Finite Group Databasebeta

← #11799123

Subgroups — #11799123

Order 1152.

304 conjugacy classes of subgroups; only the 37 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 37 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#10593334C212yesmaximal, complemented
2#10590389C211yesmaximal, characteristic, complemented
3#10590352C211yesmaximal, characteristic, complemented
4#10590150C211yesmaximal, characteristic, complemented
5#10590065C212yesmaximal, complemented
6C3×#874—21no—
7#63822C2211yescharacteristic
8C2×#3713—21no—
9C2×#3713C2212yes—
10#63815—21no—
11#63773C2212yes—
12#63735—22no—
13#63734—22no—
14C4×C3⋊(C3⋊C8)C2211yescharacteristic
15C3×#805—21no—
16#63578C2211yescharacteristic
17#5073—61no—
18#4824—61no—
19C3×#235—21no—
20C2×C3×D12—22no—
21C2×C3×D12—42no—
22C32×C42D411yescharacteristic
23C2×C3⋊(C3⋊C8)D411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×#208—21no—
26#3718D411yescharacteristic, complemented
27#3715—21no—
28#3713—22no—
29#3713—22no—
30#3713—41no—
31#3713—41no—
32#3713D411yescharacteristic, complemented
33#3711—41no—
34D3×C3⋊C8—41no—
35#3708—22no—
36#2213—91nomaximal, Sylow
37C3×#127—61no—
38#950—61no—
39#948—61no—
40C2×#213—62no—
41C2×#213—62no—
42#907—61no—
43#874—21no—
44C3×#104—61no—
45#822—61no—
46#805—21no—
47C4×C3⋊C8—61no—
48C4×C3⋊C8—61no—
49C22×C3×D3—42no—
50C2×C32×C4—21no—
51C2×C32×C4C2×D411yescharacteristic
52C3×#67—41no—
53C3×D12—21no—
54C3×D12—42no—
55C3×D12—42no—
56C3×D12—84no—
57C3×C4×D3—41no—
58C3×Dic6—21no—
59C3⋊(C3⋊C8)D811yescharacteristic
60C3⋊(C3⋊C8)D811yescharacteristic
61C3⋊(C3⋊C8)C2×D411yescharacteristic
62C3⋊(C3⋊C8)#4111yescharacteristic
63C3×C3⋊C8—41no—
64#509—92no—
65#493—91no—
66#443—91no—
67#364—91no—
68#361—92no—
69C3×#41—61no—
70C2×C3×D4—62no—
71C2×C3×D4—122no—
72#235—21no—
73C2×D12—22no—
74C2×D12—42no—
75C3×M16—61no—
76C3×C42—21no—
77C3×C42—21no—
78#216—61no—
79#215—61no—
80#214—61no—
81#213—61no—
82#213—122no—
83#213—122no—
84#213—122no—
85#213—122no—
86#208—21no—
87#208—121no—
88C2×C3⋊C8—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—121no—
93ΓL(1,𝔽25)—121no—
94D3×C8—121no—
95C22×C32AGL(1,ℤ/8)11yescharacteristic
96C2×C3×D3—41no—
97C2×C3×D3—84no—
98C2×C3×D3—82no—
99C32×C4—22no—
100C32×C4#12111yescharacteristic
101C32×C4C2×D811yescharacteristic
102C3×Dic3—41no—
103#135—91no—
104C2×D8—92no—
105C2×D8—181no—
106#131—181no—
107#127—61no—
108SD32—182no—
109D16—182no—
110M32—92no—
111#108—91no—
112#104—61no—
113C4×C8—91no—
114C23×C3—122no—
115C22×D3—42no—
116C3×Q8—61no—
117C3×D4—61no—
118C3×D4—122no—
119C3×D4—122no—
120C3×D4—121no—
121C3×D4—244no—
122C2×C3×C4—22no—
123C2×C3×C4—21no—
124C2×C3×C4—21no—
125C2×C3×C4—41no—
126C2×C3×C4—121no—
127#67—41no—
128D12—21no—
129D12—42no—
130D12—42no—
131D12—84no—
132C4×D3—41no—
133Dic6—21no—
134C3×C8—121no—
135C3⋊C8—41no—
136C3⋊C8—61no—
137C3⋊C8—61no—
138C3⋊C8—61no—
139C3⋊C8—61no—
140C3⋊C8—61no—
141C3⋊C8—61no—
142C3⋊C8—61no—
143C3⋊C8—61no—
144C2×C32—21no—
145C2×C32#45911yescharacteristic
146C3×D3—81no—
147C3×D3—162no—
148#41—61no—
149C2×D4—62no—
150C2×D4—122no—
151Q16—91no—
152SD16—181no—
153D8—91no—
154D8—182no—
155D8—182no—
156D8—361no—
157D8—361no—
158M16—61no—
159M16—361no—
160C2×C8—91no—
161C2×C8—91no—
162C2×C8—361no—
163C42GO+(4,𝔽2)11yescharacteristic
164C16—182no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—121no—
168C22×C3—242no—
169C22×C3—244no—
170C2×D3—41no—
171C2×D3—82no—
172C2×D3—84no—
173C3×C4—24no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—21no—
178C3×C4—42no—
179C3×C4—121no—
180Dic3—41no—
181C32#221311yescharacteristic, complemented, Sylow
182C23—122no—
183Q8—61no—
184D4—61no—
185D4—121no—
186D4—122no—
187D4—122no—
188D4—244no—
189C2×C4—21no—
190C2×C4—121no—
191C2×C4C2×GO+(4,𝔽2)11yescharacteristic
192C8—91no—
193C8—91no—
194C8—91no—
195C8—91no—
196C8—121no—
197C2×C3—22no—
198C2×C3—21no—
199C2×C3—21no—
200C2×C3—41no—
201C2×C3—241no—
202C2×C3—482no—
203D3—81no—
204D3—162no—
205C22—121no—
206C22—244no—
207C22—242no—
208C22#6423611yescharacteristic
209C4—22no—
210C4—121no—
211C4#6422511yescharacteristic
212C4#6423011yescharacteristic
213C3—21no—
214C3—21no—
215C2—21no—
216C2—241no—
217C2—482no—
218C2#1059342611yescharacteristic
subgroupG/H
centerC2#10593426
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC32×C42D4
socleC2×C32#459
hypercenterC42GO+(4,𝔽2)
hypocenterC32#2213
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C42

Complements

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

NH ≅ G/Ntype
1. #10593334C2semidirect
2. #10590389C2semidirect
3. #10590352C2semidirect
4. #10590150C2semidirect
5. #10590065C2semidirect
26. #3718D4semidirect
32. #3713D4semidirect
181. C32#2213semidirect

Maximal subgroups

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

subgroupindex
#105933342
#105903892
#105903522
#105901502
#105900652
#22139