Finite Group Databasebeta

← C2×#10595529 #11910219

Subgroups — C2×#10595529 #11910219

Order 1152.

3147 conjugacy classes of subgroups; only the 580 normal subgroups are shown.

normal subgroups only

This group has 3147 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×#64162C211yesmaximal, characteristic, complemented
2C2×C3×#953C212yesmaximal, complemented
3#10595529C2116yesmaximal, direct product factor
4C2×#63983C213yesmaximal, complemented
5C2×#63959C216yesmaximal, complemented
6C2×#63953C213yesmaximal, complemented
7C2×#5594—32nomaximal
8C25×C32C2211yescharacteristic, complemented
9C23×D32C2211yescharacteristic, complemented
10C22×#638C2213yes—
11C22×C3×#67C2216yes—
12C22×#627C2213yescomplemented
13#64162C2218yescomplemented
14C2×#3757C2213yescomplemented
15C3×#953C22116yescomplemented
16C2×C3×#217C2216yescomplemented
17#63983C22124yescomplemented
18C2×#3722C2213yescomplemented
19C2×(C2×D3)⋊Dic3C2216yescomplemented
20#63959C22148yescomplemented
21C2×Dic32C2213yescomplemented
22#63953C22124yescomplemented
23C2×C3×#120—32no—
24C2×#953—32no—
25C2×#953—61no—
26C2×#953D312yescomplemented
27C2×#937—36no—
28C2×#936—36no—
29#5594—332no—
30C2×#885—36no—
31C2×#885—36no—
32C24×C32—46no—
33C24×C32C2313yes—
34C24×C32C2314yescomplemented
35C23×C3⋊D3C2311yescharacteristic
36C23×C3×D3C2312yes—
37C22×D32—46no—
38C22×D32C2314yescomplemented
39C2×#638—46no—
40C2×#638C23112yes—
41C22×C3⋊Dic3C2313yes—
42C2×C3×#67—412no—
43C2×C3×#67C23124yes—
44C22×C3×Dic3C2316yes—
45C2×#627—46no—
46C2×#627C23112yescomplemented
47#3757C23112yescomplemented
48C3×#217C23124yescomplemented
49#3722C23112yescomplemented
50(C2×D3)⋊Dic3C23124yescomplemented
51Dic32C23112yescomplemented
52C2×H(3,𝔽4)—91noSylow
53C25×C3—21no—
54C25×C3C2×D312yescomplemented
55C24×D3—32no—
56C22×C3×D4—36no—
57C22×#67—36no—
58C22×#67—63no—
59C22×#67C2×D316yes—
60C22×Dic6—36no—
61C3×#120—316no—
62C2×C3×C22⋊C4—36no—
63#953—316no—
64#953—68no—
65#953C2×D3116yescomplemented
66C2×#217—36no—
67C2×#217—36no—
68C2×#217—63no—
69C2×#217C2×D316yescomplemented
70#937—348no—
71#936—348no—
72C2×(C2×D3)⋊C4—36no—
73C2×(C2×D3)⋊C4—36no—
74C2×C4×Dic3—36no—
75#885—348no—
76#885—348no—
77C23×C32—26no—
78C23×C32—212no—
79C23×C32—412no—
80C23×C32—416no—
81C23×C32C2416yes—
82C23×C32C2411yescharacteristic
83C22×C3⋊D3—26no—
84C22×C3⋊D3C2412yes—
85C22×C3×D3—212no—
86C22×C3×D3C2414yes—
87C2×D32—412no—
88C2×D32—416no—
89#638—412no—
90C2×C3⋊Dic3—26no—
91C2×C3⋊Dic3C2416yes—
92C3×#67—424no—
93C2×C3×Dic3—212no—
94C2×C3×Dic3C24112yes—
95#627—412no—
96H(3,𝔽4)—916no—
97C2×#124—93no—
98C2×#124—96no—
99C2×#120—32no—
100C2×#120—93no—
101C2×#120—91no—
102C24×C3—23no—
103C24×C3—24no—
104C24×C3—32no—
105C24×C3—412no—
106C24×C3—412no—
107C24×C3C22×D316yes—
108C24×C3C22×D318yescomplemented
109C23×D3—32no—
110C23×D3—38no—
111C23×D3—61no—
112C23×D3—1212no—
113C23×D3C22×D312yes—
114C2×C3×D4—324no—
115C2×C3×D4—1212no—
116C22×C3×C4—36no—
117C2×#67—324no—
118C2×#67—412no—
119C2×#67—612no—
120C2×#67—1212no—
121C2×#67—1212no—
122C2×#67C22×D3124yes—
123C22×Dic3—36no—
124C22×Dic3—63no—
125C22×Dic3C22×D316yes—
126C2×Dic6—324no—
127C2×Dic6—1212no—
128C3×C22⋊C4—324no—
129#217—324no—
130#217—324no—
131#217—612no—
132#217C22×D3124yescomplemented
133(C2×D3)⋊C4—324no—
134(C2×D3)⋊C4—324no—
135C4×Dic3—324no—
136C22×C32—26no—
137C22×C32—212no—
138C22×C32—416no—
139C22×C32—412no—
140C22×C32H(5,𝔽2)16yes—
141C22×C32C2511yescharacteristic
142C2×C3⋊D3—26no—
143C2×C3⋊D3—44no—
144C2×C3×D3—212no—
145C2×C3×D3—48no—
146D32—416no—
147C3⋊Dic3—26no—
148C3×Dic3—212no—
149C25—91no—
150C25D3211yescharacteristic, complemented
151C22×Q8—93no—
152C22×D4—36no—
153C22×D4—93no—
154#124—924no—
155#124—948no—
156#120—316no—
157#120—924no—
158#120—98no—
159C2×C22⋊C4—36no—
160C2×C22⋊C4—93no—
161C2×C22⋊C4—96no—
162C2×C22⋊C4—93no—
163C2×C42—93no—
164C23×C3—212no—
165C23×C3—212no—
166C23×C3—212no—
167C23×C3—212no—
168C23×C3—26no—
169C23×C3—21no—
170C23×C3—34no—
171C23×C3—412no—
172C23×C3—424no—
173C23×C3—424no—
174C23×C3—432no—
175C23×C3—432no—
176C23×C3—612no—
177C23×C3C23×D3112yes—
178C23×C3C23×D312yes—
179C22×D3—212no—
180C22×D3—34no—
181C22×D3—62no—
182C22×D3—612no—
183C22×D3—126no—
184C22×D3—1224no—
185C22×D3—1232no—
186C22×D3C23×D314yes—
187C3×D4—1224no—
188C2×C3×C4—312no—
189C2×C3×C4—612no—
190#67—424no—
191#67—1224no—
192#67—1224no—
193C2×Dic3—212no—
194C2×Dic3—312no—
195C2×Dic3—66no—
196C2×Dic3—612no—
197C2×Dic3—126no—
198C2×Dic3C23×D3112yes—
199Dic6—1224no—
200C2×C32—46no—
201C2×C32H(3,𝔽4)14yescomplemented
202C2×C32C2×H(5,𝔽2)13yes—
203C3⋊D3—42no—
204C3×D3—44no—
205C24—32no—
206C24—46no—
207C24—94no—
208C24—91no—
209C24—366no—
210C24C2×D3213yes—
211C24C2×D3214yescomplemented
212C2×Q8—912no—
213C2×Q8—366no—
214C2×D4—324no—
215C2×D4—912no—
216C2×D4—1212no—
217C2×D4—366no—
218C22×C4—36no—
219C22×C4—93no—
220C22⋊C4—324no—
221C22⋊C4—912no—
222C22⋊C4—924no—
223C22⋊C4—912no—
224C42—912no—
225C22×C3—212no—
226C22×C3—212no—
227C22×C3—212no—
228C22×C3—212no—
229C22×C3—26no—
230C22×C3—21no—
231C22×C3—412no—
232C22×C3—424no—
233C22×C3—432no—
234C22×C3—432no—
235C22×C3—424no—
236C22×C3—612no—
237C22×C3—128no—
238C22×C3#1004112yes—
239C22×C3C24×D312yes—
240C2×D3—212no—
241C2×D3—48no—
242C2×D3—612no—
243C2×D3—126no—
244C2×D3—1232no—
245C2×D3—128no—
246C2×D3—244no—
247C3×C4—612no—
248Dic3—212no—
249Dic3—612no—
250Dic3—126no—
251C32C2×H(3,𝔽4)11yescharacteristic, complemented, Sylow
252C23—212no—
253C23—26no—
254C23—34no—
255C23—412no—
256C23—416no—
257C23—612no—
258C23—92no—
259C23—186no—
260C23—3612no—
261C23—3616no—
262C23C22×D3216yes—
263C23C22×D3211yescharacteristic
264Q8—3612no—
265D4—1224no—
266D4—3612no—
267C2×C4—312no—
268C2×C4—612no—
269C2×C4—96no—
270C2×C4—186no—
271C2×C3—23no—
272C2×C3—24no—
273C2×C3—412no—
274C2×C3—412no—
275C2×C3—124no—
276C2×C3#559418yescomplemented
277C2×C3C2×#100416yes—
278D3—44no—
279D3—124no—
280D3—242no—
281C22—212no—
282C22—26no—
283C22—416no—
284C22—412no—
285C22—612no—
286C22—128no—
287C22—186no—
288C22—3616no—
289C22—364no—
290C22#6433016yes—
291C22C23×D3211yescharacteristic
292C4—612no—
293C4—186no—
294C3—21no—
295C3C2×#559412yescomplemented
296C2—46no—
297C2—124no—
298C2—362no—
299C2#1059552914yesdirect product factor
300C2C2×#6433013yes—
subgroupG/H
centerC23C22×D32
commutator, cosocleC22×C32C25
FrattiniC22C23×D32
FittingC25×C32C22
socleC23×C32C24
hypercenterC25D32
hypocenterC32C2×H(3,𝔽4)
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C23 ◁ C25

Complements

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

NH ≅ G/Ntype
1. C2×#64162C2semidirect
2. C2×C3×#953C2semidirect
3. #10595529C2direct (N × H)
4. C2×#63983C2semidirect
5. C2×#63959C2semidirect
6. C2×#63953C2semidirect
8. C25×C32C22semidirect
9. C23×D32C22semidirect
12. C22×#627C22semidirect
13. #64162C22semidirect
14. C2×#3757C22semidirect
15. C3×#953C22semidirect
16. C2×C3×#217C22semidirect
17. #63983C22semidirect
18. C2×#3722C22semidirect
19. C2×(C2×D3)⋊Dic3C22semidirect
20. #63959C22semidirect
21. C2×Dic32C22semidirect
22. #63953C22semidirect
26. C2×#953D3semidirect
34. C24×C32C23semidirect
38. C22×D32C23semidirect
46. C2×#627C23semidirect
47. #3757C23semidirect
48. C3×#217C23semidirect
49. #3722C23semidirect
50. (C2×D3)⋊Dic3C23semidirect
51. Dic32C23semidirect
54. C25×C3C2×D3semidirect
65. #953C2×D3semidirect
69. C2×#217C2×D3semidirect
108. C24×C3C22×D3semidirect
132. #217C22×D3semidirect
150. C25D32semidirect
201. C2×C32H(3,𝔽4)semidirect
211. C24C2×D32semidirect
251. C32C2×H(3,𝔽4)semidirect
276. C2×C3#5594semidirect
295. C3C2×#5594semidirect
299. C2#10595529direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#641622
C2×C3×#9532
#105955292
C2×#639832
C2×#639592
C2×#639532
C2×#55943