Finite Group Databasebeta

← #11771879

Subgroups — #11771879

Order 1152.

206 conjugacy classes of subgroups; only the 31 normal subgroups are shown.

normal subgroups only

This group has 206 conjugacy classes of subgroups — too many to draw. Only its 31 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#10590855C211yesmaximal, characteristic
2#10590182C211yesmaximal, characteristic
3#10589108C211yesmaximal, characteristic
4C2×C4⋊#157—21no—
5C2×C8×C3⋊D3C2211yescharacteristic
6#63871—21no—
7C2×#3718C411yescharacteristic, complemented
8C3×#816—21no—
9C2×C3×C3⋊C16—21no—
10#63576C411yescharacteristic, complemented
11#4813—61no—
12(C2×D3)⋊C16—61no—
13C22×#157—41no—
14C2×C4×C3⋊D3D411yescharacteristic
15C2×C3×Dic6—21no—
16C4⋊#157—22no—
17C4⋊#157—41no—
18C2×C32×C8D411yescharacteristic
19C2×C3⋊(C3⋊C8)C2×C411yescharacteristic
20C8×C3⋊D3—41no—
21C3×C4⋊Dic3—21no—
22Dic3⋊Dic3—41no—
23#3722—41no—
24#3718—41no—
25C3×C3⋊C16—41no—
26#1348—91nomaximal, Sylow
27#946—61no—
28C2×#216—61no—
29C2×D3×C8—61no—
30C2×D3×C8—61no—
31#897—61no—
32C2×C3×C16—61no—
33C3×#103—61no—
34#816—21no—
35C2×C3⋊C16—21no—
36#807—61no—
37C22×C3⋊D3D811yescharacteristic
38C2×#157—42no—
39C2×#157—81no—
40C2×#157—81no—
41C2×C32×C4C22⋊C411yescharacteristic
42C2×C3⋊Dic3SD1611yescharacteristic
43C4×C3⋊D3—21no—
44C4×C3⋊D3—21no—
45C2×C3×Dic3—41no—
46C2×C3×Dic3—41no—
47C3×Dic6—41no—
48C3×Dic6—41no—
49C32×C8—21no—
50C3⋊(C3⋊C8)—21no—
51#467—91no—
52C22⋊C16—91no—
53#340—91no—
54C2×C3×Q8—61no—
55C2×C4×D3—61no—
56C2×C4×D3—61no—
57C2×Dic6—21no—
58C2×C3×C8—21no—
59C2×C3×C8—21no—
60C3×C4⋊C4—61no—
61#216—122no—
62(C2×D3)⋊C4—121no—
63(C2×D3)⋊C4—121no—
64C4⋊Dic3—21no—
65C4⋊Dic3—121no—
66Dic3⋊C4—121no—
67C2×C3⋊C8—61no—
68C2×C3⋊C8—61no—
69D3×C8—122no—
70D3×C8—121no—
71D3×C8—121no—
72C3×C16—121no—
73C3⋊C16—41no—
74C22×C32#10211yescharacteristic
75C2×C3⋊D3—21no—
76C2×C3⋊D3—21no—
77C2×C3⋊D3SD3211yescharacteristic
78C2×C3⋊D3Q3211yescharacteristic
79#157—82no—
80C32×C4#9911yescharacteristic
81C32×C4#10411yescharacteristic
82C3⋊Dic3—21no—
83C3×Dic3—81no—
84C3×Dic3—81no—
85C2×Q16—91no—
86C22×C8—91no—
87C22⋊Q8—181no—
88C2×C4⋊C4—181no—
89C2×C16—61no—
90#107—91no—
91#103—61no—
92C22×D3—61no—
93C22×D3—61no—
94C3×Q8—121no—
95C3×Q8—121no—
96C2×C3×C4—21no—
97C2×C3×C4—21no—
98C2×C3×C4—121no—
99C2×C3×C4—121no—
100C2×Dic3—41no—
101C2×Dic3—41no—
102C2×Dic3—61no—
103C2×Dic3—61no—
104C4×D3—121no—
105C4×D3—121no—
106C4×D3—121no—
107C4×D3—121no—
108Dic6—41no—
109Dic6—41no—
110C3×C8—21no—
111C3×C8—21no—
112C3×C8—41no—
113C3⋊C8—62no—
114C3⋊C8—121no—
115C2×C32#32711yescharacteristic
116C2×C32#35811yescharacteristic
117C2×C32#36011yescharacteristic
118C3⋊D3—21no—
119C3⋊D3—21no—
120C2×Q8—61no—
121C22×C4—91no—
122C22×C4—361no—
123Q16—361no—
124C2×C8—91no—
125C2×C8—361no—
126C2×C8GO+(4,𝔽2)11yescharacteristic
127C4⋊C4—61no—
128C4⋊C4—182no—
129C4⋊C4—361no—
130C4⋊C4—361no—
131C22⋊C4—361no—
132C16—121no—
133C22×C3—21no—
134C22×C3—21no—
135C2×D3—61no—
136C2×D3—61no—
137C2×D3—61no—
138C2×D3—61no—
139C2×D3—121no—
140C2×D3—121no—
141C2×D3—121no—
142C2×D3—121no—
143C3×C4—21no—
144C3×C4—21no—
145C3×C4—21no—
146C3×C4—21no—
147C3×C4—241no—
148C3×C4—241no—
149Dic3—81no—
150Dic3—81no—
151Dic3—121no—
152Dic3—121no—
153C32#134811yescharacteristic, complemented, Sylow
154C23—91no—
155Q8—121no—
156Q8—121no—
157C2×C4—91no—
158C2×C4—121no—
159C2×C4—121no—
160C2×C4—181no—
161C2×C4—181no—
162C2×C4—362no—
163C2×C4—721no—
164C2×C4—721no—
165C2×C4D32⋊C411yescharacteristic
166C8—21no—
167C8—181no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C2×C3—21no—
172C2×C3—21no—
173C2×C3—21no—
174D3—121no—
175D3—121no—
176D3—121no—
177D3—121no—
178C22—91no—
179C22—91no—
180C22—181no—
181C22—181no—
182C22#6372911yescharacteristic
183C4—181no—
184C4—241no—
185C4—241no—
186C4—722no—
187C4#6373111yescharacteristic
188C4#6373811yescharacteristic
189C3—21no—
190C3—21no—
191C2—181no—
192C2—181no—
193C2#1059001711yescharacteristic
194C2#1059001911yescharacteristic
195C2#1059003311yescharacteristic
subgroupG/H
centerC22#63729
commutatorC2×C3⋊(C3⋊C8)C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#102
prime radicalC22×C3⋊D3D8
cosocleC2×C8×C3⋊D3C22
hypocenterC32#1348
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
7. C2×#3718C4semidirect
10. #63576C4semidirect
153. C32#1348semidirect

Maximal subgroups

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

subgroupindex
#105908552
#105901822
#105891082
#13489