Finite Group Databasebeta

← #11772037

Subgroups — #11772037

Order 1152.

196 conjugacy classes of subgroups; only the 29 normal subgroups are shown.

normal subgroups only

This group has 196 conjugacy classes of subgroups — too many to draw. Only its 29 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#10590884C211yesmaximal, characteristic
2#10590178C211yesmaximal, characteristic, complemented
3#10589135C211yesmaximal, characteristic, complemented
4C2×C3×#204—21no—
5#63914C411yescharacteristic
6#63873C411yescharacteristic
7C2×#3715—21no—
8#63773—21no—
9C8×C3⋊Dic3C2211yescharacteristic
10C3×#812—21no—
11#5175—61no—
12#4511—61no—
13C2×C3×D12—21no—
14C2×C3×Dic6—21no—
15C2×#625—41no—
16C2×C32×C8D411yescharacteristic
17C4×C3⋊Dic3C2×C411yescharacteristic
18C2×C3⋊(C3⋊C8)D411yescharacteristic
19C3×#204—41no—
20C3×#204—41no—
21#3724—41no—
22#3715—41no—
23#3715—41no—
24#3708—41no—
25C3×C3⋊C16—41no—
26#1359—91nomaximal, Sylow
27C2×C3×SD16—61no—
28#944—61no—
29C2×#215—61no—
30#940—61no—
31C2×#214—61no—
32C2×#204—21no—
33C3×M32—61no—
34C8×Dic3—61no—
35C8×Dic3—61no—
36#812—21no—
37C22×C3×D3—41no—
38C2×C32×C4C22⋊C411yescharacteristic
39C2×C3⋊Dic3—21no—
40C2×C3×Dic3—41no—
41C3×D12—41no—
42C3×D12—41no—
43C3×Dic6—41no—
44C3×Dic6—41no—
45#625—82no—
46C32×C8D811yescharacteristic
47C32×C8SD1611yescharacteristic
48C3⋊(C3⋊C8)D811yescharacteristic
49C3⋊(C3⋊C8)SD1611yescharacteristic
50#492—91no—
51#364—91no—
52#364—91no—
53C2×C3×Q8—61no—
54C2×C3×D4—61no—
55C2×#67—122no—
56C2×D12—21no—
57C2×Dic6—21no—
58C3×SD16—121no—
59C3×SD16—121no—
60C2×C3×C8—21no—
61C2×C3×C8—21no—
62#215—121no—
63#215—121no—
64#214—121no—
65#214—121no—
66Dic3⋊C4—122no—
67C4×Dic3—61no—
68C4×Dic3—61no—
69C2×C3⋊C8—61no—
70C2×C3⋊C8—61no—
71#204—41no—
72#204—41no—
73C3×C16—121no—
74C3⋊C16—41no—
75C22×C32#10011yescharacteristic
76C2×C3×D3—82no—
77C2×C3×D3—81no—
78C32×C4#10211yescharacteristic
79C32×C4#10211yescharacteristic
80C3⋊Dic3—22no—
81C3×Dic3—81no—
82C2×SD16—61no—
83C2×SD16—181no—
84C4⋊Q8—91no—
85#127—91no—
86M32—61no—
87M32—181no—
88C4×C8—91no—
89C23×C3—121no—
90C22×D3—41no—
91C3×Q8—121no—
92C3×Q8—121no—
93C3×D4—121no—
94C3×D4—121no—
95C2×C3×C4—21no—
96C2×C3×C4—21no—
97C2×C3×C4—121no—
98#67—244no—
99C2×Dic3—41no—
100C2×Dic3—62no—
101C2×Dic3—121no—
102D12—41no—
103D12—41no—
104Dic6—41no—
105Dic6—41no—
106C3×C8—21no—
107C3×C8—21no—
108C3×C8—21no—
109C3×C8—21no—
110C3⋊C8—61no—
111C3⋊C8—61no—
112C3⋊C8—61no—
113C3⋊C8—61no—
114C2×C32—21no—
115C2×C32#33111yescharacteristic
116C3×D3—161no—
117C2×Q8—61no—
118C2×D4—61no—
119C2×D4—361no—
120SD16—121no—
121SD16—121no—
122SD16—361no—
123SD16—361no—
124C2×C8—91no—
125C2×C8GO+(4,𝔽2)11yescharacteristic
126C4⋊C4—361no—
127C42—91no—
128C16—121no—
129C16—361no—
130C22×C3—21no—
131C22×C3—21no—
132C22×C3—242no—
133C22×C3—241no—
134C2×D3—81no—
135C2×D3—82no—
136C3×C4—21no—
137C3×C4—21no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—241no—
141Dic3—64no—
142Dic3—81no—
143Dic3—122no—
144C32#135911yescharacteristic, complemented, Sylow
145C23—121no—
146Q8—121no—
147Q8—121no—
148D4—121no—
149D4—121no—
150D4—722no—
151C2×C4—121no—
152C2×C4—181no—
153C2×C4D32⋊C411yescharacteristic
154C8—91no—
155C8—91no—
156C8#377411yescharacteristic
157C8#377511yescharacteristic
158C2×C3—22no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—41no—
162C2×C3—481no—
163D3—161no—
164C22—242no—
165C22—241no—
166C22#6372711yescharacteristic
167C4—182no—
168C4—241no—
169C4#6372911yescharacteristic
170C4#6373911yescharacteristic
171C3—21no—
172C3—21no—
173C2—21no—
174C2—481no—
175C2#1059003711yescharacteristic
subgroupG/H
centerC2#10590037
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×C8GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#331
prime radical#63914C4
cosocleC8×C3⋊Dic3C22
hypocenterC32#1359
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
2. #10590178C2semidirect
3. #10589135C2semidirect
144. C32#1359semidirect

Maximal subgroups

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

subgroupindex
#105908842
#105901782
#105891352
#13599