Finite Group Databasebeta

← #30613629

Subgroups — #30613629

Order 15616.

652 conjugacy classes of subgroups.

The subgroup lattice has 510 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462746C211yesmaximal, characteristic, complemented
2#21462745C211yesmaximal, characteristic, complemented
3#21461464C212yesmaximal, complemented
4#21461425C212yesmaximal, complemented
5#21461422C212yesmaximal, complemented
6#21461416C212yesmaximal, complemented
7#21461373C211yesmaximal, characteristic, complemented
8#21461156C211yesmaximal, characteristic, complemented
9#21461154C211yesmaximal, characteristic, complemented
10#21461028C211yesmaximal, characteristic, complemented
11#21454587C211yesmaximal, characteristic
12#16840813C2212yes—
13#16840812C2212yes—
14#16840794—22no—
15#16840793—22no—
16#16840790C2212yes—
17D4×#92420C2212yes—
18#16840785—21no—
19#16840782—21no—
20#16840779C2211yescharacteristic
21#16840765C2211yescharacteristic
22#16840765C2211yescharacteristic
23C2×#14519844—21no—
24D61⋊(C4⋊C8)—21no—
25C4×#11758217C2211yescharacteristic
26#16840624C2212yes—
27#16840623C2212yes—
28#16840612C2212yes—
29Q8⋊#92420C2212yes—
30#16840610C2212yes—
31D4⋊#92420C2212yes—
32#92420⋊C8C2212yes—
33#16840603C2212yes—
34C2×#14519797C411yescharacteristic
35#41×Dic61C2211yescharacteristic
36#16840230C2211yescharacteristic
37#16839854C411yescharacteristic
38#16839854C2211yescharacteristic
39#16839853C411yescharacteristic
40#16839853C2211yescharacteristic
41#16839847C411yescharacteristic
42#16839847C2211yescharacteristic
43#16839842C411yescharacteristic
44#16839842C2211yescharacteristic
45#16839798C411yescharacteristic
46#16839759C411yescharacteristic
47C2×C8×Dic61C2211yescharacteristic
48C61×#416C411yescharacteristic
49C2×#11758217—21no—
50C2×#11758217—21no—
51C2×#11758217—21no—
52C2×D61⋊C8—22no—
53C22×#92420—22no—
54#14519844—22no—
55#14519844—21no—
56#14519844—21no—
57#14519844D411yescharacteristic
58#14519844D411yescharacteristic
59C4⋊#92420—22no—
60C4⋊#92420C2312yes—
61C4⋊#92420C2312yes—
62#14519834—22no—
63C22⋊#92420—22no—
64C22⋊#92420D412yes—
65#14519832—22no—
66#14519832—22no—
67#14519832—21no—
68C4×#92420C2312yes—
69C4×#92420C2312yes—
70C2×#11758222C2×C411yescharacteristic
71#14519797—24no—
72C2×#11758202C2×C411yescharacteristic
73C2×#11758200C2×C411yescharacteristic
74C2×#11758201C2×C411yescharacteristic
75C2×#11758199C2×C411yescharacteristic
76C22×#92418C2×C411yescharacteristic
77Q8×Dic61C2×C411yescharacteristic
78Q8×Dic61C2311yescharacteristic
79#14519742C2×C411yescharacteristic
80#14519742C2311yescharacteristic
81D4×Dic61—21no—
82D4×Dic61—21no—
83D4×Dic61C2×C411yescharacteristic
84D4×Dic61C2311yescharacteristic
85#14519739C2×C411yescharacteristic
86#14519739C2311yescharacteristic
87#14519737—21no—
88#14519737—21no—
89#14519736—21no—
90#14519736C2×C411yescharacteristic
91#14519734—21no—
92C2×C4×Dic61—21no—
93C2×C4×Dic61C2311yescharacteristic
94C42×D61—21no—
95#14519710C2×C411yescharacteristic
96#14519710C2×C411yescharacteristic
97#14519708C2×C411yescharacteristic
98#14519708C2×C411yescharacteristic
99#14519702C2×C411yescharacteristic
100#14519702C2×C411yescharacteristic
101#14519699C2×C411yescharacteristic
102#14519699C2×C411yescharacteristic
103C8×Dic61C2×C411yescharacteristic
104C8×Dic61C2×C411yescharacteristic
105C8×Dic61C2311yescharacteristic
106C8×Dic61C2311yescharacteristic
107C2×#41×C61C2×C411yescharacteristic
108C22×C8×C61C2×C411yescharacteristic
109#117×C61C2×C411yescharacteristic
110#103×C61C2×C411yescharacteristic
111#103×C61C2×C411yescharacteristic
112#102×C61C2×C411yescharacteristic
113#102×C61C2×C411yescharacteristic
114#41×C61—22no—
115#41×C61—41no—
116C2×Q8×C61C22×C411yescharacteristic
117C2×D4×C61—21no—
118C2×D4×C61C22×C411yescharacteristic
119C22×C4×C61—21no—
120C22×C4×C61C22×C411yescharacteristic
121C2×C22⋊D61—21no—
122C22×Dic61—21no—
123C22×Dic61—21no—
124C22×Dic61C2×D411yescharacteristic
125C22×Dic61#4111yescharacteristic
126#11758222—22no—
127#11758222—41no—
128C2×D244C22×C411yescharacteristic
129C2×C4×D61—21no—
130C2×C4×D61—21no—
131C2×C4×D61—21no—
132C2×Dic122C22×C411yescharacteristic
133#11758217—42no—
134#11758217—81no—
135#11758217—81no—
136C2×#92420—22no—
137C2×#92420—22no—
138C2×#92420—22no—
139C2×#92420—82no—
140C2×#92420C2×D412yes—
141C2×#92420C2×D412yes—
142D61⋊C8—82no—
143C2×C8×C61—41no—
144C2×C8×C61C22×C411yescharacteristic
145C2×C8×C61C22×C411yescharacteristic
146C4⋊C4×C61C22×C411yescharacteristic
147C4⋊C4×C61C22×C411yescharacteristic
148C22⋊C4×C61—21no—
149C42×C61—21no—
150C22⋊Dic61—21no—
151C22⋊Dic61—21no—
152C22⋊Dic61—21no—
153#11758202—22no—
154#11758201—22no—
155#11758200—22no—
156#11758199M1614yescomplemented
157#11758198—21no—
158#11758198—21no—
159C4⋊Dic61—21no—
160C4⋊Dic61—21no—
161C4⋊Dic61C22×C411yescharacteristic
162C4⋊Dic61C22×C411yescharacteristic
163#11758196—21no—
164#11758196—21no—
165C4×Dic61—21no—
166C4×Dic61—21no—
167C4×Dic61—21no—
168C4×Dic61—21no—
169C4×Dic61—21no—
170C4×Dic61C22×C411yescharacteristic
171C4×Dic61C2×D411yescharacteristic
172C4×Dic61#4111yescharacteristic
173C4×Dic61C2411yescharacteristic
174C2×#92418—22no—
175C2×#92418C22×C411yescharacteristic
176C2×#92418C22×C411yescharacteristic
177C23×C61—21no—
178C23×C61C4×D411yescharacteristic
179C22×D61—21no—
180Q8×C61—21no—
181Q8×C61—21no—
182D4×C61—21no—
183D4×C61—42no—
184D4×C61C2×M1612yes—
185C2×C4×C61—21no—
186C2×C4×C61—21no—
187C2×C4×C61—21no—
188C2×C4×C61—21no—
189C2×C4×C61—21no—
190C2×C4×C61—42no—
191C2×C4×C61C4×D411yescharacteristic
192C2×C4×C61C23×C411yescharacteristic
193C22⋊D61—42no—
194C2×Dic61—21no—
195C2×Dic61—21no—
196C2×Dic61—22no—
197C2×Dic61—21no—
198C2×Dic61—21no—
199C2×Dic61—21no—
200C2×Dic61—41no—
201C2×Dic61—41no—
202C2×Dic61—42no—
203C2×Dic61C4×D411yescharacteristic
204C2×Dic61C4×D411yescharacteristic
205C2×Dic61C22×D411yescharacteristic
206C2×Dic61C2×#4111yescharacteristic
207D244—21no—
208D244C2×M1612yes—
209C4×D61—42no—
210C4×D61—41no—
211C4×D61—41no—
212C4×D61—42no—
213Dic122—21no—
214Dic122—21no—
215#92420—22no—
216#92420—22no—
217#92420—42no—
218#92420—42no—
219#92420—42no—
220C8×C61—21no—
221C8×C61—21no—
222#92418—21no—
223#92418C2×M1612yes—
224#18065—611nomaximal, Sylow
225C22×C61—21no—
226C22×C61—22no—
227C22×C61—21no—
228C22×C61—21no—
229C22×C61—41no—
230C22×C61—41no—
231C22×C61C2×C4×D411yescharacteristic
232C2×D61—22no—
233C2×D61—41no—
234C2×D61—41no—
235C4×C61—21no—
236C4×C61—41no—
237C4×C61—41no—
238C4×C61—41no—
239C4×C61C22×M1611yescharacteristic
240C4×C61#56811yescharacteristic
241Dic61—21no—
242Dic61—21no—
243Dic61—41no—
244Dic61—41no—
245Dic61—41no—
246Dic61#44412yes—
247Dic61#57711yescharacteristic
248Dic61#57711yescharacteristic
249#2990—611no—
250#2990—611no—
251C4×#135—611no—
252#1593—612no—
253#1582—612no—
254#1582—612no—
255#1580—612no—
256#1566—611no—
257#1489—611no—
258#1489—611no—
259#1451—611no—
260C2×C61—41no—
261C2×C61—42no—
262C2×C61D4×M1611yescharacteristic
263C2×C61#295211yescharacteristic
264C2×C61C2×#44411yescharacteristic
265D61—42no—
266C2×#135—611no—
267C4×#41—611no—
268C4×#41—611no—
269#446—612no—
270#446—612no—
271C4×Q16—611no—
272C4×Q16—611no—
273C4×SD16—611no—
274C4×SD16—611no—
275C4×SD16—611no—
276C4×SD16—611no—
277C4×D8—611no—
278C4×D8—611no—
279#435—1222no—
280#435—1222no—
281C8×D4—612no—
282C8×D4—612no—
283#432—1221no—
284#432—1221no—
285#431—611no—
286#427—611no—
287#423—611no—
288#423—611no—
289C2×C4⋊C8—1221no—
290C2×C4⋊C8—1221no—
291#416—611no—
292#416#692311yescharacteristic
293C4×M16—611no—
294C2×C4×C8—611no—
295#334—612no—
296#334—612no—
297Q8⋊C8—612no—
298Q8⋊C8—612no—
299D4⋊C8—612no—
300D4⋊C8—612no—
301#322—612no—
302#322—612no—
303C61#1806511yescharacteristic, complemented, Sylow
304C2×#41—611no—
305C2×#41C2×#692311yescharacteristic
306#135—1224no—
307C2×Q16—611no—
308C2×SD16—611no—
309C2×SD16—611no—
310C2×D8—611no—
311C2×M16—1221no—
312C2×M16—1221no—
313C2×M16—1221no—
314C22×C8—611no—
315C22×C8—1222no—
316C22×C8—1222no—
317C22×C8C2×#692311yescharacteristic
318C4×Q8—611no—
319C4×Q8—611no—
320C4×Q8—611no—
321C4×Q8—611no—
322C4×D4—611no—
323C4×D4—611no—
324C4×D4—611no—
325C4×D4—611no—
326C4×D4—1221no—
327C4×D4—1221no—
328C4×D4—1221no—
329C4×D4—1221no—
330#117—611no—
331#117—1221no—
332#117—1221no—
333#117C2×#692311yescharacteristic
334C2×C42—611no—
335C2×C42—1221no—
336C2×C42—1221no—
337#107—611no—
338#107—611no—
339#106—611no—
340#106—611no—
341C4⋊C8—611no—
342C4⋊C8—611no—
343C4⋊C8—612no—
344C4⋊C8—612no—
345C4⋊C8—1221no—
346C4⋊C8—1221no—
347C4⋊C8—1222no—
348C4⋊C8—1222no—
349#103—611no—
350#103—611no—
351#103C2×#692311yescharacteristic
352#103C2×#692311yescharacteristic
353#102—611no—
354#102—611no—
355#102C2×#692311yescharacteristic
356#102C2×#692311yescharacteristic
357C22⋊C8—612no—
358C22⋊C8—1222no—
359C22⋊C8—1222no—
360#97—1221no—
361#97—1222no—
362#97—1222no—
363C4×C8—612no—
364C4×C8—611no—
365C4×C8—611no—
366C4×C8—611no—
367C4×C8—611no—
368C4×C8—612no—
369#41—22no—
370#41—41no—
371#41—1222no—
372#41—2441no—
373C2×Q8—611no—
374C2×Q8C22×#692311yescharacteristic
375C2×D4—21no—
376C2×D4—611no—
377C2×D4—1221no—
378C2×D4C22×#692311yescharacteristic
379C22×C4—21no—
380C22×C4—611no—
381C22×C4—611no—
382C22×C4—1221no—
383C22×C4—1221no—
384C22×C4—1221no—
385C22×C4—1221no—
386C22×C4—1221no—
387C22×C4C22×#692311yescharacteristic
388Q16—1222no—
389SD16—1222no—
390SD16—1222no—
391D8—614no—
392M16—4881no—
393M16—4881no—
394M16—2442no—
395C2×C8—41no—
396C2×C8—611no—
397C2×C8—612no—
398C2×C8—612no—
399C2×C8—611no—
400C2×C8—1222no—
401C2×C8—1222no—
402C2×C8—1222no—
403C2×C8—1222no—
404C2×C8—4882no—
405C2×C8—4882no—
406C2×C8C22×#692311yescharacteristic
407C2×C8C22×#692311yescharacteristic
408C4⋊C4—611no—
409C4⋊C4—611no—
410C4⋊C4—1221no—
411C4⋊C4—1221no—
412C4⋊C4—1221no—
413C4⋊C4—1221no—
414C4⋊C4C22×#692311yescharacteristic
415C4⋊C4C22×#692311yescharacteristic
416C22⋊C4—21no—
417C22⋊C4—1221no—
418C22⋊C4—1221no—
419C22⋊C4—1221no—
420C22⋊C4—1221no—
421C22⋊C4—1221no—
422C42—21no—
423C42—611no—
424C42—611no—
425C42—611no—
426C42—611no—
427C42—1221no—
428C42—1221no—
429C42—1221no—
430C42—1221no—
431C42—1221no—
432C23—21no—
433C23—1221no—
434C23D4×#692311yescharacteristic
435Q8—21no—
436Q8—21no—
437Q8—1221no—
438Q8—1221no—
439D4—21no—
440D4—42no—
441D4—612no—
442D4—1221no—
443D4—2442no—
444D4D61⋊M1612yes—
445C2×C4—21no—
446C2×C4—21no—
447C2×C4—21no—
448C2×C4—21no—
449C2×C4—21no—
450C2×C4—42no—
451C2×C4—611no—
452C2×C4—611no—
453C2×C4—611no—
454C2×C4—611no—
455C2×C4—1221no—
456C2×C4—1221no—
457C2×C4—1222no—
458C2×C4—1221no—
459C2×C4—1221no—
460C2×C4—1221no—
461C2×C4—2442no—
462C2×C4—2441no—
463C2×C4—2441no—
464C2×C4—2442no—
465C2×C4—2441no—
466C2×C4—2441no—
467C2×C4—2442no—
468C2×C4D4×#692311yescharacteristic
469C2×C4C23×#692311yescharacteristic
470C8—21no—
471C8—21no—
472C8—612no—
473C8—1222no—
474C8—1222no—
475C8—1221no—
476C8—2442no—
477C8—2442no—
478C8—2442no—
479C22—21no—
480C22—22no—
481C22—21no—
482C22—21no—
483C22—41no—
484C22—41no—
485C22—1222no—
486C22—2441no—
487C22—2441no—
488C22C2×D4×#692311yescharacteristic
489C4—21no—
490C4—41no—
491C4—41no—
492C4—41no—
493C4—611no—
494C4—611no—
495C4—612no—
496C4—1221no—
497C4—1221no—
498C4—2441no—
499C4—2441no—
500C4—2441no—
501C4C2×D61⋊M1611yescharacteristic
502C4#1684084011yescharacteristic
503C2—41no—
504C2—42no—
505C2—2442no—
506C2#2146255711yescharacteristic
507C2#2146258211yescharacteristic
508C2D61⋊#44411yescharacteristic
subgroupG/H
centerC22C2×D4×#6923
commutatorC2×C4×C61C23×C4
FrattiniC2×C4C23×#6923
FittingC61×#416C4
socleC22×C61C2×C4×D4
prime radicalC2×#14519797C4
cosocleC4×Dic61C24
hypercenter#416#6923
hypocenterC61#18065
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
1. #21462746C2semidirect
2. #21462745C2semidirect
3. #21461464C2semidirect
4. #21461425C2semidirect
5. #21461422C2semidirect
6. #21461416C2semidirect
7. #21461373C2semidirect
8. #21461156C2semidirect
9. #21461154C2semidirect
10. #21461028C2semidirect
156. #11758199M16semidirect
303. C61#18065semidirect

Maximal subgroups

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

subgroupindex
#214627462
#214627452
#214614642
#214614252
#214614222
#214614162
#214613732
#214611562
#214611542
#214610282
#214545872
#1806561