Finite Group Databasebeta

← #30604145

Subgroups — #30604145

Order 15616.

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

normal subgroups only

This group has 330 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#21462189C212yesmaximal, complemented
2#21460766C212yesmaximal, complemented
3#21460751C212yesmaximal
4#21454448C211yesmaximal, characteristic
5#16840684—22no—
6#16840658C2214yes—
7#16840655—22no—
8C22×C4×Dic61C411yescharacteristic
9#16839816—22no—
10#16839812—22no—
11#16839785C411yescharacteristic
12#16839785C2211yescharacteristic
13#16839726C2211yescharacteristic
14M16×Dic61C411yescharacteristic
15M16×Dic61C2211yescharacteristic
16C61×#407C411yescharacteristic
17#14519851—24no—
18C23×Dic61—21no—
19C2×#11758194C2×C411yescharacteristic
20C2×#11758194C2311yescharacteristic
21C2×C4×Dic61—21no—
22C2×C4×Dic61—21no—
23C2×C4×Dic61—21no—
24C2×C4×Dic61—21no—
25C2×C4×Dic61—21no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61C2×C411yescharacteristic
28#14519706—22no—
29#14519706—22no—
30C22⋊#92418—22no—
31#14519687—21no—
32#14519687D412yes—
33C8×Dic61—21no—
34C8×Dic61D412yes—
35C23×C4×C61C2×C411yescharacteristic
36C2×M16×C61C2×C411yescharacteristic
37C2×M16×C61C2×C411yescharacteristic
38C22⋊C8×C61—22no—
39C24×C61M1611yescharacteristic
40C22×C4×C61—21no—
41C22×C4×C61—21no—
42C22×C4×C61—41no—
43C22×C4×C61—41no—
44C22×C4×C61M1611yescharacteristic
45C22×C4×C61C22×C411yescharacteristic
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61—21no—
50C22×Dic61—21no—
51C22×Dic61—21no—
52C22×Dic61—44no—
53M16×C61—41no—
54M16×C61—41no—
55C2×C8×C61—21no—
56C2×C8×C61C22⋊C412yes—
57C4×Dic61—21no—
58C4×Dic61—21no—
59C4×Dic61—21no—
60C4×Dic61—21no—
61C4×Dic61—21no—
62C4×Dic61—21no—
63C4×Dic61C22⋊C411yescharacteristic
64C4×Dic61C22⋊C411yescharacteristic
65C4×Dic61M1611yescharacteristic
66C4×Dic61M1611yescharacteristic
67#11758194—41no—
68#11758194—41no—
69C2×#92418—21no—
70C2×#92418C2×D412yes—
71#11758187—44no—
72C23×C61—21no—
73C23×C61—42no—
74C23×C61—41no—
75C23×C61C2×M1611yescharacteristic
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—42no—
80C2×C4×C61—41no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61C2×C22⋊C411yescharacteristic
84C2×C4×C61C2×M1611yescharacteristic
85C2×Dic61—24no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—42no—
91C2×Dic61—42no—
92C2×Dic61—42no—
93C2×Dic61—42no—
94C2×Dic61—42no—
95C8×C61—22no—
96C8×C61—41no—
97#92418—22no—
98#92418—41no—
99#11521—611nomaximal, Sylow
100C22×C61—22no—
101C22×C61—21no—
102C22×C61—41no—
103C22×C61—41no—
104C22×C61—42no—
105C22×C61—42no—
106C22×C61—41no—
107C22×C61#40711yescharacteristic
108C4×C61—21no—
109C4×C61—41no—
110C4×C61#41011yescharacteristic
111C4×C61#41311yescharacteristic
112Dic61—22no—
113Dic61—22no—
114Dic61—41no—
115Dic61—41no—
116#2920—611no—
117#2165—612no—
118#1327—612no—
119#1320—612no—
120C2×C61—21no—
121C2×C61—42no—
122C2×C61—41no—
123C2×C61#146411yescharacteristic
124C22×C42—611no—
125#432—1222no—
126#431—1222no—
127#423—611no—
128#423—611no—
129#407—611no—
130#407#692311yescharacteristic
131C4×M16—611no—
132C4×M16—611no—
133#364—1222no—
134#349—614no—
135#347—1222no—
136C61#1152111yescharacteristic, complemented, Sylow
137C23×C4—1221no—
138C23×C4C2×#692311yescharacteristic
139C2×M16—611no—
140C2×M16—611no—
141C2×M16C2×#692311yescharacteristic
142C2×M16C2×#692311yescharacteristic
143C2×C42—611no—
144C2×C42—611no—
145C2×C42—1221no—
146C2×C42—1221no—
147C2×C42—1221no—
148C2×C42—1221no—
149C2×C42—1221no—
150M32—1224no—
151C4⋊C8—1222no—
152C4⋊C8—1222no—
153C22⋊C8—22no—
154C22⋊C8—1222no—
155#97—612no—
156#97—1221no—
157C4×C8—612no—
158C4×C8—1221no—
159C24#1175821311yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—41no—
163C22×C4—41no—
164C22×C4—1221no—
165C22×C4—1221no—
166C22×C4—1221no—
167C22×C4—1221no—
168C22×C4—1221no—
169C22×C4—1221no—
170C22×C4—2444no—
171C22×C4#1175821311yescharacteristic
172C22×C4C22×#692311yescharacteristic
173M16—41no—
174M16—41no—
175M16—2441no—
176M16—2441no—
177C2×C8—21no—
178C2×C8—612no—
179C2×C8—1221no—
180C2×C8C22⋊#692312yes—
181C42—611no—
182C42—611no—
183C42—611no—
184C42—611no—
185C42—1221no—
186C42—1221no—
187C42—1221no—
188C42—1221no—
189C42—1221no—
190C42—1221no—
191C16—2444no—
192C23—21no—
193C23—41no—
194C23—42no—
195C23C2×#1175821311yescharacteristic
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—21no—
199C2×C4—42no—
200C2×C4—41no—
201C2×C4—41no—
202C2×C4—41no—
203C2×C4—1224no—
204C2×C4—1221no—
205C2×C4—1221no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—2442no—
209C2×C4—2442no—
210C2×C4—2442no—
211C2×C4—2442no—
212C2×C4—2442no—
213C2×C4C2×C22⋊#692311yescharacteristic
214C2×C4D61⋊M1611yescharacteristic
215C8—22no—
216C8—41no—
217C8—1222no—
218C8—2441no—
219C22—22no—
220C22—21no—
221C22—41no—
222C22—41no—
223C22—42no—
224C22—42no—
225C22—41no—
226C22#1684073311yescharacteristic
227C4—21no—
228C4—41no—
229C4—1222no—
230C4—1222no—
231C4—2441no—
232C4—2441no—
233C4#1684074211yescharacteristic
234C4#1684074911yescharacteristic
235C2—21no—
236C2—42no—
237C2—41no—
238C2#2146107111yescharacteristic
subgroupG/H
centerC4#16840742
commutatorC22×C4×C61C22×C4
FrattiniC22×C4C22×#6923
FittingC61×#407C4
socleC2×C61#1464
prime radicalC24×C61M16
cosocleC2×#11758194C23
hypercenter#407#6923
hypocenterC61#11521
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #407

Complements

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

NH ≅ G/Ntype
1. #21462189C2semidirect
2. #21460766C2semidirect
136. C61#11521semidirect

Maximal subgroups

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

subgroupindex
#214621892
#214607662
#214607512
#214544482
#1152161