Finite Group Databasebeta

← #29702102

Subgroups — #29702102

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#21455609C211yesmaximal, characteristic
2#21454766C211yesmaximal, characteristic, complemented
3#21454388C211yesmaximal, characteristic
4#21446799C211yesmaximal, characteristic, complemented
5#21446570C211yesmaximal, characteristic, complemented
6#21446565C211yesmaximal, characteristic, complemented
7#21446417C211yesmaximal, characteristic, complemented
8#21446417C211yesmaximal, characteristic, complemented
9#21446091C211yesmaximal, characteristic
10#21446091C211yesmaximal, characteristic
11#21445678C211yesmaximal, characteristic, complemented
12#21445662C211yesmaximal, characteristic
13#21445655C211yesmaximal, characteristic
14#21445632C211yesmaximal, characteristic
15C61×#1950C211yesmaximal, characteristic, complemented
16C2×#14519785C2211yescharacteristic
17C2×#14519785C2211yescharacteristic
18#16840319C2211yescharacteristic
19C4×#11758222C2211yescharacteristic
20#16840070C411yescharacteristic, complemented
21#16840070C411yescharacteristic, complemented
22#16840063C411yescharacteristic, complemented
23#16840063C411yescharacteristic, complemented
24#16840058C411yescharacteristic, complemented
25#16840053C411yescharacteristic, complemented
26#16840048C411yescharacteristic, complemented
27#16840043C411yescharacteristic, complemented
28#16839892—21no—
29#16839890—21no—
30#16839890—21no—
31C8×Dic122—21no—
32#16839800C2211yescharacteristic
33#16839800C2211yescharacteristic
34#16839790C2211yescharacteristic
35#16839790C2211yescharacteristic
36#16839790C2211yescharacteristic
37#16839790C2211yescharacteristic
38#16839787—21no—
39#16839787—21no—
40#16839784—21no—
41C2×C4⋊#92418C2211yescharacteristic
42C4⋊C8×D61—21no—
43C2×#14519703C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839759C2211yescharacteristic
46#16839759C2211yescharacteristic
47#16839720C2211yescharacteristic
48#16839720C2211yescharacteristic
49C2×#14519687C2211yescharacteristic
50C2×C8×Dic61C2211yescharacteristic
51#16839608C2211yescharacteristic
52#16839523C2211yescharacteristic
53#16839523C2211yescharacteristic
54#16839523C2211yescharacteristic
55#16839523C2211yescharacteristic
56#16839523C2211yescharacteristic
57#16839523C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#108×C61C2211yescharacteristic
61C2×#108×C61C2211yescharacteristic
62C61×#423C2211yescharacteristic
63C2×C4⋊C8×C61C2211yescharacteristic
64C4×M16×C61C2211yescharacteristic
65C61×#341C2211yescharacteristic
66C61×#341C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519785—22no—
69#14519785—22no—
70#14519785—41no—
71#14519785—41no—
72C2×#11758189—21no—
73C2×#11758189—21no—
74C22×#92418C2311yescharacteristic
75C22×#92418C2311yescharacteristic
76C2×C8×D61—21no—
77C2×C8×D61—21no—
78#14519777C2×C411yescharacteristic
79#14519777C2×C411yescharacteristic
80#14519769C2×C411yescharacteristic
81#14519769C2×C411yescharacteristic
82#14519756—21no—
83#14519756—21no—
84C4×Dic122—21no—
85C4×Dic122—21no—
86C4×Dic122C2×C411yescharacteristic
87C4×Dic122C2×C411yescharacteristic
88C4×D244C2×C411yescharacteristic
89C4×D244C2×C411yescharacteristic
90C4×C22⋊D61—21no—
91C4×C22⋊D61—21no—
92#14519736C2311yescharacteristic
93#14519736C2311yescharacteristic
94#14519736C2311yescharacteristic
95#14519734—21no—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—21no—
99#14519711C2×C411yescharacteristic
100#14519711C2×C411yescharacteristic
101#14519711C2×C411yescharacteristic
102#14519711C2×C411yescharacteristic
103#14519709C2×C411yescharacteristic
104#14519709C2×C411yescharacteristic
105#14519709C2×C411yescharacteristic
106#14519709C2×C411yescharacteristic
107C4⋊#92418D411yescharacteristic
108C4⋊#92418D411yescharacteristic
109C4⋊#92418D411yescharacteristic
110C4⋊#92418D411yescharacteristic
111#14519706—21no—
112#14519706—21no—
113#14519706—21no—
114#14519706—21no—
115#14519706—21no—
116#14519706—21no—
117#14519706—21no—
118#14519706—21no—
119#14519703—22no—
120#14519703Q814yescomplemented
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#14519687—21no—
130#14519687—21no—
131#14519687—41no—
132C8×Dic61—21no—
133C8×Dic61—21no—
134C8×Dic61—41no—
135#14519684—21no—
136#14519684—21no—
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C2×M16×C61C2311yescharacteristic
140C2×M16×C61C2311yescharacteristic
141C22×C8×C61C2311yescharacteristic
142C22×C8×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#108×C61—41no—
145#108×C61—41no—
146C4⋊C8×C61—21no—
147C4⋊C8×C61—21no—
148C4⋊C8×C61C2×C411yescharacteristic
149C4⋊C8×C61C2×C411yescharacteristic
150C4⋊C8×C61C2×C411yescharacteristic
151C4⋊C8×C61C2×C411yescharacteristic
152#97×C61—21no—
153C4×C8×C61—21no—
154C22×C4×C61#4111yescharacteristic
155C22×C4×C61#4111yescharacteristic
156C22×C4×C61C2411yescharacteristic
157C2×C22⋊D61—21no—
158C22×Dic61—21no—
159C22×Dic61—21no—
160#11758222—21no—
161#11758222—21no—
162#11758222C2×Q812yes—
163#11758222#4112yes—
164C2×D244C22×C411yescharacteristic
165C2×C4×D61—21no—
166C2×C4×D61—21no—
167C2×C4×D61—21no—
168C2×Dic122—21no—
169C2×Dic122—21no—
170C2×Dic122C22×C411yescharacteristic
171M16×C61—21no—
172M16×C61—21no—
173M16×C61—21no—
174M16×C61—21no—
175M16×C61—21no—
176M16×C61—21no—
177M16×C61—21no—
178M16×C61C2×Q812yes—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
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×C61C22×C411yescharacteristic
188C2×C8×C61C22×C411yescharacteristic
189C2×C8×C61C22×C411yescharacteristic
190C2×C8×C61C22×C411yescharacteristic
191C42×C61C22×C411yescharacteristic
192C42×C61C22×C411yescharacteristic
193C42×C61C2×D411yescharacteristic
194C42×C61C2×D411yescharacteristic
195C22⋊Dic61—21no—
196C22⋊Dic61—21no—
197C22⋊Dic61—21no—
198#11758198—21no—
199#11758198—21no—
200C4⋊Dic61—21no—
201C4⋊Dic61—21no—
202C4⋊Dic61C22×C411yescharacteristic
203C4⋊Dic61C22×C411yescharacteristic
204C4⋊Dic61C22×C411yescharacteristic
205C4⋊Dic61C22×C411yescharacteristic
206C4⋊Dic61C22×C411yescharacteristic
207C4⋊Dic61C22×C411yescharacteristic
208#11758196—21no—
209#11758196—21no—
210#11758196—21no—
211#11758196—21no—
212#11758196—21no—
213#11758196—21no—
214C4×Dic61—21no—
215C4×Dic61—21no—
216C4×Dic61—21no—
217C4×Dic61—21no—
218C4×Dic61—21no—
219C4×Dic61—21no—
220C4×Dic61—21no—
221C4×Dic61—21no—
222C4×Dic61C2×Q812yes—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
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—
237C2×C4×C61—41no—
238C2×C4×C61—41no—
239C2×C4×C61C4×D411yescharacteristic
240C2×C4×C61C4×D411yescharacteristic
241C2×C4×C61C4×D411yescharacteristic
242C2×C4×C61C4×D411yescharacteristic
243C2×C4×C61C23×C411yescharacteristic
244C2×C4×C61C22×D411yescharacteristic
245C2×C4×C61C22×Q811yescharacteristic
246C2×C4×C61C2×#4111yescharacteristic
247C2×C4×C61H(5,𝔽2)11yescharacteristic
248C2×C4×C612−1+411yescharacteristic
249C22⋊D61—22no—
250C22⋊D61—22no—
251C2×Dic61—21no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—21no—
256C2×Dic61—21no—
257C2×Dic61—21no—
258C2×Dic61—22no—
259C2×Dic61—41no—
260C2×Dic61—41no—
261C2×Dic61—41no—
262C2×Dic61—41no—
263C2×Dic61—41no—
264D244—21no—
265D244C4×Q812yes—
266C4×D61—22no—
267C4×D61—22no—
268C4×D61—42no—
269C4×D61—81no—
270Dic122—21no—
271Dic122—42no—
272Dic122—81no—
273Dic122C4×Q812yes—
274C8×C61—21no—
275C8×C61—21no—
276C8×C61—21no—
277C8×C61—21no—
278C8×C61—22no—
279C8×C61—41no—
280C8×C61—41no—
281C8×C61—41no—
282#92418—21no—
283#92418—21no—
284#92418—21no—
285#92418—21no—
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×C61C2×C4×Q811yescharacteristic
300C4×C61#52011yescharacteristic
301C4×C61#54611yescharacteristic
302C4×C61D4×Q811yescharacteristic
303Dic61—22no—
304Dic61—42no—
305Dic61—41no—
306Dic61—41no—
307Dic61—41no—
308Dic61—41no—
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312#3076—611no—
313#2962—611no—
314#2906—611no—
315#1995—611no—
316#1950D6111yescharacteristic, complemented
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#533—611no—
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×#108C2×D6111yescharacteristic
350C2×#108C2×D6111yescharacteristic
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—1221no—
363C2×C4⋊C8C2×D6111yescharacteristic
364C2×#104—611no—
365C2×#104—611no—
366#416—611no—
367#416—611no—
368#405—611no—
369#405—611no—
370C4×M16C2×D6111yescharacteristic
371C2×#97—611no—
372C2×C4×C8—611no—
373#376—611no—
374#341C2×D6111yescharacteristic
375#341C2×D6111yescharacteristic
376#339—611no—
377#339—611no—
378#339—611no—
379#339—611no—
380#339—611no—
381#339—611no—
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—1221no—
391C2×M16—1221no—
392C2×M16C22×D6111yescharacteristic
393C2×M16C22×D6111yescharacteristic
394C2×M16C22×D6111yescharacteristic
395C2×M16C22×D6111yescharacteristic
396C22×C8—611no—
397C22×C8—611no—
398C22×C8—1221no—
399C22×C8—1221no—
400C22×C8C22×D6111yescharacteristic
401C22×C8C22×D6111yescharacteristic
402C4⋊Q8—611no—
403C4⋊Q8—611no—
404#125—611no—
405#125—611no—
406C22⋊Q8—1221no—
407C22⋊Q8—1221no—
408C4×Q8—611no—
409C4×Q8—611no—
410C4×Q8—1221no—
411C4×Q8—1221no—
412C4×D4—611no—
413C4×D4—611no—
414C4×D4—1221no—
415C4×D4—1221no—
416#117—611no—
417#117—611no—
418#117—611no—
419#117—1221no—
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#108—41no—
425#108—41no—
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—1221no—
441C4⋊C8—1221no—
442C4⋊C8—1221no—
443C4⋊C8—1221no—
444C4⋊C8—1221no—
445C4⋊C8—1221no—
446C4⋊C8—1221no—
447C4⋊C8—1221no—
448C4⋊C8C4×D6111yescharacteristic
449C4⋊C8C4×D6111yescharacteristic
450C4⋊C8C4×D6111yescharacteristic
451C4⋊C8C4×D6111yescharacteristic
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—21no—
463#97—1221no—
464#97—1221no—
465#97—2441no—
466C4×C8—21no—
467C4×C8—1221no—
468C4×C8—1221no—
469C4×C8—2441no—
470#95—1221no—
471#95—1221no—
472#41—612no—
473#41—612no—
474#41—1221no—
475#41—1221no—
476C2×Q8—611no—
477C2×Q8—1221no—
478C2×Q8—1221no—
479C2×D4—611no—
480C2×D4—1221no—
481C22×C4—1221no—
482C22×C4—1221no—
483C22×C4—1221no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4#1175822611yescharacteristic
487C22×C4#1175822611yescharacteristic
488C22×C4C23×D6111yescharacteristic
489M16—21no—
490M16—21no—
491M16—21no—
492M16—21no—
493M16—21no—
494M16—21no—
495M16—21no—
496M16—2442no—
497M16—2442no—
498M16Q8×D6112yes—
499C2×C8—21no—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
505C2×C8—21no—
506C2×C8—21no—
507C2×C8—611no—
508C2×C8—611no—
509C2×C8—611no—
510C2×C8—611no—
511C2×C8—1221no—
512C2×C8—1221no—
513C2×C8—1221no—
514C2×C8—1221no—
515C2×C8—2442no—
516C2×C8—2442no—
517C2×C8C2×C4×D6111yescharacteristic
518C2×C8C2×C4×D6111yescharacteristic
519C2×C8C2×C4×D6111yescharacteristic
520C2×C8C2×C4×D6111yescharacteristic
521C4⋊C4—611no—
522C4⋊C4—611no—
523C4⋊C4—611no—
524C4⋊C4—611no—
525C4⋊C4—611no—
526C4⋊C4—611no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
529C4⋊C4—1221no—
530C4⋊C4—1221no—
531C4⋊C4—1221no—
532C4⋊C4—1221no—
533C4⋊C4—1221no—
534C4⋊C4—1221no—
535C22⋊C4—1221no—
536C22⋊C4—1221no—
537C22⋊C4—1221no—
538C22⋊C4—1221no—
539C22⋊C4—1221no—
540C42—612no—
541C42—1221no—
542C42—1221no—
543C42—1221no—
544C42—1221no—
545C42—1221no—
546C42—1221no—
547C42—1221no—
548C42—1221no—
549C42C2×C4×D6111yescharacteristic
550C42C2×C4×D6111yescharacteristic
551C42D4×D6111yescharacteristic
552C42D4×D6111yescharacteristic
553C23—1221no—
554C23C2×#1175822611yescharacteristic
555Q8—612no—
556Q8—1221no—
557Q8—4881no—
558Q8—2442no—
559D4—612no—
560D4—1222no—
561D4—1222no—
562D4—1221no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—1221no—
566C2×C4—1222no—
567C2×C4—1222no—
568C2×C4—1222no—
569C2×C4—1221no—
570C2×C4—1221no—
571C2×C4—1221no—
572C2×C4—1221no—
573C2×C4—1221no—
574C2×C4—1221no—
575C2×C4—4881no—
576C2×C4—2442no—
577C2×C4—2441no—
578C2×C4—2441no—
579C2×C4—2441no—
580C2×C4—2441no—
581C2×C4—2441no—
582C2×C4#1451973911yescharacteristic
583C2×C4#1451973911yescharacteristic
584C2×C4#1451973911yescharacteristic
585C2×C4#1451973911yescharacteristic
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C2×Q8×D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#1451982211yescharacteristic
591C2×C4#1451982411yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—22no—
597C8—41no—
598C8—41no—
599C8—41no—
600C8—1221no—
601C8—1221no—
602C8—1221no—
603C8—1221no—
604C22—21no—
605C22—21no—
606C22—1222no—
607C22—2441no—
608C22—2441no—
609C22C2×#1451973911yescharacteristic
610C22#1684045011yescharacteristic
611C22#1684047311yescharacteristic
612C4—21no—
613C4—21no—
614C4—21no—
615C4—21no—
616C4—1222no—
617C4—4881no—
618C4—2442no—
619C4—2441no—
620C4—2441no—
621C4—2441no—
622C4—2441no—
623C4—2441no—
624C4—2441no—
625C4C4×Q8×D6111yescharacteristic
626C4#1684024111yescharacteristic
627C4#1684040911yescharacteristic
628C4#1684042511yescharacteristic
629C2—21no—
630C2—21no—
631C2—2442no—
632C2#2144882311yescharacteristic
633C2#2145472111yescharacteristic
634C2#2145473511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1950C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenter#1950D61
hypocenterC61#22984
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1950

Complements

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

NH ≅ G/Ntype
2. #21454766C2semidirect
4. #21446799C2semidirect
5. #21446570C2semidirect
6. #21446565C2semidirect
7. #21446417C2semidirect
8. #21446417C2semidirect
11. #21445678C2semidirect
15. C61×#1950C2semidirect
20. #16840070C4semidirect
21. #16840070C4semidirect
22. #16840063C4semidirect
23. #16840063C4semidirect
24. #16840058C4semidirect
25. #16840053C4semidirect
26. #16840048C4semidirect
27. #16840043C4semidirect
120. #14519703Q8semidirect
316. #1950D61semidirect
384. C61#22984semidirect

Maximal subgroups

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

subgroupindex
#214556092
#214547662
#214543882
#214467992
#214465702
#214465652
#214464172
#214460912
#214456782
#214456622
#214456552
#214456322
C61×#19502
#2298461