Finite Group Databasebeta

← #16069342

Subgroups — #16069342

Order 3328.

1778 conjugacy classes of subgroups; only the 539 normal subgroups are shown.

normal subgroups only

This group has 1778 conjugacy classes of subgroups — too many to draw. Only its 539 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#13123100C213yesmaximal
2#13123096C2112yesmaximal, complemented
3#13118103C2112yesmaximal, complemented
4#13117214C213yesmaximal
5C13×#2840C211yesmaximal, characteristic
6C24×Dic13C2211yescharacteristic
7C2×Q8×Dic13C2214yescomplemented
8C2×#88131C2216yes—
9C13×#393C22112yes—
10C13×#379C2213yes—
11#11718908C2213yes—
12#11718890C22112yescomplemented
13#11718610C22112yes—
14#11718609C22124yes—
15#11718604C2216yes—
16#11718603C22112yes—
17C22⋊C4×Dic13C22112yes—
18#11718320C22112yescomplemented
19#11718318C22124yescomplemented
20#11718310C22112yescomplemented
21C25×C13C2311yescharacteristic
22C22×Q8×C13C2314yes—
23C23×Dic13—44no—
24C23×Dic13Q818yescomplemented
25C23×Dic13C2313yes—
26C23×Dic13C2313yes—
27C2×C13×C22⋊C4C2316yes—
28C2×C13×C22⋊C4C23112yes—
29C2×C22⋊Dic13C2316yes—
30C2×C22⋊Dic13C23112yes—
31Q8×Dic13—48no—
32C2×C4⋊Dic13C23112yes—
33C2×#6101C23112yes—
34C2×#6101C23124yes—
35C2×C4×Dic13C23112yes—
36#88131—412no—
37C13×#95C23112yes—
38#88071C23112yes—
39#88071C23124yes—
40#36674—131nomaximal, Sylow
41C24×C13—42no—
42C24×C13—44no—
43C24×C13C2×Q814yes—
44C24×C13C2413yes—
45C2×Q8×C13—44no—
46C2×Q8×C13—48no—
47C22×C4×C13C24112yes—
48C22×Dic13—212no—
49C22×Dic13—416no—
50C22×Dic13—46no—
51C22×Dic13C2×Q8112yes—
52C22×Dic13C2×Q8112yes—
53C22×Dic13C24112yes—
54C22×Dic13C2413yes—
55C22×Dic13C2411yescharacteristic
56C13×C22⋊C4—46no—
57C13×C22⋊C4—412no—
58C22⋊Dic13—46no—
59C22⋊Dic13—412no—
60C4⋊Dic13—412no—
61#6101—412no—
62#6101—424no—
63C4×Dic13—224no—
64#2842—133no—
65#2841—1312no—
66#2840D1311yescharacteristic
67#2396—1312no—
68#2280—133no—
69C23×C13—26no—
70C23×C13—212no—
71C23×C13—44no—
72C23×C13—48no—
73C23×C13—416no—
74C23×C13C22×Q816yes—
75C23×C13C2511yescharacteristic
76Q8×C13—416no—
77C2×C4×C13—212no—
78C2×C4×C13—224no—
79C2×Dic13—26no—
80C2×Dic13—224no—
81C2×Dic13—212no—
82C2×Dic13—224no—
83C2×Dic13—412no—
84C2×Dic13C22×Q816yes—
85C2×Dic13C22×Q812yes—
86C2×Dic13H(5,𝔽2)14yes—
87C24×C4—131no—
88C2×C4×Q8—134no—
89C2×#117—136no—
90#400—1312no—
91#399—1312no—
92#398—1324no—
93#396—1324no—
94#395—1312no—
95#393C2×D13112yes—
96#381—136no—
97#380—1312no—
98#379—133no—
99#379C2×D1313yes—
100C4×C4⋊C4—1312no—
101C4×C22⋊C4—1312no—
102C22×C13—26no—
103C22×C13—212no—
104C22×C13—416no—
105C22×C13—412no—
106C22×C13C23×Q811yescharacteristic
107C22×C13C2×H(5,𝔽2)12yes—
108C22×C13#58514yes—
109C4×C13—412no—
110Dic13—26no—
111Dic13—412no—
112Dic13#54314yes—
113C25C22×D1311yescharacteristic
114C22×Q8C22×D1314yes—
115C23×C4—133no—
116C23×C4—138no—
117C23×C4—133no—
118C23×C4—524no—
119C4×Q8—528no—
120#117—5212no—
121C2×C4⋊C4—1312no—
122C2×C4⋊C4—1312no—
123C2×C4⋊C4—1324no—
124C2×C22⋊C4—136no—
125C2×C22⋊C4—1312no—
126C2×C22⋊C4C22×D1316yes—
127C2×C22⋊C4C22×D13112yes—
128C2×C42—1312no—
129#95—1324no—
130#95—1312no—
131#95C22×D13112yes—
132C2×C13—46no—
133C2×C13C2×#54311yescharacteristic
134C2×C13#345812yes—
135C2×C13#352914yes—
136C24—42no—
137C24—44no—
138C24Q8×D1314yes—
139C24C23×D1313yes—
140C2×Q8—44no—
141C2×Q8—48no—
142C22×C4—131no—
143C22×C4—1312no—
144C22×C4—133no—
145C22×C4—1312no—
146C22×C4—1312no—
147C22×C4—2612no—
148C22×C4—5216no—
149C22×C4—526no—
150C22×C4C23×D13112yes—
151C4⋊C4—5212no—
152C4⋊C4—5212no—
153C4⋊C4—5224no—
154C22⋊C4—46no—
155C22⋊C4—412no—
156C22⋊C4—526no—
157C22⋊C4—5212no—
158C42—2624no—
159C13#3667411yescharacteristic, complemented, Sylow
160C23—26no—
161C23—212no—
162C23—44no—
163C23—48no—
164C23—416no—
165C23C2×Q8×D1316yes—
166C23C24×D1311yescharacteristic
167Q8—416no—
168C2×C4—212no—
169C2×C4—224no—
170C2×C4—132no—
171C2×C4—134no—
172C2×C4—136no—
173C2×C4—2624no—
174C2×C4—266no—
175C2×C4—2612no—
176C2×C4—2624no—
177C2×C4—5212no—
178C22—26no—
179C22—212no—
180C22—416no—
181C22—412no—
182C22C22×Q8×D1311yescharacteristic
183C22D13×H(5,𝔽2)12yes—
184C22#1171965014yes—
185C4—412no—
186C4—134no—
187C4—266no—
188C4—5212no—
189C2—46no—
190C2D13×#54311yescharacteristic
191C2#1312823812yes—
192C2#1312897614yes—
subgroupG/H
center, FrattiniC23C24×D13
commutator, socle, cosocleC23×C13C25
FittingC13×#2840C2
prime radicalC25×C13C23
hypercenter#2840D13
hypocenterC13#36674
LCSG ▷ C23×C13 ▷ C13
UCSC1 ◁ C23 ◁ #2840

Complements

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

NH ≅ G/Ntype
2. #13123096C2semidirect
3. #13118103C2semidirect
7. C2×Q8×Dic13C22semidirect
12. #11718890C22semidirect
18. #11718320C22semidirect
19. #11718318C22semidirect
20. #11718310C22semidirect
24. C23×Dic13Q8semidirect
159. C13#36674semidirect

Maximal subgroups

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

subgroupindex
#131231002
#131230962
#131181032
#131172142
C13×#28402
#3667413