Finite Group Databasebeta

← #11808992

Subgroups — #11808992

Order 1152.

4692 conjugacy classes of subgroups; only the 425 normal subgroups are shown.

normal subgroups only

This group has 4692 conjugacy classes of subgroups — too many to draw. Only its 425 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×#638C212yesmaximal, complemented
2C2×#64091C214yesmaximal, complemented
3C32×#379C211yesmaximal, characteristic, complemented
4#10592659C214yesmaximal, complemented
5#10592657C214yesmaximal, complemented
6#73852—34nomaximal
7C25×C32C2211yescharacteristic
8C24×C3⋊D3C2212yescomplemented
9C22×#638—216no—
10C22×#638—28no—
11C22×#638C2214yes—
12C22×#638C2214yescomplemented
13C23×C3⋊Dic3C2212yescomplemented
14C22×C4⋊(C3⋊D3)C2214yescomplemented
15C2×C32×C22⋊C4C2214yescomplemented
16C2×C32×C22⋊C4C2212yescomplemented
17C2×#3752C2218yescomplemented
18#64091—216no—
19#63658C2214yescomplemented
20C23×#67—38no—
21C2×#882—316no—
22C3×#379D314yescomplemented
23#4960—316no—
24#4958—316no—
25C24×C32—28no—
26C24×C32—42no—
27C24×C32D414yescomplemented
28C24×C32C2311yescharacteristic
29C24×C32C2312yes—
30C23×C3⋊D3—24no—
31C23×C3⋊D3—28no—
32C23×C3⋊D3—28no—
33C23×C3⋊D3—44no—
34C23×C3⋊D3C2314yes—
35C22×C32×C4C2314yes—
36C2×#638—264no—
37C2×#638—28no—
38C2×#638—28no—
39C2×#638—28no—
40C2×#638—28no—
41C2×#638—28no—
42C2×#638D4116yescomplemented
43C22×C3⋊Dic3—24no—
44C22×C3⋊Dic3—28no—
45C22×C3⋊Dic3C2314yes—
46C2×C4⋊(C3⋊D3)—216no—
47C2×C4⋊(C3⋊D3)—44no—
48C32×C22⋊C4—28no—
49C32×C22⋊C4—42no—
50#3752—216no—
51#2403—91noSylow
52C25×C3C2×D314yes—
53C24×D3—38no—
54C22×#67—316no—
55C22×#67—316no—
56C22×#67—664no—
57C22×#67—632no—
58C23×Dic3—38no—
59C22×D12—316no—
60C2×C3×C22⋊C4C2×D3116yescomplemented
61C2×C3×C22⋊C4C2×D318yescomplemented
62C2×(C2×D3)⋊C4—332no—
63#882—664no—
64C3⋊#95—316no—
65C23×C32—24no—
66C23×C32—24no—
67C23×C32—216no—
68C23×C32—24no—
69C23×C32—22no—
70C23×C32—44no—
71C23×C32—416no—
72C23×C32C2×D412yes—
73C23×C32C2×D414yes—
74C23×C32C2×D418yes—
75C23×C32C2411yescharacteristic
76C22×C3⋊D3—216no—
77C22×C3⋊D3—28no—
78C22×C3⋊D3—24no—
79C22×C3⋊D3—24no—
80C22×C3⋊D3—28no—
81C22×C3⋊D3—432no—
82C22×C3⋊D3—48no—
83C22×C3⋊D3—48no—
84C22×C3⋊D3C2×D418yescomplemented
85C2×C32×C4—28no—
86C2×C32×C4—24no—
87#638—232no—
88#638—232no—
89C2×C3⋊Dic3—216no—
90C2×C3⋊Dic3—24no—
91C2×C3⋊Dic3—24no—
92C2×C3⋊Dic3C2×D418yescomplemented
93C4⋊(C3⋊D3)—416no—
94C23×D4—92no—
95C2×#120—94no—
96#392—94no—
97#386—94no—
98#379C3⋊D311yescharacteristic, complemented
99C24×C3—232no—
100C24×C3—48no—
101C24×C3D12116yescomplemented
102C24×C3C22×D314yes—
103C24×C3C22×D318yes—
104C23×D3—316no—
105C23×D3—632no—
106C23×D3—616no—
107C23×D3—632no—
108C23×D3—1216no—
109C22×C3×C4C22×D3116yes—
110C2×#67—364no—
111C2×#67—632no—
112C2×#67—632no—
113C2×#67—6256no—
114C2×#67—632no—
115C2×#67—632no—
116C2×#67—632no—
117C22×Dic3—316no—
118C22×Dic3—632no—
119C22×Dic3—616no—
120C2×D12—664no—
121C2×D12—1216no—
122C3×C22⋊C4—232no—
123C3×C22⋊C4—48no—
124(C2×D3)⋊C4—664no—
125C22×C32—24no—
126C22×C32—24no—
127C22×C32—216no—
128C22×C32—24no—
129C22×C32—22no—
130C22×C32—416no—
131C22×C32—44no—
132C22×C32#12018yescomplemented
133C22×C32C22×D411yescharacteristic
134C22×C32C22×D414yes—
135C22×C32H(5,𝔽2)12yes—
136C2×C3⋊D3—28no—
137C2×C3⋊D3—216no—
138C2×C3⋊D3—432no—
139C2×C3⋊D3—44no—
140C2×C3⋊D3—44no—
141C2×C3⋊D3—48no—
142C32×C4—44no—
143C3⋊Dic3—28no—
144C25—92no—
145C25C2×C3⋊D311yescharacteristic
146C22×D4—94no—
147C22×D4—94no—
148C22×D4—94no—
149C22×D4—1816no—
150C22×D4—188no—
151C23×C4—92no—
152#120—1816no—
153C2×C22⋊C4—98no—
154C2×C22⋊C4C2×C3⋊D314yescomplemented
155C2×C22⋊C4C2×C3⋊D312yescomplemented
156#95—94no—
157C23×C3—216no—
158C23×C3—216no—
159C23×C3—264no—
160C23×C3—216no—
161C23×C3—28no—
162C23×C3—416no—
163C23×C3—464no—
164C23×C3C2×D1218yes—
165C23×C3C2×D12116yes—
166C23×C3D3×D4132yes—
167C23×C3C23×D314yes—
168C22×D3—332no—
169C22×D3—664no—
170C22×D3—616no—
171C22×D3—632no—
172C22×D3—616no—
173C22×D3—632no—
174C22×D3—12128no—
175C22×D3—1232no—
176C22×D3—1232no—
177C2×C3×C4—232no—
178C2×C3×C4—216no—
179#67—6128no—
180#67—6128no—
181C2×Dic3—332no—
182C2×Dic3—664no—
183C2×Dic3—616no—
184C2×Dic3—616no—
185D12—1264no—
186C2×C32—28no—
187C2×C32—42no—
188C2×C32C2×#12012yes—
189C2×C32#53411yescharacteristic
190C2×C32D4214yes—
191C3⋊D3—48no—
192C24—28no—
193C24—42no—
194C24—94no—
195C24—188no—
196C24—184no—
197C24—188no—
198C24—364no—
199C24C4⋊(C3⋊D3)14yescomplemented
200C24C22×C3⋊D311yescharacteristic
201C24C22×C3⋊D312yes—
202C2×D4—916no—
203C2×D4—1816no—
204C2×D4—188no—
205C2×D4—188no—
206C2×D4—1864no—
207C2×D4—188no—
208C2×D4—188no—
209C2×D4—188no—
210C2×D4—364no—
211C22×C4—94no—
212C22×C4—188no—
213C22×C4—184no—
214C22×C4C22×C3⋊D314yes—
215C22⋊C4—28no—
216C22⋊C4—42no—
217C22⋊C4—1816no—
218C22×C3—216no—
219C22×C3—216no—
220C22×C3—264no—
221C22×C3—216no—
222C22×C3—28no—
223C22×C3—464no—
224C22×C3—416no—
225C22×C3#882132yescomplemented
226C22×C3C22×D1214yes—
227C22×C3C2×D3×D4116yes—
228C22×C3#100418yes—
229C2×D3—632no—
230C2×D3—664no—
231C2×D3—12128no—
232C2×D3—1216no—
233C2×D3—1216no—
234C2×D3—1232no—
235C3×C4—416no—
236Dic3—632no—
237C32#240311yescharacteristic, complemented, Sylow
238C23—24no—
239C23—24no—
240C23—216no—
241C23—24no—
242C23—22no—
243C23—44no—
244C23—416no—
245C23—98no—
246C23—1816no—
247C23—184no—
248C23—188no—
249C23—184no—
250C23—188no—
251C23—3632no—
252C23—368no—
253C23—368no—
254C23C2×C4⋊(C3⋊D3)12yes—
255C23C2×C4⋊(C3⋊D3)14yes—
256C23D4×C3⋊D318yes—
257C23C23×C3⋊D311yescharacteristic
258D4—1832no—
259D4—1832no—
260D4—3616no—
261C2×C4—28no—
262C2×C4—24no—
263C2×C4—98no—
264C2×C4—1816no—
265C2×C4—184no—
266C2×C4—184no—
267C2×C3—232no—
268C2×C3—48no—
269C2×C3C2×#88218yes—
270C2×C3#549314yes—
271C2×C3#5590116yes—
272D3—1232no—
273C22—24no—
274C22—24no—
275C22—216no—
276C22—24no—
277C22—22no—
278C22—416no—
279C22—44no—
280C22—188no—
281C22—1816no—
282C22—3632no—
283C22—364no—
284C22—364no—
285C22—368no—
286C22#6409118yescomplemented
287C22C22×C4⋊(C3⋊D3)11yescharacteristic
288C22C2×D4×C3⋊D314yes—
289C22#6436112yes—
290C4—44no—
291C4—188no—
292C3#7385214yescomplemented
293C2—28no—
294C2—42no—
295C2—368no—
296C2C2×#6409112yes—
297C2#1059596411yescharacteristic
298C2#1059606114yes—
subgroupG/H
center, FrattiniC23C23×C3⋊D3
commutator, socle, cosocleC23×C32C24
FittingC32×#379C2
hypercenter#379C3⋊D3
hypocenterC32#2403
LCSG ▷ C23×C32 ▷ C32
UCSC1 ◁ C23 ◁ #379

Complements

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

NH ≅ G/Ntype
1. C23×#638C2semidirect
2. C2×#64091C2semidirect
3. C32×#379C2semidirect
4. #10592659C2semidirect
5. #10592657C2semidirect
8. C24×C3⋊D3C22semidirect
12. C22×#638C22semidirect
13. C23×C3⋊Dic3C22semidirect
14. C22×C4⋊(C3⋊D3)C22semidirect
15. C2×C32×C22⋊C4C22semidirect
16. C2×C32×C22⋊C4C22semidirect
17. C2×#3752C22semidirect
19. #63658C22semidirect
22. C3×#379D3semidirect
27. C24×C32D4semidirect
42. C2×#638D4semidirect
60. C2×C3×C22⋊C4C2×D3semidirect
61. C2×C3×C22⋊C4C2×D3semidirect
84. C22×C3⋊D3C2×D4semidirect
92. C2×C3⋊Dic3C2×D4semidirect
98. #379C3⋊D3semidirect
101. C24×C3D12semidirect
132. C22×C32#120semidirect
154. C2×C22⋊C4C2×C3⋊D3semidirect
155. C2×C22⋊C4C2×C3⋊D3semidirect
199. C24C4⋊(C3⋊D3)semidirect
225. C22×C3#882semidirect
237. C32#2403semidirect
286. C22#64091semidirect
292. C3#73852semidirect

Maximal subgroups

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

subgroupindex
C23×#6382
C2×#640912
C32×#3792
#105926592
#105926572
#738523