Finite Group Databasebeta

← #30594377

Subgroups — #30594377

Order 15616.

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

normal subgroups only

This group has 292 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#21462047C211yesmaximal, characteristic
2#21461555C211yesmaximal, characteristic
3C2×#16839541C211yesmaximal, 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
12C22×#11758185C411yescharacteristic, complemented
13#16839541—21no—
14#16839541—21no—
15C22×C16×C61C411yescharacteristic, complemented
16C2×D61⋊C8—21no—
17C2×C22⋊#6923—21no—
18C2×C4×#6923—21no—
19#14519852—41no—
20#14519852—41no—
21C2×#11758187—22no—
22#14519834C812yes—
23C22⋊#92420—21no—
24#14519831—41no—
25#14519831—41no—
26(C2×#6923)⋊C4C812yes—
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
35C2×#11758185—21no—
36C2×#11758185—41no—
37C22×C8×C61C2×C411yescharacteristic
38C2×C16×C61—21no—
39C2×C16×C61—41no—
40C23×D61M1611yescharacteristic
41C22×#6923—22no—
42C22×C4×C61C4211yescharacteristic
43C22×Dic61M1611yescharacteristic
44C2×C4×D61—41no—
45C2×C4×D61—41no—
46C2×C4×D61C22⋊C411yescharacteristic
47C2×C4×D61C4⋊C411yescharacteristic
48C2×C4×D61C2×C811yescharacteristic
49C2×C4×D61C2×C811yescharacteristic
50C22⋊#6923—41no—
51C22⋊#6923—41no—
52C2×#92420—22no—
53C4×#6923—41no—
54C4×#6923—41no—
55D61⋊C8—41no—
56D61⋊C8—41no—
57C2×C8×C61—21no—
58C2×C8×C61—21no—
59C2×C8×C61C22⋊C411yescharacteristic
60C2×C8×C61C4⋊C411yescharacteristic
61C2×#92418—41no—
62C2×#92418C22⋊C411yescharacteristic
63C2×#92418C4⋊C411yescharacteristic
64C8×D61—21no—
65C8×D61—21no—
66C8×D61—21no—
67C8×D61—21no—
68C8×D61—41no—
69C8×D61—41no—
70#11758187—42no—
71C16×C61—41no—
72#11758185—41no—
73C23×C61#9711yescharacteristic
74C22×D61—21no—
75C22×D61—21no—
76C22×D61—22no—
77C22×D61—41no—
78C22×D61C22⋊C811yescharacteristic
79C22×D61C4⋊C811yescharacteristic
80C2×#6923—42no—
81C2×#6923—42no—
82C2×#6923—42no—
83C2×C4×C61—21no—
84C2×C4×C61—21no—
85C2×C4×C61#9511yescharacteristic
86C2×C4×C61C4×C811yescharacteristic
87C2×Dic61—41no—
88C2×Dic61C22⋊C811yescharacteristic
89C2×Dic61C4⋊C811yescharacteristic
90C4×D61—21no—
91C4×D61—21no—
92C4×D61—21no—
93C4×D61—21no—
94C4×D61—41no—
95C4×D61—41no—
96#92420—42no—
97C8×C61—21no—
98C8×C61#9911yescharacteristic
99C8×C61#9911yescharacteristic
100#92418—21no—
101#92418—21no—
102#7200—611nomaximal, Sylow
103C22×C61—21no—
104C22×C61—21no—
105C22×C61#33611yescharacteristic
106C22×C61#34711yescharacteristic
107C22×C61#34711yescharacteristic
108C2×D61—21no—
109C2×D61—21no—
110C2×D61—21no—
111C2×D61—21no—
112C2×D61—21no—
113C2×D61—42no—
114C2×D61—42no—
115C2×D61#35012yes—
116#6923—82no—
117C4×C61—21no—
118C4×C61#34211yescharacteristic
119C4×C61#34411yescharacteristic
120Dic61—21no—
121Dic61—21no—
122#2112—611no—
123C2×C22⋊C16—611no—
124#1752—611no—
125C2×C61—21no—
126C2×C61—21no—
127C2×C61#128211yescharacteristic
128C2×C61#137511yescharacteristic
129C2×C61#137911yescharacteristic
130D61—22no—
131D61—41no—
132C23×C8—611no—
133C2×M32—1221no—
134C22×C16—611no—
135C22×C16#692311yescharacteristic, complemented
136C2×C22⋊C8—611no—
137C2×#97—1221no—
138C4×C22⋊C4—611no—
139C22⋊C16—612no—
140C22⋊C16—1221no—
141C22⋊C16—1221no—
142C22⋊C16—1221no—
143#336—1221no—
144C61#720011yescharacteristic, complemented, Sylow
145C23×C4—611no—
146C22×C8—611no—
147C22×C8—611no—
148C22×C8—611no—
149C22×C8—611no—
150C22×C8—611no—
151C22×C8—1221no—
152C22×C8—2441no—
153C22×C8—2441no—
154C22×C8C2×#692311yescharacteristic
155C2×C22⋊C4—1221no—
156C2×C42—1221no—
157M32—2441no—
158M32—2441no—
159C2×C16—21no—
160C2×C16—41no—
161C2×C16—1222no—
162C2×C16—1221no—
163C2×C16—2441no—
164C22⋊C8—612no—
165C22⋊C8—1221no—
166#97—2441no—
167#97—2441no—
168#95—612no—
169C24—611no—
170C22×C4—611no—
171C22×C4—611no—
172C22×C4—611no—
173C22×C4—611no—
174C22×C4—611no—
175C22×C4—1222no—
176C22×C4—2441no—
177C22×C4—2441no—
178C22×C4C4×#692311yescharacteristic
179C2×C8—21no—
180C2×C8—21no—
181C2×C8—611no—
182C2×C8—611no—
183C2×C8—1221no—
184C2×C8—1221no—
185C2×C8—1221no—
186C2×C8—1221no—
187C2×C8—1222no—
188C2×C8—2441no—
189C2×C8—2441no—
190C2×C8—2441no—
191C2×C8—2441no—
192C2×C8—2441no—
193C2×C8C4⋊#692311yescharacteristic
194C2×C8C22⋊#692311yescharacteristic
195C22⋊C4—2441no—
196C22⋊C4—2441no—
197C42—2441no—
198C42—2441no—
199C16—41no—
200C16—2442no—
201C16—2441no—
202C23—611no—
203C23—611no—
204C23—1222no—
205C23—1221no—
206C23—1221no—
207C23—2441no—
208C23#1451983111yescharacteristic
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—611no—
212C2×C4—611no—
213C2×C4—1221no—
214C2×C4—1221no—
215C2×C4—1221no—
216C2×C4—1221no—
217C2×C4—2441no—
218C2×C4—2441no—
219C2×C4—2441no—
220C2×C4—2442no—
221C2×C4—2442no—
222C2×C4—2442no—
223C2×C4(C2×#6923)⋊C411yescharacteristic
224C2×C4C8×#692311yescharacteristic
225C8—21no—
226C8—1221no—
227C8—1221no—
228C8—2442no—
229C8#1451983511yescharacteristic
230C8#1451983611yescharacteristic
231C22—21no—
232C22—21no—
233C22—612no—
234C22—1221no—
235C22—1221no—
236C22—1221no—
237C22—1221no—
238C22—1221no—
239C22—2442no—
240C22—2442no—
241C22(C2×#6923)⋊C811yescharacteristic
242C22#1684065211yescharacteristic
243C22#1684065311yescharacteristic
244C4—21no—
245C4—1221no—
246C4—1221no—
247C4—4882no—
248C4#1684064011yescharacteristic
249C4#1684064411yescharacteristic
250C2—21no—
251C2—21no—
252C2—1222no—
253C2—2441no—
254C2#2146066111yescharacteristic
255C2#2146085911yescharacteristic
256C2#2146087211yescharacteristic
subgroupG/H
centerC2×C4(C2×#6923)⋊C4
commutatorC2×C4×C61C4×C8
FrattiniC22×C8C2×#6923
FittingC22×C16×C61C4
socleC22×C61#336
prime radicalC23×D61M16
cosocleC22×C8×D61C22
hypercenterC22×C16#6923
hypocenterC61#7200
LCSG ▷ C2×C4×C61 ▷ C2×C61 ▷ C61
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ C22×C16

Complements

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

NH ≅ G/Ntype
9. C22⋊#11758187C4semidirect
12. C22×#11758185C4semidirect
15. C22×C16×C61C4semidirect
135. C22×C16#6923semidirect
144. C61#7200semidirect

Maximal subgroups

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

subgroupindex
#214620472
#214615552
C2×#168395412
#720061