Finite Group Databasebeta

← #11929216

Subgroups — #11929216

Order 1248.

292 conjugacy classes of subgroups; only the 108 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 108 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#10597792C211yesmaximal, characteristic, complemented
2C13×#237C211yesmaximal, characteristic, complemented
3C3×#6129C211yesmaximal, characteristic, complemented
4C2×#64605C212yesmaximal, complemented
5#10597748C212yesmaximal, complemented
6#10597746C212yesmaximal, complemented
7#10597745C212yesmaximal, complemented
8#10597737C211yesmaximal, characteristic, complemented
9D39⋊Q8C211yesmaximal, characteristic, complemented
10D3×Dic26C211yesmaximal, characteristic, complemented
11Dic6×D13C211yesmaximal, characteristic, complemented
12#88257—31nomaximal, Hall
13C3×D4×C13C2211yescharacteristic
14#64625C2212yes—
15C2×Dic39C2212yes—
16C4×D39C2211yescharacteristic
17Dic78C2211yescharacteristic
18C13×#67C2212yes—
19C2×Dic3×C13C2212yes—
20C4×D3×C13C2211yescharacteristic
21C13×Dic6C2211yescharacteristic
22C3×C22⋊D13C2212yes—
23C2×C3×Dic13C2212yes—
24C3×C4×D13C2211yescharacteristic
25C3×Dic26C2211yescharacteristic
26#64605C2212yes—
27#64605C2212yes—
28#64605C2212yes—
29#64605C2211yescharacteristic
30#64604C2211yescharacteristic
31#64603C2211yescharacteristic
32#64602C2211yescharacteristic
33#64601C2212yes—
34D3×Dic13C2212yes—
35Dic3×D13C2212yes—
36C13×#41—31no—
37Q8×D13—31no—
38Q8×D13—31no—
39#6129—31no—
40#6129—32no—
41#6129—32no—
42#6129D311yescharacteristic, complemented
43#6127—32no—
44#6127—31no—
45C2×Dic26—32no—
46C2×Dic26—31no—
47C22×C3×C13C2312yes—
48C2×D39C2311yescharacteristic
49C2×D3×C13C2311yescharacteristic
50C2×C3×D13C2311yescharacteristic
51C3×C4×C13C2311yescharacteristic
52Dic39C2312yes—
53Dic39C2311yescharacteristic
54C3×Dic13C2312yes—
55C3×Dic13C2311yescharacteristic
56Dic3×C13C2312yes—
57Dic3×C13C2311yescharacteristic
58Q8×C13—31no—
59D4×C13—32no—
60D4×C13C2×D311yescharacteristic
61C2×C4×C13—32no—
62C2×C4×C13—31no—
63C22⋊D13—32no—
64C22⋊D13—31no—
65C22⋊D13—31no—
66C22⋊D13C2×D312yes—
67C2×Dic13—32no—
68C2×Dic13—32no—
69C2×Dic13C2×D312yes—
70D52—31no—
71C4×D13—32no—
72C4×D13—31no—
73C4×D13—32no—
74C4×D13C2×D311yescharacteristic
75Dic26—31no—
76Dic26—31no—
77Dic26—32no—
78Dic26—32no—
79Dic26—32no—
80Dic26C2×D311yescharacteristic
81#1010—131nomaximal, Hall
82C2×C3×C13—22no—
83C2×C3×C13C2411yescharacteristic
84D39—21no—
85C3×D13—21no—
86D3×C13—21no—
87C22×C13—31no—
88C22×C13C22×D312yes—
89C2×D13—31no—
90C2×D13C22×D311yescharacteristic
91C4×C13—31no—
92C4×C13—32no—
93C4×C13C22×D311yescharacteristic
94Dic13—32no—
95Dic13—31no—
96Dic13C22×D311yescharacteristic
97Dic13C22×D312yes—
98C3×#41—131no—
99D3×Q8—131no—
100D3×Q8—131no—
101#237—131no—
102#237—132no—
103#237—132no—
104#237D1311yescharacteristic, complemented
105#235—132no—
106#235—131no—
107C2×Dic6—132no—
108C2×Dic6—131no—
109C3×C132−1+411yescharacteristic, complemented, Hall
1102−1+4—391noSylow
111C2×C13—22no—
112C2×C13—61no—
113C2×C13C23×D311yescharacteristic
114D13—21no—
115D13—61no—
116C3×Q8—131no—
117C3×D4—132no—
118C3×D4C2×D1311yescharacteristic
119C2×C3×C4—132no—
120C2×C3×C4—131no—
121#67—132no—
122#67—131no—
123#67—131no—
124#67C2×D1312yes—
125C2×Dic3—132no—
126C2×Dic3—132no—
127C2×Dic3C2×D1312yes—
128D12—131no—
129C4×D3—132no—
130C4×D3—131no—
131C4×D3—132no—
132C4×D3C2×D1311yescharacteristic
133Dic6—131no—
134Dic6—131no—
135Dic6—132no—
136Dic6—132no—
137Dic6—132no—
138Dic6C2×D1311yescharacteristic
139#41—31no—
140#41—131no—
141#41—391no—
142#41—392no—
143#41—392no—
144#41—392no—
145#41—391no—
146C2×Q8—392no—
147C2×Q8—391no—
148C2×Q8—391no—
149C2×Q8—391no—
150C13#101011yescharacteristic, complemented, Sylow
151C22×C3—131no—
152C22×C3C22×D1312yes—
153C2×D3—131no—
154C2×D3C22×D1311yescharacteristic
155C3×C4—131no—
156C3×C4—132no—
157C3×C4C22×D1311yescharacteristic
158Dic3—132no—
159Dic3—131no—
160Dic3C22×D1311yescharacteristic
161Dic3C22×D1312yes—
162Q8—31no—
163Q8—131no—
164Q8—391no—
165Q8—392no—
166Q8—392no—
167Q8—392no—
168Q8—391no—
169D4—32no—
170D4—132no—
171D4—391no—
172D4—391no—
173D4—391no—
174D4—392no—
175D4D3×D1311yescharacteristic
176C2×C4—32no—
177C2×C4—31no—
178C2×C4—132no—
179C2×C4—131no—
180C2×C4—392no—
181C2×C4—392no—
182C2×C4—392no—
183C2×C4—392no—
184C2×C4—391no—
185C2×C3—22no—
186C2×C3—261no—
187C2×C3C23×D1311yescharacteristic
188D3—21no—
189D3—261no—
190C22—31no—
191C22—131no—
192C22—391no—
193C22C2×D3×D1312yes—
194C4—31no—
195C4—32no—
196C4—131no—
197C4—132no—
198C4—392no—
199C4—391no—
200C4C2×D3×D1311yescharacteristic
201C3#8825711yescharacteristic, complemented, Sylow
202C2—22no—
203C2—61no—
204C2—261no—
205C2—781no—
206C2C22×D3×D1311yescharacteristic
subgroupG/H
center, FrattiniC2C22×D3×D13
commutator, socle, cosocleC2×C3×C13C24
FittingC3×D4×C13C22
hypercenterD4D3×D13
hypocenterC3×C132−1+4
LCSG ▷ C2×C3×C13 ▷ C3×C13
UCSC1 ◁ C2 ◁ D4

Complements

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

NH ≅ G/Ntype
1. #10597792C2semidirect
2. C13×#237C2semidirect
3. C3×#6129C2semidirect
4. C2×#64605C2semidirect
5. #10597748C2semidirect
6. #10597746C2semidirect
7. #10597745C2semidirect
8. #10597737C2semidirect
9. D39⋊Q8C2semidirect
10. D3×Dic26C2semidirect
11. Dic6×D13C2semidirect
42. #6129D3semidirect
104. #237D13semidirect
109. C3×C132−1+4semidirect
150. C13#1010semidirect
201. C3#88257semidirect

Maximal subgroups

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

subgroupindex
#105977922
C13×#2372
C3×#61292
C2×#646052
#105977482
#105977462
#105977452
#105977372
D39⋊Q82
D3×Dic262
Dic6×D132
#882573
#101013