Finite Group Databasebeta

← C73×#11504 #32920908

Subgroups — C73×#11504 #32920908

Order 18688.

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

normal subgroups only

This group has 510 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×#2310C211yesmaximal, characteristic
2C73×#1464C212yesmaximal
3C73×#1317C214yesmaximal
4C23×Q8×C73C411yescharacteristic
5C2×#117×C73C411yescharacteristic
6C2×#117×C73C2211yescharacteristic
7#432×C73—22no—
8#391×C73—22no—
9#391×C73—22no—
10#381×C73C412yes—
11#381×C73C2212yes—
12#324×C73—22no—
13#323×C73C2214yes—
14C22×Q8×C73—21no—
15C22×Q8×C73—21no—
16C22×Q8×C73—24no—
17C22×Q8×C73—41no—
18C22×Q8×C73—41no—
19C22×Q8×C73—42no—
20C23×C4×C73C2×C411yescharacteristic
21C23×C4×C73C2×C412yes—
22#117×C73—41no—
23#117×C73—41no—
24#117×C73—42no—
25C2×C4⋊C4×C73—21no—
26C2×C4⋊C4×C73D412yes—
27C2×C22⋊C4×C73C2×C412yes—
28C2×C22⋊C4×C73C2×C411yescharacteristic
29C2×C22⋊C4×C73C2311yescharacteristic
30C2×C42×C73—21no—
31C2×C42×C73D412yes—
32C4⋊C8×C73—42no—
33C22⋊C8×C73—24no—
34#97×C73—42no—
35#95×C73—24no—
36#95×C73—24no—
37C24×C73C22×C411yescharacteristic
38C2×Q8×C73—24no—
39C2×Q8×C73—24no—
40C2×Q8×C73—48no—
41C2×Q8×C73—48no—
42C2×Q8×C73—42no—
43C2×Q8×C73—42no—
44C2×Q8×C73—41no—
45C2×Q8×C73—41no—
46C2×Q8×C73—42no—
47C22×C4×C73—22no—
48C22×C4×C73—21no—
49C22×C4×C73—21no—
50C22×C4×C73—22no—
51C22×C4×C73—22no—
52C22×C4×C73—22no—
53C22×C4×C73—22no—
54C22×C4×C73—42no—
55C22×C4×C73—42no—
56C22×C4×C73C22⋊C411yescharacteristic
57C22×C4×C73C22⋊C412yes—
58C22×C4×C73C22⋊C411yescharacteristic
59C22×C4×C73M1614yes—
60C22×C4×C73C2×D412yes—
61C2×C8×C73—44no—
62C4⋊C4×C73—42no—
63C4⋊C4×C73—42no—
64C22⋊C4×C73—41no—
65C22⋊C4×C73—41no—
66C22⋊C4×C73—42no—
67C42×C73—22no—
68C42×C73—22no—
69C42×C73—42no—
70C23×C73—21no—
71C23×C73—21no—
72C23×C73—42no—
73C23×C73C2×C22⋊C411yescharacteristic
74C23×C73C2×M1612yes—
75Q8×C73—44no—
76Q8×C73—44no—
77Q8×C73—48no—
78C2×C4×C73—24no—
79C2×C4×C73—24no—
80C2×C4×C73—21no—
81C2×C4×C73—21no—
82C2×C4×C73—21no—
83C2×C4×C73—21no—
84C2×C4×C73—24no—
85C2×C4×C73—22no—
86C2×C4×C73—22no—
87C2×C4×C73—44no—
88C2×C4×C73—42no—
89C2×C4×C73—42no—
90C2×C4×C73—44no—
91C2×C4×C73—42no—
92C2×C4×C73—42no—
93C2×C4×C73—44no—
94C2×C4×C73—42no—
95C2×C4×C73#9911yescharacteristic
96C2×C4×C73#9911yescharacteristic
97C2×C4×C73#10012yes—
98C8×C73—84no—
99C22×C73—22no—
100C22×C73—22no—
101C22×C73—42no—
102C22×C73—42no—
103C22×C73—42no—
104C22×C73#40711yescharacteristic
105C22×C73C2×#9911yescharacteristic
106C22×C73C2×#10011yescharacteristic
107C4×C73—21no—
108C4×C73—21no—
109C4×C73—22no—
110C4×C73—42no—
111C4×C73—42no—
112C4×C73—44no—
113C4×C73—82no—
114#11504C7311yesmaximal, characteristic, direct product factor, Sylow
115C2×C73—21no—
116C2×C73—21no—
117C2×C73—42no—
118C2×C73#146211yescharacteristic
119C2×C73#212312yes—
120#2310C2×C7311yescharacteristic
121#1464C2×C7312yes—
122#1317C2×C7314yes—
123C73#1150411yescharacteristic, direct product factor, Sylow
124C23×Q8C4×C7311yescharacteristic
125C2×#117C4×C7311yescharacteristic
126C2×#117C22×C7311yescharacteristic
127#432—22no—
128#391—22no—
129#391—22no—
130#381C4×C7312yes—
131#381C22×C7312yes—
132#324—22no—
133#323C22×C7314yes—
134C22×Q8—21no—
135C22×Q8—21no—
136C22×Q8—24no—
137C22×Q8—41no—
138C22×Q8—41no—
139C22×Q8—42no—
140C23×C4C2×C4×C7311yescharacteristic
141C23×C4C2×C4×C7312yes—
142#117—41no—
143#117—41no—
144#117—42no—
145C2×C4⋊C4—21no—
146C2×C4⋊C4D4×C7312yes—
147C2×C22⋊C4C2×C4×C7312yes—
148C2×C22⋊C4C2×C4×C7311yescharacteristic
149C2×C22⋊C4C23×C7311yescharacteristic
150C2×C42—21no—
151C2×C42D4×C7312yes—
152C4⋊C8—42no—
153C22⋊C8—24no—
154#97—42no—
155#95—24no—
156#95—24no—
157C24C22×C4×C7311yescharacteristic
158C2×Q8—24no—
159C2×Q8—24no—
160C2×Q8—48no—
161C2×Q8—48no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—41no—
165C2×Q8—41no—
166C2×Q8—42no—
167C22×C4—22no—
168C22×C4—21no—
169C22×C4—21no—
170C22×C4—22no—
171C22×C4—22no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—42no—
175C22×C4—42no—
176C22×C4C22⋊C4×C7311yescharacteristic
177C22×C4C22⋊C4×C7311yescharacteristic
178C22×C4C22⋊C4×C7312yes—
179C22×C4M16×C7314yes—
180C22×C4C2×D4×C7312yes—
181C2×C8—44no—
182C4⋊C4—42no—
183C4⋊C4—42no—
184C22⋊C4—41no—
185C22⋊C4—41no—
186C22⋊C4—42no—
187C42—22no—
188C42—22no—
189C42—42no—
190C23—21no—
191C23—21no—
192C23—42no—
193C23C2×C22⋊C4×C7311yescharacteristic
194C23C2×M16×C7312yes—
195Q8—44no—
196Q8—44no—
197Q8—48no—
198C2×C4—24no—
199C2×C4—24no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—21no—
203C2×C4—21no—
204C2×C4—24no—
205C2×C4—22no—
206C2×C4—22no—
207C2×C4—44no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—44no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—44no—
214C2×C4—42no—
215C2×C4#99×C7311yescharacteristic
216C2×C4#99×C7311yescharacteristic
217C2×C4#100×C7312yes—
218C8—84no—
219C22—22no—
220C22—22no—
221C22—42no—
222C22—42no—
223C22—42no—
224C22#407×C7311yescharacteristic
225C22C2×#99×C7311yescharacteristic
226C22C2×#100×C7311yescharacteristic
227C4—21no—
228C4—21no—
229C4—22no—
230C4—44no—
231C4—42no—
232C4—42no—
233C4—82no—
234C2—21no—
235C2—21no—
236C2—42no—
237C2C73×#146211yescharacteristic
238C2C73×#212312yes—
subgroupG/H
center, socleC22×C73C2×#99
commutatorC24C22×C4×C73
Frattini, cosocleC2×C22⋊C4C23×C73
prime radicalC24×C73C22×C4
LCSG ▷ C24 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ C2×#117×C73 ◁ G

Complements

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

NH ≅ G/Ntype
114. #11504C73direct (N × H)
123. C73#11504direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#23102
C73×#14642
C73×#13172
#1150473