Finite Group Databasebeta

← #11774409

Subgroups — #11774409

Order 1152.

386 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 65 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#10594810C211yesmaximal, characteristic
2C2×#63779C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C22×#622—21no—
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C3×#924—21no—
8#63982C412yes—
9#63957—21no—
10#63919C411yescharacteristic
11#63873C411yescharacteristic
12#63870—21no—
13#63843—21no—
14#63838C2212yes—
15#63779—21no—
16#63779C2212yes—
17C3×#830—21no—
18#63572—21no—
19#63553C2212yes—
20#5622—61no—
21#4718—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3C2×C411yescharacteristic
24C22×C3⋊Dic3D411yescharacteristic
25C2×C3×Dic6—21no—
26C2×#627C2×C412yes—
27C2×#622—22no—
28C2×#622—42no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3D411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×#217—22no—
34C3×C4⋊Dic3—21no—
35C3×Dic3⋊C4—22no—
36C2×C3×C3⋊C8—22no—
37#3724—21no—
38#3724—21no—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic32—22no—
42#1481—91nomaximal, Sylow
43C3×C22⋊Q8—61no—
44Q8×Dic3—61no—
45#944—61no—
46#924—21no—
47C2×C4×Dic3—61no—
48C2×C4×Dic3—61no—
49#889—62no—
50#888—61no—
51#887—62no—
52#887—61no—
53#878—62no—
54#877—62no—
55C3×C22⋊C8—61no—
56#830—21no—
57Dic3⋊C8—62no—
58C8×Dic3—62no—
59C23×C32C22⋊C411yescharacteristic
60C2×C32×C4—41no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3SD1612yes—
67C2×C3⋊Dic3Q1612yes—
68C2×C3⋊Dic3C22×C411yescharacteristic
69C2×C3⋊Dic3C2×D411yescharacteristic
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C3×Dic6—42no—
73#627—24no—
74#622—42no—
75C3×C3⋊C8—42no—
76#533—91no—
77#431—91no—
78C2×C4⋊C8—91no—
79Q8⋊C8—94no—
80C2×C3×Q8—61no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×Dic3—61no—
84C22×Dic3—61no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C2×Dic6—21no—
88C2×Dic6—62no—
89C2×C3×C8—62no—
90C3×C4⋊C4—61no—
91C3×C4⋊C4—62no—
92C3×C22⋊C4—62no—
93#217—22no—
94C4⋊Dic3—21no—
95C4⋊Dic3—62no—
96Dic3⋊C4—22no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101C4×Dic3—61no—
102C4×Dic3—61no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—62no—
110C4×Dic3—62no—
111C2×C3⋊C8—22no—
112C22×C32—21no—
113C22×C32—21no—
114C22×C32#10312yes—
115C22×C32C2×C22⋊C411yescharacteristic
116C32×C4—21no—
117C32×C4—21no—
118C3⋊Dic3—21no—
119C3⋊Dic3#10312yes—
120C3⋊Dic3#13112yes—
121C3⋊Dic3C2×SD1611yescharacteristic
122C3⋊Dic3C2×Q1611yescharacteristic
123C3×Dic3—42no—
124C3×Dic3—42no—
125C22×C8—181no—
126C4⋊Q8—91no—
127C4⋊Q8—91no—
128#125—181no—
129C22⋊Q8—61no—
130C22⋊Q8—92no—
131C4×Q8—92no—
132C4×Q8—181no—
133#117—181no—
134C2×C42—91no—
135C4⋊C8—92no—
136C4⋊C8—181no—
137C4⋊C8—181no—
138C22⋊C8—61no—
139C4×C8—92no—
140C23×C3—21no—
141C23×C3—21no—
142C3×Q8—122no—
143C2×C3×C4—21no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—42no—
148C2×C3×C4—42no—
149C2×C3×C4—62no—
150C2×C3×C4—62no—
151C2×Dic3—22no—
152C2×Dic3—22no—
153C2×Dic3—61no—
154C2×Dic3—61no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—122no—
166C2×Dic3—122no—
167Dic6—42no—
168Dic6—124no—
169C3×C8—122no—
170C3⋊C8—42no—
171C2×C32—22no—
172C2×C32#40811yescharacteristic
173C2×C32C2×#10311yescharacteristic
174C2×C32#42111yescharacteristic
175C2×Q8—61no—
176C2×Q8—92no—
177C22×C4—91no—
178C22×C4—91no—
179C22×C4GO+(4,𝔽2)11yescharacteristic
180C2×C8—62no—
181C2×C8—182no—
182C2×C8—362no—
183C4⋊C4—62no—
184C4⋊C4—61no—
185C4⋊C4—92no—
186C4⋊C4—181no—
187C4⋊C4—181no—
188C4⋊C4—182no—
189C22⋊C4—62no—
190C42—91no—
191C42—91no—
192C42—91no—
193C42—91no—
194C42—182no—
195C22×C3—21no—
196C22×C3—21no—
197C22×C3—22no—
198C22×C3—22no—
199C22×C3—41no—
200C22×C3—41no—
201C22×C3—41no—
202C22×C3—41no—
203C3×C4—22no—
204C3×C4—22no—
205C3×C4—41no—
206C3×C4—41no—
207C3×C4—122no—
208C3×C4—122no—
209Dic3—42no—
210Dic3—42no—
211Dic3—62no—
212Dic3—62no—
213Dic3—62no—
214Dic3—61no—
215Dic3—61no—
216Dic3—61no—
217Dic3—61no—
218Dic3—62no—
219Dic3—121no—
220Dic3—121no—
221C32#148111yescharacteristic, complemented, Sylow
222C23D32⋊C411yescharacteristic
223Q8—122no—
224Q8—184no—
225C2×C4—41no—
226C2×C4—62no—
227C2×C4—62no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—92no—
232C2×C4—92no—
233C2×C4—91no—
234C2×C4—182no—
235C2×C4D32⋊C411yescharacteristic
236C2×C4C2×GO+(4,𝔽2)11yescharacteristic
237C8—122no—
238C8—362no—
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—42no—
246C2×C3—42no—
247C22—21no—
248C22—21no—
249C22#6373012yes—
250C22C2×D32⋊C411yescharacteristic
251C4—21no—
252C4—21no—
253C4—92no—
254C4—91no—
255C4—91no—
256C4—92no—
257C4—122no—
258C4—122no—
259C4—181no—
260C3—21no—
261C3—21no—
262C2—22no—
263C2#1059330911yescharacteristic
264C2C2×#6373011yescharacteristic
265C2#1059350611yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1481
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590031C2semidirect
221. C32#1481semidirect

Maximal subgroups

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

subgroupindex
#105948102
C2×#637792
#105910612
#105900312
#14819