Finite Group Databasebeta

← #11780731

Subgroups — #11780731

Order 1152.

552 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 552 conjugacy classes of subgroups — too many to draw. Only its 105 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#10596170C211yesmaximal, characteristic
2C32×#491C211yesmaximal, characteristic, complemented
3#10592788C211yesmaximal, characteristic
4#10592780C211yesmaximal, characteristic, complemented
5#10589409C211yesmaximal, characteristic, complemented
6#10589331C211yesmaximal, characteristic, complemented
7#10589330C211yesmaximal, characteristic
8#71253—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×#125C2211yescharacteristic
11#64107—21no—
12#64107—21no—
13#64106—21no—
14#64105—21no—
15#64103—21no—
16#64097—21no—
17#64084C2211yescharacteristic
18#64079C2211yescharacteristic
19C32×#103—21no—
20C32×#103—21no—
21C32×#97C2211yescharacteristic
22#63637—21no—
23#63636—21no—
24#63635—21no—
25#63634—21no—
26#63630C2211yescharacteristic
27#63630C2211yescharacteristic
28#5699—34no—
29C3×#491D314yescomplemented
30#5089—34no—
31#5081—34no—
32#4543—34no—
33#4465—34no—
34#4464—34no—
35C2×C32×Q8—21no—
36C2×C4⋊(C3⋊D3)D411yescharacteristic
37C2×C4×C3⋊D3—21no—
38C2×#634—21no—
39C2×#634D411yescharacteristic
40C2×C32×C8—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—21no—
43C32×C4⋊C4—21no—
44C32×C4⋊C4—21no—
45C32×C4⋊C4D411yescharacteristic
46C32×C4⋊C4D411yescharacteristic
47C32×C42C2311yescharacteristic
48#3752—21no—
49#3752—21no—
50#3752—21no—
51#3752—21no—
52#3752—21no—
53C4⋊(C3⋊Dic3)—21no—
54C4⋊(C3⋊Dic3)D411yescharacteristic
55C4⋊(C3⋊Dic3)D411yescharacteristic
56#3750—21no—
57#3750—21no—
58#3750—21no—
59C4×C3⋊Dic3—21no—
60C2×C3⋊(C3⋊C8)—21no—
61C2×C3⋊(C3⋊C8)—21no—
62#1664—91noSylow
63C3×C4⋊Q8C2×D314yes—
64C3×#125C2×D314yes—
65#898—64no—
66#898—64no—
67#897—64no—
68#896—64no—
69#894—64no—
70#888—64no—
71#875—34no—
72#870—34no—
73C3×#103—24no—
74C3×#103—24no—
75C3×#97C2×D314yes—
76#810—64no—
77#809—64no—
78#808—64no—
79#807—64no—
80#803—34no—
81#803—34no—
82C22×C3⋊D3—21no—
83C32×Q8—42no—
84C2×C32×C4—21no—
85C2×C32×C4—21no—
86C2×C32×C4—41no—
87C2×C32×C4C2×D411yescharacteristic
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C3⋊Dic3—21no—
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C4⋊(C3⋊D3)—41no—
94C4×C3⋊D3—81no—
95#634—41no—
96#634—81no—
97C32×C8—41no—
98C3⋊(C3⋊C8)—22no—
99C3⋊(C3⋊C8)—41no—
100#563—91no—
101#501—91no—
102#491C3⋊D311yescharacteristic, complemented
103#489—91no—
104#330—91no—
105#330—91no—
106#329—91no—
107C2×C3×Q8—24no—
108C2×D12—34no—
109C2×C4×D3—64no—
110C2×Dic6—34no—
111C2×Dic6—64no—
112C2×C3×C8—24no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115C3×C4⋊C4—24no—
116C3×C4⋊C4—24no—
117C3×C4⋊C4#6714yes—
118C3×C4⋊C4#6714yes—
119C3×C42C22×D314yes—
120(C2×D3)⋊C4—64no—
121(C2×D3)⋊C4—64no—
122(C2×D3)⋊C4—64no—
123(C2×D3)⋊C4—64no—
124(C2×D3)⋊C4—64no—
125C4⋊Dic3—34no—
126C4⋊Dic3—34no—
127C4⋊Dic3—64no—
128Dic3⋊C4—64no—
129Dic3⋊C4—64no—
130Dic3⋊C4—64no—
131C4×Dic3—64no—
132C2×C3⋊C8—64no—
133C2×C3⋊C8—64no—
134C22×C32#12011yescharacteristic
135C2×C3⋊D3—41no—
136C2×C3⋊D3—41no—
137C2×C3⋊D3—41no—
138C32×C4—21no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—41no—
142C32×C4—41no—
143C32×C4—81no—
144C3⋊Dic3—41no—
145C3⋊Dic3—41no—
146C3⋊Dic3—41no—
147C4⋊Q8—181no—
148C4⋊Q8C2×C3⋊D311yescharacteristic
149#126—181no—
150#126—181no—
151#125—91no—
152#125C2×C3⋊D311yescharacteristic
153#124—91no—
154#123—181no—
155C22⋊Q8—181no—
156C22⋊Q8—181no—
157#107—181no—
158#106—181no—
159#103—21no—
160#103—21no—
161#103—181no—
162#102—181no—
163#97—91no—
164#97—91no—
165#97C2×C3⋊D311yescharacteristic
166C22×D3—64no—
167C3×Q8—48no—
168C2×C3×C4—24no—
169C2×C3×C4—24no—
170C2×C3×C4—44no—
171C2×C3×C4D3×D414yes—
172C2×C3×C4D3×D414yes—
173C2×C3×C4C2×#6714yes—
174C2×Dic3—64no—
175C2×Dic3—64no—
176C2×Dic3—64no—
177D12—124no—
178C4×D3—244no—
179Dic6—124no—
180Dic6—244no—
181C3×C8—44no—
182C3⋊C8—68no—
183C3⋊C8—124no—
184C2×C32#45411yescharacteristic
185C2×C32#45511yescharacteristic
186C2×C32#45611yescharacteristic
187C3⋊D3—81no—
188C2×Q8—21no—
189C2×Q8—91no—
190C2×Q8—181no—
191C2×D4—91no—
192C22×C4—181no—
193C2×C8—21no—
194C2×C8—181no—
195C2×C8—181no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—21no—
199C4⋊C4—21no—
200C4⋊C4—91no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4—181no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4#63811yescharacteristic
207C4⋊C4#63811yescharacteristic
208C22⋊C4—181no—
209C22⋊C4—181no—
210C22⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C42—181no—
214C42C22×C3⋊D311yescharacteristic
215C22×C3#93714yes—
216C2×D3—124no—
217C2×D3—124no—
218C2×D3—124no—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—44no—
223C3×C4—44no—
224C3×C4—84no—
225Dic3—124no—
226Dic3—124no—
227Dic3—124no—
228C32#166411yescharacteristic, complemented, Sylow
229C23—181no—
230Q8—42no—
231Q8—361no—
232Q8—721no—
233D4—361no—
234C2×C4—21no—
235C2×C4—21no—
236C2×C4—41no—
237C2×C4—181no—
238C2×C4—181no—
239C2×C4—181no—
240C2×C4—721no—
241C2×C4D4×C3⋊D311yescharacteristic
242C2×C4D4×C3⋊D311yescharacteristic
243C2×C4C2×#63811yescharacteristic
244C8—41no—
245C8—182no—
246C8—361no—
247C2×C3#506214yes—
248C2×C3#520214yes—
249C2×C3#520514yes—
250D3—244no—
251C22—361no—
252C22—361no—
253C22—361no—
254C22#6414611yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—41no—
259C4—41no—
260C4—81no—
261C4—361no—
262C4—361no—
263C4—361no—
264C3#7125314yescomplemented
265C2—721no—
266C2#1059276111yescharacteristic
267C2#1059290111yescharacteristic
268C2#1059290411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#491C2
socleC22×C32#120
prime radicalC2×C4⋊(C3⋊D3)D4
hypercenter#491C3⋊D3
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #491

Complements

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

NH ≅ G/Ntype
2. C32×#491C2semidirect
4. #10592780C2semidirect
5. #10589409C2semidirect
6. #10589331C2semidirect
29. C3×#491D3semidirect
102. #491C3⋊D3semidirect
228. C32#1664semidirect
264. C3#71253semidirect

Maximal subgroups

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

subgroupindex
#105961702
C32×#4912
#105927882
#105927802
#105894092
#105893312
#105893302
#712533