Finite Group Databasebeta

← #11803833

Subgroups — #11803833

Order 1152.

1121 conjugacy classes of subgroups; only the 276 normal subgroups are shown.

normal subgroups only

This group has 1121 conjugacy classes of subgroups — too many to draw. Only its 276 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×#63873C211yesmaximal, characteristic
2C2×#63843C212yesmaximal
3#10592631C211yesmaximal, characteristic
4C3×#4929C212yesmaximal
5#10591249C218yesmaximal
6#10591230C211yesmaximal, characteristic
7#76485—32nomaximal
8C22×C3×Dic6C2212yes—
9C2×C32×C42C2211yescharacteristic
10C2×C4×C3⋊Dic3C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C2×C3×C4⋊Dic3C2212yes—
13C2×#3724C2214yes—
14C2×Dic3⋊Dic3C2214yes—
15C2×Dic32C2214yes—
16#63873C418yescomplemented
17#63843—28no—
18#63658C2214yes—
19C3×C3⋊#95C2218yes—
20#63579C2214yes—
21C2×Q8×Dic3—32no—
22C2×#944—32no—
23C2×#887—32no—
24C3×#391—32no—
25#4977—32no—
26#4932—32no—
27#4932—61no—
28#4929D312yes—
29#4655—38no—
30#4652—38no—
31C22×C32×C4C2312yes—
32C22×C32×C4C2311yescharacteristic
33C22×C3⋊Dic3C2312yes—
34C22×C3⋊Dic3C2312yes—
35C22×C3×Dic3C2314yes—
36C22×C3×Dic3C2314yes—
37C2×C3×Dic6—24no—
38C2×C3×Dic6—24no—
39C2×C3×Dic6C2×C418yes—
40C32×C42—22no—
41C4×C3⋊Dic3C2×C414yes—
42C4×C3⋊Dic3D414yes—
43C3×C4⋊Dic3—24no—
44#3724C2×C4116yes—
45Dic3⋊Dic3—28no—
46Dic32—28no—
47#2327—91noSylow
48C22×C3×Q8—32no—
49C22×Dic6C2×D312yes—
50C2×C3×C4⋊C4—32no—
51C2×C3×C42—21no—
52C2×C3×C42C2×D312yes—
53Q8×Dic3—68no—
54#944—316no—
55C2×C4⋊Dic3—34no—
56C2×C4⋊Dic3C2×D312yes—
57C2×Dic3⋊C4—38no—
58C2×Dic3⋊C4—34no—
59C2×C4×Dic3—32no—
60C2×C4×Dic3—32no—
61C2×C4×Dic3—34no—
62C2×C4×Dic3—34no—
63C2×C4×Dic3—61no—
64C2×C4×Dic3—61no—
65#887—68no—
66C3×#95—38no—
67C3⋊#95—34no—
68C3⋊#95—34no—
69C3⋊#95—38no—
70C3⋊#95—64no—
71C3⋊#95C2×D318yes—
72C23×C32C2411yescharacteristic
73C2×C32×C4—22no—
74C2×C32×C4—24no—
75C2×C32×C4C22×C412yes—
76C2×C32×C4C2×D412yes—
77C2×C32×C4#4112yes—
78C2×C3⋊Dic3—24no—
79C2×C3⋊Dic3—24no—
80C2×C3⋊Dic3C22×C414yes—
81C2×C3⋊Dic3C2×D414yes—
82C2×C3×Dic3—24no—
83C2×C3×Dic3—24no—
84C2×C3×Dic3—24no—
85C2×C3×Dic3—28no—
86C2×C3×Dic3C22×C418yes—
87C3×Dic6—216no—
88C2×C4⋊Q8—91no—
89C2×C4×Q8—92no—
90#391—32no—
91#387—98no—
92#382—91no—
93#376—91no—
94C2×C3×Q8—38no—
95C2×C3×Q8—64no—
96C2×C3×Q8—64no—
97C22×C3×C4—21no—
98C22×C3×C4—22no—
99C22×C3×C4—34no—
100C22×C3×C4—34no—
101C22×C3×C4C22×D314yes—
102C22×C3×C4C22×D312yes—
103C22×Dic3—34no—
104C22×Dic3—32no—
105C22×Dic3—32no—
106C22×Dic3—62no—
107C22×Dic3—62no—
108C22×Dic3C22×D314yes—
109C22×Dic3C22×D314yes—
110C2×Dic6—24no—
111C2×Dic6—24no—
112C2×Dic6C4×D318yes—
113C3×C4⋊C4—64no—
114C3×C42—24no—
115C3×C42—24no—
116C4⋊Dic3—24no—
117C4⋊Dic3—68no—
118Dic3⋊C4—332no—
119Dic3⋊C4—68no—
120C4×Dic3—38no—
121C4×Dic3—38no—
122C4×Dic3—64no—
123C4×Dic3—64no—
124C4×Dic3—68no—
125C4×Dic3—68no—
126C22×C32C23×C411yescharacteristic
127C22×C32C22×D411yescharacteristic
128C22×C32C2×#4111yescharacteristic
129C22×C322−1+414yes—
130C32×C4—42no—
131C32×C4C4×D414yes—
132C3⋊Dic3—24no—
133C3⋊Dic3—24no—
134C3×Dic3—28no—
135C3×Dic3—44no—
136C22×Q8—32no—
137C4⋊Q8—98no—
138C4×Q8—188no—
139C2×C4⋊C4—32no—
140C2×C4⋊C4—94no—
141C2×C4⋊C4—94no—
142C2×C42—91no—
143C2×C42—91no—
144C2×C42—94no—
145C2×C42D3211yescharacteristic
146#95—38no—
147#95—94no—
148#95—94no—
149C23×C3—21no—
150C23×C3C23×D312yes—
151C3×Q8—616no—
152C2×C3×C4—24no—
153C2×C3×C4—24no—
154C2×C3×C4—24no—
155C2×C3×C4—24no—
156C2×C3×C4—22no—
157C2×C3×C4—22no—
158C2×C3×C4—22no—
159C2×C3×C4—38no—
160C2×C3×C4—44no—
161C2×C3×C4—64no—
162C2×C3×C4—64no—
163C2×C3×C4—64no—
164C2×C3×C4—68no—
165C2×C3×C4C2×C4×D314yes—
166C2×C3×C4D3×D414yes—
167C2×C3×C4#23714yes—
168C2×Dic3—24no—
169C2×Dic3—24no—
170C2×Dic3—24no—
171C2×Dic3—28no—
172C2×Dic3—38no—
173C2×Dic3—34no—
174C2×Dic3—34no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—64no—
180C2×Dic3—64no—
181C2×Dic3—124no—
182C2×Dic3—124no—
183C2×Dic3C2×C4×D318yes—
184Dic6—216no—
185C2×C32C2×C4×D411yescharacteristic
186C2×C32#51912yes—
187C2×C32#53612yes—
188C2×C32#54112yes—
189C2×Q8—38no—
190C2×Q8—64no—
191C2×Q8—64no—
192C22×C4—34no—
193C22×C4—34no—
194C22×C4—92no—
195C22×C4—92no—
196C22×C4C2×D3212yes—
197C22×C4C2×D3211yescharacteristic
198C4⋊C4—64no—
199C4⋊C4—916no—
200C4⋊C4—188no—
201C42—22no—
202C42—94no—
203C42—94no—
204C42—188no—
205C22×C3—24no—
206C22×C3—21no—
207C22×C3—21no—
208C22×C3—21no—
209C22×C3C22×C4×D312yes—
210C22×C3C2×D3×D412yes—
211C22×C3C2×#23712yes—
212C22×C3#100714yes—
213C22×C3#101014yes—
214C3×C4—24no—
215C3×C4—44no—
216C3×C4—44no—
217C3×C4—68no—
218C3×C4—124no—
219C3×C4#67⋊C418yes—
220Dic3—28no—
221Dic3—44no—
222Dic3—64no—
223Dic3—64no—
224Dic3—68no—
225Dic3—124no—
226Dic3—124no—
227C32#232711yescharacteristic, complemented, Sylow
228C23C22×D3211yescharacteristic
229Q8—616no—
230C2×C4—24no—
231C2×C4—22no—
232C2×C4—38no—
233C2×C4—64no—
234C2×C4—64no—
235C2×C4—68no—
236C2×C4—64no—
237C2×C4—94no—
238C2×C4—94no—
239C2×C4—184no—
240C2×C4—184no—
241C2×C4C4×D3212yes—
242C2×C4#380212yes—
243C2×C4#380512yes—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—21no—
248C2×C3C2×#67⋊C412yes—
249C2×C3#557214yes—
250C2×C3#562514yes—
251C2×C3#567512yes—
252C2×C3#572412yes—
253C22#6429714yes—
254C22C2×C4×D3211yescharacteristic
255C22C2×#380211yescharacteristic
256C22C2×#380511yescharacteristic
257C4—42no—
258C4—68no—
259C4—124no—
260C4—184no—
261C4—184no—
262C4#6390214yes—
263C3—21no—
264C3#7648512yescomplemented
265C2#1059384812yes—
266C2#1059390812yes—
267C2#1059482612yes—
268C2C2×#6390211yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, prime radical, cosocleC23×C32C24
hypercenterC2×C42D32
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
16. #63873C4semidirect
227. C32#2327semidirect
264. C3#76485semidirect

Maximal subgroups

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

subgroupindex
C2×#638732
C2×#638432
#105926312
C3×#49292
#105912492
#105912302
#764853