Finite Group Databasebeta

← #11773334

Subgroups — #11773334

Order 1152.

1410 conjugacy classes of subgroups; only the 130 normal subgroups are shown.

normal subgroups only

This group has 1410 conjugacy classes of subgroups — too many to draw. Only its 130 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
1C22×C22⋊#157C212yesmaximal
2C2×C22⋊C4×C3⋊D3C211yesmaximal, characteristic
3C2×#63781C214yesmaximal, complemented
4C24×C3⋊D3C2211yescharacteristic
5C23×#157C2214yes—
6C22×C4×C3⋊D3C2212yes—
7C2×C22⋊#157—24no—
8C2×C22⋊#157—28no—
9C2×C32×C22⋊C4C411yescharacteristic, complemented
10C2×#3757C411yescharacteristic, complemented
11C2×#3752C412yescomplemented
12C22⋊C4×C3⋊D3—24no—
13#63781—28no—
14C2×D3×C22⋊C4—62no—
15C24×C32C2×C411yescharacteristic
16C23×C3⋊D3—24no—
17C23×C3⋊D3—24no—
18C23×C3⋊D3—24no—
19C23×C3⋊D3C2×C411yescharacteristic
20C23×C3⋊D3D414yes—
21C23×C3⋊D3C2311yescharacteristic
22C22×#157—24no—
23C22×#157—24no—
24C22×#157—24no—
25C22×#157—24no—
26C22×#157—24no—
27C22×#157—24no—
28C22×#157D418yes—
29C22×C32×C4C2×C412yes—
30C22×C3⋊Dic3C2×C412yes—
31C2×C4×C3⋊D3—22no—
32C2×C4×C3⋊D3—22no—
33C2×C4×C3⋊D3—24no—
34C2×C4×C3⋊D3—24no—
35C22⋊#157—216no—
36C32×C22⋊C4—22no—
37#3757—22no—
38#3752—24no—
39#1440—91nomaximal, Sylow
40C24×D3—62no—
41C22×C4×D3—64no—
42C2×C3×C22⋊C4—22no—
43C2×#217—62no—
44C2×(C2×D3)⋊C4—64no—
45D3×C22⋊C4—616no—
46C23×C32—22no—
47C23×C32—24no—
48C23×C32C22⋊C412yes—
49C23×C32C22×C411yescharacteristic
50C22×C3⋊D3—22no—
51C22×C3⋊D3—28no—
52C22×C3⋊D3—24no—
53C22×C3⋊D3—24no—
54C22×C3⋊D3—28no—
55C22×C3⋊D3—24no—
56C22×C3⋊D3—44no—
57C22×C3⋊D3—44no—
58C22×C3⋊D3—44no—
59C22×C3⋊D3—44no—
60C22×C3⋊D3C22⋊C412yes—
61C22×C3⋊D3C2×D414yes—
62C22×C3⋊D3C2×D412yes—
63C22×C3⋊D3#4114yes—
64C22×C3⋊D3#4114yes—
65C2×#157—28no—
66C2×#157—28no—
67C2×#157—28no—
68C2×#157—44no—
69C2×#157—44no—
70C2×#157—44no—
71C2×#157—44no—
72C2×C32×C4—22no—
73C2×C32×C4—24no—
74C2×C3⋊Dic3—22no—
75C2×C3⋊Dic3—24no—
76C4×C3⋊D3—42no—
77C4×C3⋊D3—44no—
78C4×C3⋊D3—42no—
79C22×C22⋊C4—91no—
80C22×C22⋊C4—92no—
81C2×#95—94no—
82C24×C3—22no—
83C23×D3—62no—
84C23×D3—62no—
85C23×D3—68no—
86C23×D3—616no—
87C23×D3—128no—
88C23×D3—128no—
89C22×C3×C4—24no—
90C22×Dic3—64no—
91C2×C4×D3—68no—
92C2×C4×D3—68no—
93C2×C4×D3—128no—
94C2×C4×D3—128no—
95C3×C22⋊C4—28no—
96#217—68no—
97(C2×D3)⋊C4—616no—
98C22×C32—22no—
99C22×C32—24no—
100C22×C32—44no—
101C22×C32C2×C22⋊C411yescharacteristic
102C22×C32#11712yes—
103C22×C32C4×D414yes—
104C2×C3⋊D3—22no—
105C2×C3⋊D3—24no—
106C2×C3⋊D3—44no—
107C2×C3⋊D3—48no—
108C2×C3⋊D3—48no—
109C2×C3⋊D3#12012yes—
110C2×C3⋊D3#12114yes—
111C2×C3⋊D3#12114yes—
112C2×C3⋊D3#12314yes—
113C2×C3⋊D3#12314yes—
114C2×C3⋊D3#12312yes—
115C2×C3⋊D3#12414yes—
116C2×C3⋊D3#12614yes—
117#157—48no—
118C32×C4—42no—
119C3⋊Dic3—42no—
120C25—91no—
121C23×C4—94no—
122C23×C4—92no—
123C2×C22⋊C4—91no—
124C2×C22⋊C4—92no—
125C2×C22⋊C4—184no—
126C2×C22⋊C4—188no—
127C2×C22⋊C4—184no—
128C2×C22⋊C4#15711yescharacteristic, complemented
129#95—188no—
130C23×C3—28no—
131C23×C3—22no—
132C23×C3—24no—
133C23×C3—48no—
134C22×D3—64no—
135C22×D3—68no—
136C22×D3—68no—
137C22×D3—68no—
138C22×D3—64no—
139C22×D3—632no—
140C22×D3—68no—
141C22×D3—128no—
142C22×D3—1216no—
143C22×D3—128no—
144C22×D3—128no—
145C22×D3—1216no—
146C22×D3—1216no—
147C22×D3—1216no—
148C22×D3—1216no—
149C2×C3×C4—28no—
150C2×C3×C4—48no—
151C2×Dic3—68no—
152C2×Dic3—128no—
153C4×D3—128no—
154C4×D3—1216no—
155C4×D3—128no—
156C2×C32—42no—
157C2×C32#38111yescharacteristic
158C2×C32#38612yes—
159C2×C32#38814yes—
160C3⋊D3—42no—
161C3⋊D3#39414yes—
162C3⋊D3#39714yes—
163C24—91no—
164C24—91no—
165C24—94no—
166C24—184no—
167C24—184no—
168C24—184no—
169C24C2×#15711yescharacteristic
170C22×C4—98no—
171C22×C4—92no—
172C22×C4—184no—
173C22×C4—182no—
174C22×C4—182no—
175C22×C4—184no—
176C22×C4—184no—
177C22×C4—184no—
178C22×C4—184no—
179C22×C4—184no—
180C22×C4—184no—
181C22×C4—184no—
182C22×C4C2×#15712yes—
183C22⋊C4—22no—
184C22⋊C4—184no—
185C22⋊C4—1816no—
186C22⋊C4—182no—
187C22×C3—28no—
188C22×C3—24no—
189C22×C3—28no—
190C22×C3—22no—
191C22×C3—48no—
192C22×C3—416no—
193C2×D3—64no—
194C2×D3—68no—
195C2×D3—64no—
196C2×D3—68no—
197C2×D3—68no—
198C2×D3—68no—
199C2×D3—68no—
200C2×D3—68no—
201C2×D3—68no—
202C2×D3—128no—
203C2×D3—1232no—
204C2×D3—1232no—
205C2×D3—1216no—
206C3×C4—48no—
207Dic3—128no—
208C32#144011yescharacteristic, complemented, Sylow
209C23—22no—
210C23—24no—
211C23—94no—
212C23—94no—
213C23—94no—
214C23—92no—
215C23—92no—
216C23—184no—
217C23—188no—
218C23—188no—
219C23—184no—
220C23—182no—
221C23—184no—
222C23—364no—
223C23—364no—
224C23—364no—
225C23—364no—
226C23C22⋊#15712yes—
227C23C22×#15711yescharacteristic
228C2×C4—24no—
229C2×C4—22no—
230C2×C4—188no—
231C2×C4—188no—
232C2×C4—188no—
233C2×C4—184no—
234C2×C4—182no—
235C2×C4—362no—
236C2×C4—364no—
237C2×C4—362no—
238C2×C4—364no—
239C2×C4—364no—
240C2×C4—364no—
241C2×C4—364no—
242C2×C3—22no—
243C2×C3—24no—
244C2×C3—28no—
245C2×C3—48no—
246D3—68no—
247D3—68no—
248D3—128no—
249C22—22no—
250C22—24no—
251C22—44no—
252C22—94no—
253C22—92no—
254C22—94no—
255C22—92no—
256C22—94no—
257C22—94no—
258C22—94no—
259C22—94no—
260C22—182no—
261C22—184no—
262C22—368no—
263C22—368no—
264C22—364no—
265C22#6428612yes—
266C22D4×#15714yes—
267C22C2×C22⋊#15711yescharacteristic
268C4—42no—
269C4—368no—
270C4—362no—
271C3—22no—
272C2—42no—
273C2—94no—
274C2—94no—
275C2—362no—
276C2#1059374714yes—
277C2#1059381111yescharacteristic
278C2#1059382612yes—
subgroupG/H
center, FrattiniC23C22×#157
commutator, socleC23×C32C22×C4
FittingC2×C32×C22⋊C4C4
prime radicalC24×C3⋊D3C22
cosocleC23×C3⋊D3C23
hypercenterC2×C22⋊C4#157
hypocenterC32#1440
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C22⋊C4

Complements

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

NH ≅ G/Ntype
3. C2×#63781C2semidirect
9. C2×C32×C22⋊C4C4semidirect
10. C2×#3757C4semidirect
11. C2×#3752C4semidirect
128. C2×C22⋊C4#157semidirect
208. C32#1440semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊#1572
C2×C22⋊C4×C3⋊D32
C2×#637812
#14409