Finite Group Databasebeta

← #11874977

Subgroups — #11874977

Order 1152.

1068 conjugacy classes of subgroups; only the 257 normal subgroups are shown.

normal subgroups only

This group has 1068 conjugacy classes of subgroups — too many to draw. Only its 257 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#10596159C212yesmaximal
2C32×#499C211yesmaximal, characteristic, complemented
3#10592764C212yesmaximal, complemented
4#10592579C212yesmaximal
5#10592573C212yesmaximal, complemented
6#10592559C212yesmaximal
7#10592554C212yesmaximal, complemented
8C4×C8×C3⋊D3C211yesmaximal, characteristic
9#10592382C211yesmaximal, characteristic, complemented
10#81916—34nomaximal
11C32×#125C2212yes—
12C2×C8×C3⋊D3C2211yescharacteristic
13C2×C8×C3⋊D3C2211yescharacteristic
14#64105—24no—
15#64101C2214yes—
16#64097C2214yes—
17#64096—24no—
18C42×C3⋊D3C2211yescharacteristic
19#64079C2212yes—
20C32×#107C2212yes—
21C32×#106C2212yes—
22C32×C4×C8C2211yescharacteristic
23#63645C2212yes—
24#63644C2212yes—
25C8×C3⋊Dic3C2211yescharacteristic
26C8×C3⋊Dic3C2211yescharacteristic
27#63635C2214yes—
28#63634C2214yes—
29C4×C3⋊(C3⋊C8)C2211yescharacteristic
30#5688—38no—
31C3×#499D314yescomplemented
32#5065—38no—
33#4880—38no—
34#4874—38no—
35#4860—38no—
36#4855—38no—
37C4×D3×C8—34no—
38#4683—34no—
39C2×C4×C3⋊D3D412yes—
40C2×C4×C3⋊D3C2311yescharacteristic
41C2×#634—24no—
42C2×C32×C8C2311yescharacteristic
43C2×C32×C8C2311yescharacteristic
44C32×C4⋊C4—24no—
45C32×C4⋊C4C2314yes—
46C32×C42C2311yescharacteristic
47#3752—24no—
48C4⋊(C3⋊Dic3)C2314yes—
49#3750—24no—
50#3750—24no—
51C4×C3⋊Dic3—24no—
52C4×C3⋊Dic3D412yes—
53C4×C3⋊Dic3C2311yescharacteristic
54C2×C3⋊(C3⋊C8)C2311yescharacteristic
55C2×C3⋊(C3⋊C8)C2311yescharacteristic
56C8×C3⋊D3Q814yescomplemented
57C8×C3⋊D3Q814yescomplemented
58#3160—91noSylow
59C3×#125C2×D318yes—
60C2×D3×C8—34no—
61C2×D3×C8—34no—
62#896—616no—
63#892—316no—
64#888—316no—
65#887—616no—
66C42×D3—34no—
67#870—38no—
68C3×#107C2×D318yes—
69C3×#106C2×D318yes—
70C3×C4×C8C2×D314yes—
71#818—38no—
72#817—38no—
73C8×Dic3—34no—
74C8×Dic3—34no—
75#808—316no—
76#807—316no—
77C4×C3⋊C8—34no—
78C22×C3⋊D3C2×D411yescharacteristic
79C2×C32×C4—24no—
80C2×C32×C4C2×D412yes—
81C2×C32×C4C2411yescharacteristic
82C2×C3⋊Dic3—24no—
83C2×C3⋊Dic3C2×D411yescharacteristic
84C2×C3⋊Dic3C2×D412yes—
85C4×C3⋊D3—24no—
86C4×C3⋊D3C2×Q812yes—
87C4×C3⋊D3C2×Q812yes—
88#634—48no—
89C32×C8C2×Q812yes—
90C32×C8C2×Q812yes—
91C3⋊(C3⋊C8)C2×Q812yes—
92C3⋊(C3⋊C8)C2×Q812yes—
93#533—92no—
94#500—92no—
95#499—92no—
96#499—91no—
97#499C3⋊D311yescharacteristic, complemented
98#498—92no—
99#427—92no—
100#427—92no—
101C2×C4×C8—91no—
102C2×C4×D3—34no—
103C2×C4×D3—38no—
104C2×Dic6—616no—
105C2×C3×C8C22×D314yes—
106C2×C3×C8C22×D314yes—
107C3×C4⋊C4—216no—
108C3×C4⋊C4C22×D3116yes—
109C3×C42C22×D314yes—
110(C2×D3)⋊C4—616no—
111C4⋊Dic3—316no—
112Dic3⋊C4—616no—
113Dic3⋊C4—616no—
114C4×Dic3—38no—
115C4×Dic3—34no—
116C4×Dic3—616no—
117C2×C3⋊C8—34no—
118C2×C3⋊C8—34no—
119D3×C8—316no—
120D3×C8—316no—
121C22×C32C22×D411yescharacteristic
122C2×C3⋊D3—22no—
123C2×C3⋊D3C4⋊Q812yes—
124C32×C4—22no—
125C32×C4—44no—
126C32×C4C22×Q811yescharacteristic
127C32×C4C22×Q811yescharacteristic
128C3⋊Dic3—44no—
129C3⋊Dic3C4⋊Q812yes—
130C3⋊Dic3#13514yes—
131C22×C8—91no—
132C22×C8—91no—
133C4⋊Q8—94no—
134#125—92no—
135#125C2×C3⋊D312yes—
136C22⋊Q8—184no—
137C4×Q8—184no—
138#117—94no—
139C2×C42—91no—
140#107—92no—
141#107—94no—
142#107C2×C3⋊D312yes—
143#106—92no—
144#106—94no—
145#106C2×C3⋊D312yes—
146C4×C8—91no—
147C4×C8—91no—
148C4×C8—91no—
149C4×C8C2×C3⋊D311yescharacteristic
150C22×D3—34no—
151C2×C3×C4—216no—
152C2×C3×C4D3×D418yes—
153C2×C3×C4C23×D314yes—
154C2×Dic3—34no—
155C2×Dic3—38no—
156C2×Dic3—616no—
157C4×D3—38no—
158C4×D3—38no—
159C4×D3—616no—
160Dic6—1232no—
161C3×C8D3×Q818yes—
162C3×C8D3×Q818yes—
163C3⋊C8—38no—
164C3⋊C8—38no—
165C2×C32C2×C4⋊Q811yescharacteristic
166C2×C32C2×#13512yes—
167C3⋊D3—22no—
168C2×Q8—184no—
169C22×C4—91no—
170C22×C4—92no—
171C2×C8—91no—
172C2×C8—91no—
173C2×C8—94no—
174C2×C8—94no—
175C2×C8C22×C3⋊D311yescharacteristic
176C2×C8C22×C3⋊D311yescharacteristic
177C4⋊C4—24no—
178C4⋊C4—94no—
179C4⋊C4—184no—
180C4⋊C4—184no—
181C4⋊C4C22×C3⋊D314yes—
182C22⋊C4—184no—
183C42—91no—
184C42—92no—
185C42—184no—
186C42C22×C3⋊D311yescharacteristic
187C22×C3C2×D3×D414yes—
188C2×D3—38no—
189C2×D3—68no—
190C3×C4—28no—
191C3×C4—416no—
192C3×C4C2×D3×Q814yes—
193C3×C4C2×D3×Q814yes—
194Dic3—38no—
195Dic3—316no—
196Dic3—1216no—
197C32#316011yescharacteristic, complemented, Sylow
198C23—91no—
199Q8—368no—
200C2×C4—24no—
201C2×C4—91no—
202C2×C4—92no—
203C2×C4—92no—
204C2×C4—92no—
205C2×C4—184no—
206C2×C4—184no—
207C2×C4D4×C3⋊D312yes—
208C2×C4C23×C3⋊D311yescharacteristic
209C8—92no—
210C8—92no—
211C8Q8×C3⋊D312yes—
212C8Q8×C3⋊D312yes—
213C2×C3D3×C4⋊Q814yes—
214C2×C3D3×#13518yes—
215D3—68no—
216C22—92no—
217C22—182no—
218C22C2×D4×C3⋊D311yescharacteristic
219C4—22no—
220C4—44no—
221C4—92no—
222C4—94no—
223C4—364no—
224C4C2×Q8×C3⋊D311yescharacteristic
225C4C2×Q8×C3⋊D311yescharacteristic
226C3#8191614yescomplemented
227C2—182no—
228C2C3⋊D3×C4⋊Q811yescharacteristic
229C2C3⋊D3×#13512yes—
subgroupG/H
centerC22C2×D4×C3⋊D3
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C23×C3⋊D3
FittingC32×#499C2
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenter#499C3⋊D3
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #499

Complements

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

NH ≅ G/Ntype
2. C32×#499C2semidirect
3. #10592764C2semidirect
5. #10592573C2semidirect
7. #10592554C2semidirect
9. #10592382C2semidirect
31. C3×#499D3semidirect
56. C8×C3⋊D3Q8semidirect
57. C8×C3⋊D3Q8semidirect
97. #499C3⋊D3semidirect
197. C32#3160semidirect
226. C3#81916semidirect

Maximal subgroups

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

subgroupindex
#105961592
C32×#4992
#105927642
#105925792
#105925732
#105925592
#105925542
C4×C8×C3⋊D32
#105923822
#819163