Finite Group Databasebeta

← #29682277

Subgroups — #29682277

Order 15616.

790 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#427×D61C211yesmaximal, characteristic
2#21454380C211yesmaximal, characteristic
3#21454235C211yesmaximal, characteristic
4#21446421C211yesmaximal, characteristic, complemented
5#21446420C211yesmaximal, characteristic, complemented
6#21446419C211yesmaximal, characteristic, complemented
7#21446418C211yesmaximal, characteristic, complemented
8#21446417C211yesmaximal, characteristic, complemented
9#21446416C211yesmaximal, characteristic, complemented
10#21446415C211yesmaximal, characteristic, complemented
11#341×D61C211yesmaximal, characteristic
12#21445527C211yesmaximal, characteristic
13#21445527C211yesmaximal, characteristic
14#21445514C211yesmaximal, characteristic
15C61×#1922C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C2×M16×D61C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C22×C8×D61C2211yescharacteristic
20C2×#14519734C2211yescharacteristic
21#117×D61C2211yescharacteristic
22#117×D61C2211yescharacteristic
23#16839800C2211yescharacteristic
24#16839799C411yescharacteristic, complemented
25#16839799C411yescharacteristic, complemented
26#16839798C2211yescharacteristic
27#16839798C2211yescharacteristic
28#16839797C411yescharacteristic, complemented
29#16839797C411yescharacteristic, complemented
30#107×D61C411yescharacteristic, complemented
31#107×D61C411yescharacteristic, complemented
32#106×D61C411yescharacteristic, complemented
33#106×D61C411yescharacteristic, complemented
34#16839790C2211yescharacteristic
35#16839789C2211yescharacteristic
36#16839788C2211yescharacteristic
37#16839787—21no—
38#16839787—21no—
39#16839784—21no—
40#16839784—21no—
41#16839720C2211yescharacteristic
42#16839719—21no—
43#16839718C2211yescharacteristic
44#16839717C2211yescharacteristic
45#16839716—21no—
46#16839714—21no—
47C4×#11758189—21no—
48#16839527C2211yescharacteristic
49#16839526C2211yescharacteristic
50#16839526C2211yescharacteristic
51#16839523C2211yescharacteristic
52#16839523C2211yescharacteristic
53#16839522C2211yescharacteristic
54#16839522C2211yescharacteristic
55#16839521C2211yescharacteristic
56#16839521C2211yescharacteristic
57#16839517C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C61×#427C2211yescharacteristic
61C61×#424C2211yescharacteristic
62C61×#405C2211yescharacteristic
63C61×#341C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C22×C4×D61C2311yescharacteristic
68C2×#11758194C2311yescharacteristic
69C2×#11758194C2311yescharacteristic
70C2×#11758189—21no—
71C2×#11758189—22no—
72C2×#11758189—22no—
73C2×#11758189—21no—
74C2×#11758189D411yescharacteristic
75C2×#11758189D411yescharacteristic
76C2×#11758189D411yescharacteristic
77C2×#11758189D411yescharacteristic
78M16×D61—22no—
79M16×D61—22no—
80M16×D61—22no—
81M16×D61Q814yes—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—21no—
85C2×C8×D61—22no—
86C2×C8×D61—22no—
87C2×C8×D61—21no—
88C2×C8×D61C2×C411yescharacteristic
89C2×C8×D61C2×C411yescharacteristic
90C2×C8×D61C2×C411yescharacteristic
91C2×C8×D61C2×C411yescharacteristic
92#14519736C2311yescharacteristic
93#14519736C2311yescharacteristic
94#14519735C2×C411yescharacteristic
95#14519735C2×C411yescharacteristic
96#14519735C2×C411yescharacteristic
97#14519735C2×C411yescharacteristic
98#14519734—21no—
99#14519734—21no—
100#14519734—22no—
101#14519734—22no—
102#14519733—21no—
103#14519733—21no—
104C2×#11758196—21no—
105C4⋊C4×D61C2×C411yescharacteristic
106C4⋊C4×D61C2×C411yescharacteristic
107C4⋊C4×D61C2×C411yescharacteristic
108C4⋊C4×D61C2×C411yescharacteristic
109C2×#11758198—21no—
110C22⋊C4×D61—21no—
111C22⋊C4×D61—21no—
112C2×C4×Dic61C2311yescharacteristic
113C42×D61—21no—
114C42×D61—21no—
115#14519711C2×C411yescharacteristic
116#14519711C2×C411yescharacteristic
117#14519710C2×C411yescharacteristic
118#14519710C2×C411yescharacteristic
119#14519710C2×C411yescharacteristic
120#14519710C2×C411yescharacteristic
121#14519709C2×C411yescharacteristic
122#14519709C2×C411yescharacteristic
123#14519708C2×C411yescharacteristic
124#14519708C2×C411yescharacteristic
125#14519708C2×C411yescharacteristic
126#14519708C2×C411yescharacteristic
127C4⋊#92418—21no—
128C4⋊#92418—21no—
129#14519706—21no—
130#14519706—21no—
131#14519706—21no—
132#14519706—21no—
133#14519688—21no—
134#14519687—21no—
135#14519687—21no—
136C4×#92418—21no—
137C8×Dic61—21no—
138C8×Dic61—21no—
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143#117×C61C2311yescharacteristic
144#117×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
146#107×C61C2×C411yescharacteristic
147#107×C61C2×C411yescharacteristic
148#106×C61C2×C411yescharacteristic
149#106×C61C2×C411yescharacteristic
150C4⋊C8×C61—21no—
151C4⋊C8×C61—21no—
152#97×C61—21no—
153C4×C8×C61—21no—
154C23×D61#4111yescharacteristic
155C22×C4×C61—21no—
156C22×C4×C61C2411yescharacteristic
157C22×Dic61—21no—
158C22×Dic61#4111yescharacteristic
159C2×C4×D61—21no—
160C2×C4×D61—21no—
161C2×C4×D61—21no—
162C2×C4×D61—21no—
163C2×C4×D61C22×C411yescharacteristic
164C2×C4×D61C22×C411yescharacteristic
165C2×C4×D61C2×D411yescharacteristic
166C2×C4×D61C2×D411yescharacteristic
167C2×C4×D61C2×Q812yes—
168C2×C4×D61#4112yes—
169C2×C4×D61#4112yes—
170C2×C4×D61#4112yes—
171M16×C61—21no—
172M16×C61—21no—
173M16×C61—21no—
174M16×C61C2×Q812yes—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61C22×C411yescharacteristic
182C2×C8×C61C22×C411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61—21no—
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197#11758198—21no—
198#11758198—21no—
199#11758198—21no—
200#11758198—21no—
201#11758198—42no—
202C4⋊Dic61C22×C411yescharacteristic
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206#11758196—21no—
207#11758196—21no—
208#11758196—21no—
209#11758196—21no—
210#11758196—42no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219#11758194—21no—
220#11758194—21no—
221#11758194—21no—
222#11758194C2×Q812yes—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418C22×C411yescharacteristic
230C2×#92418C22×C411yescharacteristic
231C2×#92418C2×D411yescharacteristic
232C2×#92418C2×D411yescharacteristic
233#11758189—24no—
234#11758189—22no—
235#11758189—22no—
236#11758189—22no—
237#11758189—22no—
238#11758189—42no—
239C8×D61—22no—
240C8×D61—22no—
241C8×D61—22no—
242C8×D61—22no—
243C8×D61—24no—
244C8×D61—42no—
245C23×C61C2×#4111yescharacteristic
246C22×D61—41no—
247C22×D61—41no—
248C22×D61C4×D411yescharacteristic
249C22×D61C4×D411yescharacteristic
250C22×D61#12512yes—
251C22×D61#12612yes—
252C2×C4×C61—21no—
253C2×C4×C61—21no—
254C2×C4×C61—21no—
255C2×C4×C61—21no—
256C2×C4×C61—41no—
257C2×C4×C61—41no—
258C2×C4×C61—41no—
259C2×C4×C61C23×C411yescharacteristic
260C2×C4×C61C22×D411yescharacteristic
261C2×C4×C61C22×Q811yescharacteristic
262C2×C4×C61C2×#4111yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×Dic61—21no—
266C2×Dic61—21no—
267C2×Dic61—21no—
268C2×Dic61—21no—
269C2×Dic61—41no—
270C2×Dic61—41no—
271C2×Dic61—41no—
272C2×Dic61C4×D411yescharacteristic
273C2×Dic61C4×D411yescharacteristic
274C2×Dic61#12512yes—
275C2×Dic61#12612yes—
276C4×D61—81no—
277C4×D61—81no—
278C4×D61—81no—
279C4×D61—81no—
280C4×D61#11712yes—
281C4×D61#11712yes—
282C4×D61C4×Q812yes—
283C4×D61C4×Q812yes—
284C4×D61C22⋊Q812yes—
285C4×D61C22⋊Q812yes—
286C4×D61#12312yes—
287C4×D61#12312yes—
288C8×C61—21no—
289C8×C61—21no—
290C8×C61—22no—
291C8×C61—21no—
292C8×C61—21no—
293C8×C61—41no—
294#92418—21no—
295#92418—21no—
296#92418—22no—
297#92418—21no—
298#92418—21no—
299#92418—41no—
300#21043—611nomaximal, Sylow
301C22×C61—21no—
302C22×C61—21no—
303C22×C61C2×C4×D411yescharacteristic
304C22×C61C2×#12511yescharacteristic
305C22×C61C2×#12611yescharacteristic
306C2×D61—21no—
307C2×D61—21no—
308C2×D61—21no—
309C2×D61—21no—
310C2×D61—42no—
311C2×D61—42no—
312C2×D61#38712yes—
313C2×D61#38712yes—
314C4×C61—41no—
315C4×C61—41no—
316C4×C61—41no—
317C4×C61—41no—
318C4×C61—81no—
319C4×C61C2×#11711yescharacteristic
320C4×C61C2×C4×Q811yescharacteristic
321C4×C61C2×C22⋊Q811yescharacteristic
322C4×C61C2×#12311yescharacteristic
323Dic61—41no—
324Dic61—41no—
325Dic61—41no—
326Dic61—41no—
327Dic61—81no—
328Dic61#38712yes—
329Dic61#38712yes—
330C2×#427—611no—
331#2905—611no—
332#2873—611no—
333#1922—611no—
334#1922—611no—
335#1922—611no—
336#1922—611no—
337#1922—611no—
338#1922—611no—
339#1922—611no—
340#1922D6111yescharacteristic, complemented
341C2×#341—611no—
342#1733—611no—
343#1733—611no—
344#1729—611no—
345C2×C61—21no—
346C2×C61—21no—
347C2×C61C2×#38711yescharacteristic
348C2×C61#295711yescharacteristic
349C2×C61#295711yescharacteristic
350D61—22no—
351D61—22no—
352C22×M16—611no—
353C22×M16—611no—
354C22×M16—611no—
355C23×C8—611no—
356C2×#117—611no—
357C2×#117—611no—
358C2×#117—611no—
359#427—611no—
360#427—611no—
361#427—611no—
362#427—611no—
363#427—611no—
364#427—611no—
365#427—611no—
366#427C2×D6111yescharacteristic
367C2×#107—611no—
368C2×#107—611no—
369C2×#106—611no—
370C2×#106—611no—
371#424—611no—
372#424—611no—
373#424—611no—
374#424—1221no—
375#424—1221no—
376#424C2×D6111yescharacteristic
377#423—1221no—
378#423—1221no—
379#405—611no—
380#405—611no—
381#405—611no—
382#405—1221no—
383#405—1221no—
384#405C2×D6111yescharacteristic
385C4×M16—1221no—
386C4×M16—1221no—
387#341—611no—
388#341—611no—
389#341—611no—
390#341C2×D6111yescharacteristic
391#339—611no—
392#339—611no—
393#339—611no—
394#339—611no—
395#339—611no—
396#339—611no—
397#339C2×D6111yescharacteristic
398#339C2×D6111yescharacteristic
399#336—611no—
400#336—611no—
401#336—611no—
402#336C2×D6111yescharacteristic
403C61#2104311yescharacteristic, complemented, Sylow
404C23×C4—611no—
405C2×M16—611no—
406C2×M16—611no—
407C2×M16—611no—
408C2×M16—611no—
409C2×M16—611no—
410C2×M16—614no—
411C2×M16—611no—
412C2×M16—1221no—
413C2×M16—1222no—
414C2×M16—1222no—
415C2×M16—1221no—
416C2×M16—1222no—
417C2×M16—1222no—
418C2×M16—1222no—
419C2×M16C22×D6111yescharacteristic
420C2×M16C22×D6111yescharacteristic
421C22×C8—611no—
422C22×C8—611no—
423C22×C8—611no—
424C22×C8—611no—
425C22×C8—611no—
426C22×C8—611no—
427C22×C8—1222no—
428C22×C8—1222no—
429C22×C8—1221no—
430C22×C8—1221no—
431C22×C8C22×D6111yescharacteristic
432C22×C8C22×D6111yescharacteristic
433#117—611no—
434#117—611no—
435#117—611no—
436#117—611no—
437#117—611no—
438#117—611no—
439#117—1221no—
440#117—1221no—
441#117—1222no—
442#117—1222no—
443#117—1221no—
444#117—1221no—
445#117C22×D6111yescharacteristic
446#117C22×D6111yescharacteristic
447C2×C4⋊C4—611no—
448C2×C4⋊C4—611no—
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—1221no—
452C2×C22⋊C4—1221no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C42—611no—
456C2×C42—1221no—
457C2×C42—1221no—
458C2×C42C22×D6111yescharacteristic
459#107—611no—
460#107—611no—
461#107—611no—
462#107—611no—
463#107—611no—
464#107—611no—
465#107C4×D6111yescharacteristic
466#107C4×D6111yescharacteristic
467#106—611no—
468#106—611no—
469#106—611no—
470#106—611no—
471#106—611no—
472#106—611no—
473#106C4×D6111yescharacteristic
474#106C4×D6111yescharacteristic
475C4⋊C8—21no—
476C4⋊C8—21no—
477C4⋊C8—1221no—
478C4⋊C8—1221no—
479C4⋊C8—1221no—
480C4⋊C8—1221no—
481C4⋊C8—1221no—
482C4⋊C8—1221no—
483#97—21no—
484#97—1221no—
485#97—1221no—
486#97—1221no—
487C4×C8—21no—
488C4×C8—1221no—
489C4×C8—1221no—
490C4×C8—1221no—
491C24—611no—
492C22×C4—21no—
493C22×C4—611no—
494C22×C4—611no—
495C22×C4—611no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—612no—
499C22×C4—612no—
500C22×C4—612no—
501C22×C4—612no—
502C22×C4—1221no—
503C22×C4—1221no—
504C22×C4—1221no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4C23×D6111yescharacteristic
508M16—21no—
509M16—21no—
510M16—21no—
511M16—612no—
512M16—1224no—
513M16—1222no—
514M16—1222no—
515M16—1222no—
516M16—1222no—
517M16—1221no—
518M16—1221no—
519M16—1221no—
520M16—2442no—
521M16Q8×D6112yes—
522C2×C8—21no—
523C2×C8—21no—
524C2×C8—21no—
525C2×C8—21no—
526C2×C8—21no—
527C2×C8—21no—
528C2×C8—611no—
529C2×C8—611no—
530C2×C8—611no—
531C2×C8—611no—
532C2×C8—1222no—
533C2×C8—1222no—
534C2×C8—1222no—
535C2×C8—1222no—
536C2×C8—1224no—
537C2×C8—1221no—
538C2×C8—1221no—
539C2×C8—1221no—
540C2×C8—1221no—
541C2×C8—1221no—
542C2×C8—1221no—
543C2×C8—2442no—
544C2×C8C2×C4×D6111yescharacteristic
545C2×C8C2×C4×D6111yescharacteristic
546C2×C8D4×D6111yescharacteristic
547C2×C8D4×D6111yescharacteristic
548C4⋊C4—611no—
549C4⋊C4—611no—
550C4⋊C4—611no—
551C4⋊C4—611no—
552C4⋊C4—1221no—
553C4⋊C4—1221no—
554C4⋊C4—1221no—
555C4⋊C4—1221no—
556C4⋊C4—2442no—
557C4⋊C4C2×C4×D6111yescharacteristic
558C4⋊C4C2×C4×D6111yescharacteristic
559C4⋊C4C2×C4×D6111yescharacteristic
560C4⋊C4C2×C4×D6111yescharacteristic
561C22⋊C4—21no—
562C22⋊C4—21no—
563C22⋊C4—1221no—
564C22⋊C4—1221no—
565C22⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C22⋊C4—1221no—
569C22⋊C4—2442no—
570C42—21no—
571C42—21no—
572C42—21no—
573C42—21no—
574C42—1221no—
575C42—1221no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C23—611no—
583C23—611no—
584C23—612no—
585C23—612no—
586C23—2441no—
587C23—2441no—
588C23#41×D6111yescharacteristic
589C2×C4—21no—
590C2×C4—21no—
591C2×C4—21no—
592C2×C4—21no—
593C2×C4—41no—
594C2×C4—41no—
595C2×C4—41no—
596C2×C4—611no—
597C2×C4—611no—
598C2×C4—612no—
599C2×C4—612no—
600C2×C4—612no—
601C2×C4—612no—
602C2×C4—612no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—612no—
606C2×C4—612no—
607C2×C4—612no—
608C2×C4—1221no—
609C2×C4—1221no—
610C2×C4—1221no—
611C2×C4—1221no—
612C2×C4—4881no—
613C2×C4—4881no—
614C2×C4—4881no—
615C2×C4—4881no—
616C2×C4—2441no—
617C2×C4—2441no—
618C2×C4—2441no—
619C2×C4C22×C4×D6111yescharacteristic
620C2×C4C2×D4×D6111yescharacteristic
621C2×C4C2×Q8×D6111yescharacteristic
622C2×C4#41×D6111yescharacteristic
623C2×C4#41×D6111yescharacteristic
624C2×C4#41×D6111yescharacteristic
625C8—21no—
626C8—21no—
627C8—22no—
628C8—21no—
629C8—21no—
630C8—41no—
631C8—1221no—
632C8—1221no—
633C8—1222no—
634C8—1221no—
635C8—1221no—
636C8—2441no—
637C22—21no—
638C22—21no—
639C22—612no—
640C22—612no—
641C22—1221no—
642C22—1221no—
643C22—1221no—
644C22—1221no—
645C22—2442no—
646C22—2442no—
647C22C4×D4×D6111yescharacteristic
648C22#125×D6111yescharacteristic
649C22#126×D6111yescharacteristic
650C4—41no—
651C4—41no—
652C4—41no—
653C4—41no—
654C4—81no—
655C4—612no—
656C4—612no—
657C4—4881no—
658C4—2441no—
659C4—2441no—
660C4—2441no—
661C4—2441no—
662C4#117×D6111yescharacteristic
663C4C4×Q8×D6111yescharacteristic
664C4C22⋊Q8×D6111yescharacteristic
665C4#123×D6111yescharacteristic
666C2—21no—
667C2—21no—
668C2—1222no—
669C2—1222no—
670C2#387×D6111yescharacteristic
671C2#2145473111yescharacteristic
672C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1922C2
socleC22×C61C2×C4×D4
prime radicalC23×D61#41
cosocleC22×C4×C61C24
hypercenter#1922D61
hypocenterC61#21043
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1922

Complements

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

NH ≅ G/Ntype
4. #21446421C2semidirect
5. #21446420C2semidirect
6. #21446419C2semidirect
7. #21446418C2semidirect
8. #21446417C2semidirect
9. #21446416C2semidirect
10. #21446415C2semidirect
15. C61×#1922C2semidirect
24. #16839799C4semidirect
25. #16839799C4semidirect
28. #16839797C4semidirect
29. #16839797C4semidirect
30. #107×D61C4semidirect
31. #107×D61C4semidirect
32. #106×D61C4semidirect
33. #106×D61C4semidirect
340. #1922D61semidirect
403. C61#21043semidirect

Maximal subgroups

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

subgroupindex
#427×D612
#214543802
#214542352
#214464212
#214464202
#214464192
#214464182
#214464172
#214464162
#214464152
#341×D612
#214455272
#214455142
C61×#19222
#2104361