Finite Group Databasebeta

← #11798863

Subgroups — #11798863

Order 1152.

334 conjugacy classes of subgroups; only the 43 normal subgroups are shown.

normal subgroups only

This group has 334 conjugacy classes of subgroups — too many to draw. Only its 43 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
1C2×#63734C212yesmaximal, complemented
2#10590886C211yesmaximal, characteristic, complemented
3#10590740C211yesmaximal, characteristic, complemented
4#10590177C211yesmaximal, characteristic, complemented
5#10590061C212yesmaximal, complemented
6C2×C3×D24—21no—
7#63914—21no—
8#63898—21no—
9C2×#3713C2212yes—
10C2×#3713C2211yescharacteristic
11C2×#3708C2212yes—
12#63734—24no—
13C8×C3⋊Dic3C2211yescharacteristic
14C3×#821—21no—
15#63576C2211yescharacteristic
16#5151—61no—
17#4756—61no—
18C2×C3×D12—21no—
19C2×C3×D12—22no—
20C2×#625—41no—
21C2×#625—41no—
22C2×D3×Dic3—41no—
23C2×C32×C8D411yescharacteristic
24C4×C3⋊Dic3D411yescharacteristic
25C2×C3⋊(C3⋊C8)C2311yescharacteristic
26C3×C4⋊Dic3—21no—
27C3×D24—42no—
28(C2×D3)⋊Dic3—41no—
29#3713—22no—
30#3713—21no—
31#3713—22no—
32#3713D412yescomplemented
33#3708—22no—
34#2206—91nomaximal, Sylow
35C2×C3×D8—61no—
36#940—62no—
37D4×Dic3—61no—
38C2×#213—61no—
39C2×#213—62no—
40C2×D24—21no—
41#893—61no—
42C3×#102—61no—
43#821—21no—
44C8×Dic3—61no—
45C8×Dic3—61no—
46#807—61no—
47C22×C3×D3—41no—
48C22×C3×D3—42no—
49C2×C32×C4C2×D411yescharacteristic
50C2×C3⋊Dic3D811yescharacteristic
51C2×C3⋊Dic3D811yescharacteristic
52C2×C3×Dic3—41no—
53C3×D12—22no—
54C3×D12—42no—
55C3×D12—41no—
56C3×D12—42no—
57#625—82no—
58#625—82no—
59D3×Dic3—82no—
60C32×C8—21no—
61C3⋊(C3⋊C8)C2×D411yescharacteristic
62C3⋊(C3⋊C8)#4111yescharacteristic
63C2×D16—92no—
64#493—91no—
65C4×D8—91no—
66C4⋊C16—91no—
67#357—92no—
68C2×C3×D4—61no—
69C2×C3×D4—62no—
70C2×#67—122no—
71C2×#67—122no—
72C22×Dic3—121no—
73C2×D12—21no—
74C2×D12—22no—
75C2×C4×D3—121no—
76C3×D8—122no—
77C2×C3×C8—21no—
78C2×C3×C8—21no—
79C3×C4⋊C4—61no—
80#217—121no—
81#213—62no—
82#213—62no—
83#213—122no—
84#213—122no—
85(C2×D3)⋊C4—121no—
86C4⋊Dic3—21no—
87C4×Dic3—61no—
88C4×Dic3—61no—
89C2×C3⋊C8—61no—
90C2×C3⋊C8—61no—
91D24—42no—
92C22×C32C2×D811yescharacteristic
93C2×C3×D3—42no—
94C2×C3×D3—81no—
95C2×C3×D3—81no—
96C2×C3×D3—82no—
97C2×C3×D3—82no—
98C2×C3×D3—82no—
99C32×C4#12111yescharacteristic
100C32×C4AGL(1,ℤ/8)11yescharacteristic
101C3⋊Dic3—21no—
102C3⋊Dic3D1612yescomplemented
103C3×Dic3—81no—
104C2×D8—61no—
105C2×D8—91no—
106C2×D8—92no—
107#127—181no—
108C4×D4—181no—
109D16—184no—
110C2×C16—92no—
111#107—91no—
112#102—61no—
113C4×C8—91no—
114C23×C3—121no—
115C23×C3—122no—
116C22×D3—41no—
117C22×D3—42no—
118C3×D4—62no—
119C3×D4—121no—
120C3×D4—122no—
121C3×D4—122no—
122C2×C3×C4—21no—
123C2×C3×C4—21no—
124C2×C3×C4—121no—
125#67—244no—
126#67—244no—
127C2×Dic3—41no—
128C2×Dic3—61no—
129C2×Dic3—61no—
130C2×Dic3—61no—
131C2×Dic3—61no—
132C2×Dic3—242no—
133D12—22no—
134D12—41no—
135D12—42no—
136D12—42no—
137C4×D3—242no—
138C3×C8—22no—
139C3×C8—41no—
140C3⋊C8—61no—
141C3⋊C8—61no—
142C3⋊C8—61no—
143C3⋊C8—61no—
144C2×C32#45911yescharacteristic
145C2×C32C2×D1611yescharacteristic
146C2×C32#50911yescharacteristic
147C3×D3—82no—
148C3×D3—162no—
149C2×D4—61no—
150C2×D4—62no—
151C2×D4—361no—
152C2×D4—361no—
153C22×C4—361no—
154D8—92no—
155D8—122no—
156D8—181no—
157D8—182no—
158D8—182no—
159C2×C8—91no—
160C2×C8GO+(4,𝔽2)11yescharacteristic
161C4⋊C4—61no—
162C22⋊C4—361no—
163C42—91no—
164C16—182no—
165C22×C3—21no—
166C22×C3—21no—
167C22×C3—122no—
168C22×C3—241no—
169C22×C3—241no—
170C22×C3—242no—
171C22×C3—242no—
172C22×C3—242no—
173C2×D3—42no—
174C2×D3—81no—
175C2×D3—81no—
176C2×D3—82no—
177C2×D3—82no—
178C2×D3—82no—
179C3×C4—21no—
180C3×C4—21no—
181C3×C4—21no—
182C3×C4—21no—
183C3×C4—241no—
184Dic3—62no—
185Dic3—62no—
186Dic3—62no—
187Dic3—81no—
188Dic3—121no—
189C32#220611yescharacteristic, complemented, Sylow
190C23—121no—
191C23—122no—
192D4—62no—
193D4—122no—
194D4—121no—
195D4—122no—
196D4—722no—
197D4—722no—
198C2×C4—91no—
199C2×C4—91no—
200C2×C4—121no—
201C2×C4—722no—
202C2×C4C2×GO+(4,𝔽2)11yescharacteristic
203C8—21no—
204C8—91no—
205C8—91no—
206C2×C3—21no—
207C2×C3—21no—
208C2×C3—21no—
209C2×C3—21no—
210C2×C3—21no—
211C2×C3—21no—
212C2×C3—242no—
213C2×C3—482no—
214D3—82no—
215D3—162no—
216C22—122no—
217C22—241no—
218C22—241no—
219C22—242no—
220C22—242no—
221C22—242no—
222C22#6422511yescharacteristic
223C4—92no—
224C4—181no—
225C4—241no—
226C4#6423011yescharacteristic
227C4#6423611yescharacteristic
228C3—21no—
229C3—21no—
230C2—242no—
231C2—482no—
232C2#1059327611yescharacteristic
233C2#1059327711yescharacteristic
234C2#1059342611yescharacteristic
subgroupG/H
centerC22#64225
commutator, cosocleC2×C3⋊(C3⋊C8)C23
FrattiniC2×C4C2×GO+(4,𝔽2)
FittingC2×C32×C8D4
socleC22×C32C2×D8
hypercenterC2×C8GO+(4,𝔽2)
hypocenterC32#2206
LCSG ▷ C2×C3⋊(C3⋊C8) ▷ C32×C4 ▷ C2×C32 ▷ C32
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8

Complements

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

NH ≅ G/Ntype
1. C2×#63734C2semidirect
2. #10590886C2semidirect
3. #10590740C2semidirect
4. #10590177C2semidirect
5. #10590061C2semidirect
32. #3713D4semidirect
102. C3⋊Dic3D16semidirect
189. C32#2206semidirect

Maximal subgroups

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

subgroupindex
C2×#637342
#105908862
#105907402
#105901772
#105900612
#22069