Finite Group Databasebeta

← #30608442

Subgroups — #30608442

Order 15616.

332 conjugacy classes of subgroups; only the 54 normal subgroups are shown.

normal subgroups only

This group has 332 conjugacy classes of subgroups — too many to draw. Only its 54 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21462119C211yesmaximal, characteristic
2#21462095C211yesmaximal, characteristic
3#21460967C211yesmaximal, characteristic, complemented
4#21460966C211yesmaximal, characteristic, complemented
5#21460948C211yesmaximal, characteristic, complemented
6#21460948C211yesmaximal, characteristic, complemented
7#21456884C211yesmaximal, characteristic
8#16840749—21no—
9D61⋊#99—21no—
10#16840671C2211yescharacteristic
11#16840671C2211yescharacteristic
12#16840670—21no—
13#16840669C2211yescharacteristic
14#16840669C2211yescharacteristic
15#16840666—21no—
16#16840373C411yescharacteristic, complemented
17#16840325C2211yescharacteristic
18#16840154C2211yescharacteristic
19#16840126C411yescharacteristic, complemented
20#16840117C2211yescharacteristic
21#16839982—21no—
22#16839960—21no—
23#16839921—21no—
24#16839911—21no—
25#16839821C411yescharacteristic, complemented
26C61×#492C411yescharacteristic, complemented
27C2×#11758217—41no—
28C2×C22⋊#6923—41no—
29#14519838—21no—
30#14519838—21no—
31#14519837—41no—
32#14519836—21no—
33#14519836—21no—
34#14519835—41no—
35C2×#11758224D411yescharacteristic
36C2×D4×D61D411yescharacteristic
37C2×#11758202—21no—
38C2×#11758201—21no—
39#14519773D411yescharacteristic
40#14519772—41no—
41#14519769C2×C411yescharacteristic, complemented
42#14519767—41no—
43#14519765C2311yescharacteristic
44#14519764D411yescharacteristic
45#14519753—21no—
46#14519749—41no—
47#14519745—41no—
48Q8×Dic61—21no—
49#14519734C2×C411yescharacteristic
50#14519706—21no—
51#14519702—21no—
52#14519699—21no—
53#14519698—21no—
54#14519698—21no—
55#14519689—21no—
56#14519688C2×C411yescharacteristic, complemented
57C2×SD16×C61—21no—
58C2×SD16×C61—21no—
59C4⋊Q8×C61C2×C411yescharacteristic, complemented
60#127×C61C2×C411yescharacteristic
61C4×C8×C61C2×C411yescharacteristic, complemented
62C23×D61—21no—
63C22×#6923—81no—
64C2×Q8×C61—21no—
65C2×D4×C61—41no—
66C2×D4×C61C22⋊C411yescharacteristic
67C2×D4×C61C22⋊C411yescharacteristic
68C2×C22⋊D61—21no—
69C2×C22⋊D61—21no—
70C2×C22⋊D61—41no—
71C22×Dic61—21no—
72#11758224—81no—
73D4×D61—81no—
74C2×D244C2×D411yescharacteristic
75C2×C4×D61C22⋊C411yescharacteristic
76C2×Dic122C2×D411yescharacteristic
77C22⋊#6923—41no—
78C22⋊#6923—41no—
79C22⋊#6923—81no—
80#11758217—41no—
81#11758217—41no—
82#11758217—81no—
83C2×#92420—81no—
84SD16×C61—81no—
85SD16×C61—81no—
86C2×C8×C61—21no—
87C4⋊C4×C61—41no—
88C42×C61C22×C411yescharacteristic
89C22⋊Dic61—41no—
90#11758202—81no—
91#11758201—81no—
92#11758198—21no—
93#11758198—41no—
94#11758198—41no—
95C4⋊Dic61—21no—
96C4⋊Dic61—41no—
97#11758196—21no—
98#11758196—41no—
99#11758196—41no—
100C4×Dic61—41no—
101C4×Dic61C22⋊C411yescharacteristic
102C2×#92418—21no—
103C23×C61—21no—
104C23×C61—21no—
105C22×D61—21no—
106C22×D61—41no—
107C22×D61—41no—
108C22×D61—161no—
109C22×D61#9911yescharacteristic
110C2×#6923—81no—
111C2×#6923—81no—
112C2×#6923—162no—
113Q8×C61—41no—
114Q8×C61—41no—
115D4×C61—41no—
116D4×C61—41no—
117D4×C61—161no—
118C2×C4×C61—21no—
119C2×C4×C61—41no—
120C2×C4×C61C2×C22⋊C411yescharacteristic
121C22⋊D61—81no—
122C22⋊D61—81no—
123C22⋊D61—161no—
124C2×Dic61—21no—
125C2×Dic61—21no—
126C2×Dic61—41no—
127C2×Dic61—41no—
128C2×Dic61—41no—
129C2×Dic61#9911yescharacteristic
130D244—41no—
131C4×D61—41no—
132Dic122—41no—
133#92420—81no—
134#92420—81no—
135C8×C61—41no—
136#92418—41no—
137#13607—611nomaximal, Sylow
138C22×C61—41no—
139C22×C61—41no—
140C22×C61—81no—
141C22×C61—81no—
142C22×C61C2×#9911yescharacteristic
143C2×D61—21no—
144C2×D61—41no—
145C2×D61—41no—
146C2×D61—82no—
147C2×D61—81no—
148C2×D61—161no—
149#6923—161no—
150#6923—161no—
151C4×C61—21no—
152C4×C61—41no—
153C4×C61—81no—
154Dic61—21no—
155Dic61—41no—
156Dic61—41no—
157Dic61—81no—
158#3222—611no—
159#2134—611no—
160#2127—611no—
161#1414—611no—
162#1414—611no—
163#1407—611no—
164#1407—611no—
165C2×C61—21no—
166C2×C61—81no—
167C2×C61—81no—
168C2×C61#212711yescharacteristic
169D61—41no—
170D61—81no—
171#541—611no—
172#535—611no—
173#497—611no—
174#492#692311yescharacteristic, complemented
175#490—611no—
176#488—611no—
177#464—1221no—
178#460—1221no—
179#452—1221no—
180#450—1221no—
181#433—611no—
182#413—1221no—
183C2×#99—1221no—
184#355—611no—
185#355—611no—
186#355—1221no—
187#354—611no—
188#354—611no—
189#353—1221no—
190C61#1360711yescharacteristic, complemented, Sylow
191C2×#41—611no—
192C22×D4—611no—
193C2×Q16—1221no—
194C2×SD16—21no—
195C2×SD16—21no—
196C2×SD16—1221no—
197C2×M16—2441no—
198C4⋊Q8C2×#692311yescharacteristic, complemented
199#127—611no—
200#127C2×#692311yescharacteristic
201#126—2441no—
202#125—611no—
203#125—2441no—
204#124—611no—
205#124—611no—
206C22⋊Q8—1221no—
207#121—2441no—
208#120—2441no—
209C4×Q8—1221no—
210#117—611no—
211C2×C22⋊C4—2441no—
212C4⋊C8—1221no—
213#103—1221no—
214#102—1221no—
215#102—1221no—
216#102—1221no—
217#101—1221no—
218#101—1221no—
219#100—2441no—
220#99—1221no—
221#99—1221no—
222#99—2441no—
223C22⋊C8—1221no—
224#97—611no—
225C4×C8C2×#692311yescharacteristic, complemented
226C24—1221no—
227#41—4881no—
228C2×Q8—21no—
229C2×Q8—611no—
230C2×D4—41no—
231C2×D4—611no—
232C2×D4—1221no—
233C2×D4—1221no—
234C2×D4—4881no—
235C2×D4—2441no—
236C2×D4C22⋊#692311yescharacteristic
237C2×D4C22⋊#692311yescharacteristic
238C22×C4—611no—
239C22×C4—1221no—
240C22×C4—4881no—
241Q16—4881no—
242SD16—81no—
243SD16—81no—
244SD16—4881no—
245M16—4881no—
246M16—2441no—
247M16—2441no—
248C2×C8—21no—
249C2×C8—1221no—
250C2×C8—4881no—
251C4⋊C4—41no—
252C4⋊C4—1221no—
253C4⋊C4—1221no—
254C4⋊C4—2441no—
255C4⋊C4—2441no—
256C4⋊C4—2441no—
257C22⋊C4—1221no—
258C22⋊C4—4881no—
259C22⋊C4—2441no—
260C22⋊C4—2441no—
261C22⋊C4—2441no—
262C22⋊C4—2441no—
263C22⋊C4—2441no—
264C42—611no—
265C42—2441no—
266C42C22×#692311yescharacteristic
267C23—21no—
268C23—21no—
269C23—611no—
270C23—1221no—
271C23—9761no—
272C23—2441no—
273C23—2441no—
274Q8—41no—
275Q8—41no—
276Q8—2441no—
277D4—41no—
278D4—41no—
279D4—161no—
280D4—9761no—
281D4—4881no—
282D4—4881no—
283D4—2441no—
284C2×C4—21no—
285C2×C4—41no—
286C2×C4—611no—
287C2×C4—1221no—
288C2×C4—1221no—
289C2×C4—9762no—
290C2×C4—4881no—
291C2×C4—4881no—
292C2×C4—2441no—
293C2×C4—2441no—
294C2×C4—2441no—
295C2×C4—2441no—
296C2×C4C2×C22⋊#692311yescharacteristic
297C8—41no—
298C8—4881no—
299C8—4881no—
300C8—2441no—
301C22—41no—
302C22—41no—
303C22—81no—
304C22—81no—
305C22—1221no—
306C22—9761no—
307C22—4881no—
308C22—4882no—
309C22—2441no—
310C22—2441no—
311C22D61⋊#9911yescharacteristic
312C4—21no—
313C4—41no—
314C4—81no—
315C4—1221no—
316C4—9761no—
317C4—9761no—
318C4—4881no—
319C4—2441no—
320C4—2441no—
321C2—21no—
322C2—81no—
323C2—81no—
324C2—4881no—
325C2—2441no—
326C2#2146209511yescharacteristic
subgroupG/H
centerC2#21462095
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#492C4
socleC2×C61#2127
prime radical#16840325C22
cosocle#14519765C23
hypercenter#492#6923
hypocenterC61#13607
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ #127 ◁ #492

Complements

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

NH ≅ G/Ntype
3. #21460967C2semidirect
4. #21460966C2semidirect
5. #21460948C2semidirect
6. #21460948C2semidirect
16. #16840373C4semidirect
19. #16840126C4semidirect
25. #16839821C4semidirect
26. C61×#492C4semidirect
41. #14519769C2×C4semidirect
56. #14519688C2×C4semidirect
59. C4⋊Q8×C61C2×C4semidirect
61. C4×C8×C61C2×C4semidirect
174. #492#6923semidirect
190. C61#13607semidirect
198. C4⋊Q8C2×#6923semidirect
225. C4×C8C2×#6923semidirect

Maximal subgroups

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

subgroupindex
#214621192
#214620952
#214609672
#214609662
#214609482
#214568842
#1360761