Finite Group Databasebeta

← #30604485

Subgroups — #30604485

Order 15616.

338 conjugacy classes of subgroups; only the 92 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 92 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#21462179C211yesmaximal, characteristic, complemented
2#21462026C211yesmaximal, characteristic, complemented
3#21460788C212yesmaximal, complemented
4#21460771C212yesmaximal, complemented
5#21454782C211yesmaximal, characteristic
6C2×#14519852—21no—
7C4⋊#11758187C2212yes—
8#16840657—21no—
9#16840650C2212yes—
10#16840648—21no—
11#16840648—21no—
12C4×#11758224C411yescharacteristic
13#16839892C411yescharacteristic
14#16839889C2211yescharacteristic
15#16839840C2211yescharacteristic
16#16839836—21no—
17#16839831—21no—
18#16839814C411yescharacteristic
19#16839812—21no—
20M16×Dic61—21no—
21C4×C8×D61C2211yescharacteristic
22C61×#436C411yescharacteristic
23#14519852—24no—
24C2×#11758187—22no—
25C2×#11758187—22no—
26C2×#11758224C811yescharacteristic
27C2×#11758194—21no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30C4×Dic122C2×C411yescharacteristic
31#14519742C811yescharacteristic
32D4×Dic61C811yescharacteristic
33C4×C22⋊D61—21no—
34#14519737—21no—
35#14519735C811yescharacteristic
36#14519733—21no—
37C2×C4×Dic61—21no—
38C42×D61C2×C411yescharacteristic
39C4⋊#92418C2×C411yescharacteristic
40#14519706—21no—
41#14519706—21no—
42C22⋊#92418—21no—
43#14519689—21no—
44#14519687—21no—
45#14519687—21no—
46C4×#92418C2311yescharacteristic
47C8×Dic61—21no—
48C8×Dic61D411yescharacteristic
49C8×Dic61D411yescharacteristic
50C2×M16×C61—21no—
51C4×D4×C61C2×C411yescharacteristic
52C4⋊C8×C61C2×C411yescharacteristic
53C22⋊C8×C61—21no—
54C4×C8×C61C2×C411yescharacteristic
55C2×D4×C61C2×C811yescharacteristic
56C22×C4×C61—21no—
57C2×C22⋊D61—21no—
58C22×Dic61—21no—
59C22×Dic61—21no—
60#11758224—42no—
61C2×C4×D61C22⋊C411yescharacteristic
62C2×C4×D61C2×C811yescharacteristic
63C2×C4×D61M1611yescharacteristic
64C2×Dic122C2×C811yescharacteristic
65M16×C61—42no—
66C2×C8×C61—21no—
67C2×C8×C61C22⋊C411yescharacteristic
68C2×C8×C61C22⋊C411yescharacteristic
69C4⋊C4×C61C2×C811yescharacteristic
70C22⋊C4×C61—21no—
71C42×C61C22×C411yescharacteristic
72C22⋊Dic61—21no—
73#11758198—21no—
74C4⋊Dic61C2×C811yescharacteristic
75#11758196—21no—
76#11758196—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C4×Dic61—21no—
80C4×Dic61C22⋊C411yescharacteristic
81C4×Dic61C2×C811yescharacteristic
82C4×Dic61M1611yescharacteristic
83#11758194—42no—
84C2×#92418—21no—
85C2×#92418C2×D411yescharacteristic
86C2×#92418C2×D411yescharacteristic
87C8×D61—22no—
88C8×D61—22no—
89#11758187—24no—
90#11758187—42no—
91C23×C61—21no—
92C22×D61C22⋊C811yescharacteristic
93D4×C61—41no—
94C2×C4×C61—21no—
95C2×C4×C61—41no—
96C2×C4×C61—41no—
97C2×C4×C61C2×C22⋊C411yescharacteristic
98C2×C4×C61C22×C811yescharacteristic
99C2×C4×C61C2×M1611yescharacteristic
100C22⋊D61—42no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—42no—
104C2×Dic61—42no—
105C2×Dic61C22⋊C811yescharacteristic
106C2×Dic61C22⋊C811yescharacteristic
107C2×Dic61C22⋊C811yescharacteristic
108C4×D61—21no—
109C4×D61—21no—
110C4×D61—22no—
111C4×D61—22no—
112Dic122—41no—
113C8×C61—21no—
114C8×C61—41no—
115C8×C61#10412yes—
116#92418—21no—
117#92418—41no—
118#92418#13512yes—
119#11617—611nomaximal, Sylow
120C22×C61—41no—
121C22×C61—41no—
122C22×C61—41no—
123C22×C61C2×C22⋊C811yescharacteristic
124C2×D61—21no—
125C2×D61—21no—
126C2×D61—21no—
127C4×C61—21no—
128C4×C61—21no—
129C4×C61—41no—
130C4×C61#41611yescharacteristic
131C4×C61C2×#10411yescharacteristic
132Dic61—21no—
133Dic61—41no—
134Dic61—41no—
135Dic61#34912yes—
136Dic61#35012yes—
137#2965—611no—
138#2162—611no—
139C4×M32—611no—
140#1338—612no—
141#1330—612no—
142C2×C61—81no—
143C2×C61#147611yescharacteristic
144C2×C61C2×#34911yescharacteristic
145C2×C61C2×#35011yescharacteristic
146D61—41no—
147C4×#41—611no—
148C2×M32—1221no—
149#446—611no—
150#446—611no—
151#436—611no—
152#436#692311yescharacteristic
153#435—1221no—
154#435—1221no—
155#431—611no—
156#431—1221no—
157C4×M16—1221no—
158C2×C4×C8—611no—
159C4⋊C16—612no—
160C22⋊C16—1221no—
161#346—612no—
162C4×C16—1221no—
163C4×C16—1221no—
164C61#1161711yescharacteristic, complemented, Sylow
165C2×#41—611no—
166C2×M16—21no—
167C2×M16—1221no—
168C22×C8—611no—
169C22×C8—611no—
170C4×Q8—611no—
171C4×Q8—611no—
172C4×D4—611no—
173C4×D4—1221no—
174C4×D4—1221no—
175C4×D4C2×#692311yescharacteristic
176#117—611no—
177#117—1221no—
178C2×C42—611no—
179C2×C42—1221no—
180M32—1224no—
181C2×C16—1222no—
182C2×C16—1222no—
183C4⋊C8—611no—
184C4⋊C8—1221no—
185C4⋊C8—1221no—
186C4⋊C8C2×#692311yescharacteristic
187C22⋊C8—21no—
188C22⋊C8—1221no—
189C22⋊C8—1221no—
190#97—1221no—
191#97—1221no—
192C4×C8—611no—
193C4×C8—611no—
194C4×C8—611no—
195C4×C8—1221no—
196C4×C8C2×#692311yescharacteristic
197#41—2442no—
198C2×Q8—611no—
199C2×D4—1221no—
200C2×D4D61⋊C811yescharacteristic
201C22×C4—21no—
202C22×C4—611no—
203C22×C4—611no—
204C22×C4—611no—
205C22×C4—1221no—
206C22×C4—1221no—
207M16—42no—
208M16—2442no—
209C2×C8—21no—
210C2×C8—611no—
211C2×C8—611no—
212C2×C8—1222no—
213C2×C8—1222no—
214C2×C8—1221no—
215C2×C8C22⋊#692311yescharacteristic
216C2×C8C22⋊#692311yescharacteristic
217C4⋊C4—611no—
218C4⋊C4—1221no—
219C4⋊C4—1221no—
220C4⋊C4D61⋊C811yescharacteristic
221C22⋊C4—21no—
222C22⋊C4—1221no—
223C22⋊C4—1221no—
224C42—611no—
225C42—611no—
226C42—611no—
227C42—1221no—
228C42—1221no—
229C42—1221no—
230C42C22×#692311yescharacteristic
231C16—1224no—
232C16—2442no—
233C23—21no—
234C23—611no—
235Q8—2441no—
236D4—41no—
237D4—2442no—
238C2×C4—21no—
239C2×C4—41no—
240C2×C4—41no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—1222no—
245C2×C4—1222no—
246C2×C4—1221no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—2442no—
251C2×C4—2442no—
252C2×C4C2×C22⋊#692311yescharacteristic
253C2×C4C2×D61⋊C811yescharacteristic
254C2×C4D61⋊M1611yescharacteristic
255C8—21no—
256C8—41no—
257C8—612no—
258C8—1221no—
259C8—2441no—
260C8#1451984112yes—
261C22—41no—
262C22—41no—
263C22—41no—
264C22—1221no—
265C22—1221no—
266C22—1221no—
267C22D61⋊(C22⋊C8)11yescharacteristic
268C4—21no—
269C4—21no—
270C4—41no—
271C4—612no—
272C4—612no—
273C4—1221no—
274C4—2441no—
275C4—2441no—
276C4#1684075211yescharacteristic
277C4C2×#1451984111yescharacteristic
278C2—81no—
279C2—2441no—
280C2#2146111111yescharacteristic
281C2D61⋊#34911yescharacteristic
282C2D61⋊#35011yescharacteristic
subgroupG/H
centerC2×C4C2×C22⋊#6923
commutatorC2×C4×C61C22×C8
FrattiniC42C22×#6923
FittingC61×#436C4
socleC22×C61C2×C22⋊C8
prime radicalC2×#11758224C8
cosocleC4×#92418C23
hypercenter#436#6923
hypocenterC61#11617
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C4×C8 ◁ #436

Complements

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

NH ≅ G/Ntype
1. #21462179C2semidirect
2. #21462026C2semidirect
3. #21460788C2semidirect
4. #21460771C2semidirect
164. C61#11617semidirect

Maximal subgroups

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

subgroupindex
#214621792
#214620262
#214607882
#214607712
#214547822
#1161761