Finite Group Databasebeta

← #11771420

Subgroups — #11771420

Order 1152.

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

normal subgroups only

This group has 252 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#10590937C211yesmaximal, characteristic
2#10590180C211yesmaximal, characteristic, complemented
3#10589110C211yesmaximal, characteristic, complemented
4C2×C4×D32C411yescharacteristic
5C2×#3743C2211yescharacteristic
6C2×#3712C411yescharacteristic
7#63773—21no—
8C3×(C2×D3)⋊C8—21no—
9C3×#812—21no—
10(C2×D3)⋊(C3⋊C8)—21no—
11#4726—61no—
12#4514—61no—
13C22×D32C811yescharacteristic
14C2×C4×C3⋊D3C2×C411yescharacteristic
15C2×C3×C4×D3—21no—
16C2×#624C811yescharacteristic
17C2×D3×Dic3—21no—
18C4×D32—41no—
19C4×D32—41no—
20C2×C32×C8D411yescharacteristic
21C2×C3⋊(C3⋊C8)D411yescharacteristic
22#3743—41no—
23C2×C3×C3⋊C8—21no—
24#3712—41no—
25#3708—41no—
26C3×C3⋊C16—41no—
27#1320—91nomaximal, Sylow
28C22×C4×D3—61no—
29C2×ΓL(1,𝔽25)—61no—
30C2×ΓL(1,𝔽25)—61no—
31C2×ΓL(1,𝔽25)—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⋊D3C2×C811yescharacteristic
39C22×C3×D3—21no—
40C2×D32—41no—
41C2×D32—42no—
42C2×C32×C4C22⋊C411yescharacteristic
43C2×C3⋊Dic3M1611yescharacteristic
44C4×C3⋊D3—21no—
45C4×C3⋊D3—21no—
46C2×C3×Dic3—21no—
47C3×C4×D3—41no—
48C3×C4×D3—41no—
49#624—41no—
50D3×Dic3—42no—
51C32×C8—21no—
52C3⋊(C3⋊C8)—21no—
53C3×C3⋊C8—41no—
54#407—91no—
55#349—91no—
56#349—91no—
57C23×D3—61no—
58C22×C3×C4—61no—
59C22×Dic3—61no—
60C2×C4×D3—21no—
61C2×C4×D3—61no—
62C2×C4×D3—61no—
63C2×C4×D3—61no—
64C2×C4×D3—61no—
65C2×C4×D3—122no—
66C2×C4×D3—122no—
67C2×C3×C8—21no—
68C2×C3×C8—21no—
69C2×C3×C8—61no—
70C2×C3⋊C8—21no—
71C2×C3⋊C8—61no—
72C2×C3⋊C8—61no—
73ΓL(1,𝔽25)—122no—
74ΓL(1,𝔽25)—121no—
75ΓL(1,𝔽25)—121no—
76ΓL(1,𝔽25)—122no—
77C3×C16—121no—
78C3⋊C16—41no—
79C22×C32C22⋊C811yescharacteristic
80C2×C3⋊D3—21no—
81C2×C3⋊D3—41no—
82C2×C3×D3—22no—
83C2×C3×D3—41no—
84C2×C3×D3—41no—
85D32—42no—
86D32—42no—
87C32×C4#9911yescharacteristic
88C32×C4#10011yescharacteristic
89C3⋊Dic3—21no—
90C3×Dic3—41no—
91C23×C4—91no—
92C2×M16—91no—
93C2×M16—91no—
94M32—61no—
95M32—181no—
96C22⋊C8—61no—
97C22⋊C8—181no—
98C23×C3—61no—
99C22×D3—21no—
100C22×D3—61no—
101C22×D3—61no—
102C22×D3—122no—
103C22×D3—122no—
104C22×D3—122no—
105C2×C3×C4—21no—
106C2×C3×C4—21no—
107C2×C3×C4—61no—
108C2×C3×C4—121no—
109C2×C3×C4—121no—
110C2×Dic3—21no—
111C2×Dic3—61no—
112C2×Dic3—61no—
113C2×Dic3—122no—
114C4×D3—41no—
115C4×D3—41no—
116C4×D3—62no—
117C4×D3—62no—
118C4×D3—121no—
119C4×D3—121no—
120C4×D3—122no—
121C4×D3—122no—
122C3×C8—21no—
123C3×C8—21no—
124C3×C8—41no—
125C3×C8—121no—
126C3⋊C8—41no—
127C3⋊C8—121no—
128C3⋊C8—121no—
129C2×C32—21no—
130C2×C32#32311yescharacteristic
131C3⋊D3—41no—
132C3×D3—42no—
133C24—91no—
134C22×C4—61no—
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—181no—
138C22×C4—361no—
139C22×C4—361no—
140M16—361no—
141M16—361no—
142C2×C8—61no—
143C2×C8—91no—
144C2×C8GO+(4,𝔽2)11yescharacteristic
145C16—121no—
146C16—361no—
147C22×C3—21no—
148C22×C3—21no—
149C22×C3—62no—
150C22×C3—121no—
151C22×C3—121no—
152C2×D3—22no—
153C2×D3—41no—
154C2×D3—41no—
155C2×D3—62no—
156C2×D3—121no—
157C2×D3—124no—
158C2×D3—124no—
159C2×D3—121no—
160C2×D3—121no—
161C2×D3—241no—
162C3×C4—21no—
163C3×C4—21no—
164C3×C4—21no—
165C3×C4—21no—
166C3×C4—121no—
167Dic3—41no—
168Dic3—62no—
169Dic3—121no—
170C32#132011yescharacteristic, complemented, Sylow
171C23—61no—
172C23—91no—
173C23—362no—
174C23—361no—
175C2×C4—61no—
176C2×C4—91no—
177C2×C4—121no—
178C2×C4—121no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—362no—
182C2×C4—361no—
183C2×C4D32⋊C411yescharacteristic
184C8—21no—
185C8—121no—
186C8—181no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—41no—
192C2×C3—122no—
193D3—42no—
194D3—122no—
195D3—241no—
196C22—62no—
197C22—121no—
198C22—121no—
199C22—181no—
200C22—361no—
201C22—362no—
202C22—362no—
203C22D32⋊C811yescharacteristic
204C4—121no—
205C4—181no—
206C4#6372711yescharacteristic
207C4#6373811yescharacteristic
208C3—21no—
209C3—21no—
210C2—21no—
211C2—122no—
212C2—361no—
213C2#1059002711yescharacteristic
subgroupG/H
centerC4#63738
commutatorC22×C3⋊D3C2×C8
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#323
prime radicalC22×D32C8
cosocleC2×#3743C22
hypocenterC32#1320
LCSG ▷ C22×C3⋊D3 ▷ 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
170. C32#1320semidirect

Maximal subgroups

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

subgroupindex
#105909372
#105901802
#105891102
#13209