Finite Group Databasebeta

← #11777188

Subgroups — #11777188

Order 1152.

302 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 302 conjugacy classes of subgroups — too many to draw. Only its 66 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
1D4×#622C211yesmaximal, characteristic
2#10593750C211yesmaximal, characteristic, complemented
3#10592457C211yesmaximal, characteristic
4D4⋊#622C211yesmaximal, characteristic
5#10590172C211yesmaximal, characteristic, complemented
6C8×#622C211yesmaximal, characteristic, complemented
7#10590161C211yesmaximal, characteristic, complemented
8C22×#622—21no—
9D4×C3⋊Dic3C2211yescharacteristic
10C2×#3754C411yescharacteristic
11#64096C2211yescharacteristic
12C22⋊#622—21no—
13#63779—21no—
14C4⋊#622C2211yescharacteristic
15C4⋊#622C2211yescharacteristic
16C4×#622—21no—
17C4×#622C2211yescharacteristic
18C4×#622C2211yescharacteristic
19C32×#102C411yescharacteristic
20#63643C411yescharacteristic
21C8×C3⋊Dic3C2211yescharacteristic
22#63635C411yescharacteristic
23#4758—62no—
24C2×C32×D4C2×C411yescharacteristic
25C22×C3⋊Dic3—21no—
26C2×#634C2×C411yescharacteristic
27C2×#622—21no—
28C2×#622—21no—
29C2×#622—21no—
30C2×#622—42no—
31C2×#622D411yescharacteristic
32C2×#622D411yescharacteristic
33C2×C32×C8C2×C411yescharacteristic
34C32×C4⋊C4C2×C411yescharacteristic
35#3757—21no—
36#3754C814yescomplemented
37C4⋊(C3⋊Dic3)C2×C411yescharacteristic
38#3750—21no—
39C4×C3⋊Dic3—21no—
40C4×C3⋊Dic3C2311yescharacteristic
41C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
42C8×SD16—91nomaximal, Sylow
43D4×Dic3—62no—
44C2×#214—62no—
45#887—62no—
46C3×#102—22no—
47#816—62no—
48C8×Dic3—62no—
49#808—62no—
50C23×C32—21no—
51C32×D4—21no—
52C32×D4C2×C812yes—
53C2×C32×C4—21no—
54C2×C32×C4C22×C411yescharacteristic
55C2×C3⋊Dic3—21no—
56C2×C3⋊Dic3—21no—
57C2×C3⋊Dic3—41no—
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3C2×D411yescharacteristic
60C2×C3⋊Dic3#4111yescharacteristic
61#634—21no—
62#634C2×C812yescomplemented
63#622—22no—
64#622—21no—
65#622—41no—
66#622—41no—
67#622SD1612yescomplemented
68C32×C8—21no—
69C3⋊(C3⋊C8)C2×C812yescomplemented
70C8×Q8—91no—
71C4×SD16—91no—
72C8×D4—91no—
73#334—91no—
74Q8⋊C8—91no—
75D4⋊C8—91no—
76C82—91no—
77C2×C3×D4—22no—
78C22×Dic3—122no—
79C2×Dic6—62no—
80C2×C3×C8—22no—
81C3×C4⋊C4—22no—
82#217—122no—
83#214—68no—
84C4⋊Dic3—62no—
85Dic3⋊C4—122no—
86C4×Dic3—62no—
87C4×Dic3—122no—
88C2×C3⋊C8—62no—
89C22×C32—22no—
90C22×C32—41no—
91C22×C32—41no—
92C22×C32C4×D411yescharacteristic
93C32×C4—41no—
94C32×C4C22×C811yescharacteristic
95C32×C4#13111yescharacteristic
96C3⋊Dic3—22no—
97C3⋊Dic3—21no—
98C3⋊Dic3—41no—
99C3⋊Dic3C2×SD1611yescharacteristic
100C3⋊Dic3#13511yescharacteristic
101C2×SD16—91no—
102C22×C8—181no—
103C4×Q8—91no—
104C4×D4—91no—
105#106—91no—
106C4⋊C8—91no—
107C4⋊C8—91no—
108C4⋊C8—181no—
109#103—91no—
110#102#15711yescharacteristic
111C22⋊C8—181no—
112C4×C8—91no—
113C4×C8—91no—
114C4×C8—91no—
115C4×C8—181no—
116C23×C3—42no—
117C3×D4—24no—
118C3×D4—42no—
119C2×C3×C4—22no—
120C2×C3×C4—42no—
121C2×Dic3—62no—
122C2×Dic3—62no—
123C2×Dic3—122no—
124C2×Dic3—122no—
125C2×Dic3—242no—
126C2×Dic3—242no—
127Dic6—64no—
128Dic6—122no—
129C3×C8—42no—
130C3⋊C8—64no—
131C2×C32—42no—
132C2×C32C8×D411yescharacteristic
133C2×C32C4×SD1611yescharacteristic
134C2×C32#44311yescharacteristic
135C2×Q8—91no—
136C2×D4C2×#15711yescharacteristic
137C22×C4—181no—
138SD16—94no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—181no—
143C2×C8—181no—
144C2×C8—181no—
145C2×C8—362no—
146C2×C8C2×#15711yescharacteristic
147C4⋊C4—91no—
148C4⋊C4—181no—
149C4⋊C4C2×#15711yescharacteristic
150C22⋊C4—181no—
151C42—91no—
152C42—181no—
153C22×C3—22no—
154C22×C3—44no—
155C22×C3—82no—
156C22×C3—82no—
157C3×C4—22no—
158C3×C4—22no—
159C3×C4—82no—
160Dic3—62no—
161Dic3—62no—
162Dic3—124no—
163Dic3—122no—
164Dic3—242no—
165C32C8×SD1611yescharacteristic, complemented, Sylow
166C23—21no—
167Q8—92no—
168Q8—181no—
169D4—21no—
170D4#378712yes—
171C2×C4—21no—
172C2×C4—91no—
173C2×C4—91no—
174C2×C4—181no—
175C2×C4—181no—
176C2×C4—361no—
177C2×C4—361no—
178C2×C4C22×#15711yescharacteristic
179C8—21no—
180C8—92no—
181C8—92no—
182C8—181no—
183C8—182no—
184C8—361no—
185C8—361no—
186C2×C3—22no—
187C2×C3—22no—
188C2×C3—22no—
189C2×C3—84no—
190C22—22no—
191C22—41no—
192C22—41no—
193C22D4×#15711yescharacteristic
194C4—41no—
195C4—91no—
196C4—91no—
197C4—182no—
198C4—181no—
199C4—361no—
200C4C2×#378711yescharacteristic
201C4#6428711yescharacteristic
202C3—22no—
203C2—42no—
204C2#1059373911yescharacteristic
205C2#1059377911yescharacteristic
206C2SD16×#15711yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC32×C4C22×C8
FrattiniC2×C4C22×#157
FittingC32×#102C4
socleC22×C32C4×D4
prime radicalC2×C32×D4C2×C4
cosocleC4×C3⋊Dic3C23
hypercenter#102#157
hypocenterC32C8×SD16
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #102

Complements

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

NH ≅ G/Ntype
2. #10593750C2semidirect
5. #10590172C2semidirect
6. C8×#622C2semidirect
7. #10590161C2semidirect
36. #3754C8semidirect
62. #634C2×C8semidirect
67. #622SD16semidirect
69. C3⋊(C3⋊C8)C2×C8semidirect
165. C32C8×SD16semidirect

Maximal subgroups

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

subgroupindex
D4×#6222
#105937502
#105924572
D4⋊#6222
#105901722
C8×#6222
#105901612
C8×SD169