Finite Group Databasebeta

← #11780974

Subgroups — #11780974

Order 1152.

468 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 141 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×#475C211yesmaximal, characteristic
2#10592791C211yesmaximal, characteristic
3Q8×C3⋊(C3⋊C8)C211yesmaximal, characteristic
4#10592719C211yesmaximal, characteristic
5#10589413C211yesmaximal, characteristic
6#10589352C211yesmaximal, characteristic
7#10589345C211yesmaximal, characteristic
8#71117—34nomaximal
9C32×C4⋊Q8C2211yescharacteristic
10C32×C4×Q8C2211yescharacteristic
11C2×#3756—21no—
12C2×#3756—21no—
13#64078C2211yescharacteristic
14C32×#106—21no—
15C32×C4⋊C8C2211yescharacteristic
16C32×#103—21no—
17#63662—21no—
18#63635—21no—
19C4⋊(C3⋊(C3⋊C8))—21no—
20C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
21C4⋊(C3⋊(C3⋊C8))C2211yescharacteristic
22C4×C3⋊(C3⋊C8)—21no—
23C4×C3⋊(C3⋊C8)C2211yescharacteristic
24C3×#475D314yes—
25#5092—34no—
26Q8×C3⋊C8—34no—
27#5020—34no—
28#4547—34no—
29#4486—34no—
30#4479—34no—
31C2×C32×Q8—21no—
32C2×C32×Q8D411yescharacteristic
33C2×#634—21no—
34C2×C32×C8—21no—
35C32×C4⋊C4—21no—
36C32×C4⋊C4—21no—
37C32×C4⋊C4—21no—
38C32×C4⋊C4D411yescharacteristic
39C32×C42—21no—
40C32×C42C2311yescharacteristic
41#3756—42no—
42#3756—42no—
43C4⋊(C3⋊Dic3)—21no—
44C4⋊(C3⋊Dic3)—21no—
45C2×C3⋊(C3⋊C8)—21no—
46C2×C3⋊(C3⋊C8)—21no—
47C2×C3⋊(C3⋊C8)D411yescharacteristic
48C2×C3⋊(C3⋊C8)D411yescharacteristic
49#1670—91noSylow
50C3×C4⋊Q8C2×D314yes—
51C3×C4×Q8C2×D314yes—
52C2×#216—64no—
53C2×#216—64no—
54#869—34no—
55C3×#106—24no—
56C3×C4⋊C8C2×D314yes—
57C3×#103—24no—
58#835—64no—
59#808—64no—
60C4⋊(C3⋊C8)—34no—
61C4⋊(C3⋊C8)—34no—
62C4⋊(C3⋊C8)—64no—
63C4×C3⋊C8—34no—
64C4×C3⋊C8—64no—
65C32×Q8—21no—
66C32×Q8—41no—
67C32×Q8—41no—
68C32×Q8Q1612yescomplemented
69C2×C32×C4—21no—
70C2×C32×C4—21no—
71C2×C32×C4—41no—
72C2×C32×C4C2×D411yescharacteristic
73C2×C32×C4C2×D411yescharacteristic
74C2×C32×C4#4111yescharacteristic
75C2×C3⋊Dic3—41no—
76#634—41no—
77#634—41no—
78C32×C8—41no—
79C3⋊(C3⋊C8)—21no—
80C3⋊(C3⋊C8)—41no—
81C3⋊(C3⋊C8)—41no—
82C3⋊(C3⋊C8)SD1612yes—
83#494—91no—
84#475—91no—
85#475C3⋊D311yescharacteristic
86C8×Q8—91no—
87#335—91no—
88#332—91no—
89#332—91no—
90C2×C3×Q8—24no—
91C2×C3×Q8#6714yes—
92C2×Dic6—64no—
93C2×C3×C8—24no—
94C3×C4⋊C4—24no—
95C3×C4⋊C4—24no—
96C3×C4⋊C4—24no—
97C3×C4⋊C4#6714yes—
98C3×C42—24no—
99C3×C42C22×D314yes—
100#216—128no—
101#216—128no—
102C4⋊Dic3—64no—
103C4⋊Dic3—64no—
104C2×C3⋊C8—34no—
105C2×C3⋊C8—34no—
106C2×C3⋊C8—64no—
107C2×C3⋊C8—64no—
108C22×C32#12111yescharacteristic
109C32×C4—22no—
110C32×C4—21no—
111C32×C4—41no—
112C32×C4—81no—
113C32×C4C2×SD1611yescharacteristic
114C32×C4C2×Q1611yescharacteristic
115C32×C4#13511yescharacteristic
116C32×C4AGL(1,ℤ/8)11yescharacteristic
117C3⋊Dic3—81no—
118C2×Q16—181no—
119C2×Q16—181no—
120C4⋊Q8—91no—
121C4⋊Q8C2×C3⋊D311yescharacteristic
122C4×Q8C2×C3⋊D311yescharacteristic
123#106—21no—
124#106—181no—
125C4⋊C8—91no—
126C4⋊C8—91no—
127C4⋊C8—181no—
128C4⋊C8C2×C3⋊D311yescharacteristic
129#103—21no—
130#103—181no—
131C4×C8—91no—
132C4×C8—181no—
133C3×Q8—24no—
134C3×Q8—44no—
135C3×Q8—44no—
136C3×Q8#21618yescomplemented
137C2×C3×C4—24no—
138C2×C3×C4—24no—
139C2×C3×C4—44no—
140C2×C3×C4D3×D414yes—
141C2×C3×C4#23714yes—
142C2×C3×C4C2×#6714yes—
143C2×Dic3—124no—
144Dic6—124no—
145Dic6—124no—
146C3×C8—44no—
147C3⋊C8—38no—
148C3⋊C8—64no—
149C3⋊C8—124no—
150C3⋊C8—124no—
151C2×C32#46011yescharacteristic
152C2×C32#46711yescharacteristic
153C2×C32#47311yescharacteristic
154C2×Q8—21no—
155C2×Q8—181no—
156C2×Q8#63811yescharacteristic
157Q16—362no—
158Q16—362no—
159C2×C8—21no—
160C2×C8—91no—
161C2×C8—91no—
162C2×C8—181no—
163C2×C8—181no—
164C4⋊C4—21no—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—181no—
168C4⋊C4—181no—
169C4⋊C4#63811yescharacteristic
170C42—21no—
171C42C22×C3⋊D311yescharacteristic
172C22×C3#93914yes—
173C3×C4—24no—
174C3×C4—28no—
175C3×C4—44no—
176C3×C4—84no—
177C3×C4D3×SD1614yes—
178C3×C4#91414yes—
179C3×C4C2×#21614yes—
180C3×C4#95014yes—
181Dic3—244no—
182C32#167011yescharacteristic, complemented, Sylow
183Q8—21no—
184Q8—41no—
185Q8—41no—
186Q8—361no—
187Q8—361no—
188Q8#375612yescomplemented
189C2×C4—21no—
190C2×C4—21no—
191C2×C4—41no—
192C2×C4—361no—
193C2×C4D4×C3⋊D311yescharacteristic
194C2×C4#383011yescharacteristic
195C2×C4C2×#63811yescharacteristic
196C8—41no—
197C8—92no—
198C8—181no—
199C8—361no—
200C8—361no—
201C2×C3#505114yes—
202C2×C3#516314yes—
203C2×C3#520414yes—
204C22#6414811yescharacteristic
205C4—21no—
206C4—22no—
207C4—41no—
208C4—81no—
209C4—721no—
210C4SD16×C3⋊D311yescharacteristic
211C4#6412311yescharacteristic
212C4C2×#375611yescharacteristic
213C4#6415911yescharacteristic
214C3#7111714yescomplemented
215C2#1059275011yescharacteristic
216C2#1059286211yescharacteristic
217C2#1059290311yescharacteristic
subgroupG/H
centerC22#64148
commutator, cosocleC32×C42C23
FrattiniC42C22×C3⋊D3
FittingC32×#475C2
socle, prime radicalC22×C32#121
hypercenter#475C3⋊D3
hypocenterC32#1670
LCSG ▷ C32×C42 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C42 ◁ #475

Complements

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

NH ≅ G/Ntype
68. C32×Q8Q16semidirect
136. C3×Q8#216semidirect
182. C32#1670semidirect
188. Q8#3756semidirect
214. C3#71117semidirect

Maximal subgroups

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

subgroupindex
C32×#4752
#105927912
Q8×C3⋊(C3⋊C8)2
#105927192
#105894132
#105893522
#105893452
#711173