Finite Group Databasebeta

← #11781276

Subgroups — #11781276

Order 1152.

480 conjugacy classes of subgroups; only the 129 normal subgroups are shown.

normal subgroups only

This group has 480 conjugacy classes of subgroups — too many to draw. Only its 129 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
1C32×#486C211yesmaximal, characteristic
2#10592790C211yesmaximal, characteristic, complemented
3#10592774C211yesmaximal, characteristic
4C8×#634C211yesmaximal, characteristic, complemented
5#10589412C211yesmaximal, characteristic, complemented
6#10589410C211yesmaximal, characteristic
7#10589323C211yesmaximal, characteristic, complemented
8#71208—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×#127C2211yescharacteristic
11C2×#3754—21no—
12C4×#634C2211yescharacteristic
13C32×#102—21no—
14C32×#102—21no—
15C32×C4×C8C2211yescharacteristic
16#63659—21no—
17#63641—21no—
18C8×C3⋊Dic3—21no—
19#63637—21no—
20#63634—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#486D314yes—
25#5091—34no—
26#5075—34no—
27C8×Dic6—34no—
28#4546—34no—
29#4544—34no—
30#4457—34no—
31C2×C32×Q8—21no—
32C2×C32×D4—21no—
33C2×C32×D4—21no—
34C2×C32×D4—21no—
35C2×#634D411yescharacteristic
36C2×C32×C8D411yescharacteristic
37C2×C32×C8D411yescharacteristic
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C42C2311yescharacteristic
41#3754—42no—
42C4⋊(C3⋊Dic3)D411yescharacteristic
43#3750—21no—
44C4×C3⋊Dic3—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)—21no—
48#1678—91noSylow
49C3×C4⋊Q8C2×D314yes—
50C3×#127C2×D314yes—
51C2×#214—64no—
52C4×Dic6—34no—
53C3×#102—24no—
54C3×#102—24no—
55C3×C4×C8C2×D314yes—
56#832—64no—
57Dic3⋊C8—64no—
58C8×Dic3—64no—
59#810—64no—
60#807—64no—
61C4⋊(C3⋊C8)—34no—
62C4⋊(C3⋊C8)—34no—
63C4⋊(C3⋊C8)—34no—
64C23×C32—41no—
65C32×Q8—81no—
66C32×D4—41no—
67C32×D4—41no—
68C32×D4—41no—
69C32×D4—41no—
70C32×D4—81no—
71C2×C32×C4—41no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—21no—
76C2×C3⋊Dic3—21no—
77#634—21no—
78#634SD1612yes—
79C32×C8—21no—
80C32×C8—21no—
81C3⋊(C3⋊C8)—41no—
82C3⋊(C3⋊C8)—41no—
83C3⋊(C3⋊C8)—41no—
84#486C3⋊D311yescharacteristic
85#477—91no—
86#460—91no—
87C8×Q8—91no—
88#334—91no—
89#333—91no—
90#331—91no—
91C2×C3×Q8—24no—
92C2×C3×D4—24no—
93C2×C3×D4—24no—
94C2×C3×D4—24no—
95C2×Dic6—34no—
96C2×C3×C8#6714yes—
97C2×C3×C8#6714yes—
98C3×C4⋊C4—24no—
99C3×C4⋊C4—24no—
100C3×C42C22×D314yes—
101#214—128no—
102C4⋊Dic3—34no—
103Dic3⋊C4—64no—
104C4×Dic3—64no—
105C2×C3⋊C8—64no—
106C2×C3⋊C8—64no—
107C2×C3⋊C8—64no—
108C22×C32—81no—
109C22×C32—81no—
110C22×C32—81no—
111C22×C32#12111yescharacteristic
112C32×C4—21no—
113C32×C4—81no—
114C32×C4C2×SD1611yescharacteristic
115C32×C4#13511yescharacteristic
116C32×C4#13511yescharacteristic
117C32×C4#13711yescharacteristic
118C3⋊Dic3—22no—
119C3⋊Dic3—41no—
120C2×SD16—181no—
121C4⋊Q8C2×C3⋊D311yescharacteristic
122#127C2×C3⋊D311yescharacteristic
123C4×Q8—91no—
124#107—181no—
125C4⋊C8—91no—
126C4⋊C8—91no—
127C4⋊C8—91no—
128C4⋊C8—181no—
129#103—181no—
130#102—21no—
131#102—21no—
132#102—181no—
133C4×C8—181no—
134C4×C8C2×C3⋊D311yescharacteristic
135C23×C3—44no—
136C3×Q8—84no—
137C3×D4—44no—
138C3×D4—44no—
139C3×D4—44no—
140C3×D4—44no—
141C3×D4—84no—
142C2×C3×C4—44no—
143C2×C3×C4D3×D414yes—
144C2×C3×C4#23714yes—
145C2×C3×C4C2×#6714yes—
146C2×Dic3—64no—
147C2×Dic3—64no—
148Dic6—38no—
149Dic6—64no—
150C3×C8—24no—
151C3×C8—24no—
152C3⋊C8—124no—
153C3⋊C8—124no—
154C3⋊C8—124no—
155C2×C32—161no—
156C2×C32#46411yescharacteristic
157C2×C32#46511yescharacteristic
158C2×C32#47211yescharacteristic
159C2×Q8—21no—
160C2×Q8—91no—
161C2×D4—21no—
162C2×D4—21no—
163C2×D4—21no—
164SD16—362no—
165C2×C8—181no—
166C2×C8—181no—
167C2×C8—181no—
168C2×C8#63811yescharacteristic
169C2×C8#63811yescharacteristic
170C4⋊C4—21no—
171C4⋊C4—21no—
172C4⋊C4—91no—
173C4⋊C4—181no—
174C42—181no—
175C42C22×C3⋊D311yescharacteristic
176C22×C3—84no—
177C22×C3—84no—
178C22×C3—84no—
179C22×C3#93814yes—
180C3×C4—24no—
181C3×C4—84no—
182C3×C4D3×SD1614yes—
183C3×C4#91614yes—
184C3×C4#95014yes—
185C3×C4#95114yes—
186Dic3—68no—
187Dic3—124no—
188C32#167811yescharacteristic, complemented, Sylow
189C23—41no—
190Q8—81no—
191Q8—92no—
192Q8—181no—
193D4—41no—
194D4—41no—
195D4—41no—
196D4—41no—
197D4—81no—
198C2×C4—41no—
199C2×C4—181no—
200C2×C4—181no—
201C2×C4D4×C3⋊D311yescharacteristic
202C2×C4#383011yescharacteristic
203C2×C4C2×#63811yescharacteristic
204C8—21no—
205C8—21no—
206C8—361no—
207C8—361no—
208C8—361no—
209C2×C3—164no—
210C2×C3#505414yes—
211C2×C3#516014yes—
212C2×C3#517114yes—
213C22—81no—
214C22—81no—
215C22—81no—
216C22#6414711yescharacteristic
217C4—21no—
218C4—81no—
219C4—182no—
220C4—361no—
221C4SD16×C3⋊D311yescharacteristic
222C4#6412511yescharacteristic
223C4#6415911yescharacteristic
224C4#6416011yescharacteristic
225C3#7120814yescomplemented
226C2—161no—
227C2#1059275311yescharacteristic
228C2#1059285911yescharacteristic
229C2#1059287011yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#486C2
socleC22×C32#121
prime radicalC32×#127C22
hypercenter#486C3⋊D3
hypocenterC32#1678
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #10592790C2semidirect
4. C8×#634C2semidirect
5. #10589412C2semidirect
7. #10589323C2semidirect
188. C32#1678semidirect
225. C3#71208semidirect

Maximal subgroups

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

subgroupindex
C32×#4862
#105927902
#105927742
C8×#6342
#105894122
#105894102
#105893232
#712083