Finite Group Databasebeta

← #32999343

Subgroups — #32999343

Order 18688.

286 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 286 conjugacy classes of subgroups — too many to draw. Only its 59 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#22612143C212yesmaximal, complemented
2#22611511C211yesmaximal, characteristic, complemented
3#22607922C212yesmaximal, complemented
4#22607884C211yesmaximal, characteristic, complemented
5C73×#3259C211yesmaximal, characteristic
6#17988636C2211yescharacteristic
7#17988409—22no—
8#17988400—22no—
9#17988369C2212yes—
10#17988357—21no—
11#17988352—21no—
12#17988345C2211yescharacteristic
13#540×C73—21no—
14#478×C73—22no—
15#469×C73C2212yes—
16#466×C73—21no—
17#459×C73—22no—
18#424×C73C2211yescharacteristic
19C2×#11924012—21no—
20C2×#11924012—21no—
21#14556531—22no—
22#14556527—22no—
23C2×D8×C73—21no—
24C2×D8×C73D412yes—
25C2×M16×C73C2311yescharacteristic
26C22×C8×C73D411yescharacteristic
27#127×C73—21no—
28#125×C73—21no—
29#123×C73—42no—
30#121×C73—22no—
31#121×C73—42no—
32C4×D4×C73—22no—
33#117×C73D411yescharacteristic
34#107×C73—21no—
35#106×C73D412yes—
36C4⋊C8×C73—22no—
37#102×C73—22no—
38#102×C73—22no—
39#11924012—41no—
40#11924012—41no—
41#11924012—41no—
42#11924012—41no—
43C2×#10596831—41no—
44C2×#10596831—41no—
45#11924003—42no—
46C2×D4×C73—22no—
47C2×D4×C73—42no—
48C2×D4×C73—42no—
49C22×C4×C73—42no—
50C22×C4×C73C2×D411yescharacteristic
51D8×C73—42no—
52D8×C73—81no—
53M16×C73—41no—
54C2×C8×C73—21no—
55C2×C8×C73—41no—
56C2×C8×C73C2×D412yes—
57C4⋊C4×C73—21no—
58C4⋊C4×C73—22no—
59C4⋊C4×C73—42no—
60C22⋊C4×C73—42no—
61C22⋊C4×C73—42no—
62C22⋊C4×C73SD1612yes—
63C42×C73—21no—
64C23×C73—42no—
65C23×C73C2×SD1611yescharacteristic
66D4×C73—42no—
67D4×C73—42no—
68D4×C73—162no—
69D4×C73—162no—
70C2×C4×C73—21no—
71C2×C4×C73—21no—
72C2×C4×C73—22no—
73C2×C4×C73—42no—
74C2×C4×C73—162no—
75C2×C4×C73#12011yescharacteristic
76C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
77C8×C73—22no—
78C8×C73—41no—
79#10596831—81no—
80#10596831—81no—
81C22×C73—21no—
82C22×C73—41no—
83C22×C73—82no—
84C22×C73—82no—
85C22×C73—82no—
86C22×C73#45011yescharacteristic
87C4×C73—21no—
88C4×C73—42no—
89C4×C73—82no—
90C4×C73#45411yescharacteristic
91C4×C73#45811yescharacteristic
92#12304—731nomaximal, Sylow
93C2×C73—21no—
94C2×C73—41no—
95C2×C73—162no—
96C2×C73#161611yescharacteristic
97#3259D7311yescharacteristic
98#2238—732no—
99#2103—731no—
100#1341—732no—
101#1328—731no—
102C73#1230411yescharacteristic, complemented, Sylow
103#540—21no—
104#478—22no—
105#469C2×D7312yes—
106#466—21no—
107#459—22no—
108#430—731no—
109#424C2×D7311yescharacteristic
110#365—1462no—
111#361—1462no—
112#349—732no—
113#344—1461no—
114#341—1461no—
115#338—731no—
116C2×D8—21no—
117C2×D8C22⋊D7312yes—
118C2×M16—1461no—
119C2×M16—1461no—
120C2×M16C22×D7311yescharacteristic
121C22×C8C22⋊D7311yescharacteristic
122#127—21no—
123#125—21no—
124#123—42no—
125#121—22no—
126#121—42no—
127C4×D4—22no—
128#117C22⋊D7311yescharacteristic
129M32—1462no—
130#108—1462no—
131#107—21no—
132#106C22⋊D7312yes—
133C4⋊C8—22no—
134#102—22no—
135#102—22no—
136C2×D4—22no—
137C2×D4—42no—
138C2×D4—42no—
139C22×C4—42no—
140C22×C4C2×C22⋊D7311yescharacteristic
141D8—42no—
142D8—81no—
143M16—41no—
144M16—2921no—
145M16—2921no—
146M16—2921no—
147M16—2921no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—2921no—
151C2×C8—2921no—
152C2×C8C2×C22⋊D7312yes—
153C4⋊C4—21no—
154C4⋊C4—22no—
155C4⋊C4—42no—
156C22⋊C4—42no—
157C22⋊C4—42no—
158C22⋊C4#1192401612yes—
159C42—21no—
160C16—2922no—
161C23—42no—
162C23C2×#1192401611yescharacteristic
163D4—42no—
164D4—42no—
165D4—162no—
166D4—162no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—162no—
172C2×C4#1455656011yescharacteristic
173C2×C4#1455661711yescharacteristic
174C8—22no—
175C8—41no—
176C8—5841no—
177C8—5841no—
178C22—21no—
179C22—41no—
180C22—82no—
181C22—82no—
182C22—82no—
183C22#1798873811yescharacteristic
184C4—21no—
185C4—42no—
186C4—82no—
187C4#1798876011yescharacteristic
188C4#1798877711yescharacteristic
189C2—21no—
190C2—41no—
191C2—162no—
192C2#2260896811yescharacteristic
subgroupG/H
centerC2#22608968
commutator, cosocleC2×M16×C73C23
FrattiniC2×M16C22×D73
Fitting, prime radicalC73×#3259C2
socleC2×C73#1616
hypercenter#3259D73
hypocenterC73#12304
LCSG ▷ C2×M16×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3259

Complements

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

NH ≅ G/Ntype
1. #22612143C2semidirect
2. #22611511C2semidirect
3. #22607922C2semidirect
4. #22607884C2semidirect
102. C73#12304semidirect

Maximal subgroups

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

subgroupindex
#226121432
#226115112
#226079222
#226078842
C73×#32592
#1230473