Finite Group Databasebeta

← #11807804

Subgroups — #11807804

Order 1152.

696 conjugacy classes of subgroups.

The subgroup lattice has 333 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C9×C22⋊Q8C211yesmaximal, characteristic
2#10588909C212yesmaximal, complemented
3#10588892C211yesmaximal, characteristic
4#10588891C211yesmaximal, characteristic
5#10588664C212yesmaximal, complemented
6#10588660C212yesmaximal, complemented
7#10588660C212yesmaximal, complemented
8#10588631C212yesmaximal
9#10588631C212yesmaximal
10#82750—31nomaximal
11C22×Q8×C9C2211yescharacteristic
12C23×C4×C9C2211yescharacteristic
13C9×C22⋊Q8C418yescomplemented
14C2×C9×C4⋊C4C2211yescharacteristic
15C2×C9×C4⋊C4C2212yes—
16C2×C9×C22⋊C4C2212yes—
17C2×#3676C2212yes—
18C2×#3676C2211yescharacteristic
19C2×#3676C2211yescharacteristic
20C2×C4⋊Dic9C2212yes—
21C2×C4⋊Dic9C2212yes—
22C2×C4⋊Dic9C2212yes—
23C2×C4×Dic9C2212yes—
24C2×C4×Dic9C2212yes—
25C9⋊#95C2212yes—
26C9⋊#95C2212yes—
27C9⋊#95C2212yes—
28C9⋊#95C2212yes—
29C9⋊#95C2212yes—
30C9⋊#95C2211yescharacteristic
31C9⋊#95C2211yescharacteristic
32C9⋊#95C2212yes—
33C2×C3×C22⋊Q8D311yescharacteristic
34#5229—32no—
35#5212—31no—
36#5211—31no—
37#4984—32no—
38#4980—32no—
39#4980—32no—
40#4951—32no—
41#4951—32no—
42C24×C9C2311yescharacteristic
43C2×Q8×C9—42no—
44C2×Q8×C9C2×C414yes—
45C22×C4×C9—42no—
46C22×C4×C9C2×C414yes—
47C22×C4×C9C2312yes—
48C22×C4×C9C2312yes—
49C22×C4×C9C2311yescharacteristic
50C22×C4×C9C2311yescharacteristic
51C22×Dic9C2312yes—
52C22×Dic9C2312yes—
53C22×Dic9C2312yes—
54C22×Dic9C2312yes—
55C9×C4⋊C4C2×C414yes—
56C9×C4⋊C4C2×C418yes—
57C9×C22⋊C4C2×C418yes—
58#3676—41no—
59#3676—42no—
60#3676—41no—
61C4⋊Dic9—42no—
62C4⋊Dic9—42no—
63C4⋊Dic9—42no—
64C4×Dic9—42no—
65C4×Dic9—42no—
66#2378—91noSylow
67C22×C3×Q8C2×D311yescharacteristic
68C23×C3×C4C2×D311yescharacteristic
69C3×C22⋊Q8Dic318yes—
70C2×C3×C4⋊C4C2×D311yescharacteristic
71C2×C3×C4⋊C4C2×D312yes—
72C2×C3×C22⋊C4C2×D312yes—
73C2×#217—32no—
74C2×#217—31no—
75C2×#217—31no—
76C2×C4⋊Dic3—32no—
77C2×C4⋊Dic3—32no—
78C2×C4⋊Dic3—32no—
79C2×C4×Dic3—32no—
80C2×C4×Dic3—32no—
81C3⋊#95—32no—
82C3⋊#95—32no—
83C3⋊#95—32no—
84C3⋊#95—32no—
85C3⋊#95—32no—
86C3⋊#95—31no—
87C3⋊#95—31no—
88C3⋊#95—32no—
89C23×C9—21no—
90C23×C9—22no—
91C23×C9—22no—
92C23×C9—21no—
93C23×C9C22×C412yes—
94C23×C9C2411yescharacteristic
95Q8×C9—44no—
96C2×C4×C9—22no—
97C2×C4×C9—22no—
98C2×C4×C9—22no—
99C2×C4×C9—22no—
100C2×C4×C9—22no—
101C2×C4×C9—22no—
102C2×C4×C9—44no—
103C2×C4×C9C22×C414yes—
104C2×C4×C9C22×C414yes—
105C2×C4×C9C22×C412yes—
106C2×C4×C9C22×C412yes—
107C2×Dic9—22no—
108C2×Dic9—22no—
109C2×Dic9—22no—
110C2×Dic9—22no—
111C2×Dic9—22no—
112C2×Dic9—22no—
113C2×Dic9—22no—
114C2×Dic9—22no—
115C2×Dic9—22no—
116C2×Dic9—22no—
117C2×Dic9—22no—
118C2×Dic9—22no—
119C2×C22⋊Q8D911yescharacteristic
120#391—92no—
121#389—92no—
122#388—92no—
123#388—92no—
124#387—92no—
125#387—92no—
126#381—91no—
127#380—91no—
128C24×C3C22×D311yescharacteristic
129C2×C3×Q8—42no—
130C2×C3×Q8C2×Dic314yes—
131C22×C3×C4—42no—
132C22×C3×C4C2×Dic314yes—
133C22×C3×C4C22×D311yescharacteristic
134C22×C3×C4C22×D312yes—
135C22×C3×C4C22×D312yes—
136C22×C3×C4C22×D311yescharacteristic
137C22×Dic3—32no—
138C22×Dic3—32no—
139C22×Dic3—32no—
140C22×Dic3—32no—
141C3×C4⋊C4C2×Dic314yes—
142C3×C4⋊C4C2×Dic318yes—
143C3×C22⋊C4C2×Dic318yes—
144#217—122no—
145#217—121no—
146#217—121no—
147C4⋊Dic3—122no—
148C4⋊Dic3—122no—
149C4⋊Dic3—122no—
150C4×Dic3—122no—
151C4×Dic3—122no—
152C22×C9—22no—
153C22×C9—22no—
154C22×C9—22no—
155C22×C9—42no—
156C22×C9—42no—
157C22×C9C23×C411yescharacteristic
158C22×C9H(5,𝔽2)12yes—
159C22×C9H(5,𝔽2)11yescharacteristic
160C22×C92−1+412yes—
161C22×C92−1+411yescharacteristic
162C4×C9—22no—
163C4×C9—22no—
164C4×C9—24no—
165C4×C9—24no—
166Dic9—42no—
167Dic9—42no—
168Dic9—42no—
169Dic9—42no—
170C22×Q8C2×D911yescharacteristic
171C23×C4C2×D911yescharacteristic
172C22⋊Q8Dic918yescomplemented
173C2×C4⋊C4—92no—
174C2×C4⋊C4—92no—
175C2×C4⋊C4—92no—
176C2×C4⋊C4C2×D911yescharacteristic
177C2×C4⋊C4C2×D912yes—
178C2×C22⋊C4—91no—
179C2×C22⋊C4—91no—
180C2×C22⋊C4—92no—
181C2×C22⋊C4C2×D912yes—
182C2×C42—92no—
183C2×C42—92no—
184#95—92no—
185#95—91no—
186#95—92no—
187#95—91no—
188#95—92no—
189#95—92no—
190#95—92no—
191#95—92no—
192C23×C3—22no—
193C23×C3—22no—
194C23×C3—21no—
195C23×C3—21no—
196C23×C3C22×Dic312yes—
197C23×C3C23×D311yescharacteristic
198C3×Q8—44no—
199C2×C3×C4—22no—
200C2×C3×C4—22no—
201C2×C3×C4—22no—
202C2×C3×C4—22no—
203C2×C3×C4—22no—
204C2×C3×C4—22no—
205C2×C3×C4—44no—
206C2×C3×C4C22×Dic314yes—
207C2×C3×C4C22×Dic314yes—
208C2×C3×C4C22×Dic312yes—
209C2×C3×C4C22×Dic312yes—
210C2×Dic3—62no—
211C2×Dic3—62no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214C2×Dic3—62no—
215C2×Dic3—62no—
216C2×Dic3—62no—
217C2×Dic3—62no—
218C2×Dic3—62no—
219C2×Dic3—62no—
220C2×Dic3—62no—
221C2×Dic3—62no—
222C2×C9—42no—
223C2×C9#51811yescharacteristic
224C2×C9#51911yescharacteristic
225C2×C9#52011yescharacteristic
226C2×C9#56212yes—
227C2×C9#56312yes—
228C24C22×D911yescharacteristic
229C2×Q8—42no—
230C2×Q8C2×Dic914yes—
231C22×C4—42no—
232C22×C4—92no—
233C22×C4—92no—
234C22×C4—92no—
235C22×C4—92no—
236C22×C4C2×Dic914yes—
237C22×C4C22×D911yescharacteristic
238C22×C4C22×D912yes—
239C22×C4C22×D912yes—
240C22×C4C22×D911yescharacteristic
241C4⋊C4—362no—
242C4⋊C4—362no—
243C4⋊C4—362no—
244C4⋊C4C2×Dic914yes—
245C4⋊C4C2×Dic918yes—
246C22⋊C4—362no—
247C22⋊C4—361no—
248C22⋊C4—361no—
249C22⋊C4C2×Dic918yes—
250C42—362no—
251C42—362no—
252C22×C3—22no—
253C22×C3—22no—
254C22×C3—22no—
255C22×C3—42no—
256C22×C3—42no—
257C22×C3#100412yes—
258C22×C3#100712yes—
259C22×C3#100911yescharacteristic
260C22×C3#101011yescharacteristic
261C22×C3C23×Dic311yescharacteristic
262C3×C4—22no—
263C3×C4—22no—
264C3×C4—24no—
265C3×C4—24no—
266Dic3—122no—
267Dic3—122no—
268Dic3—122no—
269Dic3—122no—
270C9#237811yescharacteristic, complemented, Sylow
271C23—22no—
272C23—22no—
273C23—21no—
274C23—21no—
275C23C22×Dic912yes—
276C23C23×D911yescharacteristic
277Q8—44no—
278C2×C4—22no—
279C2×C4—22no—
280C2×C4—22no—
281C2×C4—22no—
282C2×C4—22no—
283C2×C4—22no—
284C2×C4—44no—
285C2×C4—182no—
286C2×C4—182no—
287C2×C4—182no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—182no—
291C2×C4—182no—
292C2×C4—182no—
293C2×C4—182no—
294C2×C4—182no—
295C2×C4—182no—
296C2×C4—182no—
297C2×C4C22×Dic914yes—
298C2×C4C22×Dic914yes—
299C2×C4C22×Dic912yes—
300C2×C4C22×Dic912yes—
301C2×C3—42no—
302C2×C3#564612yes—
303C2×C3#564712yes—
304C2×C3#579811yescharacteristic
305C2×C3#581211yescharacteristic
306C2×C3#582711yescharacteristic
307C22—22no—
308C22—22no—
309C22—22no—
310C22—42no—
311C22—42no—
312C22#6371012yes—
313C22#6371312yes—
314C22#6371511yescharacteristic
315C22#6371611yescharacteristic
316C22C23×Dic911yescharacteristic
317C4—22no—
318C4—22no—
319C4—24no—
320C4—24no—
321C4—362no—
322C4—362no—
323C4—362no—
324C4—362no—
325C3#8275011yescharacteristic
326C2—42no—
327C2#1058974812yes—
328C2#1058974912yes—
329C2#1058990011yescharacteristic
330C2#1058991411yescharacteristic
331C2#1058992911yescharacteristic
subgroupG/H
centerC23C23×D9
commutatorC22×C9C23×C4
Frattini, socleC23×C3C23×D3
FittingC2×C9×C22⋊Q8C2
prime radicalC24×C3C22×D3
cosocleC23×C9C24
hypercenterC2×C22⋊Q8D9
hypocenterC9#2378
LCSG ▷ C22×C9 ▷ C9
UCSC1 ◁ C23 ◁ C2×C22⋊Q8

Complements

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

NH ≅ G/Ntype
2. #10588909C2semidirect
5. #10588664C2semidirect
6. #10588660C2semidirect
7. #10588660C2semidirect
13. C9×C22⋊Q8C4semidirect
172. C22⋊Q8Dic9semidirect
270. C9#2378semidirect

Maximal subgroups

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

subgroupindex
C2×C9×C22⋊Q82
#105889092
#105888922
#105888912
#105886642
#105886602
#105886312
#827503