Finite Group Databasebeta

← #30593978

Subgroups — #30593978

Order 15616.

358 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 358 conjugacy classes of subgroups — too many to draw. Only its 74 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#21461711C211yesmaximal, characteristic
2#21461676C211yesmaximal, characteristic
3#21445582C211yesmaximal, characteristic
4C2×#14519844—21no—
5C2×#14519834—21no—
6C2×#14519834C412yes—
7#16840628—21no—
8#16840628—21no—
9#16840628C412yes—
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12C2×#14519688C411yescharacteristic
13#16839516—21no—
14C2×#97×C61C411yescharacteristic
15C22×#92420—22no—
16C22×#92420—22no—
17#14519844—41no—
18#14519844—41no—
19#14519834—41no—
20#14519834—41no—
21#14519834—42no—
22C22×C4×D61C2×C411yescharacteristic
23C22×C4×D61D411yescharacteristic
24C22×C4×D61Q811yescharacteristic
25C22×#92418—21no—
26C2×C4×Dic61C2×C411yescharacteristic
27C2×C4×Dic61D411yescharacteristic
28C2×C4×Dic61D411yescharacteristic
29C42×D61—41no—
30C42×D61—41no—
31#14519689—24no—
32#14519688—41no—
33C22×C8×C61—21no—
34C2×C42×C61C2×C411yescharacteristic
35#97×C61—41no—
36C23×D61C4⋊C411yescharacteristic
37C22×C4×C61C4211yescharacteristic
38C22×C4×C61C22⋊C411yescharacteristic
39C22×C4×C61C4⋊C411yescharacteristic
40C22×Dic61C22⋊C411yescharacteristic
41C22×Dic61C22⋊C411yescharacteristic
42C22×Dic61C4⋊C411yescharacteristic
43C2×C4×D61—22no—
44C2×C4×D61—21no—
45C2×C4×D61—21no—
46C2×C4×D61—21no—
47C2×C4×D61—21no—
48C2×C4×D61—22no—
49C2×C4×D61—22no—
50C2×C4×D61—41no—
51C2×C4×D61—41no—
52C2×C4×D61—41no—
53C2×C4×D61—41no—
54C2×#92420—42no—
55C2×#92420—42no—
56C2×#92420—42no—
57C2×#92420—42no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×C8×C61—22no—
61C2×C8×C61—41no—
62C2×C8×C61—41no—
63C42×C61—21no—
64C42×C61—21no—
65C4×Dic61—21no—
66C4×Dic61—21no—
67C4×Dic61—41no—
68C4×Dic61—41no—
69C2×#92418—22no—
70C2×#92418—41no—
71C2×#92418—41no—
72C23×C61#9511yescharacteristic
73C22×D61—21no—
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—21no—
77C22×D61—21no—
78C22×D61—21no—
79C22×D61#10812yes—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61—21no—
86C2×C4×C61—21no—
87C2×C4×C61—21no—
88C2×C4×C61#9911yescharacteristic
89C2×C4×C61#9911yescharacteristic
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—21no—
93C2×Dic61—21no—
94C2×Dic61—21no—
95C2×Dic61—21no—
96C2×Dic61#10011yescharacteristic
97C2×Dic61#10111yescharacteristic
98C2×Dic61#10412yes—
99C2×Dic61#10812yes—
100C4×D61—42no—
101C4×D61—42no—
102C4×D61—44no—
103C4×D61—42no—
104C4×D61—42no—
105#92420—82no—
106#92420—82no—
107C8×C61—42no—
108#92418—42no—
109#7038—611nomaximal, Sylow
110C22×C61H(3,ℤ/4)11yescharacteristic
111C22×C61#33911yescharacteristic
112C22×C61#34111yescharacteristic
113C22×C61#34111yescharacteristic
114C22×C61#34211yescharacteristic
115C22×C61#34311yescharacteristic
116C22×C61#34411yescharacteristic
117C2×D61—22no—
118C2×D61—22no—
119C2×D61—22no—
120C2×D61—41no—
121C2×D61—41no—
122C2×D61—41no—
123C2×D61—41no—
124C4×C61—21no—
125C4×C61—21no—
126C4×C61—41no—
127C4×C61—41no—
128Dic61—22no—
129Dic61—22no—
130Dic61—21no—
131Dic61—21no—
132#1817—611no—
133#1797—611no—
134#1749—611no—
135C2×C61#128411yescharacteristic
136C2×C61#128711yescharacteristic
137C2×C61#129011yescharacteristic
138C2×C61#129811yescharacteristic
139C2×C61#129911yescharacteristic
140C2×C61#130211yescharacteristic
141C2×C61#130511yescharacteristic
142D61—42no—
143C22×C42—611no—
144C2×C4⋊C8—1221no—
145C2×C22⋊C8—612no—
146C2×C22⋊C8—1221no—
147C2×C22⋊C8—1221no—
148C2×#97—611no—
149C2×#97#692311yescharacteristic
150#336—612no—
151#336—1221no—
152#336—1221no—
153#336—1221no—
154C61#703811yescharacteristic, complemented, Sylow
155C23×C4—611no—
156C23×C4—611no—
157C23×C4—611no—
158C22×C8—21no—
159C22×C8—1221no—
160C22×C8—1222no—
161C22×C8—1222no—
162C2×C42—611no—
163C2×C42—611no—
164C2×C42—611no—
165C2×C42—2441no—
166C2×C42—2441no—
167C2×C42C2×#692311yescharacteristic
168C4⋊C8—2441no—
169C4⋊C8—2441no—
170C22⋊C8—1224no—
171C22⋊C8—2441no—
172C22⋊C8—2441no—
173C22⋊C8—2442no—
174#97—41no—
175#97—2441no—
176C24—611no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—1222no—
181C22×C4—1221no—
182C22×C4—1222no—
183C22×C4—1221no—
184C22×C4—1222no—
185C22×C4—1221no—
186C22×C4—1221no—
187C22×C4—2441no—
188C22×C4—2441no—
189C22×C4—2441no—
190C22×C4—2441no—
191C22×C4C4×#692311yescharacteristic
192C22×C4C4⋊#692311yescharacteristic
193C22×C4C22⋊#692311yescharacteristic
194C2×C8—22no—
195C2×C8—41no—
196C2×C8—41no—
197C2×C8—1222no—
198C2×C8—2442no—
199C2×C8—2442no—
200C2×C8—2442no—
201C2×C8—2442no—
202C2×C8—2442no—
203C2×C8—2442no—
204C2×C8—2441no—
205C2×C8—2441no—
206C42—21no—
207C42—21no—
208C42—1221no—
209C42—1221no—
210C42—2441no—
211C42—2441no—
212C23—612no—
213C23—1221no—
214C23—1221no—
215C23—1221no—
216C23—1221no—
217C23—1221no—
218C23—1221no—
219C23(C2×#6923)⋊C411yescharacteristic
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—21no—
227C2×C4—21no—
228C2×C4—612no—
229C2×C4—612no—
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—2442no—
239C2×C4—2442no—
240C2×C4—2444no—
241C2×C4—2442no—
242C2×C4—2442no—
243C2×C4#1451983511yescharacteristic
244C2×C4#1451983611yescharacteristic
245C8—42no—
246C8—4882no—
247C8—4882no—
248C8—2442no—
249C22—1222no—
250C22—1222no—
251C22—1222no—
252C22—2441no—
253C22—2441no—
254C22—2441no—
255C22—2441no—
256C22#1684062911yescharacteristic
257C22#1684063311yescharacteristic
258C22#1684063711yescharacteristic
259C22#1684063711yescharacteristic
260C22#1684064011yescharacteristic
261C22#1684064111yescharacteristic
262C22#1684064511yescharacteristic
263C4—21no—
264C4—21no—
265C4—41no—
266C4—41no—
267C4—1222no—
268C4—1222no—
269C4—1221no—
270C4—1221no—
271C2—2442no—
272C2#2146066711yescharacteristic
273C2#2146067511yescharacteristic
274C2#2146068311yescharacteristic
275C2#2146070111yescharacteristic
276C2#2146070411yescharacteristic
277C2#2146071311yescharacteristic
278C2#2146071911yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC2×#97×C61C4
socleC23×C61#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×D61C22
hypercenterC2×#97#6923
hypocenterC61#7038
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#97

Complements

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

NH ≅ G/Ntype
154. C61#7038semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214616762
#214455822
#703861