Finite Group Databasebeta

← #35569820

Subgroups — #35569820

Order 21248.

2600 conjugacy classes of subgroups.

The subgroup lattice has 1124 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#24910611C212yesmaximal, complemented
2#24910604C212yesmaximal, complemented
3#24910538C211yesmaximal, characteristic, complemented
4#24910505C212yesmaximal, complemented
5#24910494C211yesmaximal, characteristic, complemented
6#24910483C211yesmaximal, characteristic, complemented
7#24910436C211yesmaximal, characteristic, complemented
8#24910392C211yesmaximal, characteristic, complemented
9#24910312C212yesmaximal, complemented
10#24910304C211yesmaximal, characteristic, complemented
11D4×C22⋊Dic83C211yesmaximal, characteristic, complemented
12#24910257C212yesmaximal, complemented
13#24910230C212yesmaximal, complemented
14#24910158C211yesmaximal, characteristic, complemented
15#24910147C211yesmaximal, characteristic, complemented
16#24910124C212yesmaximal, complemented
17#24910061C212yesmaximal, complemented
18#24910055C211yesmaximal, characteristic, complemented
19#24910045C211yesmaximal, characteristic, complemented
20#124×Dic83C211yesmaximal, characteristic, complemented
21#24909928C211yesmaximal, characteristic, complemented
22#24909928C211yesmaximal, characteristic, complemented
23C2×#546×C83C211yesmaximal, characteristic
24C2×Q8×Dic83C2211yescharacteristic, complemented
25C2×Q8×Dic83C2211yescharacteristic, complemented
26C2×D4×Dic83C2211yescharacteristic
27C2×D4×Dic83C2211yescharacteristic
28C2×D4×Dic83C2212yescomplemented
29C2×#14581751C2211yescharacteristic
30C2×#14581751C2211yescharacteristic
31C2×#14581751C2211yescharacteristic, complemented
32C2×#14581751C2212yescomplemented
33C22×C4⋊Dic83C2211yescharacteristic, complemented
34C22×C22⋊Dic83C2212yes—
35#19127608C2211yescharacteristic, complemented
36#19127608C2211yescharacteristic, complemented
37#19127604C2211yescharacteristic
38#19127604C2212yes—
39#19127604C2211yescharacteristic
40#19127604C2211yescharacteristic
41#19127604C2211yescharacteristic
42#19127604C2211yescharacteristic
43#19127604C2211yescharacteristic
44#19127604C2211yescharacteristic
45#19127604C2211yescharacteristic
46#19127604C2212yes—
47#19127604C2212yescomplemented
48#19127604C2212yescomplemented
49#19127604C2212yescomplemented
50#19127600C2211yescharacteristic, complemented
51#19127600C2212yescomplemented
52#19127600C2211yescharacteristic, complemented
53#19127600C2211yescharacteristic, complemented
54#19127600C2211yescharacteristic, complemented
55#19127594C2212yes—
56#19127594C2212yes—
57#19127594C2212yes—
58#19127594C2212yes—
59#19127594C2212yes—
60#19127594C2211yescharacteristic
61#19127594C2211yescharacteristic
62#19127594C2212yescomplemented
63#19127594C2212yescomplemented
64#19127594C2212yescomplemented
65#19127594C2212yescomplemented
66#19127594C2212yescomplemented
67#19127594C2212yescomplemented
68#19127594C2212yescomplemented
69#19127594C2212yescomplemented
70#19127594C2211yescharacteristic, complemented
71#19127594C2211yescharacteristic, complemented
72#19127594C2212yescomplemented
73#19127594C2212yescomplemented
74#19127587C2212yescomplemented
75#19127587C2212yescomplemented
76#19127587C2212yescomplemented
77#19127581C2212yes—
78#19127581C2212yes—
79#19127581C2212yes—
80#19127581C2212yescomplemented
81#19127581C2212yescomplemented
82#19127581C2212yescomplemented
83#19127581C2212yescomplemented
84#19127576C2212yescomplemented
85#19127576C2212yescomplemented
86#19127576C2212yescomplemented
87#19127567C2211yescharacteristic, complemented
88#19127564C2212yescomplemented
89#19127561C2211yescharacteristic
90#19127561C2212yescomplemented
91#19127561C2212yescomplemented
92#19127561C2211yescharacteristic, complemented
93#19127561C2212yescomplemented
94#19127557C2212yes—
95#19127557C2212yes—
96#19127557C2212yes—
97C4⋊C4×Dic83C2211yescharacteristic, complemented
98C4⋊C4×Dic83C2211yescharacteristic, complemented
99C4⋊C4×Dic83C2212yescomplemented
100C4×C4⋊Dic83C2211yescharacteristic, complemented
101C4×C4⋊Dic83C2211yescharacteristic, complemented
102C22⋊C4×Dic83C2212yescomplemented
103C22⋊C4×Dic83C2212yescomplemented
104C22⋊C4×Dic83C2212yescomplemented
105C22⋊C4×Dic83C2212yescomplemented
106C4×C22⋊Dic83C2211yescharacteristic
107C4×C22⋊Dic83C2212yescomplemented
108C4×C22⋊Dic83C2211yescharacteristic, complemented
109C4×C22⋊Dic83C2212yescomplemented
110C4×C22⋊Dic83C2212yescomplemented
111C42×Dic83C2211yescharacteristic, complemented
112C22×#41×C83C2211yescharacteristic
113C23×D4×C83C2211yescharacteristic
114#546×C83C4116yescomplemented
115C2×#124×C83C2211yescharacteristic
116C2×#123×C83C2212yes—
117C2×C22⋊Q8×C83C2211yescharacteristic
118C2×#121×C83C2211yescharacteristic
119C2×#121×C83C2212yes—
120C2×#120×C83C2212yes—
121C2×C4×D4×C83C2211yescharacteristic
122C2×C4×D4×C83C2211yescharacteristic
123C22×C22⋊C4×C83C2212yes—
124C23×Dic83C2312yes—
125C23×Dic83C2312yes—
126C23×Dic83C2312yes—
127Q8×Dic83—42no—
128Q8×Dic83—42no—
129D4×Dic83—42no—
130D4×Dic83—42no—
131D4×Dic83—44no—
132#14581751—42no—
133#14581751—42no—
134#14581751—42no—
135#14581751—44no—
136C2×C4⋊Dic83—42no—
137C2×C4⋊Dic83C2311yescharacteristic
138C2×C4⋊Dic83C2311yescharacteristic
139C2×C4⋊Dic83C2311yescharacteristic
140C2×C4⋊Dic83C2311yescharacteristic
141C2×C4⋊Dic83C2312yes—
142C2×C4⋊Dic83C2311yescharacteristic
143C2×C4⋊Dic83C2311yescharacteristic
144C2×C4⋊Dic83C2311yescharacteristic
145C2×C4⋊Dic83C2312yes—
146C2×C4⋊Dic83C2311yescharacteristic
147C2×C4⋊Dic83C2312yes—
148C2×C4⋊Dic83C2312yes—
149C2×C4⋊Dic83C2312yes—
150C2×C4⋊Dic83C2311yescharacteristic
151C2×C4⋊Dic83C2311yescharacteristic
152C2×C22⋊Dic83—44no—
153C2×C22⋊Dic83C2312yes—
154C2×C22⋊Dic83C2311yescharacteristic
155C2×C22⋊Dic83C2311yescharacteristic
156C2×C22⋊Dic83C2312yes—
157C2×C22⋊Dic83C2311yescharacteristic
158C2×C22⋊Dic83C2311yescharacteristic
159C2×C22⋊Dic83C2311yescharacteristic
160C2×C22⋊Dic83C2312yes—
161C2×C22⋊Dic83C2312yes—
162C2×C22⋊Dic83C2312yes—
163C2×C22⋊Dic83C2312yes—
164C2×C22⋊Dic83C2312yes—
165C2×C22⋊Dic83C2312yes—
166C2×C22⋊Dic83C2312yes—
167C2×C22⋊Dic83C2312yes—
168C2×C22⋊Dic83C2312yes—
169C2×C22⋊Dic83C2312yes—
170C2×C22⋊Dic83C2312yes—
171C2×C22⋊Dic83C2312yes—
172C2×C22⋊Dic83C2312yes—
173C2×C22⋊Dic83C2312yes—
174C2×C22⋊Dic83C2312yes—
175C2×C22⋊Dic83C2311yescharacteristic
176C2×C22⋊Dic83C2311yescharacteristic
177C2×C22⋊Dic83C2311yescharacteristic
178C2×C4×Dic83C2311yescharacteristic
179C2×C4×Dic83C2311yescharacteristic
180C2×C4×Dic83C2311yescharacteristic
181C2×C4×Dic83C2311yescharacteristic
182C2×C4×Dic83C2311yescharacteristic
183C2×C4×Dic83C2312yes—
184C2×C4×Dic83C2312yes—
185C2×C4×Dic83C2312yes—
186C2×C4×Dic83C2312yes—
187C2×C4×Dic83C2312yes—
188C2×C4×Dic83C2312yes—
189C2×C4×Dic83C2311yescharacteristic
190C2×C4×Dic83C2311yescharacteristic
191C2×C4×Dic83C2311yescharacteristic
192C83⋊#95C2311yescharacteristic
193C83⋊#95C2312yes—
194C83⋊#95C2311yescharacteristic
195C83⋊#95C2311yescharacteristic
196C83⋊#95C2312yes—
197C83⋊#95C2312yes—
198C83⋊#95C2312yes—
199C83⋊#95C2312yes—
200C83⋊#95C2312yes—
201C83⋊#95C2311yescharacteristic
202C83⋊#95C2312yes—
203C83⋊#95C2312yes—
204C83⋊#95C2312yes—
205C83⋊#95C2312yes—
206C83⋊#95C2312yes—
207C83⋊#95C2311yescharacteristic
208C83⋊#95C2311yescharacteristic
209C83⋊#95C2312yes—
210C83⋊#95C2312yes—
211C25×C83C2312yes—
212C2×#41×C83—42no—
213C2×#41×C83—42no—
214C2×#41×C83C2×C418yescomplemented
215C22×Q8×C83C2311yescharacteristic
216C22×D4×C83—42no—
217C22×D4×C83—42no—
218C22×D4×C83C2×C418yescomplemented
219C22×D4×C83C2311yescharacteristic
220C22×D4×C83C2311yescharacteristic
221C22×D4×C83C2311yescharacteristic
222C22×D4×C83C2312yes—
223C22×D4×C83C2312yes—
224C22×D4×C83C2312yes—
225C23×C4×C83C2311yescharacteristic
226C23×C4×C83C2311yescharacteristic
227C23×C4×C83C2312yes—
228C23×C4×C83C2312yes—
229#124×C83C2×C418yescomplemented
230#123×C83C2×C4116yescomplemented
231C22⋊Q8×C83C2×C418yescomplemented
232#121×C83C2×C418yes—
233#121×C83C2×C4116yescomplemented
234#120×C83C2×C4116yescomplemented
235C4×D4×C83C2×C418yescomplemented
236C4×D4×C83C2×C418yescomplemented
237C2×C4⋊C4×C83C2311yescharacteristic
238C2×C4⋊C4×C83C2312yes—
239C2×C4⋊C4×C83C2311yescharacteristic
240C2×C22⋊C4×C83C2×C4116yescomplemented
241C2×C22⋊C4×C83C2312yes—
242C2×C22⋊C4×C83C2312yes—
243C2×C22⋊C4×C83C2311yescharacteristic
244C2×C22⋊C4×C83C2312yes—
245C2×C22⋊C4×C83C2312yes—
246C2×C22⋊C4×C83C2312yes—
247C2×C22⋊C4×C83C2311yescharacteristic
248C2×C42×C83C2311yescharacteristic
249C22×Dic83—24no—
250C22×Dic83—42no—
251C22×Dic83—42no—
252C22×Dic83—42no—
253C22×Dic83—42no—
254C22×Dic83—42no—
255C22×Dic83—42no—
256C22×Dic83—42no—
257C22×Dic83—42no—
258C22×Dic83C2411yescharacteristic
259C22×Dic83C2412yes—
260C22×Dic83C2412yes—
261C22×Dic83C2412yes—
262C22×Dic83C2411yescharacteristic
263C22×Dic83C2411yescharacteristic
264C22×Dic83C2411yescharacteristic
265C22×Dic83C2411yescharacteristic
266C22×Dic83C2412yes—
267C22×Dic83C2411yescharacteristic
268C22×Dic83C2411yescharacteristic
269C22×Dic83C2411yescharacteristic
270C4⋊Dic83—22no—
271C4⋊Dic83—22no—
272C4⋊Dic83—22no—
273C4⋊Dic83—22no—
274C4⋊Dic83—24no—
275C4⋊Dic83—42no—
276C4⋊Dic83—41no—
277C4⋊Dic83—41no—
278C4⋊Dic83—41no—
279C4⋊Dic83—41no—
280C4⋊Dic83—41no—
281C4⋊Dic83—41no—
282C4⋊Dic83—42no—
283C4⋊Dic83—42no—
284C4⋊Dic83—42no—
285C22⋊Dic83—22no—
286C22⋊Dic83—24no—
287C22⋊Dic83—22no—
288C22⋊Dic83—42no—
289C22⋊Dic83—42no—
290C22⋊Dic83—41no—
291C22⋊Dic83—42no—
292C22⋊Dic83—42no—
293C22⋊Dic83—41no—
294C22⋊Dic83—42no—
295C22⋊Dic83—42no—
296C22⋊Dic83—42no—
297C22⋊Dic83—42no—
298C22⋊Dic83—42no—
299C22⋊Dic83—42no—
300C22⋊Dic83—42no—
301C22⋊Dic83—41no—
302C22⋊Dic83—41no—
303C22⋊Dic83—41no—
304C22⋊Dic83—41no—
305C22⋊Dic83—42no—
306C22⋊Dic83—42no—
307C22⋊Dic83—42no—
308C22⋊Dic83—42no—
309C22⋊Dic83—42no—
310C4×Dic83—22no—
311C4×Dic83—22no—
312C4×Dic83—22no—
313C4×Dic83—22no—
314C4×Dic83—22no—
315C4×Dic83—41no—
316C4×Dic83—42no—
317C4×Dic83—41no—
318C4×Dic83—41no—
319C4×Dic83—42no—
320C4×Dic83—42no—
321C4×Dic83—42no—
322C4×Dic83—42no—
323C4×Dic83—42no—
324C24×C83—42no—
325C24×C83—42no—
326C24×C83—42no—
327C24×C83—42no—
328C24×C83—42no—
329C24×C83—42no—
330C24×C83C22×C418yes—
331C24×C83C2412yes—
332C24×C83C2411yescharacteristic
333C24×C83C2411yescharacteristic
334C24×C83C2412yes—
335#41×C83—416no—
336C2×Q8×C83—22no—
337C2×Q8×C83—22no—
338C2×Q8×C83C22×C414yes—
339C2×D4×C83—22no—
340C2×D4×C83—22no—
341C2×D4×C83—22no—
342C2×D4×C83—22no—
343C2×D4×C83—416no—
344C2×D4×C83—42no—
345C2×D4×C83—42no—
346C2×D4×C83—42no—
347C2×D4×C83—41no—
348C2×D4×C83—41no—
349C2×D4×C83—42no—
350C2×D4×C83—42no—
351C2×D4×C83—42no—
352C2×D4×C83C22×C414yes—
353C2×D4×C83C22×C414yes—
354C2×D4×C83C22×C414yes—
355C2×D4×C83C22×C418yes—
356C2×D4×C83C22×C418yes—
357C2×D4×C83C22×C418yes—
358C22×C4×C83—22no—
359C22×C4×C83—22no—
360C22×C4×C83—22no—
361C22×C4×C83—22no—
362C22×C4×C83—42no—
363C22×C4×C83—42no—
364C22×C4×C83—42no—
365C22×C4×C83—42no—
366C22×C4×C83C22×C414yes—
367C22×C4×C83C22×C414yes—
368C22×C4×C83C22×C418yes—
369C22×C4×C83C22×C418yes—
370C22×C4×C83C2411yescharacteristic
371C22×C4×C83C2411yescharacteristic
372C22×C4×C83C2412yes—
373C22×C4×C83C2411yescharacteristic
374C22×C4×C83C2412yes—
375C22×C4×C83C2411yescharacteristic
376C22×C4×C83C2411yescharacteristic
377C4⋊C4×C83C22×C414yes—
378C4⋊C4×C83C22×C414yes—
379C4⋊C4×C83C22×C418yes—
380C22⋊C4×C83C22×C414yes—
381C22⋊C4×C83C22×C418yes—
382C22⋊C4×C83C22×C418yes—
383C22⋊C4×C83C22×C418yes—
384C22⋊C4×C83C22×C418yes—
385C22⋊C4×C83C22×C414yes—
386C22⋊C4×C83C22×C418yes—
387C42×C83C22×C414yes—
388C23×C83—21no—
389C23×C83—21no—
390C23×C83—21no—
391C23×C83—21no—
392C23×C83—22no—
393C23×C83—22no—
394C23×C83—22no—
395C23×C83—22no—
396C23×C83—22no—
397C23×C83—21no—
398C23×C83—22no—
399C23×C83—21no—
400C23×C83—22no—
401C23×C83—21no—
402C23×C83—21no—
403C23×C83—21no—
404C23×C83—22no—
405C23×C83—21no—
406C23×C83—21no—
407C23×C83—21no—
408C23×C83—22no—
409C23×C83—22no—
410C23×C83—22no—
411C23×C83—22no—
412C23×C83—48no—
413C23×C83—48no—
414C23×C83—48no—
415C23×C83—84no—
416C23×C83—84no—
417C23×C83—84no—
418C23×C83—84no—
419C23×C83C23×C412yes—
420C23×C83C23×C414yes—
421C23×C83C23×C414yes—
422C23×C83C23×C412yes—
423C23×C83C2511yescharacteristic
424Q8×C83—28no—
425D4×C83—28no—
426D4×C83—28no—
427D4×C83—48no—
428D4×C83—44no—
429D4×C83—48no—
430D4×C83—48no—
431C2×C4×C83—21no—
432C2×C4×C83—21no—
433C2×C4×C83—21no—
434C2×C4×C83—21no—
435C2×C4×C83—21no—
436C2×C4×C83—22no—
437C2×C4×C83—22no—
438C2×C4×C83—22no—
439C2×C4×C83—21no—
440C2×C4×C83—22no—
441C2×C4×C83—21no—
442C2×C4×C83—21no—
443C2×C4×C83—28no—
444C2×C4×C83—28no—
445C2×C4×C83—48no—
446C2×C4×C83—48no—
447C2×C4×C83C23×C412yes—
448C2×C4×C83C23×C412yes—
449C2×C4×C83C23×C414yes—
450C2×C4×C83C23×C412yes—
451C2×C4×C83C23×C414yes—
452C2×C4×C83C23×C412yes—
453C2×C4×C83C23×C412yes—
454C2×C4×C83H(5,𝔽2)12yes—
455C2×C4×C83H(5,𝔽2)12yes—
456C2×Dic83—21no—
457C2×Dic83—21no—
458C2×Dic83—21no—
459C2×Dic83—21no—
460C2×Dic83—21no—
461C2×Dic83—21no—
462C2×Dic83—21no—
463C2×Dic83—21no—
464C2×Dic83—21no—
465C2×Dic83—21no—
466C2×Dic83—21no—
467C2×Dic83—22no—
468C2×Dic83—22no—
469C2×Dic83—22no—
470C2×Dic83—22no—
471C2×Dic83—22no—
472C2×Dic83—22no—
473C2×Dic83—21no—
474C2×Dic83—22no—
475C2×Dic83—21no—
476C2×Dic83—21no—
477C2×Dic83—21no—
478C2×Dic83—22no—
479C2×Dic83—21no—
480C2×Dic83—21no—
481C2×Dic83—21no—
482C2×Dic83—21no—
483C2×Dic83—22no—
484C2×Dic83—21no—
485C2×Dic83—21no—
486C2×Dic83—21no—
487C2×Dic83—22no—
488C2×Dic83—22no—
489C2×Dic83—22no—
490C2×Dic83—21no—
491C2×Dic83—84no—
492C2×Dic83—84no—
493C2×Dic83—84no—
494C2×Dic83H(5,𝔽2)12yes—
495C22×C83—22no—
496C22×C83—22no—
497C22×C83—24no—
498C22×C83—24no—
499C22×C83—22no—
500C22×C83—22no—
501C22×C83—24no—
502C22×C83—24no—
503C22×C83—24no—
504C22×C83—22no—
505C22×C83—24no—
506C22×C83—22no—
507C22×C83—42no—
508C22×C83—41no—
509C22×C83—42no—
510C22×C83—41no—
511C22×C83—41no—
512C22×C83—42no—
513C22×C83—42no—
514C22×C83—41no—
515C22×C83—41no—
516C22×C83—42no—
517C22×C83—42no—
518C22×C83—41no—
519C22×C83—41no—
520C22×C83—42no—
521C22×C83—42no—
522C22×C83—41no—
523C22×C83—816no—
524C22×C83C24×C411yescharacteristic
525C22×C83C2×H(5,𝔽2)11yescharacteristic
526C22×C83C2×H(5,𝔽2)11yescharacteristic
527C22×C83C2×H(5,𝔽2)11yescharacteristic
528C22×C83#58511yescharacteristic
529C22×C83#58511yescharacteristic
530C22×C83#58511yescharacteristic
531C4×C83—22no—
532C4×C83—22no—
533C4×C83—24no—
534C4×C83—22no—
535C4×C83—22no—
536C4×C83—24no—
537C4×C83#51814yes—
538Dic83—22no—
539Dic83—41no—
540Dic83—41no—
541Dic83—42no—
542Dic83—41no—
543Dic83—41no—
544Dic83—41no—
545Dic83—41no—
546Dic83—42no—
547Dic83—42no—
548Dic83—41no—
549Dic83—42no—
550#34495—831nomaximal, Sylow
551C2×C83—42no—
552C2×C83—44no—
553C2×C83—44no—
554C2×C83—42no—
555C2×C83C2×#51811yescharacteristic
556C2×C83#342811yescharacteristic
557C2×C83C4×H(5,𝔽2)11yescharacteristic
558C2×C83#354611yescharacteristic
559C2×C83#355111yescharacteristic
560C2×C83#355811yescharacteristic
561C2×C83#356211yescharacteristic
562C2×#546D8311yescharacteristic
563#2376—832no—
564#2375—832no—
565#2367—831no—
566#2363—832no—
567#2362—831no—
568#2361—831no—
569#2357—831no—
570#2352—831no—
571#2342—832no—
572#2341—831no—
573D4×C22⋊C4—831no—
574#2335—832no—
575#2333—832no—
576#2324—831no—
577#2323—831no—
578#2321—832no—
579#2312—832no—
580#2311—831no—
581#2309—831no—
582C4×#124—831no—
583#2293—831no—
584#2293—831no—
585C83#3449511yescharacteristic, complemented, Sylow
586C22×#41C2×D8311yescharacteristic
587C23×D4C2×D8311yescharacteristic
588#546Dic83116yescomplemented
589C2×#124C2×D8311yescharacteristic
590C2×#123C2×D8312yes—
591C2×C22⋊Q8C2×D8311yescharacteristic
592C2×#121C2×D8311yescharacteristic
593C2×#121C2×D8312yes—
594C2×#120C2×D8312yes—
595C2×C4×Q8—831no—
596C2×C4×Q8—831no—
597C2×C4×D4—832no—
598C2×C4×D4—831no—
599C2×C4×D4—831no—
600C2×C4×D4C2×D8311yescharacteristic
601C2×C4×D4C2×D8311yescharacteristic
602C2×#117—831no—
603C2×#117—831no—
604C2×#117—831no—
605C2×#117—832no—
606C22×C4⋊C4—831no—
607C22×C22⋊C4—832no—
608C22×C22⋊C4C2×D8312yes—
609#391—831no—
610#391—831no—
611#390—831no—
612#390—831no—
613#390—832no—
614#390—831no—
615#390—831no—
616#390—832no—
617#390—831no—
618#390—831no—
619#390—832no—
620#390—832no—
621#390—832no—
622#390—831no—
623#390—831no—
624#389—831no—
625#389—832no—
626#389—831no—
627#389—831no—
628#389—831no—
629#388—831no—
630#388—832no—
631#388—832no—
632#388—832no—
633#388—832no—
634#388—832no—
635#388—832no—
636#388—832no—
637#388—832no—
638#388—832no—
639#388—832no—
640#388—832no—
641#388—831no—
642#388—832no—
643#388—832no—
644#388—831no—
645#388—831no—
646#388—832no—
647#388—832no—
648#387—832no—
649#387—832no—
650#387—832no—
651#386—832no—
652#386—832no—
653#386—832no—
654#386—832no—
655#386—832no—
656#386—832no—
657#386—832no—
658#385—832no—
659#385—832no—
660#385—832no—
661#382—831no—
662#381—832no—
663#380—832no—
664#380—832no—
665#380—832no—
666#380—831no—
667#380—831no—
668#379—832no—
669#379—832no—
670#379—832no—
671C4×C4⋊C4—831no—
672C4×C4⋊C4—831no—
673C4×C4⋊C4—832no—
674C4×C4⋊C4—831no—
675C4×C4⋊C4—831no—
676C4×C22⋊C4—832no—
677C4×C22⋊C4—832no—
678C4×C22⋊C4—832no—
679C4×C22⋊C4—831no—
680C4×C22⋊C4—831no—
681C4×C22⋊C4—832no—
682C4×C22⋊C4—832no—
683C4×C22⋊C4—832no—
684C4×C22⋊C4—832no—
685C43—831no—
686C25C22×D8312yes—
687C2×#41—42no—
688C2×#41—42no—
689C2×#41C2×Dic8318yescomplemented
690C22×Q8C22×D8311yescharacteristic
691C22×D4—42no—
692C22×D4—42no—
693C22×D4C2×Dic8318yescomplemented
694C22×D4C22×D8311yescharacteristic
695C22×D4C22×D8311yescharacteristic
696C22×D4C22×D8312yes—
697C22×D4C22×D8311yescharacteristic
698C22×D4C22×D8312yes—
699C22×D4C22×D8312yes—
700C23×C4—832no—
701C23×C4—832no—
702C23×C4—832no—
703C23×C4C22×D8311yescharacteristic
704C23×C4C22×D8311yescharacteristic
705C23×C4C22×D8312yes—
706C23×C4C22×D8312yes—
707#124C2×Dic8318yescomplemented
708#123C2×Dic83116yescomplemented
709C22⋊Q8C2×Dic8318yescomplemented
710#121C2×Dic8318yes—
711#121C2×Dic83116yescomplemented
712#120C2×Dic83116yescomplemented
713C4×Q8—3322no—
714C4×Q8—3322no—
715C4×D4—3324no—
716C4×D4—3322no—
717C4×D4—3322no—
718C4×D4C2×Dic8318yescomplemented
719C4×D4C2×Dic8318yescomplemented
720#117—3322no—
721#117—3324no—
722#117—3322no—
723#117—3322no—
724C2×C4⋊C4—3322no—
725C2×C4⋊C4—832no—
726C2×C4⋊C4—831no—
727C2×C4⋊C4—831no—
728C2×C4⋊C4—832no—
729C2×C4⋊C4—831no—
730C2×C4⋊C4—831no—
731C2×C4⋊C4—832no—
732C2×C4⋊C4—832no—
733C2×C4⋊C4—831no—
734C2×C4⋊C4—831no—
735C2×C4⋊C4—831no—
736C2×C4⋊C4—831no—
737C2×C4⋊C4—832no—
738C2×C4⋊C4—831no—
739C2×C4⋊C4—831no—
740C2×C4⋊C4C22×D8311yescharacteristic
741C2×C4⋊C4C22×D8311yescharacteristic
742C2×C4⋊C4C22×D8312yes—
743C2×C22⋊C4—3324no—
744C2×C22⋊C4—832no—
745C2×C22⋊C4—832no—
746C2×C22⋊C4—832no—
747C2×C22⋊C4—831no—
748C2×C22⋊C4—831no—
749C2×C22⋊C4—832no—
750C2×C22⋊C4—831no—
751C2×C22⋊C4—831no—
752C2×C22⋊C4—832no—
753C2×C22⋊C4—832no—
754C2×C22⋊C4—832no—
755C2×C22⋊C4—831no—
756C2×C22⋊C4—832no—
757C2×C22⋊C4—832no—
758C2×C22⋊C4—832no—
759C2×C22⋊C4—832no—
760C2×C22⋊C4—832no—
761C2×C22⋊C4—832no—
762C2×C22⋊C4—832no—
763C2×C22⋊C4—832no—
764C2×C22⋊C4—832no—
765C2×C22⋊C4—831no—
766C2×C22⋊C4—831no—
767C2×C22⋊C4—832no—
768C2×C22⋊C4—831no—
769C2×C22⋊C4C2×Dic83116yescomplemented
770C2×C22⋊C4C22×D8311yescharacteristic
771C2×C22⋊C4C22×D8312yes—
772C2×C22⋊C4C22×D8312yes—
773C2×C22⋊C4C22×D8312yes—
774C2×C22⋊C4C22×D8312yes—
775C2×C22⋊C4C22×D8311yescharacteristic
776C2×C22⋊C4C22×D8312yes—
777C2×C42—832no—
778C2×C42—832no—
779C2×C42—832no—
780C2×C42—832no—
781C2×C42—832no—
782C2×C42—831no—
783C2×C42—831no—
784C2×C42—831no—
785C2×C42—832no—
786C2×C42—831no—
787C2×C42—831no—
788C2×C42—831no—
789C2×C42—831no—
790C2×C42—831no—
791C2×C42C22×D8311yescharacteristic
792#95—832no—
793#95—831no—
794#95—831no—
795#95—831no—
796#95—831no—
797#95—832no—
798#95—831no—
799#95—832no—
800#95—832no—
801#95—832no—
802#95—832no—
803#95—832no—
804#95—831no—
805#95—832no—
806#95—832no—
807#95—832no—
808#95—832no—
809#95—832no—
810#95—832no—
811C24—42no—
812C24—42no—
813C24—42no—
814C24—42no—
815C24—42no—
816C24—42no—
817C24C22×Dic8318yes—
818C24C23×D8311yescharacteristic
819C24C23×D8312yes—
820C24C23×D8312yes—
821C24C23×D8311yescharacteristic
822#41—416no—
823C2×Q8—22no—
824C2×Q8—22no—
825C2×Q8C22×Dic8314yes—
826C2×D4—22no—
827C2×D4—22no—
828C2×D4—22no—
829C2×D4—22no—
830C2×D4—416no—
831C2×D4—42no—
832C2×D4—42no—
833C2×D4—42no—
834C2×D4—42no—
835C2×D4—42no—
836C2×D4—42no—
837C2×D4—41no—
838C2×D4—41no—
839C2×D4C22×Dic8314yes—
840C2×D4C22×Dic8314yes—
841C2×D4C22×Dic8314yes—
842C2×D4C22×Dic8318yes—
843C2×D4C22×Dic8318yes—
844C2×D4C22×Dic8318yes—
845C22×C4—22no—
846C22×C4—22no—
847C22×C4—22no—
848C22×C4—22no—
849C22×C4—42no—
850C22×C4—42no—
851C22×C4—42no—
852C22×C4—42no—
853C22×C4—3322no—
854C22×C4—3322no—
855C22×C4—3322no—
856C22×C4—3322no—
857C22×C4—3322no—
858C22×C4—3322no—
859C22×C4—3322no—
860C22×C4—3322no—
861C22×C4—831no—
862C22×C4—832no—
863C22×C4—831no—
864C22×C4—831no—
865C22×C4—832no—
866C22×C4—831no—
867C22×C4—831no—
868C22×C4—831no—
869C22×C4—832no—
870C22×C4—832no—
871C22×C4—831no—
872C22×C4—831no—
873C22×C4—1664no—
874C22×C4C22×Dic8314yes—
875C22×C4C22×Dic8314yes—
876C22×C4C22×Dic8318yes—
877C22×C4C22×Dic8318yes—
878C22×C4C23×D8311yescharacteristic
879C22×C4C23×D8311yescharacteristic
880C22×C4C23×D8312yes—
881C22×C4C23×D8312yes—
882C22×C4C23×D8311yescharacteristic
883C22×C4C23×D8311yescharacteristic
884C22×C4C23×D8311yescharacteristic
885C4⋊C4—3322no—
886C4⋊C4—3322no—
887C4⋊C4—3321no—
888C4⋊C4—3321no—
889C4⋊C4—3321no—
890C4⋊C4—3321no—
891C4⋊C4—3322no—
892C4⋊C4—3322no—
893C4⋊C4—3321no—
894C4⋊C4—3321no—
895C4⋊C4—1664no—
896C4⋊C4—1662no—
897C4⋊C4—1662no—
898C4⋊C4—1662no—
899C4⋊C4—1662no—
900C4⋊C4C22×Dic8314yes—
901C4⋊C4C22×Dic8314yes—
902C4⋊C4C22×Dic8318yes—
903C22⋊C4—3322no—
904C22⋊C4—3322no—
905C22⋊C4—3322no—
906C22⋊C4—3321no—
907C22⋊C4—3322no—
908C22⋊C4—3321no—
909C22⋊C4—3321no—
910C22⋊C4—3321no—
911C22⋊C4—3322no—
912C22⋊C4—3322no—
913C22⋊C4—3322no—
914C22⋊C4—3321no—
915C22⋊C4—3322no—
916C22⋊C4—3322no—
917C22⋊C4—3321no—
918C22⋊C4—3322no—
919C22⋊C4—3322no—
920C22⋊C4—3322no—
921C22⋊C4—3322no—
922C22⋊C4—3322no—
923C22⋊C4—3322no—
924C22⋊C4—3322no—
925C22⋊C4—1662no—
926C22⋊C4—1664no—
927C22⋊C4—1662no—
928C22⋊C4C22×Dic8314yes—
929C22⋊C4C22×Dic8318yes—
930C22⋊C4C22×Dic8318yes—
931C22⋊C4C22×Dic8318yes—
932C22⋊C4C22×Dic8318yes—
933C22⋊C4C22×Dic8314yes—
934C22⋊C4C22×Dic8318yes—
935C42—3322no—
936C42—3322no—
937C42—3322no—
938C42—3322no—
939C42—3322no—
940C42—3321no—
941C42—3322no—
942C42—3321no—
943C42—3321no—
944C42—1662no—
945C42—1662no—
946C42—1662no—
947C42—1662no—
948C42—1662no—
949C42C22×Dic8314yes—
950C23—22no—
951C23—21no—
952C23—22no—
953C23—21no—
954C23—21no—
955C23—21no—
956C23—21no—
957C23—22no—
958C23—22no—
959C23—21no—
960C23—22no—
961C23—22no—
962C23—22no—
963C23—21no—
964C23—22no—
965C23—21no—
966C23—21no—
967C23—22no—
968C23—22no—
969C23—22no—
970C23—22no—
971C23—21no—
972C23—21no—
973C23—21no—
974C23—48no—
975C23—48no—
976C23—48no—
977C23—84no—
978C23—84no—
979C23—84no—
980C23—84no—
981C23C23×Dic8312yes—
982C23C23×Dic8314yes—
983C23C23×Dic8314yes—
984C23C23×Dic8312yes—
985C23C24×D8311yescharacteristic
986Q8—28no—
987D4—28no—
988D4—28no—
989D4—48no—
990D4—48no—
991D4—44no—
992D4—48no—
993C2×C4—21no—
994C2×C4—22no—
995C2×C4—21no—
996C2×C4—22no—
997C2×C4—22no—
998C2×C4—21no—
999C2×C4—21no—
1000C2×C4—21no—
1001C2×C4—21no—
1002C2×C4—22no—
1003C2×C4—21no—
1004C2×C4—21no—
1005C2×C4—28no—
1006C2×C4—28no—
1007C2×C4—48no—
1008C2×C4—48no—
1009C2×C4—832no—
1010C2×C4—6644no—
1011C2×C4—6644no—
1012C2×C4—6644no—
1013C2×C4—1661no—
1014C2×C4—1662no—
1015C2×C4—1662no—
1016C2×C4—1662no—
1017C2×C4—1661no—
1018C2×C4—1661no—
1019C2×C4—1661no—
1020C2×C4—1662no—
1021C2×C4—1662no—
1022C2×C4—1662no—
1023C2×C4—1661no—
1024C2×C4—1661no—
1025C2×C4—1661no—
1026C2×C4—1661no—
1027C2×C4—1661no—
1028C2×C4—1661no—
1029C2×C4—1662no—
1030C2×C4—1661no—
1031C2×C4—1661no—
1032C2×C4—1662no—
1033C2×C4—1661no—
1034C2×C4—1661no—
1035C2×C4—1661no—
1036C2×C4—1661no—
1037C2×C4—1661no—
1038C2×C4—1662no—
1039C2×C4—1661no—
1040C2×C4—1661no—
1041C2×C4—1661no—
1042C2×C4—1662no—
1043C2×C4—1662no—
1044C2×C4—1662no—
1045C2×C4—1661no—
1046C2×C4—1661no—
1047C2×C4—1661no—
1048C2×C4C23×Dic8312yes—
1049C2×C4C23×Dic8312yes—
1050C2×C4C23×Dic8314yes—
1051C2×C4C23×Dic8312yes—
1052C2×C4C23×Dic8314yes—
1053C2×C4C23×Dic8312yes—
1054C2×C4C23×Dic8312yes—
1055C2×C4#1458183712yes—
1056C2×C4#1458183712yes—
1057C22—22no—
1058C22—22no—
1059C22—24no—
1060C22—24no—
1061C22—22no—
1062C22—22no—
1063C22—24no—
1064C22—24no—
1065C22—24no—
1066C22—22no—
1067C22—24no—
1068C22—22no—
1069C22—41no—
1070C22—42no—
1071C22—42no—
1072C22—41no—
1073C22—41no—
1074C22—42no—
1075C22—41no—
1076C22—42no—
1077C22—41no—
1078C22—42no—
1079C22—42no—
1080C22—41no—
1081C22—42no—
1082C22—41no—
1083C22—42no—
1084C22—41no—
1085C22—816no—
1086C22C24×Dic8311yescharacteristic
1087C22H(5,𝔽2)×D8311yescharacteristic
1088C22C2×#1458183711yescharacteristic
1089C22C2×#1458183711yescharacteristic
1090C22#1912853611yescharacteristic
1091C22#1912853711yescharacteristic
1092C22#1912853711yescharacteristic
1093C4—22no—
1094C4—22no—
1095C4—24no—
1096C4—22no—
1097C4—22no—
1098C4—24no—
1099C4—3321no—
1100C4—3321no—
1101C4—3321no—
1102C4—3322no—
1103C4—3322no—
1104C4—3322no—
1105C4—3321no—
1106C4—3321no—
1107C4—3322no—
1108C4—3321no—
1109C4—3321no—
1110C4—1662no—
1111C4#1912817614yes—
1112C2—42no—
1113C2—44no—
1114C2—44no—
1115C2—42no—
1116C2C2×#1912817611yescharacteristic
1117C2#2492066611yescharacteristic
1118C2H(5,𝔽2)×Dic8311yescharacteristic
1119C2#2492182711yescharacteristic
1120C2#2492188311yescharacteristic
1121C2#2492197211yescharacteristic
1122C2#2492204111yescharacteristic
subgroupG/H
center, FrattiniC23C24×D83
commutatorC22×C83C24×C4
Fitting, prime radicalC2×#546×C83C2
socle, cosocleC23×C83C25
hypercenterC2×#546D83
hypocenterC83#34495
LCSG ▷ C22×C83 ▷ C83
UCSC1 ◁ C23 ◁ C2×#546

Complements

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

NH ≅ G/Ntype
1. #24910611C2semidirect
2. #24910604C2semidirect
3. #24910538C2semidirect
4. #24910505C2semidirect
5. #24910494C2semidirect
6. #24910483C2semidirect
7. #24910436C2semidirect
8. #24910392C2semidirect
9. #24910312C2semidirect
10. #24910304C2semidirect
11. D4×C22⋊Dic83C2semidirect
12. #24910257C2semidirect
13. #24910230C2semidirect
14. #24910158C2semidirect
15. #24910147C2semidirect
16. #24910124C2semidirect
17. #24910061C2semidirect
18. #24910055C2semidirect
19. #24910045C2semidirect
20. #124×Dic83C2semidirect
21. #24909928C2semidirect
22. #24909928C2semidirect
24. C2×Q8×Dic83C22semidirect
25. C2×Q8×Dic83C22semidirect
28. C2×D4×Dic83C22semidirect
31. C2×#14581751C22semidirect
32. C2×#14581751C22semidirect
33. C22×C4⋊Dic83C22semidirect
35. #19127608C22semidirect
36. #19127608C22semidirect
47. #19127604C22semidirect
48. #19127604C22semidirect
49. #19127604C22semidirect
50. #19127600C22semidirect
51. #19127600C22semidirect
52. #19127600C22semidirect
53. #19127600C22semidirect
54. #19127600C22semidirect
62. #19127594C22semidirect
63. #19127594C22semidirect
64. #19127594C22semidirect
65. #19127594C22semidirect
66. #19127594C22semidirect
67. #19127594C22semidirect
68. #19127594C22semidirect
69. #19127594C22semidirect
70. #19127594C22semidirect
71. #19127594C22semidirect
72. #19127594C22semidirect
73. #19127594C22semidirect
74. #19127587C22semidirect
75. #19127587C22semidirect
76. #19127587C22semidirect
80. #19127581C22semidirect
81. #19127581C22semidirect
82. #19127581C22semidirect
83. #19127581C22semidirect
84. #19127576C22semidirect
85. #19127576C22semidirect
86. #19127576C22semidirect
87. #19127567C22semidirect
88. #19127564C22semidirect
90. #19127561C22semidirect
91. #19127561C22semidirect
92. #19127561C22semidirect
93. #19127561C22semidirect
97. C4⋊C4×Dic83C22semidirect
98. C4⋊C4×Dic83C22semidirect
99. C4⋊C4×Dic83C22semidirect
100. C4×C4⋊Dic83C22semidirect
101. C4×C4⋊Dic83C22semidirect
102. C22⋊C4×Dic83C22semidirect
103. C22⋊C4×Dic83C22semidirect
104. C22⋊C4×Dic83C22semidirect
105. C22⋊C4×Dic83C22semidirect
107. C4×C22⋊Dic83C22semidirect
108. C4×C22⋊Dic83C22semidirect
109. C4×C22⋊Dic83C22semidirect
110. C4×C22⋊Dic83C22semidirect
111. C42×Dic83C22semidirect
114. #546×C83C4semidirect
214. C2×#41×C83C2×C4semidirect
218. C22×D4×C83C2×C4semidirect
229. #124×C83C2×C4semidirect
230. #123×C83C2×C4semidirect
231. C22⋊Q8×C83C2×C4semidirect
233. #121×C83C2×C4semidirect
234. #120×C83C2×C4semidirect
235. C4×D4×C83C2×C4semidirect
236. C4×D4×C83C2×C4semidirect
240. C2×C22⋊C4×C83C2×C4semidirect
585. C83#34495semidirect
588. #546Dic83semidirect
689. C2×#41C2×Dic83semidirect
693. C22×D4C2×Dic83semidirect
707. #124C2×Dic83semidirect
708. #123C2×Dic83semidirect
709. C22⋊Q8C2×Dic83semidirect
711. #121C2×Dic83semidirect
712. #120C2×Dic83semidirect
718. C4×D4C2×Dic83semidirect
719. C4×D4C2×Dic83semidirect
769. C2×C22⋊C4C2×Dic83semidirect

Maximal subgroups

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

subgroupindex
#249106112
#249106042
#249105382
#249105052
#249104942
#249104832
#249104362
#249103922
#249103122
#249103042
D4×C22⋊Dic832
#249102572
#249102302
#249101582
#249101472
#249101242
#249100612
#249100552
#249100452
#124×Dic832
#249099282
C2×#546×C832
#3449583