Finite Group Databasebeta

← #11801039

Subgroups — #11801039

Order 1152.

3264 conjugacy classes of subgroups; only the 441 normal subgroups are shown.

normal subgroups only

This group has 3264 conjugacy classes of subgroups — too many to draw. Only its 441 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
1C23×C4×C3⋊D3C211yesmaximal, characteristic
2C2×#64086C212yesmaximal, complemented
3C32×#381C211yesmaximal, characteristic, complemented
4#10592910C211yesmaximal, characteristic, complemented
5#10592654C212yesmaximal
6#10592366C214yesmaximal, complemented
7#10592365C214yesmaximal, complemented
8#74050—34nomaximal
9C24×C3⋊D3C2211yescharacteristic
10C23×C32×C4C2211yescharacteristic
11C23×C3⋊Dic3C2211yescharacteristic
12C22×C4×C3⋊D3—28no—
13C22×C4×C3⋊D3C418yescomplemented
14C22×C4×C3⋊D3C2212yes—
15C22×C4×C3⋊D3C2212yes—
16C2×C32×C22⋊C4C2212yes—
17C2×#3757C2212yes—
18C2×#3752C2218yes—
19C2×#3750C2214yescomplemented
20C2×C4×C3⋊Dic3C2214yescomplemented
21#64086—28no—
22C32×#95C2214yescomplemented
23#63658C2214yescomplemented
24C23×C4×D3—34no—
25C2×#877—38no—
26C3×#381D314yescomplemented
27#5211—34no—
28#4955—38no—
29#4667—316no—
30#4666—316no—
31C24×C32C2311yescharacteristic
32C23×C3⋊D3—24no—
33C23×C3⋊D3—28no—
34C23×C3⋊D3C2×C414yes—
35C23×C3⋊D3C2312yes—
36C22×C32×C4—24no—
37C22×C32×C4C2×C414yes—
38C22×C32×C4C2314yes—
39C22×C32×C4C2312yes—
40C22×C3⋊Dic3C2×C414yes—
41C22×C3⋊Dic3D418yes—
42C22×C3⋊Dic3C2314yes—
43C22×C3⋊Dic3C2311yescharacteristic
44C22×C3⋊Dic3C2311yescharacteristic
45C2×C4×C3⋊D3—232no—
46C2×C4×C3⋊D3—28no—
47C2×C4×C3⋊D3—28no—
48C2×C4×C3⋊D3C2×C418yes—
49C2×C4×C3⋊D3C2×C418yes—
50C32×C22⋊C4—24no—
51#3757—24no—
52#3752—216no—
53#3750—28no—
54C4×C3⋊Dic3—28no—
55#2280—91noSylow
56C24×D3—34no—
57C23×C3×C4C2×D314yes—
58C23×Dic3—34no—
59C22×C4×D3—332no—
60C22×C4×D3—38no—
61C22×C4×D3—38no—
62C22×C4×D3—632no—
63C2×C3×C22⋊C4C2×D318yes—
64C2×#217—38no—
65C2×(C2×D3)⋊C4—332no—
66C2×Dic3⋊C4—316no—
67C2×C4×Dic3—316no—
68#877—632no—
69C3×#95C2×D3116yescomplemented
70C3⋊#95—316no—
71C23×C32—24no—
72C23×C32C22×C412yes—
73C23×C32C2×D414yes—
74C23×C32C2411yescharacteristic
75C22×C3⋊D3—232no—
76C22×C3⋊D3—28no—
77C22×C3⋊D3—24no—
78C22×C3⋊D3—24no—
79C22×C3⋊D3—216no—
80C22×C3⋊D3C22×C414yes—
81C22×C3⋊D3#4118yes—
82C2×C32×C4—28no—
83C2×C32×C4—24no—
84C2×C32×C4—24no—
85C2×C32×C4—28no—
86C2×C32×C4C22×C414yes—
87C2×C3⋊Dic3—24no—
88C2×C3⋊Dic3—28no—
89C2×C3⋊Dic3C22⋊C4116yescomplemented
90C2×C3⋊Dic3C22×C412yes—
91C2×C3⋊Dic3C22×C412yes—
92C2×C3⋊Dic3C2×D414yes—
93C2×C3⋊Dic3C2×D414yes—
94C4×C3⋊D3—216no—
95C4×C3⋊D3—216no—
96C24×C4—91no—
97C2×#117—92no—
98#381—91no—
99#381C3⋊D311yescharacteristic, complemented
100#380—94no—
101#379—92no—
102C4×C22⋊C4—94no—
103C24×C3C22×D314yes—
104C23×D3—38no—
105C23×D3—316no—
106C23×D3—632no—
107C23×D3—616no—
108C22×C3×C4—216no—
109C22×C3×C4C4×D3116yes—
110C22×C3×C4C22×D3116yes—
111C22×C3×C4C22×D318yes—
112C22×Dic3—316no—
113C22×Dic3—332no—
114C22×Dic3—34no—
115C22×Dic3—34no—
116C22×Dic3—316no—
117C2×C4×D3—332no—
118C2×C4×D3—332no—
119C2×C4×D3—6128no—
120C2×C4×D3—632no—
121C2×C4×D3—632no—
122C3×C22⋊C4—216no—
123#217—616no—
124(C2×D3)⋊C4—664no—
125Dic3⋊C4—632no—
126C4×Dic3—632no—
127C22×C32—24no—
128C22×C32—28no—
129C22×C32C2×C22⋊C414yes—
130C22×C32C23×C411yescharacteristic
131C22×C32C22×D412yes—
132C22×C32C2×#4114yes—
133C2×C3⋊D3—232no—
134C2×C3⋊D3—24no—
135C2×C3⋊D3—24no—
136C2×C3⋊D3—216no—
137C2×C3⋊D3#11718yescomplemented
138C32×C4—24no—
139C32×C4—44no—
140C3⋊Dic3—44no—
141C3⋊Dic3C2×C22⋊C414yes—
142C3⋊Dic3C2×C22⋊C414yes—
143C25—91no—
144C23×C4—91no—
145C23×C4—98no—
146C23×C4—92no—
147C23×C4—92no—
148C23×C4—188no—
149C23×C4C2×C3⋊D311yescharacteristic
150#117—188no—
151C2×C4⋊C4—94no—
152C2×C22⋊C4—92no—
153C2×C22⋊C4—98no—
154C2×C22⋊C4C2×C3⋊D312yes—
155C2×C42—94no—
156#95—94no—
157#95C2×C3⋊D314yescomplemented
158C23×C3—216no—
159C23×C3C2×C4×D318yes—
160C23×C3D3×D4116yes—
161C23×C3C23×D314yes—
162C22×D3—316no—
163C22×D3—332no—
164C22×D3—664no—
165C22×D3—6128no—
166C22×D3—632no—
167C22×D3—616no—
168C22×D3—616no—
169C2×C3×C4—232no—
170C2×C3×C4—216no—
171C2×C3×C4—216no—
172C2×C3×C4—232no—
173C2×C3×C4C2×C4×D3116yes—
174C2×Dic3—364no—
175C2×Dic3—38no—
176C2×Dic3—38no—
177C2×Dic3—316no—
178C2×Dic3—316no—
179C2×Dic3—616no—
180C2×Dic3—632no—
181C4×D3—664no—
182C4×D3—664no—
183C2×C32—24no—
184C2×C32C22×C22⋊C411yescharacteristic
185C2×C32C2×#11712yes—
186C2×C32#52514yes—
187C3⋊D3—28no—
188C24—92no—
189C24—94no—
190C24—188no—
191C24—184no—
192C24C22×C3⋊D311yescharacteristic
193C22×C4—24no—
194C22×C4—91no—
195C22×C4—91no—
196C22×C4—94no—
197C22×C4—98no—
198C22×C4—98no—
199C22×C4—98no—
200C22×C4—94no—
201C22×C4—1832no—
202C22×C4—188no—
203C22×C4—188no—
204C22×C4C4×C3⋊D314yes—
205C22×C4C22×C3⋊D314yes—
206C22×C4C22×C3⋊D312yes—
207C4⋊C4—188no—
208C22⋊C4—24no—
209C22⋊C4—1816no—
210C22⋊C4—184no—
211C42—188no—
212C22×C3—232no—
213C22×C3—216no—
214C22×C3D3×C22⋊C4116yes—
215C22×C3C22×C4×D314yes—
216C22×C3C2×D3×D418yes—
217C22×C3D3×#41116yes—
218C2×D3—332no—
219C2×D3—6128no—
220C2×D3—664no—
221C2×D3—616no—
222C2×D3—616no—
223C3×C4—216no—
224C3×C4—416no—
225Dic3—316no—
226Dic3—316no—
227Dic3—1216no—
228C32#228011yescharacteristic, complemented, Sylow
229C23—24no—
230C23—94no—
231C23—98no—
232C23—1816no—
233C23—1832no—
234C23—188no—
235C23—184no—
236C23—184no—
237C23C2×C4×C3⋊D312yes—
238C23D4×C3⋊D314yes—
239C23C23×C3⋊D311yescharacteristic
240C2×C4—28no—
241C2×C4—24no—
242C2×C4—24no—
243C2×C4—28no—
244C2×C4—916no—
245C2×C4—92no—
246C2×C4—92no—
247C2×C4—94no—
248C2×C4—94no—
249C2×C4—1816no—
250C2×C4—1816no—
251C2×C4—184no—
252C2×C4—188no—
253C2×C4C2×C4×C3⋊D314yes—
254C2×C3—216no—
255C2×C3C2×D3×C22⋊C414yes—
256C2×C3D3×#11718yes—
257C2×C3#5656116yes—
258D3—632no—
259C22—28no—
260C22—24no—
261C22—98no—
262C22—1832no—
263C22—1816no—
264C22—184no—
265C22—184no—
266C22C22⋊C4×C3⋊D314yes—
267C22C22×C4×C3⋊D311yescharacteristic
268C22C2×D4×C3⋊D312yes—
269C22#41×C3⋊D314yes—
270C4—24no—
271C4—44no—
272C4—94no—
273C4—94no—
274C4—364no—
275C3#7405014yescomplemented
276C2—24no—
277C2—188no—
278C2C2×C22⋊C4×C3⋊D311yescharacteristic
279C2C3⋊D3×#11712yes—
280C2#1059612714yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutatorC22×C32C23×C4
FittingC32×#381C2
socle, cosocleC23×C32C24
prime radicalC24×C3⋊D3C22
hypercenter#381C3⋊D3
hypocenterC32#2280
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ #381

Complements

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

NH ≅ G/Ntype
2. C2×#64086C2semidirect
3. C32×#381C2semidirect
4. #10592910C2semidirect
6. #10592366C2semidirect
7. #10592365C2semidirect
13. C22×C4×C3⋊D3C4semidirect
19. C2×#3750C22semidirect
20. C2×C4×C3⋊Dic3C22semidirect
22. C32×#95C22semidirect
23. #63658C22semidirect
26. C3×#381D3semidirect
69. C3×#95C2×D3semidirect
89. C2×C3⋊Dic3C22⋊C4semidirect
99. #381C3⋊D3semidirect
137. C2×C3⋊D3#117semidirect
157. #95C2×C3⋊D3semidirect
228. C32#2280semidirect
275. C3#74050semidirect

Maximal subgroups

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

subgroupindex
C23×C4×C3⋊D32
C2×#640862
C32×#3812
#105929102
#105926542
#105923662
#105923652
#740503