Finite Group Databasebeta

← #11801240

Subgroups — #11801240

Order 1152.

986 conjugacy classes of subgroups; only the 215 normal subgroups are shown.

normal subgroups only

This group has 986 conjugacy classes of subgroups — too many to draw. Only its 215 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×C4×#157C211yesmaximal, characteristic
2#10594969C212yesmaximal
3#10593516C214yesmaximal
4#10593413C212yesmaximal, complemented
5C4×#3773C214yesmaximal, complemented
6#10593344C212yesmaximal, complemented
7C23×#157C2212yes—
8C22×C4×C3⋊D3C2211yescharacteristic
9C2×C4×#157C418yescomplemented
10C2×C4×#157C2211yescharacteristic
11C2×C4×#157C2212yes—
12C2×C4×#157C2211yescharacteristic
13C2×#3773C2218yes—
14C3×#926—22no—
15#63974C2214yes—
16#63957—22no—
17#63900C2214yes—
18C4×#624C2214yes—
19#63874—22no—
20#63849—22no—
21#63737C2218yes—
22D3×#117—62no—
23C23×C3⋊D3C2311yescharacteristic
24C22×#157—28no—
25C22×#157C2×C418yes—
26C22×#157C2312yes—
27C22×#157C2312yes—
28C22×C32×C4D411yescharacteristic
29C22×C3⋊Dic3D411yescharacteristic
30C2×C4×C3⋊D3C2×C414yes—
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3D411yescharacteristic
33C2×C4×C3⋊D3Q814yes—
34C2×C4×C3⋊D3C2311yescharacteristic
35C2×C4×C3⋊D3C2311yescharacteristic
36C2×#624C2318yes—
37C4×#157C2×C414yes—
38C4×#157C2×C418yes—
39C4×#157C2×C414yes—
40#3773—216no—
41C3×#217—24no—
42C3×C4⋊Dic3—24no—
43C3×C4×Dic3—24no—
44#3724—24no—
45#3722—24no—
46Dic32—24no—
47#2285—91nomaximal, Sylow
48C22×C4×D3—62no—
49C3×#117—62no—
50#926—22no—
51#892—64no—
52D3×C4⋊C4—64no—
53D3×C22⋊C4—64no—
54#877—64no—
55#872—64no—
56C42×D3—64no—
57C23×C32C2×D411yescharacteristic
58C22×C3⋊D3—24no—
59C22×C3⋊D3C22×C412yes—
60C22×C3⋊D3C2×D411yescharacteristic
61C22×C3⋊D3C2×Q812yes—
62C22×C3⋊D3C2411yescharacteristic
63C2×#157—24no—
64C2×#157—216no—
65C2×#157C22×C414yes—
66C2×#157C22×C414yes—
67C2×#157#4118yes—
68C2×C32×C4C4⋊C414yescomplemented
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4C2×D411yescharacteristic
71C2×C3⋊Dic3C4⋊C414yescomplemented
72C2×C3⋊Dic3C2×D411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C4×C3⋊D3C4⋊C414yescomplemented
75C4×C3⋊D3C4⋊C414yescomplemented
76C4×C3⋊D3C22×C412yes—
77C4×C3⋊D3C22×C412yes—
78C4×C3⋊D3C2×Q812yes—
79C4×C3⋊D3C2×Q812yes—
80C2×C3×Dic3—28no—
81#624—216no—
82C2×#117—92no—
83C22×C42—91no—
84#384—92no—
85#382—92no—
86#380—94no—
87C4×C4⋊C4—94no—
88C23×D3—62no—
89C22×C3×C4—22no—
90C22×Dic3—62no—
91C2×C4×D3—62no—
92C2×C4×D3—62no—
93C2×C4×D3—62no—
94C2×C4×D3—62no—
95C2×C4×D3—68no—
96C2×C4×D3—68no—
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—22no—
108C22×C32C2×C4⋊C412yes—
109C22×C32C22×D411yescharacteristic
110C2×C3⋊D3—22no—
111C2×C3⋊D3—24no—
112C2×C3⋊D3—24no—
113C2×C3⋊D3C2×C4⋊C412yes—
114C2×C3⋊D3C23×C411yescharacteristic
115C2×C3⋊D3C22×Q811yescharacteristic
116C2×C3⋊D3C2×#4114yes—
117#157—24no—
118#157#11718yescomplemented
119C32×C4C2×C4⋊C412yes—
120C32×C4C2×C4⋊C412yes—
121C3⋊Dic3C2×C4⋊C412yes—
122C3⋊Dic3C2×C4⋊C412yes—
123C3×Dic3—48no—
124C23×C4—91no—
125C23×C4—92no—
126#117—62no—
127#117—182no—
128#117—182no—
129#117—182no—
130C2×C4⋊C4—94no—
131C2×C4⋊C4—98no—
132C2×C22⋊C4—94no—
133C2×C42—94no—
134C2×C42—98no—
135C2×C42—92no—
136C2×C42—91no—
137C2×C42—91no—
138#95—98no—
139C23×C3—22no—
140C22×D3—62no—
141C22×D3—64no—
142C22×D3—62no—
143C22×D3—64no—
144C22×D3—128no—
145C2×C3×C4—22no—
146C2×C3×C4—22no—
147C2×C3×C4—28no—
148C2×C3×C4—68no—
149C2×Dic3—28no—
150C2×Dic3—68no—
151C2×Dic3—62no—
152C2×Dic3—62no—
153C4×D3—68no—
154C4×D3—68no—
155C4×D3—64no—
156C4×D3—64no—
157C4×D3—64no—
158C4×D3—64no—
159C4×D3—1216no—
160C2×C32—22no—
161C2×C32C22×C4⋊C411yescharacteristic
162C2×C32#53212yes—
163C3⋊D3—22no—
164C3⋊D3C2×#11712yes—
165C3⋊D3#53312yes—
166C24—91no—
167C22×C4—98no—
168C22×C4—92no—
169C22×C4—91no—
170C22×C4—91no—
171C22×C4—91no—
172C22×C4—91no—
173C22×C4—91no—
174C22×C4—94no—
175C22×C4—94no—
176C22×C4—98no—
177C22×C4—92no—
178C22×C4—188no—
179C22×C4GO+(4,𝔽2)11yescharacteristic
180C4⋊C4—64no—
181C4⋊C4—184no—
182C4⋊C4—1816no—
183C22⋊C4—64no—
184C22⋊C4—184no—
185C42—64no—
186C42—94no—
187C42—98no—
188C42—94no—
189C42—184no—
190C22×C3—22no—
191C22×C3—24no—
192C22×C3—44no—
193C2×D3—62no—
194C2×D3—62no—
195C2×D3—68no—
196C2×D3—64no—
197C2×D3—128no—
198C2×D3—128no—
199C2×D3—124no—
200C3×C4—24no—
201C3×C4—24no—
202C3×C4—128no—
203Dic3—48no—
204Dic3—64no—
205Dic3—64no—
206C32#228511yescharacteristic, complemented, Sylow
207C23—91no—
208C23—91no—
209C23—92no—
210C23—92no—
211C23—184no—
212C23C2×GO+(4,𝔽2)11yescharacteristic
213C2×C4—68no—
214C2×C4—94no—
215C2×C4—98no—
216C2×C4—91no—
217C2×C4—91no—
218C2×C4—94no—
219C2×C4—92no—
220C2×C4—92no—
221C2×C4—92no—
222C2×C4—94no—
223C2×C4—92no—
224C2×C4—94no—
225C2×C4—94no—
226C2×C4—1816no—
227C2×C4—1816no—
228C2×C4—184no—
229C2×C4#377314yescomplemented
230C2×C4C2×GO+(4,𝔽2)11yescharacteristic
231C2×C4C2×GO+(4,𝔽2)11yescharacteristic
232C2×C3—24no—
233C2×C3—22no—
234C2×C3—44no—
235D3—64no—
236D3—64no—
237D3—124no—
238C22—22no—
239C22—94no—
240C22—91no—
241C22—91no—
242C22—92no—
243C22—184no—
244C22—184no—
245C22—182no—
246C22C2×#377312yes—
247C22C22×GO+(4,𝔽2)11yescharacteristic
248C4—98no—
249C4—92no—
250C4—92no—
251C4—128no—
252C4—184no—
253C4C2×#377312yes—
254C4C2×#377312yes—
255C3—22no—
256C2—22no—
257C2—92no—
258C2—92no—
259C2—182no—
260C2#1059651112yes—
261C2C22×#377311yescharacteristic
subgroupG/H
centerC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FrattiniC22C22×GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32C22×D4
prime radicalC23×C3⋊D3C23
cosocleC22×C3⋊D3C24
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#2285
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10593413C2semidirect
5. C4×#3773C2semidirect
6. #10593344C2semidirect
9. C2×C4×#157C4semidirect
68. C2×C32×C4C4⋊C4semidirect
71. C2×C3⋊Dic3C4⋊C4semidirect
74. C4×C3⋊D3C4⋊C4semidirect
75. C4×C3⋊D3C4⋊C4semidirect
118. #157#117semidirect
206. C32#2285semidirect
229. C2×C4#3773semidirect

Maximal subgroups

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

subgroupindex
C22×C4×#1572
#105949692
#105935162
#105934132
C4×#37732
#105933442
#22859