Finite Group Databasebeta

← #30595216

Subgroups — #30595216

Order 15616.

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

normal subgroups only

This group has 260 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#21461950C211yesmaximal, characteristic
3#356×D61C211yesmaximal, characteristic
4C2×#14519840—21no—
5C2×#14519840—21no—
6D61⋊#101—21no—
7#16840721C411yescharacteristic
8#16840706C411yescharacteristic
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—
19#14519840—42no—
20#14519840—42no—
21#14519838—22no—
22#14519838—41no—
23#14519832—41no—
24(C2×#6923)⋊C4—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—
57#11758213—81no—
58D61⋊C8—22no—
59D61⋊C8—41no—
60D61⋊C8—81no—
61M16×C61—41no—
62C4⋊C4×C61—41no—
63C42×C61C4211yescharacteristic
64C4⋊Dic61—41no—
65#11758196—41no—
66#11758196—41no—
67C4×Dic61—21no—
68C4×Dic61C4⋊C411yescharacteristic
69#11758194—41no—
70#11758189—81no—
71C8×D61—81no—
72C22×D61#9911yescharacteristic
73C2×#6923—82no—
74C2×#6923—81no—
75Q8×C61—41no—
76Q8×C61—41no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61#9511yescharacteristic
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61#9911yescharacteristic
85C4×D61—21no—
86C4×D61—21no—
87C4×D61—42no—
88C4×D61—41no—
89C4×D61—41no—
90C4×D61—41no—
91C4×D61—41no—
92Dic122—41no—
93Dic122—41no—
94Dic122—81no—
95Dic122—81no—
96#92420—42no—
97#92420—82no—
98C8×C61—81no—
99#92418—81no—
100#7505—611nomaximal, Sylow
101C22×C61#34211yescharacteristic
102C2×D61—22no—
103C2×D61#35311yescharacteristic
104C2×D61#35411yescharacteristic
105#6923—161no—
106C4×C61—21no—
107C4×C61—41no—
108C4×C61—41no—
109C4×C61—41no—
110Dic61—21no—
111Dic61—41no—
112Dic61—41no—
113Dic61—41no—
114C2×#356—611no—
115C2×#356—611no—
116#1960—611no—
117C2×C61—21no—
118C2×C61#139311yescharacteristic
119D61—21no—
120D61#141312yes—
121C2×C4⋊Q8—611no—
122C2×#103—1221no—
123C2×#103—1221no—
124C2×#101—1221no—
125C2×#101—1221no—
126C2×#97—611no—
127#382—611no—
128#356—612no—
129#356—611no—
130#356—1221no—
131#356—1221no—
132#356#692311yescharacteristic, complemented
133C61#750511yescharacteristic, complemented, Sylow
134C22×Q8—611no—
135C22×Q8—611no—
136C2×M16—2441no—
137C2×M16—2441no—
138C22×C8—1221no—
139C4⋊Q8—611no—
140C4⋊Q8—611no—
141C4⋊Q8—611no—
142C4⋊Q8—2441no—
143C4⋊Q8C2×#692311yescharacteristic
144C2×C4⋊C4—1221no—
145C2×C4⋊C4—2441no—
146C2×C42—611no—
147#103—2442no—
148#103—2442no—
149#101—21no—
150#101—1222no—
151#101—1221no—
152#101—2441no—
153#101—2441no—
154#97—2441no—
155#95—2441no—
156C2×Q8—611no—
157C2×Q8—611no—
158C2×Q8—1221no—
159C2×Q8—1221no—
160C2×Q8—2441no—
161C2×Q8—2441no—
162C2×Q8—2441no—
163C2×Q8—2441no—
164C2×Q8C4⋊#692311yescharacteristic
165C2×Q8C22⋊#692311yescharacteristic
166C22×C4—611no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4—1221no—
170C22×C4—2441no—
171M16—41no—
172M16—4881no—
173M16—4881no—
174M16—2441no—
175M16—2442no—
176C2×C8—1222no—
177C2×C8—4881no—
178C2×C8—4881no—
179C2×C8—2441no—
180C2×C8—2441no—
181C4⋊C4—41no—
182C4⋊C4—2441no—
183C4⋊C4—2441no—
184C4⋊C4—2441no—
185C4⋊C4—2441no—
186C4⋊C4—2441no—
187C42—611no—
188C42—1221no—
189C42C4×#692311yescharacteristic
190C23—611no—
191Q8—41no—
192Q8—41no—
193Q8—4881no—
194Q8—4881no—
195Q8—2441no—
196Q8—2441no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—611no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—4881no—
207C2×C4—4882no—
208C2×C4—2441no—
209C2×C4—2441no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2442no—
213C2×C4(C2×#6923)⋊C411yescharacteristic
214C8—81no—
215C8—4881no—
216C8—4882no—
217C8—2442no—
218C22—611no—
219C22—611no—
220C22—1222no—
221C22#1684063911yescharacteristic
222C4—21no—
223C4—41no—
224C4—41no—
225C4—41no—
226C4—1221no—
227C4—9761no—
228C4—2441no—
229C4—2441no—
230C4—2441no—
231C2—21no—
232C2—612no—
233C2—1221no—
234C2#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#7505
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
132. #356#6923semidirect
133. C61#7505semidirect

Maximal subgroups

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

subgroupindex
D61⋊#3562
#214619502
#356×D612
#750561