Finite Group Databasebeta

← #30594537

Subgroups — #30594537

Order 15616.

322 conjugacy classes of subgroups; only the 52 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 52 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#21461793C211yesmaximal, characteristic
2#21461077C211yesmaximal, characteristic
3#21444158C211yesmaximal, characteristic
4C22×D61⋊C8C411yescharacteristic
5#16840732—21no—
6C2×#14519834C411yescharacteristic
7C2×C22⋊#92420—21no—
8#16840628—21no—
9#16840608C412yes—
10#16840606—21no—
11C2×#14519737C2211yescharacteristic
12#16839816—21no—
13#16839486C411yescharacteristic
14#16839485—21no—
15C61×#323C411yescharacteristic
16C2×#11758217—41no—
17C2×D61⋊C8—41no—
18C2×D61⋊C8—42no—
19C22×#92420—21no—
20C22×#92420—21no—
21#14519834—41no—
22C22⋊#92420—22no—
23C22⋊#92420—42no—
24C22⋊#92420—41no—
25C22×C22⋊D61Q811yescharacteristic
26C23×Dic61D411yescharacteristic
27C22×C4×D61C2×C411yescharacteristic
28#14519737—41no—
29#14519737—41no—
30C2×#11758196C2×C411yescharacteristic
31C2×#11758198D411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33#14519706—41no—
34C22⋊#92418—21no—
35#14519687—41no—
36C2×C22⋊C4×C61C2×C411yescharacteristic
37C22⋊C8×C61—21no—
38C24×C61C4⋊C411yescharacteristic
39C23×D61C4⋊C411yescharacteristic
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C2×C22⋊D61—22no—
43C2×C22⋊D61—41no—
44C2×C22⋊D61—41no—
45C22×Dic61—21no—
46C22×Dic61—21no—
47C22×Dic61—41no—
48C22×Dic61—41no—
49C22×Dic61C22⋊C411yescharacteristic
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C4⋊C411yescharacteristic
52C2×C4×D61—21no—
53C2×C4×D61—21no—
54C2×C4×D61—41no—
55C2×C4×D61—41no—
56#11758217—81no—
57#11758217—81no—
58C2×#92420—22no—
59C2×#92420—41no—
60C2×#92420—41no—
61C2×#92420—42no—
62C2×#92420—41no—
63C2×#92420—41no—
64C2×#92420—41no—
65D61⋊C8—42no—
66D61⋊C8—42no—
67C2×C8×C61—41no—
68C22⋊C4×C61—41no—
69#11758198—41no—
70#11758196—41no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73C2×#92418—41no—
74C23×C61—21no—
75C23×C61—21no—
76C23×C61—21no—
77C23×C61—41no—
78C23×C61—41no—
79C23×C61#9511yescharacteristic
80C22×D61—21no—
81C22×D61—21no—
82C22×D61—41no—
83C22×D61—41no—
84C22×D61#10812yes—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—41no—
88C2×C4×C61—41no—
89C22⋊D61—44no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—41no—
97C2×Dic61—41no—
98C2×Dic61—41no—
99C2×Dic61—81no—
100C2×Dic61#9911yescharacteristic
101C2×Dic61#9911yescharacteristic
102C4×D61—42no—
103C4×D61—41no—
104C4×D61—41no—
105#92420—42no—
106#92420—81no—
107#92420—82no—
108C8×C61—81no—
109#92418—81no—
110#7247—611nomaximal, Sylow
111C22×C61—21no—
112C22×C61—21no—
113C22×C61—42no—
114C22×C61—41no—
115C22×C61—41no—
116C22×C61—41no—
117C22×C61—81no—
118C22×C61#33811yescharacteristic
119C22×C61#34111yescharacteristic
120C22×C61#34211yescharacteristic
121C2×D61—22no—
122C2×D61—42no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—42no—
126C4×C61—41no—
127C4×C61—41no—
128Dic61—21no—
129Dic61—41no—
130Dic61—41no—
131Dic61AΣL(1,𝔽16)11yescharacteristic
132Dic61#35211yescharacteristic
133#1869—611no—
134#1466—611no—
135#1465—611no—
136C2×C61—21no—
137C2×C61—21no—
138C2×C61—81no—
139C2×C61#129311yescharacteristic
140C2×C61#139011yescharacteristic
141C2×C61#139511yescharacteristic
142D61—42no—
143C23×C8—611no—
144C2×C4×D4—611no—
145#432—1221no—
146#407—1221no—
147C2×C22⋊C8—611no—
148C2×C22⋊C8—1221no—
149#336—1221no—
150#324—612no—
151#323—611no—
152#323—1221no—
153#323—1221no—
154#323#692311yescharacteristic
155C61#724711yescharacteristic, complemented, Sylow
156C22×D4—611no—
157C23×C4—611no—
158C23×C4—611no—
159C2×M16—2441no—
160C22×C8—1221no—
161C22×C8—1221no—
162C22×C8—2442no—
163C22×C8—2441no—
164C4×D4—2441no—
165C4×D4—2441no—
166C2×C4⋊C4—611no—
167C2×C22⋊C4—611no—
168C2×C22⋊C4C2×#692311yescharacteristic
169C2×C42—611no—
170C4⋊C8—2441no—
171C22⋊C8—21no—
172C22⋊C8—1222no—
173C22⋊C8—1221no—
174C22⋊C8—2442no—
175C22⋊C8—2441no—
176C22⋊C8—2441no—
177#97—2441no—
178C24—611no—
179C24C4⋊#692311yescharacteristic
180C2×D4—1222no—
181C2×D4—2441no—
182C2×D4—2441no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—611no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4—1221no—
189C22×C4—1221no—
190C22×C4—2441no—
191C22×C4—2441no—
192C22×C4—2441no—
193C22×C4—2441no—
194C22×C4C4×#692311yescharacteristic
195C22×C4C22⋊#692311yescharacteristic
196M16—4881no—
197M16—4881no—
198C2×C8—41no—
199C2×C8—1222no—
200C2×C8—2441no—
201C2×C8—2441no—
202C2×C8—2442no—
203C2×C8—2441no—
204C2×C8—2441no—
205C2×C8—2441no—
206C2×C8—2441no—
207C2×C8—2442no—
208C2×C8—2442no—
209C4⋊C4—2441no—
210C22⋊C4—41no—
211C22⋊C4—2441no—
212C42—1221no—
213C42—1221no—
214C23—21no—
215C23—21no—
216C23—21no—
217C23—41no—
218C23—41no—
219C23—612no—
220C23—1221no—
221C23—1221no—
222C23—2441no—
223C23—2441no—
224C23(C2×#6923)⋊C411yescharacteristic
225D4—2444no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—41no—
229C2×C4—41no—
230C2×C4—611no—
231C2×C4—611no—
232C2×C4—1221no—
233C2×C4—1221no—
234C2×C4—1221no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—4881no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2442no—
242C2×C4—2441no—
243C2×C4—2441no—
244C2×C4—2441no—
245C8—81no—
246C8—4881no—
247C8—4881no—
248C8—4882no—
249C8—2442no—
250C22—21no—
251C22—21no—
252C22—42no—
253C22—41no—
254C22—41no—
255C22—41no—
256C22—81no—
257C22—1222no—
258C22—2442no—
259C22—2442no—
260C22—2441no—
261C22—2441no—
262C22#1684063111yescharacteristic
263C22#1684063711yescharacteristic
264C22#1684063911yescharacteristic
265C4—41no—
266C4—41no—
267C4—611no—
268C4—611no—
269C4—1221no—
270C4—2441no—
271C4—2441no—
272C2—21no—
273C2—21no—
274C2—81no—
275C2—2442no—
276C2#2146069011yescharacteristic
277C2#2146090511yescharacteristic
278C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
prime radicalC22×C22⋊D61Q8
cosocleC2×#14519737C22
hypercenter#323#6923
hypocenterC61#7247
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C22⋊C4 ◁ #323

Complements

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

NH ≅ G/Ntype
155. C61#7247semidirect

Maximal subgroups

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

subgroupindex
#214617932
#214610772
#214441582
#724761