Finite Group Databasebeta

← #29648235

Subgroups — #29648235

Order 15616.

902 conjugacy classes of subgroups.

The subgroup lattice has 860 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459715C211yesmaximal, characteristic
2#21454833C211yesmaximal, characteristic, complemented
3#21444451C211yesmaximal, characteristic, complemented
4#21444448C211yesmaximal, characteristic, complemented
5#21444442C211yesmaximal, characteristic, complemented
6#21444440C211yesmaximal, characteristic, complemented
7#21444437C211yesmaximal, characteristic, complemented
8#21444435C211yesmaximal, characteristic, complemented
9#21444433C211yesmaximal, characteristic, complemented
10#21444427C211yesmaximal, characteristic, complemented
11#21444424C211yesmaximal, characteristic, complemented
12#21444408C211yesmaximal, characteristic, complemented
13#21444405C211yesmaximal, characteristic, complemented
14C2×#16839501C211yesmaximal, characteristic, complemented
15C61×#2970C211yesmaximal, characteristic, complemented
16#16840495—21no—
17#16840495—21no—
18#16840484—21no—
19#16840484—21no—
20#16840441—21no—
21#16840441—21no—
22#16840441—21no—
23#16840441—21no—
24#16840383C411yescharacteristic
25#16840383C411yescharacteristic
26#16840383C411yescharacteristic
27#16840383C411yescharacteristic
28#16840333C411yescharacteristic
29#16840326C411yescharacteristic
30#16840319C2211yescharacteristic
31#16840296C2211yescharacteristic
32#16840296C2211yescharacteristic
33#16840296C2211yescharacteristic
34#16840296C2211yescharacteristic
35C2×#14519765C2211yescharacteristic
36#16840239C411yescharacteristic
37#16840236C411yescharacteristic
38#16839893—21no—
39#16839834—21no—
40#16839834—21no—
41D4×#92418—21no—
42#16839819C2211yescharacteristic
43#16839819C2211yescharacteristic, complemented
44#16839819C2211yescharacteristic, complemented
45C4×#11758194C2211yescharacteristic, complemented
46C2×#14519688C2211yescharacteristic
47C2×#14519688C2211yescharacteristic, complemented
48#16839503C2211yescharacteristic, complemented
49#16839503C2211yescharacteristic, complemented
50#16839503C2211yescharacteristic, complemented
51#16839503C2211yescharacteristic, complemented
52#16839503C2211yescharacteristic, complemented
53#16839503C2211yescharacteristic, complemented
54#16839503C2211yescharacteristic, complemented
55#16839503C2211yescharacteristic, complemented
56#16839501C2211yescharacteristic
57#16839501C2211yescharacteristic
58#16839501C2211yescharacteristic
59#16839501C2211yescharacteristic
60#16839501C2211yescharacteristic
61#16839501C2211yescharacteristic
62#16839501C2211yescharacteristic
63#16839501C2211yescharacteristic
64C4×#41×C61C2211yescharacteristic
65C61×#446—21no—
66C61×#435—21no—
67C61×#435—21no—
68C8×D4×C61—21no—
69C61×#432C2211yescharacteristic
70C61×#432C2211yescharacteristic, complemented
71C61×#432C2211yescharacteristic, complemented
72C4×M16×C61C2211yescharacteristic, complemented
73C2×#97×C61C2211yescharacteristic
74C2×#97×C61C2211yescharacteristic, complemented
75C22×Dic122C2×C411yescharacteristic
76C22×D244C2×C411yescharacteristic
77C2×#11758194—21no—
78C22×#92418—21no—
79C22×#92418—21no—
80#14519777C2×C411yescharacteristic
81#14519777C2×C411yescharacteristic
82#14519775—21no—
83#14519773—21no—
84#14519772—21no—
85#14519772—21no—
86#14519772—21no—
87#14519772—21no—
88#14519771—21no—
89#14519771—21no—
90#14519771—21no—
91#14519771—21no—
92#14519769C2311yescharacteristic
93#14519769C2311yescharacteristic
94#14519766—21no—
95#14519765—21no—
96#14519765—21no—
97#14519765C2×C411yescharacteristic
98#14519765C2×C411yescharacteristic
99#14519765C2311yescharacteristic
100#14519765C2311yescharacteristic
101#14519764—21no—
102#14519763—21no—
103#14519763—21no—
104#14519763—21no—
105#14519763—21no—
106#14519760—21no—
107#14519760—21no—
108#14519760—21no—
109#14519760—21no—
110#14519759—21no—
111#14519759—21no—
112#14519759—21no—
113#14519759—21no—
114#14519758—21no—
115#14519758—21no—
116#14519756—21no—
117#14519756—21no—
118#14519756C2×C411yescharacteristic
119#14519756C2×C411yescharacteristic
120#14519756C2×C411yescharacteristic
121#14519756C2×C411yescharacteristic
122#14519755—21no—
123#14519755—21no—
124#14519755—21no—
125#14519755—21no—
126#14519751C2×C411yescharacteristic
127#14519751C2×C411yescharacteristic
128#14519751C2×C411yescharacteristic
129#14519751C2×C411yescharacteristic
130#14519745—21no—
131#14519745—21no—
132C4×Dic122—21no—
133C4×Dic122—21no—
134C4×Dic122C2×C411yescharacteristic
135C4×Dic122C2×C411yescharacteristic
136C4×Dic122C2×C411yescharacteristic
137C4×Dic122C2×C411yescharacteristic
138#14519742—21no—
139#14519742—21no—
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic
142C4×D244C2×C411yescharacteristic
143C4×D244C2×C411yescharacteristic
144#14519739—21no—
145#14519739—21no—
146C4×C22⋊D61—21no—
147C4×C22⋊D61—21no—
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150#14519736C2×C411yescharacteristic
151#14519736C2×C411yescharacteristic
152#14519734—21no—
153#14519734—21no—
154#14519734—21no—
155#14519734—21no—
156#14519733—21no—
157#14519733—21no—
158C2×#11758198—21no—
159C2×#11758198—21no—
160C22⋊C4×D61—21no—
161C22⋊C4×D61—21no—
162C4⋊#92418—21no—
163C4⋊#92418—21no—
164C4⋊#92418—21no—
165C22⋊#92418—21no—
166C22⋊#92418—21no—
167C22⋊#92418—21no—
168#14519688—21no—
169#14519688—21no—
170#14519688C2311yescharacteristic
171#14519688C2311yescharacteristic
172#14519688C2311yescharacteristic
173#14519688C2311yescharacteristic
174C4×#92418—21no—
175C2×#41×C61C2×C411yescharacteristic
176C2×M16×C61—21no—
177C22×C8×C61—21no—
178C22×C8×C61—21no—
179C4×Q8×C61D411yescharacteristic
180C4×Q8×C61D411yescharacteristic
181C4×D4×C61D411yescharacteristic
182C4×D4×C61D411yescharacteristic
183C4×D4×C61D411yescharacteristic
184C4×D4×C61D411yescharacteristic
185C4×D4×C61D411yescharacteristic
186C4×D4×C61D411yescharacteristic
187#117×C61C2×C411yescharacteristic
188#117×C61C2×C411yescharacteristic
189#117×C61C2×C411yescharacteristic
190C2×C42×C61C2311yescharacteristic
191C2×C42×C61C2311yescharacteristic
192C2×C42×C61C2311yescharacteristic
193C4⋊C8×C61—21no—
194C4⋊C8×C61—21no—
195C4⋊C8×C61—21no—
196C22⋊C8×C61—21no—
197C22⋊C8×C61—21no—
198C22⋊C8×C61—21no—
199#97×C61—21no—
200#97×C61—21no—
201#97×C61C2311yescharacteristic
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205C4×C8×C61—21no—
206C23×D61—21no—
207#41×C61—42no—
208C2×Q8×C61C22⋊C411yescharacteristic
209C2×D4×C61C22⋊C411yescharacteristic
210C2×D4×C61C22⋊C411yescharacteristic
211C2×D4×C61C22⋊C411yescharacteristic
212C22×C4×C61C22×C411yescharacteristic
213C22×C4×C61C22×C411yescharacteristic
214C22×C4×C61C22×C411yescharacteristic
215C22×C4×C61C2×D411yescharacteristic
216C22×C4×C61C2×D411yescharacteristic
217C22×C4×C61C2×D411yescharacteristic
218C22×C4×C61C2×D411yescharacteristic
219C22×C4×C61C2×D411yescharacteristic
220C22×C4×C61C2×D411yescharacteristic
221C2×C22⋊D61—21no—
222C2×C22⋊D61—21no—
223C2×C22⋊D61—21no—
224C2×C22⋊D61—21no—
225C22×Dic61—21no—
226C2×D244—21no—
227C2×D244—42no—
228C2×D244C22×C411yescharacteristic
229C2×D244C22×C411yescharacteristic
230C2×C4×D61—21no—
231C2×C4×D61—21no—
232C2×C4×D61—21no—
233C2×C4×D61—21no—
234C2×Dic122—21no—
235C2×Dic122—21no—
236C2×Dic122—21no—
237C2×Dic122—42no—
238C2×Dic122C22×C411yescharacteristic
239C2×Dic122C22×C411yescharacteristic
240M16×C61—42no—
241C2×C8×C61—21no—
242C2×C8×C61—21no—
243C2×C8×C61—21no—
244C2×C8×C61—21no—
245C2×C8×C61—42no—
246C2×C8×C61—42no—
247C4⋊C4×C61C22⋊C411yescharacteristic
248C4⋊C4×C61C22⋊C411yescharacteristic
249C4⋊C4×C61C22⋊C411yescharacteristic
250C4⋊C4×C61C22⋊C411yescharacteristic
251C4⋊C4×C61C22⋊C411yescharacteristic
252C4⋊C4×C61C22⋊C411yescharacteristic
253C22⋊C4×C61C22⋊C411yescharacteristic
254C22⋊C4×C61C22⋊C411yescharacteristic
255C22⋊C4×C61C22⋊C411yescharacteristic
256C22⋊C4×C61C22⋊C411yescharacteristic
257C22⋊C4×C61C22⋊C411yescharacteristic
258C22⋊C4×C61C22⋊C411yescharacteristic
259C42×C61C22×C411yescharacteristic
260C42×C61C22×C411yescharacteristic
261C42×C61C22×C411yescharacteristic
262C42×C61C2×D411yescharacteristic
263C42×C61C2×D411yescharacteristic
264C42×C61C2×D411yescharacteristic
265C42×C61C2×D411yescharacteristic
266C42×C61C2×D411yescharacteristic
267C42×C61C2×D411yescharacteristic
268C42×C61C2411yescharacteristic
269C22⋊Dic61—21no—
270C22⋊Dic61—21no—
271C22⋊Dic61—21no—
272C22⋊Dic61—21no—
273C22⋊Dic61—21no—
274C22⋊Dic61—21no—
275#11758198—21no—
276#11758198—21no—
277#11758198—21no—
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#11758198—21no—
289#11758198—21no—
290#11758198—21no—
291C4⋊Dic61—21no—
292C4⋊Dic61—21no—
293C4⋊Dic61C22×C411yescharacteristic
294C4⋊Dic61C22×C411yescharacteristic
295C4⋊Dic61C22×C411yescharacteristic
296C4⋊Dic61C22×C411yescharacteristic
297#11758196—21no—
298#11758196—21no—
299#11758196—21no—
300#11758196—21no—
301#11758196—21no—
302#11758196—21no—
303#11758196—21no—
304#11758196—21no—
305#11758196—21no—
306#11758196—21no—
307#11758196—21no—
308#11758196—21no—
309C4×Dic61—21no—
310C4×Dic61—21no—
311C4×Dic61—21no—
312C4×Dic61—21no—
313C4×Dic61—21no—
314C4×Dic61—21no—
315#11758194—42no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—21no—
319C2×#92418—21no—
320C2×#92418—42no—
321C2×#92418—42no—
322C23×C61C2×C22⋊C411yescharacteristic
323C23×C61C2×C22⋊C411yescharacteristic
324C23×C61C2×C22⋊C411yescharacteristic
325C22×D61—21no—
326C22×D61—21no—
327C22×D61—42no—
328C22×D61—81no—
329C22×D61—81no—
330Q8×C61—41no—
331D4×C61—22no—
332D4×C61—22no—
333D4×C61—41no—
334C2×C4×C61—22no—
335C2×C4×C61—41no—
336C2×C4×C61—41no—
337C2×C4×C61—41no—
338C2×C4×C61—41no—
339C2×C4×C61—41no—
340C2×C4×C61—41no—
341C2×C4×C61—41no—
342C2×C4×C61—41no—
343C2×C4×C61C2×C22⋊C411yescharacteristic
344C2×C4×C61C2×C22⋊C411yescharacteristic
345C2×C4×C61C2×C22⋊C411yescharacteristic
346C2×C4×C61C2×C22⋊C411yescharacteristic
347C2×C4×C61C2×C22⋊C411yescharacteristic
348C2×C4×C61C2×C22⋊C411yescharacteristic
349C2×C4×C61C2×C22⋊C411yescharacteristic
350C2×C4×C61C2×C22⋊C411yescharacteristic
351C2×C4×C61C2×C22⋊C411yescharacteristic
352C2×C4×C61C23×C411yescharacteristic
353C2×C4×C61C22×D411yescharacteristic
354C2×C4×C61C22×D411yescharacteristic
355C22⋊D61—81no—
356C22⋊D61—81no—
357C22⋊D61—81no—
358C22⋊D61—81no—
359C2×Dic61—21no—
360C2×Dic61—21no—
361C2×Dic61—21no—
362C2×Dic61—21no—
363C2×Dic61—21no—
364C2×Dic61—21no—
365C2×Dic61—42no—
366D244—41no—
367D244—41no—
368D244—42no—
369C4×D61—81no—
370C4×D61—81no—
371C4×D61—81no—
372C4×D61—81no—
373Dic122—42no—
374Dic122—41no—
375Dic122—41no—
376Dic122—81no—
377Dic122—81no—
378C8×C61—22no—
379C8×C61—41no—
380C8×C61—41no—
381C8×C61—41no—
382#92418—22no—
383#92418—41no—
384#92418—41no—
385#92418—41no—
386#17686—611nomaximal, Sylow
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—21no—
390C22×C61—21no—
391C22×C61—21no—
392C22×C61—21no—
393C22×C61—21no—
394C22×C61—21no—
395C22×C61#41312yes—
396C22×C61C22×C22⋊C411yescharacteristic
397C2×D61—41no—
398C2×D61—41no—
399C2×D61—41no—
400C2×D61—41no—
401C2×D61—41no—
402C2×D61—41no—
403C2×D61—162no—
404C4×C61—21no—
405C4×C61—21no—
406C4×C61—21no—
407C4×C61—21no—
408C4×C61—21no—
409C4×C61—21no—
410C4×C61—21no—
411C4×C61—21no—
412C4×C61—21no—
413C4×C61—21no—
414C4×C61—21no—
415C4×C61—21no—
416Dic61—41no—
417Dic61—41no—
418Dic61—41no—
419Dic61—41no—
420Dic61—41no—
421Dic61—41no—
422#3510—611no—
423#2970—611no—
424#2970D6111yescharacteristic, complemented
425#1535—611no—
426#1535—611no—
427#1533—611no—
428#1532—611no—
429#1532—611no—
430#1531—611no—
431#1531—611no—
432#1529—611no—
433#1529—611no—
434#1524—611no—
435#1524—611no—
436C2×#329—611no—
437C2×C61—22no—
438C2×C61—41no—
439C2×C61—41no—
440C2×C61C2×#41311yescharacteristic
441C2×C61#290111yescharacteristic
442C2×C61#290111yescharacteristic
443D61—81no—
444D61—81no—
445#559—1221no—
446#559—1221no—
447#556—1221no—
448#556—1221no—
449#551—1221no—
450#551—1221no—
451#551—1221no—
452#551—1221no—
453#542—611no—
454#542—611no—
455#542—611no—
456#542—611no—
457#536—611no—
458#535—611no—
459#533—611no—
460#529—611no—
461#529—611no—
462#529—611no—
463#529—611no—
464C2×#124—611no—
465#519—611no—
466#518—611no—
467C4×#41C2×D6111yescharacteristic
468#446—21no—
469#446—1221no—
470#435—21no—
471#435—21no—
472#435—1221no—
473#435—1221no—
474C8×D4—21no—
475C8×D4—1221no—
476#432—611no—
477#432—611no—
478#432—611no—
479#432C2×D6111yescharacteristic
480#432C2×D6111yescharacteristic, complemented
481#432C2×D6111yescharacteristic, complemented
482C4×M16—611no—
483C4×M16C2×D6111yescharacteristic, complemented
484C2×#97—611no—
485C2×#97—611no—
486C2×#97C2×D6111yescharacteristic
487C2×#97C2×D6111yescharacteristic, complemented
488#330—611no—
489#330—611no—
490#330—611no—
491#330—611no—
492#330—611no—
493#330—611no—
494#330—611no—
495#330—611no—
496#329—611no—
497#329—611no—
498#329—611no—
499#329—611no—
500#329—611no—
501#329—611no—
502#329—611no—
503#329—611no—
504C61#1768611yescharacteristic, complemented, Sylow
505C2×#41C4×D6111yescharacteristic
506C22×Q8—611no—
507C22×D4—611no—
508C2×M16—21no—
509C2×M16—1221no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—1221no—
513C22×C8—1221no—
514C4⋊Q8—611no—
515C4⋊Q8—611no—
516C4⋊Q8—1221no—
517#127—1221no—
518#126—1221no—
519#126—1221no—
520#126—1221no—
521#126—1221no—
522#126—1221no—
523#126—1221no—
524#126—1221no—
525#126—1221no—
526#125—611no—
527#125—611no—
528#124—611no—
529#124—611no—
530#124—611no—
531#124—611no—
532#124—1221no—
533#124—1221no—
534#124—1221no—
535#124—1221no—
536#124—1221no—
537#124—1221no—
538#124—1221no—
539#124—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546#123—1221no—
547#123—1221no—
548#123—1221no—
549#123—1221no—
550C22⋊Q8—611no—
551C22⋊Q8—611no—
552C22⋊Q8—611no—
553C22⋊Q8—611no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557C22⋊Q8—1221no—
558C22⋊Q8—1221no—
559C22⋊Q8—1221no—
560#121—611no—
561#121—611no—
562#121—611no—
563#121—611no—
564#120—1221no—
565#120—1221no—
566C4×Q8—611no—
567C4×Q8—611no—
568C4×Q8—611no—
569C4×Q8—611no—
570C4×Q8—1221no—
571C4×Q8—1221no—
572C4×Q8—1221no—
573C4×Q8—1221no—
574C4×Q8D24411yescharacteristic
575C4×Q8C22⋊D6111yescharacteristic
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—611no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1221no—
585C4×D4—1221no—
586C4×D4D24411yescharacteristic
587C4×D4D24411yescharacteristic
588C4×D4D24411yescharacteristic
589C4×D4C22⋊D6111yescharacteristic
590C4×D4C22⋊D6111yescharacteristic
591C4×D4C22⋊D6111yescharacteristic
592#117—611no—
593#117—611no—
594#117—1221no—
595#117—1221no—
596#117—1221no—
597#117—1221no—
598#117—1221no—
599#117—1221no—
600#117C4×D6111yescharacteristic
601#117C4×D6111yescharacteristic
602#117C4×D6111yescharacteristic
603C2×C22⋊C4—1221no—
604C2×C22⋊C4—1221no—
605C2×C22⋊C4—1221no—
606C2×C22⋊C4—1221no—
607C2×C42C22×D6111yescharacteristic
608C2×C42C22×D6111yescharacteristic
609C2×C42C22×D6111yescharacteristic
610C4⋊C8—21no—
611C4⋊C8—21no—
612C4⋊C8—21no—
613C4⋊C8—1221no—
614C4⋊C8—1221no—
615C4⋊C8—1221no—
616C22⋊C8—21no—
617C22⋊C8—21no—
618C22⋊C8—21no—
619C22⋊C8—1221no—
620C22⋊C8—1221no—
621C22⋊C8—1221no—
622#97—21no—
623#97—21no—
624#97—611no—
625#97—611no—
626#97—611no—
627#97—611no—
628#97—1221no—
629#97—1221no—
630#97C22×D6111yescharacteristic
631#97C22×D6111yescharacteristic
632#97C22×D6111yescharacteristic
633#97C22×D6111yescharacteristic
634C4×C8—21no—
635C4×C8—1221no—
636C24—1221no—
637#41—42no—
638C2×Q8—611no—
639C2×Q8—611no—
640C2×Q8—1221no—
641C2×Q8—1221no—
642C2×Q8—1221no—
643C2×Q8—2442no—
644C2×Q8#1175819811yescharacteristic
645C2×D4—611no—
646C2×D4—611no—
647C2×D4—1221no—
648C2×D4—1221no—
649C2×D4—1221no—
650C2×D4—1221no—
651C2×D4—1221no—
652C2×D4—2442no—
653C2×D4#1175819811yescharacteristic
654C2×D4#1175819811yescharacteristic
655C2×D4#1175819811yescharacteristic
656C22×C4—1221no—
657C22×C4—1221no—
658C22×C4—1221no—
659C22×C4—1221no—
660C22×C4—1221no—
661C22×C4C2×C4×D6111yescharacteristic
662C22×C4C2×C4×D6111yescharacteristic
663C22×C4C2×C4×D6111yescharacteristic
664C22×C4C2×D24411yescharacteristic
665C22×C4C2×D24411yescharacteristic
666C22×C4C2×D24411yescharacteristic
667C22×C4C2×C22⋊D6111yescharacteristic
668C22×C4C2×C22⋊D6111yescharacteristic
669C22×C4C2×C22⋊D6111yescharacteristic
670M16—42no—
671M16—2442no—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—42no—
677C2×C8—42no—
678C2×C8—1221no—
679C2×C8—1221no—
680C2×C8—1221no—
681C2×C8—1221no—
682C2×C8—2442no—
683C2×C8—2442no—
684C4⋊C4—611no—
685C4⋊C4—611no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—1221no—
689C4⋊C4—1221no—
690C4⋊C4—1221no—
691C4⋊C4—1221no—
692C4⋊C4—1221no—
693C4⋊C4—1221no—
694C4⋊C4—1221no—
695C4⋊C4—1221no—
696C4⋊C4—1221no—
697C4⋊C4—1221no—
698C4⋊C4—1221no—
699C4⋊C4—1221no—
700C4⋊C4—1221no—
701C4⋊C4—1221no—
702C4⋊C4#1175819811yescharacteristic
703C4⋊C4#1175819811yescharacteristic
704C4⋊C4#1175819811yescharacteristic
705C4⋊C4#1175819811yescharacteristic
706C4⋊C4#1175819811yescharacteristic
707C4⋊C4#1175819811yescharacteristic
708C22⋊C4—1221no—
709C22⋊C4—1221no—
710C22⋊C4—1221no—
711C22⋊C4—1221no—
712C22⋊C4—1221no—
713C22⋊C4—1221no—
714C22⋊C4—1221no—
715C22⋊C4—1221no—
716C22⋊C4—1221no—
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—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1221no—
730C22⋊C4#1175819811yescharacteristic
731C22⋊C4#1175819811yescharacteristic
732C22⋊C4#1175819811yescharacteristic
733C22⋊C4#1175819811yescharacteristic
734C22⋊C4#1175819811yescharacteristic
735C22⋊C4#1175819811yescharacteristic
736C42—1221no—
737C42—1221no—
738C42—1221no—
739C42—1221no—
740C42—1221no—
741C42—1221no—
742C42C2×C4×D6111yescharacteristic
743C42C2×C4×D6111yescharacteristic
744C42C2×C4×D6111yescharacteristic
745C42C2×D24411yescharacteristic
746C42C2×D24411yescharacteristic
747C42C2×D24411yescharacteristic
748C42C2×C22⋊D6111yescharacteristic
749C42C2×C22⋊D6111yescharacteristic
750C42C2×C22⋊D6111yescharacteristic
751C42C23×D6111yescharacteristic
752C23—1221no—
753C23—1221no—
754C23—4881no—
755C23—4881no—
756C23—2442no—
757C23C2×#1175819811yescharacteristic
758C23C2×#1175819811yescharacteristic
759C23C2×#1175819811yescharacteristic
760Q8—41no—
761Q8—4881no—
762Q8—4881no—
763Q8—2441no—
764Q8—2441no—
765Q8—2442no—
766D4—22no—
767D4—22no—
768D4—41no—
769D4—4881no—
770D4—4881no—
771D4—4881no—
772D4—4881no—
773D4—2441no—
774D4—2441no—
775D4—2442no—
776C2×C4—22no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—41no—
781C2×C4—41no—
782C2×C4—41no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—1221no—
786C2×C4—1221no—
787C2×C4—1221no—
788C2×C4—1221no—
789C2×C4—1221no—
790C2×C4—1221no—
791C2×C4—4881no—
792C2×C4—4881no—
793C2×C4—4881no—
794C2×C4—4881no—
795C2×C4—2442no—
796C2×C4C2×#1175819811yescharacteristic
797C2×C4C2×#1175819811yescharacteristic
798C2×C4C2×#1175819811yescharacteristic
799C2×C4C2×#1175819811yescharacteristic
800C2×C4C2×#1175819811yescharacteristic
801C2×C4C2×#1175819811yescharacteristic
802C2×C4C2×#1175819811yescharacteristic
803C2×C4C2×#1175819811yescharacteristic
804C2×C4C2×#1175819811yescharacteristic
805C2×C4C22×C4×D6111yescharacteristic
806C2×C4C22×C22⋊D6111yescharacteristic
807C2×C4C22×D24411yescharacteristic
808C8—22no—
809C8—41no—
810C8—41no—
811C8—41no—
812C8—1222no—
813C8—2441no—
814C8—2441no—
815C8—2441no—
816C22—21no—
817C22—21no—
818C22—21no—
819C22—21no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—9762no—
825C22—2441no—
826C22—2441no—
827C22—2441no—
828C22—2441no—
829C22—2441no—
830C22—2441no—
831C22#1683974412yes—
832C22C22×#1175819811yescharacteristic
833C4—21no—
834C4—21no—
835C4—21no—
836C4—21no—
837C4—21no—
838C4—21no—
839C4—21no—
840C4—21no—
841C4—21no—
842C4—21no—
843C4—21no—
844C4—21no—
845C4—2441no—
846C4—2441no—
847C4—2441no—
848C4—2441no—
849C4—2441no—
850C4—2441no—
851C2—22no—
852C2—41no—
853C2—41no—
854C2—4881no—
855C2—4881no—
856C2C2×#1683974411yescharacteristic
857C2#2145436411yescharacteristic
858C2#2145436711yescharacteristic
subgroupG/H
centerC22C22×#11758198
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#2970C2
socleC22×C61C22×C22⋊C4
prime radical#16840326C4
cosocleC42×C61C24
hypercenter#2970D61
hypocenterC61#17686
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C4×#41 ◁ #2970

Complements

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

NH ≅ G/Ntype
2. #21454833C2semidirect
3. #21444451C2semidirect
4. #21444448C2semidirect
5. #21444442C2semidirect
6. #21444440C2semidirect
7. #21444437C2semidirect
8. #21444435C2semidirect
9. #21444433C2semidirect
10. #21444427C2semidirect
11. #21444424C2semidirect
12. #21444408C2semidirect
13. #21444405C2semidirect
14. C2×#16839501C2semidirect
15. C61×#2970C2semidirect
43. #16839819C22semidirect
44. #16839819C22semidirect
45. C4×#11758194C22semidirect
47. C2×#14519688C22semidirect
48. #16839503C22semidirect
49. #16839503C22semidirect
50. #16839503C22semidirect
51. #16839503C22semidirect
52. #16839503C22semidirect
53. #16839503C22semidirect
54. #16839503C22semidirect
55. #16839503C22semidirect
70. C61×#432C22semidirect
71. C61×#432C22semidirect
72. C4×M16×C61C22semidirect
74. C2×#97×C61C22semidirect
424. #2970D61semidirect
480. #432C2×D61semidirect
481. #432C2×D61semidirect
483. C4×M16C2×D61semidirect
487. C2×#97C2×D61semidirect
504. C61#17686semidirect

Maximal subgroups

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

subgroupindex
#214597152
#214548332
#214444512
#214444482
#214444422
#214444402
#214444372
#214444352
#214444332
#214444272
#214444242
#214444082
#214444052
C2×#168395012
C61×#29702
#1768661