Finite Group Databasebeta

← #29718219

Subgroups — #29718219

Order 15616.

1486 conjugacy classes of subgroups.

The subgroup lattice has 1068 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
4C22×#14519704C211yesmaximal, characteristic, complemented
5#21454118C211yesmaximal, characteristic, complemented
6#21447045C211yesmaximal, characteristic, complemented
7#21447026C211yesmaximal, characteristic, complemented
8#21446866C211yesmaximal, characteristic, complemented
9#21446846C211yesmaximal, characteristic, complemented
10#21446283C211yesmaximal, characteristic, complemented
11#21446263C211yesmaximal, characteristic, complemented
12#21446188C211yesmaximal, characteristic, complemented
13#21446052C211yesmaximal, 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
22C22×C4×Dic61C2211yescharacteristic, 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
33C2×#14519704—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#16839667C2211yescharacteristic, complemented
48#16839665C2211yescharacteristic, complemented
49#16839656—22no—
50#16839642—22no—
51#16839627C2211yescharacteristic, 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
74C23×Dic61—21no—
75#14519807—22no—
76#14519807—22no—
77#14519807—22no—
78#14519807—41no—
79#14519807—41no—
80#14519807—41no—
81C2×#11758202—21no—
82C2×#11758202—21no—
83C2×#11758202—21no—
84C2×#11758200—21no—
85C2×#11758200—21no—
86C2×#11758200—21no—
87C2×#11758194—21no—
88C2×#11758194—22no—
89C2×#11758194—41no—
90C2×#11758194C2311yescharacteristic
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C22×#92418—21no—
95#14519764—22no—
96#14519764—41no—
97#14519756—21no—
98#14519756—21no—
99#14519756—21no—
100#14519756—21no—
101C2×C4⋊Dic61C2311yescharacteristic
102C2×#11758196—21no—
103C2×C22⋊Dic61—21no—
104C2×C22⋊Dic61—22no—
105C2×C22⋊Dic61—22no—
106C2×C4×Dic61—22no—
107C2×C4×Dic61—21no—
108C2×C4×Dic61—41no—
109C2×C4×Dic61C2311yescharacteristic
110C2×C4×Dic61C2311yescharacteristic
111#14519710—21no—
112#14519708—21no—
113#14519704—22no—
114#14519704—22no—
115#14519704—22no—
116#14519704—22no—
117#14519704—41no—
118#14519704D414yescomplemented
119#14519701—21no—
120#14519701—21no—
121#14519701—21no—
122#14519700—21no—
123#14519700—21no—
124#14519698—21no—
125#14519698—21no—
126#14519698—21no—
127#14519694—22no—
128#14519694—41no—
129C22⋊#92418—21no—
130C22⋊#92418—21no—
131#14519684—22no—
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×D411yescharacteristic
209C24×C61C2×D412yes—
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—44no—
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—
301C22×Dic61—42no—
302C22×Dic61—42no—
303C22×Dic61—42no—
304C2×Dic122—21no—
305C2×Dic122—21no—
306C2×Dic122—21no—
307C2×Dic122—21no—
308C2×Dic122—21no—
309C2×Dic122—21no—
310C4⋊C4×C61—22no—
311C4⋊C4×C61—22no—
312C4⋊C4×C61—21no—
313C4⋊C4×C61—21no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61C2×D411yescharacteristic
317C4⋊C4×C61C2×D411yescharacteristic
318C22⋊C4×C61—22no—
319C22⋊C4×C61—22no—
320C22⋊C4×C61—22no—
321C22⋊C4×C61—22no—
322C22⋊C4×C61—22no—
323C22⋊C4×C61—21no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—21no—
326C22⋊C4×C61—21no—
327C22⋊C4×C61—22no—
328C22⋊C4×C61—22no—
329C22⋊C4×C61—21no—
330C42×C61—22no—
331C42×C61—21no—
332C22⋊Dic61—44no—
333C22⋊Dic61—44no—
334C22⋊Dic61—41no—
335C22⋊Dic61—41no—
336#11758202—42no—
337#11758202—42no—
338#11758202—42no—
339#11758200—42no—
340#11758200—42no—
341#11758200—42no—
342C4⋊Dic61—21no—
343C4⋊Dic61—21no—
344#11758196—41no—
345#11758196—41no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61—21no—
349C4×Dic61—42no—
350C4×Dic61C2×D412yescomplemented
351#11758194—21no—
352#11758194—21no—
353#11758194—21no—
354#11758194—21no—
355#11758194—21no—
356#11758194—21no—
357#11758194—21no—
358#11758194—42no—
359#11758194C2×D412yescomplemented
360C2×#92418—21no—
361C2×#92418—21no—
362C2×#92418—21no—
363C2×#92418—21no—
364C2×#92418—42no—
365C23×C61—21no—
366C23×C61—21no—
367C23×C61—21no—
368C23×C61—22no—
369C23×C61—22no—
370C23×C61—21no—
371C23×C61—21no—
372C23×C61—22no—
373C23×C61—22no—
374C23×C61—41no—
375C23×C61—42no—
376C23×C61—44no—
377C23×C61—42no—
378C23×C61—42no—
379C23×C61—42no—
380C23×C61—81no—
381C23×C61—82no—
382C23×C61—82no—
383C23×C61#12011yescharacteristic
384C23×C61#12011yescharacteristic
385C23×C61C22×D411yescharacteristic
386Q8×C61—21no—
387Q8×C61—21no—
388Q8×C61—21no—
389Q8×C61—21no—
390Q8×C61—21no—
391Q8×C61—42no—
392Q8×C61#12112yes—
393D4×C61—22no—
394D4×C61—22no—
395D4×C61—21no—
396D4×C61—21no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—21no—
400D4×C61—42no—
401D4×C61—42no—
402D4×C61—44no—
403D4×C61—42no—
404D4×C61—44no—
405D4×C61—41no—
406D4×C61—41no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—44no—
410D4×C61—42no—
411D4×C61—41no—
412D4×C61—41no—
413D4×C61—41no—
414D4×C61—41no—
415D4×C61—81no—
416D4×C61—82no—
417D4×C61—82no—
418D4×C61—82no—
419D4×C61—82no—
420D4×C61#12112yes—
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—21no—
430C2×C4×C61—22no—
431C2×C4×C61—21no—
432C2×C4×C61—21no—
433C2×C4×C61—22no—
434C2×C4×C61—21no—
435C2×C4×C61—22no—
436C2×C4×C61—21no—
437C2×C4×C61—21no—
438C2×C4×C61—21no—
439C2×C4×C61—42no—
440C2×C4×C61—42no—
441C2×C4×C61—42no—
442C2×C4×C61—44no—
443C2×C4×C61—41no—
444C2×C4×C61—41no—
445C2×C4×C61—41no—
446C2×C4×C61—41no—
447C2×C4×C61—42no—
448C2×C4×C61—82no—
449C2×C4×C61#12011yescharacteristic
450C2×C4×C61#12011yescharacteristic
451C2×C4×C61C22×D411yescharacteristic
452C2×C4×C61C22×D411yescharacteristic
453C2×C4×C61C22×D411yescharacteristic
454C2×C4×C61C2×#4111yescharacteristic
455C2×C4×C61H(5,𝔽2)11yescharacteristic
456C2×C4×C61H(5,𝔽2)11yescharacteristic
457C2×Dic61—22no—
458C2×Dic61—22no—
459C2×Dic61—41no—
460C2×Dic61—41no—
461C2×Dic61—41no—
462C2×Dic61—48no—
463C2×Dic61—41no—
464C2×Dic61—42no—
465C2×Dic61—41no—
466C2×Dic61—41no—
467C2×Dic61—41no—
468C2×Dic61—41no—
469Dic122—41no—
470Dic122—41no—
471Dic122—41no—
472Dic122—41no—
473#92418—22no—
474#92418—41no—
475#92418—41no—
476#92418—41no—
477#24467—611nomaximal, Sylow
478C22×C61—21no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—21no—
482C22×C61—21no—
483C22×C61—22no—
484C22×C61—21no—
485C22×C61—21no—
486C22×C61—42no—
487C22×C61—42no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61—41no—
492C22×C61—42no—
493C22×C61—42no—
494C22×C61—41no—
495C22×C61—41no—
496C22×C61—41no—
497C22×C61—42no—
498C22×C61—41no—
499C22×C61—84no—
500C22×C61—82no—
501C22×C61—82no—
502C22×C61—164no—
503C22×C61#45512yescomplemented
504C22×C61C2×#12011yescharacteristic
505C22×C61D4211yescharacteristic
506C22×C61#54611yescharacteristic
507C4×C61—21no—
508C4×C61—21no—
509C4×C61—22no—
510C4×C61—41no—
511C4×C61—41no—
512C4×C61—42no—
513C4×C61—41no—
514C4×C61—41no—
515C4×C61C2×#12111yescharacteristic
516C4×C61#53411yescharacteristic
517C4×C61D4211yescharacteristic
518C4×C61#54611yescharacteristic
519Dic61—42no—
520Dic61—42no—
521Dic61—81no—
522Dic61—81no—
523#3488D6111yescharacteristic
524#3056—611no—
525C2×#455—611no—
526#3007—611no—
527C22×#104—611no—
528#2850—611no—
529#2040—611no—
530#2037—611no—
531#2007—611no—
532#2004—611no—
533#1900—611no—
534#1896—611no—
535#1882—611no—
536#1860—611no—
537#1792—611no—
538C2×C61—21no—
539C2×C61—21no—
540C2×C61—22no—
541C2×C61—41no—
542C2×C61—42no—
543C2×C61—81no—
544C2×C61—82no—
545C2×C61—81no—
546C2×C61#241011yescharacteristic
547C2×C61C2×#45511yescharacteristic
548C2×C61#301811yescharacteristic
549C2×H(5,𝔽2)C2×D6111yescharacteristic
550C22×#41C2×D6111yescharacteristic
551C2×#137—611no—
552C2×#137—611no—
553C2×#137—611no—
554C22×M16—611no—
555#550—21no—
556#548—21no—
557#546—21no—
558#546—22no—
559D42—22no—
560D42—21no—
561#537—21no—
562#537C2×D6111yescharacteristic
563#535—21no—
564#535C2×D6111yescharacteristic
565C2×#124—611no—
566#525—21no—
567#525C2×D6111yescharacteristic
568C2×C22⋊Q8—611no—
569C2×#121—21no—
570C2×#121C2×D6111yescharacteristic
571#520C2×D6111yescharacteristic
572C22×C42—611no—
573#470—1221no—
574#468—1221no—
575#467—1221no—
576#465—1221no—
577#455—1224no—
578#452—1221no—
579#452—1221no—
580#451—1221no—
581#450—1221no—
582#428—611no—
583C2×#104—611no—
584C2×#104—611no—
585C2×#104—611no—
586C2×#104—611no—
587C2×#104—611no—
588C2×#104—611no—
589C2×#104—1224no—
590#419—611no—
591#417—611no—
592#417—611no—
593#417—611no—
594C2×#100—611no—
595C2×#100—611no—
596#407—611no—
597#391—611no—
598#390—611no—
599#388—1222no—
600#386—1222no—
601#382—611no—
602#343—611no—
603#343—611no—
604#339—611no—
605#339—611no—
606C61#2446711yescharacteristic, complemented, Sylow
607H(5,𝔽2)—22no—
608H(5,𝔽2)—22no—
609H(5,𝔽2)—41no—
610H(5,𝔽2)—41no—
611C2×#41—21no—
612C2×#41—21no—
613C2×#41—21no—
614C2×#41—21no—
615C2×#41—22no—
616C2×#41—22no—
617C2×#41—41no—
618C2×#41—41no—
619C2×#41C22⋊D6111yescharacteristic
620C2×#41C22⋊D6111yescharacteristic
621C2×#41C22×D6111yescharacteristic
622C2×#41C22×D6111yescharacteristic
623C2×#41C22×D6111yescharacteristic
624C22×Q8—611no—
625C22×Q8C22⋊D6111yescharacteristic
626C22×D4—21no—
627C22×D4—22no—
628C22×D4—22no—
629C22×D4—21no—
630C22×D4—21no—
631C22×D4C22⋊D6111yescharacteristic
632C22×D4C22⋊D6112yes—
633C22×D4C22×D6111yescharacteristic
634C23×C4—21no—
635C23×C4—1221no—
636C23×C4C22×D6111yescharacteristic
637#137—1222no—
638#137—1222no—
639#137—1222no—
640#137—2441no—
641#137—2441no—
642#137—2441no—
643C2×Q16—1221no—
644C2×Q16—1221no—
645C2×Q16—1221no—
646C2×SD16—1221no—
647C2×SD16—1221no—
648C2×SD16—1221no—
649C2×M16—611no—
650C2×M16—611no—
651C2×M16—611no—
652C2×M16—611no—
653C2×M16—1221no—
654C2×M16—1222no—
655C2×M16—2441no—
656C22×C8—1221no—
657#127—22no—
658#127—21no—
659#124—22no—
660#124—21no—
661#124—1222no—
662#124—2441no—
663#123—22no—
664#123—21no—
665C22⋊Q8—22no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—1221no—
669C22⋊Q8—1221no—
670C22⋊Q8—1221no—
671C22⋊Q8—1221no—
672C22⋊Q8C22⋊D6111yescharacteristic
673C22⋊Q8C22⋊D6111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—22no—
678#121—22no—
679#121—21no—
680#121—21no—
681#121—21no—
682#121—21no—
683#121—21no—
684#121—21no—
685#121—22no—
686#121—21no—
687#121—21no—
688#121C22⋊D6111yescharacteristic
689#121C22⋊D6111yescharacteristic
690#120—22no—
691#120—22no—
692#120—22no—
693#120—21no—
694#120—22no—
695C4×Q8—21no—
696C4×D4—22no—
697C4×D4—22no—
698C4×D4—21no—
699C4×D4—22no—
700C4×D4—21no—
701C4×D4—21no—
702#117—21no—
703#117C22×D6111yescharacteristic
704C2×C4⋊C4—21no—
705C2×C4⋊C4—611no—
706C2×C4⋊C4—1221no—
707C2×C4⋊C4C22×D6111yescharacteristic
708C2×C22⋊C4—22no—
709C2×C22⋊C4—1221no—
710C2×C22⋊C4—1222no—
711C2×C22⋊C4—1222no—
712C2×C22⋊C4C22⋊D6112yes—
713C2×C42—611no—
714C2×C42—611no—
715C2×C42—1222no—
716C2×C42—1221no—
717C2×C42—2441no—
718#107—1221no—
719#106—1221no—
720#104—614no—
721#104—1222no—
722#104—1222no—
723#104—1222no—
724#104—1222no—
725#104—2441no—
726#103—1221no—
727#103—1221no—
728#103—1221no—
729#103—1221no—
730#103—1221no—
731#102—1221no—
732#102—1221no—
733#102—1221no—
734#100—1222no—
735#100—2441no—
736C22⋊C8—1221no—
737C22⋊C8—1221no—
738#95—1222no—
739#95—1222no—
740C24—22no—
741C24—21no—
742C24C2×C22⋊D6111yescharacteristic
743C24C2×C22⋊D6112yes—
744#41—21no—
745#41—21no—
746#41—22no—
747#41—22no—
748#41—21no—
749#41—21no—
750#41—21no—
751#41—21no—
752#41—21no—
753#41—21no—
754#41—21no—
755#41—21no—
756#41—42no—
757#41—42no—
758#41—41no—
759#41—41no—
760#41—42no—
761#41—42no—
762#41—42no—
763#41—42no—
764#41—42no—
765#41—42no—
766#41D4×D6112yes—
767#41#1175822412yes—
768C2×Q8—21no—
769C2×Q8—22no—
770C2×Q8—41no—
771C2×Q8—1221no—
772C2×Q8—1221no—
773C2×Q8—1221no—
774C2×Q8—1221no—
775C2×Q8—1221no—
776C2×Q8—1221no—
777C2×Q8C2×C22⋊D6111yescharacteristic
778C2×Q8C2×C22⋊D6111yescharacteristic
779C2×Q8C2×C22⋊D6111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—22no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—22no—
787C2×D4—21no—
788C2×D4—21no—
789C2×D4—21no—
790C2×D4—22no—
791C2×D4—22no—
792C2×D4—22no—
793C2×D4—21no—
794C2×D4—22no—
795C2×D4—21no—
796C2×D4—21no—
797C2×D4—21no—
798C2×D4—21no—
799C2×D4—21no—
800C2×D4—21no—
801C2×D4—21no—
802C2×D4—41no—
803C2×D4—42no—
804C2×D4—42no—
805C2×D4—42no—
806C2×D4—42no—
807C2×D4—44no—
808C2×D4—44no—
809C2×D4—42no—
810C2×D4—42no—
811C2×D4—44no—
812C2×D4—84no—
813C2×D4C2×C22⋊D6111yescharacteristic
814C2×D4C2×C22⋊D6111yescharacteristic
815C2×D4C2×C22⋊D6111yescharacteristic
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—21no—
820C22×C4—21no—
821C22×C4—22no—
822C22×C4—21no—
823C22×C4—22no—
824C22×C4—21no—
825C22×C4—21no—
826C22×C4—21no—
827C22×C4—21no—
828C22×C4—42no—
829C22×C4—42no—
830C22×C4—1221no—
831C22×C4—1221no—
832C22×C4—1221no—
833C22×C4—1221no—
834C22×C4—2442no—
835C22×C4—2442no—
836C22×C4—2442no—
837C22×C4C2×C22⋊D6111yescharacteristic
838C22×C4C2×C22⋊D6111yescharacteristic
839C22×C4C2×C22⋊D6111yescharacteristic
840C22×C4C2×C22⋊D6111yescharacteristic
841C22×C4C2×C22⋊D6111yescharacteristic
842C22×C4C2×C22⋊D6112yes—
843C22×C4C23×D6111yescharacteristic
844Q16—2442no—
845Q16—2442no—
846Q16—2442no—
847SD16—2442no—
848SD16—2442no—
849SD16—2442no—
850M16—612no—
851M16—1221no—
852M16—1221no—
853M16—1221no—
854M16—1221no—
855M16—1221no—
856M16—1221no—
857M16—1221no—
858M16—2442no—
859C2×C8—1221no—
860C2×C8—1221no—
861C2×C8—1221no—
862C2×C8—1221no—
863C2×C8—2442no—
864C4⋊C4—22no—
865C4⋊C4—22no—
866C4⋊C4—21no—
867C4⋊C4—21no—
868C4⋊C4—21no—
869C4⋊C4—21no—
870C4⋊C4—1221no—
871C4⋊C4—1221no—
872C4⋊C4—2441no—
873C4⋊C4—2441no—
874C4⋊C4C2×C22⋊D6111yescharacteristic
875C4⋊C4C2×C22⋊D6111yescharacteristic
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—22no—
879C22⋊C4—22no—
880C22⋊C4—22no—
881C22⋊C4—21no—
882C22⋊C4—21no—
883C22⋊C4—21no—
884C22⋊C4—21no—
885C22⋊C4—22no—
886C22⋊C4—22no—
887C22⋊C4—21no—
888C22⋊C4—2444no—
889C22⋊C4—2444no—
890C22⋊C4—2441no—
891C22⋊C4—2441no—
892C42—22no—
893C42—21no—
894C42—612no—
895C42—1221no—
896C42—1221no—
897C42—1221no—
898C42—2442no—
899C23—22no—
900C23—21no—
901C23—21no—
902C23—21no—
903C23—22no—
904C23—21no—
905C23—21no—
906C23—22no—
907C23—22no—
908C23—41no—
909C23—42no—
910C23—44no—
911C23—42no—
912C23—42no—
913C23—42no—
914C23—81no—
915C23—82no—
916C23—82no—
917C23#1451974611yescharacteristic
918C23#1451974611yescharacteristic
919C23C22×C22⋊D6111yescharacteristic
920Q8—21no—
921Q8—21no—
922Q8—21no—
923Q8—21no—
924Q8—21no—
925Q8—42no—
926Q8—2441no—
927Q8—2441no—
928Q8—2441no—
929Q8—2441no—
930Q8#1451974912yes—
931D4—22no—
932D4—22no—
933D4—21no—
934D4—21no—
935D4—21no—
936D4—21no—
937D4—21no—
938D4—42no—
939D4—42no—
940D4—44no—
941D4—42no—
942D4—44no—
943D4—44no—
944D4—42no—
945D4—41no—
946D4—41no—
947D4—41no—
948D4—41no—
949D4—41no—
950D4—41no—
951D4—41no—
952D4—41no—
953D4—81no—
954D4—82no—
955D4—82no—
956D4—82no—
957D4—82no—
958D4#1451974912yes—
959C2×C4—21no—
960C2×C4—21no—
961C2×C4—21no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—21no—
965C2×C4—21no—
966C2×C4—21no—
967C2×C4—21no—
968C2×C4—22no—
969C2×C4—21no—
970C2×C4—21no—
971C2×C4—22no—
972C2×C4—21no—
973C2×C4—22no—
974C2×C4—21no—
975C2×C4—21no—
976C2×C4—21no—
977C2×C4—42no—
978C2×C4—42no—
979C2×C4—42no—
980C2×C4—44no—
981C2×C4—41no—
982C2×C4—41no—
983C2×C4—41no—
984C2×C4—41no—
985C2×C4—42no—
986C2×C4—82no—
987C2×C4—1222no—
988C2×C4—1222no—
989C2×C4—2442no—
990C2×C4—2441no—
991C2×C4—2441no—
992C2×C4—2441no—
993C2×C4—2441no—
994C2×C4—2441no—
995C2×C4—2441no—
996C2×C4—2441no—
997C2×C4—2448no—
998C2×C4—2441no—
999C2×C4#1451974611yescharacteristic
1000C2×C4#1451974611yescharacteristic
1001C2×C4C2×D4×D6111yescharacteristic
1002C2×C4C22×C22⋊D6111yescharacteristic
1003C2×C4C22×C22⋊D6111yescharacteristic
1004C2×C4C2×#1175822411yescharacteristic
1005C2×C4#1451982211yescharacteristic
1006C2×C4#1451982211yescharacteristic
1007C8—1222no—
1008C8—2441no—
1009C8—2441no—
1010C8—2441no—
1011C22—21no—
1012C22—21no—
1013C22—21no—
1014C22—21no—
1015C22—21no—
1016C22—21no—
1017C22—21no—
1018C22—22no—
1019C22—42no—
1020C22—42no—
1021C22—41no—
1022C22—41no—
1023C22—42no—
1024C22—41no—
1025C22—41no—
1026C22—41no—
1027C22—42no—
1028C22—41no—
1029C22—41no—
1030C22—41no—
1031C22—42no—
1032C22—84no—
1033C22—82no—
1034C22—82no—
1035C22—164no—
1036C22#1683994012yescomplemented
1037C22C2×#1451974611yescharacteristic
1038C22D4×C22⋊D6111yescharacteristic
1039C22#1684040611yescharacteristic
1040C4—21no—
1041C4—21no—
1042C4—22no—
1043C4—42no—
1044C4—41no—
1045C4—41no—
1046C4—41no—
1047C4—41no—
1048C4—4881no—
1049C4—4881no—
1050C4—2442no—
1051C4—2442no—
1052C4C2×#1451974911yescharacteristic
1053C4#1684032111yescharacteristic
1054C4D4×C22⋊D6111yescharacteristic
1055C4#1684040611yescharacteristic
1056C2—21no—
1057C2—22no—
1058C2—21no—
1059C2—41no—
1060C2—42no—
1061C2—81no—
1062C2—82no—
1063C2—81no—
1064C2#2144919311yescharacteristic
1065C2C2×#1683994011yescharacteristic
1066C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
Fitting, prime radicalC61×#3488C2
socleC22×C61C2×#120
hypercenter#3488D61
hypocenterC61#24467
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. C22×#14519704C2semidirect
5. #21454118C2semidirect
6. #21447045C2semidirect
7. #21447026C2semidirect
8. #21446866C2semidirect
9. #21446846C2semidirect
10. #21446283C2semidirect
11. #21446263C2semidirect
12. #21446188C2semidirect
13. #21446052C2semidirect
14. #21445773C2semidirect
17. C2×#14519807C22semidirect
18. C2×#14519807C22semidirect
19. C22×#11758194C22semidirect
20. C2×#14519764C22semidirect
21. C2×#14519756C22semidirect
22. C22×C4×Dic61C22semidirect
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
47. #16839667C22semidirect
48. #16839665C22semidirect
51. #16839627C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
118. #14519704D4semidirect
350. C4×Dic61C2×D4semidirect
359. #11758194C2×D4semidirect
503. C22×C61#455semidirect
606. C61#24467semidirect
1036. C22#16839940semidirect

Maximal subgroups

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

subgroupindex
#214554512
C2×#168399402
#214550792
C22×#145197042
#214541182
#214470452
#214470262
#214468662
#214468462
#214462832
#214462632
#214461882
#214460522
#214457732
C61×#34882
#2446761