Finite Group Databasebeta

← #30594654

Subgroups — #30594654

Order 15616.

298 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 298 conjugacy classes of subgroups — too many to draw. Only its 56 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#21461992C211yesmaximal, characteristic
2#21461572C211yesmaximal, characteristic
3#21445614C211yesmaximal, characteristic
4C2×C4⋊#92420C411yescharacteristic
5C2×#14519838—21no—
6C4×#11758217—21no—
7C2×#14519832C411yescharacteristic
8#16840642C412yes—
9#16840628—21no—
10#16840628—21no—
11C2×#14519742C2211yescharacteristic
12C2×#14519695—21no—
13M16×Dic61—21no—
14#16839531C411yescharacteristic
15C61×#343C411yescharacteristic
16C2×#11758217—22no—
17C22×#92420—21no—
18C22×#92420—21no—
19C4⋊#92420—41no—
20#14519838—22no—
21#14519838—22no—
22#14519832—41no—
23#14519832—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#14519695—24no—
35#14519687—41no—
36C8×Dic61—41no—
37C2×M16×C61—21no—
38C2×C4⋊C4×C61C2×C411yescharacteristic
39C22×C4×C61C4211yescharacteristic
40C22×C4×C61C22⋊C411yescharacteristic
41C22×C4×C61C4⋊C411yescharacteristic
42C22×Dic61C22⋊C411yescharacteristic
43C22×Dic61C22⋊C411yescharacteristic
44C22×Dic61C4⋊C411yescharacteristic
45C22×Dic61C4⋊C411yescharacteristic
46C2×Dic122—21no—
47C2×Dic122—21no—
48C2×Dic122—22no—
49C2×Dic122—41no—
50#11758217—24no—
51#11758217—42no—
52C2×#92420—22no—
53C2×#92420—42no—
54C2×#92420—41no—
55C2×#92420—41no—
56C2×#92420—42no—
57C2×#92420—41no—
58M16×C61—22no—
59M16×C61—41no—
60C2×C8×C61—41no—
61C4⋊C4×C61—41no—
62#11758196—41no—
63#11758196—41no—
64C4×Dic61—21no—
65C4×Dic61—21no—
66C4×Dic61—21no—
67C4×Dic61—21no—
68C4×Dic61—21no—
69C4×Dic61—21no—
70#11758194—22no—
71#11758194—41no—
72C2×#92418—41no—
73C23×C61#9511yescharacteristic
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61—21no—
77C2×C4×C61—21no—
78C2×C4×C61—41no—
79C2×C4×C61—41no—
80C2×C4×C61#10411yescharacteristic
81C2×C4×C61#10411yescharacteristic
82C2×Dic61—21no—
83C2×Dic61—21no—
84C2×Dic61—21no—
85C2×Dic61—21no—
86C2×Dic61—21no—
87C2×Dic61—21no—
88C2×Dic61—21no—
89C2×Dic61—21no—
90C2×Dic61—41no—
91C2×Dic61#9911yescharacteristic
92C2×Dic61#9911yescharacteristic
93C2×Dic61#10412yes—
94Dic122—42no—
95Dic122—42no—
96#92420—42no—
97#92420—44no—
98#92420—81no—
99C8×C61—42no—
100#92418—42no—
101#7284—611nomaximal, Sylow
102C22×C61—21no—
103C22×C61—21no—
104C22×C61#33911yescharacteristic
105C22×C61#33911yescharacteristic
106C22×C61#34211yescharacteristic
107C4×C61—21no—
108C4×C61—21no—
109C4×C61—41no—
110C4×C61—41no—
111Dic61—22no—
112Dic61—21no—
113Dic61—41no—
114Dic61—41no—
115Dic61#35511yescharacteristic
116Dic61#35611yescharacteristic
117#1985—611no—
118C4×#101—611no—
119C4×#101—611no—
120C2×C61—21no—
121C2×C61—21no—
122C2×C61#129711yescharacteristic
123C2×C61#139211yescharacteristic
124C2×C61#139411yescharacteristic
125C2×C4×Q8—611no—
126C2×C4⋊C8—611no—
127C2×#101—1221no—
128C2×#101—1221no—
129C4×M16—1221no—
130C4×M16—1221no—
131C2×#97—611no—
132#343—612no—
133#343—611no—
134#343#692311yescharacteristic
135#336—1221no—
136#336—1221no—
137C61#728411yescharacteristic, complemented, Sylow
138C22×Q8—611no—
139C2×M16—21no—
140C2×M16—1222no—
141C2×M16—1221no—
142C22×C8—1221no—
143C22×C8—1221no—
144C4×Q8—2441no—
145C4×Q8—2441no—
146C2×C4⋊C4—611no—
147C2×C4⋊C4—611no—
148C2×C4⋊C4C2×#692311yescharacteristic
149C2×C42—611no—
150C2×C42—611no—
151C2×C42—611no—
152C4⋊C8—2441no—
153#101—1224no—
154#101—1222no—
155#101—1222no—
156#97—2441no—
157#97—2441no—
158#97—2441no—
159C4×C8—2441no—
160C4×C8—2441no—
161C2×Q8—1222no—
162C2×Q8—1221no—
163C2×Q8—1221no—
164C2×Q8—2441no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4C4×#692311yescharacteristic
170C22×C4C4⋊#692311yescharacteristic
171C22×C4C22⋊#692311yescharacteristic
172M16—22no—
173M16—41no—
174M16—1222no—
175M16—1224no—
176M16—2442no—
177M16—2441no—
178C2×C8—41no—
179C2×C8—1222no—
180C2×C8—2441no—
181C2×C8—2442no—
182C2×C8—2441no—
183C2×C8—2441no—
184C2×C8—2442no—
185C2×C8—2441no—
186C4⋊C4—41no—
187C4⋊C4—2441no—
188C4⋊C4—2441no—
189C42—1221no—
190C42—1221no—
191C42—1221no—
192C42—1221no—
193C42—1221no—
194C42—1221no—
195C23(C2×#6923)⋊C411yescharacteristic
196Q8—2442no—
197Q8—2442no—
198C2×C4—21no—
199C2×C4—21no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—611no—
205C2×C4—612no—
206C2×C4—611no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—1221no—
211C2×C4—1221no—
212C2×C4—1221no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—2441no—
216C2×C4#1451984111yescharacteristic
217C2×C4#1451984211yescharacteristic
218C8—42no—
219C8—4881no—
220C8—2442no—
221C8—2442no—
222C8—2444no—
223C22—21no—
224C22—21no—
225C22#1684063211yescharacteristic
226C22#1684063311yescharacteristic
227C22#1684063911yescharacteristic
228C4—21no—
229C4—21no—
230C4—41no—
231C4—41no—
232C4—611no—
233C4—611no—
234C4—1221no—
235C4—1222no—
236C4—2441no—
237C4—2441no—
238C2—21no—
239C2—21no—
240C2#2146070011yescharacteristic
241C2#2146090911yescharacteristic
242C2#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#7284
LCSG ▷ C22×C4×C61 ▷ C23×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
137. C61#7284semidirect

Maximal subgroups

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

subgroupindex
#214619922
#214615722
#214456142
#728461