Finite Group Databasebeta

← #11780902

Subgroups — #11780902

Order 1152.

352 conjugacy classes of subgroups; only the 45 normal subgroups are shown.

normal subgroups only

This group has 352 conjugacy classes of subgroups — too many to draw. Only its 45 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#10593417C212yesmaximal, complemented
2#10590886C211yesmaximal, characteristic, complemented
3#10590718C211yesmaximal, characteristic, complemented
4#10590173C211yesmaximal, characteristic, complemented
5#10590037C212yesmaximal, complemented
6C2×#3774—22no—
7C2×C3×D24—21no—
8#63914C2212yes—
9C4×#625C2211yescharacteristic
10C2×#3713—21no—
11C2×D3×C3⋊C8—21no—
12C4⋊#622C2212yes—
13#63739—22no—
14C8×C3⋊Dic3C2211yescharacteristic
15C3×(C2×D3)⋊C8—21no—
16#63572C2211yescharacteristic
17#5151—61no—
18#67⋊C8—61no—
19C2×C3×D12—22no—
20C2×C3×C4×D3—21no—
21C2×#625—22no—
22C2×#625—22no—
23C2×#625D411yescharacteristic
24C2×#622—22no—
25#3774—44no—
26C2×C32×C8D411yescharacteristic
27C4×C3⋊Dic3C2311yescharacteristic
28C2×C3⋊(C3⋊C8)D411yescharacteristic
29C2×C3×C3⋊C8—21no—
30C3×D24—42no—
31#3724D411yescharacteristic
32(C2×D3)⋊Dic3—21no—
33#3713—42no—
34D3×C3⋊C8—42no—
35#1667—91nomaximal, Sylow
36C2×C3×D8—61no—
37#940—62no—
38C2×#213—62no—
39C4×#67—61no—
40C22×C3⋊C8—61no—
41C2×D24—21no—
42C2×D3×C8—61no—
43C3×C22⋊C8—61no—
44(C2×D3)⋊C8—21no—
45Dic3⋊C8—61no—
46C8×Dic3—61no—
47C8×Dic3—61no—
48C22×C3×D3—21no—
49C22×C3×D3—42no—
50C2×C32×C4C2×D411yescharacteristic
51C2×C3⋊Dic3C2×D411yescharacteristic
52C2×C3⋊Dic3#4111yescharacteristic
53C2×C3×Dic3—21no—
54C3×D12—42no—
55C3×D12—42no—
56C3×C4×D3—41no—
57C3×C4×D3—41no—
58#625—21no—
59#625—42no—
60#625—42no—
61#625—82no—
62#625D812yescomplemented
63#622—42no—
64C32×C8—21no—
65C3⋊(C3⋊C8)D812yescomplemented
66C3×C3⋊C8—41no—
67#493—91no—
68#459—92no—
69C8×D4—91no—
70#335—91no—
71#331—92no—
72C2×C3×D4—62no—
73C22×C3×C4—61no—
74C2×#67—61no—
75C2×#67—122no—
76C2×#67—122no—
77C2×D12—22no—
78C2×C4×D3—21no—
79C3×D8—122no—
80C2×C3×C8—21no—
81C2×C3×C8—21no—
82C2×C3×C8—61no—
83#217—61no—
84#213—124no—
85(C2×D3)⋊C4—61no—
86Dic3⋊C4—61no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C2×C3⋊C8—21no—
90C2×C3⋊C8—61no—
91C2×C3⋊C8—61no—
92C2×C3⋊C8—122no—
93D24—42no—
94D3×C8—122no—
95C22×C32#12111yescharacteristic
96C2×C3×D3—22no—
97C2×C3×D3—41no—
98C2×C3×D3—41no—
99C2×C3×D3—82no—
100C2×C3×D3—82no—
101C2×C3×D3—82no—
102C32×C4C2×D811yescharacteristic
103C32×C4AGL(1,ℤ/8)11yescharacteristic
104C3⋊Dic3—21no—
105C3⋊Dic3C2×D811yescharacteristic
106C3⋊Dic3#13511yescharacteristic
107C3×Dic3—41no—
108C2×D8—61no—
109C2×D8—181no—
110C2×D8—182no—
111C22×C8—181no—
112#127—92no—
113C4×D4—91no—
114C4⋊C8—91no—
115C4⋊C8—92no—
116#102—182no—
117C22⋊C8—61no—
118C4×C8—91no—
119C23×C3—61no—
120C23×C3—122no—
121C22×D3—21no—
122C22×D3—42no—
123C3×D4—122no—
124C3×D4—122no—
125C2×C3×C4—21no—
126C2×C3×C4—21no—
127C2×C3×C4—61no—
128C2×C3×C4—121no—
129C2×C3×C4—121no—
130#67—62no—
131#67—62no—
132#67—242no—
133#67—242no—
134#67—244no—
135C2×Dic3—21no—
136C2×Dic3—61no—
137C2×Dic3—61no—
138C2×Dic3—61no—
139C2×Dic3—61no—
140D12—42no—
141D12—42no—
142C4×D3—41no—
143C4×D3—41no—
144C3×C8—22no—
145C3×C8—41no—
146C3×C8—121no—
147C3⋊C8—41no—
148C3⋊C8—62no—
149C3⋊C8—62no—
150C2×C32#45911yescharacteristic
151C2×C32#46611yescharacteristic
152C2×C32#47211yescharacteristic
153C3×D3—42no—
154C3×D3—162no—
155C2×D4—62no—
156C2×D4—91no—
157C2×D4—182no—
158C2×D4—182no—
159C22×C4—61no—
160D8—122no—
161D8—362no—
162D8—364no—
163C2×C8—61no—
164C2×C8—91no—
165C2×C8—182no—
166C2×C8—362no—
167C2×C8GO+(4,𝔽2)11yescharacteristic
168C4⋊C4—91no—
169C22⋊C4—181no—
170C42—91no—
171C22×C3—21no—
172C22×C3—21no—
173C22×C3—62no—
174C22×C3—121no—
175C22×C3—121no—
176C22×C3—242no—
177C22×C3—242no—
178C22×C3—242no—
179C2×D3—22no—
180C2×D3—41no—
181C2×D3—41no—
182C2×D3—82no—
183C2×D3—82no—
184C2×D3—82no—
185C3×C4—21no—
186C3×C4—21no—
187C3×C4—21no—
188C3×C4—21no—
189C3×C4—121no—
190Dic3—41no—
191Dic3—61no—
192Dic3—61no—
193Dic3—61no—
194Dic3—61no—
195Dic3—62no—
196Dic3—121no—
197C32#166711yescharacteristic, complemented, Sylow
198C23—61no—
199C23—122no—
200D4—92no—
201D4—122no—
202D4—122no—
203D4—181no—
204D4—362no—
205D4—362no—
206D4—722no—
207C2×C4—61no—
208C2×C4—91no—
209C2×C4—91no—
210C2×C4—121no—
211C2×C4—121no—
212C2×C4C2×GO+(4,𝔽2)11yescharacteristic
213C8—21no—
214C8—92no—
215C8—121no—
216C8—362no—
217C2×C3—21no—
218C2×C3—21no—
219C2×C3—21no—
220C2×C3—21no—
221C2×C3—21no—
222C2×C3—21no—
223C2×C3—122no—
224C2×C3—482no—
225D3—42no—
226D3—162no—
227C22—62no—
228C22—121no—
229C22—121no—
230C22—242no—
231C22—242no—
232C22—242no—
233C22#6423011yescharacteristic
234C4—91no—
235C4—91no—
236C4—121no—
237C4—181no—
238C4#6422511yescharacteristic
239C4#6423611yescharacteristic
240C3—21no—
241C3—21no—
242C2—122no—
243C2—482no—
244C2#1059328511yescharacteristic
245C2#1059330311yescharacteristic
246C2#1059342611yescharacteristic
subgroupG/H
centerC22#64230
commutator, cosocleC4×C3⋊Dic3C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32#121
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#1667
LCSG ▷ C4×C3⋊Dic3 ▷ C22×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. #10593417C2semidirect
2. #10590886C2semidirect
3. #10590718C2semidirect
4. #10590173C2semidirect
5. #10590037C2semidirect
62. #625D8semidirect
65. C3⋊(C3⋊C8)D8semidirect
197. C32#1667semidirect

Maximal subgroups

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

subgroupindex
#105934172
#105908862
#105907182
#105901732
#105900372
#16679