Finite Group Databasebeta

← #11783108

Subgroups — #11783108

Order 1152.

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

normal subgroups only

This group has 746 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×#3792C211yesmaximal, characteristic
2C23×#622C211yesmaximal, characteristic
3C2×#64086C211yesmaximal, characteristic
4#10590207C214yesmaximal, complemented
5C23×C3⋊Dic3C2211yescharacteristic
6C2×#3792—22no—
7C2×#3792—22no—
8C2×#3792C414yescomplemented
9C22×#622—22no—
10C22×#622—22no—
11C22×#622C414yescomplemented
12C22×#622C2212yes—
13C22×#622C2212yes—
14C2×C32×C22⋊C4C411yescharacteristic
15C2×#3757C411yescharacteristic
16C2×#3750C412yes—
17C2×C4×C3⋊Dic3C2212yes—
18#64086—22no—
19#64086—22no—
20C2×#877—62no—
21C24×C32C2×C411yescharacteristic
22C22×C32×C4C2×C412yes—
23C22×C3⋊Dic3C2×C412yes—
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3C2×C412yes—
26C22×C3⋊Dic3C2×C412yes—
27C22×C3⋊Dic3D412yes—
28C22×C3⋊Dic3D412yes—
29C22×C3⋊Dic3D412yes—
30C22×C3⋊Dic3Q812yes—
31C22×C3⋊Dic3C2311yescharacteristic
32#3792—28no—
33C2×#622—28no—
34C2×#622—22no—
35C2×#622—22no—
36C2×#622—22no—
37C2×#622—22no—
38C2×#622C2×C414yes—
39C2×#622C2×C414yes—
40C32×C22⋊C4—22no—
41#3757—22no—
42#3750—24no—
43C4×C3⋊Dic3—22no—
44C4×C3⋊Dic3—22no—
45#1729—91nomaximal, Sylow
46C23×Dic3—62no—
47C2×C3×C22⋊C4—22no—
48C2×#217—62no—
49C2×Dic3⋊C4—64no—
50C2×C4×Dic3—64no—
51#877—68no—
52#877—68no—
53C23×C32—24no—
54C23×C32C4212yes—
55C23×C32C22⋊C412yes—
56C23×C32C4⋊C412yes—
57C23×C32C22×C411yescharacteristic
58C2×C32×C4—22no—
59C2×C32×C4—24no—
60C2×C3⋊Dic3—22no—
61C2×C3⋊Dic3—24no—
62C2×C3⋊Dic3C4212yes—
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C22⋊C414yes—
65C2×C3⋊Dic3C22⋊C414yes—
66C2×C3⋊Dic3C4⋊C412yes—
67C2×C3⋊Dic3C4⋊C414yes—
68C2×C3⋊Dic3C4⋊C414yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C22×C411yescharacteristic
71C2×C3⋊Dic3C2×D411yescharacteristic
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C2×C3⋊Dic3C2×Q811yescharacteristic
75#622—24no—
76#622—24no—
77C22×M16—91no—
78C23×C8—91no—
79C2×#117—91no—
80#336—94no—
81C24×C3—22no—
82C22×C3×C4—24no—
83C22×Dic3—64no—
84C22×Dic3—64no—
85C22×Dic3—62no—
86C22×Dic3—62no—
87C22×Dic3—64no—
88C22×Dic3—64no—
89C22×Dic3—64no—
90C22×Dic3—64no—
91C22×Dic3—64no—
92C3×C22⋊C4—28no—
93#217—68no—
94Dic3⋊C4—616no—
95C4×Dic3—68no—
96C4×Dic3—68no—
97C22×C32—24no—
98C22×C32—24no—
99C22×C32—24no—
100C22×C32#9514yes—
101C22×C32C2×C4211yescharacteristic
102C22×C32C2×C22⋊C411yescharacteristic
103C22×C32C2×C4⋊C411yescharacteristic
104C22×C32#13114yes—
105C32×C4—42no—
106C3⋊Dic3—42no—
107C3⋊Dic3#9514yes—
108C3⋊Dic3C2×C22⋊C411yescharacteristic
109C3⋊Dic3C2×C22⋊C411yescharacteristic
110C3⋊Dic3C2×C4⋊C411yescharacteristic
111C3⋊Dic3C2×C4⋊C411yescharacteristic
112C23×C4—91no—
113C2×M16—94no—
114C2×M16—182no—
115C2×M16—182no—
116C22×C8—94no—
117C22×C8—92no—
118C22×C8—92no—
119C22×C8—182no—
120C22×C8—182no—
121#117—182no—
122#117—182no—
123C2×C4⋊C4—92no—
124C2×C22⋊C4—91no—
125C2×C22⋊C4#15711yescharacteristic
126C2×C42—92no—
127C23×C3—22no—
128C23×C3—24no—
129C23×C3—24no—
130C23×C3—24no—
131C23×C3—48no—
132C2×C3×C4—28no—
133C2×C3×C4—48no—
134C2×Dic3—64no—
135C2×Dic3—64no—
136C2×Dic3—68no—
137C2×Dic3—68no—
138C2×Dic3—64no—
139C2×Dic3—68no—
140C2×Dic3—68no—
141C2×Dic3—62no—
142C2×Dic3—62no—
143C2×Dic3—62no—
144C2×Dic3—62no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—68no—
148C2×Dic3—128no—
149C2×C32—24no—
150C2×C32C2×#9511yescharacteristic
151C2×C32#40512yes—
152C2×C32#40812yes—
153C2×C32#42412yes—
154C24C2×#15711yescharacteristic
155C22×C4—91no—
156C22×C4—91no—
157C22×C4—92no—
158C22×C4—92no—
159C22×C4—92no—
160C22×C4—92no—
161C22×C4—92no—
162C22×C4—92no—
163C22×C4—92no—
164C22×C4C2×#15712yes—
165M16—188no—
166C2×C8—94no—
167C2×C8—94no—
168C2×C8—182no—
169C2×C8—188no—
170C2×C8—182no—
171C2×C8—182no—
172C2×C8—182no—
173C4⋊C4—184no—
174C22⋊C4—22no—
175C22⋊C4—182no—
176C42—182no—
177C42—182no—
178C22×C3—22no—
179C22×C3—22no—
180C22×C3—28no—
181C22×C3—28no—
182C22×C3—22no—
183C22×C3—48no—
184C22×C3—48no—
185C22×C3—48no—
186C3×C4—48no—
187Dic3—68no—
188Dic3—62no—
189Dic3—62no—
190Dic3—62no—
191Dic3—62no—
192Dic3—128no—
193C32#172911yescharacteristic, complemented, Sylow
194C23—24no—
195C23C4×#15712yes—
196C23C4⋊#15712yes—
197C23C22⋊#15712yes—
198C23C22×#15711yescharacteristic
199C2×C4—24no—
200C2×C4—22no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—92no—
204C2×C4—91no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—94no—
208C2×C4—94no—
209C2×C4—94no—
210C2×C4—94no—
211C2×C4—91no—
212C2×C4—91no—
213C2×C4—92no—
214C2×C4—184no—
215C2×C4—182no—
216C8—184no—
217C8—184no—
218C2×C3—22no—
219C2×C3—24no—
220C2×C3—24no—
221C2×C3—24no—
222C2×C3—48no—
223C22—24no—
224C22—24no—
225C22—24no—
226C22#6378114yes—
227C22C2×C4×#15711yescharacteristic
228C22C2×C4⋊#15711yescharacteristic
229C22#6428714yes—
230C22C2×C22⋊#15711yescharacteristic
231C4—42no—
232C4—91no—
233C4—91no—
234C4—91no—
235C4—91no—
236C4—94no—
237C4—362no—
238C3—22no—
239C2—24no—
240C2#1059373812yes—
241C2#1059374312yes—
242C2C2×#6378111yescharacteristic
243C2#1059382212yes—
subgroupG/H
center, FrattiniC23C22×#157
commutatorC22×C32C2×C42
FittingC2×C32×C22⋊C4C4
socleC23×C32C22×C4
prime radicalC24×C32C2×C4
cosocleC22×C3⋊Dic3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1729
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
4. #10590207C2semidirect
8. C2×#3792C4semidirect
11. C22×#622C4semidirect
193. C32#1729semidirect

Maximal subgroups

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

subgroupindex
C22×#37922
C23×#6222
C2×#640862
#105902072
#17299