Finite Group Databasebeta

← C2×#10588594 #11899544

Subgroups — C2×#10588594 #11899544

Order 1152.

600 conjugacy classes of subgroups; only the 142 normal subgroups are shown.

normal subgroups only

This group has 600 conjugacy classes of subgroups — too many to draw. Only its 142 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×#63481C211yesmaximal, characteristic, complemented
2C2×D8×D9C211yesmaximal, characteristic, complemented
3C2×C9×SD32C211yesmaximal, characteristic, complemented
4C2×#63387C211yesmaximal, characteristic, complemented
5C2×#63385C211yesmaximal, characteristic, complemented
6#10588594C218yesmaximal, direct product factor
7C2×D144C211yesmaximal, characteristic, complemented
8C2×#63357C211yesmaximal, characteristic, complemented
9C2×#4914—31nomaximal
10C2×#3701—21no—
11C2×D4×D9—21no—
12C2×C9×Q16C2211yescharacteristic, complemented
13C2×C9×D8C2211yescharacteristic
14C2×#3675—21no—
15C2×#3673—21no—
16#63481—22no—
17#63481C2214yescomplemented
18D8×D9—22no—
19D8×D9C2214yescomplemented
20C2×D72C2211yescharacteristic
21C2×D72C2211yescharacteristic, complemented
22C2×C8×D9C2211yescharacteristic
23C9×SD32C2214yescomplemented
24C2×C9×C16C2211yescharacteristic, complemented
25#63387C2214yescomplemented
26#63385C2214yescomplemented
27C2×C9⋊C16C2211yescharacteristic, complemented
28D144C2214yescomplemented
29#63357C2214yescomplemented
30C2×#919—31no—
31C2×D3×D8—31no—
32C2×C3×SD32D311yescharacteristic
33C2×#828—31no—
34C2×#826—31no—
35#4914—38no—
36C2×D48—31no—
37C2×#798—31no—
38C23×D9—41no—
39C2×Q8×C9—21no—
40C2×D4×C9—21no—
41C2×#611—41no—
42#3701—24no—
43#3701—42no—
44D4×D9—24no—
45D4×D9—42no—
46C2×D36—21no—
47C2×D36—21no—
48C2×D36—41no—
49C2×C4×D9—41no—
50C2×C4×D9D411yescharacteristic
51C9×Q16—21no—
52C9×Q16C2312yescomplemented
53C9×D8—21no—
54C9×D8C2312yes—
55C2×C8×C9C2311yescharacteristic
56#3675—24no—
57#3673—24no—
58C2×C9⋊C8D411yescharacteristic
59D72—21no—
60D72—21no—
61D72C2312yes—
62D72C2312yescomplemented
63C8×D9D412yes—
64C8×D9C2312yes—
65C9×C16C2312yescomplemented
66C9⋊C16C2312yescomplemented
67C2×#509—91noSylow
68C2×#239—61no—
69C2×D3×D4—61no—
70C2×C3×Q16C2×D311yescharacteristic
71C2×C3×D8C2×D311yescharacteristic
72C2×#215—61no—
73C2×#213—61no—
74#919—34no—
75#919—62no—
76D3×D8—34no—
77D3×D8—62no—
78C2×D24—31no—
79C2×D24—31no—
80C2×D3×C8—31no—
81C3×SD32C2×D314yes—
82C2×C3×C16C2×D311yescharacteristic
83#828—34no—
84#826—34no—
85C2×C3⋊C16—31no—
86D48—34no—
87#798—34no—
88C23×C9—41no—
89C22×D9—41no—
90C22×D9—41no—
91C22×D9—44no—
92C22×D9—84no—
93C22×D9D811yescharacteristic
94Q8×C9—22no—
95Q8×C9—41no—
96D4×C9—22no—
97D4×C9—41no—
98C2×C4×C9—41no—
99C2×C4×C9C2×D411yescharacteristic
100#611—44no—
101C2×Dic9D811yescharacteristic
102D36—22no—
103D36—22no—
104D36—44no—
105D36—41no—
106D36—41no—
107C4×D9—44no—
108C4×D9D812yes—
109C4×D9C2×D412yes—
110C8×C9C2×D411yescharacteristic
111C8×C9C2411yescharacteristic
112C9⋊C8C2×D412yes—
113C2×#135—91no—
114C22×D8—91no—
115#509—98no—
116C2×SD32—91no—
117C2×SD32D911yescharacteristic, complemented
118C2×D16—91no—
119C2×D16—91no—
120C2×M32—91no—
121C23×D3—121no—
122C2×C3×Q8—21no—
123C2×C3×D4—21no—
124C2×#67—121no—
125#239—64no—
126#239—122no—
127D3×D4—64no—
128D3×D4—122no—
129C2×D12—61no—
130C2×D12—61no—
131C2×D12—121no—
132C2×C4×D3—31no—
133C2×C4×D3—121no—
134C3×Q16—21no—
135C3×Q16C22×D312yes—
136C3×D8—21no—
137C3×D8C22×D312yes—
138C2×C3×C8C22×D311yescharacteristic
139#215—64no—
140#213—64no—
141C2×C3⋊C8—31no—
142D24—32no—
143D24—32no—
144D24—61no—
145D24—61no—
146D3×C8—32no—
147D3×C8—32no—
148C3×C16C22×D312yes—
149C3⋊C16—32no—
150C22×C9—42no—
151C22×C9—82no—
152C22×C9C2×D811yescharacteristic
153C2×D9—22no—
154C2×D9—42no—
155C2×D9—42no—
156C2×D9—88no—
157C2×D9—82no—
158C2×D9—82no—
159C2×D9C2×D812yes—
160C4×C9—42no—
161C4×C9C2×D811yescharacteristic
162C4×C9C22×D411yescharacteristic
163Dic9C2×D812yes—
164C2×#41—181no—
165C22×D4—181no—
166#135—94no—
167#135—182no—
168C2×Q16C2×D911yescharacteristic, complemented
169C2×SD16—181no—
170C2×D8—94no—
171C2×D8—91no—
172C2×D8—91no—
173C2×D8—182no—
174C2×D8—181no—
175C2×D8C2×D911yescharacteristic
176C22×C8—91no—
177SD32—94no—
178SD32C2×D914yescomplemented
179D16—94no—
180D16—94no—
181M32—94no—
182C2×C16—91no—
183C2×C16C2×D911yescharacteristic, complemented
184C23×C3—41no—
185C22×D3—31no—
186C22×D3—124no—
187C22×D3—121no—
188C22×D3—121no—
189C22×D3—244no—
190C3×Q8—22no—
191C3×Q8—41no—
192C3×D4—22no—
193C3×D4—41no—
194C2×C3×C4—41no—
195C2×C3×C4D3×D411yescharacteristic
196#67—124no—
197C2×Dic3—31no—
198D12—62no—
199D12—62no—
200D12—124no—
201D12—121no—
202D12—121no—
203C4×D3—32no—
204C4×D3—32no—
205C4×D3—124no—
206C3×C8D3×D411yescharacteristic
207C3×C8C23×D311yescharacteristic
208C3⋊C8—32no—
209C2×C9—82no—
210C2×C9#50912yescomplemented
211C2×C9C22×D811yescharacteristic
212D9—22no—
213D9—82no—
214D9—82no—
215C24—361no—
216#41—184no—
217#41—362no—
218C2×Q8—21no—
219C2×D4—21no—
220C2×D4—184no—
221C2×D4—181no—
222C2×D4—181no—
223C2×D4—361no—
224C2×D4—362no—
225C2×D4—361no—
226C22×C4—91no—
227C22×C4—361no—
228Q16—21no—
229Q16C22×D912yescomplemented
230SD16—184no—
231D8—21no—
232D8—92no—
233D8—92no—
234D8—184no—
235D8—181no—
236D8—181no—
237D8C22×D912yes—
238C2×C8—91no—
239C2×C8—92no—
240C2×C8—92no—
241C2×C8C22×D911yescharacteristic
242C16—92no—
243C16C22×D912yescomplemented
244C22×C3—42no—
245C22×C3—82no—
246C22×C3D3×D811yescharacteristic
247C2×D3—32no—
248C2×D3—62no—
249C2×D3—122no—
250C2×D3—122no—
251C2×D3—248no—
252C2×D3—242no—
253C2×D3—242no—
254C3×C4—42no—
255C3×C4D3×D811yescharacteristic
256C3×C4C2×D3×D411yescharacteristic
257Dic3—32no—
258C9C2×#50911yescharacteristic, complemented, Sylow
259C23—41no—
260C23—91no—
261C23—364no—
262C23—361no—
263C23—361no—
264C23—724no—
265Q8—22no—
266Q8—41no—
267D4—22no—
268D4—41no—
269D4—182no—
270D4—182no—
271D4—364no—
272D4—364no—
273D4—361no—
274D4—361no—
275C2×C4—41no—
276C2×C4—91no—
277C2×C4—92no—
278C2×C4—92no—
279C2×C4—364no—
280C2×C4D4×D911yescharacteristic
281C8—92no—
282C8D4×D911yescharacteristic
283C8C23×D911yescharacteristic
284C2×C3—82no—
285C2×C3#491412yes—
286C2×C3C2×D3×D811yescharacteristic
287D3—62no—
288D3—242no—
289D3—242no—
290C22—42no—
291C22—82no—
292C22—92no—
293C22—182no—
294C22—362no—
295C22—362no—
296C22—728no—
297C22—722no—
298C22—722no—
299C22D8×D911yescharacteristic
300C4—42no—
301C4—92no—
302C4D8×D911yescharacteristic
303C4C2×D4×D911yescharacteristic
304C3C2×#491411yescharacteristic
305C2—82no—
306C2—182no—
307C2—722no—
308C2—722no—
309C2#1058859412yesdirect product factor
310C2C2×D8×D911yescharacteristic
subgroupG/H
centerC22D8×D9
commutator, cosocleC8×C9C24
FrattiniC3×C8C23×D3
FittingC2×C9×SD32C2
socleC22×C3D3×D8
hypercenterC2×SD32D9
hypocenterC9C2×#509
LCSG ▷ C8×C9 ▷ C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×SD32

Complements

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

NH ≅ G/Ntype
1. C2×#63481C2semidirect
2. C2×D8×D9C2semidirect
3. C2×C9×SD32C2semidirect
4. C2×#63387C2semidirect
5. C2×#63385C2semidirect
6. #10588594C2direct (N × H)
7. C2×D144C2semidirect
8. C2×#63357C2semidirect
12. C2×C9×Q16C22semidirect
17. #63481C22semidirect
19. D8×D9C22semidirect
21. C2×D72C22semidirect
23. C9×SD32C22semidirect
24. C2×C9×C16C22semidirect
25. #63387C22semidirect
26. #63385C22semidirect
27. C2×C9⋊C16C22semidirect
28. D144C22semidirect
29. #63357C22semidirect
52. C9×Q16C23semidirect
62. D72C23semidirect
65. C9×C16C23semidirect
66. C9⋊C16C23semidirect
117. C2×SD32D9semidirect
168. C2×Q16C2×D9semidirect
178. SD32C2×D9semidirect
183. C2×C16C2×D9semidirect
210. C2×C9#509semidirect
229. Q16C22×D9semidirect
243. C16C22×D9semidirect
258. C9C2×#509semidirect
309. C2#10588594direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#634812
C2×D8×D92
C2×C9×SD322
C2×#633872
C2×#633852
#105885942
C2×D1442
C2×#633572
C2×#49143