Finite Group Databasebeta

← #11770847

Subgroups — #11770847

Order 1152.

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

normal subgroups only

This group has 458 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#10593800C211yesmaximal, characteristic
2#10591260C211yesmaximal, characteristic
3#10591152C211yesmaximal, characteristic
4C22×C4×C3⋊D3C2211yescharacteristic
5C2×#3787C412yescomplemented
6C2×#3722C412yes—
7C2×Dic32—21no—
8C2×#3710—21no—
9C22⋊#622—21no—
10#63778—21no—
11C3×C3⋊#95—21no—
12C3×#830—21no—
13#63557C412yescomplemented
14D3×C22⋊C8—61no—
15#4666—61no—
16C23×C3⋊D3C2×C411yescharacteristic
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3D411yescharacteristic
19C2×C4×C3⋊D3—42no—
20C2×C4×C3⋊D3C2×C411yescharacteristic
21C2×C4×C3⋊D3C2×C411yescharacteristic
22C2×C4×C3⋊D3D411yescharacteristic
23C2×C4×C3⋊D3Q811yescharacteristic
24C22×C3×Dic3—22no—
25C2×#622—22no—
26#3787—42no—
27C2×C3×C3⋊C8—22no—
28#3722—22no—
29#3722C814yescomplemented
30Dic32—42no—
31#3710—42no—
32#1282—91nomaximal, Sylow
33C22×C4×D3—61no—
34C22×C4×D3—61no—
35C2×(C2×D3)⋊C4—62no—
36C2×C4×Dic3—62no—
37C2×D3×C8—62no—
38C3×C22⋊C8—61no—
39C3×#95—61no—
40C3⋊#95—21no—
41#830—21no—
42(C2×D3)⋊C8—62no—
43C23×C32C22⋊C411yescharacteristic
44C22×C3⋊D3—41no—
45C22×C3⋊D3—41no—
46C22×C3⋊D3C4211yescharacteristic
47C22×C3⋊D3C4⋊C411yescharacteristic
48C22×C3⋊D3C2×C812yes—
49C22×C3⋊D3M1612yes—
50C2×C32×C4—41no—
51C2×C32×C4C22⋊C411yescharacteristic
52C2×C32×C4C4⋊C411yescharacteristic
53C2×C3⋊Dic3—22no—
54C2×C3⋊Dic3C22⋊C411yescharacteristic
55C2×C3⋊Dic3C4⋊C411yescharacteristic
56C4×C3⋊D3—22no—
57C4×C3⋊D3—22no—
58C4×C3⋊D3—41no—
59C4×C3⋊D3—41no—
60C2×C3×Dic3—24no—
61C2×C3×Dic3—42no—
62C2×C3×Dic3—42no—
63#622—42no—
64C3×C3⋊C8—42no—
65C2×C22⋊C8—91no—
66C2×C22⋊C8—91no—
67C4×C22⋊C4—91no—
68C23×D3—61no—
69C23×D3—61no—
70C22×C3×C4—21no—
71C22×C3×C4—21no—
72C22×C3×C4—62no—
73C22×Dic3—22no—
74C22×Dic3—61no—
75C22×Dic3—61no—
76C2×C4×D3—61no—
77C2×C4×D3—61no—
78C2×C4×D3—61no—
79C2×C4×D3—61no—
80C2×C4×D3—61no—
81C2×C4×D3—61no—
82C2×C4×D3—61no—
83C2×C4×D3—61no—
84C2×C4×D3—124no—
85C2×C4×D3—124no—
86C2×C3×C8—62no—
87(C2×D3)⋊C4—64no—
88(C2×D3)⋊C4—64no—
89C4×Dic3—124no—
90C2×C3⋊C8—22no—
91D3×C8—124no—
92C22×C32—21no—
93C22×C32—21no—
94C22×C32#9511yescharacteristic
95C22×C32C22⋊C812yes—
96C2×C3⋊D3—21no—
97C2×C3⋊D3—21no—
98C2×C3⋊D3—21no—
99C2×C3⋊D3—21no—
100C2×C3⋊D3—42no—
101C2×C3⋊D3—42no—
102C2×C3⋊D3C4×C811yescharacteristic
103C2×C3⋊D3#9711yescharacteristic
104C2×C3⋊D3C4⋊C812yes—
105C32×C4—21no—
106C32×C4—21no—
107C3⋊Dic3—21no—
108C3⋊Dic3#9912yes—
109C3×Dic3—44no—
110C23×C4—91no—
111C22×C8—92no—
112C22×C8—181no—
113C2×C22⋊C4—92no—
114C2×C42—181no—
115C22⋊C8—61no—
116C22⋊C8—92no—
117C22⋊C8—181no—
118C22⋊C8—181no—
119#95—61no—
120C23×C3—21no—
121C23×C3—21no—
122C22×D3—61no—
123C22×D3—61no—
124C22×D3—61no—
125C22×D3—61no—
126C22×D3—62no—
127C22×D3—62no—
128C22×D3—62no—
129C22×D3—62no—
130C22×D3—122no—
131C22×D3—122no—
132C22×D3—122no—
133C22×D3—121no—
134C22×D3—121no—
135C2×C3×C4—21no—
136C2×C3×C4—21no—
137C2×C3×C4—21no—
138C2×C3×C4—21no—
139C2×C3×C4—42no—
140C2×C3×C4—42no—
141C2×C3×C4—64no—
142C2×C3×C4—122no—
143C2×C3×C4—122no—
144C2×Dic3—24no—
145C2×Dic3—42no—
146C2×Dic3—42no—
147C2×Dic3—61no—
148C2×Dic3—61no—
149C2×Dic3—61no—
150C2×Dic3—61no—
151C2×Dic3—64no—
152C2×Dic3—122no—
153C4×D3—64no—
154C4×D3—122no—
155C4×D3—122no—
156C4×D3—122no—
157C4×D3—122no—
158C4×D3—122no—
159C4×D3—122no—
160C4×D3—122no—
161C3×C8—122no—
162C3⋊C8—42no—
163C2×C32—22no—
164C2×C32#33611yescharacteristic
165C2×C32#34211yescharacteristic
166C2×C32#34411yescharacteristic
167C3⋊D3—22no—
168C3⋊D3—21no—
169C3⋊D3—21no—
170C24—91no—
171C22×C4—62no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—91no—
175C22×C4—91no—
176C22×C4—91no—
177C22×C4—362no—
178C22×C4GO+(4,𝔽2)11yescharacteristic
179C2×C8—62no—
180C2×C8—182no—
181C2×C8—362no—
182C2×C8—362no—
183C22⋊C4—94no—
184C22⋊C4—182no—
185C42—362no—
186C22×C3—21no—
187C22×C3—22no—
188C22×C3—21no—
189C22×C3—22no—
190C22×C3—22no—
191C22×C3—21no—
192C22×C3—21no—
193C22×C3—41no—
194C22×C3—41no—
195C2×D3—62no—
196C2×D3—61no—
197C2×D3—61no—
198C2×D3—61no—
199C2×D3—61no—
200C2×D3—62no—
201C2×D3—62no—
202C2×D3—62no—
203C2×D3—121no—
204C2×D3—121no—
205C2×D3—121no—
206C2×D3—121no—
207C2×D3—121no—
208C2×D3—121no—
209C2×D3—124no—
210C2×D3—124no—
211C2×D3—122no—
212C2×D3—122no—
213C2×D3—122no—
214C2×D3—122no—
215C3×C4—22no—
216C3×C4—41no—
217C3×C4—41no—
218C3×C4—41no—
219C3×C4—124no—
220Dic3—44no—
221Dic3—62no—
222Dic3—62no—
223Dic3—62no—
224Dic3—121no—
225C32#128211yescharacteristic, complemented, Sylow
226C23—91no—
227C23—91no—
228C23—92no—
229C23—92no—
230C23—361no—
231C23—361no—
232C23D32⋊C411yescharacteristic
233C2×C4—41no—
234C2×C4—64no—
235C2×C4—91no—
236C2×C4—91no—
237C2×C4—122no—
238C2×C4—122no—
239C2×C4—182no—
240C2×C4—182no—
241C2×C4—182no—
242C2×C4—361no—
243C2×C4—361no—
244C2×C4D32⋊C411yescharacteristic
245C2×C4#377311yescharacteristic
246C8—122no—
247C8—362no—
248C2×C3—22no—
249C2×C3—22no—
250C2×C3—21no—
251C2×C3—21no—
252C2×C3—21no—
253C2×C3—21no—
254C2×C3—21no—
255C2×C3—21no—
256C2×C3—42no—
257D3—64no—
258D3—122no—
259D3—121no—
260D3—121no—
261D3—121no—
262D3—121no—
263C22—21no—
264C22—21no—
265C22—92no—
266C22—91no—
267C22—91no—
268C22—181no—
269C22—181no—
270C22—181no—
271C22—181no—
272C22—362no—
273C22—362no—
274C22D32⋊C812yes—
275C22#6373711yescharacteristic
276C4—21no—
277C4—21no—
278C4—92no—
279C4—124no—
280C4—181no—
281C3—21no—
282C3—21no—
283C2—22no—
284C2—182no—
285C2—181no—
286C2—181no—
287C2#1059004311yescharacteristic
288C2#1059005611yescharacteristic
289C2#1059007711yescharacteristic
subgroupG/H
centerC22#63737
commutatorC2×C3⋊D3C4×C8
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#95
prime radicalC23×C3⋊D3C2×C4
cosocleC22×C4×C3⋊D3C22
hypocenterC32#1282
LCSG ▷ C2×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
5. C2×#3787C4semidirect
13. #63557C4semidirect
29. #3722C8semidirect
225. C32#1282semidirect

Maximal subgroups

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

subgroupindex
#105938002
#105912602
#105911522
#12829