Finite Group Databasebeta

← #32988731

Subgroups — #32988731

Order 18688.

576 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 111 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#22621072C212yesmaximal
2#22618329C211yesmaximal, characteristic
3#22608604C212yesmaximal
4#22607764C211yesmaximal, characteristic
5C73×#1994C211yesmaximal, characteristic
6C2×#14556591—22no—
7C2×#14556591C2212yes—
8#17988983—22no—
9#17988937—22no—
10#17988915—24no—
11#17988872—24no—
12#17988640C2212yes—
13#17988457—24no—
14#17988334—24no—
15#533×C73C2211yescharacteristic
16#423×C73C2211yescharacteristic
17C43×C73C2211yescharacteristic
18#339×C73—22no—
19C22×Dic146—22no—
20#14556591—22no—
21#14556591—22no—
22#14556591—22no—
23#14556591—22no—
24#14556591—44no—
25#14556591—44no—
26C2×C4⋊Dic73—28no—
27C2×C4⋊Dic73—22no—
28C2×C4⋊Dic73D414yes—
29#14556522—28no—
30C4⋊#10596831D414yes—
31#14556515—28no—
32C22⋊#10596831—22no—
33C4×#10596831—22no—
34C2×M16×C73—21no—
35C4⋊Q8×C73D412yes—
36#125×C73—21no—
37C22⋊Q8×C73—22no—
38C4×Q8×C73—22no—
39#117×C73—21no—
40C2×C42×C73—22no—
41C2×C42×C73D412yes—
42C2×C42×C73C2311yescharacteristic
43C4⋊C8×C73—22no—
44C2×Dic146—42no—
45C2×Dic146—42no—
46C2×Dic146—44no—
47C2×Dic146—44no—
48C22×Dic73—24no—
49C2×#10596831—24no—
50C4⋊Dic73—24no—
51C4⋊Dic73—24no—
52C4⋊Dic73—416no—
53C4⋊Dic73—42no—
54C4⋊Dic73—42no—
55C2×Q8×C73—22no—
56C22×C4×C73—22no—
57C22×C4×C73C2×D412yes—
58C22×C4×C73C2×D411yescharacteristic
59M16×C73—42no—
60C2×C8×C73—41no—
61C4⋊C4×C73—22no—
62C4⋊C4×C73—22no—
63C4⋊C4×C73—42no—
64C22⋊C4×C73—41no—
65C42×C73—28no—
66C42×C73—22no—
67C42×C73—41no—
68C42×C73SD1614yes—
69C42×C73C2×D412yes—
70C42×C73C2×D411yescharacteristic
71C42×C73#4111yescharacteristic
72C23×C73#12011yescharacteristic
73Q8×C73—44no—
74C2×C4×C73—28no—
75C2×C4×C73—24no—
76C2×C4×C73—24no—
77C2×C4×C73—42no—
78C2×C4×C73#12012yes—
79C2×C4×C73#12112yes—
80C2×C4×C73#12111yescharacteristic
81C2×C4×C73#12711yescharacteristic
82C2×C4×C73C2×SD1612yes—
83C2×C4×C73AGL(1,ℤ/8)12yes—
84C2×Dic73—44no—
85C2×Dic73—48no—
86Dic146—84no—
87Dic146—82no—
88Dic146—82no—
89C8×C73—81no—
90#10596831—44no—
91C22×C73—22no—
92C22×C73#39211yescharacteristic
93C22×C73#45012yes—
94C4×C73—28no—
95C4×C73—22no—
96C4×C73—82no—
97C4×C73#45614yes—
98C4×C73#46012yes—
99C4×C73#49211yescharacteristic
100C4×C73#49611yescharacteristic
101Dic73—84no—
102#10299—731nomaximal, Sylow
103C2×C73—22no—
104C2×C73#200512yes—
105C2×C73#201411yescharacteristic
106#3229—732no—
107#2868—731no—
108#1994D7311yescharacteristic
109#1546—732no—
110#1276—731no—
111C73#1029911yescharacteristic, complemented, Sylow
112#533C2×D7311yescharacteristic
113C2×C4⋊Q8—732no—
114C2×C4⋊Q8—1462no—
115#498—1462no—
116#487—1462no—
117#483—1464no—
118#475—1464no—
119#431—732no—
120#423C2×D7311yescharacteristic
121#384—1464no—
122C43C2×D7311yescharacteristic
123#339—22no—
124#332—1464no—
125C22×Q8—1462no—
126C2×M16—21no—
127C4⋊Q8—2924no—
128C4⋊Q8—2924no—
129C4⋊Q8—1462no—
130C4⋊Q8—1462no—
131C4⋊Q8—1462no—
132C4⋊Q8—1462no—
133C4⋊Q8D29212yes—
134#125—21no—
135C22⋊Q8—22no—
136C4×Q8—22no—
137#117—21no—
138C2×C4⋊C4—734no—
139C2×C4⋊C4—1468no—
140C2×C4⋊C4—1462no—
141C2×C42—22no—
142C2×C42C22⋊D7312yes—
143C2×C42C22×D7311yescharacteristic
144#106—1468no—
145C4⋊C8—22no—
146C4⋊C8—734no—
147#103—1468no—
148C22⋊C8—1462no—
149C4×C8—1462no—
150C2×Q8—22no—
151C2×Q8—2922no—
152C2×Q8—2922no—
153C2×Q8—2924no—
154C2×Q8—2924no—
155C22×C4—22no—
156C22×C4—1464no—
157C22×C4D4×D7312yes—
158C22×C4C2×C22⋊D7311yescharacteristic
159M16—42no—
160C2×C8—41no—
161C2×C8—1464no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—29216no—
166C4⋊C4—2922no—
167C4⋊C4—2922no—
168C4⋊C4—1464no—
169C4⋊C4—1464no—
170C22⋊C4—41no—
171C42—28no—
172C42—22no—
173C42—41no—
174C42#1192401514yes—
175C42D4×D7312yes—
176C42C2×D29211yescharacteristic
177C42#1192402811yescharacteristic
178C23#1455655911yescharacteristic
179Q8—44no—
180Q8—5842no—
181Q8—5842no—
182Q8—5844no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—42no—
187C2×C4—2928no—
188C2×C4—2924no—
189C2×C4#1455656112yes—
190C2×C4#1455656412yes—
191C2×C4#1455656511yescharacteristic
192C2×C4#1455658711yescharacteristic
193C2×C4C2×#1192401512yes—
194C2×C4#1455661612yes—
195C8—81no—
196C8—2924no—
197C22—22no—
198C22#1798849611yescharacteristic
199C22#1798873712yes—
200C4—28no—
201C4—22no—
202C4—82no—
203C4—5844no—
204C4#1798877114yes—
205C4#1798878712yes—
206C4#1798896111yescharacteristic
207C4#1798897711yescharacteristic
208C2—22no—
209C2#2261096612yes—
210C2#2261101811yescharacteristic
subgroupG/H
centerC22#17988496
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1994C2
socleC22×C73#392
prime radicalC23×C73#120
hypercenter#1994D73
hypocenterC73#10299
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1994

Complements

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

NH ≅ G/Ntype
111. C73#10299semidirect

Maximal subgroups

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

subgroupindex
#226210722
#226183292
#226086042
#226077642
C73×#19942
#1029973