Finite Group Databasebeta

← #11784410

Subgroups — #11784410

Order 1152.

338 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 338 conjugacy classes of subgroups — too many to draw. Only its 90 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×#63770C211yesmaximal, characteristic
2C2×#63767C211yesmaximal, characteristic
3#10593748C212yesmaximal
4#10592579C211yesmaximal, characteristic
5#10590164C212yesmaximal
6C2×C4×#157C2211yescharacteristic
7C2×#3788C2212yes—
8C2×#3787C2211yescharacteristic
9C2×C8×C3⋊D3C2211yescharacteristic
10#64101C2212yes—
11#63777—22no—
12C4×#622—22no—
13#63770C414yescomplemented
14#63767C414yescomplemented
15C32×#107C411yescharacteristic, complemented
16#63645C411yescharacteristic, complemented
17#63635C412yescomplemented
18#4880—62no—
19C22×#157—21no—
20C2×C4×C3⋊D3C2311yescharacteristic
21C2×#622—22no—
22C2×#622D412yes—
23C4×#157—21no—
24C4×#157C2×C412yes—
25#3788—22no—
26#3788C2×C414yes—
27#3787C2×C412yes—
28#3787Q812yes—
29C2×C32×C8C2×C411yescharacteristic
30C32×C4⋊C4C2×C412yes—
31#3752—22no—
32C4⋊(C3⋊Dic3)C2×C412yes—
33C4×C3⋊Dic3—22no—
34C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
35C8×C3⋊D3C2×C412yes—
36C8×C3⋊D3C2×C412yes—
37#1773—91nomaximal, Sylow
38C2×D3×C8—62no—
39#892—64no—
40C3×#107—22no—
41#818—62no—
42#808—64no—
43C22×C3⋊D3#4111yescharacteristic
44C2×#157—22no—
45C2×#157—41no—
46C2×#157—41no—
47C2×C32×C4—22no—
48C2×C32×C4C22×C411yescharacteristic
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3C2×D411yescharacteristic
51C4×C3⋊D3C22×C411yescharacteristic
52C4×C3⋊D3C22×C411yescharacteristic
53C4×C3⋊D3C2×Q811yescharacteristic
54C4×C3⋊D3#4111yescharacteristic
55#622—24no—
56#622C4⋊C414yes—
57C32×C8C4212yes—
58C3⋊(C3⋊C8)C4212yes—
59C2×#108—91no—
60#427—91no—
61#405—92no—
62C2×#97—91no—
63#339—92no—
64C2×C4×D3—62no—
65C2×C3×C8—22no—
66C3×C4⋊C4—24no—
67(C2×D3)⋊C4—124no—
68C4⋊Dic3—64no—
69C4×Dic3—124no—
70C2×C3⋊C8—62no—
71D3×C8—64no—
72D3×C8—64no—
73C22×C32C4×D411yescharacteristic
74C2×C3⋊D3—21no—
75C2×C3⋊D3—21no—
76C2×C3⋊D3#11711yescharacteristic
77C2×C3⋊D3C4×Q811yescharacteristic
78#157—42no—
79C32×C4—42no—
80C32×C4C2×C4211yescharacteristic
81C32×C4C4×Q811yescharacteristic
82C3⋊Dic3—42no—
83C3⋊Dic3C2×C4⋊C411yescharacteristic
84C3⋊Dic3C4×D411yescharacteristic
85C2×M16—92no—
86C22×C8—91no—
87C22×C8—91no—
88#117—92no—
89C2×C42—91no—
90#108—94no—
91#107—91no—
92#107#15711yescharacteristic, complemented
93#106—92no—
94#97—94no—
95#97—182no—
96C4×C8—182no—
97C22×D3—62no—
98C2×C3×C4—22no—
99C2×C3×C4—44no—
100C2×Dic3—62no—
101C2×Dic3—124no—
102C4×D3—62no—
103C4×D3—62no—
104C4×D3—62no—
105C4×D3—62no—
106C3×C8—24no—
107C3⋊C8—64no—
108C2×C32C4×C4⋊C411yescharacteristic
109C2×C32#44411yescharacteristic
110C2×C32#44411yescharacteristic
111C3⋊D3—21no—
112C3⋊D3—21no—
113C22×C4—91no—
114C22×C4—181no—
115M16—94no—
116M16—182no—
117C2×C8—92no—
118C2×C8—92no—
119C2×C8—92no—
120C2×C8—91no—
121C2×C8—92no—
122C2×C8—92no—
123C2×C8—182no—
124C2×C8C2×#15711yescharacteristic
125C4⋊C4—92no—
126C4⋊C4C2×#15712yes—
127C22⋊C4—182no—
128C42—92no—
129C42—182no—
130C42—181no—
131C22×C3—22no—
132C2×D3—62no—
133C2×D3—62no—
134C2×D3—122no—
135C2×D3—122no—
136C3×C4—22no—
137C3×C4—22no—
138C3×C4—84no—
139Dic3—62no—
140Dic3—62no—
141Dic3—244no—
142C32#177311yescharacteristic, complemented, Sylow
143C23—91no—
144C2×C4—22no—
145C2×C4—91no—
146C2×C4—91no—
147C2×C4—91no—
148C2×C4—91no—
149C2×C4—91no—
150C2×C4—182no—
151C2×C4—182no—
152C2×C4—361no—
153C2×C4—361no—
154C2×C4C22×#15711yescharacteristic
155C8—94no—
156C8—92no—
157C8—184no—
158C8C4×#15712yes—
159C2×C3—22no—
160C2×C3—22no—
161C2×C3—22no—
162D3—122no—
163D3—122no—
164C22—91no—
165C22—91no—
166C22—181no—
167C22—181no—
168C22D4×#15711yescharacteristic
169C4—42no—
170C4—91no—
171C4—91no—
172C4—362no—
173C4—362no—
174C4C2×C4×#15711yescharacteristic
175C4Q8×#15711yescharacteristic
176C3—22no—
177C2—181no—
178C2—181no—
179C2C4⋊C4×#15711yescharacteristic
180C2#1059378011yescharacteristic
181C2#1059378811yescharacteristic
subgroupG/H
centerC22D4×#157
commutatorC32×C4C2×C42
FrattiniC2×C4C22×#157
FittingC32×#107C4
socleC22×C32C4×D4
prime radicalC22×C3⋊D3#41
cosocleC2×C4×C3⋊D3C23
hypercenter#107#157
hypocenterC32#1773
LCSG ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ #107

Complements

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

NH ≅ G/Ntype
13. #63770C4semidirect
14. #63767C4semidirect
15. C32×#107C4semidirect
16. #63645C4semidirect
17. #63635C4semidirect
92. #107#157semidirect
142. C32#1773semidirect

Maximal subgroups

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

subgroupindex
C2×#637702
C2×#637672
#105937482
#105925792
#105901642
#17739