Finite Group Databasebeta

← C2×#10589681 #11903232

Subgroups — C2×#10589681 #11903232

Order 1152.

1800 conjugacy classes of subgroups.

The subgroup lattice has 324 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×C9C211yesmaximal, characteristic, complemented
2C2×#63508C212yesmaximal, complemented
3#10589681C2116yesmaximal, direct product factor
4C2×#63458C214yesmaximal, complemented
5C2×C4⋊C4×D9C212yesmaximal, complemented
6C2×C4×D36C211yesmaximal, characteristic
7C2×C4×D36C212yesmaximal
8C2×#63432C212yesmaximal, complemented
9C2×#63431C211yesmaximal, characteristic, complemented
10C2×#5579—31nomaximal
11C22×Q8×C9C2211yescharacteristic
12C22×D36C2211yescharacteristic
13C22×C4×D9C2212yes—
14C22×C4×D9C2214yes—
15C22×Dic18C2212yes—
16C4×Q8×C9C2218yescomplemented
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C4⋊C4C2212yes—
19C2×C42×C9C2211yescharacteristic
20C2×C42×C9C2212yes—
21#63508C22116yescomplemented
22C2×(C2×D9)⋊C4C2212yes—
23C2×(C2×D9)⋊C4C2214yes—
24C2×C4⋊Dic9C2212yes—
25C2×C4⋊Dic9C2212yes—
26C2×C4⋊Dic9C2211yescharacteristic
27C2×Dic9⋊C4C2214yes—
28C2×Dic9⋊C4C2214yes—
29#63458C22132yescomplemented
30C4⋊C4×D9C22116yescomplemented
31C4×D36C22116yes—
32C4×D36C2218yes—
33#63432C22116yescomplemented
34#63431C2218yescomplemented
35C2×C3×C4×Q8D311yescharacteristic
36C2×#946—32no—
37#5579—316no—
38C2×#896—34no—
39C2×D3×C4⋊C4—32no—
40C2×C4×D12—32no—
41C2×C4×D12—31no—
42C2×#870—32no—
43C2×#869—31no—
44C23×D9C2312yes—
45C2×Q8×C9—24no—
46C2×Q8×C9C2314yes—
47C22×C4×C9C2311yescharacteristic
48C22×C4×C9C2312yes—
49C22×C4×C9C2312yes—
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2311yescharacteristic
52C22×Dic9C2314yes—
53C22×Dic9C2312yes—
54C2×D36Q818yescomplemented
55C2×D36C2314yes—
56C2×C4×D9—28no—
57C2×C4×D9—48no—
58C2×C4×D9C2318yes—
59C2×C4×D9C23116yes—
60C2×Dic18—44no—
61C2×Dic18C2318yes—
62C9×C4⋊C4C2314yes—
63C9×C4⋊C4C2318yes—
64C42×C9C2314yes—
65C42×C9C2318yes—
66(C2×D9)⋊C4C23116yes—
67(C2×D9)⋊C4C2318yes—
68C4⋊Dic9C2318yes—
69C4⋊Dic9C2318yes—
70C4⋊Dic9C2314yes—
71Dic9⋊C4C23116yes—
72Dic9⋊C4C23116yes—
73C2×#554—91noSylow
74C22×C3×Q8C2×D311yescharacteristic
75C22×D12—31no—
76C22×C4×D3—32no—
77C22×C4×D3—34no—
78C22×Dic6—32no—
79C3×C4×Q8C2×D318yes—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C4⋊C4C2×D312yes—
82C2×C3×C42C2×D311yescharacteristic
83C2×C3×C42C2×D312yes—
84#946—316no—
85C2×(C2×D3)⋊C4—32no—
86C2×(C2×D3)⋊C4—34no—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—32no—
89C2×C4⋊Dic3—31no—
90C2×Dic3⋊C4—34no—
91C2×Dic3⋊C4—34no—
92#896—332no—
93D3×C4⋊C4—316no—
94C4×D12—316no—
95C4×D12—38no—
96#870—316no—
97#869—38no—
98C23×C9C2411yescharacteristic
99C22×D9—24no—
100C22×D9—24no—
101C22×D9C2×Q818yes—
102C22×D9C2414yes—
103Q8×C9—28no—
104C2×C4×C9—24no—
105C2×C4×C9—22no—
106C2×C4×C9—24no—
107C2×C4×C9C2×Q814yes—
108C2×C4×C9#4114yes—
109C2×C4×C9C2414yes—
110C2×C4×C9C2414yes—
111C2×C4×C9C2412yes—
112C2×C4×C9C2412yes—
113C2×C4×C9C2412yes—
114C2×Dic9—24no—
115C2×Dic9—28no—
116C2×Dic9C2414yes—
117C2×Dic9C2418yes—
118D36C2×Q8116yescomplemented
119C4×D9—216no—
120C4×D9—416no—
121Dic18—48no—
122#554—916no—
123C2×C4⋊Q8—91no—
124C2×#125—92no—
125C2×C22⋊Q8—92no—
126C2×C22⋊Q8—94no—
127C2×C4×Q8D911yescharacteristic, complemented
128C2×C4×D4—92no—
129C2×C4×D4—91no—
130C22×C4⋊C4—92no—
131C23×D3—32no—
132C2×C3×Q8—24no—
133C2×C3×Q8C22×D314yes—
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D312yes—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D311yescharacteristic
139C22×Dic3—32no—
140C22×Dic3—34no—
141C2×D12—38no—
142C2×D12—34no—
143C2×C4×D3—38no—
144C2×C4×D3—316no—
145C2×C4×D3—68no—
146C2×C4×D3—128no—
147C2×Dic6—38no—
148C2×Dic6—124no—
149C3×C4⋊C4C22×D314yes—
150C3×C4⋊C4C22×D318yes—
151C3×C42C22×D314yes—
152C3×C42C22×D318yes—
153(C2×D3)⋊C4—38no—
154(C2×D3)⋊C4—316no—
155C4⋊Dic3—38no—
156C4⋊Dic3—38no—
157C4⋊Dic3—34no—
158Dic3⋊C4—316no—
159Dic3⋊C4—316no—
160C22×C9C22×Q812yes—
161C22×C9C2×#4112yes—
162C22×C9H(5,𝔽2)12yes—
163C22×C9C2511yescharacteristic
164C2×D9—216no—
165C2×D9—24no—
166C2×D9—24no—
167C2×D9C22×Q818yes—
168C4×C9—24no—
169C4×C9—22no—
170C4×C9—24no—
171C4×C9C22×Q814yes—
172C4×C9C2×#4114yes—
173Dic9—24no—
174Dic9—28no—
175C22×Q8—92no—
176C22×Q8C2×D911yescharacteristic
177C22×D4—91no—
178C23×C4—92no—
179C23×C4—94no—
180C4⋊Q8—98no—
181#125—916no—
182C22⋊Q8—916no—
183C22⋊Q8—932no—
184C4×Q8C2×D918yescomplemented
185C4×D4—916no—
186C4×D4—98no—
187C2×C4⋊C4—94no—
188C2×C4⋊C4—92no—
189C2×C4⋊C4—91no—
190C2×C4⋊C4—92no—
191C2×C4⋊C4—94no—
192C2×C4⋊C4—916no—
193C2×C4⋊C4C2×D911yescharacteristic
194C2×C4⋊C4C2×D912yes—
195C2×C22⋊C4—92no—
196C2×C22⋊C4—94no—
197C2×C42C2×D912yes—
198C2×C42C2×D911yescharacteristic
199C23×C3C23×D311yescharacteristic
200C22×D3—38no—
201C22×D3—34no—
202C22×D3—64no—
203C22×D3—64no—
204C3×Q8—28no—
205C2×C3×C4—24no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4#23514yes—
209C2×C3×C4D3×Q814yes—
210C2×C3×C4C23×D314yes—
211C2×C3×C4C23×D314yes—
212C2×C3×C4C23×D312yes—
213C2×C3×C4C23×D312yes—
214C2×C3×C4C23×D312yes—
215C2×Dic3—34no—
216C2×Dic3—38no—
217C2×Dic3—64no—
218C2×Dic3—68no—
219D12—316no—
220C4×D3—616no—
221C4×D3—1216no—
222Dic6—128no—
223C2×C9#55414yescomplemented
224C2×C9C23×Q811yescharacteristic
225C2×C9C22×#4111yescharacteristic
226C2×C9C2×H(5,𝔽2)11yescharacteristic
227D9—28no—
228C24—92no—
229C2×Q8—24no—
230C2×Q8—98no—
231C2×Q8—364no—
232C2×Q8C22×D914yes—
233C2×D4—98no—
234C2×D4—94no—
235C22×C4—92no—
236C22×C4—94no—
237C22×C4—98no—
238C22×C4—916no—
239C22×C4—188no—
240C22×C4—368no—
241C22×C4C22×D912yes—
242C22×C4C22×D911yescharacteristic
243C22×C4C22×D912yes—
244C22×C4C22×D911yescharacteristic
245C22×C4C22×D911yescharacteristic
246C4⋊C4—916no—
247C4⋊C4—98no—
248C4⋊C4—94no—
249C4⋊C4—98no—
250C4⋊C4—916no—
251C4⋊C4C22×D914yes—
252C4⋊C4C22×D918yes—
253C22⋊C4—98no—
254C22⋊C4—916no—
255C42C22×D918yes—
256C42C22×D914yes—
257C22×C3C2×#23512yes—
258C22×C3C2×D3×Q812yes—
259C22×C3#100912yes—
260C22×C3C24×D311yescharacteristic
261C2×D3—38no—
262C2×D3—64no—
263C2×D3—64no—
264C2×D3—616no—
265C3×C4—24no—
266C3×C4—22no—
267C3×C4—24no—
268C3×C4C2×#23514yes—
269C3×C4C2×D3×Q814yes—
270Dic3—64no—
271Dic3—68no—
272C9C2×#55411yescharacteristic, complemented, Sylow
273C23—94no—
274C23—98no—
275C23—184no—
276C23—184no—
277C23C23×D911yescharacteristic
278Q8—28no—
279Q8—368no—
280D4—916no—
281C2×C4—24no—
282C2×C4—24no—
283C2×C4—22no—
284C2×C4—94no—
285C2×C4—98no—
286C2×C4—184no—
287C2×C4—188no—
288C2×C4—1816no—
289C2×C4—3616no—
290C2×C4#369714yes—
291C2×C4Q8×D914yes—
292C2×C4C23×D914yes—
293C2×C4C23×D912yes—
294C2×C4C23×D914yes—
295C2×C4C23×D912yes—
296C2×C4C23×D912yes—
297C2×C3#557914yes—
298C2×C3C22×#23511yescharacteristic
299C2×C3C22×D3×Q811yescharacteristic
300C2×C3C2×#100911yescharacteristic
301D3—68no—
302C22—98no—
303C22—184no—
304C22—184no—
305C22—1816no—
306C22C2×#369712yes—
307C22C2×Q8×D912yes—
308C22#6371512yes—
309C22C24×D911yescharacteristic
310C4—24no—
311C4—24no—
312C4—22no—
313C4—184no—
314C4—188no—
315C4C2×#369714yes—
316C4C2×Q8×D914yes—
317C3C2×#557911yescharacteristic
318C2—188no—
319C2#1058968114yesdirect product factor
320C2C22×#369711yescharacteristic
321C2C22×Q8×D911yescharacteristic
322C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×Q8×C9C2
socleC23×C3C23×D3
prime radicalC22×D36C22
hypercenterC2×C4×Q8D9
hypocenterC9C2×#554
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×Q8

Complements

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

NH ≅ G/Ntype
1. C2×C4×Q8×C9C2semidirect
2. C2×#63508C2semidirect
3. #10589681C2direct (N × H)
4. C2×#63458C2semidirect
5. C2×C4⋊C4×D9C2semidirect
8. C2×#63432C2semidirect
9. C2×#63431C2semidirect
16. C4×Q8×C9C22semidirect
21. #63508C22semidirect
29. #63458C22semidirect
30. C4⋊C4×D9C22semidirect
33. #63432C22semidirect
34. #63431C22semidirect
54. C2×D36Q8semidirect
118. D36C2×Q8semidirect
127. C2×C4×Q8D9semidirect
184. C4×Q8C2×D9semidirect
223. C2×C9#554semidirect
272. C9C2×#554semidirect
319. C2#10589681direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×Q8×C92
C2×#635082
#105896812
C2×#634582
C2×C4⋊C4×D92
C2×C4×D362
C2×#634322
C2×#634312
C2×#55793