Finite Group Databasebeta

← #32999348

Subgroups — #32999348

Order 18688.

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

normal subgroups only

This group has 262 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#22612148C212yesmaximal
2#22611511C211yesmaximal, characteristic
3#22607925C212yesmaximal
4#22607884C211yesmaximal, characteristic
5C73×#3261C211yesmaximal, characteristic
6#17988636C2211yescharacteristic
7#17988409—22no—
8#17988403—22no—
9#17988369C2212yes—
10#17988357—21no—
11#17988352—21no—
12#17988345C2211yescharacteristic
13#541×C73—21no—
14#479×C73—22no—
15#470×C73C2212yes—
16#467×C73—21no—
17#462×C73—22no—
18#424×C73C2211yescharacteristic
19C2×#11924012—21no—
20C2×#11924012—21no—
21#14556531—22no—
22#14556527—22no—
23C2×Q16×C73—21no—
24C2×Q16×C73D412yes—
25C2×M16×C73C2311yescharacteristic
26C22×C8×C73D411yescharacteristic
27C4⋊Q8×C73—21no—
28#126×C73—42no—
29#125×C73—21no—
30#125×C73—42no—
31C22⋊Q8×C73—22no—
32C4×Q8×C73—22no—
33#117×C73D411yescharacteristic
34#107×C73—21no—
35#106×C73D412yes—
36C4⋊C8×C73—22no—
37#103×C73—22no—
38#103×C73—22no—
39#11924012—41no—
40#11924012—41no—
41#11924012—41no—
42#11924012—41no—
43C2×#10596831—41no—
44C2×#10596831—41no—
45#11924003—42no—
46C2×Q8×C73—22no—
47C22×C4×C73C2×D411yescharacteristic
48Q16×C73—42no—
49Q16×C73—81no—
50M16×C73—41no—
51C2×C8×C73—21no—
52C2×C8×C73—41no—
53C2×C8×C73C2×D412yes—
54C4⋊C4×C73—21no—
55C4⋊C4×C73—22no—
56C4⋊C4×C73—42no—
57C4⋊C4×C73—42no—
58C4⋊C4×C73—42no—
59C4⋊C4×C73—42no—
60C22⋊C4×C73—42no—
61C22⋊C4×C73SD1612yes—
62C42×C73—21no—
63C42×C73—42no—
64C23×C73C2×SD1611yescharacteristic
65Q8×C73—42no—
66Q8×C73—42no—
67C2×C4×C73—21no—
68C2×C4×C73—21no—
69C2×C4×C73—22no—
70C2×C4×C73—42no—
71C2×C4×C73—42no—
72C2×C4×C73#12011yescharacteristic
73C2×C4×C73AGL(1,ℤ/8)11yescharacteristic
74C8×C73—22no—
75C8×C73—41no—
76#10596831—81no—
77#10596831—81no—
78C22×C73—21no—
79C22×C73—41no—
80C22×C73#45011yescharacteristic
81C4×C73—21no—
82C4×C73—42no—
83C4×C73—82no—
84C4×C73—82no—
85C4×C73#45411yescharacteristic
86C4×C73#45811yescharacteristic
87#12305—731nomaximal, Sylow
88C2×C73—21no—
89C2×C73—41no—
90C2×C73#161611yescharacteristic
91#3261D7311yescharacteristic
92#2239—732no—
93#2103—731no—
94#1342—732no—
95#1328—731no—
96C73#1230511yescharacteristic, complemented, Sylow
97#541—21no—
98#479—22no—
99#470C2×D7312yes—
100#467—21no—
101#462—22no—
102#430—731no—
103#424C2×D7311yescharacteristic
104#365—1462no—
105#362—1462no—
106#349—732no—
107#344—1461no—
108#341—1461no—
109#338—731no—
110C2×Q16—21no—
111C2×Q16C22⋊D7312yes—
112C2×M16—1461no—
113C2×M16—1461no—
114C2×M16C22×D7311yescharacteristic
115C22×C8C22⋊D7311yescharacteristic
116C4⋊Q8—21no—
117#126—42no—
118#125—21no—
119#125—42no—
120C22⋊Q8—22no—
121C4×Q8—22no—
122#117C22⋊D7311yescharacteristic
123M32—1462no—
124#108—1462no—
125#107—21no—
126#106C22⋊D7312yes—
127C4⋊C8—22no—
128#103—22no—
129#103—22no—
130C2×Q8—22no—
131C22×C4C2×C22⋊D7311yescharacteristic
132Q16—42no—
133Q16—81no—
134M16—41no—
135M16—2921no—
136M16—2921no—
137M16—2921no—
138M16—2921no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—2921no—
142C2×C8—2921no—
143C2×C8C2×C22⋊D7312yes—
144C4⋊C4—21no—
145C4⋊C4—22no—
146C4⋊C4—42no—
147C4⋊C4—42no—
148C4⋊C4—42no—
149C4⋊C4—42no—
150C22⋊C4—42no—
151C22⋊C4#1192401612yes—
152C42—21no—
153C42—42no—
154C16—2922no—
155C23C2×#1192401611yescharacteristic
156Q8—42no—
157Q8—42no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—42no—
162C2×C4—42no—
163C2×C4#1455656011yescharacteristic
164C2×C4#1455661711yescharacteristic
165C8—22no—
166C8—41no—
167C8—5841no—
168C8—5841no—
169C22—21no—
170C22—41no—
171C22#1798873811yescharacteristic
172C4—21no—
173C4—42no—
174C4—82no—
175C4—82no—
176C4#1798876011yescharacteristic
177C4#1798877711yescharacteristic
178C2—21no—
179C2—41no—
180C2#2260896811yescharacteristic
subgroupG/H
centerC2#22608968
commutator, cosocleC2×M16×C73C23
FrattiniC2×M16C22×D73
FittingC73×#3261C2
socleC2×C73#1616
prime radicalC23×C73C2×SD16
hypercenter#3261D73
hypocenterC73#12305
LCSG ▷ C2×M16×C73 ▷ C2×C4×C73 ▷ C2×C73 ▷ C73
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #3261

Complements

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

NH ≅ G/Ntype
96. C73#12305semidirect

Maximal subgroups

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

subgroupindex
#226121482
#226115112
#226079252
#226078842
C73×#32612
#1230573