Finite Group Databasebeta

← #11882220

Subgroups — #11882220

Order 1152.

588 conjugacy classes of subgroups.

The subgroup lattice has 339 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C9×#533C211yesmaximal, characteristic, complemented
2#10589579C211yesmaximal, characteristic
3#10588769C212yesmaximal, complemented
4#10588768C212yesmaximal, complemented
5#10588731C214yesmaximal, complemented
6#10588710C212yesmaximal, complemented
7#10588702C212yesmaximal, complemented
8C2×C4⋊(C9⋊C8)C211yesmaximal, characteristic, complemented
9#83363—31nomaximal
10C2×#3697—21no—
11C9×C4⋊Q8C2211yescharacteristic
12C9×C4⋊Q8C2211yescharacteristic
13C9×#125—21no—
14C9×C22⋊Q8—21no—
15C9×C22⋊Q8C2212yes—
16C4×Q8×C9—21no—
17C4×Q8×C9C2212yes—
18C9×#117—21no—
19C2×C42×C9C2211yescharacteristic
20C2×#3675C2214yes—
21#63492—21no—
22#63492C2212yes—
23C22×C9⋊C8C2212yes—
24#63437—21no—
25#63436C2211yescharacteristic
26C4×D36—21no—
27C4×D36C2212yes—
28#63431C2211yescharacteristic
29#63395C2214yes—
30#63369C2214yes—
31#63367C2214yes—
32C4⋊(C9⋊C8)C2212yes—
33C4⋊(C9⋊C8)C2212yes—
34C3×#533D311yescharacteristic
35#5477—31no—
36#5084—32no—
37#5083—32no—
38#5048—34no—
39#5027—32no—
40#5020—32no—
41C2×C4⋊(C3⋊C8)—31no—
42C2×Q8×C9—21no—
43C2×Q8×C9C2312yes—
44C22×C4×C9D411yescharacteristic
45C22×C4×C9D411yescharacteristic
46C22×C4×C9C2311yescharacteristic
47C2×#611—22no—
48#3697—44no—
49C2×D36—21no—
50C2×D36—21no—
51C2×D36C2312yes—
52C2×C4×D9—22no—
53C2×Dic18—21no—
54C9×C4⋊C4—21no—
55C9×C4⋊C4—21no—
56C9×C4⋊C4—21no—
57C9×C4⋊C4—22no—
58C9×C4⋊C4—22no—
59C9×C4⋊C4C2312yes—
60C9×C22⋊C4—22no—
61C42×C9—22no—
62C42×C9D411yescharacteristic
63C42×C9D411yescharacteristic
64C42×C9C2311yescharacteristic
65C42×C9C2311yescharacteristic
66#3675—44no—
67(C2×D9)⋊C4—22no—
68(C2×D9)⋊C4—22no—
69C4⋊Dic9—21no—
70C4⋊Dic9C2312yes—
71C2×C9⋊C8—42no—
72C2×C9⋊C8C2314yes—
73#3246—91noSylow
74C2×#235—61no—
75C3×C4⋊Q8C2×D311yescharacteristic
76C3×C4⋊Q8C2×D311yescharacteristic
77C3×#125—21no—
78C3×C22⋊Q8—21no—
79C3×C22⋊Q8C2×D312yes—
80C3×C4×Q8—21no—
81C3×C4×Q8C2×D312yes—
82C3×#117—21no—
83C2×C3×C42C2×D311yescharacteristic
84C2×#215—34no—
85#930—32no—
86#930—61no—
87C22×C3⋊C8—32no—
88#875—61no—
89#874—31no—
90C4×D12—32no—
91C4×D12—61no—
92#869—31no—
93#835—34no—
94#809—34no—
95#808—34no—
96C4⋊(C3⋊C8)—32no—
97C4⋊(C3⋊C8)—32no—
98C23×C9C2×D411yescharacteristic
99C22×D9—22no—
100Q8×C9—22no—
101Q8×C9—22no—
102Q8×C9—42no—
103C2×C4×C9—21no—
104C2×C4×C9—21no—
105C2×C4×C9—22no—
106C2×C4×C9—22no—
107C2×C4×C9—41no—
108C2×C4×C9SD1614yescomplemented
109C2×C4×C9C2×D411yescharacteristic
110C2×C4×C9C2×D411yescharacteristic
111C2×C4×C9C2×D411yescharacteristic
112C2×C4×C9C2×D411yescharacteristic
113C2×C4×C9C2×D411yescharacteristic
114C2×C4×C9C2411yescharacteristic
115#611—44no—
116C2×Dic9—22no—
117D36—22no—
118D36—22no—
119D36—42no—
120D36—42no—
121C4×D9—44no—
122Dic18—42no—
123C9⋊C8—24no—
124#533D911yescharacteristic, complemented
125#532—91no—
126#476—92no—
127#475—92no—
128#465—94no—
129#461—92no—
130#460—92no—
131C2×C4⋊C8—91no—
132C2×C3×Q8—21no—
133C2×C3×Q8C22×D312yes—
134C22×C3×C4#6711yescharacteristic
135C22×C3×C4#6711yescharacteristic
136C22×C3×C4C22×D311yescharacteristic
137C2×#67—62no—
138#235—124no—
139C2×D12—32no—
140C2×D12—61no—
141C2×D12—61no—
142C2×C4×D3—62no—
143C2×Dic6—61no—
144C3×C4⋊C4—21no—
145C3×C4⋊C4—21no—
146C3×C4⋊C4—21no—
147C3×C4⋊C4—22no—
148C3×C4⋊C4—22no—
149C3×C4⋊C4C22×D312yes—
150C3×C22⋊C4—22no—
151C3×C42—22no—
152C3×C42#6711yescharacteristic
153C3×C42#6711yescharacteristic
154C3×C42C22×D311yescharacteristic
155C3×C42C22×D311yescharacteristic
156#215—124no—
157(C2×D3)⋊C4—62no—
158(C2×D3)⋊C4—62no—
159C4⋊Dic3—32no—
160C4⋊Dic3—61no—
161C2×C3⋊C8—34no—
162C2×C3⋊C8—122no—
163C22×C9—21no—
164C22×C9—21no—
165C22×C9C2×SD1612yes—
166C22×C9C22×D411yescharacteristic
167C2×D9—42no—
168C2×D9—42no—
169C2×D9—42no—
170C4×C9—21no—
171C4×C9—21no—
172C4×C9—21no—
173C4×C9—42no—
174C4×C9—42no—
175C4×C9C2×SD1612yes—
176C4×C9C2×SD1612yes—
177C4×C9H(5,𝔽2)11yescharacteristic
178C4×C92−1+411yescharacteristic
179Dic9—42no—
180C2×#41—181no—
181C2×SD16—94no—
182C22×C8—92no—
183C4⋊Q8—91no—
184C4⋊Q8C2×D911yescharacteristic
185C4⋊Q8C2×D911yescharacteristic
186#127—91no—
187#125—21no—
188#124—181no—
189C22⋊Q8—21no—
190C22⋊Q8C2×D912yes—
191#121—92no—
192#121—181no—
193C4×Q8—21no—
194C4×Q8C2×D912yes—
195C4×D4—92no—
196C4×D4—181no—
197#117—21no—
198C2×C42C2×D911yescharacteristic
199#106—94no—
200C4⋊C8—92no—
201C4⋊C8—92no—
202#103—94no—
203#102—94no—
204C23×C3C2×#6711yescharacteristic
205C22×D3—62no—
206C3×Q8—22no—
207C3×Q8—22no—
208C3×Q8—42no—
209C2×C3×C4—21no—
210C2×C3×C4—21no—
211C2×C3×C4—22no—
212C2×C3×C4—22no—
213C2×C3×C4—41no—
214C2×C3×C4#21514yes—
215C2×C3×C4C2×#6711yescharacteristic
216C2×C3×C4C2×#6711yescharacteristic
217C2×C3×C4C2×#6711yescharacteristic
218C2×C3×C4C2×#6711yescharacteristic
219C2×C3×C4C2×#6711yescharacteristic
220C2×C3×C4C23×D311yescharacteristic
221#67—124no—
222C2×Dic3—62no—
223D12—62no—
224D12—62no—
225D12—122no—
226D12—122no—
227C4×D3—124no—
228Dic6—122no—
229C3⋊C8—64no—
230C2×C9—22no—
231C2×C9#53711yescharacteristic
232C2×C9C22×SD1611yescharacteristic
233C2×C9#57511yescharacteristic
234D9—82no—
235#41—364no—
236C2×Q8—21no—
237C2×Q8—181no—
238C2×Q8C22×D912yes—
239C2×D4—92no—
240C2×D4—182no—
241C2×D4—181no—
242C2×D4—181no—
243C22×C4—182no—
244C22×C4#61111yescharacteristic
245C22×C4#61111yescharacteristic
246C22×C4C22×D911yescharacteristic
247SD16—364no—
248C2×C8—94no—
249C2×C8—362no—
250C4⋊C4—21no—
251C4⋊C4—21no—
252C4⋊C4—21no—
253C4⋊C4—22no—
254C4⋊C4—22no—
255C4⋊C4—92no—
256C4⋊C4—181no—
257C4⋊C4C22×D912yes—
258C22⋊C4—22no—
259C22⋊C4—182no—
260C22⋊C4—182no—
261C42—22no—
262C42#61111yescharacteristic
263C42#61111yescharacteristic
264C42C22×D911yescharacteristic
265C42C22×D911yescharacteristic
266C22×C3—21no—
267C22×C3—21no—
268C22×C3C2×#21512yes—
269C22×C3C22×#6711yescharacteristic
270C2×D3—122no—
271C2×D3—122no—
272C2×D3—122no—
273C3×C4—21no—
274C3×C4—21no—
275C3×C4—21no—
276C3×C4—42no—
277C3×C4—42no—
278C3×C4C2×#21512yes—
279C3×C4C2×#21512yes—
280C3×C4#100911yescharacteristic
281C3×C4#101011yescharacteristic
282Dic3—122no—
283C9#324611yescharacteristic, complemented, Sylow
284C23—182no—
285C23C2×#61111yescharacteristic
286Q8—22no—
287Q8—22no—
288Q8—42no—
289Q8—362no—
290D4—182no—
291D4—182no—
292D4—362no—
293D4—364no—
294D4—362no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—22no—
298C2×C4—22no—
299C2×C4—41no—
300C2×C4—182no—
301C2×C4—364no—
302C2×C4#367514yescomplemented
303C2×C4C2×#61111yescharacteristic
304C2×C4C2×#61111yescharacteristic
305C2×C4C2×#61111yescharacteristic
306C2×C4C2×#61111yescharacteristic
307C2×C4C2×#61111yescharacteristic
308C2×C4C23×D911yescharacteristic
309C8—184no—
310C2×C3—22no—
311C2×C3C22×#21511yescharacteristic
312C2×C3#582211yescharacteristic
313C2×C3#583311yescharacteristic
314D3—242no—
315C22—21no—
316C22—21no—
317C22—362no—
318C22—362no—
319C22—362no—
320C22C2×#367512yes—
321C22C22×#61111yescharacteristic
322C4—21no—
323C4—21no—
324C4—21no—
325C4—42no—
326C4—42no—
327C4—362no—
328C4C2×#367512yes—
329C4C2×#367512yes—
330C4#6371511yescharacteristic
331C4#6371611yescharacteristic
332C3#8336311yescharacteristic
333C2—22no—
334C2—722no—
335C2C22×#367511yescharacteristic
336C2#1058992511yescharacteristic
337C2#1058993511yescharacteristic
subgroupG/H
centerC22C22×#611
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#533C2
socleC22×C3C22×#67
prime radical#10589579C2
hypercenter#533D9
hypocenterC9#3246
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ C2×C42 ◁ #533

Complements

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

NH ≅ G/Ntype
1. C9×#533C2semidirect
3. #10588769C2semidirect
4. #10588768C2semidirect
5. #10588731C2semidirect
6. #10588710C2semidirect
7. #10588702C2semidirect
8. C2×C4⋊(C9⋊C8)C2semidirect
108. C2×C4×C9SD16semidirect
124. #533D9semidirect
283. C9#3246semidirect
302. C2×C4#3675semidirect

Maximal subgroups

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

subgroupindex
C9×#5332
#105895792
#105887692
#105887682
#105887312
#105887102
#105887022
C2×C4⋊(C9⋊C8)2
#833633