Finite Group Databasebeta

← #11806910

Subgroups — #11806910

Order 1152.

1913 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64083C211yesmaximal, characteristic
2C2×#63894C214yesmaximal, complemented
3C3×C4×C4⋊Dic3C212yesmaximal, complemented
4#10591380C214yesmaximal, complemented
5#10591320C214yesmaximal, complemented
6#73653—32nomaximal
7C22×C4⋊(C3⋊D3)C2214yes—
8C22×C4⋊(C3⋊D3)C2212yes—
9C22×#624C2214yes—
10C2×C32×C42C2211yescharacteristic
11#64083C418yescomplemented
12C2×C3×C4⋊Dic3C2212yes—
13C2×C3×C4⋊Dic3C2212yes—
14C2×C3×C4×Dic3C2214yes—
15C2×#3722C2218yes—
16C2×#3722C2214yes—
17#63894—216no—
18C3×C3⋊#95C2214yes—
19C2×#893—34no—
20C2×#874—32no—
21C2×#874—61no—
22C2×C4×D12—34no—
23C3×C4×C4⋊C4—32no—
24#4988—34no—
25#4939—34no—
26C4×C4⋊Dic3D312yescomplemented
27#4665—38no—
28C23×C3⋊D3C2314yes—
29C22×C32×C4C2311yescharacteristic
30C22×C32×C4C2312yes—
31C2×C4⋊(C3⋊D3)—28no—
32C2×C4⋊(C3⋊D3)—28no—
33C2×C4⋊(C3⋊D3)—42no—
34C2×C4⋊(C3⋊D3)—42no—
35C2×C4⋊(C3⋊D3)C2×C4116yescomplemented
36C2×C4⋊(C3⋊D3)C2×C418yescomplemented
37C22×C3×Dic3C2314yes—
38C22×C3×Dic3C2314yes—
39C2×#624—216no—
40C2×#624—44no—
41C32×C42C2×C414yescomplemented
42C3×C4⋊Dic3—24no—
43C3×C4⋊Dic3D418yescomplemented
44C3×C4×Dic3—28no—
45#3722—216no—
46#3722—44no—
47#2366—91noSylow
48C22×D12—34no—
49C22×D12—34no—
50C22×D12—34no—
51C22×D12—64no—
52C22×D12—62no—
53C22×C4×D3—38no—
54C2×C3×C4⋊C4—32no—
55C2×C3×C4⋊C4—32no—
56C2×C3×C42—21no—
57C2×C3×C42—34no—
58C2×C3×C42C2×D312yes—
59C2×(C2×D3)⋊C4—38no—
60C2×(C2×D3)⋊C4—38no—
61C2×(C2×D3)⋊C4—38no—
62C2×C4⋊Dic3C2×D312yes—
63C2×C4⋊Dic3C2×D312yes—
64C2×C4×Dic3C2×D314yes—
65#893—616no—
66#874—316no—
67#874—68no—
68C4×D12—616no—
69C3×#95—34no—
70C3⋊#95C2×D314yes—
71C23×C32C2411yescharacteristic
72C22×C3⋊D3—28no—
73C22×C3⋊D3—28no—
74C22×C3⋊D3—24no—
75C22×C3⋊D3—24no—
76C22×C3⋊D3C22×C418yes—
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4C22×C412yes—
80C2×C32×C4C22×C414yes—
81C2×C32×C4C2×D414yes—
82C2×C32×C4#4114yes—
83C4⋊(C3⋊D3)—232no—
84C4⋊(C3⋊D3)—48no—
85C2×C3×Dic3—24no—
86C2×C3×Dic3—24no—
87C2×C3×Dic3—24no—
88C2×C3×Dic3—24no—
89C2×C3×Dic3—24no—
90C2×C3×Dic3C2×D418yes—
91#624—416no—
92C2×#127—91no—
93C2×C4×D4—94no—
94#390—94no—
95#386—94no—
96C4×C4⋊C4—32no—
97C23×D3—38no—
98C23×D3—64no—
99C22×C3×C4—21no—
100C22×C3×C4—22no—
101C22×C3×C4—34no—
102C22×C3×C4—34no—
103C22×C3×C4C22×D312yes—
104C22×C3×C4C22×D312yes—
105C22×C3×C4C22×D312yes—
106C22×Dic3C22×D314yes—
107C22×Dic3C22×D314yes—
108C2×D12—316no—
109C2×D12—316no—
110C2×D12—316no—
111C2×D12—616no—
112C2×D12—68no—
113C2×D12—68no—
114C2×D12—68no—
115C2×D12—68no—
116C2×D12—68no—
117C2×D12—128no—
118C2×D12—128no—
119C2×D12—124no—
120C2×D12—124no—
121C2×D12—124no—
122C2×D12—124no—
123C2×C4×D3—616no—
124C2×C4×D3—616no—
125C2×C4×D3—128no—
126C3×C4⋊C4—38no—
127C3×C4⋊C4—64no—
128C3×C42—24no—
129C3×C42—68no—
130C3×C42C4×D318yescomplemented
131(C2×D3)⋊C4—616no—
132(C2×D3)⋊C4—616no—
133(C2×D3)⋊C4—128no—
134C4⋊Dic3—24no—
135C4⋊Dic3D1218yescomplemented
136C4×Dic3—28no—
137C22×C32C23×C411yescharacteristic
138C22×C32C22×D412yes—
139C22×C32C2×#4112yes—
140C22×C32H(5,𝔽2)11yescharacteristic
141C22×C32H(5,𝔽2)11yescharacteristic
142C2×C3⋊D3—216no—
143C2×C3⋊D3—28no—
144C2×C3⋊D3—44no—
145C2×C3⋊D3—48no—
146C2×C3⋊D3—44no—
147C32×C4—22no—
148C32×C4C4×D418yescomplemented
149C3×Dic3—28no—
150C3×Dic3—44no—
151C22×D4—94no—
152C22×D4—92no—
153C23×C4—94no—
154#127—98no—
155C4×D4—1816no—
156C2×C4⋊C4—32no—
157C2×C4⋊C4—32no—
158C2×C22⋊C4—98no—
159C2×C22⋊C4—94no—
160C2×C42—34no—
161C2×C42D3211yescharacteristic
162#95—34no—
163C23×C3—21no—
164C23×C3C23×D312yes—
165C22×D3—316no—
166C22×D3—68no—
167C22×D3—68no—
168C22×D3—68no—
169C22×D3—68no—
170C22×D3—68no—
171C22×D3—68no—
172C22×D3—68no—
173C22×D3—128no—
174C22×D3—128no—
175C22×D3—124no—
176C22×D3—124no—
177C2×C3×C4—22no—
178C2×C3×C4—22no—
179C2×C3×C4—22no—
180C2×C3×C4—22no—
181C2×C3×C4—24no—
182C2×C3×C4—24no—
183C2×C3×C4—22no—
184C2×C3×C4—24no—
185C2×C3×C4—38no—
186C2×C3×C4—64no—
187C2×C3×C4—64no—
188C2×C3×C4—64no—
189C2×C3×C4—64no—
190C2×C3×C4—64no—
191C2×C3×C4C2×C4×D314yes—
192C2×C3×C4C2×C4×D314yes—
193C2×C3×C4C2×C4×D314yes—
194C2×C3×C4C2×D1214yes—
195C2×C3×C4#23514yes—
196C2×C3×C4D3×D414yes—
197C2×C3×C4#23914yes—
198C2×Dic3—24no—
199C2×Dic3—24no—
200C2×Dic3—24no—
201C2×Dic3—24no—
202C2×Dic3—24no—
203C2×Dic3C2×D1218yes—
204D12—632no—
205D12—632no—
206D12—1232no—
207D12—1216no—
208D12—1216no—
209C4×D3—1232no—
210C2×C32C2×C4×D412yes—
211C2×C32#51811yescharacteristic
212C2×C32D4211yescharacteristic
213C2×C32#55012yes—
214C2×C32#55911yescharacteristic
215C3⋊D3—48no—
216C24—94no—
217C2×D4—916no—
218C2×D4—98no—
219C2×D4—188no—
220C2×D4—188no—
221C2×D4—362no—
222C2×D4—362no—
223C22×C4—34no—
224C22×C4—34no—
225C22×C4—1816no—
226C22×C4—364no—
227C22×C4C2×D3211yescharacteristic
228C22×C4C2×D3212yes—
229C4⋊C4—38no—
230C4⋊C4—64no—
231C22⋊C4—1816no—
232C22⋊C4—364no—
233C42—68no—
234C42#62414yescomplemented
235C22×C3—22no—
236C22×C3—22no—
237C22×C3—21no—
238C22×C3—21no—
239C22×C3—21no—
240C22×C3C22×C4×D312yes—
241C22×C3C22×D1212yes—
242C22×C3C2×#23512yes—
243C22×C3C2×D3×D412yes—
244C22×C3C2×#23912yes—
245C22×C3#100912yes—
246C22×C3#100912yes—
247C2×D3—616no—
248C2×D3—616no—
249C2×D3—616no—
250C2×D3—1216no—
251C2×D3—128no—
252C2×D3—128no—
253C2×D3—128no—
254C2×D3—128no—
255C2×D3—128no—
256C2×D3—248no—
257C2×D3—244no—
258C2×D3—244no—
259C3×C4—24no—
260C3×C4—24no—
261C3×C4—28no—
262C3×C4—68no—
263C3×C4—124no—
264C3×C4C4×D1218yescomplemented
265C3×C4#89318yescomplemented
266Dic3—28no—
267Dic3—44no—
268C32#236611yescharacteristic, complemented, Sylow
269C23—98no—
270C23—188no—
271C23—188no—
272C23—184no—
273C23—184no—
274C23C22×D3211yescharacteristic
275D4—1832no—
276D4—368no—
277C2×C4—21no—
278C2×C4—21no—
279C2×C4—38no—
280C2×C4—64no—
281C2×C4—64no—
282C2×C4—64no—
283C2×C4—64no—
284C2×C4—64no—
285C2×C4—3616no—
286C2×C4#379914yes—
287C2×C4D3×D1214yes—
288C2×C4C2×#62412yes—
289C2×C4C2×#62414yes—
290C2×C3—22no—
291C2×C3—22no—
292C2×C3—21no—
293C2×C3—21no—
294C2×C3—21no—
295C2×C3C2×C4×D1212yes—
296C2×C3C2×#89312yes—
297C2×C3#552112yes—
298C2×C3D4×D1212yes—
299C2×C3#555312yes—
300C2×C3#557712yes—
301C2×C3#558512yes—
302D3—1216no—
303D3—248no—
304C22—1816no—
305C22—188no—
306C22—368no—
307C22—364no—
308C22—364no—
309C22C2×#379912yes—
310C22C2×D3×D1212yes—
311C22#6430811yescharacteristic
312C22#6430811yescharacteristic
313C22C22×#62411yescharacteristic
314C4—22no—
315C4—68no—
316C4—124no—
317C4#6389418yescomplemented
318C3—21no—
319C3#7365312yescomplemented
320C2—368no—
321C2#1059390212yes—
322C2#1059396311yescharacteristic
323C2D12211yescharacteristic
324C2C2×#6389412yes—
325C2#1059499611yescharacteristic
subgroupG/H
center, FrattiniC23C22×D32
commutatorC22×C32C23×C4
FittingC2×C32×C42C22
socle, cosocleC23×C32C24
prime radicalC2×#64083C2
hypercenterC2×C42D32
hypocenterC32#2366
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
2. C2×#63894C2semidirect
3. C3×C4×C4⋊Dic3C2semidirect
4. #10591380C2semidirect
5. #10591320C2semidirect
11. #64083C4semidirect
26. C4×C4⋊Dic3D3semidirect
35. C2×C4⋊(C3⋊D3)C2×C4semidirect
36. C2×C4⋊(C3⋊D3)C2×C4semidirect
41. C32×C42C2×C4semidirect
43. C3×C4⋊Dic3D4semidirect
130. C3×C42C4×D3semidirect
135. C4⋊Dic3D12semidirect
148. C32×C4C4×D4semidirect
234. C42#624semidirect
264. C3×C4C4×D12semidirect
265. C3×C4#893semidirect
268. C32#2366semidirect
317. C4#63894semidirect
319. C3#73653semidirect

Maximal subgroups

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

subgroupindex
C2×#640832
C2×#638942
C3×C4×C4⋊Dic32
#105913802
#105913202
#736533