Finite Group Databasebeta

← #11772905

Subgroups — #11772905

Order 1152.

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

normal subgroups only

This group has 167 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#10591403C211yesmaximal, characteristic
2#10590212C211yesmaximal, characteristic
3#10589181C211yesmaximal, characteristic
4#64145C2211yescharacteristic
5#63872C411yescharacteristic, complemented
6#63780—21no—
7C3×#834—21no—
8C3×#832—21no—
9#63567—21no—
10#63553C411yescharacteristic, complemented
11#4768—61no—
12#4473—61no—
13C2×C32×D4D411yescharacteristic
14C2×#634D411yescharacteristic
15#3792—41no—
16#3757—41no—
17C4×C3⋊Dic3C2×C411yescharacteristic
18C3×#217—41no—
19C3×C4⋊Dic3—21no—
20C2×C3×C3⋊C8—21no—
21Dic3⋊Dic3—41no—
22#1414—91nomaximal, Sylow
23#936—61no—
24#936—61no—
25#890—61no—
26C3×#102—61no—
27C3×#99—61no—
28#834—21no—
29#832—21no—
30#816—61no—
31C8×Dic3—61no—
32#810—61no—
33C23×C32—21no—
34C32×D4—41no—
35C2×C32×C4C22⋊C411yescharacteristic
36C2×C3⋊Dic3—21no—
37C2×C3⋊Dic3—21no—
38#634—41no—
39C2×C3×Dic3—41no—
40C2×C3×Dic3—81no—
41#622—81no—
42C3×C3⋊C8—41no—
43#488—91no—
44#355—91no—
45#354—91no—
46C2×C3×D4—21no—
47C2×C3×D4—21no—
48C2×Dic6—61no—
49C2×Dic6—61no—
50C2×C3×C8—61no—
51C3×C4⋊C4—61no—
52C3×C22⋊C4—121no—
53#217—41no—
54#217—121no—
55#217—121no—
56#217—121no—
57#217—121no—
58C4⋊Dic3—21no—
59C4⋊Dic3—121no—
60Dic3⋊C4—121no—
61C4×Dic3—61no—
62C4×Dic3—61no—
63C2×C3⋊C8—21no—
64C22×C32—41no—
65C22×C32—81no—
66C22×C32#9911yescharacteristic
67C32×C4—21no—
68C3⋊Dic3—41no—
69C3⋊Dic3—41no—
70C3×Dic3—81no—
71C3×Dic3—161no—
72#125—91no—
73#124—91no—
74#103—181no—
75#102—61no—
76#101—181no—
77#99—61no—
78C4×C8—91no—
79C23×C3—21no—
80C23×C3—21no—
81C23×C3—41no—
82C3×D4—41no—
83C3×D4—41no—
84C3×D4—81no—
85C2×C3×C4—21no—
86C2×C3×C4—21no—
87C2×C3×C4—121no—
88C2×C3×C4—241no—
89C2×Dic3—41no—
90C2×Dic3—61no—
91C2×Dic3—61no—
92C2×Dic3—81no—
93C2×Dic3—121no—
94C2×Dic3—121no—
95C2×Dic3—121no—
96Dic6—121no—
97Dic6—121no—
98Dic6—241no—
99C3×C8—121no—
100C3⋊C8—41no—
101C2×C32—21no—
102C2×C32—81no—
103C2×C32#35411yescharacteristic
104C2×Q8—91no—
105C2×D4GO+(4,𝔽2)11yescharacteristic
106M16—361no—
107C2×C8—61no—
108C4⋊C4—61no—
109C4⋊C4—361no—
110C22⋊C4—121no—
111C22⋊C4—361no—
112C42—91no—
113C22×C3—21no—
114C22×C3—21no—
115C22×C3—41no—
116C22×C3—41no—
117C22×C3—81no—
118C22×C3—81no—
119C22×C3—81no—
120C22×C3—81no—
121C22×C3—81no—
122C3×C4—21no—
123C3×C4—21no—
124C3×C4—41no—
125C3×C4—241no—
126C3×C4—481no—
127Dic3—81no—
128Dic3—121no—
129Dic3—121no—
130Dic3—161no—
131Dic3—241no—
132Dic3—241no—
133Dic3—241no—
134C32#141411yescharacteristic, complemented, Sylow
135C23—21no—
136Q8—361no—
137D4—41no—
138C2×C4—121no—
139C2×C4—181no—
140C2×C4—181no—
141C2×C4—241no—
142C2×C4D32⋊C411yescharacteristic
143C8—121no—
144C8—721no—
145C2×C3—21no—
146C2×C3—21no—
147C2×C3—21no—
148C2×C3—21no—
149C2×C3—41no—
150C2×C3—81no—
151C2×C3—81no—
152C2×C3—161no—
153C22—41no—
154C22—81no—
155C22#6373811yescharacteristic
156C4—21no—
157C4—241no—
158C4—361no—
159C4—361no—
160C4—481no—
161C3—21no—
162C3—21no—
163C2—21no—
164C2—81no—
165C2#1059008111yescharacteristic
subgroupG/H
centerC2#10590081
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×D4GO+(4,𝔽2)
Fitting, prime radicalC2×C32×D4D4
socleC2×C32#354
cosocle#64145C22
hypocenterC32#1414
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
5. #63872C4semidirect
10. #63553C4semidirect
134. C32#1414semidirect

Maximal subgroups

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

subgroupindex
#105914032
#105902122
#105891812
#14149