Finite Group Databasebeta

← #11772408

Subgroups — #11772408

Order 1152.

242 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 242 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C22×#3708C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3#10591138C211yesmaximal, characteristic
4C22×C3⋊(C3⋊C8)C2211yescharacteristic
5C3×#926—21no—
6C2×C3×#208—21no—
7C2×#3708—21no—
8C2×#3708—21no—
9C2×#3708C412yescomplemented
10#63578—21no—
11#63578C412yescomplemented
12#63576C412yes—
13#63574—21no—
14C2×#822—61no—
15#4998—61no—
16C22×C32×C4D411yescharacteristic
17C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
18C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20C2×C3⋊(C3⋊C8)D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22C2×C3⋊(C3⋊C8)Q811yescharacteristic
23C3×#217—41no—
24C3×C4⋊Dic3—22no—
25C3×C4×Dic3—41no—
26C3×#208—22no—
27C3×#208—41no—
28C2×C3×C3⋊C8—41no—
29#3708—22no—
30#1382—91nomaximal, Sylow
31C2×C3×M16—61no—
32C3×#117—61no—
33#926—21no—
34C2×#208—21no—
35C22×C3⋊C8—61no—
36C22×C3⋊C8—61no—
37#822—62no—
38#822—62no—
39#808—62no—
40#807—62no—
41C23×C32SD1611yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C32×C4D811yescharacteristic
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4Q1611yescharacteristic
48C2×C3×Dic3—42no—
49C3⋊(C3⋊C8)C4211yescharacteristic
50C3⋊(C3⋊C8)C22⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C3⋊(C3⋊C8)C4⋊C411yescharacteristic
53C3×C3⋊C8—42no—
54C22×C16—91no—
55C2×#108—91no—
56#427—91no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C3×M16—62no—
60C3×M16—121no—
61C2×C3×C8—121no—
62C3×C4⋊C4—62no—
63C3×C22⋊C4—121no—
64C3×C42—121no—
65#217—41no—
66C4⋊Dic3—22no—
67C4×Dic3—41no—
68#208—22no—
69#208—41no—
70C2×C3⋊C8—41no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8—61no—
75C2×C3⋊C8—61no—
76C2×C3⋊C8—61no—
77C2×C3⋊C8—61no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C2×C3⋊C8—61no—
81C2×C3⋊C8—61no—
82C2×C3⋊C8—61no—
83C22×C32—22no—
84C22×C32#10211yescharacteristic
85C22×C32#10311yescharacteristic
86C22×C32#10611yescharacteristic
87C32×C4#9511yescharacteristic
88C32×C4#10211yescharacteristic
89C32×C4#10311yescharacteristic
90C32×C4#10711yescharacteristic
91C3×Dic3—82no—
92C2×M16—61no—
93C22×C8—91no—
94#117—61no—
95C2×C16—92no—
96C2×C16—181no—
97C2×C16—181no—
98#108—92no—
99#108—181no—
100#107—92no—
101#106—181no—
102C23×C3—21no—
103C23×C3—21no—
104C2×C3×C4—21no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—21no—
108C2×C3×C4—21no—
109C2×C3×C4—21no—
110C2×C3×C4—21no—
111C2×C3×C4—21no—
112C2×C3×C4—21no—
113C2×C3×C4—21no—
114C2×C3×C4—21no—
115C2×C3×C4—21no—
116C2×C3×C4—122no—
117C2×Dic3—42no—
118C3×C8—122no—
119C3⋊C8—42no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C3⋊C8—61no—
128C2×C32—21no—
129C2×C32—21no—
130C2×C32#34011yescharacteristic
131C2×C32#35912yes—
132C22×C4GO+(4,𝔽2)11yescharacteristic
133M16—62no—
134M16—121no—
135C2×C8—91no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—121no—
142C4⋊C4—62no—
143C22⋊C4—121no—
144C42—121no—
145C16—182no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—21no—
152C22×C3—42no—
153C22×C3—42no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—242no—
163Dic3—82no—
164C32#138211yescharacteristic, complemented, Sylow
165C23#377511yescharacteristic
166C2×C4—122no—
167C2×C4D32⋊C411yescharacteristic
168C2×C4D32⋊C411yescharacteristic
169C2×C4#377311yescharacteristic
170C2×C4#377411yescharacteristic
171C2×C4#377511yescharacteristic
172C2×C4#377611yescharacteristic
173C8—91no—
174C8—91no—
175C8—91no—
176C8—91no—
177C8—122no—
178C2×C3—22no—
179C2×C3—22no—
180C2×C3—21no—
181C2×C3—21no—
182C2×C3—41no—
183C2×C3—41no—
184C2×C3—41no—
185C2×C3—41no—
186C22—22no—
187C22#6373911yescharacteristic
188C22#6374011yescharacteristic
189C22#6374211yescharacteristic
190C4—242no—
191C4#6373711yescharacteristic
192C4#6373911yescharacteristic
193C4#6374011yescharacteristic
194C4#6374311yescharacteristic
195C3—21no—
196C3—21no—
197C2—21no—
198C2—21no—
199C2#1059006312yes—
200C2#1059007511yescharacteristic
subgroupG/H
centerC2×C4#3774
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC22×C32#102
prime radicalC23×C32SD16
cosocleC22×C3⋊(C3⋊C8)C22
hypocenterC32#1382
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2×C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
9. C2×#3708C4semidirect
11. #63578C4semidirect
164. C32#1382semidirect

Maximal subgroups

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

subgroupindex
C22×#37082
C2×#635782
#105911382
#13829