Finite Group Databasebeta

← #25963354

Subgroups — #25963354

Order 11008.

4732 conjugacy classes of subgroups; only the 807 normal subgroups are shown.

normal subgroups only

This group has 4732 conjugacy classes of subgroups — too many to draw. Only its 807 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#19148243C213yesmaximal, complemented
2#19144001C2112yesmaximal, complemented
3#19143987C2112yesmaximal, complemented
4#19143059C213yesmaximal, complemented
5C43×2−1+6C211yesmaximal, characteristic, complemented
6C22×Q8×D43C2211yescharacteristic, complemented
7Q8×C22⋊D43—212no—
8#14583556—212no—
9#14583470C22118yescomplemented
10#14583406C22118yescomplemented
11#14583377C2213yescomplemented
12#14583089C22148yescomplemented
13#14583086C22116yescomplemented
14#14582873C22136yescomplemented
15C43×#585—212no—
16C43×#585C22112yes—
17C2×2−1+4×C43—212no—
18C2×2−1+4×C43C2213yes—
19C22×Dic86C2313yes—
20C2×Q8×D43—212no—
21C22×C4×D43C2313yes—
22#13063323—218no—
23#13063312—218no—
24#13063306C23136yes—
25#13063304—236no—
26#13063301—218no—
27#13063296—218no—
28#13063293C23112yes—
29Q8×Dic43—212no—
30C4×C22⋊D43—236no—
31#13063284C23118yes—
32#13063240C23148yes—
332−1+4×C43—248no—
342−1+4×C43—236no—
352−1+4×C43—224no—
36H(5,𝔽2)×C43—216no—
37H(5,𝔽2)×C43—236no—
38H(5,𝔽2)×C43C23116yes—
39C2×#41×C43—248no—
40C2×#41×C43—272no—
41C2×#41×C43D4112yescomplemented
42C2×#41×C43C23118yes—
43C22×Q8×C43—216no—
44C22×Q8×C43D4112yescomplemented
45C22×Q8×C43C2311yescharacteristic
46C23×D43C2411yescharacteristic
47#41×C43—2144no—
48#41×C43—248no—
49#41×C43—248no—
50#41×C43—248no—
51#41×C43—272no—
52C2×Q8×C43—272no—
53C2×Q8×C43—248no—
54C2×Q8×C43C2×D4118yes—
55C2×Q8×C43C2×D4112yes—
56C2×D4×C43—272no—
57C2×D4×C43—248no—
58C2×D4×C43C2×D4118yes—
59C2×D4×C43C24112yes—
60C22×C4×C43—248no—
61C22×C4×C43C2×D4136yes—
62C22×C4×C43C2413yes—
63C2×C22⋊D43—212no—
64C22×Dic43C2413yes—
65Q8×D43—416no—
66C2×C4×D43—218no—
67C2×Dic86—218no—
68C22⋊Dic43—236no—
69C22⋊Dic43C24112yes—
70(C2×D43)⋊C4—212no—
71C4⋊Dic43—218no—
72Dic43⋊C4—236no—
73C4×Dic43—218no—
74C23×C43—216no—
75C23×C43C22×D4112yes—
76C23×C43C2511yescharacteristic
77C22×D43—23no—
78C22×D43—42no—
79Q8×C43—216no—
80Q8×C43—236no—
81Q8×C43#120116yes—
82D4×C43—248no—
83D4×C43—224no—
84D4×C43—236no—
85C2×C4×C43—248no—
86C2×C4×C43—272no—
87C2×C4×C43C22×D4112yes—
88C2×C4×C43C22×D4118yes—
89C22⋊D43—424no—
90C2×Dic43—212no—
91C2×Dic43—29no—
92C4×D43—412no—
93Dic86—412no—
94#60400—431nomaximal, Sylow
95C22×C43—212no—
96C22×C43—41no—
97C22×C43—412no—
98C22×C43—816no—
99C22×C43C23×D413yes—
100C2×D43—26no—
101C2×D43—43no—
102C2×D43—41no—
103C4×C43—212no—
104C4×C43C2×#120112yes—
105Dic43—412no—
106Dic43—43no—
1072−1+6D4311yescharacteristic, complemented
108#3486—433no—
109#3028—4312no—
110#3025—4312no—
111#2884—433no—
112C2×C43—23no—
113C2×C43—412no—
114C2×C43C22×#12011yescharacteristic
115D43—42no—
116#585—212no—
117#585C2×D43112yes—
118C2×2−1+4—212no—
119C2×2−1+4C2×D4313yes—
120C23×Q8—431no—
121D4×Q8—8612no—
122#548—8612no—
123#536—4318no—
124#525—4318no—
125#519—433no—
126#458—4348no—
127B(4,𝔽2)—4316no—
128#410—4336no—
129C43#6040011yescharacteristic, complemented, Sylow
1302−1+4—248no—
1312−1+4—236no—
1322−1+4—224no—
133H(5,𝔽2)—216no—
134H(5,𝔽2)—236no—
135H(5,𝔽2)C22×D43116yes—
136C2×#41—248no—
137C2×#41—272no—
138C2×#41C22⋊D43112yescomplemented
139C2×#41C22×D43118yes—
140C22×Q8—216no—
141C22×Q8—433no—
142C22×Q8—8612no—
143C22×Q8C22⋊D43112yescomplemented
144C22×Q8C22×D4311yescharacteristic
145C23×C4—433no—
146C4⋊Q8—8618no—
147#124—8618no—
148#123—4336no—
149C22⋊Q8—8618no—
150C22⋊Q8—8636no—
151#121—8618no—
152#120—4312no—
153C4×Q8—8612no—
154C4×D4—8636no—
155#117—4318no—
156#99—4348no—
157C24—431no—
158#41—2144no—
159#41—248no—
160#41—248no—
161#41—248no—
162#41—272no—
163C2×Q8—272no—
164C2×Q8—248no—
165C2×Q8—8618no—
166C2×Q8—17216no—
167C2×Q8C2×C22⋊D43118yes—
168C2×Q8C2×C22⋊D43112yes—
169C2×D4—272no—
170C2×D4—248no—
171C2×D4—8612no—
172C2×D4C2×C22⋊D43118yes—
173C2×D4C23×D43112yes—
174C22×C4—248no—
175C22×C4—433no—
176C22×C4—8618no—
177C22×C4C2×C22⋊D43136yes—
178C22×C4C23×D4313yes—
179C4⋊C4—8618no—
180C4⋊C4—8636no—
181C22⋊C4—4312no—
182C22⋊C4—8636no—
183C22⋊C4—8612no—
184C42—8618no—
185C23—216no—
186C23—863no—
187C23—1722no—
188C23C22×C22⋊D43112yes—
189C23C24×D4311yescharacteristic
190Q8—216no—
191Q8—236no—
192Q8—17212no—
193Q8#13063294116yes—
194D4—248no—
195D4—224no—
196D4—236no—
197D4—17224no—
198C2×C4—248no—
199C2×C4—272no—
200C2×C4—8612no—
201C2×C4—869no—
202C2×C4—17212no—
203C2×C4C22×C22⋊D43112yes—
204C2×C4C22×C22⋊D43118yes—
205C22—212no—
206C22—41no—
207C22—412no—
208C22—816no—
209C22—866no—
210C22—1723no—
211C22—1721no—
212C22C23×C22⋊D4313yes—
213C4—212no—
214C4—17212no—
215C4—1723no—
216C4C2×#13063294112yes—
217C2—23no—
218C2—412no—
219C2—1722no—
220C2C22×#1306329411yescharacteristic
subgroupG/H
centerC2C22×#13063294
commutator, cosocleC23×C43C25
FrattiniC23C24×D43
FittingC43×2−1+6C2
socleC2×C43C22×#120
hypercenter2−1+6D43
hypocenterC43#60400
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×Q8 ◁ 2−1+6

Complements

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

NH ≅ G/Ntype
1. #19148243C2semidirect
2. #19144001C2semidirect
3. #19143987C2semidirect
4. #19143059C2semidirect
5. C43×2−1+6C2semidirect
6. C22×Q8×D43C22semidirect
9. #14583470C22semidirect
10. #14583406C22semidirect
11. #14583377C22semidirect
12. #14583089C22semidirect
13. #14583086C22semidirect
14. #14582873C22semidirect
41. C2×#41×C43D4semidirect
44. C22×Q8×C43D4semidirect
107. 2−1+6D43semidirect
129. C43#60400semidirect
138. C2×#41C22⋊D43semidirect
143. C22×Q8C22⋊D43semidirect

Maximal subgroups

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

subgroupindex
#191482432
#191440012
#191439872
#191430592
C43×2−1+62
#6040043