Finite Group Databasebeta

← C2×#10592765 #11868319

Subgroups — C2×#10592765 #11868319

Order 1152.

1344 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×C32×#125C211yesmaximal, characteristic, complemented
2C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
3#10592765C218yesmaximal, direct product factor
4C2×#63636C211yesmaximal, characteristic
5C2×#63636C211yesmaximal, characteristic
6C2×#63635C211yesmaximal, characteristic, complemented
7C2×#63634C211yesmaximal, characteristic, complemented
8C2×C4⋊(C3⋊(C3⋊C8))C211yesmaximal, characteristic, complemented
9C2×#5066—34nomaximal
10C22×C4⋊(C3⋊D3)C2211yescharacteristic
11C22×C4×C3⋊D3—21no—
12C32×#125—22no—
13C32×#125C2214yescomplemented
14C2×C32×C4⋊C4—21no—
15C2×C32×C4⋊C4—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C4⋊C4C2211yescharacteristic
18C2×C32×C42C2211yescharacteristic
19C2×#3752—21no—
20C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
21C22×C3⋊(C3⋊C8)C2211yescharacteristic
22C22×C3⋊(C3⋊C8)C2211yescharacteristic
23C4×C4⋊(C3⋊D3)—22no—
24C4×C4⋊(C3⋊D3)C2214yes—
25#63636C2214yes—
26#63636C2214yes—
27#63635C2214yescomplemented
28#63634C2214yescomplemented
29C4⋊(C3⋊(C3⋊C8))C2214yescomplemented
30C2×C3×#125D314yescomplemented
31C2×C4×D12—34no—
32#5066—332no—
33C2×#809—34no—
34C2×#809—34no—
35C2×#808—34no—
36C2×#807—34no—
37C2×C4⋊(C3⋊C8)—34no—
38C23×C3⋊D3—21no—
39C22×C32×C4—21no—
40C22×C32×C4—21no—
41C22×C32×C4D411yescharacteristic
42C22×C32×C4D411yescharacteristic
43C22×C32×C4C2311yescharacteristic
44C22×C3⋊Dic3—21no—
45C2×C4⋊(C3⋊D3)—21no—
46C2×C4⋊(C3⋊D3)—22no—
47C2×C4⋊(C3⋊D3)Q814yes—
48C2×C4⋊(C3⋊D3)C2312yes—
49C2×C4×C3⋊D3—24no—
50C2×C4×C3⋊D3—44no—
51C32×C4⋊C4—24no—
52C32×C4⋊C4—24no—
53C32×C4⋊C4—21no—
54C32×C4⋊C4—21no—
55C32×C4⋊C4C2312yes—
56C32×C4⋊C4C2312yes—
57C32×C42D412yes—
58C32×C42C2312yes—
59#3752—24no—
60C4⋊(C3⋊Dic3)—21no—
61C4⋊(C3⋊Dic3)C2312yes—
62C2×C3⋊(C3⋊C8)—22no—
63C2×C3⋊(C3⋊C8)—22no—
64C2×C3⋊(C3⋊C8)C2312yes—
65C2×C3⋊(C3⋊C8)C2312yes—
66C2×#478—91noSylow
67C22×D12—34no—
68C22×C4×D3—64no—
69C3×#125—28no—
70C3×#125C2×D3116yescomplemented
71C2×C3×C4⋊C4—24no—
72C2×C3×C4⋊C4—24no—
73C2×C3×C4⋊C4C2×D314yes—
74C2×C3×C4⋊C4C2×D314yes—
75C2×C3×C42C2×D314yes—
76C2×(C2×D3)⋊C4—64no—
77C2×C4⋊Dic3—34no—
78C22×C3⋊C8—34no—
79C22×C3⋊C8—34no—
80C4×D12—316no—
81C4×D12—68no—
82#809—316no—
83#809—316no—
84#808—316no—
85#807—316no—
86C4⋊(C3⋊C8)—316no—
87C23×C32C2×D411yescharacteristic
88C22×C3⋊D3—24no—
89C22×C3⋊D3—22no—
90C22×C3⋊D3—42no—
91C22×C3⋊D3—42no—
92C2×C32×C4—22no—
93C2×C32×C4—22no—
94C2×C32×C4—22no—
95C2×C32×C4—22no—
96C2×C32×C4—42no—
97C2×C32×C4—42no—
98C2×C32×C4C2×D412yes—
99C2×C32×C4C2×D412yes—
100C2×C32×C4C2×D411yescharacteristic
101C2×C32×C4C2×Q812yes—
102C2×C32×C4#4112yes—
103C2×C32×C4C2411yescharacteristic
104C2×C3⋊Dic3—22no—
105C2×C3⋊Dic3—42no—
106C4⋊(C3⋊D3)—24no—
107C4⋊(C3⋊D3)—22no—
108C4⋊(C3⋊D3)C2×Q814yes—
109C4×C3⋊D3—48no—
110C3⋊(C3⋊C8)—22no—
111C3⋊(C3⋊C8)—22no—
112C2×#125C3⋊D311yescharacteristic, complemented
113C2×C4×D4—91no—
114#478—98no—
115C2×#107—91no—
116C2×#106—91no—
117C2×C4⋊C8—91no—
118C2×#102—91no—
119C2×#102—91no—
120C23×D3—64no—
121C22×C3×C4—24no—
122C22×C3×C4—24no—
123C22×C3×C4#6714yes—
124C22×C3×C4#6714yes—
125C22×C3×C4C22×D314yes—
126C22×Dic3—64no—
127C2×D12—316no—
128C2×D12—38no—
129C2×D12—68no—
130C2×D12—64no—
131C2×C4×D3—616no—
132C2×C4×D3—1216no—
133C3×C4⋊C4—216no—
134C3×C4⋊C4—216no—
135C3×C4⋊C4—24no—
136C3×C4⋊C4—24no—
137C3×C4⋊C4C22×D318yes—
138C3×C4⋊C4C22×D318yes—
139C3×C42#6718yes—
140C3×C42C22×D318yes—
141(C2×D3)⋊C4—616no—
142C4⋊Dic3—38no—
143C4⋊Dic3—64no—
144C2×C3⋊C8—38no—
145C2×C3⋊C8—38no—
146C2×C3⋊C8—68no—
147C2×C3⋊C8—68no—
148C22×C32C22⋊Q812yes—
149C22×C32#13512yes—
150C22×C32AGL(1,ℤ/8)12yes—
151C22×C32C22×D411yescharacteristic
152C2×C3⋊D3—24no—
153C2×C3⋊D3—42no—
154C2×C3⋊D3—42no—
155C2×C3⋊D3—48no—
156C32×C4—22no—
157C32×C4—22no—
158C32×C4—42no—
159C32×C4—42no—
160C32×C4C22⋊Q812yes—
161C32×C4C22×Q811yescharacteristic
162C32×C4C2×#4111yescharacteristic
163C3⋊Dic3—42no—
164C22×D4—91no—
165C23×C4—181no—
166C22×C8—91no—
167C22×C8—91no—
168#125—22no—
169#125C2×C3⋊D314yescomplemented
170C4×D4—94no—
171C4×D4—182no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4—21no—
174C2×C4⋊C4—91no—
175C2×C4⋊C4C2×C3⋊D311yescharacteristic
176C2×C4⋊C4C2×C3⋊D311yescharacteristic
177C2×C22⋊C4—181no—
178C2×C42C2×C3⋊D311yescharacteristic
179#107—94no—
180#106—94no—
181C4⋊C8—94no—
182#102—94no—
183#102—94no—
184C23×C3C2×#6714yes—
185C22×D3—616no—
186C22×D3—68no—
187C22×D3—128no—
188C22×D3—128no—
189C2×C3×C4—28no—
190C2×C3×C4—28no—
191C2×C3×C4—28no—
192C2×C3×C4—28no—
193C2×C3×C4—48no—
194C2×C3×C4—48no—
195C2×C3×C4D3×Q818yes—
196C2×C3×C4#23918yes—
197C2×C3×C4C2×#6718yes—
198C2×C3×C4C2×#6718yes—
199C2×C3×C4C2×#6714yes—
200C2×C3×C4C23×D314yes—
201C2×Dic3—68no—
202C2×Dic3—128no—
203D12—316no—
204D12—616no—
205D12—68no—
206C4×D3—1232no—
207C3⋊C8—68no—
208C3⋊C8—68no—
209C2×C32#47814yescomplemented
210C2×C32C2×C22⋊Q811yescharacteristic
211C2×C32C2×#13511yescharacteristic
212C2×C32C2×AGL(1,ℤ/8)11yescharacteristic
213C3⋊D3—44no—
214C24—181no—
215C2×D4—92no—
216C2×D4—94no—
217C2×D4—182no—
218C2×D4—181no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—181no—
222C22×C4—184no—
223C22×C4—364no—
224C22×C4#63811yescharacteristic
225C22×C4#63811yescharacteristic
226C22×C4C22×C3⋊D311yescharacteristic
227C2×C8—92no—
228C2×C8—92no—
229C2×C8—182no—
230C2×C8—182no—
231C4⋊C4—24no—
232C4⋊C4—24no—
233C4⋊C4—21no—
234C4⋊C4—21no—
235C4⋊C4—92no—
236C4⋊C4—181no—
237C4⋊C4C22×C3⋊D312yes—
238C4⋊C4C22×C3⋊D312yes—
239C22⋊C4—184no—
240C42#63812yes—
241C42C22×C3⋊D312yes—
242C22×C3#94618yes—
243C22×C3#94918yes—
244C22×C3#95018yes—
245C22×C3C22×#6714yes—
246C2×D3—616no—
247C2×D3—128no—
248C2×D3—128no—
249C2×D3—1232no—
250C3×C4—28no—
251C3×C4—28no—
252C3×C4—48no—
253C3×C4—48no—
254C3×C4#94618yes—
255C3×C4C2×D3×Q814yes—
256C3×C4C2×#23914yes—
257Dic3—128no—
258C32C2×#47811yescharacteristic, complemented, Sylow
259C23—182no—
260C23—184no—
261C23—362no—
262C23—362no—
263C23C2×#63811yescharacteristic
264D4—94no—
265D4—182no—
266D4—184no—
267C2×C4—22no—
268C2×C4—22no—
269C2×C4—22no—
270C2×C4—22no—
271C2×C4—42no—
272C2×C4—42no—
273C2×C4—182no—
274C2×C4—368no—
275C2×C4—362no—
276C2×C4Q8×C3⋊D312yes—
277C2×C4#383212yes—
278C2×C4C2×#63812yes—
279C2×C4C2×#63812yes—
280C2×C4C2×#63811yescharacteristic
281C2×C4C23×C3⋊D311yescharacteristic
282C8—182no—
283C8—182no—
284C2×C3#5066116yescomplemented
285C2×C3C2×#94614yes—
286C2×C3C2×#94914yes—
287C2×C3C2×#95014yes—
288D3—1216no—
289C22—184no—
290C22—362no—
291C22—362no—
292C22—368no—
293C22#6415512yes—
294C22#6415812yes—
295C22#6415912yes—
296C22C22×#63811yescharacteristic
297C4—22no—
298C4—22no—
299C4—42no—
300C4—42no—
301C4—362no—
302C4#6415512yes—
303C4C2×Q8×C3⋊D311yescharacteristic
304C4C2×#383211yescharacteristic
305C3C2×#506614yescomplemented
306C2—364no—
307C2#1059276514yesdirect product factor
308C2C2×#6415511yescharacteristic
309C2C2×#6415811yescharacteristic
310C2C2×#6415911yescharacteristic
subgroupG/H
centerC23C2×#638
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×#125C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenterC2×#125C3⋊D3
hypocenterC32C2×#478
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#125

Complements

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

NH ≅ G/Ntype
1. C2×C32×#125C2semidirect
3. #10592765C2direct (N × H)
6. C2×#63635C2semidirect
7. C2×#63634C2semidirect
8. C2×C4⋊(C3⋊(C3⋊C8))C2semidirect
13. C32×#125C22semidirect
27. #63635C22semidirect
28. #63634C22semidirect
29. C4⋊(C3⋊(C3⋊C8))C22semidirect
30. C2×C3×#125D3semidirect
70. C3×#125C2×D3semidirect
112. C2×#125C3⋊D3semidirect
169. #125C2×C3⋊D3semidirect
209. C2×C32#478semidirect
258. C32C2×#478semidirect
284. C2×C3#5066semidirect
305. C3C2×#5066semidirect
307. C2#10592765direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×#1252
C2×C4×C4⋊(C3⋊D3)2
#105927652
C2×#636362
C2×#636352
C2×#636342
C2×C4⋊(C3⋊(C3⋊C8))2
C2×#50663