Finite Group Databasebeta

← #30616893

Subgroups — #30616893

Order 15616.

1342 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
1C2×D61⋊#131C211yesmaximal, characteristic, complemented
2C2×#16840808C211yesmaximal, characteristic, complemented
3C2×#16840807C211yesmaximal, characteristic, complemented
4#21462535C211yesmaximal, characteristic, complemented
5#21461809C211yesmaximal, characteristic, complemented
6#21461808C211yesmaximal, characteristic, complemented
7#21461801C211yesmaximal, characteristic, complemented
8#21461788C211yesmaximal, characteristic, complemented
9#21461787C211yesmaximal, characteristic, complemented
10#21461773C211yesmaximal, characteristic, complemented
11#21461661C211yesmaximal, characteristic, complemented
12#21461600C211yesmaximal, characteristic, complemented
13#21461598C211yesmaximal, characteristic, complemented
14#21461558C211yesmaximal, characteristic, complemented
15#21455040C211yesmaximal, characteristic
16C2×#14519865C2211yescharacteristic
17C2×#14519865C2211yescharacteristic
18C2×#14519865C2211yescharacteristic, complemented
19D61⋊#131—24no—
20D61⋊#131—24no—
21C2×#14519864—21no—
22C2×#14519864—21no—
23C2×#14519864C2211yescharacteristic
24C2×#14519864C2211yescharacteristic
25C2×D61⋊M16—21no—
26C2×D61⋊M16C2211yescharacteristic
27C22×D61⋊C8—21no—
28C22×D61⋊C8C2211yescharacteristic
29#16840808—24no—
30#16840807—24no—
31#16840792—21no—
32#16840791—21no—
33#16840790—21no—
34#16840789—21no—
35C2×#14519848C2211yescharacteristic, complemented
36C2×#14519847C2211yescharacteristic, complemented
37#16840769C2211yescharacteristic, complemented
38C2×#14519842C2211yescharacteristic
39C2×#14519842C2211yescharacteristic
40C2×#14519842C2211yescharacteristic, complemented
41C2×#14519842C2211yescharacteristic, complemented
42C2×#14519841C2211yescharacteristic
43C2×#14519841C2211yescharacteristic
44#16840737C2211yescharacteristic, complemented
45#16840733C2211yescharacteristic
46#16840727C2211yescharacteristic, complemented
47C2×#14519831C2211yescharacteristic, complemented
48C2×#14519831C2211yescharacteristic, complemented
49C4×C22⋊#6923C2211yescharacteristic
50#16840638C2211yescharacteristic, complemented
51#16840638C2211yescharacteristic, complemented
52#16840632C2211yescharacteristic, complemented
53#16840632C2211yescharacteristic, complemented
54(C2×#6923)⋊C8C2211yescharacteristic, complemented
55(C2×#6923)⋊C8C2211yescharacteristic, complemented
56C2×#41×D61C2211yescharacteristic
57C2×#14519800C2211yescharacteristic
58C2×#14519798C2211yescharacteristic
59#16840275C2211yescharacteristic
60#16839922C411yescharacteristic, complemented
61#16839916C411yescharacteristic, complemented
62#16839911C411yescharacteristic, complemented
63#16839909C411yescharacteristic, complemented
64#16839907C411yescharacteristic, complemented
65#16839902C411yescharacteristic, complemented
66#16839897C411yescharacteristic, complemented
67#16839757C2211yescharacteristic
68#16839755C2211yescharacteristic
69C22⋊C8×D61C2211yescharacteristic
70C61×#452C411yescharacteristic, complemented
71#14519865—22no—
72#14519865—22no—
73#14519865—22no—
74#14519865—22no—
75#14519865—22no—
76#14519865D414yescomplemented
77#14519864—28no—
78#14519864—28no—
79#14519864—22no—
80#14519864—22no—
81#14519864—22no—
82#14519864D414yescomplemented
83C2×#11758213—21no—
84C2×#11758213—21no—
85C2×#11758213—21no—
86C2×#11758213C2311yescharacteristic
87C2×#11758213C2311yescharacteristic
88C2×#11758213C2311yescharacteristic
89C2×#11758213C2311yescharacteristic
90D61⋊M16—28no—
91D61⋊M16—22no—
92D61⋊M16—22no—
93C2×#11758217—21no—
94C2×#11758217—21no—
95C2×#11758217—21no—
96C2×D61⋊C8—28no—
97C2×D61⋊C8—21no—
98C2×D61⋊C8—21no—
99C2×D61⋊C8—21no—
100C2×D61⋊C8—22no—
101C2×D61⋊C8—22no—
102C2×D61⋊C8—21no—
103C2×D61⋊C8D411yescharacteristic
104C2×D61⋊C8D411yescharacteristic
105C2×D61⋊C8C2311yescharacteristic
106C2×D61⋊C8C2311yescharacteristic
107C22×#92420—21no—
108C22×#92420—21no—
109C22×#92420D411yescharacteristic
110C22×#92420D411yescharacteristic
111C2×C22⋊#6923—21no—
112C2×C4×#6923C2311yescharacteristic
113C2×C4×#6923C2311yescharacteristic
114#14519848—22no—
115#14519847—22no—
116#14519844—21no—
117C4⋊#92420—21no—
118#14519842—22no—
119#14519842—22no—
120#14519842—22no—
121#14519842—22no—
122#14519841—22no—
123#14519841—22no—
124#14519834—21no—
125#14519834—21no—
126#14519834—21no—
127C22⋊#92420—21no—
128#14519832—21no—
129#14519831—22no—
130#14519831—22no—
131C4×#92420—21no—
132(C2×#6923)⋊C4—21no—
133C2×#11758226C2311yescharacteristic
134C2×#11758226C2311yescharacteristic
135C2×#11758222—21no—
136C2×#11758222C2×C411yescharacteristic
137C2×#11758224—21no—
138C2×#11758224C2311yescharacteristic
139#41×D61—22no—
140#41×D61—22no—
141#41×D61—22no—
142#41×D61—22no—
143C2×Q8×D61C2×C411yescharacteristic
144C2×D4×D61—21no—
145C2×D4×D61C2×C411yescharacteristic
146C22×C4×D61—21no—
147C22×C4×D61C2311yescharacteristic
148#14519800—22no—
149#14519800—22no—
150#14519798—22no—
151#14519798—22no—
152C2×#11758202C2×C411yescharacteristic
153C2×#11758190C2×C411yescharacteristic
154C2×#11758201C2×C411yescharacteristic
155C2×#11758201C2×C411yescharacteristic
156C2×D488C2×C411yescharacteristic
157C2×#11758199C2×C411yescharacteristic
158C2×C8×D61C2311yescharacteristic
159C2×C8×D61C2311yescharacteristic
160#14519762—21no—
161#14519753C2×C411yescharacteristic
162#14519752C2×C411yescharacteristic
163#14519751C2×C411yescharacteristic
164#14519747—21no—
165#14519739—21no—
166#14519737—21no—
167#14519735C2311yescharacteristic
168#14519702C2×C411yescharacteristic
169#14519701C2×C411yescharacteristic
170#14519700C2×C411yescharacteristic
171#14519699C2×C411yescharacteristic
172#14519698C2×C411yescharacteristic
173#14519697C2×C411yescharacteristic
174C22⋊#92418C2×C411yescharacteristic
175#14519689C2×C411yescharacteristic
176#14519689C2×C411yescharacteristic
177C2×#41×C61C2×C411yescharacteristic
178C2×Q16×C61C2×C411yescharacteristic
179C2×SD16×C61C2×C411yescharacteristic
180C22⋊Q8×C61C2×C411yescharacteristic
181#103×C61C2×C411yescharacteristic
182#102×C61C2×C411yescharacteristic
183C22⋊C8×C61C2×C411yescharacteristic
184C23×D61—21no—
185C23×D61#4111yescharacteristic
186C22×#6923—21no—
187C22×#6923—21no—
188#41×C61—22no—
189#41×C61—22no—
190C2×Q8×C61C22×C411yescharacteristic
191C2×Q8×C61C22×C411yescharacteristic
192C2×D4×C61—21no—
193C2×D4×C61C22×C411yescharacteristic
194C22×C4×C61—21no—
195C22×C4×C61C22×C411yescharacteristic
196C2×C22⋊D61—21no—
197C2×C22⋊D61—21no—
198C2×C22⋊D61—21no—
199C2×C22⋊D61—21no—
200C22×Dic61—21no—
201C22×Dic61C2×D411yescharacteristic
202#11758226—21no—
203#11758226—21no—
204#11758226—21no—
205#11758226—21no—
206#11758226—21no—
207#11758226—21no—
208#11758226C2×D412yes—
209#11758226#4112yes—
210Q8×D61—22no—
211Q8×D61—22no—
212#11758224—24no—
213#11758224—24no—
214#11758224—21no—
215#11758224—21no—
216#11758224C2×D412yes—
217#11758224#4112yes—
218D4×D61—24no—
219D4×D61—24no—
220D4×D61—22no—
221D4×D61—22no—
222#11758222—24no—
223#11758222—24no—
224#11758222—22no—
225#11758222—22no—
226C2×D244—21no—
227C2×D244—21no—
228C2×D244—21no—
229C2×D244C22×C411yescharacteristic
230C2×D244C22×C411yescharacteristic
231C2×C4×D61—24no—
232C2×C4×D61—24no—
233C2×C4×D61—21no—
234C2×C4×D61—21no—
235C2×C4×D61—21no—
236C2×C4×D61—21no—
237C2×C4×D61—21no—
238C2×C4×D61—21no—
239C2×C4×D61—21no—
240C2×C4×D61—21no—
241C2×C4×D61C22×C411yescharacteristic
242C2×C4×D61C2×D411yescharacteristic
243C2×C4×D61#4111yescharacteristic
244C2×C4×D61C2411yescharacteristic
245C2×Dic122—21no—
246C2×Dic122C22×C411yescharacteristic
247C22⋊#6923—42no—
248#11758217—24no—
249#11758217—24no—
250#11758217—24no—
251C2×#92420—24no—
252C2×#92420—21no—
253C2×#92420—21no—
254C2×#92420—24no—
255C2×#92420—22no—
256C2×#92420—22no—
257C2×#92420—21no—
258C2×#92420—21no—
259C2×#92420C2×D411yescharacteristic
260C2×#92420C2×D411yescharacteristic
261C2×#92420C2×D411yescharacteristic
262C2×#92420C2×D411yescharacteristic
263C4×#6923—21no—
264C4×#6923—21no—
265C4×#6923—21no—
266C4×#6923—21no—
267#11758213—24no—
268#11758213—21no—
269#11758213—21no—
270#11758213—24no—
271#11758213—21no—
272#11758213—21no—
273#11758213—21no—
274#11758213—21no—
275#11758213—42no—
276#11758213C2×D412yes—
277#11758213C2×D412yes—
278D61⋊C8—24no—
279D61⋊C8—24no—
280D61⋊C8—21no—
281D61⋊C8—21no—
282D61⋊C8—22no—
283D61⋊C8—24no—
284D61⋊C8—22no—
285D61⋊C8—42no—
286D61⋊C8C2×D412yes—
287D61⋊C8C2×D412yes—
288Q16×C61—22no—
289SD16×C61—22no—
290C2×C8×C61C22×C411yescharacteristic
291C2×C8×C61C22×C411yescharacteristic
292C4⋊C4×C61—21no—
293C4⋊C4×C61C22×C411yescharacteristic
294C22⋊C4×C61—21no—
295#11758202—22no—
296#11758201—22no—
297#11758201—22no—
298#11758199—22no—
299#11758198—21no—
300#11758198—21no—
301#11758198—21no—
302#11758198—21no—
303C4⋊Dic61C22×C411yescharacteristic
304#11758196—21no—
305C4×Dic61—21no—
306C2×#92418C22×C411yescharacteristic
307C2×#92418C22×C411yescharacteristic
308D488—22no—
309#11758190—22no—
310C8×D61—21no—
311C8×D61—21no—
312C8×D61—21no—
313C8×D61—21no—
314C23×C61—21no—
315C23×C61C4×D411yescharacteristic
316C22×D61—24no—
317C22×D61—21no—
318C22×D61—21no—
319C22×D61—21no—
320C22×D61—22no—
321C22×D61—21no—
322C22×D61—41no—
323C22×D61—42no—
324C22×D61—42no—
325C22×D61C4×D411yescharacteristic
326C22×D61C2×#4111yescharacteristic
327C2×#6923—41no—
328C2×#6923—41no—
329C2×#6923—41no—
330C2×#6923—41no—
331C2×#6923—41no—
332C2×#6923—41no—
333Q8×C61—21no—
334Q8×C61—21no—
335Q8×C61—21no—
336Q8×C61C4×D412yes—
337D4×C61—24no—
338D4×C61—21no—
339D4×C61C4×D412yes—
340C2×C4×C61—24no—
341C2×C4×C61—21no—
342C2×C4×C61—21no—
343C2×C4×C61—21no—
344C2×C4×C61—21no—
345C2×C4×C61—21no—
346C2×C4×C61C4×D411yescharacteristic
347C2×C4×C61C23×C411yescharacteristic
348C22⋊D61—24no—
349C22⋊D61—24no—
350C22⋊D61—22no—
351C22⋊D61—22no—
352C22⋊D61—42no—
353C2×Dic61—21no—
354C2×Dic61—21no—
355C2×Dic61—22no—
356C2×Dic61—21no—
357C2×Dic61—22no—
358C2×Dic61—21no—
359C2×Dic61C4×D411yescharacteristic
360C2×Dic61C22×D411yescharacteristic
361D244—22no—
362D244—22no—
363D244—21no—
364D244—21no—
365D244—21no—
366D244—41no—
367D244—41no—
368D244—42no—
369D244C4×D412yes—
370C4×D61—24no—
371C4×D61—24no—
372C4×D61—21no—
373C4×D61—21no—
374C4×D61—21no—
375C4×D61—21no—
376C4×D61—21no—
377C4×D61—22no—
378C4×D61—21no—
379C4×D61—22no—
380C4×D61—41no—
381C4×D61—41no—
382C4×D61C22×D411yescharacteristic
383C4×D61C22×D411yescharacteristic
384C4×D61C2×#4111yescharacteristic
385C4×D61C2×#4111yescharacteristic
386Dic122—24no—
387Dic122—21no—
388Dic122C4×D412yes—
389#92420—21no—
390#92420—21no—
391#92420—22no—
392#92420—22no—
393#92420—41no—
394#92420—41no—
395#92420#12012yes—
396#92420#12012yes—
397C8×C61—21no—
398C8×C61—21no—
399#92418—21no—
400#92418—21no—
401#21467—611nomaximal, Sylow
402C22×C61—21no—
403C22×C61—21no—
404C22×C61—21no—
405C22×C61—22no—
406C22×C61—41no—
407C22×C61—41no—
408C22×C61C2×C4×D411yescharacteristic
409C2×D61—21no—
410C2×D61—21no—
411C2×D61—21no—
412C2×D61—21no—
413C2×D61—22no—
414C2×D61—42no—
415C2×D61—42no—
416C2×D61—48no—
417C2×D61—41no—
418C2×D61—41no—
419C2×D61—41no—
420C2×D61—41no—
421C2×D61—41no—
422C2×D61#44412yescomplemented
423C2×D61#52511yescharacteristic
424C2×D61#52511yescharacteristic
425#6923—81no—
426#6923—81no—
427C4×C61—22no—
428C4×C61—21no—
429C4×C61—41no—
430C4×C61—41no—
431C4×C61C2×C4×D411yescharacteristic
432C4×C61C2×C4×D411yescharacteristic
433Dic61—21no—
434Dic61—22no—
435Dic61—41no—
436Dic61C2×#12011yescharacteristic
437Dic61#52511yescharacteristic
438C22×#131—611no—
439#3002—611no—
440C2×#444—611no—
441C2×#444—611no—
442#2929—611no—
443#1876—611no—
444#1876—611no—
445#1871—611no—
446#1866—611no—
447#1866—611no—
448#1855—611no—
449#1789—611no—
450#1765—611no—
451#1765—611no—
452#1752—611no—
453C2×C61—41no—
454C2×C61—42no—
455C2×C61C4×#12011yescharacteristic
456C2×C61C2×#44411yescharacteristic
457C2×C61#295511yescharacteristic
458D61—21no—
459D61—21no—
460D61—22no—
461D61—42no—
462D61—81no—
463C22×#41—611no—
464C2×#135—611no—
465C2×#135—611no—
466C2×#131—611no—
467C2×#131—611no—
468C2×#131—611no—
469C2×#131—611no—
470C2×#131—611no—
471C2×#131—1221no—
472C2×#131—1221no—
473C2×#131—1224no—
474C2×#131—1224no—
475C22×M16—611no—
476C22×M16—1221no—
477C23×C8—611no—
478C23×C8—1221no—
479#525—611no—
480#452—611no—
481#452#692311yescharacteristic, complemented
482#451—611no—
483#450—611no—
484#449—611no—
485#449—611no—
486#448—611no—
487#447—611no—
488#444—1224no—
489#444—1224no—
490#435—1221no—
491#435—1221no—
492C8×D4—1221no—
493C8×D4—1221no—
494C2×#108—611no—
495C2×#108—611no—
496#424—611no—
497C2×#104—611no—
498C2×#104—611no—
499C2×#104—611no—
500C2×#104—611no—
501C2×#104—611no—
502C2×#104—611no—
503#416—611no—
504#416—611no—
505#408—611no—
506#407—611no—
507C2×C22⋊C8—611no—
508#405—611no—
509C2×#97—611no—
510C2×#97—611no—
511C4×C22⋊C4—611no—
512#341—611no—
513#341—611no—
514#339—611no—
515#339—611no—
516#336—611no—
517#336—611no—
518C61#2146711yescharacteristic, complemented, Sylow
519C2×#41—611no—
520C2×#41—611no—
521C2×#41—611no—
522C2×#41—611no—
523C2×#41—1221no—
524C2×#41—1221no—
525C2×#41—1222no—
526C2×#41—1222no—
527C2×#41—1222no—
528C2×#41—1222no—
529C2×#41C2×#692311yescharacteristic
530C22×Q8—611no—
531C22×D4—611no—
532C22×D4—1221no—
533C23×C4—611no—
534C23×C4—1221no—
535#135—1222no—
536#135—1222no—
537#135—1222no—
538#135—1222no—
539C2×Q16—611no—
540C2×Q16C2×#692311yescharacteristic
541C2×SD16—611no—
542C2×SD16—611no—
543C2×SD16—611no—
544C2×SD16C2×#692311yescharacteristic
545C2×D8—611no—
546C2×D8—611no—
547#131—614no—
548#131—614no—
549#131—1222no—
550#131—1222no—
551#131—1222no—
552#131—1222no—
553#131—1222no—
554#131—1222no—
555#131—1222no—
556#131—1222no—
557#131—1228no—
558#131—1228no—
559C2×M16—611no—
560C2×M16—611no—
561C2×M16—611no—
562C2×M16—611no—
563C2×M16—1221no—
564C2×M16—1221no—
565C2×M16—1221no—
566C2×M16—1221no—
567C2×M16—1221no—
568C2×M16—1222no—
569C2×M16—1222no—
570C2×M16—1221no—
571C2×M16—1228no—
572C22×C8—611no—
573C22×C8—611no—
574C22×C8—611no—
575C22×C8—611no—
576C22×C8—611no—
577C22×C8—611no—
578C22×C8—611no—
579C22×C8—611no—
580C22×C8—1221no—
581C22×C8—1221no—
582C22×C8—1222no—
583C22×C8—1222no—
584C22×C8—1221no—
585C22×C8—1221no—
586C22×C8—1221no—
587C22×C8—1221no—
588C22×C8—1228no—
589#123—1221no—
590C22⋊Q8—611no—
591C22⋊Q8C2×#692311yescharacteristic
592#121—611no—
593#121—611no—
594#120—1221no—
595C4×D4—1221no—
596C4×D4—1221no—
597#117—611no—
598C2×C22⋊C4—1221no—
599C2×C42—611no—
600C2×C42—611no—
601#108—1222no—
602#108—1222no—
603C4⋊C8—1221no—
604C4⋊C8—1221no—
605#104—1222no—
606#104—1222no—
607#104—1222no—
608#104—1222no—
609#104—1222no—
610#104—1222no—
611#103—611no—
612#103—611no—
613#103—611no—
614#103C2×#692311yescharacteristic
615#102—611no—
616#102—611no—
617#102—611no—
618#102C2×#692311yescharacteristic
619C22⋊C8—611no—
620C22⋊C8—611no—
621C22⋊C8—611no—
622C22⋊C8—1221no—
623C22⋊C8—1221no—
624C22⋊C8—1221no—
625C22⋊C8—1221no—
626C22⋊C8C2×#692311yescharacteristic
627#97—1222no—
628#97—1222no—
629#97—1221no—
630C4×C8—1221no—
631#95—1221no—
632C24—611no—
633C24—1221no—
634#41—22no—
635#41—22no—
636#41—612no—
637#41—612no—
638#41—612no—
639#41—612no—
640#41—1222no—
641#41—1222no—
642#41—1224no—
643#41—1224no—
644#41—1221no—
645#41—1221no—
646#41—1221no—
647#41—1221no—
648#41—1221no—
649#41—1221no—
650#41—1221no—
651#41—1221no—
652#41—1224no—
653#41—1224no—
654C2×Q8—611no—
655C2×Q8—1221no—
656C2×Q8—1222no—
657C2×Q8—1222no—
658C2×Q8C22×#692311yescharacteristic
659C2×Q8C22×#692311yescharacteristic
660C2×D4—21no—
661C2×D4—611no—
662C2×D4—611no—
663C2×D4—1221no—
664C2×D4—1221no—
665C2×D4—1221no—
666C2×D4—1221no—
667C2×D4—1222no—
668C2×D4—1224no—
669C2×D4—1224no—
670C2×D4—1221no—
671C2×D4—1221no—
672C2×D4—1222no—
673C2×D4—1221no—
674C2×D4C22×#692311yescharacteristic
675C22×C4—21no—
676C22×C4—611no—
677C22×C4—611no—
678C22×C4—611no—
679C22×C4—611no—
680C22×C4—611no—
681C22×C4—1221no—
682C22×C4—1221no—
683C22×C4—1221no—
684C22×C4—1221no—
685C22×C4—1221no—
686C22×C4—1221no—
687C22×C4—1221no—
688C22×C4—1224no—
689C22×C4—1224no—
690C22×C4—1221no—
691C22×C4—1221no—
692C22×C4—1221no—
693C22×C4—1221no—
694C22×C4C22×#692311yescharacteristic
695Q16—22no—
696Q16—1222no—
697SD16—22no—
698SD16—1222no—
699SD16—1222no—
700SD16—1222no—
701D8—1222no—
702D8—1222no—
703M16—612no—
704M16—612no—
705M16—1224no—
706M16—1224no—
707M16—1221no—
708M16—1221no—
709M16—1224no—
710M16—1224no—
711M16—1224no—
712M16—1221no—
713M16—1221no—
714M16—1221no—
715M16—1221no—
716M16—2442no—
717C2×C8—611no—
718C2×C8—611no—
719C2×C8—612no—
720C2×C8—612no—
721C2×C8—611no—
722C2×C8—611no—
723C2×C8—611no—
724C2×C8—611no—
725C2×C8—1221no—
726C2×C8—1221no—
727C2×C8—1221no—
728C2×C8—1221no—
729C2×C8—1222no—
730C2×C8—1222no—
731C2×C8—1222no—
732C2×C8—1222no—
733C2×C8—1224no—
734C2×C8—1224no—
735C2×C8—1221no—
736C2×C8—1221no—
737C2×C8—1221no—
738C2×C8—1221no—
739C2×C8—1224no—
740C2×C8—1224no—
741C2×C8—1224no—
742C2×C8—1221no—
743C2×C8—1221no—
744C2×C8—2442no—
745C2×C8C22×#692311yescharacteristic
746C2×C8C22×#692311yescharacteristic
747C4⋊C4—21no—
748C4⋊C4—611no—
749C4⋊C4—1221no—
750C4⋊C4C22×#692311yescharacteristic
751C22⋊C4—21no—
752C22⋊C4—1221no—
753C22⋊C4—1221no—
754C22⋊C4—1221no—
755C22⋊C4—1221no—
756C22⋊C4—2442no—
757C42—1221no—
758C42—1221no—
759C42—1221no—
760C42—1221no—
761C42—1221no—
762C23—21no—
763C23—611no—
764C23—611no—
765C23—1222no—
766C23—1221no—
767C23—1221no—
768C23—1224no—
769C23—1221no—
770C23—1221no—
771C23—2441no—
772C23—2442no—
773C23—2442no—
774C23D4×#692311yescharacteristic
775Q8—21no—
776Q8—21no—
777Q8—21no—
778Q8—612no—
779Q8—1224no—
780Q8—1221no—
781Q8D4×#692312yes—
782D4—24no—
783D4—21no—
784D4—612no—
785D4—1222no—
786D4—1222no—
787D4—1222no—
788D4—1222no—
789D4—1224no—
790D4—1224no—
791D4—1221no—
792D4—1221no—
793D4—1221no—
794D4—2442no—
795D4—2441no—
796D4—2441no—
797D4—2442no—
798D4D4×#692312yes—
799C2×C4—24no—
800C2×C4—21no—
801C2×C4—21no—
802C2×C4—21no—
803C2×C4—21no—
804C2×C4—21no—
805C2×C4—611no—
806C2×C4—611no—
807C2×C4—611no—
808C2×C4—611no—
809C2×C4—611no—
810C2×C4—611no—
811C2×C4—1221no—
812C2×C4—1222no—
813C2×C4—1221no—
814C2×C4—1222no—
815C2×C4—1221no—
816C2×C4—1221no—
817C2×C4—1224no—
818C2×C4—1224no—
819C2×C4—1221no—
820C2×C4—1222no—
821C2×C4—1221no—
822C2×C4—1222no—
823C2×C4—1221no—
824C2×C4—1221no—
825C2×C4—1221no—
826C2×C4—1221no—
827C2×C4—2441no—
828C2×C4—2441no—
829C2×C4—2441no—
830C2×C4—2441no—
831C2×C4—2441no—
832C2×C4—2441no—
833C2×C4—2441no—
834C2×C4—2441no—
835C2×C4D4×#692311yescharacteristic
836C2×C4C23×#692311yescharacteristic
837C8—21no—
838C8—21no—
839C8—612no—
840C8—612no—
841C8—1221no—
842C8—1221no—
843C8—1222no—
844C8—1222no—
845C8—1221no—
846C8—1221no—
847C8—2441no—
848C8—2441no—
849C22—21no—
850C22—22no—
851C22—21no—
852C22—21no—
853C22—41no—
854C22—41no—
855C22—611no—
856C22—611no—
857C22—612no—
858C22—1221no—
859C22—1221no—
860C22—1221no—
861C22—1221no—
862C22—1222no—
863C22—2442no—
864C22—2442no—
865C22—2448no—
866C22—2441no—
867C22—2441no—
868C22—2441no—
869C22—2441no—
870C22—2441no—
871C22C2×D4×#692311yescharacteristic
872C4—21no—
873C4—22no—
874C4—41no—
875C4—41no—
876C4—611no—
877C4—611no—
878C4—1221no—
879C4—1222no—
880C4—4881no—
881C4—4881no—
882C4—2441no—
883C4C2×D4×#692311yescharacteristic
884C4C2×D4×#692311yescharacteristic
885C2—41no—
886C2—42no—
887C2—1221no—
888C2—1221no—
889C2—1222no—
890C2—4881no—
891C2—2442no—
892C2#120×#692311yescharacteristic
893C2D61⋊#44411yescharacteristic
894C2#2146259211yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#452C4
socleC22×C61C2×C4×D4
prime radical#21455040C2
cosocleC2×C4×D61C24
hypercenter#452#6923
hypocenterC61#21467
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #452

Complements

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

NH ≅ G/Ntype
1. C2×D61⋊#131C2semidirect
2. C2×#16840808C2semidirect
3. C2×#16840807C2semidirect
4. #21462535C2semidirect
5. #21461809C2semidirect
6. #21461808C2semidirect
7. #21461801C2semidirect
8. #21461788C2semidirect
9. #21461787C2semidirect
10. #21461773C2semidirect
11. #21461661C2semidirect
12. #21461600C2semidirect
13. #21461598C2semidirect
14. #21461558C2semidirect
18. C2×#14519865C22semidirect
35. C2×#14519848C22semidirect
36. C2×#14519847C22semidirect
37. #16840769C22semidirect
40. C2×#14519842C22semidirect
41. C2×#14519842C22semidirect
44. #16840737C22semidirect
46. #16840727C22semidirect
47. C2×#14519831C22semidirect
48. C2×#14519831C22semidirect
50. #16840638C22semidirect
51. #16840638C22semidirect
52. #16840632C22semidirect
53. #16840632C22semidirect
54. (C2×#6923)⋊C8C22semidirect
55. (C2×#6923)⋊C8C22semidirect
60. #16839922C4semidirect
61. #16839916C4semidirect
62. #16839911C4semidirect
63. #16839909C4semidirect
64. #16839907C4semidirect
65. #16839902C4semidirect
66. #16839897C4semidirect
70. C61×#452C4semidirect
76. #14519865D4semidirect
82. #14519864D4semidirect
422. C2×D61#444semidirect
481. #452#6923semidirect
518. C61#21467semidirect

Maximal subgroups

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

subgroupindex
C2×D61⋊#1312
C2×#168408082
C2×#168408072
#214625352
#214618092
#214618082
#214618012
#214617882
#214617872
#214617732
#214616612
#214616002
#214615982
#214615582
#214550402
#2146761