Finite Group Databasebeta

← C73×#10388 #32919792

Subgroups — C73×#10388 #32919792

Order 18688.

594 conjugacy classes of subgroups; only the 90 normal subgroups are shown.

normal subgroups only

This group has 594 conjugacy classes of subgroups — too many to draw. Only its 90 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×#2608C211yesmaximal, characteristic, complemented
2C73×#1789C212yesmaximal
3C73×#1782C211yesmaximal, characteristic
4C73×#1306C211yesmaximal, characteristic, complemented
5C73×#1284C212yesmaximal, complemented
6C22×#41×C73C2211yescharacteristic
7C2×#104×C73—22no—
8C2×#104×C73—22no—
9C2×#99×C73—22no—
10#407×C73C2212yes—
11#396×C73—22no—
12#389×C73—22no—
13#387×C73—22no—
14#381×C73C2211yescharacteristic
15#381×C73C2211yescharacteristic
16C4×C22⋊C4×C73C2212yes—
17C2×#41×C73—22no—
18C2×#41×C73—22no—
19C2×#41×C73—44no—
20C22×Q8×C73Q811yescharacteristic
21C22×D4×C73—21no—
22C22×D4×C73Q811yescharacteristic
23C23×C4×C73—21no—
24C23×C4×C73C2311yescharacteristic
25C2×M16×C73—22no—
26C2×C4⋊C4×C73—22no—
27C2×C4⋊C4×C73—22no—
28C2×C4⋊C4×C73—22no—
29C2×C22⋊C4×C73—22no—
30C2×C22⋊C4×C73—21no—
31C2×C22⋊C4×C73D412yes—
32C2×C42×C73D412yes—
33C2×C42×C73D412yes—
34#104×C73—44no—
35#104×C73—44no—
36#99×C73—44no—
37C22⋊C8×C73—22no—
38C22⋊C8×C73—22no—
39#95×C73—22no—
40#95×C73—22no—
41#95×C73—22no—
42#95×C73—22no—
43C24×C73—21no—
44C24×C73C2×D411yescharacteristic
45#41×C73—24no—
46#41×C73—24no—
47#41×C73—42no—
48#41×C73—42no—
49#41×C73—44no—
50#41×C73—44no—
51C2×Q8×C73—22no—
52C2×Q8×C73—42no—
53C2×D4×C73—24no—
54C2×D4×C73—22no—
55C2×D4×C73—42no—
56C2×D4×C73—42no—
57C2×D4×C73—41no—
58C2×D4×C73—41no—
59C22×C4×C73—22no—
60C22×C4×C73—21no—
61C22×C4×C73—22no—
62C22×C4×C73—22no—
63C22×C4×C73—42no—
64C22×C4×C73—42no—
65C22×C4×C73—42no—
66C22×C4×C73—42no—
67C22×C4×C73—41no—
68C22×C4×C73C2×D412yes—
69C22×C4×C73C2×Q811yescharacteristic
70C22×C4×C73#4112yes—
71C22×C4×C73#4111yescharacteristic
72M16×C73—42no—
73M16×C73—42no—
74C2×C8×C73—42no—
75C4⋊C4×C73—44no—
76C4⋊C4×C73—44no—
77C4⋊C4×C73—82no—
78C22⋊C4×C73—44no—
79C22⋊C4×C73—42no—
80C22⋊C4×C73—42no—
81C42×C73—42no—
82C42×C73—42no—
83C23×C73—22no—
84C23×C73—22no—
85C23×C73—42no—
86C23×C73—41no—
87C23×C73—41no—
88C23×C73—82no—
89C23×C73#12011yescharacteristic
90C23×C73C22⋊Q811yescharacteristic
91C23×C73#12411yescharacteristic
92Q8×C73—24no—
93Q8×C73—42no—
94D4×C73—24no—
95D4×C73—42no—
96D4×C73—44no—
97D4×C73—44no—
98C2×C4×C73—22no—
99C2×C4×C73—22no—
100C2×C4×C73—24no—
101C2×C4×C73—22no—
102C2×C4×C73—41no—
103C2×C4×C73—41no—
104C2×C4×C73—42no—
105C2×C4×C73—44no—
106C2×C4×C73—44no—
107C2×C4×C73—42no—
108C2×C4×C73—41no—
109C2×C4×C73—41no—
110C2×C4×C73—42no—
111C2×C4×C73—42no—
112C2×C4×C73—42no—
113C2×C4×C73—42no—
114C2×C4×C73—42no—
115C2×C4×C73—42no—
116C2×C4×C73—42no—
117C2×C4×C73—81no—
118C2×C4×C73—82no—
119C2×C4×C73C22⋊Q812yes—
120C2×C4×C73#12412yes—
121C8×C73—82no—
122C22×C73—22no—
123C22×C73—21no—
124C22×C73—21no—
125C22×C73—22no—
126C22×C73—22no—
127C22×C73—42no—
128C22×C73—82no—
129C22×C73—82no—
130C22×C73—82no—
131C22×C73—82no—
132C22×C73#39311yescharacteristic
133C22×C73B(4,𝔽2)12yes—
134C4×C73—22no—
135C4×C73—22no—
136C4×C73—44no—
137C4×C73—42no—
138C4×C73—82no—
139C4×C73—82no—
140C4×C73—161no—
141#10388C7311yesmaximal, characteristic, direct product factor, Sylow
142C2×C73—22no—
143C2×C73—41no—
144C2×C73—41no—
145C2×C73—82no—
146C2×C73#202911yescharacteristic
147C2×C73#203112yes—
148#2608C2×C7311yescharacteristic, complemented
149#1789C2×C7312yes—
150#1782C2×C7311yescharacteristic
151#1306C2×C7311yescharacteristic, complemented
152#1284C2×C7312yescomplemented
153C73#1038811yescharacteristic, direct product factor, Sylow
154C22×#41C22×C7311yescharacteristic
155C2×#104—22no—
156C2×#104—22no—
157C2×#99—22no—
158#407C22×C7312yes—
159#396—22no—
160#389—22no—
161#387—22no—
162#381C22×C7311yescharacteristic
163#381C22×C7311yescharacteristic
164C4×C22⋊C4C22×C7312yes—
165C2×#41—22no—
166C2×#41—22no—
167C2×#41—44no—
168C22×Q8Q8×C7311yescharacteristic
169C22×D4—21no—
170C22×D4Q8×C7311yescharacteristic
171C23×C4—21no—
172C23×C4C23×C7311yescharacteristic
173C2×M16—22no—
174C2×C4⋊C4—22no—
175C2×C4⋊C4—22no—
176C2×C4⋊C4—22no—
177C2×C22⋊C4—22no—
178C2×C22⋊C4—21no—
179C2×C22⋊C4D4×C7312yes—
180C2×C42D4×C7312yes—
181C2×C42D4×C7312yes—
182#104—44no—
183#104—44no—
184#99—44no—
185C22⋊C8—22no—
186C22⋊C8—22no—
187#95—22no—
188#95—22no—
189#95—22no—
190#95—22no—
191C24—21no—
192C24C2×D4×C7311yescharacteristic
193#41—24no—
194#41—24no—
195#41—42no—
196#41—42no—
197#41—44no—
198#41—44no—
199C2×Q8—22no—
200C2×Q8—42no—
201C2×D4—24no—
202C2×D4—22no—
203C2×D4—42no—
204C2×D4—42no—
205C2×D4—41no—
206C2×D4—41no—
207C22×C4—22no—
208C22×C4—21no—
209C22×C4—22no—
210C22×C4—22no—
211C22×C4—42no—
212C22×C4—42no—
213C22×C4—42no—
214C22×C4—42no—
215C22×C4—41no—
216C22×C4C2×D4×C7312yes—
217C22×C4C2×Q8×C7311yescharacteristic
218C22×C4#41×C7312yes—
219C22×C4#41×C7311yescharacteristic
220M16—42no—
221M16—42no—
222C2×C8—42no—
223C4⋊C4—44no—
224C4⋊C4—44no—
225C4⋊C4—82no—
226C22⋊C4—44no—
227C22⋊C4—42no—
228C22⋊C4—42no—
229C42—42no—
230C42—42no—
231C23—22no—
232C23—22no—
233C23—42no—
234C23—41no—
235C23—41no—
236C23—82no—
237C23#120×C7311yescharacteristic
238C23C22⋊Q8×C7311yescharacteristic
239C23#124×C7311yescharacteristic
240Q8—24no—
241Q8—42no—
242D4—24no—
243D4—42no—
244D4—44no—
245D4—44no—
246C2×C4—22no—
247C2×C4—22no—
248C2×C4—24no—
249C2×C4—22no—
250C2×C4—41no—
251C2×C4—41no—
252C2×C4—42no—
253C2×C4—44no—
254C2×C4—44no—
255C2×C4—42no—
256C2×C4—41no—
257C2×C4—41no—
258C2×C4—42no—
259C2×C4—42no—
260C2×C4—42no—
261C2×C4—42no—
262C2×C4—42no—
263C2×C4—42no—
264C2×C4—42no—
265C2×C4—81no—
266C2×C4—82no—
267C2×C4C22⋊Q8×C7312yes—
268C2×C4#124×C7312yes—
269C8—82no—
270C22—22no—
271C22—21no—
272C22—21no—
273C22—22no—
274C22—22no—
275C22—42no—
276C22—82no—
277C22—82no—
278C22—82no—
279C22—82no—
280C22#393×C7311yescharacteristic
281C22B(4,𝔽2)×C7312yes—
282C4—22no—
283C4—22no—
284C4—44no—
285C4—42no—
286C4—82no—
287C4—82no—
288C4—161no—
289C2—22no—
290C2—41no—
291C2—41no—
292C2—82no—
293C2C73×#202911yescharacteristic
294C2C73×#203112yes—
subgroupG/H
center, socleC22×C73#393
commutator, Frattini, cosocleC23×C4C23×C73
prime radicalC22×#41×C73C22
LCSG ▷ C23×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2608C2semidirect
4. C73×#1306C2semidirect
5. C73×#1284C2semidirect
141. #10388C73direct (N × H)
148. #2608C2×C73semidirect
151. #1306C2×C73semidirect
152. #1284C2×C73semidirect
153. C73#10388direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#26082
C73×#17892
C73×#17822
C73×#13062
C73×#12842
#1038873