Finite Group Databasebeta

← #11799411

Subgroups — #11799411

Order 1152.

420 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 420 conjugacy classes of subgroups — too many to draw. Only its 95 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#10592891C211yesmaximal, characteristic
2C2×#63656C211yesmaximal, characteristic, complemented
3#10592606C211yesmaximal, characteristic
4#10592595C211yesmaximal, characteristic
5C32×#362C211yesmaximal, characteristic, complemented
6#10589383C211yesmaximal, characteristic, complemented
7#10589359C211yesmaximal, characteristic, complemented
8#69270—34nomaximal
9C2×C32×Q16C2211yescharacteristic
10#64151—21no—
11#64118—21no—
12C2×#3746C2211yescharacteristic
13#64110C2211yescharacteristic
14C32×M32C2211yescharacteristic
15C32×#108C2211yescharacteristic
16#63663—21no—
17#63656—21no—
18#63656—21no—
19#63651—21no—
20#63646C2211yescharacteristic
21C2×C3⋊(C3⋊C16)C2211yescharacteristic
22#63625—21no—
23C16×C3⋊D3—21no—
24#5192—34no—
25C2×#829—34no—
26#4907—34no—
27#4896—34no—
28C3×#362D314yescomplemented
29#4517—34no—
30#4493—34no—
31C2×C32×Q8—21no—
32#3828D411yescharacteristic
33C2×#634—21no—
34C32×Q16—21no—
35C32×Q16—21no—
36C32×M16—21no—
37C2×C32×C8C2311yescharacteristic
38#3756—41no—
39#3755—41no—
40#3748—21no—
41#3748D411yescharacteristic
42#3746—21no—
43#3746—21no—
44#3746—41no—
45#3744—41no—
46#3743—21no—
47C8×C3⋊D3—21no—
48C32×C16—21no—
49C3⋊(C3⋊C16)D411yescharacteristic
50C3⋊(C3⋊C16)D411yescharacteristic
51#2222—91noSylow
52C2×C3×Q16C2×D314yes—
53#942—64no—
54#909—64no—
55C2×Dic12—34no—
56#901—34no—
57C3×M32C2×D314yes—
58C3×#108C2×D314yes—
59#836—64no—
60#829—64no—
61#829—64no—
62#824—64no—
63#819—34no—
64C2×C3⋊C16—34no—
65#798—64no—
66D3×C16—64no—
67C32×Q8—41no—
68C32×Q8—41no—
69C2×C32×C4—41no—
70C2×C32×C4C2×D411yescharacteristic
71#638—21no—
72C2×C3⋊Dic3—41no—
73C4⋊(C3⋊D3)D811yescharacteristic
74C4×C3⋊D3—21no—
75#634—41no—
76#634—41no—
77#634D811yescharacteristic
78C32×C8—41no—
79C32×C8C2×D411yescharacteristic
80C32×C8#4111yescharacteristic
81C3⋊(C3⋊C8)—21no—
82C3⋊(C3⋊C8)—41no—
83C2×Q32—91no—
84#504—91no—
85#473—91no—
86#473—91no—
87#368—91no—
88#362—91no—
89#362C3⋊D311yescharacteristic, complemented
90C2×C3×Q8—24no—
91#235—34no—
92C2×Dic6—64no—
93C3×Q16—24no—
94C3×Q16—24no—
95C3×M16—24no—
96C2×C3×C8C22×D314yes—
97#216—124no—
98#215—124no—
99#208—34no—
100#208—64no—
101Dic12—64no—
102Dic12—64no—
103Dic12—124no—
104#204—124no—
105ΓL(1,𝔽25)—64no—
106D3×C8—64no—
107C3×C16—24no—
108C3⋊C16—34no—
109C3⋊C16—34no—
110C22×C32#13511yescharacteristic
111C2×C3⋊D3—21no—
112C32×C4—81no—
113C32×C4#12111yescharacteristic
114C32×C4C2×D811yescharacteristic
115C3⋊Dic3—21no—
116C3⋊Dic3—81no—
117#137—181no—
118#137—181no—
119C2×Q16—91no—
120C2×Q16C2×C3⋊D311yescharacteristic
121#131—91no—
122Q32—181no—
123Q32—181no—
124M32—181no—
125M32C2×C3⋊D311yescharacteristic
126C2×C16—91no—
127C2×C16—181no—
128#108—91no—
129#108C2×C3⋊D311yescharacteristic
130#101—181no—
131#101—181no—
132C3×Q8—44no—
133C3×Q8—44no—
134C2×C3×C4—44no—
135C2×C3×C4D3×D414yes—
136#67—64no—
137C2×Dic3—124no—
138D12—34no—
139C4×D3—64no—
140Dic6—34no—
141Dic6—124no—
142Dic6—124no—
143C3×C8—44no—
144C3×C8#23514yes—
145C3×C8D3×D414yes—
146C3⋊C8—64no—
147C3⋊C8—124no—
148C2×C32—21no—
149C2×C32#46611yescharacteristic
150C3⋊D3—41no—
151#41—91no—
152C2×Q8—21no—
153C2×Q8—181no—
154Q16—21no—
155Q16—21no—
156Q16—181no—
157Q16—181no—
158Q16—361no—
159Q16—361no—
160SD16—361no—
161SD16—361no—
162M16—21no—
163M16—91no—
164M16—181no—
165M16—181no—
166C2×C8—181no—
167C2×C8C22×C3⋊D311yescharacteristic
168C16—21no—
169C16—91no—
170C16—91no—
171C22×C3#91614yes—
172C2×D3—64no—
173C3×C4—84no—
174C3×C4#88414yes—
175C3×C4D3×D814yes—
176Dic3—64no—
177Dic3—244no—
178C32#222211yescharacteristic, complemented, Sylow
179Q8—41no—
180Q8—41no—
181Q8—91no—
182Q8—361no—
183Q8—361no—
184D4—91no—
185D4—181no—
186C2×C4—41no—
187C2×C4—181no—
188C2×C4—361no—
189C2×C4D4×C3⋊D311yescharacteristic
190C8—41no—
191C8—181no—
192C8—361no—
193C8#382811yescharacteristic
194C8D4×C3⋊D311yescharacteristic
195C2×C3—24no—
196C2×C3#477514yes—
197D3—124no—
198C22—181no—
199C22#6412511yescharacteristic
200C4—81no—
201C4—181no—
202C4—721no—
203C4#6409311yescharacteristic
204C4D8×C3⋊D311yescharacteristic
205C3#6927014yescomplemented
206C2—21no—
207C2—361no—
208C2#1059247411yescharacteristic
subgroupG/H
centerC2#10592474
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#362C2
socleC2×C32#466
prime radical#3828D4
hypercenter#362C3⋊D3
hypocenterC32#2222
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #362

Complements

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

NH ≅ G/Ntype
2. C2×#63656C2semidirect
5. C32×#362C2semidirect
6. #10589383C2semidirect
7. #10589359C2semidirect
28. C3×#362D3semidirect
89. #362C3⋊D3semidirect
178. C32#2222semidirect
205. C3#69270semidirect

Maximal subgroups

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

subgroupindex
#105928912
C2×#636562
#105926062
#105925952
C32×#3622
#105893832
#105893592
#692703