Finite Group Databasebeta

← #11800058

Subgroups — #11800058

Order 1152.

290 conjugacy classes of subgroups; only the 47 normal subgroups are shown.

normal subgroups only

This group has 290 conjugacy classes of subgroups — too many to draw. Only its 47 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#10590902C211yesmaximal, characteristic, complemented
2#10590886C211yesmaximal, characteristic
3#10590174C211yesmaximal, characteristic, complemented
4#10590061C214yesmaximal, complemented
5C2×C3×D24—21no—
6#63919—21no—
7#63914—21no—
8C2×#3713C2212yes—
9C2×#3708C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#818—21no—
12#63576C2212yes—
13#5151—61no—
14#4874—61no—
15C2×C3×D12—22no—
16C2×#627—41no—
17C2×#625—41no—
18C2×#625—41no—
19C2×C32×C8D411yescharacteristic
20C4×C3⋊Dic3D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×C4⋊Dic3—22no—
23C3×D24—42no—
24#3724—41no—
25#3713—24no—
26#3708—22no—
27#2240—91nomaximal, Sylow
28C2×C3×D8—61no—
29#940—62no—
30C2×#213—62no—
31C2×D24—21no—
32#888—62no—
33C3×#107—61no—
34#818—21no—
35C8×Dic3—61no—
36C8×Dic3—61no—
37#807—62no—
38C22×C3×D3—42no—
39C2×C32×C4C2×D411yescharacteristic
40C2×C3⋊Dic3D811yescharacteristic
41C2×C3⋊Dic3D811yescharacteristic
42C2×C3×Dic3—42no—
43C3×D12—42no—
44C3×D12—42no—
45#627—82no—
46#625—82no—
47#625—82no—
48C32×C8SD1612yes—
49C3⋊(C3⋊C8)#4112yes—
50#500—91no—
51#493—91no—
52#357—94no—
53C4×C16—91no—
54C2×C3×D4—62no—
55C2×#67—122no—
56C2×#67—122no—
57C2×D12—22no—
58C2×Dic6—122no—
59C3×D8—122no—
60C2×C3×C8—21no—
61C2×C3×C8—21no—
62C3×C4⋊C4—62no—
63#213—124no—
64C4⋊Dic3—22no—
65Dic3⋊C4—122no—
66C4×Dic3—61no—
67C4×Dic3—61no—
68C2×C3⋊C8—61no—
69C2×C3⋊C8—61no—
70D24—42no—
71C22×C32C2×D811yescharacteristic
72C2×C3×D3—82no—
73C2×C3×D3—82no—
74C2×C3×D3—82no—
75C32×C4#12411yescharacteristic
76C32×C4C2×SD1611yescharacteristic
77C3⋊Dic3D1612yes—
78C3⋊Dic3SD3212yes—
79C3×Dic3—82no—
80C2×D8—61no—
81C2×D8—92no—
82C4⋊Q8—181no—
83#127—181no—
84C2×C16—92no—
85#107—61no—
86#107—92no—
87C4×C8—91no—
88C23×C3—122no—
89C22×D3—42no—
90C3×D4—122no—
91C3×D4—122no—
92C2×C3×C4—21no—
93C2×C3×C4—21no—
94C2×C3×C4—122no—
95#67—244no—
96#67—244no—
97C2×Dic3—42no—
98C2×Dic3—61no—
99C2×Dic3—61no—
100C2×Dic3—61no—
101C2×Dic3—61no—
102D12—42no—
103D12—42no—
104Dic6—244no—
105C3×C8—22no—
106C3×C8—22no—
107C3⋊C8—62no—
108C3⋊C8—62no—
109C2×C32#48611yescharacteristic
110C2×C32C2×D1611yescharacteristic
111C2×C32C2×SD3211yescharacteristic
112C3×D3—162no—
113C2×Q8—361no—
114C2×D4—62no—
115C2×D4—361no—
116C2×D4—361no—
117D8—122no—
118D8—184no—
119C2×C8—91no—
120C2×C8GO+(4,𝔽2)11yescharacteristic
121C4⋊C4—62no—
122C4⋊C4—361no—
123C42—91no—
124C16—182no—
125C22×C3—21no—
126C22×C3—21no—
127C22×C3—242no—
128C22×C3—242no—
129C22×C3—242no—
130C2×D3—82no—
131C2×D3—82no—
132C2×D3—82no—
133C3×C4—21no—
134C3×C4—21no—
135C3×C4—21no—
136C3×C4—21no—
137C3×C4—242no—
138Dic3—62no—
139Dic3—62no—
140Dic3—62no—
141Dic3—62no—
142Dic3—82no—
143C32#224011yescharacteristic, complemented, Sylow
144C23—122no—
145Q8—722no—
146D4—122no—
147D4—122no—
148D4—722no—
149D4—722no—
150C2×C4—91no—
151C2×C4—91no—
152C2×C4—122no—
153C2×C4C2×GO+(4,𝔽2)11yescharacteristic
154C8—92no—
155C8#377512yes—
156C2×C3—21no—
157C2×C3—21no—
158C2×C3—21no—
159C2×C3—21no—
160C2×C3—21no—
161C2×C3—21no—
162C2×C3—482no—
163D3—162no—
164C22—242no—
165C22—242no—
166C22—242no—
167C22#6422511yescharacteristic
168C4—92no—
169C4—92no—
170C4—242no—
171C4#6422111yescharacteristic
172C4C2×#377511yescharacteristic
173C3—21no—
174C3—21no—
175C2—482no—
176C2#1059327611yescharacteristic
177C2#1059327811yescharacteristic
178C2#1059336611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
prime radical#10590886C2
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2240
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10590902C2semidirect
3. #10590174C2semidirect
4. #10590061C2semidirect
143. C32#2240semidirect

Maximal subgroups

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

subgroupindex
#105909022
#105908862
#105901742
#105900612
#22409