Finite Group Databasebeta

← #29647786

Subgroups — #29647786

Order 15616.

1074 conjugacy classes of subgroups.

The subgroup lattice has 988 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459654C211yesmaximal, characteristic
2#21454847C211yesmaximal, characteristic, complemented
3#21448730C211yesmaximal, characteristic, complemented
4#21444389C211yesmaximal, characteristic, complemented
5#21444385C211yesmaximal, characteristic, complemented
6#21444361C211yesmaximal, characteristic, complemented
7#21444359C211yesmaximal, characteristic, complemented
8#21444358C211yesmaximal, characteristic, complemented
9#21444357C211yesmaximal, characteristic, complemented
10#21444342C211yesmaximal, characteristic, complemented
11#21444322C211yesmaximal, characteristic, complemented
12#21444320C211yesmaximal, characteristic, complemented
13#328×D61C211yesmaximal, characteristic, complemented
14#327×D61C211yesmaximal, characteristic, complemented
15C61×#1509C211yesmaximal, characteristic, complemented
16#16840465C411yescharacteristic, complemented
17#16840463—21no—
18#16840462C411yescharacteristic, complemented
19#16840456—21no—
20#16840453C411yescharacteristic, complemented
21#16840450C411yescharacteristic, complemented
22#16840437—21no—
23#16840436—21no—
24#16840424C411yescharacteristic, complemented
25#16840420C411yescharacteristic, complemented
26#16840407C411yescharacteristic, complemented
27#16840405C411yescharacteristic, complemented
28#16840356—21no—
29#16840345—21no—
30#16840323—21no—
31#16840296C2211yescharacteristic
32#16840275C2211yescharacteristic
33#16840272C2211yescharacteristic
34C22⋊Q8×D61C2211yescharacteristic
35#121×D61C2211yescharacteristic
36#16840234—21no—
37C2×C4×D244—21no—
38C2×C4×D244C2211yescharacteristic
39#16839835—21no—
40#16839835—21no—
41#16839832—21no—
42#16839832—21no—
43#16839819C2211yescharacteristic, complemented
44#16839724C2211yescharacteristic, complemented
45#16839724C2211yescharacteristic, complemented
46C22⋊C8×D61C2211yescharacteristic
47C22⋊C8×D61C2211yescharacteristic
48#16839660—21no—
49#16839633—21no—
50#16839633—21no—
51#16839628C2211yescharacteristic, complemented
52#16839621C2211yescharacteristic
53#16839621C2211yescharacteristic, complemented
54#95×D61C2211yescharacteristic
55#95×D61C2211yescharacteristic, complemented
56#16839500C2211yescharacteristic, complemented
57#16839500C2211yescharacteristic, complemented
58#16839499C2211yescharacteristic, complemented
59#16839499C2211yescharacteristic, complemented
60#16839498C2211yescharacteristic, complemented
61#16839498C2211yescharacteristic, complemented
62#16839497C2211yescharacteristic
63#16839497C2211yescharacteristic
64#16839496C2211yescharacteristic
65#16839496C2211yescharacteristic
66#16839495C2211yescharacteristic
67#16839495C2211yescharacteristic
68C61×#529C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C4×C4⋊C4×C61C2211yescharacteristic, complemented
71C61×#328C2211yescharacteristic, complemented
72C61×#328C2211yescharacteristic, complemented
73C61×#327C2211yescharacteristic
74C61×#327C2211yescharacteristic
75C2×#11758226C2×C411yescharacteristic, complemented
76C2×#11758224C2×C411yescharacteristic, complemented
77C2×Q8×D61C2×C411yescharacteristic, complemented
78C22×D244D411yescharacteristic
79C2×D4×D61—21no—
80C2×D4×D61C2×C411yescharacteristic, complemented
81C22×C4×D61—21no—
82C22×C4×D61—21no—
83C22×C4×D61C2311yescharacteristic
84C22×C4×D61C2311yescharacteristic
85C2×#11758189—21no—
86C2×#11758189—21no—
87C2×C8×D61—21no—
88C2×C8×D61—21no—
89#14519772—21no—
90#14519772—21no—
91#14519771—21no—
92#14519771—21no—
93#14519770—21no—
94#14519769C2×C411yescharacteristic, complemented
95#14519768—21no—
96#14519767—21no—
97#14519765—21no—
98#14519765C2×C411yescharacteristic, complemented
99#14519763—21no—
100#14519762—21no—
101#14519762—21no—
102#14519762—21no—
103#14519762—21no—
104#14519761—21no—
105#14519760—21no—
106#14519760—21no—
107#14519759—21no—
108#14519759—21no—
109#14519757—21no—
110#14519757C2×C411yescharacteristic, complemented
111#14519757C2×C411yescharacteristic, complemented
112#14519756C2311yescharacteristic
113#14519755—21no—
114#14519754—21no—
115#14519754—21no—
116#14519753C2×C411yescharacteristic, complemented
117#14519753C2×C411yescharacteristic, complemented
118#14519752—21no—
119#14519752—21no—
120#14519752C2×C411yescharacteristic, complemented
121#14519752C2×C411yescharacteristic, complemented
122#14519751—21no—
123#14519751C2311yescharacteristic
124#14519750—21no—
125#14519750—21no—
126#14519750—21no—
127#14519750—21no—
128#14519749—21no—
129#14519748C2×C411yescharacteristic, complemented
130#14519748C2×C411yescharacteristic, complemented
131#14519747—21no—
132#14519747—21no—
133#14519747—21no—
134#14519745—21no—
135C4×Dic122C2×C411yescharacteristic, complemented
136C4×D244—21no—
137C4×D244—44no—
138C4×D244C2×C411yescharacteristic
139C4×D244C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic
142C4×D244C2×C411yescharacteristic, complemented
143C4×D244D411yescharacteristic
144C4×D244D411yescharacteristic
145C4×D244D411yescharacteristic
146C4×D244D411yescharacteristic
147D4×Dic61—21no—
148#14519739—21no—
149#14519739—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61—21no—
152#14519737—21no—
153#14519737—21no—
154#14519737—21no—
155#14519735—21no—
156#14519735C2×C411yescharacteristic, complemented
157#14519735C2×C411yescharacteristic, complemented
158#14519734—21no—
159#14519734—21no—
160C2×C4⋊Dic61—21no—
161C2×C4⋊Dic61D411yescharacteristic
162C2×#11758196—21no—
163C2×#11758196—21no—
164C4⋊C4×D61—21no—
165C4⋊C4×D61C2×C411yescharacteristic, complemented
166C4⋊C4×D61C2×C411yescharacteristic, complemented
167C2×#11758198—21no—
168C2×#11758198—21no—
169C2×#11758198—21no—
170C2×#11758198D411yescharacteristic
171C2×#11758198D411yescharacteristic
172C22⋊C4×D61—21no—
173C22⋊C4×D61—21no—
174C22⋊C4×D61—21no—
175C4⋊#92418—21no—
176C22⋊#92418C2311yescharacteristic
177C22⋊#92418C2311yescharacteristic
178#14519689—21no—
179#14519689—21no—
180#14519689—21no—
181#14519689—21no—
182#14519688—21no—
183#14519684—21no—
184#14519684—21no—
185#14519684—21no—
186#14519684C2311yescharacteristic
187#14519684C2311yescharacteristic
188#126×C61—21no—
189#125×C61C2×C411yescharacteristic, complemented
190#124×C61C2×C411yescharacteristic, complemented
191#123×C61—21no—
192C22⋊Q8×C61C2311yescharacteristic
193#121×C61C2311yescharacteristic
194C4×Q8×C61C2×C411yescharacteristic, complemented
195C4×D4×C61—21no—
196C4×D4×C61C2×C411yescharacteristic, complemented
197#117×C61—21no—
198C2×C4⋊C4×C61—21no—
199C2×C42×C61—21no—
200C2×C42×C61C2311yescharacteristic
201C4⋊C8×C61—21no—
202C22⋊C8×C61C2311yescharacteristic
203C22⋊C8×C61C2311yescharacteristic
204#97×C61—21no—
205#95×C61C2311yescharacteristic
206#95×C61C2311yescharacteristic
207C23×D61—21no—
208C23×D61C2×D411yescharacteristic
209C23×D61C2×D411yescharacteristic
210C2×Q8×C61C22×C411yescharacteristic
211C2×D4×C61—21no—
212C2×D4×C61C22×C411yescharacteristic
213C22×C4×C61—21no—
214C22×C4×C61—21no—
215C22×C4×C61—21no—
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2411yescharacteristic
219C2×C22⋊D61—21no—
220C2×C22⋊D61—21no—
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C22×Dic61—21no—
225C22×Dic61—21no—
226C22×Dic61—21no—
227C22×Dic61C2×D411yescharacteristic
228C22×Dic61C2×D411yescharacteristic
229#11758226—81no—
230Q8×D61—81no—
231#11758224—81no—
232D4×D61—42no—
233D4×D61—42no—
234D4×D61—81no—
235C2×D244—22no—
236C2×D244—22no—
237C2×D244—21no—
238C2×D244—21no—
239C2×D244—21no—
240C2×D244C22⋊C411yescharacteristic
241C2×D244C22⋊C411yescharacteristic
242C2×D244C22⋊C411yescharacteristic
243C2×D244C22⋊C411yescharacteristic
244C2×D244C22×C411yescharacteristic
245C2×C4×D61—21no—
246C2×C4×D61—21no—
247C2×C4×D61—21no—
248C2×C4×D61—21no—
249C2×C4×D61—21no—
250C2×C4×D61—42no—
251C2×C4×D61—42no—
252C2×C4×D61—42no—
253C2×C4×D61—42no—
254C2×C4×D61—81no—
255C2×C4×D61—81no—
256C2×C4×D61—81no—
257C2×C4×D61—81no—
258C2×C4×D61C22×C411yescharacteristic
259C2×C4×D61C22×C411yescharacteristic
260C2×C4×D61C22×C411yescharacteristic
261C2×C4×D61C22×C411yescharacteristic
262C2×C4×D61C2×D411yescharacteristic
263C2×C4×D61C2×D411yescharacteristic
264C2×C4×D61C2×D411yescharacteristic
265C2×C4×D61C2×D411yescharacteristic
266C2×Dic122—21no—
267C2×Dic122C22×C411yescharacteristic
268C2×C8×C61—21no—
269C2×C8×C61—21no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61—21no—
273C4⋊C4×C61—21no—
274C4⋊C4×C61—42no—
275C4⋊C4×C61C22×C411yescharacteristic
276C4⋊C4×C61C22×C411yescharacteristic
277C22⋊C4×C61—21no—
278C22⋊C4×C61—21no—
279C22⋊C4×C61—21no—
280C22⋊C4×C61—21no—
281C22⋊C4×C61—21no—
282C42×C61—21no—
283C42×C61—42no—
284C42×C61C22×C411yescharacteristic
285C42×C61C22×C411yescharacteristic
286C42×C61C2×D411yescharacteristic
287C42×C61C2×D411yescharacteristic
288C22⋊Dic61—21no—
289C22⋊Dic61—21no—
290C22⋊Dic61—21no—
291#11758198—21no—
292#11758198—21no—
293#11758198—21no—
294#11758198—21no—
295#11758198—21no—
296#11758198—21no—
297#11758198—21no—
298#11758198—21no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303#11758198—42no—
304#11758198—42no—
305#11758198C22⋊C411yescharacteristic
306#11758198C22⋊C411yescharacteristic
307#11758198C22⋊C411yescharacteristic
308#11758198C22⋊C411yescharacteristic
309#11758198C22⋊C411yescharacteristic
310#11758198C22⋊C411yescharacteristic
311#11758198C22⋊C411yescharacteristic
312#11758198C22⋊C411yescharacteristic
313C4⋊Dic61—21no—
314C4⋊Dic61—21no—
315C4⋊Dic61—42no—
316C4⋊Dic61C22⋊C411yescharacteristic
317C4⋊Dic61C22⋊C411yescharacteristic
318C4⋊Dic61C22⋊C411yescharacteristic
319C4⋊Dic61C22⋊C411yescharacteristic
320C4⋊Dic61C22×C411yescharacteristic
321C4⋊Dic61C22×C411yescharacteristic
322#11758196—21no—
323#11758196—21no—
324#11758196—21no—
325#11758196—21no—
326#11758196—21no—
327#11758196—21no—
328#11758196—21no—
329#11758196—21no—
330#11758196—81no—
331#11758196—81no—
332C4×Dic61—21no—
333C4×Dic61—21no—
334C4×Dic61—21no—
335C2×#92418—21no—
336C2×#92418—21no—
337#11758189—81no—
338#11758189—81no—
339C8×D61—81no—
340C8×D61—81no—
341C23×C61—21no—
342C23×C61C22×D411yescharacteristic
343C22×D61—21no—
344C22×D61—21no—
345C22×D61—21no—
346C22×D61—41no—
347C22×D61—41no—
348C22×D61—41no—
349C22×D61—41no—
350C22×D61—42no—
351C22×D61—81no—
352C22×D61—81no—
353C22×D61C2×C22⋊C411yescharacteristic
354C22×D61C2×C22⋊C411yescharacteristic
355C22×D61C2×C22⋊C411yescharacteristic
356C22×D61C2×C22⋊C411yescharacteristic
357C22×D61AGL(1,ℤ/8)12yes—
358C22×D61#13712yes—
359Q8×C61—41no—
360D4×C61—41no—
361D4×C61—41no—
362D4×C61—41no—
363C2×C4×C61—21no—
364C2×C4×C61—21no—
365C2×C4×C61—22no—
366C2×C4×C61—21no—
367C2×C4×C61—21no—
368C2×C4×C61—21no—
369C2×C4×C61—41no—
370C2×C4×C61—41no—
371C2×C4×C61—41no—
372C2×C4×C61—41no—
373C2×C4×C61—41no—
374C2×C4×C61—41no—
375C2×C4×C61—41no—
376C2×C4×C61—81no—
377C2×C4×C61C2×C22⋊C411yescharacteristic
378C2×C4×C61C2×C22⋊C411yescharacteristic
379C2×C4×C61C2×C22⋊C411yescharacteristic
380C2×C4×C61C2×C22⋊C411yescharacteristic
381C2×C4×C61C23×C411yescharacteristic
382C2×C4×C61C22×D411yescharacteristic
383C22⋊D61—41no—
384C22⋊D61—41no—
385C22⋊D61—42no—
386C22⋊D61—81no—
387C22⋊D61—81no—
388C22⋊D61—81no—
389C2×Dic61—21no—
390C2×Dic61—21no—
391C2×Dic61—21no—
392C2×Dic61—41no—
393C2×Dic61—41no—
394C2×Dic61—41no—
395C2×Dic61—41no—
396C2×Dic61—41no—
397C2×Dic61—41no—
398C2×Dic61—41no—
399C2×Dic61—41no—
400C2×Dic61—81no—
401C2×Dic61C2×C22⋊C411yescharacteristic
402C2×Dic61C2×C22⋊C411yescharacteristic
403C2×Dic61C2×C22⋊C411yescharacteristic
404C2×Dic61C2×C22⋊C411yescharacteristic
405D244—22no—
406D244—22no—
407D244—22no—
408D244—22no—
409D244—41no—
410D244—42no—
411D244—81no—
412D244—81no—
413C4×D61—41no—
414C4×D61—41no—
415C4×D61—41no—
416C4×D61—41no—
417C4×D61—41no—
418C4×D61—41no—
419C4×D61—41no—
420C4×D61—41no—
421C4×D61—42no—
422C4×D61—81no—
423C4×D61—81no—
424C4×D61—81no—
425C4×D61—81no—
426C4×D61—84no—
427C4×D61—84no—
428Dic122—41no—
429Dic122—81no—
430C8×C61—41no—
431C8×C61—41no—
432#92418—41no—
433#92418—41no—
434#17622—611nomaximal, Sylow
435C22×C61—21no—
436C22×C61—21no—
437C22×C61—41no—
438C22×C61—41no—
439C22×C61—41no—
440C22×C61C22×C22⋊C411yescharacteristic
441C22×C61C2×AGL(1,ℤ/8)11yescharacteristic
442C22×C61C2×#13711yescharacteristic
443C2×D61—21no—
444C2×D61—21no—
445C2×D61—21no—
446C2×D61—21no—
447C2×D61—21no—
448C2×D61—21no—
449C2×D61—21no—
450C2×D61—21no—
451C2×D61—21no—
452C2×D61—21no—
453C2×D61—42no—
454C2×D61—42no—
455C2×D61—42no—
456C2×D61—42no—
457C2×D61—41no—
458C2×D61—41no—
459C2×D61—41no—
460C2×D61—162no—
461C2×D61#41712yes—
462C2×D61#41712yes—
463C4×C61—21no—
464C4×C61—21no—
465C4×C61—21no—
466C4×C61—21no—
467C4×C61—21no—
468C4×C61—21no—
469C4×C61—42no—
470C4×C61—41no—
471C4×C61—41no—
472C4×C61—41no—
473C4×C61—81no—
474Dic61—21no—
475Dic61—21no—
476Dic61—21no—
477Dic61—21no—
478Dic61—41no—
479Dic61—41no—
480Dic61—41no—
481Dic61—81no—
482Dic61—81no—
483#3505—611no—
484#2973—611no—
485#2349—611no—
486#1520—611no—
487#1519—611no—
488#1513—611no—
489#1513—611no—
490#1512—611no—
491#1512—611no—
492#1509—611no—
493#1509D6111yescharacteristic, complemented
494#1504—611no—
495#1504—611no—
496C2×#328—611no—
497C2×#327—611no—
498C2×C61—21no—
499C2×C61—21no—
500C2×C61—81no—
501C2×C61#288311yescharacteristic
502C2×C61C2×#41711yescharacteristic
503C2×C61#290111yescharacteristic
504D61—22no—
505D61—22no—
506D61—41no—
507D61—41no—
508D61—81no—
509#553—611no—
510#553—611no—
511#553—1221no—
512#553—1221no—
513#552—611no—
514#552—611no—
515#551—1221no—
516#551—1221no—
517#548—611no—
518#548—611no—
519#546—611no—
520#546—611no—
521#539—1221no—
522#538—1221no—
523#534—1221no—
524#529—611no—
525#529C2×D6111yescharacteristic
526#525—611no—
527#525—611no—
528C2×C22⋊Q8—611no—
529C2×#121—611no—
530#518—1221no—
531C2×C4×D4—611no—
532C2×C4×D4—1221no—
533#435—1221no—
534#435—1221no—
535#435—1221no—
536#435—1221no—
537#432—611no—
538#432C2×D6111yescharacteristic, complemented
539#407—611no—
540#407—611no—
541C2×C22⋊C8—611no—
542C2×C22⋊C8—611no—
543#389—1221no—
544#385—1221no—
545#385—1221no—
546#382—611no—
547#380—611no—
548#380—611no—
549C4×C4⋊C4C2×D6111yescharacteristic, complemented
550C2×#95—611no—
551C2×#95—611no—
552#328—611no—
553#328—611no—
554#328—611no—
555#328—611no—
556#328—611no—
557#328—611no—
558#328C2×D6111yescharacteristic, complemented
559#328C2×D6111yescharacteristic, complemented
560#327—611no—
561#327—611no—
562#327—611no—
563#327—611no—
564#327—611no—
565#327—611no—
566#327C2×D6111yescharacteristic
567#327C2×D6111yescharacteristic
568C61#1762211yescharacteristic, complemented, Sylow
569C2×#41—611no—
570C2×#41—611no—
571C22×Q8—611no—
572C22×D4—611no—
573C22×D4—611no—
574C22×D4—1221no—
575C23×C4—611no—
576C23×C4—611no—
577C23×C4—1221no—
578C23×C4—1221no—
579C2×M16—1221no—
580C2×M16—1221no—
581C22×C8—1221no—
582C22×C8—1221no—
583#126—21no—
584#126—1221no—
585#126—1221no—
586#126—1221no—
587#126—1221no—
588#126—1221no—
589#125—611no—
590#125—1221no—
591#125—1221no—
592#125C4×D6111yescharacteristic, complemented
593#124—611no—
594#124—1221no—
595#124—1221no—
596#124C4×D6111yescharacteristic, complemented
597#123—21no—
598#123—1221no—
599#123—1221no—
600#123—1221no—
601#123—1221no—
602#123—1221no—
603#123—1221no—
604#123—1221no—
605#123—1221no—
606#123—1221no—
607C22⋊Q8—611no—
608C22⋊Q8—611no—
609C22⋊Q8—611no—
610C22⋊Q8—611no—
611C22⋊Q8—611no—
612C22⋊Q8—1221no—
613C22⋊Q8—1221no—
614C22⋊Q8—1221no—
615C22⋊Q8—1221no—
616C22⋊Q8C22×D6111yescharacteristic
617#121—611no—
618#121—611no—
619#121—611no—
620#121—611no—
621#121—611no—
622#121—1221no—
623#121—1221no—
624#121—1221no—
625#121—1221no—
626#121—1221no—
627#121—1221no—
628#121—1221no—
629#121—1221no—
630#121C22×D6111yescharacteristic
631#120—1221no—
632#120—1221no—
633#120—1221no—
634#120—1221no—
635C4×Q8—611no—
636C4×Q8C4×D6111yescharacteristic, complemented
637C4×D4—21no—
638C4×D4—611no—
639C4×D4—611no—
640C4×D4—611no—
641C4×D4—611no—
642C4×D4—611no—
643C4×D4—611no—
644C4×D4—611no—
645C4×D4—611no—
646C4×D4—611no—
647C4×D4—1221no—
648C4×D4—1221no—
649C4×D4—1221no—
650C4×D4—1221no—
651C4×D4—1221no—
652C4×D4—1221no—
653C4×D4—1221no—
654C4×D4—1221no—
655C4×D4—1221no—
656C4×D4—2444no—
657C4×D4C4×D6111yescharacteristic, complemented
658#117—21no—
659#117—611no—
660#117—611no—
661#117—1221no—
662#117—1221no—
663#117—1221no—
664C2×C4⋊C4—21no—
665C2×C4⋊C4—611no—
666C2×C4⋊C4—611no—
667C2×C4⋊C4—611no—
668C2×C4⋊C4—1221no—
669C2×C4⋊C4—1221no—
670C2×C4⋊C4—1221no—
671C2×C4⋊C4—1221no—
672C2×C22⋊C4—611no—
673C2×C22⋊C4—611no—
674C2×C22⋊C4—1221no—
675C2×C22⋊C4—1221no—
676C2×C22⋊C4—1221no—
677C2×C22⋊C4—1221no—
678C2×C22⋊C4—1221no—
679C2×C22⋊C4—1221no—
680C2×C42—21no—
681C2×C42C22×D6111yescharacteristic
682C4⋊C8—21no—
683C4⋊C8—1221no—
684C22⋊C8—611no—
685C22⋊C8—611no—
686C22⋊C8—1221no—
687C22⋊C8—1221no—
688C22⋊C8—1221no—
689C22⋊C8—1221no—
690C22⋊C8C22×D6111yescharacteristic
691C22⋊C8C22×D6111yescharacteristic
692#97—21no—
693#97—1221no—
694#95—611no—
695#95—611no—
696#95—1221no—
697#95—1221no—
698#95—1221no—
699#95C22×D6111yescharacteristic
700#95C22×D6111yescharacteristic
701C24—611no—
702C24—611no—
703C24—1221no—
704#41—4881no—
705#41—4881no—
706C2×Q8—611no—
707C2×Q8—1221no—
708C2×Q8—4881no—
709C2×Q8C2×C4×D6111yescharacteristic
710C2×D4—21no—
711C2×D4—611no—
712C2×D4—611no—
713C2×D4—611no—
714C2×D4—611no—
715C2×D4—611no—
716C2×D4—1222no—
717C2×D4—1222no—
718C2×D4—1221no—
719C2×D4—1221no—
720C2×D4—1221no—
721C2×D4—1221no—
722C2×D4—1221no—
723C2×D4—1221no—
724C2×D4—1221no—
725C2×D4—1221no—
726C2×D4—4881no—
727C2×D4—2442no—
728C2×D4—2442no—
729C2×D4C2×C4×D6111yescharacteristic
730C22×C4—21no—
731C22×C4—21no—
732C22×C4—21no—
733C22×C4—611no—
734C22×C4—611no—
735C22×C4—611no—
736C22×C4—611no—
737C22×C4—611no—
738C22×C4—611no—
739C22×C4—611no—
740C22×C4—611no—
741C22×C4—611no—
742C22×C4—611no—
743C22×C4—1221no—
744C22×C4—1221no—
745C22×C4—1221no—
746C22×C4—1221no—
747C22×C4—1221no—
748C22×C4—1221no—
749C22×C4—1221no—
750C22×C4—1221no—
751C22×C4—4881no—
752C22×C4—4881no—
753C22×C4—4881no—
754C22×C4—4881no—
755C22×C4—2442no—
756C22×C4—2442no—
757C22×C4—2442no—
758C22×C4—2442no—
759C22×C4D4×D6111yescharacteristic
760C22×C4D4×D6111yescharacteristic
761C22×C4C23×D6111yescharacteristic
762M16—4881no—
763M16—4881no—
764C2×C8—21no—
765C2×C8—21no—
766C2×C8—1221no—
767C2×C8—1221no—
768C2×C8—4881no—
769C2×C8—4881no—
770C4⋊C4—21no—
771C4⋊C4—21no—
772C4⋊C4—21no—
773C4⋊C4—21no—
774C4⋊C4—42no—
775C4⋊C4—611no—
776C4⋊C4—611no—
777C4⋊C4—611no—
778C4⋊C4—611no—
779C4⋊C4—611no—
780C4⋊C4—611no—
781C4⋊C4—1221no—
782C4⋊C4—1221no—
783C4⋊C4—1221no—
784C4⋊C4—1221no—
785C4⋊C4—1221no—
786C4⋊C4—1221no—
787C4⋊C4—1221no—
788C4⋊C4—1221no—
789C4⋊C4—1221no—
790C4⋊C4—1221no—
791C4⋊C4—4881no—
792C4⋊C4—4881no—
793C4⋊C4—2442no—
794C4⋊C4C2×C4×D6111yescharacteristic
795C4⋊C4C2×C4×D6111yescharacteristic
796C22⋊C4—21no—
797C22⋊C4—21no—
798C22⋊C4—21no—
799C22⋊C4—21no—
800C22⋊C4—21no—
801C22⋊C4—611no—
802C22⋊C4—611no—
803C22⋊C4—611no—
804C22⋊C4—611no—
805C22⋊C4—611no—
806C22⋊C4—611no—
807C22⋊C4—611no—
808C22⋊C4—611no—
809C22⋊C4—1221no—
810C22⋊C4—1221no—
811C22⋊C4—1221no—
812C22⋊C4—1221no—
813C22⋊C4—1221no—
814C22⋊C4—1221no—
815C22⋊C4—1221no—
816C22⋊C4—1221no—
817C22⋊C4—1221no—
818C22⋊C4—1221no—
819C22⋊C4—1221no—
820C22⋊C4—1221no—
821C22⋊C4—1221no—
822C22⋊C4—1221no—
823C22⋊C4—1221no—
824C22⋊C4—2442no—
825C22⋊C4—2442no—
826C42—21no—
827C42—42no—
828C42—1221no—
829C42—1221no—
830C42—1221no—
831C42C2×C4×D6111yescharacteristic
832C42C2×C4×D6111yescharacteristic
833C42D4×D6111yescharacteristic
834C42D4×D6111yescharacteristic
835C23—21no—
836C23—611no—
837C23—611no—
838C23—612no—
839C23—612no—
840C23—611no—
841C23—611no—
842C23—1221no—
843C23—1221no—
844C23—1221no—
845C23—4881no—
846C23—4881no—
847C23—2441no—
848C23—2441no—
849C23—2441no—
850C23—2441no—
851C23—2442no—
852C23C2×D4×D6111yescharacteristic
853Q8—41no—
854Q8—4881no—
855Q8—2441no—
856D4—41no—
857D4—41no—
858D4—41no—
859D4—1222no—
860D4—1222no—
861D4—1222no—
862D4—1222no—
863D4—4881no—
864D4—4881no—
865D4—4881no—
866D4—4881no—
867D4—4881no—
868D4—2441no—
869D4—2442no—
870D4—2442no—
871D4—2441no—
872D4—2441no—
873C2×C4—21no—
874C2×C4—21no—
875C2×C4—22no—
876C2×C4—21no—
877C2×C4—21no—
878C2×C4—21no—
879C2×C4—41no—
880C2×C4—41no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—41no—
884C2×C4—41no—
885C2×C4—41no—
886C2×C4—81no—
887C2×C4—611no—
888C2×C4—611no—
889C2×C4—611no—
890C2×C4—611no—
891C2×C4—1221no—
892C2×C4—1221no—
893C2×C4—1221no—
894C2×C4—4881no—
895C2×C4—4881no—
896C2×C4—4884no—
897C2×C4—4884no—
898C2×C4—4881no—
899C2×C4—4881no—
900C2×C4—4881no—
901C2×C4—2441no—
902C2×C4—2441no—
903C2×C4—2441no—
904C2×C4—2441no—
905C2×C4—2441no—
906C2×C4—2441no—
907C2×C4—2441no—
908C2×C4—2441no—
909C2×C4—2442no—
910C2×C4—2441no—
911C2×C4—2441no—
912C2×C4—2441no—
913C2×C4—2441no—
914C2×C4—2441no—
915C2×C4—2441no—
916C2×C4—2441no—
917C2×C4—2441no—
918C2×C4C22⋊C4×D6111yescharacteristic
919C2×C4C22⋊C4×D6111yescharacteristic
920C2×C4C22⋊C4×D6111yescharacteristic
921C2×C4C22⋊C4×D6111yescharacteristic
922C2×C4C22×C4×D6111yescharacteristic
923C2×C4C2×D4×D6111yescharacteristic
924C8—41no—
925C8—41no—
926C8—2441no—
927C8—2441no—
928C22—21no—
929C22—21no—
930C22—41no—
931C22—41no—
932C22—41no—
933C22—612no—
934C22—612no—
935C22—1221no—
936C22—1221no—
937C22—1221no—
938C22—1221no—
939C22—1221no—
940C22—1221no—
941C22—1221no—
942C22—1221no—
943C22—1221no—
944C22—1221no—
945C22—9762no—
946C22—2442no—
947C22—2442no—
948C22—2442no—
949C22—2442no—
950C22—2441no—
951C22—2441no—
952C22—2441no—
953C22C2×C22⋊C4×D6111yescharacteristic
954C22AGL(1,ℤ/8)×D6111yescharacteristic
955C22#137×D6111yescharacteristic
956C4—21no—
957C4—21no—
958C4—21no—
959C4—21no—
960C4—21no—
961C4—21no—
962C4—42no—
963C4—41no—
964C4—41no—
965C4—41no—
966C4—81no—
967C4—1221no—
968C4—1221no—
969C4—1221no—
970C4—1221no—
971C4—4881no—
972C4—4881no—
973C4—2441no—
974C4—2441no—
975C4—2441no—
976C2—21no—
977C2—21no—
978C2—81no—
979C2—1222no—
980C2—1222no—
981C2—4881no—
982C2—2441no—
983C2—2441no—
984C2#2145427811yescharacteristic
985C2#417×D6111yescharacteristic
986C2#2145436311yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1509C2
socleC22×C61C22×C22⋊C4
prime radical#21459654C2
cosocleC22×C4×C61C24
hypercenter#1509D61
hypocenterC61#17622
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1509

Complements

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

NH ≅ G/Ntype
2. #21454847C2semidirect
3. #21448730C2semidirect
4. #21444389C2semidirect
5. #21444385C2semidirect
6. #21444361C2semidirect
7. #21444359C2semidirect
8. #21444358C2semidirect
9. #21444357C2semidirect
10. #21444342C2semidirect
11. #21444322C2semidirect
12. #21444320C2semidirect
13. #328×D61C2semidirect
14. #327×D61C2semidirect
15. C61×#1509C2semidirect
16. #16840465C4semidirect
18. #16840462C4semidirect
20. #16840453C4semidirect
21. #16840450C4semidirect
24. #16840424C4semidirect
25. #16840420C4semidirect
26. #16840407C4semidirect
27. #16840405C4semidirect
43. #16839819C22semidirect
44. #16839724C22semidirect
45. #16839724C22semidirect
51. #16839628C22semidirect
53. #16839621C22semidirect
55. #95×D61C22semidirect
56. #16839500C22semidirect
57. #16839500C22semidirect
58. #16839499C22semidirect
59. #16839499C22semidirect
60. #16839498C22semidirect
61. #16839498C22semidirect
69. C61×#432C22semidirect
70. C4×C4⋊C4×C61C22semidirect
71. C61×#328C22semidirect
72. C61×#328C22semidirect
75. C2×#11758226C2×C4semidirect
76. C2×#11758224C2×C4semidirect
77. C2×Q8×D61C2×C4semidirect
80. C2×D4×D61C2×C4semidirect
94. #14519769C2×C4semidirect
98. #14519765C2×C4semidirect
110. #14519757C2×C4semidirect
111. #14519757C2×C4semidirect
116. #14519753C2×C4semidirect
117. #14519753C2×C4semidirect
120. #14519752C2×C4semidirect
121. #14519752C2×C4semidirect
129. #14519748C2×C4semidirect
130. #14519748C2×C4semidirect
135. C4×Dic122C2×C4semidirect
142. C4×D244C2×C4semidirect
156. #14519735C2×C4semidirect
157. #14519735C2×C4semidirect
165. C4⋊C4×D61C2×C4semidirect
166. C4⋊C4×D61C2×C4semidirect
189. #125×C61C2×C4semidirect
190. #124×C61C2×C4semidirect
194. C4×Q8×C61C2×C4semidirect
196. C4×D4×C61C2×C4semidirect
493. #1509D61semidirect
538. #432C2×D61semidirect
549. C4×C4⋊C4C2×D61semidirect
558. #328C2×D61semidirect
559. #328C2×D61semidirect
568. C61#17622semidirect
592. #125C4×D61semidirect
596. #124C4×D61semidirect
636. C4×Q8C4×D61semidirect
657. C4×D4C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214596542
#214548472
#214487302
#214443892
#214443852
#214443612
#214443592
#214443582
#214443572
#214443422
#214443222
#214443202
#328×D612
#327×D612
C61×#15092
#1762261