Finite Group Databasebeta

← #15783546

Subgroups — #15783546

Order 3328.

194 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 63 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#13117151C211yesmaximal, characteristic
2#13116723C211yesmaximal, characteristic, complemented
3#13116713C211yesmaximal, characteristic, complemented
4#13113042C211yesmaximal, characteristic, complemented
5#13113027C211yesmaximal, characteristic, complemented
6#13113024C211yesmaximal, characteristic, complemented
7C13×#1398C211yesmaximal, characteristic, complemented
8#11718565C2211yescharacteristic
9C2×D208C2211yescharacteristic
10#11718361—21no—
11C4×D104—21no—
12C13×M64C2211yescharacteristic
13C13×M64C2211yescharacteristic
14C13×#346C2211yescharacteristic
15#11718102—21no—
16#11718101—21no—
17#11718098C2211yescharacteristic
18#11718097C2211yescharacteristic
19#11718041C412yescomplemented
20D416C412yescomplemented
21#88158—21no—
22C2×D104—21no—
23#88155—41no—
24C4×D52—41no—
25C2×C13×C16D411yescharacteristic
26C2×C13×C16C2311yescharacteristic
27C4×C8×C13D411yescharacteristic
28#88061—41no—
29#88059—21no—
30#88058—21no—
31#88045—41no—
32Dic104C2×C411yescharacteristic, complemented
33#88040—21no—
34D208—21no—
35D208C2×C412yes—
36D208C2×C411yescharacteristic, complemented
37C13×C32—21no—
38C13×C32C2×C412yescomplemented
39#13658—131nomaximal, Sylow
40#6127—41no—
41C2×D52—41no—
42C2×C4×D13—81no—
43C2×C8×C13D811yescharacteristic
44C2×C8×C13C2×D411yescharacteristic
45C42×C13D811yescharacteristic
46#6103—81no—
47C4⋊Dic13—41no—
48#6099—41no—
49Dic52—21no—
50D104—22no—
51D104—21no—
52D104—41no—
53#6095—41no—
54#6094—81no—
55C8×D13—81no—
56C13×C16—21no—
57C13×C16C22×C411yescharacteristic
58C13×C16#4111yescharacteristic
59#2263—131no—
60#2179—131no—
61#2177—131no—
62#1426—131no—
63#1419—131no—
64#1418—131no—
65#1398D1311yescharacteristic, complemented
66C22×D13—81no—
67C2×C4×C13—21no—
68C2×C4×C13C2×D811yescharacteristic
69C22⋊D13—81no—
70C2×Dic13—81no—
71D52—41no—
72D52—42no—
73D52—81no—
74C4×D13—81no—
75C4×D13—162no—
76Dic26—41no—
77C8×C13—21no—
78C8×C13C4×D411yescharacteristic
79C8×C13#13511yescharacteristic
80#1055—81no—
81#508—131no—
82C2×D16—131no—
83#443—261no—
84C4×D8—261no—
85SD64—132no—
86D32—132no—
87M64C2×D1311yescharacteristic
88M64C2×D1311yescharacteristic
89#368—131no—
90#367—131no—
91#359—261no—
92#357—261no—
93#346C2×D1311yescharacteristic
94C22×C13#50911yescharacteristic
95C2×D13—81no—
96C2×D13—82no—
97C2×D13—161no—
98C2×D13—161no—
99C4×C13—41no—
100C4×C13C4×D811yescharacteristic
101C4×C13#50911yescharacteristic
102Dic13—81no—
103Dic13—161no—
104#135—261no—
105C2×D8—261no—
106#131—521no—
107C4×D4—521no—
108Q32—131no—
109SD32—261no—
110D16—131no—
111D16—132no—
112D16—261no—
113C2×C16D5211yescharacteristic
114C2×C16C22×D1311yescharacteristic
115#108—261no—
116#107—261no—
117#104—521no—
118#102—521no—
119C4×C8D5211yescharacteristic
120C32—21no—
121C32C4×D1312yescomplemented
122C2×C13—21no—
123C2×C13#217711yescharacteristic
124D13—161no—
125D13—162no—
126#41—521no—
127C2×D4—521no—
128C22×C4—1041no—
129Q16—261no—
130SD16—521no—
131D8—262no—
132D8—261no—
133D8—521no—
134M16—521no—
135M16—1041no—
136C2×C8—1041no—
137C2×C8D10411yescharacteristic
138C2×C8C2×D5211yescharacteristic
139C4⋊C4—521no—
140C22⋊C4—1041no—
141C42D10411yescharacteristic
142C16—21no—
143C16C2×C4×D1311yescharacteristic
144C16#612711yescharacteristic
145C13#1365811yescharacteristic, complemented, Sylow
146C23—1041no—
147Q8—521no—
148D4—522no—
149D4—521no—
150D4—1041no—
151D4—1041no—
152C2×C4—21no—
153C2×C4—1041no—
154C2×C4—1041no—
155C2×C4—2082no—
156C2×C4C2×D10411yescharacteristic
157C8—21no—
158C8—1041no—
159C8C4×D5211yescharacteristic
160C8#8815811yescharacteristic
161C22—1041no—
162C22—1042no—
163C22—2081no—
164C22—2081no—
165C22#1171856911yescharacteristic
166C4—41no—
167C4—1041no—
168C4—2081no—
169C4C4×D10411yescharacteristic
170C4#1171856911yescharacteristic
171C2—21no—
172C2—2082no—
173C2—2081no—
174C2#1311671311yescharacteristic
subgroupG/H
centerC2#13116713
commutatorC13×C16C22×C4
FrattiniC2×C16C22×D13
FittingC13×#1398C2
socleC2×C13#2177
prime radical#13117151C2
cosocleC2×C13×C16C23
hypercenter#1398D13
hypocenterC13#13658
LCSG ▷ C13×C16 ▷ C8×C13 ▷ C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #346 ◁ #1398

Complements

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

NH ≅ G/Ntype
2. #13116723C2semidirect
3. #13116713C2semidirect
4. #13113042C2semidirect
5. #13113027C2semidirect
6. #13113024C2semidirect
7. C13×#1398C2semidirect
19. #11718041C4semidirect
20. D416C4semidirect
32. Dic104C2×C4semidirect
36. D208C2×C4semidirect
38. C13×C32C2×C4semidirect
65. #1398D13semidirect
121. C32C4×D13semidirect
145. C13#13658semidirect

Maximal subgroups

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

subgroupindex
#131171512
#131167232
#131167132
#131130422
#131130272
#131130242
C13×#13982
#1365813