Finite Group Databasebeta

← #11775189

Subgroups — #11775189

Order 1152.

428 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 57 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#10595050C211yesmaximal, characteristic
2#10593804C211yesmaximal, characteristic
3#10591252C211yesmaximal, characteristic
4#10590072C214yesmaximal
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C3×#926—21no—
7#63982—21no—
8#63982C2212yes—
9C2×Dic32—21no—
10#63919C411yescharacteristic, complemented
11#63919C411yescharacteristic, complemented
12C4×#627—21no—
13C4×#627C412yescomplemented
14#63872—21no—
15C22⋊#622C2212yes—
16#63779—21no—
17#63777—21no—
18C3×C3⋊#95—21no—
19#63579C2212yes—
20#5517—61no—
21#4648—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—22no—
26C2×#627—21no—
27C2×#627C2×C412yes—
28C2×#622—22no—
29C4×C3⋊Dic3C2×C411yescharacteristic
30C4×C3⋊Dic3C2×C411yescharacteristic
31C4×C3⋊Dic3D411yescharacteristic
32C4×C3⋊Dic3D411yescharacteristic
33C3×#217—22no—
34C3×C4⋊Dic3—21no—
35C3×C4⋊Dic3—21no—
36C3×C4×Dic3—22no—
37#3724—21no—
38#3724C2×C412yes—
39Dic3⋊Dic3—22no—
40Dic3⋊Dic3—22no—
41Dic32—24no—
42#1506—91nomaximal, Sylow
43C3×#117—61no—
44#926—21no—
45C2×C4×Dic3—61no—
46C2×C4×Dic3—61no—
47C2×C4×Dic3—62no—
48#890—61no—
49#890—61no—
50#888—61no—
51#888—61no—
52#878—62no—
53#878—62no—
54C4×Dic6—62no—
55C4×Dic6—62no—
56C3×#95—61no—
57C3⋊#95—21no—
58C3⋊#95—62no—
59C23×C32C2×D411yescharacteristic
60C2×C32×C4—22no—
61C2×C32×C4C22⋊C411yescharacteristic
62C2×C32×C4C22⋊C411yescharacteristic
63C2×C3⋊Dic3—22no—
64C2×C3⋊Dic3—41no—
65C2×C3⋊Dic3C22⋊C411yescharacteristic
66C2×C3⋊Dic3C22⋊C411yescharacteristic
67C2×C3⋊Dic3C22×C411yescharacteristic
68C2×C3⋊Dic3C2×D411yescharacteristic
69C2×C3×Dic3—24no—
70C2×C3×Dic3—22no—
71C2×C3×Dic3—22no—
72C2×C3×Dic3—42no—
73C2×C3×Dic3—42no—
74#627—42no—
75#627—42no—
76#622—42no—
77#533—91no—
78#432—91no—
79#376—91no—
80#328—94no—
81C22×C3×C4—21no—
82C22×C3×C4—21no—
83C22×C3×C4—62no—
84C22×Dic3—22no—
85C22×Dic3—61no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C2×Dic6—62no—
90C2×Dic6—62no—
91C3×C4⋊C4—61no—
92C3×C4⋊C4—61no—
93C3×C22⋊C4—62no—
94C3×C42—62no—
95#217—22no—
96C4⋊Dic3—21no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99C4⋊Dic3—62no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—22no—
105C4×Dic3—61no—
106C4×Dic3—61no—
107C4×Dic3—61no—
108C4×Dic3—61no—
109C4×Dic3—61no—
110C4×Dic3—61no—
111C4×Dic3—61no—
112C4×Dic3—61no—
113C4×Dic3—68no—
114C22×C32—21no—
115C22×C32—21no—
116C22×C32C2×C22⋊C411yescharacteristic
117C22×C32#13712yes—
118C32×C4—21no—
119C32×C4—21no—
120C3⋊Dic3—21no—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3#10412yes—
124C3×Dic3—44no—
125C3×Dic3—42no—
126C3×Dic3—42no—
127C4⋊Q8—91no—
128C4⋊Q8—91no—
129#125—181no—
130C22⋊Q8—92no—
131C22⋊Q8—181no—
132C4×Q8—92no—
133C4×Q8—181no—
134#117—61no—
135C2×C42—91no—
136C2×C42—181no—
137C4⋊C8—181no—
138C22⋊C8—92no—
139#97—181no—
140#95—61no—
141#95—92no—
142C23×C3—21no—
143C23×C3—21no—
144C2×C3×C4—24no—
145C2×C3×C4—21no—
146C2×C3×C4—21no—
147C2×C3×C4—21no—
148C2×C3×C4—21no—
149C2×C3×C4—42no—
150C2×C3×C4—64no—
151C2×C3×C4—62no—
152C2×C3×C4—62no—
153C2×C3×C4—122no—
154C2×C3×C4—122no—
155C2×Dic3—22no—
156C2×Dic3—22no—
157C2×Dic3—24no—
158C2×Dic3—42no—
159C2×Dic3—42no—
160C2×Dic3—61no—
161C2×Dic3—61no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—64no—
169C2×Dic3—122no—
170C2×Dic3—122no—
171C2×Dic3—121no—
172C2×Dic3—121no—
173Dic6—124no—
174Dic6—124no—
175C2×C32—22no—
176C2×C32#41011yescharacteristic
177C2×C32#41911yescharacteristic
178C2×C32C2×#10411yescharacteristic
179C2×Q8—92no—
180C2×Q8—181no—
181C22×C4—62no—
182C22×C4—91no—
183C22×C4—91no—
184C22×C4GO+(4,𝔽2)11yescharacteristic
185C2×C8—182no—
186C4⋊C4—61no—
187C4⋊C4—61no—
188C4⋊C4—92no—
189C4⋊C4—182no—
190C4⋊C4—182no—
191C4⋊C4—181no—
192C22⋊C4—62no—
193C42—62no—
194C42—91no—
195C42—91no—
196C42—91no—
197C42—91no—
198C42—184no—
199C22×C3—22no—
200C22×C3—21no—
201C22×C3—21no—
202C22×C3—21no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—41no—
207C22×C3—41no—
208C3×C4—22no—
209C3×C4—22no—
210C3×C4—41no—
211C3×C4—41no—
212C3×C4—122no—
213C3×C4—122no—
214C3×C4—124no—
215Dic3—42no—
216Dic3—42no—
217Dic3—44no—
218Dic3—62no—
219Dic3—62no—
220Dic3—62no—
221Dic3—62no—
222Dic3—121no—
223Dic3—121no—
224Dic3—121no—
225Dic3—121no—
226C32#150611yescharacteristic, complemented, Sylow
227C23C2×GO+(4,𝔽2)11yescharacteristic
228Q8—362no—
229Q8—362no—
230C2×C4—22no—
231C2×C4—64no—
232C2×C4—62no—
233C2×C4—62no—
234C2×C4—91no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—122no—
239C2×C4—122no—
240C2×C4—182no—
241C2×C4—361no—
242C2×C4D32⋊C411yescharacteristic
243C2×C4D32⋊C411yescharacteristic
244C8—362no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—21no—
248C2×C3—21no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—42no—
254C22—21no—
255C22—21no—
256C22C2×D32⋊C411yescharacteristic
257C22#6423912yes—
258C4—21no—
259C4—21no—
260C4—92no—
261C4—124no—
262C4—122no—
263C4—122no—
264C4—181no—
265C4—181no—
266C4—181no—
267C3—21no—
268C3—21no—
269C2—22no—
270C2#1059334611yescharacteristic
271C2#1059338011yescharacteristic
272C2#1059350311yescharacteristic
subgroupG/H
centerC22C2×D32⋊C4
commutatorC2×C3⋊Dic3C22×C4
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C2×C22⋊C4
prime radicalC23×C32C2×D4
cosocleC22×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1506
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
10. #63919C4semidirect
11. #63919C4semidirect
13. C4×#627C4semidirect
226. C32#1506semidirect

Maximal subgroups

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

subgroupindex
#105950502
#105938042
#105912522
#105900722
#15069