Finite Group Databasebeta

← C2×#10589645 #11903223

Subgroups — C2×#10589645 #11903223

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×D4×C9C211yesmaximal, characteristic
2C2×D4×Dic9C212yesmaximal
3C22×C4⋊Dic9C212yesmaximal, complemented
4C2×#63486C212yesmaximal, complemented
5#10589645C2116yesmaximal, direct product factor
6C2×#63452C212yesmaximal, complemented
7C2×#63440C214yesmaximal, complemented
8C2×#63431C211yesmaximal, characteristic, complemented
9C2×C4×Dic18C211yesmaximal, characteristic, complemented
10C2×#5543—31nomaximal
11C22×D4×C9C2211yescharacteristic
12C23×C4×C9C2212yes—
13C23×Dic9C2214yes—
14C22×Dic18C2211yescharacteristic
15C22×Dic18C2212yes—
16C4×D4×C9C2218yes—
17C2×C9×C4⋊C4C2211yescharacteristic
18C2×C9×C22⋊C4C2212yes—
19C2×C42×C9C2211yescharacteristic
20C2×#3676C2214yes—
21D4×Dic9C22116yes—
22C2×C4⋊Dic9C2211yescharacteristic
23C2×C4⋊Dic9C2212yes—
24C2×C4⋊Dic9C2212yes—
25C2×C4⋊Dic9C2214yes—
26C2×C4⋊Dic9C22116yescomplemented
27#63486C22116yescomplemented
28C2×Dic9⋊C4C2212yes—
29C2×Dic9⋊C4C2214yes—
30C2×C4×Dic9C2212yes—
31#63452C22116yescomplemented
32#63440C22132yescomplemented
33#63431C2218yescomplemented
34C4×Dic18C2218yescomplemented
35C2×C3×C4×D4D311yescharacteristic
36C2×D4×Dic3—32no—
37C22×C4⋊Dic3—32no—
38C2×#924—32no—
39#5543—316no—
40C2×#890—32no—
41C2×#878—34no—
42C2×#869—31no—
43C2×C4×Dic6—31no—
44C24×C9C2312yes—
45C2×D4×C9Q818yescomplemented
46C2×D4×C9C2314yes—
47C22×C4×C9—28no—
48C22×C4×C9C2311yescharacteristic
49C22×C4×C9C2312yes—
50C22×C4×C9C2318yes—
51C22×C4×C9C2311yescharacteristic
52C22×C4×C9C2311yescharacteristic
53C22×Dic9—48no—
54C22×Dic9C2312yes—
55C22×Dic9C2314yes—
56C22×Dic9C2312yes—
57C22×Dic9C23116yes—
58C2×Dic18—24no—
59C2×Dic18—44no—
60C2×Dic18C2314yes—
61C2×Dic18C2318yes—
62C9×C4⋊C4C2314yes—
63C9×C22⋊C4C2318yes—
64C42×C9C2314yes—
65#3676C23116yes—
66C4⋊Dic9C2318yes—
67C4⋊Dic9C2314yes—
68C4⋊Dic9C2318yes—
69C4⋊Dic9C23116yes—
70Dic9⋊C4C2318yes—
71Dic9⋊C4C23116yes—
72C4×Dic9C2318yes—
73C2×#554—91noSylow
74C22×C3×D4C2×D311yescharacteristic
75C23×C3×C4C2×D312yes—
76C23×Dic3—34no—
77C22×Dic6—31no—
78C22×Dic6—32no—
79C3×C4×D4C2×D318yes—
80C2×C3×C4⋊C4C2×D311yescharacteristic
81C2×C3×C22⋊C4C2×D312yes—
82C2×C3×C42C2×D311yescharacteristic
83C2×#217—34no—
84D4×Dic3—316no—
85C2×C4⋊Dic3—31no—
86C2×C4⋊Dic3—32no—
87C2×C4⋊Dic3—32no—
88C2×C4⋊Dic3—34no—
89C2×C4⋊Dic3—316no—
90#924—316no—
91C2×Dic3⋊C4—32no—
92C2×Dic3⋊C4—34no—
93C2×C4×Dic3—32no—
94#890—316no—
95#878—332no—
96#869—38no—
97C4×Dic6—38no—
98C23×C9—24no—
99C23×C9—24no—
100C23×C9C2×Q818yes—
101C23×C9C2414yes—
102C23×C9C2411yescharacteristic
103D4×C9C2×Q8116yescomplemented
104C2×C4×C9—24no—
105C2×C4×C9—22no—
106C2×C4×C9—216no—
107C2×C4×C9C2×Q814yes—
108C2×C4×C9#4114yes—
109C2×C4×C9C2414yes—
110C2×C4×C9C2412yes—
111C2×C4×C9C2412yes—
112C2×C4×C9C2412yes—
113C2×Dic9—24no—
114C2×Dic9—28no—
115C2×Dic9—24no—
116C2×Dic9—416no—
117C2×Dic9C2414yes—
118C2×Dic9C2414yes—
119C2×Dic9C2418yes—
120Dic18—28no—
121Dic18—48no—
122#554—916no—
123C2×C4⋊Q8—91no—
124C2×#125—92no—
125C2×C22⋊Q8—92no—
126C2×C22⋊Q8—94no—
127C2×C4×Q8—91no—
128C2×C4×D4—92no—
129C2×C4×D4D911yescharacteristic
130C22×C4⋊C4—92no—
131C24×C3C22×D312yes—
132C2×C3×D4Dic618yes—
133C2×C3×D4C22×D314yes—
134C22×C3×C4—28no—
135C22×C3×C4C22×D312yes—
136C22×C3×C4C22×D311yescharacteristic
137C22×C3×C4C22×D318yes—
138C22×C3×C4C22×D311yescharacteristic
139C22×C3×C4C22×D311yescharacteristic
140C22×Dic3—32no—
141C22×Dic3—32no—
142C22×Dic3—34no—
143C22×Dic3—316no—
144C22×Dic3—128no—
145C2×Dic6—34no—
146C2×Dic6—38no—
147C2×Dic6—64no—
148C2×Dic6—124no—
149C3×C4⋊C4C22×D314yes—
150C3×C22⋊C4C22×D318yes—
151C3×C42C22×D314yes—
152#217—316no—
153C4⋊Dic3—34no—
154C4⋊Dic3—38no—
155C4⋊Dic3—38no—
156C4⋊Dic3—316no—
157Dic3⋊C4—38no—
158Dic3⋊C4—316no—
159C4×Dic3—38no—
160C22×C9—216no—
161C22×C9—24no—
162C22×C9—24no—
163C22×C9C22×Q818yes—
164C22×C9C22×Q812yes—
165C22×C9C2×#4112yes—
166C22×C9H(5,𝔽2)12yes—
167C22×C9C2511yescharacteristic
168C4×C9—24no—
169C4×C9—22no—
170C4×C9C22×Q814yes—
171C4×C9C2×#4114yes—
172Dic9—24no—
173Dic9—28no—
174Dic9—24no—
175C22×Q8—91no—
176C22×Q8—92no—
177C22×D4C2×D911yescharacteristic
178C23×C4—94no—
179C23×C4C2×D912yes—
180C4⋊Q8—98no—
181#125—916no—
182C22⋊Q8—916no—
183C22⋊Q8—932no—
184C4×Q8—98no—
185C4×D4—916no—
186C4×D4C2×D918yes—
187C2×C4⋊C4—91no—
188C2×C4⋊C4—94no—
189C2×C4⋊C4—92no—
190C2×C4⋊C4—916no—
191C2×C4⋊C4—92no—
192C2×C4⋊C4—92no—
193C2×C4⋊C4—94no—
194C2×C4⋊C4C2×D911yescharacteristic
195C2×C22⋊C4—94no—
196C2×C22⋊C4C2×D912yes—
197C2×C42—92no—
198C2×C42C2×D911yescharacteristic
199C23×C3—24no—
200C23×C3—24no—
201C23×C3C2×Dic618yes—
202C23×C3C23×D314yes—
203C23×C3C23×D311yescharacteristic
204C3×D4C2×Dic6116yes—
205C2×C3×C4—24no—
206C2×C3×C4—22no—
207C2×C3×C4—216no—
208C2×C3×C4C2×Dic614yes—
209C2×C3×C4#23714yes—
210C2×C3×C4C23×D314yes—
211C2×C3×C4C23×D312yes—
212C2×C3×C4C23×D312yes—
213C2×C3×C4C23×D312yes—
214C2×Dic3—34no—
215C2×Dic3—34no—
216C2×Dic3—38no—
217C2×Dic3—64no—
218C2×Dic3—68no—
219C2×Dic3—64no—
220C2×Dic3—1216no—
221Dic6—68no—
222Dic6—128no—
223C2×C9—28no—
224C2×C9#55414yescomplemented
225C2×C9C23×Q811yescharacteristic
226C2×C9C22×#4111yescharacteristic
227C2×C9C2×H(5,𝔽2)11yescharacteristic
228C24C22×D912yes—
229C2×Q8—94no—
230C2×Q8—98no—
231C2×Q8—184no—
232C2×Q8—364no—
233C2×D4Dic1818yescomplemented
234C2×D4C22×D914yes—
235C22×C4—28no—
236C22×C4—92no—
237C22×C4—92no—
238C22×C4—94no—
239C22×C4—916no—
240C22×C4—368no—
241C22×C4C22×D918yes—
242C22×C4C22×D911yescharacteristic
243C22×C4C22×D912yes—
244C22×C4C22×D911yescharacteristic
245C22×C4C22×D911yescharacteristic
246C4⋊C4—94no—
247C4⋊C4—916no—
248C4⋊C4—98no—
249C4⋊C4—98no—
250C4⋊C4—98no—
251C4⋊C4—916no—
252C4⋊C4C22×D914yes—
253C22⋊C4—916no—
254C22⋊C4C22×D918yes—
255C42—98no—
256C42C22×D914yes—
257C22×C3—24no—
258C22×C3—24no—
259C22×C3—216no—
260C22×C3C22×Dic618yes—
261C22×C3C22×Dic612yes—
262C22×C3C2×#23712yes—
263C22×C3#100912yes—
264C22×C3C24×D311yescharacteristic
265C3×C4—24no—
266C3×C4—22no—
267C3×C4C22×Dic614yes—
268C3×C4C2×#23714yes—
269Dic3—64no—
270Dic3—68no—
271Dic3—64no—
272C9C2×#55411yescharacteristic, complemented, Sylow
273C23—24no—
274C23—24no—
275C23C2×Dic1818yes—
276C23C23×D914yes—
277C23C23×D911yescharacteristic
278Q8—188no—
279Q8—368no—
280D4C2×Dic18116yescomplemented
281C2×C4—24no—
282C2×C4—22no—
283C2×C4—216no—
284C2×C4—94no—
285C2×C4—94no—
286C2×C4—98no—
287C2×C4—184no—
288C2×C4—184no—
289C2×C4—188no—
290C2×C4—3616no—
291C2×C4C2×Dic1814yes—
292C2×C4#369914yes—
293C2×C4C23×D912yes—
294C2×C4C23×D914yes—
295C2×C4C23×D912yes—
296C2×C4C23×D912yes—
297C2×C3—28no—
298C2×C3#554314yes—
299C2×C3C23×Dic611yescharacteristic
300C2×C3C22×#23711yescharacteristic
301C2×C3C2×#100911yescharacteristic
302C22—24no—
303C22—24no—
304C22—216no—
305C22C22×Dic1818yes—
306C22C22×Dic1812yes—
307C22C2×#369912yes—
308C22#6371512yes—
309C22C24×D911yescharacteristic
310C4—24no—
311C4—22no—
312C4—184no—
313C4—184no—
314C4—188no—
315C4C22×Dic1814yes—
316C4C2×#369914yes—
317C3C2×#554311yescharacteristic
318C2—28no—
319C2#1058964514yesdirect product factor
320C2C23×Dic1811yescharacteristic
321C2C22×#369911yescharacteristic
322C2C2×#6371511yescharacteristic
subgroupG/H
centerC23C23×D9
commutator, cosocleC22×C9C25
FrattiniC22×C3C24×D3
FittingC2×C4×D4×C9C2
socleC23×C3C23×D3
prime radicalC22×C3×D4C2×D3
hypercenterC2×C4×D4D9
hypocenterC9C2×#554
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C4×D4

Complements

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

NH ≅ G/Ntype
3. C22×C4⋊Dic9C2semidirect
4. C2×#63486C2semidirect
5. #10589645C2direct (N × H)
6. C2×#63452C2semidirect
7. C2×#63440C2semidirect
8. C2×#63431C2semidirect
9. C2×C4×Dic18C2semidirect
26. C2×C4⋊Dic9C22semidirect
27. #63486C22semidirect
31. #63452C22semidirect
32. #63440C22semidirect
33. #63431C22semidirect
34. C4×Dic18C22semidirect
45. C2×D4×C9Q8semidirect
103. D4×C9C2×Q8semidirect
224. C2×C9#554semidirect
233. C2×D4Dic18semidirect
272. C9C2×#554semidirect
280. D4C2×Dic18semidirect
319. C2#10589645direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C4×D4×C92
C2×D4×Dic92
C22×C4⋊Dic92
C2×#634862
#105896452
C2×#634522
C2×#634402
C2×#634312
C2×C4×Dic182
C2×#55433