Finite Group Databasebeta

← #11776994

Subgroups — #11776994

Order 1152.

300 conjugacy classes of subgroups; only the 65 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 65 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#10590340C211yesmaximal, characteristic
3#10590331C211yesmaximal, characteristic
4#10590041C214yesmaximal, complemented
5C42×C3⋊D3C2211yescharacteristic
6C2×#3712—21no—
7C2×#3710—21no—
8#63779C412yes—
9#63778C412yes—
10C4×#622C2212yes—
11C3×C4⋊(C3⋊C8)—21no—
12C3×C4⋊(C3⋊C8)—21no—
13#63572C2212yes—
14#63572C2212yes—
15#4837—61no—
16D3×C4⋊C8—61no—
17C2×C4×C3⋊D3C2×C411yescharacteristic
18C2×C4×C3⋊D3D411yescharacteristic
19C2×C4×C3⋊D3Q811yescharacteristic
20C2×#622C2×C414yes—
21C32×C42D411yescharacteristic
22C4×C3⋊Dic3C2×C411yescharacteristic
23C4×C3⋊Dic3Q811yescharacteristic
24C4×C3⋊Dic3C2311yescharacteristic
25C2×C3×C3⋊C8—22no—
26C2×C3×C3⋊C8—22no—
27#3712—42no—
28#3710—42no—
29#1570—91nomaximal, Sylow
30C2×ΓL(1,𝔽25)—62no—
31C2×D3×C8—62no—
32C42×D3—61no—
33C42×D3—61no—
34C3×C4⋊C8—61no—
35C3×C4⋊C8—61no—
36Dic3⋊C8—62no—
37Dic3⋊C8—62no—
38C4⋊(C3⋊C8)—21no—
39C4⋊(C3⋊C8)—21no—
40C22×C3⋊D3C4⋊C411yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C32×C4C4⋊C411yescharacteristic
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3C4⋊C411yescharacteristic
45C2×C3⋊Dic3C22×C411yescharacteristic
46C2×C3⋊Dic3C2×Q811yescharacteristic
47C4×C3⋊D3—22no—
48C4×C3⋊D3—41no—
49C4×C3⋊D3SD1612yes—
50C4×C3⋊D3SD1612yes—
51#622—24no—
52C3×C3⋊C8—42no—
53C3×C3⋊C8—42no—
54#431—91no—
55#423—91no—
56C2×C4⋊C8—91no—
57#334—94no—
58C2×C4×D3—61no—
59C2×C4×D3—61no—
60C2×C4×D3—61no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C3×C8—62no—
65C2×C3×C8—62no—
66C3×C42—21no—
67C3×C42—21no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C2×C3⋊C8—22no—
75C2×C3⋊C8—22no—
76ΓL(1,𝔽25)—124no—
77D3×C8—124no—
78C22×C32C2×C4⋊C411yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—21no—
81C2×C3⋊D3#10612yes—
82C32×C4—21no—
83C32×C4—21no—
84C32×C4C2×SD1611yescharacteristic
85C32×C4C2×SD1611yescharacteristic
86C3⋊Dic3—21no—
87C3⋊Dic3#10612yes—
88C3⋊Dic3#13112yes—
89C2×M16—181no—
90C22×C8—181no—
91C2×C42—91no—
92C4⋊C8—61no—
93C4⋊C8—61no—
94C4⋊C8—92no—
95C4⋊C8—92no—
96C4⋊C8—92no—
97C22⋊C8—92no—
98C4×C8—92no—
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—62no—
114C4×D3—62no—
115C4×D3—62no—
116C4×D3—62no—
117C4×D3—64no—
118C4×D3—122no—
119C4×D3—122no—
120C4×D3—122no—
121C3×C8—122no—
122C3×C8—122no—
123C3⋊C8—42no—
124C3⋊C8—42no—
125C2×C32#42411yescharacteristic
126C2×C32C2×#10611yescharacteristic
127C2×C32#43011yescharacteristic
128C3⋊D3—22no—
129C22×C4—91no—
130C22×C4—91no—
131C22×C4—91no—
132M16—362no—
133C2×C8—62no—
134C2×C8—62no—
135C2×C8—94no—
136C2×C8—362no—
137C42—91no—
138C42—91no—
139C42—91no—
140C42GO+(4,𝔽2)11yescharacteristic
141C22×C3—21no—
142C22×C3—21no—
143C2×D3—62no—
144C2×D3—62no—
145C2×D3—62no—
146C2×D3—62no—
147C2×D3—121no—
148C2×D3—121no—
149C3×C4—22no—
150C3×C4—22no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—41no—
156C3×C4—41no—
157Dic3—62no—
158Dic3—62no—
159Dic3—62no—
160Dic3—62no—
161Dic3—121no—
162Dic3—121no—
163C32#157011yescharacteristic, complemented, Sylow
164C23—91no—
165C2×C4—91no—
166C2×C4—91no—
167C2×C4—92no—
168C2×C4—92no—
169C2×C4—91no—
170C2×C4—182no—
171C2×C4—361no—
172C2×C4#377311yescharacteristic
173C2×C4#377311yescharacteristic
174C2×C4C2×GO+(4,𝔽2)11yescharacteristic
175C8—122no—
176C8—122no—
177C8—184no—
178C2×C3—21no—
179C2×C3—21no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184D3—64no—
185D3—122no—
186C22—92no—
187C22—181no—
188C22—181no—
189C22C2×#377311yescharacteristic
190C4—21no—
191C4—21no—
192C4—92no—
193C4—92no—
194C4—181no—
195C4#6422711yescharacteristic
196C4#6422711yescharacteristic
197C3—21no—
198C3—21no—
199C2—182no—
200C2#1059332711yescharacteristic
201C2#1059333011yescharacteristic
202C2#1059338711yescharacteristic
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#1570
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. #10590041C2semidirect
163. C32#1570semidirect

Maximal subgroups

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

subgroupindex
#105937252
#105903402
#105903312
#105900412
#15709