Finite Group Databasebeta

← #35611779

Subgroups — #35611779

Order 21248.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1758 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128288C211yesmaximal, characteristic, complemented
2C2×#19128284C211yesmaximal, characteristic, complemented
3#24915744C211yesmaximal, characteristic, complemented
4#24915742C211yesmaximal, characteristic, complemented
5#24914371C211yesmaximal, characteristic, complemented
6#24914280C211yesmaximal, characteristic, complemented
7#24914275C211yesmaximal, characteristic, complemented
8#24914236C211yesmaximal, characteristic, complemented
9#24914005C211yesmaximal, characteristic, complemented
10#24913998C211yesmaximal, characteristic, complemented
11#24913975C211yesmaximal, characteristic, complemented
12#24913945C211yesmaximal, characteristic, complemented
13#24913944C211yesmaximal, characteristic, complemented
14#24913771C211yesmaximal, characteristic, complemented
15#24913761C211yesmaximal, characteristic, complemented
16#24913753C211yesmaximal, characteristic, complemented
17#24913721C211yesmaximal, characteristic, complemented
18#24913720C211yesmaximal, characteristic, complemented
19#24913705C211yesmaximal, characteristic, complemented
20#24913695C211yesmaximal, characteristic, complemented
21#24913203C211yesmaximal, characteristic, complemented
22#24913199C211yesmaximal, characteristic, complemented
23#24912647C211yesmaximal, characteristic, complemented
24#24912639C211yesmaximal, characteristic, complemented
25#24912425C211yesmaximal, characteristic, complemented
26#24912421C211yesmaximal, characteristic, complemented
27#24910911C211yesmaximal, characteristic, complemented
28#24910908C211yesmaximal, characteristic, complemented
29#24910900C211yesmaximal, characteristic, complemented
30C2×#19127572C211yesmaximal, characteristic, complemented
31C83×#2416C211yesmaximal, characteristic, complemented
32C23×C4×D83C2211yescharacteristic
33#19128288—28no—
34#19128284—28no—
35C2×#14581787C2211yescharacteristic
36C2×#14581787C2211yescharacteristic
37C2×#14581787C2211yescharacteristic
38C2×#14581786C2211yescharacteristic
39C2×#14581780C2211yescharacteristic
40C2×#14581778C2211yescharacteristic
41C2×#14581778C2211yescharacteristic
42C2×#14581778C2211yescharacteristic
43C2×#14581777C2211yescharacteristic
44C2×#14581776C2211yescharacteristic
45C2×#14581776C2211yescharacteristic
46C2×#14581775C2211yescharacteristic
47C2×#14581772C2211yescharacteristic, complemented
48C2×#14581771C2211yescharacteristic
49C2×#14581769C2211yescharacteristic
50C2×#14581769C2211yescharacteristic, complemented
51C2×#14581766C2211yescharacteristic
52C2×#14581765C2211yescharacteristic
53C2×#14581765C2211yescharacteristic
54C2×#14581765C2211yescharacteristic
55C2×#14581764C2211yescharacteristic
56C2×#14581764C2211yescharacteristic
57C2×#14581764C2211yescharacteristic
58C2×#14581764C2211yescharacteristic
59C2×#14581764C2211yescharacteristic
60C2×#14581764C2211yescharacteristic, complemented
61C2×#14581763C2211yescharacteristic
62C2×#14581763C2211yescharacteristic
63C2×#14581762C2211yescharacteristic
64C2×#14581760C2211yescharacteristic
65C2×#14581760C2211yescharacteristic
66C2×#14581760C2211yescharacteristic
67C2×D4×Dic83C2211yescharacteristic
68C2×D4×Dic83C2211yescharacteristic
69C2×C4×C22⋊D83C2211yescharacteristic
70C22×Dic83⋊C4C2211yescharacteristic
71C22×(C2×D83)⋊C4C2211yescharacteristic
72C22×(C2×D83)⋊C4C2211yescharacteristic
73#19127643C2211yescharacteristic, complemented
74#19127640C2211yescharacteristic, complemented
75#19127637C2211yescharacteristic, complemented
76#19127637C2211yescharacteristic, complemented
77#19127635C2211yescharacteristic, complemented
78#19127634C2211yescharacteristic, complemented
79#19127633C2211yescharacteristic, complemented
80#19127632C2211yescharacteristic, complemented
81#19127631C2211yescharacteristic, complemented
82#19127631C2211yescharacteristic, complemented
83#19127630C2211yescharacteristic
84#19127630C2211yescharacteristic
85#19127629C2211yescharacteristic, complemented
86#19127627C2211yescharacteristic
87#19127627C2211yescharacteristic
88#19127627C2211yescharacteristic, complemented
89#19127624C2211yescharacteristic, complemented
90#19127624C2211yescharacteristic, complemented
91#19127624C2211yescharacteristic, complemented
92#19127623C2211yescharacteristic, complemented
93#19127623C2211yescharacteristic, complemented
94#19127623C2211yescharacteristic, complemented
95#19127622C2211yescharacteristic, complemented
96#19127621C2211yescharacteristic, complemented
97#19127619C2211yescharacteristic
98#19127619C2211yescharacteristic
99#19127617C2211yescharacteristic
100#19127617C2211yescharacteristic
101#19127617C2211yescharacteristic
102#19127617C2211yescharacteristic
103#19127617C2211yescharacteristic, complemented
104#19127616C2211yescharacteristic
105#19127616C2211yescharacteristic
106#19127616C2211yescharacteristic, complemented
107#19127615C2211yescharacteristic, complemented
108#19127615C2211yescharacteristic, complemented
109#19127613C2211yescharacteristic, complemented
110#19127613C2211yescharacteristic, complemented
111#19127610C2211yescharacteristic
112#19127610C2211yescharacteristic
113#19127609C2211yescharacteristic
114#19127609C2211yescharacteristic
115#19127609C2211yescharacteristic, complemented
116#19127609C2211yescharacteristic, complemented
117#19127606C2211yescharacteristic, complemented
118#19127605C2211yescharacteristic, complemented
119#19127601C2211yescharacteristic, complemented
120#19127600C2211yescharacteristic, complemented
121#19127598C2211yescharacteristic, complemented
122#19127596C2211yescharacteristic, complemented
123#19127595C2211yescharacteristic, complemented
124#19127591C2211yescharacteristic, complemented
125#19127589C2211yescharacteristic, complemented
126#19127589C2211yescharacteristic, complemented
127#19127588C2211yescharacteristic, complemented
128#19127585C2211yescharacteristic, complemented
129#19127585C2211yescharacteristic, complemented
130#19127584C2211yescharacteristic, complemented
131#19127581C2211yescharacteristic
132#19127581C2211yescharacteristic
133#19127581C2211yescharacteristic
134#19127581C2211yescharacteristic
135#19127581C2211yescharacteristic, complemented
136#19127580C2211yescharacteristic
137#19127580C2211yescharacteristic
138#19127579C2211yescharacteristic
139#19127579C2211yescharacteristic
140#19127578C2211yescharacteristic, complemented
141#19127577C2211yescharacteristic
142#19127577C2211yescharacteristic
143#19127577C2211yescharacteristic
144#19127577C2211yescharacteristic
145#19127577C2211yescharacteristic
146#19127577C2211yescharacteristic
147#19127577C2211yescharacteristic, complemented
148#19127577C2211yescharacteristic, complemented
149#19127576C2211yescharacteristic, complemented
150#19127574C2211yescharacteristic, complemented
151#19127574C2211yescharacteristic, complemented
152#19127573C2211yescharacteristic, complemented
153#19127572C2211yescharacteristic
154#19127572C2211yescharacteristic
155#19127572C2211yescharacteristic
156#19127572C2211yescharacteristic
157#19127572C2211yescharacteristic
158#19127572C2211yescharacteristic
159#19127572C2211yescharacteristic
160#19127572C2211yescharacteristic
161#19127561C2211yescharacteristic
162#19127561C2211yescharacteristic
163#19127560C2211yescharacteristic
164#19127560C2211yescharacteristic
165#19127559C2211yescharacteristic
166#19127559C2211yescharacteristic
167#19127559C2211yescharacteristic, complemented
168#19127559C2211yescharacteristic, complemented
169#19127558C2211yescharacteristic
170#19127558C2211yescharacteristic
171#19127558C2211yescharacteristic, complemented
172C2×C83⋊#95C2211yescharacteristic
173C2×C83⋊#95C2211yescharacteristic
174C2×#121×C83C2211yescharacteristic
175C2×#121×C83C2211yescharacteristic
176C2×#121×C83C2211yescharacteristic
177C2×#121×C83C2211yescharacteristic, complemented
178C2×C4×D4×C83C2211yescharacteristic
179C22×C4⋊C4×C83C2211yescharacteristic
180#396×C83C2211yescharacteristic, complemented
181#396×C83C2211yescharacteristic, complemented
182#394×C83C2211yescharacteristic, complemented
183#394×C83C2211yescharacteristic, complemented
184#390×C83C2211yescharacteristic, complemented
185#389×C83C2211yescharacteristic, complemented
186#386×C83C2211yescharacteristic
187#386×C83C2211yescharacteristic
188#380×C83C2211yescharacteristic, complemented
189C24×D83C2311yescharacteristic
190C22×Dic166C2311yescharacteristic
191C22×Dic166C2311yescharacteristic
192C22×D332C2311yescharacteristic
193C22×D332C2311yescharacteristic
194C22×C22⋊D83C2311yescharacteristic
195C22×C22⋊D83C2311yescharacteristic
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C22×C22⋊D83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C23×Dic83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C23×Dic83C2311yescharacteristic
208C23×Dic83C2311yescharacteristic
209C22×C4×D83—42no—
210C22×C4×D83—42no—
211C22×C4×D83—42no—
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217#14581787—24no—
218#14581787—24no—
219#14581787—24no—
220#14581786—24no—
221#14581780—24no—
222#14581778—24no—
223#14581778—24no—
224#14581778—24no—
225#14581777—24no—
226#14581776—24no—
227#14581776—24no—
228#14581775—24no—
229#14581772—42no—
230#14581771—24no—
231#14581769—24no—
232#14581769—42no—
233#14581766—24no—
234#14581765—24no—
235#14581765—42no—
236#14581765—42no—
237#14581764—24no—
238#14581764—24no—
239#14581764—24no—
240#14581764—42no—
241#14581764—42no—
242#14581764—42no—
243#14581763—42no—
244#14581763—42no—
245#14581762—24no—
246#14581760—24no—
247#14581760—24no—
248#14581760—24no—
249D4×Dic83—24no—
250D4×Dic83—24no—
251C4×C22⋊D83—24no—
252C2×C4⋊Dic83C2311yescharacteristic
253C2×C4⋊Dic83C2311yescharacteristic
254C2×C4⋊Dic83C2311yescharacteristic
255C2×C4⋊Dic83C2311yescharacteristic
256C2×C4⋊Dic83C2311yescharacteristic
257C2×C4⋊Dic83C2311yescharacteristic
258C2×C4⋊Dic83C2311yescharacteristic
259C2×C4⋊Dic83C2311yescharacteristic
260C2×Dic83⋊C4—42no—
261C2×Dic83⋊C4C2311yescharacteristic
262C2×Dic83⋊C4C2311yescharacteristic
263C2×Dic83⋊C4C2311yescharacteristic
264C2×Dic83⋊C4C2311yescharacteristic
265C2×Dic83⋊C4C2311yescharacteristic
266C2×Dic83⋊C4C2311yescharacteristic
267C2×Dic83⋊C4C2311yescharacteristic
268C2×Dic83⋊C4C2311yescharacteristic
269C2×Dic83⋊C4C2311yescharacteristic
270C2×Dic83⋊C4C2311yescharacteristic
271C2×Dic83⋊C4C2311yescharacteristic
272C2×Dic83⋊C4C2311yescharacteristic
273C2×Dic83⋊C4C2311yescharacteristic
274C2×Dic83⋊C4C2311yescharacteristic
275C2×Dic83⋊C4C2311yescharacteristic
276C2×Dic83⋊C4C2311yescharacteristic
277C2×C22⋊Dic83C2311yescharacteristic
278C2×C22⋊Dic83C2311yescharacteristic
279C2×C22⋊Dic83C2311yescharacteristic
280C2×C22⋊Dic83C2311yescharacteristic
281C2×C22⋊Dic83C2311yescharacteristic
282C2×C22⋊Dic83C2311yescharacteristic
283C2×C22⋊Dic83C2311yescharacteristic
284C2×C22⋊Dic83C2311yescharacteristic
285C2×C22⋊Dic83C2311yescharacteristic
286C2×C22⋊Dic83C2311yescharacteristic
287C2×C22⋊Dic83C2311yescharacteristic
288C2×C22⋊Dic83C2311yescharacteristic
289C2×C22⋊Dic83C2311yescharacteristic
290C2×C22⋊Dic83C2311yescharacteristic
291C2×C22⋊Dic83C2311yescharacteristic
292C2×C22⋊Dic83C2311yescharacteristic
293C2×(C2×D83)⋊C4—42no—
294C2×(C2×D83)⋊C4D418yescomplemented
295C2×(C2×D83)⋊C4C2311yescharacteristic
296C2×(C2×D83)⋊C4C2311yescharacteristic
297C2×(C2×D83)⋊C4C2311yescharacteristic
298C2×(C2×D83)⋊C4C2311yescharacteristic
299C2×(C2×D83)⋊C4C2311yescharacteristic
300C2×(C2×D83)⋊C4C2311yescharacteristic
301C2×(C2×D83)⋊C4C2311yescharacteristic
302C2×(C2×D83)⋊C4C2311yescharacteristic
303C2×(C2×D83)⋊C4C2311yescharacteristic
304C2×(C2×D83)⋊C4C2311yescharacteristic
305C2×(C2×D83)⋊C4C2311yescharacteristic
306C2×(C2×D83)⋊C4C2311yescharacteristic
307C2×(C2×D83)⋊C4C2311yescharacteristic
308C2×(C2×D83)⋊C4C2311yescharacteristic
309C2×(C2×D83)⋊C4C2311yescharacteristic
310C2×(C2×D83)⋊C4C2311yescharacteristic
311C2×(C2×D83)⋊C4C2311yescharacteristic
312C2×(C2×D83)⋊C4C2311yescharacteristic
313C2×(C2×D83)⋊C4C2311yescharacteristic
314C2×(C2×D83)⋊C4C2311yescharacteristic
315C2×(C2×D83)⋊C4C2311yescharacteristic
316C2×(C2×D83)⋊C4C2311yescharacteristic
317C2×(C2×D83)⋊C4C2311yescharacteristic
318C2×(C2×D83)⋊C4C2311yescharacteristic
319C2×C4×Dic83C2311yescharacteristic
320C2×C4×Dic83C2311yescharacteristic
321C2×C4×Dic83C2311yescharacteristic
322C83⋊#95C2311yescharacteristic
323C83⋊#95C2311yescharacteristic
324C83⋊#95C2311yescharacteristic
325C83⋊#95C2311yescharacteristic
326C83⋊#95C2311yescharacteristic
327C83⋊#95C2311yescharacteristic
328C83⋊#95C2311yescharacteristic
329C83⋊#95C2311yescharacteristic
330C83⋊#95C2311yescharacteristic
331C83⋊#95C2311yescharacteristic
332C83⋊#95C2311yescharacteristic
333C83⋊#95C2311yescharacteristic
334C83⋊#95C2311yescharacteristic
335C83⋊#95C2311yescharacteristic
336C83⋊#95C2311yescharacteristic
337C83⋊#95C2311yescharacteristic
338C83⋊#95C2311yescharacteristic
339C83⋊#95C2311yescharacteristic
340C83⋊#95C2311yescharacteristic
341C83⋊#95C2311yescharacteristic
342C83⋊#95C2311yescharacteristic
343C83⋊#95C2311yescharacteristic
344C83⋊#95C2311yescharacteristic
345C83⋊#95C2311yescharacteristic
346C83⋊#95C2311yescharacteristic
347C83⋊#95C2311yescharacteristic
348C83⋊#95C2311yescharacteristic
349C83⋊#95C2311yescharacteristic
350C22×D4×C83C2311yescharacteristic
351C22×D4×C83C2311yescharacteristic
352C22×D4×C83C2311yescharacteristic
353C22×D4×C83C2311yescharacteristic
354C22×D4×C83C2311yescharacteristic
355C22×D4×C83C2311yescharacteristic
356C23×C4×C83C2311yescharacteristic
357C23×C4×C83C2311yescharacteristic
358C23×C4×C83C2311yescharacteristic
359C23×C4×C83C2311yescharacteristic
360#121×C83—24no—
361#121×C83—42no—
362#121×C83—42no—
363#121×C83—42no—
364C4×D4×C83—24no—
365C2×C4⋊C4×C83—42no—
366C2×C4⋊C4×C83C2311yescharacteristic
367C2×C4⋊C4×C83C2311yescharacteristic
368C2×C4⋊C4×C83C2311yescharacteristic
369C2×C4⋊C4×C83C2311yescharacteristic
370C2×C4⋊C4×C83C2311yescharacteristic
371C2×C4⋊C4×C83C2311yescharacteristic
372C2×C4⋊C4×C83C2311yescharacteristic
373C2×C4⋊C4×C83C2311yescharacteristic
374C2×C22⋊C4×C83C2311yescharacteristic
375C2×C22⋊C4×C83C2311yescharacteristic
376C2×C22⋊C4×C83C2311yescharacteristic
377C2×C22⋊C4×C83C2311yescharacteristic
378C2×C22⋊C4×C83C2311yescharacteristic
379C2×C22⋊C4×C83C2311yescharacteristic
380C2×C22⋊C4×C83C2311yescharacteristic
381C2×C22⋊C4×C83C2311yescharacteristic
382C2×C22⋊C4×C83C2311yescharacteristic
383C2×C22⋊C4×C83C2311yescharacteristic
384C2×C22⋊C4×C83C2311yescharacteristic
385C2×C22⋊C4×C83C2311yescharacteristic
386C2×C42×C83C2311yescharacteristic
387#95×C83C2311yescharacteristic
388#95×C83C2311yescharacteristic
389#95×C83C2311yescharacteristic
390#95×C83C2311yescharacteristic
391C23×D83—22no—
392C23×D83—22no—
393C23×D83—41no—
394C23×D83—41no—
395C23×D83—41no—
396C23×D83—41no—
397C23×D83C2×D414yes—
398C23×D83C2411yescharacteristic
399C23×D83C2411yescharacteristic
400C23×D83C2411yescharacteristic
401C2×Dic166—22no—
402C2×Dic166—22no—
403C2×Dic166—41no—
404C2×Dic166—41no—
405C2×Dic166—41no—
406C2×Dic166—41no—
407C2×D332—22no—
408C2×D332—22no—
409C2×D332—41no—
410C2×D332—41no—
411C2×D332—41no—
412C2×D332—41no—
413C2×C22⋊D83—22no—
414C2×C22⋊D83—22no—
415C2×C22⋊D83—22no—
416C2×C22⋊D83—22no—
417C2×C22⋊D83—22no—
418C2×C22⋊D83—22no—
419C2×C22⋊D83—22no—
420C2×C22⋊D83—22no—
421C2×C22⋊D83—22no—
422C2×C22⋊D83—22no—
423C2×C22⋊D83—22no—
424C2×C22⋊D83—41no—
425C2×C22⋊D83—41no—
426C2×C22⋊D83—41no—
427C2×C22⋊D83—41no—
428C2×C22⋊D83—41no—
429C2×C22⋊D83—41no—
430C2×C22⋊D83—41no—
431C2×C22⋊D83—41no—
432C2×C22⋊D83—41no—
433C2×C22⋊D83—41no—
434C2×C22⋊D83—41no—
435C2×C22⋊D83—41no—
436C2×C22⋊D83—41no—
437C2×C22⋊D83—41no—
438C2×C22⋊D83—41no—
439C2×C22⋊D83—41no—
440C2×C22⋊D83—41no—
441C2×C22⋊D83—41no—
442C2×C22⋊D83—41no—
443C22×Dic83—22no—
444C22×Dic83—22no—
445C22×Dic83—22no—
446C22×Dic83—22no—
447C22×Dic83—22no—
448C22×Dic83—41no—
449C22×Dic83—41no—
450C22×Dic83—41no—
451C22×Dic83—41no—
452C22×Dic83—41no—
453C22×Dic83—41no—
454C22×Dic83—41no—
455C22×Dic83—41no—
456C22×Dic83—41no—
457C22×Dic83C2×D414yes—
458C22×Dic83C2411yescharacteristic
459C22×Dic83C2411yescharacteristic
460C22×Dic83C2411yescharacteristic
461C22×Dic83C2411yescharacteristic
462C22×Dic83C2411yescharacteristic
463C22×Dic83C2411yescharacteristic
464C22×Dic83C2411yescharacteristic
465C22×Dic83C2411yescharacteristic
466C22×Dic83C2411yescharacteristic
467C22×Dic83C2411yescharacteristic
468C22×Dic83C2411yescharacteristic
469C22×Dic83C2411yescharacteristic
470C22×Dic83C2411yescharacteristic
471C2×C4×D83—22no—
472C2×C4×D83—22no—
473C2×C4×D83—22no—
474C2×C4×D83—22no—
475C2×C4×D83—22no—
476C2×C4×D83—41no—
477C2×C4×D83—41no—
478C2×C4×D83—41no—
479C2×C4×D83—41no—
480C2×C4×D83—41no—
481C2×C4×D83—41no—
482C2×C4×D83—41no—
483C2×C4×D83—41no—
484C2×C4×D83—416no—
485C2×C4×D83—41no—
486C2×C4×D83—41no—
487C4⋊Dic83—22no—
488C4⋊Dic83—22no—
489C4⋊Dic83—22no—
490C4⋊Dic83—22no—
491C4⋊Dic83—22no—
492C4⋊Dic83—41no—
493C4⋊Dic83—41no—
494C4⋊Dic83—41no—
495Dic83⋊C4—22no—
496Dic83⋊C4—22no—
497Dic83⋊C4—22no—
498Dic83⋊C4—22no—
499Dic83⋊C4—22no—
500Dic83⋊C4—22no—
501Dic83⋊C4—22no—
502Dic83⋊C4—22no—
503Dic83⋊C4—22no—
504Dic83⋊C4—41no—
505Dic83⋊C4—41no—
506Dic83⋊C4—41no—
507Dic83⋊C4—41no—
508Dic83⋊C4—41no—
509Dic83⋊C4—41no—
510Dic83⋊C4—41no—
511C22⋊Dic83—22no—
512C22⋊Dic83—22no—
513C22⋊Dic83—22no—
514C22⋊Dic83—22no—
515C22⋊Dic83—22no—
516C22⋊Dic83—22no—
517C22⋊Dic83—22no—
518C22⋊Dic83—22no—
519C22⋊Dic83—41no—
520C22⋊Dic83—41no—
521C22⋊Dic83—41no—
522C22⋊Dic83—41no—
523C22⋊Dic83—41no—
524C22⋊Dic83—41no—
525C22⋊Dic83—41no—
526C22⋊Dic83—41no—
527(C2×D83)⋊C4—22no—
528(C2×D83)⋊C4—22no—
529(C2×D83)⋊C4—22no—
530(C2×D83)⋊C4—22no—
531(C2×D83)⋊C4—22no—
532(C2×D83)⋊C4—22no—
533(C2×D83)⋊C4—22no—
534(C2×D83)⋊C4—22no—
535(C2×D83)⋊C4—22no—
536(C2×D83)⋊C4—22no—
537(C2×D83)⋊C4—22no—
538(C2×D83)⋊C4—41no—
539(C2×D83)⋊C4—41no—
540(C2×D83)⋊C4—41no—
541(C2×D83)⋊C4—41no—
542(C2×D83)⋊C4—41no—
543(C2×D83)⋊C4—41no—
544(C2×D83)⋊C4—41no—
545(C2×D83)⋊C4—41no—
546(C2×D83)⋊C4—41no—
547(C2×D83)⋊C4C2×D414yes—
548(C2×D83)⋊C4C2×D414yes—
549(C2×D83)⋊C4C2×D414yes—
550(C2×D83)⋊C4C2×D414yes—
551C4×Dic83—22no—
552C4×Dic83—22no—
553C4×Dic83—22no—
554C24×C83C2411yescharacteristic
555C24×C83C2411yescharacteristic
556C24×C83C2411yescharacteristic
557C24×C83C2411yescharacteristic
558C2×D4×C83—22no—
559C2×D4×C83—22no—
560C2×D4×C83—22no—
561C2×D4×C83—22no—
562C2×D4×C83—22no—
563C2×D4×C83—22no—
564C2×D4×C83—22no—
565C2×D4×C83—22no—
566C2×D4×C83—22no—
567C2×D4×C83—22no—
568C2×D4×C83—22no—
569C2×D4×C83—41no—
570C2×D4×C83—41no—
571C2×D4×C83—41no—
572C2×D4×C83—41no—
573C2×D4×C83—41no—
574C2×D4×C83—41no—
575C2×D4×C83—41no—
576C22×C4×C83—22no—
577C22×C4×C83—22no—
578C22×C4×C83—22no—
579C22×C4×C83—22no—
580C22×C4×C83—41no—
581C22×C4×C83—41no—
582C22×C4×C83—41no—
583C22×C4×C83—41no—
584C22×C4×C83—41no—
585C22×C4×C83—41no—
586C22×C4×C83—41no—
587C22×C4×C83C2×D414yes—
588C22×C4×C83C2411yescharacteristic
589C22×C4×C83C2411yescharacteristic
590C22×C4×C83C2411yescharacteristic
591C22×C4×C83C2411yescharacteristic
592C22×C4×C83C2411yescharacteristic
593C22×C4×C83C2411yescharacteristic
594C22×C4×C83C2411yescharacteristic
595C22×C4×C83C2411yescharacteristic
596C22×C4×C83C2411yescharacteristic
597C22×C4×C83C2411yescharacteristic
598C22×C4×C83C2411yescharacteristic
599C4⋊C4×C83—22no—
600C4⋊C4×C83—22no—
601C4⋊C4×C83—22no—
602C4⋊C4×C83—22no—
603C4⋊C4×C83—41no—
604C4⋊C4×C83—41no—
605C4⋊C4×C83—41no—
606C4⋊C4×C83—41no—
607C22⋊C4×C83—22no—
608C22⋊C4×C83—22no—
609C22⋊C4×C83—22no—
610C22⋊C4×C83—22no—
611C22⋊C4×C83—22no—
612C22⋊C4×C83—41no—
613C22⋊C4×C83—41no—
614C22⋊C4×C83—41no—
615C22⋊C4×C83—41no—
616C22⋊C4×C83—41no—
617C22⋊C4×C83—41no—
618C22⋊C4×C83—41no—
619C42×C83—22no—
620C23×C83—21no—
621C23×C83—21no—
622C23×C83—21no—
623C23×C83—21no—
624C23×C83—21no—
625C23×C83—21no—
626C23×C83—21no—
627C23×C83—21no—
628C23×C83—21no—
629C23×C83—21no—
630C23×C83—21no—
631C23×C83—21no—
632C23×C83—21no—
633C23×C83—21no—
634C23×C83—21no—
635C23×C83—21no—
636C23×C83—21no—
637C23×C83—21no—
638C23×C83—21no—
639C23×C83—21no—
640C23×C83—21no—
641C23×C83—21no—
642C23×C83—21no—
643C23×C83—21no—
644C23×C83—21no—
645C23×C83C22×D412yes—
646C23×C83H(5,𝔽2)12yes—
647C23×C832−1+412yes—
648C23×C83C2511yescharacteristic
649C22×D83—28no—
650C22×D83—21no—
651C22×D83—21no—
652C22×D83—21no—
653C22×D83—21no—
654C22×D83—21no—
655C22×D83—21no—
656C22×D83—21no—
657C22×D83—21no—
658C22×D83—21no—
659C22×D83—21no—
660C22×D83—21no—
661C22×D83—21no—
662C22×D83—21no—
663C22×D83—21no—
664C22×D83—21no—
665C22×D83—21no—
666C22×D83—21no—
667C22×D83—21no—
668C22×D83—21no—
669C22×D83—44no—
670C22×D83—44no—
671C22×D83—44no—
672C22×D83—44no—
673C22×D83—44no—
674C22×D83—44no—
675C22×D83C22×D412yes—
676C22×D83C22×D412yes—
677D4×C83—44no—
678D4×C83—44no—
679D4×C83—44no—
680D4×C83—82no—
681D4×C83—82no—
682D4×C83—82no—
683C2×C4×C83—21no—
684C2×C4×C83—21no—
685C2×C4×C83—21no—
686C2×C4×C83—21no—
687C2×C4×C83—21no—
688C2×C4×C83—21no—
689C2×C4×C83—21no—
690C2×C4×C83—21no—
691C2×C4×C83—21no—
692C2×C4×C83—21no—
693C2×C4×C83—21no—
694C2×C4×C83—21no—
695C2×C4×C83—21no—
696C2×C4×C83—21no—
697C2×C4×C83—21no—
698C2×C4×C83—21no—
699C2×C4×C83—21no—
700C2×C4×C83—21no—
701C2×C4×C83—21no—
702C2×C4×C83—21no—
703C2×C4×C83—21no—
704C2×C4×C83—21no—
705C2×C4×C83—21no—
706C2×C4×C83—21no—
707C2×C4×C83—21no—
708C2×C4×C83—21no—
709C2×C4×C83—21no—
710C2×C4×C83—21no—
711C2×C4×C83—21no—
712C2×C4×C83—21no—
713C2×C4×C83—44no—
714C2×C4×C83—44no—
715C2×C4×C83—82no—
716C2×C4×C83—82no—
717C2×C4×C83C22×D412yes—
718C2×C4×C83C22×D412yes—
719C2×C4×C83H(5,𝔽2)12yes—
720C22⋊D83—44no—
721C22⋊D83—82no—
722C22⋊D83—82no—
723C22⋊D83—82no—
724C22⋊D83—82no—
725C22⋊D83—82no—
726C22⋊D83—82no—
727C22⋊D83—82no—
728C22⋊D83—82no—
729C22⋊D83—82no—
730C2×Dic83—21no—
731C2×Dic83—21no—
732C2×Dic83—21no—
733C2×Dic83—21no—
734C2×Dic83—21no—
735C2×Dic83—21no—
736C2×Dic83—21no—
737C2×Dic83—21no—
738C2×Dic83—21no—
739C2×Dic83—21no—
740C2×Dic83—21no—
741C2×Dic83—21no—
742C2×Dic83—21no—
743C2×Dic83—21no—
744C2×Dic83—21no—
745C2×Dic83—21no—
746C2×Dic83—21no—
747C2×Dic83—21no—
748C2×Dic83—21no—
749C2×Dic83—21no—
750C2×Dic83—21no—
751C2×Dic83—21no—
752C2×Dic83—21no—
753C2×Dic83—21no—
754C2×Dic83—21no—
755C2×Dic83—21no—
756C2×Dic83—21no—
757C2×Dic83—21no—
758C2×Dic83—21no—
759C2×Dic83—21no—
760C2×Dic83—21no—
761C2×Dic83—21no—
762C2×Dic83—21no—
763C2×Dic83—21no—
764C2×Dic83—21no—
765C2×Dic83—21no—
766C2×Dic83—44no—
767C2×Dic83—44no—
768C2×Dic83—82no—
769C2×Dic83—82no—
770C2×Dic83—82no—
771C2×Dic83C22×D412yes—
772C2×Dic83C22×D412yes—
773C2×Dic83H(5,𝔽2)12yes—
774D332—82no—
775D332—82no—
776C4×D83—44no—
777C4×D83—44no—
778C4×D83—44no—
779C4×D83—44no—
780C4×D83—82no—
781Dic166—82no—
782Dic166—82no—
783C22×C83—22no—
784C22×C83—22no—
785C22×C83—22no—
786C22×C83—22no—
787C22×C83—22no—
788C22×C83—22no—
789C22×C83—41no—
790C22×C83—41no—
791C22×C83—41no—
792C22×C83—41no—
793C22×C83—41no—
794C22×C83—41no—
795C22×C83—41no—
796C22×C83—41no—
797C22×C83—41no—
798C22×C83—41no—
799C22×C83—41no—
800C22×C83—41no—
801C22×C83—41no—
802C22×C83—41no—
803C22×C83—41no—
804C22×C83—41no—
805C22×C83—41no—
806C22×C83—41no—
807C22×C83—41no—
808C22×C83—41no—
809C22×C83—41no—
810C22×C83#53714yes—
811C22×C83C23×D411yescharacteristic
812C22×C83C2×H(5,𝔽2)11yescharacteristic
813C22×C83C2×H(5,𝔽2)11yescharacteristic
814C22×C83C2×H(5,𝔽2)11yescharacteristic
815C22×C83C2×2−1+411yescharacteristic
816C22×C83#58511yescharacteristic
817C22×C83#58511yescharacteristic
818C2×D83—22no—
819C2×D83—22no—
820C2×D83—22no—
821C2×D83—22no—
822C2×D83—22no—
823C2×D83—22no—
824C2×D83—416no—
825C2×D83—41no—
826C2×D83—41no—
827C2×D83—41no—
828C2×D83—41no—
829C2×D83—41no—
830C2×D83—41no—
831C2×D83—41no—
832C2×D83—41no—
833C2×D83—41no—
834C2×D83—41no—
835C2×D83—41no—
836C2×D83—41no—
837C2×D83—41no—
838C2×D83—41no—
839C2×D83—41no—
840C4×C83—22no—
841C4×C83—22no—
842C4×C83—22no—
843C4×C83—41no—
844C4×C83—41no—
845C4×C83—41no—
846C4×C83—41no—
847C4×C83—41no—
848C4×C83—41no—
849C4×C83—41no—
850C4×C83—41no—
851Dic83—22no—
852Dic83—22no—
853Dic83—22no—
854Dic83—41no—
855Dic83—41no—
856Dic83—41no—
857Dic83—41no—
858Dic83—41no—
859Dic83—41no—
860Dic83—41no—
861Dic83—41no—
862Dic83—41no—
863Dic83—41no—
864#36738—831nomaximal, Sylow
865C2×C83—24no—
866C2×C83—81no—
867C2×C83—81no—
868C2×C83—81no—
869C2×C83C2×#53711yescharacteristic
870C2×C83#349611yescharacteristic
871C2×C83#349611yescharacteristic
872C2×C83#353211yescharacteristic
873C2×C83#353311yescharacteristic
874C2×C83#354111yescharacteristic
875C2×C83#354111yescharacteristic
876D83—42no—
877D83—42no—
878D83—81no—
879C2×#538—831no—
880C2×#538—831no—
881#2847—831no—
882#2847—831no—
883#2722—831no—
884#2715—831no—
885#2715—831no—
886#2712—831no—
887#2695—831no—
888#2695—831no—
889#2693—831no—
890#2691—831no—
891#2691—831no—
892#2676—831no—
893#2676—831no—
894#2675—831no—
895#2672—831no—
896#2672—831no—
897#2671—831no—
898#2671—831no—
899#2617—831no—
900#2617—831no—
901#2564—831no—
902#2564—831no—
903#2543—831no—
904#2543—831no—
905#2417—831no—
906#2417—831no—
907#2416—831no—
908#2416D8311yescharacteristic, complemented
909C2×#385—831no—
910C83#3673811yescharacteristic, complemented, Sylow
911C24×C4—831no—
912#538—1668no—
913#538—1668no—
914C2×#126—831no—
915C2×#126—831no—
916C2×#126—831no—
917C2×#126—831no—
918C2×#124—831no—
919C2×#124—831no—
920C2×#124—831no—
921C2×#124—831no—
922C2×#123—831no—
923C2×#123—831no—
924C2×#123—831no—
925C2×#123—831no—
926C2×C22⋊Q8—831no—
927C2×C22⋊Q8—831no—
928C2×C22⋊Q8—831no—
929C2×C22⋊Q8—831no—
930C2×#121—831no—
931C2×#121—831no—
932C2×#121—831no—
933C2×#121—831no—
934C2×#121—831no—
935C2×#121—831no—
936C2×#121—831no—
937C2×#121—831no—
938C2×#121—831no—
939C2×#121—831no—
940C2×#121—831no—
941C2×#121—831no—
942C2×#121C2×D8311yescharacteristic
943C2×#121C2×D8311yescharacteristic
944C2×#121C2×D8311yescharacteristic
945C2×#121C2×D8311yescharacteristic, complemented
946C2×#120—831no—
947C2×#120—831no—
948C2×#120—831no—
949C2×#120—831no—
950C2×C4×D4—831no—
951C2×C4×D4—831no—
952C2×C4×D4—831no—
953C2×C4×D4C2×D8311yescharacteristic
954C22×C4⋊C4—831no—
955C22×C4⋊C4C2×D8311yescharacteristic
956C22×C22⋊C4—831no—
957C22×C22⋊C4—831no—
958#400—831no—
959#400—831no—
960#399—831no—
961#399—831no—
962#398—831no—
963#398—831no—
964#398—831no—
965#398—831no—
966#398—831no—
967#398—831no—
968#397—831no—
969#397—831no—
970#397—831no—
971#397—831no—
972#397—831no—
973#397—831no—
974#396—831no—
975#396—831no—
976#396—831no—
977#396—831no—
978#396—831no—
979#396—831no—
980#396C2×D8311yescharacteristic, complemented
981#396C2×D8311yescharacteristic, complemented
982#395—831no—
983#395—831no—
984#394—831no—
985#394—831no—
986#394—831no—
987#394—831no—
988#394—831no—
989#394—831no—
990#394—831no—
991#394—831no—
992#394—831no—
993#394—831no—
994#394—831no—
995#394—831no—
996#394C2×D8311yescharacteristic, complemented
997#394C2×D8311yescharacteristic, complemented
998#393—831no—
999#393—831no—
1000#392—831no—
1001#392—831no—
1002#392—831no—
1003#392—831no—
1004#392—831no—
1005#392—831no—
1006#391—831no—
1007#391—831no—
1008#390—831no—
1009#390C2×D8311yescharacteristic, complemented
1010#389—831no—
1011#389—831no—
1012#389—831no—
1013#389C2×D8311yescharacteristic, complemented
1014#388—831no—
1015#388—831no—
1016#388—831no—
1017#388—831no—
1018#387—831no—
1019#387—831no—
1020#387—831no—
1021#387—831no—
1022#386—831no—
1023#386—831no—
1024#386—831no—
1025#386—831no—
1026#386—831no—
1027#386—831no—
1028#386—831no—
1029#386—831no—
1030#386—831no—
1031#386—831no—
1032#386—831no—
1033#386—831no—
1034#386—831no—
1035#386—831no—
1036#386—831no—
1037#386—831no—
1038#386—831no—
1039#386—831no—
1040#386C2×D8311yescharacteristic
1041#386C2×D8311yescharacteristic
1042#385—831no—
1043#385—831no—
1044#385—831no—
1045#385—831no—
1046#385—831no—
1047#385—831no—
1048#385—831no—
1049#385—831no—
1050#385—831no—
1051#385—831no—
1052#385—831no—
1053#385—831no—
1054#380—831no—
1055#380—831no—
1056#380—831no—
1057#380—831no—
1058#380—831no—
1059#380—831no—
1060#380—831no—
1061#380—831no—
1062#380—831no—
1063#380—831no—
1064#380—831no—
1065#380C2×D8311yescharacteristic, complemented
1066C2×#95—831no—
1067C2×#95—831no—
1068C25—831no—
1069C22×Q8—831no—
1070C22×Q8—831no—
1071C22×D4—831no—
1072C22×D4—831no—
1073C22×D4—831no—
1074C22×D4—831no—
1075C22×D4—831no—
1076C22×D4—831no—
1077C22×D4—831no—
1078C22×D4—831no—
1079C22×D4—831no—
1080C22×D4—831no—
1081C22×D4—831no—
1082C22×D4—831no—
1083C22×D4C22×D8311yescharacteristic
1084C22×D4C22×D8311yescharacteristic
1085C22×D4C22×D8311yescharacteristic
1086C22×D4C22×D8311yescharacteristic
1087C22×D4C22×D8311yescharacteristic
1088C22×D4C22×D8311yescharacteristic
1089C23×C4—3322no—
1090C23×C4—3322no—
1091C23×C4—3322no—
1092C23×C4—831no—
1093C23×C4—831no—
1094C23×C4—831no—
1095C23×C4—831no—
1096C23×C4—831no—
1097C23×C4—831no—
1098C23×C4—831no—
1099C23×C4—831no—
1100C23×C4—831no—
1101C23×C4—831no—
1102C23×C4C22×D8311yescharacteristic
1103C23×C4C22×D8311yescharacteristic
1104C23×C4C22×D8311yescharacteristic
1105C23×C4C22×D8311yescharacteristic
1106#126—1664no—
1107#126—1664no—
1108#126—1664no—
1109#126—1664no—
1110#124—1664no—
1111#124—1664no—
1112#124—1664no—
1113#124—1664no—
1114#123—1664no—
1115#123—1664no—
1116#123—1664no—
1117#123—1664no—
1118C22⋊Q8—3322no—
1119C22⋊Q8—3322no—
1120C22⋊Q8—1664no—
1121C22⋊Q8—1664no—
1122#121—24no—
1123#121—42no—
1124#121—42no—
1125#121—42no—
1126#121—3322no—
1127#121—3322no—
1128#121—3322no—
1129#121—3322no—
1130#121—3322no—
1131#121—3322no—
1132#121—3322no—
1133#121—1664no—
1134#121—1664no—
1135#121—1664no—
1136#121—1664no—
1137#121—1664no—
1138#120—1664no—
1139#120—1664no—
1140#120—1664no—
1141#120—1664no—
1142C4×D4—24no—
1143C4×D4—1664no—
1144C4×D4—1664no—
1145C4×D4—1664no—
1146C2×C4⋊C4—42no—
1147C2×C4⋊C4—3322no—
1148C2×C4⋊C4—831no—
1149C2×C4⋊C4—831no—
1150C2×C4⋊C4—831no—
1151C2×C4⋊C4—831no—
1152C2×C4⋊C4—831no—
1153C2×C4⋊C4—831no—
1154C2×C4⋊C4—831no—
1155C2×C4⋊C4—831no—
1156C2×C4⋊C4—831no—
1157C2×C4⋊C4—831no—
1158C2×C4⋊C4—831no—
1159C2×C4⋊C4—831no—
1160C2×C4⋊C4—831no—
1161C2×C4⋊C4—831no—
1162C2×C4⋊C4—831no—
1163C2×C4⋊C4—831no—
1164C2×C4⋊C4—831no—
1165C2×C4⋊C4—831no—
1166C2×C4⋊C4—831no—
1167C2×C4⋊C4—831no—
1168C2×C4⋊C4—831no—
1169C2×C4⋊C4—831no—
1170C2×C4⋊C4—831no—
1171C2×C4⋊C4—831no—
1172C2×C4⋊C4C22×D8311yescharacteristic
1173C2×C4⋊C4C22×D8311yescharacteristic
1174C2×C4⋊C4C22×D8311yescharacteristic
1175C2×C4⋊C4C22×D8311yescharacteristic
1176C2×C4⋊C4C22×D8311yescharacteristic
1177C2×C4⋊C4C22×D8311yescharacteristic
1178C2×C4⋊C4C22×D8311yescharacteristic
1179C2×C4⋊C4C22×D8311yescharacteristic
1180C2×C22⋊C4—3322no—
1181C2×C22⋊C4—831no—
1182C2×C22⋊C4—831no—
1183C2×C22⋊C4—831no—
1184C2×C22⋊C4—831no—
1185C2×C22⋊C4—831no—
1186C2×C22⋊C4—831no—
1187C2×C22⋊C4—831no—
1188C2×C22⋊C4—831no—
1189C2×C22⋊C4—831no—
1190C2×C22⋊C4—831no—
1191C2×C22⋊C4—831no—
1192C2×C22⋊C4—831no—
1193C2×C22⋊C4—831no—
1194C2×C22⋊C4—831no—
1195C2×C22⋊C4—831no—
1196C2×C22⋊C4—831no—
1197C2×C22⋊C4—831no—
1198C2×C22⋊C4—838no—
1199C2×C22⋊C4—831no—
1200C2×C22⋊C4—831no—
1201C2×C22⋊C4—831no—
1202C2×C22⋊C4—831no—
1203C2×C22⋊C4—831no—
1204C2×C22⋊C4—831no—
1205C2×C22⋊C4—831no—
1206C2×C22⋊C4—831no—
1207C2×C22⋊C4—831no—
1208C2×C22⋊C4—831no—
1209C2×C22⋊C4—831no—
1210C2×C22⋊C4—831no—
1211C2×C22⋊C4—831no—
1212C2×C22⋊C4—831no—
1213C2×C22⋊C4—831no—
1214C2×C22⋊C4—831no—
1215C2×C22⋊C4—831no—
1216C2×C22⋊C4—831no—
1217C2×C22⋊C4—831no—
1218C2×C22⋊C4—831no—
1219C2×C22⋊C4—831no—
1220C2×C22⋊C4—831no—
1221C2×C22⋊C4—831no—
1222C2×C22⋊C4C22×D8311yescharacteristic
1223C2×C22⋊C4C22×D8311yescharacteristic
1224C2×C22⋊C4C22×D8311yescharacteristic
1225C2×C22⋊C4C22×D8311yescharacteristic
1226C2×C22⋊C4C22×D8311yescharacteristic
1227C2×C22⋊C4C22×D8311yescharacteristic
1228C2×C22⋊C4C22×D8311yescharacteristic
1229C2×C22⋊C4C22×D8311yescharacteristic
1230C2×C22⋊C4C22×D8311yescharacteristic
1231C2×C22⋊C4C22×D8311yescharacteristic
1232C2×C22⋊C4C22×D8311yescharacteristic
1233C2×C22⋊C4C22×D8311yescharacteristic
1234C2×C42—831no—
1235C2×C42—831no—
1236C2×C42—831no—
1237C2×C42C22×D8311yescharacteristic
1238#95—831no—
1239#95—831no—
1240#95—831no—
1241#95—831no—
1242#95—831no—
1243#95—831no—
1244#95—831no—
1245#95—831no—
1246#95—831no—
1247#95—831no—
1248#95—831no—
1249#95—831no—
1250#95—831no—
1251#95—831no—
1252#95—831no—
1253#95—831no—
1254#95—831no—
1255#95—831no—
1256#95—831no—
1257#95—831no—
1258#95—831no—
1259#95—831no—
1260#95—831no—
1261#95—831no—
1262#95—831no—
1263#95—831no—
1264#95—831no—
1265#95—831no—
1266#95C22×D8311yescharacteristic
1267#95C22×D8311yescharacteristic
1268#95C22×D8311yescharacteristic
1269#95C22×D8311yescharacteristic
1270C24—3321no—
1271C24—3321no—
1272C24—3321no—
1273C24—3321no—
1274C24—834no—
1275C24—831no—
1276C24—831no—
1277C24—831no—
1278C24—1662no—
1279C24—1662no—
1280C24C23×D8311yescharacteristic
1281C24C23×D8311yescharacteristic
1282C24C23×D8311yescharacteristic
1283C24C23×D8311yescharacteristic
1284C2×Q8—3321no—
1285C2×Q8—3321no—
1286C2×Q8—3321no—
1287C2×Q8—3321no—
1288C2×Q8—1662no—
1289C2×Q8—1662no—
1290C2×D4—22no—
1291C2×D4—22no—
1292C2×D4—22no—
1293C2×D4—22no—
1294C2×D4—22no—
1295C2×D4—22no—
1296C2×D4—22no—
1297C2×D4—22no—
1298C2×D4—22no—
1299C2×D4—22no—
1300C2×D4—22no—
1301C2×D4—41no—
1302C2×D4—41no—
1303C2×D4—41no—
1304C2×D4—41no—
1305C2×D4—41no—
1306C2×D4—41no—
1307C2×D4—41no—
1308C2×D4—3321no—
1309C2×D4—3321no—
1310C2×D4—3321no—
1311C2×D4—3321no—
1312C2×D4—3321no—
1313C2×D4—3321no—
1314C2×D4—3321no—
1315C2×D4—3321no—
1316C2×D4—3321no—
1317C2×D4—3321no—
1318C2×D4—3321no—
1319C2×D4—3321no—
1320C2×D4—3321no—
1321C2×D4—3321no—
1322C2×D4—3321no—
1323C2×D4—3321no—
1324C2×D4—3321no—
1325C2×D4—3321no—
1326C2×D4—3321no—
1327C2×D4—3321no—
1328C2×D4—3321no—
1329C2×D4—3321no—
1330C2×D4—3321no—
1331C2×D4—1662no—
1332C2×D4—1662no—
1333C2×D4—1662no—
1334C2×D4—1662no—
1335C2×D4—1662no—
1336C2×D4—1662no—
1337C2×D4—1662no—
1338C2×D4—1662no—
1339C2×D4—1662no—
1340C2×D4—1662no—
1341C2×D4—1662no—
1342C2×D4—1662no—
1343C2×D4—1662no—
1344C22×C4—22no—
1345C22×C4—22no—
1346C22×C4—22no—
1347C22×C4—22no—
1348C22×C4—41no—
1349C22×C4—41no—
1350C22×C4—41no—
1351C22×C4—41no—
1352C22×C4—41no—
1353C22×C4—41no—
1354C22×C4—41no—
1355C22×C4—3321no—
1356C22×C4—3321no—
1357C22×C4—3321no—
1358C22×C4—3321no—
1359C22×C4—3321no—
1360C22×C4—3321no—
1361C22×C4—3321no—
1362C22×C4—3321no—
1363C22×C4—3321no—
1364C22×C4—3321no—
1365C22×C4—33216no—
1366C22×C4—3321no—
1367C22×C4—3321no—
1368C22×C4—3321no—
1369C22×C4—3321no—
1370C22×C4—3321no—
1371C22×C4—3321no—
1372C22×C4—3321no—
1373C22×C4—3321no—
1374C22×C4—3321no—
1375C22×C4—834no—
1376C22×C4—831no—
1377C22×C4—831no—
1378C22×C4—831no—
1379C22×C4—831no—
1380C22×C4—831no—
1381C22×C4—831no—
1382C22×C4—831no—
1383C22×C4—831no—
1384C22×C4—831no—
1385C22×C4—831no—
1386C22×C4—831no—
1387C22×C4—831no—
1388C22×C4—831no—
1389C22×C4—1662no—
1390C22×C4—1662no—
1391C22×C4—1662no—
1392C22×C4—1662no—
1393C22×C4—1662no—
1394C22×C4—1662no—
1395C22×C4—1662no—
1396C22×C4—1662no—
1397C22×C4—1662no—
1398C22×C4—1662no—
1399C22×C4D4×D8314yes—
1400C22×C4C23×D8311yescharacteristic
1401C22×C4C23×D8311yescharacteristic
1402C22×C4C23×D8311yescharacteristic
1403C22×C4C23×D8311yescharacteristic
1404C22×C4C23×D8311yescharacteristic
1405C22×C4C23×D8311yescharacteristic
1406C22×C4C23×D8311yescharacteristic
1407C22×C4C23×D8311yescharacteristic
1408C22×C4C23×D8311yescharacteristic
1409C22×C4C23×D8311yescharacteristic
1410C22×C4C23×D8311yescharacteristic
1411C4⋊C4—22no—
1412C4⋊C4—22no—
1413C4⋊C4—22no—
1414C4⋊C4—22no—
1415C4⋊C4—41no—
1416C4⋊C4—41no—
1417C4⋊C4—41no—
1418C4⋊C4—41no—
1419C4⋊C4—3321no—
1420C4⋊C4—3321no—
1421C4⋊C4—3321no—
1422C4⋊C4—3321no—
1423C4⋊C4—3321no—
1424C4⋊C4—3321no—
1425C4⋊C4—3321no—
1426C4⋊C4—3321no—
1427C4⋊C4—3321no—
1428C4⋊C4—3321no—
1429C4⋊C4—1662no—
1430C4⋊C4—1662no—
1431C4⋊C4—1662no—
1432C4⋊C4—1662no—
1433C4⋊C4—1662no—
1434C4⋊C4—1662no—
1435C4⋊C4—1662no—
1436C4⋊C4—1662no—
1437C4⋊C4—1662no—
1438C4⋊C4—1662no—
1439C4⋊C4—1662no—
1440C4⋊C4—1662no—
1441C4⋊C4—1662no—
1442C4⋊C4—1662no—
1443C22⋊C4—22no—
1444C22⋊C4—22no—
1445C22⋊C4—22no—
1446C22⋊C4—22no—
1447C22⋊C4—22no—
1448C22⋊C4—41no—
1449C22⋊C4—41no—
1450C22⋊C4—41no—
1451C22⋊C4—41no—
1452C22⋊C4—41no—
1453C22⋊C4—41no—
1454C22⋊C4—41no—
1455C22⋊C4—3321no—
1456C22⋊C4—3321no—
1457C22⋊C4—3321no—
1458C22⋊C4—3321no—
1459C22⋊C4—3321no—
1460C22⋊C4—3321no—
1461C22⋊C4—3321no—
1462C22⋊C4—3321no—
1463C22⋊C4—3321no—
1464C22⋊C4—3321no—
1465C22⋊C4—3321no—
1466C22⋊C4—3321no—
1467C22⋊C4—3321no—
1468C22⋊C4—3321no—
1469C22⋊C4—3321no—
1470C22⋊C4—3321no—
1471C22⋊C4—3321no—
1472C22⋊C4—834no—
1473C22⋊C4—834no—
1474C22⋊C4—834no—
1475C22⋊C4—834no—
1476C22⋊C4—1662no—
1477C22⋊C4—1662no—
1478C22⋊C4—1662no—
1479C22⋊C4—1662no—
1480C22⋊C4—1662no—
1481C22⋊C4—1662no—
1482C22⋊C4—1662no—
1483C22⋊C4—1662no—
1484C22⋊C4—1662no—
1485C22⋊C4—1662no—
1486C22⋊C4—1662no—
1487C22⋊C4—1662no—
1488C22⋊C4—1662no—
1489C22⋊C4—1662no—
1490C22⋊C4—1662no—
1491C22⋊C4—1662no—
1492C22⋊C4—1662no—
1493C22⋊C4—1662no—
1494C22⋊C4—1662no—
1495C42—22no—
1496C42—1662no—
1497C42—1662no—
1498C42—1662no—
1499C23—21no—
1500C23—21no—
1501C23—21no—
1502C23—21no—
1503C23—21no—
1504C23—21no—
1505C23—21no—
1506C23—21no—
1507C23—21no—
1508C23—21no—
1509C23—21no—
1510C23—21no—
1511C23—21no—
1512C23—21no—
1513C23—21no—
1514C23—21no—
1515C23—21no—
1516C23—21no—
1517C23—21no—
1518C23—21no—
1519C23—21no—
1520C23—21no—
1521C23—21no—
1522C23—21no—
1523C23—21no—
1524C23—3324no—
1525C23—3324no—
1526C23—3324no—
1527C23—3324no—
1528C23—3324no—
1529C23—3324no—
1530C23—832no—
1531C23—832no—
1532C23—1661no—
1533C23—1661no—
1534C23—1661no—
1535C23—1661no—
1536C23—1661no—
1537C23—1661no—
1538C23—1661no—
1539C23—1661no—
1540C23—1661no—
1541C23—1661no—
1542C23—1661no—
1543C23—1661no—
1544C23—1661no—
1545C23—1661no—
1546C23—1661no—
1547C23—1668no—
1548C23—1661no—
1549C23—1661no—
1550C23—1661no—
1551C23—1661no—
1552C23C2×D4×D8312yes—
1553C23#1458183712yes—
1554C23#1458183912yes—
1555C23C24×D8311yescharacteristic
1556Q8—6642no—
1557Q8—6642no—
1558D4—44no—
1559D4—44no—
1560D4—44no—
1561D4—82no—
1562D4—82no—
1563D4—82no—
1564D4—3324no—
1565D4—6642no—
1566D4—6642no—
1567D4—6642no—
1568D4—6642no—
1569D4—6642no—
1570D4—6642no—
1571D4—6642no—
1572D4—6642no—
1573D4—6642no—
1574D4—6642no—
1575D4—6642no—
1576C2×C4—21no—
1577C2×C4—21no—
1578C2×C4—21no—
1579C2×C4—21no—
1580C2×C4—21no—
1581C2×C4—21no—
1582C2×C4—21no—
1583C2×C4—21no—
1584C2×C4—21no—
1585C2×C4—21no—
1586C2×C4—21no—
1587C2×C4—21no—
1588C2×C4—21no—
1589C2×C4—21no—
1590C2×C4—21no—
1591C2×C4—21no—
1592C2×C4—21no—
1593C2×C4—21no—
1594C2×C4—21no—
1595C2×C4—21no—
1596C2×C4—21no—
1597C2×C4—21no—
1598C2×C4—21no—
1599C2×C4—21no—
1600C2×C4—21no—
1601C2×C4—21no—
1602C2×C4—21no—
1603C2×C4—21no—
1604C2×C4—21no—
1605C2×C4—21no—
1606C2×C4—44no—
1607C2×C4—44no—
1608C2×C4—82no—
1609C2×C4—82no—
1610C2×C4—3324no—
1611C2×C4—3324no—
1612C2×C4—3324no—
1613C2×C4—3324no—
1614C2×C4—3324no—
1615C2×C4—3324no—
1616C2×C4—832no—
1617C2×C4—832no—
1618C2×C4—832no—
1619C2×C4—6642no—
1620C2×C4—6642no—
1621C2×C4—6642no—
1622C2×C4—6642no—
1623C2×C4—1661no—
1624C2×C4—1661no—
1625C2×C4—1661no—
1626C2×C4—1661no—
1627C2×C4—1661no—
1628C2×C4—1661no—
1629C2×C4—1661no—
1630C2×C4—1661no—
1631C2×C4—1661no—
1632C2×C4—1661no—
1633C2×C4—1661no—
1634C2×C4—1661no—
1635C2×C4—1661no—
1636C2×C4—1661no—
1637C2×C4—1661no—
1638C2×C4—1661no—
1639C2×C4—1661no—
1640C2×C4—1661no—
1641C2×C4—1661no—
1642C2×C4—1661no—
1643C2×C4—1661no—
1644C2×C4—1661no—
1645C2×C4—1661no—
1646C2×C4—1661no—
1647C2×C4—1661no—
1648C2×C4—1661no—
1649C2×C4—1661no—
1650C2×C4—1661no—
1651C2×C4—1661no—
1652C2×C4—1661no—
1653C2×C4—1661no—
1654C2×C4—1661no—
1655C2×C4—1661no—
1656C2×C4—1661no—
1657C2×C4—1661no—
1658C2×C4—1661no—
1659C2×C4C2×D4×D8312yes—
1660C2×C4C2×D4×D8312yes—
1661C2×C4#1458183712yes—
1662C22—22no—
1663C22—22no—
1664C22—22no—
1665C22—22no—
1666C22—22no—
1667C22—22no—
1668C22—41no—
1669C22—41no—
1670C22—41no—
1671C22—41no—
1672C22—41no—
1673C22—41no—
1674C22—41no—
1675C22—41no—
1676C22—41no—
1677C22—41no—
1678C22—41no—
1679C22—41no—
1680C22—41no—
1681C22—41no—
1682C22—41no—
1683C22—41no—
1684C22—41no—
1685C22—41no—
1686C22—41no—
1687C22—41no—
1688C22—41no—
1689C22—33216no—
1690C22—3321no—
1691C22—3321no—
1692C22—3321no—
1693C22—3321no—
1694C22—3321no—
1695C22—3321no—
1696C22—3321no—
1697C22—3321no—
1698C22—3321no—
1699C22—3321no—
1700C22—3321no—
1701C22—3321no—
1702C22—3321no—
1703C22—3321no—
1704C22—3321no—
1705C22—1662no—
1706C22—1662no—
1707C22—1662no—
1708C22—1662no—
1709C22—1662no—
1710C22—1662no—
1711C22#1912828014yes—
1712C22C22×D4×D8311yescharacteristic
1713C22H(5,𝔽2)×D8311yescharacteristic
1714C22C2×#1458183711yescharacteristic
1715C22C2×#1458183711yescharacteristic
1716C22C2×#1458183911yescharacteristic
1717C22#1912853711yescharacteristic
1718C22#1912853811yescharacteristic
1719C4—22no—
1720C4—22no—
1721C4—22no—
1722C4—41no—
1723C4—41no—
1724C4—41no—
1725C4—41no—
1726C4—41no—
1727C4—41no—
1728C4—41no—
1729C4—41no—
1730C4—3321no—
1731C4—3321no—
1732C4—3321no—
1733C4—3321no—
1734C4—3321no—
1735C4—3321no—
1736C4—3321no—
1737C4—3321no—
1738C4—3321no—
1739C4—3321no—
1740C4—1662no—
1741C4—1662no—
1742C4—1662no—
1743C2—24no—
1744C2—81no—
1745C2—81no—
1746C2—81no—
1747C2—3322no—
1748C2—3322no—
1749C2—6641no—
1750C2C2×#1912828011yescharacteristic
1751C2#2492122011yescharacteristic
1752C2#2492122611yescharacteristic
1753C2#2492161311yescharacteristic
1754C2#2492163311yescharacteristic
1755C2#2492174111yescharacteristic
1756C2#2492174211yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2416C2
hypercenter#2416D83
hypocenterC83#36738
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2416

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
1. C2×#19128288C2semidirect
2. C2×#19128284C2semidirect
3. #24915744C2semidirect
4. #24915742C2semidirect
5. #24914371C2semidirect
6. #24914280C2semidirect
7. #24914275C2semidirect
8. #24914236C2semidirect
9. #24914005C2semidirect
10. #24913998C2semidirect
11. #24913975C2semidirect
12. #24913945C2semidirect
13. #24913944C2semidirect
14. #24913771C2semidirect
15. #24913761C2semidirect
16. #24913753C2semidirect
17. #24913721C2semidirect
18. #24913720C2semidirect
19. #24913705C2semidirect
20. #24913695C2semidirect
21. #24913203C2semidirect
22. #24913199C2semidirect
23. #24912647C2semidirect
24. #24912639C2semidirect
25. #24912425C2semidirect
26. #24912421C2semidirect
27. #24910911C2semidirect
28. #24910908C2semidirect
29. #24910900C2semidirect
30. C2×#19127572C2semidirect
31. C83×#2416C2semidirect
47. C2×#14581772C22semidirect
50. C2×#14581769C22semidirect
60. C2×#14581764C22semidirect
73. #19127643C22semidirect
74. #19127640C22semidirect
75. #19127637C22semidirect
76. #19127637C22semidirect
77. #19127635C22semidirect
78. #19127634C22semidirect
79. #19127633C22semidirect
80. #19127632C22semidirect
81. #19127631C22semidirect
82. #19127631C22semidirect
85. #19127629C22semidirect
88. #19127627C22semidirect
89. #19127624C22semidirect
90. #19127624C22semidirect
91. #19127624C22semidirect
92. #19127623C22semidirect
93. #19127623C22semidirect
94. #19127623C22semidirect
95. #19127622C22semidirect
96. #19127621C22semidirect
103. #19127617C22semidirect
106. #19127616C22semidirect
107. #19127615C22semidirect
108. #19127615C22semidirect
109. #19127613C22semidirect
110. #19127613C22semidirect
115. #19127609C22semidirect
116. #19127609C22semidirect
117. #19127606C22semidirect
118. #19127605C22semidirect
119. #19127601C22semidirect
120. #19127600C22semidirect
121. #19127598C22semidirect
122. #19127596C22semidirect
123. #19127595C22semidirect
124. #19127591C22semidirect
125. #19127589C22semidirect
126. #19127589C22semidirect
127. #19127588C22semidirect
128. #19127585C22semidirect
129. #19127585C22semidirect
130. #19127584C22semidirect
135. #19127581C22semidirect
140. #19127578C22semidirect
147. #19127577C22semidirect
148. #19127577C22semidirect
149. #19127576C22semidirect
150. #19127574C22semidirect
151. #19127574C22semidirect
152. #19127573C22semidirect
167. #19127559C22semidirect
168. #19127559C22semidirect
171. #19127558C22semidirect
177. C2×#121×C83C22semidirect
180. #396×C83C22semidirect
181. #396×C83C22semidirect
182. #394×C83C22semidirect
183. #394×C83C22semidirect
184. #390×C83C22semidirect
185. #389×C83C22semidirect
188. #380×C83C22semidirect
294. C2×(C2×D83)⋊C4D4semidirect
908. #2416D83semidirect
910. C83#36738semidirect
945. C2×#121C2×D83semidirect
980. #396C2×D83semidirect
981. #396C2×D83semidirect
996. #394C2×D83semidirect
997. #394C2×D83semidirect
1009. #390C2×D83semidirect
1013. #389C2×D83semidirect
1065. #380C2×D83semidirect

Maximal subgroups

By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.

subgroupindex
C2×#191282882
C2×#191282842
#249157442
#249157422
#249143712
#249142802
#249142752
#249142362
#249140052
#249139982
#249139752
#249139452
#249139442
#249137712
#249137612
#249137532
#249137212
#249137202
#249137052
#249136952
#249132032
#249131992
#249126472
#249126392
#249124252
#249124212
#249109112
#249109082
#249109002
C2×#191275722
C83×#24162
#3673883