Finite Group Databasebeta

← #11872717

Subgroups — #11872717

Order 1152.

1254 conjugacy classes of subgroups; only the 253 normal subgroups are shown.

normal subgroups only

This group has 1254 conjugacy classes of subgroups — too many to draw. Only its 253 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#10596006C211yesmaximal, characteristic, complemented
2#10595992C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4#10592546C212yesmaximal, complemented
5#10592542C212yesmaximal, complemented
6#10592436C212yesmaximal, complemented
7#10592431C212yesmaximal, complemented
8#10592410C212yesmaximal, complemented
9C4×#3745C212yesmaximal, complemented
10#79386—34nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64139C2212yes—
14#64135C2211yescharacteristic
15C2×#3745C2212yes—
16C2×#3745C2212yes—
17#64103—22no—
18#64102—22no—
19#64093—22no—
20C22⋊C4×C3⋊D3—22no—
21#64083C2211yescharacteristic, complemented
22C4×C4⋊(C3⋊D3)C2212yes—
23C4×C4⋊(C3⋊D3)C2212yes—
24C4×C4⋊(C3⋊D3)C2212yescomplemented
25#64079C2211yescharacteristic, complemented
26C32×C4⋊C8C2212yescomplemented
27C32×C22⋊C8C2212yes—
28C32×#97C2211yescharacteristic, complemented
29C32×C4×C8C2211yescharacteristic, complemented
30#63648C2212yes—
31#63648C2212yes—
32#63648C2212yescomplemented
33#63648C2212yescomplemented
34#63645C2212yescomplemented
35#63644C2212yescomplemented
36#5535—34no—
37#5521—34no—
38C3×#433D314yescomplemented
39#4847—38no—
40#4843—38no—
41#4737—38no—
42#4732—38no—
43#4711—38no—
44C4×D24—38no—
45C23×C3⋊D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×#638—22no—
48C2×C4⋊(C3⋊D3)—21no—
49C2×C4⋊(C3⋊D3)—24no—
50C2×C4⋊(C3⋊D3)—22no—
51C2×C4⋊(C3⋊D3)C2312yes—
52C2×C4⋊(C3⋊D3)C2312yes—
53C2×C4×C3⋊D3—22no—
54C2×C4×C3⋊D3—22no—
55C2×C4×C3⋊D3—22no—
56C2×C32×C8C2312yes—
57C2×C32×C8C2312yes—
58C32×C4⋊C4D412yes—
59C32×C22⋊C4D412yes—
60C32×C42C2311yescharacteristic
61C32×C42C2311yescharacteristic
62#3757—21no—
63#3752—22no—
64#3752—22no—
65#3752—22no—
66#3752—22no—
67C4⋊(C3⋊Dic3)C2312yes—
68C4⋊(C3⋊Dic3)C2312yes—
69#3750—22no—
70C4×C3⋊Dic3—21no—
71#3745—24no—
72#3745—24no—
73#3122—91noSylow
74C22×D12—34no—
75C3×#117C2×D314yes—
76#930—38no—
77#926—34no—
78C2×D24—38no—
79C2×D24—38no—
80#894—68no—
81#893—68no—
82#884—68no—
83D3×C22⋊C4—68no—
84#874—34no—
85C4×D12—38no—
86C4×D12—38no—
87C4×D12—38no—
88#870—34no—
89C3×C4⋊C8C2×D318yescomplemented
90C3×C22⋊C8C2×D318yes—
91C3×#97C2×D314yescomplemented
92C3×C4×C8C2×D314yescomplemented
93#821—38no—
94#821—38no—
95#821—38no—
96#821—38no—
97#818—38no—
98#817—38no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—22no—
101C22×C3⋊D3—24no—
102C22×C3⋊D3—22no—
103C22×C3⋊D3—82no—
104C2×C32×C4—22no—
105C2×C32×C4C2×D411yescharacteristic
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2×D412yes—
108C2×C32×C4C2411yescharacteristic
109#638—82no—
110C2×C3⋊Dic3—22no—
111C2×C3⋊Dic3—22no—
112C4⋊(C3⋊D3)—24no—
113C4⋊(C3⋊D3)—22no—
114C4⋊(C3⋊D3)—22no—
115C4⋊(C3⋊D3)—22no—
116C4⋊(C3⋊D3)—82no—
117C4⋊(C3⋊D3)#4114yes—
118C4×C3⋊D3—82no—
119C4×C3⋊D3—82no—
120C4×C3⋊D3—82no—
121C32×C8—22no—
122C32×C8—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#433C3⋊D311yescharacteristic, complemented
132C23×D3—64no—
133C22×C3×C4C22×D314yes—
134C2×#67—68no—
135C2×D12—38no—
136C2×D12—38no—
137C2×D12—616no—
138C2×D12—64no—
139C2×D12—68no—
140C2×C4×D3—68no—
141C2×C4×D3—68no—
142C2×C4×D3—68no—
143C2×C3×C8C22×D318yes—
144C2×C3×C8C22×D318yes—
145C3×C4⋊C4D1218yes—
146C3×C22⋊C4D1218yes—
147C3×C42C22×D314yes—
148C3×C42C22×D314yes—
149#217—64no—
150(C2×D3)⋊C4—68no—
151(C2×D3)⋊C4—68no—
152(C2×D3)⋊C4—68no—
153(C2×D3)⋊C4—68no—
154C4⋊Dic3—38no—
155C4⋊Dic3—38no—
156Dic3⋊C4—68no—
157C4×Dic3—64no—
158D24—616no—
159D24—616no—
160C22×C32—21no—
161C22×C32—22no—
162C22×C32C22×D411yescharacteristic
163C2×C3⋊D3—24no—
164C2×C3⋊D3—42no—
165C2×C3⋊D3—42no—
166C2×C3⋊D3—42no—
167C2×C3⋊D3—42no—
168C2×C3⋊D3—42no—
169C2×C3⋊D3—84no—
170C32×C4—21no—
171C32×C4—22no—
172C32×C4—22no—
173C32×C4C2×#4112yes—
174C3⋊Dic3—42no—
175C3⋊Dic3—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×C3⋊D311yescharacteristic
190C2×C22⋊C4—182no—
191#107—92no—
192#106—92no—
193C4⋊C8C2×C3⋊D312yescomplemented
194#102—92no—
195#102—92no—
196#102—92no—
197#102—92no—
198C22⋊C8C2×C3⋊D312yes—
199#97C2×C3⋊D311yescharacteristic, complemented
200C4×C8C2×C3⋊D311yescharacteristic, complemented
201C23×C3C2×D1214yes—
202C22×D3—68no—
203C22×D3—616no—
204C22×D3—68no—
205C22×D3—248no—
206C2×C3×C4—28no—
207C2×C3×C4C2×D1214yes—
208C2×C3×C4C2×D1218yes—
209C2×C3×C4C2×D1218yes—
210C2×C3×C4C23×D314yes—
211#67—248no—
212C2×Dic3—68no—
213C2×Dic3—68no—
214D12—316no—
215D12—616no—
216D12—68no—
217D12—68no—
218D12—68no—
219D12—248no—
220C4×D3—248no—
221C4×D3—248no—
222C4×D3—248no—
223C3×C8—28no—
224C3×C8—28no—
225C2×C32—41no—
226C2×C32#52511yescharacteristic
227C2×C32#57612yes—
228C3⋊D3—44no—
229C3⋊D3—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×C3⋊D311yescharacteristic
241D8—184no—
242D8—184no—
243C2×C8C22×C3⋊D312yes—
244C2×C8C22×C3⋊D312yes—
245C4⋊C4—92no—
246C4⋊C4—92no—
247C4⋊C4—182no—
248C4⋊C4C4⋊(C3⋊D3)12yes—
249C22⋊C4—181no—
250C22⋊C4—182no—
251C22⋊C4—182no—
252C22⋊C4—182no—
253C22⋊C4—182no—
254C22⋊C4C4⋊(C3⋊D3)12yes—
255C42—181no—
256C42C22×C3⋊D311yescharacteristic
257C42C22×C3⋊D311yescharacteristic
258C22×C3—28no—
259C22×C3—24no—
260C22×C3C22×D1214yes—
261C2×D3—616no—
262C2×D3—128no—
263C2×D3—128no—
264C2×D3—128no—
265C2×D3—128no—
266C2×D3—128no—
267C2×D3—2416no—
268C3×C4—28no—
269C3×C4—28no—
270C3×C4—24no—
271C3×C4D3×#4118yes—
272Dic3—128no—
273Dic3—128no—
274C32#312211yescharacteristic, complemented, Sylow
275C23—184no—
276C23—182no—
277C23—182no—
278C23—722no—
279C23C2×C4⋊(C3⋊D3)11yescharacteristic
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×C4⋊(C3⋊D3)11yescharacteristic
294C2×C4C2×C4⋊(C3⋊D3)12yes—
295C2×C4C2×C4⋊(C3⋊D3)12yes—
296C2×C4C23×C3⋊D311yescharacteristic
297C8—22no—
298C8—22no—
299C2×C3—44no—
300C2×C3#552414yes—
301C2×C3#575218yes—
302D3—1216no—
303D3—248no—
304C22—22no—
305C22—21no—
306C22—184no—
307C22—362no—
308C22—362no—
309C22—362no—
310C22—362no—
311C22—362no—
312C22—724no—
313C22C22×C4⋊(C3⋊D3)11yescharacteristic
314C4—22no—
315C4—22no—
316C4—21no—
317C4—362no—
318C4—362no—
319C4#41×C3⋊D312yes—
320C3#7938614yescomplemented
321C2—41no—
322C2—364no—
323C2—722no—
324C2#1059599511yescharacteristic
325C2#1059622312yes—
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#433C2
socleC22×C32C22×D4
hypercenter#433C3⋊D3
hypocenterC32#3122
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ #117 ◁ #433

Complements

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

NH ≅ G/Ntype
1. #10596006C2semidirect
2. #10595992C2semidirect
3. C32×#433C2semidirect
4. #10592546C2semidirect
5. #10592542C2semidirect
6. #10592436C2semidirect
7. #10592431C2semidirect
8. #10592410C2semidirect
9. C4×#3745C2semidirect
21. #64083C22semidirect
24. C4×C4⋊(C3⋊D3)C22semidirect
25. #64079C22semidirect
26. C32×C4⋊C8C22semidirect
28. C32×#97C22semidirect
29. C32×C4×C8C22semidirect
32. #63648C22semidirect
33. #63648C22semidirect
34. #63645C22semidirect
35. #63644C22semidirect
38. C3×#433D3semidirect
89. C3×C4⋊C8C2×D3semidirect
91. C3×#97C2×D3semidirect
92. C3×C4×C8C2×D3semidirect
131. #433C3⋊D3semidirect
193. C4⋊C8C2×C3⋊D3semidirect
199. #97C2×C3⋊D3semidirect
200. C4×C8C2×C3⋊D3semidirect
274. C32#3122semidirect
320. C3#79386semidirect

Maximal subgroups

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

subgroupindex
#105960062
#105959922
C32×#4332
#105925462
#105925422
#105924362
#105924312
#105924102
C4×#37452
#793863