Finite Group Databasebeta

← #11783382

Subgroups — #11783382

Order 1152.

750 conjugacy classes of subgroups; only the 125 normal subgroups are shown.

normal subgroups only

This group has 750 conjugacy classes of subgroups — too many to draw. Only its 125 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
1C2×#64286C211yesmaximal, characteristic
2#10594969C212yesmaximal
3#10590077C214yesmaximal
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×C22⋊#157C2212yes—
6#64286—22no—
7#64286—22no—
8C2×C4⋊#157C412yescomplemented
9C2×C4×#157C412yescomplemented
10C3×#926—22no—
11#63974C2214yes—
12#63957—22no—
13#63900—22no—
14C4×#624—22no—
15#63874C414yescomplemented
16#63849C414yescomplemented
17D3×#117—62no—
18C23×C3⋊D3C2311yescharacteristic
19C22×#157C2×C414yes—
20C22×C32×C4D411yescharacteristic
21C22×C3⋊Dic3D411yescharacteristic
22C2×C4×C3⋊D3C2×C411yescharacteristic
23C2×C4×C3⋊D3C2×C411yescharacteristic
24C2×C4×C3⋊D3C2×C412yes—
25C2×C4×C3⋊D3C2×C412yes—
26C2×C4×C3⋊D3D412yes—
27C2×C4×C3⋊D3D412yes—
28C2×C4×C3⋊D3Q811yescharacteristic
29C2×C4×C3⋊D3Q811yescharacteristic
30C2×#624—24no—
31C22⋊#157—24no—
32C4⋊#157—24no—
33C4×#157—22no—
34C4×#157—22no—
35C3×#217—24no—
36C3×C4⋊Dic3—24no—
37C3×C4×Dic3—24no—
38#3724—24no—
39#3722C2×C418yes—
40Dic32—24no—
41#1740—91nomaximal, Sylow
42C22×C4×D3—62no—
43C3×#117—62no—
44#926—22no—
45#892—64no—
46D3×C4⋊C4—64no—
47D3×C22⋊C4—64no—
48#877—64no—
49#872—64no—
50C42×D3—64no—
51C23×C32C2×D411yescharacteristic
52C22×C3⋊D3—42no—
53C22×C3⋊D3C22×C411yescharacteristic
54C22×C3⋊D3C22×C412yes—
55C22×C3⋊D3C2×D412yes—
56C22×C3⋊D3C2×Q811yescharacteristic
57C2×#157—24no—
58C2×#157—44no—
59C2×C32×C4C22⋊C412yes—
60C2×C32×C4C22⋊C412yes—
61C2×C32×C4C4⋊C411yescharacteristic
62C2×C32×C4C4⋊C411yescharacteristic
63C2×C3⋊Dic3C22⋊C412yes—
64C2×C3⋊Dic3C22⋊C412yes—
65C2×C3⋊Dic3C4⋊C411yescharacteristic
66C2×C3⋊Dic3C4⋊C411yescharacteristic
67C4×C3⋊D3C4211yescharacteristic
68C4×C3⋊D3C4211yescharacteristic
69C4×C3⋊D3C4212yes—
70C4×C3⋊D3C22⋊C411yescharacteristic
71C4×C3⋊D3C22⋊C411yescharacteristic
72C4×C3⋊D3C22⋊C412yes—
73C4×C3⋊D3C4⋊C412yes—
74C4×C3⋊D3C4⋊C412yes—
75C4×C3⋊D3C4⋊C412yes—
76C4×C3⋊D3C4⋊C412yes—
77C2×C3×Dic3—28no—
78#624—48no—
79C2×#117—91no—
80C2×#117—92no—
81#342—94no—
82C23×D3—62no—
83C22×C3×C4—22no—
84C22×Dic3—62no—
85C2×C4×D3—62no—
86C2×C4×D3—62no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—62no—
90C2×C4×D3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—62no—
96C2×C4×D3—62no—
97C2×C4×D3—68no—
98C3×C4⋊C4—64no—
99C3×C22⋊C4—64no—
100C3×C42—64no—
101#217—24no—
102(C2×D3)⋊C4—68no—
103C4⋊Dic3—24no—
104Dic3⋊C4—68no—
105C4×Dic3—24no—
106C4×Dic3—68no—
107C22×C32—41no—
108C22×C32C2×C22⋊C412yes—
109C22×C32C2×C4⋊C411yescharacteristic
110C2×C3⋊D3—24no—
111C2×C3⋊D3—22no—
112C2×C3⋊D3—42no—
113C2×C3⋊D3—41no—
114C2×C3⋊D3C2×C4211yescharacteristic
115C2×C3⋊D3C2×C22⋊C411yescharacteristic
116C2×C3⋊D3C2×C4⋊C412yes—
117#157—44no—
118C32×C4#9511yescharacteristic
119C32×C4#9512yes—
120C32×C4#9511yescharacteristic
121C3⋊Dic3#9511yescharacteristic
122C3⋊Dic3#9511yescharacteristic
123C3⋊Dic3#9512yes—
124C3×Dic3—48no—
125C23×C4—91no—
126#117—62no—
127#117—94no—
128#117—94no—
129#117—182no—
130#117—182no—
131#117—182no—
132C2×C4⋊C4—92no—
133C2×C4⋊C4—182no—
134C2×C22⋊C4—94no—
135C2×C22⋊C4—92no—
136C2×C42—92no—
137C2×C42—182no—
138C23×C3—22no—
139C22×D3—62no—
140C22×D3—62no—
141C22×D3—62no—
142C22×D3—62no—
143C22×D3—62no—
144C22×D3—62no—
145C22×D3—128no—
146C2×C3×C4—22no—
147C2×C3×C4—22no—
148C2×C3×C4—22no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—22no—
152C2×C3×C4—68no—
153C2×Dic3—28no—
154C2×Dic3—62no—
155C2×Dic3—62no—
156C2×Dic3—62no—
157C2×Dic3—62no—
158C2×Dic3—62no—
159C2×Dic3—62no—
160C4×D3—62no—
161C4×D3—62no—
162C4×D3—62no—
163C4×D3—62no—
164C4×D3—62no—
165C4×D3—62no—
166C4×D3—62no—
167C4×D3—62no—
168C4×D3—62no—
169C4×D3—62no—
170C4×D3—62no—
171C4×D3—62no—
172C4×D3—62no—
173C4×D3—62no—
174C4×D3—62no—
175C4×D3—62no—
176C4×D3—1216no—
177C2×C32—22no—
178C2×C32—21no—
179C2×C32C2×#9511yescharacteristic
180C3⋊D3—22no—
181C3⋊D3—21no—
182C3⋊D3#41012yes—
183C24—91no—
184C22×C4—91no—
185C22×C4—92no—
186C22×C4—92no—
187C22×C4—92no—
188C22×C4—92no—
189C22×C4—91no—
190C22×C4—91no—
191C22×C4—91no—
192C22×C4—91no—
193C22×C4—94no—
194C22×C4—184no—
195C22×C4GO+(4,𝔽2)11yescharacteristic
196C4⋊C4—64no—
197C4⋊C4—184no—
198C4⋊C4—184no—
199C22⋊C4—64no—
200C22⋊C4—98no—
201C22⋊C4—184no—
202C42—64no—
203C42—184no—
204C42—182no—
205C42—182no—
206C22×C3—22no—
207C22×C3—22no—
208C22×C3—22no—
209C22×C3—44no—
210C2×D3—62no—
211C2×D3—62no—
212C2×D3—62no—
213C2×D3—62no—
214C2×D3—68no—
215C2×D3—124no—
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—124no—
219C2×D3—124no—
220C3×C4—22no—
221C3×C4—22no—
222C3×C4—22no—
223C3×C4—22no—
224C3×C4—128no—
225Dic3—48no—
226Dic3—62no—
227Dic3—62no—
228Dic3—62no—
229Dic3—62no—
230C32#174011yescharacteristic, complemented, Sylow
231C23—92no—
232C23—91no—
233C23—92no—
234C23—91no—
235C23—362no—
236C23C2×GO+(4,𝔽2)11yescharacteristic
237C2×C4—68no—
238C2×C4—92no—
239C2×C4—92no—
240C2×C4—91no—
241C2×C4—91no—
242C2×C4—91no—
243C2×C4—92no—
244C2×C4—92no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—91no—
248C2×C4—92no—
249C2×C4—91no—
250C2×C4—92no—
251C2×C4—91no—
252C2×C4—184no—
253C2×C4—368no—
254C2×C4—364no—
255C2×C4D32⋊C412yes—
256C2×C4D32⋊C412yes—
257C2×C4#377311yescharacteristic
258C2×C4#377311yescharacteristic
259C2×C3—24no—
260C2×C3—22no—
261C2×C3—42no—
262C2×C3—42no—
263D3—64no—
264D3—64no—
265D3—122no—
266D3—122no—
267C22—41no—
268C22—91no—
269C22—92no—
270C22—91no—
271C22—184no—
272C22—182no—
273C22—362no—
274C22—361no—
275C22C2×D32⋊C412yes—
276C22C2×#377311yescharacteristic
277C4—91no—
278C4—92no—
279C4—91no—
280C4—128no—
281C4—364no—
282C4#6373711yescharacteristic
283C4#6373712yes—
284C4#6373711yescharacteristic
285C3—22no—
286C2—22no—
287C2—21no—
288C2—92no—
289C2—182no—
290C2—181no—
291C2C2×#6373711yescharacteristic
subgroupG/H
centerC4#63737
commutatorC2×C3⋊D3C2×C42
FrattiniC23C2×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32C2×#95
prime radical, cosocleC23×C3⋊D3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1740
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
8. C2×C4⋊#157C4semidirect
9. C2×C4×#157C4semidirect
15. #63874C4semidirect
16. #63849C4semidirect
230. C32#1740semidirect

Maximal subgroups

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

subgroupindex
C2×#642862
#105949692
#105900772
#17409