Finite Group Databasebeta

← #32980360

Subgroups — #32980360

Order 18688.

428 conjugacy classes of subgroups; only the 119 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 119 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#22613117C211yesmaximal, characteristic
2#22610901C211yesmaximal, characteristic
3#22610099C212yesmaximal
4#22607813C212yesmaximal
5C2×#330×C73C211yesmaximal, characteristic
6C2×#14556525—22no—
7C2×#14556523—22no—
8C2×#14556502C2211yescharacteristic
9#17988486—22no—
10#17988473—22no—
11#17988473—22no—
12#17988457C2211yescharacteristic
13#17988453C2212yes—
14#17988349—22no—
15C2×#125×C73C2211yescharacteristic
16C2×#97×C73C2212yes—
17#330×C73C414yescomplemented
18C22×#10596831—21no—
19C2×C4⋊Dic73—22no—
20C2×C4⋊Dic73—22no—
21C2×C4⋊Dic73—21no—
22C2×C4⋊Dic73D412yes—
23C2×C4⋊Dic73D412yes—
24C2×C4×Dic73—22no—
25#14556525—44no—
26#14556523—44no—
27#14556502—22no—
28#14556498—22no—
29#14556498—22no—
30#14556498—22no—
31#14556498—22no—
32C22×C8×C73—22no—
33#125×C73—22no—
34#125×C73C2×C412yes—
35#125×C73Q812yes—
36C2×C4⋊C4×C73—22no—
37C2×C4⋊C4×C73D412yes—
38C2×C42×C73C2311yescharacteristic
39#97×C73—22no—
40#97×C73C2×C414yes—
41C22×Dic73—22no—
42C22×Dic73—22no—
43C22×Dic73—41no—
44C2×#10596831—22no—
45C2×#10596831—41no—
46C2×#10596831—41no—
47C4⋊Dic73—42no—
48C4⋊Dic73—42no—
49C4⋊Dic73—42no—
50C4⋊Dic73—42no—
51C4⋊Dic73—42no—
52C4⋊Dic73—82no—
53C4×Dic73—82no—
54C22×C4×C73—22no—
55C22×C4×C73C2×D412yes—
56C22×C4×C73C2×D411yescharacteristic
57C2×C8×C73—24no—
58C2×C8×C73—24no—
59C2×C8×C73—24no—
60C4⋊C4×C73—24no—
61C4⋊C4×C73—24no—
62C4⋊C4×C73—22no—
63C4⋊C4×C73C4⋊C414yes—
64C42×C73C22×C411yescharacteristic
65C42×C73C2×Q811yescharacteristic
66C42×C73#4112yes—
67C23×C73#12011yescharacteristic
68C2×C4×C73—22no—
69C2×C4×C73—21no—
70C2×C4×C73—22no—
71C2×C4×C73—21no—
72C2×C4×C73—24no—
73C2×C4×C73—42no—
74C2×C4×C73—42no—
75C2×C4×C73C2×C4⋊C411yescharacteristic
76C2×C4×C73C4×D412yes—
77C2×C4×C73C22⋊Q812yes—
78C2×C4×C73#12311yescharacteristic
79C2×Dic73—42no—
80C2×Dic73—42no—
81C2×Dic73—42no—
82C2×Dic73—42no—
83C2×Dic73—42no—
84C2×Dic73—42no—
85C2×Dic73—82no—
86C2×Dic73—81no—
87C8×C73—28no—
88#10596831—42no—
89C22×C73#38511yescharacteristic
90C22×C73#45312yes—
91C22×C73#45411yescharacteristic
92C22×C73#45612yes—
93C22×C73#45611yescharacteristic
94C4×C73—21no—
95C4×C73—21no—
96C4×C73—22no—
97C4×C73—22no—
98C4×C73—44no—
99Dic73—82no—
100Dic73—82no—
101Dic73—161no—
102#8913—731nomaximal, Sylow
103C2×C73#165611yescharacteristic
104C2×C73#166012yes—
105C2×C73#166311yescharacteristic
106C2×C73#185711yescharacteristic
107C2×C73#185912yes—
108#2382—731no—
109#1992—731no—
110#1847—732no—
111C2×#330D7311yescharacteristic
112#1295—732no—
113C73#891311yescharacteristic, complemented, Sylow
114C2×#125C2×D7311yescharacteristic
115C2×#107—1462no—
116C2×#106—1462no—
117C2×#97—731no—
118C2×#97C2×D7312yes—
119#389—1462no—
120#387—1462no—
121#387—1462no—
122#384—731no—
123#382—732no—
124#340—1462no—
125#330Dic7314yescomplemented
126C22×C8—22no—
127C22×C8—1461no—
128#125—22no—
129#125Dic14612yes—
130#125C2×Dic7312yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—732no—
133C2×C4⋊C4—732no—
134C2×C4⋊C4—1462no—
135C2×C4⋊C4—1461no—
136C2×C4⋊C4—1462no—
137C2×C4⋊C4D29212yes—
138C2×C42—1462no—
139C2×C42C22×D7311yescharacteristic
140#107—2924no—
141#106—2924no—
142#97—22no—
143#97—1462no—
144#97C2×Dic7314yes—
145#95—1462no—
146#95—1462no—
147#95—1462no—
148#95—1462no—
149C22×C4—22no—
150C22×C4—2921no—
151C22×C4—1462no—
152C22×C4—1462no—
153C22×C4D4×D7312yes—
154C22×C4C2×D29211yescharacteristic
155C2×C8—24no—
156C2×C8—24no—
157C2×C8—24no—
158C2×C8—2921no—
159C2×C8—2921no—
160C2×C8—1462no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—2922no—
165C4⋊C4—2922no—
166C4⋊C4—2922no—
167C4⋊C4—2922no—
168C4⋊C4—2922no—
169C4⋊C4—5842no—
170C4⋊C4C4⋊Dic7314yes—
171C42—5842no—
172C42C22×Dic7311yescharacteristic
173C42C2×Dic14611yescharacteristic
174C42#1192402712yes—
175C23#1455656111yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—2922no—
184C2×C4—2922no—
185C2×C4—2922no—
186C2×C4—2922no—
187C2×C4—2922no—
188C2×C4—2922no—
189C2×C4—5842no—
190C2×C4—5841no—
191C2×C4C2×C4⋊Dic7311yescharacteristic
192C2×C4D4×Dic7312yes—
193C2×C4#1455656812yes—
194C2×C4#1455657511yescharacteristic
195C8—28no—
196C8—2922no—
197C22#1798846211yescharacteristic
198C22#1798875612yes—
199C22#1798876211yescharacteristic
200C22#1798877112yes—
201C22#1798877211yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—5842no—
208C4—5842no—
209C4—11681no—
210C2#2260922611yescharacteristic
211C2#2260924412yes—
212C2#2260926011yescharacteristic
213C2#2261014811yescharacteristic
214C2#2261015912yes—
subgroupG/H
centerC23#14556561
commutatorC42×C73C22×C4
FrattiniC2×C42C22×D73
FittingC2×#330×C73C2
socle, prime radicalC23×C73#120
cosocleC2×C42×C73C23
hypercenterC2×#330D73
hypocenterC73#8913
LCSG ▷ C42×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#330

Complements

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

NH ≅ G/Ntype
17. #330×C73C4semidirect
113. C73#8913semidirect
125. #330Dic73semidirect

Maximal subgroups

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

subgroupindex
#226131172
#226109012
#226100992
#226078132
C2×#330×C732
#891373