Finite Group Databasebeta

← #29647550

Subgroups — #29647550

Order 15616.

996 conjugacy classes of subgroups.

The subgroup lattice has 952 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459856C211yesmaximal, characteristic
2#21454850C211yesmaximal, characteristic, complemented
3#21448448C211yesmaximal, characteristic, complemented
4#21444393C211yesmaximal, characteristic, complemented
5#21444392C211yesmaximal, characteristic, complemented
6#21444381C211yesmaximal, characteristic, complemented
7#21444368C211yesmaximal, characteristic, complemented
8#21444362C211yesmaximal, characteristic, complemented
9#21444354C211yesmaximal, characteristic, complemented
10#21444351C211yesmaximal, characteristic, complemented
11#21444337C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#21444307C211yesmaximal, characteristic, complemented
14#328×D61C211yesmaximal, characteristic, complemented
15C61×#1516C211yesmaximal, characteristic, complemented
16#16840480C411yescharacteristic, complemented
17#16840471—21no—
18#16840454C411yescharacteristic, complemented
19#16840451C411yescharacteristic, complemented
20#16840443—21no—
21#16840441—21no—
22#16840425C411yescharacteristic, complemented
23#16840419C411yescharacteristic, complemented
24#16840418C411yescharacteristic, complemented
25#16840412C411yescharacteristic, complemented
26#16840411C411yescharacteristic, complemented
27#16840399—21no—
28#16840380—21no—
29#16840355—21no—
30#16840354—21no—
31#16840314C2211yescharacteristic
32#16840293C2211yescharacteristic
33#16840272C2211yescharacteristic
34C2×#14519756C2211yescharacteristic
35C22⋊Q8×D61C2211yescharacteristic
36#16840241—21no—
37C2×C4×C22⋊D61C2211yescharacteristic
38#16839837—21no—
39#16839836—21no—
40#16839833—21no—
41C8×C22⋊D61—21no—
42#16839816C2211yescharacteristic
43#16839812C2211yescharacteristic
44#16839726C2211yescharacteristic
45#16839724C2211yescharacteristic
46C22⋊C8×D61C2211yescharacteristic
47#16839650—21no—
48#16839649—21no—
49#16839638—21no—
50#16839636—21no—
51#16839629C2211yescharacteristic
52#16839626C2211yescharacteristic
53#16839622C2211yescharacteristic
54#16839609C2211yescharacteristic
55#95×D61C2211yescharacteristic
56#16839500C2211yescharacteristic
57#16839500C2211yescharacteristic
58#16839500C2211yescharacteristic
59#16839500C2211yescharacteristic
60#16839499C2211yescharacteristic
61#16839499C2211yescharacteristic
62#16839498C2211yescharacteristic
63#16839498C2211yescharacteristic
64#16839498C2211yescharacteristic
65#16839498C2211yescharacteristic
66#16839496C2211yescharacteristic
67#16839496C2211yescharacteristic
68C61×#525C2211yescharacteristic
69C2×C22⋊C8×C61C2211yescharacteristic
70C61×#381C2211yescharacteristic
71C61×#328C2211yescharacteristic
72C61×#328C2211yescharacteristic
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758224—21no—
76C2×#11758224C2×C411yescharacteristic
77C22×Dic122C2×C411yescharacteristic, complemented
78C2×Q8×D61C2×C411yescharacteristic
79C22×C22⋊D61D411yescharacteristic
80C22×C4×D61—21no—
81C22×C4×D61C2311yescharacteristic
82C2×#11758194—21no—
83C2×#11758189—21no—
84C2×C8×D61—21no—
85#14519776—21no—
86#14519776C2×C411yescharacteristic, complemented
87#14519775C2×C411yescharacteristic, complemented
88#14519772—21no—
89#14519771—21no—
90#14519770—21no—
91#14519770—21no—
92#14519770—21no—
93#14519769—21no—
94#14519768—21no—
95#14519768C2×C411yescharacteristic, complemented
96#14519767—21no—
97#14519764—21no—
98#14519764C2×C411yescharacteristic, complemented
99#14519763—21no—
100#14519763—21no—
101#14519761—21no—
102#14519760—21no—
103#14519759—21no—
104#14519759—21no—
105#14519759—21no—
106#14519758—21no—
107#14519758—21no—
108#14519758—21no—
109#14519757C2×C411yescharacteristic
110#14519757C2×C411yescharacteristic
111#14519756—21no—
112#14519756—21no—
113#14519756—21no—
114#14519756C2×C411yescharacteristic, complemented
115#14519756C2×C411yescharacteristic, complemented
116#14519756C2311yescharacteristic
117#14519756C2311yescharacteristic
118#14519755—21no—
119#14519755—21no—
120#14519754—21no—
121#14519754—21no—
122#14519754—21no—
123#14519754—21no—
124#14519754—21no—
125#14519753C2×C411yescharacteristic
126#14519749—21no—
127#14519749—21no—
128#14519748—21no—
129#14519748C2×C411yescharacteristic
130#14519745—21no—
131Q8×Dic61C2×C411yescharacteristic, complemented
132C4×Dic122—21no—
133#14519742—21no—
134#14519742C2×C411yescharacteristic, complemented
135#14519742C2×C411yescharacteristic, complemented
136D4×Dic61—21no—
137D4×Dic61—21no—
138D4×Dic61—21no—
139D4×Dic61C2×C411yescharacteristic, complemented
140C4×C22⋊D61—21no—
141C4×C22⋊D61C2×C411yescharacteristic
142C4×C22⋊D61C2×C411yescharacteristic
143C4×C22⋊D61C2×C411yescharacteristic
144C4×C22⋊D61C2×C411yescharacteristic
145C4×C22⋊D61D411yescharacteristic
146C4×C22⋊D61D411yescharacteristic
147C4×C22⋊D61D411yescharacteristic
148C4×C22⋊D61D411yescharacteristic
149#14519737—21no—
150#14519737—21no—
151#14519735C2×C411yescharacteristic
152#14519734—21no—
153#14519733—21no—
154#14519733—21no—
155#14519733—21no—
156C2×C4⋊Dic61—21no—
157C2×C4⋊Dic61C2×C411yescharacteristic, complemented
158C2×#11758196—21no—
159C2×#11758196—21no—
160C2×#11758196—21no—
161C2×#11758196D411yescharacteristic
162C4⋊C4×D61—21no—
163C4⋊C4×D61C2×C411yescharacteristic
164C2×C22⋊Dic61—21no—
165C2×C22⋊Dic61—21no—
166C2×C22⋊Dic61D411yescharacteristic
167C2×#11758198—21no—
168C2×#11758198D411yescharacteristic
169C22⋊C4×D61—21no—
170C2×C4×Dic61—21no—
171C2×C4×Dic61C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174C22⋊#92418—21no—
175C22⋊#92418C2311yescharacteristic
176C22⋊#92418C2311yescharacteristic
177#14519689—21no—
178#14519689—21no—
179#14519687—21no—
180C8×Dic61—21no—
181#14519684—21no—
182#14519684—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684C2311yescharacteristic
186#14519684C2311yescharacteristic
187C2×#41×C61C2×C411yescharacteristic, complemented
188C23×C4×C61C2311yescharacteristic
189C22×C8×C61—21no—
190#123×C61—21no—
191C22⋊Q8×C61C2×C411yescharacteristic, complemented
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2×C411yescharacteristic, complemented
194#121×C61C2311yescharacteristic
195#120×C61—21no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61C2×C411yescharacteristic, complemented
199C2×C22⋊C4×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61C2311yescharacteristic
202C22⋊C8×C61C2311yescharacteristic
203#95×C61—21no—
204#95×C61C2311yescharacteristic
205#95×C61C2311yescharacteristic
206C24×C61C2×D411yescharacteristic
207C23×D61C2×D411yescharacteristic
208#41×C61—81no—
209C2×Q8×C61C22×C411yescharacteristic
210C2×D4×C61—21no—
211C2×D4×C61—21no—
212C2×D4×C61—21no—
213C2×D4×C61C22×C411yescharacteristic
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61—21no—
217C22×C4×C61—81no—
218C22×C4×C61C22×C411yescharacteristic
219C22×C4×C61C22×C411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C22×C4×C61C2411yescharacteristic
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—42no—
227C2×C22⋊D61C22⋊C411yescharacteristic
228C2×C22⋊D61C22⋊C411yescharacteristic
229C2×C22⋊D61C22⋊C411yescharacteristic
230C2×C22⋊D61C22⋊C411yescharacteristic
231C22×Dic61—21no—
232C22×Dic61—21no—
233C22×Dic61—21no—
234C22×Dic61—21no—
235C22×Dic61—21no—
236C22×Dic61—21no—
237C22×Dic61C2×D411yescharacteristic
238C22×Dic61C2×D411yescharacteristic
239C22×Dic61C2×D411yescharacteristic
240Q8×D61—81no—
241#11758224—44no—
242#11758224—81no—
243C2×C4×D61—21no—
244C2×C4×D61—21no—
245C2×C4×D61—42no—
246C2×C4×D61—81no—
247C2×C4×D61—81no—
248C2×C4×D61—81no—
249C2×C4×D61C22×C411yescharacteristic
250C2×C4×D61C22×C411yescharacteristic
251C2×C4×D61C2×D411yescharacteristic
252C2×C4×D61C2×D411yescharacteristic
253C2×Dic122—21no—
254C2×Dic122—21no—
255C2×Dic122—21no—
256C2×Dic122—81no—
257C2×Dic122C22×C411yescharacteristic
258C2×Dic122C22×C411yescharacteristic
259C2×C8×C61—21no—
260C2×C8×C61—21no—
261C2×C8×C61—81no—
262C4⋊C4×C61—21no—
263C4⋊C4×C61—21no—
264C4⋊C4×C61C22×C411yescharacteristic
265C4⋊C4×C61C22×C411yescharacteristic
266C22⋊C4×C61—21no—
267C22⋊C4×C61—21no—
268C22⋊C4×C61—21no—
269C22⋊C4×C61—21no—
270C22⋊C4×C61—21no—
271C22⋊C4×C61—81no—
272C42×C61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61—21no—
277C22⋊Dic61—21no—
278C22⋊Dic61—21no—
279C22⋊Dic61—21no—
280C22⋊Dic61—21no—
281C22⋊Dic61—81no—
282C22⋊Dic61C22⋊C411yescharacteristic
283C22⋊Dic61C22⋊C411yescharacteristic
284C22⋊Dic61C22⋊C411yescharacteristic
285C22⋊Dic61C22⋊C411yescharacteristic
286#11758198—21no—
287#11758198—21no—
288#11758198—21no—
289#11758198—21no—
290#11758198—42no—
291#11758198C22⋊C411yescharacteristic
292#11758198C22⋊C411yescharacteristic
293#11758198C22⋊C411yescharacteristic
294#11758198C22⋊C411yescharacteristic
295C4⋊Dic61—21no—
296C4⋊Dic61—21no—
297C4⋊Dic61—21no—
298C4⋊Dic61—21no—
299C4⋊Dic61—21no—
300C4⋊Dic61—81no—
301C4⋊Dic61C22×C411yescharacteristic
302C4⋊Dic61C22×C411yescharacteristic
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309#11758196—21no—
310#11758196—21no—
311#11758196—21no—
312#11758196—21no—
313#11758196—21no—
314#11758196—21no—
315#11758196—81no—
316#11758196C22⋊C411yescharacteristic
317#11758196C22⋊C411yescharacteristic
318#11758196C22⋊C411yescharacteristic
319#11758196C22⋊C411yescharacteristic
320C4×Dic61—21no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—81no—
325C4×Dic61C22×C411yescharacteristic
326C4×Dic61C22×C411yescharacteristic
327C4×Dic61C2×D411yescharacteristic
328C4×Dic61C2×D411yescharacteristic
329#11758194—81no—
330C2×#92418—21no—
331C2×#92418—21no—
332#11758189—81no—
333C8×D61—81no—
334C23×C61—21no—
335C23×C61—21no—
336C23×C61—21no—
337C23×C61—41no—
338C23×C61—41no—
339C23×C61C2×C22⋊C411yescharacteristic
340C23×C61C2×C22⋊C411yescharacteristic
341C23×C61C22×D411yescharacteristic
342C22×D61—21no—
343C22×D61—21no—
344C22×D61—22no—
345C22×D61—41no—
346C22×D61C2×C22⋊C411yescharacteristic
347C22×D61C2×C22⋊C411yescharacteristic
348Q8×C61—41no—
349D4×C61—41no—
350D4×C61—42no—
351D4×C61—41no—
352D4×C61—41no—
353D4×C61—81no—
354C2×C4×C61—21no—
355C2×C4×C61—21no—
356C2×C4×C61—21no—
357C2×C4×C61—41no—
358C2×C4×C61—41no—
359C2×C4×C61—41no—
360C2×C4×C61—41no—
361C2×C4×C61—41no—
362C2×C4×C61—41no—
363C2×C4×C61—41no—
364C2×C4×C61—41no—
365C2×C4×C61—41no—
366C2×C4×C61—41no—
367C2×C4×C61—41no—
368C2×C4×C61—41no—
369C2×C4×C61—81no—
370C2×C4×C61C2×C22⋊C411yescharacteristic
371C2×C4×C61C2×C22⋊C411yescharacteristic
372C2×C4×C61C23×C411yescharacteristic
373C2×C4×C61C22×D411yescharacteristic
374C22⋊D61—22no—
375C22⋊D61—22no—
376C22⋊D61—41no—
377C22⋊D61—41no—
378C22⋊D61—42no—
379C22⋊D61—81no—
380C2×Dic61—21no—
381C2×Dic61—21no—
382C2×Dic61—21no—
383C2×Dic61—21no—
384C2×Dic61—21no—
385C2×Dic61—21no—
386C2×Dic61—41no—
387C2×Dic61—41no—
388C2×Dic61—42no—
389C2×Dic61—42no—
390C2×Dic61—41no—
391C2×Dic61—41no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—81no—
397C2×Dic61—81no—
398C2×Dic61C2×C22⋊C411yescharacteristic
399C2×Dic61C2×C22⋊C411yescharacteristic
400C2×Dic61C2×C22⋊C411yescharacteristic
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C4×D61—41no—
405C4×D61—41no—
406C4×D61—41no—
407C4×D61—41no—
408C4×D61—42no—
409C4×D61—81no—
410C4×D61—84no—
411Dic122—42no—
412Dic122—41no—
413Dic122—41no—
414Dic122—81no—
415Dic122—81no—
416C8×C61—41no—
417C8×C61—41no—
418#92418—41no—
419#92418—41no—
420#17598—611nomaximal, Sylow
421C22×C61—21no—
422C22×C61—21no—
423C22×C61—21no—
424C22×C61—21no—
425C22×C61—21no—
426C22×C61—21no—
427C22×C61—21no—
428C22×C61—21no—
429C22×C61—41no—
430C22×C61—41no—
431C22×C61—41no—
432C22×C61—81no—
433C22×C61—81no—
434C22×C61C22×C22⋊C411yescharacteristic
435C22×C61#57711yescharacteristic
436C22×C61#57811yescharacteristic
437C2×D61—21no—
438C2×D61—21no—
439C2×D61—21no—
440C2×D61—21no—
441C2×D61—21no—
442C2×D61—42no—
443C2×D61—42no—
444C2×D61#42112yes—
445C4×C61—21no—
446C4×C61—21no—
447C4×C61—21no—
448C4×C61—21no—
449C4×C61—41no—
450C4×C61—41no—
451C4×C61—41no—
452C4×C61—81no—
453C4×C61—81no—
454Dic61—21no—
455Dic61—21no—
456Dic61—21no—
457Dic61—21no—
458Dic61—21no—
459Dic61—21no—
460Dic61—41no—
461Dic61—41no—
462Dic61—41no—
463Dic61—41no—
464Dic61—81no—
465Dic61—81no—
466#3520—611no—
467#2974—611no—
468#2318—611no—
469#1521—611no—
470#1520—611no—
471#1518—611no—
472#1516D6111yescharacteristic, complemented
473#1515—611no—
474#1513—611no—
475#1512—611no—
476#1511—611no—
477#1508—611no—
478#1504—611no—
479#1501—611no—
480C2×#328—611no—
481C2×C61—21no—
482C2×C61—21no—
483C2×C61—41no—
484C2×C61—41no—
485C2×C61—81no—
486C2×C61#288311yescharacteristic
487C2×C61#289811yescharacteristic
488C2×C61C2×#42111yescharacteristic
489D61—22no—
490D61—41no—
491#556—611no—
492#554—1221no—
493#552—611no—
494#552—611no—
495#551—1221no—
496#551—1221no—
497D4×Q8—611no—
498#548—611no—
499#548—611no—
500#547—611no—
501#547—611no—
502#546—1221no—
503#542—1221no—
504#539—1221no—
505#539—1221no—
506#533—611no—
507#529—611no—
508#525—611no—
509#525C2×D6111yescharacteristic
510C2×C22⋊Q8—611no—
511C2×C22⋊Q8—611no—
512#520—1221no—
513C2×C4×D4—611no—
514#436—1221no—
515#435—1221no—
516#435—1221no—
517C8×D4—1221no—
518#432—611no—
519#431—611no—
520#407—611no—
521#407—611no—
522C2×C22⋊C8—611no—
523C2×C22⋊C8C2×D6111yescharacteristic
524#388—1221no—
525#387—1221no—
526#386—1221no—
527#385—1221no—
528#383—611no—
529#382—611no—
530#381C2×D6111yescharacteristic
531#380—611no—
532C4×C22⋊C4—611no—
533C2×#95—611no—
534#328—611no—
535#328—611no—
536#328—611no—
537#328—611no—
538#328—611no—
539#328—611no—
540#328—611no—
541#328—611no—
542#328—611no—
543#328—611no—
544#328C2×D6111yescharacteristic
545#328C2×D6111yescharacteristic
546#327—611no—
547#327—611no—
548#327C2×D6111yescharacteristic
549#327C2×D6111yescharacteristic
550C61#1759811yescharacteristic, complemented, Sylow
551C2×#41—611no—
552C2×#41—1221no—
553C2×#41C4×D6111yescharacteristic, complemented
554C22×Q8—611no—
555C22×Q8—611no—
556C22×D4—611no—
557C23×C4—611no—
558C23×C4—1221no—
559C23×C4C22×D6111yescharacteristic
560C2×M16—1221no—
561C2×M16—1221no—
562C22×C8—21no—
563C22×C8—1221no—
564C4⋊Q8—611no—
565C4⋊Q8—611no—
566C4⋊Q8—1221no—
567#126—1221no—
568#126—1221no—
569#126—1221no—
570#126—1221no—
571#126—1221no—
572#125—611no—
573#125—1221no—
574#125—1221no—
575#125—1221no—
576#124—611no—
577#124—1221no—
578#124—1221no—
579#124—1221no—
580#123—21no—
581#123—1221no—
582#123—1221no—
583#123—1221no—
584#123—1221no—
585#123—1221no—
586#123—1221no—
587#123—1221no—
588#123—1221no—
589C22⋊Q8—611no—
590C22⋊Q8—611no—
591C22⋊Q8—611no—
592C22⋊Q8—611no—
593C22⋊Q8—611no—
594C22⋊Q8—611no—
595C22⋊Q8—611no—
596C22⋊Q8—1221no—
597C22⋊Q8—1221no—
598C22⋊Q8—1221no—
599C22⋊Q8—1221no—
600C22⋊Q8—1221no—
601C22⋊Q8—1221no—
602C22⋊Q8—1221no—
603C22⋊Q8—1221no—
604C22⋊Q8—1221no—
605C22⋊Q8—1221no—
606C22⋊Q8C4×D6111yescharacteristic, complemented
607C22⋊Q8C22×D6111yescharacteristic
608#121—611no—
609#121—1221no—
610#121—1221no—
611#121—1221no—
612#121C4×D6111yescharacteristic, complemented
613#121C22×D6111yescharacteristic
614#120—21no—
615#120—1221no—
616C4×Q8—611no—
617C4×Q8—611no—
618C4×Q8—611no—
619C4×Q8—1221no—
620C4×Q8—1221no—
621C4×D4—21no—
622C4×D4—21no—
623C4×D4—611no—
624C4×D4—611no—
625C4×D4—611no—
626C4×D4—611no—
627C4×D4—611no—
628C4×D4—611no—
629C4×D4—611no—
630C4×D4—611no—
631C4×D4—611no—
632C4×D4—1221no—
633C4×D4—1221no—
634C4×D4—1221no—
635C4×D4—1221no—
636C4×D4—1221no—
637C4×D4—1221no—
638#117—611no—
639#117—1221no—
640#117—1221no—
641#117—1221no—
642#117—1221no—
643#117C4×D6111yescharacteristic, complemented
644C2×C4⋊C4—611no—
645C2×C4⋊C4—611no—
646C2×C4⋊C4—611no—
647C2×C4⋊C4—1221no—
648C2×C4⋊C4—1221no—
649C2×C4⋊C4—1221no—
650C2×C4⋊C4—1221no—
651C2×C4⋊C4—1221no—
652C2×C22⋊C4—21no—
653C2×C22⋊C4—611no—
654C2×C22⋊C4—611no—
655C2×C22⋊C4—1221no—
656C2×C22⋊C4—1221no—
657C2×C22⋊C4—1221no—
658C2×C22⋊C4—1221no—
659C2×C42—611no—
660C2×C42—1221no—
661C4⋊C8—1221no—
662C4⋊C8—1221no—
663C22⋊C8—21no—
664C22⋊C8—611no—
665C22⋊C8—611no—
666C22⋊C8—1221no—
667C22⋊C8—1221no—
668C22⋊C8—1221no—
669C22⋊C8C22×D6111yescharacteristic
670C22⋊C8C22×D6111yescharacteristic
671#97—1221no—
672C4×C8—1221no—
673#95—21no—
674#95—611no—
675#95—611no—
676#95—1221no—
677#95—1221no—
678#95—1221no—
679#95—1221no—
680#95C22×D6111yescharacteristic
681#95C22×D6111yescharacteristic
682C24—611no—
683C24D4×D6111yescharacteristic
684#41—81no—
685#41—4881no—
686#41—2444no—
687C2×Q8—611no—
688C2×Q8—611no—
689C2×Q8—1221no—
690C2×Q8—1221no—
691C2×Q8—1221no—
692C2×Q8—4881no—
693C2×Q8—4881no—
694C2×Q8C2×C4×D6111yescharacteristic
695C2×D4—21no—
696C2×D4—21no—
697C2×D4—21no—
698C2×D4—611no—
699C2×D4—611no—
700C2×D4—611no—
701C2×D4—611no—
702C2×D4—1221no—
703C2×D4—1221no—
704C2×D4—2442no—
705C2×D4C2×C4×D6111yescharacteristic
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—81no—
710C22×C4—611no—
711C22×C4—611no—
712C22×C4—611no—
713C22×C4—611no—
714C22×C4—611no—
715C22×C4—611no—
716C22×C4—611no—
717C22×C4—1221no—
718C22×C4—1221no—
719C22×C4—1221no—
720C22×C4—1221no—
721C22×C4—1221no—
722C22×C4—1221no—
723C22×C4—1221no—
724C22×C4—1221no—
725C22×C4—4881no—
726C22×C4—4881no—
727C22×C4—4881no—
728C22×C4—2442no—
729C22×C4C2×C4×D6111yescharacteristic
730C22×C4C2×C4×D6111yescharacteristic
731C22×C4D4×D6111yescharacteristic
732C22×C4D4×D6111yescharacteristic
733C22×C4D4×D6111yescharacteristic
734C22×C4C23×D6111yescharacteristic
735M16—4881no—
736M16—4881no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—81no—
740C2×C8—1221no—
741C2×C8—1221no—
742C2×C8—4881no—
743C4⋊C4—21no—
744C4⋊C4—21no—
745C4⋊C4—611no—
746C4⋊C4—611no—
747C4⋊C4—611no—
748C4⋊C4—611no—
749C4⋊C4—611no—
750C4⋊C4—611no—
751C4⋊C4—1221no—
752C4⋊C4—1221no—
753C4⋊C4—1221no—
754C4⋊C4—1221no—
755C4⋊C4—1221no—
756C4⋊C4—1221no—
757C4⋊C4—1221no—
758C4⋊C4—1221no—
759C4⋊C4—1221no—
760C4⋊C4—1221no—
761C4⋊C4—1221no—
762C4⋊C4—1221no—
763C4⋊C4—1221no—
764C4⋊C4—1221no—
765C4⋊C4—1221no—
766C4⋊C4—1221no—
767C4⋊C4—1221no—
768C4⋊C4—4881no—
769C4⋊C4—4881no—
770C4⋊C4C2×C4×D6111yescharacteristic
771C4⋊C4C2×C4×D6111yescharacteristic
772C22⋊C4—21no—
773C22⋊C4—21no—
774C22⋊C4—21no—
775C22⋊C4—21no—
776C22⋊C4—21no—
777C22⋊C4—81no—
778C22⋊C4—611no—
779C22⋊C4—611no—
780C22⋊C4—611no—
781C22⋊C4—611no—
782C22⋊C4—611no—
783C22⋊C4—611no—
784C22⋊C4—611no—
785C22⋊C4—611no—
786C22⋊C4—1221no—
787C22⋊C4—1221no—
788C22⋊C4—1221no—
789C22⋊C4—1221no—
790C22⋊C4—1221no—
791C22⋊C4—1221no—
792C22⋊C4—1221no—
793C22⋊C4—1221no—
794C22⋊C4—1221no—
795C22⋊C4—1221no—
796C22⋊C4—1221no—
797C22⋊C4—1221no—
798C22⋊C4—4881no—
799C22⋊C4—2442no—
800C42—21no—
801C42—611no—
802C42—611no—
803C42—611no—
804C42—611no—
805C42—1221no—
806C42—1221no—
807C42—1221no—
808C42—1221no—
809C42—4881no—
810C23—21no—
811C23—21no—
812C23—21no—
813C23—41no—
814C23—41no—
815C23—611no—
816C23—611no—
817C23—1222no—
818C23—1221no—
819C23—1221no—
820C23—2441no—
821C23C22⋊C4×D6111yescharacteristic
822C23C22⋊C4×D6111yescharacteristic
823C23C2×D4×D6111yescharacteristic
824Q8—41no—
825Q8—4881no—
826Q8—4881no—
827Q8—2441no—
828Q8—2441no—
829Q8—2442no—
830D4—41no—
831D4—42no—
832D4—41no—
833D4—41no—
834D4—81no—
835D4—1222no—
836D4—1222no—
837D4—4881no—
838D4—2441no—
839D4—2441no—
840D4—2442no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—81no—
857C2×C4—611no—
858C2×C4—611no—
859C2×C4—611no—
860C2×C4—611no—
861C2×C4—611no—
862C2×C4—611no—
863C2×C4—1221no—
864C2×C4—1221no—
865C2×C4—1221no—
866C2×C4—1221no—
867C2×C4—1221no—
868C2×C4—1221no—
869C2×C4—4881no—
870C2×C4—4884no—
871C2×C4—4881no—
872C2×C4—4881no—
873C2×C4—2441no—
874C2×C4—2441no—
875C2×C4—2441no—
876C2×C4—2441no—
877C2×C4—2442no—
878C2×C4—2441no—
879C2×C4—2441no—
880C2×C4—2442no—
881C2×C4—2441no—
882C2×C4—2441no—
883C2×C4—2441no—
884C2×C4—2441no—
885C2×C4—2441no—
886C2×C4—2441no—
887C2×C4—2442no—
888C2×C4C22⋊C4×D6111yescharacteristic
889C2×C4C22⋊C4×D6111yescharacteristic
890C2×C4C22×C4×D6111yescharacteristic
891C2×C4C2×D4×D6111yescharacteristic
892C8—41no—
893C8—41no—
894C8—2441no—
895C8—2441no—
896C22—21no—
897C22—21no—
898C22—21no—
899C22—21no—
900C22—21no—
901C22—21no—
902C22—21no—
903C22—21no—
904C22—41no—
905C22—41no—
906C22—41no—
907C22—81no—
908C22—81no—
909C22—612no—
910C22—1221no—
911C22—1221no—
912C22—1221no—
913C22—1221no—
914C22—1221no—
915C22—2442no—
916C22—2442no—
917C22C2×C22⋊C4×D6111yescharacteristic
918C22#1684056911yescharacteristic
919C22#1684057611yescharacteristic
920C4—21no—
921C4—21no—
922C4—21no—
923C4—21no—
924C4—41no—
925C4—41no—
926C4—41no—
927C4—81no—
928C4—81no—
929C4—1221no—
930C4—1221no—
931C4—1221no—
932C4—1221no—
933C4—1221no—
934C4—1221no—
935C4—4881no—
936C4—4881no—
937C4—2441no—
938C4—2441no—
939C4—2441no—
940C4—2441no—
941C2—21no—
942C2—21no—
943C2—41no—
944C2—41no—
945C2—81no—
946C2—1222no—
947C2—2441no—
948C2#2145427711yescharacteristic
949C2#2145434811yescharacteristic
950C2#421×D6111yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1516C2
socleC22×C61C22×C22⋊C4
prime radical#21459856C2
cosocleC22×C4×C61C24
hypercenter#1516D61
hypocenterC61#17598
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1516

Complements

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

NH ≅ G/Ntype
2. #21454850C2semidirect
3. #21448448C2semidirect
4. #21444393C2semidirect
5. #21444392C2semidirect
6. #21444381C2semidirect
7. #21444368C2semidirect
8. #21444362C2semidirect
9. #21444354C2semidirect
10. #21444351C2semidirect
11. #21444337C2semidirect
12. #21444320C2semidirect
13. #21444307C2semidirect
14. #328×D61C2semidirect
15. C61×#1516C2semidirect
16. #16840480C4semidirect
18. #16840454C4semidirect
19. #16840451C4semidirect
22. #16840425C4semidirect
23. #16840419C4semidirect
24. #16840418C4semidirect
25. #16840412C4semidirect
26. #16840411C4semidirect
77. C22×Dic122C2×C4semidirect
86. #14519776C2×C4semidirect
87. #14519775C2×C4semidirect
95. #14519768C2×C4semidirect
98. #14519764C2×C4semidirect
114. #14519756C2×C4semidirect
115. #14519756C2×C4semidirect
131. Q8×Dic61C2×C4semidirect
134. #14519742C2×C4semidirect
135. #14519742C2×C4semidirect
139. D4×Dic61C2×C4semidirect
157. C2×C4⋊Dic61C2×C4semidirect
187. C2×#41×C61C2×C4semidirect
191. C22⋊Q8×C61C2×C4semidirect
193. #121×C61C2×C4semidirect
198. #117×C61C2×C4semidirect
472. #1516D61semidirect
550. C61#17598semidirect
553. C2×#41C4×D61semidirect
606. C22⋊Q8C4×D61semidirect
612. #121C4×D61semidirect
643. #117C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214598562
#214548502
#214484482
#214443932
#214443922
#214443812
#214443682
#214443622
#214443542
#214443512
#214443372
#214443202
#214443072
#328×D612
C61×#15162
#1759861