Finite Group Databasebeta

← #11772868

Subgroups — #11772868

Order 1152.

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

normal subgroups only

This group has 185 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#10591628C211yesmaximal, characteristic
2#10590218C211yesmaximal, characteristic
3#10589185C211yesmaximal, characteristic
4#64153C2211yescharacteristic
5C2×C3×#216—21no—
6#63873C411yescharacteristic
7C2×#3719—21no—
8#63780—21no—
9C3×#836—21no—
10#63553C411yescharacteristic
11#5183—61no—
12#4478—61no—
13C2×C32×Q8D411yescharacteristic
14C2×#634D411yescharacteristic
15C2×C3×Dic6—21no—
16#3792—41no—
17#3750—41no—
18C4×C3⋊Dic3C2×C411yescharacteristic
19C3×#216—42no—
20C3×#208—41no—
21C2×C3×C3⋊C8—21no—
22#3724—41no—
23#3719—42no—
24#1411—91nomaximal, Sylow
25C2×C3×Q16—61no—
26#944—61no—
27#944—61no—
28#944—61no—
29C2×#216—21no—
30C2×#216—61no—
31C2×Dic12—61no—
32C3×#101—61no—
33#836—21no—
34C8×Dic3—61no—
35C32×Q8—41no—
36C2×C32×C4—21no—
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C3⋊Dic3—21no—
39C2×C3⋊Dic3—21no—
40#634—41no—
41C2×C3×Dic3—41no—
42C3×Dic6—41no—
43C3×Dic6—41no—
44#622—81no—
45C3×C3⋊C8—22no—
46C3×C3⋊C8—81no—
47#494—91no—
48#356—91no—
49#356—91no—
50C2×C3×Q8—21no—
51C2×C3×Q8—21no—
52C2×C3×Q8—61no—
53C2×Dic6—21no—
54C2×Dic6—61no—
55C2×Dic6—61no—
56C3×Q16—122no—
57C3×M16—121no—
58C2×C3×C8—61no—
59#216—42no—
60#216—122no—
61Dic3⋊C4—122no—
62Dic3⋊C4—122no—
63Dic3⋊C4—121no—
64Dic3⋊C4—121no—
65C4×Dic3—61no—
66C4×Dic3—61no—
67#208—41no—
68C2×C3⋊C8—21no—
69Dic12—122no—
70C22×C32#9911yescharacteristic
71C32×C4—21no—
72C32×C4—41no—
73C3⋊Dic3—22no—
74C3⋊Dic3—41no—
75C3×Dic3—81no—
76C2×Q16—61no—
77C2×Q16—181no—
78C4⋊Q8—91no—
79C4⋊Q8—91no—
80#101—61no—
81#101—181no—
82C4×C8—91no—
83C3×Q8—41no—
84C3×Q8—41no—
85C3×Q8—81no—
86C3×Q8—121no—
87C3×Q8—121no—
88C2×C3×C4—21no—
89C2×C3×C4—21no—
90C2×C3×C4—21no—
91C2×C3×C4—21no—
92C2×C3×C4—41no—
93C2×C3×C4—121no—
94C2×Dic3—41no—
95C2×Dic3—62no—
96C2×Dic3—121no—
97C2×Dic3—121no—
98C2×Dic3—121no—
99Dic6—41no—
100Dic6—41no—
101Dic6—121no—
102Dic6—121no—
103Dic6—241no—
104C3×C8—62no—
105C3×C8—241no—
106C3⋊C8—22no—
107C3⋊C8—81no—
108C2×C32—21no—
109C2×C32#35311yescharacteristic
110C2×Q8—61no—
111C2×Q8—91no—
112C2×Q8GO+(4,𝔽2)11yescharacteristic
113Q16—122no—
114Q16—362no—
115M16—121no—
116M16—361no—
117C2×C8—61no—
118C4⋊C4—361no—
119C4⋊C4—361no—
120C42—91no—
121C22×C3—21no—
122C22×C3—21no—
123C3×C4—21no—
124C3×C4—21no—
125C3×C4—41no—
126C3×C4—41no—
127C3×C4—41no—
128C3×C4—81no—
129C3×C4—241no—
130Dic3—64no—
131Dic3—81no—
132Dic3—122no—
133Dic3—241no—
134Dic3—241no—
135C32#141111yescharacteristic, complemented, Sylow
136Q8—41no—
137Q8—121no—
138Q8—121no—
139Q8—361no—
140C2×C4—21no—
141C2×C4—121no—
142C2×C4—181no—
143C2×C4—181no—
144C2×C4D32⋊C411yescharacteristic
145C8—62no—
146C8—241no—
147C8—721no—
148C2×C3—22no—
149C2×C3—21no—
150C2×C3—21no—
151C2×C3—41no—
152C22#6373811yescharacteristic
153C4—21no—
154C4—41no—
155C4—182no—
156C4—241no—
157C4—361no—
158C3—21no—
159C3—21no—
160C2—21no—
161C2#1059008011yescharacteristic
subgroupG/H
centerC2#10590080
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×Q8GO+(4,𝔽2)
FittingC2×C32×Q8D4
socleC2×C32#353
prime radicalC22×C32#99
cosocle#64153C22
hypocenterC32#1411
LCSG ▷ C4×C3⋊Dic3 ▷ C2×C32×C4 ▷ C22×C32 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C22 ◁ C2×C4 ◁ C2×Q8

Complements

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

NH ≅ G/Ntype
135. C32#1411semidirect

Maximal subgroups

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

subgroupindex
#105916282
#105902182
#105891852
#14119