Finite Group Databasebeta

← #35611466

Subgroups — #35611466

Order 21248.

2432 conjugacy classes of subgroups.

The subgroup lattice has 1672 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128292C211yesmaximal, characteristic, complemented
2C2×#19128213C211yesmaximal, characteristic, complemented
3#24915754C211yesmaximal, characteristic, complemented
4#24915749C211yesmaximal, characteristic, complemented
5#24914165C211yesmaximal, characteristic, complemented
6#24914146C211yesmaximal, characteristic, complemented
7#24914120C211yesmaximal, characteristic, complemented
8#24914101C211yesmaximal, characteristic, complemented
9#24914075C211yesmaximal, characteristic, complemented
10#24914032C211yesmaximal, characteristic, complemented
11#24914021C211yesmaximal, characteristic, complemented
12#24913851C211yesmaximal, characteristic, complemented
13#24913832C211yesmaximal, characteristic, complemented
14#24913823C211yesmaximal, characteristic, complemented
15#24913821C211yesmaximal, characteristic, complemented
16#24913810C211yesmaximal, characteristic, complemented
17#24913801C211yesmaximal, characteristic, complemented
18#24913801C211yesmaximal, characteristic, complemented
19#24913794C211yesmaximal, characteristic, complemented
20#24913783C211yesmaximal, characteristic, complemented
21#24913387C211yesmaximal, characteristic, complemented
22#24913310C211yesmaximal, characteristic, complemented
23#24913161C211yesmaximal, characteristic, complemented
24#24913092C211yesmaximal, characteristic, complemented
25#24913048C211yesmaximal, characteristic, complemented
26#24912814C211yesmaximal, characteristic, complemented
27#24912663C211yesmaximal, characteristic, complemented
28#24910805C211yesmaximal, characteristic, complemented
29#24910796C211yesmaximal, characteristic, complemented
30#24910101C211yesmaximal, characteristic, complemented
31C83×#2601C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C23×C4×D83C2211yescharacteristic
34#19128292—28no—
35C2×#14581787C2211yescharacteristic
36C2×#14581784C2211yescharacteristic, complemented
37C2×#14581783C2211yescharacteristic, complemented
38#19128213—28no—
39C2×#14581777C2211yescharacteristic
40C2×#14581777C2211yescharacteristic, complemented
41C2×#14581776C2211yescharacteristic
42C2×#14581776C2211yescharacteristic
43C2×#14581776C2211yescharacteristic
44C2×#14581774C2211yescharacteristic
45C2×#14581774C2211yescharacteristic
46C2×#14581774C2211yescharacteristic
47C2×#14581774C2211yescharacteristic, complemented
48C2×#14581772C2211yescharacteristic
49C2×#14581772C2211yescharacteristic
50C2×#14581772C2211yescharacteristic, complemented
51C2×#14581770C2211yescharacteristic
52C2×#14581770C2211yescharacteristic
53C2×#14581769C2211yescharacteristic
54C2×#14581769C2211yescharacteristic, complemented
55C2×#14581769C2211yescharacteristic, complemented
56C2×#14581767C2211yescharacteristic
57C2×#14581767C2211yescharacteristic
58C2×#14581765C2211yescharacteristic
59C2×#14581764C2211yescharacteristic
60C2×#14581762C2211yescharacteristic
61C2×#14581762C2211yescharacteristic
62C2×#14581760C2211yescharacteristic
63C2×C4×D332C2211yescharacteristic
64C2×C4×D332C2211yescharacteristic
65C2×C4×D332C2211yescharacteristic
66C2×C4×D332C2211yescharacteristic
67C2×(C22⋊D83)⋊C4C2211yescharacteristic, complemented
68C2×C4⋊C4×D83C2211yescharacteristic, complemented
69#19127640C2211yescharacteristic, complemented
70#19127637C2211yescharacteristic
71#19127635C2211yescharacteristic, complemented
72#19127634C2211yescharacteristic, complemented
73#19127633C2211yescharacteristic, complemented
74#19127633C2211yescharacteristic, complemented
75#19127631C2211yescharacteristic, complemented
76#19127631C2211yescharacteristic, complemented
77#19127630C2211yescharacteristic
78#19127630C2211yescharacteristic, complemented
79#19127628C2211yescharacteristic
80#19127628C2211yescharacteristic, complemented
81#19127627C2211yescharacteristic
82#19127626C2211yescharacteristic
83#19127626C2211yescharacteristic, complemented
84#19127625C2211yescharacteristic
85#19127624C2211yescharacteristic, complemented
86#19127623C2211yescharacteristic
87#19127623C2211yescharacteristic
88#19127623C2211yescharacteristic
89#19127623C2211yescharacteristic, complemented
90#19127623C2211yescharacteristic, complemented
91#19127623C2211yescharacteristic, complemented
92#19127622C2211yescharacteristic, complemented
93#19127622C2211yescharacteristic, complemented
94#19127621C2211yescharacteristic, complemented
95#19127619C2211yescharacteristic
96#19127619C2211yescharacteristic
97#19127619C2211yescharacteristic, complemented
98#19127618C2211yescharacteristic
99#19127618C2211yescharacteristic
100#19127618C2211yescharacteristic
101#19127617C2211yescharacteristic
102#19127617C2211yescharacteristic
103#19127617C2211yescharacteristic
104#19127616C2211yescharacteristic
105#19127616C2211yescharacteristic, complemented
106#19127616C2211yescharacteristic, complemented
107#19127614C2211yescharacteristic, complemented
108#19127610C2211yescharacteristic
109#19127610C2211yescharacteristic
110#19127610C2211yescharacteristic
111#19127610C2211yescharacteristic, complemented
112#19127609C2211yescharacteristic
113#19127605C2211yescharacteristic, complemented
114#19127603C2211yescharacteristic
115#19127603C2211yescharacteristic
116#19127602C2211yescharacteristic
117#19127602C2211yescharacteristic
118#19127601C2211yescharacteristic
119#19127601C2211yescharacteristic
120#19127601C2211yescharacteristic, complemented
121#19127597C2211yescharacteristic, complemented
122#19127597C2211yescharacteristic, complemented
123#19127596C2211yescharacteristic, complemented
124#19127596C2211yescharacteristic, complemented
125#19127595C2211yescharacteristic
126#19127595C2211yescharacteristic
127#19127592C2211yescharacteristic
128#19127592C2211yescharacteristic
129#19127592C2211yescharacteristic, complemented
130#19127592C2211yescharacteristic, complemented
131#19127591C2211yescharacteristic
132#19127591C2211yescharacteristic, complemented
133#19127590C2211yescharacteristic
134#19127587C2211yescharacteristic, complemented
135#19127585C2211yescharacteristic, complemented
136#19127585C2211yescharacteristic, complemented
137#19127581C2211yescharacteristic
138#19127579C2211yescharacteristic
139#19127579C2211yescharacteristic
140#19127579C2211yescharacteristic, complemented
141#19127578C2211yescharacteristic
142#19127577C2211yescharacteristic
143#19127577C2211yescharacteristic
144#19127577C2211yescharacteristic
145#19127577C2211yescharacteristic, complemented
146#19127576C2211yescharacteristic
147#19127576C2211yescharacteristic, complemented
148#19127575C2211yescharacteristic
149#19127575C2211yescharacteristic
150#19127575C2211yescharacteristic
151#19127575C2211yescharacteristic
152#19127575C2211yescharacteristic, complemented
153#19127575C2211yescharacteristic, complemented
154#19127575C2211yescharacteristic, complemented
155#19127574C2211yescharacteristic
156#19127574C2211yescharacteristic
157#19127572C2211yescharacteristic
158#19127572C2211yescharacteristic
159#19127572C2211yescharacteristic, complemented
160#19127572C2211yescharacteristic, complemented
161#19127571C2211yescharacteristic, complemented
162#19127567C2211yescharacteristic, complemented
163#19127563C2211yescharacteristic
164#19127563C2211yescharacteristic
165#19127563C2211yescharacteristic, complemented
166#19127560C2211yescharacteristic
167#19127560C2211yescharacteristic
168#19127560C2211yescharacteristic, complemented
169#19127559C2211yescharacteristic
170#19127556C2211yescharacteristic
171#19127556C2211yescharacteristic
172#19127556C2211yescharacteristic
173#19127547C2211yescharacteristic, complemented
174C2×#126×C83C2211yescharacteristic, complemented
175C2×#117×C83C2211yescharacteristic
176#398×C83C2211yescharacteristic, complemented
177#396×C83C2211yescharacteristic
178#396×C83C2211yescharacteristic, complemented
179#394×C83C2211yescharacteristic
180#390×C83C2211yescharacteristic
181#389×C83C2211yescharacteristic, complemented
182#388×C83C2211yescharacteristic
183#388×C83C2211yescharacteristic, complemented
184#388×C83C2211yescharacteristic, complemented
185#387×C83C2211yescharacteristic, complemented
186#386×C83C2211yescharacteristic
187#385×C83C2211yescharacteristic
188C4×C4⋊C4×C83C2211yescharacteristic, complemented
189C24×D83C2311yescharacteristic
190C2×#13050590—24no—
191C2×#13050590—42no—
192C2×#13050590—42no—
193C22×Dic166C2311yescharacteristic
194C22×Dic166C2311yescharacteristic
195C22×D332C2311yescharacteristic
196C22×D332C2311yescharacteristic
197C22×D332C2311yescharacteristic
198C22×D332C2311yescharacteristic
199C22×D332C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C22×C22⋊D83C2311yescharacteristic
204C22×C22⋊D83C2311yescharacteristic
205C22×C22⋊D83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C23×Dic83C2311yescharacteristic
208C22×C4×D83—24no—
209C22×C4×D83—42no—
210C22×C4×D83—42no—
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215C22×C4×D83C2311yescharacteristic
216C22×C4×D83C2311yescharacteristic
217C22×C4×D83C2311yescharacteristic
218C22×C4×D83C2311yescharacteristic
219#14581787—24no—
220#14581784—24no—
221#14581783—24no—
222#14581777—24no—
223#14581777—42no—
224#14581776—24no—
225#14581776—24no—
226#14581776—24no—
227#14581774—24no—
228#14581774—24no—
229#14581774—42no—
230#14581774—42no—
231#14581772—24no—
232#14581772—24no—
233#14581772—24no—
234#14581770—24no—
235#14581770—42no—
236#14581769—24no—
237#14581769—42no—
238#14581769—42no—
239#14581767—24no—
240#14581767—24no—
241#14581765—24no—
242#14581764—42no—
243#14581762—24no—
244#14581762—24no—
245#14581760—42no—
246C4×D332—24no—
247C4×D332—24no—
248C4×D332—24no—
249C4×D332D418yescomplemented
250(C22⋊D83)⋊C4—24no—
251C2×C4⋊Dic83C2311yescharacteristic
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×C4⋊Dic83C2311yescharacteristic
261C2×C4⋊Dic83C2311yescharacteristic
262C2×C4⋊Dic83C2311yescharacteristic
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×Dic83⋊C4C2311yescharacteristic
278C2×Dic83⋊C4C2311yescharacteristic
279C4⋊C4×D83—24no—
280C2×C22⋊Dic83C2311yescharacteristic
281C2×C22⋊Dic83C2311yescharacteristic
282C2×C22⋊Dic83C2311yescharacteristic
283C2×C22⋊Dic83C2311yescharacteristic
284C2×C22⋊Dic83C2311yescharacteristic
285C2×C22⋊Dic83C2311yescharacteristic
286C2×C22⋊Dic83C2311yescharacteristic
287C2×(C2×D83)⋊C4C2311yescharacteristic
288C2×(C2×D83)⋊C4C2311yescharacteristic
289C2×(C2×D83)⋊C4C2311yescharacteristic
290C2×(C2×D83)⋊C4C2311yescharacteristic
291C2×(C2×D83)⋊C4C2311yescharacteristic
292C2×(C2×D83)⋊C4C2311yescharacteristic
293C2×(C2×D83)⋊C4C2311yescharacteristic
294C2×(C2×D83)⋊C4C2311yescharacteristic
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×(C2×D83)⋊C4C2311yescharacteristic
320C2×(C2×D83)⋊C4C2311yescharacteristic
321C2×C4×Dic83C2311yescharacteristic
322C2×C4×Dic83C2311yescharacteristic
323C2×C4×Dic83C2311yescharacteristic
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
348C22×D4×C83C2311yescharacteristic
349C23×C4×C83C2311yescharacteristic
350#126×C83—24no—
351#117×C83—24no—
352C2×C4⋊C4×C83C2311yescharacteristic
353C2×C4⋊C4×C83C2311yescharacteristic
354C2×C4⋊C4×C83C2311yescharacteristic
355C2×C4⋊C4×C83C2311yescharacteristic
356C2×C4⋊C4×C83C2311yescharacteristic
357C2×C4⋊C4×C83C2311yescharacteristic
358C2×C4⋊C4×C83C2311yescharacteristic
359C2×C4⋊C4×C83C2311yescharacteristic
360C2×C4⋊C4×C83C2311yescharacteristic
361C2×C4⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C22⋊C4×C83C2311yescharacteristic
365C2×C22⋊C4×C83C2311yescharacteristic
366C2×C22⋊C4×C83C2311yescharacteristic
367C2×C22⋊C4×C83C2311yescharacteristic
368C2×C22⋊C4×C83C2311yescharacteristic
369C2×C22⋊C4×C83C2311yescharacteristic
370C2×C22⋊C4×C83C2311yescharacteristic
371C2×C22⋊C4×C83C2311yescharacteristic
372C2×C22⋊C4×C83C2311yescharacteristic
373C2×C42×C83C2311yescharacteristic
374C2×C42×C83C2311yescharacteristic
375C2×C42×C83C2311yescharacteristic
376C2×C42×C83C2311yescharacteristic
377#95×C83C2311yescharacteristic
378#95×C83C2311yescharacteristic
379#95×C83C2311yescharacteristic
380#95×C83C2311yescharacteristic
381#95×C83C2311yescharacteristic
382#95×C83C2311yescharacteristic
383#95×C83C2311yescharacteristic
384#95×C83C2311yescharacteristic
385C23×D83—22no—
386C23×D83—22no—
387C23×D83—22no—
388C23×D83—41no—
389C23×D83—41no—
390C23×D83—41no—
391C23×D83—41no—
392C23×D83C2411yescharacteristic
393C23×D83C2411yescharacteristic
394C23×D83C2411yescharacteristic
395C23×D83C2411yescharacteristic
396#13050590—416no—
397C2×Dic166—22no—
398C2×Dic166—22no—
399C2×Dic166—22no—
400C2×Dic166—41no—
401C2×Dic166—41no—
402C2×Dic166—41no—
403C2×D332—22no—
404C2×D332—22no—
405C2×D332—22no—
406C2×D332—22no—
407C2×D332—22no—
408C2×D332—22no—
409C2×D332—22no—
410C2×D332—41no—
411C2×D332—41no—
412C2×D332—41no—
413C2×D332—41no—
414C2×D332—41no—
415C2×D332—41no—
416C2×D332—41no—
417C2×D332C2×D414yes—
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—22no—
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—
436C22×Dic83—22no—
437C22×Dic83—22no—
438C22×Dic83—22no—
439C22×Dic83—41no—
440C22×Dic83—41no—
441C22×Dic83—41no—
442C22×Dic83C2411yescharacteristic
443C22×Dic83C2411yescharacteristic
444C22×Dic83C2411yescharacteristic
445C22×Dic83C2411yescharacteristic
446C22×Dic83C2411yescharacteristic
447C22×Dic83C2411yescharacteristic
448C22×Dic83C2411yescharacteristic
449C22×Dic83C2411yescharacteristic
450C22×Dic83C2411yescharacteristic
451C22×Dic83C2411yescharacteristic
452C22×Dic83C2411yescharacteristic
453C22×Dic83C2411yescharacteristic
454C2×C4×D83—22no—
455C2×C4×D83—22no—
456C2×C4×D83—22no—
457C2×C4×D83—22no—
458C2×C4×D83—22no—
459C2×C4×D83—22no—
460C2×C4×D83—22no—
461C2×C4×D83—22no—
462C2×C4×D83—41no—
463C2×C4×D83—41no—
464C2×C4×D83—41no—
465C2×C4×D83—41no—
466C2×C4×D83—41no—
467C2×C4×D83—41no—
468C2×C4×D83—41no—
469C2×C4×D83—41no—
470C2×C4×D83—41no—
471C2×C4×D83—41no—
472C2×C4×D83—41no—
473C2×C4×D83—41no—
474C2×C4×D83—416no—
475C2×C4×D83—41no—
476C2×C4×D83—41no—
477C2×C4×D83C2×D414yes—
478C2×C4×D83C2×D414yes—
479C4⋊Dic83—22no—
480C4⋊Dic83—22no—
481C4⋊Dic83—22no—
482C4⋊Dic83—22no—
483C4⋊Dic83—22no—
484C4⋊Dic83—22no—
485C4⋊Dic83—22no—
486C4⋊Dic83—41no—
487C4⋊Dic83—41no—
488C4⋊Dic83—41no—
489C4⋊Dic83—41no—
490C4⋊Dic83C2×D414yes—
491Dic83⋊C4—22no—
492Dic83⋊C4—22no—
493Dic83⋊C4—22no—
494Dic83⋊C4—22no—
495Dic83⋊C4—22no—
496Dic83⋊C4—22no—
497Dic83⋊C4—22no—
498Dic83⋊C4—22no—
499Dic83⋊C4—41no—
500Dic83⋊C4—41no—
501Dic83⋊C4—41no—
502Dic83⋊C4—41no—
503Dic83⋊C4—41no—
504Dic83⋊C4—41no—
505Dic83⋊C4—41no—
506Dic83⋊C4—41no—
507C22⋊Dic83—22no—
508C22⋊Dic83—22no—
509C22⋊Dic83—22no—
510C22⋊Dic83—41no—
511C22⋊Dic83—41no—
512C22⋊Dic83—41no—
513C22⋊Dic83—41no—
514(C2×D83)⋊C4—22no—
515(C2×D83)⋊C4—22no—
516(C2×D83)⋊C4—22no—
517(C2×D83)⋊C4—22no—
518(C2×D83)⋊C4—22no—
519(C2×D83)⋊C4—22no—
520(C2×D83)⋊C4—22no—
521(C2×D83)⋊C4—22no—
522(C2×D83)⋊C4—22no—
523(C2×D83)⋊C4—22no—
524(C2×D83)⋊C4—22no—
525(C2×D83)⋊C4—41no—
526(C2×D83)⋊C4—41no—
527(C2×D83)⋊C4—41no—
528(C2×D83)⋊C4—41no—
529(C2×D83)⋊C4—41no—
530(C2×D83)⋊C4—41no—
531(C2×D83)⋊C4—41no—
532(C2×D83)⋊C4—41no—
533(C2×D83)⋊C4—41no—
534(C2×D83)⋊C4—41no—
535(C2×D83)⋊C4—41no—
536(C2×D83)⋊C4—41no—
537(C2×D83)⋊C4—41no—
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)⋊C4C2×D414yes—
547(C2×D83)⋊C4C2×D414yes—
548C4×Dic83—22no—
549C4×Dic83—41no—
550C4×Dic83—41no—
551C24×C83C2411yescharacteristic
552C24×C83C2411yescharacteristic
553C2×D4×C83—22no—
554C2×D4×C83—41no—
555C2×D4×C83—41no—
556C22×C4×C83—22no—
557C22×C4×C83—22no—
558C22×C4×C83—22no—
559C22×C4×C83C2411yescharacteristic
560C22×C4×C83C2411yescharacteristic
561C22×C4×C83C2411yescharacteristic
562C22×C4×C83C2411yescharacteristic
563C22×C4×C83C2411yescharacteristic
564C22×C4×C83C2411yescharacteristic
565C22×C4×C83C2411yescharacteristic
566C22×C4×C83C2411yescharacteristic
567C22×C4×C83C2411yescharacteristic
568C22×C4×C83C2411yescharacteristic
569C22×C4×C83C2411yescharacteristic
570C22×C4×C83C2411yescharacteristic
571C22×C4×C83C2411yescharacteristic
572C4⋊C4×C83—22no—
573C4⋊C4×C83—22no—
574C4⋊C4×C83—22no—
575C4⋊C4×C83—22no—
576C4⋊C4×C83—22no—
577C4⋊C4×C83—22no—
578C4⋊C4×C83—41no—
579C4⋊C4×C83—41no—
580C4⋊C4×C83—41no—
581C4⋊C4×C83—41no—
582C22⋊C4×C83—22no—
583C22⋊C4×C83—22no—
584C22⋊C4×C83—22no—
585C22⋊C4×C83—22no—
586C22⋊C4×C83—22no—
587C22⋊C4×C83—22no—
588C22⋊C4×C83—22no—
589C22⋊C4×C83—41no—
590C22⋊C4×C83—41no—
591C22⋊C4×C83—41no—
592C22⋊C4×C83—41no—
593C42×C83—22no—
594C42×C83—41no—
595C42×C83—41no—
596C42×C83C2×D414yes—
597C23×C83—21no—
598C23×C83—21no—
599C23×C83—21no—
600C23×C83—21no—
601C23×C83—21no—
602C23×C83—21no—
603C23×C83—21no—
604C23×C83—21no—
605C23×C83—21no—
606C23×C83—21no—
607C23×C83—21no—
608C23×C83—21no—
609C23×C83—21no—
610C23×C83H(5,𝔽2)12yes—
611C23×C83C2511yescharacteristic
612C22×D83—21no—
613C22×D83—21no—
614C22×D83—21no—
615C22×D83—21no—
616C22×D83—21no—
617C22×D83—21no—
618C22×D83—21no—
619C22×D83—21no—
620C22×D83—21no—
621C22×D83—21no—
622C22×D83—21no—
623C22×D83—21no—
624C22×D83—21no—
625C22×D83—21no—
626C22×D83—21no—
627C22×D83—21no—
628C22×D83—21no—
629C22×D83—21no—
630C22×D83—21no—
631C22×D83—21no—
632C22×D83—21no—
633C22×D83—21no—
634C22×D83—21no—
635C22×D83—21no—
636C22×D83—21no—
637C22×D83—44no—
638C22×D83—44no—
639C22×D83—44no—
640C22×D83—44no—
641C22×D83—44no—
642C22×D83—44no—
643C22×D83—44no—
644C22×D83C22×D412yes—
645C22×D83C22×D412yes—
646C22×D832−1+412yes—
647D4×C83—82no—
648C2×C4×C83—28no—
649C2×C4×C83—21no—
650C2×C4×C83—21no—
651C2×C4×C83—21no—
652C2×C4×C83—21no—
653C2×C4×C83—21no—
654C2×C4×C83—21no—
655C2×C4×C83—21no—
656C2×C4×C83—21no—
657C2×C4×C83—21no—
658C2×C4×C83—21no—
659C2×C4×C83—21no—
660C2×C4×C83—21no—
661C2×C4×C83—21no—
662C2×C4×C83—21no—
663C2×C4×C83—21no—
664C2×C4×C83—21no—
665C2×C4×C83—21no—
666C2×C4×C83—21no—
667C2×C4×C83—21no—
668C2×C4×C83—21no—
669C2×C4×C83—21no—
670C2×C4×C83—21no—
671C2×C4×C83—21no—
672C2×C4×C83—21no—
673C2×C4×C83—21no—
674C2×C4×C83—21no—
675C2×C4×C83—21no—
676C2×C4×C83—21no—
677C2×C4×C83—21no—
678C2×C4×C83—21no—
679C2×C4×C83—21no—
680C2×C4×C83—21no—
681C2×C4×C83—21no—
682C2×C4×C83—21no—
683C2×C4×C83—21no—
684C2×C4×C83C22×D412yes—
685C2×C4×C83C22×D412yes—
686C2×C4×C83C22×D412yes—
687C2×C4×C83H(5,𝔽2)12yes—
688C22⋊D83—44no—
689C22⋊D83—44no—
690C22⋊D83—44no—
691C22⋊D83—82no—
692C22⋊D83—82no—
693C22⋊D83—82no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—21no—
697C2×Dic83—21no—
698C2×Dic83—21no—
699C2×Dic83—21no—
700C2×Dic83—21no—
701C2×Dic83—21no—
702C2×Dic83—21no—
703C2×Dic83—21no—
704C2×Dic83—21no—
705C2×Dic83—21no—
706C2×Dic83—21no—
707C2×Dic83—21no—
708C2×Dic83—21no—
709C2×Dic83—21no—
710C2×Dic83—21no—
711C2×Dic83—21no—
712C2×Dic83—21no—
713C2×Dic83—21no—
714C2×Dic83—21no—
715C2×Dic83—21no—
716C2×Dic83—21no—
717C2×Dic83—21no—
718C2×Dic83—21no—
719C2×Dic83—21no—
720C2×Dic83—21no—
721C2×Dic83—21no—
722C2×Dic83—21no—
723C2×Dic83—21no—
724C2×Dic83—21no—
725C2×Dic83—21no—
726C2×Dic83—21no—
727C2×Dic83—21no—
728C2×Dic83—44no—
729C2×Dic83—82no—
730C2×Dic83C22×D412yes—
731C2×Dic83C22×D412yes—
732D332—44no—
733D332—44no—
734D332—44no—
735D332—44no—
736D332—44no—
737C4×D83—44no—
738C4×D83—44no—
739C4×D83—44no—
740C4×D83—44no—
741C4×D83—44no—
742C4×D83—44no—
743C4×D83—44no—
744C4×D83—82no—
745Dic166—44no—
746Dic166—82no—
747C22×C83—22no—
748C22×C83—22no—
749C22×C83—22no—
750C22×C83—41no—
751C22×C83—41no—
752C22×C83—41no—
753C22×C83—41no—
754C22×C83—41no—
755C22×C83—41no—
756C22×C83—41no—
757C22×C83—41no—
758C22×C83—41no—
759C22×C83—41no—
760C22×C83—41no—
761C22×C83C23×D411yescharacteristic
762C22×C83C2×H(5,𝔽2)11yescharacteristic
763C22×C83C2×H(5,𝔽2)11yescharacteristic
764C22×C83C2×2−1+411yescharacteristic
765C22×C83#58511yescharacteristic
766C22×C83#58511yescharacteristic
767C22×C83#58511yescharacteristic
768C2×D83—22no—
769C2×D83—22no—
770C2×D83—22no—
771C2×D83—22no—
772C2×D83—22no—
773C2×D83—22no—
774C2×D83—22no—
775C2×D83—22no—
776C2×D83—22no—
777C2×D83—416no—
778C2×D83—41no—
779C2×D83—41no—
780C2×D83—41no—
781C2×D83—41no—
782C2×D83—41no—
783C2×D83—41no—
784C2×D83—41no—
785C2×D83—41no—
786C2×D83—41no—
787C2×D83—41no—
788C2×D83—41no—
789C2×D83—41no—
790C2×D83—41no—
791C2×D83—41no—
792C2×D83—41no—
793C2×D83—41no—
794C2×D83—41no—
795C2×D83—41no—
796C2×D83—41no—
797C4×C83—22no—
798C4×C83—22no—
799C4×C83—22no—
800C4×C83—22no—
801C4×C83—41no—
802C4×C83—41no—
803C4×C83—41no—
804C4×C83—41no—
805C4×C83—41no—
806C4×C83—41no—
807C4×C83—41no—
808C4×C83—41no—
809C4×C83—41no—
810Dic83—22no—
811Dic83—22no—
812Dic83—41no—
813Dic83—41no—
814Dic83—41no—
815Dic83—41no—
816Dic83—41no—
817Dic83—41no—
818Dic83—41no—
819Dic83—41no—
820Dic83—41no—
821Dic83—41no—
822#36723—831nomaximal, Sylow
823C2×C83—42no—
824C2×C83—81no—
825C2×C83#344911yescharacteristic
826C2×C83#348411yescharacteristic
827C2×C83#348911yescharacteristic
828C2×C83#353311yescharacteristic
829C2×C83#353511yescharacteristic
830C2×C83#353911yescharacteristic
831C2×C83#354111yescharacteristic
832D83—42no—
833D83—42no—
834D83—42no—
835D83—81no—
836C2×#539—831no—
837C2×#525—831no—
838#2849—831no—
839#2848—831no—
840#2707—831no—
841#2706—831no—
842#2704—831no—
843#2703—831no—
844#2701—831no—
845#2698—831no—
846#2697—831no—
847#2685—831no—
848#2683—831no—
849#2682—831no—
850#2681—831no—
851#2681—831no—
852#2680—831no—
853#2680—831no—
854#2678—831no—
855#2678—831no—
856#2638—831no—
857#2630—831no—
858#2611—831no—
859#2603—831no—
860#2601D8311yescharacteristic, complemented
861#2600—831no—
862#2579—831no—
863#2566—831no—
864#2407—831no—
865#2406—831no—
866#2319—831no—
867C83#3672311yescharacteristic, complemented, Sylow
868C22×#41—831no—
869C24×C4—831no—
870#539—1668no—
871C2×#126—831no—
872C2×#126C2×D8311yescharacteristic, complemented
873C2×#125—831no—
874C2×#125—831no—
875#525—1668no—
876C2×#123—831no—
877C2×#123—831no—
878C2×#123—831no—
879C2×#123—831no—
880C2×#123—831no—
881C2×#123—831no—
882C2×#123—831no—
883C2×#123—831no—
884C2×#123—831no—
885C2×C22⋊Q8—831no—
886C2×C22⋊Q8—831no—
887C2×C22⋊Q8—831no—
888C2×C22⋊Q8—831no—
889C2×C22⋊Q8—831no—
890C2×C22⋊Q8—831no—
891C2×C22⋊Q8—831no—
892C2×C22⋊Q8—831no—
893C2×#121—831no—
894C2×#121—831no—
895C2×#121—831no—
896C2×#121—831no—
897C2×#120—831no—
898C2×#120—831no—
899C2×#120—831no—
900C2×C4×D4—831no—
901C2×C4×D4—831no—
902C2×C4×D4—831no—
903C2×C4×D4—831no—
904C2×C4×D4—831no—
905C2×#117C2×D8311yescharacteristic
906C22×C4⋊C4—831no—
907#400—831no—
908#399—831no—
909#398—831no—
910#398—831no—
911#398—831no—
912#398—831no—
913#398—831no—
914#398—831no—
915#398C2×D8311yescharacteristic, complemented
916#397—831no—
917#397—831no—
918#397—831no—
919#397—831no—
920#397—831no—
921#397—831no—
922#397—831no—
923#396—831no—
924#396—831no—
925#396—831no—
926#396—831no—
927#396—831no—
928#396—831no—
929#396—831no—
930#396—831no—
931#396C2×D8311yescharacteristic
932#396C2×D8311yescharacteristic, complemented
933#395—831no—
934#395—831no—
935#395—831no—
936#394—831no—
937#394—831no—
938#394—831no—
939#394—831no—
940#394—831no—
941#394—831no—
942#394—831no—
943#394—831no—
944#394—831no—
945#394—831no—
946#394—831no—
947#394—831no—
948#394C2×D8311yescharacteristic
949#393—831no—
950#392—831no—
951#392—831no—
952#392—831no—
953#392—831no—
954#392—831no—
955#391—831no—
956#390—831no—
957#390—831no—
958#390—831no—
959#390—831no—
960#390—831no—
961#390—831no—
962#390—831no—
963#390C2×D8311yescharacteristic
964#389—831no—
965#389—831no—
966#389—831no—
967#389—831no—
968#389C2×D8311yescharacteristic, complemented
969#388—831no—
970#388—831no—
971#388—831no—
972#388—831no—
973#388—831no—
974#388—831no—
975#388—831no—
976#388—831no—
977#388—831no—
978#388C2×D8311yescharacteristic
979#388C2×D8311yescharacteristic, complemented
980#388C2×D8311yescharacteristic, complemented
981#387—831no—
982#387—831no—
983#387—831no—
984#387C2×D8311yescharacteristic, complemented
985#386—831no—
986#386—831no—
987#386—831no—
988#386—831no—
989#386—831no—
990#386—831no—
991#386—831no—
992#386—831no—
993#386—831no—
994#386C2×D8311yescharacteristic
995#385—831no—
996#385—831no—
997#385—831no—
998#385—831no—
999#385—831no—
1000#385—831no—
1001#385—831no—
1002#385—831no—
1003#385—831no—
1004#385—831no—
1005#385—831no—
1006#385—831no—
1007#385—831no—
1008#385—831no—
1009#385—831no—
1010#385C2×D8311yescharacteristic
1011#384—831no—
1012#382—831no—
1013#381—831no—
1014#381—831no—
1015#381—831no—
1016#380—831no—
1017#380—831no—
1018#380—831no—
1019#380—831no—
1020#379—831no—
1021#379—831no—
1022#379—831no—
1023C4×C4⋊C4C2×D8311yescharacteristic, complemented
1024#376—831no—
1025C25—831no—
1026C2×#41—3322no—
1027C2×#41—3322no—
1028C2×#41—1664no—
1029C22×Q8—831no—
1030C22×Q8—831no—
1031C22×D4—831no—
1032C22×D4—831no—
1033C22×D4—831no—
1034C22×D4—831no—
1035C22×D4—831no—
1036C22×D4—831no—
1037C22×D4—831no—
1038C22×D4—831no—
1039C22×D4—831no—
1040C22×D4—831no—
1041C22×D4—831no—
1042C22×D4C22×D8311yescharacteristic
1043C23×C4—3322no—
1044C23×C4—3322no—
1045C23×C4—831no—
1046C23×C4—831no—
1047C23×C4—831no—
1048C23×C4—831no—
1049C23×C4—831no—
1050C23×C4—831no—
1051C23×C4—831no—
1052C23×C4—831no—
1053C23×C4—831no—
1054C23×C4—831no—
1055C23×C4—1664no—
1056C23×C4C22×D8311yescharacteristic
1057#126—24no—
1058#126—1664no—
1059#125—1664no—
1060#125—1664no—
1061#123—3322no—
1062#123—3322no—
1063#123—3322no—
1064#123—1664no—
1065#123—1664no—
1066#123—1664no—
1067#123—1664no—
1068#123—1664no—
1069#123—1664no—
1070C22⋊Q8—3322no—
1071C22⋊Q8—3322no—
1072C22⋊Q8—3322no—
1073C22⋊Q8—1664no—
1074C22⋊Q8—1664no—
1075C22⋊Q8—1664no—
1076C22⋊Q8—1664no—
1077C22⋊Q8—1664no—
1078#121—3322no—
1079#121—1664no—
1080#121—1664no—
1081#121—1664no—
1082#120—3322no—
1083#120—1664no—
1084#120—1664no—
1085C4×D4—838no—
1086C4×D4—1664no—
1087C4×D4—1664no—
1088C4×D4—1664no—
1089C4×D4—1664no—
1090#117—24no—
1091C2×C4⋊C4—831no—
1092C2×C4⋊C4—831no—
1093C2×C4⋊C4—831no—
1094C2×C4⋊C4—831no—
1095C2×C4⋊C4—831no—
1096C2×C4⋊C4—831no—
1097C2×C4⋊C4—831no—
1098C2×C4⋊C4—831no—
1099C2×C4⋊C4—831no—
1100C2×C4⋊C4—831no—
1101C2×C4⋊C4—831no—
1102C2×C4⋊C4—831no—
1103C2×C4⋊C4—831no—
1104C2×C4⋊C4—831no—
1105C2×C4⋊C4—831no—
1106C2×C4⋊C4—831no—
1107C2×C4⋊C4—831no—
1108C2×C4⋊C4—831no—
1109C2×C4⋊C4—831no—
1110C2×C4⋊C4—831no—
1111C2×C4⋊C4—831no—
1112C2×C4⋊C4—831no—
1113C2×C4⋊C4—831no—
1114C2×C4⋊C4—831no—
1115C2×C4⋊C4—831no—
1116C2×C4⋊C4—831no—
1117C2×C4⋊C4—831no—
1118C2×C4⋊C4—831no—
1119C2×C4⋊C4—1664no—
1120C2×C4⋊C4C22×D8311yescharacteristic
1121C2×C4⋊C4C22×D8311yescharacteristic
1122C2×C4⋊C4C22×D8311yescharacteristic
1123C2×C4⋊C4C22×D8311yescharacteristic
1124C2×C4⋊C4C22×D8311yescharacteristic
1125C2×C4⋊C4C22×D8311yescharacteristic
1126C2×C4⋊C4C22×D8311yescharacteristic
1127C2×C4⋊C4C22×D8311yescharacteristic
1128C2×C4⋊C4C22×D8311yescharacteristic
1129C2×C4⋊C4C22×D8311yescharacteristic
1130C2×C22⋊C4—831no—
1131C2×C22⋊C4—831no—
1132C2×C22⋊C4—831no—
1133C2×C22⋊C4—831no—
1134C2×C22⋊C4—831no—
1135C2×C22⋊C4—831no—
1136C2×C22⋊C4—831no—
1137C2×C22⋊C4—831no—
1138C2×C22⋊C4—831no—
1139C2×C22⋊C4—831no—
1140C2×C22⋊C4—831no—
1141C2×C22⋊C4—831no—
1142C2×C22⋊C4—831no—
1143C2×C22⋊C4—831no—
1144C2×C22⋊C4—831no—
1145C2×C22⋊C4—831no—
1146C2×C22⋊C4—831no—
1147C2×C22⋊C4—831no—
1148C2×C22⋊C4—831no—
1149C2×C22⋊C4—831no—
1150C2×C22⋊C4—831no—
1151C2×C22⋊C4—831no—
1152C2×C22⋊C4—831no—
1153C2×C22⋊C4—831no—
1154C2×C22⋊C4—831no—
1155C2×C22⋊C4—831no—
1156C2×C22⋊C4—831no—
1157C2×C22⋊C4—831no—
1158C2×C22⋊C4—831no—
1159C2×C22⋊C4—831no—
1160C2×C22⋊C4—831no—
1161C2×C22⋊C4—831no—
1162C2×C22⋊C4—831no—
1163C2×C22⋊C4—831no—
1164C2×C22⋊C4—831no—
1165C2×C22⋊C4—831no—
1166C2×C22⋊C4—831no—
1167C2×C22⋊C4—831no—
1168C2×C22⋊C4—831no—
1169C2×C22⋊C4—831no—
1170C2×C22⋊C4—831no—
1171C2×C22⋊C4C22×D8311yescharacteristic
1172C2×C22⋊C4C22×D8311yescharacteristic
1173C2×C22⋊C4C22×D8311yescharacteristic
1174C2×C22⋊C4C22×D8311yescharacteristic
1175C2×C22⋊C4C22×D8311yescharacteristic
1176C2×C22⋊C4C22×D8311yescharacteristic
1177C2×C22⋊C4C22×D8311yescharacteristic
1178C2×C22⋊C4C22×D8311yescharacteristic
1179C2×C22⋊C4C22×D8311yescharacteristic
1180C2×C22⋊C4C22×D8311yescharacteristic
1181C2×C22⋊C4C22×D8311yescharacteristic
1182C2×C42—831no—
1183C2×C42—831no—
1184C2×C42—831no—
1185C2×C42C22×D8311yescharacteristic
1186C2×C42C22×D8311yescharacteristic
1187C2×C42C22×D8311yescharacteristic
1188C2×C42C22×D8311yescharacteristic
1189#95—831no—
1190#95—831no—
1191#95—831no—
1192#95—831no—
1193#95—831no—
1194#95—831no—
1195#95—831no—
1196#95—831no—
1197#95—831no—
1198#95—831no—
1199#95—831no—
1200#95—831no—
1201#95—831no—
1202#95—831no—
1203#95—831no—
1204#95—831no—
1205#95—831no—
1206#95—831no—
1207#95—831no—
1208#95—831no—
1209#95—831no—
1210#95—831no—
1211#95—831no—
1212#95—831no—
1213#95C22×D8311yescharacteristic
1214#95C22×D8311yescharacteristic
1215#95C22×D8311yescharacteristic
1216#95C22×D8311yescharacteristic
1217#95C22×D8311yescharacteristic
1218#95C22×D8311yescharacteristic
1219#95C22×D8311yescharacteristic
1220#95C22×D8311yescharacteristic
1221C24—3321no—
1222C24—3321no—
1223C24—3321no—
1224C24—3321no—
1225C24—831no—
1226C24—831no—
1227C24—831no—
1228C24—831no—
1229C24—1662no—
1230C24—1662no—
1231C24—1662no—
1232C24C23×D8311yescharacteristic
1233C24C23×D8311yescharacteristic
1234#41—33216no—
1235C2×Q8—3321no—
1236C2×Q8—3321no—
1237C2×Q8—3321no—
1238C2×Q8—1662no—
1239C2×Q8—1662no—
1240C2×Q8—1662no—
1241C2×D4—22no—
1242C2×D4—41no—
1243C2×D4—41no—
1244C2×D4—3321no—
1245C2×D4—3321no—
1246C2×D4—3321no—
1247C2×D4—3321no—
1248C2×D4—3321no—
1249C2×D4—3321no—
1250C2×D4—3321no—
1251C2×D4—3321no—
1252C2×D4—3321no—
1253C2×D4—3321no—
1254C2×D4—3321no—
1255C2×D4—3321no—
1256C2×D4—3321no—
1257C2×D4—3321no—
1258C2×D4—3321no—
1259C2×D4—3321no—
1260C2×D4—3321no—
1261C2×D4—3321no—
1262C2×D4—834no—
1263C2×D4—1662no—
1264C2×D4—1662no—
1265C2×D4—1662no—
1266C2×D4—1662no—
1267C2×D4—1662no—
1268C2×D4—1662no—
1269C2×D4—1662no—
1270C2×D4—1662no—
1271C2×D4—1662no—
1272C2×D4—1662no—
1273C2×D4—1662no—
1274C2×D4—1662no—
1275C2×D4—1662no—
1276C2×D4—1662no—
1277C22×C4—22no—
1278C22×C4—22no—
1279C22×C4—22no—
1280C22×C4—33216no—
1281C22×C4—3321no—
1282C22×C4—3321no—
1283C22×C4—3321no—
1284C22×C4—3321no—
1285C22×C4—3321no—
1286C22×C4—3321no—
1287C22×C4—3321no—
1288C22×C4—3321no—
1289C22×C4—3321no—
1290C22×C4—3321no—
1291C22×C4—3321no—
1292C22×C4—3321no—
1293C22×C4—3321no—
1294C22×C4—3321no—
1295C22×C4—3321no—
1296C22×C4—3321no—
1297C22×C4—3321no—
1298C22×C4—834no—
1299C22×C4—834no—
1300C22×C4—831no—
1301C22×C4—831no—
1302C22×C4—831no—
1303C22×C4—831no—
1304C22×C4—831no—
1305C22×C4—831no—
1306C22×C4—831no—
1307C22×C4—831no—
1308C22×C4—831no—
1309C22×C4—831no—
1310C22×C4—831no—
1311C22×C4—831no—
1312C22×C4—1662no—
1313C22×C4—1662no—
1314C22×C4—1662no—
1315C22×C4—1662no—
1316C22×C4—1662no—
1317C22×C4—1662no—
1318C22×C4—1662no—
1319C22×C4—1662no—
1320C22×C4—1662no—
1321C22×C4—1662no—
1322C22×C4—1662no—
1323C22×C4C23×D8311yescharacteristic
1324C22×C4C23×D8311yescharacteristic
1325C22×C4C23×D8311yescharacteristic
1326C22×C4C23×D8311yescharacteristic
1327C22×C4C23×D8311yescharacteristic
1328C22×C4C23×D8311yescharacteristic
1329C22×C4C23×D8311yescharacteristic
1330C22×C4C23×D8311yescharacteristic
1331C22×C4C23×D8311yescharacteristic
1332C22×C4C23×D8311yescharacteristic
1333C22×C4C23×D8311yescharacteristic
1334C22×C4C23×D8311yescharacteristic
1335C22×C4C23×D8311yescharacteristic
1336C4⋊C4—22no—
1337C4⋊C4—22no—
1338C4⋊C4—22no—
1339C4⋊C4—22no—
1340C4⋊C4—22no—
1341C4⋊C4—22no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—41no—
1345C4⋊C4—41no—
1346C4⋊C4—3321no—
1347C4⋊C4—3321no—
1348C4⋊C4—3321no—
1349C4⋊C4—3321no—
1350C4⋊C4—3321no—
1351C4⋊C4—3321no—
1352C4⋊C4—3321no—
1353C4⋊C4—3321no—
1354C4⋊C4—3321no—
1355C4⋊C4—3321no—
1356C4⋊C4—3321no—
1357C4⋊C4—3321no—
1358C4⋊C4—834no—
1359C4⋊C4—1662no—
1360C4⋊C4—1662no—
1361C4⋊C4—1662no—
1362C4⋊C4—1662no—
1363C4⋊C4—1662no—
1364C4⋊C4—1662no—
1365C4⋊C4—1662no—
1366C4⋊C4—1662no—
1367C4⋊C4—1662no—
1368C4⋊C4—1662no—
1369C4⋊C4—1662no—
1370C4⋊C4—1662no—
1371C4⋊C4—1662no—
1372C4⋊C4—1662no—
1373C4⋊C4—1662no—
1374C22⋊C4—22no—
1375C22⋊C4—22no—
1376C22⋊C4—22no—
1377C22⋊C4—22no—
1378C22⋊C4—22no—
1379C22⋊C4—22no—
1380C22⋊C4—22no—
1381C22⋊C4—41no—
1382C22⋊C4—41no—
1383C22⋊C4—41no—
1384C22⋊C4—41no—
1385C22⋊C4—3321no—
1386C22⋊C4—3321no—
1387C22⋊C4—3321no—
1388C22⋊C4—3321no—
1389C22⋊C4—3321no—
1390C22⋊C4—3321no—
1391C22⋊C4—3321no—
1392C22⋊C4—3321no—
1393C22⋊C4—3321no—
1394C22⋊C4—3321no—
1395C22⋊C4—3321no—
1396C22⋊C4—3321no—
1397C22⋊C4—3321no—
1398C22⋊C4—3321no—
1399C22⋊C4—3321no—
1400C22⋊C4—3321no—
1401C22⋊C4—3321no—
1402C22⋊C4—3321no—
1403C22⋊C4—3321no—
1404C22⋊C4—3321no—
1405C22⋊C4—3321no—
1406C22⋊C4—3321no—
1407C22⋊C4—3321no—
1408C22⋊C4—3321no—
1409C22⋊C4—3321no—
1410C22⋊C4—834no—
1411C22⋊C4—834no—
1412C22⋊C4—1662no—
1413C22⋊C4—1662no—
1414C22⋊C4—1662no—
1415C22⋊C4—1662no—
1416C22⋊C4—1662no—
1417C22⋊C4—1662no—
1418C22⋊C4—1662no—
1419C22⋊C4—1662no—
1420C22⋊C4—1662no—
1421C22⋊C4—1662no—
1422C22⋊C4—1662no—
1423C22⋊C4—1662no—
1424C22⋊C4—1662no—
1425C22⋊C4—1662no—
1426C42—22no—
1427C42—41no—
1428C42—41no—
1429C42—3321no—
1430C42—3321no—
1431C42—1662no—
1432C42D4×D8314yes—
1433C23—21no—
1434C23—21no—
1435C23—21no—
1436C23—21no—
1437C23—21no—
1438C23—21no—
1439C23—21no—
1440C23—21no—
1441C23—21no—
1442C23—21no—
1443C23—21no—
1444C23—21no—
1445C23—21no—
1446C23—3324no—
1447C23—3324no—
1448C23—3324no—
1449C23—3324no—
1450C23—3324no—
1451C23—3324no—
1452C23—3324no—
1453C23—832no—
1454C23—832no—
1455C23—832no—
1456C23—1661no—
1457C23—1661no—
1458C23—1661no—
1459C23—1661no—
1460C23—1661no—
1461C23—1661no—
1462C23—1661no—
1463C23—1661no—
1464C23—1661no—
1465C23—1661no—
1466C23—1661no—
1467C23—1661no—
1468C23—1661no—
1469C23—1661no—
1470C23—1661no—
1471C23—1661no—
1472C23—1661no—
1473C23—1661no—
1474C23—1661no—
1475C23—1661no—
1476C23—1661no—
1477C23—1661no—
1478C23—1661no—
1479C23—1661no—
1480C23—1661no—
1481C23#1458183812yes—
1482C23C24×D8311yescharacteristic
1483Q8—3324no—
1484Q8—6642no—
1485D4—82no—
1486D4—3324no—
1487D4—3324no—
1488D4—3324no—
1489D4—3324no—
1490D4—3324no—
1491D4—3324no—
1492D4—3324no—
1493D4—3324no—
1494D4—6642no—
1495D4—6642no—
1496D4—6642no—
1497C2×C4—28no—
1498C2×C4—21no—
1499C2×C4—21no—
1500C2×C4—21no—
1501C2×C4—21no—
1502C2×C4—21no—
1503C2×C4—21no—
1504C2×C4—21no—
1505C2×C4—21no—
1506C2×C4—21no—
1507C2×C4—21no—
1508C2×C4—21no—
1509C2×C4—21no—
1510C2×C4—21no—
1511C2×C4—21no—
1512C2×C4—21no—
1513C2×C4—21no—
1514C2×C4—21no—
1515C2×C4—21no—
1516C2×C4—21no—
1517C2×C4—21no—
1518C2×C4—21no—
1519C2×C4—21no—
1520C2×C4—21no—
1521C2×C4—21no—
1522C2×C4—21no—
1523C2×C4—21no—
1524C2×C4—21no—
1525C2×C4—21no—
1526C2×C4—21no—
1527C2×C4—21no—
1528C2×C4—21no—
1529C2×C4—21no—
1530C2×C4—21no—
1531C2×C4—21no—
1532C2×C4—21no—
1533C2×C4—3324no—
1534C2×C4—3324no—
1535C2×C4—3324no—
1536C2×C4—3324no—
1537C2×C4—3324no—
1538C2×C4—3324no—
1539C2×C4—3324no—
1540C2×C4—3324no—
1541C2×C4—832no—
1542C2×C4—832no—
1543C2×C4—6642no—
1544C2×C4—6642no—
1545C2×C4—1661no—
1546C2×C4—1661no—
1547C2×C4—1661no—
1548C2×C4—1661no—
1549C2×C4—1661no—
1550C2×C4—1661no—
1551C2×C4—1661no—
1552C2×C4—1661no—
1553C2×C4—1661no—
1554C2×C4—1661no—
1555C2×C4—1661no—
1556C2×C4—1661no—
1557C2×C4—1661no—
1558C2×C4—1661no—
1559C2×C4—1661no—
1560C2×C4—1661no—
1561C2×C4—1661no—
1562C2×C4—1661no—
1563C2×C4—1661no—
1564C2×C4—1661no—
1565C2×C4—1661no—
1566C2×C4—1661no—
1567C2×C4—1661no—
1568C2×C4—1661no—
1569C2×C4—1661no—
1570C2×C4—1661no—
1571C2×C4—1661no—
1572C2×C4—1661no—
1573C2×C4—1661no—
1574C2×C4—1661no—
1575C2×C4—1661no—
1576C2×C4—1661no—
1577C2×C4—1661no—
1578C2×C4—1661no—
1579C2×C4C2×D4×D8312yes—
1580C2×C4C2×D4×D8312yes—
1581C2×C4C2×D4×D8312yes—
1582C2×C4#1458183812yes—
1583C22—22no—
1584C22—22no—
1585C22—22no—
1586C22—41no—
1587C22—41no—
1588C22—41no—
1589C22—41no—
1590C22—41no—
1591C22—41no—
1592C22—41no—
1593C22—41no—
1594C22—41no—
1595C22—41no—
1596C22—41no—
1597C22—33216no—
1598C22—3321no—
1599C22—3321no—
1600C22—3321no—
1601C22—3321no—
1602C22—3321no—
1603C22—3321no—
1604C22—3321no—
1605C22—3321no—
1606C22—3321no—
1607C22—3321no—
1608C22—3321no—
1609C22—3321no—
1610C22—3321no—
1611C22—3321no—
1612C22—3321no—
1613C22—3321no—
1614C22—3321no—
1615C22—3321no—
1616C22—3321no—
1617C22—1662no—
1618C22—1662no—
1619C22—1662no—
1620C22—1662no—
1621C22—1662no—
1622C22—1662no—
1623C22—1662no—
1624C22—1662no—
1625C22—1662no—
1626C22C22×D4×D8311yescharacteristic
1627C22C2×#1458183811yescharacteristic
1628C22C2×#1458183811yescharacteristic
1629C222−1+4×D8311yescharacteristic
1630C22#1912853611yescharacteristic
1631C22#1912853711yescharacteristic
1632C22#1912853711yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—22no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—41no—
1646C4—3321no—
1647C4—3321no—
1648C4—3321no—
1649C4—3321no—
1650C4—3321no—
1651C4—3321no—
1652C4—3321no—
1653C4—3321no—
1654C4—3321no—
1655C4—3321no—
1656C4—1662no—
1657C4—1662no—
1658C2—42no—
1659C2—81no—
1660C2—3322no—
1661C2—3322no—
1662C2—3322no—
1663C2—6641no—
1664C2#2492079011yescharacteristic
1665C2#2492109611yescharacteristic
1666C2#2492113811yescharacteristic
1667C2#2492163511yescharacteristic
1668C2#2492167511yescharacteristic
1669C2#2492172011yescharacteristic
1670C2#2492176311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2601C2
hypercenter#2601D83
hypocenterC83#36723
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2601

Complements

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

NH ≅ G/Ntype
1. C2×#19128292C2semidirect
2. C2×#19128213C2semidirect
3. #24915754C2semidirect
4. #24915749C2semidirect
5. #24914165C2semidirect
6. #24914146C2semidirect
7. #24914120C2semidirect
8. #24914101C2semidirect
9. #24914075C2semidirect
10. #24914032C2semidirect
11. #24914021C2semidirect
12. #24913851C2semidirect
13. #24913832C2semidirect
14. #24913823C2semidirect
15. #24913821C2semidirect
16. #24913810C2semidirect
17. #24913801C2semidirect
18. #24913801C2semidirect
19. #24913794C2semidirect
20. #24913783C2semidirect
21. #24913387C2semidirect
22. #24913310C2semidirect
23. #24913161C2semidirect
24. #24913092C2semidirect
25. #24913048C2semidirect
26. #24912814C2semidirect
27. #24912663C2semidirect
28. #24910805C2semidirect
29. #24910796C2semidirect
30. #24910101C2semidirect
31. C83×#2601C2semidirect
36. C2×#14581784C22semidirect
37. C2×#14581783C22semidirect
40. C2×#14581777C22semidirect
47. C2×#14581774C22semidirect
50. C2×#14581772C22semidirect
54. C2×#14581769C22semidirect
55. C2×#14581769C22semidirect
67. C2×(C22⋊D83)⋊C4C22semidirect
68. C2×C4⋊C4×D83C22semidirect
69. #19127640C22semidirect
71. #19127635C22semidirect
72. #19127634C22semidirect
73. #19127633C22semidirect
74. #19127633C22semidirect
75. #19127631C22semidirect
76. #19127631C22semidirect
78. #19127630C22semidirect
80. #19127628C22semidirect
83. #19127626C22semidirect
85. #19127624C22semidirect
89. #19127623C22semidirect
90. #19127623C22semidirect
91. #19127623C22semidirect
92. #19127622C22semidirect
93. #19127622C22semidirect
94. #19127621C22semidirect
97. #19127619C22semidirect
105. #19127616C22semidirect
106. #19127616C22semidirect
107. #19127614C22semidirect
111. #19127610C22semidirect
113. #19127605C22semidirect
120. #19127601C22semidirect
121. #19127597C22semidirect
122. #19127597C22semidirect
123. #19127596C22semidirect
124. #19127596C22semidirect
129. #19127592C22semidirect
130. #19127592C22semidirect
132. #19127591C22semidirect
134. #19127587C22semidirect
135. #19127585C22semidirect
136. #19127585C22semidirect
140. #19127579C22semidirect
145. #19127577C22semidirect
147. #19127576C22semidirect
152. #19127575C22semidirect
153. #19127575C22semidirect
154. #19127575C22semidirect
159. #19127572C22semidirect
160. #19127572C22semidirect
161. #19127571C22semidirect
162. #19127567C22semidirect
165. #19127563C22semidirect
168. #19127560C22semidirect
173. #19127547C22semidirect
174. C2×#126×C83C22semidirect
176. #398×C83C22semidirect
178. #396×C83C22semidirect
181. #389×C83C22semidirect
183. #388×C83C22semidirect
184. #388×C83C22semidirect
185. #387×C83C22semidirect
188. C4×C4⋊C4×C83C22semidirect
249. C4×D332D4semidirect
860. #2601D83semidirect
867. C83#36723semidirect
872. C2×#126C2×D83semidirect
915. #398C2×D83semidirect
932. #396C2×D83semidirect
968. #389C2×D83semidirect
979. #388C2×D83semidirect
980. #388C2×D83semidirect
984. #387C2×D83semidirect
1023. C4×C4⋊C4C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282922
C2×#191282132
#249157542
#249157492
#249141652
#249141462
#249141202
#249141012
#249140752
#249140322
#249140212
#249138512
#249138322
#249138232
#249138212
#249138102
#249138012
#249137942
#249137832
#249133872
#249133102
#249131612
#249130922
#249130482
#249128142
#249126632
#249108052
#249107962
#249101012
C83×#26012
#3672383