Finite Group Databasebeta

← #11776203

Subgroups — #11776203

Order 1152.

382 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 67 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×C4⋊#622C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590040C212yesmaximal, complemented
5#10590038C212yesmaximal, complemented
6C22×#622—21no—
7C2×C4×C3⋊Dic3C2211yescharacteristic
8C3×#924—21no—
9#63982C412yes—
10#63957—21no—
11#63919C2211yescharacteristic
12#63873C2211yescharacteristic
13#63870—21no—
14#63843—21no—
15#63838C412yes—
16C4⋊#622—21no—
17C4⋊#622C2212yes—
18C3×#830—21no—
19#63572C2212yes—
20#63553—21no—
21#5622—61no—
22#4718—61no—
23C22×C32×C4D411yescharacteristic
24C22×C3⋊Dic3C2×C411yescharacteristic
25C22×C3⋊Dic3D411yescharacteristic
26C2×C3×Dic6—21no—
27C2×#627C2×C412yes—
28C2×#622—22no—
29C2×#622—42no—
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C4×C3⋊Dic3C2311yescharacteristic
34C3×#217—22no—
35C3×C4⋊Dic3—21no—
36C3×Dic3⋊C4—22no—
37C2×C3×C3⋊C8—22no—
38#3724—21no—
39#3724—21no—
40#3724C2×C412yes—
41Dic3⋊Dic3—22no—
42Dic32—22no—
43#1542—91nomaximal, Sylow
44C3×C22⋊Q8—61no—
45Q8×Dic3—61no—
46#944—61no—
47#924—21no—
48C2×C4×Dic3—61no—
49C2×C4×Dic3—61no—
50#889—62no—
51#888—61no—
52#887—62no—
53#887—61no—
54#878—62no—
55#877—62no—
56C3×C22⋊C8—61no—
57#830—21no—
58Dic3⋊C8—62no—
59C8×Dic3—62no—
60C23×C32C22⋊C411yescharacteristic
61C2×C32×C4—22no—
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3SD1612yes—
68C2×C3⋊Dic3Q1612yes—
69C2×C3⋊Dic3C22×C411yescharacteristic
70C2×C3⋊Dic3C2×D411yescharacteristic
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73C3×Dic6—42no—
74#627—42no—
75#622—42no—
76C3×C3⋊C8—42no—
77#533—91no—
78#431—91no—
79C2×C4⋊C8—91no—
80#333—92no—
81#332—92no—
82C2×C3×Q8—61no—
83C22×C3×C4—21no—
84C22×C3×C4—21no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C2×Dic6—21no—
90C2×Dic6—62no—
91C2×C3×C8—62no—
92C3×C4⋊C4—61no—
93C3×C4⋊C4—62no—
94C3×C22⋊C4—62no—
95#217—22no—
96C4⋊Dic3—21no—
97C4⋊Dic3—62no—
98Dic3⋊C4—22no—
99Dic3⋊C4—62no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103C4×Dic3—61no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—62no—
112C4×Dic3—62no—
113C2×C3⋊C8—22no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32#10312yes—
117C22×C32C2×C22⋊C411yescharacteristic
118C32×C4—21no—
119C32×C4#13512yes—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3#10312yes—
123C3⋊Dic3C2×SD1611yescharacteristic
124C3⋊Dic3C2×Q1611yescharacteristic
125C3×Dic3—42no—
126C3×Dic3—42no—
127C22×C8—181no—
128C4⋊Q8—91no—
129C4⋊Q8—91no—
130#125—181no—
131C22⋊Q8—61no—
132C22⋊Q8—92no—
133C4×Q8—92no—
134C4×Q8—181no—
135#117—181no—
136C2×C42—91no—
137C4⋊C8—92no—
138C4⋊C8—92no—
139C4⋊C8—181no—
140C22⋊C8—61no—
141C4×C8—181no—
142C23×C3—21no—
143C23×C3—21no—
144C3×Q8—122no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—42no—
150C2×C3×C4—42no—
151C2×C3×C4—62no—
152C2×C3×C4—62no—
153C2×Dic3—22no—
154C2×Dic3—22no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C2×Dic3—62no—
161C2×Dic3—62no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—122no—
168C2×Dic3—122no—
169Dic6—42no—
170Dic6—124no—
171C3×C8—122no—
172C3⋊C8—42no—
173C2×C32—22no—
174C2×C32#41311yescharacteristic
175C2×C32C2×#10311yescharacteristic
176C2×C32#41611yescharacteristic
177C2×Q8—61no—
178C2×Q8—92no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4GO+(4,𝔽2)11yescharacteristic
182C2×C8—62no—
183C2×C8—182no—
184C2×C8—362no—
185C4⋊C4—61no—
186C4⋊C4—62no—
187C4⋊C4—92no—
188C4⋊C4—181no—
189C4⋊C4—181no—
190C4⋊C4—182no—
191C22⋊C4—62no—
192C42—91no—
193C42—91no—
194C42—91no—
195C42—91no—
196C42—182no—
197C22×C3—21no—
198C22×C3—21no—
199C22×C3—22no—
200C22×C3—22no—
201C22×C3—41no—
202C22×C3—41no—
203C22×C3—41no—
204C22×C3—41no—
205C3×C4—22no—
206C3×C4—22no—
207C3×C4—41no—
208C3×C4—41no—
209C3×C4—122no—
210C3×C4—122no—
211Dic3—42no—
212Dic3—42no—
213Dic3—62no—
214Dic3—62no—
215Dic3—61no—
216Dic3—61no—
217Dic3—61no—
218Dic3—61no—
219Dic3—62no—
220Dic3—62no—
221Dic3—121no—
222Dic3—121no—
223C32#154211yescharacteristic, complemented, Sylow
224C23D32⋊C411yescharacteristic
225Q8—122no—
226Q8—362no—
227C2×C4—22no—
228C2×C4—62no—
229C2×C4—62no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—92no—
233C2×C4—92no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—361no—
237C2×C4D32⋊C411yescharacteristic
238C2×C4C2×GO+(4,𝔽2)11yescharacteristic
239C8—122no—
240C8—362no—
241C2×C3—21no—
242C2×C3—21no—
243C2×C3—21no—
244C2×C3—21no—
245C2×C3—21no—
246C2×C3—21no—
247C2×C3—42no—
248C2×C3—42no—
249C22—21no—
250C22—21no—
251C22#6373012yes—
252C22C2×D32⋊C411yescharacteristic
253C4—21no—
254C4—91no—
255C4—92no—
256C4—91no—
257C4—122no—
258C4—122no—
259C4—181no—
260C4—181no—
261C4#6423712yes—
262C3—21no—
263C3—21no—
264C2—22no—
265C2#1059331311yescharacteristic
266C2C2×#6373011yescharacteristic
267C2#1059349811yescharacteristic
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#1542
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590040C2semidirect
5. #10590038C2semidirect
223. C32#1542semidirect

Maximal subgroups

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

subgroupindex
#105948102
C2×C4⋊#6222
#105910612
#105900402
#105900382
#15429