Finite Group Databasebeta

← C2×#10594023 #11910194

Subgroups — C2×#10594023 #11910194

Order 1152.

2937 conjugacy classes of subgroups; only the 580 normal subgroups are shown.

normal subgroups only

This group has 2937 conjugacy classes of subgroups — too many to draw. Only its 580 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#64083C211yesmaximal, characteristic, complemented
2C2×C3×#876C212yesmaximal, complemented
3C2×#63923C213yesmaximal, complemented
4C2×#63910C216yesmaximal, complemented
5C2×#63897C213yesmaximal, complemented
6#10594023C2116yesmaximal, direct product factor
7C2×#5711—32nomaximal
8C23×D32C2211yescharacteristic
9C22×C4⋊(C3⋊D3)C2213yes—
10C22×C4⋊(C3⋊D3)C2213yescomplemented
11C22×#626C2216yes—
12C22×#624C2213yescomplemented
13C2×C32×C42C2211yescharacteristic, complemented
14#64083C2218yescomplemented
15C2×C3×(C2×D3)⋊C4C2216yes—
16C2×C3×Dic3⋊C4C2216yescomplemented
17C3×#876C22116yescomplemented
18C2×#3722C2213yes—
19C2×#3722C2213yescomplemented
20#63923C22124yescomplemented
21#63910C22148yescomplemented
22#63897C22124yescomplemented
23C2×C3×#126—32no—
24#5711—332no—
25C2×#895—36no—
26C2×#894—36no—
27C2×#884—36no—
28C2×#882—36no—
29C2×#876D312yescomplemented
30C2×#874—32no—
31C2×#874—61no—
32C23×C3⋊D3C2313yes—
33C23×C3⋊D3C2311yescharacteristic
34C23×C3×D3C2312yes—
35C22×D32—46no—
36C22×D32C2314yes—
37C22×C32×C4C2313yes—
38C2×C4⋊(C3⋊D3)—46no—
39C2×C4⋊(C3⋊D3)—46no—
40C2×C4⋊(C3⋊D3)C23112yes—
41C2×C4⋊(C3⋊D3)C23112yescomplemented
42C22×C3×Dic3C2316yes—
43C2×#626—412no—
44C2×#626C23124yes—
45C2×#624—46no—
46C2×#624C23112yescomplemented
47C32×C42C2314yescomplemented
48C3×(C2×D3)⋊C4C23124yes—
49C3×Dic3⋊C4C23124yescomplemented
50#3722C23112yes—
51#3722C23112yescomplemented
52C2×#560—91noSylow
53C24×D3—32no—
54C22×#67—36no—
55C22×D12—36no—
56C22×D12—36no—
57C22×D12—36no—
58C22×D12—63no—
59C22×D12—63no—
60C22×C4×D3—36no—
61C3×#126—316no—
62C2×C3×C4⋊C4—36no—
63C2×C3×C22⋊C4—36no—
64C2×C3×C42—21no—
65C2×C3×C42C2×D312yescomplemented
66C2×(C2×D3)⋊C4—36no—
67C2×(C2×D3)⋊C4—36no—
68C2×(C2×D3)⋊C4C2×D316yes—
69C2×Dic3⋊C4C2×D316yescomplemented
70#895—348no—
71#894—348no—
72#884—348no—
73#882—348no—
74#876C2×D3116yescomplemented
75#874—316no—
76#874—68no—
77C23×C32C2411yescharacteristic
78C22×C3⋊D3—26no—
79C22×C3⋊D3—26no—
80C22×C3⋊D3—212no—
81C22×C3⋊D3C2412yes—
82C22×C3⋊D3C2416yes—
83C22×C3×D3—212no—
84C22×C3×D3C2414yes—
85C2×D32—412no—
86C2×D32—416no—
87C2×C32×C4—26no—
88C2×C32×C4C2416yes—
89C4⋊(C3⋊D3)—412no—
90C4⋊(C3⋊D3)—412no—
91C2×C3×Dic3—212no—
92C2×C3×Dic3C24112yes—
93#626—424no—
94#624—412no—
95#560—916no—
96C2×#127—91no—
97C2×#126—32no—
98C2×#123—93no—
99C2×#121—96no—
100C2×#120—93no—
101C24×C3—32no—
102C23×D3—32no—
103C23×D3—36no—
104C23×D3—38no—
105C23×D3—61no—
106C23×D3—63no—
107C23×D3—1212no—
108C23×D3C22×D312yes—
109C22×C3×C4—23no—
110C22×C3×C4—36no—
111C22×C3×C4C22×D316yes—
112C2×#67—324no—
113C2×#67—1212no—
114C22×Dic3C22×D316yes—
115C2×D12—324no—
116C2×D12—324no—
117C2×D12—324no—
118C2×D12—612no—
119C2×D12—612no—
120C2×D12—1212no—
121C2×D12—1212no—
122C2×D12—1212no—
123C2×D12—1212no—
124C2×D12—1212no—
125C2×C4×D3—324no—
126C2×C4×D3—1212no—
127C3×C4⋊C4—324no—
128C3×C22⋊C4—324no—
129C3×C42—24no—
130C3×C42C22×D318yescomplemented
131(C2×D3)⋊C4—324no—
132(C2×D3)⋊C4—324no—
133(C2×D3)⋊C4C22×D3124yes—
134Dic3⋊C4C22×D3124yescomplemented
135C22×C32H(5,𝔽2)16yes—
136C22×C32C2511yescharacteristic
137C2×C3⋊D3—26no—
138C2×C3⋊D3—212no—
139C2×C3⋊D3—26no—
140C2×C3⋊D3—44no—
141C2×C3⋊D3—412no—
142C2×C3×D3—212no—
143C2×C3×D3—48no—
144D32—416no—
145C32×C4—26no—
146C3×Dic3—212no—
147C25—91no—
148C22×D4—96no—
149C22×D4—93no—
150C22×D4—93no—
151C23×C4—93no—
152#127—98no—
153#126—316no—
154#123—924no—
155#121—948no—
156#120—924no—
157C2×C4⋊C4—36no—
158C2×C22⋊C4—36no—
159C2×C22⋊C4—93no—
160C2×C22⋊C4—93no—
161C2×C42D3211yescharacteristic, complemented
162C23×C3—21no—
163C23×C3—34no—
164C23×C3—612no—
165C23×C3C23×D312yes—
166C22×D3—212no—
167C22×D3—34no—
168C22×D3—312no—
169C22×D3—62no—
170C22×D3—66no—
171C22×D3—612no—
172C22×D3—612no—
173C22×D3—612no—
174C22×D3—612no—
175C22×D3—126no—
176C22×D3—1212no—
177C22×D3—126no—
178C22×D3—1224no—
179C22×D3—1232no—
180C22×D3C23×D314yes—
181C2×C3×C4—212no—
182C2×C3×C4—212no—
183C2×C3×C4—26no—
184C2×C3×C4—312no—
185C2×C3×C4—612no—
186C2×C3×C4C23×D3112yes—
187#67—1224no—
188C2×Dic3—212no—
189C2×Dic3C23×D3112yes—
190D12—1224no—
191D12—1224no—
192D12—1224no—
193D12—1224no—
194D12—1224no—
195C4×D3—1224no—
196C2×C32#56014yescomplemented
197C2×C32C2×H(5,𝔽2)13yes—
198C3⋊D3—42no—
199C3⋊D3—46no—
200C3×D3—44no—
201C24—32no—
202C24—94no—
203C24—91no—
204C24—93no—
205C24—366no—
206C2×D4—924no—
207C2×D4—912no—
208C2×D4—912no—
209C2×D4—366no—
210C2×D4—366no—
211C2×D4—3612no—
212C22×C4—36no—
213C22×C4—912no—
214C22×C4—366no—
215C22×C4C2×D3213yes—
216C4⋊C4—324no—
217C22⋊C4—324no—
218C22⋊C4—912no—
219C22⋊C4—912no—
220C42C2×D3214yescomplemented
221C22×C3—26no—
222C22×C3—21no—
223C22×C3—612no—
224C22×C3—128no—
225C22×C3#1009112yes—
226C22×C3C24×D312yes—
227C2×D3—212no—
228C2×D3—48no—
229C2×D3—612no—
230C2×D3—612no—
231C2×D3—612no—
232C2×D3—612no—
233C2×D3—126no—
234C2×D3—1212no—
235C2×D3—126no—
236C2×D3—1232no—
237C2×D3—128no—
238C2×D3—1224no—
239C2×D3—244no—
240C2×D3—2412no—
241C3×C4—212no—
242C3×C4—212no—
243C3×C4—612no—
244Dic3—212no—
245C32C2×#56011yescharacteristic, complemented, Sylow
246C23—34no—
247C23—612no—
248C23—92no—
249C23—96no—
250C23—186no—
251C23—1812no—
252C23—186no—
253C23—3612no—
254C23—3616no—
255C23C22×D3211yescharacteristic
256D4—3612no—
257D4—3612no—
258D4—3624no—
259C2×C4—26no—
260C2×C4—312no—
261C2×C4—612no—
262C2×C4—3612no—
263C2×C4C22×D3216yes—
264C2×C3—23no—
265C2×C3—24no—
266C2×C3—124no—
267C2×C3#571118yescomplemented
268C2×C3C2×#100916yes—
269D3—44no—
270D3—124no—
271D3—1212no—
272D3—242no—
273D3—246no—
274C22—612no—
275C22—128no—
276C22—186no—
277C22—1812no—
278C22—186no—
279C22—3616no—
280C22—364no—
281C22—3612no—
282C22#6430816yes—
283C22C23×D3211yescharacteristic
284C4—26no—
285C4—612no—
286C3—21no—
287C3C2×#571112yescomplemented
288C2—124no—
289C2—362no—
290C2—366no—
291C2#1059402314yesdirect product factor
292C2C2×#6430813yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC2×C32×C42C22
socleC23×C32C24
hypercenterC2×C42D32
hypocenterC32C2×#560
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C2×C42

Complements

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

NH ≅ G/Ntype
1. C2×#64083C2semidirect
2. C2×C3×#876C2semidirect
3. C2×#63923C2semidirect
4. C2×#63910C2semidirect
5. C2×#63897C2semidirect
6. #10594023C2direct (N × H)
10. C22×C4⋊(C3⋊D3)C22semidirect
12. C22×#624C22semidirect
13. C2×C32×C42C22semidirect
14. #64083C22semidirect
16. C2×C3×Dic3⋊C4C22semidirect
17. C3×#876C22semidirect
19. C2×#3722C22semidirect
20. #63923C22semidirect
21. #63910C22semidirect
22. #63897C22semidirect
29. C2×#876D3semidirect
41. C2×C4⋊(C3⋊D3)C23semidirect
46. C2×#624C23semidirect
47. C32×C42C23semidirect
49. C3×Dic3⋊C4C23semidirect
51. #3722C23semidirect
65. C2×C3×C42C2×D3semidirect
69. C2×Dic3⋊C4C2×D3semidirect
74. #876C2×D3semidirect
130. C3×C42C22×D3semidirect
134. Dic3⋊C4C22×D3semidirect
161. C2×C42D32semidirect
196. C2×C32#560semidirect
220. C42C2×D32semidirect
245. C32C2×#560semidirect
267. C2×C3#5711semidirect
287. C3C2×#5711semidirect
291. C2#10594023direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#640832
C2×C3×#8762
C2×#639232
C2×#639102
C2×#638972
#105940232
C2×#57113