Finite Group Databasebeta

← #11772807

Subgroups — #11772807

Order 1152.

215 conjugacy classes of subgroups; only the 19 normal subgroups are shown.

normal subgroups only

This group has 215 conjugacy classes of subgroups — too many to draw. Only its 19 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#10591485C211yesmaximal, characteristic
2#10590212C211yesmaximal, characteristic, complemented
3#10589181C211yesmaximal, characteristic, complemented
4#64145C2211yescharacteristic
5C2×C3×#213—21no—
6#63914C411yescharacteristic, complemented
7C2×#3716—21no—
8#63780—21no—
9C3×#834—21no—
10#63555C411yescharacteristic, complemented
11#5154—61no—
12#4473—61no—
13C2×C32×D4D411yescharacteristic
14C2×#634D411yescharacteristic
15C2×C3×D12—21no—
16C2×#625—41no—
17#3792—41no—
18#3757—41no—
19C4×C3⋊Dic3C2×C411yescharacteristic
20C3×#217—41no—
21C3×#213—42no—
22C2×C3×C3⋊C8—21no—
23#3716—42no—
24#1406—91nomaximal, Sylow
25C2×C3×D8—61no—
26#940—61no—
27#936—61no—
28#936—61no—
29C2×#214—61no—
30C2×#213—21no—
31C2×#204—61no—
32C3×#99—61no—
33#834—21no—
34#815—61no—
35C23×C32—21no—
36C22×C3×D3—41no—
37C32×D4—41no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C3⋊Dic3—21no—
40C2×C3⋊Dic3—21no—
41#634—41no—
42C2×C3×Dic3—81no—
43C3×D12—41no—
44C3×D12—41no—
45#625—82no—
46#622—81no—
47C3×C3⋊C8—22no—
48#496—91no—
49#355—91no—
50#354—91no—
51C2×C3×D4—21no—
52C2×C3×D4—21no—
53C2×C3×D4—61no—
54C2×#67—122no—
55C2×D12—21no—
56C2×Dic6—61no—
57C2×Dic6—61no—
58C3×D8—122no—
59C2×C3×C8—61no—
60C3×C22⋊C4—121no—
61#217—41no—
62#217—122no—
63#217—121no—
64#217—121no—
65#214—122no—
66#213—42no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C2×C3⋊C8—21no—
70#204—122no—
71C22×C32—41no—
72C22×C32—81no—
73C22×C32#9911yescharacteristic
74C2×C3×D3—82no—
75C2×C3×D3—81no—
76C32×C4—21no—
77C3⋊Dic3—41no—
78C3⋊Dic3—41no—
79C3×Dic3—161no—
80C2×SD16—181no—
81C2×D8—61no—
82#127—91no—
83#124—91no—
84#101—181no—
85#99—61no—
86#97—91no—
87C23×C3—21no—
88C23×C3—21no—
89C23×C3—41no—
90C23×C3—121no—
91C22×D3—41no—
92C3×D4—41no—
93C3×D4—41no—
94C3×D4—81no—
95C3×D4—121no—
96C3×D4—121no—
97C2×C3×C4—21no—
98C2×C3×C4—21no—
99C2×C3×C4—241no—
100#67—244no—
101C2×Dic3—62no—
102C2×Dic3—81no—
103C2×Dic3—121no—
104C2×Dic3—121no—
105C2×Dic3—121no—
106D12—41no—
107D12—41no—
108Dic6—121no—
109Dic6—121no—
110Dic6—241no—
111C3×C8—62no—
112C3⋊C8—22no—
113C2×C32—21no—
114C2×C32—81no—
115C2×C32#35311yescharacteristic
116C3×D3—161no—
117C2×Q8—91no—
118C2×D4—61no—
119C2×D4—361no—
120C2×D4GO+(4,𝔽2)11yescharacteristic
121SD16—362no—
122D8—122no—
123M16—361no—
124C2×C8—61no—
125C22⋊C4—121no—
126C22⋊C4—361no—
127C42—91no—
128C22×C3—21no—
129C22×C3—21no—
130C22×C3—41no—
131C22×C3—41no—
132C22×C3—81no—
133C22×C3—82no—
134C22×C3—81no—
135C22×C3—81no—
136C22×C3—242no—
137C22×C3—241no—
138C2×D3—81no—
139C2×D3—82no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—41no—
143C3×C4—481no—
144Dic3—122no—
145Dic3—161no—
146Dic3—241no—
147Dic3—241no—
148Dic3—241no—
149C32#140611yescharacteristic, complemented, Sylow
150C23—21no—
151C23—121no—
152Q8—361no—
153D4—41no—
154D4—121no—
155D4—121no—
156D4—722no—
157C2×C4—181no—
158C2×C4—181no—
159C2×C4—241no—
160C2×C4D32⋊C411yescharacteristic
161C8—62no—
162C8—721no—
163C2×C3—22no—
164C2×C3—21no—
165C2×C3—21no—
166C2×C3—41no—
167C2×C3—81no—
168C2×C3—81no—
169C2×C3—161no—
170C2×C3—481no—
171D3—161no—
172C22—41no—
173C22—81no—
174C22—242no—
175C22—241no—
176C22#6373811yescharacteristic
177C4—21no—
178C4—361no—
179C4—361no—
180C4—481no—
181C3—21no—
182C3—21no—
183C2—21no—
184C2—81no—
185C2—481no—
186C2#1059008011yescharacteristic
subgroupG/H
centerC2#10590080
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×D4GO+(4,𝔽2)
FittingC2×C32×D4D4
socleC2×C32#353
prime radical#10591485C2
cosocle#64145C22
hypocenterC32#1406
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×D4

Complements

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

NH ≅ G/Ntype
2. #10590212C2semidirect
3. #10589181C2semidirect
6. #63914C4semidirect
10. #63555C4semidirect
149. C32#1406semidirect

Maximal subgroups

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

subgroupindex
#105914852
#105902122
#105891812
#14069