Finite Group Databasebeta

← #29648008

Subgroups — #29648008

Order 15616.

964 conjugacy classes of subgroups.

The subgroup lattice has 846 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459791C211yesmaximal, characteristic
2#21454828C211yesmaximal, characteristic, complemented
3#21454248C211yesmaximal, characteristic, complemented
4#21444440C211yesmaximal, characteristic, complemented
5#21444438C211yesmaximal, characteristic, complemented
6#21444432C211yesmaximal, characteristic, complemented
7#21444425C211yesmaximal, characteristic, complemented
8#21444419C211yesmaximal, characteristic, complemented
9#21444412C211yesmaximal, characteristic, complemented
10#21444408C211yesmaximal, characteristic, complemented
11#21444406C211yesmaximal, characteristic, complemented
12#21444406C211yesmaximal, characteristic, complemented
13C2×#16839504C211yesmaximal, characteristic, complemented
14#330×D61C211yesmaximal, characteristic, complemented
15C61×#1528C211yesmaximal, characteristic, complemented
16C2×#14519785—21no—
17#16840489C411yescharacteristic
18#16840468C411yescharacteristic
19#16840467C411yescharacteristic
20#16840465C411yescharacteristic
21#16840460C411yescharacteristic
22#16840450C411yescharacteristic
23#16840447—21no—
24#16840447C411yescharacteristic
25#16840444—21no—
26#16840444—21no—
27#16840413—21no—
28#16840413C411yescharacteristic
29#16840371—21no—
30#16840360—21no—
31#16840359—21no—
32#16840318C2211yescharacteristic
33#16840297C2211yescharacteristic
34#16840297C2211yescharacteristic
35#16840296C2211yescharacteristic
36#125×D61C2211yescharacteristic
37#16840243—21no—
38C4×#11758222C2211yescharacteristic
39#16839891—21no—
40#16839832—21no—
41#16839830—21no—
42#16839825—21no—
43#16839817C2211yescharacteristic
44#16839817C2211yescharacteristic
45#16839720—21no—
46#16839716—21no—
47#16839716—21no—
48#16839714C2211yescharacteristic
49#16839714C2211yescharacteristic
50#16839714C2211yescharacteristic
51C2×#14519688C2211yescharacteristic
52C2×#14519688C2211yescharacteristic
53#97×D61C2211yescharacteristic
54#97×D61C2211yescharacteristic
55#97×D61C2211yescharacteristic
56#16839504C2211yescharacteristic
57#16839504C2211yescharacteristic
58#16839504C2211yescharacteristic
59#16839504C2211yescharacteristic
60#16839503C2211yescharacteristic
61#16839503C2211yescharacteristic
62#16839503C2211yescharacteristic
63#16839503C2211yescharacteristic
64#16839501C2211yescharacteristic
65#16839501C2211yescharacteristic
66#16839501C2211yescharacteristic
67#16839501C2211yescharacteristic
68C2×#125×C61C2211yescharacteristic
69C61×#432C2211yescharacteristic
70C4×M16×C61C2211yescharacteristic
71C61×#330C2211yescharacteristic
72C61×#330C2211yescharacteristic
73C61×#330C2211yescharacteristic
74C61×#330C2211yescharacteristic
75C2×#11758222—21no—
76C2×#11758222D411yescharacteristic
77#14519785—28no—
78C2×#11758189—21no—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C22×#92418—21no—
82C22×#92418—21no—
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86#14519776—21no—
87#14519776C2×C411yescharacteristic
88#14519776C2×C411yescharacteristic
89#14519772—21no—
90#14519772—21no—
91#14519772—21no—
92#14519772—21no—
93#14519772—21no—
94#14519772—21no—
95#14519771—21no—
96#14519769C2311yescharacteristic
97#14519768—21no—
98#14519768C2×C411yescharacteristic
99#14519768C2×C411yescharacteristic
100#14519767—21no—
101#14519767—21no—
102#14519767—21no—
103#14519767—21no—
104#14519767—21no—
105#14519767—21no—
106#14519765C2311yescharacteristic
107#14519762—21no—
108#14519762—21no—
109#14519762—21no—
110#14519762—21no—
111#14519762—21no—
112#14519762—21no—
113#14519760—21no—
114#14519760—21no—
115#14519760—21no—
116#14519757—21no—
117#14519757C2×C411yescharacteristic
118#14519757C2×C411yescharacteristic
119#14519756—21no—
120#14519756C2×C411yescharacteristic
121#14519755—21no—
122#14519755—21no—
123#14519755—21no—
124#14519755—21no—
125#14519755—21no—
126#14519755—21no—
127#14519752—21no—
128#14519752C2×C411yescharacteristic
129#14519752C2×C411yescharacteristic
130#14519751—21no—
131#14519751C2×C411yescharacteristic
132C4×Dic122C2×C411yescharacteristic
133C4×Dic122C2×C411yescharacteristic
134C4×Dic122D411yescharacteristic
135#14519742—21no—
136#14519742—21no—
137#14519742—21no—
138#14519742C2×C411yescharacteristic
139#14519742C2×C411yescharacteristic
140C4×D244C2×C411yescharacteristic
141C4×D244C2×C411yescharacteristic
142C4×D244D411yescharacteristic
143#14519739—21no—
144#14519739—21no—
145#14519739—21no—
146#14519739C2×C411yescharacteristic
147#14519739C2×C411yescharacteristic
148C4×C22⋊D61—21no—
149C4×C22⋊D61—21no—
150C4×C22⋊D61—21no—
151C4×C22⋊D61C2×C411yescharacteristic
152C4×C22⋊D61C2×C411yescharacteristic
153C4×C22⋊D61D411yescharacteristic
154C4×C22⋊D61D411yescharacteristic
155#14519736—21no—
156#14519736D411yescharacteristic
157#14519735—21no—
158#14519735—21no—
159#14519735—21no—
160#14519735C2×C411yescharacteristic
161#14519735C2×C411yescharacteristic
162#14519734—21no—
163#14519734D411yescharacteristic
164#14519734D411yescharacteristic
165C4⋊C4×D61—21no—
166C4⋊C4×D61—21no—
167C4⋊C4×D61—21no—
168C4⋊C4×D61C2×C411yescharacteristic
169C4⋊C4×D61C2×C411yescharacteristic
170C42×D61C2311yescharacteristic
171C42×D61C2311yescharacteristic
172#14519706—21no—
173#14519706—21no—
174#14519689—21no—
175#14519689—21no—
176#14519688—21no—
177#14519688—21no—
178#14519688C2311yescharacteristic
179#14519688C2311yescharacteristic
180#14519688C2311yescharacteristic
181#14519688C2311yescharacteristic
182#14519687—21no—
183#14519687—21no—
184#14519687—21no—
185C8×Dic61—21no—
186C8×Dic61—21no—
187C8×Dic61—21no—
188C2×M16×C61—21no—
189#125×C61—21no—
190#125×C61—21no—
191#125×C61C2×C411yescharacteristic
192#125×C61C2×C411yescharacteristic
193#125×C61C2311yescharacteristic
194#125×C61C2311yescharacteristic
195C2×C4⋊C4×C61—21no—
196C2×C4⋊C4×C61—21no—
197C2×C4⋊C4×C61C2×C411yescharacteristic
198C2×C4⋊C4×C61C2×C411yescharacteristic
199C2×C42×C61C2311yescharacteristic
200C4⋊C8×C61—21no—
201C22⋊C8×C61—21no—
202#97×C61C2311yescharacteristic
203#97×C61C2311yescharacteristic
204#97×C61C2311yescharacteristic
205#97×C61C2311yescharacteristic
206C4×C8×C61—21no—
207C22×C4×C61—21no—
208C22×C4×C61—21no—
209C22×C4×C61C22×C411yescharacteristic
210C22×C4×C61C2×D411yescharacteristic
211C22×C4×C61C2×D411yescharacteristic
212C2×C22⋊D61—21no—
213C2×C22⋊D61C22⋊C411yescharacteristic
214C2×C22⋊D61C22⋊C411yescharacteristic
215#11758222—24no—
216#11758222—44no—
217C2×D244—21no—
218C2×D244—21no—
219C2×D244C22⋊C411yescharacteristic
220C2×D244C22×C411yescharacteristic
221C2×C4×D61—21no—
222C2×C4×D61—21no—
223C2×C4×D61—21no—
224C2×C4×D61—21no—
225C2×C4×D61—21no—
226C2×C4×D61C22×C411yescharacteristic
227C2×C4×D61C22×C411yescharacteristic
228C2×C4×D61C2×D411yescharacteristic
229C2×C4×D61C2×D411yescharacteristic
230C2×C4×D61C2×D411yescharacteristic
231C2×C4×D61C2×D411yescharacteristic
232C2×Dic122—21no—
233C2×Dic122—21no—
234C2×Dic122C22⋊C411yescharacteristic
235C2×Dic122C22×C411yescharacteristic
236M16×C61—24no—
237C2×C8×C61—21no—
238C2×C8×C61—21no—
239C2×C8×C61—21no—
240C2×C8×C61—21no—
241C4⋊C4×C61—21no—
242C4⋊C4×C61—21no—
243C4⋊C4×C61—21no—
244C4⋊C4×C61—21no—
245C4⋊C4×C61—21no—
246C4⋊C4×C61—21no—
247C4⋊C4×C61—21no—
248C4⋊C4×C61—21no—
249C4⋊C4×C61—21no—
250C4⋊C4×C61—21no—
251C4⋊C4×C61C22×C411yescharacteristic
252C4⋊C4×C61C22×C411yescharacteristic
253C4⋊C4×C61C22×C411yescharacteristic
254C4⋊C4×C61C22×C411yescharacteristic
255C42×C61C22×C411yescharacteristic
256C42×C61C2×D411yescharacteristic
257C42×C61C2×D411yescharacteristic
258C42×C61C2411yescharacteristic
259C22⋊Dic61—21no—
260C22⋊Dic61C22⋊C411yescharacteristic
261C22⋊Dic61C22⋊C411yescharacteristic
262#11758198—21no—
263#11758198—21no—
264#11758198—21no—
265#11758198—21no—
266#11758198—21no—
267#11758198—21no—
268#11758198—21no—
269#11758198—21no—
270#11758198—21no—
271#11758198—21no—
272#11758198—21no—
273#11758198—21no—
274#11758198C22⋊C411yescharacteristic
275#11758198C22⋊C411yescharacteristic
276#11758198C22⋊C411yescharacteristic
277#11758198C22⋊C411yescharacteristic
278C4⋊Dic61—21no—
279C4⋊Dic61—21no—
280C4⋊Dic61—21no—
281C4⋊Dic61—21no—
282C4⋊Dic61C22⋊C411yescharacteristic
283C4⋊Dic61C22⋊C411yescharacteristic
284C4⋊Dic61C22×C411yescharacteristic
285C4⋊Dic61C22×C411yescharacteristic
286#11758196—21no—
287#11758196—21no—
288#11758196—21no—
289#11758196—21no—
290#11758196—21no—
291#11758196—21no—
292#11758196—21no—
293#11758196—21no—
294#11758196—21no—
295#11758196—21no—
296#11758196—21no—
297#11758196—21no—
298#11758196C22⋊C411yescharacteristic
299#11758196C22⋊C411yescharacteristic
300#11758196C22⋊C411yescharacteristic
301#11758196C22⋊C411yescharacteristic
302C4×Dic61—21no—
303C4×Dic61—21no—
304C4×Dic61—21no—
305C4×Dic61—21no—
306C4×Dic61—21no—
307C4×Dic61C22×C411yescharacteristic
308C4×Dic61C22×C411yescharacteristic
309C4×Dic61C2×D411yescharacteristic
310C4×Dic61C2×D411yescharacteristic
311C4×Dic61C2×D411yescharacteristic
312C4×Dic61C2×D411yescharacteristic
313C2×#92418—24no—
314C2×#92418—21no—
315C2×#92418—21no—
316C2×#92418—21no—
317C2×#92418—21no—
318C2×#92418—42no—
319#11758189—24no—
320#11758189—24no—
321#11758189—42no—
322C8×D61—24no—
323C8×D61—24no—
324C8×D61—42no—
325C23×C61C2×C22⋊C411yescharacteristic
326C22×D61—21no—
327C22×D61C2×C22⋊C411yescharacteristic
328C22×D61C2×C22⋊C411yescharacteristic
329C2×C4×C61—22no—
330C2×C4×C61—21no—
331C2×C4×C61—21no—
332C2×C4×C61—21no—
333C2×C4×C61—21no—
334C2×C4×C61—41no—
335C2×C4×C61—41no—
336C2×C4×C61—42no—
337C2×C4×C61—81no—
338C2×C4×C61C2×C22⋊C411yescharacteristic
339C2×C4×C61C2×C22⋊C411yescharacteristic
340C2×C4×C61C2×C22⋊C411yescharacteristic
341C2×C4×C61C23×C411yescharacteristic
342C2×C4×C61C22×D411yescharacteristic
343C2×C4×C61C22×D411yescharacteristic
344C22⋊D61—22no—
345C22⋊D61—42no—
346C22⋊D61#10414yes—
347C2×Dic61—21no—
348C2×Dic61—21no—
349C2×Dic61—21no—
350C2×Dic61C2×C22⋊C411yescharacteristic
351C2×Dic61C2×C22⋊C411yescharacteristic
352C2×Dic61C2×C22⋊C411yescharacteristic
353C2×Dic61C2×C22⋊C411yescharacteristic
354C2×Dic61C2×C22⋊C411yescharacteristic
355C2×Dic61C2×C22⋊C411yescharacteristic
356D244—22no—
357D244—41no—
358D244—42no—
359D244—81no—
360C4×D61—22no—
361C4×D61—22no—
362C4×D61—41no—
363C4×D61—41no—
364C4×D61—41no—
365C4×D61—41no—
366C4×D61—42no—
367C4×D61—42no—
368C4×D61—81no—
369C4×D61—81no—
370C4×D61—81no—
371Dic122—22no—
372Dic122—42no—
373Dic122—41no—
374Dic122—81no—
375C8×C61—22no—
376C8×C61—22no—
377C8×C61—41no—
378C8×C61—41no—
379#92418—22no—
380#92418—22no—
381#92418—22no—
382#92418—41no—
383#17653—611nomaximal, Sylow
384C22×C61—21no—
385C22×C61—21no—
386C22×C61C2×#10412yes—
387C22×C61C22×C22⋊C411yescharacteristic
388C2×D61—21no—
389C2×D61—21no—
390C2×D61—21no—
391C2×D61—21no—
392C2×D61—21no—
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C2×D61C2×#10412yes—
397C4×C61—21no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—21no—
401C4×C61—21no—
402C4×C61—21no—
403C4×C61—41no—
404C4×C61—41no—
405C4×C61—41no—
406C4×C61—41no—
407Dic61—21no—
408Dic61—21no—
409Dic61—21no—
410Dic61—21no—
411Dic61—21no—
412Dic61—41no—
413Dic61—41no—
414Dic61—41no—
415Dic61C2×#10412yes—
416#3515—611no—
417#2970—611no—
418#2875—611no—
419#1532—611no—
420#1532—611no—
421#1531—611no—
422#1529—611no—
423#1528—611no—
424#1528D6111yescharacteristic, complemented
425#1526—611no—
426#1524—611no—
427#1524—611no—
428#1524—611no—
429C2×#330—611no—
430C2×#330—611no—
431C2×C61—22no—
432C2×C61#288911yescharacteristic
433C2×C61C22×#10411yescharacteristic
434C2×C61#290111yescharacteristic
435D61—22no—
436D61—41no—
437D61—81no—
438C2×#131—1221no—
439#557—611no—
440#554—611no—
441#554—611no—
442#553—611no—
443#553—611no—
444#552—611no—
445#552—611no—
446#552—1221no—
447#552—1221no—
448#552—1221no—
449#547—611no—
450#547—1221no—
451#541—1221no—
452#539—1221no—
453#539—1221no—
454#533—611no—
455#529—611no—
456#529—611no—
457#529—611no—
458C2×#125—611no—
459C2×#125C2×D6111yescharacteristic
460#520—1221no—
461C4×#41—611no—
462#446—1221no—
463#435—1221no—
464#435—1221no—
465C8×D4—1221no—
466#432—611no—
467#432—611no—
468#432C2×D6111yescharacteristic
469#405—1221no—
470#405—1221no—
471#405—1221no—
472C4×M16—611no—
473C4×M16—611no—
474C4×M16—611no—
475C4×M16C2×D6111yescharacteristic
476C2×#97—611no—
477C2×#97—611no—
478C2×#97—611no—
479C2×#97—611no—
480C2×#97—611no—
481#330—611no—
482#330—611no—
483#330—611no—
484#330—611no—
485#330—611no—
486#330—611no—
487#330—611no—
488#330—611no—
489#330C2×D6111yescharacteristic
490#330C2×D6111yescharacteristic
491#330C2×D6111yescharacteristic
492#330C2×D6111yescharacteristic
493#329—611no—
494#329—611no—
495#329—611no—
496#329—611no—
497C61#1765311yescharacteristic, complemented, Sylow
498C2×#41—611no—
499C2×#41—1221no—
500#131—1228no—
501C2×M16—21no—
502C2×M16—1221no—
503C2×M16—1221no—
504C2×M16—1221no—
505C22×C8—1221no—
506C22×C8—1221no—
507C22×C8—1221no—
508C22×C8—1221no—
509C22×C8—1221no—
510C4⋊Q8—611no—
511C4⋊Q8—611no—
512C4⋊Q8—1221no—
513#126—1221no—
514#126—1221no—
515#126—1221no—
516#126—1221no—
517#126—1221no—
518#126—1221no—
519#126—1221no—
520#125—21no—
521#125—21no—
522#125—611no—
523#125—611no—
524#125—611no—
525#125—1221no—
526#125—1221no—
527#125—1221no—
528#125—1221no—
529#125—1221no—
530#125—1221no—
531#125—1221no—
532#125C4×D6111yescharacteristic
533#125C4×D6111yescharacteristic
534#125C22×D6111yescharacteristic
535#125C22×D6111yescharacteristic
536#124—611no—
537#123—1221no—
538#123—1221no—
539#123—1221no—
540#123—1221no—
541#123—1221no—
542#123—1221no—
543#123—1221no—
544#123—1221no—
545#123—1221no—
546C22⋊Q8—611no—
547C22⋊Q8—611no—
548C22⋊Q8—611no—
549C22⋊Q8—1221no—
550C22⋊Q8—1221no—
551C22⋊Q8—1221no—
552C22⋊Q8—1221no—
553C22⋊Q8—1221no—
554C22⋊Q8—1221no—
555C22⋊Q8—1221no—
556C22⋊Q8—1221no—
557#121—611no—
558#121—611no—
559#121—611no—
560#121—1221no—
561#121—1221no—
562C4×Q8—611no—
563C4×Q8—611no—
564C4×Q8—611no—
565C4×Q8—611no—
566C4×Q8—611no—
567C4×Q8—1221no—
568C4×Q8—1221no—
569C4×Q8—1221no—
570C4×D4—611no—
571C4×D4—611no—
572C4×D4—611no—
573C4×D4—611no—
574C4×D4—611no—
575C4×D4—611no—
576C4×D4—611no—
577C4×D4—611no—
578C4×D4—611no—
579C4×D4—1221no—
580C4×D4—1221no—
581C4×D4—1221no—
582C4×D4—1221no—
583C4×D4—1221no—
584C4×D4—1221no—
585#117—611no—
586#117—611no—
587#117—611no—
588#117—611no—
589#117—611no—
590#117—1221no—
591#117—1221no—
592#117—1221no—
593#117—1221no—
594#117—1221no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—21no—
597C2×C4⋊C4—611no—
598C2×C4⋊C4—611no—
599C2×C4⋊C4—1221no—
600C2×C4⋊C4—1221no—
601C2×C4⋊C4—1221no—
602C2×C4⋊C4C4×D6111yescharacteristic
603C2×C4⋊C4C4×D6111yescharacteristic
604C2×C42—611no—
605C2×C42—611no—
606C2×C42C22×D6111yescharacteristic
607C4⋊C8—21no—
608C4⋊C8—1221no—
609C4⋊C8—1221no—
610C22⋊C8—21no—
611C22⋊C8—1221no—
612C22⋊C8—1221no—
613#97—611no—
614#97—611no—
615#97—611no—
616#97—611no—
617#97—1221no—
618#97—1221no—
619#97—1221no—
620#97—1221no—
621#97—1221no—
622#97C22×D6111yescharacteristic
623#97C22×D6111yescharacteristic
624#97C22×D6111yescharacteristic
625#97C22×D6111yescharacteristic
626C4×C8—21no—
627C4×C8—1221no—
628C4×C8—1221no—
629C4×C8—1221no—
630#41—1224no—
631#41—2444no—
632C2×Q8—611no—
633C2×Q8—611no—
634C2×Q8—1221no—
635C2×Q8—1221no—
636C2×D4—611no—
637C2×D4—611no—
638C2×D4—611no—
639C2×D4—611no—
640C2×D4—1221no—
641C2×D4—1221no—
642C2×D4—1221no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—611no—
646C22×C4—611no—
647C22×C4—611no—
648C22×C4—611no—
649C22×C4—611no—
650C22×C4—611no—
651C22×C4—1221no—
652C22×C4—1221no—
653C22×C4—1221no—
654C22×C4—1221no—
655C22×C4—1221no—
656C22×C4C2×C4×D6111yescharacteristic
657C22×C4D4×D6111yescharacteristic
658C22×C4D4×D6111yescharacteristic
659M16—24no—
660M16—1224no—
661M16—1224no—
662M16—2442no—
663C2×C8—21no—
664C2×C8—21no—
665C2×C8—21no—
666C2×C8—21no—
667C2×C8—1224no—
668C2×C8—1224no—
669C2×C8—1224no—
670C2×C8—1221no—
671C2×C8—1221no—
672C2×C8—1221no—
673C2×C8—1221no—
674C2×C8—2442no—
675C2×C8—2442no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—611no—
687C4⋊C4—611no—
688C4⋊C4—611no—
689C4⋊C4—611no—
690C4⋊C4—611no—
691C4⋊C4—611no—
692C4⋊C4—611no—
693C4⋊C4—611no—
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—1221no—
703C4⋊C4—1221no—
704C4⋊C4—1221no—
705C4⋊C4—1221no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1221no—
709C4⋊C4—1221no—
710C4⋊C4C2×C4×D6111yescharacteristic
711C4⋊C4C2×C4×D6111yescharacteristic
712C4⋊C4C2×C4×D6111yescharacteristic
713C4⋊C4C2×C4×D6111yescharacteristic
714C22⋊C4—611no—
715C22⋊C4—611no—
716C22⋊C4—611no—
717C22⋊C4—611no—
718C22⋊C4—611no—
719C22⋊C4—611no—
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—1221no—
731C22⋊C4—1221no—
732C22⋊C4—1221no—
733C42—611no—
734C42—611no—
735C42—611no—
736C42—611no—
737C42—611no—
738C42—611no—
739C42—1221no—
740C42—1221no—
741C42—1221no—
742C42—1221no—
743C42—1221no—
744C42C2×C4×D6111yescharacteristic
745C42D4×D6111yescharacteristic
746C42D4×D6111yescharacteristic
747C42C23×D6111yescharacteristic
748C23—611no—
749C23—611no—
750C23—1221no—
751C23C22⋊C4×D6111yescharacteristic
752Q8—1222no—
753Q8—4881no—
754Q8—2441no—
755Q8—2442no—
756D4—614no—
757D4—1222no—
758D4—1222no—
759D4—4881no—
760D4—2441no—
761D4—2442no—
762D4—2442no—
763C2×C4—22no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—42no—
771C2×C4—81no—
772C2×C4—611no—
773C2×C4—611no—
774C2×C4—611no—
775C2×C4—611no—
776C2×C4—611no—
777C2×C4—611no—
778C2×C4—1222no—
779C2×C4—1222no—
780C2×C4—1221no—
781C2×C4—1221no—
782C2×C4—1221no—
783C2×C4—4881no—
784C2×C4—4881no—
785C2×C4—4881no—
786C2×C4—2441no—
787C2×C4—2441no—
788C2×C4—2441no—
789C2×C4—2441no—
790C2×C4—2442no—
791C2×C4—2442no—
792C2×C4C22⋊C4×D6111yescharacteristic
793C2×C4C22⋊C4×D6111yescharacteristic
794C2×C4C22⋊C4×D6111yescharacteristic
795C2×C4C22×C4×D6111yescharacteristic
796C2×C4C2×D4×D6111yescharacteristic
797C2×C4C2×D4×D6111yescharacteristic
798C8—22no—
799C8—22no—
800C8—41no—
801C8—41no—
802C8—1222no—
803C8—1222no—
804C8—1222no—
805C8—2441no—
806C22—21no—
807C22—21no—
808C22—612no—
809C22—1221no—
810C22—1221no—
811C22—1221no—
812C22—1221no—
813C22—1221no—
814C22—2441no—
815C22—2441no—
816C22—2441no—
817C22#104×D6112yes—
818C22C2×C22⋊C4×D6111yescharacteristic
819C4—21no—
820C4—21no—
821C4—21no—
822C4—21no—
823C4—21no—
824C4—21no—
825C4—41no—
826C4—41no—
827C4—41no—
828C4—41no—
829C4—612no—
830C4—1221no—
831C4—1221no—
832C4—1221no—
833C4—1221no—
834C4—1221no—
835C4—2441no—
836C4—2441no—
837C4—2441no—
838C2—22no—
839C2—1222no—
840C2—4881no—
841C2—2441no—
842C2#2145429911yescharacteristic
843C2C2×#104×D6111yescharacteristic
844C2#2145436511yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D61
commutatorC2×C4×C61C23×C4
FrattiniC42C23×D61
FittingC61×#1528C2
socleC22×C61C22×C22⋊C4
prime radical#21459791C2
cosocleC42×C61C24
hypercenter#1528D61
hypocenterC61#17653
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1528

Complements

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

NH ≅ G/Ntype
2. #21454828C2semidirect
3. #21454248C2semidirect
4. #21444440C2semidirect
5. #21444438C2semidirect
6. #21444432C2semidirect
7. #21444425C2semidirect
8. #21444419C2semidirect
9. #21444412C2semidirect
10. #21444408C2semidirect
11. #21444406C2semidirect
12. #21444406C2semidirect
13. C2×#16839504C2semidirect
14. #330×D61C2semidirect
15. C61×#1528C2semidirect
424. #1528D61semidirect
497. C61#17653semidirect

Maximal subgroups

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

subgroupindex
#214597912
#214548282
#214542482
#214444402
#214444382
#214444322
#214444252
#214444192
#214444122
#214444082
#214444062
C2×#168395042
#330×D612
C61×#15282
#1765361