Finite Group Databasebeta

← #11781971

Subgroups — #11781971

Order 1152.

351 conjugacy classes of subgroups; only the 88 normal subgroups are shown.

normal subgroups only

This group has 351 conjugacy classes of subgroups — too many to draw. Only its 88 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#10592723C211yesmaximal, characteristic
2C3×#5031C212yesmaximal
3#10590312C211yesmaximal, characteristic
4#10589098C211yesmaximal, characteristic
5#10589093C212yesmaximal
6#71057—32nomaximal
7C32×C4×Q8C2211yescharacteristic
8C2×C3×#216—22no—
9C3×#869C2212yes—
10C4⋊(C3⋊(C3⋊C8))—21no—
11C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
12#63630—21no—
13C4×C3⋊(C3⋊C8)C2211yescharacteristic
14C3×#810—22no—
15C3×C4⋊(C3⋊C8)C2212yes—
16#63576—21no—
17#63576—21no—
18C3×#462—32no—
19#5078—32no—
20#5031D312yes—
21#5024—32no—
22#5024—61no—
23#4547—32no—
24#4482—32no—
25#4480—32no—
26C2×C32×Q8D411yescharacteristic
27C2×C3×Dic6—22no—
28C32×C4⋊C4—21no—
29C32×C4⋊C4D411yescharacteristic
30C32×C42—21no—
31C32×C42C2311yescharacteristic
32C2×C3⋊(C3⋊C8)—21no—
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C2×C3⋊(C3⋊C8)D411yescharacteristic
35C3×#216—44no—
36C3×C4⋊Dic3—22no—
37C3×C4⋊Dic3—22no—
38C2×C3×C3⋊C8—22no—
39#1694—91noSylow
40C2×C3×Q16—62no—
41C3×C4⋊Q8—32no—
42C3×C4×Q8—21no—
43C3×C4×Q8C2×D312yes—
44C2×#216—22no—
45#869C2×D312yes—
46C3×C4⋊C8—32no—
47C3×#103—62no—
48#810—22no—
49#807—62no—
50#807—62no—
51C4⋊(C3⋊C8)—32no—
52C4⋊(C3⋊C8)—61no—
53C4⋊(C3⋊C8)—62no—
54C4⋊(C3⋊C8)—62no—
55C4⋊(C3⋊C8)C2×D312yes—
56#803—62no—
57#803—62no—
58C4×C3⋊C8—32no—
59C4×C3⋊C8—61no—
60C32×Q8—22no—
61C2×C32×C4—21no—
62C2×C32×C4—21no—
63C2×C32×C4C2×D411yescharacteristic
64C2×C32×C4C2×D411yescharacteristic
65C2×C32×C4#4111yescharacteristic
66C2×C3×Dic3—42no—
67C3×Dic6—42no—
68C3×Dic6—42no—
69C3⋊(C3⋊C8)—21no—
70C3⋊(C3⋊C8)—41no—
71C3⋊(C3⋊C8)Q1612yescomplemented
72C3×C3⋊C8—42no—
73#500—91no—
74#462—32no—
75#446—91no—
76#334—91no—
77#332—92no—
78C2×C3×Q8—21no—
79C2×C3×Q8—62no—
80C2×C3×Q8#6712yes—
81C2×Dic6—22no—
82C3×Q16—124no—
83C2×C3×C8—62no—
84C3×C4⋊C4—22no—
85C3×C4⋊C4—22no—
86C3×C4⋊C4—21no—
87C3×C4⋊C4—62no—
88C3×C4⋊C4—62no—
89C3×C4⋊C4#6712yes—
90C3×C42—22no—
91C3×C42—22no—
92C3×C42—21no—
93C3×C42C22×D312yes—
94#216—44no—
95C4⋊Dic3—22no—
96C4⋊Dic3—22no—
97C2×C3⋊C8—22no—
98C2×C3⋊C8—32no—
99C2×C3⋊C8—32no—
100C2×C3⋊C8—61no—
101C2×C3⋊C8—61no—
102C2×C3⋊C8—62no—
103C2×C3⋊C8—62no—
104C22×C32#12111yescharacteristic
105C32×C4—21no—
106C32×C4—41no—
107C32×C4—41no—
108C32×C4C2×Q1611yescharacteristic
109C32×C4AGL(1,ℤ/8)12yes—
110C32×C4#13711yescharacteristic
111C3×Dic3—82no—
112C2×Q16—62no—
113C4⋊Q8—32no—
114C4×Q8D3211yescharacteristic
115#107—181no—
116#107—181no—
117C4⋊C8—32no—
118C4⋊C8—91no—
119C4⋊C8—181no—
120#103—62no—
121#97—181no—
122C4×C8—91no—
123C3×Q8—22no—
124C3×Q8—22no—
125C3×Q8—42no—
126C3×Q8—122no—
127C3×Q8—122no—
128C2×C3×C4—22no—
129C2×C3×C4—22no—
130C2×C3×C4—22no—
131C2×C3×C4—22no—
132C2×C3×C4—21no—
133C2×C3×C4—21no—
134C2×C3×C4—21no—
135C2×C3×C4—122no—
136C2×C3×C4D3×D412yes—
137C2×C3×C4#23712yes—
138C2×C3×C4C2×#6712yes—
139C2×Dic3—42no—
140Dic6—42no—
141Dic6—42no—
142C3×C8—122no—
143C3⋊C8—34no—
144C3⋊C8—42no—
145C3⋊C8—62no—
146C3⋊C8—62no—
147C3⋊C8—121no—
148C3⋊C8—122no—
149C3⋊C8—122no—
150C2×C32#46211yescharacteristic
151C2×C32#46911yescharacteristic
152C2×C32#47311yescharacteristic
153C2×Q8—62no—
154C2×Q8#62511yescharacteristic
155Q16—124no—
156C2×C8—62no—
157C2×C8—91no—
158C2×C8—91no—
159C2×C8—181no—
160C4⋊C4—21no—
161C4⋊C4—62no—
162C4⋊C4—62no—
163C4⋊C4#62511yescharacteristic
164C42—21no—
165C42C2×D3211yescharacteristic
166C22×C3—21no—
167C22×C3#93912yes—
168C3×C4—22no—
169C3×C4—22no—
170C3×C4—21no—
171C3×C4—21no—
172C3×C4—41no—
173C3×C4—42no—
174C3×C4—42no—
175C3×C4—42no—
176C3×C4—42no—
177C3×C4—242no—
178C3×C4D3×Q1612yes—
179C3×C4#91812yes—
180C3×C4#93212yes—
181C3×C4#94912yes—
182Dic3—82no—
183C32#169411yescharacteristic, complemented, Sylow
184Q8—22no—
185Q8—122no—
186Q8—122no—
187C2×C4—21no—
188C2×C4—21no—
189C2×C4—122no—
190C2×C4#380511yescharacteristic
191C2×C4C2×#62511yescharacteristic
192C2×C4#381111yescharacteristic
193C8—92no—
194C8—122no—
195C8—181no—
196C8—361no—
197C2×C3—21no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3#503912yes—
201C2×C3#518212yes—
202C2×C3#520412yes—
203C22#6398011yescharacteristic
204C4—21no—
205C4—41no—
206C4—41no—
207C4—242no—
208C4#6382312yes—
209C4#6394411yescharacteristic
210C4#6394511yescharacteristic
211C3—21no—
212C3#7105712yescomplemented
213C2#1059116711yescharacteristic
214C2#1059163311yescharacteristic
215C2#1059168311yescharacteristic
subgroupG/H
centerC22#63980
commutator, cosocleC32×C42C23
FrattiniC42C2×D32
FittingC32×C4×Q8C22
socle, prime radicalC22×C32#121
hypercenterC4×Q8D32
hypocenterC32#1694
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
71. C3⋊(C3⋊C8)Q16semidirect
183. C32#1694semidirect
212. C3#71057semidirect

Maximal subgroups

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

subgroupindex
#105927232
C3×#50312
#105903122
#105890982
#105890932
#710573