Finite Group Databasebeta

← C2×C8×#625 #11859178

Subgroups — C2×C8×#625 #11859178

Order 1152.

1313 conjugacy classes of subgroups.

The subgroup lattice has 331 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C3×D3×C8C212yesmaximal, complemented
2C2×C4×#625C211yesmaximal, characteristic
3C2×C8×C3⋊Dic3C211yesmaximal, characteristic, complemented
4C2×#63572C211yesmaximal, characteristic, complemented
5C2×(C2×D3)⋊(C3⋊C8)C212yesmaximal, complemented
6C8×#625C218yesmaximal, direct product factor
7C2×C8×#67—32nomaximal
8C22×C3×C4×D3C2212yes—
9C22×#625C411yescharacteristic
10C22×C32×C8C2211yescharacteristic
11C2×C4×C3⋊Dic3C2211yescharacteristic
12C22×C3⋊(C3⋊C8)C2211yescharacteristic
13C22×C3×C3⋊C8C2212yes—
14C2×C3×D3×C8—28no—
15C2×C3×D3×C8C2218yescomplemented
16C2×#3724C411yescharacteristic
17C2×(C2×D3)⋊Dic3C412yes—
18C4×#625C414yes—
19C4×#625C2214yes—
20C8×C3⋊Dic3C2214yescomplemented
21#63572C2214yescomplemented
22(C2×D3)⋊(C3⋊C8)C2218yescomplemented
23C23×C3×C8—32no—
24C2×C4×#67—32no—
25C22×D3×C8D312yescomplemented
26C2×#830—32no—
27C8×#67—316no—
28C2×(C2×D3)⋊C8—32no—
29C2×Dic3⋊C8—32no—
30C2×C8×Dic3—32no—
31C2×C8×Dic3—61no—
32C23×C3×D3C2×C412yes—
33C22×C32×C4C2311yescharacteristic
34C22×C3⋊Dic3C2×C411yescharacteristic
35C22×C3⋊Dic3C2×C411yescharacteristic
36C22×C3×Dic3C2×C412yes—
37C2×C3×C4×D3—24no—
38C2×C3×C4×D3—24no—
39C2×C3×C4×D3C2×C414yes—
40C2×C3×C4×D3C2314yes—
41C2×#625C818yesdirect product factor
42C2×#625C2×C414yes—
43C2×C32×C8D414yescomplemented
44C2×C32×C8C2312yes—
45C4×C3⋊Dic3C2×C412yes—
46C4×C3⋊Dic3C2312yes—
47C2×C3⋊(C3⋊C8)—22no—
48C2×C3⋊(C3⋊C8)C2312yes—
49C2×C3×C3⋊C8—24no—
50C2×C3×C3⋊C8C2314yes—
51C3×D3×C8—216no—
52#3724C2×C414yes—
53(C2×D3)⋊Dic3C2×C418yes—
54C2×C8×D4—91noSylow
55C23×C3×C4—32no—
56C22×#67—32no—
57C22×C4×D3C2×D312yes—
58C22×C3×C8—21no—
59C22×C3×C8—32no—
60C22×C3×C8—38no—
61C22×C3×C8—68no—
62C22×C3×C8C2×D312yes—
63C2×#217—32no—
64C4×#67—38no—
65C4×#67—38no—
66C2×(C2×D3)⋊C4—32no—
67C2×Dic3⋊C4—32no—
68C2×C4×Dic3—32no—
69C2×C4×Dic3—61no—
70C22×C3⋊C8—32no—
71C22×C3⋊C8—61no—
72C22×C3⋊C8C2×D312yes—
73C2×D3×C8—28no—
74C2×D3×C8C2×D318yescomplemented
75#830—38no—
76(C2×D3)⋊C8—38no—
77Dic3⋊C8—38no—
78C8×Dic3—38no—
79C8×Dic3—64no—
80C23×C32C22×C411yescharacteristic
81C22×C3×D3—24no—
82C22×C3×D3—24no—
83C22×C3×D3C2×C818yescomplemented
84C22×C3×D3C22×C414yes—
85C2×C32×C4C22×C411yescharacteristic
86C2×C32×C4C2×D412yes—
87C2×C32×C4#4112yes—
88C2×C32×C4C2411yescharacteristic
89C2×C3⋊Dic3—22no—
90C2×C3⋊Dic3C2×C814yescomplemented
91C2×C3⋊Dic3C22×C412yes—
92C2×C3⋊Dic3C22×C412yes—
93C2×C3×Dic3—24no—
94C2×C3×Dic3C22×C414yes—
95C3×C4×D3—28no—
96C3×C4×D3—24no—
97C3×C4×D3—24no—
98#625C2×C8116yesdirect product factor
99C32×C8C2×D414yescomplemented
100C3⋊(C3⋊C8)—22no—
101C3×C3⋊C8—24no—
102C23×C8—32no—
103C2×C4×D4—91no—
104C8×D4—98no—
105C2×C4⋊C8—91no—
106C2×C22⋊C8—92no—
107C2×C4×C8—91no—
108C24×C3—32no—
109C23×D3C4×D312yes—
110C22×C3×C4—21no—
111C22×C3×C4—32no—
112C22×C3×C4—34no—
113C22×C3×C4—34no—
114C22×C3×C4—64no—
115C22×C3×C4—64no—
116C22×C3×C4C22×D312yes—
117C2×#67—316no—
118C2×#67—38no—
119C22×Dic3—32no—
120C22×Dic3—32no—
121C22×Dic3—61no—
122C22×Dic3—61no—
123C22×Dic3C4×D312yes—
124C2×C4×D3—24no—
125C2×C4×D3—24no—
126C2×C4×D3C4×D314yes—
127C2×C4×D3C22×D314yes—
128C2×C3×C8—24no—
129C2×C3×C8—22no—
130C2×C3×C8—34no—
131C2×C3×C8—64no—
132C2×C3×C8—616no—
133C2×C3×C8#6718yescomplemented
134C2×C3×C8C22×D314yes—
135#217—38no—
136(C2×D3)⋊C4—38no—
137Dic3⋊C4—38no—
138C4×Dic3—34no—
139C4×Dic3—34no—
140C4×Dic3—62no—
141C4×Dic3—62no—
142C2×C3⋊C8—24no—
143C2×C3⋊C8—34no—
144C2×C3⋊C8—62no—
145C2×C3⋊C8—64no—
146C2×C3⋊C8—64no—
147C2×C3⋊C8C22×D314yes—
148D3×C8—216no—
149C22×C32C4×D412yes—
150C22×C32C22×C812yes—
151C22×C32#13112yes—
152C22×C32C23×C411yescharacteristic
153C2×C3×D3—24no—
154C2×C3×D3—24no—
155C2×C3×D3—216no—
156C2×C3×D3C22×C818yescomplemented
157C32×C4C4×D412yes—
158C32×C4C22×D411yescharacteristic
159C32×C4C2×#4111yescharacteristic
160C3⋊Dic3—22no—
161C3⋊Dic3C22×C814yescomplemented
162C3×Dic3—24no—
163C22×D4—91no—
164C23×C4—32no—
165C22×C8—32no—
166C22×C8—38no—
167C22×C8—68no—
168C22×C8—91no—
169C22×C8D3211yescharacteristic
170C4×D4—94no—
171C4×D4—94no—
172C2×C4⋊C4—91no—
173C2×C22⋊C4—92no—
174C2×C42—91no—
175C4⋊C8—94no—
176C22⋊C8—98no—
177C4×C8—94no—
178C23×C3—21no—
179C23×C3—38no—
180C23×C3—34no—
181C23×C3—64no—
182C23×C3—64no—
183C23×C3C2×C4×D312yes—
184C22×D3—24no—
185C22×D3—24no—
186C22×D3D3×C818yescomplemented
187C22×D3C2×C4×D314yes—
188C2×C3×C4—21no—
189C2×C3×C4—22no—
190C2×C3×C4—21no—
191C2×C3×C4—22no—
192C2×C3×C4—34no—
193C2×C3×C4—64no—
194C2×C3×C4—68no—
195C2×C3×C4—64no—
196C2×C3×C4—64no—
197C2×C3×C4C2×C4×D312yes—
198C2×C3×C4#23514yes—
199C2×C3×C4C2×#6714yes—
200C2×C3×C4C23×D312yes—
201#67—332no—
202C2×Dic3—24no—
203C2×Dic3—38no—
204C2×Dic3—34no—
205C2×Dic3—34no—
206C2×Dic3—64no—
207C2×Dic3—62no—
208C2×Dic3—62no—
209C2×Dic3—64no—
210C2×Dic3—64no—
211C2×Dic3C2×C4×D314yes—
212C4×D3—28no—
213C4×D3—24no—
214C4×D3—24no—
215C3×C8—24no—
216C3×C8—64no—
217C3×C8C2×#6718yescomplemented
218C3⋊C8—24no—
219C3⋊C8—64no—
220C3⋊C8—64no—
221C2×C32C8×D414yescomplemented
222C2×C32C2×C4×D411yescharacteristic
223C2×C32C23×C811yescharacteristic
224C2×C32C2×#13111yescharacteristic
225C3×D3—28no—
226C24—32no—
227C2×D4—94no—
228C2×D4—98no—
229C22×C4—32no—
230C22×C4—34no—
231C22×C4—34no—
232C22×C4—64no—
233C22×C4—64no—
234C22×C4—91no—
235C22×C4—91no—
236C22×C4C2×D3211yescharacteristic
237C2×C8—34no—
238C2×C8—64no—
239C2×C8—616no—
240C2×C8—92no—
241C2×C8—182no—
242C2×C8#62514yesdirect product factor
243C2×C8C2×D3212yes—
244C4⋊C4—94no—
245C22⋊C4—98no—
246C42—92no—
247C42—92no—
248C22×C3—22no—
249C22×C3—21no—
250C22×C3—22no—
251C22×C3—22no—
252C22×C3—38no—
253C22×C3—64no—
254C22×C3—64no—
255C22×C3—616no—
256C22×C3C2×D3×C814yes—
257C22×C3#90114yes—
258C22×C3C4×#6714yes—
259C22×C3C22×C4×D312yes—
260C2×D3—24no—
261C2×D3—24no—
262C2×D3—216no—
263C2×D3C2×D3×C818yescomplemented
264C3×C4—21no—
265C3×C4—21no—
266C3×C4—22no—
267C3×C4—64no—
268C3×C4C4×#6714yes—
269C3×C4C2×#23512yes—
270C3×C4C22×#6712yes—
271Dic3—24no—
272Dic3—38no—
273Dic3—64no—
274Dic3—64no—
275Dic3—64no—
276C32C2×C8×D411yescharacteristic, complemented, Sylow
277C23—38no—
278C23—34no—
279C23—64no—
280C23—64no—
281C23C4×D3211yescharacteristic
282D4—916no—
283C2×C4—34no—
284C2×C4—64no—
285C2×C4—64no—
286C2×C4—64no—
287C2×C4—68no—
288C2×C4—94no—
289C2×C4—92no—
290C2×C4—92no—
291C2×C4—182no—
292C2×C4#379812yes—
293C2×C4C4×D3211yescharacteristic
294C2×C4C2×#62512yes—
295C2×C4C22×D3211yescharacteristic
296C8—64no—
297C8—182no—
298C8C2×#62514yesdirect product factor
299C2×C3—21no—
300C2×C3—21no—
301C2×C3—21no—
302C2×C3—24no—
303C2×C3—68no—
304C2×C3C8×#6718yescomplemented
305C2×C3C22×D3×C812yes—
306C2×C3C2×#90112yes—
307C2×C3C2×C4×#6712yes—
308D3—28no—
309C22—38no—
310C22—64no—
311C22—64no—
312C22—616no—
313C22D32×C812yes—
314C22#6380312yes—
315C22C4×#62512yes—
316C22C2×C4×D3211yescharacteristic
317C4—64no—
318C4—94no—
319C4—182no—
320C4C4×#62512yes—
321C4C2×#379811yescharacteristic
322C4C22×#62511yescharacteristic
323C3—21no—
324C3C2×C8×#6712yescomplemented
325C2—68no—
326C2C8×#62514yesdirect product factor
327C2C2×D32×C811yescharacteristic
328C2C2×#6380311yescharacteristic
329C2C2×C4×#62511yescharacteristic
subgroupG/H
center, hypercenterC22×C8D32
commutatorC2×C32C23×C8
FrattiniC2×C4C22×D32
FittingC22×C32×C8C22
socleC23×C32C22×C4
prime radicalC22×#625C4
cosocleC2×C32×C4C24
hypocenterC32C2×C8×D4
LCSG ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
1. C22×C3×D3×C8C2semidirect
3. C2×C8×C3⋊Dic3C2semidirect
4. C2×#63572C2semidirect
5. C2×(C2×D3)⋊(C3⋊C8)C2semidirect
6. C8×#625C2direct (N × H)
15. C2×C3×D3×C8C22semidirect
20. C8×C3⋊Dic3C22semidirect
21. #63572C22semidirect
22. (C2×D3)⋊(C3⋊C8)C22semidirect
25. C22×D3×C8D3semidirect
41. C2×#625C8direct (N × H)
43. C2×C32×C8D4semidirect
74. C2×D3×C8C2×D3semidirect
83. C22×C3×D3C2×C8semidirect
90. C2×C3⋊Dic3C2×C8semidirect
98. #625C2×C8direct (N × H)
99. C32×C8C2×D4semidirect
133. C2×C3×C8#67semidirect
156. C2×C3×D3C22×C8semidirect
161. C3⋊Dic3C22×C8semidirect
186. C22×D3D3×C8semidirect
217. C3×C8C2×#67semidirect
221. C2×C32C8×D4semidirect
242. C2×C8#625direct (N × H)
263. C2×D3C2×D3×C8semidirect
276. C32C2×C8×D4semidirect
298. C8C2×#625direct (N × H)
304. C2×C3C8×#67semidirect
324. C3C2×C8×#67semidirect
326. C2C8×#625direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C3×D3×C82
C2×C4×#6252
C2×C8×C3⋊Dic32
C2×#635722
C2×(C2×D3)⋊(C3⋊C8)2
C8×#6252
C2×C8×#673