Finite Group Databasebeta

← #29718189

Subgroups — #29718189

Order 15616.

1444 conjugacy classes of subgroups.

The subgroup lattice has 1056 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455440C211yesmaximal, characteristic, complemented
2C2×#16839935C211yesmaximal, characteristic, complemented
3#21455071C211yesmaximal, characteristic, complemented
4C22×#14519704C211yesmaximal, characteristic, complemented
5#21454122C211yesmaximal, characteristic, complemented
6#21447045C211yesmaximal, characteristic, complemented
7#21447033C211yesmaximal, characteristic, complemented
8#21446861C211yesmaximal, characteristic, complemented
9#21446839C211yesmaximal, characteristic, complemented
10#21446288C211yesmaximal, characteristic, complemented
11#21446263C211yesmaximal, characteristic, complemented
12#21446195C211yesmaximal, characteristic, complemented
13#21446052C211yesmaximal, characteristic, complemented
14#21445778C211yesmaximal, characteristic, complemented
15C61×#3489C211yesmaximal, characteristic, complemented
16C2×#14519802C2211yescharacteristic
17C2×#14519802C2211yescharacteristic
18C2×#14519802C2211yescharacteristic, complemented
19C22×#11758194C2211yescharacteristic
20C2×#14519766C2211yescharacteristic, complemented
21C2×#14519751C2211yescharacteristic
22C22×C4×Dic61C2211yescharacteristic
23#16840013—21no—
24#16840010—21no—
25#16839996—21no—
26#16839993—21no—
27#16839935—24no—
28#16839907—21no—
29#16839907—21no—
30#16839901—21no—
31#16839896—21no—
32#16839805C2211yescharacteristic, complemented
33C2×#14519704—24no—
34C2×#14519704C2211yescharacteristic
35C2×#14519704C2211yescharacteristic
36C2×#14519704C2211yescharacteristic
37C2×#14519704C2211yescharacteristic
38C2×#14519704C2211yescharacteristic, complemented
39C2×#14519704C2211yescharacteristic, complemented
40#16839766C2211yescharacteristic, complemented
41#16839763C2211yescharacteristic
42#16839763C2211yescharacteristic
43#16839763C2211yescharacteristic, complemented
44C2×#14519696C2211yescharacteristic, complemented
45C2×#14519696C2211yescharacteristic, complemented
46#16839726C2211yescharacteristic
47#16839669C2211yescharacteristic, complemented
48#16839663C2211yescharacteristic, complemented
49#16839652—22no—
50#16839639—22no—
51#16839627C2211yescharacteristic, complemented
52#16839531C2211yescharacteristic, complemented
53#16839531C2211yescharacteristic, complemented
54#16839521C2211yescharacteristic, complemented
55#16839521C2211yescharacteristic, complemented
56C2×2−1+4×C61C2211yescharacteristic
57C22×#41×C61C2211yescharacteristic
58D4×Q8×C61—21no—
59C61×#548—21no—
60C61×#547—21no—
61C61×#547—22no—
62C61×#546—21no—
63C61×#546—22no—
64C61×#537—21no—
65C61×#537C2211yescharacteristic
66C61×#536—21no—
67C61×#536C2211yescharacteristic
68C61×#525—21no—
69C61×#525C2211yescharacteristic
70C2×C22⋊Q8×C61—21no—
71C2×C22⋊Q8×C61C2211yescharacteristic
72C61×#520C2211yescharacteristic
73C22×D244C2311yescharacteristic
74C22×C22⋊D61—21no—
75C23×Dic61—21no—
76#14519802—22no—
77#14519802—22no—
78#14519802—22no—
79#14519802—41no—
80#14519802—41no—
81#14519802—41no—
82C2×#11758201—21no—
83C2×#11758201—21no—
84C2×#11758201—21no—
85C2×#11758199—21no—
86C2×#11758199—21no—
87C2×#11758199—21no—
88C2×#11758194—21no—
89C2×#11758194—22no—
90C2×#11758194—41no—
91C2×#11758194C2311yescharacteristic
92C2×#11758194C2311yescharacteristic
93C2×#11758194C2311yescharacteristic
94C2×#11758194C2311yescharacteristic
95C22×#92418—21no—
96#14519766—22no—
97#14519766—41no—
98#14519751—21no—
99#14519751—21no—
100#14519751—21no—
101#14519751—21no—
102C2×C4⋊Dic61C2311yescharacteristic
103C2×#11758198—21no—
104C2×#11758198—22no—
105C2×#11758198—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#14519698—21no—
123#14519698—21no—
124#14519698—21no—
125#14519697—21no—
126#14519697—21no—
127#14519696—22no—
128#14519696—41no—
129C22⋊#92418—21no—
130C22⋊#92418—21no—
131#14519684—22no—
132#14519684—22no—
1332−1+4×C61—22no—
1342−1+4×C61—22no—
1352−1+4×C61—41no—
1362−1+4×C61—41no—
137C2×#41×C61—21no—
138C2×#41×C61—21no—
139C2×#41×C61—21no—
140C2×#41×C61—22no—
141C2×#41×C61—21no—
142C2×#41×C61—22no—
143C2×#41×C61—22no—
144C2×#41×C61—41no—
145C2×#41×C61—41no—
146C2×#41×C61D411yescharacteristic
147C2×#41×C61D411yescharacteristic
148C2×#41×C61C2311yescharacteristic
149C2×#41×C61C2311yescharacteristic
150C2×#41×C61C2311yescharacteristic
151C22×Q8×C61—21no—
152C22×Q8×C61—21no—
153C22×Q8×C61D411yescharacteristic
154C22×Q8×C61C2311yescharacteristic
155C22×D4×C61—21no—
156C22×D4×C61D411yescharacteristic
157C23×C4×C61—21no—
158C23×C4×C61C2311yescharacteristic
159C4⋊Q8×C61—22no—
160C4⋊Q8×C61—21no—
161#124×C61—22no—
162#124×C61—21no—
163#123×C61—22no—
164#123×C61—22no—
165#123×C61—22no—
166#123×C61—22no—
167#123×C61—21no—
168C22⋊Q8×C61—22no—
169C22⋊Q8×C61—22no—
170C22⋊Q8×C61—22no—
171C22⋊Q8×C61—21no—
172C22⋊Q8×C61—21no—
173C22⋊Q8×C61—21no—
174C22⋊Q8×C61—21no—
175C22⋊Q8×C61—21no—
176C22⋊Q8×C61—21no—
177C22⋊Q8×C61—21no—
178C22⋊Q8×C61—21no—
179C22⋊Q8×C61D411yescharacteristic
180C22⋊Q8×C61D411yescharacteristic
181#121×C61—22no—
182#121×C61—22no—
183#121×C61—22no—
184#121×C61—21no—
185#121×C61—21no—
186#121×C61—22no—
187#121×C61D411yescharacteristic
188#121×C61D411yescharacteristic
189#120×C61—22no—
190#120×C61—21no—
191C4×Q8×C61—21no—
192C4×D4×C61—22no—
193C4×D4×C61—22no—
194C4×D4×C61—21no—
195C4×D4×C61—22no—
196C4×D4×C61—21no—
197C4×D4×C61—21no—
198#117×C61—21no—
199#117×C61C2311yescharacteristic
200C2×C4⋊C4×C61—22no—
201C2×C4⋊C4×C61—21no—
202C2×C4⋊C4×C61D412yes—
203C2×C4⋊C4×C61C2311yescharacteristic
204C2×C22⋊C4×C61—22no—
205C2×C22⋊C4×C61D412yes—
206C24×C61—21no—
207C24×C61C2×D411yescharacteristic
208C23×D61—21no—
209#41×C61—21no—
210#41×C61—21no—
211#41×C61—22no—
212#41×C61—22no—
213#41×C61—21no—
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—42no—
222#41×C61—42no—
223#41×C61—41no—
224#41×C61—41no—
225#41×C61—42no—
226#41×C61—42no—
227#41×C61—42no—
228#41×C61—42no—
229#41×C61—44no—
230#41×C61—44no—
231#41×C61—42no—
232#41×C61—42no—
233#41×C61C2×D412yes—
234#41×C61#4112yes—
235C2×Q8×C61—22no—
236C2×Q8×C61—21no—
237C2×Q8×C61—21no—
238C2×Q8×C61—21no—
239C2×Q8×C61—21no—
240C2×Q8×C61—21no—
241C2×Q8×C61—21no—
242C2×Q8×C61—21no—
243C2×Q8×C61—22no—
244C2×Q8×C61—41no—
245C2×Q8×C61—42no—
246C2×Q8×C61—42no—
247C2×Q8×C61—42no—
248C2×Q8×C61—42no—
249C2×Q8×C61C2×D411yescharacteristic
250C2×Q8×C61C2×D411yescharacteristic
251C2×Q8×C61C2×D411yescharacteristic
252C2×D4×C61—21no—
253C2×D4×C61—22no—
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—22no—
261C2×D4×C61—21no—
262C2×D4×C61—21no—
263C2×D4×C61—41no—
264C2×D4×C61—42no—
265C2×D4×C61—42no—
266C2×D4×C61C2×D411yescharacteristic
267C2×D4×C61C2×D411yescharacteristic
268C2×D4×C61C2×D411yescharacteristic
269C22×C4×C61—21no—
270C22×C4×C61—21no—
271C22×C4×C61—21no—
272C22×C4×C61—21no—
273C22×C4×C61—21no—
274C22×C4×C61—22no—
275C22×C4×C61—22no—
276C22×C4×C61—21no—
277C22×C4×C61—22no—
278C22×C4×C61—21no—
279C22×C4×C61—21no—
280C22×C4×C61—21no—
281C22×C4×C61—21no—
282C22×C4×C61—42no—
283C22×C4×C61—42no—
284C22×C4×C61C2×D412yes—
285C22×C4×C61C2×D411yescharacteristic
286C22×C4×C61C2×D411yescharacteristic
287C22×C4×C61C2×D411yescharacteristic
288C22×C4×C61C2×D411yescharacteristic
289C22×C4×C61C2×D411yescharacteristic
290C22×C4×C61C2×D412yes—
291C22×C4×C61C2411yescharacteristic
292C2×C22⋊D61—44no—
293C2×C22⋊D61—41no—
294C2×C22⋊D61—41no—
295C22×Dic61—21no—
296C22×Dic61—21no—
297C22×Dic61—21no—
298C22×Dic61—42no—
299C22×Dic61—42no—
300C22×Dic61—42no—
301C2×D244—21no—
302C2×D244—21no—
303C2×D244—21no—
304C2×D244—21no—
305C2×D244—21no—
306C2×D244—21no—
307C4⋊C4×C61—22no—
308C4⋊C4×C61—22no—
309C4⋊C4×C61—22no—
310C4⋊C4×C61—22no—
311C4⋊C4×C61—21no—
312C4⋊C4×C61—22no—
313C4⋊C4×C61—22no—
314C4⋊C4×C61—21no—
315C4⋊C4×C61—21no—
316C4⋊C4×C61—21no—
317C4⋊C4×C61C2×D411yescharacteristic
318C4⋊C4×C61C2×D411yescharacteristic
319C22⋊C4×C61—22no—
320C22⋊C4×C61—22no—
321C22⋊C4×C61—22no—
322C22⋊C4×C61—22no—
323C22⋊C4×C61—22no—
324C22⋊C4×C61—21no—
325C22⋊C4×C61—22no—
326C22⋊C4×C61—22no—
327C22⋊C4×C61—21no—
328C22⋊C4×C61—21no—
329C22⋊C4×C61—21no—
330C22⋊C4×C61—21no—
331C42×C61—22no—
332C42×C61—21no—
333#11758201—42no—
334#11758201—42no—
335#11758201—42no—
336#11758199—42no—
337#11758199—42no—
338#11758199—42no—
339#11758198—44no—
340#11758198—44no—
341#11758198—41no—
342#11758198—41no—
343C4⋊Dic61—21no—
344C4⋊Dic61—21no—
345C4×Dic61—21no—
346C4×Dic61—21no—
347C4×Dic61—21no—
348C4×Dic61—42no—
349C4×Dic61C2×D412yes—
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×D412yes—
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—41no—
371C23×C61—42no—
372C23×C61—42no—
373C23×C61—81no—
374C23×C61#12011yescharacteristic
375C23×C61#12011yescharacteristic
376C23×C61C22×D411yescharacteristic
377C22×D61—42no—
378C22×D61—42no—
379C22×D61—41no—
380C22×D61—41no—
381C22×D61—41no—
382Q8×C61—21no—
383Q8×C61—21no—
384Q8×C61—21no—
385Q8×C61—21no—
386Q8×C61—21no—
387Q8×C61—42no—
388Q8×C61—44no—
389Q8×C61—41no—
390Q8×C61—41no—
391Q8×C61—41no—
392Q8×C61—41no—
393Q8×C61#12112yes—
394D4×C61—22no—
395D4×C61—22no—
396D4×C61—21no—
397D4×C61—21no—
398D4×C61—21no—
399D4×C61—21no—
400D4×C61—21no—
401D4×C61—42no—
402D4×C61—42no—
403D4×C61—42no—
404D4×C61—44no—
405D4×C61—41no—
406D4×C61—41no—
407D4×C61—41no—
408D4×C61—41no—
409D4×C61—42no—
410D4×C61—81no—
411D4×C61—82no—
412D4×C61#12112yes—
413C2×C4×C61—21no—
414C2×C4×C61—21no—
415C2×C4×C61—21no—
416C2×C4×C61—21no—
417C2×C4×C61—21no—
418C2×C4×C61—21no—
419C2×C4×C61—21no—
420C2×C4×C61—21no—
421C2×C4×C61—21no—
422C2×C4×C61—22no—
423C2×C4×C61—21no—
424C2×C4×C61—21no—
425C2×C4×C61—22no—
426C2×C4×C61—21no—
427C2×C4×C61—22no—
428C2×C4×C61—21no—
429C2×C4×C61—21no—
430C2×C4×C61—22no—
431C2×C4×C61—21no—
432C2×C4×C61—22no—
433C2×C4×C61—22no—
434C2×C4×C61—42no—
435C2×C4×C61—42no—
436C2×C4×C61—42no—
437C2×C4×C61—44no—
438C2×C4×C61—44no—
439C2×C4×C61—41no—
440C2×C4×C61—41no—
441C2×C4×C61—41no—
442C2×C4×C61—41no—
443C2×C4×C61—42no—
444C2×C4×C61—82no—
445C2×C4×C61#12011yescharacteristic
446C2×C4×C61#12011yescharacteristic
447C2×C4×C61C22×D411yescharacteristic
448C2×C4×C61C22×D411yescharacteristic
449C2×C4×C61C22×D411yescharacteristic
450C2×C4×C61C2×#4111yescharacteristic
451C2×C4×C61H(5,𝔽2)11yescharacteristic
452C2×C4×C61H(5,𝔽2)11yescharacteristic
453C22⋊D61—82no—
454C22⋊D61—82no—
455C2×Dic61—22no—
456C2×Dic61—22no—
457C2×Dic61—41no—
458C2×Dic61—41no—
459C2×Dic61—41no—
460C2×Dic61—48no—
461C2×Dic61—41no—
462C2×Dic61—42no—
463C2×Dic61—41no—
464D244—41no—
465D244—41no—
466D244—41no—
467D244—41no—
468#92418—22no—
469#92418—41no—
470#92418—41no—
471#92418—41no—
472#24465—611nomaximal, Sylow
473C22×C61—21no—
474C22×C61—21no—
475C22×C61—21no—
476C22×C61—21no—
477C22×C61—21no—
478C22×C61—22no—
479C22×C61—21no—
480C22×C61—21no—
481C22×C61—42no—
482C22×C61—42no—
483C22×C61—41no—
484C22×C61—41no—
485C22×C61—41no—
486C22×C61—41no—
487C22×C61—41no—
488C22×C61—41no—
489C22×C61—41no—
490C22×C61—41no—
491C22×C61—84no—
492C22×C61#45412yescomplemented
493C22×C61C2×#12011yescharacteristic
494C22×C61D4211yescharacteristic
495C22×C61#54611yescharacteristic
496C2×D61—82no—
497C2×D61—82no—
498C2×D61—81no—
499C2×D61—81no—
500C2×D61—81no—
501C4×C61—21no—
502C4×C61—21no—
503C4×C61—22no—
504C4×C61—42no—
505C4×C61—41no—
506C4×C61—41no—
507C4×C61—41no—
508C4×C61—42no—
509C4×C61—41no—
510C4×C61C2×#12111yescharacteristic
511C4×C61#53411yescharacteristic
512C4×C61D4211yescharacteristic
513C4×C61#54611yescharacteristic
514Dic61—42no—
515Dic61—42no—
516Dic61—81no—
517#3489D6111yescharacteristic, complemented
518#3055—611no—
519C2×#454—611no—
520#3006—611no—
521C22×#104—611no—
522#2850—611no—
523#2040—611no—
524#2038—611no—
525#2006—611no—
526#2003—611no—
527#1901—611no—
528#1896—611no—
529#1883—611no—
530#1860—611no—
531#1793—611no—
532C2×C61—21no—
533C2×C61—21no—
534C2×C61—22no—
535C2×C61—41no—
536C2×C61—42no—
537C2×C61—81no—
538C2×C61—81no—
539C2×C61#241011yescharacteristic
540C2×C61C2×#45411yescharacteristic
541C2×C61#301811yescharacteristic
542D61—161no—
543C2×2−1+4C2×D6111yescharacteristic
544C22×#41C2×D6111yescharacteristic
545C2×AGL(1,ℤ/8)—611no—
546C2×AGL(1,ℤ/8)—611no—
547C2×AGL(1,ℤ/8)—611no—
548C22×M16—611no—
549D4×Q8—21no—
550#548—21no—
551#547—21no—
552#547—22no—
553#546—21no—
554#546—22no—
555#537—21no—
556#537C2×D6111yescharacteristic
557#536—21no—
558#536C2×D6111yescharacteristic
559C2×#124—611no—
560#525—21no—
561#525C2×D6111yescharacteristic
562C2×C22⋊Q8—21no—
563C2×C22⋊Q8C2×D6111yescharacteristic
564C2×#121—611no—
565#520C2×D6111yescharacteristic
566C22×C42—611no—
567#469—1221no—
568#468—1221no—
569#466—1221no—
570#465—1221no—
571#454—1224no—
572#449—1221no—
573#449—1221no—
574#448—1221no—
575#447—1221no—
576#428—611no—
577C2×#104—611no—
578C2×#104—611no—
579C2×#104—611no—
580C2×#104—611no—
581C2×#104—611no—
582C2×#104—611no—
583C2×#104—1224no—
584#418—611no—
585#417—611no—
586#417—611no—
587#417—611no—
588C2×#101—611no—
589C2×#101—611no—
590#407—611no—
591#391—611no—
592#390—611no—
593#388—1222no—
594#386—1222no—
595#382—611no—
596#343—611no—
597#343—611no—
598#339—611no—
599#339—611no—
600C61#2446511yescharacteristic, complemented, Sylow
6012−1+4—22no—
6022−1+4—22no—
6032−1+4—41no—
6042−1+4—41no—
605C2×#41—21no—
606C2×#41—21no—
607C2×#41—21no—
608C2×#41—22no—
609C2×#41—21no—
610C2×#41—22no—
611C2×#41—22no—
612C2×#41—41no—
613C2×#41—41no—
614C2×#41C22⋊D6111yescharacteristic
615C2×#41C22⋊D6111yescharacteristic
616C2×#41C22×D6111yescharacteristic
617C2×#41C22×D6111yescharacteristic
618C2×#41C22×D6111yescharacteristic
619C22×Q8—21no—
620C22×Q8—21no—
621C22×Q8C22⋊D6111yescharacteristic
622C22×Q8C22×D6111yescharacteristic
623C22×D4—21no—
624C22×D4—611no—
625C22×D4—1221no—
626C22×D4C22⋊D6111yescharacteristic
627C23×C4—21no—
628C23×C4—1221no—
629C23×C4C22×D6111yescharacteristic
630AGL(1,ℤ/8)—1222no—
631AGL(1,ℤ/8)—1222no—
632AGL(1,ℤ/8)—1222no—
633AGL(1,ℤ/8)—2441no—
634AGL(1,ℤ/8)—2441no—
635AGL(1,ℤ/8)—2441no—
636C2×SD16—1221no—
637C2×SD16—1221no—
638C2×SD16—1221no—
639C2×D8—1221no—
640C2×D8—1221no—
641C2×D8—1221no—
642C2×M16—611no—
643C2×M16—611no—
644C2×M16—611no—
645C2×M16—611no—
646C2×M16—1221no—
647C2×M16—1222no—
648C2×M16—2441no—
649C22×C8—1221no—
650C4⋊Q8—22no—
651C4⋊Q8—21no—
652#124—22no—
653#124—21no—
654#124—1222no—
655#124—2441no—
656#123—22no—
657#123—22no—
658#123—22no—
659#123—21no—
660#123—22no—
661C22⋊Q8—22no—
662C22⋊Q8—22no—
663C22⋊Q8—22no—
664C22⋊Q8—21no—
665C22⋊Q8—21no—
666C22⋊Q8—21no—
667C22⋊Q8—21no—
668C22⋊Q8—21no—
669C22⋊Q8—21no—
670C22⋊Q8—21no—
671C22⋊Q8—21no—
672C22⋊Q8C22⋊D6111yescharacteristic
673C22⋊Q8C22⋊D6111yescharacteristic
674#121—22no—
675#121—22no—
676#121—22no—
677#121—21no—
678#121—21no—
679#121—22no—
680#121—1221no—
681#121—1221no—
682#121—1221no—
683#121—1221no—
684#121C22⋊D6111yescharacteristic
685#121C22⋊D6111yescharacteristic
686#120—22no—
687#120—21no—
688C4×Q8—21no—
689C4×D4—22no—
690C4×D4—22no—
691C4×D4—21no—
692C4×D4—22no—
693C4×D4—21no—
694C4×D4—21no—
695#117—21no—
696#117C22×D6111yescharacteristic
697C2×C4⋊C4—22no—
698C2×C4⋊C4—21no—
699C2×C4⋊C4—611no—
700C2×C4⋊C4C22⋊D6112yes—
701C2×C4⋊C4C22×D6111yescharacteristic
702C2×C22⋊C4—22no—
703C2×C22⋊C4—1221no—
704C2×C22⋊C4—1222no—
705C2×C22⋊C4—1222no—
706C2×C22⋊C4C22⋊D6112yes—
707C2×C42—611no—
708C2×C42—611no—
709C2×C42—1222no—
710C2×C42—1221no—
711C2×C42—2441no—
712#107—1221no—
713#106—1221no—
714#104—614no—
715#104—1222no—
716#104—1222no—
717#104—1222no—
718#104—1222no—
719#104—2441no—
720#103—1221no—
721#103—1221no—
722#103—1221no—
723#102—1221no—
724#102—1221no—
725#102—1221no—
726#102—1221no—
727#102—1221no—
728#101—1222no—
729#101—2441no—
730C22⋊C8—1221no—
731C22⋊C8—1221no—
732#95—1222no—
733#95—1222no—
734C24—21no—
735C24—1221no—
736C24C2×C22⋊D6111yescharacteristic
737#41—21no—
738#41—21no—
739#41—22no—
740#41—22no—
741#41—21no—
742#41—21no—
743#41—21no—
744#41—21no—
745#41—21no—
746#41—21no—
747#41—21no—
748#41—21no—
749#41—42no—
750#41—42no—
751#41—41no—
752#41—41no—
753#41—42no—
754#41—42no—
755#41—42no—
756#41—42no—
757#41—44no—
758#41—44no—
759#41—42no—
760#41—42no—
761#41D4×D6112yes—
762#41#1175822412yes—
763C2×Q8—22no—
764C2×Q8—21no—
765C2×Q8—21no—
766C2×Q8—21no—
767C2×Q8—21no—
768C2×Q8—21no—
769C2×Q8—21no—
770C2×Q8—21no—
771C2×Q8—22no—
772C2×Q8—41no—
773C2×Q8—42no—
774C2×Q8—42no—
775C2×Q8—42no—
776C2×Q8—42no—
777C2×Q8C2×C22⋊D6111yescharacteristic
778C2×Q8C2×C22⋊D6111yescharacteristic
779C2×Q8C2×C22⋊D6111yescharacteristic
780C2×D4—21no—
781C2×D4—22no—
782C2×D4—22no—
783C2×D4—21no—
784C2×D4—21no—
785C2×D4—21no—
786C2×D4—21no—
787C2×D4—21no—
788C2×D4—22no—
789C2×D4—21no—
790C2×D4—21no—
791C2×D4—41no—
792C2×D4—42no—
793C2×D4—42no—
794C2×D4—1221no—
795C2×D4—1221no—
796C2×D4—1221no—
797C2×D4—1221no—
798C2×D4—1221no—
799C2×D4—1221no—
800C2×D4—2444no—
801C2×D4—2441no—
802C2×D4—2441no—
803C2×D4C2×C22⋊D6111yescharacteristic
804C2×D4C2×C22⋊D6111yescharacteristic
805C2×D4C2×C22⋊D6111yescharacteristic
806C22×C4—21no—
807C22×C4—21no—
808C22×C4—21no—
809C22×C4—21no—
810C22×C4—21no—
811C22×C4—22no—
812C22×C4—22no—
813C22×C4—21no—
814C22×C4—22no—
815C22×C4—21no—
816C22×C4—21no—
817C22×C4—21no—
818C22×C4—21no—
819C22×C4—42no—
820C22×C4—42no—
821C22×C4—1221no—
822C22×C4—1221no—
823C22×C4—1221no—
824C22×C4—2442no—
825C22×C4—2442no—
826C22×C4—2442no—
827C22×C4C2×C22⋊D6112yes—
828C22×C4C2×C22⋊D6111yescharacteristic
829C22×C4C2×C22⋊D6111yescharacteristic
830C22×C4C2×C22⋊D6111yescharacteristic
831C22×C4C2×C22⋊D6111yescharacteristic
832C22×C4C2×C22⋊D6111yescharacteristic
833C22×C4C2×C22⋊D6112yes—
834C22×C4C23×D6111yescharacteristic
835SD16—2442no—
836SD16—2442no—
837SD16—2442no—
838D8—2442no—
839D8—2442no—
840D8—2442no—
841M16—612no—
842M16—1221no—
843M16—1221no—
844M16—1221no—
845M16—1221no—
846M16—1221no—
847M16—1221no—
848M16—1221no—
849M16—2442no—
850C2×C8—1221no—
851C2×C8—1221no—
852C2×C8—1221no—
853C2×C8—1221no—
854C2×C8—2442no—
855C4⋊C4—22no—
856C4⋊C4—22no—
857C4⋊C4—22no—
858C4⋊C4—22no—
859C4⋊C4—21no—
860C4⋊C4—21no—
861C4⋊C4—21no—
862C4⋊C4—22no—
863C4⋊C4—22no—
864C4⋊C4—21no—
865C4⋊C4—1221no—
866C4⋊C4—1221no—
867C4⋊C4C2×C22⋊D6111yescharacteristic
868C4⋊C4C2×C22⋊D6111yescharacteristic
869C22⋊C4—22no—
870C22⋊C4—22no—
871C22⋊C4—22no—
872C22⋊C4—22no—
873C22⋊C4—22no—
874C22⋊C4—21no—
875C22⋊C4—21no—
876C22⋊C4—22no—
877C22⋊C4—22no—
878C22⋊C4—21no—
879C22⋊C4—21no—
880C22⋊C4—21no—
881C22⋊C4—2444no—
882C22⋊C4—2444no—
883C22⋊C4—2441no—
884C22⋊C4—2441no—
885C42—22no—
886C42—21no—
887C42—612no—
888C42—1221no—
889C42—1221no—
890C42—1221no—
891C42—2442no—
892C23—21no—
893C23—21no—
894C23—21no—
895C23—22no—
896C23—21no—
897C23—21no—
898C23—41no—
899C23—42no—
900C23—42no—
901C23—81no—
902C23—2442no—
903C23—2442no—
904C23—2441no—
905C23—2441no—
906C23—2441no—
907C23#1451974611yescharacteristic
908C23#1451974611yescharacteristic
909C23C22×C22⋊D6111yescharacteristic
910Q8—21no—
911Q8—21no—
912Q8—21no—
913Q8—21no—
914Q8—21no—
915Q8—42no—
916Q8—44no—
917Q8—41no—
918Q8—41no—
919Q8—41no—
920Q8—41no—
921Q8#1451974912yes—
922D4—22no—
923D4—22no—
924D4—21no—
925D4—21no—
926D4—21no—
927D4—21no—
928D4—21no—
929D4—42no—
930D4—42no—
931D4—42no—
932D4—44no—
933D4—41no—
934D4—41no—
935D4—41no—
936D4—41no—
937D4—42no—
938D4—81no—
939D4—82no—
940D4—4882no—
941D4—4882no—
942D4—2441no—
943D4—2441no—
944D4—2441no—
945D4—2441no—
946D4#1451974912yes—
947C2×C4—21no—
948C2×C4—21no—
949C2×C4—21no—
950C2×C4—21no—
951C2×C4—21no—
952C2×C4—21no—
953C2×C4—21no—
954C2×C4—21no—
955C2×C4—21no—
956C2×C4—22no—
957C2×C4—21no—
958C2×C4—21no—
959C2×C4—22no—
960C2×C4—21no—
961C2×C4—22no—
962C2×C4—21no—
963C2×C4—21no—
964C2×C4—22no—
965C2×C4—21no—
966C2×C4—22no—
967C2×C4—22no—
968C2×C4—42no—
969C2×C4—42no—
970C2×C4—42no—
971C2×C4—44no—
972C2×C4—44no—
973C2×C4—41no—
974C2×C4—41no—
975C2×C4—41no—
976C2×C4—41no—
977C2×C4—42no—
978C2×C4—82no—
979C2×C4—1222no—
980C2×C4—1222no—
981C2×C4—2442no—
982C2×C4—2441no—
983C2×C4—2441no—
984C2×C4—2441no—
985C2×C4—2441no—
986C2×C4—2448no—
987C2×C4—2441no—
988C2×C4#1451974611yescharacteristic
989C2×C4#1451974611yescharacteristic
990C2×C4C2×D4×D6111yescharacteristic
991C2×C4C22×C22⋊D6111yescharacteristic
992C2×C4C22×C22⋊D6111yescharacteristic
993C2×C4C2×#1175822411yescharacteristic
994C2×C4#1451982211yescharacteristic
995C2×C4#1451982211yescharacteristic
996C8—1222no—
997C8—2441no—
998C8—2441no—
999C8—2441no—
1000C22—21no—
1001C22—21no—
1002C22—21no—
1003C22—21no—
1004C22—21no—
1005C22—21no—
1006C22—21no—
1007C22—22no—
1008C22—42no—
1009C22—42no—
1010C22—41no—
1011C22—41no—
1012C22—41no—
1013C22—41no—
1014C22—41no—
1015C22—41no—
1016C22—41no—
1017C22—41no—
1018C22—84no—
1019C22—4882no—
1020C22—4882no—
1021C22—4881no—
1022C22—4881no—
1023C22—4881no—
1024C22#1683993512yescomplemented
1025C22C2×#1451974611yescharacteristic
1026C22D4×C22⋊D6111yescharacteristic
1027C22#1684040611yescharacteristic
1028C4—21no—
1029C4—21no—
1030C4—22no—
1031C4—41no—
1032C4—42no—
1033C4—41no—
1034C4—42no—
1035C4—41no—
1036C4—41no—
1037C4—4881no—
1038C4—2442no—
1039C4—2442no—
1040C4C2×#1451974911yescharacteristic
1041C4#1684032111yescharacteristic
1042C4D4×C22⋊D6111yescharacteristic
1043C4#1684040611yescharacteristic
1044C2—21no—
1045C2—22no—
1046C2—21no—
1047C2—41no—
1048C2—42no—
1049C2—81no—
1050C2—81no—
1051C2—9761no—
1052C2#2144919311yescharacteristic
1053C2C2×#1683993511yescharacteristic
1054C2#2145516811yescharacteristic
subgroupG/H
centerC22C2×#14519746
commutator, cosocleC22×C4×C61C24
FrattiniC22×C4C23×D61
FittingC61×#3489C2
socleC22×C61C2×#120
hypercenter#3489D61
hypocenterC61#24465
LCSG ▷ C22×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3489

Complements

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

NH ≅ G/Ntype
1. #21455440C2semidirect
2. C2×#16839935C2semidirect
3. #21455071C2semidirect
4. C22×#14519704C2semidirect
5. #21454122C2semidirect
6. #21447045C2semidirect
7. #21447033C2semidirect
8. #21446861C2semidirect
9. #21446839C2semidirect
10. #21446288C2semidirect
11. #21446263C2semidirect
12. #21446195C2semidirect
13. #21446052C2semidirect
14. #21445778C2semidirect
15. C61×#3489C2semidirect
18. C2×#14519802C22semidirect
20. C2×#14519766C22semidirect
32. #16839805C22semidirect
38. C2×#14519704C22semidirect
39. C2×#14519704C22semidirect
40. #16839766C22semidirect
43. #16839763C22semidirect
44. C2×#14519696C22semidirect
45. C2×#14519696C22semidirect
47. #16839669C22semidirect
48. #16839663C22semidirect
51. #16839627C22semidirect
52. #16839531C22semidirect
53. #16839531C22semidirect
54. #16839521C22semidirect
55. #16839521C22semidirect
118. #14519704D4semidirect
492. C22×C61#454semidirect
517. #3489D61semidirect
600. C61#24465semidirect
1024. C22#16839935semidirect

Maximal subgroups

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

subgroupindex
#214554402
C2×#168399352
#214550712
C22×#145197042
#214541222
#214470452
#214470332
#214468612
#214468392
#214462882
#214462632
#214461952
#214460522
#214457782
C61×#34892
#2446561