Finite Group Databasebeta

← #11802803

Subgroups — #11802803

Order 1152.

930 conjugacy classes of subgroups; only the 162 normal subgroups are shown.

normal subgroups only

This group has 930 conjugacy classes of subgroups — too many to draw. Only its 162 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
1C2×C4⋊C4×C3⋊D3C211yesmaximal, characteristic
2#10593812C212yesmaximal
3#10593811C212yesmaximal
4C4×C22⋊#157C212yesmaximal
5#10593758C218yesmaximal, complemented
6C22×C4×C3⋊D3C2211yescharacteristic
7C22×C4×C3⋊D3C2211yescharacteristic
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C22⋊#157C2214yes—
10C2×C4⋊#157C2214yes—
11C2×C4×#157C2214yes—
12C2×C32×C4⋊C4C411yescharacteristic, complemented
13C2×C4⋊(C3⋊Dic3)C411yescharacteristic, complemented
14C2×#3750C411yescharacteristic, complemented
15C2×#3750C411yescharacteristic, complemented
16C4⋊C4×C3⋊D3C414yescomplemented
17C4⋊C4×C3⋊D3C2214yes—
18#63781C2214yes—
19#63781C2218yes—
20#63781C2214yes—
21C2×D3×C4⋊C4—62no—
22C23×C3⋊D3C2311yescharacteristic
23C22×#157C2318yes—
24C22×C32×C4C2×C411yescharacteristic
25C22×C32×C4C2×C411yescharacteristic
26C22×C32×C4C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C411yescharacteristic
28C22×C3⋊Dic3C2×C411yescharacteristic
29C22×C3⋊Dic3C2×C411yescharacteristic
30C2×C4×C3⋊D3—24no—
31C2×C4×C3⋊D3—42no—
32C2×C4×C3⋊D3—42no—
33C2×C4×C3⋊D3C2×C412yes—
34C2×C4×C3⋊D3C2×C412yes—
35C2×C4×C3⋊D3C2×C412yes—
36C2×C4×C3⋊D3C2312yes—
37C2×C4×C3⋊D3C2312yes—
38C2×C4×C3⋊D3C2312yes—
39C22⋊#157—28no—
40C4⋊#157—44no—
41C4×#157—44no—
42C32×C4⋊C4C2×C414yes—
43C4⋊(C3⋊Dic3)C2×C414yes—
44#3750C2×C414yes—
45#3750C2×C414yes—
46#2313—91nomaximal, Sylow
47C22×C4×D3—62no—
48C22×C4×D3—62no—
49C22×C4×D3—62no—
50C2×C3×C4⋊C4—22no—
51C2×C4⋊Dic3—62no—
52C2×Dic3⋊C4—62no—
53C2×Dic3⋊C4—62no—
54D3×C4⋊C4—68no—
55D3×C4⋊C4—68no—
56C23×C32C22×C411yescharacteristic
57C22×C3⋊D3—22no—
58C22×C3⋊D3—22no—
59C22×C3⋊D3C22×C411yescharacteristic
60C22×C3⋊D3#4114yes—
61C22×C3⋊D3C2411yescharacteristic
62C2×#157—28no—
63C2×#157—28no—
64C2×#157—28no—
65C2×C32×C4—22no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C22×C412yes—
69C2×C32×C4C22×C412yes—
70C2×C32×C4C22×C412yes—
71C2×C3⋊Dic3—22no—
72C2×C3⋊Dic3—41no—
73C2×C3⋊Dic3—41no—
74C2×C3⋊Dic3C22×C412yes—
75C2×C3⋊Dic3C22×C412yes—
76C2×C3⋊Dic3C22×C412yes—
77C4×C3⋊D3—24no—
78C4×C3⋊D3—24no—
79C4×C3⋊D3—24no—
80C4×C3⋊D3—24no—
81C4×C3⋊D3—42no—
82C4×C3⋊D3—42no—
83C22×C4⋊C4—91no—
84#387—98no—
85#381—92no—
86#380—92no—
87C4×C22⋊C4—92no—
88C23×D3—62no—
89C22×C3×C4—22no—
90C22×C3×C4—22no—
91C22×C3×C4—22no—
92C22×Dic3—62no—
93C22×Dic3—62no—
94C22×Dic3—62no—
95C2×C4×D3—64no—
96C2×C4×D3—64no—
97C2×C4×D3—64no—
98C2×C4×D3—64no—
99C2×C4×D3—64no—
100C2×C4×D3—64no—
101C2×C4×D3—616no—
102C2×C4×D3—128no—
103C2×C4×D3—128no—
104C3×C4⋊C4—28no—
105C4⋊Dic3—68no—
106Dic3⋊C4—68no—
107Dic3⋊C4—68no—
108C22×C32—21no—
109C22×C32—21no—
110C22×C32#11712yes—
111C22×C32C23×C411yescharacteristic
112C2×C3⋊D3—21no—
113C2×C3⋊D3—21no—
114C2×C3⋊D3—28no—
115C2×C3⋊D3#11712yes—
116C2×C3⋊D3C2×#4112yes—
117C2×C3⋊D3H(5,𝔽2)12yes—
118C2×C3⋊D32−1+412yes—
119#157—48no—
120C32×C4—22no—
121C32×C4—22no—
122C32×C4—22no—
123C3⋊Dic3—22no—
124C3⋊Dic3—22no—
125C3⋊Dic3—22no—
126C23×C4—91no—
127C23×C4—91no—
128C23×C4—91no—
129C2×C4⋊C4—91no—
130C2×C4⋊C4—91no—
131C2×C4⋊C4—91no—
132C2×C4⋊C4—94no—
133C2×C4⋊C4—94no—
134C2×C4⋊C4—94no—
135C2×C4⋊C4#15711yescharacteristic, complemented
136C2×C22⋊C4—94no—
137C2×C42—94no—
138#95—94no—
139#95—94no—
140#95—98no—
141C23×C3—22no—
142C22×D3—62no—
143C22×D3—68no—
144C22×D3—62no—
145C22×D3—68no—
146C22×D3—68no—
147C2×C3×C4—28no—
148C2×C3×C4—24no—
149C2×C3×C4—24no—
150C2×C3×C4—24no—
151C2×C3×C4—44no—
152C2×C3×C4—44no—
153C2×Dic3—64no—
154C2×Dic3—64no—
155C2×Dic3—64no—
156C2×Dic3—68no—
157C2×Dic3—124no—
158C2×Dic3—124no—
159C4×D3—616no—
160C4×D3—616no—
161C4×D3—128no—
162C4×D3—128no—
163C4×D3—128no—
164C4×D3—128no—
165C2×C32—22no—
166C2×C32C2×#11711yescharacteristic
167C2×C32#51811yescharacteristic
168C2×C32#51911yescharacteristic
169C3⋊D3—22no—
170C3⋊D3#53914yes—
171C24—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—92no—
176C22×C4—92no—
177C22×C4—92no—
178C22×C4—92no—
179C22×C4—92no—
180C22×C4—92no—
181C22×C4—98no—
182C22×C4—184no—
183C22×C4—362no—
184C22×C4—362no—
185C22×C4C2×#15711yescharacteristic
186C22×C4C2×#15711yescharacteristic
187C22×C4C2×#15711yescharacteristic
188C4⋊C4—94no—
189C4⋊C4—94no—
190C4⋊C4—94no—
191C4⋊C4—364no—
192C4⋊C4C2×#15714yes—
193C22⋊C4—188no—
194C42—364no—
195C22×C3—24no—
196C22×C3—24no—
197C22×C3—24no—
198C22×C3—22no—
199C2×D3—64no—
200C2×D3—64no—
201C2×D3—64no—
202C2×D3—64no—
203C2×D3—64no—
204C2×D3—632no—
205C2×D3—64no—
206C3×C4—28no—
207C3×C4—44no—
208C3×C4—44no—
209Dic3—68no—
210Dic3—124no—
211Dic3—124no—
212C32#231311yescharacteristic, complemented, Sylow
213C23—91no—
214C23—94no—
215C23—91no—
216C23—182no—
217C23—182no—
218C23C22×#15711yescharacteristic
219C2×C4—22no—
220C2×C4—41no—
221C2×C4—41no—
222C2×C4—92no—
223C2×C4—92no—
224C2×C4—92no—
225C2×C4—184no—
226C2×C4—184no—
227C2×C4—184no—
228C2×C4—184no—
229C2×C4—182no—
230C2×C4—188no—
231C2×C4—188no—
232C2×C4—188no—
233C2×C4—362no—
234C2×C4—362no—
235C2×C4—361no—
236C2×C4—361no—
237C2×C4C22×#15712yes—
238C2×C4C22×#15712yes—
239C2×C4C22×#15712yes—
240C2×C3—28no—
241C2×C3—22no—
242C2×C3—22no—
243C2×C3—22no—
244D3—68no—
245D3—68no—
246C22—21no—
247C22—21no—
248C22—92no—
249C22—92no—
250C22—92no—
251C22—92no—
252C22—188no—
253C22—181no—
254C22—181no—
255C22#6428612yes—
256C22C23×#15711yescharacteristic
257C4—22no—
258C4—22no—
259C4—22no—
260C4—182no—
261C4—182no—
262C4—182no—
263C4—368no—
264C3—22no—
265C2—22no—
266C2—94no—
267C2—182no—
268C2C2×#6428611yescharacteristic
269C2#1059664211yescharacteristic
270C2#1059664611yescharacteristic
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC2×C32×C4⋊C4C4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC2×C4⋊C4#157
hypocenterC32#2313
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
5. #10593758C2semidirect
12. C2×C32×C4⋊C4C4semidirect
13. C2×C4⋊(C3⋊Dic3)C4semidirect
14. C2×#3750C4semidirect
15. C2×#3750C4semidirect
16. C4⋊C4×C3⋊D3C4semidirect
135. C2×C4⋊C4#157semidirect
212. C32#2313semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊C4×C3⋊D32
#105938122
#105938112
C4×C22⋊#1572
#105937582
#23139