Finite Group Databasebeta

← #33000381

Subgroups — #33000381

Order 18688.

172 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 172 conjugacy classes of subgroups — too many to draw. Only its 55 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#22612207C211yesmaximal, characteristic, complemented
2#22612108C211yesmaximal, characteristic
3#22612104C211yesmaximal, characteristic
4#22611767C211yesmaximal, characteristic
5#22608006C211yesmaximal, characteristic, complemented
6#22607993C211yesmaximal, characteristic, complemented
7C73×#1366C211yesmaximal, characteristic, complemented
8#17989005—21no—
9#17988989C2211yescharacteristic
10#17988705C2211yescharacteristic
11#17988414—21no—
12#17988412—21no—
13#17988410—21no—
14#17988409—21no—
15#17988408C2211yescharacteristic
16#17988398—21no—
17#17988396—21no—
18#17988372—21no—
19C4×#11924003C2211yescharacteristic
20#499×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#364×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24#14556597—21no—
25#14556583—21no—
26#14556531—21no—
27#14556530—41no—
28C2×#11924003D411yescharacteristic
29C2×#11924003D411yescharacteristic
30C16×D73—41no—
31#14556527D411yescharacteristic
32#14556525—21no—
33#14556523—21no—
34#14556519—21no—
35#125×C73—21no—
36M32×C73—21no—
37M32×C73—21no—
38#107×C73—21no—
39#106×C73—21no—
40C4×C8×C73C2311yescharacteristic
41#11924028—21no—
42Dic292Q1611yescharacteristic
43#11924017—21no—
44D584Q1611yescharacteristic
45#11924012—21no—
46#11924011—41no—
47C8×D73—41no—
48C4⋊Dic73—41no—
49#11924007—81no—
50#11924003—21no—
51#11924003—41no—
52#11924003SD1611yescharacteristic
53#11924003SD1611yescharacteristic
54C2×C8×C73C2×D411yescharacteristic
55C2×C8×C73C2×D411yescharacteristic
56C4⋊C4×C73—41no—
57C4⋊C4×C73—81no—
58C42×C73#4111yescharacteristic
59C16×C73—41no—
60C16×C73—41no—
61C2×C4×C73—21no—
62C2×C4×C73—81no—
63C2×C4×C73#12111yescharacteristic
64C22⋊D73—41no—
65C2×Dic73—81no—
66D292—21no—
67C4×D73—41no—
68Dic146—21no—
69C8×C73C2×SD1611yescharacteristic
70C8×C73C2×Q1611yescharacteristic
71C8×C73#13511yescharacteristic
72C8×C73#13711yescharacteristic
73#10596831—41no—
74C22×C73#47211yescharacteristic
75C2×D73—41no—
76C4×C73—41no—
77C4×C73—161no—
78C4×C73#46111yescharacteristic
79C4×C73#46711yescharacteristic
80Dic73—41no—
81Dic73—161no—
82#12464—731nomaximal, Sylow
83C2×C73—21no—
84C2×C73#167511yescharacteristic
85D73—81no—
86#2253—731no—
87#2231—731no—
88#2231—731no—
89#2170—731no—
90#1373—731no—
91#1366—731no—
92#1366D7311yescharacteristic, complemented
93C73#1246411yescharacteristic, complemented, Sylow
94#504—1461no—
95#499—731no—
96#499C2×D7311yescharacteristic
97#443—731no—
98#367—1461no—
99#366—1461no—
100#365—1461no—
101#365—1461no—
102#364—731no—
103#364C2×D7311yescharacteristic
104#364C2×D7311yescharacteristic
105#360—1461no—
106#360—1461no—
107#350—1461no—
108C4×C16—731no—
109#135—731no—
110#131—1461no—
111#125—21no—
112#125—1461no—
113M32—21no—
114M32—21no—
115M32—2921no—
116M32—1461no—
117C2×C16—2921no—
118C2×C16—731no—
119C2×C16—731no—
120#108—731no—
121#107—21no—
122#107—1461no—
123#106—21no—
124#106—1461no—
125#104—1461no—
126C4×C8C22×D7311yescharacteristic
127#41—1461no—
128Q16—731no—
129SD16—1461no—
130D8—731no—
131M16—2921no—
132M16—1461no—
133C2×C8—2921no—
134C2×C8D4×D7311yescharacteristic
135C2×C8D4×D7311yescharacteristic
136C4⋊C4—41no—
137C4⋊C4—81no—
138C4⋊C4—2921no—
139C4⋊C4—5841no—
140C42#1192402811yescharacteristic
141C16—41no—
142C16—41no—
143C16—2921no—
144C16—731no—
145C16—731no—
146C16—1461no—
147Q8—1461no—
148D4—2921no—
149D4—1461no—
150C2×C4—21no—
151C2×C4—81no—
152C2×C4—2921no—
153C2×C4—5841no—
154C2×C4#1455656411yescharacteristic
155C8—2921no—
156C8SD16×D7311yescharacteristic
157C8Q16×D7311yescharacteristic
158C8#1455661211yescharacteristic
159C8#1455662311yescharacteristic
160C22—2921no—
161C22#1798885611yescharacteristic
162C4—41no—
163C4—161no—
164C4—2921no—
165C4—11681no—
166C4#1798879111yescharacteristic
167C4#1798882711yescharacteristic
168C2—21no—
169C2—5841no—
170C2#2260932911yescharacteristic
subgroupG/H
centerC2#22609329
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1366C2
socleC2×C73#1675
prime radical#14556613D4
hypercenter#1366D73
hypocenterC73#12464
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1366

Complements

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

NH ≅ G/Ntype
1. #22612207C2semidirect
5. #22608006C2semidirect
6. #22607993C2semidirect
7. C73×#1366C2semidirect
92. #1366D73semidirect
93. C73#12464semidirect

Maximal subgroups

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

subgroupindex
#226122072
#226121082
#226121042
#226117672
#226080062
#226079932
C73×#13662
#1246473