Finite Group Databasebeta

← #30594384

Subgroups — #30594384

Order 15616.

304 conjugacy classes of subgroups; only the 68 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 68 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#21462048C211yesmaximal, characteristic
2C8×C22⋊#6923C211yesmaximal, characteristic
3C22⋊C16×D61C211yesmaximal, characteristic
4C2×#14519851C412yescomplemented
5D61⋊(C22⋊C8)C411yescharacteristic
6C2×C8×#6923—21no—
7C4×C22⋊#6923C411yescharacteristic
8#16840657—21no—
9#16840657—21no—
10(C2×#6923)⋊C8—21no—
11C22×C8×D61C2211yescharacteristic
12C2×C16×D61—21no—
13C22⋊#11758185C411yescharacteristic, complemented
14#16839541—21no—
15C61×C22⋊C16C411yescharacteristic, complemented
16C2×D61⋊C8—21no—
17C2×C22⋊#6923—21no—
18C2×C4×#6923—21no—
19#14519851—42no—
20C2×#11758187—22no—
21#14519834C812yes—
22C22⋊#92420—21no—
23C8×#6923—42no—
24(C2×#6923)⋊C4C812yes—
25C22×C4×D61C2×C411yescharacteristic
26C22×#92418C2×C411yescharacteristic
27C2×C8×D61—42no—
28C2×C8×D61D411yescharacteristic
29C2×C8×D61D411yescharacteristic
30C2×C8×D61D411yescharacteristic
31C2×C8×D61Q811yescharacteristic
32C2×#11758185—21no—
33C16×D61—42no—
34C22×C8×C61C2×C411yescharacteristic
35C2×C16×C61—21no—
36C23×D61M1611yescharacteristic
37C22×#6923—22no—
38C22×C4×C61C4211yescharacteristic
39C22×Dic61M1611yescharacteristic
40C2×C4×D61—41no—
41C2×C4×D61—41no—
42C2×C4×D61C22⋊C411yescharacteristic
43C2×C4×D61C4⋊C411yescharacteristic
44C2×C4×D61C2×C811yescharacteristic
45C2×C4×D61C2×C811yescharacteristic
46C22⋊#6923—24no—
47C2×#92420—22no—
48C4×#6923—41no—
49C4×#6923—41no—
50D61⋊C8—41no—
51D61⋊C8—41no—
52C2×C8×C61—41no—
53C2×C8×C61C22⋊C411yescharacteristic
54C2×C8×C61C4⋊C411yescharacteristic
55C2×#92418—22no—
56C2×#92418C22⋊C411yescharacteristic
57C2×#92418C4⋊C411yescharacteristic
58C8×D61—22no—
59C8×D61—22no—
60C8×D61—41no—
61C8×D61—41no—
62#11758187—42no—
63C16×C61—41no—
64#11758185—41no—
65C23×C61#9711yescharacteristic
66C22×D61—22no—
67C22×D61—22no—
68C22×D61—41no—
69C22×D61C22⋊C811yescharacteristic
70C22×D61C4⋊C811yescharacteristic
71C2×#6923—24no—
72C2×#6923—42no—
73C2×#6923—42no—
74C2×C4×C61—21no—
75C2×C4×C61—21no—
76C2×C4×C61#9511yescharacteristic
77C2×C4×C61C4×C811yescharacteristic
78C2×Dic61—41no—
79C2×Dic61C22⋊C811yescharacteristic
80C2×Dic61C4⋊C811yescharacteristic
81C4×D61—21no—
82C4×D61—21no—
83C4×D61—21no—
84C4×D61—21no—
85C4×D61—41no—
86C4×D61—41no—
87#92420—42no—
88C8×C61—21no—
89C8×C61—21no—
90#92418—21no—
91#92418#9912yes—
92#7202—611nomaximal, Sylow
93C22×C61—21no—
94C22×C61—21no—
95C22×C61—21no—
96C22×C61#33611yescharacteristic
97C2×D61—21no—
98C2×D61—21no—
99C2×D61—21no—
100C2×D61—21no—
101C2×D61—44no—
102C2×D61#35012yes—
103C2×D61#36412yes—
104#6923—44no—
105C4×C61—21no—
106C4×C61#34211yescharacteristic
107C4×C61#34411yescharacteristic
108Dic61—21no—
109Dic61—21no—
110#2112—611no—
111C2×C22⋊C16—611no—
112C8×C22⋊C4—611no—
113C2×C61—41no—
114C2×C61#128211yescharacteristic
115C2×C61#137611yescharacteristic
116C2×C61#137911yescharacteristic
117D61—22no—
118D61—22no—
119C23×C8—611no—
120C2×M32—612no—
121C22×C16—1221no—
122C2×C22⋊C8—611no—
123C2×C4×C8—1221no—
124C4×C22⋊C4—611no—
125C22⋊C16—611no—
126C22⋊C16—1221no—
127C22⋊C16—1221no—
128C22⋊C16—1221no—
129C22⋊C16#692311yescharacteristic, complemented
130#336—1221no—
131C61#720211yescharacteristic, complemented, Sylow
132C23×C4—611no—
133C22×C8—611no—
134C22×C8—611no—
135C22×C8—611no—
136C22×C8—611no—
137C22×C8—611no—
138C22×C8—1221no—
139C22×C8—2442no—
140C22×C8C2×#692311yescharacteristic
141C2×C22⋊C4—1221no—
142C2×C42—1221no—
143M32—2442no—
144C2×C16—21no—
145C2×C16—1222no—
146C2×C16—1221no—
147C2×C16—2442no—
148C22⋊C8—612no—
149C22⋊C8—1221no—
150C4×C8—2442no—
151#95—612no—
152C24—611no—
153C22×C4—611no—
154C22×C4—611no—
155C22×C4—611no—
156C22×C4—611no—
157C22×C4—611no—
158C22×C4—1222no—
159C22×C4—2441no—
160C22×C4—2441no—
161C22×C4C4×#692311yescharacteristic
162C2×C8—41no—
163C2×C8—611no—
164C2×C8—611no—
165C2×C8—1222no—
166C2×C8—1222no—
167C2×C8—1222no—
168C2×C8—1222no—
169C2×C8—2441no—
170C2×C8—2441no—
171C2×C8—2441no—
172C2×C8—2441no—
173C2×C8C4⋊#692311yescharacteristic
174C2×C8C22⋊#692311yescharacteristic
175C22⋊C4—1224no—
176C42—2441no—
177C42—2441no—
178C16—41no—
179C16—2441no—
180C16—2442no—
181C23—611no—
182C23—611no—
183C23—1222no—
184C23—1222no—
185C23—2441no—
186C23#1451983111yescharacteristic
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—611no—
190C2×C4—611no—
191C2×C4—1221no—
192C2×C4—1221no—
193C2×C4—1221no—
194C2×C4—1221no—
195C2×C4—1224no—
196C2×C4—2441no—
197C2×C4—2441no—
198C2×C4—2441no—
199C2×C4—2442no—
200C2×C4—2442no—
201C2×C4(C2×#6923)⋊C411yescharacteristic
202C2×C4C8×#692311yescharacteristic
203C8—21no—
204C8—21no—
205C8—612no—
206C8—1221no—
207C8—2442no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22—612no—
212C22—612no—
213C22—1221no—
214C22—1221no—
215C22—1221no—
216C22—1221no—
217C22—2444no—
218C22(C2×#6923)⋊C811yescharacteristic
219C4—21no—
220C4—1221no—
221C4—1221no—
222C4—2444no—
223C4#1684063911yescharacteristic
224C4#1684064511yescharacteristic
225C2—41no—
226C2—1222no—
227C2—1222no—
228C2#2146066011yescharacteristic
229C2#2146086211yescharacteristic
230C2#2146087211yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC2×C4×C61C4×C8
FrattiniC22×C8C2×#6923
FittingC61×C22⋊C16C4
socleC22×C61#336
prime radicalC23×D61M16
cosocleC22×C8×D61C22
hypercenterC22⋊C16#6923
hypocenterC61#7202
LCSG ▷ C2×C4×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22⋊C16

Complements

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

NH ≅ G/Ntype
4. C2×#14519851C4semidirect
13. C22⋊#11758185C4semidirect
15. C61×C22⋊C16C4semidirect
129. C22⋊C16#6923semidirect
131. C61#7202semidirect

Maximal subgroups

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

subgroupindex
#214620482
C8×C22⋊#69232
C22⋊C16×D612
#720261