Finite Group Databasebeta

← #11799604

Subgroups — #11799604

Order 1152.

234 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 43 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
2#10590790C211yesmaximal, characteristic
3#10590177C211yesmaximal, characteristic
4#10590068C212yesmaximal
5#10590062C212yesmaximal
6#63919—21no—
7#63843—21no—
8C2×#3718C2211yescharacteristic
9C2×#3708C2212yes—
10C8×C3⋊Dic3C2211yescharacteristic
11C3×#818—21no—
12C3×#816—21no—
13#63576C2211yescharacteristic
14#63576C2212yes—
15#4874—61no—
16#4790—61no—
17C2×C3×Dic6—21no—
18C2×#627—41no—
19C2×C32×C8D411yescharacteristic
20C4×C3⋊Dic3D411yescharacteristic
21C2×C3⋊(C3⋊C8)C2311yescharacteristic
22C3×C4⋊Dic3—21no—
23C3×C4⋊Dic3—22no—
24#3724—41no—
25Dic3⋊Dic3—41no—
26Dic32—41no—
27#3718—21no—
28#3718Q812yescomplemented
29#3708—22no—
30#2227—91nomaximal, Sylow
31Q8×Dic3—61no—
32C2×#216—61no—
33#888—62no—
34#887—61no—
35C3×#107—61no—
36C3×#103—61no—
37#818—21no—
38#816—21no—
39C8×Dic3—61no—
40C8×Dic3—61no—
41#807—62no—
42#807—61no—
43C2×C32×C4C2×D411yescharacteristic
44C2×C3⋊Dic3D811yescharacteristic
45C2×C3⋊Dic3D811yescharacteristic
46C2×C3×Dic3—41no—
47C2×C3×Dic3—41no—
48C2×C3×Dic3—42no—
49C3×Dic6—22no—
50C3×Dic6—41no—
51#627—82no—
52C32×C8—21no—
53C3⋊(C3⋊C8)C2×Q811yescharacteristic
54C3⋊(C3⋊C8)#4111yescharacteristic
55#500—91no—
56C4×Q16—91no—
57#366—92no—
58C4⋊C16—91no—
59#358—92no—
60C2×C3×Q8—61no—
61C2×Dic6—21no—
62C2×Dic6—122no—
63C2×C3×C8—21no—
64C2×C3×C8—21no—
65C3×C4⋊C4—61no—
66C3×C4⋊C4—62no—
67#216—62no—
68#216—62no—
69C4⋊Dic3—21no—
70C4⋊Dic3—22no—
71C4⋊Dic3—121no—
72Dic3⋊C4—121no—
73Dic3⋊C4—122no—
74C4×Dic3—61no—
75C4×Dic3—61no—
76C4×Dic3—121no—
77C4×Dic3—121no—
78C2×C3⋊C8—61no—
79C2×C3⋊C8—61no—
80C22×C32C2×D811yescharacteristic
81C32×C4C22⋊Q811yescharacteristic
82C32×C4#13711yescharacteristic
83C3⋊Dic3—21no—
84C3⋊Dic3Q3212yes—
85C3×Dic3—42no—
86C3×Dic3—82no—
87C3×Dic3—81no—
88C2×Q16—91no—
89C4⋊Q8—181no—
90C4×Q8—181no—
91C2×C16—92no—
92#107—61no—
93#107—92no—
94#107—91no—
95#103—61no—
96C4×C8—91no—
97C3×Q8—62no—
98C3×Q8—121no—
99C2×C3×C4—21no—
100C2×C3×C4—21no—
101C2×C3×C4—121no—
102C2×C3×C4—121no—
103C2×C3×C4—122no—
104C2×Dic3—41no—
105C2×Dic3—41no—
106C2×Dic3—42no—
107C2×Dic3—61no—
108C2×Dic3—61no—
109C2×Dic3—61no—
110C2×Dic3—61no—
111Dic6—22no—
112Dic6—41no—
113Dic6—244no—
114C3×C8—22no—
115C3×C8—41no—
116C3⋊C8—61no—
117C3⋊C8—61no—
118C3⋊C8—61no—
119C3⋊C8—61no—
120C2×C32#47411yescharacteristic
121C2×C32C2×Q3211yescharacteristic
122C2×C32#50911yescharacteristic
123C2×Q8—61no—
124C2×Q8—361no—
125Q16—92no—
126Q16—181no—
127C2×C8—91no—
128C2×C8GO+(4,𝔽2)11yescharacteristic
129C4⋊C4—61no—
130C4⋊C4—62no—
131C4⋊C4—361no—
132C4⋊C4—361no—
133C42—91no—
134C42—361no—
135C16—182no—
136C22×C3—21no—
137C22×C3—21no—
138C3×C4—21no—
139C3×C4—21no—
140C3×C4—21no—
141C3×C4—21no—
142C3×C4—122no—
143C3×C4—242no—
144C3×C4—241no—
145Dic3—42no—
146Dic3—62no—
147Dic3—62no—
148Dic3—62no—
149Dic3—82no—
150Dic3—81no—
151Dic3—121no—
152C32#222711yescharacteristic, complemented, Sylow
153Q8—62no—
154Q8—121no—
155Q8—722no—
156C2×C4—91no—
157C2×C4—91no—
158C2×C4—121no—
159C2×C4—121no—
160C2×C4—122no—
161C2×C4C2×GO+(4,𝔽2)11yescharacteristic
162C8—21no—
163C8—91no—
164C8—91no—
165C2×C3—21no—
166C2×C3—21no—
167C2×C3—21no—
168C2×C3—21no—
169C2×C3—21no—
170C2×C3—21no—
171C22#6422511yescharacteristic
172C4—92no—
173C4—122no—
174C4—181no—
175C4—242no—
176C4—241no—
177C4D32⋊Q811yescharacteristic
178C4#6423911yescharacteristic
179C3—21no—
180C3—21no—
181C2#1059327711yescharacteristic
182C2#1059328011yescharacteristic
183C2#1059336711yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socle, prime radicalC22×C32C2×D8
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2227
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
28. #3718Q8semidirect
152. C32#2227semidirect

Maximal subgroups

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

subgroupindex
#105909022
#105907902
#105901772
#105900682
#105900622
#22279