Finite Group Databasebeta

← #11799443

Subgroups — #11799443

Order 1152.

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

normal subgroups only

This group has 432 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#10592859C211yesmaximal, characteristic
2C2×#63654C211yesmaximal, characteristic, complemented
3#10592606C211yesmaximal, characteristic, complemented
4#10592595C211yesmaximal, characteristic, complemented
5C32×#361C211yesmaximal, characteristic, complemented
6#10589383C211yesmaximal, characteristic, complemented
7#10589359C211yesmaximal, characteristic, complemented
8#69261—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64141—21no—
11#64118—21no—
12C2×#3746C2211yescharacteristic
13#64110C2211yescharacteristic
14C32×M32C2211yescharacteristic
15C32×#108C2211yescharacteristic
16#63660—21no—
17#63654—21no—
18#63654—21no—
19#63651—21no—
20#63646C2211yescharacteristic
21C2×C3⋊(C3⋊C16)C2211yescharacteristic
22#63625—21no—
23C16×C3⋊D3—21no—
24#5160—34no—
25C2×#827—34no—
26#4907—34no—
27#4896—34no—
28C3×#361D314yescomplemented
29#4517—34no—
30#4493—34no—
31C2×C32×D4—21no—
32#3828D411yescharacteristic
33C2×#634—21no—
34C32×D8—21no—
35C32×D8—21no—
36C32×M16—21no—
37C2×C32×C8C2311yescharacteristic
38#3754—41no—
39#3753—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#2223—91noSylow
52C2×C3×D8C2×D314yes—
53#932—64no—
54#909—64no—
55C2×Dic12—34no—
56#901—34no—
57C3×M32C2×D314yes—
58C3×#108C2×D314yes—
59#833—64no—
60#827—64no—
61#827—64no—
62#824—64no—
63#819—34no—
64C2×C3⋊C16—34no—
65#798—64no—
66D3×C16—64no—
67C23×C32—41no—
68C32×D4—41no—
69C32×D4—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×SD32—91no—
84#504—91no—
85#473—91no—
86#472—91no—
87#368—91no—
88#362—91no—
89#361C3⋊D311yescharacteristic, complemented
90C2×C3×D4—24no—
91#235—34no—
92C2×Dic6—64no—
93C3×D8—24no—
94C3×D8—24no—
95C3×M16—24no—
96C2×C3×C8C22×D314yes—
97#214—124no—
98#213—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—81no—
111C22×C32—161no—
112C22×C32#13511yescharacteristic
113C2×C3⋊D3—21no—
114C32×C4#12111yescharacteristic
115C32×C4C2×D811yescharacteristic
116C3⋊Dic3—21no—
117C3⋊Dic3—81no—
118#137—181no—
119AGL(1,ℤ/8)—181no—
120C2×Q16—91no—
121C2×D8C2×C3⋊D311yescharacteristic
122#131—91no—
123SD32—181no—
124SD32—181no—
125M32—181no—
126M32C2×C3⋊D311yescharacteristic
127C2×C16—91no—
128C2×C16—181no—
129#108—91no—
130#108C2×C3⋊D311yescharacteristic
131#101—181no—
132#100—181no—
133C23×C3—44no—
134C3×D4—44no—
135C3×D4—44no—
136C2×C3×C4D3×D414yes—
137#67—64no—
138C2×Dic3—124no—
139D12—34no—
140C4×D3—64no—
141Dic6—34no—
142Dic6—124no—
143Dic6—124no—
144C3×C8—44no—
145C3×C8#23514yes—
146C3×C8D3×D414yes—
147C3⋊C8—64no—
148C3⋊C8—124no—
149C2×C32—21no—
150C2×C32—161no—
151C2×C32#46611yescharacteristic
152C3⋊D3—41no—
153#41—91no—
154C2×Q8—181no—
155C2×D4—21no—
156Q16—181no—
157Q16—181no—
158Q16—361no—
159SD16—361no—
160SD16—361no—
161D8—21no—
162D8—21no—
163D8—361no—
164M16—21no—
165M16—91no—
166M16—181no—
167M16—181no—
168C2×C8—181no—
169C2×C8C22×C3⋊D311yescharacteristic
170C16—21no—
171C16—91no—
172C16—91no—
173C22×C3—84no—
174C22×C3—164no—
175C22×C3#91614yes—
176C2×D3—64no—
177C3×C4#88414yes—
178C3×C4D3×D814yes—
179Dic3—64no—
180Dic3—244no—
181C32#222311yescharacteristic, complemented, Sylow
182C23—41no—
183Q8—91no—
184Q8—361no—
185Q8—361no—
186D4—41no—
187D4—41no—
188D4—91no—
189D4—181no—
190C2×C4—181no—
191C2×C4—361no—
192C2×C4D4×C3⋊D311yescharacteristic
193C8—41no—
194C8—181no—
195C8—361no—
196C8#382811yescharacteristic
197C8D4×C3⋊D311yescharacteristic
198C2×C3—24no—
199C2×C3—164no—
200C2×C3#477514yes—
201D3—124no—
202C22—81no—
203C22—161no—
204C22—181no—
205C22#6412511yescharacteristic
206C4—181no—
207C4—721no—
208C4#6409311yescharacteristic
209C4D8×C3⋊D311yescharacteristic
210C3#6926114yescomplemented
211C2—21no—
212C2—161no—
213C2—361no—
214C2#1059247411yescharacteristic
subgroupG/H
centerC2#10592474
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#361C2
socleC2×C32#466
prime radical#10592859C2
hypercenter#361C3⋊D3
hypocenterC32#2223
LCSG ▷ C2×C32×C8 ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ #361

Complements

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

NH ≅ G/Ntype
2. C2×#63654C2semidirect
3. #10592606C2semidirect
4. #10592595C2semidirect
5. C32×#361C2semidirect
6. #10589383C2semidirect
7. #10589359C2semidirect
28. C3×#361D3semidirect
89. #361C3⋊D3semidirect
181. C32#2223semidirect
210. C3#69261semidirect

Maximal subgroups

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

subgroupindex
#105928592
C2×#636542
#105926062
#105925952
C32×#3612
#105893832
#105893592
#692613