Finite Group Databasebeta

← #30594381

Subgroups — #30594381

Order 15616.

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

normal subgroups only

This group has 286 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#21462047C211yesmaximal, characteristic
2#21461555C211yesmaximal, characteristic
3#21447429C211yesmaximal, characteristic
4C2×#14519852—21no—
5D61⋊(C22⋊C8)C411yescharacteristic
6C2×#14519831—21no—
7C4×C22⋊#6923C411yescharacteristic
8#16840657—21no—
9C22⋊#11758187C412yescomplemented
10(C2×#6923)⋊C8—21no—
11C22×C8×D61C2211yescharacteristic
12C2×#14519717C411yescharacteristic, complemented
13#16839541—21no—
14#16839541—21no—
15C2×M32×C61C411yescharacteristic, complemented
16C2×D61⋊C8—21no—
17C2×C22⋊#6923C812yes—
18C2×C4×#6923—21no—
19#14519852—41no—
20#14519852—41no—
21C2×#11758187—22no—
22#14519834—21no—
23C22⋊#92420C812yes—
24#14519831—41no—
25#14519831—41no—
26(C2×#6923)⋊C4—21no—
27C22×C4×D61C2×C411yescharacteristic
28C22×#92418C2×C411yescharacteristic
29C2×C8×D61—41no—
30C2×C8×D61—41no—
31C2×C8×D61D411yescharacteristic
32C2×C8×D61D411yescharacteristic
33C2×C8×D61D411yescharacteristic
34C2×C8×D61Q811yescharacteristic
35#14519717—41no—
36C2×#11758185—21no—
37C22×C8×C61C2×C411yescharacteristic
38M32×C61—41no—
39C2×C16×C61—21no—
40C23×D61C2×C811yescharacteristic
41C22×#6923—22no—
42C22×C4×C61C4211yescharacteristic
43C22×Dic61C2×C811yescharacteristic
44C2×C4×D61—41no—
45C2×C4×D61—41no—
46C2×C4×D61C22⋊C411yescharacteristic
47C2×C4×D61C4⋊C411yescharacteristic
48C2×C4×D61M1611yescharacteristic
49C2×C4×D61M1611yescharacteristic
50C22⋊#6923—42no—
51C2×#92420—22no—
52C4×#6923—41no—
53C4×#6923—41no—
54D61⋊C8—41no—
55D61⋊C8—41no—
56C2×C8×C61—21no—
57C2×C8×C61—21no—
58C2×C8×C61C22⋊C411yescharacteristic
59C2×C8×C61C4⋊C411yescharacteristic
60C2×#92418—41no—
61C2×#92418C22⋊C411yescharacteristic
62C2×#92418C4⋊C411yescharacteristic
63C8×D61—21no—
64C8×D61—21no—
65C8×D61—21no—
66C8×D61—21no—
67C8×D61—41no—
68C8×D61—41no—
69#11758187—42no—
70C16×C61—41no—
71#11758185—41no—
72C23×C61C4×C811yescharacteristic
73C22×D61—22no—
74C22×D61—41no—
75C22×D61—41no—
76C22×D61C22⋊C811yescharacteristic
77C22×D61C4⋊C811yescharacteristic
78C2×#6923—42no—
79C2×#6923—42no—
80C2×#6923—42no—
81C2×C4×C61—21no—
82C2×C4×C61—21no—
83C2×C4×C61#9511yescharacteristic
84C2×C4×C61#9711yescharacteristic
85C2×Dic61—41no—
86C2×Dic61C22⋊C811yescharacteristic
87C2×Dic61C4⋊C811yescharacteristic
88C4×D61—21no—
89C4×D61—21no—
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—41no—
93C4×D61—41no—
94#92420—42no—
95C8×C61—21no—
96C8×C61#9911yescharacteristic
97C8×C61#9911yescharacteristic
98#92418—21no—
99#92418—21no—
100#7201—611nomaximal, Sylow
101C22×C61—21no—
102C22×C61—21no—
103C22×C61—21no—
104C22×C61#33611yescharacteristic
105C2×D61—21no—
106C2×D61—21no—
107C2×D61—21no—
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—44no—
111C2×D61#34912yes—
112#6923—82no—
113C4×C61—21no—
114C4×C61#34211yescharacteristic
115C4×C61#34411yescharacteristic
116Dic61—21no—
117Dic61—21no—
118#2112—611no—
119#2112—611no—
120#1752—611no—
121C2×C61—41no—
122C2×C61#128211yescharacteristic
123C2×C61#137711yescharacteristic
124C2×C61#137811yescharacteristic
125D61—22no—
126D61—41no—
127C23×C8—611no—
128C2×M32—611no—
129C2×M32—1221no—
130C2×M32#692311yescharacteristic, complemented
131C2×C22⋊C8—611no—
132C2×#97—1221no—
133C4×C22⋊C4—611no—
134C22⋊C16—612no—
135C22⋊C16—1221no—
136C22⋊C16—1221no—
137C22⋊C16—1221no—
138#336—1221no—
139C61#720111yescharacteristic, complemented, Sylow
140C23×C4—611no—
141C22×C8—611no—
142C22×C8—611no—
143C22×C8—611no—
144C22×C8—611no—
145C22×C8—611no—
146C22×C8—1221no—
147C22×C8—2441no—
148C22×C8—2441no—
149C22×C8C2×#692311yescharacteristic
150C2×C22⋊C4—612no—
151C2×C42—1221no—
152M32—41no—
153M32—2441no—
154M32—2441no—
155M32—2441no—
156C2×C16—21no—
157C2×C16—1222no—
158C2×C16—1221no—
159C22⋊C8—612no—
160C22⋊C8—1221no—
161#97—2441no—
162#97—2441no—
163#95—1221no—
164C24—611no—
165C22×C4—611no—
166C22×C4—611no—
167C22×C4—611no—
168C22×C4—611no—
169C22×C4—611no—
170C22×C4—1222no—
171C22×C4—2441no—
172C22×C4—2441no—
173C22×C4C4×#692311yescharacteristic
174C2×C8—21no—
175C2×C8—21no—
176C2×C8—611no—
177C2×C8—611no—
178C2×C8—1221no—
179C2×C8—1221no—
180C2×C8—1221no—
181C2×C8—1221no—
182C2×C8—1222no—
183C2×C8—2441no—
184C2×C8—2441no—
185C2×C8—2441no—
186C2×C8—2441no—
187C2×C8—2441no—
188C2×C8C4⋊#692311yescharacteristic
189C2×C8C22⋊#692311yescharacteristic
190C22⋊C4—2442no—
191C42—2441no—
192C42—2441no—
193C16—41no—
194C16—2442no—
195C16—2441no—
196C23—611no—
197C23—611no—
198C23—1222no—
199C23—2441no—
200C23—2441no—
201C23C8×#692311yescharacteristic
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—611no—
205C2×C4—611no—
206C2×C4—1221no—
207C2×C4—1221no—
208C2×C4—1221no—
209C2×C4—1221no—
210C2×C4—2441no—
211C2×C4—2441no—
212C2×C4—2441no—
213C2×C4—2442no—
214C2×C4—2442no—
215C2×C4—2442no—
216C2×C4(C2×#6923)⋊C411yescharacteristic
217C2×C4#1451983111yescharacteristic
218C8—21no—
219C8—1221no—
220C8—1221no—
221C8—2442no—
222C8#1451983511yescharacteristic
223C8#1451983611yescharacteristic
224C22—21no—
225C22—21no—
226C22—21no—
227C22—612no—
228C22—1221no—
229C22—1221no—
230C22—1221no—
231C22—1221no—
232C22—1221no—
233C22—2444no—
234C22(C2×#6923)⋊C811yescharacteristic
235C4—21no—
236C4—1221no—
237C4—1221no—
238C4—4882no—
239C4#1684064011yescharacteristic
240C4#1684064411yescharacteristic
241C2—41no—
242C2—1222no—
243C2—2441no—
244C2#2146066111yescharacteristic
245C2#2146086511yescharacteristic
246C2#2146087111yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC23×C61C4×C8
FrattiniC22×C8C2×#6923
FittingC2×M32×C61C4
socleC22×C61#336
prime radicalC23×D61C2×C8
cosocleC22×C8×D61C22
hypercenterC2×M32#6923
hypocenterC61#7201
LCSG ▷ C23×C61 ▷ C22×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C2×M32

Complements

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

NH ≅ G/Ntype
9. C22⋊#11758187C4semidirect
12. C2×#14519717C4semidirect
15. C2×M32×C61C4semidirect
130. C2×M32#6923semidirect
139. C61#7201semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214615552
#214474292
#720161