Finite Group Databasebeta

← #11777091

Subgroups — #11777091

Order 1152.

284 conjugacy classes of subgroups; only the 61 normal subgroups are shown.

normal subgroups only

This group has 284 conjugacy classes of subgroups — too many to draw. Only its 61 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#10593801C211yesmaximal, characteristic
2C2×#63572C211yesmaximal, characteristic
3#10591066C211yesmaximal, characteristic
4#10590042C212yesmaximal, complemented
5#10590041C212yesmaximal, complemented
6C2×C4×C3⋊Dic3C2211yescharacteristic
7C22×C3×C3⋊C8—21no—
8C22⋊#622C412yes—
9#63779C412yes—
10C4×#622C2212yes—
11C3×#830—21no—
12#63572—21no—
13#63572C2211yescharacteristic
14#63572C2212yes—
15#63572C2211yescharacteristic
16#63555—21no—
17C2×Dic3⋊C8—61no—
18#4719—61no—
19C22×C32×C4D411yescharacteristic
20C22×C3⋊Dic3C2×C411yescharacteristic
21C22×C3⋊Dic3Q811yescharacteristic
22C2×#622C2×C414yes—
23C4×C3⋊Dic3C2×C411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C4×C3⋊Dic3Q811yescharacteristic
26C4×C3⋊Dic3C2311yescharacteristic
27C2×C3×C3⋊C8—22no—
28C2×C3×C3⋊C8—21no—
29C2×C3×C3⋊C8—21no—
30C2×C3×C3⋊C8—42no—
31#1573—91nomaximal, Sylow
32C22×C3×C8—61no—
33C2×C4×Dic3—61no—
34C2×C4×Dic3—61no—
35C22×C3⋊C8—21no—
36C3×C22⋊C8—61no—
37#830—21no—
38#815—61no—
39#815—61no—
40Dic3⋊C8—61no—
41Dic3⋊C8—61no—
42Dic3⋊C8—62no—
43Dic3⋊C8—62no—
44C23×C32C4⋊C411yescharacteristic
45C2×C32×C4—21no—
46C2×C32×C4—21no—
47C2×C32×C4C4⋊C411yescharacteristic
48C2×C32×C4C2×D411yescharacteristic
49C2×C3⋊Dic3—22no—
50C2×C3⋊Dic3—22no—
51C2×C3⋊Dic3C4⋊C411yescharacteristic
52C2×C3⋊Dic3C4⋊C411yescharacteristic
53C2×C3⋊Dic3C22×C411yescharacteristic
54C2×C3⋊Dic3C2×Q811yescharacteristic
55#622—24no—
56C3×C3⋊C8—41no—
57C3×C3⋊C8—42no—
58C3×C3⋊C8—41no—
59#432—91no—
60#431—91no—
61C2×C4⋊C8—91no—
62#335—92no—
63#334—92no—
64C22×C3×C4—21no—
65C22×C3×C4—21no—
66C22×Dic3—61no—
67C22×Dic3—61no—
68C22×Dic3—61no—
69C22×Dic3—61no—
70C2×C3×C8—62no—
71C2×C3×C8—61no—
72C2×C3×C8—61no—
73C2×C3×C8—122no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C4×Dic3—61no—
77C4×Dic3—61no—
78C4×Dic3—61no—
79C4×Dic3—61no—
80C4×Dic3—61no—
81C4×Dic3—61no—
82C2×C3⋊C8—22no—
83C2×C3⋊C8—21no—
84C2×C3⋊C8—21no—
85C2×C3⋊C8—42no—
86C22×C32—21no—
87C22×C32—21no—
88C22×C32#10812yes—
89C22×C32C2×C4⋊C411yescharacteristic
90C32×C4—21no—
91C32×C4AGL(1,ℤ/8)11yescharacteristic
92C32×C4#13711yescharacteristic
93C3⋊Dic3—21no—
94C3⋊Dic3—21no—
95C3⋊Dic3—21no—
96C3⋊Dic3#13112yes—
97C22×C8—61no—
98C2×C42—91no—
99C4⋊C8—91no—
100C4⋊C8—92no—
101C4⋊C8—91no—
102C4⋊C8—92no—
103C4⋊C8—181no—
104C22⋊C8—61no—
105C22⋊C8—92no—
106#97—181no—
107C4×C8—92no—
108C23×C3—21no—
109C23×C3—21no—
110C2×C3×C4—22no—
111C2×C3×C4—22no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—41no—
117C2×C3×C4—41no—
118C2×Dic3—61no—
119C2×Dic3—61no—
120C2×Dic3—61no—
121C2×Dic3—61no—
122C2×Dic3—61no—
123C2×Dic3—61no—
124C2×Dic3—61no—
125C2×Dic3—61no—
126C2×Dic3—64no—
127C2×Dic3—122no—
128C2×Dic3—122no—
129C2×Dic3—122no—
130C3×C8—121no—
131C3×C8—121no—
132C3×C8—122no—
133C3⋊C8—41no—
134C3⋊C8—41no—
135C3⋊C8—42no—
136C2×C32—22no—
137C2×C32#42411yescharacteristic
138C2×C32#42811yescharacteristic
139C2×C32C2×#10811yescharacteristic
140C22×C4—91no—
141C22×C4—91no—
142C22×C4GO+(4,𝔽2)11yescharacteristic
143C2×C8—61no—
144C2×C8—61no—
145C2×C8—62no—
146C2×C8—94no—
147C2×C8—122no—
148C42—91no—
149C42—91no—
150C42—91no—
151C42—91no—
152C22×C3—22no—
153C22×C3—22no—
154C22×C3—21no—
155C22×C3—21no—
156C22×C3—22no—
157C22×C3—22no—
158C22×C3—41no—
159C22×C3—41no—
160C3×C4—22no—
161C3×C4—21no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—41no—
166Dic3—62no—
167Dic3—62no—
168Dic3—62no—
169Dic3—121no—
170Dic3—121no—
171Dic3—121no—
172Dic3—121no—
173Dic3—121no—
174C32#157311yescharacteristic, complemented, Sylow
175C23#377311yescharacteristic
176C2×C4—21no—
177C2×C4—21no—
178C2×C4—91no—
179C2×C4—91no—
180C2×C4—91no—
181C2×C4—91no—
182C2×C4—182no—
183C2×C4—182no—
184C2×C4#377311yescharacteristic
185C2×C4C2×GO+(4,𝔽2)11yescharacteristic
186C8—122no—
187C8—121no—
188C8—121no—
189C8—184no—
190C2×C3—24no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—21no—
194C2×C3—21no—
195C2×C3—21no—
196C2×C3—21no—
197C2×C3—42no—
198C22—21no—
199C22—21no—
200C22#6373312yes—
201C22C2×#377311yescharacteristic
202C4—21no—
203C4—92no—
204C4—181no—
205C4—181no—
206C4—181no—
207C4#6423611yescharacteristic
208C4#6423911yescharacteristic
209C3—21no—
210C3—21no—
211C2—22no—
212C2#1059332711yescharacteristic
213C2C2×#6373311yescharacteristic
214C2#1059350711yescharacteristic
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#1573
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
174. C32#1573semidirect

Maximal subgroups

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

subgroupindex
#105938012
C2×#635722
#105910662
#105900422
#105900412
#15739