Finite Group Databasebeta

← #11786284

Subgroups — #11786284

Order 1152.

402 conjugacy classes of subgroups; only the 94 normal subgroups are shown.

normal subgroups only

This group has 402 conjugacy classes of subgroups — too many to draw. Only its 94 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×#63769C212yesmaximal
2C2×#63768C212yesmaximal
3#10593736C211yesmaximal, characteristic
4#10593735C211yesmaximal, characteristic
5C3⋊D3×#97C211yesmaximal, characteristic
6C2×C4⋊#157—22no—
7C2×C4⋊#157C2212yes—
8C2×C4⋊#157C2211yescharacteristic
9C2×C4⋊#157C2211yescharacteristic
10C2×C8×C3⋊D3C2212yes—
11C42×C3⋊D3C2211yescharacteristic
12#63781—22no—
13#63769—24no—
14#63768—24no—
15C32×#97C411yescharacteristic, complemented
16#63642C412yescomplemented
17#63630C411yescharacteristic, complemented
18D3×#97—62no—
19C22×#157—22no—
20C22×#157—21no—
21C22×#157—21no—
22C2×C4×C3⋊D3D412yes—
23C2×C4×C3⋊D3C2311yescharacteristic
24C4⋊#157—22no—
25C4⋊#157—22no—
26C4⋊#157—22no—
27C4⋊#157—22no—
28C4⋊#157—44no—
29C2×C32×C8C2×C412yes—
30C32×C42C2×C411yescharacteristic
31C4×C3⋊Dic3C2×C411yescharacteristic
32C4×C3⋊Dic3Q812yes—
33C2×C3⋊(C3⋊C8)C2×C412yes—
34C8×C3⋊D3D414yes—
35C8×C3⋊D3Q814yes—
36#1847—91nomaximal, Sylow
37C2×D3×C8—64no—
38C42×D3—62no—
39C3×#97—22no—
40#815—64no—
41#803—62no—
42C22×C3⋊D3C2×D411yescharacteristic
43C2×#157—42no—
44C2×#157—41no—
45C2×#157—41no—
46C2×#157—42no—
47C2×#157—44no—
48C2×#157—42no—
49C2×C32×C4C4⋊C412yes—
50C2×C32×C4C22×C411yescharacteristic
51C2×C3⋊Dic3C4⋊C412yes—
52C2×C3⋊Dic3C2×Q811yescharacteristic
53C4×C3⋊D3—22no—
54C4×C3⋊D3—22no—
55C4×C3⋊D3C2×D412yes—
56C4×C3⋊D3C2×Q812yes—
57C32×C8C4⋊C414yescomplemented
58C3⋊(C3⋊C8)C4⋊C414yescomplemented
59C2×#107—92no—
60C2×#106—92no—
61C2×#97—91no—
62#384—91no—
63#382—91no—
64C2×C4×D3—62no—
65C2×C4×D3—64no—
66C2×C3×C8—24no—
67C3×C42—22no—
68C4×Dic3—62no—
69C4×Dic3—64no—
70C2×C3⋊C8—64no—
71D3×C8—68no—
72D3×C8—68no—
73C22×C32C2×C4⋊C411yescharacteristic
74C2×C3⋊D3#12711yescharacteristic
75C2×C3⋊D3C4⋊Q811yescharacteristic
76C2×C3⋊D3AGL(1,ℤ/8)12yes—
77C2×C3⋊D3#13712yes—
78#157—81no—
79#157—82no—
80#157—81no—
81C32×C4—22no—
82C32×C4C2×C4⋊C412yes—
83C3⋊Dic3—22no—
84C3⋊Dic3C4⋊Q812yes—
85C22×C8—92no—
86C2×C4⋊C4—91no—
87C2×C4⋊C4—91no—
88C2×C4⋊C4—92no—
89C2×C4⋊C4—182no—
90C2×C42—91no—
91#107—184no—
92#106—184no—
93#97—92no—
94#97—91no—
95#97#15711yescharacteristic, complemented
96#95—182no—
97C22×D3—62no—
98C2×C3×C4—22no—
99C2×C3×C4—24no—
100C2×Dic3—62no—
101C2×Dic3—64no—
102C4×D3—64no—
103C4×D3—64no—
104C4×D3—124no—
105C4×D3—124no—
106C3×C8—28no—
107C3⋊C8—68no—
108C2×C32#38411yescharacteristic
109C2×C32#42812yes—
110C3⋊D3#49611yescharacteristic
111C3⋊D3#49711yescharacteristic
112C3⋊D3#50112yes—
113C22×C4—91no—
114C22×C4—92no—
115C22×C4—181no—
116C22×C4—181no—
117C22×C4—182no—
118C2×C8—92no—
119C2×C8—94no—
120C2×C8—94no—
121C2×C8C2×#15712yes—
122C4⋊C4—182no—
123C4⋊C4—182no—
124C4⋊C4—182no—
125C4⋊C4—182no—
126C4⋊C4—364no—
127C42—91no—
128C42—92no—
129C42C2×#15711yescharacteristic
130C22×C3—22no—
131C2×D3—62no—
132C2×D3—62no—
133C2×D3—64no—
134C2×D3—64no—
135C3×C4—24no—
136C3×C4—44no—
137Dic3—64no—
138Dic3—124no—
139C32#184711yescharacteristic, complemented, Sylow
140C23—91no—
141C2×C4—91no—
142C2×C4—92no—
143C2×C4—92no—
144C2×C4—92no—
145C2×C4—182no—
146C2×C4—182no—
147C2×C4—361no—
148C2×C4—362no—
149C2×C4—361no—
150C2×C4—364no—
151C2×C4—362no—
152C2×C4—362no—
153C2×C4C4⋊#15712yes—
154C2×C4C22×#15711yescharacteristic
155C8—94no—
156C8C4⋊#15714yescomplemented
157C2×C3—22no—
158C2×C3—24no—
159D3—62no—
160D3—62no—
161D3—64no—
162C22—91no—
163C22—91no—
164C22—92no—
165C22—92no—
166C22C2×C4⋊#15711yescharacteristic
167C4—22no—
168C4—92no—
169C4—182no—
170C4—722no—
171C4—721no—
172C4—721no—
173C4C2×C4⋊#15712yes—
174C3—22no—
175C2—91no—
176C2—91no—
177C2—92no—
178C2#1059373511yescharacteristic
179C2#1059377412yes—
subgroupG/H
centerC22C2×C4⋊#157
commutatorC2×C32×C4C22×C4
FrattiniC2×C4C22×#157
FittingC32×#97C4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C2×D4
cosocleC2×C4×C3⋊D3C23
hypercenter#97#157
hypocenterC32#1847
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #97

Complements

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

NH ≅ G/Ntype
15. C32×#97C4semidirect
16. #63642C4semidirect
17. #63630C4semidirect
57. C32×C8C4⋊C4semidirect
58. C3⋊(C3⋊C8)C4⋊C4semidirect
95. #97#157semidirect
139. C32#1847semidirect
156. C8C4⋊#157semidirect

Maximal subgroups

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

subgroupindex
C2×#637692
C2×#637682
#105937362
#105937352
C3⋊D3×#972
#18479