Finite Group Databasebeta

← #35568359

Subgroups — #35568359

Order 21248.

2522 conjugacy classes of subgroups.

The subgroup lattice has 1608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128280C211yesmaximal, characteristic
2#24910627C211yesmaximal, characteristic, complemented
3#24910623C211yesmaximal, characteristic, complemented
4#24910614C211yesmaximal, characteristic, complemented
5#24910545C211yesmaximal, characteristic, complemented
6#24910544C211yesmaximal, characteristic, complemented
7#24910515C211yesmaximal, characteristic, complemented
8#24910512C211yesmaximal, characteristic, complemented
9#24910511C211yesmaximal, characteristic, complemented
10#24910507C211yesmaximal, characteristic, complemented
11#24910484C211yesmaximal, characteristic, complemented
12#24910482C211yesmaximal, characteristic, complemented
13#24910291C211yesmaximal, characteristic, complemented
14#24910289C211yesmaximal, characteristic, complemented
15#24910289C211yesmaximal, characteristic, complemented
16#24910287C211yesmaximal, characteristic, complemented
17#24910224C211yesmaximal, characteristic, complemented
18#24910222C211yesmaximal, characteristic, complemented
19#24910220C211yesmaximal, characteristic, complemented
20#24910216C211yesmaximal, characteristic, complemented
21#24910194C211yesmaximal, characteristic, complemented
22#24910193C211yesmaximal, characteristic, complemented
23#24910165C211yesmaximal, characteristic, complemented
24#24910165C211yesmaximal, characteristic, complemented
25#24910164C211yesmaximal, characteristic, complemented
26#24910160C211yesmaximal, characteristic, complemented
27#24910062C211yesmaximal, characteristic, complemented
28#24909979C211yesmaximal, characteristic, complemented
29#24909975C211yesmaximal, characteristic, complemented
30#387×D83C211yesmaximal, characteristic, complemented
31C83×#2377C211yesmaximal, characteristic, complemented
32C22×#13050590C2211yescharacteristic
33C22×#13050589C2211yescharacteristic
34#19128280C4116yescomplemented
35C2×#14581772C2211yescharacteristic
36C2×#14581771C2211yescharacteristic
37C2×#14581769C2211yescharacteristic
38C2×#14581769C2211yescharacteristic
39C2×#14581765C2211yescharacteristic
40C2×#14581765C2211yescharacteristic
41C2×#14581764C2211yescharacteristic
42C2×#14581764C2211yescharacteristic
43C2×#14581763C2211yescharacteristic
44C2×#14581763C2211yescharacteristic
45C2×#14581763C2211yescharacteristic
46C2×D4×Dic83C2211yescharacteristic
47C2×D4×Dic83C2211yescharacteristic
48C2×#14581754C2211yescharacteristic
49C2×#14581754C2211yescharacteristic
50C2×C4×C22⋊D83C2211yescharacteristic
51C2×C4×C22⋊D83C2211yescharacteristic
52C2×C4×C22⋊D83C2211yescharacteristic
53C2×(C22⋊D83)⋊C4C2211yescharacteristic
54C2×(C22⋊D83)⋊C4C2211yescharacteristic
55C2×(C22⋊D83)⋊C4C2211yescharacteristic
56C2×(C22⋊D83)⋊C4C2211yescharacteristic
57C2×(C22⋊D83)⋊C4C2211yescharacteristic
58C2×C4⋊C4×D83C2211yescharacteristic
59C2×C4⋊C4×D83C2211yescharacteristic
60C2×C42×D83C2211yescharacteristic
61#19127606C2211yescharacteristic
62#19127606C2211yescharacteristic
63#19127605C2211yescharacteristic
64#19127605C2211yescharacteristic
65#19127605C2211yescharacteristic
66#19127605C2211yescharacteristic
67#19127605C2211yescharacteristic
68#19127605C2211yescharacteristic
69#19127601C2211yescharacteristic
70#19127601C2211yescharacteristic
71#19127599C2211yescharacteristic
72#19127597C2211yescharacteristic
73#19127596C2211yescharacteristic
74#19127596C2211yescharacteristic
75#19127595C2211yescharacteristic
76#19127595C2211yescharacteristic
77#19127595C2211yescharacteristic
78#19127595C2211yescharacteristic
79#19127594C2211yescharacteristic
80#19127594C2211yescharacteristic
81#19127593C2211yescharacteristic
82#19127592C2211yescharacteristic
83#19127591C2211yescharacteristic
84#19127590C2211yescharacteristic
85#19127589C2211yescharacteristic
86#19127589C2211yescharacteristic
87#19127589C2211yescharacteristic
88#19127589C2211yescharacteristic
89#19127588C2211yescharacteristic
90#19127588C2211yescharacteristic
91#19127587C2211yescharacteristic
92#19127587C2211yescharacteristic
93#19127586C2211yescharacteristic
94#19127586C2211yescharacteristic
95#19127586C2211yescharacteristic
96#19127586C2211yescharacteristic
97#19127585C2211yescharacteristic
98#19127585C2211yescharacteristic
99#19127584C2211yescharacteristic
100#19127584C2211yescharacteristic
101#19127584C2211yescharacteristic
102#19127584C2211yescharacteristic
103#19127583C2211yescharacteristic
104#19127583C2211yescharacteristic
105#19127583C2211yescharacteristic
106#19127583C2211yescharacteristic
107#19127582C2211yescharacteristic
108#19127582C2211yescharacteristic
109#19127582C2211yescharacteristic
110#19127582C2211yescharacteristic
111#19127581C2211yescharacteristic
112#19127581C2211yescharacteristic
113#19127581C2211yescharacteristic
114#19127581C2211yescharacteristic
115#19127580C2211yescharacteristic
116#19127579C2211yescharacteristic
117#19127579C2211yescharacteristic
118#19127578C2211yescharacteristic
119#19127578C2211yescharacteristic
120#19127578C2211yescharacteristic
121#19127577C2211yescharacteristic
122#19127577C2211yescharacteristic
123#19127577C2211yescharacteristic
124#19127577C2211yescharacteristic
125#19127577C2211yescharacteristic
126#19127577C2211yescharacteristic
127#19127577C2211yescharacteristic
128#19127577C2211yescharacteristic
129#19127577C2211yescharacteristic
130#19127577C2211yescharacteristic
131#19127575C2211yescharacteristic
132#19127574C2211yescharacteristic
133#19127573C2211yescharacteristic
134#19127573C2211yescharacteristic
135#19127573C2211yescharacteristic
136#19127572C2211yescharacteristic
137#19127563C2211yescharacteristic
138#19127563C2211yescharacteristic
139#19127563C2211yescharacteristic
140#19127562C2211yescharacteristic
141#19127562C2211yescharacteristic
142#19127560C2211yescharacteristic
143#19127560C2211yescharacteristic
144#19127559C2211yescharacteristic
145#19127559C2211yescharacteristic
146#19127558C2211yescharacteristic
147C4⋊C4×Dic83C2211yescharacteristic
148C4×C4⋊Dic83C2211yescharacteristic
149#19127552C2211yescharacteristic
150#19127552C2211yescharacteristic
151C22⋊C4×Dic83C2211yescharacteristic
152C22⋊C4×Dic83C2211yescharacteristic
153C22⋊C4×Dic83C2211yescharacteristic
154C22⋊C4×Dic83C2211yescharacteristic
155C22⋊C4×Dic83C2211yescharacteristic
156C22⋊C4×Dic83C2211yescharacteristic
157C22⋊C4×Dic83C2211yescharacteristic
158C4×(C2×D83)⋊C4C2211yescharacteristic
159C4×(C2×D83)⋊C4C2211yescharacteristic
160C4×C22⋊Dic83C2211yescharacteristic
161C4×C22⋊Dic83C2211yescharacteristic
162#19127548C2211yescharacteristic
163#19127548C2211yescharacteristic
164#19127548C2211yescharacteristic
165C2×C83⋊#95C2211yescharacteristic
166C2×C83⋊#95C2211yescharacteristic
167C2×C83⋊#95C2211yescharacteristic
168#95×D83C2211yescharacteristic
169#95×D83C2211yescharacteristic
170#95×D83C2211yescharacteristic
171#95×D83C2211yescharacteristic
172#95×D83C2211yescharacteristic
173C2×#121×C83C2211yescharacteristic
174#390×C83C2211yescharacteristic
175#390×C83C2211yescharacteristic
176#388×C83C2211yescharacteristic
177#388×C83C2211yescharacteristic
178#387×C83C2211yescharacteristic
179#387×C83C2211yescharacteristic
180#386×C83C2211yescharacteristic
181#386×C83C2211yescharacteristic
182#386×C83C2211yescharacteristic
183#386×C83C2211yescharacteristic
184#385×C83C2211yescharacteristic
185#385×C83C2211yescharacteristic
186#381×C83C2211yescharacteristic
187#380×C83C2211yescharacteristic
188C2×#13050590—42no—
189C2×#13050590—42no—
190C2×#13050590C2×C418yescomplemented
191C2×#13050589—42no—
192C2×#13050589—42no—
193C2×#13050589C2×C418yescomplemented
194C22×Dic166C2311yescharacteristic
195C22×Dic166C2311yescharacteristic
196C22×D332C2311yescharacteristic
197C22×C22⋊D83C2311yescharacteristic
198C22×C22⋊D83C2311yescharacteristic
199C22×C22⋊D83C2311yescharacteristic
200C22×C22⋊D83C2311yescharacteristic
201C22×C22⋊D83C2311yescharacteristic
202C22×C22⋊D83C2311yescharacteristic
203C23×Dic83C2311yescharacteristic
204C23×Dic83C2311yescharacteristic
205C23×Dic83C2311yescharacteristic
206C23×Dic83C2311yescharacteristic
207C23×Dic83C2311yescharacteristic
208C23×Dic83C2311yescharacteristic
209C22×C4×D83C2311yescharacteristic
210C22×C4×D83C2311yescharacteristic
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#14581772C2×C418yescomplemented
220#14581771C2×C418yescomplemented
221#14581769C2×C418yescomplemented
222#14581769C2×C418yescomplemented
223#14581765C2×C418yescomplemented
224#14581765C2×C418yescomplemented
225#14581764C2×C418yescomplemented
226#14581764C2×C418yescomplemented
227#14581763C2×C418yescomplemented
228#14581763C2×C418yescomplemented
229#14581763C2×C418yescomplemented
230D4×Dic83—42no—
231D4×Dic83—42no—
232#14581754—42no—
233#14581754—42no—
234C4×C22⋊D83—42no—
235C4×C22⋊D83—42no—
236C4×C22⋊D83—42no—
237(C22⋊D83)⋊C4—42no—
238(C22⋊D83)⋊C4—42no—
239(C22⋊D83)⋊C4—42no—
240(C22⋊D83)⋊C4—42no—
241(C22⋊D83)⋊C4—42no—
242C2×C4⋊Dic83C2311yescharacteristic
243C2×C4⋊Dic83C2311yescharacteristic
244C2×C4⋊Dic83C2311yescharacteristic
245C2×C4⋊Dic83C2311yescharacteristic
246C2×C4⋊Dic83C2311yescharacteristic
247C2×Dic83⋊C4C2311yescharacteristic
248C2×Dic83⋊C4C2311yescharacteristic
249C2×Dic83⋊C4C2311yescharacteristic
250C2×Dic83⋊C4C2311yescharacteristic
251C2×Dic83⋊C4C2311yescharacteristic
252C2×Dic83⋊C4C2311yescharacteristic
253C2×Dic83⋊C4C2311yescharacteristic
254C2×Dic83⋊C4C2311yescharacteristic
255C2×Dic83⋊C4C2311yescharacteristic
256C2×Dic83⋊C4C2311yescharacteristic
257C2×Dic83⋊C4C2311yescharacteristic
258C2×Dic83⋊C4C2311yescharacteristic
259C2×Dic83⋊C4C2311yescharacteristic
260C2×Dic83⋊C4C2311yescharacteristic
261C4⋊C4×D83—42no—
262C4⋊C4×D83C2×C418yescomplemented
263C2×C22⋊Dic83C2311yescharacteristic
264C2×C22⋊Dic83C2311yescharacteristic
265C2×C22⋊Dic83C2311yescharacteristic
266C2×C22⋊Dic83C2311yescharacteristic
267C2×C22⋊Dic83C2311yescharacteristic
268C2×C22⋊Dic83C2311yescharacteristic
269C2×C22⋊Dic83C2311yescharacteristic
270C2×C22⋊Dic83C2311yescharacteristic
271C2×C22⋊Dic83C2311yescharacteristic
272C2×C22⋊Dic83C2311yescharacteristic
273C2×C22⋊Dic83C2311yescharacteristic
274C2×C22⋊Dic83C2311yescharacteristic
275C2×(C2×D83)⋊C4C2311yescharacteristic
276C2×(C2×D83)⋊C4C2311yescharacteristic
277C2×(C2×D83)⋊C4C2311yescharacteristic
278C2×(C2×D83)⋊C4C2311yescharacteristic
279C2×(C2×D83)⋊C4C2311yescharacteristic
280C2×(C2×D83)⋊C4C2311yescharacteristic
281C2×(C2×D83)⋊C4C2311yescharacteristic
282C2×(C2×D83)⋊C4C2311yescharacteristic
283C2×(C2×D83)⋊C4C2311yescharacteristic
284C2×(C2×D83)⋊C4C2311yescharacteristic
285C2×(C2×D83)⋊C4C2311yescharacteristic
286C2×(C2×D83)⋊C4C2311yescharacteristic
287C2×C4×Dic83C2311yescharacteristic
288C2×C4×Dic83C2311yescharacteristic
289C2×C4×Dic83C2311yescharacteristic
290C2×C4×Dic83C2311yescharacteristic
291C2×C4×Dic83C2311yescharacteristic
292C2×C4×Dic83C2311yescharacteristic
293C2×C4×Dic83C2311yescharacteristic
294C2×C4×Dic83C2311yescharacteristic
295C2×C4×Dic83C2311yescharacteristic
296C2×C4×Dic83C2311yescharacteristic
297C2×C4×Dic83C2311yescharacteristic
298C2×C4×Dic83C2311yescharacteristic
299C2×C4×Dic83C2311yescharacteristic
300C2×C4×Dic83C2311yescharacteristic
301C42×D83—42no—
302C83⋊#95C2311yescharacteristic
303C83⋊#95C2311yescharacteristic
304C83⋊#95C2311yescharacteristic
305C83⋊#95C2311yescharacteristic
306C83⋊#95C2311yescharacteristic
307C83⋊#95C2311yescharacteristic
308C83⋊#95C2311yescharacteristic
309C83⋊#95C2311yescharacteristic
310C83⋊#95C2311yescharacteristic
311C83⋊#95C2311yescharacteristic
312C83⋊#95C2311yescharacteristic
313C83⋊#95C2311yescharacteristic
314C83⋊#95C2311yescharacteristic
315C83⋊#95C2311yescharacteristic
316C83⋊#95C2311yescharacteristic
317C83⋊#95C2311yescharacteristic
318C83⋊#95C2311yescharacteristic
319C83⋊#95C2311yescharacteristic
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
340C22×D4×C83C2311yescharacteristic
341C22×D4×C83C2311yescharacteristic
342C22×D4×C83C2311yescharacteristic
343C23×C4×C83C2311yescharacteristic
344C23×C4×C83C2311yescharacteristic
345C23×C4×C83C2311yescharacteristic
346#121×C83C2×C418yescomplemented
347C2×C4⋊C4×C83C2311yescharacteristic
348C2×C4⋊C4×C83C2311yescharacteristic
349C2×C4⋊C4×C83C2311yescharacteristic
350C2×C4⋊C4×C83C2311yescharacteristic
351C2×C4⋊C4×C83C2311yescharacteristic
352C2×C22⋊C4×C83C2311yescharacteristic
353C2×C22⋊C4×C83C2311yescharacteristic
354C2×C22⋊C4×C83C2311yescharacteristic
355C2×C22⋊C4×C83C2311yescharacteristic
356C2×C22⋊C4×C83C2311yescharacteristic
357C2×C22⋊C4×C83C2311yescharacteristic
358C2×C22⋊C4×C83C2311yescharacteristic
359C2×C22⋊C4×C83C2311yescharacteristic
360C2×C22⋊C4×C83C2311yescharacteristic
361C2×C22⋊C4×C83C2311yescharacteristic
362C2×C22⋊C4×C83C2311yescharacteristic
363C2×C22⋊C4×C83C2311yescharacteristic
364C2×C42×C83C2311yescharacteristic
365C2×C42×C83C2311yescharacteristic
366#95×C83C2311yescharacteristic
367#95×C83C2311yescharacteristic
368#95×C83C2311yescharacteristic
369#95×C83C2311yescharacteristic
370#95×C83C2311yescharacteristic
371#95×C83C2311yescharacteristic
372#95×C83C2311yescharacteristic
373#95×C83C2311yescharacteristic
374#95×C83C2311yescharacteristic
375#95×C83C2311yescharacteristic
376C23×D83C2411yescharacteristic
377C23×D83C2411yescharacteristic
378#13050590—416no—
379#13050589—416no—
380C2×Dic166—41no—
381C2×Dic166—41no—
382C2×Dic166—41no—
383C2×Dic166—41no—
384C2×Dic166C22×C414yes—
385C2×Dic166C22×C414yes—
386C2×D332—22no—
387C2×D332—22no—
388C2×D332C22×C414yes—
389C2×C22⋊D83—22no—
390C2×C22⋊D83—22no—
391C2×C22⋊D83—22no—
392C2×C22⋊D83—22no—
393C2×C22⋊D83—22no—
394C2×C22⋊D83—22no—
395C2×C22⋊D83—41no—
396C2×C22⋊D83—41no—
397C2×C22⋊D83—41no—
398C2×C22⋊D83—41no—
399C2×C22⋊D83—41no—
400C2×C22⋊D83—41no—
401C2×C22⋊D83C22×C414yes—
402C2×C22⋊D83C22×C414yes—
403C2×C22⋊D83C22×C414yes—
404C2×C22⋊D83C22×C414yes—
405C2×C22⋊D83C22×C414yes—
406C2×C22⋊D83C22×C414yes—
407C22×Dic83—22no—
408C22×Dic83—22no—
409C22×Dic83—22no—
410C22×Dic83—41no—
411C22×Dic83—41no—
412C22×Dic83—41no—
413C22×Dic83—41no—
414C22×Dic83—41no—
415C22×Dic83—41no—
416C22×Dic83—41no—
417C22×Dic83—41no—
418C22×Dic83—41no—
419C22×Dic83—41no—
420C22×Dic83—41no—
421C22×Dic83—41no—
422C22×Dic83—41no—
423C22×Dic83C22×C414yes—
424C22×Dic83C22×C414yes—
425C22×Dic83C2411yescharacteristic
426C22×Dic83C2411yescharacteristic
427C22×Dic83C2411yescharacteristic
428C22×Dic83C2411yescharacteristic
429C22×Dic83C2411yescharacteristic
430C22×Dic83C2411yescharacteristic
431C22×Dic83C2411yescharacteristic
432C22×Dic83C2411yescharacteristic
433C22×Dic83C2411yescharacteristic
434C22×Dic83C2411yescharacteristic
435C22×Dic83C2411yescharacteristic
436C22×Dic83C2411yescharacteristic
437C22×Dic83C2411yescharacteristic
438C22×Dic83C2411yescharacteristic
439C2×C4×D83—22no—
440C2×C4×D83—22no—
441C2×C4×D83—22no—
442C2×C4×D83—22no—
443C2×C4×D83—22no—
444C2×C4×D83—22no—
445C2×C4×D83—22no—
446C2×C4×D83—22no—
447C2×C4×D83—22no—
448C2×C4×D83—41no—
449C2×C4×D83—41no—
450C2×C4×D83—41no—
451C2×C4×D83—41no—
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—41no—
463C2×C4×D83—41no—
464C2×C4×D83—41no—
465C2×C4×D83C22×C414yes—
466C2×C4×D83C22×C414yes—
467C2×C4×D83C22×C414yes—
468C2×C4×D83C22×C414yes—
469C4⋊Dic83—22no—
470C4⋊Dic83—41no—
471C4⋊Dic83C22×C414yes—
472C4⋊Dic83C22×C414yes—
473C4⋊Dic83C22×C414yes—
474Dic83⋊C4—22no—
475Dic83⋊C4—41no—
476Dic83⋊C4—41no—
477Dic83⋊C4—41no—
478Dic83⋊C4—41no—
479Dic83⋊C4—41no—
480Dic83⋊C4—41no—
481Dic83⋊C4—41no—
482Dic83⋊C4—41no—
483Dic83⋊C4—41no—
484Dic83⋊C4C22×C414yes—
485Dic83⋊C4C22×C414yes—
486Dic83⋊C4C22×C414yes—
487Dic83⋊C4C22×C414yes—
488C22⋊Dic83—22no—
489C22⋊Dic83—22no—
490C22⋊Dic83—22no—
491C22⋊Dic83—41no—
492C22⋊Dic83—41no—
493C22⋊Dic83—41no—
494C22⋊Dic83—41no—
495C22⋊Dic83—41no—
496C22⋊Dic83C22×C414yes—
497C22⋊Dic83C22×C414yes—
498C22⋊Dic83C22×C414yes—
499C22⋊Dic83C22×C414yes—
500(C2×D83)⋊C4—22no—
501(C2×D83)⋊C4—22no—
502(C2×D83)⋊C4—22no—
503(C2×D83)⋊C4—22no—
504(C2×D83)⋊C4—22no—
505(C2×D83)⋊C4—41no—
506(C2×D83)⋊C4—41no—
507(C2×D83)⋊C4—41no—
508(C2×D83)⋊C4—41no—
509(C2×D83)⋊C4—41no—
510(C2×D83)⋊C4C22×C414yes—
511(C2×D83)⋊C4C22×C414yes—
512C4×Dic83—22no—
513C4×Dic83—22no—
514C4×Dic83—41no—
515C4×Dic83—41no—
516C4×Dic83—41no—
517C4×Dic83—41no—
518C4×Dic83—41no—
519C4×Dic83—41no—
520C4×Dic83—41no—
521C4×Dic83—41no—
522C4×Dic83—41no—
523C4×Dic83—41no—
524C4×Dic83—41no—
525C4×Dic83—41no—
526C24×C83C2411yescharacteristic
527C24×C83C2411yescharacteristic
528C24×C83C2411yescharacteristic
529C2×D4×C83—41no—
530C2×D4×C83—41no—
531C2×D4×C83—41no—
532C2×D4×C83—41no—
533C2×D4×C83—41no—
534C2×D4×C83—41no—
535C2×D4×C83C22×C414yes—
536C2×D4×C83C22×C414yes—
537C2×D4×C83C22×C414yes—
538C22×C4×C83—41no—
539C22×C4×C83—41no—
540C22×C4×C83—41no—
541C22×C4×C83—41no—
542C22×C4×C83—41no—
543C22×C4×C83—41no—
544C22×C4×C83—41no—
545C22×C4×C83—41no—
546C22×C4×C83C22×C414yes—
547C22×C4×C83C2411yescharacteristic
548C22×C4×C83C2411yescharacteristic
549C22×C4×C83C2411yescharacteristic
550C22×C4×C83C2411yescharacteristic
551C22×C4×C83C2411yescharacteristic
552C22×C4×C83C2411yescharacteristic
553C22×C4×C83C2411yescharacteristic
554C22×C4×C83C2411yescharacteristic
555C22×C4×C83C2411yescharacteristic
556C22×C4×C83C2411yescharacteristic
557C22×C4×C83C2411yescharacteristic
558C22×C4×C83C2411yescharacteristic
559C4⋊C4×C83—41no—
560C4⋊C4×C83—41no—
561C4⋊C4×C83—41no—
562C4⋊C4×C83—41no—
563C4⋊C4×C83C22×C414yes—
564C22⋊C4×C83—41no—
565C22⋊C4×C83—41no—
566C22⋊C4×C83—41no—
567C22⋊C4×C83—41no—
568C22⋊C4×C83—41no—
569C22⋊C4×C83—41no—
570C22⋊C4×C83—41no—
571C22⋊C4×C83—41no—
572C22⋊C4×C83—41no—
573C22⋊C4×C83—41no—
574C22⋊C4×C83C22×C414yes—
575C22⋊C4×C83C22×C414yes—
576C42×C83—41no—
577C42×C83—41no—
578C23×C83—21no—
579C23×C83—21no—
580C23×C83—21no—
581C23×C83—21no—
582C23×C83—21no—
583C23×C83—21no—
584C23×C83—21no—
585C23×C83—21no—
586C23×C83—21no—
587C23×C83—21no—
588C23×C83—21no—
589C23×C83—21no—
590C23×C83—21no—
591C23×C83—21no—
592C23×C83—21no—
593C23×C83—21no—
594C23×C83—21no—
595C23×C83—21no—
596C23×C83C23×C412yes—
597C23×C83C23×C412yes—
598C23×C83C23×C412yes—
599C23×C83C2511yescharacteristic
600C22×D83—21no—
601C22×D83—21no—
602C22×D83—21no—
603C22×D83—21no—
604C22×D83—21no—
605C22×D83—21no—
606C22×D83—21no—
607C22×D83—21no—
608C22×D83—21no—
609C22×D83—21no—
610C22×D83C23×C412yes—
611C22×D83C23×C412yes—
612C22×D83H(5,𝔽2)12yes—
613C22×D83H(5,𝔽2)12yes—
614D4×C83—44no—
615D4×C83—44no—
616D4×C83—44no—
617C2×C4×C83—21no—
618C2×C4×C83—21no—
619C2×C4×C83—21no—
620C2×C4×C83—21no—
621C2×C4×C83—21no—
622C2×C4×C83—21no—
623C2×C4×C83—21no—
624C2×C4×C83—21no—
625C2×C4×C83—21no—
626C2×C4×C83—21no—
627C2×C4×C83—21no—
628C2×C4×C83—21no—
629C2×C4×C83—21no—
630C2×C4×C83—21no—
631C2×C4×C83—21no—
632C2×C4×C83—21no—
633C2×C4×C83—21no—
634C2×C4×C83—21no—
635C2×C4×C83—21no—
636C2×C4×C83—21no—
637C2×C4×C83—21no—
638C2×C4×C83—21no—
639C2×C4×C83—21no—
640C2×C4×C83—21no—
641C2×C4×C83—21no—
642C2×C4×C83—21no—
643C2×C4×C83—21no—
644C2×C4×C83—21no—
645C2×C4×C83—21no—
646C2×C4×C83—21no—
647C2×C4×C83—21no—
648C2×C4×C83—21no—
649C2×C4×C83—44no—
650C2×C4×C83—82no—
651C2×C4×C83—82no—
652C2×C4×C83C23×C412yes—
653C2×C4×C83C23×C412yes—
654C2×C4×C83C23×C412yes—
655C2×C4×C83C23×C412yes—
656C22⋊D83—28no—
657C22⋊D83—28no—
658C22⋊D83—28no—
659C22⋊D83—44no—
660C22⋊D83—44no—
661C22⋊D83—44no—
662C2×Dic83—21no—
663C2×Dic83—21no—
664C2×Dic83—21no—
665C2×Dic83—21no—
666C2×Dic83—21no—
667C2×Dic83—21no—
668C2×Dic83—21no—
669C2×Dic83—21no—
670C2×Dic83—21no—
671C2×Dic83—21no—
672C2×Dic83—21no—
673C2×Dic83—21no—
674C2×Dic83—21no—
675C2×Dic83—21no—
676C2×Dic83—21no—
677C2×Dic83—21no—
678C2×Dic83—21no—
679C2×Dic83—21no—
680C2×Dic83—21no—
681C2×Dic83—21no—
682C2×Dic83—21no—
683C2×Dic83—21no—
684C2×Dic83—21no—
685C2×Dic83—21no—
686C2×Dic83—21no—
687C2×Dic83—21no—
688C2×Dic83—21no—
689C2×Dic83—21no—
690C2×Dic83—21no—
691C2×Dic83—21no—
692C2×Dic83—21no—
693C2×Dic83—21no—
694C2×Dic83—21no—
695C2×Dic83—21no—
696C2×Dic83—44no—
697C2×Dic83—44no—
698C2×Dic83—82no—
699C2×Dic83—82no—
700C2×Dic83—82no—
701C2×Dic83—82no—
702C2×Dic83C23×C412yes—
703C2×Dic83C23×C412yes—
704C2×Dic83C23×C412yes—
705C2×Dic83C23×C412yes—
706C2×Dic83C23×C412yes—
707C2×Dic83C23×C412yes—
708C2×Dic83H(5,𝔽2)12yes—
709C2×Dic832−1+412yes—
710D332—28no—
711C4×D83—28no—
712C4×D83—44no—
713C4×D83—44no—
714C4×D83—44no—
715C4×D83—44no—
716C4×D83—44no—
717C4×D83—82no—
718C4×D83—82no—
719C4×D83—82no—
720C4×D83—82no—
721Dic166—44no—
722Dic166—44no—
723C22×C83—22no—
724C22×C83—22no—
725C22×C83—22no—
726C22×C83—22no—
727C22×C83—22no—
728C22×C83—22no—
729C22×C83—22no—
730C22×C83—22no—
731C22×C83—22no—
732C22×C83—41no—
733C22×C83—41no—
734C22×C83—41no—
735C22×C83—41no—
736C22×C83—41no—
737C22×C83—41no—
738C22×C83—41no—
739C22×C83—41no—
740C22×C83—41no—
741C22×C83—41no—
742C22×C83—41no—
743C22×C83—41no—
744C22×C83C24×C411yescharacteristic
745C22×C83C2×H(5,𝔽2)11yescharacteristic
746C22×C83C2×H(5,𝔽2)11yescharacteristic
747C22×C83C2×H(5,𝔽2)11yescharacteristic
748C22×C83C2×2−1+411yescharacteristic
749C22×C83#58511yescharacteristic
750C22×C83#58511yescharacteristic
751C2×D83—22no—
752C2×D83—22no—
753C2×D83—22no—
754C2×D83—22no—
755C2×D83—22no—
756C2×D83—22no—
757C2×D83—22no—
758C2×D83—22no—
759C2×D83—22no—
760C2×D83—41no—
761C2×D83—41no—
762C2×D83—41no—
763C2×D83—41no—
764C2×D83#51814yes—
765C4×C83—22no—
766C4×C83—22no—
767C4×C83—22no—
768C4×C83—22no—
769C4×C83—41no—
770C4×C83—41no—
771C4×C83—41no—
772C4×C83—41no—
773C4×C83—41no—
774C4×C83—41no—
775C4×C83—41no—
776C4×C83—41no—
777Dic83—22no—
778Dic83—22no—
779Dic83—22no—
780Dic83—22no—
781Dic83—22no—
782Dic83—22no—
783Dic83—22no—
784Dic83—22no—
785Dic83—41no—
786Dic83—41no—
787Dic83—41no—
788Dic83—41no—
789Dic83—41no—
790Dic83—41no—
791#34436—831nomaximal, Sylow
792C2×C83—42no—
793C2×C83—42no—
794C2×C83—42no—
795C2×C83C2×#51811yescharacteristic
796C2×C83C4×H(5,𝔽2)11yescharacteristic
797C2×C83C4×2−1+411yescharacteristic
798C2×C83#353411yescharacteristic
799C2×C83#353611yescharacteristic
800C2×C83#355911yescharacteristic
801C2×C83#356011yescharacteristic
802D83—24no—
803D83—42no—
804C2×#537—831no—
805#2378—831no—
806#2378—831no—
807#2377—831no—
808#2377D8311yescharacteristic, complemented
809#2368—831no—
810#2368—831no—
811#2364—831no—
812#2364—831no—
813#2364—831no—
814#2364—831no—
815#2361—831no—
816#2361—831no—
817#2339—831no—
818#2339—831no—
819#2339—831no—
820#2339—831no—
821#2333—831no—
822#2333—831no—
823#2332—831no—
824#2332—831no—
825#2329—831no—
826#2329—831no—
827#2325—831no—
828#2325—831no—
829#2325—831no—
830#2325—831no—
831#2313—831no—
832C4×#121—831no—
833C4×#121—831no—
834C2×#387—831no—
835C83#3443611yescharacteristic, complemented, Sylow
836C22×#41—831no—
837C22×#41—831no—
838#537—8316no—
839C2×C22⋊Q8—831no—
840C2×C22⋊Q8—831no—
841C2×C22⋊Q8—831no—
842C2×C22⋊Q8—831no—
843C2×#121—831no—
844C2×#121—831no—
845C2×#121—831no—
846C2×#121—831no—
847C2×#121—831no—
848C2×#121—831no—
849C2×#121—831no—
850C2×#121C2×D8311yescharacteristic
851C2×C4×D4—831no—
852C2×C4×D4—831no—
853C2×C4×D4—831no—
854C2×C4×D4—831no—
855C2×C4×D4—831no—
856C2×C4×D4—831no—
857C2×C4×D4—831no—
858C2×C4×D4—831no—
859C2×C4×D4—831no—
860C2×C4×D4—831no—
861C2×C4×D4—831no—
862C2×C4×D4—831no—
863C22×C4⋊C4—831no—
864C22×C4⋊C4—831no—
865C22×C42—831no—
866#391—831no—
867#391—831no—
868#391—831no—
869#391—831no—
870#391—831no—
871#391—831no—
872#391—831no—
873#391—831no—
874#390—831no—
875#390—831no—
876#390C2×D8311yescharacteristic
877#390C2×D8311yescharacteristic
878#389—831no—
879#389—831no—
880#389—831no—
881#389—831no—
882#388—831no—
883#388—831no—
884#388—831no—
885#388—831no—
886#388—831no—
887#388—831no—
888#388—831no—
889#388—831no—
890#388—831no—
891#388—831no—
892#388—831no—
893#388—831no—
894#388—831no—
895#388—831no—
896#388C2×D8311yescharacteristic
897#388C2×D8311yescharacteristic
898#387—831no—
899#387—831no—
900#387—831no—
901#387—831no—
902#387—831no—
903#387—831no—
904#387—831no—
905#387—831no—
906#387—831no—
907#387—831no—
908#387—831no—
909#387—831no—
910#387—831no—
911#387—831no—
912#387—831no—
913#387—831no—
914#387—831no—
915#387—831no—
916#387—831no—
917#387—831no—
918#387—831no—
919#387—831no—
920#387C2×D8311yescharacteristic
921#387C2×D8311yescharacteristic
922#386—831no—
923#386—831no—
924#386—831no—
925#386—831no—
926#386—831no—
927#386—831no—
928#386—831no—
929#386—831no—
930#386—831no—
931#386—831no—
932#386—831no—
933#386—831no—
934#386—831no—
935#386—831no—
936#386—831no—
937#386—831no—
938#386—831no—
939#386—831no—
940#386—831no—
941#386—831no—
942#386C2×D8311yescharacteristic
943#386C2×D8311yescharacteristic
944#386C2×D8311yescharacteristic
945#386C2×D8311yescharacteristic
946#385—831no—
947#385—831no—
948#385—831no—
949#385—831no—
950#385—831no—
951#385—831no—
952#385C2×D8311yescharacteristic
953#385C2×D8311yescharacteristic
954#381—831no—
955#381—831no—
956#381—831no—
957#381—831no—
958#381—831no—
959#381C2×D8311yescharacteristic
960#380—831no—
961#380—831no—
962#380—831no—
963#380—831no—
964#380—831no—
965#380C2×D8311yescharacteristic
966C4×C4⋊C4—831no—
967C4×C4⋊C4—831no—
968C4×C4⋊C4—831no—
969C4×C4⋊C4—831no—
970C4×C22⋊C4—831no—
971C4×C22⋊C4—831no—
972C4×C22⋊C4—831no—
973C4×C22⋊C4—831no—
974C4×C22⋊C4—831no—
975C4×C22⋊C4—831no—
976C4×C22⋊C4—831no—
977C4×C22⋊C4—831no—
978C4×C22⋊C4—831no—
979C4×C22⋊C4—831no—
980C4×C22⋊C4—831no—
981C4×C22⋊C4—831no—
982C4×C22⋊C4—831no—
983C4×C22⋊C4—831no—
984C2×#95—831no—
985C2×#95—831no—
986C2×#95—831no—
987C2×#95—831no—
988C2×#95—831no—
989C2×#95—831no—
990C2×#95—831no—
991C2×#95—831no—
992C2×#41—3322no—
993C2×#41—3322no—
994C2×#41—3322no—
995C2×#41—3322no—
996C2×#41—838no—
997C2×#41—838no—
998C22×Q8—831no—
999C22×Q8—831no—
1000C22×D4—831no—
1001C22×D4—831no—
1002C22×D4—831no—
1003C22×D4—831no—
1004C22×D4—831no—
1005C22×D4—831no—
1006C22×D4—831no—
1007C22×D4C22×D8311yescharacteristic
1008C22×D4C22×D8311yescharacteristic
1009C22×D4C22×D8311yescharacteristic
1010C23×C4—831no—
1011C23×C4—831no—
1012C23×C4—831no—
1013C23×C4—831no—
1014C23×C4—831no—
1015C23×C4—831no—
1016C23×C4—831no—
1017C23×C4—831no—
1018C23×C4—831no—
1019C23×C4—831no—
1020C23×C4—831no—
1021C23×C4—831no—
1022C23×C4—831no—
1023C23×C4—831no—
1024C23×C4—831no—
1025C23×C4—831no—
1026C23×C4C22×D8311yescharacteristic
1027C23×C4C22×D8311yescharacteristic
1028C23×C4C22×D8311yescharacteristic
1029C22⋊Q8—838no—
1030C22⋊Q8—838no—
1031C22⋊Q8—838no—
1032C22⋊Q8—838no—
1033#121—838no—
1034#121—838no—
1035#121—838no—
1036#121—838no—
1037#121—838no—
1038#121—838no—
1039#121—838no—
1040#121C4×D8318yescomplemented
1041C4×D4—3322no—
1042C4×D4—3322no—
1043C4×D4—3322no—
1044C4×D4—3322no—
1045C4×D4—3322no—
1046C4×D4—3322no—
1047C4×D4—3322no—
1048C4×D4—3322no—
1049C4×D4—3322no—
1050C4×D4—3322no—
1051C4×D4—3322no—
1052C4×D4—3322no—
1053C2×C4⋊C4—3322no—
1054C2×C4⋊C4—831no—
1055C2×C4⋊C4—831no—
1056C2×C4⋊C4—831no—
1057C2×C4⋊C4—831no—
1058C2×C4⋊C4—831no—
1059C2×C4⋊C4—831no—
1060C2×C4⋊C4—831no—
1061C2×C4⋊C4—831no—
1062C2×C4⋊C4—831no—
1063C2×C4⋊C4—831no—
1064C2×C4⋊C4—831no—
1065C2×C4⋊C4—831no—
1066C2×C4⋊C4—831no—
1067C2×C4⋊C4—831no—
1068C2×C4⋊C4—831no—
1069C2×C4⋊C4—831no—
1070C2×C4⋊C4—831no—
1071C2×C4⋊C4—838no—
1072C2×C4⋊C4—831no—
1073C2×C4⋊C4—831no—
1074C2×C4⋊C4C22×D8311yescharacteristic
1075C2×C4⋊C4C22×D8311yescharacteristic
1076C2×C4⋊C4C22×D8311yescharacteristic
1077C2×C4⋊C4C22×D8311yescharacteristic
1078C2×C4⋊C4C22×D8311yescharacteristic
1079C2×C22⋊C4—831no—
1080C2×C22⋊C4—831no—
1081C2×C22⋊C4—831no—
1082C2×C22⋊C4—831no—
1083C2×C22⋊C4—831no—
1084C2×C22⋊C4—831no—
1085C2×C22⋊C4—831no—
1086C2×C22⋊C4—831no—
1087C2×C22⋊C4—831no—
1088C2×C22⋊C4—831no—
1089C2×C22⋊C4—831no—
1090C2×C22⋊C4—831no—
1091C2×C22⋊C4—831no—
1092C2×C22⋊C4—831no—
1093C2×C22⋊C4—831no—
1094C2×C22⋊C4—831no—
1095C2×C22⋊C4—831no—
1096C2×C22⋊C4—831no—
1097C2×C22⋊C4—831no—
1098C2×C22⋊C4—831no—
1099C2×C22⋊C4—831no—
1100C2×C22⋊C4—831no—
1101C2×C22⋊C4—831no—
1102C2×C22⋊C4—831no—
1103C2×C22⋊C4C22×D8311yescharacteristic
1104C2×C22⋊C4C22×D8311yescharacteristic
1105C2×C22⋊C4C22×D8311yescharacteristic
1106C2×C22⋊C4C22×D8311yescharacteristic
1107C2×C22⋊C4C22×D8311yescharacteristic
1108C2×C22⋊C4C22×D8311yescharacteristic
1109C2×C22⋊C4C22×D8311yescharacteristic
1110C2×C22⋊C4C22×D8311yescharacteristic
1111C2×C22⋊C4C22×D8311yescharacteristic
1112C2×C22⋊C4C22×D8311yescharacteristic
1113C2×C22⋊C4C22×D8311yescharacteristic
1114C2×C22⋊C4C22×D8311yescharacteristic
1115C2×C42—3322no—
1116C2×C42—831no—
1117C2×C42—831no—
1118C2×C42—831no—
1119C2×C42—831no—
1120C2×C42—831no—
1121C2×C42—831no—
1122C2×C42—831no—
1123C2×C42—831no—
1124C2×C42—831no—
1125C2×C42—831no—
1126C2×C42—831no—
1127C2×C42—831no—
1128C2×C42—831no—
1129C2×C42—831no—
1130C2×C42C22×D8311yescharacteristic
1131C2×C42C22×D8311yescharacteristic
1132#95—831no—
1133#95—831no—
1134#95—831no—
1135#95—831no—
1136#95—831no—
1137#95—831no—
1138#95—831no—
1139#95—831no—
1140#95—831no—
1141#95—831no—
1142#95—831no—
1143#95—831no—
1144#95—831no—
1145#95—831no—
1146#95—831no—
1147#95—831no—
1148#95—831no—
1149#95—831no—
1150#95—831no—
1151#95—831no—
1152#95—831no—
1153#95—831no—
1154#95—831no—
1155#95—831no—
1156#95—831no—
1157#95—831no—
1158#95—831no—
1159#95—831no—
1160#95—831no—
1161#95—831no—
1162#95—831no—
1163#95—831no—
1164#95—831no—
1165#95—831no—
1166#95—831no—
1167#95—831no—
1168#95—831no—
1169#95—831no—
1170#95C22×D8311yescharacteristic
1171#95C22×D8311yescharacteristic
1172#95C22×D8311yescharacteristic
1173#95C22×D8311yescharacteristic
1174#95C22×D8311yescharacteristic
1175#95C22×D8311yescharacteristic
1176#95C22×D8311yescharacteristic
1177#95C22×D8311yescharacteristic
1178#95C22×D8311yescharacteristic
1179#95C22×D8311yescharacteristic
1180C24—831no—
1181C24—831no—
1182C24C23×D8311yescharacteristic
1183C24C23×D8311yescharacteristic
1184C24C23×D8311yescharacteristic
1185#41—33216no—
1186#41—33216no—
1187C2×Q8—3321no—
1188C2×Q8—3321no—
1189C2×Q8—3321no—
1190C2×Q8—3321no—
1191C2×Q8—834no—
1192C2×Q8—834no—
1193C2×D4—41no—
1194C2×D4—41no—
1195C2×D4—41no—
1196C2×D4—41no—
1197C2×D4—41no—
1198C2×D4—41no—
1199C2×D4—3321no—
1200C2×D4—3321no—
1201C2×D4—3321no—
1202C2×D4—3321no—
1203C2×D4—3321no—
1204C2×D4—3321no—
1205C2×D4—834no—
1206C2×D4—834no—
1207C2×D4—834no—
1208C2×D4—834no—
1209C2×D4—834no—
1210C2×D4—834no—
1211C2×D4—834no—
1212C2×D4—1662no—
1213C2×D4—1662no—
1214C2×D4—1662no—
1215C2×D4—1662no—
1216C2×D4—1662no—
1217C2×D4—1662no—
1218C2×D4—1662no—
1219C2×D4—1662no—
1220C2×D4C2×C4×D8314yes—
1221C2×D4C2×C4×D8314yes—
1222C2×D4C2×C4×D8314yes—
1223C22×C4—41no—
1224C22×C4—41no—
1225C22×C4—41no—
1226C22×C4—41no—
1227C22×C4—41no—
1228C22×C4—41no—
1229C22×C4—41no—
1230C22×C4—41no—
1231C22×C4—3321no—
1232C22×C4—3321no—
1233C22×C4—3321no—
1234C22×C4—3321no—
1235C22×C4—3321no—
1236C22×C4—3321no—
1237C22×C4—3321no—
1238C22×C4—3321no—
1239C22×C4—3321no—
1240C22×C4—3321no—
1241C22×C4—3321no—
1242C22×C4—3321no—
1243C22×C4—3321no—
1244C22×C4—3321no—
1245C22×C4—3321no—
1246C22×C4—3321no—
1247C22×C4—3321no—
1248C22×C4—3321no—
1249C22×C4—3321no—
1250C22×C4—3321no—
1251C22×C4—3321no—
1252C22×C4—3321no—
1253C22×C4—3321no—
1254C22×C4—3321no—
1255C22×C4—3321no—
1256C22×C4—3321no—
1257C22×C4—3321no—
1258C22×C4—3321no—
1259C22×C4—3321no—
1260C22×C4—3321no—
1261C22×C4—834no—
1262C22×C4—834no—
1263C22×C4—834no—
1264C22×C4—834no—
1265C22×C4—834no—
1266C22×C4—831no—
1267C22×C4—831no—
1268C22×C4—831no—
1269C22×C4—831no—
1270C22×C4—831no—
1271C22×C4—831no—
1272C22×C4—831no—
1273C22×C4—831no—
1274C22×C4—834no—
1275C22×C4—831no—
1276C22×C4—831no—
1277C22×C4—831no—
1278C22×C4—831no—
1279C22×C4—831no—
1280C22×C4—831no—
1281C22×C4—1662no—
1282C22×C4—1662no—
1283C22×C4—1662no—
1284C22×C4—1662no—
1285C22×C4—1662no—
1286C22×C4—1662no—
1287C22×C4—1662no—
1288C22×C4—1662no—
1289C22×C4—1662no—
1290C22×C4—1662no—
1291C22×C4—1662no—
1292C22×C4—1662no—
1293C22×C4C2×C4×D8314yes—
1294C22×C4C23×D8311yescharacteristic
1295C22×C4C23×D8311yescharacteristic
1296C22×C4C23×D8311yescharacteristic
1297C22×C4C23×D8311yescharacteristic
1298C22×C4C23×D8311yescharacteristic
1299C22×C4C23×D8311yescharacteristic
1300C22×C4C23×D8311yescharacteristic
1301C22×C4C23×D8311yescharacteristic
1302C22×C4C23×D8311yescharacteristic
1303C22×C4C23×D8311yescharacteristic
1304C22×C4C23×D8311yescharacteristic
1305C22×C4C23×D8311yescharacteristic
1306C4⋊C4—41no—
1307C4⋊C4—41no—
1308C4⋊C4—41no—
1309C4⋊C4—41no—
1310C4⋊C4—3321no—
1311C4⋊C4—3321no—
1312C4⋊C4—3321no—
1313C4⋊C4—3321no—
1314C4⋊C4—3321no—
1315C4⋊C4—3321no—
1316C4⋊C4—3321no—
1317C4⋊C4—3321no—
1318C4⋊C4—3321no—
1319C4⋊C4—3321no—
1320C4⋊C4—834no—
1321C4⋊C4—834no—
1322C4⋊C4—834no—
1323C4⋊C4—834no—
1324C4⋊C4—834no—
1325C4⋊C4—834no—
1326C4⋊C4—834no—
1327C4⋊C4—1662no—
1328C4⋊C4—1662no—
1329C4⋊C4C2×C4×D8314yes—
1330C22⋊C4—41no—
1331C22⋊C4—41no—
1332C22⋊C4—41no—
1333C22⋊C4—41no—
1334C22⋊C4—41no—
1335C22⋊C4—41no—
1336C22⋊C4—41no—
1337C22⋊C4—41no—
1338C22⋊C4—41no—
1339C22⋊C4—41no—
1340C22⋊C4—3321no—
1341C22⋊C4—3321no—
1342C22⋊C4—3321no—
1343C22⋊C4—3321no—
1344C22⋊C4—3321no—
1345C22⋊C4—3321no—
1346C22⋊C4—3321no—
1347C22⋊C4—3321no—
1348C22⋊C4—3321no—
1349C22⋊C4—3321no—
1350C22⋊C4—834no—
1351C22⋊C4—834no—
1352C22⋊C4—834no—
1353C22⋊C4—834no—
1354C22⋊C4—834no—
1355C22⋊C4—834no—
1356C22⋊C4—1662no—
1357C22⋊C4—1662no—
1358C22⋊C4—1662no—
1359C22⋊C4—1662no—
1360C22⋊C4—1662no—
1361C22⋊C4—1662no—
1362C22⋊C4—1662no—
1363C22⋊C4—1662no—
1364C22⋊C4C2×C4×D8314yes—
1365C22⋊C4C2×C4×D8314yes—
1366C42—41no—
1367C42—41no—
1368C42—3321no—
1369C42—3321no—
1370C42—3321no—
1371C42—3321no—
1372C42—3321no—
1373C42—3321no—
1374C42—3321no—
1375C42—3321no—
1376C42—3321no—
1377C42—3321no—
1378C42—3321no—
1379C42—3321no—
1380C42—1662no—
1381C42—1662no—
1382C23—21no—
1383C23—21no—
1384C23—21no—
1385C23—21no—
1386C23—21no—
1387C23—21no—
1388C23—21no—
1389C23—21no—
1390C23—21no—
1391C23—21no—
1392C23—21no—
1393C23—21no—
1394C23—21no—
1395C23—21no—
1396C23—21no—
1397C23—21no—
1398C23—21no—
1399C23—21no—
1400C23—832no—
1401C23—832no—
1402C23—832no—
1403C23—832no—
1404C23—1661no—
1405C23—1661no—
1406C23—1661no—
1407C23—1661no—
1408C23—1661no—
1409C23—1661no—
1410C23—1661no—
1411C23—1661no—
1412C23—1661no—
1413C23—1661no—
1414C23C22×C4×D8312yes—
1415C23C22×C4×D8312yes—
1416C23C22×C4×D8312yes—
1417C23C24×D8311yescharacteristic
1418Q8—3324no—
1419Q8—3324no—
1420D4—44no—
1421D4—44no—
1422D4—44no—
1423D4—3324no—
1424D4—3324no—
1425D4—3324no—
1426D4—1668no—
1427D4—1668no—
1428D4—1668no—
1429D4—1668no—
1430C2×C4—21no—
1431C2×C4—21no—
1432C2×C4—21no—
1433C2×C4—21no—
1434C2×C4—21no—
1435C2×C4—21no—
1436C2×C4—21no—
1437C2×C4—21no—
1438C2×C4—21no—
1439C2×C4—21no—
1440C2×C4—21no—
1441C2×C4—21no—
1442C2×C4—21no—
1443C2×C4—21no—
1444C2×C4—21no—
1445C2×C4—21no—
1446C2×C4—21no—
1447C2×C4—21no—
1448C2×C4—21no—
1449C2×C4—21no—
1450C2×C4—21no—
1451C2×C4—21no—
1452C2×C4—21no—
1453C2×C4—21no—
1454C2×C4—21no—
1455C2×C4—21no—
1456C2×C4—21no—
1457C2×C4—21no—
1458C2×C4—21no—
1459C2×C4—21no—
1460C2×C4—21no—
1461C2×C4—21no—
1462C2×C4—44no—
1463C2×C4—82no—
1464C2×C4—82no—
1465C2×C4—3324no—
1466C2×C4—3324no—
1467C2×C4—3324no—
1468C2×C4—3324no—
1469C2×C4—3324no—
1470C2×C4—3324no—
1471C2×C4—3324no—
1472C2×C4—832no—
1473C2×C4—832no—
1474C2×C4—832no—
1475C2×C4—832no—
1476C2×C4—832no—
1477C2×C4—832no—
1478C2×C4—832no—
1479C2×C4—832no—
1480C2×C4—6642no—
1481C2×C4—6642no—
1482C2×C4—6642no—
1483C2×C4—6642no—
1484C2×C4—6642no—
1485C2×C4—6642no—
1486C2×C4—6642no—
1487C2×C4—6642no—
1488C2×C4—1668no—
1489C2×C4—1661no—
1490C2×C4—1661no—
1491C2×C4—1661no—
1492C2×C4—1661no—
1493C2×C4—1661no—
1494C2×C4—1661no—
1495C2×C4—1661no—
1496C2×C4—1661no—
1497C2×C4—1661no—
1498C2×C4—1661no—
1499C2×C4—1661no—
1500C2×C4—1661no—
1501C2×C4—1661no—
1502C2×C4—1661no—
1503C2×C4—1661no—
1504C2×C4—1661no—
1505C2×C4—1661no—
1506C2×C4—1661no—
1507C2×C4—1661no—
1508C2×C4—1661no—
1509C2×C4—1661no—
1510C2×C4—1661no—
1511C2×C4—1661no—
1512C2×C4—1661no—
1513C2×C4—1661no—
1514C2×C4—1661no—
1515C2×C4—1661no—
1516C2×C4—1661no—
1517C2×C4—1661no—
1518C2×C4—1661no—
1519C2×C4—1661no—
1520C2×C4—1661no—
1521C2×C4—1661no—
1522C2×C4—1661no—
1523C2×C4C22×C4×D8312yes—
1524C2×C4C22×C4×D8312yes—
1525C2×C4C22×C4×D8312yes—
1526C2×C4C22×C4×D8312yes—
1527C22—22no—
1528C22—22no—
1529C22—22no—
1530C22—22no—
1531C22—22no—
1532C22—22no—
1533C22—22no—
1534C22—22no—
1535C22—22no—
1536C22—41no—
1537C22—41no—
1538C22—41no—
1539C22—41no—
1540C22—41no—
1541C22—41no—
1542C22—41no—
1543C22—41no—
1544C22—41no—
1545C22—41no—
1546C22—41no—
1547C22—41no—
1548C22—3321no—
1549C22—3321no—
1550C22—3321no—
1551C22—3321no—
1552C22—834no—
1553C22—1662no—
1554C22—1662no—
1555C22—1662no—
1556C22—1662no—
1557C22—1662no—
1558C22—1662no—
1559C22—1662no—
1560C22—1662no—
1561C22—1662no—
1562C22C23×C4×D8311yescharacteristic
1563C22H(5,𝔽2)×D8311yescharacteristic
1564C22H(5,𝔽2)×D8311yescharacteristic
1565C22H(5,𝔽2)×D8311yescharacteristic
1566C222−1+4×D8311yescharacteristic
1567C22#1912853611yescharacteristic
1568C22#1912853611yescharacteristic
1569C4—22no—
1570C4—22no—
1571C4—22no—
1572C4—22no—
1573C4—41no—
1574C4—41no—
1575C4—41no—
1576C4—41no—
1577C4—41no—
1578C4—41no—
1579C4—41no—
1580C4—41no—
1581C4—3321no—
1582C4—3321no—
1583C4—3321no—
1584C4—3321no—
1585C4—3321no—
1586C4—3321no—
1587C4—1662no—
1588C4—1662no—
1589C4—1662no—
1590C4—1662no—
1591C4—1662no—
1592C4—1662no—
1593C4—1662no—
1594C4—1662no—
1595C2—42no—
1596C2—42no—
1597C2—42no—
1598C2—3322no—
1599C2—1664no—
1600C2#518×D8311yescharacteristic
1601C2#2492066711yescharacteristic
1602C2#2492067411yescharacteristic
1603C2#2492164411yescharacteristic
1604C2#2492168211yescharacteristic
1605C2#2492199111yescharacteristic
1606C2#2492201311yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2377C2
socle, cosocleC23×C83C25
prime radicalC2×#19128280C2
hypercenter#2377D83
hypocenterC83#34436
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2377

Complements

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

NH ≅ G/Ntype
2. #24910627C2semidirect
3. #24910623C2semidirect
4. #24910614C2semidirect
5. #24910545C2semidirect
6. #24910544C2semidirect
7. #24910515C2semidirect
8. #24910512C2semidirect
9. #24910511C2semidirect
10. #24910507C2semidirect
11. #24910484C2semidirect
12. #24910482C2semidirect
13. #24910291C2semidirect
14. #24910289C2semidirect
15. #24910289C2semidirect
16. #24910287C2semidirect
17. #24910224C2semidirect
18. #24910222C2semidirect
19. #24910220C2semidirect
20. #24910216C2semidirect
21. #24910194C2semidirect
22. #24910193C2semidirect
23. #24910165C2semidirect
24. #24910165C2semidirect
25. #24910164C2semidirect
26. #24910160C2semidirect
27. #24910062C2semidirect
28. #24909979C2semidirect
29. #24909975C2semidirect
30. #387×D83C2semidirect
31. C83×#2377C2semidirect
34. #19128280C4semidirect
190. C2×#13050590C2×C4semidirect
193. C2×#13050589C2×C4semidirect
219. #14581772C2×C4semidirect
220. #14581771C2×C4semidirect
221. #14581769C2×C4semidirect
222. #14581769C2×C4semidirect
223. #14581765C2×C4semidirect
224. #14581765C2×C4semidirect
225. #14581764C2×C4semidirect
226. #14581764C2×C4semidirect
227. #14581763C2×C4semidirect
228. #14581763C2×C4semidirect
229. #14581763C2×C4semidirect
262. C4⋊C4×D83C2×C4semidirect
346. #121×C83C2×C4semidirect
808. #2377D83semidirect
835. C83#34436semidirect
1040. #121C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282802
#249106272
#249106232
#249106142
#249105452
#249105442
#249105152
#249105122
#249105112
#249105072
#249104842
#249104822
#249102912
#249102892
#249102872
#249102242
#249102222
#249102202
#249102162
#249101942
#249101932
#249101652
#249101642
#249101602
#249100622
#249099792
#249099752
#387×D832
C83×#23772
#3443683