Finite Group Databasebeta

← #11771433

Subgroups — #11771433

Order 1152.

220 conjugacy classes of subgroups; only the 27 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 27 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#10590959C211yesmaximal, characteristic
2#10590180C211yesmaximal, characteristic, complemented
3#10589110C211yesmaximal, characteristic, complemented
4C2×#3798C411yescharacteristic
5C2×#3743C2211yescharacteristic
6C2×#3710C411yescharacteristic
7#63773—21no—
8C3×(C2×D3)⋊C8—21no—
9C3×#812—21no—
10(C2×D3)⋊(C3⋊C8)—21no—
11#4727—61no—
12#4514—61no—
13C2×C4×C3⋊D3C2×C411yescharacteristic
14C2×C3×C4×D3—21no—
15C2×#627C811yescharacteristic
16C2×#626—21no—
17C2×#625C811yescharacteristic
18#3798—41no—
19#3798—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3743—41no—
23C2×C3×C3⋊C8—21no—
24#3710—41no—
25#3708—41no—
26C3×C3⋊C16—41no—
27#1321—91nomaximal, Sylow
28C2×#235—61no—
29C2×ΓL(1,𝔽25)—61no—
30C2×ΓL(1,𝔽25)—61no—
31C2×D3×C8—61no—
32C3×M32—61no—
33C3×C22⋊C8—61no—
34#830—61no—
35(C2×D3)⋊C8—21no—
36(C2×D3)⋊C8—61no—
37#812—21no—
38C22×C3⋊D3M1611yescharacteristic
39C22×C3×D3—21no—
40C2×C32×C4C22⋊C411yescharacteristic
41C2×C3⋊Dic3C2×C811yescharacteristic
42C4×C3⋊D3—21no—
43C4×C3⋊D3—21no—
44C2×C3×Dic3—21no—
45C3×C4×D3—41no—
46C3×C4×D3—41no—
47#627—41no—
48#626—42no—
49#625—41no—
50C32×C8—21no—
51C3⋊(C3⋊C8)—21no—
52C3×C3⋊C8—41no—
53#408—91no—
54#349—91no—
55#349—91no—
56C22×C3×C4—61no—
57C2×#67—61no—
58C2×#67—61no—
59#235—122no—
60#235—122no—
61C2×D12—61no—
62C2×C4×D3—21no—
63C2×C4×D3—61no—
64C2×C4×D3—61no—
65C2×Dic6—61no—
66C2×C3×C8—21no—
67C2×C3×C8—21no—
68C2×C3×C8—61no—
69C2×C3⋊C8—21no—
70C2×C3⋊C8—61no—
71C2×C3⋊C8—61no—
72ΓL(1,𝔽25)—121no—
73ΓL(1,𝔽25)—121no—
74ΓL(1,𝔽25)—122no—
75D3×C8—122no—
76C3×C16—121no—
77C3⋊C16—41no—
78C22×C32C22⋊C811yescharacteristic
79C2×C3⋊D3—21no—
80C2×C3⋊D3—41no—
81C2×C3×D3—42no—
82C2×C3×D3—41no—
83C32×C4#9911yescharacteristic
84C32×C4#10011yescharacteristic
85C3⋊Dic3—21no—
86C3×Dic3—41no—
87C2×#41—91no—
88C2×M16—91no—
89C22×C8—91no—
90M32—61no—
91M32—181no—
92C22⋊C8—61no—
93C22⋊C8—181no—
94C23×C3—61no—
95C22×D3—21no—
96C22×D3—61no—
97C22×D3—61no—
98C2×C3×C4—21no—
99C2×C3×C4—21no—
100C2×C3×C4—61no—
101C2×C3×C4—121no—
102C2×C3×C4—121no—
103#67—122no—
104#67—122no—
105C2×Dic3—21no—
106C2×Dic3—61no—
107C2×Dic3—61no—
108D12—122no—
109C4×D3—41no—
110C4×D3—41no—
111C4×D3—62no—
112C4×D3—62no—
113C4×D3—121no—
114C4×D3—121no—
115Dic6—122no—
116C3×C8—21no—
117C3×C8—21no—
118C3×C8—41no—
119C3×C8—121no—
120C3⋊C8—41no—
121C3⋊C8—121no—
122C3⋊C8—121no—
123C2×C32—21no—
124C2×C32#32311yescharacteristic
125C3⋊D3—41no—
126C3×D3—81no—
127#41—361no—
128#41—361no—
129C2×Q8—91no—
130C2×D4—91no—
131C2×D4—181no—
132C22×C4—61no—
133C22×C4—91no—
134M16—361no—
135C2×C8—61no—
136C2×C8—91no—
137C2×C8—361no—
138C2×C8GO+(4,𝔽2)11yescharacteristic
139C16—121no—
140C16—361no—
141C22×C3—21no—
142C22×C3—21no—
143C22×C3—121no—
144C22×C3—122no—
145C2×D3—41no—
146C2×D3—42no—
147C2×D3—62no—
148C2×D3—121no—
149C2×D3—122no—
150C2×D3—241no—
151C3×C4—21no—
152C3×C4—21no—
153C3×C4—21no—
154C3×C4—21no—
155C3×C4—121no—
156Dic3—41no—
157Dic3—62no—
158Dic3—121no—
159C32#132111yescharacteristic, complemented, Sylow
160C23—61no—
161C23—91no—
162Q8—361no—
163D4—362no—
164D4—361no—
165C2×C4—61no—
166C2×C4—91no—
167C2×C4—121no—
168C2×C4—121no—
169C2×C4—181no—
170C2×C4—181no—
171C2×C4D32⋊C411yescharacteristic
172C8—21no—
173C8—121no—
174C8—181no—
175C2×C3—22no—
176C2×C3—21no—
177C2×C3—21no—
178C2×C3—41no—
179C2×C3—241no—
180D3—81no—
181D3—122no—
182D3—241no—
183C22—122no—
184C22—121no—
185C22—181no—
186C22—361no—
187C22D32⋊C811yescharacteristic
188C4—121no—
189C4—181no—
190C4#6372711yescharacteristic
191C4#6373811yescharacteristic
192C3—21no—
193C3—21no—
194C2—21no—
195C2—241no—
196C2—361no—
197C2#1059002711yescharacteristic
subgroupG/H
centerC4#63738
commutatorC2×C3⋊Dic3C2×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#323
prime radicalC2×#3798C4
cosocleC2×#3743C22
hypocenterC32#1321
LCSG ▷ C2×C3⋊Dic3 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590180C2semidirect
3. #10589110C2semidirect
159. C32#1321semidirect

Maximal subgroups

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

subgroupindex
#105909592
#105901802
#105891102
#13219