Finite Group Databasebeta

← C73×#21908 #32931312

Subgroups — C73×#21908 #32931312

Order 18688.

950 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2280C211yesmaximal, characteristic
2C73×#1924C214yesmaximal, complemented
3C73×#1923C214yesmaximal, complemented
4C73×#1798C212yesmaximal, complemented
5C73×#1779C212yesmaximal
6C73×#1750C212yesmaximal, complemented
7C24×C4×C73C2211yescharacteristic
8C2×#117×C73C2211yescharacteristic
9C2×#117×C73C2211yescharacteristic
10C2×C4⋊C8×C73C2212yescomplemented
11C2×C4⋊C8×C73C2212yescomplemented
12C2×C22⋊C8×C73C2214yes—
13C2×C22⋊C8×C73C2212yes—
14C2×C22⋊C8×C73C2214yes—
15C2×C22⋊C8×C73C2212yes—
16C2×#97×C73C2212yescomplemented
17C2×C4×C8×C73C2212yescomplemented
18#381×C73C412yes—
19#380×C73C412yes—
20#380×C73C412yes—
21#379×C73C412yes—
22C4×C22⋊C4×C73C2214yes—
23#336×C73C2214yescomplemented
24#336×C73C2214yescomplemented
25C25×C73C2×C411yescharacteristic
26C23×C4×C73—24no—
27C23×C4×C73—42no—
28C23×C4×C73—41no—
29C23×C4×C73—41no—
30C23×C4×C73C2×C412yes—
31C23×C4×C73C2×C411yescharacteristic
32C23×C4×C73C2312yes—
33C23×C4×C73C2311yescharacteristic
34C22×C8×C73C2314yes—
35C22×C8×C73C2314yes—
36#117×C73—41no—
37#117×C73—41no—
38#117×C73—42no—
39C2×C4⋊C4×C73C2×C412yes—
40C2×C4⋊C4×C73C2×C411yescharacteristic
41C2×C4⋊C4×C73C2×C411yescharacteristic
42C2×C22⋊C4×C73C2×C414yes—
43C2×C22⋊C4×C73C2×C414yes—
44C2×C22⋊C4×C73C2×C412yes—
45C2×C22⋊C4×C73C2×C412yes—
46C2×C42×C73C2312yes—
47C2×C42×C73C2312yes—
48C4⋊C8×C73—42no—
49C4⋊C8×C73—42no—
50C22⋊C8×C73—28no—
51C22⋊C8×C73—42no—
52C22⋊C8×C73—42no—
53C22⋊C8×C73—44no—
54#97×C73—42no—
55C4×C8×C73—42no—
56#95×C73C2×C414yes—
57#95×C73C2×C414yes—
58C24×C73—22no—
59C24×C73—24no—
60C24×C73—41no—
61C24×C73—41no—
62C24×C73—42no—
63C24×C73C22×C411yescharacteristic
64C24×C73C22×C412yes—
65C22×C4×C73—21no—
66C22×C4×C73—21no—
67C22×C4×C73—22no—
68C22×C4×C73—22no—
69C22×C4×C73—24no—
70C22×C4×C73—24no—
71C22×C4×C73—22no—
72C22×C4×C73—22no—
73C22×C4×C73—24no—
74C22×C4×C73—42no—
75C22×C4×C73—42no—
76C22×C4×C73—41no—
77C22×C4×C73—41no—
78C22×C4×C73—48no—
79C22×C4×C73—48no—
80C22×C4×C73C22×C412yes—
81C22×C4×C73C22×C412yes—
82C22×C4×C73C22×C414yes—
83C22×C4×C73C22×C412yes—
84C22×C4×C73C22×C411yescharacteristic
85C22×C4×C73#4114yes—
86C22×C4×C73C2411yescharacteristic
87C2×C8×C73—24no—
88C2×C8×C73—24no—
89C2×C8×C73—24no—
90C2×C8×C73—24no—
91C2×C8×C73—24no—
92C2×C8×C73—24no—
93C4⋊C4×C73—42no—
94C4⋊C4×C73—41no—
95C4⋊C4×C73—41no—
96C22⋊C4×C73—28no—
97C22⋊C4×C73—44no—
98C22⋊C4×C73—42no—
99C22⋊C4×C73—42no—
100C42×C73—22no—
101C42×C73—22no—
102C42×C73—22no—
103C42×C73—22no—
104C23×C73—22no—
105C23×C73—21no—
106C23×C73—21no—
107C23×C73—22no—
108C23×C73—22no—
109C23×C73—22no—
110C23×C73—22no—
111C23×C73—22no—
112C23×C73—22no—
113C23×C73—22no—
114C23×C73—48no—
115C23×C73—44no—
116C23×C73—44no—
117C23×C73—48no—
118C23×C73—44no—
119C23×C73#11712yes—
120C23×C73#13114yes—
121C23×C73C23×C411yescharacteristic
122C2×C4×C73—21no—
123C2×C4×C73—21no—
124C2×C4×C73—24no—
125C2×C4×C73—24no—
126C2×C4×C73—22no—
127C2×C4×C73—24no—
128C2×C4×C73—22no—
129C2×C4×C73—22no—
130C2×C4×C73—22no—
131C2×C4×C73—22no—
132C2×C4×C73—24no—
133C2×C4×C73—24no—
134C2×C4×C73—24no—
135C2×C4×C73—24no—
136C2×C4×C73—48no—
137C2×C4×C73—44no—
138C2×C4×C73—44no—
139C2×C4×C73—44no—
140C2×C4×C73#11712yes—
141C2×C4×C73C2×#4112yes—
142C2×C4×C73H(5,𝔽2)11yescharacteristic
143C2×C4×C73H(5,𝔽2)11yescharacteristic
144C2×C4×C73H(5,𝔽2)12yes—
145C8×C73—44no—
146C8×C73—44no—
147C22×C73—22no—
148C22×C73—24no—
149C22×C73—24no—
150C22×C73—24no—
151C22×C73—24no—
152C22×C73—416no—
153C22×C73—42no—
154C22×C73—42no—
155C22×C73—42no—
156C22×C73—42no—
157C22×C73—41no—
158C22×C73—41no—
159C22×C73—42no—
160C22×C73C2×#11711yescharacteristic
161C22×C73#51811yescharacteristic
162C22×C73#51811yescharacteristic
163C22×C73C2×#13112yes—
164C22×C73#56812yes—
165C4×C73—22no—
166C4×C73—42no—
167C4×C73—44no—
168C4×C73—42no—
169C4×C73—42no—
170C4×C73#53812yes—
171C4×C73#53812yes—
172#21908C7311yesmaximal, characteristic, direct product factor, Sylow
173C2×C73—42no—
174C2×C73—44no—
175C2×C73#231211yescharacteristic
176C2×C73#292412yes—
177C2×C73#297612yes—
178C2×C73#297711yescharacteristic
179C2×C73#297811yescharacteristic
180#2280C2×C7311yescharacteristic
181#1924C2×C7314yescomplemented
182#1923C2×C7314yescomplemented
183#1798C2×C7312yescomplemented
184#1779C2×C7312yes—
185#1750C2×C7312yescomplemented
186C73#2190811yescharacteristic, direct product factor, Sylow
187C24×C4C22×C7311yescharacteristic
188C2×#117C22×C7311yescharacteristic
189C2×#117C22×C7311yescharacteristic
190C2×C4⋊C8C22×C7312yescomplemented
191C2×C4⋊C8C22×C7312yescomplemented
192C2×C22⋊C8C22×C7314yes—
193C2×C22⋊C8C22×C7312yes—
194C2×C22⋊C8C22×C7314yes—
195C2×C22⋊C8C22×C7312yes—
196C2×#97C22×C7312yescomplemented
197C2×C4×C8C22×C7312yescomplemented
198#381C4×C7312yes—
199#380C4×C7312yes—
200#380C4×C7312yes—
201#379C4×C7312yes—
202C4×C22⋊C4C22×C7314yes—
203#336C22×C7314yescomplemented
204#336C22×C7314yescomplemented
205C25C2×C4×C7311yescharacteristic
206C23×C4—24no—
207C23×C4—42no—
208C23×C4—41no—
209C23×C4—41no—
210C23×C4C2×C4×C7312yes—
211C23×C4C2×C4×C7311yescharacteristic
212C23×C4C23×C7312yes—
213C23×C4C23×C7311yescharacteristic
214C22×C8C23×C7314yes—
215C22×C8C23×C7314yes—
216#117—41no—
217#117—41no—
218#117—42no—
219C2×C4⋊C4C2×C4×C7311yescharacteristic
220C2×C4⋊C4C2×C4×C7311yescharacteristic
221C2×C4⋊C4C2×C4×C7312yes—
222C2×C22⋊C4C2×C4×C7314yes—
223C2×C22⋊C4C2×C4×C7312yes—
224C2×C22⋊C4C2×C4×C7312yes—
225C2×C22⋊C4C2×C4×C7314yes—
226C2×C42C23×C7312yes—
227C2×C42C23×C7312yes—
228C4⋊C8—42no—
229C4⋊C8—42no—
230C22⋊C8—28no—
231C22⋊C8—42no—
232C22⋊C8—42no—
233C22⋊C8—44no—
234#97—42no—
235C4×C8—42no—
236#95C2×C4×C7314yes—
237#95C2×C4×C7314yes—
238C24—22no—
239C24—24no—
240C24—41no—
241C24—41no—
242C24—42no—
243C24C22×C4×C7311yescharacteristic
244C24C22×C4×C7312yes—
245C22×C4—21no—
246C22×C4—21no—
247C22×C4—22no—
248C22×C4—22no—
249C22×C4—24no—
250C22×C4—24no—
251C22×C4—22no—
252C22×C4—22no—
253C22×C4—24no—
254C22×C4—42no—
255C22×C4—42no—
256C22×C4—41no—
257C22×C4—41no—
258C22×C4—48no—
259C22×C4—48no—
260C22×C4C22×C4×C7312yes—
261C22×C4C22×C4×C7312yes—
262C22×C4C22×C4×C7314yes—
263C22×C4C22×C4×C7312yes—
264C22×C4C22×C4×C7311yescharacteristic
265C22×C4#41×C7314yes—
266C22×C4C24×C7311yescharacteristic
267C2×C8—24no—
268C2×C8—24no—
269C2×C8—24no—
270C2×C8—24no—
271C2×C8—24no—
272C2×C8—24no—
273C4⋊C4—42no—
274C4⋊C4—41no—
275C4⋊C4—41no—
276C22⋊C4—28no—
277C22⋊C4—44no—
278C22⋊C4—42no—
279C22⋊C4—42no—
280C42—22no—
281C42—22no—
282C42—22no—
283C42—22no—
284C23—22no—
285C23—21no—
286C23—21no—
287C23—22no—
288C23—22no—
289C23—22no—
290C23—22no—
291C23—22no—
292C23—22no—
293C23—22no—
294C23—44no—
295C23—48no—
296C23—44no—
297C23—48no—
298C23—44no—
299C23#117×C7312yes—
300C23#131×C7314yes—
301C23C23×C4×C7311yescharacteristic
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—24no—
305C2×C4—24no—
306C2×C4—22no—
307C2×C4—24no—
308C2×C4—22no—
309C2×C4—22no—
310C2×C4—22no—
311C2×C4—22no—
312C2×C4—24no—
313C2×C4—24no—
314C2×C4—24no—
315C2×C4—24no—
316C2×C4—48no—
317C2×C4—44no—
318C2×C4—44no—
319C2×C4—44no—
320C2×C4#117×C7312yes—
321C2×C4C2×#41×C7312yes—
322C2×C4H(5,𝔽2)×C7311yescharacteristic
323C2×C4H(5,𝔽2)×C7311yescharacteristic
324C2×C4H(5,𝔽2)×C7312yes—
325C8—44no—
326C8—44no—
327C22—24no—
328C22—24no—
329C22—22no—
330C22—24no—
331C22—24no—
332C22—416no—
333C22—42no—
334C22—42no—
335C22—41no—
336C22—41no—
337C22—42no—
338C22—42no—
339C22—42no—
340C22C2×#117×C7311yescharacteristic
341C22#518×C7311yescharacteristic
342C22#518×C7311yescharacteristic
343C22C2×#131×C7312yes—
344C22#568×C7312yes—
345C4—22no—
346C4—44no—
347C4—42no—
348C4—42no—
349C4—42no—
350C4#538×C7312yes—
351C4#538×C7312yes—
352C2—44no—
353C2—42no—
354C2C73×#231211yescharacteristic
355C2C73×#292412yes—
356C2C73×#297612yes—
357C2C73×#297711yescharacteristic
358C2C73×#297811yescharacteristic
subgroupG/H
centerC22×C4×C73C24
commutatorC23C23×C4×C73
Frattini, cosocleC22×C4C24×C73
socleC23×C73C23×C4
prime radicalC25×C73C2×C4
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#1924C2semidirect
3. C73×#1923C2semidirect
4. C73×#1798C2semidirect
6. C73×#1750C2semidirect
10. C2×C4⋊C8×C73C22semidirect
11. C2×C4⋊C8×C73C22semidirect
16. C2×#97×C73C22semidirect
17. C2×C4×C8×C73C22semidirect
23. #336×C73C22semidirect
24. #336×C73C22semidirect
172. #21908C73direct (N × H)
181. #1924C2×C73semidirect
182. #1923C2×C73semidirect
183. #1798C2×C73semidirect
185. #1750C2×C73semidirect
186. C73#21908direct (N × H)
190. C2×C4⋊C8C22×C73semidirect
191. C2×C4⋊C8C22×C73semidirect
196. C2×#97C22×C73semidirect
197. C2×C4×C8C22×C73semidirect
203. #336C22×C73semidirect
204. #336C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#22802
C73×#19242
C73×#19232
C73×#17982
C73×#17792
C73×#17502
#2190873