Finite Group Databasebeta

← #11799122

Subgroups — #11799122

Order 1152.

304 conjugacy classes of subgroups; only the 39 normal subgroups are shown.

normal subgroups only

This group has 304 conjugacy classes of subgroups — too many to draw. Only its 39 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#10590921C211yesmaximal, characteristic, complemented
3#10590886C211yesmaximal, characteristic, complemented
4#10590178C211yesmaximal, characteristic, complemented
5#10590065C212yesmaximal, complemented
6C2×C3×D24—21no—
7C3×#901—21no—
8#63914—21no—
9#63822C2211yescharacteristic
10C2×#3713C2212yes—
11#63773C2212yes—
12#63735—22no—
13#63734—22no—
14C8×C3⋊Dic3C2211yescharacteristic
15#63578C2211yescharacteristic
16#63568—21no—
17#5151—61no—
18#5144—61no—
19C3×#235—21no—
20C2×C3×D12—22no—
21C2×#625—42no—
22C2×C32×C8D411yescharacteristic
23C4×C3⋊Dic3D411yescharacteristic
24C2×C3⋊(C3⋊C8)C2311yescharacteristic
25C3×#208—21no—
26C3×D24—41no—
27C3×D24—41no—
28C3×ΓL(1,𝔽25)—41no—
29C3×D3×C8—41no—
30#3718D411yescharacteristic, complemented
31#3715—21no—
32#3713—22no—
33#3713—22no—
34#3713D411yescharacteristic, complemented
35#3708—22no—
36#2213—91nomaximal, Sylow
37C2×C3×D8—61no—
38C3×#131—61no—
39#950—61no—
40#940—62no—
41C2×#213—62no—
42C2×D24—21no—
43#901—21no—
44#837—61no—
45#825—61no—
46#822—61no—
47C8×Dic3—61no—
48C8×Dic3—61no—
49C22×C3×D3—42no—
50C2×C32×C4C2×D411yescharacteristic
51C2×C3⋊Dic3—21no—
52C3×#67—41no—
53C3×D12—21no—
54C3×D12—42no—
55C3×D12—42no—
56C3×C4×D3—41no—
57C3×Dic6—21no—
58#625—84no—
59C32×C8D811yescharacteristic
60C32×C8D811yescharacteristic
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×#67—124no—
72#235—21no—
73C2×D12—22no—
74C3×D8—121no—
75C3×D8—121no—
76C3×M16—61no—
77C3×M16—121no—
78C2×C3×C8—21no—
79C2×C3×C8—21no—
80C2×C3×C8—121no—
81#216—61no—
82#215—61no—
83#214—61no—
84#213—61no—
85#213—122no—
86#213—122no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89#208—21no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92D24—41no—
93D24—41no—
94ΓL(1,𝔽25)—41no—
95D3×C8—41no—
96C22×C32AGL(1,ℤ/8)11yescharacteristic
97C2×C3×D3—41no—
98C2×C3×D3—84no—
99C2×C3×D3—82no—
100C32×C4#12111yescharacteristic
101C32×C4C2×D811yescharacteristic
102C3⋊Dic3—22no—
103C3×Dic3—41no—
104#135—91no—
105C2×D8—61no—
106C2×D8—92no—
107#131—61no—
108#127—181no—
109SD32—182no—
110D16—182no—
111M32—92no—
112#108—91no—
113#104—181no—
114C4×C8—91no—
115C23×C3—122no—
116C22×D3—42no—
117C3×Q8—61no—
118C3×D4—61no—
119C3×D4—122no—
120C3×D4—122no—
121C3×D4—121no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—121no—
125#67—41no—
126#67—248no—
127C2×Dic3—62no—
128C2×Dic3—121no—
129D12—21no—
130D12—42no—
131D12—42no—
132C4×D3—41no—
133Dic6—21no—
134C3×C8—21no—
135C3×C8—21no—
136C3×C8—21no—
137C3×C8—21no—
138C3×C8—121no—
139C3⋊C8—41no—
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—362no—
151Q16—91no—
152SD16—181no—
153D8—91no—
154D8—121no—
155D8—121no—
156D8—182no—
157D8—182no—
158M16—61no—
159M16—121no—
160C2×C8—91no—
161C2×C8—121no—
162C2×C8GO+(4,𝔽2)11yescharacteristic
163C42—91no—
164C16—182no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—121no—
168C22×C3—244no—
169C22×C3—242no—
170C2×D3—41no—
171C2×D3—82no—
172C2×D3—84no—
173C3×C4—21no—
174C3×C4—21no—
175C3×C4—21no—
176C3×C4—21no—
177C3×C4—121no—
178Dic3—41no—
179Dic3—64no—
180Dic3—122no—
181C32#221311yescharacteristic, complemented, Sylow
182C23—122no—
183Q8—61no—
184D4—61no—
185D4—121no—
186D4—122no—
187D4—122no—
188D4—724no—
189C2×C4—121no—
190C2×C4—181no—
191C2×C4C2×GO+(4,𝔽2)11yescharacteristic
192C8—91no—
193C8—91no—
194C8—121no—
195C8#377411yescharacteristic
196C8#377411yescharacteristic
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#6422411yescharacteristic
209C4—121no—
210C4—182no—
211C4#6423011yescharacteristic
212C4C2×#377411yescharacteristic
213C3—21no—
214C3—21no—
215C2—21no—
216C2—241no—
217C2—482no—
218C2#1059341711yescharacteristic
subgroupG/H
centerC2#10593417
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC2×C32#459
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2213
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10593334C2semidirect
2. #10590921C2semidirect
3. #10590886C2semidirect
4. #10590178C2semidirect
5. #10590065C2semidirect
30. #3718D4semidirect
34. #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
#105909212
#105908862
#105901782
#105900652
#22139