Finite Group Databasebeta

← #11872803

Subgroups — #11872803

Order 1152.

1182 conjugacy classes of subgroups; only the 253 normal subgroups are shown.

normal subgroups only

This group has 1182 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#10595992C211yesmaximal, characteristic
2#10595989C211yesmaximal, characteristic, complemented
3C32×#433C211yesmaximal, characteristic, complemented
4#10592546C212yesmaximal, complemented
5#10592540C212yesmaximal, complemented
6#10592430C212yesmaximal
7#10592422C212yesmaximal, complemented
8#10592409C212yesmaximal, complemented
9C4×#3744C212yesmaximal, complemented
10#79387—34nomaximal
11C22×C4⋊(C3⋊D3)C2211yescharacteristic
12C32×#117C2211yescharacteristic
13#64135C2211yescharacteristic
14#64133C2212yes—
15C2×#3744C2212yes—
16C2×#3744C2212yes—
17#64102—22no—
18#64098—22no—
19C22⋊C4×C3⋊D3—22no—
20#64088—22no—
21C4×C4⋊(C3⋊D3)C2212yes—
22C4×C4⋊(C3⋊D3)C2212yes—
23#64079C2211yescharacteristic, complemented
24#64078C2211yescharacteristic, complemented
25C4×#634C2212yescomplemented
26C32×C4⋊C8C2212yescomplemented
27C32×C22⋊C8C2212yes—
28C32×#97C2211yescharacteristic, complemented
29C32×C4×C8C2211yescharacteristic, complemented
30#63648C2212yes—
31#63648C2212yes—
32#63645C2212yescomplemented
33#63644C2212yescomplemented
34#63643C2212yescomplemented
35#63643C2212yescomplemented
36#5521—34no—
37#5518—34no—
38C3×#433D314yescomplemented
39#4847—38no—
40#4841—38no—
41#4731—38no—
42#4723—38no—
43#4710—38no—
44C4×#204—38no—
45C23×C3⋊D3—21no—
46C22×C32×C4C2311yescharacteristic
47C2×C4⋊(C3⋊D3)—21no—
48C2×C4⋊(C3⋊D3)—24no—
49C2×C4⋊(C3⋊D3)C2312yes—
50C2×C4×C3⋊D3—22no—
51C2×C4×C3⋊D3—22no—
52C2×#634C2312yes—
53C2×C32×C8C2312yes—
54C2×C32×C8C2312yes—
55C32×C4⋊C4D412yes—
56C32×C22⋊C4D412yes—
57C32×C42C2311yescharacteristic
58C32×C42C2311yescharacteristic
59#3757—22no—
60#3757—21no—
61#3752—22no—
62#3752—22no—
63C4⋊(C3⋊Dic3)—22no—
64C4⋊(C3⋊Dic3)C2312yes—
65C4⋊(C3⋊Dic3)C2312yes—
66#3750—22no—
67#3750—22no—
68#3750—22no—
69C4×C3⋊Dic3—22no—
70C4×C3⋊Dic3—21no—
71#3744—24no—
72#3744—24no—
73#3123—91noSylow
74C22×D12—34no—
75C3×#117C2×D314yes—
76#926—34no—
77#924—38no—
78C2×#204—38no—
79C2×#204—38no—
80#893—68no—
81#889—68no—
82D3×C22⋊C4—68no—
83#879—68no—
84C4×D12—38no—
85C4×D12—38no—
86#870—34no—
87#869—34no—
88C4×Dic6—38no—
89C3×C4⋊C8C2×D318yescomplemented
90C3×C22⋊C8C2×D318yes—
91C3×#97C2×D314yescomplemented
92C3×C4×C8C2×D314yescomplemented
93#821—38no—
94#821—38no—
95#818—38no—
96#817—38no—
97#816—38no—
98#816—38no—
99C23×C32C2×D411yescharacteristic
100C22×C3⋊D3—22no—
101C22×C3⋊D3—24no—
102C22×C3⋊D3—82no—
103C2×C32×C4—22no—
104C2×C32×C4C2×D411yescharacteristic
105C2×C32×C4C2×D412yes—
106C2×C32×C4C2×D412yes—
107C2×C32×C4C2411yescharacteristic
108C2×C3⋊Dic3—22no—
109C2×C3⋊Dic3—22no—
110C2×C3⋊Dic3—22no—
111C4⋊(C3⋊D3)—24no—
112C4⋊(C3⋊D3)—22no—
113C4⋊(C3⋊D3)#4114yes—
114C4×C3⋊D3—82no—
115C4×C3⋊D3—82no—
116#634—22no—
117#634—22no—
118C32×C8—22no—
119C32×C8—22no—
120#541—91no—
121#518—91no—
122#485—92no—
123#478—92no—
124#461—92no—
125#450—92no—
126#440—92no—
127C4×SD16—92no—
128#433C3⋊D311yescharacteristic, complemented
129C23×D3—64no—
130C22×C3×C4C22×D314yes—
131C2×D12—38no—
132C2×D12—616no—
133C2×D12—64no—
134C2×C4×D3—68no—
135C2×C4×D3—68no—
136C2×Dic6—38no—
137C2×C3×C8C22×D318yes—
138C2×C3×C8C22×D318yes—
139C3×C4⋊C4D1218yes—
140C3×C22⋊C4D1218yes—
141C3×C42C22×D314yes—
142C3×C42C22×D314yes—
143#217—68no—
144#217—64no—
145(C2×D3)⋊C4—68no—
146(C2×D3)⋊C4—68no—
147C4⋊Dic3—38no—
148C4⋊Dic3—38no—
149C4⋊Dic3—68no—
150Dic3⋊C4—68no—
151Dic3⋊C4—68no—
152Dic3⋊C4—68no—
153C4×Dic3—68no—
154C4×Dic3—64no—
155#204—616no—
156#204—616no—
157C22×C32—21no—
158C22×C32—22no—
159C22×C32C22×D411yescharacteristic
160C2×C3⋊D3—24no—
161C2×C3⋊D3—42no—
162C2×C3⋊D3—42no—
163C2×C3⋊D3—84no—
164C32×C4—21no—
165C32×C4—22no—
166C32×C4—22no—
167C32×C4C2×#4112yes—
168C3⋊Dic3—42no—
169C3⋊Dic3—42no—
170C3⋊Dic3—42no—
171C22×D4—91no—
172C2×SD16—92no—
173C2×SD16—92no—
174C4⋊Q8—91no—
175#126—182no—
176#125—91no—
177#125—182no—
178C22⋊Q8—92no—
179C4×Q8—92no—
180C4×D4—92no—
181C4×D4—92no—
182C4×D4—182no—
183#117—91no—
184#117C2×C3⋊D311yescharacteristic
185C2×C22⋊C4—182no—
186#107—92no—
187#106—92no—
188C4⋊C8C2×C3⋊D312yescomplemented
189#103—92no—
190#103—92no—
191#102—92no—
192#102—92no—
193C22⋊C8C2×C3⋊D312yes—
194#97C2×C3⋊D311yescharacteristic, complemented
195C4×C8C2×C3⋊D311yescharacteristic, complemented
196C23×C3C2×D1214yes—
197C22×D3—68no—
198C22×D3—616no—
199C22×D3—248no—
200C2×C3×C4—28no—
201C2×C3×C4C2×D1214yes—
202C2×C3×C4C2×D1218yes—
203C2×C3×C4C2×D1218yes—
204C2×C3×C4C23×D314yes—
205C2×Dic3—68no—
206C2×Dic3—68no—
207C2×Dic3—68no—
208D12—316no—
209D12—616no—
210D12—68no—
211C4×D3—248no—
212C4×D3—248no—
213Dic6—68no—
214Dic6—68no—
215C3×C8—28no—
216C3×C8—28no—
217C2×C32—41no—
218C2×C32#52511yescharacteristic
219C2×C32#57712yes—
220C3⋊D3—44no—
221C24—181no—
222C2×Q8—92no—
223C2×D4—92no—
224C2×D4—184no—
225C2×D4—181no—
226C22×C4—182no—
227C22×C4—182no—
228C22×C4C22×C3⋊D311yescharacteristic
229SD16—184no—
230SD16—184no—
231C2×C8C22×C3⋊D312yes—
232C2×C8C22×C3⋊D312yes—
233C4⋊C4—92no—
234C4⋊C4—92no—
235C4⋊C4—182no—
236C4⋊C4—182no—
237C4⋊C4—182no—
238C4⋊C4—182no—
239C4⋊C4C4⋊(C3⋊D3)12yes—
240C22⋊C4—181no—
241C22⋊C4—182no—
242C22⋊C4—182no—
243C22⋊C4—182no—
244C22⋊C4C4⋊(C3⋊D3)12yes—
245C42—181no—
246C42—182no—
247C42C22×C3⋊D311yescharacteristic
248C42C22×C3⋊D311yescharacteristic
249C22×C3—28no—
250C22×C3—24no—
251C22×C3C22×D1214yes—
252C2×D3—616no—
253C2×D3—128no—
254C2×D3—128no—
255C2×D3—2416no—
256C3×C4—28no—
257C3×C4—28no—
258C3×C4—24no—
259C3×C4D3×#4118yes—
260Dic3—128no—
261Dic3—128no—
262Dic3—128no—
263C32#312311yescharacteristic, complemented, Sylow
264C23—184no—
265C23—182no—
266C23—722no—
267C23C2×C4⋊(C3⋊D3)11yescharacteristic
268Q8—182no—
269Q8—182no—
270D4—94no—
271D4—184no—
272D4—182no—
273C2×C4—22no—
274C2×C4—182no—
275C2×C4—182no—
276C2×C4—182no—
277C2×C4—722no—
278C2×C4—722no—
279C2×C4C2×C4⋊(C3⋊D3)12yes—
280C2×C4C2×C4⋊(C3⋊D3)11yescharacteristic
281C2×C4C2×C4⋊(C3⋊D3)12yes—
282C2×C4C23×C3⋊D311yescharacteristic
283C8—22no—
284C8—22no—
285C2×C3—44no—
286C2×C3#552414yes—
287C2×C3#575118yes—
288D3—1216no—
289C22—22no—
290C22—21no—
291C22—184no—
292C22—362no—
293C22—362no—
294C22—724no—
295C22C22×C4⋊(C3⋊D3)11yescharacteristic
296C4—22no—
297C4—22no—
298C4—21no—
299C4—362no—
300C4—362no—
301C4—362no—
302C4#41×C3⋊D312yes—
303C3#7938714yescomplemented
304C2—41no—
305C2—364no—
306C2#1059599511yescharacteristic
307C2#1059622212yes—
subgroupG/H
centerC22C22×C4⋊(C3⋊D3)
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#433C2
socleC22×C32C22×D4
prime radicalC22×C4⋊(C3⋊D3)C22
hypercenter#433C3⋊D3
hypocenterC32#3123
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
2. #10595989C2semidirect
3. C32×#433C2semidirect
4. #10592546C2semidirect
5. #10592540C2semidirect
7. #10592422C2semidirect
8. #10592409C2semidirect
9. C4×#3744C2semidirect
23. #64079C22semidirect
24. #64078C22semidirect
25. C4×#634C22semidirect
26. C32×C4⋊C8C22semidirect
28. C32×#97C22semidirect
29. C32×C4×C8C22semidirect
32. #63645C22semidirect
33. #63644C22semidirect
34. #63643C22semidirect
35. #63643C22semidirect
38. C3×#433D3semidirect
89. C3×C4⋊C8C2×D3semidirect
91. C3×#97C2×D3semidirect
92. C3×C4×C8C2×D3semidirect
128. #433C3⋊D3semidirect
188. C4⋊C8C2×C3⋊D3semidirect
194. #97C2×C3⋊D3semidirect
195. C4×C8C2×C3⋊D3semidirect
263. C32#3123semidirect
303. C3#79387semidirect

Maximal subgroups

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

subgroupindex
#105959922
#105959892
C32×#4332
#105925462
#105925402
#105924302
#105924222
#105924092
C4×#37442
#793873