Finite Group Databasebeta

← #11777057

Subgroups — #11777057

Order 1152.

264 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 264 conjugacy classes of subgroups — too many to draw. Only its 57 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#10593795C211yesmaximal, characteristic
2#10591066C211yesmaximal, characteristic
3#10591061C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C22⋊#622C412yes—
8C4⋊#622C412yes—
9C4×#622C2211yescharacteristic
10C4×#622C2211yescharacteristic
11C3×#830—21no—
12C3×#830—21no—
13#63572C2212yes—
14#63572C2212yes—
15#63555—21no—
16#63553—21no—
17#4719—61no—
18#4718—61no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22C2×#622C2×C412yes—
23C2×#622C2×C412yes—
24C4×C3⋊Dic3C2×C411yescharacteristic
25C4×C3⋊Dic3D411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C2×C3×C3⋊C8—22no—
29C2×C3×C3⋊C8—22no—
30#1572—91nomaximal, Sylow
31C2×C4×Dic3—61no—
32C2×C4×Dic3—61no—
33C3×C22⋊C8—61no—
34C3×C22⋊C8—61no—
35#830—21no—
36#830—21no—
37#815—62no—
38Dic3⋊C8—62no—
39Dic3⋊C8—62no—
40C8×Dic3—62no—
41C23×C32C4⋊C411yescharacteristic
42C2×C32×C4—22no—
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3—22no—
46C2×C3⋊Dic3—41no—
47C2×C3⋊Dic3C4⋊C411yescharacteristic
48C2×C3⋊Dic3C4⋊C411yescharacteristic
49C2×C3⋊Dic3C22×C411yescharacteristic
50C2×C3⋊Dic3C2×Q811yescharacteristic
51#622—22no—
52#622—22no—
53C3×C3⋊C8—42no—
54C3×C3⋊C8—42no—
55#432—91no—
56#431—91no—
57#431—91no—
58#335—92no—
59#334—92no—
60C22×C3×C4—21no—
61C22×C3×C4—21no—
62C22×Dic3—61no—
63C22×Dic3—61no—
64C22×Dic3—61no—
65C22×Dic3—61no—
66C2×C3×C8—62no—
67C2×C3×C8—62no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C2×C3⋊C8—22no—
77C2×C3⋊C8—22no—
78C22×C32—21no—
79C22×C32—21no—
80C22×C32—21no—
81C22×C32C2×C4⋊C411yescharacteristic
82C32×C4—21no—
83C32×C4#13512yes—
84C3⋊Dic3—21no—
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C3⋊Dic3#13112yes—
88C2×C42—91no—
89C4⋊C8—92no—
90C4⋊C8—92no—
91C4⋊C8—92no—
92C22⋊C8—61no—
93C22⋊C8—61no—
94C22⋊C8—92no—
95#97—181no—
96C4×C8—91no—
97C4×C8—91no—
98C4×C8—181no—
99C23×C3—21no—
100C23×C3—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—42no—
106C2×C3×C4—42no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—64no—
116C2×Dic3—122no—
117C2×Dic3—122no—
118C2×Dic3—122no—
119C3×C8—122no—
120C3×C8—122no—
121C3⋊C8—42no—
122C3⋊C8—42no—
123C2×C32—41no—
124C2×C32#42411yescharacteristic
125C2×C32#42711yescharacteristic
126C2×C32#43011yescharacteristic
127C22×C4—91no—
128C22×C4—91no—
129C22×C4GO+(4,𝔽2)11yescharacteristic
130C2×C8—62no—
131C2×C8—62no—
132C2×C8—92no—
133C2×C8—92no—
134C42—91no—
135C42—91no—
136C42—91no—
137C42—91no—
138C22×C3—22no—
139C22×C3—22no—
140C22×C3—21no—
141C22×C3—21no—
142C22×C3—41no—
143C22×C3—41no—
144C22×C3—41no—
145C22×C3—41no—
146C3×C4—22no—
147C3×C4—22no—
148C3×C4—41no—
149C3×C4—41no—
150Dic3—62no—
151Dic3—62no—
152Dic3—62no—
153Dic3—62no—
154Dic3—121no—
155Dic3—121no—
156Dic3—121no—
157Dic3—121no—
158C32#157211yescharacteristic, complemented, Sylow
159C23#377311yescharacteristic
160C2×C4—22no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—91no—
164C2×C4—91no—
165C2×C4—182no—
166C2×C4—361no—
167C2×C4#377311yescharacteristic
168C2×C4C2×GO+(4,𝔽2)11yescharacteristic
169C8—122no—
170C8—122no—
171C8—182no—
172C8—182no—
173C2×C3—21no—
174C2×C3—21no—
175C2×C3—21no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—42no—
180C2×C3—42no—
181C22—21no—
182C22—21no—
183C22—21no—
184C22C2×#377311yescharacteristic
185C4—21no—
186C4—92no—
187C4—181no—
188C4—181no—
189C4—181no—
190C4#6423712yes—
191C3—21no—
192C3—21no—
193C2—41no—
194C2#1059332711yescharacteristic
195C2#1059333011yescharacteristic
196C2#1059351111yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC22×C32×C4D4
socleC22×C32C2×C4⋊C4
prime radicalC23×C32C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC22×C4GO+(4,𝔽2)
hypocenterC32#1572
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
4. #10590042C2semidirect
5. #10590041C2semidirect
158. C32#1572semidirect

Maximal subgroups

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

subgroupindex
#105937952
#105910662
#105910612
#105900422
#105900412
#15729