Finite Group Databasebeta

← #33000397

Subgroups — #33000397

Order 18688.

186 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 186 conjugacy classes of subgroups — too many to draw. Only its 53 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#22612178C211yesmaximal, characteristic, complemented
2#22612104C211yesmaximal, characteristic
3#22612013C211yesmaximal, characteristic
4#22611772C211yesmaximal, characteristic
5#22607998C211yesmaximal, characteristic, complemented
6#22607969C211yesmaximal, characteristic, complemented
7C73×#1366C211yesmaximal, characteristic, complemented
8#17989030—21no—
9#17989005—21no—
10#17988967C2211yescharacteristic
11#17988705C2211yescharacteristic
12#17988409—21no—
13#17988408C2211yescharacteristic
14#17988404—21no—
15#17988396—21no—
16#17988390—21no—
17#17988390—21no—
18#17988372—21no—
19#17988363C2211yescharacteristic
20#499×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#364×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24C2×Dic292—21no—
25C2×Dic292—21no—
26#14556597—21no—
27#14556591—21no—
28Dic584—41no—
29#14556536—41no—
30#14556531—21no—
31#14556530—41no—
32C2×#11924003D411yescharacteristic
33C2×#11924003D411yescharacteristic
34C16×D73—41no—
35#14556527D411yescharacteristic
36#14556519—21no—
37#125×C73—21no—
38M32×C73—21no—
39M32×C73—21no—
40#107×C73—21no—
41#106×C73—21no—
42C4×C8×C73C2311yescharacteristic
43#11924028—21no—
44C2×Dic146—41no—
45Dic292—41no—
46Dic292—41no—
47Dic292—41no—
48Dic292—41no—
49Dic292SD1611yescharacteristic
50#11924017—21no—
51D584SD1611yescharacteristic
52#11924012—21no—
53#11924011—41no—
54C8×D73—41no—
55C4⋊Dic73—81no—
56#11924003—21no—
57#11924003—21no—
58#11924003—41no—
59C2×C8×C73C2×D411yescharacteristic
60C2×C8×C73C2×D411yescharacteristic
61C4⋊C4×C73—41no—
62C4⋊C4×C73—81no—
63C42×C73#4111yescharacteristic
64C16×C73—41no—
65C16×C73—41no—
66C2×C4×C73—21no—
67C2×C4×C73—81no—
68C2×C4×C73#12111yescharacteristic
69C22⋊D73—41no—
70C2×Dic73—81no—
71D292—21no—
72C4×D73—41no—
73Dic146—21no—
74Dic146—81no—
75Dic146—81no—
76C8×C73C2×SD1611yescharacteristic
77C8×C73#13511yescharacteristic
78C8×C73#13511yescharacteristic
79C8×C73AGL(1,ℤ/8)11yescharacteristic
80#10596831—41no—
81C22×C73#47211yescharacteristic
82C2×D73—41no—
83C4×C73—41no—
84C4×C73—161no—
85C4×C73#46311yescharacteristic
86C4×C73#46511yescharacteristic
87Dic73—41no—
88Dic73—161no—
89#12466—731nomaximal, Sylow
90C2×C73—21no—
91C2×C73#167711yescharacteristic
92D73—81no—
93#2245—731no—
94#2231—731no—
95#2214—731no—
96#2171—731no—
97#1369—731no—
98#1366D7311yescharacteristic, complemented
99#1358—731no—
100C73#1246611yescharacteristic, complemented, Sylow
101#510—1461no—
102#504—1461no—
103#499C2×D7311yescharacteristic
104#494—731no—
105#443—731no—
106#365—1461no—
107#364—731no—
108#364C2×D7311yescharacteristic
109#364C2×D7311yescharacteristic
110#362—1461no—
111#360—1461no—
112#358—1461no—
113#358—1461no—
114#350—1461no—
115#346—731no—
116#135—731no—
117C2×Q16—1461no—
118C2×Q16—1461no—
119#131—1461no—
120C4⋊Q8—1461no—
121#125—21no—
122Q32—2921no—
123SD32—2921no—
124M32—21no—
125M32—21no—
126M32—2921no—
127M32—1461no—
128C2×C16—2921no—
129C2×C16—731no—
130C2×C16—731no—
131#108—731no—
132#107—21no—
133#106—21no—
134#104—1461no—
135C4×C8C22×D7311yescharacteristic
136#41—1461no—
137C2×Q8—2921no—
138Q16—2921no—
139Q16—2921no—
140Q16—2921no—
141Q16—2921no—
142Q16—731no—
143SD16—1461no—
144D8—731no—
145M16—2921no—
146M16—1461no—
147C2×C8—2921no—
148C2×C8D4×D7311yescharacteristic
149C2×C8D4×D7311yescharacteristic
150C4⋊C4—41no—
151C4⋊C4—81no—
152C4⋊C4—5841no—
153C42#1192402811yescharacteristic
154C16—41no—
155C16—41no—
156C16—2921no—
157C16—1461no—
158C16—1461no—
159Q8—5841no—
160Q8—5841no—
161Q8—1461no—
162D4—2921no—
163D4—1461no—
164C2×C4—21no—
165C2×C4—81no—
166C2×C4—2921no—
167C2×C4—5841no—
168C2×C4#1455656411yescharacteristic
169C8—2921no—
170C8SD16×D7311yescharacteristic
171C8#1455661411yescharacteristic
172C8#1455661411yescharacteristic
173C8#1455661811yescharacteristic
174C22—2921no—
175C22#1798885611yescharacteristic
176C4—41no—
177C4—161no—
178C4—2921no—
179C4—11681no—
180C4#1798880511yescharacteristic
181C4#1798881911yescharacteristic
182C2—21no—
183C2—5841no—
184C2#2260934311yescharacteristic
subgroupG/H
centerC2#22609343
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1366C2
socleC2×C73#1677
prime radical#14556613D4
hypercenter#1366D73
hypocenterC73#12466
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. #22612178C2semidirect
5. #22607998C2semidirect
6. #22607969C2semidirect
7. C73×#1366C2semidirect
98. #1366D73semidirect
100. C73#12466semidirect

Maximal subgroups

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

subgroupindex
#226121782
#226121042
#226120132
#226117722
#226079982
#226079692
C73×#13662
#1246673