Finite Group Databasebeta

← #30595196

Subgroups — #30595196

Order 15616.

272 conjugacy classes of subgroups; only the 44 normal subgroups are shown.

normal subgroups only

This group has 272 conjugacy classes of subgroups — too many to draw. Only its 44 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
1D61⋊#356C211yesmaximal, characteristic
2#21461946C211yesmaximal, characteristic
3#356×D61C211yesmaximal, characteristic
4C2×#14519840—21no—
5C2×#14519840—21no—
6D61⋊#101—21no—
7C4×D61⋊C8C411yescharacteristic
8#16840708C411yescharacteristic
9#16840673C412yescomplemented
10#16840672—21no—
11C4⋊Q8×D61C2211yescharacteristic
12#101×D61—21no—
13#16839561C411yescharacteristic, complemented
14#16839560—21no—
15C61×#356C411yescharacteristic, complemented
16D61⋊M16—41no—
17C2×D61⋊C8—21no—
18C2×C4⋊#6923—21no—
19C2×C4⋊#6923—41no—
20#14519840—42no—
21#14519840—42no—
22#14519838—22no—
23#14519838—41no—
24C4×#92420—41no—
25C2×Q8×D61D411yescharacteristic
26C2×Q8×D61D411yescharacteristic
27M16×D61—41no—
28#14519777C2×C411yescharacteristic
29#14519776—41no—
30#14519775D411yescharacteristic
31#14519775Q811yescharacteristic
32C4⋊C4×D61—41no—
33C42×D61C2×C411yescharacteristic
34#14519696—21no—
35#14519695—41no—
36C4⋊Q8×C61C2×C411yescharacteristic
37#101×C61—21no—
38C22×#6923—41no—
39C2×Q8×C61C22⋊C411yescharacteristic
40C2×Q8×C61C4⋊C411yescharacteristic
41Q8×D61—41no—
42Q8×D61—41no—
43Q8×D61—41no—
44Q8×D61—41no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61C22⋊C411yescharacteristic
49C2×Dic122—21no—
50C2×Dic122—21no—
51C2×Dic122C22⋊C411yescharacteristic
52C2×Dic122C4⋊C411yescharacteristic
53#11758217—42no—
54C2×#92420—41no—
55C4⋊#6923—41no—
56C4⋊#6923—41no—
57C4⋊#6923—82no—
58#11758213—81no—
59D61⋊C8—22no—
60D61⋊C8—41no—
61D61⋊C8—81no—
62M16×C61—41no—
63C4⋊C4×C61—41no—
64C42×C61C4211yescharacteristic
65C4⋊Dic61—41no—
66#11758196—41no—
67#11758196—41no—
68C4×Dic61—21no—
69C4×Dic61C4⋊C411yescharacteristic
70#11758194—41no—
71#11758189—81no—
72C8×D61—81no—
73C22×D61#9911yescharacteristic
74C2×#6923—82no—
75C2×#6923—81no—
76Q8×C61—41no—
77Q8×C61—41no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61#9511yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61#9911yescharacteristic
86C4×D61—22no—
87C4×D61—22no—
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—41no—
91C4×D61—41no—
92C4×D61—41no—
93C4×D61—41no—
94Dic122—41no—
95Dic122—41no—
96Dic122—81no—
97Dic122—81no—
98#92420—42no—
99#92420—82no—
100C8×C61—81no—
101#92418—81no—
102#7499—611nomaximal, Sylow
103C22×C61#34211yescharacteristic
104C2×D61—21no—
105C2×D61—21no—
106C2×D61#35311yescharacteristic
107C2×D61#35411yescharacteristic
108#6923—161no—
109C4×C61—22no—
110C4×C61—21no—
111C4×C61—41no—
112C4×C61—41no—
113Dic61—22no—
114Dic61—21no—
115Dic61—41no—
116Dic61—41no—
117C2×#356—611no—
118C2×#356—611no—
119#1956—611no—
120C2×C61—21no—
121C2×C61#139311yescharacteristic
122D61—21no—
123D61#141011yescharacteristic
124D61#141111yescharacteristic
125C2×C4⋊Q8—611no—
126C2×#103—1221no—
127C2×#103—1221no—
128C2×#101—1221no—
129C2×#101—1221no—
130C2×C4×C8—611no—
131#384—611no—
132#356—612no—
133#356—611no—
134#356—1221no—
135#356—1221no—
136#356#692311yescharacteristic, complemented
137C61#749911yescharacteristic, complemented, Sylow
138C22×Q8—611no—
139C22×Q8—611no—
140C2×M16—2441no—
141C2×M16—2441no—
142C22×C8—1221no—
143C4⋊Q8—611no—
144C4⋊Q8—611no—
145C4⋊Q8—611no—
146C4⋊Q8—2441no—
147C4⋊Q8C2×#692311yescharacteristic
148C2×C4⋊C4—1221no—
149C2×C4⋊C4—2441no—
150C2×C4⋊C4—2441no—
151C2×C42—611no—
152#103—2442no—
153#103—2442no—
154#101—21no—
155#101—1222no—
156#101—1221no—
157#101—2441no—
158#101—2441no—
159C4×C8—2441no—
160C2×Q8—611no—
161C2×Q8—611no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—2441no—
165C2×Q8—2441no—
166C2×Q8—2441no—
167C2×Q8—2441no—
168C2×Q8C4⋊#692311yescharacteristic
169C2×Q8C22⋊#692311yescharacteristic
170C22×C4—611no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—1221no—
174C22×C4—2441no—
175M16—41no—
176M16—4881no—
177M16—4881no—
178M16—2441no—
179M16—2442no—
180C2×C8—1222no—
181C2×C8—4881no—
182C2×C8—4881no—
183C2×C8—2441no—
184C2×C8—2441no—
185C4⋊C4—41no—
186C4⋊C4—4882no—
187C4⋊C4—2441no—
188C4⋊C4—2441no—
189C4⋊C4—2441no—
190C4⋊C4—2441no—
191C4⋊C4—2441no—
192C42—611no—
193C42—1221no—
194C42C4×#692311yescharacteristic
195C23—611no—
196Q8—41no—
197Q8—41no—
198Q8—4881no—
199Q8—4881no—
200Q8—2441no—
201Q8—2441no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—21no—
205C2×C4—611no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1222no—
209C2×C4—1222no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—4881no—
214C2×C4—4882no—
215C2×C4—2441no—
216C2×C4—2441no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4(C2×#6923)⋊C411yescharacteristic
220C8—81no—
221C8—4881no—
222C8—4882no—
223C8—2442no—
224C22—611no—
225C22—611no—
226C22—1221no—
227C22—1221no—
228C22#1684063911yescharacteristic
229C4—22no—
230C4—21no—
231C4—41no—
232C4—41no—
233C4—1222no—
234C4—1221no—
235C4—9761no—
236C4—2441no—
237C4—2441no—
238C2—21no—
239C2—611no—
240C2—611no—
241C2—1221no—
242C2#2146091211yescharacteristic
subgroupG/H
centerC2#21460912
commutatorC42×C61C42
FrattiniC4⋊Q8C2×#6923
FittingC61×#356C4
socleC2×C61#1393
prime radicalC22×D61#99
cosocleC4⋊Q8×D61C22
hypercenter#356#6923
hypocenterC61#7499
LCSG ▷ C42×C61 ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C4⋊Q8 ◁ #356

Complements

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

NH ≅ G/Ntype
9. #16840673C4semidirect
13. #16839561C4semidirect
15. C61×#356C4semidirect
136. #356#6923semidirect
137. C61#7499semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3562
#214619462
#356×D612
#749961