Finite Group Databasebeta

← #11776851

Subgroups — #11776851

Order 1152.

419 conjugacy classes of subgroups.

The subgroup lattice has 314 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10592624C211yesmaximal, characteristic
2C2×C3×C4⋊(C3⋊C8)C211yesmaximal, characteristic
3C3×C4×#208C211yesmaximal, characteristic
4#10589099C212yesmaximal, complemented
5#10589097C212yesmaximal, complemented
6#70420—31nomaximal
7#69850—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C2×C3×#208C411yescharacteristic
10C2×C3×#208C411yescharacteristic
11C22×C3×C3⋊C8—21no—
12#63657—21no—
13C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
14C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
15C4×C3⋊(C3⋊C8)—21no—
16C3×C4⋊(C3⋊C8)—21no—
17C3×C4⋊(C3⋊C8)C2212yes—
18C3×#803C412yes—
19C3×C4×C3⋊C8C2212yes—
20C2×C3×C4⋊C8—31no—
21C3×C4×M16—31no—
22#4925—31no—
23#4925—31no—
24#4925—61no—
25C2×C4⋊(C3⋊C8)D311yescharacteristic
26C4×#208D311yescharacteristic
27#4480—32no—
28#4479—32no—
29#4458—32no—
30#4457—32no—
31C22×C32×C4C2×C411yescharacteristic
32C22×C32×C4D411yescharacteristic
33C22×C32×C4Q811yescharacteristic
34C32×C42C2×C411yescharacteristic
35C32×C42D411yescharacteristic
36C32×C42Q811yescharacteristic
37C32×C42C2311yescharacteristic
38C2×C3⋊(C3⋊C8)—21no—
39C2×C3⋊(C3⋊C8)—21no—
40C3×#208—22no—
41C3×#208C814yescomplemented
42C2×C3×C3⋊C8—22no—
43C2×C3×C3⋊C8—42no—
44C2×C3×C3⋊C8C2×C412yes—
45C2×C3×C3⋊C8C2×C412yes—
46#1565—91noSylow
47C2×C3×M16—31no—
48C2×C3×M16—31no—
49C22×C3×C8—61no—
50C2×C3×C42—21no—
51C2×C3×C42C2×D311yescharacteristic
52C2×C3×C42C2×D311yescharacteristic
53C2×#208Dic311yescharacteristic
54C2×#208Dic311yescharacteristic
55C22×C3⋊C8—21no—
56C3×C4⋊C8—32no—
57C3×C4⋊C8—61no—
58C3×#97—32no—
59C3×C4×C8—32no—
60#830—62no—
61#830—61no—
62#830—61no—
63C4⋊(C3⋊C8)—21no—
64C4⋊(C3⋊C8)—31no—
65C4⋊(C3⋊C8)—31no—
66C4⋊(C3⋊C8)—31no—
67C4⋊(C3⋊C8)—31no—
68C4⋊(C3⋊C8)—61no—
69C4⋊(C3⋊C8)—61no—
70C4⋊(C3⋊C8)C2×D312yes—
71#803Dic312yes—
72C4×C3⋊C8—62no—
73C4×C3⋊C8—61no—
74C4×C3⋊C8—61no—
75C4×C3⋊C8C2×D312yes—
76C23×C32C4⋊C411yescharacteristic
77C2×C32×C4—21no—
78C2×C32×C4—21no—
79C2×C32×C4—41no—
80C2×C32×C4C4⋊C411yescharacteristic
81C2×C32×C4C4⋊C411yescharacteristic
82C2×C32×C4C4⋊C411yescharacteristic
83C2×C32×C4C2×C812yes—
84C2×C32×C4M1612yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D411yescharacteristic
87C2×C32×C4C2×Q811yescharacteristic
88C3⋊(C3⋊C8)—41no—
89C3⋊(C3⋊C8)—41no—
90C3×C3⋊C8—22no—
91C3×C3⋊C8—42no—
92C3×C3⋊C8C2×C814yescomplemented
93#431—91no—
94C2×C4⋊C8—31no—
95C4×M16—31no—
96#335—92no—
97#334—92no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4—21no—
101C22×C3×C4Dic611yescharacteristic
102C22×C3×C4Dic611yescharacteristic
103C22×C3×C4C4×D311yescharacteristic
104C22×C3×C4D1211yescharacteristic
105C22×C3×C4C2×Dic311yescharacteristic
106C22×C3×C4#6711yescharacteristic
107C3×M16—34no—
108C3×M16—62no—
109C2×C3×C8—32no—
110C2×C3×C8—32no—
111C2×C3×C8—62no—
112C2×C3×C8—122no—
113C3×C42—21no—
114C3×C42—21no—
115C3×C42—21no—
116C3×C42—21no—
117C3×C42Dic611yescharacteristic
118C3×C42Dic611yescharacteristic
119C3×C42C4×D311yescharacteristic
120C3×C42D1211yescharacteristic
121C3×C42C2×Dic311yescharacteristic
122C3×C42#6711yescharacteristic
123C3×C42C22×D311yescharacteristic
124C3×C42C22×D311yescharacteristic
125#208—22no—
126#208C3⋊C814yescomplemented
127C2×C3⋊C8—22no—
128C2×C3⋊C8—42no—
129C2×C3⋊C8—62no—
130C2×C3⋊C8—62no—
131C2×C3⋊C8—61no—
132C2×C3⋊C8—61no—
133C2×C3⋊C8—61no—
134C2×C3⋊C8—61no—
135C2×C3⋊C8C2×Dic312yes—
136C2×C3⋊C8C2×Dic312yes—
137C22×C32—21no—
138C22×C32—21no—
139C22×C32C4⋊C812yes—
140C22×C32C2×C4⋊C411yescharacteristic
141C32×C4—21no—
142C32×C4—21no—
143C32×C4—21no—
144C32×C4C4⋊C812yes—
145C32×C4C22×C811yescharacteristic
146C32×C4C2×M1611yescharacteristic
147C32×C4AGL(1,ℤ/8)11yescharacteristic
148C32×C4#13711yescharacteristic
149C2×M16—31no—
150C2×M16—31no—
151C22×C8—61no—
152C2×C42D3211yescharacteristic
153C4⋊C8—32no—
154C4⋊C8—61no—
155C4⋊C8—91no—
156C4⋊C8—91no—
157C22⋊C8—181no—
158#97—32no—
159C4×C8—32no—
160C4×C8—181no—
161C23×C3—21no—
162C23×C3Dic3⋊C411yescharacteristic
163C23×C3C4⋊Dic311yescharacteristic
164C2×C3×C4—21no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—22no—
169C2×C3×C4—22no—
170C2×C3×C4—21no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—41no—
177C2×C3×C4—41no—
178C2×C3×C4—41no—
179C2×C3×C4—41no—
180C2×C3×C4—42no—
181C2×C3×C4D3×C812yes—
182C2×C3×C4ΓL(1,𝔽25)12yes—
183C2×C3×C4C2×C3⋊C812yes—
184C2×C3×C4#20812yes—
185C2×C3×C4Dic3⋊C411yescharacteristic
186C2×C3×C4Dic3⋊C411yescharacteristic
187C2×C3×C4Dic3⋊C411yescharacteristic
188C2×C3×C4C4⋊Dic311yescharacteristic
189C2×C3×C4C4⋊Dic311yescharacteristic
190C2×C3×C4C4⋊Dic311yescharacteristic
191C2×C3×C4C2×Dic611yescharacteristic
192C2×C3×C4C2×Dic611yescharacteristic
193C2×C3×C4C2×C4×D311yescharacteristic
194C2×C3×C4C2×D1211yescharacteristic
195C2×C3×C4C22×Dic311yescharacteristic
196C2×C3×C4C2×#6711yescharacteristic
197C3×C8—34no—
198C3×C8—62no—
199C3×C8—122no—
200C3⋊C8—22no—
201C3⋊C8—42no—
202C3⋊C8—122no—
203C3⋊C8—122no—
204C3⋊C8—121no—
205C3⋊C8—121no—
206C3⋊C8—121no—
207C3⋊C8—121no—
208C3⋊C8C2×C3⋊C814yescomplemented
209C2×C32—22no—
210C2×C32C2×C4⋊C811yescharacteristic
211C2×C32#42811yescharacteristic
212C2×C32#43011yescharacteristic
213C22×C4D3×Dic311yescharacteristic
214C22×C4#62611yescharacteristic
215C22×C4#62711yescharacteristic
216M16—34no—
217M16—62no—
218C2×C8—32no—
219C2×C8—32no—
220C2×C8—62no—
221C2×C8—122no—
222C2×C8—181no—
223C2×C8—181no—
224C42D3×Dic311yescharacteristic
225C42#62611yescharacteristic
226C42#62711yescharacteristic
227C42C2×D3211yescharacteristic
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3—41no—
235C22×C3—41no—
236C22×C3C4⋊(C3⋊C8)12yes—
237C22×C3Dic3⋊C812yes—
238C22×C3C2×Dic3⋊C411yescharacteristic
239C22×C3C2×C4⋊Dic311yescharacteristic
240C3×C4—22no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—21no—
249C3×C4—22no—
250C3×C4—21no—
251C3×C4—21no—
252C3×C4—41no—
253C3×C4—41no—
254C3×C4C4⋊(C3⋊C8)12yes—
255C3×C4Dic3⋊C812yes—
256C3×C4C2×D3×C811yescharacteristic
257C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
258C3×C4#90811yescharacteristic
259C3×C4#90911yescharacteristic
260C3×C4C22×C3⋊C811yescharacteristic
261C3×C4C2×#20811yescharacteristic
262C3×C4#93211yescharacteristic
263C3×C4#94211yescharacteristic
264C32#156511yescharacteristic, complemented, Sylow
265C23Dic3⋊Dic311yescharacteristic
266C2×C4—21no—
267C2×C4—21no—
268C2×C4—41no—
269C2×C4D3×C3⋊C812yes—
270C2×C4#371112yes—
271C2×C4Dic3⋊Dic311yescharacteristic
272C2×C4Dic3⋊Dic311yescharacteristic
273C2×C4Dic3⋊Dic311yescharacteristic
274C2×C4C2×D3×Dic311yescharacteristic
275C2×C4C2×#62611yescharacteristic
276C2×C4C2×#62711yescharacteristic
277C8—34no—
278C8—62no—
279C8—122no—
280C8—361no—
281C8—361no—
282C2×C3—22no—
283C2×C3—22no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3—21no—
287C2×C3—42no—
288C2×C3C2×C4⋊(C3⋊C8)11yescharacteristic
289C2×C3#496411yescharacteristic
290C2×C3C2×Dic3⋊C811yescharacteristic
291C2×C3#512111yescharacteristic
292C2×C3#512411yescharacteristic
293C2×C3#512511yescharacteristic
294C22—21no—
295C22—21no—
296C22Dic3⋊(C3⋊C8)12yes—
297C22C2×Dic3⋊Dic311yescharacteristic
298C4—21no—
299C4—21no—
300C4—21no—
301C4Dic3⋊(C3⋊C8)12yes—
302C4C2×D3×C3⋊C811yescharacteristic
303C4C2×#371111yescharacteristic
304C4#6383011yescharacteristic
305C4#6383311yescharacteristic
306C3—21no—
307C3#6985011yescharacteristic, complemented
308C3#7042011yescharacteristic, complemented
309C2—22no—
310C2C2×Dic3⋊(C3⋊C8)11yescharacteristic
311C2#1059113011yescharacteristic
312C2#1059114111yescharacteristic
subgroupG/H
centerC2×C4C2×#626
commutatorC32×C4C22×C8
FrattiniC42C2×D32
FittingC2×C32×C42C22
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC32×C42C23
hypercenterC2×C42D32
hypocenterC32#1565
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
4. #10589099C2semidirect
5. #10589097C2semidirect
41. C3×#208C8semidirect
92. C3×C3⋊C8C2×C8semidirect
126. #208C3⋊C8semidirect
208. C3⋊C8C2×C3⋊C8semidirect
264. C32#1565semidirect
307. C3#69850semidirect
308. C3#70420semidirect

Maximal subgroups

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

subgroupindex
#105926242
C2×C3×C4⋊(C3⋊C8)2
C3×C4×#2082
#105890992
#105890972
#704203
#698503