Finite Group Databasebeta

← #35567923

Subgroups — #35567923

Order 21248.

2766 conjugacy classes of subgroups.

The subgroup lattice has 1192 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#19128270C211yesmaximal, characteristic
2#24910634C212yesmaximal, complemented
3#24910603C212yesmaximal, complemented
4#24910573C212yesmaximal, complemented
5#24910503C211yesmaximal, characteristic, complemented
6#24910500C211yesmaximal, characteristic, complemented
7#24910481C211yesmaximal, characteristic, complemented
8#24910478C211yesmaximal, characteristic, complemented
9#24910441C212yesmaximal, complemented
10#24910348C211yesmaximal, characteristic, complemented
11C22⋊C4×D332C211yesmaximal, characteristic, complemented
12#24910283C211yesmaximal, characteristic, complemented
13#24910188C212yesmaximal, complemented
14#24910186C212yesmaximal, complemented
15#24910157C211yesmaximal, characteristic, complemented
16#24910154C211yesmaximal, characteristic, complemented
17#24910125C212yesmaximal, complemented
18#24910116C212yesmaximal, complemented
19#24910052C211yesmaximal, characteristic, complemented
20C4×#14581767C211yesmaximal, characteristic, complemented
21#24909971C211yesmaximal, characteristic, complemented
22#24909949C211yesmaximal, characteristic, complemented
23C83×#2346C211yesmaximal, characteristic, complemented
24C22×#13050590C2211yescharacteristic
25C23×D332C2211yescharacteristic
26#19128270C4116yescomplemented
27C2×#14581789C2212yes—
28C2×#14581780C2212yes—
29C2×#14581767C2211yescharacteristic
30C2×#14581767C2211yescharacteristic
31C2×#14581767C2211yescharacteristic
32C2×#14581767C2211yescharacteristic
33C2×#14581762C2212yes—
34C2×#14581762C2212yes—
35C2×C4×D332C2211yescharacteristic
36C2×C4×D332C2211yescharacteristic
37C2×C4×D332C2212yescomplemented
38C2×C4×D332C2212yescomplemented
39C2×#14581754C2211yescharacteristic
40C2×#14581754C2211yescharacteristic
41C2×#14581754C2212yescomplemented
42C2×#14581754C2212yescomplemented
43C2×#14581750C2211yescharacteristic, complemented
44C2×#14581749C2211yescharacteristic, complemented
45C2×C4⋊C4×D83C2211yescharacteristic, complemented
46C2×C22⋊C4×D83C2212yes—
47C2×C22⋊C4×D83C2212yes—
48C2×C42×D83C2211yescharacteristic, complemented
49#19127605C2211yescharacteristic, complemented
50#19127605C2212yescomplemented
51#19127605C2211yescharacteristic, complemented
52#19127603C2211yescharacteristic
53#19127603C2211yescharacteristic
54#19127603C2212yescomplemented
55#19127603C2212yescomplemented
56#19127602C2211yescharacteristic
57#19127602C2211yescharacteristic
58#19127602C2212yescomplemented
59#19127602C2212yescomplemented
60#19127601C2211yescharacteristic
61#19127601C2212yes—
62#19127601C2211yescharacteristic
63#19127600C2211yescharacteristic, complemented
64#19127600C2211yescharacteristic, complemented
65#19127594C2212yes—
66#19127594C2212yes—
67#19127593C2212yescomplemented
68#19127593C2212yescomplemented
69#19127592C2212yescomplemented
70#19127592C2212yescomplemented
71#19127591C2212yescomplemented
72#19127591C2212yescomplemented
73#19127590C2212yescomplemented
74#19127590C2212yescomplemented
75#19127579C2212yes—
76#19127579C2212yes—
77#19127579C2212yes—
78#19127579C2212yes—
79#19127579C2212yescomplemented
80#19127579C2212yescomplemented
81#19127579C2212yescomplemented
82#19127579C2212yescomplemented
83#19127579C2212yescomplemented
84#19127579C2212yescomplemented
85#19127579C2212yescomplemented
86#19127579C2212yescomplemented
87#19127579C2211yescharacteristic, complemented
88#19127579C2212yescomplemented
89#19127579C2211yescharacteristic, complemented
90#19127577C2212yes—
91#19127577C2211yescharacteristic
92#19127577C2211yescharacteristic
93#19127575C2212yescomplemented
94#19127575C2212yescomplemented
95#19127572C2212yescomplemented
96#19127572C2212yescomplemented
97#19127567C2212yescomplemented
98#19127561C2211yescharacteristic
99#19127558C2211yescharacteristic, complemented
100#19127558C2211yescharacteristic, complemented
101#19127556C2212yes—
102#19127556C2212yes—
103C4⋊C4×Dic83C2211yescharacteristic, complemented
104C4⋊C4×Dic83C2211yescharacteristic, complemented
105C4×(C2×D83)⋊C4C2212yescomplemented
106C4×(C2×D83)⋊C4C2212yescomplemented
107C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
108C4×(C2×D83)⋊C4C2211yescharacteristic, complemented
109C4×C22⋊Dic83C2211yescharacteristic
110#19127548C2212yescomplemented
111#19127548C2212yescomplemented
112#19127547C2212yescomplemented
113C2×#117×C83C2211yescharacteristic
114#389×C83C2211yescharacteristic, complemented
115#389×C83C2211yescharacteristic, complemented
116#388×C83C2212yes—
117#388×C83C2212yes—
118#382×C83C2212yescomplemented
119#380×C83C2211yescharacteristic
120C4×C4⋊C4×C83C2211yescharacteristic, complemented
121C4×C4⋊C4×C83C2211yescharacteristic, complemented
122C4×C22⋊C4×C83C2211yescharacteristic
123#376×C83C2212yescomplemented
124C24×D83C2312yes—
125C2×#13050590—42no—
126C2×#13050590—42no—
127C2×#13050590C2×C418yescomplemented
128C22×Dic166C2311yescharacteristic
129C22×D332—42no—
130C22×D332—42no—
131C22×D332C2×C418yescomplemented
132C22×D332C2311yescharacteristic
133C22×D332C2311yescharacteristic
134C22×D332C2312yes—
135C22×D332C2311yescharacteristic
136C22×D332C2312yes—
137C22×D332C2312yes—
138C22×D332C2312yes—
139C22×D332C2312yes—
140C22×C22⋊D83C2311yescharacteristic
141C22×C22⋊D83C2311yescharacteristic
142C22×C4×D83C2311yescharacteristic
143C22×C4×D83C2311yescharacteristic
144C22×C4×D83C2311yescharacteristic
145C22×C4×D83C2311yescharacteristic
146C22×C4×D83C2312yes—
147C22×C4×D83C2312yes—
148C22×C4×D83C2312yes—
149C22×C4×D83C2312yes—
150C22×C4×D83C2312yes—
151#14581789C2×C4116yescomplemented
152#14581780C2×C4116yescomplemented
153#14581767C2×C418yescomplemented
154#14581767C2×C418yescomplemented
155#14581767C2×C418yescomplemented
156#14581767C2×C418yescomplemented
157#14581762C2×C4116yescomplemented
158#14581762C2×C4116yescomplemented
159C4×D332—44no—
160C4×D332—42no—
161C4×D332—42no—
162C4×D332—44no—
163#14581754—42no—
164#14581754—42no—
165#14581754—44no—
166#14581754—44no—
167#14581750—42no—
168#14581749—42no—
169C2×C4⋊Dic83C2311yescharacteristic
170C2×C4⋊Dic83C2311yescharacteristic
171C2×C4⋊Dic83C2312yes—
172C2×C4⋊Dic83C2312yes—
173C2×Dic83⋊C4C2311yescharacteristic
174C2×Dic83⋊C4C2312yes—
175C2×Dic83⋊C4C2311yescharacteristic
176C4⋊C4×D83—42no—
177C2×C22⋊Dic83C2311yescharacteristic
178C2×C22⋊Dic83C2311yescharacteristic
179C2×C22⋊Dic83C2312yes—
180C2×(C2×D83)⋊C4C2312yes—
181C2×(C2×D83)⋊C4C2312yes—
182C2×(C2×D83)⋊C4C2311yescharacteristic
183C2×(C2×D83)⋊C4C2311yescharacteristic
184C2×(C2×D83)⋊C4C2312yes—
185C2×(C2×D83)⋊C4C2312yes—
186C2×(C2×D83)⋊C4C2312yes—
187C2×(C2×D83)⋊C4C2312yes—
188C2×(C2×D83)⋊C4C2312yes—
189C2×(C2×D83)⋊C4C2312yes—
190C2×(C2×D83)⋊C4C2312yes—
191C2×(C2×D83)⋊C4C2312yes—
192C2×(C2×D83)⋊C4C2312yes—
193C2×(C2×D83)⋊C4C2312yes—
194C2×(C2×D83)⋊C4C2312yes—
195C2×(C2×D83)⋊C4C2312yes—
196C2×(C2×D83)⋊C4C2311yescharacteristic
197C2×(C2×D83)⋊C4C2312yes—
198C2×(C2×D83)⋊C4C2311yescharacteristic
199C2×(C2×D83)⋊C4C2311yescharacteristic
200C2×(C2×D83)⋊C4C2311yescharacteristic
201C2×(C2×D83)⋊C4C2312yes—
202C2×(C2×D83)⋊C4C2312yes—
203C2×(C2×D83)⋊C4C2312yes—
204C2×(C2×D83)⋊C4C2312yes—
205C22⋊C4×D83—44no—
206C22⋊C4×D83—44no—
207C2×C4×Dic83C2312yes—
208C2×C4×Dic83C2311yescharacteristic
209C2×C4×Dic83C2311yescharacteristic
210C2×C4×Dic83C2312yes—
211C2×C4×Dic83C2311yescharacteristic
212C2×C4×Dic83C2312yes—
213C2×C4×Dic83C2311yescharacteristic
214C42×D83—42no—
215C83⋊#95C2312yes—
216C83⋊#95C2312yes—
217C83⋊#95C2312yes—
218C83⋊#95C2312yes—
219C83⋊#95C2312yes—
220C83⋊#95C2311yescharacteristic
221C83⋊#95C2311yescharacteristic
222C83⋊#95C2311yescharacteristic
223C83⋊#95C2311yescharacteristic
224C83⋊#95C2311yescharacteristic
225C83⋊#95C2311yescharacteristic
226C83⋊#95C2312yes—
227C83⋊#95C2312yes—
228C23×C4×C83C2311yescharacteristic
229#117×C83C2×C418yescomplemented
230C2×C4⋊C4×C83C2311yescharacteristic
231C2×C4⋊C4×C83C2311yescharacteristic
232C2×C4⋊C4×C83C2312yes—
233C2×C4⋊C4×C83C2312yes—
234C2×C4⋊C4×C83C2311yescharacteristic
235C2×C4⋊C4×C83C2311yescharacteristic
236C2×C22⋊C4×C83C2311yescharacteristic
237C2×C22⋊C4×C83C2311yescharacteristic
238C2×C22⋊C4×C83C2312yes—
239C2×C22⋊C4×C83C2312yes—
240C2×C42×C83C2312yes—
241C2×C42×C83C2311yescharacteristic
242C2×C42×C83C2311yescharacteristic
243C2×C42×C83C2312yes—
244C2×C42×C83C2312yes—
245#95×C83C2312yes—
246#95×C83C2312yes—
247#95×C83C2311yescharacteristic
248#95×C83C2312yes—
249#95×C83C2311yescharacteristic
250#95×C83C2312yes—
251#95×C83C2312yes—
252C23×D83—42no—
253C23×D83—42no—
254C23×D83—42no—
255C23×D83—42no—
256C23×D83—42no—
257C23×D83—42no—
258C23×D83C22×C418yes—
259C23×D83C2411yescharacteristic
260C23×D83C2411yescharacteristic
261C23×D83C2412yes—
262C23×D83C2412yes—
263#13050590—416no—
264C2×Dic166—41no—
265C2×Dic166—41no—
266C2×Dic166C22×C414yes—
267C2×D332—22no—
268C2×D332—22no—
269C2×D332—22no—
270C2×D332—22no—
271C2×D332—416no—
272C2×D332—42no—
273C2×D332—42no—
274C2×D332—42no—
275C2×D332—42no—
276C2×D332—42no—
277C2×D332—42no—
278C2×D332—41no—
279C2×D332—41no—
280C2×D332—42no—
281C2×D332—42no—
282C2×D332—42no—
283C2×D332—42no—
284C2×D332C22×C414yes—
285C2×D332C22×C414yes—
286C2×D332C22×C418yes—
287C2×D332C22×C418yes—
288C2×D332C22×C418yes—
289C2×D332C22×C418yes—
290C2×D332C22×C418yes—
291C2×D332C22×C414yes—
292C2×C22⋊D83—41no—
293C2×C22⋊D83—41no—
294C2×C22⋊D83—41no—
295C2×C22⋊D83—41no—
296C2×C22⋊D83C22×C414yes—
297C2×C22⋊D83C22×C414yes—
298C22×Dic83C2412yes—
299C22×Dic83C2411yescharacteristic
300C22×Dic83C2411yescharacteristic
301C22×Dic83C2412yes—
302C22×Dic83C2411yescharacteristic
303C22×Dic83C2411yescharacteristic
304C22×Dic83C2411yescharacteristic
305C22×Dic83C2411yescharacteristic
306C2×C4×D83—22no—
307C2×C4×D83—22no—
308C2×C4×D83—22no—
309C2×C4×D83—22no—
310C2×C4×D83—22no—
311C2×C4×D83—22no—
312C2×C4×D83—24no—
313C2×C4×D83—24no—
314C2×C4×D83—41no—
315C2×C4×D83—41no—
316C2×C4×D83—41no—
317C2×C4×D83—41no—
318C2×C4×D83—42no—
319C2×C4×D83—42no—
320C2×C4×D83—42no—
321C2×C4×D83—42no—
322C2×C4×D83—42no—
323C2×C4×D83—42no—
324C2×C4×D83—42no—
325C2×C4×D83—42no—
326C2×C4×D83—42no—
327C2×C4×D83—42no—
328C2×C4×D83—42no—
329C2×C4×D83—42no—
330C2×C4×D83—42no—
331C2×C4×D83C22×C414yes—
332C2×C4×D83C22×C414yes—
333C4⋊Dic83—22no—
334C4⋊Dic83—22no—
335C4⋊Dic83—42no—
336C4⋊Dic83—42no—
337Dic83⋊C4—42no—
338Dic83⋊C4—41no—
339Dic83⋊C4—41no—
340C22⋊Dic83—22no—
341C22⋊Dic83—42no—
342C22⋊Dic83—41no—
343(C2×D83)⋊C4—24no—
344(C2×D83)⋊C4—22no—
345(C2×D83)⋊C4—24no—
346(C2×D83)⋊C4—22no—
347(C2×D83)⋊C4—42no—
348(C2×D83)⋊C4—42no—
349(C2×D83)⋊C4—42no—
350(C2×D83)⋊C4—42no—
351(C2×D83)⋊C4—41no—
352(C2×D83)⋊C4—41no—
353(C2×D83)⋊C4—41no—
354(C2×D83)⋊C4—41no—
355(C2×D83)⋊C4—42no—
356(C2×D83)⋊C4—42no—
357(C2×D83)⋊C4—42no—
358(C2×D83)⋊C4—42no—
359(C2×D83)⋊C4—42no—
360(C2×D83)⋊C4—42no—
361(C2×D83)⋊C4—42no—
362(C2×D83)⋊C4—42no—
363(C2×D83)⋊C4—42no—
364(C2×D83)⋊C4C22×C418yes—
365(C2×D83)⋊C4C22×C418yes—
366(C2×D83)⋊C4C22×C418yes—
367(C2×D83)⋊C4C22×C418yes—
368C4×Dic83—22no—
369C4×Dic83—22no—
370C4×Dic83—24no—
371C4×Dic83—41no—
372C4×Dic83—41no—
373C4×Dic83—42no—
374C4×Dic83—42no—
375C24×C83C2411yescharacteristic
376C22×C4×C83—22no—
377C22×C4×C83—22no—
378C22×C4×C83C22×C414yes—
379C22×C4×C83C2412yes—
380C22×C4×C83C2411yescharacteristic
381C22×C4×C83C2411yescharacteristic
382C22×C4×C83C2412yes—
383C22×C4×C83C2411yescharacteristic
384C22×C4×C83C2411yescharacteristic
385C22×C4×C83C2412yes—
386C22×C4×C83C2412yes—
387C22×C4×C83C2411yescharacteristic
388C22×C4×C83C2411yescharacteristic
389C4⋊C4×C83—22no—
390C4⋊C4×C83—22no—
391C4⋊C4×C83—42no—
392C4⋊C4×C83—42no—
393C4⋊C4×C83C22×C414yes—
394C4⋊C4×C83C22×C414yes—
395C22⋊C4×C83—22no—
396C22⋊C4×C83—41no—
397C22⋊C4×C83—42no—
398C22⋊C4×C83C22×C418yes—
399C42×C83—22no—
400C42×C83—22no—
401C42×C83—24no—
402C42×C83—42no—
403C42×C83C22×C418yes—
404C23×C83—21no—
405C23×C83—21no—
406C23×C83—21no—
407C23×C83—21no—
408C23×C83—21no—
409C23×C83—21no—
410C23×C83C23×C412yes—
411C23×C83C2511yescharacteristic
412C22×D83—22no—
413C22×D83—22no—
414C22×D83—21no—
415C22×D83—21no—
416C22×D83—21no—
417C22×D83—21no—
418C22×D83—21no—
419C22×D83—21no—
420C22×D83—22no—
421C22×D83—22no—
422C22×D83—22no—
423C22×D83—22no—
424C22×D83—22no—
425C22×D83—22no—
426C22×D83—21no—
427C22×D83—21no—
428C22×D83—21no—
429C22×D83—21no—
430C22×D83—22no—
431C22×D83—22no—
432C22×D83—21no—
433C22×D83—21no—
434C22×D83—22no—
435C22×D83—22no—
436C22×D83—48no—
437C22×D83—48no—
438C22×D83—48no—
439C22×D83—84no—
440C22×D83—84no—
441C22×D83—84no—
442C22×D83—84no—
443C22×D83C23×C414yes—
444C22×D83C23×C414yes—
445C22×D83C23×C412yes—
446C22×D83C23×C412yes—
447C2×C4×C83—21no—
448C2×C4×C83—22no—
449C2×C4×C83—22no—
450C2×C4×C83—21no—
451C2×C4×C83—21no—
452C2×C4×C83—22no—
453C2×C4×C83—22no—
454C2×C4×C83—21no—
455C2×C4×C83—28no—
456C2×C4×C83—21no—
457C2×C4×C83—21no—
458C2×C4×C83—22no—
459C2×C4×C83—21no—
460C2×C4×C83—21no—
461C2×C4×C83—22no—
462C2×C4×C83—22no—
463C2×C4×C83—22no—
464C2×C4×C83—22no—
465C2×C4×C83—21no—
466C2×C4×C83—21no—
467C2×C4×C83—21no—
468C2×C4×C83—22no—
469C2×C4×C83—21no—
470C2×C4×C83—21no—
471C2×C4×C83C23×C412yes—
472C2×C4×C83C23×C414yes—
473C2×C4×C83C23×C414yes—
474C2×C4×C83C23×C412yes—
475C2×C4×C83H(5,𝔽2)12yes—
476C2×C4×C83H(5,𝔽2)12yes—
477C2×C4×C83H(5,𝔽2)12yes—
478C22⋊D83—44no—
479C22⋊D83—44no—
480C2×Dic83—21no—
481C2×Dic83—21no—
482C2×Dic83—21no—
483C2×Dic83—21no—
484C2×Dic83—21no—
485C2×Dic83—21no—
486C2×Dic83—21no—
487C2×Dic83—21no—
488C2×Dic83—22no—
489C2×Dic83—21no—
490C2×Dic83—22no—
491C2×Dic83—22no—
492C2×Dic83—21no—
493C2×Dic83—21no—
494C2×Dic83—22no—
495C2×Dic83—21no—
496C2×Dic83—22no—
497C2×Dic83—21no—
498C2×Dic83—22no—
499C2×Dic83—21no—
500C2×Dic83—21no—
501C2×Dic83C23×C412yes—
502C2×Dic83C23×C412yes—
503C2×Dic83H(5,𝔽2)12yes—
504D332—28no—
505D332—28no—
506D332—48no—
507D332—48no—
508D332—48no—
509D332—48no—
510D332—48no—
511D332—44no—
512C4×D83—28no—
513C4×D83—28no—
514C4×D83—44no—
515C4×D83—44no—
516C4×D83—84no—
517C4×D83—84no—
518C4×D83—84no—
519C4×D83—84no—
520C4×D83—84no—
521Dic166—44no—
522C22×C83—22no—
523C22×C83—22no—
524C22×C83—22no—
525C22×C83—41no—
526C22×C83—41no—
527C22×C83—41no—
528C22×C83—41no—
529C22×C83C24×C411yescharacteristic
530C22×C83C2×H(5,𝔽2)11yescharacteristic
531C22×C83C2×H(5,𝔽2)11yescharacteristic
532C22×C83C2×H(5,𝔽2)11yescharacteristic
533C22×C83C2×H(5,𝔽2)11yescharacteristic
534C22×C83#58511yescharacteristic
535C22×C83#58511yescharacteristic
536C2×D83—22no—
537C2×D83—22no—
538C2×D83—24no—
539C2×D83—24no—
540C2×D83—22no—
541C2×D83—22no—
542C2×D83—22no—
543C2×D83—22no—
544C2×D83—24no—
545C2×D83—24no—
546C2×D83—24no—
547C2×D83—24no—
548C2×D83—41no—
549C2×D83—41no—
550C2×D83—42no—
551C2×D83—42no—
552C2×D83—41no—
553C2×D83—41no—
554C2×D83—42no—
555C2×D83—42no—
556C2×D83—41no—
557C2×D83—42no—
558C2×D83—42no—
559C2×D83—41no—
560C2×D83—41no—
561C2×D83—41no—
562C2×D83—42no—
563C2×D83—42no—
564C2×D83—816no—
565C4×C83—22no—
566C4×C83—24no—
567C4×C83—24no—
568C4×C83—22no—
569C4×C83—41no—
570C4×C83—42no—
571C4×C83—42no—
572C4×C83—41no—
573C4×C83—41no—
574C4×C83#51814yes—
575Dic83—22no—
576Dic83—22no—
577Dic83—22no—
578Dic83—41no—
579Dic83—42no—
580Dic83—42no—
581Dic83—41no—
582Dic83—41no—
583#34415—831nomaximal, Sylow
584C2×C83—42no—
585C2×C83C2×#51811yescharacteristic
586C2×C83C4×H(5,𝔽2)11yescharacteristic
587C2×C83C4×H(5,𝔽2)11yescharacteristic
588C2×C83#354211yescharacteristic
589C2×C83#354211yescharacteristic
590C2×C83#354911yescharacteristic
591C2×C83#355111yescharacteristic
592D83—42no—
593D83—42no—
594D83—44no—
595D83—44no—
596C2×#535—831no—
597#2379—832no—
598#2375—832no—
599#2372—832no—
600#2363—831no—
601#2363—831no—
602#2361—831no—
603#2361—831no—
604#2358—832no—
605#2346—831no—
606#2346D8311yescharacteristic, complemented
607D4×C22⋊C4—831no—
608D4×C22⋊C4—831no—
609#2328—832no—
610#2328—832no—
611#2324—831no—
612#2324—831no—
613#2321—832no—
614#2321—832no—
615#2311—831no—
616C4×#121—831no—
617C4×#121—831no—
618#2297—831no—
619C83#3441511yescharacteristic, complemented, Sylow
620C22×#41—831no—
621C23×D4—831no—
622#535—8316no—
623C2×#127—832no—
624C2×#124—832no—
625C2×#121—831no—
626C2×#121—831no—
627C2×#121—831no—
628C2×#121—831no—
629C2×#120—832no—
630C2×#120—832no—
631C2×C4×D4—832no—
632C2×C4×D4—831no—
633C2×C4×D4—832no—
634C2×C4×D4—831no—
635C2×C4×D4—832no—
636C2×C4×D4—831no—
637C2×C4×D4—832no—
638C2×C4×D4—831no—
639C2×#117—831no—
640C2×#117—831no—
641C2×#117C2×D8311yescharacteristic
642C22×C4⋊C4—831no—
643C22×C22⋊C4—832no—
644C22×C22⋊C4—832no—
645C22×C42—831no—
646#391—832no—
647#391—831no—
648#391—831no—
649#390—832no—
650#390—831no—
651#390—832no—
652#390—831no—
653#390—832no—
654#390—831no—
655#390—831no—
656#390—832no—
657#390—831no—
658#390—832no—
659#390—831no—
660#389—831no—
661#389—831no—
662#389C2×D8311yescharacteristic, complemented
663#389C2×D8311yescharacteristic, complemented
664#388—832no—
665#388—832no—
666#388—832no—
667#388—832no—
668#388—832no—
669#388—832no—
670#388—832no—
671#388—832no—
672#388—832no—
673#388—832no—
674#388C2×D8312yes—
675#388C2×D8312yes—
676#386—832no—
677#386—831no—
678#386—831no—
679#386—832no—
680#386—832no—
681#386—832no—
682#386—832no—
683#386—832no—
684#386—831no—
685#386—831no—
686#386—832no—
687#386—832no—
688#386—832no—
689#386—832no—
690#386—832no—
691#386—832no—
692#386—832no—
693#386—832no—
694#385—832no—
695#385—832no—
696#385—832no—
697#385—832no—
698#382—832no—
699#382C2×D8312yescomplemented
700#380—831no—
701#380—831no—
702#380—831no—
703#380C2×D8311yescharacteristic
704#379—832no—
705#379—832no—
706C4×C4⋊C4—831no—
707C4×C4⋊C4—831no—
708C4×C4⋊C4C2×D8311yescharacteristic, complemented
709C4×C4⋊C4C2×D8311yescharacteristic, complemented
710C4×C22⋊C4—831no—
711C4×C22⋊C4—832no—
712C4×C22⋊C4—832no—
713C4×C22⋊C4—831no—
714C4×C22⋊C4—831no—
715C4×C22⋊C4—832no—
716C4×C22⋊C4—832no—
717C4×C22⋊C4C2×D8311yescharacteristic
718#376—832no—
719#376C2×D8312yescomplemented
720C25—832no—
721C2×#41—3322no—
722C2×#41—3322no—
723C2×#41—838no—
724C22×Q8—831no—
725C22×D4—3322no—
726C22×D4—3322no—
727C22×D4—831no—
728C22×D4—831no—
729C22×D4—838no—
730C22×D4—832no—
731C22×D4—832no—
732C22×D4—832no—
733C22×D4—832no—
734C22×D4—832no—
735C22×D4—831no—
736C22×D4—831no—
737C22×D4—831no—
738C23×C4—832no—
739C23×C4—832no—
740C23×C4—832no—
741C23×C4—832no—
742C23×C4—832no—
743C23×C4—831no—
744C23×C4—831no—
745C23×C4—831no—
746C23×C4—831no—
747C23×C4C22×D8311yescharacteristic
748#127—8316no—
749#124—8316no—
750#121—838no—
751#121—838no—
752#121—838no—
753#121—838no—
754#120—8316no—
755#120—8316no—
756C4×D4—3324no—
757C4×D4—3322no—
758C4×D4—3322no—
759C4×D4—3324no—
760C4×D4—3322no—
761C4×D4—3322no—
762C4×D4—3324no—
763C4×D4—3324no—
764#117—3322no—
765#117—3322no—
766#117C4×D8318yescomplemented
767C2×C4⋊C4—3322no—
768C2×C4⋊C4—832no—
769C2×C4⋊C4—831no—
770C2×C4⋊C4—831no—
771C2×C4⋊C4—832no—
772C2×C4⋊C4—832no—
773C2×C4⋊C4—831no—
774C2×C4⋊C4—831no—
775C2×C4⋊C4C22×D8311yescharacteristic
776C2×C4⋊C4C22×D8311yescharacteristic
777C2×C4⋊C4C22×D8312yes—
778C2×C4⋊C4C22×D8312yes—
779C2×C4⋊C4C22×D8311yescharacteristic
780C2×C4⋊C4C22×D8311yescharacteristic
781C2×C22⋊C4—3324no—
782C2×C22⋊C4—3324no—
783C2×C22⋊C4—832no—
784C2×C22⋊C4—831no—
785C2×C22⋊C4—832no—
786C2×C22⋊C4—832no—
787C2×C22⋊C4—831no—
788C2×C22⋊C4—832no—
789C2×C22⋊C4—831no—
790C2×C22⋊C4—832no—
791C2×C22⋊C4—832no—
792C2×C22⋊C4—832no—
793C2×C22⋊C4—832no—
794C2×C22⋊C4—832no—
795C2×C22⋊C4—832no—
796C2×C22⋊C4—832no—
797C2×C22⋊C4—832no—
798C2×C22⋊C4—832no—
799C2×C22⋊C4—832no—
800C2×C22⋊C4—831no—
801C2×C22⋊C4—831no—
802C2×C22⋊C4—832no—
803C2×C22⋊C4—832no—
804C2×C22⋊C4—832no—
805C2×C22⋊C4—832no—
806C2×C22⋊C4—831no—
807C2×C22⋊C4—832no—
808C2×C22⋊C4—832no—
809C2×C22⋊C4—831no—
810C2×C22⋊C4—831no—
811C2×C22⋊C4C22×D8311yescharacteristic
812C2×C22⋊C4C22×D8312yes—
813C2×C22⋊C4C22×D8311yescharacteristic
814C2×C22⋊C4C22×D8312yes—
815C2×C42—3322no—
816C2×C42—832no—
817C2×C42—832no—
818C2×C42—831no—
819C2×C42—831no—
820C2×C42—831no—
821C2×C42—832no—
822C2×C42—831no—
823C2×C42C22×D8311yescharacteristic
824C2×C42C22×D8312yes—
825C2×C42C22×D8311yescharacteristic
826C2×C42C22×D8312yes—
827C2×C42C22×D8312yes—
828#95—831no—
829#95—832no—
830#95—832no—
831#95—832no—
832#95—831no—
833#95—831no—
834#95—832no—
835#95—832no—
836#95—831no—
837#95—831no—
838#95—831no—
839#95—832no—
840#95—832no—
841#95C22×D8311yescharacteristic
842#95C22×D8312yes—
843#95C22×D8312yes—
844#95C22×D8312yes—
845#95C22×D8311yescharacteristic
846#95C22×D8312yes—
847#95C22×D8312yes—
848C24—3322no—
849C24—3322no—
850C24—3322no—
851C24—3322no—
852C24—3322no—
853C24—3322no—
854C24—838no—
855C24—832no—
856C24—832no—
857C24—831no—
858C24—831no—
859C24C23×D8311yescharacteristic
860#41—33216no—
861C2×Q8—3321no—
862C2×Q8—3321no—
863C2×Q8—834no—
864C2×D4—3322no—
865C2×D4—3322no—
866C2×D4—3322no—
867C2×D4—3322no—
868C2×D4—3322no—
869C2×D4—3322no—
870C2×D4—3321no—
871C2×D4—3321no—
872C2×D4—3322no—
873C2×D4—3322no—
874C2×D4—3322no—
875C2×D4—3322no—
876C2×D4—33216no—
877C2×D4—3321no—
878C2×D4—3321no—
879C2×D4—3321no—
880C2×D4—3321no—
881C2×D4—834no—
882C2×D4—834no—
883C2×D4—838no—
884C2×D4—838no—
885C2×D4—838no—
886C2×D4—838no—
887C2×D4—838no—
888C2×D4—834no—
889C2×D4—834no—
890C2×D4—834no—
891C2×D4—1662no—
892C2×D4—1662no—
893C2×D4—1662no—
894C2×D4—1662no—
895C22×C4—22no—
896C22×C4—22no—
897C22×C4—3321no—
898C22×C4—3321no—
899C22×C4—3321no—
900C22×C4—3321no—
901C22×C4—3322no—
902C22×C4—3322no—
903C22×C4—3322no—
904C22×C4—3322no—
905C22×C4—3322no—
906C22×C4—3322no—
907C22×C4—3322no—
908C22×C4—3322no—
909C22×C4—3322no—
910C22×C4—3322no—
911C22×C4—3322no—
912C22×C4—3322no—
913C22×C4—3322no—
914C22×C4—831no—
915C22×C4—831no—
916C22×C4—831no—
917C22×C4—834no—
918C22×C4—834no—
919C22×C4—831no—
920C22×C4—831no—
921C22×C4—832no—
922C22×C4—832no—
923C22×C4—831no—
924C22×C4—1662no—
925C22×C4—1664no—
926C22×C4—1662no—
927C22×C4—1664no—
928C22×C4—1662no—
929C22×C4—1662no—
930C22×C4—1662no—
931C22×C4—1662no—
932C22×C4C2×C4×D8314yes—
933C22×C4C23×D8312yes—
934C22×C4C23×D8311yescharacteristic
935C22×C4C23×D8311yescharacteristic
936C22×C4C23×D8312yes—
937C22×C4C23×D8311yescharacteristic
938C22×C4C23×D8311yescharacteristic
939C22×C4C23×D8312yes—
940C22×C4C23×D8312yes—
941C22×C4C23×D8311yescharacteristic
942C22×C4C23×D8311yescharacteristic
943C4⋊C4—22no—
944C4⋊C4—22no—
945C4⋊C4—42no—
946C4⋊C4—42no—
947C4⋊C4—3322no—
948C4⋊C4—3321no—
949C4⋊C4—3321no—
950C4⋊C4—3322no—
951C4⋊C4—3322no—
952C4⋊C4—1662no—
953C4⋊C4—1662no—
954C4⋊C4C2×C4×D8314yes—
955C4⋊C4C2×C4×D8314yes—
956C22⋊C4—22no—
957C22⋊C4—42no—
958C22⋊C4—41no—
959C22⋊C4—3322no—
960C22⋊C4—3322no—
961C22⋊C4—3321no—
962C22⋊C4—3321no—
963C22⋊C4—3322no—
964C22⋊C4—3322no—
965C22⋊C4—3322no—
966C22⋊C4—3322no—
967C22⋊C4—3322no—
968C22⋊C4—3322no—
969C22⋊C4—3322no—
970C22⋊C4—3322no—
971C22⋊C4—3322no—
972C22⋊C4—3322no—
973C22⋊C4—3321no—
974C22⋊C4—3322no—
975C22⋊C4—3321no—
976C22⋊C4—3322no—
977C22⋊C4—3321no—
978C22⋊C4—838no—
979C22⋊C4—838no—
980C22⋊C4—838no—
981C22⋊C4—838no—
982C22⋊C4—1664no—
983C22⋊C4—1662no—
984C22⋊C4—1662no—
985C22⋊C4—1664no—
986C22⋊C4—1662no—
987C22⋊C4C2×C4×D8318yes—
988C42—22no—
989C42—22no—
990C42—24no—
991C42—42no—
992C42—3321no—
993C42—3321no—
994C42—3322no—
995C42—3322no—
996C42—1664no—
997C42—1662no—
998C42—1662no—
999C42C2×C4×D8318yes—
1000C23—21no—
1001C23—21no—
1002C23—21no—
1003C23—21no—
1004C23—21no—
1005C23—21no—
1006C23—3328no—
1007C23—3328no—
1008C23—3328no—
1009C23—834no—
1010C23—834no—
1011C23—832no—
1012C23—832no—
1013C23—6644no—
1014C23—6644no—
1015C23—6644no—
1016C23—6644no—
1017C23—1661no—
1018C23—1662no—
1019C23—1662no—
1020C23—1661no—
1021C23—1661no—
1022C23—1661no—
1023C23—1661no—
1024C23—1662no—
1025C23—1662no—
1026C23—1662no—
1027C23—1662no—
1028C23—1662no—
1029C23—1662no—
1030C23—1661no—
1031C23—1661no—
1032C23—1661no—
1033C23—1661no—
1034C23—1662no—
1035C23—1661no—
1036C23—1662no—
1037C23—1661no—
1038C23—1662no—
1039C23—1661no—
1040C23—1662no—
1041C23C22×C4×D8312yes—
1042C23C24×D8311yescharacteristic
1043Q8—3324no—
1044D4—3328no—
1045D4—3324no—
1046D4—3328no—
1047D4—3328no—
1048D4—3328no—
1049D4—3328no—
1050D4—3324no—
1051D4—3324no—
1052D4—1668no—
1053D4—1668no—
1054C2×C4—22no—
1055C2×C4—21no—
1056C2×C4—22no—
1057C2×C4—21no—
1058C2×C4—21no—
1059C2×C4—22no—
1060C2×C4—22no—
1061C2×C4—21no—
1062C2×C4—28no—
1063C2×C4—22no—
1064C2×C4—22no—
1065C2×C4—21no—
1066C2×C4—21no—
1067C2×C4—21no—
1068C2×C4—21no—
1069C2×C4—22no—
1070C2×C4—21no—
1071C2×C4—22no—
1072C2×C4—21no—
1073C2×C4—22no—
1074C2×C4—21no—
1075C2×C4—22no—
1076C2×C4—21no—
1077C2×C4—21no—
1078C2×C4—3324no—
1079C2×C4—3324no—
1080C2×C4—832no—
1081C2×C4—832no—
1082C2×C4—832no—
1083C2×C4—6644no—
1084C2×C4—6644no—
1085C2×C4—6644no—
1086C2×C4—6644no—
1087C2×C4—6644no—
1088C2×C4—1662no—
1089C2×C4—1661no—
1090C2×C4—1661no—
1091C2×C4—1662no—
1092C2×C4—1661no—
1093C2×C4—1661no—
1094C2×C4—1662no—
1095C2×C4—1661no—
1096C2×C4—1662no—
1097C2×C4—1662no—
1098C2×C4—1661no—
1099C2×C4—1661no—
1100C2×C4—1661no—
1101C2×C4—1662no—
1102C2×C4—1661no—
1103C2×C4—1661no—
1104C2×C4—1661no—
1105C2×C4—1661no—
1106C2×C4—1661no—
1107C2×C4—1661no—
1108C2×C4—1661no—
1109C2×C4—1668no—
1110C2×C4—1668no—
1111C2×C4C22×C4×D8312yes—
1112C2×C4C22×C4×D8314yes—
1113C2×C4C22×C4×D8314yes—
1114C2×C4C22×C4×D8312yes—
1115C2×C4#1458183812yes—
1116C2×C4#1458183812yes—
1117C2×C4#1458183812yes—
1118C22—22no—
1119C22—22no—
1120C22—22no—
1121C22—41no—
1122C22—41no—
1123C22—41no—
1124C22—41no—
1125C22—3321no—
1126C22—3322no—
1127C22—3322no—
1128C22—3321no—
1129C22—3322no—
1130C22—3322no—
1131C22—3321no—
1132C22—3321no—
1133C22—3321no—
1134C22—3322no—
1135C22—3322no—
1136C22—3321no—
1137C22—3321no—
1138C22—3322no—
1139C22—3322no—
1140C22—3321no—
1141C22—66416no—
1142C22—1662no—
1143C22—1662no—
1144C22—1664no—
1145C22—1664no—
1146C22—1662no—
1147C22—1662no—
1148C22—1664no—
1149C22—1664no—
1150C22—1662no—
1151C22—1662no—
1152C22—1664no—
1153C22—1664no—
1154C22C23×C4×D8311yescharacteristic
1155C22H(5,𝔽2)×D8311yescharacteristic
1156C22C2×#1458183811yescharacteristic
1157C22C2×#1458183811yescharacteristic
1158C22C2×#1458183811yescharacteristic
1159C22#1912853711yescharacteristic
1160C22#1912853811yescharacteristic
1161C4—22no—
1162C4—24no—
1163C4—24no—
1164C4—22no—
1165C4—42no—
1166C4—41no—
1167C4—41no—
1168C4—41no—
1169C4—42no—
1170C4—3322no—
1171C4—3321no—
1172C4—3321no—
1173C4—3321no—
1174C4—3322no—
1175C4—1662no—
1176C4—1662no—
1177C4—1662no—
1178C4#1912817514yes—
1179C2—42no—
1180C2—3324no—
1181C2—3324no—
1182C2—3322no—
1183C2—3322no—
1184C2C2×#1912817511yescharacteristic
1185C2#2492066911yescharacteristic
1186C2C4×#1458183811yescharacteristic
1187C2#2492177311yescharacteristic
1188C2#2492178611yescharacteristic
1189C2#2492186411yescharacteristic
1190C2#2492189111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
FittingC83×#2346C2
socle, cosocleC23×C83C25
prime radicalC2×#19128270C2
hypercenter#2346D83
hypocenterC83#34415
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ #2346

Complements

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

NH ≅ G/Ntype
2. #24910634C2semidirect
3. #24910603C2semidirect
4. #24910573C2semidirect
5. #24910503C2semidirect
6. #24910500C2semidirect
7. #24910481C2semidirect
8. #24910478C2semidirect
9. #24910441C2semidirect
10. #24910348C2semidirect
11. C22⋊C4×D332C2semidirect
12. #24910283C2semidirect
13. #24910188C2semidirect
14. #24910186C2semidirect
15. #24910157C2semidirect
16. #24910154C2semidirect
17. #24910125C2semidirect
18. #24910116C2semidirect
19. #24910052C2semidirect
20. C4×#14581767C2semidirect
21. #24909971C2semidirect
22. #24909949C2semidirect
23. C83×#2346C2semidirect
26. #19128270C4semidirect
37. C2×C4×D332C22semidirect
38. C2×C4×D332C22semidirect
41. C2×#14581754C22semidirect
42. C2×#14581754C22semidirect
43. C2×#14581750C22semidirect
44. C2×#14581749C22semidirect
45. C2×C4⋊C4×D83C22semidirect
48. C2×C42×D83C22semidirect
49. #19127605C22semidirect
50. #19127605C22semidirect
51. #19127605C22semidirect
54. #19127603C22semidirect
55. #19127603C22semidirect
58. #19127602C22semidirect
59. #19127602C22semidirect
63. #19127600C22semidirect
64. #19127600C22semidirect
67. #19127593C22semidirect
68. #19127593C22semidirect
69. #19127592C22semidirect
70. #19127592C22semidirect
71. #19127591C22semidirect
72. #19127591C22semidirect
73. #19127590C22semidirect
74. #19127590C22semidirect
79. #19127579C22semidirect
80. #19127579C22semidirect
81. #19127579C22semidirect
82. #19127579C22semidirect
83. #19127579C22semidirect
84. #19127579C22semidirect
85. #19127579C22semidirect
86. #19127579C22semidirect
87. #19127579C22semidirect
88. #19127579C22semidirect
89. #19127579C22semidirect
93. #19127575C22semidirect
94. #19127575C22semidirect
95. #19127572C22semidirect
96. #19127572C22semidirect
97. #19127567C22semidirect
99. #19127558C22semidirect
100. #19127558C22semidirect
103. C4⋊C4×Dic83C22semidirect
104. C4⋊C4×Dic83C22semidirect
105. C4×(C2×D83)⋊C4C22semidirect
106. C4×(C2×D83)⋊C4C22semidirect
107. C4×(C2×D83)⋊C4C22semidirect
108. C4×(C2×D83)⋊C4C22semidirect
110. #19127548C22semidirect
111. #19127548C22semidirect
112. #19127547C22semidirect
114. #389×C83C22semidirect
115. #389×C83C22semidirect
118. #382×C83C22semidirect
120. C4×C4⋊C4×C83C22semidirect
121. C4×C4⋊C4×C83C22semidirect
123. #376×C83C22semidirect
127. C2×#13050590C2×C4semidirect
131. C22×D332C2×C4semidirect
151. #14581789C2×C4semidirect
152. #14581780C2×C4semidirect
153. #14581767C2×C4semidirect
154. #14581767C2×C4semidirect
155. #14581767C2×C4semidirect
156. #14581767C2×C4semidirect
157. #14581762C2×C4semidirect
158. #14581762C2×C4semidirect
229. #117×C83C2×C4semidirect
606. #2346D83semidirect
619. C83#34415semidirect
662. #389C2×D83semidirect
663. #389C2×D83semidirect
699. #382C2×D83semidirect
708. C4×C4⋊C4C2×D83semidirect
709. C4×C4⋊C4C2×D83semidirect
719. #376C2×D83semidirect
766. #117C4×D83semidirect

Maximal subgroups

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

subgroupindex
C2×#191282702
#249106342
#249106032
#249105732
#249105032
#249105002
#249104812
#249104782
#249104412
#249103482
C22⋊C4×D3322
#249102832
#249101882
#249101862
#249101572
#249101542
#249101252
#249101162
#249100522
C4×#145817672
#249099712
#249099492
C83×#23462
#3441583