Finite Group Databasebeta

← C2×C4×#3755 #11859864

Subgroups — C2×C4×#3755 #11859864

Order 1152.

1656 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C32×C4×Q8C211yesmaximal, characteristic, complemented
2C22×#3755C211yesmaximal, characteristic
3C2×C4×C4⋊(C3⋊D3)C211yesmaximal, characteristic
4C2×#63662C211yesmaximal, characteristic, complemented
5C4×#3755C218yesmaximal, direct product factor
6C2×#63636C211yesmaximal, characteristic
7C2×#63635C211yesmaximal, characteristic, complemented
8C2×C4×C3⋊(C3⋊C8)C211yesmaximal, characteristic, complemented
9C2×C4×#215—34nomaximal
10C22×C32×Q8C2211yescharacteristic
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C22×C4×C3⋊D3—21no—
13C32×C4×Q8—22no—
14C32×C4×Q8C2214yescomplemented
15C2×C32×C4⋊C4—21no—
16C2×C32×C4⋊C4C2211yescharacteristic
17C2×C32×C42—21no—
18C2×C32×C42C2211yescharacteristic
19C2×#3755C418yesdirect product factor
20C2×#3755C2214yes—
21C2×#3752—21no—
22C2×C4⋊(C3⋊Dic3)C2211yescharacteristic
23C22×C3⋊(C3⋊C8)C2211yescharacteristic
24C22×C3⋊(C3⋊C8)C2211yescharacteristic
25C4×C4⋊(C3⋊D3)—22no—
26C4×C4⋊(C3⋊D3)C2214yes—
27#63662C2214yescomplemented
28#63636C2214yes—
29#63635C2214yescomplemented
30C4×C3⋊(C3⋊C8)C2214yescomplemented
31C2×C3×C4×Q8D314yescomplemented
32C22×#215—34no—
33C2×C4×D12—34no—
34C2×#835—34no—
35C4×#215—332no—
36C2×#809—34no—
37C2×#808—34no—
38C2×C4×C3⋊C8—34no—
39C23×C3⋊D3—21no—
40C2×C32×Q8—21no—
41C2×C32×Q8—22no—
42C2×C32×Q8C2×C414yescomplemented
43C2×C32×Q8C2312yes—
44C22×C32×C4—21no—
45C22×C32×C4—21no—
46C22×C32×C4D411yescharacteristic
47C22×C32×C4D411yescharacteristic
48C22×C32×C4C2311yescharacteristic
49C22×C3⋊Dic3—21no—
50C2×C4⋊(C3⋊D3)—21no—
51C2×C4⋊(C3⋊D3)—22no—
52C2×C4⋊(C3⋊D3)C2×C414yes—
53C2×C4⋊(C3⋊D3)C2312yes—
54C2×C4×C3⋊D3—24no—
55C2×C4×C3⋊D3—44no—
56C32×C4⋊C4—24no—
57C32×C4⋊C4—21no—
58C32×C4⋊C4C2312yes—
59C32×C42—24no—
60C32×C42D412yes—
61C32×C42C2312yes—
62#3755C2×C4116yesdirect product factor
63#3752—24no—
64C4⋊(C3⋊Dic3)—21no—
65C4⋊(C3⋊Dic3)C2312yes—
66C2×C3⋊(C3⋊C8)—22no—
67C2×C3⋊(C3⋊C8)C2×C414yescomplemented
68C2×C3⋊(C3⋊C8)C2312yes—
69C2×C3⋊(C3⋊C8)C2312yes—
70C2×C4×SD16—91noSylow
71C22×C3×Q8C2×D314yes—
72C22×D12—34no—
73C22×C4×D3—64no—
74C3×C4×Q8—28no—
75C3×C4×Q8C2×D3116yescomplemented
76C2×C3×C4⋊C4—24no—
77C2×C3×C4⋊C4C2×D314yes—
78C2×C3×C42—24no—
79C2×C3×C42C2×D314yes—
80C2×#215—332no—
81C2×#215—316no—
82C2×(C2×D3)⋊C4—64no—
83C2×C4⋊Dic3—34no—
84C22×C3⋊C8—34no—
85C22×C3⋊C8—34no—
86C4×D12—316no—
87C4×D12—68no—
88#835—316no—
89#809—316no—
90#808—316no—
91C4×C3⋊C8—316no—
92C23×C32C2×D411yescharacteristic
93C22×C3⋊D3—24no—
94C22×C3⋊D3—22no—
95C22×C3⋊D3—42no—
96C22×C3⋊D3—42no—
97C32×Q8—24no—
98C32×Q8—22no—
99C32×Q8C22×C414yescomplemented
100C2×C32×C4—24no—
101C2×C32×C4—22no—
102C2×C32×C4—22no—
103C2×C32×C4—22no—
104C2×C32×C4—42no—
105C2×C32×C4SD1614yescomplemented
106C2×C32×C4C22×C412yes—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2×D411yescharacteristic
109C2×C32×C4C2×D412yes—
110C2×C32×C4#4112yes—
111C2×C32×C4C2411yescharacteristic
112C2×C3⋊Dic3—22no—
113C2×C3⋊Dic3—42no—
114C4⋊(C3⋊D3)—24no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)C22×C414yes—
117C4×C3⋊D3—48no—
118C3⋊(C3⋊C8)—22no—
119C3⋊(C3⋊C8)C22×C414yescomplemented
120C22×SD16—91no—
121C2×C4×Q8C3⋊D311yescharacteristic, complemented
122C2×C4×D4—91no—
123C4×SD16—98no—
124C2×#106—91no—
125C2×#103—91no—
126C2×#102—91no—
127C2×C4×C8—91no—
128C23×D3—64no—
129C2×C3×Q8—28no—
130C2×C3×Q8—24no—
131C2×C3×Q8C4×D3116yescomplemented
132C2×C3×Q8C22×D318yes—
133C22×C3×C4—24no—
134C22×C3×C4—24no—
135C22×C3×C4#6714yes—
136C22×C3×C4#6714yes—
137C22×C3×C4C22×D314yes—
138C22×Dic3—64no—
139C2×D12—316no—
140C2×D12—38no—
141C2×D12—68no—
142C2×D12—64no—
143C2×C4×D3—616no—
144C2×C4×D3—1216no—
145C3×C4⋊C4—216no—
146C3×C4⋊C4—24no—
147C3×C4⋊C4C22×D318yes—
148C3×C42—216no—
149C3×C42#6718yes—
150C3×C42C22×D318yes—
151#215—364no—
152(C2×D3)⋊C4—616no—
153C4⋊Dic3—38no—
154C4⋊Dic3—64no—
155C2×C3⋊C8—316no—
156C2×C3⋊C8—38no—
157C2×C3⋊C8—38no—
158C2×C3⋊C8—68no—
159C22×C32C4×D412yes—
160C22×C32C2×SD1612yes—
161C22×C32#13512yes—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—24no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—48no—
167C32×C4—24no—
168C32×C4—22no—
169C32×C4—42no—
170C32×C4C4×D412yes—
171C32×C4C2×SD1614yescomplemented
172C32×C4C23×C411yescharacteristic
173C32×C4C2×#4111yescharacteristic
174C3⋊Dic3—42no—
175C22×Q8C2×C3⋊D311yescharacteristic
176C22×D4—91no—
177C23×C4—181no—
178C2×SD16—98no—
179C2×SD16—94no—
180C22×C8—91no—
181C22×C8—91no—
182C4×Q8—22no—
183C4×Q8C2×C3⋊D314yescomplemented
184C4×D4—94no—
185C4×D4—182no—
186C2×C4⋊C4—21no—
187C2×C4⋊C4—91no—
188C2×C4⋊C4C2×C3⋊D311yescharacteristic
189C2×C22⋊C4—181no—
190C2×C42—21no—
191C2×C42C2×C3⋊D311yescharacteristic
192#106—94no—
193#103—94no—
194#102—94no—
195C4×C8—94no—
196C23×C3C2×#6714yes—
197C22×D3—616no—
198C22×D3—68no—
199C22×D3—128no—
200C22×D3—128no—
201C3×Q8—216no—
202C3×Q8—28no—
203C3×Q8C2×C4×D3116yescomplemented
204C2×C3×C4—216no—
205C2×C3×C4—28no—
206C2×C3×C4—28no—
207C2×C3×C4—28no—
208C2×C3×C4—48no—
209C2×C3×C4#215116yescomplemented
210C2×C3×C4C2×C4×D318yes—
211C2×C3×C4#23518yes—
212C2×C3×C4C2×#6718yes—
213C2×C3×C4C2×#6714yes—
214C2×C3×C4C2×#6718yes—
215C2×C3×C4C23×D314yes—
216C2×Dic3—68no—
217C2×Dic3—128no—
218D12—316no—
219D12—616no—
220D12—68no—
221C4×D3—1232no—
222C3⋊C8—316no—
223C3⋊C8—68no—
224C2×C32C4×SD1614yescomplemented
225C2×C32C2×C4×D411yescharacteristic
226C2×C32C22×SD1611yescharacteristic
227C2×C32C2×#13511yescharacteristic
228C3⋊D3—44no—
229C24—181no—
230C2×Q8—22no—
231C2×Q8—21no—
232C2×Q8C4×C3⋊D314yescomplemented
233C2×Q8C22×C3⋊D312yes—
234C2×D4—92no—
235C2×D4—94no—
236C2×D4—182no—
237C2×D4—181no—
238C22×C4—21no—
239C22×C4—21no—
240C22×C4—181no—
241C22×C4—184no—
242C22×C4—364no—
243C22×C4#63811yescharacteristic
244C22×C4#63811yescharacteristic
245C22×C4C22×C3⋊D311yescharacteristic
246SD16—916no—
247C2×C8—92no—
248C2×C8—94no—
249C2×C8—92no—
250C2×C8—182no—
251C4⋊C4—24no—
252C4⋊C4—21no—
253C4⋊C4—92no—
254C4⋊C4—181no—
255C4⋊C4C22×C3⋊D312yes—
256C22⋊C4—184no—
257C42—24no—
258C42#63812yes—
259C42C22×C3⋊D312yes—
260C22×C3C4×#6718yes—
261C22×C3C2×#21518yes—
262C22×C3#95018yes—
263C22×C3C22×#6714yes—
264C2×D3—616no—
265C2×D3—1232no—
266C2×D3—128no—
267C2×D3—128no—
268C3×C4—216no—
269C3×C4—28no—
270C3×C4—48no—
271C3×C4C4×#6718yes—
272C3×C4C2×#215116yescomplemented
273C3×C4C22×C4×D314yes—
274C3×C4C2×#23514yes—
275Dic3—128no—
276C32C2×C4×SD1611yescharacteristic, complemented, Sylow
277C23—182no—
278C23—184no—
279C23—362no—
280C23—362no—
281C23C2×#63811yescharacteristic
282Q8—22no—
283Q8—24no—
284Q8C2×C4×C3⋊D314yescomplemented
285D4—94no—
286D4—182no—
287D4—184no—
288C2×C4—22no—
289C2×C4—24no—
290C2×C4—22no—
291C2×C4—22no—
292C2×C4—42no—
293C2×C4—182no—
294C2×C4—362no—
295C2×C4—368no—
296C2×C4#375514yesdirect product factor
297C2×C4C2×C4×C3⋊D312yes—
298C2×C4#382812yes—
299C2×C4C2×#63812yes—
300C2×C4C2×#63811yescharacteristic
301C2×C4C2×#63812yes—
302C2×C4C23×C3⋊D311yescharacteristic
303C8—94no—
304C8—182no—
305C2×C3C4×#215116yescomplemented
306C2×C3C2×C4×#6714yes—
307C2×C3C22×#21514yes—
308C2×C3C2×#95014yes—
309D3—1216no—
310C22—184no—
311C22—362no—
312C22—362no—
313C22—368no—
314C22C4×#63812yes—
315C22C2×#375512yes—
316C22#6415912yes—
317C22C22×#63811yescharacteristic
318C4—24no—
319C4—22no—
320C4—42no—
321C4—362no—
322C4C4×#63812yes—
323C4C2×#375514yesdirect product factor
324C4C22×C4×C3⋊D311yescharacteristic
325C4C2×#382811yescharacteristic
326C3C2×C4×#21514yescomplemented
327C2—364no—
328C2C4×#375514yesdirect product factor
329C2C2×C4×#63811yescharacteristic
330C2C22×#375511yescharacteristic
331C2C2×#6415911yescharacteristic
subgroupG/H
centerC22×C4#638
commutatorC32×C4C23×C4
FrattiniC2×C4C23×C3⋊D3
FittingC2×C32×C4×Q8C2
socleC23×C32C2×D4
prime radicalC22×C4⋊(C3⋊D3)C22
cosocleC2×C32×C4C24
hypercenterC2×C4×Q8C3⋊D3
hypocenterC32C2×C4×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C32×C4×Q8C2semidirect
4. C2×#63662C2semidirect
5. C4×#3755C2direct (N × H)
7. C2×#63635C2semidirect
8. C2×C4×C3⋊(C3⋊C8)C2semidirect
14. C32×C4×Q8C22semidirect
19. C2×#3755C4direct (N × H)
27. #63662C22semidirect
29. #63635C22semidirect
30. C4×C3⋊(C3⋊C8)C22semidirect
31. C2×C3×C4×Q8D3semidirect
42. C2×C32×Q8C2×C4semidirect
62. #3755C2×C4direct (N × H)
67. C2×C3⋊(C3⋊C8)C2×C4semidirect
75. C3×C4×Q8C2×D3semidirect
99. C32×Q8C22×C4semidirect
105. C2×C32×C4SD16semidirect
119. C3⋊(C3⋊C8)C22×C4semidirect
121. C2×C4×Q8C3⋊D3semidirect
131. C2×C3×Q8C4×D3semidirect
171. C32×C4C2×SD16semidirect
183. C4×Q8C2×C3⋊D3semidirect
203. C3×Q8C2×C4×D3semidirect
209. C2×C3×C4#215semidirect
224. C2×C32C4×SD16semidirect
232. C2×Q8C4×C3⋊D3semidirect
272. C3×C4C2×#215semidirect
276. C32C2×C4×SD16semidirect
284. Q8C2×C4×C3⋊D3semidirect
296. C2×C4#3755direct (N × H)
305. C2×C3C4×#215semidirect
323. C4C2×#3755direct (N × H)
326. C3C2×C4×#215semidirect
328. C2C4×#3755direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C32×C4×Q82
C22×#37552
C2×C4×C4⋊(C3⋊D3)2
C2×#636622
C4×#37552
C2×#636362
C2×#636352
C2×C4×C3⋊(C3⋊C8)2
C2×C4×#2153