Finite Group Databasebeta

← C73×#11514 #32920918

Subgroups — C73×#11514 #32920918

Order 18688.

434 conjugacy classes of subgroups; only the 110 normal subgroups are shown.

normal subgroups only

This group has 434 conjugacy classes of subgroups — too many to draw. Only its 110 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
1C73×#2317C211yesmaximal, characteristic
2C73×#1463C212yesmaximal
3C73×#1325C212yesmaximal, complemented
4C73×#1324C212yesmaximal, complemented
5C2×#117×C73C411yescharacteristic
6C2×#117×C73C411yescharacteristic
7C22×C4⋊C4×C73C2211yescharacteristic
8#407×C73—22no—
9#389×C73—22no—
10#385×C73—22no—
11#384×C73C411yescharacteristic
12#384×C73C2211yescharacteristic
13#382×C73C411yescharacteristic
14#382×C73C2211yescharacteristic
15#324×C73—22no—
16#324×C73C2214yes—
17C23×C4×C73C2×C411yescharacteristic
18C23×C4×C73D412yes—
19C2×M16×C73—42no—
20#117×C73—22no—
21#117×C73—22no—
22#117×C73—42no—
23C2×C4⋊C4×C73—21no—
24C2×C4⋊C4×C73—22no—
25C2×C4⋊C4×C73—22no—
26C2×C4⋊C4×C73—42no—
27C2×C4⋊C4×C73C2×C411yescharacteristic
28C2×C4⋊C4×C73C2×C411yescharacteristic
29C2×C4⋊C4×C73C2×C411yescharacteristic
30C2×C4⋊C4×C73D412yes—
31C2×C4⋊C4×C73C2311yescharacteristic
32C2×C22⋊C4×C73—21no—
33C2×C22⋊C4×C73—21no—
34C2×C42×C73—21no—
35C2×C42×C73C2×C411yescharacteristic
36C2×C42×C73C2×C411yescharacteristic
37C22⋊C8×C73—24no—
38C22⋊C8×C73—42no—
39#95×C73—22no—
40#95×C73—22no—
41C24×C73C22⋊C411yescharacteristic
42C22×C4×C73—22no—
43C22×C4×C73—22no—
44C22×C4×C73—21no—
45C22×C4×C73—21no—
46C22×C4×C73—22no—
47C22×C4×C73—21no—
48C22×C4×C73—21no—
49C22×C4×C73—22no—
50C22×C4×C73—21no—
51C22×C4×C73—21no—
52C22×C4×C73—82no—
53C22×C4×C73C22⋊C411yescharacteristic
54C22×C4×C73C22⋊C412yes—
55C22×C4×C73C22×C411yescharacteristic
56C22×C4×C73C2×D412yes—
57M16×C73—84no—
58C2×C8×C73—44no—
59C4⋊C4×C73—24no—
60C4⋊C4×C73—41no—
61C4⋊C4×C73—42no—
62C4⋊C4×C73—41no—
63C4⋊C4×C73—41no—
64C4⋊C4×C73—41no—
65C4⋊C4×C73—82no—
66C4⋊C4×C73—82no—
67C22⋊C4×C73—24no—
68C22⋊C4×C73—42no—
69C42×C73—21no—
70C42×C73—21no—
71C42×C73—42no—
72C42×C73M1612yescomplemented
73C42×C73M1612yescomplemented
74C23×C73—21no—
75C23×C73—21no—
76C23×C73—41no—
77C23×C73—41no—
78C23×C73#9912yes—
79C23×C73C2×C22⋊C411yescharacteristic
80C2×C4×C73—24no—
81C2×C4×C73—24no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—21no—
85C2×C4×C73—21no—
86C2×C4×C73—22no—
87C2×C4×C73—22no—
88C2×C4×C73—22no—
89C2×C4×C73—22no—
90C2×C4×C73—41no—
91C2×C4×C73—41no—
92C2×C4×C73—44no—
93C2×C4×C73—41no—
94C2×C4×C73—41no—
95C2×C4×C73—42no—
96C2×C4×C73—42no—
97C2×C4×C73—42no—
98C2×C4×C73—42no—
99C2×C4×C73—41no—
100C2×C4×C73—41no—
101C2×C4×C73—82no—
102C2×C4×C73#10112yes—
103C2×C4×C73C2×M1611yescharacteristic
104C2×C4×C73C2×M1611yescharacteristic
105C8×C73—84no—
106C22×C73—21no—
107C22×C73—21no—
108C22×C73—22no—
109C22×C73—22no—
110C22×C73—22no—
111C22×C73—42no—
112C22×C73—42no—
113C22×C73#40711yescharacteristic
114C22×C73C2×#9911yescharacteristic
115C22×C73C2×#10111yescharacteristic
116C4×C73—22no—
117C4×C73—21no—
118C4×C73—21no—
119C4×C73—42no—
120C4×C73—42no—
121C4×C73—42no—
122C4×C73—42no—
123C4×C73—81no—
124C4×C73—81no—
125#11514C7311yesmaximal, characteristic, direct product factor, Sylow
126C2×C73—21no—
127C2×C73—21no—
128C2×C73—42no—
129C2×C73#146311yescharacteristic
130C2×C73#212711yescharacteristic
131C2×C73#213311yescharacteristic
132#2317C2×C7311yescharacteristic
133#1463C2×C7312yes—
134#1325C2×C7312yescomplemented
135#1324C2×C7312yescomplemented
136C73#1151411yescharacteristic, direct product factor, Sylow
137C2×#117C4×C7311yescharacteristic
138C2×#117C4×C7311yescharacteristic
139C22×C4⋊C4C22×C7311yescharacteristic
140#407—22no—
141#389—22no—
142#385—22no—
143#384C4×C7311yescharacteristic
144#384C22×C7311yescharacteristic
145#382C4×C7311yescharacteristic
146#382C22×C7311yescharacteristic
147#324—22no—
148#324C22×C7314yes—
149C23×C4C2×C4×C7311yescharacteristic
150C23×C4D4×C7312yes—
151C2×M16—42no—
152#117—22no—
153#117—22no—
154#117—42no—
155C2×C4⋊C4—21no—
156C2×C4⋊C4—22no—
157C2×C4⋊C4—22no—
158C2×C4⋊C4—42no—
159C2×C4⋊C4C2×C4×C7311yescharacteristic
160C2×C4⋊C4C2×C4×C7311yescharacteristic
161C2×C4⋊C4C2×C4×C7311yescharacteristic
162C2×C4⋊C4D4×C7312yes—
163C2×C4⋊C4C23×C7311yescharacteristic
164C2×C22⋊C4—21no—
165C2×C22⋊C4—21no—
166C2×C42—21no—
167C2×C42C2×C4×C7311yescharacteristic
168C2×C42C2×C4×C7311yescharacteristic
169C22⋊C8—24no—
170C22⋊C8—42no—
171#95—22no—
172#95—22no—
173C24C22⋊C4×C7311yescharacteristic
174C22×C4—22no—
175C22×C4—22no—
176C22×C4—21no—
177C22×C4—21no—
178C22×C4—22no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—22no—
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—82no—
185C22×C4C22⋊C4×C7311yescharacteristic
186C22×C4C22⋊C4×C7312yes—
187C22×C4C22×C4×C7311yescharacteristic
188C22×C4C2×D4×C7312yes—
189M16—84no—
190C2×C8—44no—
191C4⋊C4—24no—
192C4⋊C4—41no—
193C4⋊C4—42no—
194C4⋊C4—41no—
195C4⋊C4—41no—
196C4⋊C4—41no—
197C4⋊C4—82no—
198C4⋊C4—82no—
199C22⋊C4—24no—
200C22⋊C4—42no—
201C42—21no—
202C42—21no—
203C42—42no—
204C42M16×C7312yescomplemented
205C42M16×C7312yescomplemented
206C23—21no—
207C23—21no—
208C23—41no—
209C23—41no—
210C23#99×C7312yes—
211C23C2×C22⋊C4×C7311yescharacteristic
212C2×C4—24no—
213C2×C4—24no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—22no—
220C2×C4—22no—
221C2×C4—22no—
222C2×C4—41no—
223C2×C4—41no—
224C2×C4—44no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—42no—
228C2×C4—42no—
229C2×C4—42no—
230C2×C4—42no—
231C2×C4—41no—
232C2×C4—41no—
233C2×C4—82no—
234C2×C4#101×C7312yes—
235C2×C4C2×M16×C7311yescharacteristic
236C2×C4C2×M16×C7311yescharacteristic
237C8—84no—
238C22—21no—
239C22—21no—
240C22—22no—
241C22—22no—
242C22—22no—
243C22—42no—
244C22—42no—
245C22#407×C7311yescharacteristic
246C22C2×#99×C7311yescharacteristic
247C22C2×#101×C7311yescharacteristic
248C4—22no—
249C4—21no—
250C4—21no—
251C4—42no—
252C4—42no—
253C4—42no—
254C4—42no—
255C4—81no—
256C4—81no—
257C2—21no—
258C2—21no—
259C2—42no—
260C2C73×#146311yescharacteristic
261C2C73×#212711yescharacteristic
262C2C73×#213311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#99
commutatorC22×C4C22×C4×C73
Frattini, cosocleC2×C4⋊C4C23×C73
prime radicalC24×C73C22⋊C4
LCSG ▷ C22×C4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C24×C73 ◁ C22×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
3. C73×#1325C2semidirect
4. C73×#1324C2semidirect
72. C42×C73M16semidirect
73. C42×C73M16semidirect
125. #11514C73direct (N × H)
134. #1325C2×C73semidirect
135. #1324C2×C73semidirect
136. C73#11514direct (N × H)
204. C42M16×C73semidirect
205. C42M16×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#23172
C73×#14632
C73×#13252
C73×#13242
#1151473