Finite Group Databasebeta

← #11799379

Subgroups — #11799379

Order 1152.

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

normal subgroups only

This group has 444 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, complemented
2C2×#63653C211yesmaximal, characteristic, complemented
3#10592606C211yesmaximal, characteristic, complemented
4#10592596C211yesmaximal, characteristic, complemented
5C32×#361C211yesmaximal, characteristic, complemented
6#10589382C211yesmaximal, characteristic, complemented
7#10589359C211yesmaximal, characteristic, complemented
8#69260—34nomaximal
9C2×C32×D8C2211yescharacteristic
10#64141—21no—
11#64117—21no—
12C2×#3745C2211yescharacteristic
13#64110C2211yescharacteristic
14C32×M32C2211yescharacteristic
15C32×#108C2211yescharacteristic
16#63660—21no—
17#63653—21no—
18#63653—21no—
19#63650—21no—
20#63646C2211yescharacteristic
21C2×C3⋊(C3⋊C16)C2211yescharacteristic
22#63625—21no—
23C16×C3⋊D3—21no—
24#5160—34no—
25C2×#826—34no—
26#4907—34no—
27#4897—34no—
28C3×#361D314yescomplemented
29#4516—34no—
30#4493—34no—
31C2×C32×D4—21no—
32#3828D411yescharacteristic
33C2×C4⋊(C3⋊D3)—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#3745—21no—
43#3745—21no—
44#3745—41no—
45#3744—41no—
46#3743—21no—
47C8×C3⋊D3—21no—
48C32×C16—21no—
49C3⋊(C3⋊C16)D411yescharacteristic
50C3⋊(C3⋊C16)D411yescharacteristic
51#2221—91noSylow
52C2×C3×D8C2×D314yes—
53#932—64no—
54#908—64no—
55C2×D24—34no—
56#901—34no—
57C3×M32C2×D314yes—
58C3×#108C2×D314yes—
59#833—64no—
60#826—64no—
61#826—64no—
62#823—64no—
63#819—34no—
64C2×C3⋊C16—34no—
65#798—64no—
66D3×C16—64no—
67C23×C32—41no—
68C22×C3⋊D3—41no—
69C32×D4—41no—
70C32×D4—41no—
71C2×C32×C4C2×D411yescharacteristic
72#638—21no—
73C4⋊(C3⋊D3)—41no—
74C4⋊(C3⋊D3)—41no—
75C4⋊(C3⋊D3)D811yescharacteristic
76C4×C3⋊D3—21no—
77#634D811yescharacteristic
78C32×C8—41no—
79C32×C8C2×D411yescharacteristic
80C32×C8#4111yescharacteristic
81C3⋊(C3⋊C8)—21no—
82C3⋊(C3⋊C8)—41no—
83C2×D16—91no—
84#504—91no—
85#472—91no—
86#472—91no—
87#368—91no—
88#361—91no—
89#361C3⋊D311yescharacteristic, complemented
90C2×C3×D4—24no—
91#235—34no—
92C2×D12—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—
101D24—64no—
102D24—64no—
103D24—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—
114C2×C3⋊D3—81no—
115C2×C3⋊D3—161no—
116C32×C4#12111yescharacteristic
117C32×C4C2×D811yescharacteristic
118C3⋊Dic3—21no—
119AGL(1,ℤ/8)—181no—
120AGL(1,ℤ/8)—181no—
121C2×D8—91no—
122C2×D8C2×C3⋊D311yescharacteristic
123#131—91no—
124D16—181no—
125D16—181no—
126M32—181no—
127M32C2×C3⋊D311yescharacteristic
128C2×C16—91no—
129C2×C16—181no—
130#108—91no—
131#108C2×C3⋊D311yescharacteristic
132#100—181no—
133#100—181no—
134C23×C3—44no—
135C22×D3—124no—
136C3×D4—44no—
137C3×D4—44no—
138C2×C3×C4D3×D414yes—
139#67—64no—
140D12—34no—
141D12—124no—
142D12—124no—
143C4×D3—64no—
144Dic6—34no—
145C3×C8—44no—
146C3×C8#23514yes—
147C3×C8D3×D414yes—
148C3⋊C8—64no—
149C3⋊C8—124no—
150C2×C32—21no—
151C2×C32—161no—
152C2×C32#46611yescharacteristic
153C3⋊D3—41no—
154C3⋊D3—161no—
155#41—91no—
156C2×D4—21no—
157C2×D4—181no—
158SD16—361no—
159SD16—361no—
160D8—21no—
161D8—21no—
162D8—181no—
163D8—181no—
164D8—361no—
165D8—361no—
166M16—21no—
167M16—91no—
168M16—181no—
169M16—181no—
170C2×C8—181no—
171C2×C8C22×C3⋊D311yescharacteristic
172C16—21no—
173C16—91no—
174C16—91no—
175C22×C3—84no—
176C22×C3—164no—
177C22×C3#91614yes—
178C2×D3—64no—
179C2×D3—244no—
180C2×D3—484no—
181C3×C4#88414yes—
182C3×C4D3×D814yes—
183Dic3—64no—
184C32#222111yescharacteristic, complemented, Sylow
185C23—41no—
186C23—361no—
187Q8—91no—
188D4—41no—
189D4—41no—
190D4—91no—
191D4—181no—
192D4—361no—
193D4—361no—
194C2×C4—181no—
195C2×C4D4×C3⋊D311yescharacteristic
196C8—41no—
197C8—181no—
198C8—361no—
199C8#382811yescharacteristic
200C8D4×C3⋊D311yescharacteristic
201C2×C3—24no—
202C2×C3—164no—
203C2×C3#477514yes—
204D3—124no—
205D3—484no—
206C22—81no—
207C22—161no—
208C22—181no—
209C22—721no—
210C22—1441no—
211C22#6412511yescharacteristic
212C4—181no—
213C4#6409311yescharacteristic
214C4D8×C3⋊D311yescharacteristic
215C3#6926014yescomplemented
216C2—21no—
217C2—161no—
218C2—361no—
219C2—1441no—
220C2#1059247411yescharacteristic
subgroupG/H
centerC2#10592474
commutator, cosocleC2×C32×C8C23
FrattiniC2×C8C22×C3⋊D3
FittingC32×#361C2
socleC2×C32#466
hypercenter#361C3⋊D3
hypocenterC32#2221
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
1. #10592859C2semidirect
2. C2×#63653C2semidirect
3. #10592606C2semidirect
4. #10592596C2semidirect
5. C32×#361C2semidirect
6. #10589382C2semidirect
7. #10589359C2semidirect
28. C3×#361D3semidirect
89. #361C3⋊D3semidirect
184. C32#2221semidirect
215. C3#69260semidirect

Maximal subgroups

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

subgroupindex
#105928592
C2×#636532
#105926062
#105925962
C32×#3612
#105893822
#105893592
#692603