Finite Group Databasebeta

← #11874189

Subgroups — #11874189

Order 1152.

1601 conjugacy classes of subgroups; only the 220 normal subgroups are shown.

normal subgroups only

This group has 1601 conjugacy classes of subgroups — too many to draw. Only its 220 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
1C2×#63797C214yesmaximal, complemented
2#10594008C212yesmaximal, complemented
3C4×C8×C3⋊D3C211yesmaximal, characteristic, complemented
4C3×#4695C212yesmaximal, complemented
5#10590886C214yesmaximal, complemented
6#10590352C212yesmaximal, complemented
7D3×#493—32nomaximal
8C2×#3802—24no—
9C2×#3802C2214yes—
10C2×C8×C3⋊D3C2212yes—
11C42×C3⋊D3C2211yescharacteristic
12C2×C3×D24C2218yescomplemented
13C3×#874C2214yescomplemented
14#63914—24no—
15#63914C2214yescomplemented
16C2×#3713C2218yescomplemented
17#63797—216no—
18C32×C4×C8C2211yescharacteristic, complemented
19C8×C3⋊Dic3C2212yescomplemented
20C4×C3⋊(C3⋊C8)C2211yescharacteristic, complemented
21C2×D3×D8—38no—
22D3×#127—34no—
23C3×#493—32no—
24#5151—38no—
25#5073—34no—
26#4695D312yescomplemented
27C4×D3×C8—32no—
28C4×D3×C8—61no—
29C22×D32—24no—
30C2×C4×C3⋊D3D412yes—
31C2×C4×C3⋊D3C2311yescharacteristic
32C2×C3×D12—28no—
33C2×C3×D12C2318yes—
34C2×#625—28no—
35C2×#625—24no—
36#3802—216no—
37#3802—416no—
38C2×C32×C8C2312yes—
39C32×C42C2311yescharacteristic
40C4×C3⋊Dic3D412yes—
41C4×C3⋊Dic3C2311yescharacteristic
42C2×C3⋊(C3⋊C8)C2312yes—
43C8×C3⋊D3D418yescomplemented
44C3×D24—216no—
45#3713—216no—
46C2×#493—91noSylow
47C2×D3×D4—38no—
48C2×D3×D4—68no—
49C2×C3×D8—38no—
50C3×#127—34no—
51#940—38no—
52#940—68no—
53C2×#213—316no—
54D3×D8—632no—
55C2×D24C2×D318yescomplemented
56C2×D3×C8—34no—
57C2×D3×C8—62no—
58#874C2×D314yescomplemented
59C42×D3—32no—
60C42×D3—61no—
61C3×C4×C8—21no—
62C3×C4×C8C2×D312yescomplemented
63C8×Dic3—34no—
64C8×Dic3—62no—
65C4×C3⋊C8—32no—
66C4×C3⋊C8—61no—
67C22×C3⋊D3C2×D411yescharacteristic
68C22×C3×D3—28no—
69C2×D32—48no—
70C2×D32—416no—
71C2×C32×C4C2×D412yes—
72C2×C32×C4C2411yescharacteristic
73C2×C3⋊Dic3C2×D411yescharacteristic
74C2×C3⋊Dic3C2×D412yes—
75C4×C3⋊D3D818yescomplemented
76C4×C3⋊D3C2×D414yes—
77C3×D12—216no—
78C3×D12—416no—
79#625—48no—
80#625—416no—
81C32×C8C2×D414yescomplemented
82C3⋊(C3⋊C8)C2×D414yescomplemented
83C22×D8—94no—
84C2×#127—92no—
85#493—32no—
86#493—92no—
87#493—94no—
88C2×C4×C8—91no—
89C23×D3—68no—
90C2×C3×D4—38no—
91C2×C3×D4—68no—
92C2×#67—616no—
93C2×#67—68no—
94D3×D4—632no—
95D3×D4—1232no—
96C2×D12—28no—
97C2×D12C22×D318yes—
98C2×C4×D3—34no—
99C2×C4×D3—32no—
100C2×C4×D3—61no—
101C2×C4×D3—62no—
102C3×D8—616no—
103C2×C3×C8—22no—
104C2×C3×C8C22×D314yes—
105C3×C42—21no—
106C3×C42C22×D312yes—
107#213—632no—
108C4×Dic3—34no—
109C4×Dic3—32no—
110C4×Dic3—61no—
111C4×Dic3—62no—
112C2×C3⋊C8—34no—
113C2×C3⋊C8—62no—
114D24—216no—
115D3×C8—316no—
116D3×C8—68no—
117C22×C32C22×D411yescharacteristic
118C2×C3⋊D3#12712yes—
119C2×C3⋊D3C2×D814yes—
120C2×C3×D3—48no—
121C2×C3×D3—416no—
122D32—816no—
123C32×C4C2×D814yescomplemented
124C32×C4C22×D412yes—
125C3⋊Dic3#12712yes—
126C3⋊Dic3C2×D814yescomplemented
127C22×D4—94no—
128C22×D4—184no—
129C2×D8—38no—
130C2×D8—98no—
131C2×D8—1816no—
132C22×C8—92no—
133#127—34no—
134#127—94no—
135#127—184no—
136C2×C42—91no—
137C4×C8—92no—
138C4×C8—91no—
139C4×C8D3211yescharacteristic, complemented
140C23×C3—68no—
141C22×D3—28no—
142C22×D3—32no—
143C22×D3—61no—
144C22×D3—1216no—
145C22×D3—1232no—
146C3×D4—616no—
147C3×D4—1216no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4D3×D414yes—
151C2×C3×C4C23×D312yes—
152#67—1216no—
153#67—1232no—
154C2×Dic3—32no—
155C2×Dic3—34no—
156C2×Dic3—61no—
157C2×Dic3—62no—
158D12—216no—
159D12—416no—
160C4×D3—316no—
161C4×D3—38no—
162C4×D3—68no—
163C4×D3—64no—
164C3×C8—24no—
165C3×C8D3×D418yescomplemented
166C3⋊C8—38no—
167C3⋊C8—64no—
168C2×C32C2×#12711yescharacteristic
169C2×C32C22×D812yes—
170C3⋊D3#49314yescomplemented
171C3×D3—88no—
172C24—184no—
173C2×D4—38no—
174C2×D4—68no—
175C2×D4—1816no—
176C2×D4—188no—
177C2×D4—184no—
178C2×D4—3616no—
179C22×C4—91no—
180C22×C4—92no—
181D8—616no—
182D8—1816no—
183C2×C8—92no—
184C2×C8—98no—
185C2×C8C2×D3212yes—
186C42—91no—
187C42—92no—
188C42C2×D3211yescharacteristic
189C22×C3—21no—
190C22×C3—128no—
191C22×C3—1216no—
192C22×C3C2×D3×D412yes—
193C2×D3—34no—
194C2×D3—38no—
195C2×D3—48no—
196C2×D3—416no—
197C2×D3—62no—
198C2×D3—64no—
199C2×D3—2432no—
200C3×C4—22no—
201C3×C4—24no—
202C3×C4D3×D818yescomplemented
203C3×C4C2×D3×D414yes—
204Dic3—34no—
205Dic3—38no—
206Dic3—62no—
207Dic3—64no—
208C32C2×#49311yescharacteristic, complemented, Sylow
209C23—68no—
210C23—91no—
211C23—368no—
212C23—3616no—
213D4—616no—
214D4—1216no—
215D4—368no—
216D4—3616no—
217C2×C4—92no—
218C2×C4—91no—
219C2×C4—94no—
220C2×C4—98no—
221C2×C4#380212yes—
222C2×C4C22×D3211yescharacteristic
223C8—94no—
224C8#380214yescomplemented
225C2×C3—22no—
226C2×C3—21no—
227C2×C3—248no—
228C2×C3D3×#12712yes—
229C2×C3C2×D3×D814yes—
230D3—38no—
231D3—64no—
232D3—88no—
233C22—94no—
234C22—92no—
235C22—1216no—
236C22—128no—
237C22—7216no—
238C22C2×#380211yescharacteristic
239C4—94no—
240C4—92no—
241C4#6379714yescomplemented
242C4C2×#380212yes—
243C3—21no—
244C3D3×#49312yescomplemented
245C2—94no—
246C2—248no—
247C2#1059400811yescharacteristic
248C2C2×#6379712yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
hypercenterC4×C8D32
hypocenterC32C2×#493
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63797C2semidirect
2. #10594008C2semidirect
3. C4×C8×C3⋊D3C2semidirect
4. C3×#4695C2semidirect
5. #10590886C2semidirect
6. #10590352C2semidirect
12. C2×C3×D24C22semidirect
13. C3×#874C22semidirect
15. #63914C22semidirect
16. C2×#3713C22semidirect
18. C32×C4×C8C22semidirect
19. C8×C3⋊Dic3C22semidirect
20. C4×C3⋊(C3⋊C8)C22semidirect
26. #4695D3semidirect
43. C8×C3⋊D3D4semidirect
55. C2×D24C2×D3semidirect
58. #874C2×D3semidirect
62. C3×C4×C8C2×D3semidirect
75. C4×C3⋊D3D8semidirect
81. C32×C8C2×D4semidirect
82. C3⋊(C3⋊C8)C2×D4semidirect
123. C32×C4C2×D8semidirect
126. C3⋊Dic3C2×D8semidirect
139. C4×C8D32semidirect
165. C3×C8D3×D4semidirect
170. C3⋊D3#493semidirect
202. C3×C4D3×D8semidirect
208. C32C2×#493semidirect
224. C8#3802semidirect
241. C4#63797semidirect
244. C3D3×#493semidirect

Maximal subgroups

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

subgroupindex
C2×#637972
#105940082
C4×C8×C3⋊D32
C3×#46952
#105908862
#105903522
D3×#4933