Finite Group Databasebeta

← #29699483

Subgroups — #29699483

Order 15616.

740 conjugacy classes of subgroups.

The subgroup lattice has 680 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21454621C211yesmaximal, characteristic
2#21454487C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic, complemented
4#21446528C211yesmaximal, characteristic, complemented
5#21446521C211yesmaximal, characteristic, complemented
6#21446417C211yesmaximal, characteristic, complemented
7#21446417C211yesmaximal, characteristic, complemented
8#21446147C211yesmaximal, characteristic
9#21446147C211yesmaximal, characteristic
10#21445836C211yesmaximal, characteristic, complemented
11#21445836C211yesmaximal, characteristic, complemented
12#21445691C211yesmaximal, characteristic, complemented
13#21445662C211yesmaximal, characteristic, complemented
14#21445655C211yesmaximal, characteristic, complemented
15C61×#1838C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519785C2211yescharacteristic
19C4×#11758222C2211yescharacteristic
20C4×#11758222C2211yescharacteristic
21#16839875C411yescharacteristic, complemented
22#16839875C411yescharacteristic, complemented
23#16839870C411yescharacteristic, complemented
24#16839870C411yescharacteristic, complemented
25#16839864C411yescharacteristic, complemented
26#16839864C411yescharacteristic, complemented
27#16839864C411yescharacteristic, complemented
28#16839864C411yescharacteristic, complemented
29#16839822—21no—
30#16839822—21no—
31#16839818—21no—
32#16839814—21no—
33#16839800C2211yescharacteristic
34#16839790C2211yescharacteristic
35#16839790C2211yescharacteristic
36#16839787—21no—
37#16839787—21no—
38#16839784—21no—
39C2×C4⋊#92418C2211yescharacteristic
40C4⋊C8×D61—21no—
41C2×#14519703C2211yescharacteristic
42C2×#14519703C2211yescharacteristic
43C2×#14519703C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839759C2211yescharacteristic
46#16839759C2211yescharacteristic
47#16839730C2211yescharacteristic
48#16839730C2211yescharacteristic
49#16839720C2211yescharacteristic
50#16839720C2211yescharacteristic
51C2×#14519687C2211yescharacteristic
52C2×C8×Dic61C2211yescharacteristic
53C4×C4⋊Dic61C2211yescharacteristic
54#16839523C2211yescharacteristic
55#16839523C2211yescharacteristic
56#16839523C2211yescharacteristic
57#16839523C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C61×#423C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C61×#341C2211yescharacteristic
64C61×#341C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#341C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68C2×#11758222C2311yescharacteristic
69#14519799—22no—
70#14519799—22no—
71C2×Dic244C2×C411yescharacteristic
72C2×#11758190C2×C411yescharacteristic
73C2×#11758190C2×C411yescharacteristic
74C2×D488C2×C411yescharacteristic
75#14519785—22no—
76#14519785—22no—
77#14519785—41no—
78#14519785—41no—
79C2×#11758189—21no—
80C2×#11758189—21no—
81C22×#92418C2311yescharacteristic
82C22×#92418C2311yescharacteristic
83C2×C8×D61—21no—
84C2×C8×D61—21no—
85C4×Dic122C2×C411yescharacteristic
86C4×Dic122C2×C411yescharacteristic
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122C2×C411yescharacteristic
89C4×D244C2×C411yescharacteristic
90C4×D244C2×C411yescharacteristic
91C4×D244C2×C411yescharacteristic
92C4×D244C2×C411yescharacteristic
93C4×C22⋊D61—21no—
94C4×C22⋊D61—21no—
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97#14519736C2311yescharacteristic
98#14519736C2311yescharacteristic
99#14519734—21no—
100#14519734—21no—
101C2×C4⋊Dic61—21no—
102C2×C4×Dic61C2311yescharacteristic
103C2×C4×Dic61C2311yescharacteristic
104C42×D61—21no—
105C42×D61—21no—
106#14519711C2×C411yescharacteristic
107#14519711C2×C411yescharacteristic
108#14519709C2×C411yescharacteristic
109#14519709C2×C411yescharacteristic
110C4⋊#92418D411yescharacteristic
111C4⋊#92418D411yescharacteristic
112C4⋊#92418D411yescharacteristic
113C4⋊#92418D411yescharacteristic
114#14519706—21no—
115#14519706—21no—
116#14519706—21no—
117#14519706—21no—
118#14519703—22no—
119#14519703—22no—
120#14519703—41no—
121#14519703—41no—
122#14519702C2×C411yescharacteristic
123#14519702C2×C411yescharacteristic
124#14519702C2×C411yescharacteristic
125#14519702C2×C411yescharacteristic
126#14519699C2×C411yescharacteristic
127#14519699C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519699C2×C411yescharacteristic
130#14519689—21no—
131#14519689—21no—
132#14519689—21no—
133#14519689—21no—
134#14519687—21no—
135#14519687—21no—
136#14519687—41no—
137C8×Dic61—21no—
138C8×Dic61—21no—
139C8×Dic61—41no—
140#14519684—21no—
141C2×M16×C61C2311yescharacteristic
142C2×M16×C61C2311yescharacteristic
143C2×M16×C61C2311yescharacteristic
144C2×M16×C61C2311yescharacteristic
145C22×C8×C61C2311yescharacteristic
146C22×C8×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C4⋊C8×C61—21no—
149C4⋊C8×C61—21no—
150C4⋊C8×C61—21no—
151C4⋊C8×C61—21no—
152#97×C61C2×C411yescharacteristic
153#97×C61C2×C411yescharacteristic
154#97×C61C2×C411yescharacteristic
155#97×C61C2×C411yescharacteristic
156C22×C4×C61#4111yescharacteristic
157C22×C4×C61#4111yescharacteristic
158C22×C4×C61C2411yescharacteristic
159C2×C22⋊D61—21no—
160C2×C22⋊D61—21no—
161C22×Dic61—21no—
162C22×Dic61—21no—
163#11758222—21no—
164#11758222—21no—
165#11758222—21no—
166#11758222—21no—
167#11758222—21no—
168#11758222—21no—
169#11758222#4112yes—
170#11758222#4112yes—
171C2×D244C22×C411yescharacteristic
172C2×D244C22×C411yescharacteristic
173C2×C4×D61—21no—
174C2×C4×D61—21no—
175C2×C4×D61—21no—
176C2×C4×D61—21no—
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×Dic122C22×C411yescharacteristic
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185M16×C61—21no—
186M16×C61—21no—
187M16×C61—21no—
188M16×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61—21no—
192C2×C8×C61—21no—
193C2×C8×C61—21no—
194C2×C8×C61—21no—
195C2×C8×C61—21no—
196C2×C8×C61—21no—
197C2×C8×C61C22×C411yescharacteristic
198C2×C8×C61C22×C411yescharacteristic
199C2×C8×C61C22×C411yescharacteristic
200C2×C8×C61C22×C411yescharacteristic
201C42×C61C22×C411yescharacteristic
202C42×C61C22×C411yescharacteristic
203C42×C61C2×D411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C22⋊Dic61—21no—
206C22⋊Dic61—21no—
207#11758198—21no—
208#11758198—21no—
209#11758198—21no—
210#11758198—21no—
211C4⋊Dic61—42no—
212C4⋊Dic61C22×C411yescharacteristic
213C4⋊Dic61C22×C411yescharacteristic
214C4⋊Dic61C22×C411yescharacteristic
215C4⋊Dic61C22×C411yescharacteristic
216#11758196—21no—
217#11758196—21no—
218#11758196—21no—
219#11758196—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61—21no—
225C4×Dic61—21no—
226C4×Dic61—21no—
227C4×Dic61—21no—
228C4×Dic61—21no—
229C4×Dic61—21no—
230C2×#92418—21no—
231C2×#92418—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418C2×D411yescharacteristic
235C2×#92418C2×D411yescharacteristic
236C2×#92418C2×D411yescharacteristic
237C2×#92418C2×D411yescharacteristic
238Dic244—22no—
239D488—22no—
240#11758190—22no—
241#11758190—22no—
242#11758189—42no—
243#11758189—42no—
244C8×D61—42no—
245C8×D61—42no—
246C23×C61C2×#4111yescharacteristic
247C22×D61—21no—
248C22×D61—21no—
249C2×C4×C61—41no—
250C2×C4×C61—41no—
251C2×C4×C61C4×D411yescharacteristic
252C2×C4×C61C4×D411yescharacteristic
253C2×C4×C61C4×D411yescharacteristic
254C2×C4×C61C4×D411yescharacteristic
255C2×C4×C61C23×C411yescharacteristic
256C2×C4×C61C22×D411yescharacteristic
257C2×C4×C61C2×#4111yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C22⋊D61—22no—
262C22⋊D61—22no—
263C22⋊D61—41no—
264C22⋊D61—41no—
265C2×Dic61—21no—
266C2×Dic61—22no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61—41no—
275C2×Dic61—41no—
276C2×Dic61—41no—
277D244—21no—
278D244—21no—
279D244—21no—
280D244#11712yes—
281C4×D61—22no—
282C4×D61—22no—
283C4×D61—42no—
284C4×D61—42no—
285C4×D61—41no—
286C4×D61—41no—
287C4×D61—81no—
288C4×D61—81no—
289Dic122—21no—
290Dic122—21no—
291Dic122—21no—
292Dic122#11712yes—
293C8×C61—21no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297C8×C61—41no—
298C8×C61—41no—
299C8×C61—41no—
300C8×C61—41no—
301#92418—21no—
302#92418—21no—
303#92418—21no—
304#92418—21no—
305#22784—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61C2×C4×D411yescharacteristic
309C22×C61#55211yescharacteristic
310C22×C61#55311yescharacteristic
311C2×D61—22no—
312C2×D61—41no—
313C2×D61—41no—
314C2×D61—41no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—21no—
318C4×C61—21no—
319C4×C61—21no—
320C4×C61—21no—
321C4×C61C2×#11711yescharacteristic
322C4×C61#52011yescharacteristic
323C4×C61#54611yescharacteristic
324C4×C61#54811yescharacteristic
325Dic61—22no—
326Dic61—42no—
327Dic61—41no—
328Dic61—41no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—81no—
333#2943—611no—
334#2925—611no—
335#2906—611no—
336#1938—611no—
337#1937—611no—
338#1922—611no—
339#1922—611no—
340#1876—611no—
341#1876—611no—
342#1838D6111yescharacteristic, complemented
343#1806—611no—
344#1806—611no—
345#1771—611no—
346#1765—611no—
347#1764—611no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61#235211yescharacteristic
351C2×C61#295511yescharacteristic
352C2×C61#295611yescharacteristic
353D61—42no—
354D61—81no—
355C2×#135—611no—
356C2×#131—611no—
357C2×#131—611no—
358C4×#41—611no—
359C4×#41—611no—
360#442—611no—
361#442—611no—
362#441—611no—
363#441—611no—
364#440—611no—
365#440—611no—
366#440—611no—
367#440—611no—
368#433—1221no—
369#433—1221no—
370#432—1221no—
371#431—1221no—
372#427—611no—
373#424—611no—
374#424—611no—
375#424—1221no—
376#424—1221no—
377#423—1221no—
378#423C2×D6111yescharacteristic
379#423C2×D6111yescharacteristic
380C2×C4⋊C8—611no—
381C2×C4⋊C8—1221no—
382C2×#104—611no—
383C2×#104—611no—
384C2×#104—611no—
385C2×#104—611no—
386#416—611no—
387#416—611no—
388#408—611no—
389#408—611no—
390#405—611no—
391#405—611no—
392C2×#97—611no—
393C2×#97C2×D6111yescharacteristic
394C2×C4×C8—611no—
395C4×C4⋊C4—611no—
396#341C2×D6111yescharacteristic
397#341C2×D6111yescharacteristic
398#341C2×D6111yescharacteristic
399#341C2×D6111yescharacteristic
400#339—611no—
401#339—611no—
402#339—611no—
403#339—611no—
404#336—611no—
405#336—611no—
406C61#2278411yescharacteristic, complemented, Sylow
407C2×#41—611no—
408C2×#41—611no—
409#135—1222no—
410#135—1222no—
411C2×Q16—611no—
412C2×SD16—611no—
413C2×SD16—611no—
414C2×D8—611no—
415#131—1222no—
416#131—1222no—
417#131—2441no—
418#131—2441no—
419C2×M16—1221no—
420C2×M16—1221no—
421C2×M16C22×D6111yescharacteristic
422C2×M16C22×D6111yescharacteristic
423C2×M16C22×D6111yescharacteristic
424C2×M16C22×D6111yescharacteristic
425C22×C8—611no—
426C22×C8—611no—
427C22×C8—1221no—
428C22×C8—1221no—
429C22×C8C22×D6111yescharacteristic
430C22×C8C22×D6111yescharacteristic
431C4×Q8—611no—
432C4×Q8—611no—
433C4×Q8—611no—
434C4×Q8—611no—
435C4×D4—611no—
436C4×D4—611no—
437C4×D4—611no—
438C4×D4—611no—
439C4×D4—1221no—
440C4×D4—1221no—
441C4×D4—1221no—
442C4×D4—1221no—
443#117—611no—
444#117—611no—
445#117—1221no—
446#117—1221no—
447C2×C4⋊C4—1221no—
448C2×C42—611no—
449C2×C42—611no—
450C2×C42—1221no—
451C2×C42—1221no—
452C2×C42C22×D6111yescharacteristic
453#107—611no—
454#107—611no—
455#106—611no—
456#106—611no—
457C4⋊C8—21no—
458C4⋊C8—21no—
459C4⋊C8—21no—
460C4⋊C8—21no—
461C4⋊C8—611no—
462C4⋊C8—611no—
463C4⋊C8—611no—
464C4⋊C8—611no—
465C4⋊C8—1221no—
466C4⋊C8—1221no—
467C4⋊C8—1221no—
468C4⋊C8—1221no—
469#104—1222no—
470#104—1222no—
471#104—2441no—
472#104—2441no—
473#103—611no—
474#103—611no—
475#103—611no—
476#103—611no—
477#102—611no—
478#102—611no—
479#102—611no—
480#102—611no—
481C22⋊C8—1221no—
482C22⋊C8—1221no—
483C22⋊C8—1221no—
484C22⋊C8—1221no—
485#97—1221no—
486#97—1221no—
487#97—2441no—
488#97C4×D6111yescharacteristic
489#97C4×D6111yescharacteristic
490#97C4×D6111yescharacteristic
491#97C4×D6111yescharacteristic
492C4×C8—1221no—
493C4×C8—1221no—
494C4×C8—2441no—
495#95—1221no—
496#41—612no—
497#41—612no—
498#41—1221no—
499#41—1221no—
500#41—1221no—
501#41—1221no—
502#41—1221no—
503#41—1221no—
504C2×Q8—611no—
505C2×Q8—611no—
506C2×D4—611no—
507C2×D4—611no—
508C2×D4—1221no—
509C2×D4—1221no—
510C22×C4—1221no—
511C22×C4—1221no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4#1175822611yescharacteristic
519C22×C4#1175822611yescharacteristic
520C22×C4C23×D6111yescharacteristic
521Q16—1222no—
522SD16—1222no—
523SD16—1222no—
524D8—1222no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—21no—
530M16—21no—
531M16—21no—
532M16—21no—
533M16—2442no—
534M16—2442no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—611no—
544C2×C8—611no—
545C2×C8—611no—
546C2×C8—611no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—1221no—
550C2×C8—1221no—
551C2×C8—2442no—
552C2×C8—2442no—
553C2×C8C2×C4×D6111yescharacteristic
554C2×C8C2×C4×D6111yescharacteristic
555C2×C8C2×C4×D6111yescharacteristic
556C2×C8C2×C4×D6111yescharacteristic
557C4⋊C4—611no—
558C4⋊C4—611no—
559C4⋊C4—611no—
560C4⋊C4—611no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—2442no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C42—1221no—
573C42—1221no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42C2×C4×D6111yescharacteristic
583C42C2×C4×D6111yescharacteristic
584C42D4×D6111yescharacteristic
585C42D4×D6111yescharacteristic
586C23—1221no—
587C23—1221no—
588C23C2×#1175822611yescharacteristic
589Q8—612no—
590Q8—1221no—
591Q8—1221no—
592Q8—1221no—
593D4—612no—
594D4—1222no—
595D4—1222no—
596D4—1221no—
597D4—1221no—
598D4—1221no—
599D4—2441no—
600D4—2441no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—1221no—
604C2×C4—1222no—
605C2×C4—1222no—
606C2×C4—1222no—
607C2×C4—1221no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—4881no—
613C2×C4—4881no—
614C2×C4—2442no—
615C2×C4—2442no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4—2441no—
620C2×C4—2441no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4#1451973911yescharacteristic
624C2×C4#1451973911yescharacteristic
625C2×C4#1451973911yescharacteristic
626C2×C4#1451973911yescharacteristic
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4#1451982311yescharacteristic
632C2×C4#1451982411yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—41no—
640C8—41no—
641C8—1221no—
642C8—1221no—
643C8—1221no—
644C8—1221no—
645C22—21no—
646C22—21no—
647C22—1222no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22C2×#1451973911yescharacteristic
654C22#1684045011yescharacteristic
655C22#1684046511yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—1222no—
661C4—4881no—
662C4—2442no—
663C4—2441no—
664C4—2441no—
665C4—2441no—
666C4—2441no—
667C4—2441no—
668C4#117×D6111yescharacteristic
669C4#1684024211yescharacteristic
670C4#1684040511yescharacteristic
671C4#1684042011yescharacteristic
672C2—21no—
673C2—21no—
674C2—4881no—
675C2—2442no—
676C2#2144874511yescharacteristic
677C2#2145472111yescharacteristic
678C2#2145472811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1838C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C22
cosocleC22×C4×C61C24
hypercenter#1838D61
hypocenterC61#22784
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1838

Complements

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

NH ≅ G/Ntype
2. #21454487C2semidirect
3. #21454388C2semidirect
4. #21446528C2semidirect
5. #21446521C2semidirect
6. #21446417C2semidirect
7. #21446417C2semidirect
10. #21445836C2semidirect
11. #21445836C2semidirect
12. #21445691C2semidirect
13. #21445662C2semidirect
14. #21445655C2semidirect
15. C61×#1838C2semidirect
21. #16839875C4semidirect
22. #16839875C4semidirect
23. #16839870C4semidirect
24. #16839870C4semidirect
25. #16839864C4semidirect
26. #16839864C4semidirect
27. #16839864C4semidirect
28. #16839864C4semidirect
342. #1838D61semidirect
406. C61#22784semidirect

Maximal subgroups

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

subgroupindex
#214546212
#214544872
#214543882
#214465282
#214465212
#214464172
#214461472
#214458362
#214456912
#214456622
#214456552
C61×#18382
#2278461