Finite Group Databasebeta

← #29699463

Subgroups — #29699463

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#21454587C211yesmaximal, characteristic
2#21454481C211yesmaximal, characteristic, complemented
3#21454386C211yesmaximal, characteristic, complemented
4#21446532C211yesmaximal, characteristic, complemented
5#21446421C211yesmaximal, characteristic, complemented
6#21446415C211yesmaximal, characteristic, complemented
7#21446149C211yesmaximal, characteristic
8#21446143C211yesmaximal, characteristic
9#21445955C211yesmaximal, characteristic, complemented
10#21445838C211yesmaximal, characteristic, complemented
11#21445837C211yesmaximal, characteristic, complemented
12#21445687C211yesmaximal, characteristic, complemented
13#21445663C211yesmaximal, characteristic, complemented
14#21445662C211yesmaximal, characteristic, complemented
15C61×#1938C211yesmaximal, characteristic, complemented
16C2×#14519797C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
19#41×Dic61C2211yescharacteristic
20#16840230C2211yescharacteristic
21#16839854C411yescharacteristic, complemented
22#16839854C411yescharacteristic, complemented
23#16839853C411yescharacteristic, complemented
24#16839853C411yescharacteristic, complemented
25#16839847C411yescharacteristic, complemented
26#16839847C411yescharacteristic, complemented
27#16839842C411yescharacteristic, complemented
28#16839842C411yescharacteristic, complemented
29#16839820—21no—
30#16839820—21no—
31#16839816—21no—
32#16839812—21no—
33#16839798C2211yescharacteristic
34#16839789C2211yescharacteristic
35#16839787—21no—
36#16839787—21no—
37#16839785C2211yescharacteristic
38#16839785C2211yescharacteristic
39#16839784—21no—
40C2×#14519706C2211yescharacteristic
41C4⋊C8×D61—21no—
42C2×#14519705C2211yescharacteristic
43C2×#14519704C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839759C2211yescharacteristic
46#16839729C2211yescharacteristic
47#16839720C2211yescharacteristic
48#16839717C2211yescharacteristic
49C2×#14519687C2211yescharacteristic
50C2×C8×Dic61C2211yescharacteristic
51C4×#11758196C2211yescharacteristic
52#16839527C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839523C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839521C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839516C2211yescharacteristic
60C61×#424C2211yescharacteristic
61C2×#104×C61C2211yescharacteristic
62C61×#416C2211yescharacteristic
63C61×#408C2211yescharacteristic
64C2×#97×C61C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519797—22no—
69#14519797—22no—
70C2×#11758202C2×C411yescharacteristic
71C2×#11758200C2×C411yescharacteristic
72C2×#11758201C2×C411yescharacteristic
73C2×#11758199C2×C411yescharacteristic
74#14519785—22no—
75#14519785—41no—
76#14519783—22no—
77#14519783—41no—
78C2×#11758194C2311yescharacteristic
79C2×#11758194C2311yescharacteristic
80C2×#11758189—21no—
81C2×#11758189—21no—
82C22×#92418C2311yescharacteristic
83C22×#92418C2311yescharacteristic
84C2×C8×D61—21no—
85C2×C8×D61—21no—
86Q8×Dic61C2×C411yescharacteristic
87Q8×Dic61C2×C411yescharacteristic
88#14519742C2×C411yescharacteristic
89#14519742C2×C411yescharacteristic
90D4×Dic61—21no—
91D4×Dic61—21no—
92D4×Dic61C2×C411yescharacteristic
93D4×Dic61C2×C411yescharacteristic
94#14519739C2×C411yescharacteristic
95#14519739C2×C411yescharacteristic
96#14519737—21no—
97#14519737—21no—
98#14519736—21no—
99#14519736C2311yescharacteristic
100#14519734—21no—
101C2×#11758196—21no—
102C2×C4×Dic61—21no—
103C2×C4×Dic61C2311yescharacteristic
104C2×C4×Dic61C2311yescharacteristic
105C42×D61—21no—
106#14519710C2×C411yescharacteristic
107#14519710C2×C411yescharacteristic
108#14519708C2×C411yescharacteristic
109#14519708C2×C411yescharacteristic
110C4⋊#92418—21no—
111C4⋊#92418—21no—
112#14519706—21no—
113#14519706—21no—
114#14519706—21no—
115#14519706—21no—
116#14519706D411yescharacteristic
117#14519706D411yescharacteristic
118#14519706D411yescharacteristic
119#14519706D411yescharacteristic
120#14519705—22no—
121#14519704—41no—
122#14519703—22no—
123#14519702C2×C411yescharacteristic
124#14519702C2×C411yescharacteristic
125#14519699C2×C411yescharacteristic
126#14519699C2×C411yescharacteristic
127C22⋊#92418—21no—
128C22⋊#92418—21no—
129#14519687—21no—
130#14519687—21no—
131#14519687—41no—
132C8×Dic61—21no—
133C8×Dic61—21no—
134C8×Dic61C2×C411yescharacteristic
135C8×Dic61C2×C411yescharacteristic
136C8×Dic61C2×C411yescharacteristic
137C8×Dic61C2×C411yescharacteristic
138#14519684—21no—
139C2×#41×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C2×M16×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C22×C8×C61C2311yescharacteristic
144#117×C61C2311yescharacteristic
145C2×C42×C61C2311yescharacteristic
146C4⋊C8×C61—21no—
147C4⋊C8×C61—21no—
148#104×C61—41no—
149#103×C61C2×C411yescharacteristic
150#103×C61C2×C411yescharacteristic
151#102×C61C2×C411yescharacteristic
152#102×C61C2×C411yescharacteristic
153C22⋊C8×C61—21no—
154C22⋊C8×C61—21no—
155#97×C61—41no—
156#41×C61—21no—
157#41×C61—21no—
158#41×C61—21no—
159#41×C61—21no—
160C2×Q8×C61C22×C411yescharacteristic
161C2×D4×C61—21no—
162C2×D4×C61C22×C411yescharacteristic
163C22×C4×C61—21no—
164C22×C4×C61—21no—
165C22×C4×C61C2411yescharacteristic
166C2×C22⋊D61—21no—
167C22×Dic61—21no—
168C22×Dic61—21no—
169C22×Dic61—21no—
170C22×Dic61#4111yescharacteristic
171C22×Dic61#4111yescharacteristic
172#11758222—21no—
173#11758222—21no—
174#11758222#4112yes—
175#11758222#4112yes—
176C2×D244C22×C411yescharacteristic
177C2×C4×D61—21no—
178C2×C4×D61—21no—
179C2×C4×D61—21no—
180C2×Dic122C22×C411yescharacteristic
181M16×C61—21no—
182M16×C61—21no—
183M16×C61—21no—
184M16×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61—21no—
190C2×C8×C61—21no—
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2×D411yescharacteristic
195C4⋊C4×C61C22×C411yescharacteristic
196C4⋊C4×C61C22×C411yescharacteristic
197C22⋊C4×C61—21no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C22⋊Dic61—21no—
202C22⋊Dic61—21no—
203C22⋊Dic61—21no—
204#11758202—22no—
205#11758201—22no—
206#11758200—22no—
207#11758199—22no—
208#11758198—21no—
209#11758198—21no—
210C4⋊Dic61—21no—
211C4⋊Dic61—21no—
212C4⋊Dic61C22×C411yescharacteristic
213C4⋊Dic61C22×C411yescharacteristic
214#11758196—21no—
215#11758196—21no—
216#11758196—42no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61—21no—
223C4×Dic61—21no—
224C4×Dic61C22×C411yescharacteristic
225C4×Dic61C22×C411yescharacteristic
226C4×Dic61C2×D411yescharacteristic
227C4×Dic61C2×D411yescharacteristic
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232C2×#92418—21no—
233C2×#92418—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
238C2×#92418C22×C411yescharacteristic
239C2×#92418C22×C411yescharacteristic
240C2×#92418C2×D411yescharacteristic
241C2×#92418C2×D411yescharacteristic
242#11758189—42no—
243#11758189—42no—
244C8×D61—42no—
245C8×D61—42no—
246C23×C61—21no—
247C23×C61C2×#4111yescharacteristic
248C22×D61—21no—
249Q8×C61—21no—
250Q8×C61—21no—
251D4×C61—21no—
252D4×C61—21no—
253D4×C61—41no—
254D4×C61—41no—
255C2×C4×C61—21no—
256C2×C4×C61—21no—
257C2×C4×C61—21no—
258C2×C4×C61—41no—
259C2×C4×C61—41no—
260C2×C4×C61—41no—
261C2×C4×C61—41no—
262C2×C4×C61—41no—
263C2×C4×C61C23×C411yescharacteristic
264C2×C4×C61C22×D411yescharacteristic
265C2×C4×C61C2×#4111yescharacteristic
266C2×C4×C61C2×#4111yescharacteristic
267C2×C4×C61H(5,𝔽2)11yescharacteristic
268C2×C4×C612−1+411yescharacteristic
269C22⋊D61—22no—
270C22⋊D61—22no—
271C2×Dic61—21no—
272C2×Dic61—22no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—41no—
276C2×Dic61—42no—
277C2×Dic61—41no—
278C2×Dic61—41no—
279C2×Dic61—41no—
280C2×Dic61—81no—
281C2×Dic61C4×D411yescharacteristic
282C2×Dic61C4×D411yescharacteristic
283C2×Dic61C4×D411yescharacteristic
284C2×Dic61C4×D411yescharacteristic
285D244—21no—
286D244#11712yes—
287C4×D61—22no—
288C4×D61—22no—
289C4×D61—42no—
290C4×D61—81no—
291Dic122—21no—
292Dic122#11712yes—
293C8×C61—21no—
294C8×C61—21no—
295C8×C61—21no—
296C8×C61—21no—
297C8×C61—41no—
298C8×C61—41no—
299#92418—21no—
300#92418—21no—
301#92418—21no—
302#92418—21no—
303#92418—41no—
304#92418—41no—
305#22782—611nomaximal, Sylow
306C22×C61—21no—
307C22×C61—21no—
308C22×C61—41no—
309C22×C61—41no—
310C22×C61—41no—
311C22×C61C2×C4×D411yescharacteristic
312C22×C61#55211yescharacteristic
313C22×C61#55311yescharacteristic
314C2×D61—22no—
315C2×D61—41no—
316C2×D61—41no—
317C4×C61—41no—
318C4×C61—41no—
319C4×C61—41no—
320C4×C61—81no—
321C4×C61C2×#11711yescharacteristic
322C4×C61#52011yescharacteristic
323C4×C61#54611yescharacteristic
324C4×C61#54811yescharacteristic
325Dic61—22no—
326Dic61—21no—
327Dic61—21no—
328Dic61—21no—
329Dic61—41no—
330Dic61—41no—
331Dic61—81no—
332Dic61#44412yes—
333C4×#135—611no—
334#2925—611no—
335#2906—611no—
336#1938—611no—
337#1938D6111yescharacteristic, complemented
338#1922—611no—
339#1922—611no—
340#1876—611no—
341#1876—611no—
342#1837—611no—
343#1806—611no—
344#1806—611no—
345#1770—611no—
346#1765—611no—
347#1765—611no—
348C2×C61—21no—
349C2×C61—21no—
350C2×C61—81no—
351C2×C61#235211yescharacteristic
352C2×C61C2×#44411yescharacteristic
353C2×C61#295711yescharacteristic
354D61—42no—
355C2×#135—611no—
356C2×#131—611no—
357C2×#131—611no—
358C4×#41—611no—
359C4×#41—611no—
360C4×Q16—611no—
361C4×Q16—611no—
362C4×SD16—611no—
363C4×SD16—611no—
364C4×SD16—611no—
365C4×SD16—611no—
366C4×D8—611no—
367C4×D8—611no—
368#433—1221no—
369#433—1221no—
370#432—1221no—
371#431—1221no—
372#427—611no—
373#424—611no—
374#424—1221no—
375#424—1221no—
376#424C2×D6111yescharacteristic
377#423—611no—
378#423—611no—
379#423—1221no—
380C2×C4⋊C8—611no—
381C2×C4⋊C8—1221no—
382C2×#104—611no—
383C2×#104—611no—
384C2×#104—611no—
385C2×#104C2×D6111yescharacteristic
386#416—611no—
387#416C2×D6111yescharacteristic
388#408—611no—
389#408C2×D6111yescharacteristic
390#405—611no—
391#405—611no—
392C2×#97—611no—
393C2×#97C2×D6111yescharacteristic
394C2×C4×C8—611no—
395C4×C4⋊C4—611no—
396#341—611no—
397#341—611no—
398#341—611no—
399#341C2×D6111yescharacteristic
400#339—611no—
401#339—611no—
402#339—611no—
403#339C2×D6111yescharacteristic
404#336—611no—
405#336—611no—
406C61#2278211yescharacteristic, complemented, Sylow
407C2×#41—611no—
408C2×#41C22×D6111yescharacteristic
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—611no—
420C2×M16—611no—
421C2×M16—1221no—
422C2×M16—1221no—
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—1221no—
445#117—1221no—
446#117C22×D6111yescharacteristic
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—611no—
460C4⋊C8—611no—
461C4⋊C8—611no—
462C4⋊C8—611no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465C4⋊C8—1221no—
466C4⋊C8—1221no—
467C4⋊C8—1221no—
468C4⋊C8—1221no—
469#104—41no—
470#104—1222no—
471#104—1222no—
472#104—2441no—
473#103—611no—
474#103—611no—
475#103C4×D6111yescharacteristic
476#103C4×D6111yescharacteristic
477#102—611no—
478#102—611no—
479#102C4×D6111yescharacteristic
480#102C4×D6111yescharacteristic
481C22⋊C8—21no—
482C22⋊C8—21no—
483C22⋊C8—1221no—
484C22⋊C8—1221no—
485#97—41no—
486#97—1221no—
487#97—1221no—
488#97—2441no—
489C4×C8—611no—
490C4×C8—611no—
491C4×C8—611no—
492C4×C8—611no—
493C4×C8—1221no—
494C4×C8—1221no—
495#95—1221no—
496#41—21no—
497#41—21no—
498#41—21no—
499#41—21no—
500#41—612no—
501#41—612no—
502#41—1221no—
503#41—1221no—
504C2×Q8—611no—
505C2×Q8C2×C4×D6111yescharacteristic
506C2×D4—21no—
507C2×D4—611no—
508C2×D4—1221no—
509C2×D4C2×C4×D6111yescharacteristic
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—611no—
513C22×C4—611no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4—1221no—
519C22×C4—1221no—
520C22×C4C23×D6111yescharacteristic
521Q16—1222no—
522SD16—1222no—
523SD16—1222no—
524D8—1222no—
525M16—21no—
526M16—21no—
527M16—21no—
528M16—21no—
529M16—1221no—
530M16—1221no—
531M16—1221no—
532M16—1221no—
533M16—2442no—
534M16—2442no—
535C2×C8—21no—
536C2×C8—21no—
537C2×C8—21no—
538C2×C8—21no—
539C2×C8—21no—
540C2×C8—21no—
541C2×C8—611no—
542C2×C8—611no—
543C2×C8—611no—
544C2×C8—611no—
545C2×C8—1221no—
546C2×C8—1221no—
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×C8D4×D6111yescharacteristic
556C2×C8D4×D6111yescharacteristic
557C4⋊C4—611no—
558C4⋊C4—611no—
559C4⋊C4—1221no—
560C4⋊C4—1221no—
561C4⋊C4—1221no—
562C4⋊C4—1221no—
563C4⋊C4—2442no—
564C4⋊C4C2×C4×D6111yescharacteristic
565C4⋊C4C2×C4×D6111yescharacteristic
566C22⋊C4—21no—
567C22⋊C4—1221no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—611no—
576C42—611no—
577C42—611no—
578C42—611no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42—1221no—
583C42—1221no—
584C42—1221no—
585C42—1221no—
586C23—21no—
587C23—1221no—
588C23#41×D6111yescharacteristic
589Q8—21no—
590Q8—21no—
591Q8—612no—
592Q8—1221no—
593D4—21no—
594D4—21no—
595D4—41no—
596D4—41no—
597D4—612no—
598D4—1222no—
599D4—1222no—
600D4—1221no—
601C2×C4—21no—
602C2×C4—21no—
603C2×C4—21no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—611no—
610C2×C4—611no—
611C2×C4—611no—
612C2×C4—611no—
613C2×C4—1222no—
614C2×C4—1221no—
615C2×C4—1222no—
616C2×C4—1222no—
617C2×C4—1221no—
618C2×C4—1221no—
619C2×C4—4881no—
620C2×C4—4881no—
621C2×C4—2442no—
622C2×C4—2442no—
623C2×C4—2441no—
624C2×C4—2441no—
625C2×C4—2441no—
626C2×C4—2441no—
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C2×D4×D6111yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982411yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—41no—
638C8—41no—
639C8—1221no—
640C8—1221no—
641C8—1221no—
642C8—1221no—
643C8—2441no—
644C8—2441no—
645C22—21no—
646C22—21no—
647C22—41no—
648C22—41no—
649C22—41no—
650C22—1222no—
651C22—2441no—
652C22—2441no—
653C22C4×D4×D6111yescharacteristic
654C22#1684044811yescharacteristic
655C22#1684045711yescharacteristic
656C4—41no—
657C4—41no—
658C4—41no—
659C4—81no—
660C4—612no—
661C4—1222no—
662C4—1221no—
663C4—1221no—
664C4—1221no—
665C4—4881no—
666C4—2441no—
667C4—2441no—
668C4#117×D6111yescharacteristic
669C4#1684024111yescharacteristic
670C4#1684040111yescharacteristic
671C4#1684042011yescharacteristic
672C2—21no—
673C2—21no—
674C2—81no—
675C2—2442no—
676C2#2144874711yescharacteristic
677C2#444×D6111yescharacteristic
678C2#2145473311yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1938C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C22
cosocleC22×C4×C61C24
hypercenter#1938D61
hypocenterC61#22782
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1938

Complements

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

NH ≅ G/Ntype
2. #21454481C2semidirect
3. #21454386C2semidirect
4. #21446532C2semidirect
5. #21446421C2semidirect
6. #21446415C2semidirect
9. #21445955C2semidirect
10. #21445838C2semidirect
11. #21445837C2semidirect
12. #21445687C2semidirect
13. #21445663C2semidirect
14. #21445662C2semidirect
15. C61×#1938C2semidirect
21. #16839854C4semidirect
22. #16839854C4semidirect
23. #16839853C4semidirect
24. #16839853C4semidirect
25. #16839847C4semidirect
26. #16839847C4semidirect
27. #16839842C4semidirect
28. #16839842C4semidirect
337. #1938D61semidirect
406. C61#22782semidirect

Maximal subgroups

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

subgroupindex
#214545872
#214544812
#214543862
#214465322
#214464212
#214464152
#214461492
#214461432
#214459552
#214458382
#214458372
#214456872
#214456632
#214456622
C61×#19382
#2278261