Finite Group Databasebeta

← #32988734

Subgroups — #32988734

Order 18688.

576 conjugacy classes of subgroups; only the 113 normal subgroups are shown.

normal subgroups only

This group has 576 conjugacy classes of subgroups — too many to draw. Only its 113 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#22621077C212yesmaximal
2#22618329C211yesmaximal, characteristic
3#22610908C211yesmaximal, characteristic
4#22608602C212yesmaximal
5C73×#1276C211yesmaximal, characteristic
6#17989144C2211yescharacteristic
7C2×#14556591—22no—
8C2×#14556591C2212yes—
9#17988985—22no—
10#17988938—22no—
11#17988918—24no—
12#17988873—24no—
13#17988611C2211yescharacteristic
14#17988457—24no—
15#17988347—22no—
16#17988332—24no—
17#431×C73C2212yes—
18C43×C73C2211yescharacteristic
19C22×Dic146—22no—
20C2×#11924012—21no—
21#14556591—22no—
22#14556591—22no—
23#14556591—22no—
24#14556591—22no—
25#14556591—44no—
26#14556591—44no—
27#14556591D412yes—
28#14556583—21no—
29#14556570—22no—
30C4×Dic146—22no—
31#14556550—21no—
32C2×C4⋊Dic73—28no—
33C2×C4⋊Dic73—22no—
34C2×C4⋊Dic73D414yes—
35#14556523—28no—
36C4⋊#10596831—22no—
37#14556516—28no—
38C2×C42×C73—22no—
39C2×C42×C73D412yes—
40C2×C42×C73C2311yescharacteristic
41C4⋊C8×C73D414yes—
42C22⋊C8×C73—22no—
43C4×C8×C73—22no—
44C2×Dic146—22no—
45C2×Dic146—42no—
46C2×Dic146—42no—
47C2×Dic146—44no—
48C2×Dic146—44no—
49C22×Dic73—24no—
50#11924012—42no—
51C2×#10596831—41no—
52C4⋊Dic73—24no—
53C4⋊Dic73—22no—
54C4⋊Dic73—24no—
55C4⋊Dic73—22no—
56C4⋊Dic73—416no—
57C4⋊Dic73—42no—
58C4⋊Dic73—42no—
59#11924007—42no—
60C22⋊Dic73—41no—
61C4×Dic73—41no—
62C22×C4×C73—22no—
63C22×C4×C73C2×D412yes—
64C22×C4×C73C2×D411yescharacteristic
65C2×C8×C73—24no—
66C42×C73—28no—
67C42×C73—22no—
68C42×C73SD1614yes—
69C42×C73C2×D411yescharacteristic
70C42×C73C2×D412yes—
71C42×C73#4111yescharacteristic
72C23×C73#12011yescharacteristic
73C2×C4×C73—28no—
74C2×C4×C73—24no—
75C2×C4×C73—24no—
76C2×C4×C73#12012yes—
77C2×C4×C73#12112yes—
78C2×C4×C73#12111yescharacteristic
79C2×C4×C73#12711yescharacteristic
80C2×C4×C73C2×SD1612yes—
81C2×C4×C73AGL(1,ℤ/8)12yes—
82C2×Dic73—42no—
83C2×Dic73—44no—
84C2×Dic73—48no—
85Dic146—44no—
86Dic146—84no—
87Dic146—82no—
88Dic146—82no—
89C8×C73—44no—
90#10596831—81no—
91C22×C73—22no—
92C22×C73#39211yescharacteristic
93C22×C73#45012yes—
94C4×C73—28no—
95C4×C73—22no—
96C4×C73#45614yes—
97C4×C73#46012yes—
98C4×C73#49211yescharacteristic
99C4×C73#49611yescharacteristic
100Dic73—82no—
101Dic73—84no—
102#10299—731nomaximal, Sylow
103C2×C73—22no—
104C2×C73#200512yes—
105C2×C73#201411yescharacteristic
106#3229—732no—
107#2868—731no—
108#1994—731no—
109#1546—732no—
110#1276D7311yescharacteristic
111C73#1029911yescharacteristic, complemented, Sylow
112#533—731no—
113C2×C4⋊Q8—732no—
114C2×C4⋊Q8—1462no—
115#498—1462no—
116#487—1462no—
117#483—1464no—
118#475—1464no—
119#431C2×D7312yes—
120#423—731no—
121#384—1464no—
122C43C2×D7311yescharacteristic
123#339—1462no—
124#332—1464no—
125C22×Q8—1462no—
126C2×M16—1461no—
127C4⋊Q8—2924no—
128C4⋊Q8—2924no—
129C4⋊Q8—732no—
130C4⋊Q8—1462no—
131C4⋊Q8—1462no—
132C4⋊Q8—1462no—
133C4⋊Q8—1462no—
134#125—1461no—
135C22⋊Q8—1462no—
136C4×Q8—1462no—
137#117—1461no—
138C2×C4⋊C4—734no—
139C2×C4⋊C4—1468no—
140C2×C4⋊C4—1462no—
141C2×C42—22no—
142C2×C42D29212yes—
143C2×C42C22×D7311yescharacteristic
144#106—1468no—
145C4⋊C8—1462no—
146C4⋊C8D29214yes—
147#103—1468no—
148C22⋊C8—22no—
149C4×C8—22no—
150C2×Q8—2922no—
151C2×Q8—2922no—
152C2×Q8—2924no—
153C2×Q8—2924no—
154C2×Q8—1462no—
155C22×C4—22no—
156C22×C4—1464no—
157C22×C4D4×D7312yes—
158C22×C4C2×D29211yescharacteristic
159M16—2922no—
160C2×C8—24no—
161C2×C8—2921no—
162C4⋊C4—29216no—
163C4⋊C4—2922no—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C4⋊C4—1464no—
167C4⋊C4—1462no—
168C4⋊C4—1464no—
169C4⋊C4—1462no—
170C22⋊C4—2921no—
171C42—28no—
172C42—22no—
173C42—2921no—
174C42#1192401714yes—
175C42D4×D7311yescharacteristic
176C42C2×D29212yes—
177C42#1192402911yescharacteristic
178C23#1455656111yescharacteristic
179Q8—2924no—
180Q8—5842no—
181Q8—5842no—
182Q8—5844no—
183C2×C4—28no—
184C2×C4—24no—
185C2×C4—24no—
186C2×C4—2928no—
187C2×C4—2922no—
188C2×C4—2924no—
189C2×C4#1455656112yes—
190C2×C4#1455656612yes—
191C2×C4#1455656611yescharacteristic
192C2×C4#1455658811yescharacteristic
193C2×C4C2×#1192401712yes—
194C2×C4#1455661912yes—
195C8—44no—
196C8—5841no—
197C22—22no—
198C22#1798849711yescharacteristic
199C22#1798874012yes—
200C4—28no—
201C4—22no—
202C4—5842no—
203C4—5844no—
204C4#1798877114yes—
205C4#1798878812yes—
206C4#1798896011yescharacteristic
207C4#1798897611yescharacteristic
208C2—22no—
209C2#2261097012yes—
210C2#2261102111yescharacteristic
subgroupG/H
centerC22#17988497
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#1276C2
socleC22×C73#392
prime radicalC23×C73#120
hypercenter#1276D73
hypocenterC73#10299
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1276

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
#226210772
#226183292
#226109082
#226086022
C73×#12762
#1029973