Finite Group Databasebeta

← #11776205

Subgroups — #11776205

Order 1152.

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

normal subgroups only

This group has 392 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#10593854C211yesmaximal, characteristic
2#10593727C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4#10590040C212yesmaximal, complemented
5#10590039C212yesmaximal, complemented
6C42×C3⋊D3C2211yescharacteristic
7C3×#870—21no—
8#63919C2211yescharacteristic
9#63919C2211yescharacteristic
10#63865—21no—
11#63865C412yes—
12#63849—21no—
13#63838—21no—
14#63838C412yes—
15C2×#3710—21no—
16#63778—21no—
17C4⋊#622C2212yes—
18C4×#622—21no—
19C3×C4⋊(C3⋊C8)—21no—
20#63572C2212yes—
21#5688—61no—
22D3×C4⋊C8—61no—
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×C4×C3⋊D3D411yescharacteristic
26C2×#627—21no—
27C2×#627C2×C412yes—
28C2×#622—22no—
29C32×C42D411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3C2311yescharacteristic
33C3×C4⋊Dic3—21no—
34C3×C4⋊Dic3—21no—
35C3×Dic3⋊C4—22no—
36C3×Dic3⋊C4—22no—
37C2×C3×C3⋊C8—22no—
38#3724—21no—
39#3724C2×C412yes—
40#3722—22no—
41Dic32—22no—
42#3710—42no—
43#1542—91nomaximal, Sylow
44C3×#125—61no—
45C2×D3×C8—62no—
46#896—62no—
47#896—62no—
48#892—61no—
49#892—61no—
50#888—61no—
51#888—61no—
52#887—62no—
53#887—62no—
54C42×D3—61no—
55C42×D3—61no—
56#870—21no—
57C3×C4⋊C8—61no—
58Dic3⋊C8—62no—
59C4⋊(C3⋊C8)—21no—
60C22×C3⋊D3C22⋊C411yescharacteristic
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C32×C4C2×D411yescharacteristic
64C2×C3⋊Dic3C22⋊C411yescharacteristic
65C2×C3⋊Dic3C22×C411yescharacteristic
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4×C3⋊D3—22no—
68C4×C3⋊D3—41no—
69C4×C3⋊D3SD1612yes—
70C4×C3⋊D3Q1612yes—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73#627—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×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×C4×D3—61no—
88C2×Dic6—62no—
89C2×Dic6—62no—
90C2×C3×C8—62no—
91C3×C4⋊C4—62no—
92C3×C4⋊C4—62no—
93C3×C4⋊C4—61no—
94C3×C4⋊C4—61no—
95C3×C42—21no—
96C3×C42—21no—
97(C2×D3)⋊C4—62no—
98(C2×D3)⋊C4—62no—
99C4⋊Dic3—21no—
100C4⋊Dic3—21no—
101Dic3⋊C4—22no—
102Dic3⋊C4—22no—
103Dic3⋊C4—62no—
104Dic3⋊C4—62no—
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—
114D3×C8—124no—
115C22×C32C2×C22⋊C411yescharacteristic
116C2×C3⋊D3—21no—
117C2×C3⋊D3—21no—
118C2×C3⋊D3#10312yes—
119C32×C4—21no—
120C32×C4—21no—
121C32×C4C2×SD1611yescharacteristic
122C32×C4C2×Q1611yescharacteristic
123C3⋊Dic3—21no—
124C3⋊Dic3#10312yes—
125C3⋊Dic3#13512yes—
126C3×Dic3—42no—
127C3×Dic3—42no—
128C22×C8—181no—
129C4⋊Q8—91no—
130C4⋊Q8—91no—
131#125—61no—
132C22⋊Q8—92no—
133C22⋊Q8—181no—
134C4×Q8—92no—
135C4×Q8—181no—
136#117—181no—
137C2×C42—91no—
138C4⋊C8—61no—
139C4⋊C8—92no—
140C4⋊C8—92no—
141C22⋊C8—181no—
142C4×C8—181no—
143C22×D3—61no—
144C22×D3—61no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
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—61no—
159C2×Dic3—61no—
160C2×Dic3—61no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—64no—
166C4×D3—122no—
167C4×D3—122no—
168C4×D3—122no—
169Dic6—124no—
170Dic6—124no—
171C3×C8—122no—
172C3⋊C8—42no—
173C2×C32#41311yescharacteristic
174C2×C32C2×#10311yescharacteristic
175C2×C32#41611yescharacteristic
176C3⋊D3—22no—
177C2×Q8—92no—
178C2×Q8—181no—
179C22×C4—91no—
180C22×C4—91no—
181C22×C4—91no—
182C2×C8—62no—
183C2×C8—182no—
184C2×C8—362no—
185C4⋊C4—61no—
186C4⋊C4—61no—
187C4⋊C4—62no—
188C4⋊C4—62no—
189C4⋊C4—92no—
190C4⋊C4—181no—
191C22⋊C4—182no—
192C42—91no—
193C42—91no—
194C42—91no—
195C42—182no—
196C42GO+(4,𝔽2)11yescharacteristic
197C22×C3—21no—
198C22×C3—21no—
199C2×D3—62no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—62no—
203C2×D3—121no—
204C2×D3—121no—
205C3×C4—22no—
206C3×C4—21no—
207C3×C4—21no—
208C3×C4—21no—
209C3×C4—21no—
210C3×C4—41no—
211C3×C4—41no—
212C3×C4—41no—
213C3×C4—122no—
214C3×C4—122no—
215Dic3—42no—
216Dic3—42no—
217Dic3—62no—
218Dic3—62no—
219Dic3—62no—
220Dic3—62no—
221Dic3—62no—
222Dic3—121no—
223C32#154211yescharacteristic, complemented, Sylow
224C23—91no—
225Q8—362no—
226Q8—362no—
227C2×C4—62no—
228C2×C4—62no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—92no—
232C2×C4—92no—
233C2×C4—91no—
234C2×C4—182no—
235C2×C4—361no—
236C2×C4D32⋊C411yescharacteristic
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—
247D3—64no—
248D3—122no—
249C22—92no—
250C22—181no—
251C22—181no—
252C22C2×D32⋊C411yescharacteristic
253C4—21no—
254C4—21no—
255C4—92no—
256C4—92no—
257C4—122no—
258C4—122no—
259C4—181no—
260C4#6422711yescharacteristic
261C4#6422811yescharacteristic
262C3—21no—
263C3—21no—
264C2—182no—
265C2#1059331311yescharacteristic
266C2#1059331711yescharacteristic
267C2#1059337511yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32C2×C22⋊C4
prime radicalC22×C3⋊D3C22⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1542
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590040C2semidirect
5. #10590039C2semidirect
223. C32#1542semidirect

Maximal subgroups

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

subgroupindex
#105938542
#105937272
#105903312
#105900402
#105900392
#15429