Finite Group Databasebeta

← #29699491

Subgroups — #29699491

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#21454484C211yesmaximal, characteristic, complemented
3#21454384C211yesmaximal, characteristic, complemented
4#21446530C211yesmaximal, characteristic, complemented
5#21446523C211yesmaximal, characteristic, complemented
6#21446419C211yesmaximal, characteristic, complemented
7#21446419C211yesmaximal, characteristic, complemented
8#21446145C211yesmaximal, characteristic
9#21446145C211yesmaximal, characteristic
10#21445960C211yesmaximal, characteristic, complemented
11#21445840C211yesmaximal, characteristic, complemented
12#21445840C211yesmaximal, characteristic, complemented
13#21445663C211yesmaximal, characteristic, complemented
14#21445656C211yesmaximal, characteristic, complemented
15C61×#1771C211yesmaximal, characteristic, complemented
16C2×#14519799C2211yescharacteristic
17C2×#14519783C2211yescharacteristic
18C2×#14519783C2211yescharacteristic
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#16839788C2211yescharacteristic
35#16839788C2211yescharacteristic
36#16839787—21no—
37#16839787—21no—
38#16839786C2211yescharacteristic
39#16839786C2211yescharacteristic
40#16839784—21no—
41C4⋊C8×D61—21no—
42C2×#14519705C2211yescharacteristic
43C2×#14519705C2211yescharacteristic
44C2×#14519705C2211yescharacteristic
45C2×#14519705C2211yescharacteristic
46#16839759C2211yescharacteristic
47#16839759C2211yescharacteristic
48#16839728C2211yescharacteristic
49#16839728C2211yescharacteristic
50#16839717C2211yescharacteristic
51#16839717C2211yescharacteristic
52#16839527C2211yescharacteristic
53#16839527C2211yescharacteristic
54#16839527C2211yescharacteristic
55#16839527C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839522C2211yescharacteristic
59#16839522C2211yescharacteristic
60C2×C4⋊C8×C61C2211yescharacteristic
61C2×#97×C61C2211yescharacteristic
62C2×#97×C61C2211yescharacteristic
63C2×C4×C8×C61C2211yescharacteristic
64C4×C4⋊C4×C61C2211yescharacteristic
65C61×#336C2211yescharacteristic
66C61×#336C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68C2×#11758222C2311yescharacteristic
69#14519799—22no—
70#14519799—22no—
71C2×Dic244C2×C411yescharacteristic
72C2×#11758190C2×C411yescharacteristic
73C2×#11758190C2×C411yescharacteristic
74C2×D488C2×C411yescharacteristic
75#14519783—22no—
76#14519783—22no—
77#14519783—41no—
78#14519783—41no—
79C2×#11758194C2311yescharacteristic
80C2×#11758194C2311yescharacteristic
81C2×#11758194C2311yescharacteristic
82C2×#11758194C2311yescharacteristic
83C2×#11758189—21no—
84C2×#11758189—21no—
85C2×C8×D61—21no—
86C2×C8×D61—21no—
87C4×Dic122C2×C411yescharacteristic
88C4×Dic122C2×C411yescharacteristic
89C4×Dic122C2×C411yescharacteristic
90C4×Dic122C2×C411yescharacteristic
91C4×D244C2×C411yescharacteristic
92C4×D244C2×C411yescharacteristic
93C4×D244C2×C411yescharacteristic
94C4×D244C2×C411yescharacteristic
95C4×C22⋊D61—21no—
96C4×C22⋊D61—21no—
97C4×C22⋊D61—21no—
98C4×C22⋊D61—21no—
99#14519736C2311yescharacteristic
100#14519736C2311yescharacteristic
101#14519734—21no—
102#14519734—21no—
103C42×D61—21no—
104C42×D61—21no—
105#14519711C2×C411yescharacteristic
106#14519711C2×C411yescharacteristic
107#14519709C2×C411yescharacteristic
108#14519709C2×C411yescharacteristic
109C4⋊#92418—21no—
110C4⋊#92418—21no—
111C4⋊#92418—21no—
112C4⋊#92418—21no—
113#14519706—21no—
114#14519706—21no—
115#14519706—21no—
116#14519706—21no—
117#14519705—22no—
118#14519705—22no—
119#14519705—41no—
120#14519705—41no—
121#14519702C2×C411yescharacteristic
122#14519702C2×C411yescharacteristic
123#14519702C2×C411yescharacteristic
124#14519702C2×C411yescharacteristic
125#14519699C2×C411yescharacteristic
126#14519699C2×C411yescharacteristic
127#14519699C2×C411yescharacteristic
128#14519699C2×C411yescharacteristic
129#14519689—21no—
130#14519689—21no—
131#14519689—21no—
132#14519689—21no—
133#14519687—21no—
134#14519687—21no—
135C8×Dic61—21no—
136C8×Dic61—21no—
137C22×C8×C61C2311yescharacteristic
138C22×C8×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141C2×C4⋊C4×C61—21no—
142C2×C42×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144C2×C42×C61C2311yescharacteristic
145C4⋊C8×C61D411yescharacteristic
146C4⋊C8×C61D411yescharacteristic
147C4⋊C8×C61D411yescharacteristic
148C4⋊C8×C61D411yescharacteristic
149#97×C61—41no—
150#97×C61C2×C411yescharacteristic
151#97×C61C2×C411yescharacteristic
152#97×C61C2×C411yescharacteristic
153#97×C61C2×C411yescharacteristic
154C4×C8×C61—41no—
155#95×C61—21no—
156C22×C4×C61—21no—
157C22×C4×C61—21no—
158C22×C4×C61#4111yescharacteristic
159C22×C4×C61#4111yescharacteristic
160C22×C4×C61C2411yescharacteristic
161C2×C22⋊D61—21no—
162C2×C22⋊D61—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
181C2×C8×C61—21no—
182C2×C8×C61—21no—
183C2×C8×C61—21no—
184C2×C8×C61—21no—
185C2×C8×C61—21no—
186C2×C8×C61—21no—
187C2×C8×C61—21no—
188C2×C8×C61—21no—
189C2×C8×C61C22×C411yescharacteristic
190C2×C8×C61C22×C411yescharacteristic
191C2×C8×C61C22×C411yescharacteristic
192C2×C8×C61C22×C411yescharacteristic
193C2×C8×C61C2×D411yescharacteristic
194C2×C8×C61C2×D411yescharacteristic
195C2×C8×C61C2×D411yescharacteristic
196C2×C8×C61C2×D411yescharacteristic
197C4⋊C4×C61—42no—
198C42×C61—21no—
199C42×C61—21no—
200C42×C61—21no—
201C42×C61—21no—
202C42×C61C22×C411yescharacteristic
203C42×C61C22×C411yescharacteristic
204C42×C61C2×D411yescharacteristic
205C42×C61C2×D411yescharacteristic
206C22⋊Dic61—21no—
207C22⋊Dic61—21no—
208#11758198—21no—
209#11758198—21no—
210#11758198—21no—
211#11758198—21no—
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—
226#11758194—21no—
227#11758194—21no—
228#11758194—21no—
229#11758194—21no—
230#11758194—21no—
231#11758194—21no—
232#11758194—21no—
233#11758194—21no—
234C2×#92418—21no—
235C2×#92418—21no—
236C2×#92418—21no—
237C2×#92418—21no—
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—22no—
250C2×C4×C61—41no—
251C2×C4×C61—41no—
252C2×C4×C61—41no—
253C2×C4×C61—41no—
254C2×C4×C61—41no—
255C2×C4×C61—41no—
256C2×C4×C61—41no—
257C2×C4×C61C4×D411yescharacteristic
258C2×C4×C61C4×D411yescharacteristic
259C2×C4×C61C4×D411yescharacteristic
260C2×C4×C61C4×D411yescharacteristic
261C2×C4×C61C23×C411yescharacteristic
262C2×C4×C61C22×D411yescharacteristic
263C2×C4×C61C2×#4111yescharacteristic
264C2×C4×C61C2×#4111yescharacteristic
265C2×C4×C61H(5,𝔽2)11yescharacteristic
266C2×C4×C612−1+411yescharacteristic
267C22⋊D61—22no—
268C22⋊D61—22no—
269C22⋊D61—41no—
270C22⋊D61—41no—
271C2×Dic61—21no—
272C2×Dic61—21no—
273C2×Dic61—21no—
274C2×Dic61—21no—
275C2×Dic61—21no—
276C2×Dic61—21no—
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—21no—
298C8×C61—21no—
299C8×C61—21no—
300C8×C61—21no—
301#92418—41no—
302#92418—41no—
303#92418—41no—
304#92418—41no—
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×C61—42no—
322C4×C61—81no—
323C4×C61C2×#11711yescharacteristic
324C4×C61#52011yescharacteristic
325C4×C61#54611yescharacteristic
326C4×C61#54811yescharacteristic
327Dic61—22no—
328Dic61—41no—
329Dic61—41no—
330Dic61—41no—
331Dic61—41no—
332Dic61—41no—
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#1838—611no—
343#1806—611no—
344#1806—611no—
345#1771D6111yescharacteristic, complemented
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—611no—
378#423—611no—
379#423—1221no—
380C2×C4⋊C8—1221no—
381C2×C4⋊C8C2×D6111yescharacteristic
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×#97C2×D6111yescharacteristic
393C2×#97C2×D6111yescharacteristic
394C2×C4×C8C2×D6111yescharacteristic
395C4×C4⋊C4C2×D6111yescharacteristic
396#341—611no—
397#341—611no—
398#341—611no—
399#341—611no—
400#339—611no—
401#339—611no—
402#339—611no—
403#339—611no—
404#336C2×D6111yescharacteristic
405#336C2×D6111yescharacteristic
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—611no—
420C2×M16—611no—
421C2×M16—611no—
422C2×M16—611no—
423C2×M16—1221no—
424C2×M16—1221no—
425C22×C8—1221no—
426C22×C8—1221no—
427C22×C8C22×D6111yescharacteristic
428C22×C8C22×D6111yescharacteristic
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—21no—
448C2×C42—1221no—
449C2×C42—1221no—
450C2×C42C22×D6111yescharacteristic
451C2×C42C22×D6111yescharacteristic
452C2×C42C22×D6111yescharacteristic
453#107—611no—
454#107—611no—
455#106—611no—
456#106—611no—
457C4⋊C8—1221no—
458C4⋊C8—1221no—
459C4⋊C8—1221no—
460C4⋊C8—1221no—
461C4⋊C8—1221no—
462C4⋊C8—1221no—
463C4⋊C8—1221no—
464C4⋊C8—1221no—
465C4⋊C8D24411yescharacteristic
466C4⋊C8D24411yescharacteristic
467C4⋊C8D24411yescharacteristic
468C4⋊C8D24411yescharacteristic
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—41no—
486#97—1221no—
487#97—1221no—
488#97C4×D6111yescharacteristic
489#97C4×D6111yescharacteristic
490#97C4×D6111yescharacteristic
491#97C4×D6111yescharacteristic
492C4×C8—41no—
493C4×C8—1221no—
494C4×C8—1221no—
495#95—21no—
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—21no—
511C22×C4—21no—
512C22×C4—1221no—
513C22×C4—1221no—
514C22×C4—1221no—
515C22×C4—1221no—
516C22×C4—1221no—
517C22×C4—1221no—
518C22×C4#1175822211yescharacteristic
519C22×C4#1175822211yescharacteristic
520C22×C4C23×D6111yescharacteristic
521Q16—1222no—
522SD16—1222no—
523SD16—1222no—
524D8—1222no—
525M16—1221no—
526M16—1221no—
527M16—1221no—
528M16—1221no—
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—21no—
542C2×C8—21no—
543C2×C8—1221no—
544C2×C8—1221no—
545C2×C8—1221no—
546C2×C8—1221no—
547C2×C8—2442no—
548C2×C8—2442no—
549C2×C8C2×C4×D6111yescharacteristic
550C2×C8C2×C4×D6111yescharacteristic
551C2×C8C2×C4×D6111yescharacteristic
552C2×C8C2×C4×D6111yescharacteristic
553C2×C8C2×D24411yescharacteristic
554C2×C8C2×D24411yescharacteristic
555C2×C8C2×D24411yescharacteristic
556C2×C8C2×D24411yescharacteristic
557C4⋊C4—42no—
558C4⋊C4—611no—
559C4⋊C4—611no—
560C4⋊C4—611no—
561C4⋊C4—611no—
562C4⋊C4—1221no—
563C4⋊C4—1221no—
564C4⋊C4—1221no—
565C4⋊C4—1221no—
566C22⋊C4—1221no—
567C22⋊C4—1221no—
568C22⋊C4—1221no—
569C22⋊C4—1221no—
570C22⋊C4—1221no—
571C22⋊C4—1221no—
572C42—21no—
573C42—21no—
574C42—21no—
575C42—21no—
576C42—1221no—
577C42—1221no—
578C42—1221no—
579C42—1221no—
580C42—1221no—
581C42—1221no—
582C42C2×C4×D6111yescharacteristic
583C42C2×C4×D6111yescharacteristic
584C42C2×D24411yescharacteristic
585C42C2×D24411yescharacteristic
586C23—1221no—
587C23—1221no—
588C23C2×#1175822211yescharacteristic
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—22no—
602C2×C4—41no—
603C2×C4—41no—
604C2×C4—41no—
605C2×C4—41no—
606C2×C4—41no—
607C2×C4—41no—
608C2×C4—41no—
609C2×C4—1221no—
610C2×C4—1222no—
611C2×C4—1222no—
612C2×C4—1221no—
613C2×C4—1221no—
614C2×C4—1221no—
615C2×C4—1221no—
616C2×C4—1221no—
617C2×C4—4881no—
618C2×C4—4881no—
619C2×C4—2442no—
620C2×C4—2442no—
621C2×C4—2441no—
622C2×C4—2441no—
623C2×C4C4×D24411yescharacteristic
624C2×C4C4×D24411yescharacteristic
625C2×C4C4×D24411yescharacteristic
626C2×C4C4×D24411yescharacteristic
627C2×C4C22×C4×D6111yescharacteristic
628C2×C4C22×D24411yescharacteristic
629C2×C4#41×D6111yescharacteristic
630C2×C4#41×D6111yescharacteristic
631C2×C4#1451982211yescharacteristic
632C2×C4#1451982511yescharacteristic
633C8—21no—
634C8—21no—
635C8—21no—
636C8—21no—
637C8—21no—
638C8—21no—
639C8—21no—
640C8—21no—
641C8—2441no—
642C8—2441no—
643C8—2441no—
644C8—2441no—
645C22—21no—
646C22—21no—
647C22—1222no—
648C22—2441no—
649C22—2441no—
650C22—2441no—
651C22—2441no—
652C22—2441no—
653C22C2×C4×D24411yescharacteristic
654C22#1684045311yescharacteristic
655C22#1684046211yescharacteristic
656C4—21no—
657C4—21no—
658C4—21no—
659C4—21no—
660C4—42no—
661C4—81no—
662C4—1222no—
663C4—2441no—
664C4—2441no—
665C4—2441no—
666C4—2441no—
667C4—2441no—
668C4#117×D6111yescharacteristic
669C4#1684024311yescharacteristic
670C4#1684040711yescharacteristic
671C4#1684042411yescharacteristic
672C2—21no—
673C2—21no—
674C2—4881no—
675C2—2442no—
676C2#2144875111yescharacteristic
677C2#2145472311yescharacteristic
678C2#2145473011yescharacteristic
subgroupG/H
centerC2×C4C22×D244
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1771C2
socleC22×C61C2×C4×D4
prime radicalC2×#14519799C22
cosocleC22×C4×C61C24
hypercenter#1771D61
hypocenterC61#22784
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C4⋊C8 ◁ #1771

Complements

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

NH ≅ G/Ntype
2. #21454484C2semidirect
3. #21454384C2semidirect
4. #21446530C2semidirect
5. #21446523C2semidirect
6. #21446419C2semidirect
7. #21446419C2semidirect
10. #21445960C2semidirect
11. #21445840C2semidirect
12. #21445840C2semidirect
13. #21445663C2semidirect
14. #21445656C2semidirect
15. C61×#1771C2semidirect
21. #16839875C4semidirect
22. #16839875C4semidirect
23. #16839870C4semidirect
24. #16839870C4semidirect
25. #16839864C4semidirect
26. #16839864C4semidirect
27. #16839864C4semidirect
28. #16839864C4semidirect
345. #1771D61semidirect
406. C61#22784semidirect

Maximal subgroups

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

subgroupindex
#214546212
#214544842
#214543842
#214465302
#214465232
#214464192
#214461452
#214459602
#214458402
#214456632
#214456562
C61×#17712
#2278461