Finite Group Databasebeta

← #11875004

Subgroups — #11875004

Order 1152.

793 conjugacy classes of subgroups; only the 200 normal subgroups are shown.

normal subgroups only

This group has 793 conjugacy classes of subgroups — too many to draw. Only its 200 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#10593866C212yesmaximal
2C4×C8×C3⋊D3C211yesmaximal, characteristic
3C3×#4682C212yesmaximal, complemented
4#10590875C214yesmaximal, complemented
5#10590714C214yesmaximal
6#10590309C212yesmaximal, complemented
7#81938—32nomaximal
8C2×C8×C3⋊D3C2212yes—
9C42×C3⋊D3C2211yescharacteristic
10C3×#869C2214yes—
11#63872C2214yes—
12#63871—24no—
13#63849C2214yes—
14#63843—24no—
15C32×C4×C8C2211yescharacteristic
16C8×C3⋊Dic3C2212yes—
17C4×C3⋊(C3⋊C8)C2211yescharacteristic
18C3×#818C2218yes—
19#63574C2218yes—
20#5728—34no—
21C3×#500—32no—
22#5080—34no—
23#4880—38no—
24#4878—38no—
25C4×D3×C8—32no—
26C4×D3×C8—61no—
27#4682D312yescomplemented
28C2×C4×C3⋊D3D412yes—
29C2×C4×C3⋊D3C2311yescharacteristic
30C2×C3×Dic6—24no—
31C2×C32×C8C2312yes—
32C32×C42C2311yescharacteristic
33C4×C3⋊Dic3D412yes—
34C4×C3⋊Dic3C2311yescharacteristic
35C2×C3⋊(C3⋊C8)C2312yes—
36C8×C3⋊D3Q818yescomplemented
37C3×C4⋊Dic3—24no—
38C3×C4⋊Dic3C2318yes—
39Dic3⋊Dic3—28no—
40#3722—24no—
41Dic32—24no—
42#3160—91noSylow
43C3×C4⋊Q8—34no—
44#946—64no—
45Q8×Dic3—64no—
46C2×D3×C8—34no—
47C2×D3×C8—62no—
48#897—64no—
49#892—38no—
50#890—38no—
51#887—64no—
52C42×D3—32no—
53C42×D3—61no—
54#869C2×D314yes—
55C3×#107—38no—
56C3×C4×C8—21no—
57C3×C4×C8C2×D312yes—
58#818C2×D318yes—
59C8×Dic3—34no—
60C8×Dic3—62no—
61#808—316no—
62C4×C3⋊C8—32no—
63C4×C3⋊C8—61no—
64C22×C3⋊D3C2×D411yescharacteristic
65C2×C32×C4C2×D412yes—
66C2×C32×C4C2411yescharacteristic
67C2×C3⋊Dic3C2×D412yes—
68C2×C3⋊Dic3C2×D411yescharacteristic
69C4×C3⋊D3—24no—
70C4×C3⋊D3C2×Q814yes—
71C2×C3×Dic3—28no—
72C3×Dic6—48no—
73C32×C8C2×Q814yes—
74C3⋊(C3⋊C8)C2×Q814yes—
75#533—92no—
76#500—32no—
77#499—94no—
78#498—92no—
79#427—94no—
80C2×C4×C8—91no—
81C2×C3×Q8—64no—
82C2×C4×D3—32no—
83C2×C4×D3—32no—
84C2×C4×D3—32no—
85C2×C4×D3—61no—
86C2×C4×D3—62no—
87C2×Dic6—24no—
88C2×C3×C8—22no—
89C2×C3×C8C22×D314yes—
90C3×C4⋊C4—38no—
91C3×C4⋊C4—64no—
92C3×C42—21no—
93C3×C42C22×D312yes—
94(C2×D3)⋊C4—68no—
95C4⋊Dic3—24no—
96C4⋊Dic3—68no—
97C4⋊Dic3C22×D318yes—
98Dic3⋊C4—68no—
99C4×Dic3—32no—
100C4×Dic3—32no—
101C4×Dic3—32no—
102C4×Dic3—61no—
103C4×Dic3—62no—
104C4×Dic3—68no—
105C2×C3⋊C8—34no—
106C2×C3⋊C8—62no—
107D3×C8—316no—
108D3×C8—68no—
109C22×C32C22×D411yescharacteristic
110C2×C3⋊D3—22no—
111C2×C3⋊D3C4⋊Q812yes—
112C32×C4#13514yes—
113C32×C4C22×Q812yes—
114C3⋊Dic3—22no—
115C3⋊Dic3C4⋊Q812yes—
116C3×Dic3—48no—
117C22×C8—92no—
118C4⋊Q8—34no—
119#125—94no—
120C22⋊Q8—184no—
121C4×Q8—184no—
122#117—94no—
123C2×C42—91no—
124#107—38no—
125#106—98no—
126C4×C8—92no—
127C4×C8—91no—
128C4×C8D3211yescharacteristic
129C22×D3—32no—
130C22×D3—61no—
131C3×Q8—128no—
132C2×C3×C4—21no—
133C2×C3×C4—22no—
134C2×C3×C4—68no—
135C2×C3×C4D3×D412yes—
136C2×C3×C4D3×D412yes—
137C2×C3×C4C23×D312yes—
138C2×Dic3—28no—
139C2×Dic3—32no—
140C2×Dic3—32no—
141C2×Dic3—32no—
142C2×Dic3—61no—
143C2×Dic3—62no—
144C4×D3—38no—
145C4×D3—64no—
146C4×D3—68no—
147C4×D3—64no—
148C4×D3—64no—
149Dic6—48no—
150C3×C8—24no—
151C3×C8D3×Q818yes—
152C3⋊C8—38no—
153C3⋊C8—64no—
154C2×C32C2×C4⋊Q811yescharacteristic
155C2×C32C2×#13512yes—
156C3⋊D3—22no—
157C2×Q8—64no—
158C22×C4—91no—
159C22×C4—92no—
160C2×C8—92no—
161C2×C8—98no—
162C2×C8C2×D3212yes—
163C4⋊C4—38no—
164C4⋊C4—64no—
165C4⋊C4—188no—
166C22⋊C4—184no—
167C42—91no—
168C42—92no—
169C42—184no—
170C42C2×D3211yescharacteristic
171C22×C3—21no—
172C22×C3C2×D3×D412yes—
173C2×D3—34no—
174C2×D3—62no—
175C2×D3—64no—
176C2×D3—62no—
177C2×D3—62no—
178C3×C4—22no—
179C3×C4—24no—
180C3×C4—128no—
181C3×C4#91214yes—
182C3×C4#91914yes—
183C3×C4C2×D3×Q814yes—
184Dic3—34no—
185Dic3—48no—
186Dic3—62no—
187Dic3—64no—
188Dic3—62no—
189Dic3—62no—
190C32#316011yescharacteristic, complemented, Sylow
191C23—91no—
192Q8—128no—
193C2×C4—68no—
194C2×C4—91no—
195C2×C4—94no—
196C2×C4—92no—
197C2×C4—184no—
198C2×C4#380212yes—
199C2×C4C22×D3211yescharacteristic
200C8—94no—
201C8#379714yes—
202C2×C3—21no—
203C2×C3—22no—
204C2×C3D3×C4⋊Q812yes—
205C2×C3C2×#91212yes—
206C2×C3C2×#91912yes—
207D3—64no—
208D3—64no—
209C22—92no—
210C22—182no—
211C22C2×#380211yescharacteristic
212C4—92no—
213C4—128no—
214C4—182no—
215C4#6381014yes—
216C4C2×#379712yes—
217C3—21no—
218C3#8193812yescomplemented
219C2—182no—
220C2#1059390911yescharacteristic
221C2C2×#6381012yes—
subgroupG/H
centerC22C2×#3802
commutator, cosocleC2×C32×C4C24
FrattiniC2×C4C22×D32
FittingC32×C4×C8C22
socleC22×C32C22×D4
prime radicalC22×C3⋊D3C2×D4
hypercenterC4×C8D32
hypocenterC32#3160
LCSG ▷ C2×C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8

Complements

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

NH ≅ G/Ntype
3. C3×#4682C2semidirect
4. #10590875C2semidirect
6. #10590309C2semidirect
27. #4682D3semidirect
36. C8×C3⋊D3Q8semidirect
190. C32#3160semidirect
218. C3#81938semidirect

Maximal subgroups

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

subgroupindex
#105938662
C4×C8×C3⋊D32
C3×#46822
#105908752
#105907142
#105903092
#819383