Finite Group Databasebeta

← #11782042

Subgroups — #11782042

Order 1152.

236 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593393C212yesmaximal
2#10590902C211yesmaximal, characteristic
3#10590787C211yesmaximal, characteristic
4#10590170C211yesmaximal, characteristic
5#10590040C212yesmaximal
6#63919C2212yes—
7C4×#627C2211yescharacteristic
8C4⋊#622C2212yes—
9#63743—22no—
10#63740—22no—
11C8×C3⋊Dic3C2211yescharacteristic
12C3×#818—21no—
13C3×#815—21no—
14#63576—21no—
15#63572C2211yescharacteristic
16Dic3⋊(C3⋊C8)—21no—
17#4874—61no—
18#4701—61no—
19C2×#627—22no—
20C2×#627D411yescharacteristic
21C2×#622—22no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3C2311yescharacteristic
24C2×C3⋊(C3⋊C8)D411yescharacteristic
25C3×C4⋊Dic3—22no—
26C3×C4×Dic3—21no—
27C2×C3×C3⋊C8—21no—
28#3724—22no—
29#3724D411yescharacteristic
30Dic3⋊Dic3—21no—
31#1696—91nomaximal, Sylow
32#888—62no—
33C4×Dic6—61no—
34C3×#107—61no—
35C3×#97—61no—
36#818—21no—
37#815—21no—
38Dic3⋊C8—61no—
39Dic3⋊C8—61no—
40C8×Dic3—61no—
41C8×Dic3—61no—
42#807—62no—
43C4⋊(C3⋊C8)—61no—
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3C2×D411yescharacteristic
46C2×C3⋊Dic3#4111yescharacteristic
47C2×C3×Dic3—21no—
48C2×C3×Dic3—21no—
49C2×C3×Dic3—42no—
50#627—22no—
51#627—82no—
52#622—42no—
53C32×C8Q1612yes—
54C3⋊(C3⋊C8)—21no—
55C3×C3⋊C8—41no—
56#500—91no—
57#477—92no—
58#446—91no—
59#334—91no—
60#333—92no—
61C2×Dic6—61no—
62C2×Dic6—122no—
63C2×C3×C8—21no—
64C2×C3×C8—21no—
65C2×C3×C8—61no—
66C3×C4⋊C4—62no—
67C3×C42—61no—
68C4⋊Dic3—22no—
69C4⋊Dic3—61no—
70Dic3⋊C4—61no—
71Dic3⋊C4—61no—
72Dic3⋊C4—122no—
73C4×Dic3—21no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C2×C3⋊C8—21no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C22×C32#12111yescharacteristic
80C32×C4C2×Q1611yescharacteristic
81C32×C4#13711yescharacteristic
82C3⋊Dic3—21no—
83C3⋊Dic3#13712yes—
84C3×Dic3—41no—
85C3×Dic3—41no—
86C3×Dic3—82no—
87C4⋊Q8—92no—
88C4×Q8—91no—
89#107—61no—
90#107—181no—
91#107—182no—
92C4⋊C8—91no—
93C4⋊C8—92no—
94C4⋊C8—181no—
95#103—182no—
96#97—61no—
97C4×C8—91no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—61no—
101C2×C3×C4—61no—
102C2×C3×C4—122no—
103C2×Dic3—21no—
104C2×Dic3—21no—
105C2×Dic3—42no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110Dic6—122no—
111Dic6—244no—
112C3×C8—22no—
113C3×C8—22no—
114C3×C8—121no—
115C3⋊C8—41no—
116C3⋊C8—62no—
117C3⋊C8—121no—
118C2×C32#46211yescharacteristic
119C2×C32#47011yescharacteristic
120C2×C32#47211yescharacteristic
121C2×Q8—91no—
122C2×Q8—182no—
123C2×C8—61no—
124C2×C8—91no—
125C2×C8—182no—
126C2×C8GO+(4,𝔽2)11yescharacteristic
127C4⋊C4—62no—
128C4⋊C4—91no—
129C4⋊C4—181no—
130C4⋊C4—182no—
131C42—61no—
132C42—91no—
133C22×C3—21no—
134C22×C3—21no—
135C3×C4—21no—
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—21no—
139C3×C4—121no—
140C3×C4—121no—
141C3×C4—242no—
142Dic3—41no—
143Dic3—41no—
144Dic3—62no—
145Dic3—62no—
146Dic3—62no—
147Dic3—82no—
148Dic3—121no—
149C32#169611yescharacteristic, complemented, Sylow
150Q8—182no—
151Q8—722no—
152C2×C4—61no—
153C2×C4—61no—
154C2×C4—91no—
155C2×C4—91no—
156C2×C4—122no—
157C2×C4C2×GO+(4,𝔽2)11yescharacteristic
158C8—121no—
159C8—181no—
160C8—362no—
161C8#377612yes—
162C2×C3—21no—
163C2×C3—21no—
164C2×C3—21no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3—21no—
168C22#6423011yescharacteristic
169C4—92no—
170C4—121no—
171C4—121no—
172C4—181no—
173C4—242no—
174C4#6422611yescharacteristic
175C4C2×#377611yescharacteristic
176C3—21no—
177C3—21no—
178C2#1059328911yescharacteristic
179C2#1059330311yescharacteristic
180C2#1059344711yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32#121
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1696
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
149. C32#1696semidirect

Maximal subgroups

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

subgroupindex
#105933932
#105909022
#105907872
#105901702
#105900402
#16969