Finite Group Databasebeta

← #11719336

Subgroups — #11719336

Order 832.

292 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 105 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×#6131C211yesmaximal, characteristic, complemented
2C2×#6127C211yesmaximal, characteristic, complemented
3C13×C22⋊Q8C211yesmaximal, characteristic, complemented
4#88198C211yesmaximal, characteristic, complemented
5C4×C22⋊D13C211yesmaximal, characteristic, complemented
6#88151C211yesmaximal, characteristic, complemented
7#88148C212yesmaximal, complemented
8#88147C211yesmaximal, characteristic, complemented
9C4⋊C4×D13C212yesmaximal, complemented
10#88138C212yesmaximal, complemented
11#88137C212yesmaximal, complemented
12C2×Q8×C13C2211yescharacteristic
13C22×C4×C13C2211yescharacteristic
14C2×C22⋊D13C2212yes—
15C2×C22⋊D13C2211yescharacteristic
16#6131—24no—
17#6127—24no—
18C2×D52C2212yes—
19C2×D52C2211yescharacteristic
20C2×C4×D13C2212yes—
21C2×C4×D13C2212yes—
22C2×C4×D13C2212yes—
23C2×C4×D13C2211yescharacteristic
24C2×Dic26C2211yescharacteristic
25C13×C4⋊C4C2212yes—
26C13×C4⋊C4C2211yescharacteristic
27C13×C22⋊C4C2212yes—
28C22⋊Dic13C2211yescharacteristic
29#6103C2212yes—
30#6103C2212yes—
31#6103C2211yescharacteristic
32C4⋊Dic13C2212yes—
33#6101C2212yes—
34#6101C2212yes—
35#6101C2211yescharacteristic
36C4×Dic13C2211yescharacteristic
37C23×C13C2311yescharacteristic
38C22×D13C2311yescharacteristic
39C22×D13C2312yes—
40Q8×C13—22no—
41C2×C4×C13—22no—
42C2×C4×C13C2312yes—
43C2×C4×C13C2311yescharacteristic
44C2×C4×C13C2312yes—
45C2×C4×C13C2311yescharacteristic
46C22⋊D13—24no—
47C22⋊D13—22no—
48C2×Dic13C2311yescharacteristic
49C2×Dic13C2312yes—
50C2×Dic13C2311yescharacteristic
51C2×Dic13C2311yescharacteristic
52D52—24no—
53D52D414yescomplemented
54C4×D13—24no—
55C4×D13—24no—
56C4×D13—22no—
57C4×D13—24no—
58Dic26—22no—
59#547—131nomaximal, Sylow
60C22×C13—21no—
61C22×C13—21no—
62C22×C13—21no—
63C22×C13C2411yescharacteristic
64C2×D13—22no—
65C2×D13—22no—
66C2×D13—21no—
67C2×D13—21no—
68C2×D13—21no—
69C2×D13C2×D414yes—
70C4×C13—21no—
71C4×C13—22no—
72C4×C13—22no—
73C4×C13C2×D412yes—
74Dic13—22no—
75Dic13—21no—
76Dic13—21no—
77Dic13#4112yescomplemented
78C2×#41—131no—
79C2×#41—131no—
80C4⋊Q8—131no—
81#123—132no—
82#123—132no—
83C22⋊Q8—131no—
84C22⋊Q8D1311yescharacteristic, complemented
85#121—132no—
86C4×D4—131no—
87C4×D4—131no—
88C2×C4⋊C4—132no—
89C2×C13—41no—
90C2×C13C22×D411yescharacteristic
91C2×C13C2×#4111yescharacteristic
92C2×C132−1+411yescharacteristic
93D13—24no—
94D13—41no—
95#41—264no—
96#41—264no—
97C2×Q8—131no—
98C2×Q8C2×D1311yescharacteristic
99C2×D4—131no—
100C2×D4—132no—
101C2×D4—131no—
102C2×D4—132no—
103C22×C4—132no—
104C22×C4—132no—
105C22×C4—132no—
106C22×C4—131no—
107C22×C4C2×D1311yescharacteristic
108C4⋊C4—131no—
109C4⋊C4—132no—
110C4⋊C4—132no—
111C4⋊C4—132no—
112C4⋊C4C2×D1312yes—
113C4⋊C4C2×D1311yescharacteristic
114C22⋊C4—131no—
115C22⋊C4—132no—
116C22⋊C4—131no—
117C22⋊C4—132no—
118C22⋊C4C2×D1312yes—
119C42—131no—
120C13#54711yescharacteristic, complemented, Sylow
121C23—132no—
122C23—131no—
123C23C22×D1311yescharacteristic
124Q8—22no—
125Q8—262no—
126D4—134no—
127D4—264no—
128D4—262no—
129D4—264no—
130C2×C4—22no—
131C2×C4—131no—
132C2×C4—131no—
133C2×C4—131no—
134C2×C4—132no—
135C2×C4—264no—
136C2×C4—264no—
137C2×C4—264no—
138C2×C4—262no—
139C2×C4C22×D1312yes—
140C2×C4C22×D1311yescharacteristic
141C2×C4C22×D1312yes—
142C2×C4C22×D1311yescharacteristic
143C22—21no—
144C22—21no—
145C22—21no—
146C22—134no—
147C22—262no—
148C22—262no—
149C22—261no—
150C22—261no—
151C22—261no—
152C22C23×D1311yescharacteristic
153C4—21no—
154C4—22no—
155C4—22no—
156C4—132no—
157C4—261no—
158C4—262no—
159C4—261no—
160C4D4×D1312yes—
161C2—41no—
162C2—264no—
163C2—521no—
164C2C2×D4×D1311yescharacteristic
165C2#8825411yescharacteristic
166C2#41×D1311yescharacteristic
subgroupG/H
center, FrattiniC22C23×D13
commutator, socle, cosocleC22×C13C24
FittingC13×C22⋊Q8C2
hypercenterC22⋊Q8D13
hypocenterC13#547
LCSG ▷ C22×C13 ▷ C13
UCSC1 ◁ C22 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C2×#6131C2semidirect
2. C2×#6127C2semidirect
3. C13×C22⋊Q8C2semidirect
4. #88198C2semidirect
5. C4×C22⋊D13C2semidirect
6. #88151C2semidirect
7. #88148C2semidirect
8. #88147C2semidirect
9. C4⋊C4×D13C2semidirect
10. #88138C2semidirect
11. #88137C2semidirect
53. D52D4semidirect
77. Dic13#41semidirect
84. C22⋊Q8D13semidirect
120. C13#547semidirect

Maximal subgroups

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

subgroupindex
C2×#61312
C2×#61272
C13×C22⋊Q82
#881982
C4×C22⋊D132
#881512
#881482
#881472
C4⋊C4×D132
#881382
#881372
#54713