Finite Group Databasebeta

← #11777056

Subgroups — #11777056

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#10593725C211yesmaximal, characteristic
2#10590299C211yesmaximal, characteristic
3#10590297C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C42×C3⋊D3C2211yescharacteristic
7#63779C412yes—
8#63778C412yes—
9C4×#622C2211yescharacteristic
10C4×#622C2211yescharacteristic
11C3×#803—21no—
12C3×C4×C3⋊C8—21no—
13#63572C2212yes—
14#63572C2212yes—
15#63557—21no—
16#63557—21no—
17#4705—61no—
18#4685—61no—
19C2×C4×C3⋊D3C2×C411yescharacteristic
20C2×C4×C3⋊D3D411yescharacteristic
21C2×C4×C3⋊D3Q811yescharacteristic
22C2×#622C2×C412yes—
23C2×#622C2×C412yes—
24C32×C42D411yescharacteristic
25C4×C3⋊Dic3C2×C411yescharacteristic
26C4×C3⋊Dic3Q811yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C2×C3×C3⋊C8—22no—
29C2×C3×C3⋊C8—22no—
30#1572—91nomaximal, Sylow
31C42×D3—61no—
32C42×D3—61no—
33C3×#97—61no—
34C3×C4×C8—61no—
35(C2×D3)⋊C8—62no—
36(C2×D3)⋊C8—62no—
37Dic3⋊C8—62no—
38Dic3⋊C8—62no—
39#803—21no—
40C4×C3⋊C8—21no—
41C22×C3⋊D3C4⋊C411yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C32×C4C4⋊C411yescharacteristic
44C2×C32×C4C2×D411yescharacteristic
45C2×C3⋊Dic3C4⋊C411yescharacteristic
46C2×C3⋊Dic3C22×C411yescharacteristic
47C2×C3⋊Dic3C2×Q811yescharacteristic
48C4×C3⋊D3—22no—
49C4×C3⋊D3—22no—
50C4×C3⋊D3—41no—
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—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C4×D3—61no—
65C2×C4×D3—61no—
66C2×C3×C8—62no—
67C2×C3×C8—62no—
68C3×C42—21no—
69C3×C42—21no—
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×C32C2×C4⋊C411yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3—21no—
82C32×C4—21no—
83C32×C4—21no—
84C32×C4#13512yes—
85C3⋊Dic3—21no—
86C3⋊Dic3—21no—
87C3⋊Dic3#13112yes—
88C2×C42—91no—
89C4⋊C8—92no—
90C4⋊C8—92no—
91C4⋊C8—92no—
92C22⋊C8—92no—
93C22⋊C8—181no—
94C22⋊C8—181no—
95#97—61no—
96C4×C8—61no—
97C4×C8—91no—
98C4×C8—91no—
99C22×D3—61no—
100C22×D3—61no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C4×D3—64no—
114C4×D3—122no—
115C4×D3—122no—
116C4×D3—122no—
117C4×D3—122no—
118C4×D3—122no—
119C3×C8—122no—
120C3×C8—122no—
121C3⋊C8—42no—
122C3⋊C8—42no—
123C2×C32#42411yescharacteristic
124C2×C32#42711yescharacteristic
125C2×C32#43011yescharacteristic
126C3⋊D3—41no—
127C22×C4—91no—
128C22×C4—91no—
129C22×C4—91no—
130C2×C8—62no—
131C2×C8—62no—
132C2×C8—92no—
133C2×C8—92no—
134C42—91no—
135C42—91no—
136C42—91no—
137C42GO+(4,𝔽2)11yescharacteristic
138C22×C3—21no—
139C22×C3—21no—
140C2×D3—62no—
141C2×D3—62no—
142C2×D3—121no—
143C2×D3—121no—
144C2×D3—121no—
145C2×D3—121no—
146C3×C4—22no—
147C3×C4—22no—
148C3×C4—22no—
149C3×C4—22no—
150C3×C4—41no—
151C3×C4—41no—
152Dic3—62no—
153Dic3—62no—
154Dic3—121no—
155Dic3—121no—
156Dic3—121no—
157Dic3—121no—
158C32#157211yescharacteristic, complemented, Sylow
159C23—91no—
160C2×C4—91no—
161C2×C4—91no—
162C2×C4—91no—
163C2×C4—182no—
164C2×C4—182no—
165C2×C4—361no—
166C2×C4#377311yescharacteristic
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—
179D3—122no—
180D3—122no—
181C22—181no—
182C22—181no—
183C22—181no—
184C22C2×#377311yescharacteristic
185C4—21no—
186C4—21no—
187C4—92no—
188C4—181no—
189C4—181no—
190C4#6422312yes—
191C3—21no—
192C3—21no—
193C2—361no—
194C2#1059332711yescharacteristic
195C2#1059333011yescharacteristic
196C2#1059338911yescharacteristic
subgroupG/H
center, FrattiniC2×C4C2×GO+(4,𝔽2)
commutatorC2×C3⋊Dic3C22×C4
FittingC32×C42D4
socleC22×C32C2×C4⋊C4
prime radicalC22×C3⋊D3C4⋊C4
cosocleC4×C3⋊Dic3C23
hypercenterC42GO+(4,𝔽2)
hypocenterC32#1572
LCSG ▷ C2×C3⋊Dic3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C42

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
#105937252
#105902992
#105902972
#105900422
#105900412
#15729