Finite Group Databasebeta

← #11775188

Subgroups — #11775188

Order 1152.

428 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 59 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
2#10593806C211yesmaximal, characteristic
3#10591222C211yesmaximal, characteristic
4#10590072C214yesmaximal
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C3×#924—21no—
7C2×C3×C4×Dic3—21no—
8#63982C2212yes—
9#63957—21no—
10#63919C411yescharacteristic, complemented
11#63873C411yescharacteristic, complemented
12#63870—21no—
13#63843—21no—
14#63838C412yescomplemented
15C22⋊#622C2212yes—
16#63777—21no—
17C4⋊#622—21no—
18#63579—21no—
19#63579C2212yes—
20#5622—61no—
21#4932—61no—
22C22×C32×C4D411yescharacteristic
23C22×C3⋊Dic3D411yescharacteristic
24C22×C3⋊Dic3C2311yescharacteristic
25C22×C3×Dic3—22no—
26C2×C3×Dic6—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×Dic3⋊C4—22no—
36C3×C4×Dic3—24no—
37#3724—21no—
38#3724—21no—
39#3724C2×C412yes—
40Dic3⋊Dic3—22no—
41Dic32—22no—
42#1506—91nomaximal, Sylow
43C3×C22⋊Q8—61no—
44C2×C3×C42—61no—
45Q8×Dic3—61no—
46#944—61no—
47#924—21no—
48C2×C4×Dic3—21no—
49C2×C4×Dic3—61no—
50C2×C4×Dic3—61no—
51#889—62no—
52#888—61no—
53#887—62no—
54#887—61no—
55#878—62no—
56#877—62no—
57C3⋊#95—62no—
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—
74C3×Dic6—42no—
75#627—42no—
76#622—42no—
77#533—91no—
78#432—91no—
79#376—91no—
80#328—94no—
81C2×C3×Q8—61no—
82C22×C3×C4—21no—
83C22×C3×C4—21no—
84C22×C3×C4—62no—
85C22×Dic3—22no—
86C22×Dic3—61no—
87C22×Dic3—61no—
88C22×Dic3—61no—
89C22×Dic3—61no—
90C2×Dic6—21no—
91C2×Dic6—62no—
92C3×C4⋊C4—61no—
93C3×C4⋊C4—62no—
94C3×C22⋊C4—62no—
95C3×C42—64no—
96#217—22no—
97C4⋊Dic3—21no—
98C4⋊Dic3—62no—
99Dic3⋊C4—22no—
100Dic3⋊C4—62no—
101Dic3⋊C4—62no—
102Dic3⋊C4—62no—
103Dic3⋊C4—62no—
104C4×Dic3—24no—
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—62no—
114C4×Dic3—62no—
115C22×C32—21no—
116C22×C32—21no—
117C22×C32C2×C22⋊C411yescharacteristic
118C22×C32#13712yes—
119C32×C4—21no—
120C32×C4#10412yes—
121C3⋊Dic3—21no—
122C3⋊Dic3—21no—
123C3⋊Dic3—21no—
124C3⋊Dic3—21no—
125C3×Dic3—44no—
126C3×Dic3—42no—
127C3×Dic3—42no—
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—61no—
137C2×C42—91no—
138C4⋊C8—181no—
139C22⋊C8—92no—
140#97—181no—
141#95—92no—
142#95—181no—
143C23×C3—21no—
144C23×C3—21no—
145C3×Q8—122no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—21no—
149C2×C3×C4—21no—
150C2×C3×C4—21no—
151C2×C3×C4—21no—
152C2×C3×C4—42no—
153C2×C3×C4—62no—
154C2×C3×C4—62no—
155C2×C3×C4—64no—
156C2×C3×C4—122no—
157C2×C3×C4—122no—
158C2×Dic3—24no—
159C2×Dic3—22no—
160C2×Dic3—22no—
161C2×Dic3—42no—
162C2×Dic3—42no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C2×Dic3—61no—
166C2×Dic3—61no—
167C2×Dic3—61no—
168C2×Dic3—61no—
169C2×Dic3—61no—
170C2×Dic3—61no—
171C2×Dic3—64no—
172C2×Dic3—122no—
173C2×Dic3—122no—
174C2×Dic3—122no—
175Dic6—42no—
176Dic6—124no—
177C2×C32—22no—
178C2×C32#41011yescharacteristic
179C2×C32#41911yescharacteristic
180C2×C32C2×#10411yescharacteristic
181C2×Q8—61no—
182C2×Q8—92no—
183C22×C4—62no—
184C22×C4—91no—
185C22×C4—91no—
186C22×C4GO+(4,𝔽2)11yescharacteristic
187C2×C8—182no—
188C4⋊C4—62no—
189C4⋊C4—61no—
190C4⋊C4—92no—
191C4⋊C4—181no—
192C4⋊C4—181no—
193C4⋊C4—182no—
194C22⋊C4—62no—
195C42—64no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42—91no—
200C42—182no—
201C22×C3—21no—
202C22×C3—22no—
203C22×C3—21no—
204C22×C3—22no—
205C22×C3—22no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—41no—
209C22×C3—41no—
210C3×C4—22no—
211C3×C4—22no—
212C3×C4—22no—
213C3×C4—41no—
214C3×C4—122no—
215C3×C4—124no—
216C3×C4—122no—
217Dic3—42no—
218Dic3—42no—
219Dic3—44no—
220Dic3—62no—
221Dic3—62no—
222Dic3—62no—
223Dic3—121no—
224Dic3—121no—
225Dic3—121no—
226Dic3—121no—
227Dic3—121no—
228C32#150611yescharacteristic, complemented, Sylow
229C23C2×GO+(4,𝔽2)11yescharacteristic
230Q8—122no—
231Q8—362no—
232C2×C4—22no—
233C2×C4—64no—
234C2×C4—62no—
235C2×C4—62no—
236C2×C4—91no—
237C2×C4—91no—
238C2×C4—91no—
239C2×C4—91no—
240C2×C4—122no—
241C2×C4—122no—
242C2×C4—182no—
243C2×C4—361no—
244C2×C4D32⋊C411yescharacteristic
245C2×C4D32⋊C411yescharacteristic
246C8—362no—
247C2×C3—22no—
248C2×C3—22no—
249C2×C3—21no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—42no—
256C22—21no—
257C22—21no—
258C22#6422612yes—
259C22C2×D32⋊C411yescharacteristic
260C4—21no—
261C4—124no—
262C4—122no—
263C4—122no—
264C4—181no—
265C4—181no—
266C4—181no—
267C4—181no—
268C4#6374112yes—
269C3—21no—
270C3—21no—
271C2—22no—
272C2#1059334511yescharacteristic
273C2#1059337411yescharacteristic
274C2C2×#6374111yescharacteristic
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. #63873C4semidirect
14. #63838C4semidirect
228. C32#1506semidirect

Maximal subgroups

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

subgroupindex
#105948102
#105938062
#105912222
#105900722
#15069