Finite Group Databasebeta

← #32989475

Subgroups — #32989475

Order 18688.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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#22610901C212yesmaximal
2#22610064C211yesmaximal, characteristic
3C2×#17988329C212yesmaximal
4#22607812C211yesmaximal, characteristic
5C73×#2822C211yesmaximal, characteristic
6C2×#14556502C2212yes—
7C2×#14556502C2211yescharacteristic
8#17988457C2211yescharacteristic
9#17988349—22no—
10#17988349—22no—
11#17988349—22no—
12#17988329—24no—
13C2×#125×C73C2212yes—
14#400×C73—22no—
15#398×C73—22no—
16#398×C73—22no—
17#382×C73C2211yescharacteristic
18C22×#10596831—22no—
19C22×#10596831—21no—
20C2×C4⋊Dic73—22no—
21C2×C4⋊Dic73—21no—
22#14556502—22no—
23#14556502—21no—
24#14556502—22no—
25#14556502D412yes—
26#125×C73—22no—
27#125×C73—22no—
28#125×C73—22no—
29#125×C73—22no—
30C2×C4⋊C4×C73—22no—
31C2×C4⋊C4×C73—22no—
32C2×C4⋊C4×C73—22no—
33C2×C4⋊C4×C73D412yes—
34C2×C4⋊C4×C73D412yes—
35C2×C4⋊C4×C73D412yes—
36C2×C42×C73C2311yescharacteristic
37#95×C73—24no—
38#95×C73—22no—
39#95×C73—22no—
40C22×Dic73—41no—
41C2×#10596831—24no—
42C2×#10596831—22no—
43C2×#10596831—42no—
44C2×#10596831—41no—
45C2×#10596831—41no—
46C2×#10596831—42no—
47C4⋊Dic73—42no—
48C4⋊Dic73—44no—
49C22×C4×C73—22no—
50C22×C4×C73—22no—
51C22×C4×C73—22no—
52C22×C4×C73C2×D412yes—
53C22×C4×C73C2×D411yescharacteristic
54C4⋊C4×C73—22no—
55C4⋊C4×C73—22no—
56C4⋊C4×C73—22no—
57C4⋊C4×C73—22no—
58C4⋊C4×C73—42no—
59C4⋊C4×C73—42no—
60C4⋊C4×C73—42no—
61C4⋊C4×C73—42no—
62C4⋊C4×C73—42no—
63C4⋊C4×C73—82no—
64C42×C73C2×D411yescharacteristic
65C42×C73#4111yescharacteristic
66C42×C73#4112yes—
67C23×C73#12011yescharacteristic
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—21no—
71C2×C4×C73—22no—
72C2×C4×C73—42no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73—42no—
76C2×C4×C73—42no—
77C2×C4×C73—42no—
78C2×C4×C73—42no—
79C2×C4×C73—42no—
80C2×C4×C73—42no—
81C2×C4×C73#12111yescharacteristic
82C2×C4×C73#12112yes—
83C2×C4×C73#12312yes—
84C2×C4×C73#12411yescharacteristic
85C2×Dic73—81no—
86C2×Dic73—82no—
87#10596831—44no—
88#10596831—42no—
89C22×C73#39411yescharacteristic
90C22×C73#45411yescharacteristic
91C22×C73#45412yes—
92C22×C73#45511yescharacteristic
93C22×C73#45612yes—
94C4×C73—22no—
95C4×C73—22no—
96C4×C73—21no—
97C4×C73—21no—
98C4×C73—82no—
99C4×C73—82no—
100C4×C73—82no—
101Dic73—161no—
102#10428—731nomaximal, Sylow
103C2×C73#165811yescharacteristic
104C2×C73#166311yescharacteristic
105C2×C73#166412yes—
106C2×C73#203812yes—
107C2×C73#204011yescharacteristic
108#2822D7311yescharacteristic
109#1992—732no—
110#1836—731no—
111C2×#330—732no—
112#1295—731no—
113C73#1042811yescharacteristic, complemented, Sylow
114C2×#125C2×D7312yes—
115C2×#97—731no—
116C2×#97—732no—
117#400—22no—
118#398—22no—
119#398—22no—
120#384—731no—
121#382C2×D7311yescharacteristic
122#340—1462no—
123#340—1462no—
124#340—1462no—
125#330—1464no—
126C22×C8—1461no—
127C22×C8—1462no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—1461no—
136C2×C4⋊C4—1462no—
137C2×C4⋊C4C22⋊D7312yes—
138C2×C4⋊C4C22⋊D7312yes—
139C2×C4⋊C4C22⋊D7312yes—
140C2×C42C22×D7311yescharacteristic
141#97—732no—
142#97—1462no—
143#97—1462no—
144#97—1461no—
145#95—24no—
146#95—22no—
147#95—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—2921no—
152C22×C4C2×C22⋊D7311yescharacteristic
153C22×C4C2×C22⋊D7312yes—
154C2×C8—2922no—
155C2×C8—2921no—
156C2×C8—2921no—
157C2×C8—2922no—
158C2×C8—1464no—
159C2×C8—1462no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—82no—
170C4⋊C4—2924no—
171C4⋊C4—2922no—
172C42D4×D7311yescharacteristic
173C42#1192402711yescharacteristic
174C42#1192402712yes—
175C23#1455656011yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—5841no—
190C2×C4—5842no—
191C2×C4#1455656211yescharacteristic
192C2×C4#1455656312yes—
193C2×C4#1455657212yes—
194C2×C4#1455657811yescharacteristic
195C8—2924no—
196C8—2922no—
197C22#1798850111yescharacteristic
198C22#1798876011yescharacteristic
199C22#1798876012yes—
200C22#1798876511yescharacteristic
201C22#1798877012yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—11681no—
210C2#2260923311yescharacteristic
211C2#2260925911yescharacteristic
212C2#2260926512yes—
213C2#2261114512yes—
214C2#2261115711yescharacteristic
subgroupG/H
centerC23#14556560
commutator, cosocleC2×C42×C73C23
FrattiniC2×C42C22×D73
FittingC73×#2822C2
socle, prime radicalC23×C73#120
hypercenter#2822D73
hypocenterC73#10428
LCSG ▷ C2×C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

Complements

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

NH ≅ G/Ntype
113. C73#10428semidirect

Maximal subgroups

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

subgroupindex
#226109012
#226100642
C2×#179883292
#226078122
C73×#28222
#1042873