Finite Group Databasebeta

← #29677102

Subgroups — #29677102

Order 15616.

590 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21458537C211yesmaximal, characteristic
2#21458533C211yesmaximal, characteristic
3#21458104C211yesmaximal, characteristic, complemented
4#21445427C211yesmaximal, characteristic, complemented
5#21445375C211yesmaximal, characteristic, complemented
6#21445371C211yesmaximal, characteristic, complemented
7#21445366C211yesmaximal, characteristic, complemented
8#21445363C211yesmaximal, characteristic, complemented
9#21445075C211yesmaximal, characteristic, complemented
10#21445074C211yesmaximal, characteristic, complemented
11#21445068C211yesmaximal, characteristic, complemented
12#21445066C211yesmaximal, characteristic, complemented
13#21444716C211yesmaximal, characteristic, complemented
14#21444702C211yesmaximal, characteristic
15C61×#3328C211yesmaximal, characteristic, complemented
16#16840485C2211yescharacteristic
17Q8×D244C2211yescharacteristic
18#16840165C2211yescharacteristic
19#16840165C2211yescharacteristic
20#16840124—21no—
21#16840121—21no—
22#16840114C2211yescharacteristic
23#16840113C2211yescharacteristic
24#16840112C2211yescharacteristic
25#16840105—21no—
26#16840057—21no—
27#16840054—21no—
28#16840047C2211yescharacteristic
29#16840042C2211yescharacteristic
30#16840039C2211yescharacteristic
31#16840019—21no—
32#16839977—21no—
33#16839974—21no—
34#16839972C2211yescharacteristic
35#16839967C2211yescharacteristic
36#16839964C2211yescharacteristic
37#16839916—21no—
38#16839893C2211yescharacteristic
39#16839893C2211yescharacteristic
40#16839862—21no—
41#16839860—21no—
42C4×#11758199C2211yescharacteristic
43#16839841C2211yescharacteristic
44#16839769—21no—
45#16839515C2211yescharacteristic
46#16839514C2211yescharacteristic
47#16839509C2211yescharacteristic
48#16839508C2211yescharacteristic
49#16839508C2211yescharacteristic
50#16839507C2211yescharacteristic
51Q8⋊#92418C2211yescharacteristic
52Q8⋊#92418C2211yescharacteristic
53D4⋊#92418C2211yescharacteristic
54#16839489C2211yescharacteristic
55C8×#92418C2211yescharacteristic
56C61×#556C2211yescharacteristic
57D4×Q8×C61C2211yescharacteristic
58C61×#487C2211yescharacteristic
59C61×#485—21no—
60C61×#475C2211yescharacteristic
61C61×#470—21no—
62C61×#462C2211yescharacteristic
63C61×#451—21no—
64C4×Q16×C61C2211yescharacteristic
65C61×#436C2211yescharacteristic
66C61×#419—21no—
67C2×Q8×D61—21no—
68C2×#11758202—21no—
69C2×#11758200—21no—
70C2×#11758201—21no—
71C2×#11758199D411yescharacteristic
72C2×#11758189—21no—
73#14519777—21no—
74#14519777C2311yescharacteristic
75#14519777C2311yescharacteristic
76#14519772—41no—
77#14519765—21no—
78#14519757—21no—
79#14519757—41no—
80#14519753—21no—
81C4×Dic122—21no—
82C4×D244—21no—
83C4×D244C2311yescharacteristic
84#14519735—21no—
85#14519710—21no—
86#14519710—21no—
87#14519710—41no—
88#14519710—41no—
89#14519710D411yescharacteristic
90#14519708—21no—
91C4⋊#92418—21no—
92C4⋊#92418—21no—
93C4⋊#92418C2311yescharacteristic
94C4⋊#92418C2311yescharacteristic
95C4⋊#92418C2311yescharacteristic
96#14519702—21no—
97#14519702—21no—
98#14519701—21no—
99#14519701—21no—
100#14519701—21no—
101#14519701—21no—
102#14519700—21no—
103#14519700—21no—
104#14519700—21no—
105#14519700—21no—
106#14519698—21no—
107#14519698D411yescharacteristic
108#14519697—21no—
109#14519697D411yescharacteristic
110#14519689—21no—
111#14519688—21no—
112#14519688—21no—
113C4×#92418C2311yescharacteristic
114C4×#92418C2311yescharacteristic
115C22×Q8×C61—21no—
116C2×Q16×C61—21no—
117C2×Q16×C61D411yescharacteristic
118C2×M16×C61—21no—
119C4⋊Q8×C61—21no—
120C4⋊Q8×C61C2311yescharacteristic
121C4⋊Q8×C61C2311yescharacteristic
122#126×C61—41no—
123#124×C61—21no—
124C22⋊Q8×C61—21no—
125C22⋊Q8×C61—21no—
126C22⋊Q8×C61—41no—
127C4×Q8×C61—21no—
128C4×Q8×C61C2311yescharacteristic
129C4×Q8×C61C2311yescharacteristic
130C4×D4×C61—21no—
131C4×D4×C61C2311yescharacteristic
132#117×C61—21no—
133#107×C61D411yescharacteristic
134#106×C61—21no—
135C4⋊C8×C61C2311yescharacteristic
136#103×C61—21no—
137#103×C61—21no—
138#103×C61—21no—
139#103×C61—21no—
140#103×C61D411yescharacteristic
141#103×C61D411yescharacteristic
142C22⋊C8×C61—21no—
143C4×C8×C61C2311yescharacteristic
144C2×Q8×C61—21no—
145C2×Q8×C61—21no—
146C2×Q8×C61—41no—
147C2×Q8×C61—42no—
148C2×Q8×C61—81no—
149C2×Q8×C61C2×D411yescharacteristic
150C2×Q8×C61C2×D411yescharacteristic
151C2×D4×C61C2×D411yescharacteristic
152C22×C4×C61—21no—
153C22×C4×C61—41no—
154Q8×D61—42no—
155Q8×D61—81no—
156C2×D244C2×D411yescharacteristic
157C2×C4×D61—21no—
158C2×C4×D61—41no—
159C2×Dic122—21no—
160C2×Dic122—21no—
161C2×Dic122—41no—
162Q16×C61—41no—
163Q16×C61—81no—
164M16×C61—81no—
165C2×C8×C61—21no—
166C2×C8×C61C2×D411yescharacteristic
167C2×C8×C61C2×D411yescharacteristic
168C4⋊C4×C61—21no—
169C4⋊C4×C61—21no—
170C4⋊C4×C61—21no—
171C4⋊C4×C61—21no—
172C4⋊C4×C61—21no—
173C4⋊C4×C61—21no—
174C4⋊C4×C61—41no—
175C4⋊C4×C61—41no—
176C4⋊C4×C61C2×D411yescharacteristic
177C4⋊C4×C61C2×D411yescharacteristic
178C4⋊C4×C61C2×D411yescharacteristic
179C22⋊C4×C61—21no—
180C22⋊C4×C61—41no—
181C22⋊C4×C61—41no—
182C22⋊C4×C61—41no—
183C42×C61—21no—
184C42×C61—21no—
185C42×C61—41no—
186C42×C61C2411yescharacteristic
187#11758202—81no—
188#11758201—42no—
189#11758200—42no—
190#11758199—41no—
191#11758198—21no—
192#11758198—41no—
193#11758198—41no—
194#11758198—41no—
195C4⋊Dic61—21no—
196C4⋊Dic61—21no—
197C4⋊Dic61—21no—
198C4⋊Dic61—21no—
199C4⋊Dic61—41no—
200C4⋊Dic61C2×D411yescharacteristic
201#11758196—41no—
202C4×Dic61—41no—
203C2×#92418—21no—
204C2×#92418—21no—
205C2×#92418—21no—
206C2×#92418—21no—
207C2×#92418C2×D411yescharacteristic
208C2×#92418C2×D411yescharacteristic
209#11758189—81no—
210C23×C61—21no—
211C22×D61—21no—
212Q8×C61—21no—
213Q8×C61—21no—
214Q8×C61—21no—
215Q8×C61—21no—
216Q8×C61—41no—
217Q8×C61—41no—
218Q8×C61—41no—
219Q8×C61—41no—
220Q8×C61—82no—
221D4×C61—21no—
222D4×C61—21no—
223C2×C4×C61—21no—
224C2×C4×C61—21no—
225C2×C4×C61—21no—
226C2×C4×C61—21no—
227C2×C4×C61—21no—
228C2×C4×C61—41no—
229C2×C4×C61—41no—
230C2×C4×C61—41no—
231C2×C4×C61—41no—
232C2×C4×C61—82no—
233C2×C4×C61C22×D411yescharacteristic
234C2×C4×C61C22×D411yescharacteristic
235C2×C4×C61H(5,𝔽2)11yescharacteristic
236C2×Dic61—21no—
237C2×Dic61—41no—
238C2×Dic61—41no—
239D244—21no—
240D244—21no—
241C4×D61—41no—
242C4×D61—41no—
243C4×D61—82no—
244Dic122—41no—
245Dic122—41no—
246Dic122—41no—
247Dic122—41no—
248Dic122—82no—
249C8×C61—21no—
250C8×C61—21no—
251C8×C61—41no—
252#92418—22no—
253#92418—21no—
254#92418—21no—
255#92418—41no—
256#92418—41no—
257#92418—41no—
258#20306—611nomaximal, Sylow
259C22×C61—41no—
260C22×C61—41no—
261C22×C61—41no—
262C22×C61D4211yescharacteristic
263C2×D61—41no—
264C2×D61—41no—
265C2×D61—41no—
266C4×C61—21no—
267C4×C61—41no—
268C4×C61—41no—
269C4×C61—41no—
270C4×C61—41no—
271C4×C61—41no—
272C4×C61—81no—
273C4×C61—81no—
274C4×C61#57511yescharacteristic
275C4×C61#57511yescharacteristic
276C4×C61#57611yescharacteristic
277C4×C61#57811yescharacteristic
278Dic61—41no—
279Dic61—81no—
280Dic61—81no—
281#3367—611no—
282#3367—611no—
283#3328—611no—
284#3328D6111yescharacteristic, complemented
285#1710—611no—
286#1700—611no—
287#1700—611no—
288#1699—611no—
289#1699—611no—
290#1650—611no—
291#1650—611no—
292#1649—611no—
293#1649—611no—
294#1591—611no—
295#1589—611no—
296C2×C61—81no—
297C2×C61#327311yescharacteristic
298C2×C61#327711yescharacteristic
299C2×C61#329311yescharacteristic
300D61—81no—
301#556—611no—
302#556C2×D6111yescharacteristic
303D4×Q8—611no—
304D4×Q8C2×D6111yescharacteristic
305#500—611no—
306#500—611no—
307#489—1221no—
308#489—1221no—
309#487—611no—
310#487—611no—
311#487—611no—
312#487C2×D6111yescharacteristic
313#485—21no—
314#485—1221no—
315#477—1221no—
316#477—1221no—
317#475—611no—
318#475C2×D6111yescharacteristic
319#474—611no—
320#474—611no—
321#470—21no—
322#470—1221no—
323#463—1221no—
324#463—1221no—
325#462—611no—
326#462C2×D6111yescharacteristic
327#461—611no—
328#461—611no—
329#451—21no—
330#451—1221no—
331#446—611no—
332#446—611no—
333#440—1221no—
334#440—1221no—
335C4×Q16C2×D6111yescharacteristic
336C4×D8—611no—
337#436—611no—
338#436C2×D6111yescharacteristic
339#419—21no—
340#419—1221no—
341#335—611no—
342#335—611no—
343#332—611no—
344#332—611no—
345#332—611no—
346#332—611no—
347Q8⋊C8—611no—
348Q8⋊C8—611no—
349D4⋊C8—611no—
350D4⋊C8—611no—
351C82—611no—
352C61#2030611yescharacteristic, complemented, Sylow
353C22×Q8—21no—
354C22×Q8—1221no—
355C2×Q16—21no—
356C2×Q16—1221no—
357C2×Q16C22⋊D6111yescharacteristic
358C2×SD16—1221no—
359C2×SD16—1221no—
360C2×D8—611no—
361C2×M16—21no—
362C2×M16—1221no—
363C4⋊Q8—21no—
364C4⋊Q8—611no—
365C4⋊Q8—611no—
366C4⋊Q8—1221no—
367C4⋊Q8C22×D6111yescharacteristic
368C4⋊Q8C22×D6111yescharacteristic
369#126—41no—
370#126—2441no—
371#124—21no—
372#124—1221no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376C22⋊Q8—1221no—
377C22⋊Q8—1221no—
378C22⋊Q8—2441no—
379C4×Q8—21no—
380C4×Q8—1221no—
381C4×Q8C22×D6111yescharacteristic
382C4×Q8C22×D6111yescharacteristic
383C4×D4—21no—
384C4×D4—611no—
385C4×D4—1221no—
386C4×D4C22×D6111yescharacteristic
387#117—21no—
388#117—1221no—
389#107—611no—
390#107—1221no—
391#107—1221no—
392#107—2441no—
393#107—2441no—
394#107C22⋊D6111yescharacteristic
395#106—21no—
396#106—1221no—
397C4⋊C8—611no—
398C4⋊C8—611no—
399C4⋊C8—611no—
400C4⋊C8—1221no—
401C4⋊C8—1221no—
402C4⋊C8C22×D6111yescharacteristic
403#103—21no—
404#103—21no—
405#103—21no—
406#103—21no—
407#103—1221no—
408#103—1221no—
409#103—1221no—
410#103—1221no—
411#103—1221no—
412#103—1221no—
413#103—1221no—
414#103—1221no—
415#103—1221no—
416#103—1221no—
417#103C22⋊D6111yescharacteristic
418#103C22⋊D6111yescharacteristic
419#102—611no—
420#102—611no—
421#102—1221no—
422#102—1221no—
423C22⋊C8—21no—
424C22⋊C8—1221no—
425#97—1221no—
426#97—1221no—
427C4×C8—611no—
428C4×C8—611no—
429C4×C8C22×D6111yescharacteristic
430C2×Q8—21no—
431C2×Q8—21no—
432C2×Q8—41no—
433C2×Q8—42no—
434C2×Q8—81no—
435C2×Q8—1221no—
436C2×Q8—1221no—
437C2×Q8—4881no—
438C2×Q8—2441no—
439C2×Q8—2442no—
440C2×Q8C2×C22⋊D6111yescharacteristic
441C2×Q8C2×C22⋊D6111yescharacteristic
442C2×D4—611no—
443C2×D4D4×D6111yescharacteristic
444C22×C4—21no—
445C22×C4—41no—
446C22×C4—1221no—
447C22×C4—2441no—
448Q16—41no—
449Q16—81no—
450Q16—4881no—
451SD16—2442no—
452SD16—2442no—
453D8—2441no—
454M16—81no—
455M16—4881no—
456C2×C8—21no—
457C2×C8—611no—
458C2×C8—611no—
459C2×C8—1221no—
460C2×C8—1221no—
461C2×C8—1221no—
462C2×C8—1221no—
463C2×C8C2×C22⋊D6111yescharacteristic
464C2×C8C2×C22⋊D6111yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—41no—
472C4⋊C4—41no—
473C4⋊C4—611no—
474C4⋊C4—1221no—
475C4⋊C4—1221no—
476C4⋊C4—1221no—
477C4⋊C4—1221no—
478C4⋊C4—2441no—
479C4⋊C4—2441no—
480C4⋊C4D4×D6111yescharacteristic
481C4⋊C4C2×C22⋊D6111yescharacteristic
482C4⋊C4C2×C22⋊D6111yescharacteristic
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—1221no—
488C22⋊C4—2441no—
489C22⋊C4—2441no—
490C22⋊C4—2441no—
491C42—21no—
492C42—21no—
493C42—41no—
494C42—2441no—
495C42C23×D6111yescharacteristic
496C23—21no—
497C23—1221no—
498Q8—21no—
499Q8—21no—
500Q8—21no—
501Q8—21no—
502Q8—41no—
503Q8—41no—
504Q8—41no—
505Q8—41no—
506Q8—82no—
507Q8—4882no—
508Q8—2441no—
509Q8—2441no—
510Q8—2441no—
511Q8—2441no—
512D4—21no—
513D4—21no—
514D4—1221no—
515D4—1221no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—82no—
526C2×C4—1221no—
527C2×C4—4882no—
528C2×C4—2441no—
529C2×C4—2441no—
530C2×C4—2441no—
531C2×C4—2441no—
532C2×C4C2×D4×D6111yescharacteristic
533C2×C4C22×C22⋊D6111yescharacteristic
534C2×C4#1451982211yescharacteristic
535C8—21no—
536C8—21no—
537C8—41no—
538C8—1222no—
539C8—1221no—
540C8—1221no—
541C8—2441no—
542C8—2441no—
543C8—2441no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—2441no—
548C22—2441no—
549C22—2441no—
550C22D4×C22⋊D6111yescharacteristic
551C4—21no—
552C4—41no—
553C4—41no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—81no—
558C4—81no—
559C4—4881no—
560C4—4881no—
561C4—2441no—
562C4#1684056011yescharacteristic
563C4#1684056111yescharacteristic
564C4#1684056511yescharacteristic
565C4#1684057811yescharacteristic
566C2—81no—
567C2—4881no—
568C2#2145742611yescharacteristic
569C2#2145747011yescharacteristic
570C2#2145762111yescharacteristic
subgroupG/H
centerC22D4×C22⋊D61
commutator, cosocleC42×C61C24
FrattiniC42C23×D61
FittingC61×#3328C2
socleC22×C61D42
prime radicalC2×#11758199D4
hypercenter#3328D61
hypocenterC61#20306
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #3328

Complements

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

NH ≅ G/Ntype
3. #21458104C2semidirect
4. #21445427C2semidirect
5. #21445375C2semidirect
6. #21445371C2semidirect
7. #21445366C2semidirect
8. #21445363C2semidirect
9. #21445075C2semidirect
10. #21445074C2semidirect
11. #21445068C2semidirect
12. #21445066C2semidirect
13. #21444716C2semidirect
15. C61×#3328C2semidirect
284. #3328D61semidirect
352. C61#20306semidirect

Maximal subgroups

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

subgroupindex
#214585372
#214585332
#214581042
#214454272
#214453752
#214453712
#214453662
#214453632
#214450752
#214450742
#214450682
#214450662
#214447162
#214447022
C61×#33282
#2030661