Finite Group Databasebeta

← #33000393

Subgroups — #33000393

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#22612176C211yesmaximal, characteristic, complemented
2#22612108C211yesmaximal, characteristic
3#22612009C211yesmaximal, characteristic
4#22611772C211yesmaximal, characteristic
5#22607998C211yesmaximal, characteristic, complemented
6#22607993C211yesmaximal, characteristic, complemented
7C73×#1358C211yesmaximal, characteristic, complemented
8#17989028—21no—
9#17989005—21no—
10#17988989C2211yescharacteristic
11#17988705C2211yescharacteristic
12#17988410—21no—
13#17988408C2211yescharacteristic
14#17988403—21no—
15#17988398—21no—
16#17988391—21no—
17#17988391—21no—
18#17988372—21no—
19#17988363C2211yescharacteristic
20#494×C73C2211yescharacteristic
21#364×C73C2211yescharacteristic
22#364×C73C2211yescharacteristic
23#14556613D411yescharacteristic
24#14556597—21no—
25#14556583—21no—
26#14556537—41no—
27#14556534—41no—
28#14556531—21no—
29#14556530—41no—
30C2×#11924003D411yescharacteristic
31C2×#11924003D411yescharacteristic
32C16×D73—41no—
33#14556527D411yescharacteristic
34#14556525—21no—
35#14556523—21no—
36#14556519—21no—
37C2×Q16×C73—21no—
38C2×Q16×C73—21no—
39C4⋊Q8×C73—21no—
40M32×C73—21no—
41M32×C73—21no—
42C4×C8×C73C2311yescharacteristic
43#11924028—21no—
44Dic292SD1611yescharacteristic
45#11924017—21no—
46D584SD1611yescharacteristic
47#11924012—21no—
48#11924011—41no—
49C8×D73—41no—
50C4⋊Dic73—41no—
51#11924007—81no—
52#11924003—21no—
53#11924003—21no—
54#11924003—41no—
55C2×Q8×C73—41no—
56Q16×C73—41no—
57Q16×C73—41no—
58Q16×C73—41no—
59Q16×C73—41no—
60C2×C8×C73C2×D411yescharacteristic
61C2×C8×C73C2×D411yescharacteristic
62C4⋊C4×C73—81no—
63C42×C73#4111yescharacteristic
64C16×C73—41no—
65C16×C73—41no—
66Q8×C73—81no—
67Q8×C73—81no—
68C2×C4×C73—21no—
69C2×C4×C73—81no—
70C2×C4×C73#12111yescharacteristic
71C22⋊D73—41no—
72C2×Dic73—81no—
73D292—21no—
74C4×D73—41no—
75Dic146—21no—
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#1366—731no—
99#1358D7311yescharacteristic, complemented
100C73#1246611yescharacteristic, complemented, Sylow
101#510—1461no—
102#504—1461no—
103#499—731no—
104#494C2×D7311yescharacteristic
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—21no—
118C2×Q16—21no—
119#131—1461no—
120C4⋊Q8—21no—
121#125—1461no—
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—1461no—
133#106—1461no—
134#104—1461no—
135C4×C8C22×D7311yescharacteristic
136#41—1461no—
137C2×Q8—41no—
138Q16—41no—
139Q16—41no—
140Q16—41no—
141Q16—41no—
142Q16—731no—
143SD16—1461no—
144D8—731no—
145M16—2921no—
146M16—1461no—
147C2×C8—2921no—
148C2×C8D4×D7311yescharacteristic
149C2×C8D4×D7311yescharacteristic
150C4⋊C4—81no—
151C4⋊C4—2921no—
152C4⋊C4—5841no—
153C42#1192402811yescharacteristic
154C16—41no—
155C16—41no—
156C16—2921no—
157C16—1461no—
158C16—1461no—
159Q8—81no—
160Q8—81no—
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#1455661011yescharacteristic
172C8#1455661211yescharacteristic
173C8#1455661511yescharacteristic
174C22—2921no—
175C22#1798885611yescharacteristic
176C4—41no—
177C4—161no—
178C4—2921no—
179C4—11681no—
180C4#1798880111yescharacteristic
181C4#1798881511yescharacteristic
182C2—21no—
183C2—5841no—
184C2#2260933911yescharacteristic
subgroupG/H
centerC2#22609339
commutator, cosocleC4×C8×C73C23
FrattiniC4×C8C22×D73
FittingC73×#1358C2
socleC2×C73#1677
prime radical#14556613D4
hypercenter#1358D73
hypocenterC73#12466
LCSG ▷ C4×C8×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #22612176C2semidirect
5. #22607998C2semidirect
6. #22607993C2semidirect
7. C73×#1358C2semidirect
99. #1358D73semidirect
100. C73#12466semidirect

Maximal subgroups

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

subgroupindex
#226121762
#226121082
#226120092
#226117722
#226079982
#226079932
C73×#13582
#1246673