Finite Group Databasebeta

← #11776849

Subgroups — #11776849

Order 1152.

429 conjugacy classes of subgroups.

The subgroup lattice has 312 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic
2C3×#4925C211yesmaximal, characteristic
3C3×C4×#208C211yesmaximal, characteristic
4#10589099C212yesmaximal, complemented
5#10589097C212yesmaximal, complemented
6#70746—31nomaximal
7#69850—31nomaximal
8C2×C32×C42C2211yescharacteristic
9C22×C3⋊(C3⋊C8)—21no—
10C2×C3×#208C411yescharacteristic
11C2×C3×#208C411yescharacteristic
12C4⋊(C3⋊(C3⋊C8))—21no—
13C4⋊(C3⋊(C3⋊C8))C2212yes—
14C3×#830—21no—
15C3×C4⋊(C3⋊C8)C2211yescharacteristic
16C3×C4⋊(C3⋊C8)C2211yescharacteristic
17C3×#803C412yes—
18C3×C4×C3⋊C8—21no—
19C3×C4×C3⋊C8C2212yes—
20C3×#431—31no—
21C3×C4×M16—31no—
22#4925D311yescharacteristic
23C2×C4⋊(C3⋊C8)—31no—
24C2×C4⋊(C3⋊C8)—31no—
25C2×C4⋊(C3⋊C8)—61no—
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)—22no—
39C2×C3⋊(C3⋊C8)—42no—
40C3×#208—22no—
41C3×#208C814yescomplemented
42C2×C3×C3⋊C8—21no—
43C2×C3×C3⋊C8—21no—
44C2×C3×C3⋊C8C2×C412yes—
45C2×C3×C3⋊C8C2×C412yes—
46#1565—91noSylow
47C2×C3×M16—31no—
48C2×C3×M16—31no—
49C2×C3×C42—21no—
50C2×C3×C42C2×D311yescharacteristic
51C2×C3×C42C2×D311yescharacteristic
52C2×#208Dic311yescharacteristic
53C2×#208Dic311yescharacteristic
54C22×C3⋊C8—62no—
55C22×C3⋊C8—61no—
56C22×C3⋊C8—61no—
57C3×C4⋊C8—31no—
58C3×C4⋊C8—31no—
59C3×C22⋊C8—61no—
60C3×#97—32no—
61C3×C4×C8—32no—
62C3×C4×C8—61no—
63#830—21no—
64C4⋊(C3⋊C8)—32no—
65C4⋊(C3⋊C8)—32no—
66C4⋊(C3⋊C8)—62no—
67C4⋊(C3⋊C8)—62no—
68C4⋊(C3⋊C8)—61no—
69C4⋊(C3⋊C8)—61no—
70C4⋊(C3⋊C8)C2×D311yescharacteristic
71C4⋊(C3⋊C8)C2×D311yescharacteristic
72#803Dic312yes—
73C4×C3⋊C8—21no—
74C4×C3⋊C8C2×D312yes—
75C23×C32C4⋊C411yescharacteristic
76C2×C32×C4—21no—
77C2×C32×C4—21no—
78C2×C32×C4—41no—
79C2×C32×C4C4⋊C411yescharacteristic
80C2×C32×C4C4⋊C411yescharacteristic
81C2×C32×C4C4⋊C411yescharacteristic
82C2×C32×C4C2×C812yes—
83C2×C32×C4M1612yes—
84C2×C32×C4C22×C411yescharacteristic
85C2×C32×C4C2×D411yescharacteristic
86C2×C32×C4C2×Q811yescharacteristic
87C3⋊(C3⋊C8)—42no—
88C3×C3⋊C8—22no—
89C3×C3⋊C8—41no—
90C3×C3⋊C8—41no—
91C3×C3⋊C8C2×C814yescomplemented
92#431—31no—
93C2×C4⋊C8—91no—
94C4×M16—31no—
95#335—92no—
96#334—92no—
97C22×C3×C4—21no—
98C22×C3×C4—21no—
99C22×C3×C4—21no—
100C22×C3×C4Dic611yescharacteristic
101C22×C3×C4Dic611yescharacteristic
102C22×C3×C4C4×D311yescharacteristic
103C22×C3×C4D1211yescharacteristic
104C22×C3×C4C2×Dic311yescharacteristic
105C22×C3×C4#6711yescharacteristic
106C3×M16—34no—
107C3×M16—62no—
108C2×C3×C8—32no—
109C2×C3×C8—32no—
110C2×C3×C8—61no—
111C2×C3×C8—61no—
112C3×C42—21no—
113C3×C42—21no—
114C3×C42—21no—
115C3×C42—21no—
116C3×C42Dic611yescharacteristic
117C3×C42Dic611yescharacteristic
118C3×C42C4×D311yescharacteristic
119C3×C42D1211yescharacteristic
120C3×C42C2×Dic311yescharacteristic
121C3×C42#6711yescharacteristic
122C3×C42C22×D311yescharacteristic
123C3×C42C22×D311yescharacteristic
124#208—22no—
125#208C3⋊C814yescomplemented
126C2×C3⋊C8—21no—
127C2×C3⋊C8—21no—
128C2×C3⋊C8—64no—
129C2×C3⋊C8—62no—
130C2×C3⋊C8—62no—
131C2×C3⋊C8—124no—
132C2×C3⋊C8—122no—
133C2×C3⋊C8—122no—
134C2×C3⋊C8C2×Dic312yes—
135C2×C3⋊C8C2×Dic312yes—
136C22×C32—21no—
137C22×C32—21no—
138C22×C32C4⋊C812yes—
139C22×C32C2×C4⋊C411yescharacteristic
140C32×C4—21no—
141C32×C4—21no—
142C32×C4—21no—
143C32×C4C4⋊C812yes—
144C32×C4C22×C811yescharacteristic
145C32×C4C2×M1611yescharacteristic
146C32×C4AGL(1,ℤ/8)11yescharacteristic
147C32×C4#13711yescharacteristic
148C2×M16—31no—
149C2×M16—31no—
150C22×C8—181no—
151C2×C42D3211yescharacteristic
152C4⋊C8—31no—
153C4⋊C8—31no—
154C4⋊C8—92no—
155C4⋊C8—181no—
156C22⋊C8—61no—
157#97—32no—
158C4×C8—32no—
159C4×C8—61no—
160C23×C3—21no—
161C23×C3Dic3⋊C411yescharacteristic
162C23×C3C4⋊Dic311yescharacteristic
163C2×C3×C4—22no—
164C2×C3×C4—22no—
165C2×C3×C4—21no—
166C2×C3×C4—21no—
167C2×C3×C4—21no—
168C2×C3×C4—21no—
169C2×C3×C4—22no—
170C2×C3×C4—22no—
171C2×C3×C4—21no—
172C2×C3×C4—21no—
173C2×C3×C4—21no—
174C2×C3×C4—21no—
175C2×C3×C4—21no—
176C2×C3×C4—21no—
177C2×C3×C4—41no—
178C2×C3×C4—41no—
179C2×C3×C4—42no—
180C2×C3×C4D3×C812yes—
181C2×C3×C4ΓL(1,𝔽25)12yes—
182C2×C3×C4C2×C3⋊C812yes—
183C2×C3×C4#20812yes—
184C2×C3×C4Dic3⋊C411yescharacteristic
185C2×C3×C4Dic3⋊C411yescharacteristic
186C2×C3×C4Dic3⋊C411yescharacteristic
187C2×C3×C4C4⋊Dic311yescharacteristic
188C2×C3×C4C4⋊Dic311yescharacteristic
189C2×C3×C4C4⋊Dic311yescharacteristic
190C2×C3×C4C2×Dic611yescharacteristic
191C2×C3×C4C2×Dic611yescharacteristic
192C2×C3×C4C2×C4×D311yescharacteristic
193C2×C3×C4C2×D1211yescharacteristic
194C2×C3×C4C22×Dic311yescharacteristic
195C2×C3×C4C2×#6711yescharacteristic
196C3×C8—34no—
197C3×C8—62no—
198C3×C8—121no—
199C3×C8—121no—
200C3⋊C8—22no—
201C3⋊C8—41no—
202C3⋊C8—41no—
203C3⋊C8—124no—
204C3⋊C8—122no—
205C3⋊C8—122no—
206C3⋊C8C2×C3⋊C814yescomplemented
207C2×C32—22no—
208C2×C32C2×C4⋊C811yescharacteristic
209C2×C32#42811yescharacteristic
210C2×C32#43011yescharacteristic
211C22×C4D3×Dic311yescharacteristic
212C22×C4#62611yescharacteristic
213C22×C4#62711yescharacteristic
214M16—34no—
215M16—62no—
216C2×C8—32no—
217C2×C8—32no—
218C2×C8—61no—
219C2×C8—61no—
220C2×C8—182no—
221C2×C8—362no—
222C42D3×Dic311yescharacteristic
223C42#62611yescharacteristic
224C42#62711yescharacteristic
225C42C2×D3211yescharacteristic
226C22×C3—22no—
227C22×C3—22no—
228C22×C3—21no—
229C22×C3—21no—
230C22×C3—21no—
231C22×C3—21no—
232C22×C3—22no—
233C22×C3—21no—
234C22×C3C4⋊(C3⋊C8)12yes—
235C22×C3Dic3⋊C812yes—
236C22×C3C2×Dic3⋊C411yescharacteristic
237C22×C3C2×C4⋊Dic311yescharacteristic
238C3×C4—22no—
239C3×C4—21no—
240C3×C4—21no—
241C3×C4—21no—
242C3×C4—21no—
243C3×C4—21no—
244C3×C4—21no—
245C3×C4—21no—
246C3×C4—21no—
247C3×C4—21no—
248C3×C4—22no—
249C3×C4—21no—
250C3×C4—41no—
251C3×C4—41no—
252C3×C4C4⋊(C3⋊C8)12yes—
253C3×C4Dic3⋊C812yes—
254C3×C4C2×D3×C811yescharacteristic
255C3×C4C2×ΓL(1,𝔽25)11yescharacteristic
256C3×C4#90811yescharacteristic
257C3×C4#90911yescharacteristic
258C3×C4C22×C3⋊C811yescharacteristic
259C3×C4C2×#20811yescharacteristic
260C3×C4#94911yescharacteristic
261C3×C4#95111yescharacteristic
262C32#156511yescharacteristic, complemented, Sylow
263C23Dic3⋊Dic311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—41no—
267C2×C4D3×C3⋊C812yes—
268C2×C4#371112yes—
269C2×C4Dic3⋊Dic311yescharacteristic
270C2×C4Dic3⋊Dic311yescharacteristic
271C2×C4Dic3⋊Dic311yescharacteristic
272C2×C4C2×D3×Dic311yescharacteristic
273C2×C4C2×#62611yescharacteristic
274C2×C4C2×#62711yescharacteristic
275C8—34no—
276C8—62no—
277C8—121no—
278C8—121no—
279C8—362no—
280C2×C3—24no—
281C2×C3—22no—
282C2×C3—22no—
283C2×C3—21no—
284C2×C3—21no—
285C2×C3—21no—
286C2×C3C2×C4⋊(C3⋊C8)11yescharacteristic
287C2×C3#499511yescharacteristic
288C2×C3C2×Dic3⋊C811yescharacteristic
289C2×C3#512111yescharacteristic
290C2×C3#512411yescharacteristic
291C2×C3#512511yescharacteristic
292C22—21no—
293C22—21no—
294C22Dic3⋊(C3⋊C8)12yes—
295C22C2×Dic3⋊Dic311yescharacteristic
296C4—21no—
297C4—21no—
298C4—21no—
299C4Dic3⋊(C3⋊C8)12yes—
300C4C2×D3×C3⋊C811yescharacteristic
301C4C2×#371111yescharacteristic
302C4#6382511yescharacteristic
303C4#6383111yescharacteristic
304C3—21no—
305C3#6985011yescharacteristic, complemented
306C3#7074611yescharacteristic, complemented
307C2—22no—
308C2C2×Dic3⋊(C3⋊C8)11yescharacteristic
309C2#1059113111yescharacteristic
310C2#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
91. C3×C3⋊C8C2×C8semidirect
125. #208C3⋊C8semidirect
206. C3⋊C8C2×C3⋊C8semidirect
262. C32#1565semidirect
305. C3#69850semidirect
306. C3#70746semidirect

Maximal subgroups

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

subgroupindex
C2×C4⋊(C3⋊(C3⋊C8))2
C3×#49252
C3×C4×#2082
#105890992
#105890972
#707463
#698503