Finite Group Databasebeta

← #30603927

Subgroups — #30603927

Order 15616.

386 conjugacy classes of subgroups; only the 106 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 106 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#21462177C212yesmaximal, complemented
2#21460755C212yesmaximal, complemented
3#21460740C212yesmaximal
4C2×#16839814C211yesmaximal, characteristic
5#16840683—22no—
6C22⋊#11758187C2214yes—
7#16840648—22no—
8C2×C42×D61C411yescharacteristic
9#16839814—22no—
10#16839814—22no—
11C2×C4⋊#92418C2211yescharacteristic
12C2×#14519689C411yescharacteristic
13C2×#14519689C2211yescharacteristic
14C2×C8×Dic61C411yescharacteristic
15C2×C8×Dic61C2211yescharacteristic
16C2×C4⋊C8×C61C411yescharacteristic
17C2×#11758187—24no—
18C22×C4×D61C811yescharacteristic
19C22×C4×D61C811yescharacteristic
20C22×C4×D61C2×C411yescharacteristic
21C22×#92418C2×C411yescharacteristic
22C22×#92418C2311yescharacteristic
23C2×C4×Dic61C811yescharacteristic
24C2×C4×Dic61C811yescharacteristic
25C2×C4×Dic61C2×C411yescharacteristic
26C42×D61—21no—
27C42×D61—21no—
28C42×D61—21no—
29C42×D61—21no—
30C4⋊#92418—22no—
31#14519689—22no—
32#14519689—22no—
33C8×Dic61—21no—
34C8×Dic61—21no—
35C8×Dic61D412yes—
36C8×Dic61D412yes—
37C22×C8×C61C2×C411yescharacteristic
38C22×C8×C61C2×C411yescharacteristic
39C2×C42×C61C2×C411yescharacteristic
40C4⋊C8×C61—22no—
41C23×D61C2×C811yescharacteristic
42C22×C4×C61C2×C811yescharacteristic
43C22×C4×C61C2×C811yescharacteristic
44C22×C4×C61C22×C411yescharacteristic
45C22×Dic61C2×C811yescharacteristic
46C22×Dic61C2×C811yescharacteristic
47C22×Dic61C2×C811yescharacteristic
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—22no—
51C2×C4×D61—21no—
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—21no—
55C2×C4×D61—42no—
56C2×C4×D61—41no—
57C2×C4×D61—41no—
58C2×C4×D61C1614yescomplemented
59C2×C8×C61—21no—
60C2×C8×C61—41no—
61C2×C8×C61—41no—
62C2×C8×C61C22⋊C412yes—
63C42×C61—21no—
64C42×C61—21no—
65C4×Dic61—21no—
66C4×Dic61—21no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61C22⋊C411yescharacteristic
70C4×Dic61C22⋊C411yescharacteristic
71C4×Dic61M1611yescharacteristic
72C4×Dic61M1611yescharacteristic
73C2×#92418—21no—
74C2×#92418—41no—
75C2×#92418—41no—
76C2×#92418C2×D412yes—
77#11758187—44no—
78C23×C61C22×C811yescharacteristic
79C22×D61—21no—
80C22×D61—21no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61C2×C1612yes—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—41no—
90C2×C4×C61C2×C1612yes—
91C2×C4×C61C2×C22⋊C411yescharacteristic
92C2×C4×C61C2×M1611yescharacteristic
93C2×Dic61—22no—
94C2×Dic61—21no—
95C2×Dic61—41no—
96C2×Dic61C22⋊C811yescharacteristic
97C2×Dic61C22⋊C811yescharacteristic
98C2×Dic61C22⋊C811yescharacteristic
99C2×Dic61C22⋊C811yescharacteristic
100C2×Dic61C2×C1612yes—
101C2×Dic61M3212yes—
102C4×D61—24no—
103C4×D61—24no—
104C4×D61—42no—
105C4×D61—42no—
106C4×D61—41no—
107C4×D61—41no—
108C4×D61—42no—
109C8×C61—22no—
110C8×C61—41no—
111#92418—22no—
112#92418—41no—
113#11459—611nomaximal, Sylow
114C22×C61—21no—
115C22×C61—21no—
116C22×C61C2×C22⋊C811yescharacteristic
117C22×C61C22×C1611yescharacteristic
118C22×C61C2×M3211yescharacteristic
119C2×D61—22no—
120C2×D61—42no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—42no—
124C4×C61—22no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61#41011yescharacteristic
128C4×C61#41311yescharacteristic
129Dic61—21no—
130Dic61—41no—
131Dic61C22⋊C1612yes—
132Dic61C22⋊C1612yes—
133Dic61#34912yes—
134C2×#431—611no—
135#2162—612no—
136#1322—612no—
137#1314—612no—
138C2×C61—21no—
139C2×C61—21no—
140C2×C61#145811yescharacteristic
141C2×C61C2×C22⋊C1611yescharacteristic
142C2×C61C2×#34911yescharacteristic
143D61—42no—
144C22×C42—611no—
145#431—1222no—
146#431—1222no—
147C2×C4⋊C8—611no—
148C2×C4⋊C8#692311yescharacteristic
149C2×C22⋊C8—611no—
150C2×C22⋊C8—611no—
151C2×C4×C8—611no—
152C2×C4×C8—611no—
153C4⋊C16—1222no—
154C22⋊C16—614no—
155C4×C16—1222no—
156C61#1145911yescharacteristic, complemented, Sylow
157C23×C4—611no—
158C23×C4—611no—
159C23×C4—611no—
160C22×C8—611no—
161C22×C8—611no—
162C22×C8C2×#692311yescharacteristic
163C22×C8C2×#692311yescharacteristic
164C2×C42—611no—
165C2×C42—611no—
166C2×C42—611no—
167C2×C42—1221no—
168C2×C42—1221no—
169C2×C42—1221no—
170C2×C42—1221no—
171C2×C42C2×#692311yescharacteristic
172C2×C16—1224no—
173C4⋊C8—22no—
174C4⋊C8—1222no—
175C22⋊C8—1222no—
176C22⋊C8—1222no—
177C4×C8—612no—
178C4×C8—612no—
179C4×C8—1221no—
180C4×C8—1221no—
181C24—611no—
182C22×C4—611no—
183C22×C4—611no—
184C22×C4—614no—
185C22×C4—611no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4—1222no—
189C22×C4—1221no—
190C22×C4—1221no—
191C22×C4—1221no—
192C22×C4—1221no—
193C22×C4—2441no—
194C22×C4—2441no—
195C22×C4—2442no—
196C22×C4D61⋊C811yescharacteristic
197C22×C4D61⋊C811yescharacteristic
198C22×C4C22×#692311yescharacteristic
199C2×C8—21no—
200C2×C8—41no—
201C2×C8—41no—
202C2×C8—612no—
203C2×C8—1221no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8C22⋊#692312yes—
207C42—21no—
208C42—21no—
209C42—611no—
210C42—611no—
211C42—611no—
212C42—611no—
213C42—1221no—
214C42—1221no—
215C42—1221no—
216C42—1221no—
217C16—2444no—
218C23—612no—
219C23—1221no—
220C23—1221no—
221C23—2441no—
222C23—2441no—
223C23C2×D61⋊C811yescharacteristic
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—41no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—611no—
233C2×C4—612no—
234C2×C4—612no—
235C2×C4—611no—
236C2×C4—1224no—
237C2×C4—1224no—
238C2×C4—1222no—
239C2×C4—1221no—
240C2×C4—2442no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4—2441no—
244C2×C4—2441no—
245C2×C4—2441no—
246C2×C4D61⋊C1612yes—
247C2×C4C2×C22⋊#692311yescharacteristic
248C2×C4D61⋊M1611yescharacteristic
249C8—22no—
250C8—41no—
251C8—1222no—
252C8—2441no—
253C22—21no—
254C22—21no—
255C22—1222no—
256C22—2442no—
257C22—2442no—
258C22—2441no—
259C22—2441no—
260C22D61⋊(C22⋊C8)11yescharacteristic
261C22C2×D61⋊C1611yescharacteristic
262C22D61⋊M3211yescharacteristic
263C4—22no—
264C4—21no—
265C4—41no—
266C4—612no—
267C4—612no—
268C4—612no—
269C4—1221no—
270C4—2441no—
271C4#1684074311yescharacteristic
272C4#1684074911yescharacteristic
273C2—21no—
274C2—21no—
275C2—2442no—
276C2#2146105311yescharacteristic
277C2D61⋊(C22⋊C16)11yescharacteristic
278C2D61⋊#34911yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC22×C61C22×C16
FrattiniC22×C4C22×#6923
FittingC2×C4⋊C8×C61C4
socleC22×C61C2×C22⋊C8
prime radicalC23×D61C2×C8
cosocleC22×#92418C23
hypercenterC2×C4⋊C8#6923
hypocenterC61#11459
LCSG ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×C4⋊C8

Complements

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

NH ≅ G/Ntype
1. #21462177C2semidirect
2. #21460755C2semidirect
58. C2×C4×D61C16semidirect
156. C61#11459semidirect

Maximal subgroups

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

subgroupindex
#214621772
#214607552
#214607402
C2×#168398142
#1145961