Finite Group Databasebeta

← #11780737

Subgroups — #11780737

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#10596143C211yesmaximal, characteristic
2C32×#489C211yesmaximal, characteristic
3#10592781C211yesmaximal, characteristic, complemented
4#10592780C211yesmaximal, characteristic, complemented
5#10589406C211yesmaximal, characteristic
6#10589331C211yesmaximal, characteristic, complemented
7#10589331C211yesmaximal, characteristic, complemented
8#71247—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×#124C2211yescharacteristic
11#64153—21no—
12#64144—21no—
13#64088—21no—
14#64088—21no—
15#64087—21no—
16#64087—21no—
17#64079C2211yescharacteristic
18#64079C2211yescharacteristic
19C32×#103—21no—
20C32×#102—21no—
21C32×#97C2211yescharacteristic
22#63662—21no—
23#63662—21no—
24#63635—21no—
25#63634—21no—
26#63630C2211yescharacteristic
27#63630C2211yescharacteristic
28#5672—34no—
29C3×#489D314yes—
30#5082—34no—
31#5081—34no—
32#4540—34no—
33#4465—34no—
34#4465—34no—
35C2×C32×Q8—21no—
36C2×C32×Q8D411yescharacteristic
37C2×C32×D4D411yescharacteristic
38C22×C3⋊Dic3—21no—
39C2×#634—21no—
40C2×C32×C8—21no—
41C32×C4⋊C4—21no—
42C32×C4⋊C4—21no—
43C32×C22⋊C4—21no—
44C32×C22⋊C4—21no—
45C32×C42C2311yescharacteristic
46#3757—21no—
47#3757—21no—
48#3757—21no—
49C4⋊(C3⋊Dic3)D411yescharacteristic
50C4⋊(C3⋊Dic3)D411yescharacteristic
51C4⋊(C3⋊Dic3)D411yescharacteristic
52C4⋊(C3⋊Dic3)D411yescharacteristic
53#3750—21no—
54#3750—21no—
55#3750—21no—
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×#124C2×D314yes—
65#944—64no—
66#935—64no—
67#879—64no—
68#879—64no—
69#878—64no—
70#878—64no—
71#870—34no—
72#870—34no—
73C3×#103—24no—
74C3×#102—24no—
75C3×#97C2×D314yes—
76#835—64no—
77#835—64no—
78#808—64no—
79#807—64no—
80#803—34no—
81#803—34no—
82C23×C32—21no—
83C32×Q8—41no—
84C32×Q8—42no—
85C32×D4—41no—
86C2×C32×C4—21no—
87C2×C32×C4—41no—
88C2×C32×C4C2×D411yescharacteristic
89C2×C32×C4C2×D411yescharacteristic
90C2×C32×C4C2×D411yescharacteristic
91C2×C3⋊Dic3—21no—
92C2×C3⋊Dic3—21no—
93C2×C3⋊Dic3—21no—
94C2×C3⋊Dic3—21no—
95C2×C3⋊Dic3—81no—
96#634—81no—
97C32×C8—41no—
98C3⋊(C3⋊C8)—22no—
99C3⋊(C3⋊C8)—41no—
100#563—91no—
101#501—91no—
102#491—91no—
103#489C3⋊D311yescharacteristic
104#330—91no—
105#330—91no—
106#329—91no—
107C2×C3×Q8—24no—
108C2×C3×Q8#6714yes—
109C2×C3×D4#6714yes—
110C22×Dic3—64no—
111C2×Dic6—64no—
112C2×C3×C8—24no—
113C3×C4⋊C4—24no—
114C3×C4⋊C4—24no—
115C3×C22⋊C4—24no—
116C3×C22⋊C4—24no—
117C3×C42C22×D314yes—
118#217—64no—
119#217—64no—
120#217—64no—
121C4⋊Dic3—34no—
122C4⋊Dic3—34no—
123C4⋊Dic3—34no—
124C4⋊Dic3—34no—
125Dic3⋊C4—64no—
126Dic3⋊C4—64no—
127Dic3⋊C4—64no—
128Dic3⋊C4—64no—
129Dic3⋊C4—64no—
130Dic3⋊C4—64no—
131C4×Dic3—64no—
132C2×C3⋊C8—64no—
133C2×C3⋊C8—64no—
134C22×C32—41no—
135C22×C32—41no—
136C22×C32—41no—
137C22×C32#12011yescharacteristic
138C32×C4—21no—
139C32×C4—21no—
140C32×C4—21no—
141C32×C4—41no—
142C32×C4—81no—
143C3⋊Dic3—41no—
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#125—91no—
153#124C2×C3⋊D311yescharacteristic
154#123—181no—
155C22⋊Q8—181no—
156C22⋊Q8—181no—
157#107—181no—
158#106—181no—
159#103—21no—
160#103—181no—
161#103—181no—
162#102—21no—
163#97—91no—
164#97—91no—
165#97C2×C3⋊D311yescharacteristic
166C23×C3—24no—
167C3×Q8—44no—
168C3×Q8—48no—
169C3×D4—44no—
170C2×C3×C4—24no—
171C2×C3×C4—44no—
172C2×C3×C4D3×D414yes—
173C2×C3×C4D3×D414yes—
174C2×C3×C4C2×#6714yes—
175C2×Dic3—64no—
176C2×Dic3—64no—
177C2×Dic3—64no—
178C2×Dic3—64no—
179C2×Dic3—244no—
180Dic6—244no—
181C3×C8—44no—
182C3⋊C8—68no—
183C3⋊C8—124no—
184C2×C32—81no—
185C2×C32#45411yescharacteristic
186C2×C32#45511yescharacteristic
187C2×C32#45611yescharacteristic
188C2×Q8—21no—
189C2×Q8—181no—
190C2×Q8#63811yescharacteristic
191C2×D4#63811yescharacteristic
192C22×C4—181no—
193C2×C8—21no—
194C2×C8—181no—
195C2×C8—181no—
196C4⋊C4—21no—
197C4⋊C4—21no—
198C4⋊C4—91no—
199C4⋊C4—91no—
200C4⋊C4—91no—
201C4⋊C4—91no—
202C4⋊C4—181no—
203C4⋊C4—181no—
204C4⋊C4—181no—
205C4⋊C4—181no—
206C4⋊C4—181no—
207C4⋊C4—181no—
208C22⋊C4—21no—
209C22⋊C4—21no—
210C22⋊C4—181no—
211C22⋊C4—181no—
212C22⋊C4—181no—
213C42—181no—
214C42C22×C3⋊D311yescharacteristic
215C22×C3—44no—
216C22×C3—44no—
217C22×C3—44no—
218C22×C3#93714yes—
219C3×C4—24no—
220C3×C4—24no—
221C3×C4—24no—
222C3×C4—44no—
223C3×C4—84no—
224Dic3—124no—
225Dic3—124no—
226Dic3—124no—
227Dic3—124no—
228C32#166411yescharacteristic, complemented, Sylow
229C23—21no—
230Q8—41no—
231Q8—42no—
232Q8—721no—
233D4—41no—
234C2×C4—21no—
235C2×C4—41no—
236C2×C4—181no—
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—84no—
248C2×C3#506114yes—
249C2×C3#520114yes—
250C2×C3#520514yes—
251C22—41no—
252C22—41no—
253C22—41no—
254C22#6414611yescharacteristic
255C4—21no—
256C4—21no—
257C4—21no—
258C4—41no—
259C4—81no—
260C4—361no—
261C4—361no—
262C4—361no—
263C4—361no—
264C3#7124714yescomplemented
265C2—81no—
266C2#1059276011yescharacteristic
267C2#1059290011yescharacteristic
268C2#1059290411yescharacteristic
subgroupG/H
centerC22#64146
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#489C2
socleC22×C32#120
prime radicalC2×C32×D4D4
hypercenter#489C3⋊D3
hypocenterC32#1664
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #489

Complements

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

NH ≅ G/Ntype
3. #10592781C2semidirect
4. #10592780C2semidirect
6. #10589331C2semidirect
7. #10589331C2semidirect
228. C32#1664semidirect
264. C3#71247semidirect

Maximal subgroups

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

subgroupindex
#105961432
C32×#4892
#105927812
#105927802
#105894062
#105893312
#712473