Finite Group Databasebeta

← #30594534

Subgroups — #30594534

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#21461795C211yesmaximal, characteristic
2#21461080C211yesmaximal, characteristic
3#21444156C211yesmaximal, characteristic
4C22×D61⋊C8C411yescharacteristic
5#16840782—21no—
6C2×#14519834—21no—
7C2×#14519834C411yescharacteristic
8#16840628—21no—
9#16840606—21no—
10#16840606C412yes—
11C2×#14519739C2211yescharacteristic
12#16839724—21no—
13#16839488C411yescharacteristic
14#16839485—21no—
15C61×#324C411yescharacteristic
16C2×D61⋊C8—41no—
17C2×D61⋊C8—42no—
18C22×#92420—21no—
19C22×#92420—21no—
20#14519844—41no—
21#14519834—42no—
22#14519834—41no—
23C22⋊#92420—22no—
24#14519832—41no—
25C22×D244Q811yescharacteristic
26C22×C4×D61C2×C411yescharacteristic
27C22×C4×D61D411yescharacteristic
28C2×#11758189—41no—
29#14519739—41no—
30#14519739—41no—
31C2×#11758198C2×C411yescharacteristic
32C2×#11758198D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34C22⋊#92418—21no—
35#14519689—41no—
36C2×C4⋊C4×C61C2×C411yescharacteristic
37C22⋊C8×C61—21no—
38C23×D61C4⋊C411yescharacteristic
39C23×D61C4⋊C411yescharacteristic
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C4⋊C411yescharacteristic
43C22×Dic61C22⋊C411yescharacteristic
44C22×Dic61C22⋊C411yescharacteristic
45C2×D244—22no—
46C2×D244—41no—
47C2×D244—41no—
48C2×C4×D61—21no—
49C2×C4×D61—21no—
50C2×C4×D61—21no—
51C2×C4×D61—21no—
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×C4×D61—41no—
55C2×C4×D61—41no—
56C2×#92420—22no—
57C2×#92420—41no—
58C2×#92420—41no—
59C2×#92420—42no—
60C2×#92420—41no—
61C2×#92420—41no—
62C2×#92420—41no—
63D61⋊C8—42no—
64D61⋊C8—42no—
65C2×C8×C61—41no—
66C4⋊C4×C61—41no—
67#11758198—41no—
68#11758198—41no—
69C4×Dic61—21no—
70C4×Dic61—21no—
71C2×#92418—41no—
72#11758189—81no—
73#11758189—81no—
74C23×C61#9511yescharacteristic
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61—21no—
80C22×D61—41no—
81C22×D61—41no—
82C22×D61—41no—
83C22×D61—41no—
84C22×D61#10812yes—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—21no—
90C2×C4×C61—41no—
91C2×C4×C61—41no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—41no—
96C2×Dic61#9911yescharacteristic
97C2×Dic61#9911yescharacteristic
98D244—44no—
99C4×D61—42no—
100C4×D61—41no—
101C4×D61—41no—
102C4×D61—41no—
103C4×D61—41no—
104C4×D61—81no—
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#33811yescharacteristic
114C22×C61#34111yescharacteristic
115C22×C61#34211yescharacteristic
116C2×D61—22no—
117C2×D61—42no—
118C2×D61—41no—
119C2×D61—41no—
120C2×D61—42no—
121C2×D61—42no—
122C2×D61—41no—
123C2×D61—41no—
124C2×D61—41no—
125C2×D61—81no—
126C4×C61—41no—
127C4×C61—41no—
128C4×C61—41no—
129Dic61—21no—
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#129311yescharacteristic
139C2×C61#139011yescharacteristic
140C2×C61#139511yescharacteristic
141D61—42no—
142D61—81no—
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—611no—
151#324#692311yescharacteristic
152#323—612no—
153#323—1221no—
154#323—1221no—
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⋊C4C2×#692311yescharacteristic
167C2×C22⋊C4—611no—
168C2×C22⋊C4—611no—
169C2×C42—611no—
170C4⋊C8—2441no—
171C22⋊C8—21no—
172C22⋊C8—1222no—
173C22⋊C8—1221no—
174C22⋊C8—2441no—
175C22⋊C8—2442no—
176C22⋊C8—2441no—
177#97—2441no—
178C24—611no—
179C24—611no—
180C2×D4—1222no—
181C2×D4—2441no—
182C2×D4—2441no—
183C22×C4—611no—
184C22×C4—611no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—1221no—
188C22×C4—1221no—
189C22×C4—2441no—
190C22×C4—2441no—
191C22×C4—2441no—
192C22×C4—2441no—
193C22×C4C4×#692311yescharacteristic
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—41no—
210C22⋊C4—2441no—
211C22⋊C4—2441no—
212C42—1221no—
213C42—1221no—
214C23—612no—
215C23—1221no—
216C23—1221no—
217C23—1221no—
218C23—1221no—
219C23—1221no—
220C23—2441no—
221C23—2441no—
222C23—2441no—
223C23—2441no—
224C23(C2×#6923)⋊C411yescharacteristic
225D4—2444no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—611no—
234C2×C4—611no—
235C2×C4—1221no—
236C2×C4—1221no—
237C2×C4—1221no—
238C2×C4—4881no—
239C2×C4—2441no—
240C2×C4—2441no—
241C2×C4—2441no—
242C2×C4—2441no—
243C2×C4—2442no—
244C2×C4—2441no—
245C8—81no—
246C8—4881no—
247C8—4881no—
248C8—4882no—
249C8—2442no—
250C22—21no—
251C22—21no—
252C22—1222no—
253C22—4881no—
254C22—2442no—
255C22—2442no—
256C22—2442no—
257C22—2441no—
258C22—2441no—
259C22—2441no—
260C22—2441no—
261C22—2441no—
262C22#1684063111yescharacteristic
263C22#1684063711yescharacteristic
264C22#1684063911yescharacteristic
265C4—41no—
266C4—41no—
267C4—41no—
268C4—611no—
269C4—611no—
270C4—1221no—
271C4—2441no—
272C2—21no—
273C2—21no—
274C2—4881no—
275C2—2442no—
276C2#2146069011yescharacteristic
277C2#2146090211yescharacteristic
278C2#2146092111yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#324C4
socleC22×C61#342
prime radicalC22×D244Q8
cosocleC2×#14519739C22
hypercenter#324#6923
hypocenterC61#7247
LCSG ▷ C22×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
155. C61#7247semidirect

Maximal subgroups

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

subgroupindex
#214617952
#214610802
#214441562
#724761