Finite Group Databasebeta

← #11800163

Subgroups — #11800163

Order 1152.

347 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 347 conjugacy classes of subgroups — too many to draw. Only its 74 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#10592577C211yesmaximal, characteristic, complemented
2#10590886C211yesmaximal, characteristic
3C3×#4491C212yesmaximal, complemented
4#10589115C212yesmaximal, complemented
5#10589104C211yesmaximal, characteristic, complemented
6#69186—32nomaximal
7#64099—21no—
8C2×C3×D24C2212yes—
9#63914—21no—
10C2×#3713—21no—
11C32×#107C2211yescharacteristic
12#63645C2211yescharacteristic
13C8×C3⋊Dic3C2211yescharacteristic
14#63635—21no—
15C2×C3×C3⋊C16C2212yes—
16#5151—32no—
17#4878—32no—
18#4878—61no—
19C3×#357—32no—
20#4562—32no—
21#4509—32no—
22#4502—32no—
23#4491D312yescomplemented
24C2×C3×D12—22no—
25C2×#625—41no—
26C2×#625—41no—
27C2×C32×C8C2311yescharacteristic
28C32×C4⋊C4—21no—
29C4⋊(C3⋊Dic3)—21no—
30C4⋊(C3⋊Dic3)—41no—
31#3750—41no—
32C4×C3⋊Dic3D411yescharacteristic
33C2×C3⋊(C3⋊C8)D411yescharacteristic
34C3×D24—22no—
35C3×D24—22no—
36#3713—42no—
37C3×C3⋊C16—22no—
38#2244—91noSylow
39C2×C3×D8—32no—
40#940—62no—
41C2×#213—62no—
42C2×D24C2×D312yes—
43#890—62no—
44#890—62no—
45C2×C3×C16—32no—
46C3×#107—21no—
47C3×#107C2×D312yes—
48#818—32no—
49#818—61no—
50C8×Dic3—32no—
51C8×Dic3—61no—
52C2×C3⋊C16C2×D312yes—
53#808—62no—
54#808—62no—
55C22×C3×D3—42no—
56C2×C32×C4—41no—
57C2×C32×C4C2×D411yescharacteristic
58C2×C3⋊Dic3—41no—
59C2×C3⋊Dic3D811yescharacteristic
60C2×C3⋊Dic3D811yescharacteristic
61C3×D12—42no—
62C3×D12—42no—
63#625—82no—
64#625—82no—
65C32×C8#4112yes—
66C3⋊(C3⋊C8)SD1612yes—
67#499—91no—
68#493—91no—
69#357—32no—
70#357—92no—
71#346—91no—
72C2×C3×D4—62no—
73C2×#67—122no—
74C2×#67—122no—
75C2×D12—22no—
76C3×D8—62no—
77C3×D8—62no—
78C2×C3×C8—21no—
79C2×C3×C8C22×D312yes—
80C3×C4⋊C4—22no—
81C3×C4⋊C4—22no—
82#213—124no—
83C4⋊Dic3—62no—
84C4⋊Dic3—62no—
85C4⋊Dic3—122no—
86C4⋊Dic3—122no—
87Dic3⋊C4—122no—
88Dic3⋊C4—122no—
89C4×Dic3—32no—
90C4×Dic3—61no—
91C2×C3⋊C8—32no—
92C2×C3⋊C8—61no—
93D24—22no—
94D24—22no—
95C3×C16—62no—
96C3⋊C16—22no—
97C22×C32C2×D811yescharacteristic
98C2×C3×D3—82no—
99C2×C3×D3—82no—
100C2×C3×D3—82no—
101C32×C4—81no—
102C32×C4#12411yescharacteristic
103C32×C4C2×SD1611yescharacteristic
104C3⋊Dic3—21no—
105C3⋊Dic3—21no—
106C3⋊Dic3—81no—
107C2×D8—32no—
108C2×D8—181no—
109#127—181no—
110#125—181no—
111C2×C16—32no—
112#107—91no—
113#107D3211yescharacteristic
114#106—181no—
115C4×C8—91no—
116C23×C3—122no—
117C22×D3—42no—
118C3×D4—122no—
119C3×D4—122no—
120C2×C3×C4—21no—
121C2×C3×C4—42no—
122C2×C3×C4—42no—
123C2×C3×C4D3×D412yes—
124#67—244no—
125#67—244no—
126C2×Dic3—32no—
127C2×Dic3—32no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—122no—
131C2×Dic3—122no—
132D12—42no—
133D12—42no—
134C3×C8—22no—
135C3×C8#23512yes—
136C3×C8#23712yes—
137C3⋊C8—34no—
138C3⋊C8—62no—
139C2×C32#48611yescharacteristic
140C2×C32#50911yescharacteristic
141C2×C32#50911yescharacteristic
142C3×D3—162no—
143C2×D4—62no—
144C2×D4—361no—
145C2×D4—361no—
146D8—62no—
147D8—62no—
148D8—362no—
149C2×C8—91no—
150C2×C8C2×D3211yescharacteristic
151C4⋊C4—21no—
152C4⋊C4—181no—
153C4⋊C4—361no—
154C4⋊C4—361no—
155C42—91no—
156C16—62no—
157C22×C3—21no—
158C22×C3—242no—
159C22×C3—242no—
160C22×C3—242no—
161C22×C3D3×D812yes—
162C2×D3—82no—
163C2×D3—82no—
164C2×D3—82no—
165C3×C4—21no—
166C3×C4—21no—
167C3×C4—82no—
168C3×C4—82no—
169C3×C4#88512yes—
170C3×C4D3×SD1612yes—
171Dic3—62no—
172Dic3—62no—
173Dic3—121no—
174Dic3—121no—
175Dic3—242no—
176Dic3—242no—
177C32#224411yescharacteristic, complemented, Sylow
178C23—122no—
179D4—122no—
180D4—122no—
181D4—722no—
182D4—722no—
183C2×C4—41no—
184C2×C4—91no—
185C2×C4—91no—
186C2×C4—361no—
187C2×C4#381111yescharacteristic
188C8—92no—
189C8#379512yes—
190C2×C3—21no—
191C2×C3—21no—
192C2×C3—21no—
193C2×C3—482no—
194C2×C3#476012yes—
195C2×C3#491112yes—
196C2×C3#491412yes—
197D3—162no—
198C22—242no—
199C22—242no—
200C22—242no—
201C22#6392611yescharacteristic
202C4—81no—
203C4—181no—
204C4—181no—
205C4—721no—
206C4#6391311yescharacteristic
207C4#6394011yescharacteristic
208C3—21no—
209C3#6918612yescomplemented
210C2—482no—
211C2#1059055211yescharacteristic
212C2#1059102611yescharacteristic
213C2#1059104011yescharacteristic
subgroupG/H
centerC22#63926
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C2×D32
FittingC32×#107C22
socleC22×C32C2×D8
prime radical#10590886C2
hypercenter#107D32
hypocenterC32#2244
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ #107

Complements

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

NH ≅ G/Ntype
1. #10592577C2semidirect
3. C3×#4491C2semidirect
4. #10589115C2semidirect
5. #10589104C2semidirect
23. #4491D3semidirect
177. C32#2244semidirect
209. C3#69186semidirect

Maximal subgroups

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

subgroupindex
#105925772
#105908862
C3×#44912
#105891152
#105891042
#691863