Finite Group Databasebeta

← #30602113

Subgroups — #30602113

Order 15616.

498 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 498 conjugacy classes of subgroups — too many to draw. Only its 92 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#21461743C211yesmaximal, characteristic, complemented
2#21461166C212yesmaximal, complemented
3#21461166C212yesmaximal, complemented
4#21461015C211yesmaximal, characteristic, complemented
5#21456248C211yesmaximal, characteristic
6#16840766C2212yes—
7C4×D61⋊C8C2211yescharacteristic
8C4×D61⋊C8C2211yescharacteristic
9#16840638—22no—
10#16840610—24no—
11#16840610—24no—
12#92420⋊C8—22no—
13C2×#14519800—22no—
14#16840313C2212yes—
15#16840147—22no—
16#16840139C411yescharacteristic
17#16840136C412yes—
18C4×C8×D61C2211yescharacteristic
19C61×#494C411yescharacteristic
20C2×#11758213—22no—
21C2×D61⋊C8—21no—
22C2×D61⋊C8—21no—
23C4⋊#92420—22no—
24C4⋊#92420—22no—
25C4×#92420—21no—
26C4×#92420—21no—
27C4×#92420D412yes—
28C4×#92420D412yes—
29C2×#11758226—22no—
30#14519800—48no—
31C2×#11758201—24no—
32C2×D488—22no—
33C2×C8×D61D412yes—
34#14519774C2×C412yes—
35#14519766—22no—
36#14519752—22no—
37#14519752—22no—
38#14519739—22no—
39#14519739—22no—
40C42×D61C2311yescharacteristic
41C4×#92418C2×C411yescharacteristic
42C8×Dic61D412yes—
43C2×Q16×C61—22no—
44C4⋊Q8×C61C2×C412yes—
45C4×C8×C61C2×C411yescharacteristic
46C2×Q8×C61—22no—
47#11758226—48no—
48C2×D244—22no—
49C2×D244—22no—
50C2×D244—22no—
51C2×D244—42no—
52C2×C4×D61—42no—
53C2×C4×D61C2×D411yescharacteristic
54C2×C4×D61#4111yescharacteristic
55C2×C4×D61#4111yescharacteristic
56C2×#92420—22no—
57C2×#92420—22no—
58C2×#92420—42no—
59#11758213—44no—
60D61⋊C8—24no—
61D61⋊C8—42no—
62Q16×C61—44no—
63C2×C8×C61C22⋊C412yes—
64C4⋊C4×C61—22no—
65C4⋊C4×C61—22no—
66C42×C61C22×C411yescharacteristic
67#11758201—48no—
68#11758198—42no—
69#11758198—42no—
70C4×Dic61C2×D411yescharacteristic
71C4×Dic61C2×D411yescharacteristic
72C4×Dic61C2×D411yescharacteristic
73C2×#92418C22⋊C412yes—
74D488—44no—
75C8×D61—24no—
76C22×D61—42no—
77C22×D61#12411yescharacteristic
78Q8×C61—44no—
79C2×C4×C61—42no—
80C2×C4×C61C2×C22⋊C411yescharacteristic
81C2×C4×C61C4×D411yescharacteristic
82C2×C4×C61C4×D411yescharacteristic
83C2×Dic61#12111yescharacteristic
84C2×Dic61#12111yescharacteristic
85C2×Dic61#12711yescharacteristic
86D244—44no—
87D244—44no—
88D244—44no—
89D244—84no—
90C4×D61—22no—
91C4×D61—22no—
92C4×D61—84no—
93C4×D61AGL(1,ℤ/8)14yes—
94#92420—24no—
95#92420—42no—
96#92420—82no—
97C8×C61—22no—
98#92418—22no—
99#9860—611nomaximal, Sylow
100C22×C61#39011yescharacteristic
101C2×D61—21no—
102C2×D61—21no—
103C2×D61—82no—
104C2×D61—82no—
105C2×D61—82no—
106C2×D61#49012yes—
107C4×C61—82no—
108C4×C61#41812yes—
109C4×C61#44312yes—
110C4×C61#44412yes—
111Dic61—21no—
112Dic61—21no—
113Dic61#49612yes—
114#3147—611no—
115#1837—611no—
116#1492—612no—
117#1492—612no—
118C2×#322—611no—
119C2×C61#196111yescharacteristic
120C2×C61#197411yescharacteristic
121C2×C61#197511yescharacteristic
122D61—22no—
123D61—162no—
124C2×#135—1222no—
125#532—612no—
126#495—1222no—
127#494#692311yescharacteristic
128#493—611no—
129#492—612no—
130#423—612no—
131C2×C4×C8—611no—
132C2×C4×C8—611no—
133C2×C4×C8—611no—
134#341—1222no—
135D4⋊C8—1224no—
136D4⋊C8—1224no—
137#322—1222no—
138C61#986011yescharacteristic, complemented, Sylow
139C2×#41—1222no—
140#135—2448no—
141C2×Q16—22no—
142C2×SD16—1224no—
143C2×D8—1222no—
144C2×M16—1222no—
145C22×C8—612no—
146C22×C8—1221no—
147C22×C8—1221no—
148C4⋊Q8C2×#692312yes—
149#127—612no—
150#124—1222no—
151#121—1222no—
152#121—1222no—
153C4×D4—1222no—
154C4×D4—1222no—
155C2×C42—611no—
156C4⋊C8—1222no—
157C4⋊C8—1222no—
158C4×C8—612no—
159C4×C8—612no—
160C4×C8—612no—
161C4×C8—611no—
162C4×C8—1221no—
163C4×C8—1221no—
164C4×C8C2×#692311yescharacteristic
165#41—2448no—
166C2×Q8—22no—
167C2×D4—1222no—
168C2×D4—1222no—
169C2×D4—1222no—
170C2×D4—2442no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—2442no—
175Q16—44no—
176SD16—2448no—
177D8—2444no—
178M16—2444no—
179C2×C8—612no—
180C2×C8—1224no—
181C2×C8—1222no—
182C2×C8—1224no—
183C2×C8—1222no—
184C2×C8—2442no—
185C2×C8—2442no—
186C2×C8C22⋊#692312yes—
187C4⋊C4—22no—
188C4⋊C4—22no—
189C22⋊C4—2442no—
190C22⋊C4—2442no—
191C42—611no—
192C42—611no—
193C42—611no—
194C42C22×#692311yescharacteristic
195C23—611no—
196C23—2442no—
197Q8—44no—
198D4—4884no—
199D4—2444no—
200D4—2444no—
201D4—2444no—
202C2×C4—42no—
203C2×C4—611no—
204C2×C4—614no—
205C2×C4—611no—
206C2×C4—611no—
207C2×C4—1222no—
208C2×C4—1222no—
209C2×C4—4884no—
210C2×C4C2×C22⋊#692311yescharacteristic
211C2×C4D4×#692311yescharacteristic
212C2×C4D4×#692311yescharacteristic
213C8—22no—
214C8—1224no—
215C8—1222no—
216C8—4882no—
217C8—2442no—
218C22—612no—
219C22—1221no—
220C22—1221no—
221C22—4882no—
222C22—4882no—
223C22—4882no—
224C22#1684071411yescharacteristic
225C4—82no—
226C4—612no—
227C4—1221no—
228C4—1221no—
229C4#1684075412yes—
230C4#1684080612yes—
231C4#1684080812yes—
232C2—1222no—
233C2—9762no—
234C2#2146195111yescharacteristic
235C2#2146197011yescharacteristic
236C2#2146197311yescharacteristic
subgroupG/H
centerC22#16840714
commutatorC42×C61C22×C4
FrattiniC42C22×#6923
FittingC61×#494C4
socleC22×C61#390
prime radical#21456248C2
cosocleC42×D61C23
hypercenter#494#6923
hypocenterC61#9860
LCSG ▷ C42×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C22 ◁ C42 ◁ #494

Complements

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

NH ≅ G/Ntype
1. #21461743C2semidirect
2. #21461166C2semidirect
3. #21461166C2semidirect
4. #21461015C2semidirect
138. C61#9860semidirect

Maximal subgroups

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

subgroupindex
#214617432
#214611662
#214610152
#214562482
#986061