Finite Group Databasebeta

← #30594400

Subgroups — #30594400

Order 15616.

284 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 66 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#21461989C211yesmaximal, characteristic
2#21461572C211yesmaximal, characteristic
3#21444141C211yesmaximal, characteristic
4C2×C4⋊#92420C411yescharacteristic
5C2×#14519838C412yes—
6C4×#11758217—21no—
7C2×C4×#92420C411yescharacteristic
8#16840642—21no—
9#16840628—21no—
10#16840628—21no—
11C2×#14519742C2211yescharacteristic
12#16839812—21no—
13#16839488C411yescharacteristic
14#16839487—21no—
15C61×#324C411yescharacteristic
16C2×#11758217—22no—
17C22×#92420—21no—
18C22×#92420—21no—
19C4⋊#92420—41no—
20#14519838—22no—
21#14519838C814yescomplemented
22#14519832—41no—
23C4×#92420—41no—
24C4×#92420—41no—
25C22×Dic122C2×C411yescharacteristic
26#14519742—41no—
27#14519742—41no—
28C2×#11758196D411yescharacteristic
29C2×#11758196Q811yescharacteristic
30C2×C4×Dic61C2×C411yescharacteristic
31C2×C4×Dic61D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33#14519706—41no—
34C22⋊#92418—21no—
35C8×Dic61—41no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C22⋊C8×C61—21no—
38C22×C4×C61C4211yescharacteristic
39C22×C4×C61C22⋊C411yescharacteristic
40C22×C4×C61C4⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C22⋊C411yescharacteristic
43C22×Dic61C4⋊C411yescharacteristic
44C22×Dic61C4⋊C411yescharacteristic
45C2×Dic122—41no—
46C2×Dic122—41no—
47C2×Dic122C2×C812yes—
48C2×Dic122M1612yes—
49#11758217—24no—
50#11758217—42no—
51C2×#92420—22no—
52C2×#92420—42no—
53C2×#92420—41no—
54C2×#92420—41no—
55C2×#92420—42no—
56C2×#92420—41no—
57C2×C8×C61—41no—
58C4⋊C4×C61—41no—
59#11758196—41no—
60#11758196—41no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C4×Dic61—21no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C4×Dic61—21no—
67C2×#92418—41no—
68C23×C61#9511yescharacteristic
69C2×C4×C61—21no—
70C2×C4×C61—21no—
71C2×C4×C61—21no—
72C2×C4×C61—21no—
73C2×C4×C61—41no—
74C2×C4×C61—41no—
75C2×C4×C61C4×C811yescharacteristic
76C2×C4×C61#9711yescharacteristic
77C2×Dic61—21no—
78C2×Dic61—21no—
79C2×Dic61—21no—
80C2×Dic61—21no—
81C2×Dic61—21no—
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—41no—
85C2×Dic61C22⋊C812yes—
86C2×Dic61#9911yescharacteristic
87C2×Dic61#9911yescharacteristic
88C2×Dic61C4⋊C812yes—
89Dic122—42no—
90Dic122—42no—
91#92420—42no—
92#92420—44no—
93#92420—81no—
94C8×C61—81no—
95#92418—81no—
96#7206—611nomaximal, Sylow
97C22×C61—21no—
98C22×C61—21no—
99C22×C61#33611yescharacteristic
100C22×C61#34211yescharacteristic
101C22×C61#34411yescharacteristic
102C4×C61—21no—
103C4×C61—21no—
104C4×C61—41no—
105C4×C61—41no—
106Dic61—22no—
107Dic61—22no—
108Dic61—21no—
109Dic61—41no—
110Dic61#35511yescharacteristic
111Dic61#35611yescharacteristic
112#1984—611no—
113C4×#101—611no—
114#1461—611no—
115C2×C61—21no—
116C2×C61—21no—
117C2×C61#128211yescharacteristic
118C2×C61#139411yescharacteristic
119C2×C61#139511yescharacteristic
120C2×C4×Q8—611no—
121#431—1221no—
122C2×C4⋊C8—611no—
123C2×#101—612no—
124C4×M16—1221no—
125C2×C4×C8—611no—
126#343—1221no—
127#336—1221no—
128#336—1221no—
129#324—611no—
130#324—1221no—
131#324#692311yescharacteristic
132C61#720611yescharacteristic, complemented, Sylow
133C22×Q8—611no—
134C2×M16—1222no—
135C22×C8—1221no—
136C22×C8—1221no—
137C4×Q8—2441no—
138C4×Q8—2441no—
139C2×C4⋊C4—611no—
140C2×C4⋊C4—611no—
141C2×C4⋊C4C2×#692311yescharacteristic
142C2×C42—611no—
143C2×C42—611no—
144C2×C42—611no—
145C4⋊C8—2441no—
146C4⋊C8—2441no—
147#101—614no—
148#101—1222no—
149C22⋊C8—21no—
150C22⋊C8—1221no—
151#97—2441no—
152C4×C8—2441no—
153C4×C8—2441no—
154C4×C8—2441no—
155C2×Q8—612no—
156C2×Q8—612no—
157C2×Q8—2441no—
158C2×Q8—2441no—
159C22×C4—611no—
160C22×C4—611no—
161C22×C4—611no—
162C22×C4—611no—
163C22×C4C4×#692311yescharacteristic
164C22×C4C4⋊#692311yescharacteristic
165C22×C4C22⋊#692311yescharacteristic
166M16—1224no—
167M16—2442no—
168C2×C8—41no—
169C2×C8—1222no—
170C2×C8—2441no—
171C2×C8—2441no—
172C2×C8—2442no—
173C2×C8—2441no—
174C2×C8—2442no—
175C2×C8—2441no—
176C4⋊C4—41no—
177C4⋊C4—2441no—
178C4⋊C4—2441no—
179C42—1221no—
180C42—1221no—
181C42—1221no—
182C42—1221no—
183C42—1221no—
184C42—1221no—
185C23(C2×#6923)⋊C411yescharacteristic
186Q8—2442no—
187Q8—2442no—
188C2×C4—21no—
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—611no—
195C2×C4—612no—
196C2×C4—612no—
197C2×C4—611no—
198C2×C4—1221no—
199C2×C4—1221no—
200C2×C4—1221no—
201C2×C4—1221no—
202C2×C4—1221no—
203C2×C4—1221no—
204C2×C4—1221no—
205C2×C4—2441no—
206C2×C4C8×#692311yescharacteristic
207C2×C4#1451983111yescharacteristic
208C8—81no—
209C8—4881no—
210C8—4881no—
211C8—2442no—
212C8—2444no—
213C22—21no—
214C22—21no—
215C22(C2×#6923)⋊C811yescharacteristic
216C22#1684063911yescharacteristic
217C22#1684064511yescharacteristic
218C4—21no—
219C4—21no—
220C4—41no—
221C4—41no—
222C4—611no—
223C4—611no—
224C4—1221no—
225C4—1222no—
226C4—1222no—
227C4—2441no—
228C2—21no—
229C2—21no—
230C2#2146066011yescharacteristic
231C2#2146091511yescharacteristic
232C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC2×C4×C61C4×C8
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC23×C61#95
cosocleC2×#14519742C22
hypercenter#324#6923
hypocenterC61#7206
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #324

Complements

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

NH ≅ G/Ntype
21. #14519838C8semidirect
132. C61#7206semidirect

Maximal subgroups

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

subgroupindex
#214619892
#214615722
#214441412
#720661