Finite Group Databasebeta

← #30594559

Subgroups — #30594559

Order 15616.

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

normal subgroups only

This group has 328 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#21461677C211yesmaximal, characteristic
2#21461525C211yesmaximal, characteristic
3#21444130C211yesmaximal, characteristic
4C22×#11758217—21no—
5C2×#14519844C411yescharacteristic
6C2×C4⋊#92420C411yescharacteristic
7C2×C22⋊#92420—21no—
8#16840642—21no—
9#16840642C412yes—
10#16840628—21no—
11C2×#14519733C2211yescharacteristic
12#16839812—21no—
13#16839487—21no—
14#16839486C411yescharacteristic
15C61×#323C411yescharacteristic
16C2×#11758217—22no—
17C2×#11758217—22no—
18C2×#11758217—22no—
19C2×#11758217—41no—
20C2×#11758217—41no—
21C2×#11758217—41no—
22C22×#92420—21no—
23C22×#92420—21no—
24C22×#92420—41no—
25#14519844—41no—
26C4⋊#92420—41no—
27C22⋊#92420—41no—
28C22⋊#92420—41no—
29C23×Dic61D411yescharacteristic
30#14519733—41no—
31#14519733—41no—
32C2×#11758196C2×C411yescharacteristic
33C2×#11758196D411yescharacteristic
34C2×C22⋊Dic61Q811yescharacteristic
35C2×C4×Dic61C2×C411yescharacteristic
36C2×C4×Dic61D411yescharacteristic
37#14519706—41no—
38C22⋊#92418—21no—
39C8×Dic61—41no—
40C2×C22⋊C4×C61C2×C411yescharacteristic
41C22⋊C8×C61—21no—
42C24×C61C4⋊C411yescharacteristic
43C22×C4×C61C4211yescharacteristic
44C22×C4×C61C22⋊C411yescharacteristic
45C22×Dic61—21no—
46C22×Dic61—21no—
47C22×Dic61—21no—
48C22×Dic61—21no—
49C22×Dic61C22⋊C411yescharacteristic
50C22×Dic61C22⋊C411yescharacteristic
51C22×Dic61C4⋊C411yescharacteristic
52C22×Dic61C4⋊C411yescharacteristic
53C22×Dic61D811yescharacteristic
54C22×Dic61SD1611yescharacteristic
55C22×Dic61SD1611yescharacteristic
56C22×Dic61Q1611yescharacteristic
57#11758217—24no—
58#11758217—42no—
59#11758217—42no—
60#11758217—42no—
61C2×#92420—42no—
62C2×#92420—42no—
63C2×#92420—42no—
64C2×#92420—41no—
65C2×#92420—41no—
66C2×#92420—41no—
67C2×#92420—41no—
68C2×#92420—41no—
69C2×#92420—41no—
70C2×C8×C61—41no—
71C22⋊C4×C61—41no—
72C22⋊Dic61—41no—
73#11758196—41no—
74#11758196—41no—
75C4×Dic61—21no—
76C4×Dic61—21no—
77C4×Dic61—21no—
78C4×Dic61—21no—
79C2×#92418—41no—
80C23×C61—21no—
81C23×C61—21no—
82C23×C61—41no—
83C23×C61—41no—
84C23×C61#9511yescharacteristic
85C23×C61#10611yescharacteristic
86C23×C61#10711yescharacteristic
87C2×C4×C61—21no—
88C2×C4×C61—21no—
89C2×C4×C61—41no—
90C2×C4×C61—41no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61—21no—
97C2×Dic61—21no—
98C2×Dic61—21no—
99C2×Dic61—21no—
100C2×Dic61—21no—
101C2×Dic61—21no—
102C2×Dic61—21no—
103C2×Dic61—41no—
104C2×Dic61—41no—
105C2×Dic61#9911yescharacteristic
106C2×Dic61#9911yescharacteristic
107C2×Dic61#10211yescharacteristic
108C2×Dic61#10211yescharacteristic
109C2×Dic61#10311yescharacteristic
110C2×Dic61#10311yescharacteristic
111C2×Dic61#10411yescharacteristic
112C2×Dic61#10411yescharacteristic
113#92420—44no—
114#92420—81no—
115#92420—81no—
116C8×C61—81no—
117#92418—81no—
118#7253—611nomaximal, Sylow
119C22×C61—21no—
120C22×C61—21no—
121C22×C61—21no—
122C22×C61—21no—
123C22×C61—41no—
124C22×C61—41no—
125C22×C61—41no—
126C22×C61—41no—
127C22×C61—81no—
128C22×C61#33911yescharacteristic
129C22×C61#34011yescharacteristic
130C22×C61#34211yescharacteristic
131C4×C61—41no—
132C4×C61—41no—
133Dic61—21no—
134Dic61—21no—
135Dic61—41no—
136Dic61—41no—
137Dic61#32711yescharacteristic
138Dic61#32711yescharacteristic
139Dic61#32811yescharacteristic
140Dic61#32811yescharacteristic
141#1798—611no—
142#1742—611no—
143#1458—611no—
144C2×C61—21no—
145C2×C61—21no—
146C2×C61—41no—
147C2×C61—41no—
148C2×C61#129411yescharacteristic
149C2×C61#139211yescharacteristic
150C2×C61#139511yescharacteristic
151C22×M16—1221no—
152C2×#117—611no—
153#431—1221no—
154C2×C4⋊C8—611no—
155C2×C4⋊C8—611no—
156C2×C22⋊C8—1221no—
157#343—612no—
158#343—1221no—
159#336—1221no—
160#324—1221no—
161#323—611no—
162#323#692311yescharacteristic
163C61#725311yescharacteristic, complemented, Sylow
164C23×C4—611no—
165C2×M16—1222no—
166C2×M16—1222no—
167C2×M16—1222no—
168C2×M16—2441no—
169C2×M16—2441no—
170C2×M16—2441no—
171C22×C8—1221no—
172C22×C8—1221no—
173C22×C8—2441no—
174#117—2441no—
175#117—2441no—
176C2×C4⋊C4—611no—
177C2×C4⋊C4—611no—
178C2×C22⋊C4—611no—
179C2×C22⋊C4C2×#692311yescharacteristic
180C2×C42—611no—
181C2×C42—611no—
182C4⋊C8—2441no—
183C4⋊C8—2441no—
184C4⋊C8—2441no—
185C22⋊C8—21no—
186C22⋊C8—1221no—
187C22⋊C8—2441no—
188C22⋊C8—2441no—
189C4×C8—2441no—
190C24C4⋊#692311yescharacteristic
191C22×C4—611no—
192C22×C4—611no—
193C22×C4—611no—
194C22×C4—611no—
195C22×C4—611no—
196C22×C4—611no—
197C22×C4—611no—
198C22×C4—611no—
199C22×C4—1221no—
200C22×C4—1221no—
201C22×C4—1221no—
202C22×C4—1221no—
203C22×C4C4×#692311yescharacteristic
204C22×C4C22⋊#692311yescharacteristic
205M16—1224no—
206M16—2442no—
207M16—2442no—
208M16—2442no—
209C2×C8—41no—
210C2×C8—2441no—
211C2×C8—2441no—
212C2×C8—2441no—
213C2×C8—2441no—
214C2×C8—2441no—
215C2×C8—2441no—
216C2×C8—2441no—
217C2×C8—2442no—
218C2×C8—2442no—
219C2×C8—2442no—
220C4⋊C4—2441no—
221C4⋊C4—2441no—
222C22⋊C4—41no—
223C22⋊C4—2441no—
224C42—1221no—
225C42—1221no—
226C42—1221no—
227C42—1221no—
228C23—21no—
229C23—21no—
230C23—41no—
231C23—41no—
232C23(C2×#6923)⋊C411yescharacteristic
233C23#1451984511yescharacteristic
234C23#1451984611yescharacteristic
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—41no—
238C2×C4—41no—
239C2×C4—611no—
240C2×C4—611no—
241C2×C4—611no—
242C2×C4—611no—
243C2×C4—611no—
244C2×C4—611no—
245C2×C4—611no—
246C2×C4—611no—
247C2×C4—1221no—
248C2×C4—1221no—
249C2×C4—1221no—
250C2×C4—1221no—
251C2×C4—1221no—
252C2×C4—1221no—
253C2×C4—1221no—
254C2×C4—1221no—
255C2×C4—1221no—
256C2×C4—1221no—
257C2×C4—1221no—
258C2×C4—1221no—
259C2×C4—2441no—
260C2×C4—2441no—
261C8—81no—
262C8—4881no—
263C8—4881no—
264C8—4881no—
265C8—2444no—
266C22—21no—
267C22—21no—
268C22—21no—
269C22—21no—
270C22—41no—
271C22—41no—
272C22—41no—
273C22—41no—
274C22—81no—
275C22#1684063411yescharacteristic
276C22#1684063611yescharacteristic
277C22#1684063911yescharacteristic
278C4—41no—
279C4—41no—
280C4—611no—
281C4—611no—
282C4—611no—
283C4—611no—
284C4—1221no—
285C4—1221no—
286C4—2441no—
287C4—2441no—
288C2—21no—
289C2—21no—
290C2—41no—
291C2—41no—
292C2#2146069411yescharacteristic
293C2#2146090911yescharacteristic
294C2#2146091811yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C22⋊C4C2×#6923
FittingC61×#323C4
socleC22×C61#342
prime radicalC24×C61C4⋊C4
cosocleC2×#14519733C22
hypercenter#323#6923
hypocenterC61#7253
LCSG ▷ C22×C4×C61 ▷ C23×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
163. C61#7253semidirect

Maximal subgroups

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

subgroupindex
#214616772
#214615252
#214441302
#725361