Finite Group Databasebeta

← #11874953

Subgroups — #11874953

Order 1152.

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

normal subgroups only

This group has 929 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
1#10593909C212yesmaximal
2C4×C8×C3⋊D3C211yesmaximal, characteristic
3C3×#4682C212yesmaximal, complemented
4#10590902C214yesmaximal, complemented
5#10590687C214yesmaximal
6#10590312C212yesmaximal, complemented
7D3×#500—32nomaximal
8C2×#3797—22no—
9C2×C8×C3⋊D3C2212yes—
10C42×C3⋊D3C2211yescharacteristic
11C3×#869C2214yes—
12#63919—22no—
13#63919C2214yes—
14#63900—22no—
15#63900C2214yes—
16#63873—22no—
17C32×C4×C8C2211yescharacteristic
18C8×C3⋊Dic3C2212yes—
19C4×C3⋊(C3⋊C8)C2211yescharacteristic
20C3×#818C2218yes—
21#63576C2218yes—
22D3×C4⋊Q8—34no—
23C3×#500—32no—
24#5078—34no—
25D3×#107—38no—
26#4874—38no—
27C4×D3×C8—32no—
28C4×D3×C8—61no—
29#4682D312yescomplemented
30C2×C4×C3⋊D3D411yescharacteristic
31C2×C4×C3⋊D3D411yescharacteristic
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×C3×Dic6—24no—
34C2×#627—24no—
35C2×#624—24no—
36#3797—48no—
37C2×C32×C8C2312yes—
38C32×C42C2311yescharacteristic
39C4×C3⋊Dic3D411yescharacteristic
40C4×C3⋊Dic3D411yescharacteristic
41C4×C3⋊Dic3C2311yescharacteristic
42C2×C3⋊(C3⋊C8)C2312yes—
43C8×C3⋊D3Q818yescomplemented
44C3×C4⋊Dic3—24no—
45C3×C4⋊Dic3C2318yes—
46#3724—24no—
47#3724—24no—
48C2×#500—91noSylow
49C2×D3×Q8—64no—
50C3×C4⋊Q8—34no—
51#944—64no—
52C2×D3×C8—34no—
53C2×D3×C8—62no—
54D3×C4⋊C4—38no—
55D3×C4⋊C4—64no—
56#888—38no—
57#888—64no—
58C42×D3—32no—
59C42×D3—61no—
60#869C2×D314yes—
61C3×#107—38no—
62C3×C4×C8—21no—
63C3×C4×C8C2×D312yes—
64#818C2×D318yes—
65C8×Dic3—34no—
66C8×Dic3—62no—
67#807—316no—
68C4×C3⋊C8—32no—
69C4×C3⋊C8—61no—
70C22×C3⋊D3C2×D411yescharacteristic
71C2×C32×C4C2×D411yescharacteristic
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2411yescharacteristic
74C2×C3⋊Dic3C2×D411yescharacteristic
75C2×C3⋊Dic3C2×D411yescharacteristic
76C2×C3⋊Dic3C2×D411yescharacteristic
77C4×C3⋊D3D814yes—
78C4×C3⋊D3Q1614yes—
79C4×C3⋊D3C2×Q814yes—
80C2×C3×Dic3—28no—
81C3×Dic6—48no—
82#627—48no—
83#624—48no—
84C32×C8C2×Q814yescomplemented
85C3⋊(C3⋊C8)C2×Q814yescomplemented
86C2×C4⋊Q8—92no—
87#500—32no—
88#500—94no—
89#500—92no—
90C2×#107—94no—
91C2×C4×C8—91no—
92C2×C3×Q8—64no—
93D3×Q8—1216no—
94C2×C4×D3—32no—
95C2×C4×D3—32no—
96C2×C4×D3—32no—
97C2×C4×D3—61no—
98C2×C4×D3—61no—
99C2×C4×D3—61no—
100C2×C4×D3—68no—
101C2×Dic6—24no—
102C2×Dic6—68no—
103C2×C3×C8—22no—
104C2×C3×C8C22×D314yes—
105C3×C4⋊C4—38no—
106C3×C4⋊C4—64no—
107C3×C42—21no—
108C3×C42C22×D312yes—
109C4⋊Dic3—24no—
110C4⋊Dic3C22×D318yes—
111Dic3⋊C4—68no—
112Dic3⋊C4—68no—
113C4×Dic3—32no—
114C4×Dic3—32no—
115C4×Dic3—32no—
116C4×Dic3—61no—
117C4×Dic3—61no—
118C4×Dic3—61no—
119C2×C3⋊C8—34no—
120C2×C3⋊C8—62no—
121D3×C8—316no—
122D3×C8—68no—
123C22×C32C22×D411yescharacteristic
124C2×C3⋊D3C4⋊Q812yes—
125C2×C3⋊D3C2×D812yes—
126C2×C3⋊D3C2×Q1612yes—
127C32×C4C2×D812yes—
128C32×C4C2×Q1612yes—
129C32×C4C22×Q812yes—
130C3⋊Dic3C4⋊Q812yes—
131C3⋊Dic3C2×D812yes—
132C3⋊Dic3C2×Q1612yes—
133C3×Dic3—48no—
134C22×Q8—182no—
135C22×C8—92no—
136C4⋊Q8—34no—
137C4⋊Q8—94no—
138C4⋊Q8—182no—
139C4⋊Q8—182no—
140C2×C4⋊C4—94no—
141C2×C4⋊C4—182no—
142C2×C42—91no—
143#107—38no—
144#107—98no—
145C4×C8—92no—
146C4×C8—91no—
147C4×C8D3211yescharacteristic
148C22×D3—32no—
149C22×D3—61no—
150C3×Q8—128no—
151C2×C3×C4—21no—
152C2×C3×C4—21no—
153C2×C3×C4—21no—
154C2×C3×C4—68no—
155C2×C3×C4D3×D412yes—
156C2×C3×C4D3×D412yes—
157C2×C3×C4C23×D312yes—
158C2×Dic3—28no—
159C2×Dic3—32no—
160C2×Dic3—32no—
161C2×Dic3—32no—
162C2×Dic3—61no—
163C2×Dic3—61no—
164C2×Dic3—61no—
165C4×D3—38no—
166C4×D3—38no—
167C4×D3—38no—
168C4×D3—64no—
169C4×D3—64no—
170C4×D3—64no—
171C4×D3—1216no—
172Dic6—48no—
173Dic6—1216no—
174C3×C8—24no—
175C3×C8D3×Q818yescomplemented
176C3⋊C8—38no—
177C3⋊C8—64no—
178C2×C32C2×C4⋊Q811yescharacteristic
179C2×C32C22×D811yescharacteristic
180C2×C32C22×Q1611yescharacteristic
181C3⋊D3#50014yescomplemented
182C2×Q8—64no—
183C2×Q8—184no—
184C2×Q8—368no—
185C22×C4—91no—
186C22×C4—91no—
187C22×C4—91no—
188C22×C4—184no—
189C2×C8—92no—
190C2×C8—98no—
191C2×C8C2×D3212yes—
192C4⋊C4—38no—
193C4⋊C4—64no—
194C4⋊C4—184no—
195C4⋊C4—184no—
196C42—91no—
197C42—91no—
198C42—91no—
199C42C2×D3211yescharacteristic
200C22×C3—21no—
201C22×C3C2×D3×D412yes—
202C2×D3—34no—
203C2×D3—34no—
204C2×D3—34no—
205C2×D3—62no—
206C2×D3—62no—
207C2×D3—62no—
208C3×C4—22no—
209C3×C4—22no—
210C3×C4—22no—
211C3×C4—128no—
212C3×C4D3×D814yes—
213C3×C4D3×Q1614yes—
214C3×C4C2×D3×Q814yes—
215Dic3—34no—
216Dic3—34no—
217Dic3—34no—
218Dic3—48no—
219Dic3—62no—
220Dic3—62no—
221Dic3—62no—
222C32C2×#50011yescharacteristic, complemented, Sylow
223C23—91no—
224Q8—128no—
225Q8—368no—
226C2×C4—68no—
227C2×C4—91no—
228C2×C4—91no—
229C2×C4—91no—
230C2×C4—94no—
231C2×C4—94no—
232C2×C4—94no—
233C2×C4—368no—
234C2×C4#380211yescharacteristic
235C2×C4#380211yescharacteristic
236C2×C4C22×D3211yescharacteristic
237C8—94no—
238C8#379714yescomplemented
239C2×C3—21no—
240C2×C3—21no—
241C2×C3—21no—
242C2×C3D3×C4⋊Q812yes—
243C2×C3C2×D3×D812yes—
244C2×C3C2×D3×Q1612yes—
245D3—38no—
246D3—64no—
247C22—92no—
248C22—92no—
249C22—92no—
250C22C2×#380211yescharacteristic
251C4—92no—
252C4—92no—
253C4—92no—
254C4—128no—
255C4#6379712yes—
256C4#6380212yes—
257C4C2×#379712yes—
258C3—21no—
259C3D3×#50012yescomplemented
260C2—94no—
261C2#1059390911yescharacteristic
262C2C2×#6379711yescharacteristic
263C2C2×#6380211yescharacteristic
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32C2×#500
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
3. C3×#4682C2semidirect
4. #10590902C2semidirect
6. #10590312C2semidirect
29. #4682D3semidirect
43. C8×C3⋊D3Q8semidirect
84. C32×C8C2×Q8semidirect
85. C3⋊(C3⋊C8)C2×Q8semidirect
175. C3×C8D3×Q8semidirect
181. C3⋊D3#500semidirect
222. C32C2×#500semidirect
238. C8#3797semidirect
259. C3D3×#500semidirect

Maximal subgroups

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

subgroupindex
#105939092
C4×C8×C3⋊D32
C3×#46822
#105909022
#105906872
#105903122
D3×#5003