Finite Group Databasebeta

← #11780997

Subgroups — #11780997

Order 1152.

363 conjugacy classes of subgroups; only the 84 normal subgroups are shown.

normal subgroups only

This group has 363 conjugacy classes of subgroups — too many to draw. Only its 84 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#10592529C211yesmaximal, characteristic
2#10590387C211yesmaximal, characteristic
3#10590307C212yesmaximal
4C3×#4482C212yesmaximal
5#10589100C211yesmaximal, characteristic
6#68465—32nomaximal
7C4×#634C2211yescharacteristic
8C3×#869C2212yes—
9C2×#3718—21no—
10C2×#3718—21no—
11C32×C4⋊C8C2211yescharacteristic
12#63641—21no—
13C8×C3⋊Dic3—21no—
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×C4⋊(C3⋊C8)C2212yes—
16#63573—22no—
17#63567—22no—
18#5094—32no—
19#5092—32no—
20#4851—32no—
21#4830—32no—
22#4830—61no—
23C3×#332—32no—
24#4482D312yes—
25#4479—32no—
26C2×#634D411yescharacteristic
27C2×C3×Dic6—22no—
28C2×C32×C8—21no—
29C32×C42C2311yescharacteristic
30C4⋊(C3⋊Dic3)D411yescharacteristic
31#3750—21no—
32C4×C3⋊Dic3—21no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×C4⋊Dic3—22no—
36C3×C4⋊Dic3—22no—
37C2×C3×C3⋊C8—22no—
38#3718—42no—
39#3718—42no—
40#1670—91noSylow
41C3×C4⋊Q8—32no—
42C2×#216—62no—
43C2×#216—62no—
44#869C2×D312yes—
45C4×Dic6—32no—
46C4×Dic6—61no—
47C3×C4⋊C8—21no—
48C3×C4⋊C8—32no—
49C3×C4⋊C8C2×D312yes—
50#817—62no—
51#816—62no—
52Dic3⋊C8—62no—
53Dic3⋊C8—62no—
54C8×Dic3—62no—
55C8×Dic3—62no—
56#810—62no—
57#808—62no—
58C4⋊(C3⋊C8)C2×D312yes—
59C4×C3⋊C8—32no—
60C4×C3⋊C8—61no—
61C2×C32×C4C2×D411yescharacteristic
62C2×C32×C4C2×D411yescharacteristic
63C2×C32×C4#4111yescharacteristic
64C2×C3⋊Dic3—21no—
65C2×C3⋊Dic3—21no—
66#634—21no—
67#634Q1612yescomplemented
68C2×C3×Dic3—42no—
69C3×Dic6—42no—
70C3×Dic6—42no—
71C32×C8—41no—
72C3⋊(C3⋊C8)—21no—
73C3⋊(C3⋊C8)SD1612yes—
74C3×C3⋊C8—42no—
75#494—91no—
76#475—92no—
77C8×Q8—91no—
78#335—91no—
79#332—32no—
80C2×C3×Q8—62no—
81C2×Dic6—22no—
82C2×Dic6—32no—
83C2×Dic6—61no—
84C2×C3×C8—22no—
85C2×C3×C8—22no—
86C2×C3×C8—62no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C3×C42—21no—
90C3×C42C22×D312yes—
91#216—124no—
92#216—124no—
93C4⋊Dic3—22no—
94C4⋊Dic3—22no—
95C4⋊Dic3—32no—
96C4⋊Dic3—61no—
97Dic3⋊C4—62no—
98Dic3⋊C4—62no—
99C4×Dic3—62no—
100C4×Dic3—62no—
101C2×C3⋊C8—22no—
102C2×C3⋊C8—32no—
103C2×C3⋊C8—32no—
104C2×C3⋊C8—61no—
105C2×C3⋊C8—61no—
106C22×C32#12111yescharacteristic
107C32×C4—21no—
108C32×C4C2×SD1611yescharacteristic
109C32×C4C2×Q1611yescharacteristic
110C32×C4#13511yescharacteristic
111C32×C4AGL(1,ℤ/8)11yescharacteristic
112C3⋊Dic3—22no—
113C3⋊Dic3—41no—
114C3×Dic3—82no—
115C2×Q16—181no—
116C2×Q16—181no—
117C4⋊Q8—32no—
118C4×Q8—91no—
119#106—182no—
120C4⋊C8—32no—
121C4⋊C8—181no—
122C4⋊C8D3211yescharacteristic
123#103—182no—
124C4×C8—91no—
125C4×C8—181no—
126C3×Q8—122no—
127C3×Q8—122no—
128C2×C3×C4—21no—
129C2×C3×C4—21no—
130C2×C3×C4—21no—
131C2×C3×C4—122no—
132C2×C3×C4#23512yes—
133C2×C3×C4D3×D412yes—
134C2×C3×C4D3×D412yes—
135C2×Dic3—42no—
136C2×Dic3—62no—
137C2×Dic3—62no—
138C2×Dic3—62no—
139C2×Dic3—62no—
140Dic6—34no—
141Dic6—42no—
142Dic6—42no—
143Dic6—62no—
144Dic6—62no—
145Dic6—62no—
146C3×C8—42no—
147C3×C8—42no—
148C3×C8—122no—
149C3⋊C8—34no—
150C3⋊C8—42no—
151C3⋊C8—62no—
152C3⋊C8—62no—
153C3⋊C8—121no—
154C2×C32#46011yescharacteristic
155C2×C32#46711yescharacteristic
156C2×C32#47311yescharacteristic
157C2×Q8—62no—
158C2×Q8—91no—
159Q16—362no—
160Q16—362no—
161C2×C8—21no—
162C2×C8—62no—
163C2×C8—91no—
164C2×C8—91no—
165C4⋊C4—62no—
166C4⋊C4—62no—
167C4⋊C4—91no—
168C4⋊C4—181no—
169C42—181no—
170C42C2×D3211yescharacteristic
171C22×C3—21no—
172C22×C3#88412yes—
173C3×C4—22no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—41no—
179C3×C4—242no—
180C3×C4#91112yes—
181C3×C4D3×SD1612yes—
182C3×C4#91612yes—
183C3×C4D3×Q1612yes—
184Dic3—64no—
185Dic3—64no—
186Dic3—82no—
187Dic3—122no—
188Dic3—122no—
189C32#167011yescharacteristic, complemented, Sylow
190Q8—92no—
191Q8—122no—
192Q8—122no—
193Q8—181no—
194C2×C4—122no—
195C2×C4—181no—
196C2×C4—181no—
197C2×C4#379811yescharacteristic
198C2×C4#380211yescharacteristic
199C2×C4#381111yescharacteristic
200C8—41no—
201C8—92no—
202C8—122no—
203C8—181no—
204C2×C3—21no—
205C2×C3—21no—
206C2×C3—21no—
207C2×C3#475512yes—
208C2×C3#476212yes—
209C2×C3#481312yes—
210C22#6391211yescharacteristic
211C4—21no—
212C4—182no—
213C4—242no—
214C4—361no—
215C4#6380211yescharacteristic
216C4#6380911yescharacteristic
217C4#6392711yescharacteristic
218C4#6394011yescharacteristic
219C3—21no—
220C3#6846512yescomplemented
221C2#1059055311yescharacteristic
222C2#1059085511yescharacteristic
223C2#1059099311yescharacteristic
subgroupG/H
centerC22#63912
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4⋊C8C22
socle, prime radicalC22×C32#121
hypercenterC4⋊C8D32
hypocenterC32#1670
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊C8

Complements

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

NH ≅ G/Ntype
67. #634Q16semidirect
189. C32#1670semidirect
220. C3#68465semidirect

Maximal subgroups

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

subgroupindex
#105925292
#105903872
#105903072
C3×#44822
#105891002
#684653