Finite Group Databasebeta

← #11799694

Subgroups — #11799694

Order 1152.

222 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 222 conjugacy classes of subgroups — too many to draw. Only its 41 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#10590874C211yesmaximal, characteristic
2#10590790C211yesmaximal, characteristic
3#10590177C211yesmaximal, characteristic
4#10590069C211yesmaximal, characteristic
5#10590068C211yesmaximal, characteristic
6#10590062C211yesmaximal, characteristic
7#10590062C211yesmaximal, characteristic
8#63872—21no—
9#63843—21no—
10C2×#3718C2211yescharacteristic
11C2×#3708C2211yescharacteristic
12C2×#3708C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14C3×#817—21no—
15C3×#816—21no—
16#63576C2211yescharacteristic
17#63576C2211yescharacteristic
18#63576C2211yescharacteristic
19#4858—61no—
20#4790—61no—
21C2×C3×Dic6—21no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×C4⋊Dic3—21no—
26C3×C4⋊Dic3—21no—
27C3×C4⋊Dic3—21no—
28Dic3⋊Dic3—41no—
29Dic3⋊Dic3—41no—
30Dic3⋊Dic3—41no—
31Dic32—41no—
32#3718—21no—
33#3718Q812yes—
34#3708—21no—
35#3708—21no—
36#2229—91nomaximal, Sylow
37Q8×Dic3—61no—
38C2×#216—61no—
39#890—61no—
40#890—61no—
41#887—61no—
42C3×#106—61no—
43C3×#103—61no—
44#817—21no—
45#816—21no—
46C8×Dic3—61no—
47C8×Dic3—61no—
48#807—61no—
49#807—61no—
50#807—61no—
51C2×C32×C4C2×D411yescharacteristic
52C2×C3⋊Dic3D811yescharacteristic
53C2×C3⋊Dic3D811yescharacteristic
54C2×C3×Dic3—41no—
55C2×C3×Dic3—41no—
56C2×C3×Dic3—41no—
57C2×C3×Dic3—41no—
58C3×Dic6—22no—
59C3×Dic6—41no—
60C32×C8—21no—
61C3⋊(C3⋊C8)C2×Q811yescharacteristic
62C3⋊(C3⋊C8)#4111yescharacteristic
63#499—91no—
64C4×Q16—91no—
65#367—91no—
66#366—91no—
67C4⋊C16—91no—
68#358—91no—
69#358—91no—
70C2×C3×Q8—61no—
71C2×Dic6—21no—
72C2×C3×C8—21no—
73C2×C3×C8—21no—
74C3×C4⋊C4—61no—
75C3×C4⋊C4—61no—
76C3×C4⋊C4—61no—
77#216—62no—
78#216—62no—
79C4⋊Dic3—21no—
80C4⋊Dic3—21no—
81C4⋊Dic3—21no—
82C4⋊Dic3—121no—
83C4⋊Dic3—121no—
84C4⋊Dic3—121no—
85Dic3⋊C4—121no—
86Dic3⋊C4—121no—
87Dic3⋊C4—121no—
88C4×Dic3—61no—
89C4×Dic3—61no—
90C4×Dic3—121no—
91C4×Dic3—121no—
92C2×C3⋊C8—61no—
93C2×C3⋊C8—61no—
94C22×C32C2×D811yescharacteristic
95C32×C4C22⋊Q811yescharacteristic
96C32×C4#13711yescharacteristic
97C3⋊Dic3—21no—
98C3⋊Dic3—21no—
99C3×Dic3—42no—
100C3×Dic3—81no—
101C3×Dic3—81no—
102C3×Dic3—81no—
103C2×Q16—91no—
104#125—181no—
105C4×Q8—181no—
106C2×C16—91no—
107C2×C16—91no—
108#107—91no—
109#107—91no—
110#107—91no—
111#106—61no—
112#103—61no—
113C4×C8—91no—
114C3×Q8—62no—
115C3×Q8—121no—
116C2×C3×C4—21no—
117C2×C3×C4—21no—
118C2×C3×C4—121no—
119C2×C3×C4—121no—
120C2×C3×C4—121no—
121C2×C3×C4—121no—
122C2×Dic3—41no—
123C2×Dic3—41no—
124C2×Dic3—41no—
125C2×Dic3—41no—
126C2×Dic3—61no—
127C2×Dic3—61no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130Dic6—22no—
131Dic6—41no—
132C3×C8—22no—
133C3×C8—41no—
134C3⋊C8—61no—
135C3⋊C8—61no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C2×C32#47411yescharacteristic
139C2×C32#50811yescharacteristic
140C2×C32#51011yescharacteristic
141C2×Q8—61no—
142Q16—92no—
143Q16—181no—
144C2×C8—91no—
145C2×C8GO+(4,𝔽2)11yescharacteristic
146C4⋊C4—61no—
147C4⋊C4—61no—
148C4⋊C4—61no—
149C4⋊C4—361no—
150C4⋊C4—361no—
151C4⋊C4—361no—
152C42—91no—
153C42—361no—
154C16—181no—
155C16—181no—
156C22×C3—21no—
157C22×C3—21no—
158C3×C4—21no—
159C3×C4—21no—
160C3×C4—21no—
161C3×C4—21no—
162C3×C4—122no—
163C3×C4—241no—
164C3×C4—241no—
165C3×C4—241no—
166Dic3—42no—
167Dic3—62no—
168Dic3—81no—
169Dic3—81no—
170Dic3—81no—
171Dic3—121no—
172Dic3—121no—
173Dic3—121no—
174C32#222911yescharacteristic, complemented, Sylow
175Q8—62no—
176Q8—121no—
177C2×C4—91no—
178C2×C4—91no—
179C2×C4—121no—
180C2×C4—121no—
181C2×C4—121no—
182C2×C4—121no—
183C2×C4C2×GO+(4,𝔽2)11yescharacteristic
184C8—21no—
185C8—91no—
186C8—91no—
187C2×C3—21no—
188C2×C3—21no—
189C2×C3—21no—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C22#6422511yescharacteristic
194C4—122no—
195C4—181no—
196C4—181no—
197C4—241no—
198C4—241no—
199C4—241no—
200C4D32⋊Q811yescharacteristic
201C4#6423911yescharacteristic
202C3—21no—
203C3—21no—
204C2#1059327511yescharacteristic
205C2#1059327911yescharacteristic
206C2#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#2229
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
174. C32#2229semidirect

Maximal subgroups

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

subgroupindex
#105908742
#105907902
#105901772
#105900692
#105900682
#105900622
#22299