Finite Group Databasebeta

← #11861536

Subgroups — #11861536

Order 1152.

1368 conjugacy classes of subgroups.

The subgroup lattice has 315 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C4×#3828C211yesmaximal, characteristic
2C32×#431C211yesmaximal, characteristic, complemented
3C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
4#10592533C212yesmaximal, complemented
5#10592529C212yesmaximal, complemented
6#10592424C214yesmaximal, complemented
7#10592384C212yesmaximal, complemented
8C4×C8×C3⋊D3C212yesmaximal, complemented
9#79276—34nomaximal
10C2×#3828C411yescharacteristic
11C2×C32×C42C2211yescharacteristic
12C4×#638C412yes—
13C4×#638C2212yes—
14#64135C411yescharacteristic
15C22×C3⋊(C3⋊C8)C2212yes—
16C2×C8×C3⋊D3C2214yes—
17C4×C4⋊(C3⋊D3)C411yescharacteristic
18C4×C4⋊(C3⋊D3)C2211yescharacteristic
19#64081C412yes—
20C42×C3⋊D3C2212yes—
21C4×#634C411yescharacteristic
22C4×#634C2211yescharacteristic
23C32×C4⋊C8C2212yes—
24C32×C22⋊C8C2212yes—
25C32×C4×C8C2212yes—
26#63647C2214yes—
27#63641C2214yes—
28C8×C3⋊Dic3C2214yes—
29C4×C3⋊(C3⋊C8)C2212yes—
30C4×C3⋊(C3⋊C8)C2211yescharacteristic
31C4×C3⋊(C3⋊C8)C2211yescharacteristic
32C4×#235—34no—
33C3×#431D314yescomplemented
34C2×C4×C3⋊C8—34no—
35#4834—38no—
36#4830—38no—
37#67⋊C8—316no—
38#4685—38no—
39C4×D3×C8—38no—
40C22×C32×C4C2×C411yescharacteristic
41C22×C32×C4C2×C411yescharacteristic
42C22×C32×C4C2311yescharacteristic
43C2×#638C2×C412yes—
44#3828C818yescomplemented
45C2×C4⋊(C3⋊D3)C2×C411yescharacteristic
46C2×C4×C3⋊D3C2×C412yes—
47C2×C4×C3⋊D3C2×C412yes—
48C2×C4×C3⋊D3C2312yes—
49C2×#634C2×C411yescharacteristic
50C2×C32×C8C2314yes—
51C32×C42C2×C411yescharacteristic
52C32×C42C2×C411yescharacteristic
53C32×C42C2311yescharacteristic
54C32×C42C2311yescharacteristic
55#3757C2×C412yes—
56#3752C2×C412yes—
57#3752C2×C412yes—
58C4⋊(C3⋊Dic3)C2×C411yescharacteristic
59C4⋊(C3⋊Dic3)C2×C411yescharacteristic
60#3750C2×C412yes—
61#3750C2×C412yes—
62C4×C3⋊Dic3C2×C412yes—
63C4×C3⋊Dic3C2×C412yes—
64C4×C3⋊Dic3C2312yes—
65C2×C3⋊(C3⋊C8)—24no—
66C2×C3⋊(C3⋊C8)C2312yes—
67C2×C3⋊(C3⋊C8)C2312yes—
68C8×C3⋊D3—28no—
69C8×#41—91noSylow
70C2×#235—34no—
71C2×C3×C42C2×D314yes—
72C4×#67—38no—
73C4×#67—38no—
74#926—34no—
75C22×C3⋊C8—38no—
76C2×D3×C8—316no—
77C4×D12—34no—
78C4×D12—34no—
79#872—38no—
80C42×D3—38no—
81C4×Dic6—34no—
82C4×Dic6—34no—
83C3×C4⋊C8C2×D318yes—
84C3×C22⋊C8C2×D318yes—
85C3×C4×C8C2×D318yes—
86(C2×D3)⋊C8—316no—
87Dic3⋊C8—316no—
88C8×Dic3—316no—
89C4×C3⋊C8—34no—
90C4×C3⋊C8—34no—
91C4×C3⋊C8—38no—
92C23×C32C22×C411yescharacteristic
93C22×C3⋊D3C22×C412yes—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4C2×C814yescomplemented
97C2×C32×C4C22×C411yescharacteristic
98C2×C32×C4C22×C411yescharacteristic
99C2×C32×C4C22×C411yescharacteristic
100C2×C32×C4C22×C411yescharacteristic
101C2×C32×C4C22×C411yescharacteristic
102C2×C32×C4C2411yescharacteristic
103#638C2×C818yescomplemented
104C2×C3⋊Dic3C22×C412yes—
105C2×C3⋊Dic3C22×C412yes—
106C2×C3⋊Dic3C22×C412yes—
107C4⋊(C3⋊D3)C2×C814yescomplemented
108C4×C3⋊D3—24no—
109C4×C3⋊D3—24no—
110C4×C3⋊D3C2×C818yescomplemented
111#634C2×C814yescomplemented
112C32×C8—24no—
113C3⋊(C3⋊C8)—22no—
114C3⋊(C3⋊C8)#4114yescomplemented
115C4×#41—91no—
116C8×Q8—92no—
117C8×D4—92no—
118C8×D4—94no—
119#431—92no—
120#431C3⋊D311yescharacteristic, complemented
121C2×C4×C8—91no—
122C2×C4×C8—92no—
123C22×C3×C4C4×D314yes—
124C22×C3×C4C4×D314yes—
125C22×C3×C4C22×D314yes—
126C2×#67—38no—
127#235—332no—
128C2×D12—34no—
129C2×C4×D3—38no—
130C2×C4×D3—38no—
131C2×C4×D3—38no—
132C2×Dic6—34no—
133C2×C3×C8C22×D3116yes—
134C3×C42C4×D314yes—
135C3×C42C4×D314yes—
136C3×C42C22×D314yes—
137C3×C42C22×D314yes—
138#217—38no—
139(C2×D3)⋊C4—38no—
140(C2×D3)⋊C4—38no—
141C4⋊Dic3—34no—
142C4⋊Dic3—34no—
143Dic3⋊C4—38no—
144Dic3⋊C4—38no—
145C4×Dic3—38no—
146C4×Dic3—38no—
147C4×Dic3—38no—
148C2×C3⋊C8—38no—
149C2×C3⋊C8—38no—
150C2×C3⋊C8—616no—
151D3×C8—632no—
152C22×C32—21no—
153C22×C32—21no—
154C22×C32C22×C812yes—
155C22×C32C23×C411yescharacteristic
156C2×C3⋊D3—22no—
157C2×C3⋊D3—22no—
158C2×C3⋊D3C22×C814yes—
159C32×C4—21no—
160C32×C4—21no—
161C32×C4C22×C812yes—
162C32×C4C22×C812yes—
163C32×C4#13112yes—
164C32×C4C2×#4112yes—
165C3⋊Dic3—22no—
166C3⋊Dic3—22no—
167C3⋊Dic3C22×C814yes—
168C2×#41—91no—
169C22×C8—92no—
170C22×C8—94no—
171C4×Q8—91no—
172C4×Q8—91no—
173C4×D4—92no—
174C4×D4—92no—
175C4×D4—91no—
176C4×D4—91no—
177#117—91no—
178#117—92no—
179C2×C42—92no—
180C2×C42C2×C3⋊D311yescharacteristic
181C4⋊C8—94no—
182C4⋊C8C2×C3⋊D312yes—
183C22⋊C8—94no—
184C22⋊C8C2×C3⋊D312yes—
185C4×C8—94no—
186C4×C8—92no—
187C4×C8—91no—
188C4×C8—91no—
189C4×C8C2×C3⋊D312yes—
190C23×C3C2×C4×D314yes—
191C22×D3—38no—
192C2×C3×C4—28no—
193C2×C3×C4—28no—
194C2×C3×C4D3×C8116yescomplemented
195C2×C3×C4C2×C4×D314yes—
196C2×C3×C4C2×C4×D314yes—
197C2×C3×C4C2×C4×D314yes—
198C2×C3×C4C2×C4×D314yes—
199C2×C3×C4C2×C4×D314yes—
200C2×C3×C4C23×D314yes—
201#67—332no—
202C2×Dic3—38no—
203C2×Dic3—38no—
204C2×Dic3—38no—
205D12—316no—
206C4×D3—332no—
207C4×D3—616no—
208C4×D3—616no—
209Dic6—316no—
210C3×C8—216no—
211C3⋊C8—316no—
212C3⋊C8—68no—
213C2×C32—22no—
214C2×C32C4×#4111yescharacteristic
215C2×C32C23×C811yescharacteristic
216C2×C32C2×#13111yescharacteristic
217C3⋊D3—24no—
218#41—98no—
219C2×Q8—91no—
220C2×D4—92no—
221C2×D4—91no—
222C22×C4—92no—
223C22×C4—92no—
224C22×C4—92no—
225C22×C4C4×C3⋊D311yescharacteristic
226C22×C4C4×C3⋊D311yescharacteristic
227C22×C4C22×C3⋊D311yescharacteristic
228C2×C8—92no—
229C2×C8—92no—
230C2×C8—188no—
231C2×C8—184no—
232C2×C8C22×C3⋊D314yes—
233C4⋊C4—92no—
234C4⋊C4—92no—
235C4⋊C4—91no—
236C4⋊C4—91no—
237C22⋊C4—92no—
238C22⋊C4—92no—
239C22⋊C4—92no—
240C42—92no—
241C42—92no—
242C42—92no—
243C42C4×C3⋊D311yescharacteristic
244C42C4×C3⋊D311yescharacteristic
245C42C22×C3⋊D311yescharacteristic
246C42C22×C3⋊D311yescharacteristic
247C22×C3—24no—
248C22×C3—24no—
249C22×C3C2×D3×C818yes—
250C22×C3C22×C4×D314yes—
251C2×D3—316no—
252C2×D3—68no—
253C2×D3—68no—
254C3×C4—24no—
255C3×C4—24no—
256C3×C4C2×D3×C818yes—
257C3×C4C2×D3×C818yes—
258C3×C4#90718yes—
259C3×C4D3×#4118yes—
260Dic3—316no—
261Dic3—68no—
262Dic3—68no—
263C32C8×#4111yescharacteristic, complemented, Sylow
264C23—92no—
265C23C2×C4×C3⋊D311yescharacteristic
266Q8—94no—
267D4—98no—
268D4—94no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—92no—
272C2×C4—98no—
273C2×C4—92no—
274C2×C4—92no—
275C2×C4—184no—
276C2×C4—184no—
277C2×C4C8×C3⋊D314yescomplemented
278C2×C4C2×C4×C3⋊D311yescharacteristic
279C2×C4C2×C4×C3⋊D311yescharacteristic
280C2×C4C2×C4×C3⋊D311yescharacteristic
281C2×C4C2×C4×C3⋊D311yescharacteristic
282C2×C4C2×C4×C3⋊D311yescharacteristic
283C2×C4C23×C3⋊D311yescharacteristic
284C8—24no—
285C8—94no—
286C8—182no—
287C2×C3—28no—
288C2×C3#552214yes—
289C2×C3C22×D3×C814yes—
290C2×C3C2×#90714yes—
291D3—616no—
292C22—21no—
293C22—21no—
294C22—94no—
295C22—182no—
296C22—182no—
297C22C2×C8×C3⋊D312yes—
298C22C22×C4×C3⋊D311yescharacteristic
299C4—21no—
300C4—21no—
301C4—94no—
302C4—182no—
303C4—182no—
304C4C2×C8×C3⋊D312yes—
305C4C2×C8×C3⋊D312yes—
306C4#6411612yes—
307C4#41×C3⋊D312yes—
308C3#7927614yescomplemented
309C2—22no—
310C2—184no—
311C2#1059599311yescharacteristic
312C2C22×C8×C3⋊D311yescharacteristic
313C2C2×#6411611yescharacteristic
subgroupG/H
centerC42C22×C3⋊D3
commutatorC2×C32C23×C8
FrattiniC2×C4C23×C3⋊D3
FittingC32×#431C2
socleC22×C32C23×C4
prime radicalC2×#3828C4
cosocleC2×C32×C4C24
hypercenter#431C3⋊D3
hypocenterC32C8×#41
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C42 ◁ #431

Complements

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

NH ≅ G/Ntype
2. C32×#431C2semidirect
3. C2×C4×C3⋊(C3⋊C8)C2semidirect
4. #10592533C2semidirect
5. #10592529C2semidirect
6. #10592424C2semidirect
7. #10592384C2semidirect
8. C4×C8×C3⋊D3C2semidirect
33. C3×#431D3semidirect
44. #3828C8semidirect
96. C2×C32×C4C2×C8semidirect
103. #638C2×C8semidirect
107. C4⋊(C3⋊D3)C2×C8semidirect
110. C4×C3⋊D3C2×C8semidirect
111. #634C2×C8semidirect
114. C3⋊(C3⋊C8)#41semidirect
120. #431C3⋊D3semidirect
194. C2×C3×C4D3×C8semidirect
263. C32C8×#41semidirect
277. C2×C4C8×C3⋊D3semidirect
308. C3#79276semidirect

Maximal subgroups

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

subgroupindex
C4×#38282
C32×#4312
C2×C4×C3⋊(C3⋊C8)2
#105925332
#105925292
#105924242
#105923842
C4×C8×C3⋊D32
#792763