Finite Group Databasebeta

← #29702110

Subgroups — #29702110

Order 15616.

692 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21455601C211yesmaximal, characteristic
2#21454768C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic
4#21446592C211yesmaximal, characteristic, complemented
5#21446571C211yesmaximal, characteristic, complemented
6#21446566C211yesmaximal, characteristic, complemented
7#21446416C211yesmaximal, characteristic, complemented
8#21446416C211yesmaximal, characteristic, complemented
9#21446095C211yesmaximal, characteristic
10#21446095C211yesmaximal, characteristic
11#21445676C211yesmaximal, characteristic, complemented
12#21445660C211yesmaximal, characteristic
13#21445653C211yesmaximal, characteristic
14#21445630C211yesmaximal, characteristic
15C61×#1995C211yesmaximal, characteristic, complemented
16C2×#14519785C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18C4×#11758222C2211yescharacteristic
19#16840066C411yescharacteristic, complemented
20#16840066C411yescharacteristic, complemented
21#16840059C411yescharacteristic, complemented
22#16840059C411yescharacteristic, complemented
23#16840054C411yescharacteristic, complemented
24#16840049C411yescharacteristic, complemented
25#16840044C411yescharacteristic, complemented
26#16840039C411yescharacteristic, complemented
27#16839893—21no—
28#16839893—21no—
29#16839893—21no—
30Q8×#92418—21no—
31C2×#14519712C2211yescharacteristic
32C2×#14519712C2211yescharacteristic
33#16839798C2211yescharacteristic
34#16839798C2211yescharacteristic
35#16839790C2211yescharacteristic
36#16839790C2211yescharacteristic
37#16839789C2211yescharacteristic
38#16839789C2211yescharacteristic
39#16839787—21no—
40#16839787—21no—
41#16839784—21no—
42C2×C4⋊#92418C2211yescharacteristic
43C2×C4⋊#92418C2211yescharacteristic
44C4⋊C8×D61—21no—
45C2×#14519705C2211yescharacteristic
46C2×#14519705C2211yescharacteristic
47#16839756C2211yescharacteristic
48#16839756C2211yescharacteristic
49#16839718C2211yescharacteristic
50#16839718C2211yescharacteristic
51C4×#11758194C2211yescharacteristic
52C2×#14519688C2211yescharacteristic
53C2×C4×#92418C2211yescharacteristic
54#16839526C2211yescharacteristic
55#16839526C2211yescharacteristic
56#16839522C2211yescharacteristic
57#16839522C2211yescharacteristic
58#16839517C2211yescharacteristic
59#16839517C2211yescharacteristic
60C61×#533C2211yescharacteristic
61C61×#423C2211yescharacteristic
62C61×#376C2211yescharacteristic
63C61×#339C2211yescharacteristic
64C61×#339C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519785—22no—
69#14519785—22no—
70#14519785—41no—
71#14519785—41no—
72C2×#11758194C2311yescharacteristic
73C2×#11758194C2311yescharacteristic
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C22×#92418C2311yescharacteristic
79C22×#92418C2311yescharacteristic
80C2×C8×D61—21no—
81C2×C8×D61—21no—
82C4×Dic122C2×C411yescharacteristic
83C4×Dic122C2×C411yescharacteristic
84C4×D244C2×C411yescharacteristic
85C4×D244C2×C411yescharacteristic
86C4×C22⋊D61—21no—
87C4×C22⋊D61—21no—
88#14519736C2311yescharacteristic
89#14519734—21no—
90C42×D61—21no—
91#14519712—41no—
92#14519712—41no—
93#14519710C2×C411yescharacteristic
94#14519710C2×C411yescharacteristic
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99#14519708C2×C411yescharacteristic
100#14519708C2×C411yescharacteristic
101C4⋊#92418—21no—
102C4⋊#92418—21no—
103C4⋊#92418—21no—
104C4⋊#92418—21no—
105C4⋊#92418C2×C411yescharacteristic
106C4⋊#92418C2×C411yescharacteristic
107C4⋊#92418C2×C411yescharacteristic
108C4⋊#92418C2×C411yescharacteristic
109C4⋊#92418D411yescharacteristic
110C4⋊#92418D411yescharacteristic
111C4⋊#92418D411yescharacteristic
112C4⋊#92418D411yescharacteristic
113#14519706—21no—
114#14519706—21no—
115#14519706—21no—
116#14519706—21no—
117#14519705—22no—
118#14519705Q814yescomplemented
119#14519700C2×C411yescharacteristic
120#14519700C2×C411yescharacteristic
121#14519700C2×C411yescharacteristic
122#14519700C2×C411yescharacteristic
123#14519697C2×C411yescharacteristic
124#14519697C2×C411yescharacteristic
125#14519697C2×C411yescharacteristic
126#14519697C2×C411yescharacteristic
127#14519688—21no—
128#14519688—21no—
129#14519688—21no—
130#14519688—41no—
131C4×#92418—21no—
132C4×#92418—21no—
133C4×#92418—21no—
134C4×#92418—41no—
135C2×M16×C61C2311yescharacteristic
136C2×M16×C61C2311yescharacteristic
137C4⋊Q8×C61C2×C411yescharacteristic
138C4⋊Q8×C61C2×C411yescharacteristic
139#125×C61C2×C411yescharacteristic
140#125×C61C2×C411yescharacteristic
141C22⋊Q8×C61—21no—
142C22⋊Q8×C61—21no—
143C4×Q8×C61—21no—
144C4×Q8×C61—21no—
145#117×C61C2311yescharacteristic
146#117×C61C2311yescharacteristic
147C2×C42×C61C2311yescharacteristic
148C2×C42×C61C2311yescharacteristic
149C2×C42×C61C2311yescharacteristic
150C4⋊C8×C61—21no—
151C4⋊C8×C61—21no—
152#95×C61—21no—
153#95×C61—21no—
154C2×Q8×C61—21no—
155C2×Q8×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—
162#11758222—21no—
163#11758222—21no—
164#11758222C2×Q812yes—
165#11758222#4112yes—
166C2×D244C22×C411yescharacteristic
167C2×C4×D61—21no—
168C2×C4×D61—21no—
169C2×C4×D61—21no—
170C2×Dic122C22×C411yescharacteristic
171M16×C61—21no—
172M16×C61—21no—
173M16×C61—21no—
174M16×C61—21no—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C4⋊C4×C61—21no—
178C4⋊C4×C61—21no—
179C4⋊C4×C61—21no—
180C4⋊C4×C61—21no—
181C4⋊C4×C61—21no—
182C4⋊C4×C61—21no—
183C4⋊C4×C61C22×C411yescharacteristic
184C4⋊C4×C61C22×C411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C22⋊C4×C61—21no—
188C22⋊C4×C61—21no—
189C42×C61—21no—
190C42×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61C22×C411yescharacteristic
195C42×C61C22×C411yescharacteristic
196C42×C61C2×D411yescharacteristic
197C42×C61C2×D411yescharacteristic
198C42×C61C2×Q812yes—
199C22⋊Dic61—21no—
200#11758198—21no—
201#11758198—21no—
202C4⋊Dic61C22×C411yescharacteristic
203C4⋊Dic61C22×C411yescharacteristic
204#11758196—21no—
205#11758196—21no—
206C4×Dic61—21no—
207C4×Dic61—21no—
208C4×Dic61—21no—
209#11758194—21no—
210#11758194—21no—
211#11758194—21no—
212#11758194C2×Q812yes—
213C2×#92418—21no—
214C2×#92418—21no—
215C2×#92418—21no—
216C2×#92418—21no—
217C2×#92418—21no—
218C2×#92418—21no—
219C2×#92418—21no—
220C2×#92418—21no—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418C22×C411yescharacteristic
224C2×#92418C22×C411yescharacteristic
225C2×#92418C22×C411yescharacteristic
226C2×#92418C22×C411yescharacteristic
227C2×#92418C2×D411yescharacteristic
228C2×#92418C2×D411yescharacteristic
229C2×#92418C2×D411yescharacteristic
230C2×#92418C2×D411yescharacteristic
231#11758189—42no—
232#11758189—42no—
233C8×D61—42no—
234C8×D61—42no—
235C23×C61C2×#4111yescharacteristic
236C22×D61—21no—
237Q8×C61—42no—
238Q8×C61—81no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—21no—
242C2×C4×C61—21no—
243C2×C4×C61—22no—
244C2×C4×C61—41no—
245C2×C4×C61—41no—
246C2×C4×C61—41no—
247C2×C4×C61—41no—
248C2×C4×C61—41no—
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×C61C22×Q811yescharacteristic
258C2×C4×C61C2×#4111yescharacteristic
259C2×C4×C61H(5,𝔽2)11yescharacteristic
260C2×C4×C612−1+411yescharacteristic
261C22⋊D61—22no—
262C22⋊D61—22no—
263C2×Dic61—21no—
264C2×Dic61—21no—
265C2×Dic61—21no—
266D244—21no—
267D244C4×Q812yes—
268C4×D61—22no—
269C4×D61—22no—
270C4×D61—42no—
271C4×D61—81no—
272Dic122—21no—
273Dic122C4×Q812yes—
274C8×C61—41no—
275C8×C61—41no—
276#92418—21no—
277#92418—21no—
278#92418—21no—
279#92418—21no—
280#92418—21no—
281#92418—21no—
282#92418—21no—
283#92418—21no—
284#92418—22no—
285#92418—41no—
286#22984—611nomaximal, Sylow
287C22×C61—21no—
288C22×C61—21no—
289C22×C61C2×C4×D411yescharacteristic
290C22×C61#55211yescharacteristic
291C22×C61#55411yescharacteristic
292C2×D61—22no—
293C2×D61—41no—
294C2×D61—41no—
295C4×C61—21no—
296C4×C61—21no—
297C4×C61—21no—
298C4×C61—21no—
299C4×C61—42no—
300C4×C61—41no—
301C4×C61—41no—
302C4×C61—41no—
303C4×C61—41no—
304C4×C61—81no—
305C4×C61C2×C4×Q811yescharacteristic
306C4×C61#52011yescharacteristic
307C4×C61#54611yescharacteristic
308C4×C61D4×Q811yescharacteristic
309Dic61—22no—
310Dic61—41no—
311Dic61—41no—
312#3076—611no—
313#2962—611no—
314#2906—611no—
315#1995D6111yescharacteristic, complemented
316#1950—611no—
317#1946—611no—
318#1945—611no—
319#1922—611no—
320#1922—611no—
321#1866—611no—
322#1866—611no—
323#1768—611no—
324#1765—611no—
325#1764—611no—
326#1759—611no—
327C2×C61—21no—
328C2×C61—21no—
329C2×C61#236011yescharacteristic
330C2×C61#295511yescharacteristic
331C2×C61#295711yescharacteristic
332D61—42no—
333C2×#131—611no—
334C2×#131—611no—
335#533C2×D6111yescharacteristic
336C4×#41—611no—
337#479—611no—
338#479—611no—
339#478—611no—
340#478—611no—
341#477—611no—
342#476—611no—
343#475—611no—
344#474—611no—
345#446—1221no—
346#446—1221no—
347#446—1221no—
348C8×Q8—1221no—
349C2×#108—611no—
350C2×#108—611no—
351#427—611no—
352#427—611no—
353#424—611no—
354#424—611no—
355#424—611no—
356#424—611no—
357#424—1221no—
358#424—1221no—
359#423—1221no—
360#423C2×D6111yescharacteristic
361C2×C4⋊C8—611no—
362C2×C4⋊C8—611no—
363C2×C4⋊C8—1221no—
364C2×#104—611no—
365C2×#104—611no—
366#416—611no—
367#416—611no—
368#405—611no—
369#405—611no—
370C4×M16—611no—
371C2×#97—611no—
372C2×C4×C8—611no—
373#376C2×D6111yescharacteristic
374#341—611no—
375#341—611no—
376#339—611no—
377#339—611no—
378#339C2×D6111yescharacteristic
379#339C2×D6111yescharacteristic
380#339C2×D6111yescharacteristic
381#339C2×D6111yescharacteristic
382#336—611no—
383#336—611no—
384C61#2298411yescharacteristic, complemented, Sylow
385C2×#41—611no—
386#131—1222no—
387#131—1222no—
388#131—2441no—
389#131—2441no—
390C2×M16—611no—
391C2×M16—611no—
392C2×M16—1221no—
393C2×M16—1221no—
394C2×M16C22×D6111yescharacteristic
395C2×M16C22×D6111yescharacteristic
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—611no—
399C22×C8—611no—
400C22×C8—1221no—
401C22×C8—1221no—
402C4⋊Q8C4×D6111yescharacteristic
403C4⋊Q8C4×D6111yescharacteristic
404#125C4×D6111yescharacteristic
405#125C4×D6111yescharacteristic
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C4×Q8—21no—
409C4×Q8—21no—
410C4×Q8—611no—
411C4×Q8—611no—
412C4×D4—611no—
413C4×D4—611no—
414C4×D4—1221no—
415C4×D4—1221no—
416#117—611no—
417#117—1221no—
418#117C22×D6111yescharacteristic
419#117C22×D6111yescharacteristic
420C2×C42—1221no—
421C2×C42C22×D6111yescharacteristic
422C2×C42C22×D6111yescharacteristic
423C2×C42C22×D6111yescharacteristic
424#108—2441no—
425#108—2441no—
426#107—611no—
427#107—611no—
428#107—611no—
429#107—611no—
430#106—611no—
431#106—611no—
432#106—611no—
433#106—611no—
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—611no—
437C4⋊C8—611no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—611no—
443C4⋊C8—611no—
444C4⋊C8—1221no—
445C4⋊C8—1221no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8—1221no—
449C4⋊C8—1221no—
450C4⋊C8—1221no—
451C4⋊C8—1221no—
452#104—614no—
453#104—1222no—
454#103—611no—
455#103—611no—
456#103—611no—
457#103—611no—
458#102—611no—
459#102—611no—
460#102—611no—
461#102—611no—
462#97—1221no—
463#97—1221no—
464#97—1221no—
465#97—2441no—
466C4×C8—1221no—
467C4×C8—1221no—
468C4×C8—1221no—
469C4×C8—2441no—
470#95—21no—
471#95—21no—
472#41—612no—
473#41—612no—
474#41—1221no—
475#41—1221no—
476C2×Q8—21no—
477C2×Q8—21no—
478C2×Q8—611no—
479C2×D4—611no—
480C2×D4—1221no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4#1175822411yescharacteristic
487C22×C4#1175822411yescharacteristic
488C22×C4C23×D6111yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—612no—
494M16—1221no—
495M16—1221no—
496M16—1221no—
497M16—2442no—
498M16—2442no—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—611no—
502C2×C8—611no—
503C2×C8—611no—
504C2×C8—611no—
505C2×C8—611no—
506C2×C8—611no—
507C2×C8—611no—
508C2×C8—611no—
509C2×C8—1221no—
510C2×C8—1221no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—1221no—
516C2×C8—1221no—
517C2×C8—1221no—
518C2×C8—1221no—
519C2×C8—2442no—
520C2×C8—2442no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—611no—
528C4⋊C4—611no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4C2×C4×D6111yescharacteristic
532C4⋊C4C2×C4×D6111yescharacteristic
533C4⋊C4C2×C4×D6111yescharacteristic
534C4⋊C4C2×C4×D6111yescharacteristic
535C22⋊C4—21no—
536C22⋊C4—21no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C42—21no—
541C42—21no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42C2×C4×D6111yescharacteristic
549C42C2×C4×D6111yescharacteristic
550C42D4×D6111yescharacteristic
551C42D4×D6111yescharacteristic
552C42Q8×D6112yes—
553C23—1221no—
554C23C2×#1175822411yescharacteristic
555Q8—42no—
556Q8—81no—
557Q8—612no—
558Q8—1221no—
559D4—612no—
560D4—1222no—
561D4—1222no—
562D4—1221no—
563C2×C4—22no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—1221no—
576C2×C4—1222no—
577C2×C4—1222no—
578C2×C4—1221no—
579C2×C4—1221no—
580C2×C4—4881no—
581C2×C4—2442no—
582C2×C4#1451973711yescharacteristic
583C2×C4#1451973711yescharacteristic
584C2×C4#1451973711yescharacteristic
585C2×C4#1451973711yescharacteristic
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C2×Q8×D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#1451982311yescharacteristic
591C2×C4#1451982511yescharacteristic
592C8—41no—
593C8—41no—
594C8—1221no—
595C8—1221no—
596C8—1221no—
597C8—1221no—
598C8—1221no—
599C8—1221no—
600C8—1221no—
601C8—1221no—
602C8—1222no—
603C8—2441no—
604C22—21no—
605C22—21no—
606C22—1222no—
607C22—2441no—
608C22—2441no—
609C22C2×#1451973711yescharacteristic
610C22#1684044611yescharacteristic
611C22#1684047011yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—42no—
617C4—41no—
618C4—41no—
619C4—41no—
620C4—41no—
621C4—81no—
622C4—1222no—
623C4—2441no—
624C4—2441no—
625C4C4×Q8×D6111yescharacteristic
626C4#1684024411yescharacteristic
627C4#1684040511yescharacteristic
628C4#1684042711yescharacteristic
629C2—21no—
630C2—21no—
631C2—2442no—
632C2#2144882911yescharacteristic
633C2#2145471811yescharacteristic
634C2#2145473211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1995C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenter#1995D61
hypocenterC61#22984
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1995

Complements

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

NH ≅ G/Ntype
2. #21454768C2semidirect
4. #21446592C2semidirect
5. #21446571C2semidirect
6. #21446566C2semidirect
7. #21446416C2semidirect
8. #21446416C2semidirect
11. #21445676C2semidirect
15. C61×#1995C2semidirect
19. #16840066C4semidirect
20. #16840066C4semidirect
21. #16840059C4semidirect
22. #16840059C4semidirect
23. #16840054C4semidirect
24. #16840049C4semidirect
25. #16840044C4semidirect
26. #16840039C4semidirect
118. #14519705Q8semidirect
315. #1995D61semidirect
384. C61#22984semidirect

Maximal subgroups

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

subgroupindex
#214556012
#214547682
#214543882
#214465922
#214465712
#214465662
#214464162
#214460952
#214456762
#214456602
#214456532
#214456302
C61×#19952
#2298461