Finite Group Databasebeta

← #11803837

Subgroups — #11803837

Order 1152.

814 conjugacy classes of subgroups; only the 159 normal subgroups are shown.

normal subgroups only

This group has 814 conjugacy classes of subgroups — too many to draw. Only its 159 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×#64222C211yesmaximal, characteristic
2C4×#3797C212yesmaximal
3#10593733C211yesmaximal, characteristic
4#10593344C211yesmaximal, characteristic
5#10593342C212yesmaximal
6#10593338C218yesmaximal
7C2×#3797C2212yes—
8C2×C4×#157C2211yescharacteristic
9C2×C4×#157C2211yescharacteristic
10C2×#3773C2214yes—
11#64222C418yescomplemented
12C42×C3⋊D3C2211yescharacteristic
13C3×C4×Dic6—22no—
14C4×#627—22no—
15#63900C2212yes—
16#63883C2214yes—
17C4×#624C2214yes—
18#63843—22no—
19#63838—22no—
20#63781C2214yes—
21#63737C2218yes—
22#63737C2214yes—
23C4×D3×Q8—62no—
24C22×#157C2312yes—
25C22×#157C2312yes—
26C2×C4×C3⋊D3C2312yes—
27C2×C4×C3⋊D3C2311yescharacteristic
28C2×C3×Dic6—22no—
29C2×#627—22no—
30C2×#624C2314yes—
31C2×#624C2314yes—
32#3797—24no—
33#3797C2×C418yes—
34C4×#157—22no—
35C4×#157C2×C414yes—
36#3773C2×C4116yes—
37C32×C42D411yescharacteristic
38C4×C3⋊Dic3D412yes—
39C4×C3⋊Dic3D411yescharacteristic
40C3×C4⋊Dic3—22no—
41C3×Dic3⋊C4—24no—
42C3×C4×Dic3—24no—
43#3724—22no—
44Dic3⋊Dic3—24no—
45Dic32—24no—
46#2327—91nomaximal, Sylow
47C2×D3×Q8—62no—
48C3×C4×Q8—62no—
49Q8×Dic3—62no—
50D3×C4⋊C4—64no—
51D3×C4⋊C4—62no—
52#887—64no—
53#887—62no—
54C42×D3—64no—
55C42×D3—62no—
56C4×Dic6—22no—
57C4×Dic6—64no—
58C22×C3⋊D3C2411yescharacteristic
59C2×#157—24no—
60C2×#157—22no—
61C2×#157—24no—
62C2×#157C22×C414yes—
63C2×C32×C4C2×D412yes—
64C2×C32×C4C2×D411yescharacteristic
65C2×C3⋊Dic3C2×D412yes—
66C2×C3⋊Dic3C2×D411yescharacteristic
67C4×C3⋊D3—24no—
68C4×C3⋊D3C22×C412yes—
69C4×C3⋊D3#4112yes—
70C2×C3×Dic3—24no—
71C2×C3×Dic3—24no—
72C3×Dic6—28no—
73#627—28no—
74#624—24no—
75#624—28no—
76#624C22×C418yes—
77C2×C4⋊Q8—91no—
78C2×C4×Q8—92no—
79#391—92no—
80#387—98no—
81#382—91no—
82#376—91no—
83C2×C3×Q8—62no—
84D3×Q8—68no—
85D3×Q8—68no—
86C2×C4×D3—64no—
87C2×C4×D3—62no—
88C2×C4×D3—62no—
89C2×C4×D3—64no—
90C2×C4×D3—62no—
91C2×Dic6—22no—
92C2×Dic6—64no—
93C3×C4⋊C4—64no—
94C3×C4⋊C4—62no—
95C3×C42—22no—
96C3×C42—64no—
97C4⋊Dic3—22no—
98C4⋊Dic3—64no—
99Dic3⋊C4—24no—
100Dic3⋊C4—64no—
101Dic3⋊C4—64no—
102C4×Dic3—24no—
103C4×Dic3—62no—
104C4×Dic3—62no—
105C4×Dic3—62no—
106C4×Dic3—64no—
107C4×Dic3—64no—
108C22×C32C22×D411yescharacteristic
109C2×C3⋊D3C23×C411yescharacteristic
110C2×C3⋊D3C2×#4111yescharacteristic
111C2×C3⋊D32−1+414yes—
112#157—24no—
113#157—42no—
114C32×C4—22no—
115C32×C4C4×D412yes—
116C3⋊Dic3—22no—
117C3⋊Dic3C4×D412yes—
118C3×Dic3—28no—
119C3×Dic3—44no—
120C22×Q8—92no—
121C4⋊Q8—98no—
122C4×Q8—62no—
123C4×Q8—182no—
124C4×Q8—182no—
125C4×Q8—182no—
126C2×C4⋊C4—92no—
127C2×C4⋊C4—94no—
128C2×C4⋊C4—94no—
129C2×C42—94no—
130C2×C42—91no—
131C2×C42—91no—
132C2×C42—91no—
133#95—94no—
134#95—94no—
135#95—98no—
136C22×D3—62no—
137C3×Q8—68no—
138C2×C3×C4—22no—
139C2×C3×C4—22no—
140C2×C3×C4—22no—
141C2×C3×C4—64no—
142C2×C3×C4—64no—
143C2×Dic3—24no—
144C2×Dic3—24no—
145C2×Dic3—62no—
146C2×Dic3—62no—
147C2×Dic3—62no—
148C4×D3—68no—
149C4×D3—64no—
150C4×D3—64no—
151C4×D3—68no—
152C4×D3—68no—
153C4×D3—128no—
154C4×D3—124no—
155Dic6—28no—
156Dic6—616no—
157C2×C32C2×C4×D411yescharacteristic
158C2×C32#53612yes—
159C3⋊D3#51912yes—
160C3⋊D3#54112yes—
161C2×Q8—62no—
162C2×Q8—98no—
163C2×Q8—182no—
164C2×Q8—184no—
165C22×C4—94no—
166C22×C4—94no—
167C22×C4—91no—
168C22×C4—92no—
169C22×C4—92no—
170C22×C4—92no—
171C4⋊C4—64no—
172C4⋊C4—62no—
173C4⋊C4—916no—
174C4⋊C4—182no—
175C4⋊C4—184no—
176C42—64no—
177C42—94no—
178C42—92no—
179C42—91no—
180C42—184no—
181C42—182no—
182C42GO+(4,𝔽2)11yescharacteristic
183C22×C3—22no—
184C2×D3—62no—
185C2×D3—62no—
186C2×D3—64no—
187C2×D3—64no—
188C3×C4—24no—
189C3×C4—24no—
190C3×C4—42no—
191C3×C4—68no—
192C3×C4—124no—
193Dic3—28no—
194Dic3—44no—
195Dic3—64no—
196Dic3—64no—
197Dic3—122no—
198C32#232711yescharacteristic, complemented, Sylow
199C23—91no—
200Q8—68no—
201Q8—188no—
202C2×C4—64no—
203C2×C4—64no—
204C2×C4—98no—
205C2×C4—91no—
206C2×C4—92no—
207C2×C4—92no—
208C2×C4—94no—
209C2×C4—92no—
210C2×C4—184no—
211C2×C4—184no—
212C2×C4—188no—
213C2×C4—184no—
214C2×C4—182no—
215C2×C4—184no—
216C2×C4C2×GO+(4,𝔽2)12yes—
217C2×C4C2×GO+(4,𝔽2)11yescharacteristic
218C2×C3—22no—
219C2×C3—22no—
220C2×C3—22no—
221D3—64no—
222D3—64no—
223C22—94no—
224C22—91no—
225C22—91no—
226C22C22×GO+(4,𝔽2)11yescharacteristic
227C4—22no—
228C4—68no—
229C4—92no—
230C4—124no—
231C4—184no—
232C4—182no—
233C4—362no—
234C4C4×GO+(4,𝔽2)12yes—
235C3—22no—
236C2—92no—
237C2—92no—
238C2#1059649412yes—
239C2C2×C4×GO+(4,𝔽2)11yescharacteristic
subgroupG/H
center, FrattiniC22C22×GO+(4,𝔽2)
commutatorC2×C3⋊D3C23×C4
FittingC32×C42D4
socleC22×C32C22×D4
prime radical, cosocleC22×C3⋊D3C24
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2327
LCSG ▷ C2×C3⋊D3 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
11. #64222C4semidirect
198. C32#2327semidirect

Maximal subgroups

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

subgroupindex
C2×#642222
C4×#37972
#105937332
#105933442
#105933422
#105933382
#23279