Finite Group Databasebeta

← #30594511

Subgroups — #30594511

Order 15616.

280 conjugacy classes of subgroups; only the 62 normal subgroups are shown.

normal subgroups only

This group has 280 conjugacy classes of subgroups — too many to draw. Only its 62 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#21461990C211yesmaximal, characteristic
2#21461686C211yesmaximal, characteristic
3#21445814C211yesmaximal, characteristic
4#16840765—21no—
5C2×#14519844C411yescharacteristic
6C2×#14519838—21no—
7C2×C4×#92420C411yescharacteristic
8#16840642C412yes—
9#16840628—21no—
10#16840628—21no—
11C2×#14519742C2211yescharacteristic
12#16839785—21no—
13C2×#14519695—21no—
14#16839531C411yescharacteristic
15C61×#343C411yescharacteristic
16C2×#11758217—22no—
17C22×#92420—21no—
18C22×#92420—21no—
19#14519844—41no—
20#14519844—41no—
21C4⋊#92420—41no—
22#14519838—41no—
23#14519838—41no—
24C4×#92420—41no—
25C22×Dic122D411yescharacteristic
26C2×#11758194—21no—
27#14519742—41no—
28#14519742—41no—
29C2×#11758196C2×C411yescharacteristic
30C2×#11758196Q811yescharacteristic
31C2×C4×Dic61C2×C411yescharacteristic
32C2×C4×Dic61D411yescharacteristic
33C2×C4×Dic61D411yescharacteristic
34#14519706—41no—
35#14519706—41no—
36#14519695—41no—
37#14519695—41no—
38C2×M16×C61—21no—
39C2×C4⋊C4×C61C2×C411yescharacteristic
40C22×C4×C61C4211yescharacteristic
41C22×C4×C61C22⋊C411yescharacteristic
42C22×C4×C61C4⋊C411yescharacteristic
43C22×Dic61C22⋊C411yescharacteristic
44C22×Dic61C22⋊C411yescharacteristic
45C22×Dic61C4⋊C411yescharacteristic
46C22×Dic61C4⋊C411yescharacteristic
47C2×Dic122—41no—
48C2×Dic122—41no—
49C2×Dic122D811yescharacteristic
50C2×Dic122SD1611yescharacteristic
51C2×Dic122SD1611yescharacteristic
52C2×Dic122Q1611yescharacteristic
53#11758217—42no—
54#11758217—42no—
55C2×#92420—22no—
56C2×#92420—41no—
57C2×#92420—41no—
58C2×#92420—42no—
59C2×#92420—42no—
60C2×#92420—41no—
61M16×C61—41no—
62M16×C61—41no—
63C2×C8×C61—41no—
64C4⋊C4×C61—41no—
65#11758196—41no—
66#11758196—41no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61—21no—
70C4×Dic61—21no—
71C4×Dic61—21no—
72C4×Dic61—21no—
73#11758194—41no—
74#11758194—41no—
75C2×#92418—41no—
76C23×C61#9511yescharacteristic
77C2×C4×C61—21no—
78C2×C4×C61—21no—
79C2×C4×C61—21no—
80C2×C4×C61—21no—
81C2×C4×C61—41no—
82C2×C4×C61—41no—
83C2×C4×C61#10211yescharacteristic
84C2×C4×C61#10311yescharacteristic
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—21no—
91C2×Dic61—21no—
92C2×Dic61—41no—
93C2×Dic61#9911yescharacteristic
94C2×Dic61#9911yescharacteristic
95C2×Dic61#10211yescharacteristic
96C2×Dic61#10311yescharacteristic
97C2×Dic61#10611yescharacteristic
98C2×Dic61#10711yescharacteristic
99Dic122—41no—
100Dic122—41no—
101Dic122—41no—
102Dic122—41no—
103#92420—42no—
104#92420—82no—
105#92420—81no—
106C8×C61—81no—
107#92418—81no—
108#7238—611nomaximal, Sylow
109C22×C61—21no—
110C22×C61—21no—
111C22×C61H(3,ℤ/4)11yescharacteristic
112C22×C61#34011yescharacteristic
113C22×C61#34211yescharacteristic
114C4×C61—21no—
115C4×C61—21no—
116C4×C61—41no—
117C4×C61—41no—
118Dic61—21no—
119Dic61—21no—
120Dic61—21no—
121Dic61—21no—
122Dic61—21no—
123Dic61—41no—
124Dic61#35511yescharacteristic
125Dic61#35611yescharacteristic
126#1984—611no—
127#1801—611no—
128#1801—611no—
129C2×C61—21no—
130C2×C61—21no—
131C2×C61#128911yescharacteristic
132C2×C61#139211yescharacteristic
133C2×C61#139411yescharacteristic
134C2×C4×Q8—611no—
135#423—1221no—
136#423—1221no—
137C2×C4⋊C8—611no—
138C2×#101—1221no—
139C2×#101—1221no—
140C2×C4×C8—611no—
141#343—612no—
142#343—611no—
143#343#692311yescharacteristic
144#336—1221no—
145#336—1221no—
146C61#723811yescharacteristic, complemented, Sylow
147C22×Q8—611no—
148C2×M16—21no—
149C2×M16—1222no—
150C2×M16—1221no—
151C22×C8—1221no—
152C22×C8—1221no—
153C4×Q8—2441no—
154C4×Q8—2441no—
155C2×C4⋊C4—611no—
156C2×C4⋊C4—611no—
157C2×C4⋊C4C2×#692311yescharacteristic
158C2×C42—611no—
159C2×C42—611no—
160C2×C42—611no—
161C4⋊C8—2441no—
162C4⋊C8—2441no—
163C4⋊C8—2441no—
164C4⋊C8—2441no—
165C4⋊C8—2441no—
166#101—2441no—
167#101—2441no—
168#101—2441no—
169#101—2441no—
170C4×C8—2441no—
171C2×Q8—611no—
172C2×Q8—611no—
173C2×Q8—611no—
174C2×Q8—611no—
175C2×Q8—2441no—
176C2×Q8—2441no—
177C22×C4—611no—
178C22×C4—611no—
179C22×C4—611no—
180C22×C4—611no—
181C22×C4C4×#692311yescharacteristic
182C22×C4C4⋊#692311yescharacteristic
183C22×C4C22⋊#692311yescharacteristic
184M16—41no—
185M16—41no—
186M16—2441no—
187M16—2442no—
188M16—2442no—
189M16—2441no—
190C2×C8—41no—
191C2×C8—1222no—
192C2×C8—2441no—
193C2×C8—2441no—
194C2×C8—2442no—
195C2×C8—2442no—
196C2×C8—2441no—
197C2×C8—2441no—
198C4⋊C4—41no—
199C4⋊C4—2441no—
200C4⋊C4—2441no—
201C42—1221no—
202C42—1221no—
203C42—1221no—
204C42—1221no—
205C42—1221no—
206C42—1221no—
207C23(C2×#6923)⋊C411yescharacteristic
208Q8—2441no—
209Q8—2441no—
210Q8—2441no—
211Q8—2441no—
212C2×C4—21no—
213C2×C4—21no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—41no—
217C2×C4—41no—
218C2×C4—611no—
219C2×C4—611no—
220C2×C4—611no—
221C2×C4—611no—
222C2×C4—611no—
223C2×C4—611no—
224C2×C4—1221no—
225C2×C4—1221no—
226C2×C4—1221no—
227C2×C4—1221no—
228C2×C4—1221no—
229C2×C4—1221no—
230C2×C4—1221no—
231C2×C4—2441no—
232C2×C4#1451983911yescharacteristic
233C2×C4#1451984011yescharacteristic
234C8—81no—
235C8—4881no—
236C8—4881no—
237C8—4882no—
238C8—2442no—
239C22—21no—
240C22—21no—
241C22#1684062911yescharacteristic
242C22#1684063511yescharacteristic
243C22#1684063911yescharacteristic
244C4—21no—
245C4—21no—
246C4—41no—
247C4—41no—
248C4—611no—
249C4—611no—
250C4—1221no—
251C4—1221no—
252C4—1221no—
253C4—1221no—
254C4—1221no—
255C4—2441no—
256C2—21no—
257C2—21no—
258C2#2146068111yescharacteristic
259C2#2146090911yescharacteristic
260C2#2146091511yescharacteristic
subgroupG/H
centerC22#16840639
commutatorC22×C4×C61C42
FrattiniC2×C4⋊C4C2×#6923
FittingC61×#343C4
socleC22×C61#342
prime radicalC23×C61#95
cosocleC2×#14519742C22
hypercenter#343#6923
hypocenterC61#7238
LCSG ▷ C22×C4×C61 ▷ C22×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C22 ◁ C23 ◁ C2×C4⋊C4 ◁ #343

Complements

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

NH ≅ G/Ntype
146. C61#7238semidirect

Maximal subgroups

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

subgroupindex
#214619902
#214616862
#214458142
#723861