Finite Group Databasebeta

← #32979521

Subgroups — #32979521

Order 18688.

394 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 91 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#22612534C211yesmaximal, characteristic
2#22608261C211yesmaximal, characteristic
3#22607838C212yesmaximal
4#22607836C212yesmaximal
5C73×#1463C211yesmaximal, characteristic
6#17988551C2212yes—
7#17988473—22no—
8#17988473—22no—
9#17988450C412yes—
10#17988447C2211yescharacteristic
11#17988447C2211yescharacteristic
12C4×C22⋊Dic73C412yes—
13#17988313—22no—
14C22×C4⋊C4×C73C2211yescharacteristic
15#407×C73C2212yes—
16#324×C73—22no—
17C2×#11924012—22no—
18C2×C4⋊Dic73—21no—
19C2×C4⋊Dic73—21no—
20C2×C22⋊Dic73C2×C412yes—
21C2×C22⋊Dic73C2×C412yes—
22C2×C4×Dic73—22no—
23C22⋊#10596831—22no—
24C22⋊#10596831—22no—
25#14556498—22no—
26#14556498—24no—
27#14556498—21no—
28#14556498—21no—
29C23×C4×C73C2×C411yescharacteristic
30C23×C4×C73C2×C411yescharacteristic
31C23×C4×C73C2311yescharacteristic
32C2×M16×C73—22no—
33C2×C4⋊C4×C73—22no—
34C2×C4⋊C4×C73—22no—
35C2×C4⋊C4×C73D412yes—
36C2×C4⋊C4×C73D412yes—
37C22⋊C8×C73—22no—
38C22⋊C8×C73—22no—
39C22×Dic73—22no—
40C22×Dic73—22no—
41#11924012—82no—
42C2×#10596831—42no—
43C4⋊Dic73—81no—
44C4⋊Dic73—81no—
45C22⋊Dic73—42no—
46C22⋊Dic73—42no—
47C4×Dic73—82no—
48C24×C73C22×C411yescharacteristic
49C22×C4×C73—21no—
50C22×C4×C73—21no—
51C22×C4×C73—21no—
52C22×C4×C73—21no—
53C22×C4×C73—41no—
54C22×C4×C73—41no—
55C22×C4×C73—81no—
56C22×C4×C73—81no—
57C22×C4×C73C22⋊C412yes—
58C22×C4×C73C22⋊C412yes—
59C22×C4×C73C2×D411yescharacteristic
60C22×C4×C73C2×D411yescharacteristic
61C22×C4×C73#4112yes—
62C22×C4×C73#4112yes—
63M16×C73—82no—
64C2×C8×C73—42no—
65C4⋊C4×C73—24no—
66C4⋊C4×C73—24no—
67C23×C73—21no—
68C23×C73—21no—
69C23×C73—41no—
70C23×C73—41no—
71C23×C73C2×C22⋊C411yescharacteristic
72C23×C73#11711yescharacteristic
73C23×C73#11711yescharacteristic
74C2×C4×C73—22no—
75C2×C4×C73—22no—
76C2×C4×C73—22no—
77C2×C4×C73—22no—
78C2×C4×C73—42no—
79C2×C4×C73—41no—
80C2×C4×C73—41no—
81C2×C4×C73—42no—
82C2×C4×C73—42no—
83C2×C4×C73—42no—
84C2×C4×C73—42no—
85C2×C4×C73—81no—
86C2×C4×C73—81no—
87C2×C4×C73#12312yes—
88C2×C4×C73#12312yes—
89C2×Dic73—42no—
90C2×Dic73—42no—
91C2×Dic73—42no—
92C2×Dic73—42no—
93C2×Dic73—42no—
94C2×Dic73—42no—
95C8×C73—82no—
96#10596831—82no—
97C22×C73—21no—
98C22×C73—21no—
99C22×C73—21no—
100C22×C73—21no—
101C22×C73—21no—
102C22×C73—21no—
103C22×C73—21no—
104C22×C73—21no—
105C22×C73—42no—
106C22×C73—42no—
107C22×C73#38111yescharacteristic
108C22×C73#41311yescharacteristic
109C22×C73#41311yescharacteristic
110C4×C73—22no—
111C4×C73—22no—
112C4×C73—42no—
113C4×C73—42no—
114Dic73—82no—
115Dic73—82no—
116#8758—731nomaximal, Sylow
117C2×C73—21no—
118C2×C73—21no—
119C2×C73—41no—
120C2×C73—41no—
121C2×C73#182211yescharacteristic
122C2×C73#182811yescharacteristic
123C2×C73#183011yescharacteristic
124#2313—731no—
125#1463—731no—
126#1463D7311yescharacteristic
127#1305—732no—
128#1305—732no—
129C73#875811yescharacteristic, complemented, Sylow
130C22×C4⋊C4C2×D7311yescharacteristic
131#407—732no—
132#407C2×D7312yes—
133#387—1462no—
134#387—1462no—
135#381—732no—
136#380—731no—
137#380—731no—
138C4×C22⋊C4—732no—
139#324—22no—
140#324—1462no—
141C23×C4C4×D7311yescharacteristic
142C23×C4C4×D7311yescharacteristic
143C23×C4C22×D7311yescharacteristic
144C2×M16—22no—
145C2×M16—1462no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—22no—
148C2×C4⋊C4—1461no—
149C2×C4⋊C4—1461no—
150C2×C4⋊C4D29212yes—
151C2×C4⋊C4C22⋊D7312yes—
152C2×C22⋊C4—732no—
153C2×C22⋊C4—732no—
154C2×C42—1462no—
155C22⋊C8—22no—
156C22⋊C8—22no—
157C22⋊C8—1462no—
158C22⋊C8—1462no—
159#95—1462no—
160#95—1464no—
161#95—1461no—
162#95—1461no—
163C24C2×C4×D7311yescharacteristic
164C22×C4—21no—
165C22×C4—21no—
166C22×C4—21no—
167C22×C4—21no—
168C22×C4—41no—
169C22×C4—41no—
170C22×C4—81no—
171C22×C4—81no—
172C22×C4—1462no—
173C22×C4—1462no—
174C22×C4#1192400512yes—
175C22×C4#1192400512yes—
176C22×C4C2×C22⋊D7311yescharacteristic
177C22×C4C2×D29211yescharacteristic
178C22×C4#1192402712yes—
179C22×C4#1192402712yes—
180M16—82no—
181M16—5842no—
182C2×C8—42no—
183C2×C8—2922no—
184C4⋊C4—24no—
185C4⋊C4—24no—
186C4⋊C4—5841no—
187C4⋊C4—5841no—
188C22⋊C4—2922no—
189C22⋊C4—2922no—
190C42—5842no—
191C23—21no—
192C23—21no—
193C23—41no—
194C23—41no—
195C23C2×#1192400511yescharacteristic
196C23#1455654711yescharacteristic
197C23#1455654711yescharacteristic
198C2×C4—22no—
199C2×C4—22no—
200C2×C4—22no—
201C2×C4—22no—
202C2×C4—41no—
203C2×C4—41no—
204C2×C4—42no—
205C2×C4—42no—
206C2×C4—42no—
207C2×C4—42no—
208C2×C4—42no—
209C2×C4—81no—
210C2×C4—81no—
211C2×C4—2922no—
212C2×C4—2922no—
213C2×C4—2922no—
214C2×C4—2922no—
215C2×C4—2922no—
216C2×C4—2922no—
217C2×C4#1455657212yes—
218C2×C4#1455657512yes—
219C8—82no—
220C8—5842no—
221C22—21no—
222C22—21no—
223C22—21no—
224C22—21no—
225C22—21no—
226C22—21no—
227C22—21no—
228C22—21no—
229C22—42no—
230C22—42no—
231C22#1798844811yescharacteristic
232C22#1798856911yescharacteristic
233C22#1798856911yescharacteristic
234C4—22no—
235C4—22no—
236C4—42no—
237C4—42no—
238C4—5842no—
239C4—5842no—
240C2—21no—
241C2—21no—
242C2—41no—
243C2—41no—
244C2#2261001211yescharacteristic
245C2#2261003711yescharacteristic
246C2#2261004311yescharacteristic
subgroupG/H
centerC22#17988448
commutator, prime radicalC24×C73C22×C4
FrattiniC23×C4C22×D73
FittingC73×#1463C2
socleC22×C73#381
cosocleC23×C4×C73C23
hypercenter#1463D73
hypocenterC73#8758
LCSG ▷ C24×C73 ▷ C22×C73 ▷ C73
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1463

Complements

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

NH ≅ G/Ntype
129. C73#8758semidirect

Maximal subgroups

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

subgroupindex
#226125342
#226082612
#226078382
#226078362
C73×#14632
#875873