Finite Group Databasebeta

← #11787107

Subgroups — #11787107

Order 1152.

599 conjugacy classes of subgroups; only the 122 normal subgroups are shown.

normal subgroups only

This group has 599 conjugacy classes of subgroups — too many to draw. Only its 122 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#10594780C211yesmaximal, characteristic
2#10592809C211yesmaximal, characteristic
3C3×#5102C212yesmaximal, complemented
4#10591232C211yesmaximal, characteristic
5#10589169C212yesmaximal, complemented
6#70546—32nomaximal
7C2×#3828C2211yescharacteristic
8C22×C32×C8C2211yescharacteristic
9C2×#3748C2211yescharacteristic
10C3×#926C2212yes—
11C2×C3×#208C2212yes—
12#63818—22no—
13#63817—24no—
14#63647—22no—
15C3×Dic3⋊C8—24no—
16#63581C414yes—
17#5745—32no—
18C3×#424—32no—
19#5110—32no—
20#5110—61no—
21#5102D312yescomplemented
22#5006—32no—
23#4556—32no—
24#4533—32no—
25C22×C32×C4C2311yescharacteristic
26C2×#638C2×C412yes—
27#3828—22no—
28#3828—22no—
29C2×C4⋊(C3⋊D3)Q811yescharacteristic
30C2×C4×C3⋊D3D412yes—
31C2×#634Q811yescharacteristic
32C2×C32×C8—21no—
33C2×C32×C8—22no—
34#3748—22no—
35C2×C3⋊(C3⋊C8)—21no—
36C3×#217C2×C414yes—
37C3×C4⋊Dic3—22no—
38C3×C4×Dic3—22no—
39C3×#208—22no—
40C3×#208—22no—
41C2×C3×C3⋊C8D414yes—
42#3712—24no—
43#3710—24no—
44#1868—91noSylow
45C2×#235—32no—
46C2×#235—61no—
47C2×C3×M16—32no—
48C22×C3×C8—21no—
49C22×C3×C8C2×D312yes—
50C3×#117—32no—
51#926C2×D312yes—
52C2×#208—32no—
53C2×#208—61no—
54C2×#208C2×D312yes—
55#907—64no—
56D3×M16—64no—
57#901—64no—
58C3×C4⋊C8—64no—
59(C2×D3)⋊C8—64no—
60(C2×D3)⋊C8—64no—
61Dic3⋊C8—24no—
62#806—38no—
63C23×C32C22×C411yescharacteristic
64C22×C3⋊D3C4⋊C412yes—
65C2×C32×C4C2×D411yescharacteristic
66C2×C32×C4C2×D412yes—
67C2×C32×C4C2×Q811yescharacteristic
68C2×C32×C4#4112yes—
69#638—24no—
70C2×C3⋊Dic3C4⋊C412yes—
71C4⋊(C3⋊D3)—22no—
72C4×C3⋊D3—22no—
73C4×C3⋊D3—22no—
74#634—22no—
75C2×C3×Dic3—24no—
76C32×C8—41no—
77C3⋊(C3⋊C8)—41no—
78C3×C3⋊C8—24no—
79#568—91no—
80#424—32no—
81#410—91no—
82#408—91no—
83#344—92no—
84C22×C3×C4—21no—
85C22×C3×C4C22×D312yes—
86C2×#67—34no—
87C2×#67—62no—
88#235—62no—
89#235—62no—
90#235—62no—
91#235—62no—
92#235—122no—
93#235—122no—
94C2×D12—32no—
95C2×D12—61no—
96C2×C4×D3—34no—
97C2×C4×D3—62no—
98C2×Dic6—32no—
99C2×Dic6—61no—
100C3×M16—62no—
101C3×M16—62no—
102C2×C3×C8—22no—
103C2×C3×C8—22no—
104C2×C3×C8—22no—
105C2×C3×C8—22no—
106C2×C3×C8—34no—
107C2×C3×C8—42no—
108C3×C4⋊C4—62no—
109C3×C22⋊C4—34no—
110C3×C42—62no—
111#217C4×D314yes—
112C4⋊Dic3—22no—
113C4×Dic3—22no—
114#208—22no—
115#208—22no—
116#208—62no—
117#208—62no—
118#208—122no—
119C2×C3⋊C8—62no—
120C2×C3⋊C8—62no—
121C2×C3⋊C8#6714yes—
122ΓL(1,𝔽25)—68no—
123D3×C8—68no—
124C22×C32—41no—
125C22×C32C2×C4⋊C411yescharacteristic
126C22×C32C4×D412yes—
127C2×C3⋊D3—22no—
128C2×C3⋊D3—42no—
129C32×C4#12011yescharacteristic
130C32×C4C22⋊Q812yes—
131C32×C4#12311yescharacteristic
132C3⋊Dic3—22no—
133C3×Dic3—44no—
134C2×#41—91no—
135#131—184no—
136C2×M16—32no—
137C2×M16—91no—
138C2×M16—182no—
139C22×C8D3211yescharacteristic
140#117—32no—
141C4⋊C8—64no—
142#99—94no—
143C22⋊C8—182no—
144C23×C3—21no—
145C23×C3C2×C4×D312yes—
146C22×D3—34no—
147C22×D3—62no—
148C2×C3×C4—21no—
149C2×C3×C4—22no—
150C2×C3×C4—22no—
151C2×C3×C4—21no—
152C2×C3×C4—64no—
153C2×C3×C4#23512yes—
154C2×C3×C4D3×D412yes—
155C2×C3×C4D3×D412yes—
156C2×C3×C4D3×Q812yes—
157C2×C3×C4#23912yes—
158C2×C3×C4C2×#6712yes—
159#67—64no—
160#67—64no—
161#67—124no—
162C2×Dic3—24no—
163C2×Dic3—34no—
164C2×Dic3—62no—
165D12—62no—
166D12—62no—
167D12—122no—
168C4×D3—64no—
169C4×D3—64no—
170C4×D3—122no—
171C4×D3—122no—
172Dic6—62no—
173Dic6—62no—
174Dic6—122no—
175C3×C8—42no—
176C3×C8—42no—
177C3×C8—64no—
178C3⋊C8—24no—
179C3⋊C8—122no—
180C3⋊C8—122no—
181C2×C32—21no—
182C2×C32—22no—
183C2×C32#38511yescharacteristic
184C3⋊D3—42no—
185#41—182no—
186#41—182no—
187C2×Q8—91no—
188C2×D4—92no—
189C2×D4—91no—
190C22×C4—92no—
191C22×C4C2×D3211yescharacteristic
192M16—62no—
193M16—62no—
194M16—184no—
195M16—182no—
196C2×C8—22no—
197C2×C8—21no—
198C2×C8—34no—
199C2×C8—184no—
200C2×C8—181no—
201C4⋊C4—62no—
202C22⋊C4—34no—
203C42—62no—
204C22×C3—21no—
205C22×C3—22no—
206C22×C3—42no—
207C22×C3—42no—
208C22×C3D3×C4⋊C412yes—
209C22×C3#89312yes—
210C22×C3C4×#6712yes—
211C2×D3—64no—
212C2×D3—122no—
213C2×D3—124no—
214C2×D3—124no—
215C3×C4—22no—
216C3×C4—21no—
217C3×C4—21no—
218C3×C4—124no—
219C3×C4#89412yes—
220C3×C4#89612yes—
221C3×C4#93712yes—
222C3×C4#94612yes—
223Dic3—44no—
224Dic3—64no—
225Dic3—122no—
226C32#186811yescharacteristic, complemented, Sylow
227C23—92no—
228C23C4×D3211yescharacteristic
229Q8—182no—
230D4—184no—
231D4—182no—
232C2×C4—64no—
233C2×C4—92no—
234C2×C4—182no—
235C2×C4—182no—
236C2×C4#379711yescharacteristic
237C2×C4#379912yes—
238C2×C4D3×#6712yes—
239C2×C4#381111yescharacteristic
240C8—41no—
241C8—64no—
242C8—361no—
243C2×C3—22no—
244C2×C3—22no—
245C2×C3—22no—
246C2×C3—22no—
247C2×C3—21no—
248C2×C3—42no—
249C2×C3#498912yes—
250D3—124no—
251D3—242no—
252C22—41no—
253C22—182no—
254C22—362no—
255C22#6388311yescharacteristic
256C22#6390412yes—
257C4—124no—
258C4—182no—
259C4#6388812yes—
260C4#6389711yescharacteristic
261C4#6398311yescharacteristic
262C3—21no—
263C3#7054612yescomplemented
264C2—22no—
265C2—21no—
266C2—362no—
267C2#1059137411yescharacteristic
subgroupG/H
centerC4#63983
commutatorC23×C32C22×C4
FrattiniC22×C4C2×D32
FittingC22×C32×C8C22
socleC2×C32#385
prime radicalC2×#3828C22
cosocleC22×C32×C4C23
hypercenterC22×C8D32
hypocenterC32#1868
LCSG ▷ C23×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×C8

Complements

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

NH ≅ G/Ntype
3. C3×#5102C2semidirect
5. #10589169C2semidirect
21. #5102D3semidirect
226. C32#1868semidirect
263. C3#70546semidirect

Maximal subgroups

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

subgroupindex
#105947802
#105928092
C3×#51022
#105912322
#105891692
#705463