Finite Group Databasebeta

← #11804816

Subgroups — #11804816

Order 1152.

1392 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C9×#41C211yesmaximal, characteristic
2C2×D4×Dic9C212yesmaximal, complemented
3#10588909C212yesmaximal, complemented
4#10588900C214yesmaximal, complemented
5#10588892C211yesmaximal, characteristic, complemented
6#10588891C212yesmaximal, complemented
7C4×#3676C211yesmaximal, characteristic, complemented
8C2×C9⋊#95C212yesmaximal, complemented
9#84088—31nomaximal
10C2×C9×#41—28no—
11C2×C9×#41C418yescomplemented
12C22×Q8×C9C2211yescharacteristic
13C22×D4×C9C2212yes—
14C22×D4×C9C2211yescharacteristic
15C23×C4×C9C2212yes—
16C23×C4×C9C2211yescharacteristic
17C23×Dic9C2214yes—
18C2×#3676C2214yes—
19C2×#3676C2212yes—
20C2×#3676C2212yes—
21D4×Dic9—28no—
22C2×C4⋊Dic9C2212yes—
23C2×C4×Dic9C2212yes—
24C9⋊#95C2211yescharacteristic
25C9⋊#95C2212yes—
26C9⋊#95C2214yes—
27C9⋊#95C2211yescharacteristic
28C9⋊#95C2214yes—
29C22×C3×#41D311yescharacteristic
30C2×D4×Dic3—32no—
31#5229—32no—
32#5220—34no—
33#5212—31no—
34#5211—32no—
35C4×#217—31no—
36C2×C3⋊#95—32no—
37C24×C9C2311yescharacteristic
38C24×C9C2312yes—
39C9×#41—232no—
40C2×Q8×C9—24no—
41C2×Q8×C9C2×C414yescomplemented
42C2×D4×C9—28no—
43C2×D4×C9C2×C414yes—
44C2×D4×C9C2×C418yescomplemented
45C2×D4×C9D418yes—
46C22×C4×C9—28no—
47C22×C4×C9—24no—
48C22×C4×C9C2×C418yescomplemented
49C22×C4×C9C2×C414yescomplemented
50C22×C4×C9C2311yescharacteristic
51C22×C4×C9C2312yes—
52C22×C4×C9C2311yescharacteristic
53C22×Dic9—28no—
54C22×Dic9—28no—
55C22×Dic9—44no—
56C22×Dic9C2312yes—
57C22×Dic9C2314yes—
58C22×Dic9C2312yes—
59#3676—28no—
60#3676—24no—
61#3676—42no—
62C4⋊Dic9—24no—
63C4×Dic9—24no—
64#2339—91noSylow
65C2×C3×#41—28no—
66C2×C3×#41Dic318yes—
67C22×C3×Q8C2×D311yescharacteristic
68C22×C3×D4C2×D312yes—
69C22×C3×D4C2×D311yescharacteristic
70C23×C3×C4C2×D312yes—
71C23×C3×C4C2×D311yescharacteristic
72C23×Dic3—34no—
73C2×#217—32no—
74C2×#217—34no—
75C2×#217—32no—
76D4×Dic3—68no—
77C2×C4⋊Dic3—32no—
78C2×C4×Dic3—32no—
79C3⋊#95—31no—
80C3⋊#95—32no—
81C3⋊#95—34no—
82C3⋊#95—31no—
83C3⋊#95—34no—
84C23×C9—24no—
85C23×C9—22no—
86C23×C9—22no—
87C23×C9—22no—
88C23×C9—22no—
89C23×C9—21no—
90C23×C9—21no—
91C23×C9C22×C412yes—
92C23×C9C22×C414yes—
93C23×C9C2×D418yes—
94C23×C9C2411yescharacteristic
95Q8×C9—28no—
96D4×C9—216no—
97D4×C9C22⋊C4116yescomplemented
98C2×C4×C9—216no—
99C2×C4×C9—22no—
100C2×C4×C9—24no—
101C2×C4×C9—28no—
102C2×C4×C9C22×C412yes—
103C2×C4×C9C22×C414yes—
104C2×C4×C9C22×C412yes—
105C2×C4×C9C2×D414yes—
106C2×Dic9—22no—
107C2×Dic9—22no—
108C2×Dic9—22no—
109C2×Dic9—24no—
110C2×Dic9—22no—
111C2×Dic9—24no—
112C2×Dic9—24no—
113C2×Dic9—22no—
114C2×Dic9—416no—
115C2×Dic9#4114yescomplemented
116C22×#41D911yescharacteristic
117C2×C4×D4—92no—
118#391—92no—
119#386—94no—
120#381—92no—
121#380—91no—
122C4×C22⋊C4—91no—
123C2×#95—92no—
124C24×C3C22×D311yescharacteristic
125C24×C3C22×D312yes—
126C3×#41—232no—
127C2×C3×Q8—24no—
128C2×C3×Q8C2×Dic314yes—
129C2×C3×D4—28no—
130C2×C3×D4C2×Dic314yes—
131C2×C3×D4C2×Dic318yes—
132C2×C3×D4#6718yes—
133C22×C3×C4—28no—
134C22×C3×C4—24no—
135C22×C3×C4C2×Dic318yes—
136C22×C3×C4C2×Dic314yes—
137C22×C3×C4C22×D311yescharacteristic
138C22×C3×C4C22×D312yes—
139C22×C3×C4C22×D311yescharacteristic
140C22×Dic3—32no—
141C22×Dic3—32no—
142C22×Dic3—34no—
143C22×Dic3—68no—
144C22×Dic3—68no—
145C22×Dic3—124no—
146#217—64no—
147#217—68no—
148#217—122no—
149C4⋊Dic3—64no—
150C4×Dic3—64no—
151C22×C9—24no—
152C22×C9—24no—
153C22×C9—28no—
154C22×C9—28no—
155C22×C9—22no—
156C22×C9—22no—
157C22×C9—22no—
158C22×C9—42no—
159C22×C9—42no—
160C22×C9C2×C22⋊C418yes—
161C22×C9C23×C411yescharacteristic
162C22×C9C22×D412yes—
163C22×C9C2×#4112yes—
164C22×C9H(5,𝔽2)11yescharacteristic
165C22×C92−1+411yescharacteristic
166C4×C9—22no—
167C4×C9—24no—
168C4×C9C2×C22⋊C414yes—
169Dic9—24no—
170Dic9—44no—
171Dic9—42no—
172C2×#41—28no—
173C2×#41Dic918yescomplemented
174C22×Q8C2×D911yescharacteristic
175C22×D4C2×D912yes—
176C22×D4C2×D911yescharacteristic
177C23×C4—94no—
178C23×C4C2×D912yes—
179C23×C4C2×D911yescharacteristic
180C4×D4—188no—
181C2×C4⋊C4—92no—
182C2×C22⋊C4—94no—
183C2×C22⋊C4—92no—
184C2×C22⋊C4—92no—
185C2×C42—92no—
186#95—91no—
187#95—92no—
188#95—94no—
189#95—91no—
190#95—94no—
191C23×C3—24no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—22no—
195C23×C3—21no—
196C23×C3—21no—
197C23×C3—22no—
198C23×C3C22×Dic312yes—
199C23×C3C22×Dic314yes—
200C23×C3C2×#6718yes—
201C23×C3C23×D311yescharacteristic
202C3×Q8—28no—
203C3×D4—216no—
204C3×D4#217116yes—
205C2×C3×C4—216no—
206C2×C3×C4—22no—
207C2×C3×C4—24no—
208C2×C3×C4—28no—
209C2×C3×C4C22×Dic312yes—
210C2×C3×C4C22×Dic314yes—
211C2×C3×C4C22×Dic312yes—
212C2×C3×C4C2×#6714yes—
213C2×Dic3—34no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—64no—
218C2×Dic3—64no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—64no—
222C2×Dic3—1216no—
223C2×C9—28no—
224C2×C9—42no—
225C2×C9C22×C22⋊C411yescharacteristic
226C2×C9C4×#4111yescharacteristic
227C2×C9#52011yescharacteristic
228C2×C9#54612yes—
229C2×C9#54712yes—
230C24C22×D911yescharacteristic
231C24C22×D912yes—
232#41—232no—
233C2×Q8—24no—
234C2×Q8C2×Dic914yescomplemented
235C2×D4—28no—
236C2×D4C2×Dic914yes—
237C2×D4C2×Dic918yescomplemented
238C2×D4#61118yes—
239C22×C4—28no—
240C22×C4—24no—
241C22×C4—92no—
242C22×C4—92no—
243C22×C4—94no—
244C22×C4—188no—
245C22×C4—188no—
246C22×C4—364no—
247C22×C4C2×Dic918yescomplemented
248C22×C4C2×Dic914yescomplemented
249C22×C4C22×D911yescharacteristic
250C22×C4C22×D912yes—
251C22×C4C22×D911yescharacteristic
252C4⋊C4—184no—
253C22⋊C4—184no—
254C22⋊C4—188no—
255C22⋊C4—362no—
256C42—184no—
257C22×C3—28no—
258C22×C3—24no—
259C22×C3—24no—
260C22×C3—28no—
261C22×C3—22no—
262C22×C3—22no—
263C22×C3—22no—
264C22×C3—42no—
265C22×C3—42no—
266C22×C3C2×#21718yes—
267C22×C3D3×#4112yes—
268C22×C3#100911yescharacteristic
269C22×C3#101011yescharacteristic
270C22×C3C23×Dic311yescharacteristic
271C22×C3C22×#6712yes—
272C3×C4—22no—
273C3×C4—24no—
274C3×C4C2×#21714yes—
275Dic3—64no—
276Dic3—122no—
277Dic3—124no—
278C9#233911yescharacteristic, complemented, Sylow
279C23—24no—
280C23—22no—
281C23—22no—
282C23—22no—
283C23—21no—
284C23—21no—
285C23—22no—
286C23C22×Dic912yes—
287C23C22×Dic914yes—
288C23C2×#61118yes—
289C23C23×D911yescharacteristic
290Q8—28no—
291D4—216no—
292D4#3676116yescomplemented
293C2×C4—216no—
294C2×C4—22no—
295C2×C4—24no—
296C2×C4—28no—
297C2×C4—94no—
298C2×C4—182no—
299C2×C4—182no—
300C2×C4—182no—
301C2×C4—184no—
302C2×C4—184no—
303C2×C4—182no—
304C2×C4—182no—
305C2×C4—184no—
306C2×C4—3616no—
307C2×C4C22×Dic912yes—
308C2×C4C22×Dic914yes—
309C2×C4C22×Dic912yes—
310C2×C4C2×#61114yes—
311C2×C3—28no—
312C2×C3—42no—
313C2×C3#582412yes—
314C2×C3Dic3×#4111yescharacteristic
315C2×C3#582711yescharacteristic
316C2×C3#582912yes—
317C2×C3C22×#21711yescharacteristic
318C22—28no—
319C22—24no—
320C22—24no—
321C22—28no—
322C22—22no—
323C22—22no—
324C22—22no—
325C22—42no—
326C22—42no—
327C22C2×#367618yes—
328C22#41×D912yes—
329C22#6371511yescharacteristic
330C22#6371611yescharacteristic
331C22C23×Dic911yescharacteristic
332C22C22×#61112yes—
333C4—22no—
334C4—24no—
335C4—184no—
336C4—362no—
337C4—364no—
338C4C2×#367614yes—
339C3#8408811yescharacteristic
340C2—28no—
341C2—42no—
342C2#1058992612yes—
343C2#41×Dic911yescharacteristic
344C2#1058992911yescharacteristic
345C2#1058993112yes—
346C2C22×#367611yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC22×C9×#41C2
prime radicalC22×C3×#41D3
cosocleC23×C9C24
hypercenterC22×#41D9
hypocenterC9#2339
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C22×#41

Complements

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

NH ≅ G/Ntype
2. C2×D4×Dic9C2semidirect
3. #10588909C2semidirect
4. #10588900C2semidirect
5. #10588892C2semidirect
6. #10588891C2semidirect
7. C4×#3676C2semidirect
8. C2×C9⋊#95C2semidirect
11. C2×C9×#41C4semidirect
41. C2×Q8×C9C2×C4semidirect
44. C2×D4×C9C2×C4semidirect
48. C22×C4×C9C2×C4semidirect
49. C22×C4×C9C2×C4semidirect
97. D4×C9C22⋊C4semidirect
115. C2×Dic9#41semidirect
173. C2×#41Dic9semidirect
234. C2×Q8C2×Dic9semidirect
237. C2×D4C2×Dic9semidirect
247. C22×C4C2×Dic9semidirect
248. C22×C4C2×Dic9semidirect
278. C9#2339semidirect
292. D4#3676semidirect

Maximal subgroups

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

subgroupindex
C22×C9×#412
C2×D4×Dic92
#105889092
#105889002
#105888922
#105888912
C4×#36762
C2×C9⋊#952
#840883