Finite Group Databasebeta

← #11781555

Subgroups — #11781555

Order 1152.

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

normal subgroups only

This group has 432 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×#487C211yesmaximal, characteristic
2#10592793C211yesmaximal, characteristic
3#10592790C211yesmaximal, characteristic
4C8×#634C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589412C211yesmaximal, characteristic
7#10589324C211yesmaximal, characteristic
8#71241—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4⋊Q8C2211yescharacteristic
11C4×#634C2211yescharacteristic
12C32×#103—21no—
13C32×#103—21no—
14C32×C4×C8C2211yescharacteristic
15#63641—21no—
16C8×C3⋊Dic3—21no—
17#63637—21no—
18#63637—21no—
19#63635—21no—
20#63634—21no—
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
23C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
24C3×#487D314yes—
25#5094—34no—
26#5091—34no—
27C8×Dic6—34no—
28#4547—34no—
29#4546—34no—
30#4458—34no—
31C2×C32×Q8—21no—
32C2×C32×Q8—21no—
33C2×#634D411yescharacteristic
34C2×C32×C8D411yescharacteristic
35C2×C32×C8D411yescharacteristic
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4—21no—
39C32×C4⋊C4—21no—
40C32×C42C2311yescharacteristic
41C4⋊(C3⋊Dic3)D411yescharacteristic
42#3750—21no—
43C4×C3⋊Dic3—21no—
44C2×C3⋊(C3⋊C8)—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—21no—
47#1684—91noSylow
48C3×C4⋊Q8C2×D314yes—
49C3×C4⋊Q8C2×D314yes—
50C4×Dic6—34no—
51C3×#103—24no—
52C3×#103—24no—
53C3×C4×C8C2×D314yes—
54Dic3⋊C8—64no—
55C8×Dic3—64no—
56#810—64no—
57#810—64no—
58#808—64no—
59#807—64no—
60C4⋊(C3⋊C8)—34no—
61C4⋊(C3⋊C8)—34no—
62C4⋊(C3⋊C8)—34no—
63C32×Q8—41no—
64C32×Q8—41no—
65C32×Q8—81no—
66C2×C32×C4—41no—
67C2×C32×C4—41no—
68C2×C32×C4C2×D411yescharacteristic
69C2×C32×C4C2×D411yescharacteristic
70C2×C32×C4#4111yescharacteristic
71C2×C3⋊Dic3—21no—
72C2×C3⋊Dic3—21no—
73#634—21no—
74#634Q1612yes—
75C32×C8—21no—
76C32×C8—21no—
77C3⋊(C3⋊C8)—41no—
78C3⋊(C3⋊C8)—41no—
79C3⋊(C3⋊C8)—41no—
80#487C3⋊D311yescharacteristic
81#477—91no—
82#475—91no—
83C8×Q8—91no—
84#335—91no—
85#333—91no—
86#332—91no—
87C2×C3×Q8—24no—
88C2×C3×Q8—24no—
89C2×Dic6—34no—
90C2×C3×C8#6714yes—
91C2×C3×C8#6714yes—
92C3×C4⋊C4—24no—
93C3×C4⋊C4—24no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C42C22×D314yes—
97C4⋊Dic3—34no—
98Dic3⋊C4—64no—
99C4×Dic3—64no—
100C2×C3⋊C8—64no—
101C2×C3⋊C8—64no—
102C2×C3⋊C8—64no—
103C22×C32#12111yescharacteristic
104C32×C4—21no—
105C32×C4—81no—
106C32×C4—81no—
107C32×C4C2×Q1611yescharacteristic
108C32×C4#13511yescharacteristic
109C32×C4#13511yescharacteristic
110C32×C4#13711yescharacteristic
111C3⋊Dic3—22no—
112C3⋊Dic3—41no—
113C4⋊Q8C2×C3⋊D311yescharacteristic
114C4⋊Q8C2×C3⋊D311yescharacteristic
115C4×Q8—91no—
116#107—181no—
117#106—181no—
118C4⋊C8—91no—
119C4⋊C8—91no—
120C4⋊C8—91no—
121C4⋊C8—181no—
122#103—21no—
123#103—21no—
124#103—181no—
125#103—181no—
126C4×C8—181no—
127C4×C8C2×C3⋊D311yescharacteristic
128C3×Q8—44no—
129C3×Q8—44no—
130C3×Q8—84no—
131C2×C3×C4—44no—
132C2×C3×C4—44no—
133C2×C3×C4D3×D414yes—
134C2×C3×C4#23714yes—
135C2×C3×C4C2×#6714yes—
136C2×Dic3—64no—
137C2×Dic3—64no—
138Dic6—38no—
139Dic6—64no—
140C3×C8—24no—
141C3×C8—24no—
142C3⋊C8—124no—
143C3⋊C8—124no—
144C3⋊C8—124no—
145C2×C32#46411yescharacteristic
146C2×C32#46711yescharacteristic
147C2×C32#47111yescharacteristic
148C2×Q8—21no—
149C2×Q8—21no—
150C2×Q8—91no—
151C2×C8—181no—
152C2×C8—181no—
153C2×C8—181no—
154C2×C8#63811yescharacteristic
155C2×C8#63811yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—21no—
159C4⋊C4—21no—
160C4⋊C4—91no—
161C4⋊C4—181no—
162C42—181no—
163C42C22×C3⋊D311yescharacteristic
164C22×C3#93814yes—
165C3×C4—24no—
166C3×C4—84no—
167C3×C4—84no—
168C3×C4D3×Q1614yes—
169C3×C4#91914yes—
170C3×C4#95014yes—
171C3×C4#95114yes—
172Dic3—68no—
173Dic3—124no—
174C32#168411yescharacteristic, complemented, Sylow
175Q8—41no—
176Q8—41no—
177Q8—81no—
178Q8—92no—
179Q8—181no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—181no—
183C2×C4—181no—
184C2×C4D4×C3⋊D311yescharacteristic
185C2×C4#383011yescharacteristic
186C2×C4C2×#63811yescharacteristic
187C8—21no—
188C8—21no—
189C8—361no—
190C8—361no—
191C8—361no—
192C2×C3#505414yes—
193C2×C3#517714yes—
194C2×C3#518814yes—
195C22#6414711yescharacteristic
196C4—21no—
197C4—81no—
198C4—81no—
199C4—182no—
200C4—361no—
201C4Q16×C3⋊D311yescharacteristic
202C4#6412811yescharacteristic
203C4#6415911yescharacteristic
204C4#6416011yescharacteristic
205C3#7124114yescomplemented
206C2#1059275311yescharacteristic
207C2#1059287611yescharacteristic
208C2#1059288711yescharacteristic
subgroupG/H
centerC22#64147
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#487C2
socle, prime radicalC22×C32#121
hypercenter#487C3⋊D3
hypocenterC32#1684
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #487

Complements

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

NH ≅ G/Ntype
174. C32#1684semidirect
205. C3#71241semidirect

Maximal subgroups

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

subgroupindex
C32×#4872
#105927932
#105927902
C8×#6342
#105894132
#105894122
#105893242
#712413