Finite Group Databasebeta

← #11872716

Subgroups — #11872716

Order 1152.

627 conjugacy classes of subgroups; only the 154 normal subgroups are shown.

normal subgroups only

This group has 627 conjugacy classes of subgroups — too many to draw. Only its 154 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#10589637C211yesmaximal, characteristic, complemented
2#10589623C211yesmaximal, characteristic, complemented
3C9×#433C211yesmaximal, characteristic, complemented
4#10588531C212yesmaximal, complemented
5#10588527C212yesmaximal, complemented
6#10588419C212yesmaximal, complemented
7#10588414C212yesmaximal, complemented
8#10588392C212yesmaximal, complemented
9C4×D72C212yesmaximal, complemented
10#79386—31nomaximal
11C22×D36C2211yescharacteristic
12C9×#117C2211yescharacteristic
13#63492C2212yes—
14#63488C2211yescharacteristic
15C2×D72C2212yes—
16C2×D72C2212yes—
17#63456—22no—
18#63455—22no—
19#63446—22no—
20C22⋊C4×D9—22no—
21#63436C2211yescharacteristic, complemented
22C4×D36C2212yes—
23C4×D36C2212yes—
24C4×D36C2212yescomplemented
25#63432C2211yescharacteristic, complemented
26C9×C4⋊C8C2212yescomplemented
27C9×C22⋊C8C2212yes—
28C9×#97C2211yescharacteristic, complemented
29C4×C8×C9C2211yescharacteristic, complemented
30#63380C2212yes—
31#63380C2212yes—
32#63380C2212yescomplemented
33#63380C2212yescomplemented
34#63378C2212yescomplemented
35#63377C2212yescomplemented
36#5535—31no—
37#5521—31no—
38C3×#433D311yescharacteristic
39#4847—32no—
40#4843—32no—
41#4737—32no—
42#4732—32no—
43#4711—32no—
44C4×D24—32no—
45C23×D9—21no—
46C22×C4×C9C2311yescharacteristic
47C2×#611—22no—
48C2×D36—21no—
49C2×D36—24no—
50C2×D36—22no—
51C2×D36C2312yes—
52C2×D36C2312yes—
53C2×C4×D9—22no—
54C2×C4×D9—22no—
55C2×C4×D9—22no—
56C2×C8×C9C2312yes—
57C2×C8×C9C2312yes—
58C9×C4⋊C4D412yes—
59C9×C22⋊C4D412yes—
60C42×C9C2311yescharacteristic
61C42×C9C2311yescharacteristic
62#3676—21no—
63(C2×D9)⋊C4—22no—
64(C2×D9)⋊C4—22no—
65(C2×D9)⋊C4—22no—
66(C2×D9)⋊C4—22no—
67C4⋊Dic9C2312yes—
68C4⋊Dic9C2312yes—
69Dic9⋊C4—22no—
70C4×Dic9—21no—
71D72—24no—
72D72—24no—
73#3122—91noSylow
74C22×D12—31no—
75C3×#117C2×D311yescharacteristic
76#930—32no—
77#926—31no—
78C2×D24—32no—
79C2×D24—32no—
80#894—62no—
81#893—62no—
82#884—62no—
83D3×C22⋊C4—62no—
84#874—31no—
85C4×D12—32no—
86C4×D12—32no—
87C4×D12—32no—
88#870—31no—
89C3×C4⋊C8C2×D312yes—
90C3×C22⋊C8C2×D312yes—
91C3×#97C2×D311yescharacteristic
92C3×C4×C8C2×D311yescharacteristic
93#821—32no—
94#821—32no—
95#821—32no—
96#821—32no—
97#818—32no—
98#817—32no—
99C23×C9C2×D411yescharacteristic
100C22×D9—22no—
101C22×D9—24no—
102C22×D9—22no—
103C22×D9—82no—
104C2×C4×C9—22no—
105C2×C4×C9C2×D411yescharacteristic
106C2×C4×C9C2×D412yes—
107C2×C4×C9C2×D412yes—
108C2×C4×C9C2411yescharacteristic
109#611—82no—
110C2×Dic9—22no—
111C2×Dic9—22no—
112D36—24no—
113D36—22no—
114D36—22no—
115D36—22no—
116D36—82no—
117D36#4114yes—
118C4×D9—82no—
119C4×D9—82no—
120C4×D9—82no—
121C8×C9—22no—
122C8×C9—22no—
123#540—91no—
124#518—91no—
125#482—92no—
126#478—92no—
127#459—92no—
128#447—92no—
129#442—92no—
130C4×D8—92no—
131#433D911yescharacteristic, complemented
132C23×D3—61no—
133C22×C3×C4C22×D311yescharacteristic
134C2×#67—62no—
135C2×D12—32no—
136C2×D12—32no—
137C2×D12—64no—
138C2×D12—61no—
139C2×D12—62no—
140C2×C4×D3—62no—
141C2×C4×D3—62no—
142C2×C4×D3—62no—
143C2×C3×C8C22×D312yes—
144C2×C3×C8C22×D312yes—
145C3×C4⋊C4D1212yes—
146C3×C22⋊C4D1212yes—
147C3×C42C22×D311yescharacteristic
148C3×C42C22×D311yescharacteristic
149#217—61no—
150(C2×D3)⋊C4—62no—
151(C2×D3)⋊C4—62no—
152(C2×D3)⋊C4—62no—
153(C2×D3)⋊C4—62no—
154C4⋊Dic3—32no—
155C4⋊Dic3—32no—
156Dic3⋊C4—62no—
157C4×Dic3—61no—
158D24—64no—
159D24—64no—
160C22×C9—21no—
161C22×C9—22no—
162C22×C9C22×D411yescharacteristic
163C2×D9—24no—
164C2×D9—42no—
165C2×D9—42no—
166C2×D9—42no—
167C2×D9—42no—
168C2×D9—42no—
169C2×D9—84no—
170C4×C9—21no—
171C4×C9—22no—
172C4×C9—22no—
173C4×C9C2×#4112yes—
174Dic9—42no—
175Dic9—42no—
176C22×D4—91no—
177C2×D8—92no—
178C2×D8—92no—
179#127—91no—
180#125—91no—
181#123—182no—
182#121—92no—
183#121—182no—
184C4×D4—92no—
185C4×D4—92no—
186C4×D4—92no—
187C4×D4—182no—
188#117—91no—
189#117C2×D911yescharacteristic
190C2×C22⋊C4—182no—
191#107—92no—
192#106—92no—
193C4⋊C8C2×D912yescomplemented
194#102—92no—
195#102—92no—
196#102—92no—
197#102—92no—
198C22⋊C8C2×D912yes—
199#97C2×D911yescharacteristic, complemented
200C4×C8C2×D911yescharacteristic, complemented
201C23×C3C2×D1211yescharacteristic
202C22×D3—62no—
203C22×D3—64no—
204C22×D3—62no—
205C22×D3—242no—
206C2×C3×C4—22no—
207C2×C3×C4C2×D1211yescharacteristic
208C2×C3×C4C2×D1212yes—
209C2×C3×C4C2×D1212yes—
210C2×C3×C4C23×D311yescharacteristic
211#67—242no—
212C2×Dic3—62no—
213C2×Dic3—62no—
214D12—34no—
215D12—64no—
216D12—62no—
217D12—62no—
218D12—62no—
219D12—242no—
220C4×D3—242no—
221C4×D3—242no—
222C4×D3—242no—
223C3×C8—22no—
224C3×C8—22no—
225C2×C9—41no—
226C2×C9#52511yescharacteristic
227C2×C9#57612yes—
228D9—44no—
229D9—82no—
230C24—181no—
231C2×D4—92no—
232C2×D4—92no—
233C2×D4—184no—
234C2×D4—182no—
235C2×D4—181no—
236C2×D4—182no—
237C22×C4—182no—
238C22×C4—182no—
239C22×C4—182no—
240C22×C4C22×D911yescharacteristic
241D8—184no—
242D8—184no—
243C2×C8C22×D912yes—
244C2×C8C22×D912yes—
245C4⋊C4—92no—
246C4⋊C4—92no—
247C4⋊C4—182no—
248C4⋊C4D3612yes—
249C22⋊C4—181no—
250C22⋊C4—182no—
251C22⋊C4—182no—
252C22⋊C4—182no—
253C22⋊C4—182no—
254C22⋊C4D3612yes—
255C42—181no—
256C42C22×D911yescharacteristic
257C42C22×D911yescharacteristic
258C22×C3—22no—
259C22×C3—21no—
260C22×C3C22×D1211yescharacteristic
261C2×D3—64no—
262C2×D3—122no—
263C2×D3—122no—
264C2×D3—122no—
265C2×D3—122no—
266C2×D3—122no—
267C2×D3—244no—
268C3×C4—22no—
269C3×C4—22no—
270C3×C4—21no—
271C3×C4D3×#4112yes—
272Dic3—122no—
273Dic3—122no—
274C9#312211yescharacteristic, complemented, Sylow
275C23—184no—
276C23—182no—
277C23—182no—
278C23—722no—
279C23C2×D3611yescharacteristic
280D4—94no—
281D4—184no—
282D4—182no—
283D4—182no—
284D4—182no—
285D4—722no—
286D4—722no—
287C2×C4—22no—
288C2×C4—182no—
289C2×C4—182no—
290C2×C4—722no—
291C2×C4—722no—
292C2×C4—722no—
293C2×C4C2×D3611yescharacteristic
294C2×C4C2×D3612yes—
295C2×C4C2×D3612yes—
296C2×C4C23×D911yescharacteristic
297C8—22no—
298C8—22no—
299C2×C3—41no—
300C2×C3#552411yescharacteristic
301C2×C3#575212yes—
302D3—124no—
303D3—242no—
304C22—22no—
305C22—21no—
306C22—184no—
307C22—362no—
308C22—362no—
309C22—362no—
310C22—362no—
311C22—362no—
312C22—724no—
313C22C22×D3611yescharacteristic
314C4—22no—
315C4—22no—
316C4—21no—
317C4—362no—
318C4—362no—
319C4#41×D912yes—
320C3#7938611yescharacteristic
321C2—41no—
322C2—364no—
323C2—722no—
324C2#1058962611yescharacteristic
325C2#1058985412yes—
subgroupG/H
centerC22C22×D36
commutator, cosocleC2×C4×C9C24
FrattiniC2×C3×C4C23×D3
FittingC9×#433C2
socleC22×C3C22×D12
hypercenter#433D9
hypocenterC9#3122
LCSG ▷ C2×C4×C9 ▷ C2×C9 ▷ C9
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #10589637C2semidirect
2. #10589623C2semidirect
3. C9×#433C2semidirect
4. #10588531C2semidirect
5. #10588527C2semidirect
6. #10588419C2semidirect
7. #10588414C2semidirect
8. #10588392C2semidirect
9. C4×D72C2semidirect
21. #63436C22semidirect
24. C4×D36C22semidirect
25. #63432C22semidirect
26. C9×C4⋊C8C22semidirect
28. C9×#97C22semidirect
29. C4×C8×C9C22semidirect
32. #63380C22semidirect
33. #63380C22semidirect
34. #63378C22semidirect
35. #63377C22semidirect
131. #433D9semidirect
193. C4⋊C8C2×D9semidirect
199. #97C2×D9semidirect
200. C4×C8C2×D9semidirect
274. C9#3122semidirect

Maximal subgroups

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

subgroupindex
#105896372
#105896232
C9×#4332
#105885312
#105885272
#105884192
#105884142
#105883922
C4×D722
#793863