Finite Group Databasebeta

← #29702099

Subgroups — #29702099

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#21455605C211yesmaximal, characteristic
2#21454765C211yesmaximal, characteristic, complemented
3#21454386C211yesmaximal, characteristic
4#21446798C211yesmaximal, characteristic, complemented
5#21446591C211yesmaximal, characteristic, complemented
6#21446571C211yesmaximal, characteristic, complemented
7#21446420C211yesmaximal, characteristic, complemented
8#21446415C211yesmaximal, characteristic, complemented
9#21446093C211yesmaximal, characteristic
10#21446091C211yesmaximal, characteristic
11#21445677C211yesmaximal, characteristic, complemented
12#21445660C211yesmaximal, characteristic
13#21445656C211yesmaximal, characteristic
14#21445628C211yesmaximal, characteristic
15C61×#1945C211yesmaximal, characteristic, complemented
16C2×#14519785C2211yescharacteristic
17C2×#14519783C2211yescharacteristic
18#16840315C2211yescharacteristic
19#16840230C2211yescharacteristic
20#16840072C411yescharacteristic, complemented
21#16840068C411yescharacteristic, complemented
22#16840065C411yescharacteristic, complemented
23#16840061C411yescharacteristic, complemented
24#16840056C411yescharacteristic, complemented
25#16840051C411yescharacteristic, complemented
26#16840046C411yescharacteristic, complemented
27#16840041C411yescharacteristic, complemented
28#16839891—21no—
29#16839891—21no—
30#16839889—21no—
31#16839886—21no—
32C2×#14519712C2211yescharacteristic
33#16839798C2211yescharacteristic
34#16839790C2211yescharacteristic
35#16839789C2211yescharacteristic
36#16839787—21no—
37#16839787—21no—
38#16839785C2211yescharacteristic
39#16839784—21no—
40C2×#14519706C2211yescharacteristic
41C2×#14519706C2211yescharacteristic
42C4⋊C8×D61—21no—
43C2×#14519705C2211yescharacteristic
44C2×#14519703C2211yescharacteristic
45#16839759C2211yescharacteristic
46#16839756C2211yescharacteristic
47#16839718C2211yescharacteristic
48#16839717C2211yescharacteristic
49M16×Dic61C2211yescharacteristic
50C2×#14519688C2211yescharacteristic
51#16839608C2211yescharacteristic
52#16839527C2211yescharacteristic
53#16839526C2211yescharacteristic
54#16839523C2211yescharacteristic
55#16839522C2211yescharacteristic
56#16839521C2211yescharacteristic
57#16839521C2211yescharacteristic
58#16839516C2211yescharacteristic
59#16839516C2211yescharacteristic
60C2×#108×C61C2211yescharacteristic
61C61×#427C2211yescharacteristic
62C61×#424C2211yescharacteristic
63C61×#424C2211yescharacteristic
64C2×C4×C8×C61C2211yescharacteristic
65C61×#339C2211yescharacteristic
66C61×#339C2211yescharacteristic
67C2×#11758222C2311yescharacteristic
68#14519785—22no—
69#14519785—41no—
70#14519783—22no—
71#14519783—41no—
72C2×#11758194C2311yescharacteristic
73C2×#11758194C2311yescharacteristic
74C2×#11758189—21no—
75C2×#11758189—21no—
76C22×#92418C2311yescharacteristic
77C22×#92418C2311yescharacteristic
78C2×C8×D61—21no—
79C2×C8×D61—21no—
80#14519776C2×C411yescharacteristic
81#14519776C2×C411yescharacteristic
82#14519768C2×C411yescharacteristic
83#14519768C2×C411yescharacteristic
84#14519754—21no—
85#14519754—21no—
86C4×Dic122—21no—
87C4×Dic122—21no—
88#14519742C2×C411yescharacteristic
89#14519742C2×C411yescharacteristic
90#14519739C2×C411yescharacteristic
91#14519739C2×C411yescharacteristic
92#14519737—21no—
93#14519737—21no—
94#14519736C2311yescharacteristic
95#14519734—21no—
96C2×C4×Dic61C2311yescharacteristic
97C2×C4×Dic61C2311yescharacteristic
98C42×D61—21no—
99#14519712—41no—
100#14519710C2×C411yescharacteristic
101#14519710C2×C411yescharacteristic
102#14519708C2×C411yescharacteristic
103#14519708C2×C411yescharacteristic
104C4⋊#92418—21no—
105C4⋊#92418—21no—
106#14519706—21no—
107#14519706—21no—
108#14519706—21no—
109#14519706—21no—
110#14519706C2×C411yescharacteristic
111#14519706C2×C411yescharacteristic
112#14519706C2×C411yescharacteristic
113#14519706C2×C411yescharacteristic
114#14519706D411yescharacteristic
115#14519706D411yescharacteristic
116#14519706D411yescharacteristic
117#14519706D411yescharacteristic
118#14519705Q814yescomplemented
119#14519703—22no—
120#14519702C2×C411yescharacteristic
121#14519702C2×C411yescharacteristic
122#14519700C2×C411yescharacteristic
123#14519700C2×C411yescharacteristic
124#14519699C2×C411yescharacteristic
125#14519699C2×C411yescharacteristic
126#14519697C2×C411yescharacteristic
127#14519697C2×C411yescharacteristic
128#14519688—21no—
129#14519688—41no—
130#14519687—21no—
131#14519687—21no—
132C4×#92418—21no—
133C8×Dic61—21no—
134C8×Dic61—21no—
135#14519684—21no—
136#14519684—21no—
137C2×M16×C61C2311yescharacteristic
138C2×M16×C61C2311yescharacteristic
139C22×C8×C61C2311yescharacteristic
140C22×C8×C61C2311yescharacteristic
141#117×C61C2311yescharacteristic
142#117×C61C2311yescharacteristic
143C2×C42×C61C2311yescharacteristic
144#108×C61—41no—
145#107×C61C2×C411yescharacteristic
146#107×C61C2×C411yescharacteristic
147#106×C61C2×C411yescharacteristic
148#106×C61C2×C411yescharacteristic
149C4⋊C8×C61—21no—
150C4⋊C8×C61—21no—
151C4⋊C8×C61—21no—
152C4⋊C8×C61—21no—
153C4×C8×C61—41no—
154C22×C4×C61—21no—
155C22×C4×C61C2411yescharacteristic
156C2×C22⋊D61—21no—
157C22×Dic61—21no—
158C22×Dic61#4111yescharacteristic
159C22×Dic61#4111yescharacteristic
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—
175C2×C8×C61—21no—
176C2×C8×C61—21no—
177C2×C8×C61—21no—
178C2×C8×C61—21no—
179C2×C8×C61—21no—
180C2×C8×C61—21no—
181C2×C8×C61C22×C411yescharacteristic
182C2×C8×C61C22×C411yescharacteristic
183C2×C8×C61C2×D411yescharacteristic
184C2×C8×C61C2×D411yescharacteristic
185C4⋊C4×C61C22×C411yescharacteristic
186C4⋊C4×C61C22×C411yescharacteristic
187C4⋊C4×C61C22×C411yescharacteristic
188C4⋊C4×C61C22×C411yescharacteristic
189C22⋊C4×C61—21no—
190C22⋊C4×C61—21no—
191C42×C61—21no—
192C42×C61—21no—
193C42×C61—21no—
194C42×C61C2×Q812yes—
195C22⋊Dic61—21no—
196#11758198—21no—
197#11758198—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—21no—
200C4⋊Dic61C22×C411yescharacteristic
201C4⋊Dic61C22×C411yescharacteristic
202#11758196—21no—
203#11758196—21no—
204#11758196—21no—
205#11758196—21no—
206#11758196—21no—
207#11758196—21no—
208C4×Dic61—21no—
209C4×Dic61—21no—
210C4×Dic61—21no—
211C4×Dic61—21no—
212C4×Dic61—21no—
213C4×Dic61C22×C411yescharacteristic
214C4×Dic61C22×C411yescharacteristic
215C4×Dic61C2×D411yescharacteristic
216C4×Dic61C2×D411yescharacteristic
217#11758194—21no—
218#11758194—21no—
219#11758194—21no—
220#11758194C2×Q812yes—
221C2×#92418—21no—
222C2×#92418—21no—
223C2×#92418—21no—
224C2×#92418—21no—
225C2×#92418—21no—
226C2×#92418—21no—
227C2×#92418C22×C411yescharacteristic
228C2×#92418C22×C411yescharacteristic
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—21no—
238C2×C4×C61—21no—
239C2×C4×C61—21no—
240C2×C4×C61—21no—
241C2×C4×C61—22no—
242C2×C4×C61—41no—
243C2×C4×C61—41no—
244C2×C4×C61C23×C411yescharacteristic
245C2×C4×C61C22×D411yescharacteristic
246C2×C4×C61C22×Q811yescharacteristic
247C2×C4×C61C2×#4111yescharacteristic
248C2×C4×C61H(5,𝔽2)11yescharacteristic
249C2×C4×C612−1+411yescharacteristic
250C22⋊D61—22no—
251C22⋊D61—22no—
252C2×Dic61—21no—
253C2×Dic61—21no—
254C2×Dic61—21no—
255C2×Dic61—41no—
256C2×Dic61—41no—
257C2×Dic61—41no—
258C2×Dic61—41no—
259C2×Dic61—41no—
260C2×Dic61C4×D411yescharacteristic
261C2×Dic61C4×D411yescharacteristic
262C2×Dic61C4×D411yescharacteristic
263C2×Dic61C4×D411yescharacteristic
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—41no—
279C8×C61—41no—
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—42no—
296C4×C61—41no—
297C4×C61—41no—
298C4×C61—41no—
299C4×C61—41no—
300C4×C61C2×C4×Q811yescharacteristic
301C4×C61#52011yescharacteristic
302C4×C61#54611yescharacteristic
303C4×C61D4×Q811yescharacteristic
304Dic61—22no—
305Dic61—21no—
306Dic61—21no—
307Dic61—21no—
308Dic61—21no—
309Dic61—41no—
310Dic61—41no—
311Dic61—81no—
312#3076—611no—
313#2962—611no—
314#2906—611no—
315#1995—611no—
316#1950—611no—
317#1946—611no—
318#1945D6111yescharacteristic, complemented
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×#108—611no—
350C2×#108C2×D6111yescharacteristic
351#427—611no—
352#427C2×D6111yescharacteristic
353#424—611no—
354#424—611no—
355#424—1221no—
356#424—1221no—
357#424C2×D6111yescharacteristic
358#424C2×D6111yescharacteristic
359#423—611no—
360#423—1221no—
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×C8C2×D6111yescharacteristic
373#376—611no—
374#341—611no—
375#341—611no—
376#339—611no—
377#339—611no—
378#339—611no—
379#339—611no—
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—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—1221no—
418#117C22×D6111yescharacteristic
419#117C22×D6111yescharacteristic
420C2×C42—611no—
421C2×C42—611no—
422C2×C42—1221no—
423C2×C42C22×D6111yescharacteristic
424#108—41no—
425#108—2441no—
426#107—611no—
427#107—611no—
428#107C4×D6111yescharacteristic
429#107C4×D6111yescharacteristic
430#106—611no—
431#106—611no—
432#106C4×D6111yescharacteristic
433#106C4×D6111yescharacteristic
434C4⋊C8—21no—
435C4⋊C8—21no—
436C4⋊C8—21no—
437C4⋊C8—21no—
438C4⋊C8—611no—
439C4⋊C8—611no—
440C4⋊C8—611no—
441C4⋊C8—611no—
442C4⋊C8—611no—
443C4⋊C8—611no—
444C4⋊C8—611no—
445C4⋊C8—611no—
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—41no—
467C4×C8—1221no—
468C4×C8—1221no—
469C4×C8—1221no—
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—21no—
482C22×C4—611no—
483C22×C4—611no—
484C22×C4—1221no—
485C22×C4—1221no—
486C22×C4—1221no—
487C22×C4—1221no—
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—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—21no—
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—2442no—
516C2×C8—2442no—
517C2×C8C2×C4×D6111yescharacteristic
518C2×C8C2×C4×D6111yescharacteristic
519C2×C8D4×D6111yescharacteristic
520C2×C8D4×D6111yescharacteristic
521C4⋊C4—611no—
522C4⋊C4—611no—
523C4⋊C4—1221no—
524C4⋊C4—1221no—
525C4⋊C4—1221no—
526C4⋊C4—1221no—
527C4⋊C4—1221no—
528C4⋊C4—1221no—
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—611no—
544C42—611no—
545C42—611no—
546C42—611no—
547C42—1221no—
548C42—1221no—
549C42—1221no—
550C42—1221no—
551C42—1221no—
552C42Q8×D6112yes—
553C23—1221no—
554C23#41×D6111yescharacteristic
555Q8—612no—
556Q8—1221no—
557Q8—4881no—
558Q8—2442no—
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—611no—
571C2×C4—611no—
572C2×C4—611no—
573C2×C4—611no—
574C2×C4—1221no—
575C2×C4—1222no—
576C2×C4—1222no—
577C2×C4—1221no—
578C2×C4—1221no—
579C2×C4—4881no—
580C2×C4—2442no—
581C2×C4—2441no—
582C2×C4—2441no—
583C2×C4—2441no—
584C2×C4—2441no—
585C2×C4—2441no—
586C2×C4C22×C4×D6111yescharacteristic
587C2×C4C2×D4×D6111yescharacteristic
588C2×C4C2×Q8×D6111yescharacteristic
589C2×C4#41×D6111yescharacteristic
590C2×C4#1451982211yescharacteristic
591C2×C4#1451982511yescharacteristic
592C8—21no—
593C8—21no—
594C8—21no—
595C8—21no—
596C8—41no—
597C8—41no—
598C8—1221no—
599C8—1221no—
600C8—1221no—
601C8—1221no—
602C8—1222no—
603C8—2441no—
604C22—21no—
605C22—21no—
606C22—1222no—
607C22—2441no—
608C22—2441no—
609C22C4×D4×D6111yescharacteristic
610C22#1684044411yescharacteristic
611C22#1684046611yescharacteristic
612C4—42no—
613C4—41no—
614C4—41no—
615C4—41no—
616C4—41no—
617C4—1222no—
618C4—1221no—
619C4—1221no—
620C4—1221no—
621C4—1221no—
622C4—4881no—
623C4—2441no—
624C4—2441no—
625C4C4×Q8×D6111yescharacteristic
626C4#1684024311yescharacteristic
627C4#1684040111yescharacteristic
628C4#1684042711yescharacteristic
629C2—21no—
630C2—21no—
631C2—2442no—
632C2#2144882111yescharacteristic
633C2#2145471711yescharacteristic
634C2#2145473111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D61
commutatorC2×C4×C61C23×C4
FrattiniC22×C4C23×D61
FittingC61×#1945C2
socleC22×C61C2×C4×D4
prime radicalC2×#11758222C23
cosocleC22×C4×C61C24
hypercenter#1945D61
hypocenterC61#22984
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1945

Complements

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

NH ≅ G/Ntype
2. #21454765C2semidirect
4. #21446798C2semidirect
5. #21446591C2semidirect
6. #21446571C2semidirect
7. #21446420C2semidirect
8. #21446415C2semidirect
11. #21445677C2semidirect
15. C61×#1945C2semidirect
20. #16840072C4semidirect
21. #16840068C4semidirect
22. #16840065C4semidirect
23. #16840061C4semidirect
24. #16840056C4semidirect
25. #16840051C4semidirect
26. #16840046C4semidirect
27. #16840041C4semidirect
118. #14519705Q8semidirect
318. #1945D61semidirect
384. C61#22984semidirect

Maximal subgroups

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

subgroupindex
#214556052
#214547652
#214543862
#214467982
#214465912
#214465712
#214464202
#214464152
#214460932
#214460912
#214456772
#214456602
#214456562
#214456282
C61×#19452
#2298461