Finite Group Databasebeta

← C22×#63513 #11918595

Subgroups — C22×#63513 #11918595

Order 1152.

2256 conjugacy classes of subgroups.

The subgroup lattice has 327 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×#41C211yesmaximal, characteristic, complemented
2C22×#3697C211yesmaximal, characteristic, complemented
3C2×#63513C2124yesmaximal, direct product factor
4C22×#3675C211yesmaximal, characteristic, complemented
5C22×#3674C211yesmaximal, characteristic, complemented
6C22×#3673C211yesmaximal, characteristic, complemented
7C22×#3672C211yesmaximal, characteristic, complemented
8C23×C9⋊C8C211yesmaximal, characteristic, complemented
9C22×#950—31nomaximal
10C2×C9×#41—26no—
11C2×C9×#41C22112yescomplemented
12C22×Q8×C9C2211yescharacteristic
13C22×D4×C9—21no—
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9—21no—
16C23×C4×C9C2211yescharacteristic
17C22×#611—21no—
18C2×#3697—26no—
19C2×#3697C22112yescomplemented
20C22×D36C2211yescharacteristic
21C22×C4×D9—21no—
22C22×Dic18C2211yescharacteristic
23#63513C22164yesdirect product factor
24C2×#3675C22112yescomplemented
25C2×#3674C22112yescomplemented
26C2×#3673C22112yescomplemented
27C2×#3672C22112yescomplemented
28C22×C9⋊C8C2211yescharacteristic
29C22×C9⋊C8C2211yescharacteristic
30C22×C9⋊C8C22112yescomplemented
31C22×C3×#41D311yescharacteristic
32C22×#235—31no—
33C2×#950—324no—
34C22×#216—31no—
35C22×#215—31no—
36C22×#214—31no—
37C22×#213—31no—
38C23×C3⋊C8—31no—
39C24×C9—21no—
40C24×C9D411yescharacteristic
41C23×D9—21no—
42C9×#41—224no—
43C9×#41C23116yescomplemented
44C2×Q8×C9—23no—
45C2×Q8×C9C2316yes—
46C2×D4×C9—212no—
47C2×D4×C9—23no—
48C2×D4×C9C2316yes—
49C22×C4×C9—21no—
50C22×C4×C9—212no—
51C22×C4×C9D411yescharacteristic
52C22×C4×C9D416yes—
53C22×C4×C9C2311yescharacteristic
54C22×C4×C9C2316yes—
55C2×#611—212no—
56C22×Dic9—21no—
57#3697—224no—
58#3697C23116yescomplemented
59C2×D36—23no—
60C2×D36C2316yes—
61C2×C4×D9—212no—
62C2×Dic18—23no—
63C2×Dic18C2316yes—
64#3675C23116yescomplemented
65#3674C23116yescomplemented
66#3673C23116yescomplemented
67#3672C23116yescomplemented
68C2×C9⋊C8C2316yes—
69C2×C9⋊C8C2316yes—
70C2×C9⋊C8C23116yescomplemented
71C22×#135—91noSylow
72C2×C3×#41—26no—
73C2×C3×#41C2×D3112yes—
74C22×C3×Q8C2×D311yescharacteristic
75C22×C3×D4—21no—
76C22×C3×D4C2×D311yescharacteristic
77C23×C3×C4—21no—
78C23×C3×C4C2×D311yescharacteristic
79C22×#67—61no—
80C2×#235—312no—
81C2×#235—66no—
82C22×D12—31no—
83C22×C4×D3—61no—
84C22×Dic6—31no—
85#950—364no—
86C2×#216—312no—
87C2×#215—312no—
88C2×#214—312no—
89C2×#213—312no—
90C22×C3⋊C8—31no—
91C22×C3⋊C8—31no—
92C22×C3⋊C8—312no—
93C23×C9—24no—
94C23×C9—26no—
95C23×C9—44no—
96C23×C9C2×D416yes—
97C23×C9C2×D411yescharacteristic
98C22×D9—26no—
99C22×D9—44no—
100Q8×C9—26no—
101Q8×C9C2414yes—
102D4×C9—216no—
103D4×C9—26no—
104D4×C9C2414yes—
105C2×C4×C9—26no—
106C2×C4×C9—216no—
107C2×C4×C9C2×D413yes—
108C2×C4×C9C2×D416yes—
109C2×C4×C9C2×D4112yes—
110C2×C4×C9C2413yes—
111C2×C4×C9C2414yes—
112#611—216no—
113C2×Dic9—26no—
114D36—26no—
115D36C2414yes—
116C4×D9—216no—
117Dic18—26no—
118Dic18C2414yes—
119C9⋊C8C2414yes—
120C9⋊C8C2414yes—
121C22×#41—91no—
122C22×#41D911yescharacteristic, complemented
123C2×#135—924no—
124C22×Q16—91no—
125C22×SD16—91no—
126C22×SD16—91no—
127C22×D8—91no—
128C23×C8—91no—
129C24×C3—21no—
130C24×C3#6711yescharacteristic
131C23×D3—61no—
132C3×#41—224no—
133C3×#41C22×D3116yes—
134C2×C3×Q8—23no—
135C2×C3×Q8C22×D316yes—
136C2×C3×D4—212no—
137C2×C3×D4—23no—
138C2×C3×D4C22×D316yes—
139C22×C3×C4—21no—
140C22×C3×C4—212no—
141C22×C3×C4#6716yes—
142C22×C3×C4#6711yescharacteristic
143C22×C3×C4C22×D311yescharacteristic
144C22×C3×C4C22×D316yes—
145C2×#67—612no—
146C22×Dic3—61no—
147#235—316no—
148#235—624no—
149C2×D12—36no—
150C2×D12—63no—
151C2×C4×D3—612no—
152C2×Dic6—36no—
153C2×Dic6—63no—
154#216—316no—
155#215—316no—
156#214—316no—
157#213—316no—
158C2×C3⋊C8—36no—
159C2×C3⋊C8—36no—
160C2×C3⋊C8—316no—
161C22×C9—212no—
162C22×C9—24no—
163C22×C9—412no—
164C22×C9#13514yescomplemented
165C22×C9C22×D414yes—
166C22×C9C22×D413yes—
167C2×D9—24no—
168C2×D9—412no—
169C4×C9—24no—
170C4×C9C22×D413yes—
171C4×C9C22×D414yes—
172C4×C9C2511yescharacteristic
173Dic9—24no—
174C2×#41—26no—
175C2×#41—912no—
176C2×#41—186no—
177C2×#41C2×D9112yescomplemented
178C22×Q8—91no—
179C22×Q8C2×D911yescharacteristic
180C22×D4—21no—
181C22×D4—91no—
182C22×D4—181no—
183C22×D4C2×D911yescharacteristic
184C23×C4—21no—
185C23×C4—181no—
186C23×C4C2×D911yescharacteristic
187#135—964no—
188C2×Q16—912no—
189C2×SD16—912no—
190C2×SD16—912no—
191C2×D8—912no—
192C22×C8—91no—
193C22×C8—91no—
194C22×C8—912no—
195C23×C3—24no—
196C23×C3—26no—
197C23×C3—44no—
198C23×C3C2×#6716yes—
199C23×C3C2×#6711yescharacteristic
200C22×D3—66no—
201C22×D3—124no—
202C3×Q8—26no—
203C3×Q8C23×D314yes—
204C3×D4—216no—
205C3×D4—26no—
206C3×D4C23×D314yes—
207C2×C3×C4—26no—
208C2×C3×C4—216no—
209C2×C3×C4C2×#6713yes—
210C2×C3×C4C2×#6716yes—
211C2×C3×C4C2×#67112yes—
212C2×C3×C4C23×D313yes—
213C2×C3×C4C23×D314yes—
214#67—616no—
215C2×Dic3—66no—
216D12—34no—
217D12—66no—
218C4×D3—616no—
219Dic6—34no—
220Dic6—66no—
221C3⋊C8—34no—
222C3⋊C8—34no—
223C2×C9—24no—
224C2×C9—44no—
225C2×C9C2×#13516yescomplemented
226C2×C9C23×D411yescharacteristic
227D9—44no—
228C24—21no—
229C24—181no—
230C24#61111yescharacteristic
231#41—224no—
232#41—916no—
233#41—1824no—
234#41C22×D9116yescomplemented
235C2×Q8—23no—
236C2×Q8—96no—
237C2×Q8—183no—
238C2×Q8C22×D916yes—
239C2×D4—212no—
240C2×D4—23no—
241C2×D4—96no—
242C2×D4—1812no—
243C2×D4—183no—
244C2×D4C22×D916yes—
245C22×C4—21no—
246C22×C4—212no—
247C22×C4—181no—
248C22×C4—1812no—
249C22×C4#61116yes—
250C22×C4#61111yescharacteristic
251C22×C4C22×D911yescharacteristic
252C22×C4C22×D916yes—
253Q16—916no—
254SD16—916no—
255SD16—916no—
256D8—916no—
257C2×C8—96no—
258C2×C8—96no—
259C2×C8—916no—
260C22×C3—212no—
261C22×C3—24no—
262C22×C3—412no—
263C22×C3#95014yes—
264C22×C3C22×#6714yes—
265C22×C3C22×#6713yes—
266C2×D3—64no—
267C2×D3—1212no—
268C3×C4—24no—
269C3×C4C22×#6713yes—
270C3×C4C22×#6714yes—
271C3×C4C24×D311yescharacteristic
272Dic3—64no—
273C9C22×#13511yescharacteristic, complemented, Sylow
274C23—24no—
275C23—26no—
276C23—44no—
277C23—186no—
278C23—364no—
279C23C2×#61116yes—
280C23C2×#61111yescharacteristic
281Q8—26no—
282Q8—94no—
283Q8—186no—
284Q8C23×D914yes—
285D4—216no—
286D4—26no—
287D4—94no—
288D4—1816no—
289D4—186no—
290D4C23×D914yes—
291C2×C4—26no—
292C2×C4—216no—
293C2×C4—186no—
294C2×C4—1816no—
295C2×C4C2×#61116yes—
296C2×C4C2×#61113yes—
297C2×C4C2×#611112yes—
298C2×C4C23×D913yes—
299C2×C4C23×D914yes—
300C8—94no—
301C8—94no—
302C2×C3—24no—
303C2×C3—44no—
304C2×C3C2×#95016yes—
305C2×C3C23×#6711yescharacteristic
306D3—124no—
307C22—212no—
308C22—24no—
309C22—412no—
310C22—184no—
311C22—3612no—
312C22#6351314yesdirect product factor
313C22C22×#61114yes—
314C22C22×#61113yes—
315C4—24no—
316C4—184no—
317C4C22×#61114yes—
318C4C22×#61113yes—
319C4C24×D911yescharacteristic
320C3C22×#95011yescharacteristic
321C2—24no—
322C2—44no—
323C2—364no—
324C2C2×#6351316yesdirect product factor
325C2C23×#61111yescharacteristic
subgroupG/H
centerC22×C4#611
commutator, cosocleC4×C9C25
FrattiniC3×C4C24×D3
FittingC22×C9×#41C2
socleC23×C3C2×#67
hypercenterC22×#41D9
hypocenterC9C22×#135
LCSG ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22×C4 ◁ C23×C4 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
1. C22×C9×#41C2semidirect
2. C22×#3697C2semidirect
3. C2×#63513C2direct (N × H)
4. C22×#3675C2semidirect
5. C22×#3674C2semidirect
6. C22×#3673C2semidirect
7. C22×#3672C2semidirect
8. C23×C9⋊C8C2semidirect
11. C2×C9×#41C22semidirect
19. C2×#3697C22semidirect
23. #63513C22direct (N × H)
24. C2×#3675C22semidirect
25. C2×#3674C22semidirect
26. C2×#3673C22semidirect
27. C2×#3672C22semidirect
30. C22×C9⋊C8C22semidirect
43. C9×#41C23semidirect
58. #3697C23semidirect
64. #3675C23semidirect
65. #3674C23semidirect
66. #3673C23semidirect
67. #3672C23semidirect
70. C2×C9⋊C8C23semidirect
122. C22×#41D9semidirect
164. C22×C9#135semidirect
177. C2×#41C2×D9semidirect
225. C2×C9C2×#135semidirect
234. #41C22×D9semidirect
273. C9C22×#135semidirect
312. C22#63513direct (N × H)
324. C2C2×#63513direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C9×#412
C22×#36972
C2×#635132
C22×#36752
C22×#36742
C22×#36732
C22×#36722
C23×C9⋊C82
C22×#9503