Finite Group Databasebeta

← #11772053

Subgroups — #11772053

Order 1152.

194 conjugacy classes of subgroups; only the 33 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 33 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#10590353C211yesmaximal, characteristic
2C4⋊#3708C211yesmaximal, characteristic, complemented
3#10589098C211yesmaximal, characteristic, complemented
4C3×#875—21no—
5C2×#3718C411yescharacteristic
6C2×#3715—21no—
7C2×#3713C411yescharacteristic
8C2×#3708—21no—
9C4×C3⋊(C3⋊C8)C2211yescharacteristic
10C3×C4⋊(C3⋊C8)—21no—
11#5059—61no—
12#4480—61no—
13C2×C3×D12—21no—
14C2×C3×Dic6—21no—
15C32×C42D411yescharacteristic
16C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
17C2×C3⋊(C3⋊C8)D411yescharacteristic
18C3×(C2×D3)⋊C4—41no—
19C3×(C2×D3)⋊C4—41no—
20C2×C3×C3⋊C8—41no—
21#3718—41no—
22#3715—41no—
23#3715—41no—
24#3713—41no—
25#3708—41no—
26#1360—91nomaximal, Sylow
27C3×#124—61no—
28C2×#216—61no—
29C2×#215—61no—
30C2×#214—61no—
31C2×#213—61no—
32#875—21no—
33C3×C4⋊C8—61no—
34C4⋊(C3⋊C8)—21no—
35C4×C3⋊C8—61no—
36C4×C3⋊C8—61no—
37C22×C3×D3—41no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C32×C4D811yescharacteristic
40C2×C32×C4SD1611yescharacteristic
41C2×C3×Dic3—41no—
42C3×D12—41no—
43C3×D12—41no—
44C3×Dic6—41no—
45C3×Dic6—41no—
46C3⋊(C3⋊C8)—21no—
47C3⋊(C3⋊C8)D811yescharacteristic
48C3⋊(C3⋊C8)SD1611yescharacteristic
49C3×C3⋊C8—81no—
50#495—91no—
51C4⋊C16—91no—
52#334—91no—
53C2×C3×Q8—61no—
54C2×C3×D4—61no—
55C2×D12—21no—
56C2×Dic6—21no—
57C2×C3×C8—121no—
58C3×C22⋊C4—121no—
59C3×C22⋊C4—121no—
60C3×C42—21no—
61C3×C42—21no—
62#216—122no—
63#215—121no—
64#215—121no—
65#214—121no—
66#214—121no—
67#213—122no—
68(C2×D3)⋊C4—41no—
69(C2×D3)⋊C4—41no—
70C2×C3⋊C8—41no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8—61no—
73C2×C3⋊C8—61no—
74C2×C3⋊C8—61no—
75C22×C32#10211yescharacteristic
76C2×C3×D3—81no—
77C2×C3×D3—81no—
78C2×C3×D3—81no—
79C32×C4—21no—
80C32×C4—21no—
81C32×C4#10011yescharacteristic
82C32×C4#10211yescharacteristic
83C3×Dic3—81no—
84C2×Q16—91no—
85C2×SD16—181no—
86C2×D8—91no—
87#124—61no—
88C2×C16—181no—
89C4⋊C8—61no—
90C4×C8—91no—
91C23×C3—121no—
92C22×D3—41no—
93C3×Q8—121no—
94C3×Q8—121no—
95C3×D4—121no—
96C3×D4—121no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—21no—
102C2×C3×C4—21no—
103C2×C3×C4—121no—
104C2×Dic3—41no—
105D12—41no—
106D12—41no—
107Dic6—41no—
108Dic6—41no—
109C3×C8—241no—
110C3⋊C8—61no—
111C3⋊C8—61no—
112C3⋊C8—61no—
113C3⋊C8—61no—
114C3⋊C8—62no—
115C3⋊C8—81no—
116C3⋊C8—121no—
117C2×C32#33111yescharacteristic
118C2×C32#35911yescharacteristic
119C2×C32#36011yescharacteristic
120C3×D3—161no—
121C2×Q8—61no—
122C2×D4—61no—
123Q16—361no—
124SD16—361no—
125SD16—361no—
126D8—361no—
127C2×C8—91no—
128C2×C8—91no—
129C2×C8—121no—
130C22⋊C4—121no—
131C22⋊C4—121no—
132C42GO+(4,𝔽2)11yescharacteristic
133C16—361no—
134C22×C3—21no—
135C22×C3—21no—
136C22×C3—241no—
137C22×C3—241no—
138C22×C3—241no—
139C2×D3—81no—
140C2×D3—81no—
141C2×D3—81no—
142C3×C4—21no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—21no—
148C3×C4—41no—
149C3×C4—41no—
150C3×C4—41no—
151C3×C4—241no—
152Dic3—81no—
153C32#136011yescharacteristic, complemented, Sylow
154C23—121no—
155Q8—121no—
156Q8—121no—
157D4—121no—
158D4—121no—
159C2×C4—121no—
160C2×C4D32⋊C411yescharacteristic
161C2×C4#377411yescharacteristic
162C2×C4#377511yescharacteristic
163C8—91no—
164C8—91no—
165C8—181no—
166C8—241no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—481no—
174D3—161no—
175C22—241no—
176C22—241no—
177C22—241no—
178C22#6373911yescharacteristic
179C4—21no—
180C4—21no—
181C4—241no—
182C4#6372711yescharacteristic
183C4#6372911yescharacteristic
184C3—21no—
185C3—21no—
186C2—481no—
187C2#1059003711yescharacteristic
188C2#1059006311yescharacteristic
189C2#1059006411yescharacteristic
subgroupG/H
centerC22#63739
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC42GO+(4,𝔽2)
FittingC32×C42D4
socleC22×C32#102
prime radicalC2×#3713C4
cosocleC4×C3⋊(C3⋊C8)C22
hypocenterC32#1360
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42

Complements

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

NH ≅ G/Ntype
2. C4⋊#3708C2semidirect
3. #10589098C2semidirect
153. C32#1360semidirect

Maximal subgroups

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

subgroupindex
#105903532
C4⋊#37082
#105890982
#13609