Finite Group Databasebeta

← #11803810

Subgroups — #11803810

Order 1152.

806 conjugacy classes of subgroups; only the 170 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 170 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×Q8×#157C212yesmaximal
2C3⋊D3×C4⋊Q8C211yesmaximal, characteristic
3#10593837C212yesmaximal
4#10593758C218yesmaximal
5#10593736C211yesmaximal, characteristic
6#10593733C211yesmaximal, characteristic
7C2×Q8×C3⋊D3C2212yes—
8Q8×#157—28no—
9C2×C4⋊#157C2212yes—
10C2×C4⋊#157C2214yes—
11C2×C4×#157C2214yes—
12C2×C4×#157C2211yescharacteristic
13C2×C4×#157C2211yescharacteristic
14C32×C4⋊Q8C411yescharacteristic, complemented
15#64153C412yescomplemented
16C4⋊C4×C3⋊D3C2214yes—
17#64097C414yescomplemented
18C42×C3⋊D3C2211yescharacteristic
19#64078C411yescharacteristic, complemented
20#63781C2218yes—
21#63781C2214yes—
22#63781C2214yes—
23D3×C4⋊Q8—62no—
24C22×#157C2314yes—
25C22×#157C2312yes—
26C22×#157C2312yes—
27C2×C32×Q8C2×C412yes—
28Q8×C3⋊D3—24no—
29Q8×C3⋊D3—24no—
30C2×C4×C3⋊D3C2314yes—
31C2×C4×C3⋊D3C2312yes—
32C2×C4×C3⋊D3C2311yescharacteristic
33C2×#634C2×C412yes—
34C2×#634C2×C414yes—
35C4⋊#157—28no—
36C4⋊#157—24no—
37C4×#157—28no—
38C4×#157—22no—
39C4×#157D414yes—
40C32×C4⋊C4C2×C414yes—
41C32×C42C2×C411yescharacteristic
42C4⋊(C3⋊Dic3)C2×C414yes—
43#3750C2×C418yes—
44C4×C3⋊Dic3C2×C412yes—
45C4×C3⋊Dic3C2×C411yescharacteristic
46#2327—91nomaximal, Sylow
47C2×D3×Q8—64no—
48C3×C4⋊Q8—22no—
49#944—64no—
50D3×C4⋊C4—68no—
51#888—68no—
52C42×D3—62no—
53#869—62no—
54C22×C3⋊D3C2411yescharacteristic
55C2×#157—24no—
56C2×#157—24no—
57C2×#157—22no—
58C2×#157—28no—
59C2×#157—24no—
60C2×#157C2×D414yes—
61C32×Q8—24no—
62C2×C32×C4C22×C412yes—
63C2×C32×C4C22×C414yes—
64C2×C32×C4C22×C411yescharacteristic
65C2×C3⋊Dic3C22×C412yes—
66C2×C3⋊Dic3C22×C414yes—
67C2×C3⋊Dic3C22×C411yescharacteristic
68C4×C3⋊D3—24no—
69C4×C3⋊D3—24no—
70C4×C3⋊D3—24no—
71C4×C3⋊D3C2×D412yes—
72C4×C3⋊D3#4112yes—
73#634—24no—
74#634—28no—
75C2×C4⋊Q8—91no—
76C2×C4×Q8—92no—
77#391—92no—
78#387—98no—
79#382—91no—
80#376—91no—
81C2×C3×Q8—24no—
82D3×Q8—128no—
83D3×Q8—128no—
84C2×C4×D3—64no—
85C2×C4×D3—62no—
86C2×C4×D3—68no—
87C2×Dic6—64no—
88C2×Dic6—68no—
89C3×C4⋊C4—28no—
90C3×C42—22no—
91C4⋊Dic3—68no—
92Dic3⋊C4—616no—
93C4×Dic3—64no—
94C4×Dic3—62no—
95C22×C32C23×C411yescharacteristic
96C2×C3⋊D3C22×D411yescharacteristic
97C2×C3⋊D3C2×#4111yescharacteristic
98C2×C3⋊D32−1+414yes—
99#157—24no—
100#157—44no—
101#157—42no—
102C32×C4—22no—
103C32×C4—24no—
104C32×C4C4×D412yes—
105C3⋊Dic3—22no—
106C3⋊Dic3—24no—
107C3⋊Dic3C4×D412yes—
108C22×Q8—92no—
109C4⋊Q8—92no—
110C4⋊Q8—94no—
111C4⋊Q8—91no—
112C4⋊Q8#15711yescharacteristic, complemented
113C4×Q8—188no—
114C2×C4⋊C4—94no—
115C2×C4⋊C4—92no—
116C2×C4⋊C4—94no—
117C2×C42—91no—
118C2×C42—91no—
119C2×C42—94no—
120C2×C42—91no—
121#95—94no—
122#95—94no—
123#95—98no—
124C22×D3—62no—
125C3×Q8—48no—
126C2×C3×C4—24no—
127C2×C3×C4—22no—
128C2×C3×C4—28no—
129C2×Dic3—64no—
130C2×Dic3—62no—
131C2×Dic3—68no—
132C4×D3—64no—
133C4×D3—64no—
134C4×D3—616no—
135C4×D3—128no—
136C4×D3—128no—
137Dic6—1216no—
138Dic6—128no—
139C2×C32C2×C4×D411yescharacteristic
140C2×C32#51912yes—
141C3⋊D3#53612yes—
142C3⋊D3#54112yes—
143C2×Q8—94no—
144C2×Q8—92no—
145C2×Q8—184no—
146C2×Q8—184no—
147C2×Q8C2×#15712yes—
148C22×C4—91no—
149C22×C4—92no—
150C22×C4—92no—
151C22×C4—94no—
152C22×C4—92no—
153C22×C4—94no—
154C4⋊C4—98no—
155C4⋊C4—94no—
156C4⋊C4—184no—
157C4⋊C4—188no—
158C4⋊C4C2×#15714yes—
159C42—94no—
160C42—92no—
161C42—91no—
162C42—188no—
163C42—182no—
164C42C2×#15711yescharacteristic
165C22×C3—22no—
166C2×D3—62no—
167C2×D3—62no—
168C2×D3—68no—
169C3×C4—28no—
170C3×C4—24no—
171C3×C4—48no—
172Dic3—64no—
173Dic3—68no—
174Dic3—128no—
175C32#232711yescharacteristic, complemented, Sylow
176C23—91no—
177Q8—24no—
178Q8—188no—
179Q8—184no—
180C2×C4—91no—
181C2×C4—92no—
182C2×C4—92no—
183C2×C4—94no—
184C2×C4—92no—
185C2×C4—94no—
186C2×C4—184no—
187C2×C4—184no—
188C2×C4—184no—
189C2×C4—184no—
190C2×C4—184no—
191C2×C4—182no—
192C2×C4—184no—
193C2×C4—188no—
194C2×C4C22×#15712yes—
195C2×C4C22×#15714yes—
196C2×C4C22×#15711yescharacteristic
197C2×C3—22no—
198C2×C3—24no—
199D3—64no—
200D3—64no—
201C22—91no—
202C22—91no—
203C22—94no—
204C22C23×#15711yescharacteristic
205C4—24no—
206C4—22no—
207C4—92no—
208C4—184no—
209C4—184no—
210C4—182no—
211C4—364no—
212C4—362no—
213C4D4×#15712yes—
214C3—22no—
215C2—92no—
216C2—92no—
217C2C2×D4×#15711yescharacteristic
218C2#1059664612yes—
subgroupG/H
center, FrattiniC22C23×#157
commutator, socleC22×C32C23×C4
FittingC32×C4⋊Q8C4
prime radical, cosocleC22×C3⋊D3C24
hypercenterC4⋊Q8#157
hypocenterC32#2327
LCSG ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
14. C32×C4⋊Q8C4semidirect
15. #64153C4semidirect
17. #64097C4semidirect
19. #64078C4semidirect
112. C4⋊Q8#157semidirect
175. C32#2327semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×#1572
C3⋊D3×C4⋊Q82
#105938372
#105937582
#105937362
#105937332
#23279