Finite Group Databasebeta

← #35611467

Subgroups — #35611467

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×#19128297C211yesmaximal, characteristic, complemented
2C2×#19128209C211yesmaximal, characteristic, complemented
3#24915754C211yesmaximal, characteristic, complemented
4#24915747C211yesmaximal, characteristic, complemented
5#24914162C211yesmaximal, characteristic, complemented
6#24914155C211yesmaximal, characteristic, complemented
7#24914119C211yesmaximal, characteristic, complemented
8#24914112C211yesmaximal, characteristic, complemented
9#24914069C211yesmaximal, characteristic, complemented
10#24914042C211yesmaximal, characteristic, complemented
11#24914023C211yesmaximal, characteristic, complemented
12#24913859C211yesmaximal, characteristic, complemented
13#24913833C211yesmaximal, characteristic, complemented
14#24913826C211yesmaximal, characteristic, complemented
15#24913822C211yesmaximal, characteristic, complemented
16#24913805C211yesmaximal, characteristic, complemented
17#24913802C211yesmaximal, characteristic, complemented
18#24913794C211yesmaximal, characteristic, complemented
19#24913791C211yesmaximal, characteristic, complemented
20#24913386C211yesmaximal, characteristic, complemented
21#24913307C211yesmaximal, characteristic, complemented
22#24913158C211yesmaximal, characteristic, complemented
23#24913086C211yesmaximal, characteristic, complemented
24#24913053C211yesmaximal, characteristic, complemented
25#24913049C211yesmaximal, characteristic, complemented
26#24912811C211yesmaximal, characteristic, complemented
27#24912658C211yesmaximal, characteristic, complemented
28#24910804C211yesmaximal, characteristic, complemented
29#24910793C211yesmaximal, characteristic, complemented
30#24910102C211yesmaximal, characteristic, complemented
31C83×#2681C211yesmaximal, characteristic, complemented
32C22×#13050589C2211yescharacteristic
33C23×C4×D83C2211yescharacteristic
34#19128297—28no—
35C2×#14581787C2211yescharacteristic
36C2×#14581785C2211yescharacteristic, complemented
37C2×#14581782C2211yescharacteristic, complemented
38C2×#14581782C2211yescharacteristic, complemented
39#19128209—28no—
40C2×#14581777C2211yescharacteristic
41C2×#14581775C2211yescharacteristic
42C2×#14581775C2211yescharacteristic
43C2×#14581774C2211yescharacteristic
44C2×#14581774C2211yescharacteristic
45C2×#14581774C2211yescharacteristic
46C2×#14581774C2211yescharacteristic, complemented
47C2×#14581774C2211yescharacteristic, complemented
48C2×#14581771C2211yescharacteristic, complemented
49C2×#14581770C2211yescharacteristic
50C2×#14581770C2211yescharacteristic
51C2×#14581768C2211yescharacteristic
52C2×#14581768C2211yescharacteristic
53C2×#14581768C2211yescharacteristic, complemented
54C2×#14581765C2211yescharacteristic
55C2×#14581765C2211yescharacteristic
56C2×#14581765C2211yescharacteristic
57C2×#14581762C2211yescharacteristic
58C2×#14581760C2211yescharacteristic
59C2×#14581760C2211yescharacteristic
60C2×#14581754C2211yescharacteristic
61C2×#14581754C2211yescharacteristic
62C2×C4×C22⋊D83C2211yescharacteristic, complemented
63C2×(C22⋊D83)⋊C4C2211yescharacteristic
64C2×(C22⋊D83)⋊C4C2211yescharacteristic
65C2×#14581748C2211yescharacteristic
66C2×C4⋊C4×D83C2211yescharacteristic, complemented
67#19127642C2211yescharacteristic, complemented
68#19127637C2211yescharacteristic
69#19127635C2211yescharacteristic, complemented
70#19127634C2211yescharacteristic, complemented
71#19127634C2211yescharacteristic, complemented
72#19127633C2211yescharacteristic, complemented
73#19127631C2211yescharacteristic, complemented
74#19127631C2211yescharacteristic, complemented
75#19127630C2211yescharacteristic
76#19127630C2211yescharacteristic
77#19127630C2211yescharacteristic
78#19127629C2211yescharacteristic
79#19127629C2211yescharacteristic, complemented
80#19127627C2211yescharacteristic, complemented
81#19127626C2211yescharacteristic, complemented
82#19127624C2211yescharacteristic
83#19127624C2211yescharacteristic, complemented
84#19127624C2211yescharacteristic, complemented
85#19127624C2211yescharacteristic, complemented
86#19127624C2211yescharacteristic, complemented
87#19127623C2211yescharacteristic
88#19127623C2211yescharacteristic
89#19127623C2211yescharacteristic
90#19127623C2211yescharacteristic
91#19127622C2211yescharacteristic, complemented
92#19127621C2211yescharacteristic, complemented
93#19127620C2211yescharacteristic, complemented
94#19127619C2211yescharacteristic
95#19127617C2211yescharacteristic
96#19127617C2211yescharacteristic
97#19127617C2211yescharacteristic
98#19127617C2211yescharacteristic
99#19127617C2211yescharacteristic, complemented
100#19127616C2211yescharacteristic
101#19127616C2211yescharacteristic
102#19127616C2211yescharacteristic, complemented
103#19127615C2211yescharacteristic
104#19127610C2211yescharacteristic
105#19127609C2211yescharacteristic
106#19127609C2211yescharacteristic
107#19127609C2211yescharacteristic
108#19127609C2211yescharacteristic, complemented
109#19127606C2211yescharacteristic, complemented
110#19127604C2211yescharacteristic
111#19127604C2211yescharacteristic
112#19127603C2211yescharacteristic
113#19127602C2211yescharacteristic
114#19127601C2211yescharacteristic
115#19127601C2211yescharacteristic
116#19127601C2211yescharacteristic
117#19127600C2211yescharacteristic, complemented
118#19127599C2211yescharacteristic, complemented
119#19127598C2211yescharacteristic, complemented
120#19127596C2211yescharacteristic, complemented
121#19127595C2211yescharacteristic
122#19127595C2211yescharacteristic, complemented
123#19127595C2211yescharacteristic, complemented
124#19127594C2211yescharacteristic
125#19127593C2211yescharacteristic
126#19127593C2211yescharacteristic
127#19127593C2211yescharacteristic, complemented
128#19127592C2211yescharacteristic
129#19127591C2211yescharacteristic
130#19127591C2211yescharacteristic, complemented
131#19127589C2211yescharacteristic, complemented
132#19127588C2211yescharacteristic, complemented
133#19127584C2211yescharacteristic, complemented
134#19127584C2211yescharacteristic, complemented
135#19127582C2211yescharacteristic, complemented
136#19127581C2211yescharacteristic
137#19127581C2211yescharacteristic, complemented
138#19127580C2211yescharacteristic
139#19127579C2211yescharacteristic
140#19127579C2211yescharacteristic
141#19127577C2211yescharacteristic
142#19127577C2211yescharacteristic
143#19127577C2211yescharacteristic
144#19127577C2211yescharacteristic, complemented
145#19127576C2211yescharacteristic
146#19127576C2211yescharacteristic, complemented
147#19127575C2211yescharacteristic
148#19127575C2211yescharacteristic
149#19127575C2211yescharacteristic, complemented
150#19127574C2211yescharacteristic
151#19127573C2211yescharacteristic
152#19127573C2211yescharacteristic
153#19127573C2211yescharacteristic, complemented
154#19127573C2211yescharacteristic, complemented
155#19127572C2211yescharacteristic
156#19127572C2211yescharacteristic
157#19127572C2211yescharacteristic
158#19127572C2211yescharacteristic
159#19127572C2211yescharacteristic, complemented
160#19127570C2211yescharacteristic, complemented
161#19127565C2211yescharacteristic, complemented
162#19127563C2211yescharacteristic
163#19127563C2211yescharacteristic
164#19127563C2211yescharacteristic, complemented
165#19127561C2211yescharacteristic
166#19127558C2211yescharacteristic
167#19127558C2211yescharacteristic
168#19127558C2211yescharacteristic, complemented
169#19127556C2211yescharacteristic
170#19127556C2211yescharacteristic
171#19127556C2211yescharacteristic
172C4⋊C4×Dic83C2211yescharacteristic, complemented
173#19127547C2211yescharacteristic, complemented
174C2×#123×C83C2211yescharacteristic
175C2×C22⋊Q8×C83C2211yescharacteristic
176C2×C22⋊Q8×C83C2211yescharacteristic, complemented
177C2×#121×C83C2211yescharacteristic
178#398×C83C2211yescharacteristic, complemented
179#396×C83C2211yescharacteristic, complemented
180#394×C83C2211yescharacteristic
181#394×C83C2211yescharacteristic
182#394×C83C2211yescharacteristic, complemented
183#393×C83C2211yescharacteristic, complemented
184#390×C83C2211yescharacteristic, complemented
185#389×C83C2211yescharacteristic, complemented
186#388×C83C2211yescharacteristic
187#386×C83C2211yescharacteristic
188#385×C83C2211yescharacteristic, complemented
189C24×D83C2311yescharacteristic
190C2×#13050589—24no—
191C2×#13050589—42no—
192C2×#13050589—42no—
193C22×Dic166C2311yescharacteristic
194C22×D332C2311yescharacteristic
195C22×D332C2311yescharacteristic
196C22×C22⋊D83C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C23×Dic83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C22×C4×D83—24no—
206C22×C4×D83—42no—
207C22×C4×D83—42no—
208C22×C4×D83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
211C22×C4×D83C2311yescharacteristic
212C22×C4×D83C2311yescharacteristic
213C22×C4×D83C2311yescharacteristic
214C22×C4×D83C2311yescharacteristic
215#14581787—24no—
216#14581785—24no—
217#14581782—24no—
218#14581782—24no—
219#14581777—24no—
220#14581775—24no—
221#14581775—24no—
222#14581774—24no—
223#14581774—24no—
224#14581774—42no—
225#14581774—42no—
226#14581774—42no—
227#14581771—42no—
228#14581770—24no—
229#14581770—24no—
230#14581768—24no—
231#14581768—24no—
232#14581768—42no—
233#14581765—24no—
234#14581765—24no—
235#14581765—24no—
236#14581762—24no—
237#14581760—24no—
238#14581760—42no—
239#14581754—24no—
240#14581754D418yescomplemented
241C4×C22⋊D83—24no—
242(C22⋊D83)⋊C4—24no—
243(C22⋊D83)⋊C4—24no—
244#14581748—24no—
245C2×C4⋊Dic83C2311yescharacteristic
246C2×C4⋊Dic83C2311yescharacteristic
247C2×C4⋊Dic83C2311yescharacteristic
248C2×C4⋊Dic83C2311yescharacteristic
249C2×C4⋊Dic83C2311yescharacteristic
250C2×C4⋊Dic83C2311yescharacteristic
251C2×C4⋊Dic83C2311yescharacteristic
252C2×C4⋊Dic83C2311yescharacteristic
253C2×C4⋊Dic83C2311yescharacteristic
254C2×C4⋊Dic83C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C2×Dic83⋊C4C2311yescharacteristic
258C2×Dic83⋊C4C2311yescharacteristic
259C2×Dic83⋊C4C2311yescharacteristic
260C2×Dic83⋊C4C2311yescharacteristic
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
274C4⋊C4×D83—24no—
275C2×C22⋊Dic83C2311yescharacteristic
276C2×C22⋊Dic83C2311yescharacteristic
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×(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×C4×Dic83C2311yescharacteristic
315C2×C4×Dic83C2311yescharacteristic
316C2×C4×Dic83C2311yescharacteristic
317C2×C4×Dic83C2311yescharacteristic
318C2×C4×Dic83C2311yescharacteristic
319C2×C4×Dic83C2311yescharacteristic
320C83⋊#95C2311yescharacteristic
321C83⋊#95C2311yescharacteristic
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
346C22×Q8×C83C2311yescharacteristic
347C22×D4×C83C2311yescharacteristic
348C22×D4×C83C2311yescharacteristic
349C22×D4×C83C2311yescharacteristic
350C23×C4×C83C2311yescharacteristic
351C23×C4×C83C2311yescharacteristic
352#123×C83—24no—
353C22⋊Q8×C83—24no—
354C22⋊Q8×C83—42no—
355#121×C83—42no—
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×C4⋊C4×C83C2311yescharacteristic
363C2×C4⋊C4×C83C2311yescharacteristic
364C2×C4⋊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×C22⋊C4×C83C2311yescharacteristic
374C2×C22⋊C4×C83C2311yescharacteristic
375C2×C22⋊C4×C83C2311yescharacteristic
376C2×C22⋊C4×C83C2311yescharacteristic
377C2×C22⋊C4×C83C2311yescharacteristic
378C2×C42×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
395#13050589—416no—
396C2×Dic166—22no—
397C2×Dic166—22no—
398C2×Dic166—41no—
399C2×D332—22no—
400C2×D332—22no—
401C2×D332—41no—
402C2×D332—41no—
403C2×D332—41no—
404C2×D332C2×D414yes—
405C2×C22⋊D83—22no—
406C2×C22⋊D83—22no—
407C2×C22⋊D83—22no—
408C2×C22⋊D83—22no—
409C2×C22⋊D83—22no—
410C2×C22⋊D83—22no—
411C2×C22⋊D83—22no—
412C2×C22⋊D83—22no—
413C2×C22⋊D83—22no—
414C2×C22⋊D83—22no—
415C2×C22⋊D83—41no—
416C2×C22⋊D83—41no—
417C2×C22⋊D83—41no—
418C2×C22⋊D83—41no—
419C2×C22⋊D83—41no—
420C2×C22⋊D83—41no—
421C2×C22⋊D83—41no—
422C2×C22⋊D83—41no—
423C2×C22⋊D83—41no—
424C2×C22⋊D83—41no—
425C2×C22⋊D83—41no—
426C22×Dic83—22no—
427C22×Dic83—22no—
428C22×Dic83—22no—
429C22×Dic83—22no—
430C22×Dic83—41no—
431C22×Dic83—41no—
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C22×Dic83C2411yescharacteristic
440C22×Dic83C2411yescharacteristic
441C22×Dic83C2411yescharacteristic
442C22×Dic83C2411yescharacteristic
443C22×Dic83C2411yescharacteristic
444C22×Dic83C2411yescharacteristic
445C2×C4×D83—22no—
446C2×C4×D83—22no—
447C2×C4×D83—22no—
448C2×C4×D83—22no—
449C2×C4×D83—22no—
450C2×C4×D83—22no—
451C2×C4×D83—22no—
452C2×C4×D83—41no—
453C2×C4×D83—41no—
454C2×C4×D83—41no—
455C2×C4×D83—41no—
456C2×C4×D83—41no—
457C2×C4×D83—41no—
458C2×C4×D83—41no—
459C2×C4×D83—41no—
460C2×C4×D83—41no—
461C2×C4×D83—41no—
462C2×C4×D83—416no—
463C2×C4×D83—41no—
464C2×C4×D83—41no—
465C2×C4×D83C2×D414yes—
466C2×C4×D83C2×D414yes—
467C4⋊Dic83—22no—
468C4⋊Dic83—22no—
469C4⋊Dic83—22no—
470C4⋊Dic83—22no—
471C4⋊Dic83—41no—
472C4⋊Dic83—41no—
473C4⋊Dic83—41no—
474C4⋊Dic83—41no—
475C4⋊Dic83—41no—
476C4⋊Dic83—41no—
477Dic83⋊C4—22no—
478Dic83⋊C4—22no—
479Dic83⋊C4—22no—
480Dic83⋊C4—22no—
481Dic83⋊C4—22no—
482Dic83⋊C4—22no—
483Dic83⋊C4—22no—
484Dic83⋊C4—22no—
485Dic83⋊C4—22no—
486Dic83⋊C4—22no—
487Dic83⋊C4—22no—
488Dic83⋊C4—22no—
489Dic83⋊C4—22no—
490Dic83⋊C4—22no—
491Dic83⋊C4—41no—
492Dic83⋊C4—41no—
493Dic83⋊C4—41no—
494Dic83⋊C4—41no—
495Dic83⋊C4—41no—
496C22⋊Dic83—22no—
497C22⋊Dic83—22no—
498C22⋊Dic83—22no—
499C22⋊Dic83—22no—
500C22⋊Dic83—22no—
501C22⋊Dic83—41no—
502C22⋊Dic83—41no—
503C22⋊Dic83—41no—
504C22⋊Dic83—41no—
505C22⋊Dic83—41no—
506C22⋊Dic83—41no—
507C22⋊Dic83—41no—
508C22⋊Dic83—41no—
509C22⋊Dic83—41no—
510(C2×D83)⋊C4—22no—
511(C2×D83)⋊C4—22no—
512(C2×D83)⋊C4—22no—
513(C2×D83)⋊C4—22no—
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—41no—
520(C2×D83)⋊C4—41no—
521(C2×D83)⋊C4—41no—
522(C2×D83)⋊C4—41no—
523(C2×D83)⋊C4—41no—
524(C2×D83)⋊C4—41no—
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)⋊C4C2×D414yes—
534(C2×D83)⋊C4C2×D414yes—
535C4×Dic83—22no—
536C4×Dic83—22no—
537C4×Dic83—41no—
538C4×Dic83—41no—
539C4×Dic83—41no—
540C4×Dic83C2×D414yes—
541C24×C83C2411yescharacteristic
542C24×C83C2411yescharacteristic
543C24×C83C2411yescharacteristic
544C2×Q8×C83—22no—
545C2×Q8×C83—41no—
546C2×Q8×C83—41no—
547C2×D4×C83—22no—
548C2×D4×C83—22no—
549C2×D4×C83—22no—
550C2×D4×C83—41no—
551C2×D4×C83—41no—
552C2×D4×C83—41no—
553C2×D4×C83—41no—
554C2×D4×C83—41no—
555C2×D4×C83—41no—
556C22×C4×C83—22no—
557C22×C4×C83—22no—
558C22×C4×C83—22no—
559C22×C4×C83—41no—
560C22×C4×C83—41no—
561C22×C4×C83—41no—
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
572C22×C4×C83C2411yescharacteristic
573C22×C4×C83C2411yescharacteristic
574C4⋊C4×C83—22no—
575C4⋊C4×C83—22no—
576C4⋊C4×C83—22no—
577C4⋊C4×C83—41no—
578C4⋊C4×C83—41no—
579C4⋊C4×C83—41no—
580C4⋊C4×C83—41no—
581C4⋊C4×C83—41no—
582C4⋊C4×C83C2×D414yes—
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—22no—
590C22⋊C4×C83—41no—
591C22⋊C4×C83—41no—
592C22⋊C4×C83—41no—
593C22⋊C4×C83—41no—
594C22⋊C4×C83—41no—
595C22⋊C4×C83—41no—
596C42×C83—41no—
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×C83—21no—
611C23×C83—21no—
612C23×C83—21no—
613C23×C83—21no—
614C23×C83—21no—
615C23×C83—21no—
616C23×C83—21no—
617C23×C83H(5,𝔽2)12yes—
618C23×C83C2511yescharacteristic
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—
647Q8×C83—82no—
648D4×C83—44no—
649D4×C83—82no—
650D4×C83—82no—
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×C83—44no—
685C2×C4×C83—82no—
686C2×C4×C83C22×D412yes—
687C2×C4×C83C22×D412yes—
688C2×C4×C83C22×D412yes—
689C22⋊D83—44no—
690C22⋊D83—44no—
691C22⋊D83—44no—
692C22⋊D83—44no—
693C22⋊D83—44no—
694C22⋊D83—82no—
695C22⋊D83—82no—
696C2×Dic83—28no—
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—21no—
729C2×Dic83—21no—
730C2×Dic83—21no—
731C2×Dic83—21no—
732C2×Dic83—21no—
733C2×Dic83—44no—
734C2×Dic83C22×D412yes—
735C2×Dic83C22×D412yes—
736C2×Dic83H(5,𝔽2)12yes—
737D332—44no—
738D332—44no—
739C4×D83—44no—
740C4×D83—44no—
741C4×D83—44no—
742C4×D83—44no—
743C4×D83—44no—
744C4×D83—44no—
745C4×D83—82no—
746Dic166—44no—
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×C83—41no—
762C22×C83—41no—
763C22×C83—41no—
764C22×C83—41no—
765C22×C83—41no—
766C22×C83—41no—
767C22×C83—41no—
768C22×C83C23×D411yescharacteristic
769C22×C83C2×H(5,𝔽2)11yescharacteristic
770C22×C83C2×H(5,𝔽2)11yescharacteristic
771C22×C83C2×2−1+411yescharacteristic
772C22×C83#58511yescharacteristic
773C22×C83#58511yescharacteristic
774C22×C83#58511yescharacteristic
775C2×D83—22no—
776C2×D83—22no—
777C2×D83—22no—
778C2×D83—22no—
779C2×D83—22no—
780C2×D83—22no—
781C2×D83—22no—
782C2×D83—22no—
783C2×D83—22no—
784C2×D83—416no—
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—41no—
801C4×C83—41no—
802C4×C83—41no—
803C4×C83—41no—
804C4×C83—41no—
805C4×C83—41no—
806C4×C83—41no—
807C4×C83—41no—
808C4×C83—41no—
809Dic83—22no—
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—81no—
826C2×C83#344911yescharacteristic
827C2×C83#348411yescharacteristic
828C2×C83#348911yescharacteristic
829C2×C83#353311yescharacteristic
830C2×C83#353511yescharacteristic
831C2×C83#353911yescharacteristic
832C2×C83#354111yescharacteristic
833D83—42no—
834D83—42no—
835D83—42no—
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#2681D8311yescharacteristic, complemented
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#2601—831no—
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×#126—831no—
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×#123C2×D8311yescharacteristic
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⋊Q8C2×D8311yescharacteristic
892C2×C22⋊Q8C2×D8311yescharacteristic, complemented
893C2×#121—831no—
894C2×#121—831no—
895C2×#121—831no—
896C2×#121C2×D8311yescharacteristic
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×#117—831no—
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#396—831no—
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#394C2×D8311yescharacteristic
947#394C2×D8311yescharacteristic
948#394C2×D8311yescharacteristic, complemented
949#393C2×D8311yescharacteristic, complemented
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, complemented
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#388—831no—
979#388—831no—
980#388C2×D8311yescharacteristic
981#387—831no—
982#387—831no—
983#387—831no—
984#387—831no—
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, complemented
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⋊C4—831no—
1024#376—831no—
1025C25—831no—
1026C2×#41—3322no—
1027C2×#41—3322no—
1028C2×#41—1664no—
1029C22×Q8—831no—
1030C22×Q8C22×D8311yescharacteristic
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×D4C22×D8311yescharacteristic
1041C22×D4C22×D8311yescharacteristic
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—1664no—
1055C23×C4C22×D8311yescharacteristic
1056C23×C4C22×D8311yescharacteristic
1057#126—1664no—
1058#126—1664no—
1059#125—1664no—
1060#125—1664no—
1061#123—24no—
1062#123—3322no—
1063#123—3322no—
1064#123—3322no—
1065#123—1664no—
1066#123—1664no—
1067#123—1664no—
1068#123—1664no—
1069#123—1664no—
1070C22⋊Q8—24no—
1071C22⋊Q8—42no—
1072C22⋊Q8—3322no—
1073C22⋊Q8—3322no—
1074C22⋊Q8—1664no—
1075C22⋊Q8—1664no—
1076C22⋊Q8—1664no—
1077C22⋊Q8—1664no—
1078#121—42no—
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—1664no—
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—831no—
1120C2×C4⋊C4—1664no—
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⋊C4C22×D8311yescharacteristic
1170C2×C22⋊C4C22×D8311yescharacteristic
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×C42—831no—
1186C2×C42—831no—
1187C2×C42—831no—
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#95—831no—
1214#95—831no—
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—1662no—
1229C24—1662no—
1230C24—1662no—
1231C24C23×D8311yescharacteristic
1232C24C23×D8311yescharacteristic
1233C24C23×D8311yescharacteristic
1234#41—33216no—
1235C2×Q8—22no—
1236C2×Q8—41no—
1237C2×Q8—41no—
1238C2×Q8—3321no—
1239C2×Q8—1662no—
1240C2×Q8—1662no—
1241C2×D4—22no—
1242C2×D4—22no—
1243C2×D4—22no—
1244C2×D4—41no—
1245C2×D4—41no—
1246C2×D4—41no—
1247C2×D4—41no—
1248C2×D4—41no—
1249C2×D4—41no—
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—3321no—
1263C2×D4—3321no—
1264C2×D4—834no—
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—41no—
1281C22×C4—41no—
1282C22×C4—41no—
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—33216no—
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—831no—
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×C4—1662no—
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—41no—
1340C4⋊C4—41no—
1341C4⋊C4—41no—
1342C4⋊C4—41no—
1343C4⋊C4—41no—
1344C4⋊C4—3321no—
1345C4⋊C4—3321no—
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—1662no—
1356C4⋊C4—1662no—
1357C4⋊C4—1662no—
1358C4⋊C4—1662no—
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⋊C4D4×D8314yes—
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—41no—
1386C22⋊C4—41no—
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—41no—
1427C42—3321no—
1428C42—3321no—
1429C42—3321no—
1430C42—834no—
1431C42—1662no—
1432C42—1662no—
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—21no—
1447C23—21no—
1448C23—21no—
1449C23—21no—
1450C23—21no—
1451C23—21no—
1452C23—21no—
1453C23—3324no—
1454C23—3324no—
1455C23—3324no—
1456C23—3324no—
1457C23—3324no—
1458C23—3324no—
1459C23—3324no—
1460C23—832no—
1461C23—832no—
1462C23—832no—
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#1458183712yes—
1482C23C24×D8311yescharacteristic
1483Q8—82no—
1484Q8—3324no—
1485D4—44no—
1486D4—82no—
1487D4—82no—
1488D4—3324no—
1489D4—3324no—
1490D4—3324no—
1491D4—3324no—
1492D4—3324no—
1493D4—3324no—
1494D4—3324no—
1495D4—6642no—
1496D4—6642no—
1497C2×C4—21no—
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—44no—
1531C2×C4—82no—
1532C2×C4—3324no—
1533C2×C4—3324no—
1534C2×C4—3324no—
1535C2×C4—3324no—
1536C2×C4—3324no—
1537C2×C4—3324no—
1538C2×C4—3324no—
1539C2×C4—832no—
1540C2×C4—832no—
1541C2×C4—832no—
1542C2×C4—6642no—
1543C2×C4—1661no—
1544C2×C4—1661no—
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—1668no—
1574C2×C4—1661no—
1575C2×C4—1661no—
1576C2×C4—1661no—
1577C2×C4—1661no—
1578C2×C4—1661no—
1579C2×C4—1661no—
1580C2×C4C2×D4×D8312yes—
1581C2×C4C2×D4×D8312yes—
1582C2×C4C2×D4×D8312yes—
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—41no—
1598C22—41no—
1599C22—41no—
1600C22—41no—
1601C22—41no—
1602C22—41no—
1603C22—41no—
1604C22—33216no—
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
1627C22H(5,𝔽2)×D8311yescharacteristic
1628C22C2×#1458183711yescharacteristic
1629C222−1+4×D8311yescharacteristic
1630C22#1912853611yescharacteristic
1631C22#1912853711yescharacteristic
1632C22#1912853811yescharacteristic
1633C4—22no—
1634C4—22no—
1635C4—22no—
1636C4—41no—
1637C4—41no—
1638C4—41no—
1639C4—41no—
1640C4—41no—
1641C4—41no—
1642C4—41no—
1643C4—41no—
1644C4—41no—
1645C4—3321no—
1646C4—3321no—
1647C4—3321no—
1648C4—3321no—
1649C4—3321no—
1650C4—3321no—
1651C4—3321no—
1652C4—3321no—
1653C4—3321no—
1654C4—3321no—
1655C4—1662no—
1656C4—1662no—
1657C4—1662no—
1658C2—42no—
1659C2—81no—
1660C2—81no—
1661C2—3322no—
1662C2—3322no—
1663C2—3322no—
1664C2#2492079111yescharacteristic
1665C2#2492109111yescharacteristic
1666C2#2492114211yescharacteristic
1667C2#2492162211yescharacteristic
1668C2#2492166211yescharacteristic
1669C2#2492172111yescharacteristic
1670C2#2492174511yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutator, socle, cosocleC23×C83C25
FittingC83×#2681C2
hypercenter#2681D83
hypocenterC83#36723
LCSG ▷ C23×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2681

Complements

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

NH ≅ G/Ntype
1. C2×#19128297C2semidirect
2. C2×#19128209C2semidirect
3. #24915754C2semidirect
4. #24915747C2semidirect
5. #24914162C2semidirect
6. #24914155C2semidirect
7. #24914119C2semidirect
8. #24914112C2semidirect
9. #24914069C2semidirect
10. #24914042C2semidirect
11. #24914023C2semidirect
12. #24913859C2semidirect
13. #24913833C2semidirect
14. #24913826C2semidirect
15. #24913822C2semidirect
16. #24913805C2semidirect
17. #24913802C2semidirect
18. #24913794C2semidirect
19. #24913791C2semidirect
20. #24913386C2semidirect
21. #24913307C2semidirect
22. #24913158C2semidirect
23. #24913086C2semidirect
24. #24913053C2semidirect
25. #24913049C2semidirect
26. #24912811C2semidirect
27. #24912658C2semidirect
28. #24910804C2semidirect
29. #24910793C2semidirect
30. #24910102C2semidirect
31. C83×#2681C2semidirect
36. C2×#14581785C22semidirect
37. C2×#14581782C22semidirect
38. C2×#14581782C22semidirect
46. C2×#14581774C22semidirect
47. C2×#14581774C22semidirect
48. C2×#14581771C22semidirect
53. C2×#14581768C22semidirect
62. C2×C4×C22⋊D83C22semidirect
66. C2×C4⋊C4×D83C22semidirect
67. #19127642C22semidirect
69. #19127635C22semidirect
70. #19127634C22semidirect
71. #19127634C22semidirect
72. #19127633C22semidirect
73. #19127631C22semidirect
74. #19127631C22semidirect
79. #19127629C22semidirect
80. #19127627C22semidirect
81. #19127626C22semidirect
83. #19127624C22semidirect
84. #19127624C22semidirect
85. #19127624C22semidirect
86. #19127624C22semidirect
91. #19127622C22semidirect
92. #19127621C22semidirect
93. #19127620C22semidirect
99. #19127617C22semidirect
102. #19127616C22semidirect
108. #19127609C22semidirect
109. #19127606C22semidirect
117. #19127600C22semidirect
118. #19127599C22semidirect
119. #19127598C22semidirect
120. #19127596C22semidirect
122. #19127595C22semidirect
123. #19127595C22semidirect
127. #19127593C22semidirect
130. #19127591C22semidirect
131. #19127589C22semidirect
132. #19127588C22semidirect
133. #19127584C22semidirect
134. #19127584C22semidirect
135. #19127582C22semidirect
137. #19127581C22semidirect
144. #19127577C22semidirect
146. #19127576C22semidirect
149. #19127575C22semidirect
153. #19127573C22semidirect
154. #19127573C22semidirect
159. #19127572C22semidirect
160. #19127570C22semidirect
161. #19127565C22semidirect
164. #19127563C22semidirect
168. #19127558C22semidirect
172. C4⋊C4×Dic83C22semidirect
173. #19127547C22semidirect
176. C2×C22⋊Q8×C83C22semidirect
178. #398×C83C22semidirect
179. #396×C83C22semidirect
182. #394×C83C22semidirect
183. #393×C83C22semidirect
184. #390×C83C22semidirect
185. #389×C83C22semidirect
188. #385×C83C22semidirect
240. #14581754D4semidirect
851. #2681D83semidirect
867. C83#36723semidirect
892. C2×C22⋊Q8C2×D83semidirect
915. #398C2×D83semidirect
932. #396C2×D83semidirect
948. #394C2×D83semidirect
949. #393C2×D83semidirect
963. #390C2×D83semidirect
968. #389C2×D83semidirect
1010. #385C2×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282972
C2×#191282092
#249157542
#249157472
#249141622
#249141552
#249141192
#249141122
#249140692
#249140422
#249140232
#249138592
#249138332
#249138262
#249138222
#249138052
#249138022
#249137942
#249137912
#249133862
#249133072
#249131582
#249130862
#249130532
#249130492
#249128112
#249126582
#249108042
#249107932
#249101022
C83×#26812
#3672383