Finite Group Databasebeta

← #15777306

Subgroups — #15777306

Order 3328.

194 conjugacy classes of subgroups; only the 67 normal subgroups are shown.

normal subgroups only

This group has 194 conjugacy classes of subgroups — too many to draw. Only its 67 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#13117118C211yesmaximal, characteristic
2#13116744C211yesmaximal, characteristic
3#13114241C211yesmaximal, characteristic
4#13114231C211yesmaximal, characteristic
5#13112895C211yesmaximal, characteristic
6#13112892C211yesmaximal, characteristic
7C13×#1371C211yesmaximal, characteristic
8#11718511—21no—
9#11718510—21no—
10#11718343C2211yescharacteristic
11#11718343C2211yescharacteristic
12C8×Dic26C2211yescharacteristic
13C4×C13×C16C2211yescharacteristic
14C13×#335C2211yescharacteristic
15C13×#335C2211yescharacteristic
16#11718097—21no—
17#11718097—21no—
18#11718094—21no—
19#11718093—21no—
20#11718074—21no—
21#11718073—21no—
22C4⋊#6090C2211yescharacteristic
23C2×Dic52—41no—
24#88123—21no—
25#88123—21no—
26C4×Dic26D411yescharacteristic
27C2×C13×C16D411yescharacteristic
28C2×C13×C16D411yescharacteristic
29C13×C4⋊C8—21no—
30C13×C4⋊C8—21no—
31C4×C8×C13C2311yescharacteristic
32#88058—21no—
33#88058—21no—
34#88058—21no—
35#88058—21no—
36#88058—41no—
37#88056—41no—
38#88056—41no—
39#88054—21no—
40C8×Dic13—21no—
41C2×#6090—21no—
42C4⋊#1055D411yescharacteristic
43#12462—131nomaximal, Sylow
44C2×Dic26—41no—
45C2×Dic26—41no—
46C2×Dic26D811yescharacteristic
47C2×C8×C13—41no—
48C2×C8×C13—41no—
49C2×C8×C13C2×D411yescharacteristic
50C2×C8×C13#4111yescharacteristic
51C42×C13C2×D411yescharacteristic
52C4⋊Dic13—41no—
53C4⋊Dic13—41no—
54C4⋊Dic13—41no—
55C4⋊Dic13—41no—
56C4⋊Dic13D811yescharacteristic
57#6101—21no—
58C4×Dic13—21no—
59C2×#1055—21no—
60Dic52—82no—
61C13×C16—21no—
62C13×C16Q1612yescomplemented
63#6090—41no—
64#2254—131no—
65#2183—131no—
66#1676—131no—
67#1674—131no—
68#1371D1311yescharacteristic
69#1365—131no—
70#1364—131no—
71C2×C4×C13#12111yescharacteristic
72C2×C4×C13C2×D811yescharacteristic
73C2×C4×C13#13511yescharacteristic
74C2×Dic13—21no—
75C2×Dic13—21no—
76C2×Dic13—81no—
77C2×Dic13—81no—
78Dic26—21no—
79Dic26—21no—
80Dic26—81no—
81Dic26—81no—
82Dic26—161no—
83C8×C13—21no—
84C8×C13—81no—
85C8×C13—81no—
86C8×C13C2×Q1611yescharacteristic
87C8×C13#13711yescharacteristic
88#1055—41no—
89#500—131no—
90#500—131no—
91#477—261no—
92#462—261no—
93C8×Q8—131no—
94#367—261no—
95#367—261no—
96C4⋊C16—131no—
97C4⋊C16—261no—
98#346—261no—
99C4×C16C2×D1311yescharacteristic
100#335C2×D1311yescharacteristic
101#335C2×D1311yescharacteristic
102#333—261no—
103#332—261no—
104C22×C13#46611yescharacteristic
105C4×C13—21no—
106C4×C13#46211yescharacteristic
107C4×C13#47311yescharacteristic
108C4×C13#50911yescharacteristic
109C4×C13#51011yescharacteristic
110Dic13—41no—
111Dic13—41no—
112Dic13—161no—
113Dic13—161no—
114C2×Q16—521no—
115C4⋊Q8—261no—
116C4⋊Q8—261no—
117C4×Q8—131no—
118C2×C16—261no—
119C2×C16D5211yescharacteristic
120C2×C16D5211yescharacteristic
121#107—261no—
122#107—261no—
123#107—261no—
124#107—261no—
125#107—521no—
126C4⋊C8—21no—
127C4⋊C8—21no—
128C4⋊C8—131no—
129C4⋊C8—261no—
130#103—521no—
131#103—521no—
132C4×C8—261no—
133C4×C8C22×D1311yescharacteristic
134C2×C13#167411yescharacteristic
135C2×C13#222011yescharacteristic
136C2×C13#222311yescharacteristic
137C2×Q8—131no—
138C2×Q8—521no—
139C2×Q8—521no—
140Q16—1042no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8—261no—
144C2×C8C2×D5211yescharacteristic
145C2×C8#613111yescharacteristic
146C4⋊C4—131no—
147C4⋊C4—261no—
148C4⋊C4—521no—
149C4⋊C4—521no—
150C4⋊C4—521no—
151C4⋊C4—521no—
152C42—261no—
153C42D4×D1311yescharacteristic
154C16—21no—
155C16—521no—
156C16Dic5212yescomplemented
157C13#1246211yescharacteristic, complemented, Sylow
158Q8—261no—
159Q8—261no—
160Q8—1041no—
161Q8—1041no—
162Q8—2081no—
163C2×C4—261no—
164C2×C4—261no—
165C2×C4—1041no—
166C2×C4—1041no—
167C2×C4#8814911yescharacteristic
168C2×C4D8×D1311yescharacteristic
169C2×C4#8817311yescharacteristic
170C8—21no—
171C8—81no—
172C8—81no—
173C8—521no—
174C8C2×Dic5211yescharacteristic
175C8#8816311yescharacteristic
176C22#1171854411yescharacteristic
177C4—21no—
178C4—521no—
179C4—521no—
180C4—2081no—
181C4—2081no—
182C4#1171851011yescharacteristic
183C4#1171855711yescharacteristic
184C4#1171857211yescharacteristic
185C4#1171857911yescharacteristic
186C2#1311423111yescharacteristic
187C2#1311695011yescharacteristic
188C2#1311696711yescharacteristic
subgroupG/H
centerC22#11718544
commutator, cosocleC4×C8×C13C23
FrattiniC4×C8C22×D13
FittingC13×#1371C2
socle, prime radicalC22×C13#466
hypercenter#1371D13
hypocenterC13#12462
LCSG ▷ C4×C8×C13 ▷ C2×C4×C13 ▷ C2×C13 ▷ C13
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1371

Complements

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

NH ≅ G/Ntype
62. C13×C16Q16semidirect
156. C16Dic52semidirect
157. C13#12462semidirect

Maximal subgroups

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

subgroupindex
#131171182
#131167442
#131142412
#131142312
#131128952
#131128922
C13×#13712
#1246213