Finite Group Databasebeta

← #11776993

Subgroups — #11776993

Order 1152.

300 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 300 conjugacy classes of subgroups — too many to draw. Only its 73 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#10591120C211yesmaximal, characteristic
3C2×#63572C211yesmaximal, characteristic
4#10590041C214yesmaximal, complemented
5C2×C4×C3⋊Dic3C2211yescharacteristic
6C2×C3×#208—21no—
7C22×C3×C3⋊C8—21no—
8C22⋊#622C412yes—
9C4⋊#622C412yes—
10C4×#622C2212yes—
11#63572—21no—
12#63572—21no—
13#63572C2212yes—
14#63572C2212yes—
15#5118—61no—
16C2×Dic3⋊C8—61no—
17C22×C32×C4D411yescharacteristic
18C22×C3⋊Dic3C2×C411yescharacteristic
19C22×C3⋊Dic3Q811yescharacteristic
20C2×#622C2×C414yes—
21C4×C3⋊Dic3C2×C411yescharacteristic
22C4×C3⋊Dic3D411yescharacteristic
23C4×C3⋊Dic3Q811yescharacteristic
24C4×C3⋊Dic3C2311yescharacteristic
25C3×#208—42no—
26C2×C3×C3⋊C8—22no—
27C2×C3×C3⋊C8—22no—
28C2×C3×C3⋊C8—42no—
29#1570—91nomaximal, Sylow
30C2×C3×M16—61no—
31C22×C3×C8—61no—
32C2×C4×Dic3—61no—
33C2×C4×Dic3—61no—
34C2×#208—21no—
35C22×C3⋊C8—21no—
36Dic3⋊C8—62no—
37Dic3⋊C8—62no—
38Dic3⋊C8—62no—
39Dic3⋊C8—62no—
40C23×C32C4⋊C411yescharacteristic
41C2×C32×C4C4⋊C411yescharacteristic
42C2×C32×C4SD1612yes—
43C2×C32×C4SD1612yes—
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—24no—
52C3×C3⋊C8—42no—
53C3×C3⋊C8—42no—
54#431—91no—
55#423—91no—
56C2×C4⋊C8—91no—
57#334—94no—
58C22×C3×C4—21no—
59C22×C3×C4—21no—
60C22×Dic3—61no—
61C22×Dic3—61no—
62C22×Dic3—61no—
63C22×Dic3—61no—
64C3×M16—122no—
65C2×C3×C8—62no—
66C2×C3×C8—62no—
67C2×C3×C8—122no—
68C4×Dic3—61no—
69C4×Dic3—61no—
70C4×Dic3—61no—
71C4×Dic3—61no—
72C4×Dic3—61no—
73C4×Dic3—61no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76#208—42no—
77C2×C3⋊C8—22no—
78C2×C3⋊C8—22no—
79C2×C3⋊C8—42no—
80C22×C32—21no—
81C22×C32—21no—
82C22×C32#10612yes—
83C22×C32C2×C4⋊C411yescharacteristic
84C32×C4#10612yes—
85C32×C4C2×SD1611yescharacteristic
86C32×C4C2×SD1611yescharacteristic
87C3⋊Dic3—21no—
88C3⋊Dic3—21no—
89C3⋊Dic3—21no—
90C3⋊Dic3#13112yes—
91C2×M16—61no—
92C22×C8—61no—
93C2×C42—91no—
94C4⋊C8—92no—
95C4⋊C8—92no—
96C4⋊C8—92no—
97C4⋊C8—181no—
98C4⋊C8—181no—
99C22⋊C8—92no—
100C4×C8—92no—
101C23×C3—21no—
102C23×C3—21no—
103C2×C3×C4—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—22no—
108C2×C3×C4—22no—
109C2×C3×C4—22no—
110C2×C3×C4—22no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—61no—
114C2×Dic3—61no—
115C2×Dic3—61no—
116C2×Dic3—61no—
117C2×Dic3—61no—
118C2×Dic3—61no—
119C2×Dic3—64no—
120C2×Dic3—122no—
121C2×Dic3—122no—
122C2×Dic3—122no—
123C3×C8—122no—
124C3×C8—122no—
125C3⋊C8—42no—
126C3⋊C8—42no—
127C2×C32—22no—
128C2×C32#42411yescharacteristic
129C2×C32C2×#10611yescharacteristic
130C2×C32#43011yescharacteristic
131C22×C4—91no—
132C22×C4—91no—
133C22×C4GO+(4,𝔽2)11yescharacteristic
134M16—122no—
135C2×C8—62no—
136C2×C8—62no—
137C2×C8—94no—
138C2×C8—122no—
139C42—91no—
140C42—91no—
141C42—91no—
142C42—91no—
143C22×C3—22no—
144C22×C3—22no—
145C22×C3—21no—
146C22×C3—21no—
147C22×C3—22no—
148C22×C3—22no—
149C22×C3—41no—
150C22×C3—41no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—22no—
156C3×C4—22no—
157Dic3—62no—
158Dic3—62no—
159Dic3—62no—
160Dic3—62no—
161Dic3—121no—
162Dic3—121no—
163Dic3—121no—
164Dic3—121no—
165C32#157011yescharacteristic, complemented, Sylow
166C23#377311yescharacteristic
167C2×C4—91no—
168C2×C4—91no—
169C2×C4—91no—
170C2×C4—91no—
171C2×C4—182no—
172C2×C4—361no—
173C2×C4#377311yescharacteristic
174C2×C4#377512yes—
175C2×C4#377512yes—
176C2×C4C2×GO+(4,𝔽2)11yescharacteristic
177C8—122no—
178C8—122no—
179C8—184no—
180C2×C3—24no—
181C2×C3—21no—
182C2×C3—21no—
183C2×C3—21no—
184C2×C3—21no—
185C2×C3—21no—
186C2×C3—21no—
187C2×C3—42no—
188C22—21no—
189C22—21no—
190C22#6374212yes—
191C22C2×#377311yescharacteristic
192C4—92no—
193C4—181no—
194C4—181no—
195C4—181no—
196C4#6374212yes—
197C4C2×#377511yescharacteristic
198C4C2×#377511yescharacteristic
199C3—21no—
200C3—21no—
201C2—22no—
202C2#1059332711yescharacteristic
203C2#1059333011yescharacteristic
204C2C2×#6374211yescharacteristic
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#1570
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. #10590041C2semidirect
165. C32#1570semidirect

Maximal subgroups

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

subgroupindex
#105937952
#105911202
C2×#635722
#105900412
#15709