Finite Group Databasebeta

← #11795096

Subgroups — #11795096

Order 1152.

360 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 360 conjugacy classes of subgroups — too many to draw. Only its 63 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#10593759C211yesmaximal, characteristic
2#10593413C211yesmaximal, characteristic
3#10590573C212yesmaximal
4#10590049C212yesmaximal
5#10590044C211yesmaximal, characteristic
6C2×C4⋊#157—21no—
7C2×C4⋊#157C2211yescharacteristic
8C2×C4×#157C2211yescharacteristic
9C2×#3773—21no—
10C2×#3773—21no—
11C4⋊C4×C3⋊D3C2211yescharacteristic
12#63900C2212yes—
13C2×#3710C2212yes—
14#63781—21no—
15C3×#807—22no—
16#63575—22no—
17D3×#107—62no—
18C22×#157—21no—
19C22×#157D411yescharacteristic
20C22×#157D411yescharacteristic
21C2×C4×C3⋊D3—21no—
22C2×C4×C3⋊D3C2311yescharacteristic
23C2×#624—22no—
24C4⋊#157—22no—
25C4⋊#157—42no—
26C4×#157—22no—
27#3773—42no—
28#3773—42no—
29C32×C4⋊C4D411yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31#3750—21no—
32C3×C4⋊Dic3—22no—
33C2×C3×C3⋊C8—22no—
34#3724—22no—
35#3710—22no—
36#3710Q814yes—
37#2083—91nomaximal, Sylow
38C2×D3×C8—62no—
39D3×C4⋊C4—62no—
40D3×C4⋊C4—62no—
41C3×#107—62no—
42#818—62no—
43#807—22no—
44#807—62no—
45C22×C3⋊D3C2×D411yescharacteristic
46C2×#157—21no—
47C2×#157—21no—
48C2×#157—21no—
49C2×#157—21no—
50C2×#157—41no—
51C2×#157—41no—
52C2×#157—41no—
53C2×#157D812yes—
54C2×#157Q1612yes—
55C2×C32×C4—21no—
56C2×C32×C4C2×D411yescharacteristic
57C2×C3⋊Dic3—21no—
58C2×C3⋊Dic3#4111yescharacteristic
59C4×C3⋊D3—41no—
60C4×C3⋊D3—41no—
61C4×C3⋊D3C2×Q812yes—
62C4×C3⋊D3#4112yes—
63C2×C3×Dic3—42no—
64#624—42no—
65#624—42no—
66C3×C3⋊C8—24no—
67C2×#107—92no—
68#389—91no—
69#384—91no—
70#340—92no—
71#336—91no—
72C2×C4×D3—62no—
73C2×C4×D3—122no—
74C2×C4×D3—122no—
75C2×C3×C8—62no—
76C3×C4⋊C4—22no—
77C3×C4⋊C4—62no—
78C4⋊Dic3—22no—
79C4⋊Dic3—62no—
80Dic3⋊C4—122no—
81Dic3⋊C4—122no—
82C2×C3⋊C8—22no—
83D3×C8—64no—
84D3×C8—64no—
85C22×C32#12111yescharacteristic
86C2×C3⋊D3#12311yescharacteristic
87C2×C3⋊D3C4⋊Q811yescharacteristic
88C2×C3⋊D3C2×D811yescharacteristic
89C2×C3⋊D3C2×Q1611yescharacteristic
90C2×C3⋊D3AGL(1,ℤ/8)11yescharacteristic
91C2×C3⋊D3#13711yescharacteristic
92#157—22no—
93#157—22no—
94#157—81no—
95C32×C4—41no—
96C32×C4C22⋊Q812yes—
97C3⋊Dic3—41no—
98C3⋊Dic3#12512yes—
99C3×Dic3—82no—
100C22×C8—92no—
101C2×C4⋊C4—92no—
102C2×C4⋊C4—91no—
103C2×C4⋊C4—91no—
104C2×C4⋊C4—181no—
105C2×C4⋊C4—181no—
106C2×C4⋊C4—181no—
107C2×C42—91no—
108#107—62no—
109#107—182no—
110#95—181no—
111C22×D3—62no—
112C2×C3×C4—22no—
113C2×C3×C4—42no—
114C2×C3×C4—122no—
115C2×Dic3—42no—
116C2×Dic3—62no—
117C2×Dic3—122no—
118C4×D3—62no—
119C4×D3—62no—
120C4×D3—62no—
121C4×D3—62no—
122C4×D3—242no—
123C4×D3—242no—
124C4×D3—242no—
125C4×D3—242no—
126C3×C8—64no—
127C3⋊C8—24no—
128C2×C32#39811yescharacteristic
129C2×C32#45911yescharacteristic
130C2×C32#46211yescharacteristic
131C3⋊D3#48011yescharacteristic
132C3⋊D3#48411yescharacteristic
133C3⋊D3#50011yescharacteristic
134C3⋊D3#50111yescharacteristic
135C22×C4—91no—
136C22×C4—91no—
137C22×C4—91no—
138C22×C4—181no—
139C22×C4—182no—
140C22×C4—181no—
141C2×C8—62no—
142C2×C8—94no—
143C2×C8—182no—
144C4⋊C4—62no—
145C4⋊C4—91no—
146C4⋊C4—181no—
147C4⋊C4—182no—
148C4⋊C4—182no—
149C4⋊C4—362no—
150C4⋊C4—362no—
151C4⋊C4—362no—
152C4⋊C4GO+(4,𝔽2)11yescharacteristic
153C42—182no—
154C22×C3—22no—
155C2×D3—62no—
156C2×D3—62no—
157C2×D3—62no—
158C2×D3—62no—
159C2×D3—62no—
160C2×D3—62no—
161C3×C4—22no—
162C3×C4—22no—
163C3×C4—82no—
164C3×C4—242no—
165Dic3—62no—
166Dic3—62no—
167Dic3—82no—
168Dic3—242no—
169C32#208311yescharacteristic, complemented, Sylow
170C23—91no—
171C2×C4—21no—
172C2×C4—91no—
173C2×C4—92no—
174C2×C4—92no—
175C2×C4—92no—
176C2×C4—92no—
177C2×C4—122no—
178C2×C4—181no—
179C2×C4—181no—
180C2×C4—181no—
181C2×C4—181no—
182C2×C4—181no—
183C2×C4—361no—
184C2×C4—361no—
185C2×C4—362no—
186C2×C4—362no—
187C2×C4—361no—
188C2×C4—361no—
189C2×C4—361no—
190C2×C4C2×GO+(4,𝔽2)11yescharacteristic
191C8—64no—
192C2×C3—22no—
193C2×C3—22no—
194C2×C3—22no—
195D3—62no—
196D3—62no—
197D3—62no—
198D3—62no—
199C22—91no—
200C22—91no—
201C22—91no—
202C22—91no—
203C22—91no—
204C22—91no—
205C22#6424211yescharacteristic
206C4—41no—
207C4—92no—
208C4—182no—
209C4—182no—
210C4—242no—
211C4—361no—
212C4—721no—
213C4D32⋊Q812yes—
214C3—22no—
215C2—91no—
216C2—91no—
217C2—91no—
218C2—91no—
219C2#1059334011yescharacteristic
220C2#1059346411yescharacteristic
221C2#1059347711yescharacteristic
subgroupG/H
centerC22#64242
commutator, cosocleC2×C4×C3⋊D3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C4⋊C4D4
socleC22×C32#121
prime radicalC22×C3⋊D3C2×D4
hypercenterC4⋊C4GO+(4,𝔽2)
hypocenterC32#2083
LCSG ▷ C2×C4×C3⋊D3 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C4⋊C4

Complements

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

NH ≅ G/Ntype
169. C32#2083semidirect

Maximal subgroups

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

subgroupindex
#105937592
#105934132
#105905732
#105900492
#105900442
#20839