Finite Group Databasebeta

← #11861364

Subgroups — #11861364

Order 1152.

809 conjugacy classes of subgroups; only the 248 normal subgroups are shown.

normal subgroups only

This group has 809 conjugacy classes of subgroups — too many to draw. Only its 248 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#10595050C211yesmaximal, characteristic
2C2×C8×C3⋊Dic3C211yesmaximal, characteristic
3C3×#5102C212yesmaximal
4#10591120C211yesmaximal, characteristic
5#10591057C212yesmaximal
6#10590788C214yesmaximal, complemented
7#10590645C214yesmaximal, complemented
8#79076—32nomaximal
9C22×C32×C8C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C22×C3⋊(C3⋊C8)C2211yescharacteristic
12C3×#926C2212yes—
13C2×C3×#208C2212yes—
14#63982C414yes—
15#63919C412yes—
16C4×#627C2214yes—
17#63872C412yes—
18C8×C3⋊Dic3C2212yes—
19C8×C3⋊Dic3C2212yes—
20C3×Dic3⋊C8C2218yes—
21#63572C2214yes—
22#63554C2214yes—
23Dic3×C3⋊C8C2214yes—
24#5517—32no—
25C3×#424—32no—
26#5122—32no—
27#5118—32no—
28#5102D312yes—
29C2×C8×Dic3—32no—
30C2×C8×Dic3—61no—
31#4997—32no—
32#4830—38no—
33#4828—38no—
34C22×C32×C4C2311yescharacteristic
35C22×C3⋊Dic3C2×C412yes—
36C2×#627C2×C414yes—
37C2×C32×C8—22no—
38C2×C32×C8C2312yes—
39C4×C3⋊Dic3C2×C411yescharacteristic
40C4×C3⋊Dic3C2×C411yescharacteristic
41C4×C3⋊Dic3C2312yes—
42C2×C3⋊(C3⋊C8)Q814yescomplemented
43C2×C3⋊(C3⋊C8)C2311yescharacteristic
44C2×C3⋊(C3⋊C8)C2311yescharacteristic
45C3×#217C2×C414yes—
46C3×C4⋊Dic3C2×C414yes—
47C3×C4×Dic3C2314yes—
48C3×#208—24no—
49C2×C3×C3⋊C8C2314yes—
50#3724C2×C414yes—
51Dic3⋊Dic3C2×C418yes—
52#2960—91noSylow
53C2×C3×M16—32no—
54C22×C3×C8—21no—
55C22×C3×C8C2×D312yes—
56C3×#117—32no—
57#926C2×D312yes—
58C2×C4×Dic3—32no—
59C2×C4×Dic3—61no—
60C2×#208C2×D312yes—
61C22×C3⋊C8—32no—
62C22×C3⋊C8—61no—
63#890—34no—
64#888—34no—
65#878—38no—
66C4×Dic6—38no—
67C3×C4⋊C8—38no—
68#815—34no—
69Dic3⋊C8—38no—
70Dic3⋊C8C2×D318yes—
71C8×Dic3—34no—
72C8×Dic3—34no—
73C8×Dic3—34no—
74C8×Dic3—62no—
75C8×Dic3—62no—
76#803—34no—
77C4×C3⋊C8—34no—
78C23×C32C22×C411yescharacteristic
79C2×C32×C4C22×C411yescharacteristic
80C2×C32×C4C2×Q812yes—
81C2×C32×C4#4112yes—
82C2×C32×C4C2411yescharacteristic
83C2×C3⋊Dic3—24no—
84C2×C3⋊Dic3C22×C412yes—
85C2×C3⋊Dic3C22×C412yes—
86C2×C3×Dic3C22×C418yes—
87#627—28no—
88C32×C8—22no—
89C3⋊(C3⋊C8)C2×Q812yes—
90C3⋊(C3⋊C8)C2×Q812yes—
91C3×C3⋊C8—24no—
92#533—91no—
93#446—94no—
94C8×Q8—94no—
95#424—32no—
96#423—91no—
97#405—92no—
98C2×C4×C8—91no—
99C22×C3×C4—21no—
100C22×C3×C4C22×D312yes—
101C22×Dic3—34no—
102C22×Dic3—62no—
103C2×Dic6—38no—
104C3×M16—64no—
105C2×C3×C8—24no—
106C2×C3×C8—24no—
107C2×C3×C8—22no—
108C2×C3×C8—34no—
109C2×C3×C8C22×D314yes—
110C3×C4⋊C4—34no—
111C3×C22⋊C4—34no—
112C3×C42—34no—
113#217C4×D314yes—
114C4⋊Dic3—38no—
115C4⋊Dic3C4×D314yes—
116Dic3⋊C4—38no—
117Dic3⋊C4—38no—
118C4×Dic3—32no—
119C4×Dic3—32no—
120C4×Dic3—34no—
121C4×Dic3—62no—
122C4×Dic3—61no—
123C4×Dic3—61no—
124C4×Dic3C22×D314yes—
125#208—24no—
126C2×C3⋊C8—38no—
127C2×C3⋊C8—32no—
128C2×C3⋊C8—32no—
129C2×C3⋊C8—61no—
130C2×C3⋊C8—61no—
131C2×C3⋊C8—64no—
132C2×C3⋊C8C22×D314yes—
133C22×C32—22no—
134C22×C32C4×Q812yes—
135C22×C32C23×C411yescharacteristic
136C32×C4C4×Q812yes—
137C32×C4C22×Q811yescharacteristic
138C32×C4C2×#4111yescharacteristic
139C3⋊Dic3—22no—
140C3⋊Dic3#13114yes—
141C3×Dic3—28no—
142C2×M16—32no—
143C22×C8—91no—
144C22×C8D3211yescharacteristic
145C4⋊Q8—92no—
146#125—92no—
147C22⋊Q8—94no—
148C4×Q8—94no—
149#117—32no—
150C2×C42—91no—
151C4⋊C8—38no—
152C4⋊C8—94no—
153#97—94no—
154C4×C8—94no—
155C4×C8—92no—
156C4×C8—92no—
157C23×C3—21no—
158C23×C3C2×C4×D312yes—
159C2×C3×C4—21no—
160C2×C3×C4—22no—
161C2×C3×C4—21no—
162C2×C3×C4—22no—
163C2×C3×C4—38no—
164C2×C3×C4C2×C4×D312yes—
165C2×C3×C4#23714yes—
166C2×C3×C4D3×Q814yes—
167C2×C3×C4C23×D312yes—
168C2×Dic3—34no—
169C2×Dic3—34no—
170C2×Dic3—62no—
171C2×Dic3—62no—
172C2×Dic3—68no—
173C2×Dic3—68no—
174C2×Dic3C2×C4×D318yes—
175Dic6—616no—
176C3×C8—24no—
177C3×C8—24no—
178C3×C8—64no—
179C3⋊C8—24no—
180C3⋊C8—34no—
181C3⋊C8—34no—
182C3⋊C8—62no—
183C3⋊C8—62no—
184C2×C32—22no—
185C2×C32C2×C4×Q811yescharacteristic
186C2×C32C2×#13112yes—
187C2×Q8—94no—
188C22×C4—92no—
189C22×C4C2×D3211yescharacteristic
190M16—64no—
191C2×C8—22no—
192C2×C8—34no—
193C2×C8—91no—
194C2×C8—91no—
195C2×C8—94no—
196C2×C8C2×D3212yes—
197C4⋊C4—34no—
198C4⋊C4—98no—
199C4⋊C4—94no—
200C22⋊C4—34no—
201C42—34no—
202C42—92no—
203C42—91no—
204C42—91no—
205C22×C3—24no—
206C22×C3—24no—
207C22×C3—21no—
208C22×C3—22no—
209C22×C3#88714yes—
210C22×C3C22×C4×D312yes—
211C3×C4—21no—
212C3×C4—21no—
213C3×C4—22no—
214C3×C4—68no—
215C3×C4#88714yes—
216C3×C4C2×#23712yes—
217C3×C4C2×D3×Q812yes—
218Dic3—28no—
219Dic3—38no—
220Dic3—64no—
221Dic3—64no—
222Dic3—64no—
223C32#296011yescharacteristic, complemented, Sylow
224C23C4×D3211yescharacteristic
225Q8—188no—
226C2×C4—38no—
227C2×C4—92no—
228C2×C4—92no—
229C2×C4—184no—
230C2×C4#379712yes—
231C2×C4C4×D3211yescharacteristic
232C2×C4#380512yes—
233C2×C4C22×D3211yescharacteristic
234C8—22no—
235C8—64no—
236C8—92no—
237C8—92no—
238C2×C3—24no—
239C2×C3—24no—
240C2×C3—22no—
241C2×C3—21no—
242C2×C3C2×#88712yes—
243C2×C3D3×#13114yes—
244C22—22no—
245C22#6383812yes—
246C22C2×C4×D3211yescharacteristic
247C4—68no—
248C4—94no—
249C4—182no—
250C4#6383812yes—
251C4C2×#379711yescharacteristic
252C4C2×#380511yescharacteristic
253C3—21no—
254C3#7907612yescomplemented
255C2—22no—
256C2#1059466912yes—
257C2C2×#6383811yescharacteristic
subgroupG/H
center, FrattiniC2×C4C22×D32
commutator, socleC22×C32C23×C4
FittingC22×C32×C8C22
prime radicalC23×C32C22×C4
cosocleC2×C32×C4C24
hypercenterC22×C8D32
hypocenterC32#2960
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
6. #10590788C2semidirect
7. #10590645C2semidirect
42. C2×C3⋊(C3⋊C8)Q8semidirect
223. C32#2960semidirect
254. C3#79076semidirect

Maximal subgroups

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

subgroupindex
#105950502
C2×C8×C3⋊Dic32
C3×#51022
#105911202
#105910572
#105907882
#105906452
#790763