Finite Group Databasebeta

← #29712933

Subgroups — #29712933

Order 15616.

1334 conjugacy classes of subgroups.

The subgroup lattice has 1008 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455748C211yesmaximal, characteristic, complemented
2#21454338C211yesmaximal, characteristic, complemented
3#21450282C211yesmaximal, characteristic, complemented
4#21447045C211yesmaximal, characteristic, complemented
5#21447040C211yesmaximal, characteristic, complemented
6#21447026C211yesmaximal, characteristic, complemented
7#21447026C211yesmaximal, characteristic, complemented
8#21446283C211yesmaximal, characteristic, complemented
9#21446122C211yesmaximal, characteristic, complemented
10#21446052C211yesmaximal, characteristic, complemented
11#21446045C211yesmaximal, characteristic, complemented
12#21445773C211yesmaximal, characteristic, complemented
13#21445773C211yesmaximal, characteristic, complemented
14#21445763C211yesmaximal, characteristic, complemented
15C61×#3488C211yesmaximal, characteristic
16C22×#11758194C2211yescharacteristic, complemented
17C2×#14519736C2211yescharacteristic, complemented
18#16840100—21no—
19#16840100—21no—
20#16840083—21no—
21#16840083—21no—
22#16839805C2211yescharacteristic, complemented
23#16839805C2211yescharacteristic, complemented
24C2×#14519704C2211yescharacteristic
25C2×#14519704C2211yescharacteristic
26C2×#14519704C2211yescharacteristic, complemented
27C2×#14519704C2211yescharacteristic, complemented
28C2×#14519704C2211yescharacteristic, complemented
29C2×#14519704C2211yescharacteristic, complemented
30#16839771—21no—
31#16839767—21no—
32#16839763C2211yescharacteristic
33#16839763C2211yescharacteristic
34#16839763C2211yescharacteristic, complemented
35#16839763C2211yescharacteristic, complemented
36#16839763C2211yescharacteristic, complemented
37#16839763C2211yescharacteristic, complemented
38#16839758—21no—
39#16839758—21no—
40C2×#14519694C2211yescharacteristic, complemented
41C2×#14519694C2211yescharacteristic, complemented
42#16839726C2211yescharacteristic, complemented
43#16839676—22no—
44#16839665C2211yescharacteristic, complemented
45#16839665C2211yescharacteristic, complemented
46#16839650—22no—
47#16839631C2211yescharacteristic, complemented
48#16839627C2211yescharacteristic, complemented
49C4×C22⋊Dic61C2211yescharacteristic, complemented
50#16839531C2211yescharacteristic, complemented
51#16839531C2211yescharacteristic, complemented
52#16839521C2211yescharacteristic, complemented
53#16839521C2211yescharacteristic, complemented
54C2×H(5,𝔽2)×C61C2211yescharacteristic
55C22×#41×C61C2211yescharacteristic
56C61×#550—21no—
57C61×#548—21no—
58C61×#546—21no—
59C61×#546—22no—
60D42×C61—22no—
61D42×C61—21no—
62C61×#537—21no—
63C61×#537C2211yescharacteristic
64C61×#535—21no—
65C61×#535C2211yescharacteristic
66C61×#525—21no—
67C61×#525C2211yescharacteristic
68C2×#121×C61—21no—
69C2×#121×C61C2211yescharacteristic
70C61×#520C2211yescharacteristic
71C2×#11758194—21no—
72C2×#11758194—41no—
73C2×#11758194—41no—
74C2×#11758194C2311yescharacteristic
75C2×#11758194C2311yescharacteristic
76C2×#11758194C2311yescharacteristic
77C2×#11758194C2311yescharacteristic
78C22×#92418—21no—
79#14519736—21no—
80#14519736—21no—
81#14519736—21no—
82#14519736—21no—
83C2×C4⋊Dic61C2311yescharacteristic
84C2×C4⋊Dic61C2311yescharacteristic
85C2×#11758196—22no—
86C2×C22⋊Dic61—21no—
87C2×C22⋊Dic61—21no—
88C2×C22⋊Dic61—22no—
89C2×C22⋊Dic61—22no—
90C2×C4×Dic61—21no—
91C2×C4×Dic61C2311yescharacteristic
92C2×C4×Dic61C2311yescharacteristic
93#14519710—21no—
94#14519710—21no—
95#14519708—21no—
96#14519708—21no—
97#14519704—22no—
98#14519704—22no—
99#14519704—41no—
100#14519704—41no—
101#14519704—41no—
102#14519704—41no—
103#14519701—21no—
104#14519701—21no—
105#14519701—21no—
106#14519701—21no—
107#14519701—21no—
108#14519701—21no—
109#14519698—21no—
110#14519698—21no—
111#14519698—21no—
112#14519698—21no—
113#14519698—21no—
114#14519698—21no—
115#14519694—41no—
116#14519694—41no—
117C22⋊#92418—21no—
118C22⋊#92418—21no—
119#14519684—21no—
120#14519684—22no—
121H(5,𝔽2)×C61—22no—
122H(5,𝔽2)×C61—22no—
123H(5,𝔽2)×C61—41no—
124H(5,𝔽2)×C61—41no—
125C2×#41×C61—21no—
126C2×#41×C61—21no—
127C2×#41×C61—21no—
128C2×#41×C61—21no—
129C2×#41×C61—22no—
130C2×#41×C61—22no—
131C2×#41×C61—41no—
132C2×#41×C61—41no—
133C2×#41×C61D411yescharacteristic
134C2×#41×C61D411yescharacteristic
135C2×#41×C61C2311yescharacteristic
136C2×#41×C61C2311yescharacteristic
137C2×#41×C61C2311yescharacteristic
138C22×Q8×C61D411yescharacteristic
139C22×D4×C61—21no—
140C22×D4×C61—22no—
141C22×D4×C61—22no—
142C22×D4×C61—21no—
143C22×D4×C61—21no—
144C22×D4×C61D411yescharacteristic
145C22×D4×C61D412yes—
146C22×D4×C61C2311yescharacteristic
147C23×C4×C61—21no—
148C23×C4×C61C2311yescharacteristic
149#127×C61—22no—
150#127×C61—21no—
151#124×C61—22no—
152#124×C61—21no—
153#123×C61—22no—
154#123×C61—21no—
155C22⋊Q8×C61—22no—
156C22⋊Q8×C61—21no—
157C22⋊Q8×C61—21no—
158C22⋊Q8×C61D411yescharacteristic
159C22⋊Q8×C61D411yescharacteristic
160#121×C61—22no—
161#121×C61—22no—
162#121×C61—22no—
163#121×C61—22no—
164#121×C61—22no—
165#121×C61—21no—
166#121×C61—21no—
167#121×C61—21no—
168#121×C61—22no—
169#121×C61—21no—
170#121×C61—21no—
171#121×C61—21no—
172#121×C61—21no—
173#121×C61—21no—
174#121×C61D411yescharacteristic
175#121×C61D411yescharacteristic
176#120×C61—22no—
177#120×C61—22no—
178#120×C61—22no—
179#120×C61—22no—
180#120×C61—21no—
181C4×Q8×C61—21no—
182C4×D4×C61—22no—
183C4×D4×C61—22no—
184C4×D4×C61—21no—
185C4×D4×C61—22no—
186C4×D4×C61—21no—
187C4×D4×C61—21no—
188#117×C61—21no—
189#117×C61C2311yescharacteristic
190C2×C4⋊C4×C61—21no—
191C2×C4⋊C4×C61C2311yescharacteristic
192C2×C22⋊C4×C61—22no—
193C2×C22⋊C4×C61D412yes—
194C24×C61—22no—
195C24×C61—21no—
196C24×C61C2×D412yes—
197C24×C61C2×D411yescharacteristic
198#41×C61—21no—
199#41×C61—21no—
200#41×C61—22no—
201#41×C61—22no—
202#41×C61—21no—
203#41×C61—21no—
204#41×C61—21no—
205#41×C61—21no—
206#41×C61—21no—
207#41×C61—21no—
208#41×C61—21no—
209#41×C61—21no—
210#41×C61—42no—
211#41×C61—42no—
212#41×C61—41no—
213#41×C61—41no—
214#41×C61—42no—
215#41×C61—42no—
216#41×C61—42no—
217#41×C61—42no—
218#41×C61—42no—
219#41×C61—42no—
220#41×C61#4112yes—
221#41×C61#4112yes—
222C2×Q8×C61—21no—
223C2×Q8×C61—22no—
224C2×Q8×C61—41no—
225C2×Q8×C61C2×D411yescharacteristic
226C2×Q8×C61C2×D411yescharacteristic
227C2×Q8×C61C2×D411yescharacteristic
228C2×D4×C61—21no—
229C2×D4×C61—22no—
230C2×D4×C61—22no—
231C2×D4×C61—22no—
232C2×D4×C61—22no—
233C2×D4×C61—21no—
234C2×D4×C61—21no—
235C2×D4×C61—21no—
236C2×D4×C61—21no—
237C2×D4×C61—21no—
238C2×D4×C61—22no—
239C2×D4×C61—22no—
240C2×D4×C61—22no—
241C2×D4×C61—21no—
242C2×D4×C61—22no—
243C2×D4×C61—21no—
244C2×D4×C61—21no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—41no—
251C2×D4×C61—42no—
252C2×D4×C61—42no—
253C2×D4×C61—42no—
254C2×D4×C61—42no—
255C2×D4×C61—44no—
256C2×D4×C61—44no—
257C2×D4×C61—42no—
258C2×D4×C61—42no—
259C2×D4×C61—82no—
260C2×D4×C61—84no—
261C2×D4×C61C2×D411yescharacteristic
262C2×D4×C61C2×D411yescharacteristic
263C2×D4×C61C2×D411yescharacteristic
264C22×C4×C61—21no—
265C22×C4×C61—21no—
266C22×C4×C61—21no—
267C22×C4×C61—21no—
268C22×C4×C61—21no—
269C22×C4×C61—22no—
270C22×C4×C61—21no—
271C22×C4×C61—22no—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—21no—
275C22×C4×C61—21no—
276C22×C4×C61—42no—
277C22×C4×C61—42no—
278C22×C4×C61C2×D411yescharacteristic
279C22×C4×C61C2×D411yescharacteristic
280C22×C4×C61C2×D411yescharacteristic
281C22×C4×C61C2×D411yescharacteristic
282C22×C4×C61C2×D411yescharacteristic
283C22×C4×C61C2×D412yes—
284C22×C4×C61C2411yescharacteristic
285C22×Dic61—21no—
286C22×Dic61—21no—
287C22×Dic61—21no—
288C22×Dic61—21no—
289C4⋊C4×C61—22no—
290C4⋊C4×C61—22no—
291C4⋊C4×C61—21no—
292C4⋊C4×C61—21no—
293C4⋊C4×C61—21no—
294C4⋊C4×C61—21no—
295C4⋊C4×C61C2×D411yescharacteristic
296C4⋊C4×C61C2×D411yescharacteristic
297C22⋊C4×C61—22no—
298C22⋊C4×C61—22no—
299C22⋊C4×C61—22no—
300C22⋊C4×C61—22no—
301C22⋊C4×C61—22no—
302C22⋊C4×C61—21no—
303C22⋊C4×C61—21no—
304C22⋊C4×C61—21no—
305C22⋊C4×C61—21no—
306C22⋊C4×C61—22no—
307C22⋊C4×C61—22no—
308C22⋊C4×C61—21no—
309C42×C61—22no—
310C42×C61—21no—
311C22⋊Dic61—42no—
312C22⋊Dic61—44no—
313C22⋊Dic61—41no—
314C22⋊Dic61—41no—
315C22⋊Dic61—82no—
316C4⋊Dic61—21no—
317C4⋊Dic61—21no—
318C4⋊Dic61—21no—
319C4⋊Dic61—21no—
320#11758196—82no—
321C4×Dic61—21no—
322C4×Dic61—21no—
323C4×Dic61—21no—
324C4×Dic61—21no—
325C4×Dic61—41no—
326C4×Dic61—41no—
327#11758194—21no—
328#11758194—21no—
329#11758194—21no—
330#11758194—21no—
331#11758194—21no—
332#11758194—21no—
333#11758194—21no—
334#11758194—21no—
335#11758194—42no—
336C2×#92418—21no—
337C2×#92418—21no—
338C2×#92418—21no—
339C2×#92418—21no—
340C2×#92418—42no—
341C23×C61—21no—
342C23×C61—21no—
343C23×C61—21no—
344C23×C61—22no—
345C23×C61—21no—
346C23×C61—21no—
347C23×C61—22no—
348C23×C61—22no—
349C23×C61—41no—
350C23×C61—41no—
351C23×C61—42no—
352C23×C61—42no—
353C23×C61—44no—
354C23×C61—42no—
355C23×C61—42no—
356C23×C61—81no—
357C23×C61—82no—
358C23×C61—82no—
359C23×C61#12011yescharacteristic
360C23×C61#12011yescharacteristic
361C23×C61C22×D411yescharacteristic
362Q8×C61—21no—
363Q8×C61—21no—
364Q8×C61—21no—
365Q8×C61—21no—
366Q8×C61—21no—
367Q8×C61—42no—
368Q8×C61#12312yes—
369D4×C61—22no—
370D4×C61—22no—
371D4×C61—21no—
372D4×C61—21no—
373D4×C61—21no—
374D4×C61—21no—
375D4×C61—21no—
376D4×C61—42no—
377D4×C61—42no—
378D4×C61—44no—
379D4×C61—42no—
380D4×C61—44no—
381D4×C61—44no—
382D4×C61—42no—
383D4×C61—41no—
384D4×C61—41no—
385D4×C61—41no—
386D4×C61—41no—
387D4×C61—41no—
388D4×C61—41no—
389D4×C61—41no—
390D4×C61—41no—
391D4×C61—81no—
392D4×C61—82no—
393D4×C61—82no—
394D4×C61—82no—
395D4×C61—82no—
396D4×C61#12312yes—
397C2×C4×C61—21no—
398C2×C4×C61—21no—
399C2×C4×C61—21no—
400C2×C4×C61—21no—
401C2×C4×C61—21no—
402C2×C4×C61—21no—
403C2×C4×C61—21no—
404C2×C4×C61—21no—
405C2×C4×C61—21no—
406C2×C4×C61—21no—
407C2×C4×C61—21no—
408C2×C4×C61—22no—
409C2×C4×C61—22no—
410C2×C4×C61—21no—
411C2×C4×C61—22no—
412C2×C4×C61—21no—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—42no—
416C2×C4×C61—42no—
417C2×C4×C61—42no—
418C2×C4×C61—44no—
419C2×C4×C61—41no—
420C2×C4×C61—41no—
421C2×C4×C61—41no—
422C2×C4×C61—41no—
423C2×C4×C61—42no—
424C2×C4×C61—82no—
425C2×C4×C61#12011yescharacteristic
426C2×C4×C61#12011yescharacteristic
427C2×C4×C61C22×D411yescharacteristic
428C2×C4×C61C22×D411yescharacteristic
429C2×C4×C61C2×#4111yescharacteristic
430C2×C4×C61C2×#4111yescharacteristic
431C2×C4×C61H(5,𝔽2)11yescharacteristic
432C2×C4×C61H(5,𝔽2)11yescharacteristic
433C2×Dic61—22no—
434C2×Dic61—41no—
435C2×Dic61—41no—
436C2×Dic61—42no—
437C2×Dic61—41no—
438C2×Dic61—42no—
439C2×Dic61—41no—
440C2×Dic61—41no—
441C2×Dic61—41no—
442C2×Dic61—41no—
443#92418—41no—
444#92418—41no—
445#92418—41no—
446#92418—41no—
447#24031—611nomaximal, Sylow
448C22×C61—21no—
449C22×C61—21no—
450C22×C61—21no—
451C22×C61—21no—
452C22×C61—22no—
453C22×C61—21no—
454C22×C61—21no—
455C22×C61—21no—
456C22×C61—21no—
457C22×C61—41no—
458C22×C61—41no—
459C22×C61—41no—
460C22×C61—41no—
461C22×C61—42no—
462C22×C61—41no—
463C22×C61—42no—
464C22×C61—41no—
465C22×C61—42no—
466C22×C61—41no—
467C22×C61—41no—
468C22×C61—81no—
469C22×C61—81no—
470C22×C61—82no—
471C22×C61—82no—
472C22×C61—84no—
473C22×C61—164no—
474C22×C61C2×#12011yescharacteristic
475C22×C61#54611yescharacteristic
476C22×C61#54611yescharacteristic
477C4×C61—21no—
478C4×C61—21no—
479C4×C61—22no—
480C4×C61—41no—
481C4×C61—41no—
482C4×C61—41no—
483C4×C61—42no—
484C4×C61—41no—
485C4×C61C2×#12311yescharacteristic
486C4×C61#53411yescharacteristic
487C4×C61#54611yescharacteristic
488C4×C61#54611yescharacteristic
489Dic61—42no—
490Dic61—81no—
491Dic61—81no—
492Dic61—81no—
493#3488D6111yescharacteristic
494#3093—611no—
495#2896—611no—
496#2500—611no—
497#2040—611no—
498#2039—611no—
499#2037—611no—
500#2037—611no—
501#1900—611no—
502#1871—611no—
503#1860—611no—
504#1859—611no—
505#1792—611no—
506#1792—611no—
507#1789—611no—
508C2×C61—21no—
509C2×C61—21no—
510C2×C61—41no—
511C2×C61—41no—
512C2×C61—42no—
513C2×C61—81no—
514C2×C61—82no—
515C2×C61—81no—
516C2×C61#240511yescharacteristic
517C2×C61#301811yescharacteristic
518C2×C61#301911yescharacteristic
519C2×H(5,𝔽2)C2×D6111yescharacteristic
520C22×#41C2×D6111yescharacteristic
521C22×M16—611no—
522#550—21no—
523#548—21no—
524#546—21no—
525#546—22no—
526D42—22no—
527D42—21no—
528#537—21no—
529#537C2×D6111yescharacteristic
530#535—21no—
531#535C2×D6111yescharacteristic
532#525—21no—
533#525C2×D6111yescharacteristic
534C2×#121—21no—
535C2×#121C2×D6111yescharacteristic
536#520C2×D6111yescharacteristic
537C2×#117—611no—
538#485—1221no—
539#485—1221no—
540#482—1221no—
541#482—1221no—
542#428—611no—
543#428—611no—
544C2×#104—611no—
545C2×#104—611no—
546C2×#104—611no—
547C2×#104—611no—
548C2×#104—611no—
549C2×#104—611no—
550#419—1221no—
551#418—1221no—
552#417—611no—
553#417—611no—
554#417—611no—
555#417—611no—
556#417—611no—
557#417—611no—
558#416—1221no—
559#416—1221no—
560C2×#100—611no—
561C2×#100—611no—
562#407—611no—
563#394—1222no—
564#390—611no—
565#390—611no—
566#388—1222no—
567#384—611no—
568#382—611no—
569C4×C22⋊C4—611no—
570#343—611no—
571#343—611no—
572#339—611no—
573#339—611no—
574C61#2403111yescharacteristic, complemented, Sylow
575H(5,𝔽2)—22no—
576H(5,𝔽2)—22no—
577H(5,𝔽2)—41no—
578H(5,𝔽2)—41no—
579C2×#41—21no—
580C2×#41—21no—
581C2×#41—21no—
582C2×#41—21no—
583C2×#41—22no—
584C2×#41—22no—
585C2×#41—41no—
586C2×#41—41no—
587C2×#41C22⋊D6111yescharacteristic
588C2×#41C22⋊D6111yescharacteristic
589C2×#41C22×D6111yescharacteristic
590C2×#41C22×D6111yescharacteristic
591C2×#41C22×D6111yescharacteristic
592C22×Q8C22⋊D6111yescharacteristic
593C22×D4—21no—
594C22×D4—22no—
595C22×D4—22no—
596C22×D4—21no—
597C22×D4—21no—
598C22×D4C22⋊D6111yescharacteristic
599C22×D4C22⋊D6112yes—
600C22×D4C22×D6111yescharacteristic
601C23×C4—21no—
602C23×C4C22×D6111yescharacteristic
603C2×M16—611no—
604C2×M16—611no—
605C2×M16—611no—
606C2×M16—611no—
607C2×M16—1221no—
608C2×M16—2441no—
609C2×M16—2441no—
610C22×C8—1221no—
611#127—22no—
612#127—21no—
613#124—22no—
614#124—21no—
615#123—22no—
616#123—21no—
617C22⋊Q8—22no—
618C22⋊Q8—21no—
619C22⋊Q8—21no—
620C22⋊Q8C22⋊D6111yescharacteristic
621C22⋊Q8C22⋊D6111yescharacteristic
622#121—22no—
623#121—22no—
624#121—22no—
625#121—22no—
626#121—22no—
627#121—21no—
628#121—21no—
629#121—21no—
630#121—21no—
631#121—21no—
632#121—21no—
633#121—22no—
634#121—21no—
635#121—21no—
636#121C22⋊D6111yescharacteristic
637#121C22⋊D6111yescharacteristic
638#120—22no—
639#120—22no—
640#120—22no—
641#120—21no—
642#120—22no—
643C4×Q8—21no—
644C4×D4—22no—
645C4×D4—22no—
646C4×D4—21no—
647C4×D4—22no—
648C4×D4—21no—
649C4×D4—21no—
650#117—21no—
651#117—1221no—
652#117—1221no—
653#117—1221no—
654#117—1221no—
655#117C22×D6111yescharacteristic
656C2×C4⋊C4—21no—
657C2×C4⋊C4—611no—
658C2×C4⋊C4—611no—
659C2×C4⋊C4—1222no—
660C2×C4⋊C4C22×D6111yescharacteristic
661C2×C22⋊C4—22no—
662C2×C22⋊C4—1222no—
663C2×C22⋊C4—1221no—
664C2×C22⋊C4—1221no—
665C2×C22⋊C4—1222no—
666C2×C22⋊C4C22⋊D6112yes—
667C2×C42—611no—
668C2×C42—611no—
669C2×C42—1221no—
670#107—1221no—
671#107—1221no—
672#106—1221no—
673#106—1221no—
674#104—1222no—
675#104—1222no—
676#104—2441no—
677#104—2441no—
678#104—2441no—
679#104—2441no—
680#103—1221no—
681#103—1221no—
682#103—1221no—
683#103—1221no—
684#103—1221no—
685#103—1221no—
686#102—1221no—
687#102—1221no—
688#102—1221no—
689#102—1221no—
690#102—1221no—
691#102—1221no—
692#100—2441no—
693#100—2441no—
694C22⋊C8—1221no—
695C22⋊C8—1221no—
696#95—1221no—
697#95—1222no—
698C24—22no—
699C24—21no—
700C24C2×C22⋊D6112yes—
701C24C2×C22⋊D6111yescharacteristic
702#41—21no—
703#41—21no—
704#41—22no—
705#41—22no—
706#41—21no—
707#41—21no—
708#41—21no—
709#41—21no—
710#41—21no—
711#41—21no—
712#41—21no—
713#41—21no—
714#41—42no—
715#41—42no—
716#41—41no—
717#41—41no—
718#41—42no—
719#41—42no—
720#41—42no—
721#41—42no—
722#41—42no—
723#41—42no—
724#41#1175822412yes—
725#41#1175822412yes—
726C2×Q8—21no—
727C2×Q8—22no—
728C2×Q8—41no—
729C2×Q8C2×C22⋊D6111yescharacteristic
730C2×Q8C2×C22⋊D6111yescharacteristic
731C2×Q8C2×C22⋊D6111yescharacteristic
732C2×D4—21no—
733C2×D4—22no—
734C2×D4—22no—
735C2×D4—22no—
736C2×D4—21no—
737C2×D4—21no—
738C2×D4—22no—
739C2×D4—21no—
740C2×D4—21no—
741C2×D4—21no—
742C2×D4—22no—
743C2×D4—22no—
744C2×D4—22no—
745C2×D4—21no—
746C2×D4—22no—
747C2×D4—21no—
748C2×D4—21no—
749C2×D4—21no—
750C2×D4—21no—
751C2×D4—21no—
752C2×D4—21no—
753C2×D4—21no—
754C2×D4—41no—
755C2×D4—42no—
756C2×D4—42no—
757C2×D4—42no—
758C2×D4—42no—
759C2×D4—44no—
760C2×D4—44no—
761C2×D4—42no—
762C2×D4—42no—
763C2×D4—82no—
764C2×D4—84no—
765C2×D4C2×C22⋊D6111yescharacteristic
766C2×D4C2×C22⋊D6111yescharacteristic
767C2×D4C2×C22⋊D6111yescharacteristic
768C22×C4—21no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—21no—
772C22×C4—21no—
773C22×C4—22no—
774C22×C4—21no—
775C22×C4—22no—
776C22×C4—21no—
777C22×C4—21no—
778C22×C4—21no—
779C22×C4—21no—
780C22×C4—42no—
781C22×C4—42no—
782C22×C4—1221no—
783C22×C4—1221no—
784C22×C4—1221no—
785C22×C4—1221no—
786C22×C4C2×C22⋊D6111yescharacteristic
787C22×C4C2×C22⋊D6111yescharacteristic
788C22×C4C2×C22⋊D6111yescharacteristic
789C22×C4C2×C22⋊D6111yescharacteristic
790C22×C4C2×C22⋊D6111yescharacteristic
791C22×C4C2×C22⋊D6112yes—
792C22×C4C23×D6111yescharacteristic
793M16—1221no—
794M16—1221no—
795M16—1221no—
796M16—1221no—
797M16—1221no—
798M16—1221no—
799M16—1221no—
800M16—1221no—
801M16—2442no—
802C2×C8—1221no—
803C2×C8—1221no—
804C2×C8—1221no—
805C2×C8—1221no—
806C2×C8—2442no—
807C4⋊C4—22no—
808C4⋊C4—22no—
809C4⋊C4—21no—
810C4⋊C4—21no—
811C4⋊C4—21no—
812C4⋊C4—21no—
813C4⋊C4—1221no—
814C4⋊C4—1221no—
815C4⋊C4—1221no—
816C4⋊C4—1221no—
817C4⋊C4—4882no—
818C4⋊C4C2×C22⋊D6111yescharacteristic
819C4⋊C4C2×C22⋊D6111yescharacteristic
820C22⋊C4—22no—
821C22⋊C4—22no—
822C22⋊C4—22no—
823C22⋊C4—22no—
824C22⋊C4—22no—
825C22⋊C4—21no—
826C22⋊C4—21no—
827C22⋊C4—21no—
828C22⋊C4—21no—
829C22⋊C4—22no—
830C22⋊C4—22no—
831C22⋊C4—21no—
832C22⋊C4—4882no—
833C22⋊C4—2442no—
834C22⋊C4—2444no—
835C22⋊C4—2441no—
836C22⋊C4—2441no—
837C42—22no—
838C42—21no—
839C42—1221no—
840C42—1221no—
841C42—1221no—
842C42—1221no—
843C42—2441no—
844C42—2441no—
845C23—21no—
846C23—21no—
847C23—21no—
848C23—22no—
849C23—21no—
850C23—21no—
851C23—22no—
852C23—22no—
853C23—41no—
854C23—41no—
855C23—42no—
856C23—42no—
857C23—44no—
858C23—42no—
859C23—42no—
860C23—81no—
861C23—82no—
862C23—82no—
863C23#1451974611yescharacteristic
864C23#1451974611yescharacteristic
865C23C22×C22⋊D6111yescharacteristic
866Q8—21no—
867Q8—21no—
868Q8—21no—
869Q8—21no—
870Q8—21no—
871Q8—42no—
872Q8#1451975812yes—
873D4—22no—
874D4—22no—
875D4—21no—
876D4—21no—
877D4—21no—
878D4—21no—
879D4—21no—
880D4—42no—
881D4—42no—
882D4—44no—
883D4—42no—
884D4—44no—
885D4—44no—
886D4—42no—
887D4—41no—
888D4—41no—
889D4—41no—
890D4—41no—
891D4—41no—
892D4—41no—
893D4—41no—
894D4—41no—
895D4—81no—
896D4—82no—
897D4—82no—
898D4—82no—
899D4—82no—
900D4#1451975812yes—
901C2×C4—21no—
902C2×C4—21no—
903C2×C4—21no—
904C2×C4—21no—
905C2×C4—21no—
906C2×C4—21no—
907C2×C4—21no—
908C2×C4—21no—
909C2×C4—21no—
910C2×C4—21no—
911C2×C4—21no—
912C2×C4—22no—
913C2×C4—22no—
914C2×C4—21no—
915C2×C4—22no—
916C2×C4—21no—
917C2×C4—21no—
918C2×C4—21no—
919C2×C4—42no—
920C2×C4—42no—
921C2×C4—42no—
922C2×C4—44no—
923C2×C4—41no—
924C2×C4—41no—
925C2×C4—41no—
926C2×C4—41no—
927C2×C4—42no—
928C2×C4—82no—
929C2×C4—1222no—
930C2×C4—2441no—
931C2×C4—2442no—
932C2×C4—2441no—
933C2×C4—2442no—
934C2×C4—2441no—
935C2×C4—2441no—
936C2×C4—2441no—
937C2×C4—2441no—
938C2×C4—2441no—
939C2×C4#1451974611yescharacteristic
940C2×C4#1451974611yescharacteristic
941C2×C4C22×C22⋊D6111yescharacteristic
942C2×C4C22×C22⋊D6111yescharacteristic
943C2×C4C2×#1175822411yescharacteristic
944C2×C4C2×#1175822411yescharacteristic
945C2×C4#1451982211yescharacteristic
946C2×C4#1451982211yescharacteristic
947C8—2441no—
948C8—2441no—
949C8—2441no—
950C8—2441no—
951C22—21no—
952C22—21no—
953C22—21no—
954C22—21no—
955C22—21no—
956C22—21no—
957C22—21no—
958C22—21no—
959C22—22no—
960C22—41no—
961C22—41no—
962C22—41no—
963C22—42no—
964C22—41no—
965C22—42no—
966C22—41no—
967C22—41no—
968C22—41no—
969C22—41no—
970C22—42no—
971C22—81no—
972C22—81no—
973C22—82no—
974C22—82no—
975C22—84no—
976C22—164no—
977C22C2×#1451974611yescharacteristic
978C22#1684040611yescharacteristic
979C22#1684040611yescharacteristic
980C4—21no—
981C4—21no—
982C4—22no—
983C4—41no—
984C4—42no—
985C4—41no—
986C4—41no—
987C4—41no—
988C4—4881no—
989C4—4881no—
990C4—4881no—
991C4—2442no—
992C4C2×#1451975811yescharacteristic
993C4#1684032111yescharacteristic
994C4#1684040611yescharacteristic
995C4#1684040611yescharacteristic
996C2—21no—
997C2—21no—
998C2—41no—
999C2—41no—
1000C2—42no—
1001C2—81no—
1002C2—82no—
1003C2—81no—
1004C2#2144914211yescharacteristic
1005C2#2145516811yescharacteristic
1006C2#2145517611yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#24031
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3488

Complements

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

NH ≅ G/Ntype
1. #21455748C2semidirect
2. #21454338C2semidirect
3. #21450282C2semidirect
4. #21447045C2semidirect
5. #21447040C2semidirect
6. #21447026C2semidirect
7. #21447026C2semidirect
8. #21446283C2semidirect
9. #21446122C2semidirect
10. #21446052C2semidirect
11. #21446045C2semidirect
12. #21445773C2semidirect
13. #21445773C2semidirect
14. #21445763C2semidirect
16. C22×#11758194C22semidirect
17. C2×#14519736C22semidirect
22. #16839805C22semidirect
23. #16839805C22semidirect
26. C2×#14519704C22semidirect
27. C2×#14519704C22semidirect
28. C2×#14519704C22semidirect
29. C2×#14519704C22semidirect
34. #16839763C22semidirect
35. #16839763C22semidirect
36. #16839763C22semidirect
37. #16839763C22semidirect
40. C2×#14519694C22semidirect
41. C2×#14519694C22semidirect
42. #16839726C22semidirect
44. #16839665C22semidirect
45. #16839665C22semidirect
47. #16839631C22semidirect
48. #16839627C22semidirect
49. C4×C22⋊Dic61C22semidirect
50. #16839531C22semidirect
51. #16839531C22semidirect
52. #16839521C22semidirect
53. #16839521C22semidirect
574. C61#24031semidirect

Maximal subgroups

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

subgroupindex
#214557482
#214543382
#214502822
#214470452
#214470402
#214470262
#214462832
#214461222
#214460522
#214460452
#214457732
#214457632
C61×#34882
#2403161