Finite Group Databasebeta

← #11772520

Subgroups — #11772520

Order 1152.

230 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 55 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
1C2×#63773C211yesmaximal, characteristic
2C2×#63578C211yesmaximal, characteristic
3C2×#63578C211yesmaximal, characteristic
4C22×C3⋊(C3⋊C8)C2211yescharacteristic
5C2×C3×#208—21no—
6C2×C3×#208—21no—
7#63773—21no—
8#63773C412yes—
9C2×#3708—21no—
10#63578—21no—
11#63578—21no—
12#63578C412yes—
13#63578C412yes—
14C2×#822—61no—
15C2×#822—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×#208—22no—
24C3×#208—22no—
25C3×#208—41no—
26C3×#208—41no—
27C2×C3×C3⋊C8—41no—
28C2×C3×C3⋊C8—41no—
29#3708—22no—
30#1388—91nomaximal, Sylow
31C2×C3×M16—61no—
32C2×C3×M16—61no—
33C2×#208—21no—
34C2×#208—21no—
35C22×C3⋊C8—61no—
36C22×C3⋊C8—61no—
37#822—62no—
38#822—62no—
39#822—62no—
40#822—62no—
41C23×C32Q1611yescharacteristic
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C32×C4C22⋊C411yescharacteristic
44C2×C32×C4C4⋊C411yescharacteristic
45C2×C32×C4D811yescharacteristic
46C2×C32×C4SD1611yescharacteristic
47C2×C32×C4SD1611yescharacteristic
48C3⋊(C3⋊C8)C4211yescharacteristic
49C3⋊(C3⋊C8)C22⋊C411yescharacteristic
50C3⋊(C3⋊C8)C4⋊C411yescharacteristic
51C3⋊(C3⋊C8)C4⋊C411yescharacteristic
52C3×C3⋊C8—42no—
53C3×C3⋊C8—42no—
54C2×M32—91no—
55C2×#108—91no—
56C2×#108—91no—
57C22×C3×C4—21no—
58C22×C3×C4—21no—
59C3×M16—62no—
60C3×M16—62no—
61C3×M16—121no—
62C3×M16—121no—
63C2×C3×C8—121no—
64C2×C3×C8—121no—
65#208—22no—
66#208—22no—
67#208—41no—
68#208—41no—
69C2×C3⋊C8—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—41no—
84C22×C32#10311yescharacteristic
85C22×C32#10311yescharacteristic
86C22×C32#10711yescharacteristic
87C32×C4#9511yescharacteristic
88C32×C4#10211yescharacteristic
89C32×C4#10211yescharacteristic
90C32×C4#10611yescharacteristic
91C2×M16—61no—
92C2×M16—61no—
93C22×C8—91no—
94M32—92no—
95M32—181no—
96C2×C16—181no—
97#108—92no—
98#108—92no—
99#108—181no—
100#108—181no—
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—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—
115C3×C8—122no—
116C3×C8—122no—
117C3⋊C8—42no—
118C3⋊C8—42no—
119C3⋊C8—61no—
120C3⋊C8—61no—
121C3⋊C8—61no—
122C3⋊C8—61no—
123C3⋊C8—61no—
124C3⋊C8—61no—
125C3⋊C8—61no—
126C3⋊C8—61no—
127C2×C32—21no—
128C2×C32—21no—
129C2×C32—21no—
130C2×C32#34011yescharacteristic
131C22×C4GO+(4,𝔽2)11yescharacteristic
132M16—62no—
133M16—62no—
134M16—121no—
135M16—121no—
136C2×C8—91no—
137C2×C8—91no—
138C2×C8—91no—
139C2×C8—91no—
140C2×C8—91no—
141C2×C8—91no—
142C2×C8—121no—
143C2×C8—121no—
144C16—182no—
145C22×C3—21no—
146C22×C3—21no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—21no—
150C22×C3—21no—
151C22×C3—42no—
152C22×C3—42no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—21no—
156C3×C4—21no—
157C3×C4—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C32#138811yescharacteristic, complemented, Sylow
162C23#377611yescharacteristic
163C2×C4D32⋊C411yescharacteristic
164C2×C4D32⋊C411yescharacteristic
165C2×C4#377311yescharacteristic
166C2×C4#377411yescharacteristic
167C2×C4#377511yescharacteristic
168C2×C4#377511yescharacteristic
169C8—91no—
170C8—91no—
171C8—91no—
172C8—91no—
173C8—122no—
174C8—122no—
175C2×C3—22no—
176C2×C3—22no—
177C2×C3—21no—
178C2×C3—21no—
179C2×C3—41no—
180C2×C3—41no—
181C2×C3—41no—
182C2×C3—41no—
183C22—41no—
184C22#6374011yescharacteristic
185C22#6374011yescharacteristic
186C22#6374311yescharacteristic
187C4#6373711yescharacteristic
188C4#6373911yescharacteristic
189C4#6373911yescharacteristic
190C4#6374211yescharacteristic
191C3—21no—
192C3—21no—
193C2—21no—
194C2—21no—
195C2—21no—
196C2#1059007511yescharacteristic
subgroupG/H
centerC4#63739
commutatorC3⋊(C3⋊C8)C42
Frattini, hypercenterC22×C4GO+(4,𝔽2)
FittingC22×C32×C4D4
socleC2×C32#340
prime radicalC23×C32Q16
cosocleC22×C3⋊(C3⋊C8)C22
hypocenterC32#1388
LCSG ▷ C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C22×C4

Complements

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

NH ≅ G/Ntype
161. C32#1388semidirect

Maximal subgroups

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

subgroupindex
C2×#637732
C2×#635782
#13889