Finite Group Databasebeta

← #14583576

Subgroups — #14583576

Order 2752.

248 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 248 conjugacy classes of subgroups — too many to draw. Only its 97 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#13063320C211yesmaximal, characteristic, complemented
2#13063320C211yesmaximal, characteristic, complemented
3#13063314C211yesmaximal, characteristic, complemented
4#13063310C211yesmaximal, characteristic, complemented
5#13063310C211yesmaximal, characteristic, complemented
6#13063309C211yesmaximal, characteristic, complemented
7#13063301C211yesmaximal, characteristic, complemented
8#13063295C211yesmaximal, characteristic
9#13063287C211yesmaximal, characteristic, complemented
10C4×C22⋊D43C211yesmaximal, characteristic, complemented
11#13063283C211yesmaximal, characteristic, complemented
12#13063281C211yesmaximal, characteristic, complemented
13C2×(C2×D43)⋊C4C211yesmaximal, characteristic, complemented
14C22⋊C4×D43C211yesmaximal, characteristic, complemented
15C22⋊Q8×C43C211yesmaximal, characteristic, complemented
16C23×D43C2211yescharacteristic
17C2×Q8×C43C2211yescharacteristic, complemented
18C22×C4×C43C2211yescharacteristic
19C2×C22⋊D43C2211yescharacteristic
20C22×Dic43C2211yescharacteristic
21C2×D172C2211yescharacteristic
22C2×D172C2211yescharacteristic
23C2×C4×D43C2211yescharacteristic
24C2×C4×D43C2211yescharacteristic
25C2×C4×D43C2211yescharacteristic, complemented
26C4⋊C4×C43C2211yescharacteristic, complemented
27C4⋊C4×C43C2211yescharacteristic, complemented
28C4⋊C4×C43C2211yescharacteristic, complemented
29C22⋊C4×C43C2211yescharacteristic
30C22⋊C4×C43C2211yescharacteristic
31C22⋊Dic43C2211yescharacteristic
32(C2×D43)⋊C4C2211yescharacteristic
33(C2×D43)⋊C4C2211yescharacteristic
34(C2×D43)⋊C4C2211yescharacteristic
35(C2×D43)⋊C4C2211yescharacteristic
36(C2×D43)⋊C4C2211yescharacteristic
37(C2×D43)⋊C4C2211yescharacteristic
38(C2×D43)⋊C4C2211yescharacteristic
39(C2×D43)⋊C4C2211yescharacteristic
40(C2×D43)⋊C4C2211yescharacteristic, complemented
41(C2×D43)⋊C4C2211yescharacteristic, complemented
42(C2×D43)⋊C4C2211yescharacteristic, complemented
43C4⋊Dic43C2211yescharacteristic, complemented
44C4⋊Dic43C2211yescharacteristic, complemented
45Dic43⋊C4C2211yescharacteristic, complemented
46Dic43⋊C4C2211yescharacteristic, complemented
47Dic43⋊C4C2211yescharacteristic, complemented
48C4×Dic43C2211yescharacteristic, complemented
49C4×Dic43C2211yescharacteristic, complemented
50C4×Dic43C2211yescharacteristic, complemented
51C23×C43C2311yescharacteristic
52C22×D43—22no—
53C22×D43—22no—
54C22×D43—41no—
55C22×D43C2311yescharacteristic
56C22×D43C2311yescharacteristic
57C22×D43C2311yescharacteristic
58Q8×C43—41no—
59C2×C4×C43—41no—
60C2×C4×C43C2311yescharacteristic
61C2×C4×C43C2311yescharacteristic
62C2×C4×C43C2311yescharacteristic
63C2×C4×C43C2311yescharacteristic
64C2×C4×C43C2311yescharacteristic
65C2×C4×C43C2311yescharacteristic
66C22⋊D43—22no—
67C2×Dic43—22no—
68C2×Dic43C2311yescharacteristic
69C2×Dic43C2311yescharacteristic
70C2×Dic43C2311yescharacteristic
71C2×Dic43C2311yescharacteristic
72C2×Dic43C2311yescharacteristic
73D172—22no—
74D172—41no—
75C4×D43—22no—
76C4×D43—41no—
77C4×D43—41no—
78C22×C43—21no—
79C22×C43—21no—
80C22×C43#4112yes—
81C22×C43C2411yescharacteristic
82C2×D43—21no—
83C2×D43—21no—
84C2×D43—21no—
85C2×D43—21no—
86C2×D43—21no—
87C2×D43—21no—
88C2×D43—21no—
89C2×D43—21no—
90C2×D43—44no—
91C2×D43#4112yes—
92C4×C43—21no—
93C4×C43—21no—
94C4×C43—21no—
95C4×C43—21no—
96C4×C43—21no—
97C4×C43—21no—
98Dic43—21no—
99Dic43—21no—
100Dic43—21no—
101Dic43—21no—
102Dic43—21no—
103C2×C43—22no—
104C2×C43C2×#4111yescharacteristic
105C2×C43C2×#4111yescharacteristic
106C2×C43H(5,𝔽2)11yescharacteristic
107D43—22no—
108D43—41no—
109D43—41no—
110#551—431nomaximal, Sylow
111C43#55111yescharacteristic, complemented, Sylow
112#126—431no—
113#126—431no—
114#124—431no—
115#123—431no—
116#123—431no—
117#123—431no—
118C22⋊Q8—431no—
119C22⋊Q8D4311yescharacteristic, complemented
120#120—431no—
121C4×D4—431no—
122C4×D4—431no—
123#117—431no—
124#117—431no—
125C2×C22⋊C4—431no—
126C2×C22⋊C4—431no—
127C24—431no—
128C2×Q8C2×D4311yescharacteristic, complemented
129C2×D4—431no—
130C2×D4—431no—
131C2×D4—431no—
132C22×C4—431no—
133C22×C4—431no—
134C22×C4—431no—
135C22×C4—431no—
136C22×C4C2×D4311yescharacteristic
137C4⋊C4—431no—
138C4⋊C4—431no—
139C4⋊C4—431no—
140C4⋊C4—431no—
141C4⋊C4—431no—
142C4⋊C4C2×D4311yescharacteristic, complemented
143C4⋊C4C2×D4311yescharacteristic, complemented
144C4⋊C4C2×D4311yescharacteristic, complemented
145C22⋊C4—431no—
146C22⋊C4—431no—
147C22⋊C4—431no—
148C22⋊C4—431no—
149C22⋊C4—431no—
150C22⋊C4—431no—
151C22⋊C4—431no—
152C22⋊C4—431no—
153C22⋊C4—431no—
154C22⋊C4—431no—
155C22⋊C4—431no—
156C22⋊C4—431no—
157C22⋊C4C2×D4311yescharacteristic
158C22⋊C4C2×D4311yescharacteristic
159C42—431no—
160C42—431no—
161C42—431no—
162C23—431no—
163C23—431no—
164C23—431no—
165C23—862no—
166C23—862no—
167C23—1721no—
168C23C22×D4311yescharacteristic
169Q8—41no—
170D4—862no—
171D4—862no—
172D4—1721no—
173C2×C4—41no—
174C2×C4—431no—
175C2×C4—431no—
176C2×C4—431no—
177C2×C4—431no—
178C2×C4—431no—
179C2×C4—862no—
180C2×C4—862no—
181C2×C4—1721no—
182C2×C4—1721no—
183C2×C4C22×D4311yescharacteristic
184C2×C4C22×D4311yescharacteristic
185C2×C4C22×D4311yescharacteristic
186C2×C4C22×D4311yescharacteristic
187C2×C4C22×D4311yescharacteristic
188C2×C4C22×D4311yescharacteristic
189C22—21no—
190C22—21no—
191C22—432no—
192C22—861no—
193C22—861no—
194C22—861no—
195C22—861no—
196C22—861no—
197C22—861no—
198C22—861no—
199C22—861no—
200C22—1724no—
201C22#1062190212yes—
202C22C23×D4311yescharacteristic
203C4—21no—
204C4—21no—
205C4—21no—
206C4—21no—
207C4—21no—
208C4—21no—
209C4—861no—
210C4—861no—
211C4—861no—
212C4—861no—
213C4—861no—
214C2—22no—
215C2—862no—
216C2—1721no—
217C2—1721no—
218C2#41×D4311yescharacteristic
219C2C2×#1062190211yescharacteristic
220C2#1306337011yescharacteristic
subgroupG/H
center, FrattiniC22C23×D43
commutator, socle, cosocleC22×C43C24
FittingC22⋊Q8×C43C2
prime radical#13063295C2
hypercenterC22⋊Q8D43
hypocenterC43#551
LCSG ▷ C22×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13063320C2semidirect
2. #13063320C2semidirect
3. #13063314C2semidirect
4. #13063310C2semidirect
5. #13063310C2semidirect
6. #13063309C2semidirect
7. #13063301C2semidirect
9. #13063287C2semidirect
10. C4×C22⋊D43C2semidirect
11. #13063283C2semidirect
12. #13063281C2semidirect
13. C2×(C2×D43)⋊C4C2semidirect
14. C22⋊C4×D43C2semidirect
15. C22⋊Q8×C43C2semidirect
17. C2×Q8×C43C22semidirect
25. C2×C4×D43C22semidirect
26. C4⋊C4×C43C22semidirect
27. C4⋊C4×C43C22semidirect
28. C4⋊C4×C43C22semidirect
40. (C2×D43)⋊C4C22semidirect
41. (C2×D43)⋊C4C22semidirect
42. (C2×D43)⋊C4C22semidirect
43. C4⋊Dic43C22semidirect
44. C4⋊Dic43C22semidirect
45. Dic43⋊C4C22semidirect
46. Dic43⋊C4C22semidirect
47. Dic43⋊C4C22semidirect
48. C4×Dic43C22semidirect
49. C4×Dic43C22semidirect
50. C4×Dic43C22semidirect
111. C43#551semidirect
119. C22⋊Q8D43semidirect
128. C2×Q8C2×D43semidirect
142. C4⋊C4C2×D43semidirect
143. C4⋊C4C2×D43semidirect
144. C4⋊C4C2×D43semidirect

Maximal subgroups

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

subgroupindex
#130633202
#130633142
#130633102
#130633092
#130633012
#130632952
#130632872
C4×C22⋊D432
#130632832
#130632812
C2×(C2×D43)⋊C42
C22⋊C4×D432
C22⋊Q8×C432
#55143