Finite Group Databasebeta

← #30552422

Subgroups — #30552422

Order 15616.

1682 conjugacy classes of subgroups.

The subgroup lattice has 838 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21459571C211yesmaximal, characteristic
2#21457117C214yesmaximal, complemented
3#21457087C214yesmaximal, complemented
4#21457040C212yesmaximal, complemented
5#21457025C212yesmaximal, complemented
6#21456987C212yesmaximal, complemented
7#21456963C212yesmaximal, complemented
8#21456345C212yesmaximal, complemented
9#21456189C212yesmaximal, complemented
10#21455767C211yesmaximal, characteristic, complemented
11#21455742C211yesmaximal, characteristic
12#21455732C211yesmaximal, characteristic
13C2×#16840092C211yesmaximal, characteristic, complemented
14#21455677C212yesmaximal, complemented
15#21455655C212yesmaximal, complemented
16#21454477C211yesmaximal, characteristic, complemented
17C2×C61×#544C211yesmaximal, characteristic, complemented
18#16840480—21no—
19#16840467—21no—
20#16840451—21no—
21#16840447—21no—
22#16840445—22no—
23#16840438—22no—
24#16840390C2211yescharacteristic
25#16840383C2212yes—
26#16840374C2212yes—
27#16840338C2211yescharacteristic
28#16840319C2212yes—
29#16840296C2212yes—
30#16840273C2211yescharacteristic
31C2×#14519756C2211yescharacteristic
32#16840242C2211yescharacteristic
33#16840239C2211yescharacteristic
34#16840172C2214yescomplemented
35#16840168C2214yescomplemented
36#16840161C2214yescomplemented
37#16840158C2214yescomplemented
38#16840132C2214yescomplemented
39#16840124C2214yescomplemented
40#16840119C2214yescomplemented
41#16840114C2214yescomplemented
42#16840103C2212yes—
43#16840103C2214yes—
44#16840097C2212yes—
45#16840097C2211yescharacteristic
46#16840097C2212yes—
47#16840092C2211yescharacteristic
48#16840092C2212yes—
49#16840092C2212yes—
50#16840092C2212yes—
51#16840092C2212yes—
52#16840092C2214yes—
53#16840086C2212yes—
54#16840080C2211yescharacteristic
55#16840080C2212yes—
56#16840075C2212yes—
57#16840075C2211yescharacteristic
58#16840066C2214yescomplemented
59#16840066C2214yescomplemented
60#16840066C2214yescomplemented
61#16840059C2214yescomplemented
62#16840054C2214yescomplemented
63#16840049C2214yescomplemented
64#16840044C2214yescomplemented
65#16840044C2214yescomplemented
66#16839823C2214yes—
67#16839819C2212yes—
68#16839815C2212yes—
69#16839805C2212yes—
70#16839802C2212yes—
71#16839798C2212yes—
72C2×#14519708C2212yes—
73#16839789C2212yes—
74#16839770C2212yes—
75#16839761C2212yes—
76#16839756C2212yes—
77C2×#14519700C2212yes—
78#16839726C2211yescharacteristic
79C2×C22⋊#92418C2211yescharacteristic
80#16839718C2212yes—
81C61×#544—21no—
82C61×#544—21no—
83C61×#544—22no—
84C61×#544C2212yes—
85C61×#544C2212yes—
86C61×#544C2214yes—
87C2×C4⋊Q8×C61—21no—
88C2×C4⋊Q8×C61C2212yes—
89C2×#125×C61—21no—
90C2×#125×C61C2212yes—
91C2×C22⋊Q8×C61—22no—
92C2×#117×C61C2211yescharacteristic
93C2×#117×C61C2211yescharacteristic
94C22×C4⋊C4×C61C2211yescharacteristic
95C2×#11758222C2311yescharacteristic
96C22×Dic122C2311yescharacteristic
97C2×#11758194C2312yes—
98C22×#92418C2312yes—
99#14519777C2312yes—
100#14519777C2312yes—
101#14519776—21no—
102#14519772—22no—
103#14519771—22no—
104#14519770—22no—
105#14519770—22no—
106#14519769—22no—
107#14519769C2312yes—
108#14519768—21no—
109#14519767—22no—
110#14519767—22no—
111#14519765C2312yes—
112#14519763—22no—
113#14519761—22no—
114#14519760—21no—
115#14519760—22no—
116#14519759—22no—
117#14519757—21no—
118#14519757—21no—
119#14519756—21no—
120#14519756—21no—
121#14519756—22no—
122#14519756C2312yes—
123#14519756C2312yes—
124#14519756C2311yescharacteristic
125#14519756C2311yescharacteristic
126#14519755—22no—
127#14519754—22no—
128#14519751C2311yescharacteristic
129#14519751C2311yescharacteristic
130#14519746—21no—
131C4×Dic122—22no—
132C4×Dic122C2312yes—
133C4×Dic122C2312yes—
134C4×Dic122C2312yes—
135#14519742—21no—
136#14519742—21no—
137C4×D244C2312yes—
138C4×C22⋊D61—21no—
139C4×C22⋊D61—21no—
140C4×C22⋊D61—22no—
141#14519737—22no—
142#14519736—22no—
143#14519736C2311yescharacteristic
144#14519735—21no—
145#14519734—22no—
146#14519733—22no—
147C2×C4⋊Dic61C2311yescharacteristic
148C2×#11758196—21no—
149C4⋊C4×D61—21no—
150C2×C22⋊Dic61—21no—
151#14519710C2312yes—
152#14519710C2312yes—
153#14519710C2314yes—
154#14519710C2314yes—
155#14519708C2312yes—
156#14519708C2314yes—
157#14519708C2314yes—
158#14519708C2314yes—
159#14519708C2314yes—
160#14519708C2312yes—
161C4⋊#92418C2314yes—
162C4⋊#92418C2314yes—
163#14519700C2314yes—
164#14519700C2314yes—
165#14519700C2312yes—
166#14519700C2312yes—
167#14519700C2314yes—
168#14519700C2314yes—
169#14519700C2314yes—
170#14519697C2312yes—
171#14519697C2312yes—
172#14519697C2314yes—
173C22⋊#92418C2311yescharacteristic
174C22⋊#92418C2311yescharacteristic
175C22⋊#92418C2312yes—
176C22⋊#92418C2312yes—
177C22⋊#92418C2312yes—
178#14519688C2314yes—
179C4×#92418C2314yes—
180C22×Q8×C61—22no—
181C23×C4×C61—21no—
182C23×C4×C61C2311yescharacteristic
183C4⋊Q8×C61—22no—
184C4⋊Q8×C61—22no—
185C4⋊Q8×C61—24no—
186C4⋊Q8×C61—22no—
187C4⋊Q8×C61—22no—
188C4⋊Q8×C61C2314yes—
189C4⋊Q8×C61C2314yes—
190#125×C61—22no—
191#125×C61—24no—
192#125×C61—22no—
193#125×C61—22no—
194#125×C61—22no—
195#125×C61C2314yes—
196#125×C61C2314yes—
197C22⋊Q8×C61—24no—
198C22⋊Q8×C61—24no—
199C22⋊Q8×C61—24no—
200C22⋊Q8×C61—24no—
201#117×C61—21no—
202#117×C61—21no—
203#117×C61D411yescharacteristic
204#117×C61D411yescharacteristic
205#117×C61D412yes—
206#117×C61C2312yes—
207#117×C61C2312yes—
208#117×C61C2311yescharacteristic
209#117×C61C2311yescharacteristic
210#117×C61C2312yes—
211C2×C4⋊C4×C61—21no—
212C2×C4⋊C4×C61—22no—
213C2×C4⋊C4×C61—22no—
214C2×C4⋊C4×C61—21no—
215C2×C4⋊C4×C61—21no—
216C2×C4⋊C4×C61—22no—
217C2×C4⋊C4×C61D411yescharacteristic
218C2×C4⋊C4×C61D411yescharacteristic
219C2×C4⋊C4×C61C2311yescharacteristic
220C2×C4⋊C4×C61C2312yes—
221C2×C4⋊C4×C61C2312yes—
222C2×C4⋊C4×C61C2312yes—
223C2×C4⋊C4×C61C2311yescharacteristic
224C2×C22⋊C4×C61—21no—
225C2×C22⋊C4×C61D412yes—
226C2×C42×C61—21no—
227C2×C42×C61C2312yes—
228C24×C61C2×D411yescharacteristic
229C2×Q8×C61—24no—
230C2×Q8×C61—24no—
231C2×Q8×C61—84no—
232C22×C4×C61—24no—
233C22×C4×C61—21no—
234C22×C4×C61—21no—
235C22×C4×C61—22no—
236C22×C4×C61—22no—
237C22×C4×C61—22no—
238C22×C4×C61—82no—
239C22×C4×C61C2×D411yescharacteristic
240C22×C4×C61C2×D412yes—
241C22×C4×C61C2×D411yescharacteristic
242C22×C4×C61C2×D411yescharacteristic
243C22×C4×C61C2×D412yes—
244C22×C4×C61C2411yescharacteristic
245C22×C4×C61C2411yescharacteristic
246C22×C4×C61C2411yescharacteristic
247C2×C22⋊D61—21no—
248C2×C22⋊D61—21no—
249C2×C22⋊D61—21no—
250C22×Dic61—21no—
251C22×Dic61—21no—
252#11758222—24no—
253C2×D244C2411yescharacteristic
254C2×C4×D61—21no—
255C2×C4×D61—22no—
256C2×Dic122—24no—
257C2×Dic122—21no—
258C2×Dic122—22no—
259C2×Dic122C2412yes—
260C2×Dic122C2411yescharacteristic
261C4⋊C4×C61—22no—
262C4⋊C4×C61—22no—
263C4⋊C4×C61—22no—
264C4⋊C4×C61—24no—
265C4⋊C4×C61—24no—
266C4⋊C4×C61—24no—
267C4⋊C4×C61—24no—
268C4⋊C4×C61—24no—
269C4⋊C4×C61—24no—
270C4⋊C4×C61—21no—
271C4⋊C4×C61—21no—
272C4⋊C4×C61C2×D411yescharacteristic
273C4⋊C4×C61C2×D412yes—
274C4⋊C4×C61C2×D411yescharacteristic
275C4⋊C4×C61C2×D411yescharacteristic
276C4⋊C4×C61C2×D411yescharacteristic
277C4⋊C4×C61C2×D412yes—
278C4⋊C4×C61C2414yes—
279C4⋊C4×C61C2412yes—
280C4⋊C4×C61C2412yes—
281C22⋊C4×C61—22no—
282C22⋊C4×C61—22no—
283C22⋊C4×C61C2×D412yes—
284C22⋊C4×C61C2×D412yes—
285C22⋊C4×C61C2×D412yes—
286C22⋊C4×C61C2×D412yes—
287C42×C61—22no—
288C42×C61—22no—
289C42×C61C2×D412yes—
290C42×C61C2×D412yes—
291C42×C61C2412yes—
292C42×C61C2412yes—
293C22⋊Dic61—22no—
294C22⋊Dic61—22no—
295C22⋊Dic61—21no—
296C22⋊Dic61—21no—
297C22⋊Dic61—21no—
298#11758198—21no—
299#11758198—22no—
300#11758198—22no—
301#11758198—21no—
302#11758198—22no—
303C4⋊Dic61—21no—
304C4⋊Dic61—22no—
305C4⋊Dic61—22no—
306C4⋊Dic61—22no—
307C4⋊Dic61C2412yes—
308C4⋊Dic61C2411yescharacteristic
309C4⋊Dic61C2411yescharacteristic
310#11758196—22no—
311#11758196—22no—
312#11758196—22no—
313#11758196—22no—
314#11758196—22no—
315#11758196—22no—
316#11758196—21no—
317#11758196—22no—
318#11758196—21no—
319C4×Dic61—22no—
320C4×Dic61—22no—
321C4×Dic61—22no—
322C4×Dic61—21no—
323#11758194—24no—
324C2×#92418—24no—
325C2×#92418C2412yes—
326C2×#92418C2414yes—
327C2×#92418C2412yes—
328C23×C61—22no—
329C23×C61—22no—
330C23×C61—41no—
331C23×C61C22×D411yescharacteristic
332C23×C61C22×D411yescharacteristic
333C23×C61C22×D411yescharacteristic
334C22×D61—21no—
335Q8×C61—84no—
336Q8×C61—84no—
337C2×C4×C61—22no—
338C2×C4×C61—24no—
339C2×C4×C61—22no—
340C2×C4×C61—22no—
341C2×C4×C61—22no—
342C2×C4×C61—22no—
343C2×C4×C61—22no—
344C2×C4×C61—22no—
345C2×C4×C61—24no—
346C2×C4×C61—42no—
347C2×C4×C61—42no—
348C2×C4×C61—44no—
349C2×C4×C61—42no—
350C2×C4×C61—82no—
351C2×C4×C61—82no—
352C2×C4×C61C22×D412yes—
353C2×C4×C61C22×D412yes—
354C2×C4×C61C22×D411yescharacteristic
355C2×C4×C61C22×D411yescharacteristic
356C2×C4×C61C22×D412yes—
357C2×C4×C61C22×D412yes—
358C2×C4×C61C22×D411yescharacteristic
359C2×C4×C612−1+414yes—
360C2×C4×C61C2511yescharacteristic
361C22⋊D61—42no—
362C22⋊D61—42no—
363C22⋊D61—81no—
364C2×Dic61—21no—
365C2×Dic61—21no—
366C2×Dic61—21no—
367C2×Dic61—22no—
368C2×Dic61—22no—
369C2×Dic61—42no—
370C2×Dic61—81no—
371D244—22no—
372C4×D61—42no—
373C4×D61—82no—
374Dic122—24no—
375Dic122—22no—
376Dic122—42no—
377Dic122—82no—
378#92418—22no—
379#92418—22no—
380#92418—24no—
381#60872—611nomaximal, Sylow
382C22×C61—21no—
383C22×C61—21no—
384C22×C61—21no—
385C22×C61—21no—
386C22×C61—21no—
387C22×C61—21no—
388C22×C61—21no—
389C22×C61—44no—
390C22×C61#53612yes—
391C22×C61#57712yes—
392C22×C61C23×D411yescharacteristic
393C2×D61—41no—
394C2×D61—41no—
395C2×D61—41no—
396C4×C61—22no—
397C4×C61—22no—
398C4×C61—21no—
399C4×C61—21no—
400C4×C61—22no—
401C4×C61—22no—
402C4×C61—42no—
403C4×C61—44no—
404C4×C61—42no—
405C4×C61#53612yes—
406C4×C61C2×2−1+412yes—
407Dic61—41no—
408Dic61—42no—
409Dic61—42no—
410Dic61—41no—
411Dic61—41no—
412#3495—611no—
413C2×#544D6111yescharacteristic, complemented
414#3244—614no—
415#3242—614no—
416#3238—612no—
417#3236—612no—
418#3232—612no—
419#3229—612no—
420#3163—612no—
421#3137—612no—
422#3095—611no—
423#3092—611no—
424#3091—611no—
425C2×#483—611no—
426#3084—612no—
427#3082—612no—
428#2924—611no—
429C2×C61—22no—
430C2×C61—22no—
431C2×C61—41no—
432C2×C61C2×#53611yescharacteristic
433C2×C61C2×#57711yescharacteristic
434C2×C61#358611yescharacteristic
435D61—81no—
436#556—1221no—
437#554—1221no—
438#552—1221no—
439#552—1222no—
440#552—1221no—
441#551—1222no—
442#544—22no—
443#544—21no—
444#544—21no—
445#544—611no—
446#544C2×D6112yes—
447#544C2×D6112yes—
448#544C2×D6114yes—
449#542—612no—
450#541—612no—
451#536—611no—
452#533—612no—
453C2×C4⋊Q8—21no—
454C2×C4⋊Q8C2×D6112yes—
455#529—612no—
456C2×#125—21no—
457C2×#125C2×D6112yes—
458#525—611no—
459C2×C22⋊Q8—22no—
460C2×C22⋊Q8—611no—
461#520—611no—
462#519—611no—
463C2×#117C2×D6111yescharacteristic
464C2×#117C2×D6111yescharacteristic
465C22×C4⋊C4C2×D6111yescharacteristic
466#501—614no—
467#501—614no—
468#499—614no—
469#498—614no—
470#491—614no—
471#489—614no—
472#488—614no—
473#487—614no—
474#485—612no—
475#485—614no—
476#484—611no—
477#484—612no—
478#484—612no—
479#483—612no—
480#483—612no—
481#483—614no—
482#483—611no—
483#483—612no—
484#483—612no—
485#482—612no—
486#481—611no—
487#481—612no—
488#480—611no—
489#480—612no—
490#479—614no—
491#479—614no—
492#479—614no—
493#478—614no—
494#477—614no—
495#476—614no—
496#475—614no—
497#475—614no—
498#433—614no—
499#432—612no—
500#431—612no—
501#428—612no—
502#428—612no—
503#427—612no—
504C2×#106—612no—
505#424—612no—
506#419—612no—
507#417—612no—
508#416—612no—
509C2×#103—612no—
510#407—611no—
511C2×C22⋊C8—611no—
512#405—612no—
513C61#6087211yescharacteristic, complemented, Sylow
514C2×#41—611no—
515C22×Q8—22no—
516C22×Q8—611no—
517C23×C4—21no—
518C23×C4C22×D6111yescharacteristic
519C2×M16—612no—
520C22×C8—612no—
521C4⋊Q8—22no—
522C4⋊Q8—22no—
523C4⋊Q8—24no—
524C4⋊Q8—22no—
525C4⋊Q8—22no—
526C4⋊Q8—612no—
527C4⋊Q8—612no—
528C4⋊Q8—1221no—
529C4⋊Q8C22×D6114yes—
530C4⋊Q8C22×D6114yes—
531#126—1222no—
532#126—1222no—
533#126—1222no—
534#126—1222no—
535#125—22no—
536#125—24no—
537#125—22no—
538#125—22no—
539#125—22no—
540#125—612no—
541#125—1222no—
542#125—1222no—
543#125—1221no—
544#125—1222no—
545#125C22×D6114yes—
546#125C22×D6114yes—
547#124—612no—
548#124—1222no—
549#123—1221no—
550#123—1222no—
551#123—1222no—
552#123—1222no—
553C22⋊Q8—24no—
554C22⋊Q8—24no—
555C22⋊Q8—24no—
556C22⋊Q8—24no—
557C22⋊Q8—612no—
558C22⋊Q8—612no—
559C22⋊Q8—611no—
560C22⋊Q8—611no—
561C22⋊Q8—1221no—
562C22⋊Q8—1221no—
563C22⋊Q8—1222no—
564C22⋊Q8—1221no—
565C22⋊Q8—1221no—
566C22⋊Q8—1222no—
567C22⋊Q8—1222no—
568#121—611no—
569#121—611no—
570#120—1221no—
571C4×Q8—612no—
572C4×Q8—612no—
573C4×Q8—612no—
574C4×Q8—1221no—
575C4×Q8—1221no—
576C4×Q8—1222no—
577C4×D4—612no—
578C4×D4—1221no—
579C4×D4—1221no—
580C4×D4—1222no—
581C4×D4—1222no—
582#117—21no—
583#117—21no—
584#117—611no—
585#117—1222no—
586#117—1221no—
587#117—1222no—
588#117—1222no—
589#117C22⋊D6111yescharacteristic
590#117C22⋊D6112yes—
591#117C22⋊D6111yescharacteristic
592#117C22×D6112yes—
593#117C22×D6112yes—
594#117C22×D6111yescharacteristic
595#117C22×D6111yescharacteristic
596#117C22×D6112yes—
597C2×C4⋊C4—21no—
598C2×C4⋊C4—21no—
599C2×C4⋊C4—21no—
600C2×C4⋊C4—22no—
601C2×C4⋊C4—22no—
602C2×C4⋊C4—22no—
603C2×C4⋊C4—611no—
604C2×C4⋊C4—1221no—
605C2×C4⋊C4—1221no—
606C2×C4⋊C4C22⋊D6111yescharacteristic
607C2×C4⋊C4C22⋊D6111yescharacteristic
608C2×C4⋊C4C22×D6112yes—
609C2×C4⋊C4C22×D6112yes—
610C2×C4⋊C4C22×D6112yes—
611C2×C4⋊C4C22×D6111yescharacteristic
612C2×C4⋊C4C22×D6111yescharacteristic
613C2×C22⋊C4—21no—
614C2×C22⋊C4—1221no—
615C2×C22⋊C4C22⋊D6112yes—
616C2×C42—21no—
617C2×C42C22×D6112yes—
618#107—612no—
619#107—612no—
620#107—614no—
621#107—614no—
622#106—614no—
623#106—614no—
624#106—612no—
625#106—612no—
626#106—614no—
627#106—614no—
628C4⋊C8—614no—
629C4⋊C8—614no—
630#103—614no—
631#103—614no—
632#103—612no—
633#103—612no—
634#103—614no—
635#103—614no—
636#103—614no—
637#102—612no—
638#102—612no—
639#102—614no—
640C22⋊C8—611no—
641C22⋊C8—611no—
642C22⋊C8—612no—
643C22⋊C8—612no—
644C22⋊C8—612no—
645#97—614no—
646C4×C8—614no—
647C24C2×C22⋊D6111yescharacteristic
648#41—1224no—
649C2×Q8—24no—
650C2×Q8—24no—
651C2×Q8—84no—
652C2×Q8—612no—
653C2×Q8—611no—
654C2×Q8—1222no—
655C2×Q8—1221no—
656C2×Q8—1224no—
657C2×D4—611no—
658C2×D4—1221no—
659C2×D4—1221no—
660C2×D4—1221no—
661C22×C4—24no—
662C22×C4—21no—
663C22×C4—21no—
664C22×C4—22no—
665C22×C4—22no—
666C22×C4—22no—
667C22×C4—82no—
668C22×C4—1221no—
669C22×C4—1221no—
670C22×C4—1222no—
671C22×C4—1221no—
672C22×C4C2×C22⋊D6111yescharacteristic
673C22×C4C2×C22⋊D6112yes—
674C22×C4C2×C22⋊D6111yescharacteristic
675C22×C4C2×C22⋊D6111yescharacteristic
676C22×C4C2×C22⋊D6112yes—
677C22×C4C23×D6111yescharacteristic
678C22×C4C23×D6111yescharacteristic
679C22×C4C23×D6111yescharacteristic
680M16—1224no—
681C2×C8—612no—
682C2×C8—614no—
683C2×C8—612no—
684C2×C8—1224no—
685C4⋊C4—22no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—24no—
689C4⋊C4—24no—
690C4⋊C4—24no—
691C4⋊C4—24no—
692C4⋊C4—24no—
693C4⋊C4—24no—
694C4⋊C4—21no—
695C4⋊C4—21no—
696C4⋊C4—612no—
697C4⋊C4—611no—
698C4⋊C4—611no—
699C4⋊C4—1221no—
700C4⋊C4—1222no—
701C4⋊C4—1222no—
702C4⋊C4—1222no—
703C4⋊C4—1222no—
704C4⋊C4—1222no—
705C4⋊C4—1222no—
706C4⋊C4—1221no—
707C4⋊C4—1221no—
708C4⋊C4—1222no—
709C4⋊C4—1222no—
710C4⋊C4—1222no—
711C4⋊C4—1222no—
712C4⋊C4C2×C22⋊D6111yescharacteristic
713C4⋊C4C2×C22⋊D6111yescharacteristic
714C4⋊C4C2×C22⋊D6112yes—
715C4⋊C4C2×C22⋊D6111yescharacteristic
716C4⋊C4C2×C22⋊D6111yescharacteristic
717C4⋊C4C2×C22⋊D6112yes—
718C4⋊C4C23×D6114yes—
719C4⋊C4C23×D6112yes—
720C4⋊C4C23×D6112yes—
721C22⋊C4—22no—
722C22⋊C4—22no—
723C22⋊C4—1222no—
724C22⋊C4—1222no—
725C22⋊C4—1221no—
726C22⋊C4—1221no—
727C22⋊C4—1221no—
728C22⋊C4—1221no—
729C22⋊C4—1222no—
730C22⋊C4—1222no—
731C22⋊C4—1221no—
732C22⋊C4—1222no—
733C22⋊C4C2×C22⋊D6112yes—
734C22⋊C4C2×C22⋊D6112yes—
735C22⋊C4C2×C22⋊D6112yes—
736C22⋊C4C2×C22⋊D6112yes—
737C42—22no—
738C42—22no—
739C42—1221no—
740C42—1222no—
741C42—1222no—
742C42—1222no—
743C42C2×C22⋊D6112yes—
744C42C2×C22⋊D6112yes—
745C42C23×D6112yes—
746C42C23×D6112yes—
747C23—22no—
748C23—22no—
749C23—41no—
750C23—1221no—
751C23C22×C22⋊D6111yescharacteristic
752C23C22×C22⋊D6111yescharacteristic
753C23C22×C22⋊D6111yescharacteristic
754Q8—84no—
755Q8—84no—
756Q8—1224no—
757Q8—1222no—
758Q8—4882no—
759Q8—2442no—
760D4—1222no—
761D4—4881no—
762D4—2442no—
763D4—2442no—
764C2×C4—24no—
765C2×C4—22no—
766C2×C4—22no—
767C2×C4—22no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—22no—
772C2×C4—24no—
773C2×C4—42no—
774C2×C4—42no—
775C2×C4—44no—
776C2×C4—42no—
777C2×C4—82no—
778C2×C4—82no—
779C2×C4—1221no—
780C2×C4—1221no—
781C2×C4—1222no—
782C2×C4—1221no—
783C2×C4—1222no—
784C2×C4—4882no—
785C2×C4—4881no—
786C2×C4—2442no—
787C2×C4—2442no—
788C2×C4C22×C22⋊D6111yescharacteristic
789C2×C4C22×C22⋊D6112yes—
790C2×C4C22×C22⋊D6112yes—
791C2×C4C22×C22⋊D6111yescharacteristic
792C2×C4C22×C22⋊D6112yes—
793C2×C4C22×C22⋊D6112yes—
794C2×C4C22×C22⋊D6111yescharacteristic
795C2×C4#1451982514yes—
796C2×C4C24×D6111yescharacteristic
797C8—1222no—
798C8—1222no—
799C8—1224no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—21no—
805C22—21no—
806C22—21no—
807C22—44no—
808C22—2441no—
809C22—2441no—
810C22—2441no—
811C22#1684033612yes—
812C22#1684057312yes—
813C22C23×C22⋊D6111yescharacteristic
814C4—22no—
815C4—22no—
816C4—22no—
817C4—22no—
818C4—21no—
819C4—21no—
820C4—44no—
821C4—42no—
822C4—42no—
823C4—2441no—
824C4—2442no—
825C4—2441no—
826C4—2441no—
827C4—2442no—
828C4#1684033612yes—
829C4C2×#1451982512yes—
830C2—22no—
831C2—22no—
832C2—41no—
833C2—4881no—
834C2C2×#1684033611yescharacteristic
835C2C2×#1684057311yescharacteristic
836C2#2146060611yescharacteristic
subgroupG/H
centerC22C23×C22⋊D61
commutator, cosocleC2×C4×C61C25
FrattiniC2×C4C24×D61
FittingC2×C61×#544C2
socleC22×C61C23×D4
prime radical#16840273C22
hypercenterC2×#544D61
hypocenterC61#60872
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C2×#117 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
2. #21457117C2semidirect
3. #21457087C2semidirect
4. #21457040C2semidirect
5. #21457025C2semidirect
6. #21456987C2semidirect
7. #21456963C2semidirect
8. #21456345C2semidirect
9. #21456189C2semidirect
10. #21455767C2semidirect
13. C2×#16840092C2semidirect
14. #21455677C2semidirect
15. #21455655C2semidirect
16. #21454477C2semidirect
17. C2×C61×#544C2semidirect
34. #16840172C22semidirect
35. #16840168C22semidirect
36. #16840161C22semidirect
37. #16840158C22semidirect
38. #16840132C22semidirect
39. #16840124C22semidirect
40. #16840119C22semidirect
41. #16840114C22semidirect
58. #16840066C22semidirect
59. #16840066C22semidirect
60. #16840066C22semidirect
61. #16840059C22semidirect
62. #16840054C22semidirect
63. #16840049C22semidirect
64. #16840044C22semidirect
65. #16840044C22semidirect
413. C2×#544D61semidirect
513. C61#60872semidirect

Maximal subgroups

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

subgroupindex
#214595712
#214571172
#214570872
#214570402
#214570252
#214569872
#214569632
#214563452
#214561892
#214557672
#214557422
#214557322
C2×#168400922
#214556772
#214556552
#214544772
C2×C61×#5442
#6087261