Finite Group Databasebeta

← #29648165

Subgroups — #29648165

Order 15616.

942 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459775C211yesmaximal, characteristic
2#21454828C211yesmaximal, characteristic, complemented
3#21454465C211yesmaximal, characteristic, complemented
4#21444451C211yesmaximal, characteristic, complemented
5#21444447C211yesmaximal, characteristic, complemented
6#21444441C211yesmaximal, characteristic, complemented
7#21444440C211yesmaximal, characteristic, complemented
8#21444436C211yesmaximal, characteristic, complemented
9#21444430C211yesmaximal, characteristic, complemented
10#21444423C211yesmaximal, characteristic, complemented
11#21444415C211yesmaximal, characteristic, complemented
12#21444415C211yesmaximal, characteristic, complemented
13#21444404C211yesmaximal, characteristic, complemented
14#329×D61C211yesmaximal, characteristic, complemented
15C61×#1536C211yesmaximal, characteristic, complemented
16#16840498C411yescharacteristic
17#16840486C411yescharacteristic
18#16840476—21no—
19#16840441—21no—
20#16840441—21no—
21#16840427C411yescharacteristic
22#16840419C411yescharacteristic
23#16840419C411yescharacteristic
24#16840409—21no—
25#16840400C411yescharacteristic
26#16840400C411yescharacteristic
27#16840397C411yescharacteristic
28#16840377—21no—
29#16840344—21no—
30#16840344—21no—
31#16840296C2211yescharacteristic
32#16840291C2211yescharacteristic
33#16840291C2211yescharacteristic
34#124×D61C2211yescharacteristic
35#124×D61C2211yescharacteristic
36#16840234—21no—
37C4×#11758222C2211yescharacteristic
38#16839891—21no—
39#16839832—21no—
40#16839830—21no—
41#16839825—21no—
42#16839822—21no—
43#16839820—21no—
44#16839819C2211yescharacteristic, complemented
45#16839817C2211yescharacteristic, complemented
46#16839817C2211yescharacteristic, complemented
47#16839817C2211yescharacteristic, complemented
48#16839817C2211yescharacteristic, complemented
49#16839787—21no—
50#16839727—21no—
51#16839714C2211yescharacteristic, complemented
52#16839714C2211yescharacteristic, complemented
53C2×#14519688C2211yescharacteristic, complemented
54#97×D61C2211yescharacteristic, complemented
55#97×D61C2211yescharacteristic, complemented
56#16839503C2211yescharacteristic, complemented
57#16839503C2211yescharacteristic, complemented
58#16839503C2211yescharacteristic, complemented
59#16839503C2211yescharacteristic, complemented
60#16839502C2211yescharacteristic, complemented
61#16839502C2211yescharacteristic, complemented
62#16839502C2211yescharacteristic, complemented
63#16839502C2211yescharacteristic, complemented
64#16839501C2211yescharacteristic
65#16839501C2211yescharacteristic
66#16839501C2211yescharacteristic
67#16839501C2211yescharacteristic
68C61×#532C2211yescharacteristic
69C61×#432C2211yescharacteristic, complemented
70C61×#432C2211yescharacteristic, complemented
71C61×#329C2211yescharacteristic, complemented
72C61×#329C2211yescharacteristic, complemented
73C61×#329C2211yescharacteristic, complemented
74C61×#329C2211yescharacteristic, complemented
75C2×#11758222D411yescharacteristic
76C2×Q8×D61C2×C411yescharacteristic
77C2×Q8×D61C2×C411yescharacteristic
78C2×D4×D61—21no—
79C2×D4×D61C2×C411yescharacteristic
80C2×D4×D61C2×C411yescharacteristic
81C2×#11758189—21no—
82C2×#11758189—21no—
83C22×#92418—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86#14519776—21no—
87#14519772—21no—
88#14519772—21no—
89#14519771—21no—
90#14519770—21no—
91#14519770—21no—
92#14519769C2311yescharacteristic
93#14519766C2×C411yescharacteristic
94#14519766C2×C411yescharacteristic
95#14519765C2311yescharacteristic
96#14519764—21no—
97#14519764—21no—
98#14519764—21no—
99#14519764C2×C411yescharacteristic
100#14519764C2×C411yescharacteristic
101#14519763—21no—
102#14519763—21no—
103#14519763—21no—
104#14519763—21no—
105#14519760—21no—
106#14519760—21no—
107#14519760—21no—
108#14519759—21no—
109#14519759—21no—
110#14519758—21no—
111#14519758—21no—
112#14519757—21no—
113#14519756—21no—
114#14519756—21no—
115#14519756C2×C411yescharacteristic
116#14519755—21no—
117#14519755—21no—
118#14519753C2×C411yescharacteristic
119#14519753C2×C411yescharacteristic
120#14519751C2×C411yescharacteristic
121#14519749—21no—
122#14519749—21no—
123#14519748—21no—
124#14519748—21no—
125#14519748—21no—
126#14519748C2×C411yescharacteristic
127#14519748C2×C411yescharacteristic
128#14519745—21no—
129#14519745—21no—
130#14519745—21no—
131#14519745—21no—
132Q8×Dic61C2×C411yescharacteristic
133Q8×Dic61C2×C411yescharacteristic
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122C2×C411yescharacteristic
136C4×Dic122D411yescharacteristic
137C4×D244C2×C411yescharacteristic
138C4×D244C2×C411yescharacteristic
139C4×D244D411yescharacteristic
140D4×Dic61—21no—
141D4×Dic61C2×C411yescharacteristic
142D4×Dic61C2×C411yescharacteristic
143#14519739—21no—
144C4×C22⋊D61—21no—
145C4×C22⋊D61—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61C2×C411yescharacteristic
148C4×C22⋊D61C2×C411yescharacteristic
149C4×C22⋊D61D411yescharacteristic
150C4×C22⋊D61D411yescharacteristic
151#14519737—21no—
152#14519737—21no—
153#14519736D411yescharacteristic
154#14519735—21no—
155#14519734—21no—
156#14519734D411yescharacteristic
157#14519734D411yescharacteristic
158#14519733—21no—
159#14519733—21no—
160C2×#11758198—21no—
161C2×#11758198—21no—
162C22⋊C4×D61—21no—
163C22⋊C4×D61—21no—
164C22⋊C4×D61—21no—
165C22⋊C4×D61—21no—
166C42×D61C2311yescharacteristic
167C42×D61C2311yescharacteristic
168C4⋊#92418—21no—
169#14519706—21no—
170#14519706—21no—
171#14519706—21no—
172#14519706—21no—
173C22⋊#92418—21no—
174#14519689—21no—
175#14519689—21no—
176#14519689—21no—
177#14519689—21no—
178#14519688—21no—
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519688C2311yescharacteristic
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C2×#41×C61C2×C411yescharacteristic
188C2×#41×C61C2×C411yescharacteristic
189C4⋊Q8×C61C2×C411yescharacteristic
190#127×C61C2×C411yescharacteristic
191#124×C61C2311yescharacteristic
192#124×C61C2311yescharacteristic
193#121×C61—21no—
194#121×C61—21no—
195C4×D4×C61—21no—
196C4×D4×C61—21no—
197C2×C42×C61C2311yescharacteristic
198C4⋊C8×C61—21no—
199C4⋊C8×C61—21no—
200C22⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C23×D61—21no—
207C23×D61—21no—
208#41×C61—81no—
209#41×C61—81no—
210C2×Q8×C61C22×C411yescharacteristic
211C2×Q8×C61C22×C411yescharacteristic
212C2×D4×C61—21no—
213C2×D4×C61—21no—
214C2×D4×C61—21no—
215C2×D4×C61—21no—
216C2×D4×C61C22×C411yescharacteristic
217C2×D4×C61C22×C411yescharacteristic
218C22×C4×C61—21no—
219C22×C4×C61—21no—
220C22×C4×C61C22×C411yescharacteristic
221C22×C4×C61C2×D411yescharacteristic
222C22×C4×C61C2×D411yescharacteristic
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C2×C22⋊D61—21no—
226C2×C22⋊D61—21no—
227C2×C22⋊D61—21no—
228C2×C22⋊D61C22⋊C411yescharacteristic
229C2×C22⋊D61C22⋊C411yescharacteristic
230C22×Dic61—21no—
231C22×Dic61—21no—
232Q8×D61—81no—
233Q8×D61—81no—
234D4×D61—44no—
235D4×D61—81no—
236D4×D61—81no—
237#11758222—42no—
238C2×D244C22⋊C411yescharacteristic
239C2×D244C22×C411yescharacteristic
240C2×C4×D61—21no—
241C2×C4×D61—21no—
242C2×C4×D61—21no—
243C2×C4×D61C22×C411yescharacteristic
244C2×C4×D61C22×C411yescharacteristic
245C2×C4×D61C2×D411yescharacteristic
246C2×C4×D61C2×D411yescharacteristic
247C2×C4×D61C2×D411yescharacteristic
248C2×C4×D61C2×D411yescharacteristic
249C2×Dic122—21no—
250C2×Dic122—21no—
251C2×Dic122C22⋊C411yescharacteristic
252C2×Dic122C22×C411yescharacteristic
253C2×C8×C61—21no—
254C2×C8×C61—21no—
255C2×C8×C61—21no—
256C2×C8×C61—21no—
257C4⋊C4×C61—21no—
258C4⋊C4×C61—21no—
259C22⋊C4×C61—21no—
260C22⋊C4×C61—21no—
261C22⋊C4×C61—21no—
262C22⋊C4×C61—21no—
263C42×C61C22×C411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2411yescharacteristic
267C22⋊Dic61—21no—
268C22⋊Dic61—21no—
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275C22⋊Dic61—21no—
276C22⋊Dic61C22⋊C411yescharacteristic
277C22⋊Dic61C22⋊C411yescharacteristic
278#11758198—21no—
279#11758198—21no—
280#11758198—21no—
281#11758198—21no—
282#11758198—21no—
283#11758198—21no—
284#11758198—21no—
285#11758198—21no—
286#11758198—21no—
287#11758198—21no—
288#11758198C22⋊C411yescharacteristic
289#11758198C22⋊C411yescharacteristic
290#11758198C22⋊C411yescharacteristic
291#11758198C22⋊C411yescharacteristic
292C4⋊Dic61—21no—
293C4⋊Dic61—21no—
294C4⋊Dic61C22⋊C411yescharacteristic
295C4⋊Dic61C22⋊C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297C4⋊Dic61C22×C411yescharacteristic
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196C22⋊C411yescharacteristic
305#11758196C22⋊C411yescharacteristic
306#11758196C22⋊C411yescharacteristic
307#11758196C22⋊C411yescharacteristic
308C4×Dic61—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61C22×C411yescharacteristic
312C4×Dic61C22×C411yescharacteristic
313C4×Dic61C2×D411yescharacteristic
314C4×Dic61C2×D411yescharacteristic
315C4×Dic61C2×D411yescharacteristic
316C4×Dic61C2×D411yescharacteristic
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—21no—
321C2×#92418—42no—
322#11758189—42no—
323#11758189—42no—
324C8×D61—42no—
325C8×D61—42no—
326C23×C61—21no—
327C23×C61—21no—
328C23×C61C2×C22⋊C411yescharacteristic
329C22×D61—21no—
330C22×D61—42no—
331C22×D61—42no—
332C22×D61—81no—
333C22×D61—81no—
334C22×D61—81no—
335C22×D61—81no—
336C22×D61C2×C22⋊C411yescharacteristic
337C22×D61C2×C22⋊C411yescharacteristic
338Q8×C61—41no—
339Q8×C61—41no—
340D4×C61—41no—
341D4×C61—41no—
342D4×C61—42no—
343D4×C61—81no—
344D4×C61—81no—
345D4×C61—81no—
346C2×C4×C61—21no—
347C2×C4×C61—21no—
348C2×C4×C61—41no—
349C2×C4×C61—41no—
350C2×C4×C61—41no—
351C2×C4×C61—81no—
352C2×C4×C61—81no—
353C2×C4×C61C2×C22⋊C411yescharacteristic
354C2×C4×C61C2×C22⋊C411yescharacteristic
355C2×C4×C61C2×C22⋊C411yescharacteristic
356C2×C4×C61C23×C411yescharacteristic
357C2×C4×C61C22×D411yescharacteristic
358C2×C4×C61C22×D411yescharacteristic
359C22⋊D61—22no—
360C22⋊D61—41no—
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—81no—
364C22⋊D61—81no—
365C22⋊D61—81no—
366C2×Dic61—21no—
367C2×Dic61—21no—
368C2×Dic61—21no—
369C2×Dic61—81no—
370C2×Dic61—81no—
371C2×Dic61C2×C22⋊C411yescharacteristic
372C2×Dic61C2×C22⋊C411yescharacteristic
373C2×Dic61C2×C22⋊C411yescharacteristic
374C2×Dic61C2×C22⋊C411yescharacteristic
375C2×Dic61C2×C22⋊C411yescharacteristic
376C2×Dic61C2×C22⋊C411yescharacteristic
377D244—22no—
378D244—41no—
379C4×D61—22no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61—41no—
383C4×D61—41no—
384C4×D61—41no—
385C4×D61—42no—
386C4×D61—81no—
387C4×D61—81no—
388Dic122—41no—
389Dic122—41no—
390Dic122—81no—
391Dic122—81no—
392C8×C61—41no—
393C8×C61—41no—
394C8×C61—41no—
395C8×C61—41no—
396#92418—22no—
397#92418—41no—
398#92418—41no—
399#92418—41no—
400#17679—611nomaximal, Sylow
401C22×C61—21no—
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—41no—
405C22×C61—41no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61—41no—
409C22×C61—41no—
410C22×C61C22×C22⋊C411yescharacteristic
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—21no—
414C2×D61—21no—
415C2×D61—21no—
416C2×D61—41no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—162no—
420C2×D61—162no—
421C2×D61#42112yes—
422C4×C61—21no—
423C4×C61—21no—
424C4×C61—21no—
425C4×C61—21no—
426C4×C61—21no—
427C4×C61—21no—
428C4×C61—41no—
429C4×C61—41no—
430Dic61—21no—
431Dic61—21no—
432Dic61—21no—
433Dic61—21no—
434Dic61—21no—
435Dic61—21no—
436Dic61—41no—
437Dic61—41no—
438Dic61—41no—
439#3514—611no—
440#2970—611no—
441#2923—611no—
442#1536D6111yescharacteristic, complemented
443#1535—611no—
444#1535—611no—
445#1533—611no—
446#1532—611no—
447#1532—611no—
448#1530—611no—
449#1529—611no—
450#1527—611no—
451#1527—611no—
452#1524—611no—
453C2×#329—611no—
454C2×C61—41no—
455C2×C61—81no—
456C2×C61—81no—
457C2×C61#288811yescharacteristic
458C2×C61C2×#42111yescharacteristic
459C2×C61#290111yescharacteristic
460D61—22no—
461D61—41no—
462D61—81no—
463#559—611no—
464#556—611no—
465#555—1221no—
466#551—1221no—
467#551—1221no—
468D4×Q8—611no—
469#548—611no—
470#548—611no—
471#546—611no—
472#546—611no—
473#546—1221no—
474D42—611no—
475#542—1221no—
476#538—1221no—
477#538—1221no—
478#532C2×D6111yescharacteristic
479#529—611no—
480#529—611no—
481#529—611no—
482C2×#124—611no—
483C2×#124—611no—
484#518—1221no—
485C4×#41—611no—
486#446—1221no—
487#435—1221no—
488#435—1221no—
489C8×D4—1221no—
490#433—1221no—
491#433—1221no—
492#432—611no—
493#432—611no—
494#432—611no—
495#432—611no—
496#432—611no—
497#432C2×D6111yescharacteristic, complemented
498#432C2×D6111yescharacteristic, complemented
499#424—1221no—
500#408—1221no—
501C4×M16—611no—
502C4×M16—611no—
503C2×#97—611no—
504C2×#97—611no—
505C2×#97—611no—
506#330—611no—
507#330—611no—
508#330—611no—
509#330—611no—
510#329—611no—
511#329—611no—
512#329—611no—
513#329—611no—
514#329—611no—
515#329—611no—
516#329—611no—
517#329—611no—
518#329C2×D6111yescharacteristic, complemented
519#329C2×D6111yescharacteristic, complemented
520#329C2×D6111yescharacteristic, complemented
521#329C2×D6111yescharacteristic, complemented
522C61#1767911yescharacteristic, complemented, Sylow
523C2×#41—611no—
524C2×#41C4×D6111yescharacteristic
525C2×#41C4×D6111yescharacteristic
526C22×Q8—611no—
527C22×Q8—611no—
528C22×D4—611no—
529C22×D4—611no—
530C22×D4—1221no—
531C2×M16—1221no—
532C2×M16—1221no—
533C22×C8—1221no—
534C22×C8—1221no—
535C22×C8—1221no—
536C4⋊Q8—1221no—
537C4⋊Q8C4×D6111yescharacteristic
538#127C4×D6111yescharacteristic
539#126—1221no—
540#126—1221no—
541#126—1221no—
542#126—1221no—
543#126—1221no—
544#125—611no—
545#124—611no—
546#124—611no—
547#124—611no—
548#124—611no—
549#124—611no—
550#124—1221no—
551#124—1221no—
552#124—1221no—
553#124—1221no—
554#124—1221no—
555#124—1221no—
556#124—1221no—
557#124C22×D6111yescharacteristic
558#124C22×D6111yescharacteristic
559#123—1221no—
560#123—1221no—
561#123—1221no—
562#123—1221no—
563#123—1221no—
564#123—1221no—
565#123—1221no—
566C22⋊Q8—611no—
567C22⋊Q8—611no—
568C22⋊Q8—611no—
569C22⋊Q8—1221no—
570C22⋊Q8—1221no—
571C22⋊Q8—1221no—
572C22⋊Q8—1221no—
573C22⋊Q8—1221no—
574#121—21no—
575#121—21no—
576#121—611no—
577#121—611no—
578#121—611no—
579#121—1221no—
580#121—1221no—
581#121—1221no—
582#121—1221no—
583#121—1221no—
584#120—1221no—
585#120—1221no—
586#120—1221no—
587#120—1221no—
588C4×Q8—611no—
589C4×Q8—611no—
590C4×Q8—611no—
591C4×Q8—611no—
592C4×Q8—611no—
593C4×D4—21no—
594C4×D4—21no—
595C4×D4—611no—
596C4×D4—611no—
597C4×D4—611no—
598C4×D4—611no—
599C4×D4—611no—
600C4×D4—611no—
601C4×D4—611no—
602C4×D4—611no—
603C4×D4—611no—
604C4×D4—1221no—
605C4×D4—1221no—
606C4×D4—1221no—
607C4×D4—1221no—
608C4×D4—1221no—
609C4×D4—1221no—
610C4×D4—1221no—
611#117—611no—
612#117—611no—
613#117—611no—
614#117—1221no—
615#117—1221no—
616#117—1221no—
617#117—1221no—
618C2×C22⋊C4—1221no—
619C2×C22⋊C4—1221no—
620C2×C22⋊C4—1221no—
621C2×C22⋊C4—1221no—
622C2×C22⋊C4—1221no—
623C2×C22⋊C4—1221no—
624C2×C42—611no—
625C2×C42—611no—
626C2×C42C22×D6111yescharacteristic
627C4⋊C8—21no—
628C4⋊C8—21no—
629C4⋊C8—1221no—
630C4⋊C8—1221no—
631C4⋊C8—1221no—
632C4⋊C8—1221no—
633C4⋊C8—1221no—
634C22⋊C8—21no—
635C22⋊C8—21no—
636C22⋊C8—1221no—
637C22⋊C8—1221no—
638C22⋊C8—1221no—
639C22⋊C8—1221no—
640C22⋊C8—1221no—
641#97—611no—
642#97—611no—
643#97—611no—
644#97—611no—
645#97—1221no—
646#97—1221no—
647#97—1221no—
648#97C22×D6111yescharacteristic
649#97C22×D6111yescharacteristic
650#97C22×D6111yescharacteristic
651#97C22×D6111yescharacteristic
652C4×C8—1221no—
653C4×C8—1221no—
654C24—1221no—
655C24—1221no—
656#41—81no—
657#41—81no—
658#41—2442no—
659C2×Q8—611no—
660C2×Q8—611no—
661C2×Q8—1221no—
662C2×Q8—1221no—
663C2×Q8—4881no—
664C2×Q8—4881no—
665C2×Q8C2×C4×D6111yescharacteristic
666C2×Q8C2×C4×D6111yescharacteristic
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—611no—
672C2×D4—611no—
673C2×D4—611no—
674C2×D4—611no—
675C2×D4—1221no—
676C2×D4—1221no—
677C2×D4—1221no—
678C2×D4—1221no—
679C2×D4—1221no—
680C2×D4—4881no—
681C2×D4—4881no—
682C2×D4—2444no—
683C2×D4C2×C4×D6111yescharacteristic
684C2×D4C2×C4×D6111yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—611no—
688C22×C4—611no—
689C22×C4—611no—
690C22×C4—611no—
691C22×C4—611no—
692C22×C4—611no—
693C22×C4—1221no—
694C22×C4—1221no—
695C22×C4—1221no—
696C22×C4—1221no—
697C22×C4—1221no—
698C22×C4C2×C4×D6111yescharacteristic
699C22×C4D4×D6111yescharacteristic
700C22×C4D4×D6111yescharacteristic
701M16—2442no—
702M16—2442no—
703C2×C8—21no—
704C2×C8—21no—
705C2×C8—21no—
706C2×C8—21no—
707C2×C8—1221no—
708C2×C8—1221no—
709C2×C8—1221no—
710C2×C8—1221no—
711C2×C8—2442no—
712C2×C8—2442no—
713C2×C8—2442no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—611no—
717C4⋊C4—611no—
718C4⋊C4—611no—
719C4⋊C4—611no—
720C4⋊C4—611no—
721C4⋊C4—611no—
722C4⋊C4—611no—
723C4⋊C4—611no—
724C4⋊C4—1221no—
725C4⋊C4—1221no—
726C4⋊C4—1221no—
727C4⋊C4—1221no—
728C4⋊C4—1221no—
729C4⋊C4—1221no—
730C4⋊C4—1221no—
731C4⋊C4—1221no—
732C22⋊C4—21no—
733C22⋊C4—21no—
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—611no—
737C22⋊C4—611no—
738C22⋊C4—611no—
739C22⋊C4—611no—
740C22⋊C4—611no—
741C22⋊C4—611no—
742C22⋊C4—1221no—
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—1221no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—1221no—
757C22⋊C4—1221no—
758C22⋊C4—1221no—
759C22⋊C4—1221no—
760C22⋊C4—1221no—
761C42—611no—
762C42—611no—
763C42—611no—
764C42—611no—
765C42—611no—
766C42—611no—
767C42—1221no—
768C42—1221no—
769C42—1221no—
770C42C2×C4×D6111yescharacteristic
771C42D4×D6111yescharacteristic
772C42D4×D6111yescharacteristic
773C42C23×D6111yescharacteristic
774C23—21no—
775C23—21no—
776C23—611no—
777C23—611no—
778C23—1221no—
779C23—4881no—
780C23—4881no—
781C23—4881no—
782C23—4881no—
783C23—2442no—
784C23—2442no—
785C23C22⋊C4×D6111yescharacteristic
786Q8—41no—
787Q8—41no—
788Q8—4881no—
789Q8—4881no—
790Q8—2441no—
791Q8—2441no—
792D4—41no—
793D4—41no—
794D4—42no—
795D4—81no—
796D4—81no—
797D4—81no—
798D4—1222no—
799D4—1222no—
800D4—4881no—
801D4—4881no—
802D4—4881no—
803D4—2441no—
804D4—2441no—
805D4—2442no—
806D4—2442no—
807C2×C4—21no—
808C2×C4—21no—
809C2×C4—41no—
810C2×C4—41no—
811C2×C4—41no—
812C2×C4—81no—
813C2×C4—81no—
814C2×C4—611no—
815C2×C4—611no—
816C2×C4—611no—
817C2×C4—611no—
818C2×C4—611no—
819C2×C4—611no—
820C2×C4—1222no—
821C2×C4—1221no—
822C2×C4—1221no—
823C2×C4—1221no—
824C2×C4—4881no—
825C2×C4—4881no—
826C2×C4—4881no—
827C2×C4—4881no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2442no—
834C2×C4C22⋊C4×D6111yescharacteristic
835C2×C4C22⋊C4×D6111yescharacteristic
836C2×C4C22⋊C4×D6111yescharacteristic
837C2×C4C22×C4×D6111yescharacteristic
838C2×C4C2×D4×D6111yescharacteristic
839C2×C4C2×D4×D6111yescharacteristic
840C8—41no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—1222no—
845C8—2441no—
846C8—2441no—
847C8—2441no—
848C22—21no—
849C22—21no—
850C22—21no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—612no—
858C22—1221no—
859C22—1221no—
860C22—1221no—
861C22—1221no—
862C22—1221no—
863C22—9762no—
864C22—9762no—
865C22—2441no—
866C22—2441no—
867C22—2441no—
868C22C2×C22⋊C4×D6111yescharacteristic
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—21no—
874C4—21no—
875C4—41no—
876C4—41no—
877C4—1221no—
878C4—1221no—
879C4—1221no—
880C4—1221no—
881C4—1221no—
882C4—1221no—
883C4—2441no—
884C4—2441no—
885C4—2441no—
886C2—41no—
887C2—81no—
888C2—81no—
889C2—1222no—
890C2—4881no—
891C2—2441no—
892C2#2145429511yescharacteristic
893C2#421×D6111yescharacteristic
894C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1536C2
socleC22×C61C22×C22⋊C4
prime radical#21459775C2
cosocleC42×C61C24
hypercenter#1536D61
hypocenterC61#17679
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1536

Complements

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

NH ≅ G/Ntype
2. #21454828C2semidirect
3. #21454465C2semidirect
4. #21444451C2semidirect
5. #21444447C2semidirect
6. #21444441C2semidirect
7. #21444440C2semidirect
8. #21444436C2semidirect
9. #21444430C2semidirect
10. #21444423C2semidirect
11. #21444415C2semidirect
12. #21444415C2semidirect
13. #21444404C2semidirect
14. #329×D61C2semidirect
15. C61×#1536C2semidirect
44. #16839819C22semidirect
45. #16839817C22semidirect
46. #16839817C22semidirect
47. #16839817C22semidirect
48. #16839817C22semidirect
51. #16839714C22semidirect
52. #16839714C22semidirect
53. C2×#14519688C22semidirect
54. #97×D61C22semidirect
55. #97×D61C22semidirect
56. #16839503C22semidirect
57. #16839503C22semidirect
58. #16839503C22semidirect
59. #16839503C22semidirect
60. #16839502C22semidirect
61. #16839502C22semidirect
62. #16839502C22semidirect
63. #16839502C22semidirect
69. C61×#432C22semidirect
70. C61×#432C22semidirect
71. C61×#329C22semidirect
72. C61×#329C22semidirect
73. C61×#329C22semidirect
74. C61×#329C22semidirect
442. #1536D61semidirect
497. #432C2×D61semidirect
498. #432C2×D61semidirect
518. #329C2×D61semidirect
519. #329C2×D61semidirect
520. #329C2×D61semidirect
521. #329C2×D61semidirect
522. C61#17679semidirect

Maximal subgroups

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

subgroupindex
#214597752
#214548282
#214544652
#214444512
#214444472
#214444412
#214444402
#214444362
#214444302
#214444232
#214444152
#214444042
#329×D612
C61×#15362
#1767961