Finite Group Databasebeta

← #29718279

Subgroups — #29718279

Order 15616.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1064 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455451C211yesmaximal, characteristic, complemented
2C2×#16839940C211yesmaximal, characteristic, complemented
3#21455079C211yesmaximal, characteristic, complemented
4C2×#16839779C211yesmaximal, characteristic, complemented
5#21451580C211yesmaximal, characteristic, complemented
6#21447040C211yesmaximal, characteristic, complemented
7#21447026C211yesmaximal, characteristic, complemented
8#21446866C211yesmaximal, characteristic, complemented
9#21446846C211yesmaximal, characteristic, complemented
10#21446283C211yesmaximal, characteristic, complemented
11#21446268C211yesmaximal, characteristic, complemented
12#21446188C211yesmaximal, characteristic, complemented
13#21446045C211yesmaximal, characteristic, complemented
14#21445773C211yesmaximal, characteristic, complemented
15C61×#3488C211yesmaximal, characteristic
16C2×#14519807C2211yescharacteristic
17C2×#14519807C2211yescharacteristic, complemented
18C2×#14519807C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic, complemented
20C2×#14519764C2211yescharacteristic, complemented
21C2×#14519756C2211yescharacteristic, complemented
22C2×#14519736C2211yescharacteristic, complemented
23#16840018—21no—
24#16840006—21no—
25#16840001—21no—
26#16839989—21no—
27#16839940—24no—
28#16839924—21no—
29#16839924—21no—
30#16839918—21no—
31#16839913—21no—
32#16839805C2211yescharacteristic, complemented
33#16839779—24no—
34C2×#14519704C2211yescharacteristic
35C2×#14519704C2211yescharacteristic
36C2×#14519704C2211yescharacteristic, complemented
37C2×#14519704C2211yescharacteristic, complemented
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40#16839770C2211yescharacteristic, complemented
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic, complemented
43#16839763C2211yescharacteristic, complemented
44C2×#14519694C2211yescharacteristic, complemented
45C2×#14519694C2211yescharacteristic, complemented
46#16839726C2211yescharacteristic, complemented
47#16839685—22no—
48#16839676—22no—
49#16839667C2211yescharacteristic, complemented
50#16839665C2211yescharacteristic, complemented
51#16839631C2211yescharacteristic, complemented
52#16839531C2211yescharacteristic, complemented
53#16839531C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56C2×H(5,𝔽2)×C61C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58C61×#550—21no—
59C61×#548—21no—
60C61×#546—21no—
61C61×#546—22no—
62D42×C61—22no—
63D42×C61—21no—
64C61×#537—21no—
65C61×#537C2211yescharacteristic
66C61×#535—21no—
67C61×#535C2211yescharacteristic
68C61×#525—21no—
69C61×#525C2211yescharacteristic
70C2×#121×C61—21no—
71C2×#121×C61C2211yescharacteristic
72C61×#520C2211yescharacteristic
73C22×Dic122C2311yescharacteristic
74#14519807—22no—
75#14519807—22no—
76#14519807—22no—
77#14519807—41no—
78#14519807—41no—
79#14519807—41no—
80C2×#11758202—21no—
81C2×#11758202—21no—
82C2×#11758202—21no—
83C2×#11758200—21no—
84C2×#11758200—21no—
85C2×#11758200—21no—
86C2×#11758194—21no—
87C2×#11758194—22no—
88C2×#11758194—41no—
89C2×#11758194C2311yescharacteristic
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C22×#92418—21no—
94#14519764—22no—
95#14519764—41no—
96#14519756—21no—
97#14519756—21no—
98#14519756—21no—
99#14519756—21no—
100#14519736—22no—
101#14519736—41no—
102C2×C4⋊Dic61—21no—
103C2×C4⋊Dic61C2311yescharacteristic
104C2×#11758196—21no—
105C2×#11758196—22no—
106C2×C22⋊Dic61—22no—
107C2×C22⋊Dic61—21no—
108C2×C22⋊Dic61—21no—
109C2×C22⋊Dic61—22no—
110C2×C4×Dic61C2311yescharacteristic
111C2×C4×Dic61C2311yescharacteristic
112#14519710—21no—
113#14519708—21no—
114#14519704—22no—
115#14519704—22no—
116#14519704—22no—
117#14519704—22no—
118#14519704—41no—
119#14519704D414yescomplemented
120#14519701—21no—
121#14519701—21no—
122#14519701—21no—
123#14519700—21no—
124#14519700—21no—
125#14519698—21no—
126#14519698—21no—
127#14519698—21no—
128#14519694—22no—
129#14519694—41no—
130C22⋊#92418—21no—
131C22⋊#92418—21no—
132#14519684—22no—
133H(5,𝔽2)×C61—22no—
134H(5,𝔽2)×C61—22no—
135H(5,𝔽2)×C61—41no—
136H(5,𝔽2)×C61—41no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—21no—
141C2×#41×C61—22no—
142C2×#41×C61—22no—
143C2×#41×C61—41no—
144C2×#41×C61—41no—
145C2×#41×C61D411yescharacteristic
146C2×#41×C61D411yescharacteristic
147C2×#41×C61C2311yescharacteristic
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150C22×Q8×C61D411yescharacteristic
151C22×D4×C61—21no—
152C22×D4×C61—22no—
153C22×D4×C61—22no—
154C22×D4×C61—21no—
155C22×D4×C61—21no—
156C22×D4×C61D411yescharacteristic
157C22×D4×C61D412yes—
158C22×D4×C61C2311yescharacteristic
159C23×C4×C61—21no—
160C23×C4×C61C2311yescharacteristic
161#127×C61—22no—
162#127×C61—21no—
163#124×C61—22no—
164#124×C61—21no—
165#123×C61—22no—
166#123×C61—21no—
167C22⋊Q8×C61—22no—
168C22⋊Q8×C61—21no—
169C22⋊Q8×C61—21no—
170C22⋊Q8×C61D411yescharacteristic
171C22⋊Q8×C61D411yescharacteristic
172#121×C61—22no—
173#121×C61—22no—
174#121×C61—22no—
175#121×C61—22no—
176#121×C61—22no—
177#121×C61—21no—
178#121×C61—21no—
179#121×C61—21no—
180#121×C61—22no—
181#121×C61—21no—
182#121×C61—21no—
183#121×C61—21no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61D411yescharacteristic
187#121×C61D411yescharacteristic
188#120×C61—22no—
189#120×C61—22no—
190#120×C61—22no—
191#120×C61—22no—
192#120×C61—21no—
193C4×Q8×C61—21no—
194C4×D4×C61—22no—
195C4×D4×C61—22no—
196C4×D4×C61—21no—
197C4×D4×C61—22no—
198C4×D4×C61—21no—
199C4×D4×C61—21no—
200#117×C61—21no—
201#117×C61C2311yescharacteristic
202C2×C4⋊C4×C61—21no—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—22no—
205C2×C22⋊C4×C61D412yes—
206C24×C61—22no—
207C24×C61—21no—
208C24×C61C2×D412yes—
209C24×C61C2×D411yescharacteristic
210#41×C61—21no—
211#41×C61—21no—
212#41×C61—22no—
213#41×C61—22no—
214#41×C61—21no—
215#41×C61—21no—
216#41×C61—21no—
217#41×C61—21no—
218#41×C61—21no—
219#41×C61—21no—
220#41×C61—21no—
221#41×C61—21no—
222#41×C61—42no—
223#41×C61—42no—
224#41×C61—41no—
225#41×C61—41no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61—42no—
229#41×C61—42no—
230#41×C61—42no—
231#41×C61—42no—
232#41×C61C2×D412yes—
233#41×C61#4112yes—
234C2×Q8×C61—21no—
235C2×Q8×C61—22no—
236C2×Q8×C61—41no—
237C2×Q8×C61C2×D411yescharacteristic
238C2×Q8×C61C2×D411yescharacteristic
239C2×Q8×C61C2×D411yescharacteristic
240C2×D4×C61—21no—
241C2×D4×C61—22no—
242C2×D4×C61—22no—
243C2×D4×C61—22no—
244C2×D4×C61—22no—
245C2×D4×C61—21no—
246C2×D4×C61—21no—
247C2×D4×C61—21no—
248C2×D4×C61—21no—
249C2×D4×C61—21no—
250C2×D4×C61—22no—
251C2×D4×C61—22no—
252C2×D4×C61—22no—
253C2×D4×C61—21no—
254C2×D4×C61—22no—
255C2×D4×C61—21no—
256C2×D4×C61—21no—
257C2×D4×C61—21no—
258C2×D4×C61—21no—
259C2×D4×C61—21no—
260C2×D4×C61—21no—
261C2×D4×C61—21no—
262C2×D4×C61—41no—
263C2×D4×C61—42no—
264C2×D4×C61—42no—
265C2×D4×C61—42no—
266C2×D4×C61—42no—
267C2×D4×C61—44no—
268C2×D4×C61—44no—
269C2×D4×C61—42no—
270C2×D4×C61—42no—
271C2×D4×C61—82no—
272C2×D4×C61—84no—
273C2×D4×C61C2×D411yescharacteristic
274C2×D4×C61C2×D411yescharacteristic
275C2×D4×C61C2×D411yescharacteristic
276C22×C4×C61—21no—
277C22×C4×C61—21no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—22no—
282C22×C4×C61—21no—
283C22×C4×C61—22no—
284C22×C4×C61—21no—
285C22×C4×C61—21no—
286C22×C4×C61—21no—
287C22×C4×C61—21no—
288C22×C4×C61—42no—
289C22×C4×C61—42no—
290C22×C4×C61C2×D411yescharacteristic
291C22×C4×C61C2×D411yescharacteristic
292C22×C4×C61C2×D411yescharacteristic
293C22×C4×C61C2×D411yescharacteristic
294C22×C4×C61C2×D411yescharacteristic
295C22×C4×C61C2×D412yes—
296C22×C4×C61C2411yescharacteristic
297C22×Dic61—21no—
298C22×Dic61—21no—
299C22×Dic61—21no—
300C22×Dic61—21no—
301C2×Dic122—21no—
302C2×Dic122—21no—
303C2×Dic122—21no—
304C2×Dic122—21no—
305C2×Dic122—21no—
306C2×Dic122—21no—
307C4⋊C4×C61—22no—
308C4⋊C4×C61—22no—
309C4⋊C4×C61—21no—
310C4⋊C4×C61—21no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61C2×D411yescharacteristic
314C4⋊C4×C61C2×D411yescharacteristic
315C22⋊C4×C61—22no—
316C22⋊C4×C61—22no—
317C22⋊C4×C61—22no—
318C22⋊C4×C61—22no—
319C22⋊C4×C61—22no—
320C22⋊C4×C61—21no—
321C22⋊C4×C61—21no—
322C22⋊C4×C61—21no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—22no—
325C22⋊C4×C61—22no—
326C22⋊C4×C61—21no—
327C42×C61—22no—
328C42×C61—21no—
329C22⋊Dic61—42no—
330C22⋊Dic61—44no—
331C22⋊Dic61—41no—
332C22⋊Dic61—41no—
333C22⋊Dic61—82no—
334#11758202—42no—
335#11758202—42no—
336#11758202—42no—
337#11758200—42no—
338#11758200—42no—
339#11758200—42no—
340C4⋊Dic61—21no—
341C4⋊Dic61—21no—
342C4⋊Dic61—42no—
343#11758196—41no—
344#11758196—41no—
345#11758196—82no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61C2×D412yescomplemented
350#11758194—21no—
351#11758194—21no—
352#11758194—21no—
353#11758194—21no—
354#11758194—21no—
355#11758194—21no—
356#11758194—21no—
357#11758194—42no—
358#11758194C2×D412yescomplemented
359C2×#92418—21no—
360C2×#92418—21no—
361C2×#92418—21no—
362C2×#92418—21no—
363C2×#92418—42no—
364C23×C61—21no—
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—22no—
368C23×C61—21no—
369C23×C61—21no—
370C23×C61—22no—
371C23×C61—22no—
372C23×C61—41no—
373C23×C61—41no—
374C23×C61—42no—
375C23×C61—42no—
376C23×C61—44no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—81no—
380C23×C61—82no—
381C23×C61—82no—
382C23×C61#12011yescharacteristic
383C23×C61#12011yescharacteristic
384C23×C61C22×D411yescharacteristic
385Q8×C61—21no—
386Q8×C61—21no—
387Q8×C61—21no—
388Q8×C61—21no—
389Q8×C61—21no—
390Q8×C61—42no—
391Q8×C61#12112yes—
392D4×C61—22no—
393D4×C61—22no—
394D4×C61—21no—
395D4×C61—21no—
396D4×C61—21no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—42no—
400D4×C61—42no—
401D4×C61—44no—
402D4×C61—42no—
403D4×C61—44no—
404D4×C61—44no—
405D4×C61—42no—
406D4×C61—41no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—41no—
410D4×C61—41no—
411D4×C61—41no—
412D4×C61—41no—
413D4×C61—41no—
414D4×C61—81no—
415D4×C61—82no—
416D4×C61—82no—
417D4×C61—82no—
418D4×C61—82no—
419D4×C61#12112yes—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—21no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—21no—
426C2×C4×C61—21no—
427C2×C4×C61—21no—
428C2×C4×C61—21no—
429C2×C4×C61—22no—
430C2×C4×C61—21no—
431C2×C4×C61—21no—
432C2×C4×C61—22no—
433C2×C4×C61—21no—
434C2×C4×C61—22no—
435C2×C4×C61—21no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—42no—
439C2×C4×C61—42no—
440C2×C4×C61—42no—
441C2×C4×C61—44no—
442C2×C4×C61—41no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—42no—
447C2×C4×C61—82no—
448C2×C4×C61#12011yescharacteristic
449C2×C4×C61#12011yescharacteristic
450C2×C4×C61C22×D411yescharacteristic
451C2×C4×C61C22×D411yescharacteristic
452C2×C4×C61C22×D411yescharacteristic
453C2×C4×C61C2×#4111yescharacteristic
454C2×C4×C61H(5,𝔽2)11yescharacteristic
455C2×C4×C61H(5,𝔽2)11yescharacteristic
456C2×Dic61—22no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—42no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—41no—
463C2×Dic61—41no—
464C2×Dic61—41no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467Dic122—41no—
468Dic122—41no—
469Dic122—41no—
470Dic122—41no—
471#92418—22no—
472#92418—41no—
473#92418—41no—
474#92418—41no—
475#24471—611nomaximal, Sylow
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—22no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—21no—
484C22×C61—21no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—41no—
489C22×C61—42no—
490C22×C61—42no—
491C22×C61—41no—
492C22×C61—41no—
493C22×C61—41no—
494C22×C61—42no—
495C22×C61—41no—
496C22×C61—81no—
497C22×C61—81no—
498C22×C61—82no—
499C22×C61—82no—
500C22×C61—84no—
501C22×C61—164no—
502C22×C61C2×#12011yescharacteristic
503C22×C61D4211yescharacteristic
504C22×C61#54611yescharacteristic
505C4×C61—21no—
506C4×C61—21no—
507C4×C61—22no—
508C4×C61—41no—
509C4×C61—41no—
510C4×C61—42no—
511C4×C61—41no—
512C4×C61—41no—
513C4×C61C2×#12111yescharacteristic
514C4×C61#53411yescharacteristic
515C4×C61D4211yescharacteristic
516C4×C61#54611yescharacteristic
517Dic61—42no—
518Dic61—81no—
519Dic61—81no—
520Dic61—81no—
521#3488D6111yescharacteristic
522#3056—611no—
523C2×#455—611no—
524#3007—611no—
525C2×#421—611no—
526#2620—611no—
527#2039—611no—
528#2037—611no—
529#2007—611no—
530#2004—611no—
531#1900—611no—
532#1897—611no—
533#1882—611no—
534#1859—611no—
535#1792—611no—
536C2×C61—21no—
537C2×C61—21no—
538C2×C61—41no—
539C2×C61—41no—
540C2×C61—42no—
541C2×C61—81no—
542C2×C61—82no—
543C2×C61—81no—
544C2×C61#241011yescharacteristic
545C2×C61#301911yescharacteristic
546C2×C61#302211yescharacteristic
547C2×H(5,𝔽2)C2×D6111yescharacteristic
548C22×#41C2×D6111yescharacteristic
549C2×#137—611no—
550C2×#137—611no—
551C2×#137—611no—
552C22×M16—611no—
553#550—21no—
554#548—21no—
555#546—21no—
556#546—22no—
557D42—22no—
558D42—21no—
559#537—21no—
560#537C2×D6111yescharacteristic
561#535—21no—
562#535C2×D6111yescharacteristic
563C2×#124—611no—
564#525—21no—
565#525C2×D6111yescharacteristic
566C2×C22⋊Q8—611no—
567C2×#121—21no—
568C2×#121C2×D6111yescharacteristic
569#520C2×D6111yescharacteristic
570C2×#117—611no—
571#470—1221no—
572#468—1221no—
573#467—1221no—
574#465—1221no—
575#455—1224no—
576#452—1221no—
577#452—1221no—
578#451—1221no—
579#450—1221no—
580#428—611no—
581#421—1224no—
582C2×#104—611no—
583C2×#104—611no—
584C2×#104—611no—
585C2×#104—611no—
586C2×#104—611no—
587C2×#104—611no—
588#419—611no—
589#417—611no—
590#417—611no—
591#417—611no—
592C2×#100—611no—
593C2×#100—611no—
594#407—611no—
595#396—1222no—
596#394—1222no—
597#391—611no—
598#390—611no—
599#384—611no—
600#343—611no—
601#343—611no—
602#339—611no—
603#339—611no—
604C61#2447111yescharacteristic, complemented, Sylow
605H(5,𝔽2)—22no—
606H(5,𝔽2)—22no—
607H(5,𝔽2)—41no—
608H(5,𝔽2)—41no—
609C2×#41—21no—
610C2×#41—21no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—22no—
614C2×#41—22no—
615C2×#41—41no—
616C2×#41—41no—
617C2×#41C22⋊D6111yescharacteristic
618C2×#41C22⋊D6111yescharacteristic
619C2×#41C22×D6111yescharacteristic
620C2×#41C22×D6111yescharacteristic
621C2×#41C22×D6111yescharacteristic
622C22×Q8—611no—
623C22×Q8C22⋊D6111yescharacteristic
624C22×D4—21no—
625C22×D4—22no—
626C22×D4—22no—
627C22×D4—21no—
628C22×D4—21no—
629C22×D4C22⋊D6111yescharacteristic
630C22×D4C22⋊D6112yes—
631C22×D4C22×D6111yescharacteristic
632C23×C4—21no—
633C23×C4C22×D6111yescharacteristic
634#137—1222no—
635#137—1222no—
636#137—1222no—
637#137—2441no—
638#137—2441no—
639#137—2441no—
640C2×Q16—1221no—
641C2×Q16—1221no—
642C2×Q16—1221no—
643C2×SD16—1221no—
644C2×SD16—1221no—
645C2×SD16—1221no—
646C2×M16—611no—
647C2×M16—611no—
648C2×M16—611no—
649C2×M16—611no—
650C2×M16—1221no—
651C2×M16—1222no—
652C2×M16—2441no—
653C22×C8—1221no—
654#127—22no—
655#127—21no—
656#124—22no—
657#124—21no—
658#124—1222no—
659#124—2441no—
660#123—22no—
661#123—21no—
662C22⋊Q8—22no—
663C22⋊Q8—21no—
664C22⋊Q8—21no—
665C22⋊Q8—1221no—
666C22⋊Q8—1221no—
667C22⋊Q8—1221no—
668C22⋊Q8—1221no—
669C22⋊Q8C22⋊D6111yescharacteristic
670C22⋊Q8C22⋊D6111yescharacteristic
671#121—22no—
672#121—22no—
673#121—22no—
674#121—22no—
675#121—22no—
676#121—21no—
677#121—21no—
678#121—21no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—22no—
683#121—21no—
684#121—21no—
685#121C22⋊D6111yescharacteristic
686#121C22⋊D6111yescharacteristic
687#120—22no—
688#120—22no—
689#120—22no—
690#120—21no—
691#120—22no—
692C4×Q8—21no—
693C4×D4—22no—
694C4×D4—22no—
695C4×D4—21no—
696C4×D4—22no—
697C4×D4—21no—
698C4×D4—21no—
699#117—21no—
700#117—1222no—
701#117—2441no—
702#117C22×D6111yescharacteristic
703C2×C4⋊C4—21no—
704C2×C4⋊C4—611no—
705C2×C4⋊C4—1222no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4—1221no—
708C2×C4⋊C4C22×D6111yescharacteristic
709C2×C22⋊C4—22no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1221no—
712C2×C22⋊C4—1221no—
713C2×C22⋊C4—1222no—
714C2×C22⋊C4C22⋊D6112yes—
715C2×C42—611no—
716C2×C42—611no—
717#107—1221no—
718#106—1221no—
719#104—614no—
720#104—1222no—
721#104—1222no—
722#104—1222no—
723#104—1222no—
724#104—2441no—
725#103—1221no—
726#103—1221no—
727#103—1221no—
728#103—1221no—
729#103—1221no—
730#102—1221no—
731#102—1221no—
732#102—1221no—
733#100—1222no—
734#100—2441no—
735C22⋊C8—1221no—
736C22⋊C8—1221no—
737#95—1222no—
738C24—22no—
739C24—21no—
740C24C2×C22⋊D6112yes—
741C24C2×C22⋊D6111yescharacteristic
742#41—21no—
743#41—21no—
744#41—22no—
745#41—22no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—42no—
755#41—42no—
756#41—41no—
757#41—41no—
758#41—42no—
759#41—42no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41D4×D6112yes—
765#41#1175822412yes—
766C2×Q8—21no—
767C2×Q8—22no—
768C2×Q8—41no—
769C2×Q8—1221no—
770C2×Q8—1221no—
771C2×Q8—1221no—
772C2×Q8—1221no—
773C2×Q8—1221no—
774C2×Q8—1221no—
775C2×Q8C2×C22⋊D6111yescharacteristic
776C2×Q8C2×C22⋊D6111yescharacteristic
777C2×Q8C2×C22⋊D6111yescharacteristic
778C2×D4—21no—
779C2×D4—22no—
780C2×D4—22no—
781C2×D4—22no—
782C2×D4—21no—
783C2×D4—21no—
784C2×D4—22no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—22no—
790C2×D4—22no—
791C2×D4—21no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—21no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—41no—
801C2×D4—42no—
802C2×D4—42no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—44no—
806C2×D4—44no—
807C2×D4—42no—
808C2×D4—42no—
809C2×D4—82no—
810C2×D4—84no—
811C2×D4C2×C22⋊D6111yescharacteristic
812C2×D4C2×C22⋊D6111yescharacteristic
813C2×D4C2×C22⋊D6111yescharacteristic
814C22×C4—21no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—22no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—21no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—42no—
827C22×C4—42no—
828C22×C4—1221no—
829C22×C4—1221no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4C2×C22⋊D6111yescharacteristic
833C22×C4C2×C22⋊D6111yescharacteristic
834C22×C4C2×C22⋊D6111yescharacteristic
835C22×C4C2×C22⋊D6111yescharacteristic
836C22×C4C2×C22⋊D6111yescharacteristic
837C22×C4C2×C22⋊D6112yes—
838C22×C4C23×D6111yescharacteristic
839Q16—2442no—
840Q16—2442no—
841Q16—2442no—
842SD16—2442no—
843SD16—2442no—
844SD16—2442no—
845M16—612no—
846M16—1221no—
847M16—1221no—
848M16—1221no—
849M16—1221no—
850M16—1221no—
851M16—1221no—
852M16—1221no—
853M16—2442no—
854C2×C8—1221no—
855C2×C8—1221no—
856C2×C8—1221no—
857C2×C8—1221no—
858C2×C8—2442no—
859C4⋊C4—22no—
860C4⋊C4—22no—
861C4⋊C4—21no—
862C4⋊C4—21no—
863C4⋊C4—21no—
864C4⋊C4—21no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4—4882no—
868C4⋊C4—2442no—
869C4⋊C4—2441no—
870C4⋊C4—2441no—
871C4⋊C4C2×C22⋊D6111yescharacteristic
872C4⋊C4C2×C22⋊D6111yescharacteristic
873C22⋊C4—22no—
874C22⋊C4—22no—
875C22⋊C4—22no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—21no—
882C22⋊C4—22no—
883C22⋊C4—22no—
884C22⋊C4—21no—
885C22⋊C4—4882no—
886C22⋊C4—2442no—
887C22⋊C4—2444no—
888C22⋊C4—2441no—
889C22⋊C4—2441no—
890C42—22no—
891C42—21no—
892C42—612no—
893C42—1221no—
894C42—1221no—
895C42—1221no—
896C23—21no—
897C23—21no—
898C23—21no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—22no—
903C23—22no—
904C23—41no—
905C23—41no—
906C23—42no—
907C23—42no—
908C23—44no—
909C23—42no—
910C23—42no—
911C23—81no—
912C23—82no—
913C23—82no—
914C23#1451974611yescharacteristic
915C23#1451974611yescharacteristic
916C23C22×C22⋊D6111yescharacteristic
917Q8—21no—
918Q8—21no—
919Q8—21no—
920Q8—21no—
921Q8—21no—
922Q8—42no—
923Q8—2441no—
924Q8—2441no—
925Q8—2441no—
926Q8—2441no—
927Q8#1451974912yes—
928D4—22no—
929D4—22no—
930D4—21no—
931D4—21no—
932D4—21no—
933D4—21no—
934D4—21no—
935D4—42no—
936D4—42no—
937D4—44no—
938D4—42no—
939D4—44no—
940D4—44no—
941D4—42no—
942D4—41no—
943D4—41no—
944D4—41no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—81no—
951D4—82no—
952D4—82no—
953D4—82no—
954D4—82no—
955D4#1451974912yes—
956C2×C4—21no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—22no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—22no—
971C2×C4—21no—
972C2×C4—21no—
973C2×C4—21no—
974C2×C4—42no—
975C2×C4—42no—
976C2×C4—42no—
977C2×C4—44no—
978C2×C4—41no—
979C2×C4—41no—
980C2×C4—41no—
981C2×C4—41no—
982C2×C4—42no—
983C2×C4—82no—
984C2×C4—1222no—
985C2×C4—2441no—
986C2×C4—2442no—
987C2×C4—2441no—
988C2×C4—2441no—
989C2×C4—2441no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4#1451974611yescharacteristic
996C2×C4#1451974611yescharacteristic
997C2×C4C2×D4×D6111yescharacteristic
998C2×C4C22×C22⋊D6111yescharacteristic
999C2×C4C22×C22⋊D6111yescharacteristic
1000C2×C4C2×#1175822411yescharacteristic
1001C2×C4#1451982211yescharacteristic
1002C2×C4#1451982211yescharacteristic
1003C8—1222no—
1004C8—2441no—
1005C8—2441no—
1006C8—2441no—
1007C22—21no—
1008C22—21no—
1009C22—21no—
1010C22—21no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—22no—
1016C22—41no—
1017C22—41no—
1018C22—42no—
1019C22—41no—
1020C22—41no—
1021C22—41no—
1022C22—42no—
1023C22—41no—
1024C22—41no—
1025C22—41no—
1026C22—42no—
1027C22—81no—
1028C22—81no—
1029C22—82no—
1030C22—82no—
1031C22—84no—
1032C22—164no—
1033C22C2×#1451974611yescharacteristic
1034C22D4×C22⋊D6111yescharacteristic
1035C22#1684040611yescharacteristic
1036C4—21no—
1037C4—21no—
1038C4—22no—
1039C4—42no—
1040C4—41no—
1041C4—41no—
1042C4—41no—
1043C4—41no—
1044C4—4881no—
1045C4—4881no—
1046C4—4881no—
1047C4—2442no—
1048C4C2×#1451974911yescharacteristic
1049C4#1684032111yescharacteristic
1050C4D4×C22⋊D6111yescharacteristic
1051C4#1684040611yescharacteristic
1052C2—21no—
1053C2—21no—
1054C2—41no—
1055C2—41no—
1056C2—42no—
1057C2—81no—
1058C2—82no—
1059C2—81no—
1060C2#2144919311yescharacteristic
1061C2#2145517611yescharacteristic
1062C2#2145519811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#24471
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. #21455451C2semidirect
2. C2×#16839940C2semidirect
3. #21455079C2semidirect
4. C2×#16839779C2semidirect
5. #21451580C2semidirect
6. #21447040C2semidirect
7. #21447026C2semidirect
8. #21446866C2semidirect
9. #21446846C2semidirect
10. #21446283C2semidirect
11. #21446268C2semidirect
12. #21446188C2semidirect
13. #21446045C2semidirect
14. #21445773C2semidirect
17. C2×#14519807C22semidirect
18. C2×#14519807C22semidirect
19. C22×#11758194C22semidirect
20. C2×#14519764C22semidirect
21. C2×#14519756C22semidirect
22. C2×#14519736C22semidirect
32. #16839805C22semidirect
36. C2×#14519704C22semidirect
37. C2×#14519704C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. #16839770C22semidirect
42. #16839763C22semidirect
43. #16839763C22semidirect
44. C2×#14519694C22semidirect
45. C2×#14519694C22semidirect
46. #16839726C22semidirect
49. #16839667C22semidirect
50. #16839665C22semidirect
51. #16839631C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
119. #14519704D4semidirect
349. C4×Dic61C2×D4semidirect
358. #11758194C2×D4semidirect
604. C61#24471semidirect

Maximal subgroups

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

subgroupindex
#214554512
C2×#168399402
#214550792
C2×#168397792
#214515802
#214470402
#214470262
#214468662
#214468462
#214462832
#214462682
#214461882
#214460452
#214457732
C61×#34882
#2447161