Finite Group Databasebeta

← #11774782

Subgroups — #11774782

Order 1152.

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

normal subgroups only

This group has 424 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#10593854C211yesmaximal, characteristic
2#10593729C211yesmaximal, characteristic
3C4×#3710C211yesmaximal, characteristic
4#10590031C214yesmaximal, complemented
5C2×#3788—21no—
6C42×C3⋊D3C2211yescharacteristic
7C3×#870—21no—
8#63919C411yescharacteristic
9#63919C411yescharacteristic
10#63865—21no—
11#63865C412yes—
12#63849—21no—
13#63838—21no—
14#63838C2212yes—
15C2×#3710—21no—
16#63779—21no—
17#63779C2212yes—
18C3×C4×C3⋊C8—21no—
19#63553C2212yes—
20#5688—61no—
21C4×D3×C8—61no—
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3D411yescharacteristic
24C2×C4×C3⋊D3D411yescharacteristic
25C2×#627—21no—
26C2×#627C2×C412yes—
27C2×#622—22no—
28#3788—42no—
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—24no—
43#1493—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—
58C8×Dic3—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—22no—
69C4×C3⋊D3SD1612yes—
70C4×C3⋊D3Q1612yes—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—22no—
73#627—24no—
74#627—42no—
75#622—42no—
76C3×C3⋊C8—24no—
77#533—91no—
78#423—91no—
79C2×C4×C8—91no—
80Q8⋊C8—94no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—61no—
85C2×C4×D3—61no—
86C2×C4×D3—61no—
87C2×Dic6—62no—
88C2×Dic6—62no—
89C2×C3×C8—62no—
90C3×C4⋊C4—62no—
91C3×C4⋊C4—62no—
92C3×C4⋊C4—61no—
93C3×C4⋊C4—61no—
94C3×C42—21no—
95C3×C42—21no—
96(C2×D3)⋊C4—62no—
97(C2×D3)⋊C4—62no—
98C4⋊Dic3—21no—
99C4⋊Dic3—21no—
100Dic3⋊C4—22no—
101Dic3⋊C4—22no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—61no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—62no—
111C4×Dic3—62no—
112C2×C3⋊C8—22no—
113D3×C8—68no—
114C22×C32C2×C22⋊C411yescharacteristic
115C2×C3⋊D3—21no—
116C2×C3⋊D3—21no—
117C2×C3⋊D3#10312yes—
118C32×C4—21no—
119C32×C4—21no—
120C32×C4#10312yes—
121C3⋊Dic3#10412yes—
122C3⋊Dic3#13112yes—
123C3⋊Dic3C2×SD1611yescharacteristic
124C3⋊Dic3C2×Q1611yescharacteristic
125C3×Dic3—42no—
126C3×Dic3—42no—
127C2×M16—181no—
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—92no—
139C4⋊C8—181no—
140C4×C8—61no—
141C4×C8—92no—
142C22×D3—61no—
143C22×D3—61no—
144C2×C3×C4—21no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—62no—
151C2×C3×C4—62no—
152C2×Dic3—22no—
153C2×Dic3—22no—
154C2×Dic3—61no—
155C2×Dic3—61no—
156C2×Dic3—61no—
157C2×Dic3—61no—
158C2×Dic3—61no—
159C2×Dic3—61no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—64no—
165C4×D3—64no—
166C4×D3—122no—
167C4×D3—122no—
168Dic6—124no—
169Dic6—124no—
170C3×C8—64no—
171C3⋊C8—24no—
172C2×C32#40811yescharacteristic
173C2×C32C2×#10311yescharacteristic
174C2×C32C2×#10411yescharacteristic
175C3⋊D3—22no—
176C2×Q8—92no—
177C2×Q8—181no—
178C22×C4—91no—
179C22×C4—91no—
180C22×C4—91no—
181M16—362no—
182C2×C8—62no—
183C2×C8—184no—
184C2×C8—182no—
185C4⋊C4—62no—
186C4⋊C4—61no—
187C4⋊C4—61no—
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—22no—
207C3×C4—22no—
208C3×C4—22no—
209C3×C4—41no—
210C3×C4—41no—
211C3×C4—122no—
212C3×C4—122no—
213Dic3—42no—
214Dic3—42no—
215Dic3—62no—
216Dic3—62no—
217Dic3—62no—
218Dic3—62no—
219Dic3—61no—
220Dic3—61no—
221Dic3—61no—
222Dic3—61no—
223C32#149311yescharacteristic, complemented, Sylow
224C23—91no—
225Q8—184no—
226Q8—362no—
227C2×C4—62no—
228C2×C4—62no—
229C2×C4—91no—
230C2×C4—91no—
231C2×C4—91no—
232C2×C4—92no—
233C2×C4—92no—
234C2×C4—182no—
235C2×C4—182no—
236C2×C4D32⋊C411yescharacteristic
237C2×C4D32⋊C411yescharacteristic
238C2×C4C2×GO+(4,𝔽2)11yescharacteristic
239C8—64no—
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—91no—
257C4—91no—
258C4—92no—
259C4—122no—
260C4—122no—
261C4#6373012yes—
262C3—21no—
263C3—21no—
264C2—182no—
265C2#1059330811yescharacteristic
266C2C2×#6373011yescharacteristic
267C2#1059338011yescharacteristic
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#1493
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
4. #10590031C2semidirect
223. C32#1493semidirect

Maximal subgroups

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

subgroupindex
#105938542
#105937292
C4×#37102
#105900312
#14939