Finite Group Databasebeta

← D13×C22⋊Q8 #11719331

Subgroups — D13×C22⋊Q8 #11719331

Order 832.

322 conjugacy classes of subgroups; only the 121 normal subgroups are shown.

normal subgroups only

This group has 322 conjugacy classes of subgroups — too many to draw. Only its 121 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×Q8×D13C211yesmaximal, characteristic, complemented
2C22×C4×D13C211yesmaximal, characteristic
3C13×C22⋊Q8C211yesmaximal, characteristic, complemented
4#88200C211yesmaximal, characteristic, complemented
5#88178C211yesmaximal, characteristic, complemented
6#88151C211yesmaximal, characteristic, complemented
7#88150C212yesmaximal, complemented
8C4⋊C4×D13C211yesmaximal, characteristic, complemented
9C4⋊C4×D13C212yesmaximal, complemented
10C22⋊C4×D13C212yesmaximal
11#88132C212yesmaximal, complemented
12C23×D13C2211yescharacteristic
13C2×Q8×C13C2211yescharacteristic, complemented
14C22×C4×C13C2211yescharacteristic
15C22×Dic13C2211yescharacteristic
16Q8×D13—24no—
17C2×C4×D13—24no—
18C2×C4×D13C2212yes—
19C2×C4×D13C2212yes—
20C2×C4×D13C2211yescharacteristic
21C2×C4×D13C2211yescharacteristic
22C2×C4×D13C2211yescharacteristic
23C2×C4×D13C2211yescharacteristic
24C2×Dic26C2212yescomplemented
25C2×Dic26C2211yescharacteristic, complemented
26C13×C4⋊C4C2212yescomplemented
27C13×C4⋊C4C2211yescharacteristic, complemented
28C13×C22⋊C4C2212yes—
29C22⋊Dic13C2212yes—
30#6103C2212yes—
31#6103C2212yes—
32C4⋊Dic13C2212yescomplemented
33C4⋊Dic13C2211yescharacteristic, complemented
34#6101C2212yescomplemented
35#6101C2212yescomplemented
36#6101C2212yescomplemented
37C23×C13C2311yescharacteristic
38C22×D13—22no—
39C22×D13—22no—
40C22×D13Q814yescomplemented
41C22×D13C2311yescharacteristic
42C22×D13C2311yescharacteristic
43Q8×C13—22no—
44C2×C4×C13—22no—
45C2×C4×C13C2311yescharacteristic
46C2×C4×C13C2312yes—
47C2×C4×C13C2312yes—
48C2×C4×C13C2311yescharacteristic
49C2×Dic13—22no—
50C2×Dic13C2312yes—
51C2×Dic13C2311yescharacteristic
52C2×Dic13C2312yes—
53C2×Dic13C2311yescharacteristic
54C4×D13—22no—
55C4×D13—24no—
56C4×D13—24no—
57C4×D13—22no—
58C4×D13—22no—
59C4×D13D414yes—
60Dic26—22no—
61Dic26—24no—
62C2×C22⋊Q8—131nomaximal, Sylow
63C22×C13—21no—
64C22×C13—21no—
65C22×C13C2×Q812yescomplemented
66C22×C13C2411yescharacteristic
67C2×D13—21no—
68C2×D13—21no—
69C2×D13—28no—
70C2×D13C2×D412yes—
71C2×D13C2×Q812yes—
72C2×D13C2×Q812yescomplemented
73C2×D13#4112yes—
74C4×C13—22no—
75C4×C13—21no—
76C4×C13—22no—
77C4×C13C2×D412yes—
78Dic13—22no—
79Dic13—21no—
80Dic13—22no—
81Dic13C2×D412yes—
82C22×Q8—131no—
83C23×C4—131no—
84C22⋊Q8—131no—
85C22⋊Q8—131no—
86C22⋊Q8—132no—
87C22⋊Q8—131no—
88C22⋊Q8—132no—
89C22⋊Q8D1311yescharacteristic, direct product factor
90C2×C4⋊C4—131no—
91C2×C4⋊C4—132no—
92C2×C22⋊C4—132no—
93C2×C13—22no—
94C2×C13C22×D411yescharacteristic
95C2×C13C22×Q811yescharacteristic
96C2×C13C2×#4111yescharacteristic
97D13—22no—
98D13C22⋊Q814yesdirect product factor
99C24—131no—
100C2×Q8—132no—
101C2×Q8—131no—
102C2×Q8—264no—
103C2×Q8C2×D1311yescharacteristic, complemented
104C22×C4—131no—
105C22×C4—131no—
106C22×C4—132no—
107C22×C4—132no—
108C22×C4—131no—
109C22×C4—131no—
110C22×C4—131no—
111C22×C4—264no—
112C22×C4C2×D1311yescharacteristic
113C4⋊C4—132no—
114C4⋊C4—132no—
115C4⋊C4—132no—
116C4⋊C4—131no—
117C4⋊C4—132no—
118C4⋊C4C2×D1311yescharacteristic, complemented
119C4⋊C4C2×D1312yescomplemented
120C22⋊C4—132no—
121C22⋊C4—132no—
122C22⋊C4—132no—
123C22⋊C4C2×D1312yes—
124C13C2×C22⋊Q811yescharacteristic, complemented, Sylow
125C23—131no—
126C23—134no—
127C23—131no—
128C23—262no—
129C23—262no—
130C23C22×D1311yescharacteristic
131Q8—22no—
132Q8—264no—
133Q8—262no—
134C2×C4—22no—
135C2×C4—131no—
136C2×C4—134no—
137C2×C4—132no—
138C2×C4—132no—
139C2×C4—131no—
140C2×C4—262no—
141C2×C4—264no—
142C2×C4—262no—
143C2×C4—264no—
144C2×C4—262no—
145C2×C4—262no—
146C2×C4C22×D1312yes—
147C2×C4C22×D1312yes—
148C2×C4C22×D1311yescharacteristic
149C2×C4C22×D1311yescharacteristic
150C22—21no—
151C22—21no—
152C22—132no—
153C22—132no—
154C22—132no—
155C22—132no—
156C22—268no—
157C22—261no—
158C22—261no—
159C22Q8×D1312yescomplemented
160C22C23×D1311yescharacteristic
161C4—21no—
162C4—22no—
163C4—22no—
164C4—132no—
165C4—261no—
166C4—262no—
167C4—262no—
168C4D4×D1312yes—
169C2—22no—
170C2—134no—
171C2—262no—
172C2C2×D4×D1311yescharacteristic
173C2C2×Q8×D1311yescharacteristic
174C2#41×D1311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D13
commutator, socle, cosocleC22×C13C24
FittingC13×C22⋊Q8C2
prime radicalC23×D13C22
hypercenterC22⋊Q8D13
hypocenterC13C2×C22⋊Q8
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×Q8×D13C2semidirect
3. C13×C22⋊Q8C2semidirect
4. #88200C2semidirect
5. #88178C2semidirect
6. #88151C2semidirect
7. #88150C2semidirect
8. C4⋊C4×D13C2semidirect
9. C4⋊C4×D13C2semidirect
11. #88132C2semidirect
13. C2×Q8×C13C22semidirect
24. C2×Dic26C22semidirect
25. C2×Dic26C22semidirect
26. C13×C4⋊C4C22semidirect
27. C13×C4⋊C4C22semidirect
32. C4⋊Dic13C22semidirect
33. C4⋊Dic13C22semidirect
34. #6101C22semidirect
35. #6101C22semidirect
36. #6101C22semidirect
40. C22×D13Q8semidirect
65. C22×C13C2×Q8semidirect
72. C2×D13C2×Q8semidirect
89. C22⋊Q8D13direct (N × H)
98. D13C22⋊Q8direct (N × H)
103. C2×Q8C2×D13semidirect
118. C4⋊C4C2×D13semidirect
119. C4⋊C4C2×D13semidirect
124. C13C2×C22⋊Q8semidirect
159. C22Q8×D13semidirect

Maximal subgroups

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

subgroupindex
C2×Q8×D132
C22×C4×D132
C13×C22⋊Q82
#882002
#881782
#881512
#881502
C4⋊C4×D132
C22⋊C4×D132
#881322
C2×C22⋊Q813