Finite Group Databasebeta

← #11797131

Subgroups — #11797131

Order 1152.

345 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 345 conjugacy classes of subgroups — too many to draw. Only its 90 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#10592559C211yesmaximal, characteristic
2#10590913C211yesmaximal, characteristic
3#10590625C211yesmaximal, characteristic
4C3×#4487C212yesmaximal, complemented
5#10589137C212yesmaximal, complemented
6#69312—32nomaximal
7C2×C8×C3⋊D3C2211yescharacteristic
8#64101—21no—
9#63818—21no—
10C32×#106C2211yescharacteristic
11#63644C2211yescharacteristic
12#63634—21no—
13C3×#819C2212yes—
14C3×#812C2212yes—
15#63578—21no—
16#63544C412yescomplemented
17#63542C412yescomplemented
18D3×M32—32no—
19D3×#108—32no—
20#4860—32no—
21#4860—61no—
22C3×#365—32no—
23#4513—32no—
24#4494—32no—
25#4487D312yescomplemented
26C2×C4×C3⋊D3D411yescharacteristic
27C2×C32×C8C2311yescharacteristic
28C32×C4⋊C4—21no—
29#3752—41no—
30C4⋊(C3⋊Dic3)—21no—
31C4×C3⋊Dic3—41no—
32C2×C3⋊(C3⋊C8)D411yescharacteristic
33C8×C3⋊D3C2×C411yescharacteristic
34C8×C3⋊D3C2×C411yescharacteristic
35C8×C3⋊D3Q811yescharacteristic
36C8×C3⋊D3Q811yescharacteristic
37C3×#208—22no—
38#3712—41no—
39#3710—41no—
40C3×C3⋊C16C2×C414yes—
41#2155—91noSylow
42D3×M16—62no—
43C2×D3×C8—32no—
44C2×D3×C8—61no—
45#892—62no—
46#892—62no—
47C3×M32—32no—
48C3×#108—32no—
49C3×#106—21no—
50C3×#106C2×D312yes—
51#822—62no—
52#819C2×D312yes—
53#817—32no—
54#817—61no—
55#812C2×D312yes—
56#807—62no—
57#807—62no—
58#798—34no—
59D3×C16—34no—
60C22×C3⋊D3SD1611yescharacteristic
61C2×C32×C4—41no—
62C2×C32×C4C2×D411yescharacteristic
63C2×C3⋊Dic3—41no—
64C2×C3⋊Dic3SD1611yescharacteristic
65C4×C3⋊D3C4⋊C411yescharacteristic
66C4×C3⋊D3C4⋊C411yescharacteristic
67C4×C3⋊D3SD1611yescharacteristic
68C4×C3⋊D3SD1611yescharacteristic
69C32×C8C22×C411yescharacteristic
70C32×C8C2×Q811yescharacteristic
71C3⋊(C3⋊C8)C4⋊C411yescharacteristic
72C3⋊(C3⋊C8)C4⋊C411yescharacteristic
73C3×C3⋊C8—42no—
74C2×M32—91no—
75C2×#108—91no—
76#427—91no—
77#365—32no—
78#365—92no—
79C2×C4×D3—32no—
80C2×C4×D3—61no—
81C3×M16—62no—
82C2×C3×C8—21no—
83C2×C3×C8C22×D312yes—
84C3×C4⋊C4—22no—
85C3×C4⋊C4—22no—
86(C2×D3)⋊C4—122no—
87(C2×D3)⋊C4—122no—
88C4⋊Dic3—62no—
89C4⋊Dic3—62no—
90C4×Dic3—122no—
91C4×Dic3—122no—
92#208—22no—
93C2×C3⋊C8—32no—
94C2×C3⋊C8—61no—
95ΓL(1,𝔽25)—122no—
96D3×C8—32no—
97D3×C8—32no—
98D3×C8—32no—
99D3×C8—32no—
100D3×C8—61no—
101D3×C8—61no—
102D3×C8—61no—
103D3×C8—61no—
104D3×C8—122no—
105C3×C16—34no—
106C3⋊C16C4×D314yes—
107C22×C32C2×SD1611yescharacteristic
108C2×C3⋊D3—41no—
109C2×C3⋊D3#10611yescharacteristic
110C2×C3⋊D3#10611yescharacteristic
111C32×C4—81no—
112C32×C4C2×C4⋊C411yescharacteristic
113C32×C4C2×SD1611yescharacteristic
114C3⋊Dic3—81no—
115C3⋊Dic3#10611yescharacteristic
116C3⋊Dic3#10611yescharacteristic
117C2×M16—181no—
118C22×C8—91no—
119#117—181no—
120M32—32no—
121M32—92no—
122C2×C16—92no—
123#108—32no—
124#108—181no—
125#107—181no—
126#106—91no—
127#106D3211yescharacteristic
128C22×D3—32no—
129C22×D3—61no—
130C2×C3×C4—21no—
131C2×C3×C4—42no—
132C2×C3×C4—42no—
133C2×C3×C4D3×D412yes—
134C2×Dic3—32no—
135C2×Dic3—61no—
136C2×Dic3—122no—
137C2×Dic3—122no—
138C4×D3—32no—
139C4×D3—32no—
140C4×D3—32no—
141C4×D3—32no—
142C4×D3—61no—
143C4×D3—61no—
144C4×D3—61no—
145C4×D3—61no—
146C3×C8—21no—
147C3×C8—21no—
148C3×C8—122no—
149C3×C8C2×C4×D312yes—
150C3×C8D3×Q812yes—
151C3⋊C8—32no—
152C3⋊C8—32no—
153C3⋊C8—42no—
154C3⋊C8—61no—
155C3⋊C8—61no—
156C2×C32—21no—
157C2×C32C2×#10611yescharacteristic
158C3⋊D3—21no—
159C3⋊D3—21no—
160C22×C4—91no—
161M16—62no—
162M16—361no—
163C2×C8—91no—
164C2×C8—91no—
165C2×C8—91no—
166C2×C8—91no—
167C2×C8—91no—
168C2×C8—361no—
169C2×C8C2×D3211yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—181no—
172C22⋊C4—361no—
173C42—361no—
174C16—34no—
175C22×C3—21no—
176C22×C3D3×SD1612yes—
177C2×D3—32no—
178C2×D3—32no—
179C2×D3—61no—
180C2×D3—61no—
181C2×D3—122no—
182C2×D3—122no—
183C3×C4—21no—
184C3×C4—21no—
185C3×C4—82no—
186C3×C4—82no—
187C3×C4D3×C4⋊C412yes—
188C3×C4D3×SD1612yes—
189Dic3—32no—
190Dic3—32no—
191Dic3—61no—
192Dic3—61no—
193Dic3—242no—
194Dic3—242no—
195C32#215511yescharacteristic, complemented, Sylow
196C23—91no—
197C2×C4—41no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—91no—
201C2×C4—91no—
202C2×C4—91no—
203C2×C4—361no—
204C2×C4#381111yescharacteristic
205C8—91no—
206C8—91no—
207C8—122no—
208C8#379711yescharacteristic
209C8C4×D3211yescharacteristic
210C2×C3—22no—
211C2×C3—22no—
212C2×C3—21no—
213C2×C3D3×#10612yes—
214D3—62no—
215D3—62no—
216D3—121no—
217D3—121no—
218C22—91no—
219C22—91no—
220C22—361no—
221C22#6393011yescharacteristic
222C4—81no—
223C4—91no—
224C4—91no—
225C4—721no—
226C4#6388311yescharacteristic
227C4#6394011yescharacteristic
228C3—21no—
229C3#6931212yescomplemented
230C2—21no—
231C2—181no—
232C2—181no—
233C2#1059057511yescharacteristic
subgroupG/H
centerC2#10590575
commutatorC32×C8C22×C4
FrattiniC2×C8C2×D32
FittingC32×#106C22
socleC2×C32C2×#106
prime radicalC22×C3⋊D3SD16
cosocleC2×C32×C8C23
hypercenter#106D32
hypocenterC32#2155
LCSG ▷ C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #106

Complements

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

NH ≅ G/Ntype
4. C3×#4487C2semidirect
5. #10589137C2semidirect
16. #63544C4semidirect
17. #63542C4semidirect
25. #4487D3semidirect
195. C32#2155semidirect
229. C3#69312semidirect

Maximal subgroups

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

subgroupindex
#105925592
#105909132
#105906252
C3×#44872
#105891372
#693123