Finite Group Databasebeta

← #30594000

Subgroups — #30594000

Order 15616.

364 conjugacy classes of subgroups; only the 72 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 72 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#21461546C211yesmaximal, characteristic
3#21445580C211yesmaximal, characteristic
4C2×#14519834—21no—
5C2×#14519834C412yes—
6C2×#14519832—21no—
7#16840628—21no—
8#16840628—21no—
9#16840628C412yes—
10C2×C42×D61C2211yescharacteristic
11C2×#14519689—21no—
12C2×#14519687—21no—
13#16839517C411yescharacteristic
14C61×#336C411yescharacteristic
15C22×#92420—22no—
16C22×#92420—22no—
17#14519834—22no—
18#14519834—22no—
19#14519834—42no—
20#14519832—42no—
21C22×C4×D61C2×C411yescharacteristic
22C22×C4×D61D411yescharacteristic
23C22×C4×D61Q811yescharacteristic
24C22×#92418—21no—
25C2×C4×Dic61C2×C411yescharacteristic
26C2×C4×Dic61D411yescharacteristic
27C2×C4×Dic61D411yescharacteristic
28C42×D61—42no—
29#14519689—24no—
30#14519687—42no—
31C22×C8×C61—21no—
32C2×C42×C61C2×C411yescharacteristic
33C23×D61C4⋊C411yescharacteristic
34C22×C4×C61C4211yescharacteristic
35C22×C4×C61C22⋊C411yescharacteristic
36C22×C4×C61C4⋊C411yescharacteristic
37C22×Dic61C22⋊C411yescharacteristic
38C22×Dic61C22⋊C411yescharacteristic
39C22×Dic61C4⋊C411yescharacteristic
40C2×C4×D61—22no—
41C2×C4×D61—21no—
42C2×C4×D61—21no—
43C2×C4×D61—22no—
44C2×C4×D61—22no—
45C2×C4×D61—41no—
46C2×C4×D61—41no—
47C2×C4×D61—41no—
48C2×C4×D61—41no—
49C2×C4×D61—41no—
50C2×#92420—24no—
51C2×#92420—42no—
52C2×#92420—42no—
53C2×#92420—42no—
54C2×#92420—42no—
55C2×#92420—42no—
56C2×C8×C61—22no—
57C2×C8×C61—41no—
58C2×C8×C61—41no—
59C42×C61—41no—
60C4×Dic61—22no—
61C4×Dic61—22no—
62C4×Dic61—41no—
63C2×#92418—22no—
64C2×#92418—41no—
65C2×#92418—41no—
66C23×C61#9511yescharacteristic
67C22×D61—21no—
68C22×D61—21no—
69C22×D61—21no—
70C22×D61—21no—
71C22×D61—21no—
72C22×D61—21no—
73C22×D61#10812yes—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—21no—
82C2×C4×C61#10411yescharacteristic
83C2×C4×C61#10411yescharacteristic
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61#9912yes—
92C2×Dic61#10412yes—
93C4×D61—42no—
94C4×D61—42no—
95C4×D61—44no—
96C4×D61—44no—
97#92420—44no—
98#92420—82no—
99C8×C61—42no—
100#92418—42no—
101#7046—611nomaximal, Sylow
102C22×C61#33811yescharacteristic
103C22×C61#33911yescharacteristic
104C22×C61#33911yescharacteristic
105C22×C61#34111yescharacteristic
106C22×C61#34211yescharacteristic
107C22×C61#34411yescharacteristic
108C22×C61#34411yescharacteristic
109C2×D61—22no—
110C2×D61—22no—
111C2×D61—22no—
112C2×D61—41no—
113C2×D61—41no—
114C2×D61—41no—
115C2×D61—41no—
116C4×C61—21no—
117C4×C61—21no—
118C4×C61—41no—
119C4×C61—41no—
120Dic61—22no—
121Dic61—22no—
122Dic61—41no—
123#1817—611no—
124#1749—611no—
125#1749—611no—
126C2×C61#129111yescharacteristic
127C2×C61#129111yescharacteristic
128C2×C61#129311yescharacteristic
129C2×C61#129711yescharacteristic
130C2×C61#130211yescharacteristic
131C2×C61#130211yescharacteristic
132C2×C61#130611yescharacteristic
133D61—42no—
134C22×C42—611no—
135C2×C22⋊C8—612no—
136C2×C22⋊C8—1221no—
137C2×C22⋊C8—1221no—
138C2×#97—1221no—
139C2×#97—1221no—
140#336—612no—
141#336—611no—
142#336—1221no—
143#336—1221no—
144#336#692311yescharacteristic
145C61#704611yescharacteristic, complemented, Sylow
146C23×C4—611no—
147C23×C4—611no—
148C23×C4—611no—
149C22×C8—21no—
150C22×C8—1222no—
151C22×C8—1221no—
152C22×C8—1222no—
153C2×C42—611no—
154C2×C42—611no—
155C2×C42—611no—
156C2×C42—2442no—
157C2×C42C2×#692311yescharacteristic
158C22⋊C8—1224no—
159C22⋊C8—1222no—
160C22⋊C8—1222no—
161C22⋊C8—2442no—
162#97—2442no—
163#97—2442no—
164C24—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—1222no—
169C22×C4—1222no—
170C22×C4—1222no—
171C22×C4—1221no—
172C22×C4—1221no—
173C22×C4—2441no—
174C22×C4—2441no—
175C22×C4—2441no—
176C22×C4—2441no—
177C22×C4—2441no—
178C22×C4C4×#692311yescharacteristic
179C22×C4C4⋊#692311yescharacteristic
180C22×C4C22⋊#692311yescharacteristic
181C2×C8—22no—
182C2×C8—41no—
183C2×C8—41no—
184C2×C8—1222no—
185C2×C8—1224no—
186C2×C8—2442no—
187C2×C8—2442no—
188C2×C8—2442no—
189C2×C8—2441no—
190C2×C8—2442no—
191C2×C8—2442no—
192C2×C8—2441no—
193C42—41no—
194C42—1222no—
195C42—1222no—
196C42—2441no—
197C23—612no—
198C23—1221no—
199C23—1221no—
200C23—1221no—
201C23—1221no—
202C23—1221no—
203C23—1221no—
204C23(C2×#6923)⋊C411yescharacteristic
205C2×C4—21no—
206C2×C4—21no—
207C2×C4—21no—
208C2×C4—21no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—21no—
212C2×C4—21no—
213C2×C4—612no—
214C2×C4—612no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—1221no—
218C2×C4—1221no—
219C2×C4—1221no—
220C2×C4—1221no—
221C2×C4—1221no—
222C2×C4—2442no—
223C2×C4—2442no—
224C2×C4—2444no—
225C2×C4—2444no—
226C2×C4#1451984111yescharacteristic
227C2×C4#1451984211yescharacteristic
228C8—42no—
229C8—4882no—
230C8—2442no—
231C8—2444no—
232C22—1222no—
233C22—1222no—
234C22—1222no—
235C22—2441no—
236C22—2441no—
237C22—2441no—
238C22—2441no—
239C22#1684063111yescharacteristic
240C22#1684063211yescharacteristic
241C22#1684063311yescharacteristic
242C22#1684063711yescharacteristic
243C22#1684063911yescharacteristic
244C22#1684064411yescharacteristic
245C22#1684064511yescharacteristic
246C4—21no—
247C4—21no—
248C4—41no—
249C4—41no—
250C4—1222no—
251C4—1222no—
252C4—2441no—
253C2—2442no—
254C2#2146068511yescharacteristic
255C2#2146068611yescharacteristic
256C2#2146069011yescharacteristic
257C2#2146070011yescharacteristic
258C2#2146071211yescharacteristic
259C2#2146071311yescharacteristic
260C2#2146072311yescharacteristic
subgroupG/H
centerC23(C2×#6923)⋊C4
commutatorC22×C4×C61C42
FrattiniC2×C42C2×#6923
FittingC61×#336C4
socleC23×C61#95
prime radicalC23×D61C4⋊C4
cosocleC2×C42×D61C22
hypercenter#336#6923
hypocenterC61#7046
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C23 ◁ C2×C42 ◁ #336

Complements

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

NH ≅ G/Ntype
145. C61#7046semidirect

Maximal subgroups

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

subgroupindex
#214617112
#214615462
#214455802
#704661