Finite Group Databasebeta

← #29682269

Subgroups — #29682269

Order 15616.

822 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#21454407C211yesmaximal, 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#21445544C211yesmaximal, characteristic
12#339×D61C211yesmaximal, characteristic
13#339×D61C211yesmaximal, characteristic
14#21445511C211yesmaximal, characteristic
15C61×#1922C211yesmaximal, characteristic, complemented
16C22×#11758189C2211yescharacteristic
17C22×#11758189C2211yescharacteristic
18C2×M16×D61C2211yescharacteristic
19C2×M16×D61C2211yescharacteristic
20#117×D61C2211yescharacteristic
21#117×D61C2211yescharacteristic
22C2×C42×D61C2211yescharacteristic
23#16839803C411yescharacteristic, complemented
24#16839803C411yescharacteristic, complemented
25#16839803C411yescharacteristic, complemented
26#16839803C411yescharacteristic, complemented
27#16839801C411yescharacteristic, complemented
28#16839801C411yescharacteristic, complemented
29#16839801C411yescharacteristic, complemented
30#16839801C411yescharacteristic, complemented
31#16839800C2211yescharacteristic
32#16839798C2211yescharacteristic
33#16839798C2211yescharacteristic
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×D61—21no—
68C22×C4×D61C2311yescharacteristic
69C2×#11758194C2311yescharacteristic
70C2×#11758194C2311yescharacteristic
71C2×#11758189—21no—
72C2×#11758189—22no—
73C2×#11758189—22no—
74C2×#11758189—22no—
75C2×#11758189—22no—
76C2×#11758189—21no—
77C2×#11758189C2×C411yescharacteristic
78C2×#11758189C2×C411yescharacteristic
79C2×#11758189C2×C411yescharacteristic
80C2×#11758189C2×C411yescharacteristic
81C2×#11758189D411yescharacteristic
82C2×#11758189D411yescharacteristic
83C2×#11758189D411yescharacteristic
84C2×#11758189D411yescharacteristic
85M16×D61—22no—
86M16×D61—22no—
87M16×D61—22no—
88M16×D61Q814yes—
89C22×#92418C2311yescharacteristic
90C22×#92418C2311yescharacteristic
91C2×C8×D61—21no—
92C2×C8×D61—21no—
93#14519736C2311yescharacteristic
94#14519736C2311yescharacteristic
95#14519735C2×C411yescharacteristic
96#14519735C2×C411yescharacteristic
97#14519735C2×C411yescharacteristic
98#14519735C2×C411yescharacteristic
99#14519734—21no—
100#14519734—21no—
101#14519733—21no—
102#14519733—21no—
103C4⋊C4×D61C2×C411yescharacteristic
104C4⋊C4×D61C2×C411yescharacteristic
105C4⋊C4×D61C2×C411yescharacteristic
106C4⋊C4×D61C2×C411yescharacteristic
107C22⋊C4×D61—21no—
108C22⋊C4×D61—21no—
109C2×C4×Dic61—21no—
110C2×C4×Dic61C2311yescharacteristic
111C42×D61—21no—
112C42×D61—21no—
113C42×D61—22no—
114C42×D61—22no—
115#14519711C2×C411yescharacteristic, complemented
116#14519711C2×C411yescharacteristic, complemented
117#14519710C2×C411yescharacteristic, complemented
118#14519710C2×C411yescharacteristic, complemented
119#14519710C2×C411yescharacteristic, complemented
120#14519710C2×C411yescharacteristic, complemented
121#14519709C2×C411yescharacteristic, complemented
122#14519709C2×C411yescharacteristic, complemented
123#14519708C2×C411yescharacteristic, complemented
124#14519708C2×C411yescharacteristic, complemented
125#14519708C2×C411yescharacteristic, complemented
126#14519708C2×C411yescharacteristic, complemented
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, complemented
147#107×C61C2×C411yescharacteristic, complemented
148#106×C61C2×C411yescharacteristic, complemented
149#106×C61C2×C411yescharacteristic, complemented
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×D61—42no—
164C2×C4×D61—42no—
165C2×C4×D61—42no—
166C2×C4×D61C22×C411yescharacteristic
167C2×C4×D61C22×C411yescharacteristic
168C2×C4×D61C2×D411yescharacteristic
169C2×C4×D61C2×D411yescharacteristic
170C2×C4×D61C2×Q812yes—
171C2×C4×D61#4112yes—
172C2×C4×D61#4112yes—
173C2×C4×D61#4112yes—
174M16×C61—21no—
175M16×C61—21no—
176M16×C61—21no—
177M16×C61C2×Q812yes—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61C22×C411yescharacteristic
185C2×C8×C61C22×C411yescharacteristic
186C2×C8×C61C2×D411yescharacteristic
187C2×C8×C61C2×D411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C4⋊C4×C61C22×C411yescharacteristic
190C4⋊C4×C61C22×C411yescharacteristic
191C4⋊C4×C61C22×C411yescharacteristic
192C22⋊C4×C61—21no—
193C22⋊C4×C61—21no—
194C42×C61—21no—
195C42×C61—21no—
196C42×C61—21no—
197C42×C61—21no—
198C22⋊Dic61—21no—
199C22⋊Dic61—21no—
200#11758198—21no—
201#11758198—21no—
202#11758198—21no—
203#11758198—21no—
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208#11758196—21no—
209#11758196—21no—
210#11758196—21no—
211#11758196—21no—
212C4×Dic61—21no—
213C4×Dic61—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61—42no—
221#11758194—21no—
222#11758194—21no—
223#11758194—21no—
224#11758194C2×Q812yes—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418—21no—
228C2×#92418—21no—
229C2×#92418—21no—
230C2×#92418—21no—
231C2×#92418C22×C411yescharacteristic
232C2×#92418C22×C411yescharacteristic
233C2×#92418C2×D411yescharacteristic
234C2×#92418C2×D411yescharacteristic
235#11758189—22no—
236#11758189—22no—
237#11758189—22no—
238#11758189—22no—
239#11758189—24no—
240#11758189—22no—
241#11758189—22no—
242#11758189—22no—
243#11758189—22no—
244#11758189—42no—
245C8×D61—24no—
246C8×D61—42no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—41no—
249C22×D61—41no—
250C22×D61C4×D411yescharacteristic
251C22×D61C4×D411yescharacteristic
252C22×D61#12512yes—
253C22×D61#12612yes—
254C2×C4×C61—22no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—21no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61C23×C411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C22×Q811yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×Dic61—22no—
268C2×Dic61—21no—
269C2×Dic61—21no—
270C2×Dic61—21no—
271C2×Dic61—21no—
272C2×Dic61—41no—
273C2×Dic61—41no—
274C2×Dic61C4×D411yescharacteristic
275C2×Dic61C4×D411yescharacteristic
276C2×Dic61#12512yes—
277C2×Dic61#12612yes—
278C4×D61—48no—
279C4×D61—81no—
280C4×D61—81no—
281C4×D61—81no—
282C4×D61—81no—
283C4×D61#11712yes—
284C4×D61#11712yes—
285C4×D61C4×Q812yes—
286C4×D61C4×Q812yes—
287C4×D61C22⋊Q812yes—
288C4×D61C22⋊Q812yes—
289C4×D61#12312yes—
290C4×D61#12312yes—
291C8×C61—21no—
292C8×C61—21no—
293C8×C61—22no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—41no—
297#92418—21no—
298#92418—21no—
299#92418—22no—
300#92418—21no—
301#92418—21no—
302#92418—41no—
303#21042—611nomaximal, Sylow
304C22×C61—21no—
305C22×C61—21no—
306C22×C61C2×C4×D411yescharacteristic
307C22×C61C2×#12511yescharacteristic
308C22×C61C2×#12611yescharacteristic
309C2×D61—21no—
310C2×D61—21no—
311C2×D61—21no—
312C2×D61—21no—
313C2×D61—42no—
314C2×D61—42no—
315C2×D61#38712yes—
316C2×D61#38712yes—
317C4×C61—42no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—41no—
321C4×C61—41no—
322C4×C61C2×#11711yescharacteristic
323C4×C61C2×C4×Q811yescharacteristic
324C4×C61C2×C22⋊Q811yescharacteristic
325C4×C61C2×#12311yescharacteristic
326Dic61—42no—
327Dic61—41no—
328Dic61—41no—
329Dic61—41no—
330Dic61—41no—
331Dic61#38712yes—
332Dic61#38712yes—
333#2911—611no—
334#2905—611no—
335#2873—611no—
336#1922—611no—
337#1922—611no—
338#1922—611no—
339#1922—611no—
340#1922—611no—
341#1922—611no—
342#1922—611no—
343#1922D6111yescharacteristic, complemented
344#1738—611no—
345C2×#339—611no—
346C2×#339—611no—
347#1728—611no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61C2×#38711yescharacteristic
351C2×C61#295611yescharacteristic
352C2×C61#295611yescharacteristic
353D61—22no—
354D61—22no—
355C22×M16—611no—
356C22×M16—611no—
357C22×M16—611no—
358C22×M16—611no—
359C2×#117—611no—
360C2×#117—611no—
361C22×C42—611no—
362#428—611no—
363#428—611no—
364#428—611no—
365#428—611no—
366#428—611no—
367#428—611no—
368#428—611no—
369#428—611no—
370#427—611no—
371#427—611no—
372#427—611no—
373#427C2×D6111yescharacteristic
374#424—611no—
375#424—611no—
376#424—611no—
377#424—1221no—
378#424—1221no—
379#424C2×D6111yescharacteristic
380#423—1221no—
381#423—1221no—
382#405—611no—
383#405—611no—
384#405—611no—
385#405—1221no—
386#405—1221no—
387#405C2×D6111yescharacteristic
388C4×M16—1221no—
389C4×M16—1221no—
390#341—611no—
391#341—611no—
392#341—611no—
393#341C2×D6111yescharacteristic
394#339—611no—
395#339—611no—
396#339—611no—
397#339—611no—
398#339—611no—
399#339—611no—
400#339C2×D6111yescharacteristic
401#339C2×D6111yescharacteristic
402#336—611no—
403#336—611no—
404#336—611no—
405#336C2×D6111yescharacteristic
406C61#2104211yescharacteristic, complemented, Sylow
407C23×C4—611no—
408C23×C4—1221no—
409C2×M16—611no—
410C2×M16—611no—
411C2×M16—611no—
412C2×M16—611no—
413C2×M16—611no—
414C2×M16—611no—
415C2×M16—611no—
416C2×M16—611no—
417C2×M16—611no—
418C2×M16—614no—
419C2×M16—611no—
420C2×M16—1221no—
421C2×M16—1222no—
422C2×M16—1222no—
423C2×M16—1222no—
424C2×M16—1222no—
425C2×M16—1221no—
426C2×M16—1222no—
427C2×M16—1222no—
428C2×M16—1222no—
429C2×M16C22×D6111yescharacteristic
430C2×M16C22×D6111yescharacteristic
431C22×C8—611no—
432C22×C8—611no—
433C22×C8—1221no—
434C22×C8—1221no—
435C22×C8C22×D6111yescharacteristic
436C22×C8C22×D6111yescharacteristic
437#117—611no—
438#117—611no—
439#117—611no—
440#117—611no—
441#117—611no—
442#117—611no—
443#117—1221no—
444#117—1221no—
445#117—1221no—
446#117—1221no—
447#117C22×D6111yescharacteristic
448#117C22×D6111yescharacteristic
449C2×C4⋊C4—611no—
450C2×C4⋊C4—611no—
451C2×C4⋊C4—611no—
452C2×C4⋊C4—611no—
453C2×C22⋊C4—1221no—
454C2×C22⋊C4—1221no—
455C2×C42—611no—
456C2×C42—1221no—
457C2×C42—1221no—
458C2×C42—1222no—
459C2×C42—1222no—
460C2×C42—1221no—
461C2×C42C22×D6111yescharacteristic
462#107—611no—
463#107—611no—
464#107—611no—
465#107—611no—
466#107—611no—
467#107—611no—
468#107C4×D6111yescharacteristic, complemented
469#107C4×D6111yescharacteristic, complemented
470#106—611no—
471#106—611no—
472#106—611no—
473#106—611no—
474#106—611no—
475#106—611no—
476#106C4×D6111yescharacteristic, complemented
477#106C4×D6111yescharacteristic, complemented
478C4⋊C8—21no—
479C4⋊C8—21no—
480C4⋊C8—1221no—
481C4⋊C8—1221no—
482C4⋊C8—1221no—
483C4⋊C8—1221no—
484C4⋊C8—1221no—
485C4⋊C8—1221no—
486#97—21no—
487#97—1221no—
488#97—1221no—
489#97—1221no—
490C4×C8—21no—
491C4×C8—1221no—
492C4×C8—1221no—
493C4×C8—1221no—
494C24—611no—
495C22×C4—21no—
496C22×C4—611no—
497C22×C4—611no—
498C22×C4—611no—
499C22×C4—611no—
500C22×C4—611no—
501C22×C4—612no—
502C22×C4—612no—
503C22×C4—612no—
504C22×C4—612no—
505C22×C4—1221no—
506C22×C4—1221no—
507C22×C4—1221no—
508C22×C4—1221no—
509C22×C4—1221no—
510C22×C4—2442no—
511C22×C4—2442no—
512C22×C4—2442no—
513C22×C4C23×D6111yescharacteristic
514M16—21no—
515M16—21no—
516M16—21no—
517M16—612no—
518M16—1222no—
519M16—1222no—
520M16—1222no—
521M16—1222no—
522M16—1224no—
523M16—1222no—
524M16—1222no—
525M16—1222no—
526M16—1222no—
527M16—1221no—
528M16—1221no—
529M16—1221no—
530M16—2442no—
531M16Q8×D6112yes—
532C2×C8—21no—
533C2×C8—21no—
534C2×C8—21no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—611no—
539C2×C8—611no—
540C2×C8—611no—
541C2×C8—611no—
542C2×C8—1224no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—1221no—
548C2×C8—1221no—
549C2×C8—2442no—
550C2×C8C2×C4×D6111yescharacteristic
551C2×C8C2×C4×D6111yescharacteristic
552C2×C8D4×D6111yescharacteristic
553C2×C8D4×D6111yescharacteristic
554C4⋊C4—611no—
555C4⋊C4—611no—
556C4⋊C4—611no—
557C4⋊C4—611no—
558C4⋊C4—1221no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4C2×C4×D6111yescharacteristic
563C4⋊C4C2×C4×D6111yescharacteristic
564C4⋊C4C2×C4×D6111yescharacteristic
565C4⋊C4C2×C4×D6111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—21no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C22⋊C4—1221no—
573C22⋊C4—1221no—
574C42—21no—
575C42—21no—
576C42—21no—
577C42—21no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1221no—
586C42—2442no—
587C23—611no—
588C23—611no—
589C23—612no—
590C23—612no—
591C23—2441no—
592C23—2441no—
593C23#41×D6111yescharacteristic
594C2×C4—22no—
595C2×C4—21no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—21no—
599C2×C4—41no—
600C2×C4—41no—
601C2×C4—611no—
602C2×C4—611no—
603C2×C4—612no—
604C2×C4—612no—
605C2×C4—612no—
606C2×C4—612no—
607C2×C4—612no—
608C2×C4—612no—
609C2×C4—612no—
610C2×C4—612no—
611C2×C4—612no—
612C2×C4—612no—
613C2×C4—1222no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—1221no—
618C2×C4—4881no—
619C2×C4—4881no—
620C2×C4—4881no—
621C2×C4—4881no—
622C2×C4—2448no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4C22×C4×D6111yescharacteristic
626C2×C4C2×D4×D6111yescharacteristic
627C2×C4C2×Q8×D6111yescharacteristic
628C2×C4#41×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C8—21no—
632C8—21no—
633C8—22no—
634C8—21no—
635C8—21no—
636C8—41no—
637C8—1221no—
638C8—1221no—
639C8—1222no—
640C8—1221no—
641C8—1221no—
642C8—2441no—
643C22—21no—
644C22—21no—
645C22—612no—
646C22—612no—
647C22—1221no—
648C22—1221no—
649C22—1221no—
650C22—1221no—
651C22—2442no—
652C22—2442no—
653C22C4×D4×D6111yescharacteristic
654C22#125×D6111yescharacteristic
655C22#126×D6111yescharacteristic
656C4—42no—
657C4—41no—
658C4—41no—
659C4—41no—
660C4—41no—
661C4—612no—
662C4—612no—
663C4—2442no—
664C4—2441no—
665C4—2441no—
666C4—2441no—
667C4—2441no—
668C4#117×D6111yescharacteristic
669C4C4×Q8×D6111yescharacteristic
670C4C22⋊Q8×D6111yescharacteristic
671C4#123×D6111yescharacteristic
672C2—21no—
673C2—21no—
674C2—1222no—
675C2—1222no—
676C2#387×D6111yescharacteristic
677C2#2145472411yescharacteristic
678C2#2145472711yescharacteristic
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#21042
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
23. #16839803C4semidirect
24. #16839803C4semidirect
25. #16839803C4semidirect
26. #16839803C4semidirect
27. #16839801C4semidirect
28. #16839801C4semidirect
29. #16839801C4semidirect
30. #16839801C4semidirect
115. #14519711C2×C4semidirect
116. #14519711C2×C4semidirect
117. #14519710C2×C4semidirect
118. #14519710C2×C4semidirect
119. #14519710C2×C4semidirect
120. #14519710C2×C4semidirect
121. #14519709C2×C4semidirect
122. #14519709C2×C4semidirect
123. #14519708C2×C4semidirect
124. #14519708C2×C4semidirect
125. #14519708C2×C4semidirect
126. #14519708C2×C4semidirect
146. #107×C61C2×C4semidirect
147. #107×C61C2×C4semidirect
148. #106×C61C2×C4semidirect
149. #106×C61C2×C4semidirect
343. #1922D61semidirect
406. C61#21042semidirect
468. #107C4×D61semidirect
469. #107C4×D61semidirect
476. #106C4×D61semidirect
477. #106C4×D61semidirect

Maximal subgroups

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

subgroupindex
#214544072
#214543802
#214542352
#214464212
#214464202
#214464192
#214464182
#214464172
#214464162
#214464152
#214455442
#339×D612
#214455112
C61×#19222
#2104261