Finite Group Databasebeta

← C2×#10590208 #11783396

Subgroups — C2×#10590208 #11783396

Order 1152.

850 conjugacy classes of subgroups; only the 146 normal subgroups are shown.

normal subgroups only

This group has 850 conjugacy classes of subgroups — too many to draw. Only its 146 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
1C22×#3792C212yesmaximal
2C22×#3750C211yesmaximal, characteristic
3#10590208C214yesmaximal, direct product factor
4C23×C32×C4C411yescharacteristic
5C23×C3⋊Dic3C411yescharacteristic
6C23×C3⋊Dic3C2211yescharacteristic
7C2×#3792—24no—
8C2×#3792—22no—
9C2×#3792C418yescomplemented
10C2×#3792C2214yes—
11C22×#622—22no—
12C2×#3750—22no—
13C2×#3750—22no—
14C2×#3750C412yes—
15C2×#3750C2212yes—
16C22×Dic3⋊C4—62no—
17C24×C32C2×C411yescharacteristic
18C22×C32×C4—21no—
19C22×C32×C4—21no—
20C22×C32×C4—42no—
21C22×C32×C4C2×C412yes—
22C22×C3⋊Dic3—21no—
23C22×C3⋊Dic3—21no—
24C22×C3⋊Dic3—42no—
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3C2×C411yescharacteristic
27C22×C3⋊Dic3C2×C414yes—
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3D412yes—
30C22×C3⋊Dic3D412yes—
31C22×C3⋊Dic3Q812yes—
32C22×C3⋊Dic3C2311yescharacteristic
33#3792—28no—
34#3792—24no—
35#3792C2×C418yescomplemented
36C2×#622—28no—
37C2×#622—24no—
38#3750—24no—
39#3750—24no—
40C2×#343—91nomaximal, Sylow
41C23×C3×C4—22no—
42C23×Dic3—62no—
43C23×Dic3—62no—
44C2×Dic3⋊C4—64no—
45C2×Dic3⋊C4—64no—
46C2×Dic3⋊C4—68no—
47C2×Dic3⋊C4—68no—
48C23×C32—22no—
49C23×C32—22no—
50C23×C32C4212yes—
51C23×C32C22⋊C411yescharacteristic
52C23×C32C22⋊C411yescharacteristic
53C23×C32C4⋊C412yes—
54C23×C32C22×C411yescharacteristic
55C2×C32×C4—22no—
56C2×C32×C4—42no—
57C2×C32×C4—42no—
58C2×C32×C4—42no—
59C2×C3⋊Dic3—22no—
60C2×C3⋊Dic3—42no—
61C2×C3⋊Dic3—42no—
62C2×C3⋊Dic3—42no—
63C2×C3⋊Dic3C4212yes—
64C2×C3⋊Dic3C22⋊C412yes—
65C2×C3⋊Dic3C22⋊C414yes—
66C2×C3⋊Dic3C22⋊C414yes—
67C2×C3⋊Dic3C4⋊C412yes—
68C2×C3⋊Dic3C4⋊C414yes—
69C2×C3⋊Dic3C4⋊C414yes—
70C2×C3⋊Dic3C22×C412yes—
71C2×C3⋊Dic3C2×D411yescharacteristic
72C2×C3⋊Dic3C2×D412yes—
73C2×C3⋊Dic3C2×Q811yescharacteristic
74#622—28no—
75C22×M16—92no—
76C22×C4⋊C4—91no—
77#343—94no—
78C24×C3—22no—
79C22×C3×C4—24no—
80C22×C3×C4—24no—
81C22×C3×C4—24no—
82C22×C3×C4—48no—
83C22×Dic3—62no—
84C22×Dic3—64no—
85C22×Dic3—64no—
86C22×Dic3—62no—
87C22×Dic3—68no—
88C22×Dic3—64no—
89C22×Dic3—64no—
90C22×Dic3—64no—
91C22×Dic3—64no—
92C22×Dic3—64no—
93C22×Dic3—128no—
94Dic3⋊C4—616no—
95Dic3⋊C4—616no—
96C22×C32—24no—
97C22×C32—24no—
98C22×C32—21no—
99C22×C32—21no—
100C22×C32—21no—
101C22×C32—21no—
102C22×C32#9512yes—
103C22×C32#9512yes—
104C22×C32#10012yes—
105C22×C32#10112yes—
106C22×C32C2×C4211yescharacteristic
107C22×C32C2×C22⋊C411yescharacteristic
108C22×C32C2×C4⋊C411yescharacteristic
109C32×C4—42no—
110C3⋊Dic3—42no—
111C3⋊Dic3#9514yes—
112C3⋊Dic3C2×C22⋊C412yes—
113C3⋊Dic3C2×C4⋊C412yes—
114C23×C4—91no—
115C23×C4—91no—
116C23×C4#15711yescharacteristic
117C2×M16—98no—
118C2×M16—94no—
119C2×M16—184no—
120C2×M16—182no—
121C22×C8—182no—
122C2×C4⋊C4—92no—
123C2×C4⋊C4—92no—
124C2×C4⋊C4—182no—
125C2×C4⋊C4—182no—
126C23×C3—28no—
127C23×C3—28no—
128C23×C3—22no—
129C23×C3—24no—
130C23×C3—24no—
131C23×C3—22no—
132C23×C3—22no—
133C2×C3×C4—28no—
134C2×C3×C4—48no—
135C2×C3×C4—48no—
136C2×C3×C4—48no—
137C2×Dic3—64no—
138C2×Dic3—64no—
139C2×Dic3—68no—
140C2×Dic3—68no—
141C2×Dic3—64no—
142C2×Dic3—68no—
143C2×Dic3—68no—
144C2×Dic3—64no—
145C2×Dic3—64no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C2×Dic3—68no—
149C2×Dic3—128no—
150C2×Dic3—128no—
151C2×Dic3—128no—
152C2×C32—22no—
153C2×C32—21no—
154C2×C32—21no—
155C2×C32#34314yescomplemented
156C2×C32C2×#9511yescharacteristic
157C2×C32C2×#10011yescharacteristic
158C2×C32C2×#10111yescharacteristic
159C24C2×#15711yescharacteristic
160C22×C4—21no—
161C22×C4—21no—
162C22×C4—42no—
163C22×C4—91no—
164C22×C4—91no—
165C22×C4—94no—
166C22×C4—92no—
167C22×C4—92no—
168C22×C4—92no—
169C22×C4—92no—
170C22×C4—92no—
171C22×C4—181no—
172C22×C4—181no—
173C22×C4—362no—
174C22×C4C2×#15712yes—
175M16—98no—
176M16—184no—
177M16—188no—
178C2×C8—188no—
179C2×C8—184no—
180C4⋊C4—184no—
181C4⋊C4—184no—
182C22×C3—24no—
183C22×C3—24no—
184C22×C3—216no—
185C22×C3—216no—
186C22×C3—24no—
187C22×C3—24no—
188C22×C3—22no—
189C22×C3—22no—
190C22×C3—24no—
191C22×C3—24no—
192C22×C3—24no—
193C22×C3—22no—
194C22×C3—24no—
195C3×C4—48no—
196Dic3—68no—
197Dic3—64no—
198Dic3—64no—
199Dic3—128no—
200C32C2×#34311yescharacteristic, complemented, Sylow
201C23—22no—
202C23—22no—
203C23C4×#15712yes—
204C23C4⋊#15712yes—
205C23C22⋊#15711yescharacteristic
206C23C22⋊#15711yescharacteristic
207C23C22×#15711yescharacteristic
208C2×C4—22no—
209C2×C4—42no—
210C2×C4—42no—
211C2×C4—42no—
212C2×C4—92no—
213C2×C4—92no—
214C2×C4—91no—
215C2×C4—91no—
216C2×C4—92no—
217C2×C4—94no—
218C2×C4—94no—
219C2×C4—94no—
220C2×C4—94no—
221C2×C4—92no—
222C2×C4—92no—
223C2×C4—182no—
224C2×C4—362no—
225C2×C4—362no—
226C2×C4—362no—
227C8—188no—
228C2×C3—24no—
229C2×C3—24no—
230C2×C3—28no—
231C2×C3—28no—
232C2×C3—22no—
233C2×C3—22no—
234C2×C3—22no—
235C22—24no—
236C22—24no—
237C22—21no—
238C22—21no—
239C22—21no—
240C22—21no—
241C22#6378012yes—
242C22#6378112yes—
243C22#6378112yes—
244C22#6378812yes—
245C22C2×C4×#15711yescharacteristic
246C22C2×C4⋊#15711yescharacteristic
247C22C2×C22⋊#15711yescharacteristic
248C4—42no—
249C4—92no—
250C4—92no—
251C4—94no—
252C4—362no—
253C3—22no—
254C2—21no—
255C2—21no—
256C2—22no—
257C2#1059020814yesdirect product factor
258C2C2×#6378011yescharacteristic
259C2C2×#6378111yescharacteristic
260C2C2×#6378811yescharacteristic
subgroupG/H
centerC23C22⋊#157
commutatorC22×C32C2×C42
FrattiniC23C22×#157
FittingC23×C32×C4C4
socleC23×C32C22⋊C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC23×C4#157
hypocenterC32C2×#343
LCSG ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C24 ◁ C23×C4

Complements

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

NH ≅ G/Ntype
3. #10590208C2direct (N × H)
9. C2×#3792C4semidirect
35. #3792C2×C4semidirect
155. C2×C32#343semidirect
200. C32C2×#343semidirect
257. C2#10590208direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#37922
C22×#37502
#105902082
C2×#3439