Finite Group Databasebeta

← #32980368

Subgroups — #32980368

Order 18688.

396 conjugacy classes of subgroups; only the 115 normal subgroups are shown.

normal subgroups only

This group has 396 conjugacy classes of subgroups — too many to draw. Only its 115 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#22610901C211yesmaximal, characteristic
2#22610064C212yesmaximal
3C2×#17988329C211yesmaximal, characteristic
4#22607812C212yesmaximal
5C73×#2382C211yesmaximal, characteristic
6C2×#14556502C2211yescharacteristic
7C2×#14556502C2212yes—
8#17988457C2211yescharacteristic
9#17988349—22no—
10#17988349—22no—
11#17988349—22no—
12#17988329C414yescomplemented
13C2×#125×C73C2211yescharacteristic
14#389×C73—22no—
15#387×C73—22no—
16#387×C73—22no—
17#382×C73C2212yes—
18C22×#10596831—21no—
19C22×#10596831—22no—
20C2×C4⋊Dic73—21no—
21C2×C4⋊Dic73—22no—
22#14556502—22no—
23#14556502—22no—
24#14556502C2×C414yes—
25#125×C73—22no—
26#125×C73C2×C412yes—
27#125×C73Q812yes—
28C2×C4⋊C4×C73—22no—
29C2×C4⋊C4×C73—22no—
30C2×C4⋊C4×C73D412yes—
31C2×C4⋊C4×C73D412yes—
32C2×C4⋊C4×C73D412yes—
33C2×C42×C73—22no—
34C2×C42×C73C2311yescharacteristic
35#95×C73—22no—
36#95×C73—22no—
37#95×C73—22no—
38#95×C73—22no—
39C22×Dic73—41no—
40C2×#10596831—22no—
41C2×#10596831—24no—
42C2×#10596831—41no—
43C2×#10596831—42no—
44C2×#10596831—42no—
45C2×#10596831—41no—
46C4⋊Dic73—42no—
47C4⋊Dic73—44no—
48C22×C4×C73—22no—
49C22×C4×C73—22no—
50C22×C4×C73—22no—
51C22×C4×C73C2×D411yescharacteristic
52C22×C4×C73C2×D412yes—
53C4⋊C4×C73—24no—
54C4⋊C4×C73—24no—
55C4⋊C4×C73—22no—
56C4⋊C4×C73—42no—
57C4⋊C4×C73—42no—
58C4⋊C4×C73—82no—
59C4⋊C4×C73C4⋊C414yes—
60C42×C73—82no—
61C42×C73C22×C411yescharacteristic
62C42×C73C2×Q811yescharacteristic
63C42×C73#4112yes—
64C23×C73#12011yescharacteristic
65C2×C4×C73—21no—
66C2×C4×C73—22no—
67C2×C4×C73—22no—
68C2×C4×C73—21no—
69C2×C4×C73—24no—
70C2×C4×C73—42no—
71C2×C4×C73—42no—
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×C73C2×C4⋊C411yescharacteristic
79C2×C4×C73C4×D412yes—
80C2×C4×C73C22⋊Q812yes—
81C2×C4×C73#12311yescharacteristic
82C2×Dic73—81no—
83C2×Dic73—82no—
84#10596831—42no—
85#10596831—44no—
86C22×C73#38511yescharacteristic
87C22×C73#45411yescharacteristic
88C22×C73#45412yes—
89C22×C73#45512yes—
90C22×C73#45611yescharacteristic
91C4×C73—21no—
92C4×C73—21no—
93C4×C73—22no—
94C4×C73—22no—
95C4×C73—44no—
96C4×C73—82no—
97C4×C73—82no—
98Dic73—161no—
99#8915—731nomaximal, Sylow
100C2×C73#165811yescharacteristic
101C2×C73#166211yescharacteristic
102C2×C73#166412yes—
103C2×C73#185711yescharacteristic
104C2×C73#186012yes—
105#2382D7311yescharacteristic
106#1992—731no—
107#1836—732no—
108C2×#330—731no—
109#1295—732no—
110C73#891511yescharacteristic, complemented, Sylow
111C2×#125C2×D7311yescharacteristic
112C2×#97—732no—
113C2×#97—731no—
114#389—22no—
115#387—22no—
116#387—22no—
117#384—731no—
118#382C2×D7312yes—
119#340—1462no—
120#340—1462no—
121#340—1462no—
122#330—734no—
123C22×C8—1462no—
124C22×C8—1461no—
125#125—22no—
126#125Dic14612yes—
127#125C4×D7312yes—
128C2×C4⋊C4—22no—
129C2×C4⋊C4—22no—
130C2×C4⋊C4—1461no—
131C2×C4⋊C4—1462no—
132C2×C4⋊C4C22⋊D7312yes—
133C2×C4⋊C4C22⋊D7312yes—
134C2×C4⋊C4C22⋊D7312yes—
135C2×C42—22no—
136C2×C42C22×D7311yescharacteristic
137#97—734no—
138#97—1462no—
139#97—1462no—
140#95—22no—
141#95—22no—
142#95—22no—
143#95—22no—
144C22×C4—22no—
145C22×C4—22no—
146C22×C4—22no—
147C22×C4—2921no—
148C22×C4C2×C22⋊D7311yescharacteristic
149C22×C4C2×C22⋊D7312yes—
150C2×C8—2921no—
151C2×C8—2922no—
152C2×C8—2922no—
153C2×C8—2921no—
154C2×C8—1462no—
155C2×C8—1464no—
156C4⋊C4—24no—
157C4⋊C4—24no—
158C4⋊C4—22no—
159C4⋊C4—42no—
160C4⋊C4—42no—
161C4⋊C4—82no—
162C4⋊C4—2922no—
163C4⋊C4—2924no—
164C4⋊C4#1192400714yes—
165C42—82no—
166C42C2×C4×D7311yescharacteristic
167C42C2×Dic14611yescharacteristic
168C42#1192402812yes—
169C23#1455656011yescharacteristic
170C2×C4—21no—
171C2×C4—22no—
172C2×C4—22no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—42no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—5841no—
184C2×C4—5842no—
185C2×C4C2×#1192400711yescharacteristic
186C2×C4C4×C22⋊D7312yes—
187C2×C4#1455657012yes—
188C2×C4#1455657411yescharacteristic
189C8—2922no—
190C8—2924no—
191C22#1798846011yescharacteristic
192C22#1798876011yescharacteristic
193C22#1798876012yes—
194C22#1798876512yes—
195C22#1798877011yescharacteristic
196C4—21no—
197C4—21no—
198C4—22no—
199C4—22no—
200C4—44no—
201C4—82no—
202C4—82no—
203C4—11681no—
204C2#2260923311yescharacteristic
205C2#2260925411yescharacteristic
206C2#2260926512yes—
207C2#2261014611yescharacteristic
208C2#2261016412yes—
subgroupG/H
centerC23#14556560
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC73×#2382C2
socle, prime radicalC23×C73#120
cosocleC2×C42×C73C23
hypercenter#2382D73
hypocenterC73#8915
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2382

Complements

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

NH ≅ G/Ntype
12. #17988329C4semidirect
110. C73#8915semidirect

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×#23822
#891573