Finite Group Databasebeta

← #11772823

Subgroups — #11772823

Order 1152.

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

normal subgroups only

This group has 195 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#10591493C211yesmaximal, characteristic
2#10590212C211yesmaximal, characteristic
3#10589181C211yesmaximal, characteristic
4#64145C2211yescharacteristic
5C2×C3×#214—21no—
6#63873C411yescharacteristic, complemented
7C2×#3719—21no—
8#63780—21no—
9C3×#834—21no—
10#63555C411yescharacteristic, complemented
11#5167—61no—
12#4473—61no—
13C2×C32×D4D411yescharacteristic
14C2×#634D411yescharacteristic
15C2×C3×Dic6—21no—
16#3792—41no—
17#3757—41no—
18C4×C3⋊Dic3C2×C411yescharacteristic
19C3×#217—41no—
20C3×#214—42no—
21C2×C3×C3⋊C8—21no—
22#3724—41no—
23#3719—42no—
24#1407—91nomaximal, Sylow
25C2×C3×SD16—61no—
26#944—61no—
27C2×#216—61no—
28#936—61no—
29#936—61no—
30C2×#214—21no—
31C2×Dic12—61no—
32C3×#99—61no—
33#834—21no—
34#815—61no—
35C23×C32—21no—
36C32×D4—41no—
37C2×C32×C4C22⋊C411yescharacteristic
38C2×C3⋊Dic3—21no—
39C2×C3⋊Dic3—21no—
40#634—41no—
41C2×C3×Dic3—41no—
42C2×C3×Dic3—81no—
43C3×Dic6—41no—
44C3×Dic6—41no—
45#622—81no—
46C3×C3⋊C8—22no—
47#497—91no—
48#355—91no—
49#354—91no—
50C2×C3×Q8—61no—
51C2×C3×D4—21no—
52C2×C3×D4—21no—
53C2×Dic6—21no—
54C2×Dic6—61no—
55C2×Dic6—61no—
56C3×SD16—122no—
57C2×C3×C8—61no—
58C3×C22⋊C4—121no—
59#217—41no—
60#217—122no—
61#217—121no—
62#217—121no—
63#216—122no—
64#214—42no—
65Dic3⋊C4—122no—
66C4×Dic3—61no—
67C4×Dic3—61no—
68C2×C3⋊C8—21no—
69Dic12—122no—
70C22×C32—41no—
71C22×C32—81no—
72C22×C32#9911yescharacteristic
73C32×C4—21no—
74C3⋊Dic3—41no—
75C3⋊Dic3—41no—
76C3×Dic3—81no—
77C3×Dic3—161no—
78C2×Q16—181no—
79C2×SD16—61no—
80C4⋊Q8—91no—
81#124—91no—
82#101—181no—
83#99—61no—
84#97—91no—
85C23×C3—21no—
86C23×C3—21no—
87C23×C3—41no—
88C3×Q8—121no—
89C3×Q8—121no—
90C3×D4—41no—
91C3×D4—41no—
92C3×D4—81no—
93C2×C3×C4—21no—
94C2×C3×C4—21no—
95C2×C3×C4—121no—
96C2×C3×C4—241no—
97C2×Dic3—41no—
98C2×Dic3—62no—
99C2×Dic3—81no—
100C2×Dic3—121no—
101C2×Dic3—121no—
102C2×Dic3—121no—
103Dic6—41no—
104Dic6—41no—
105Dic6—121no—
106Dic6—121no—
107Dic6—241no—
108C3×C8—62no—
109C3⋊C8—22no—
110C2×C32—21no—
111C2×C32—81no—
112C2×C32#35311yescharacteristic
113C2×Q8—61no—
114C2×Q8—91no—
115C2×D4GO+(4,𝔽2)11yescharacteristic
116Q16—362no—
117SD16—122no—
118M16—361no—
119C2×C8—61no—
120C4⋊C4—361no—
121C22⋊C4—121no—
122C22⋊C4—361no—
123C42—91no—
124C22×C3—21no—
125C22×C3—21no—
126C22×C3—41no—
127C22×C3—41no—
128C22×C3—81no—
129C22×C3—82no—
130C22×C3—81no—
131C22×C3—81no—
132C3×C4—21no—
133C3×C4—21no—
134C3×C4—41no—
135C3×C4—241no—
136C3×C4—481no—
137Dic3—81no—
138Dic3—122no—
139Dic3—161no—
140Dic3—241no—
141Dic3—241no—
142Dic3—241no—
143C32#140711yescharacteristic, complemented, Sylow
144C23—21no—
145Q8—121no—
146Q8—121no—
147Q8—361no—
148D4—41no—
149C2×C4—121no—
150C2×C4—181no—
151C2×C4—181no—
152C2×C4—241no—
153C2×C4D32⋊C411yescharacteristic
154C8—62no—
155C8—721no—
156C2×C3—22no—
157C2×C3—21no—
158C2×C3—21no—
159C2×C3—41no—
160C2×C3—81no—
161C2×C3—81no—
162C2×C3—161no—
163C22—41no—
164C22—81no—
165C22#6373811yescharacteristic
166C4—21no—
167C4—241no—
168C4—361no—
169C4—361no—
170C4—481no—
171C3—21no—
172C3—21no—
173C2—21no—
174C2—81no—
175C2#1059008011yescharacteristic
subgroupG/H
centerC2#10590080
commutatorC4×C3⋊Dic3C2×C4
Frattini, hypercenterC2×D4GO+(4,𝔽2)
Fitting, prime radicalC2×C32×D4D4
socleC2×C32#353
cosocle#64145C22
hypocenterC32#1407
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
6. #63873C4semidirect
10. #63555C4semidirect
143. C32#1407semidirect

Maximal subgroups

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

subgroupindex
#105914932
#105902122
#105891812
#14079