Finite Group Databasebeta

← C73×#36692 #32946096

Subgroups — C73×#36692 #32946096

Order 18688.

1716 conjugacy classes of subgroups.

The subgroup lattice has 454 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2837C214yesmaximal, complemented
2C73×#2836C214yesmaximal, complemented
3C73×#2829C214yesmaximal, complemented
4C73×#2828C214yesmaximal, complemented
5C73×#2402C211yesmaximal, characteristic, complemented
6C73×#2397C211yesmaximal, characteristic, complemented
7C73×#2395C214yesmaximal, complemented
8C73×#2392C214yesmaximal, complemented
9C73×#2392C212yesmaximal, complemented
10C73×#2298C211yesmaximal, characteristic, complemented
11C73×#2293C212yesmaximal, complemented
12C2×C4×D4×C73C2212yes—
13C2×C4×D4×C73C2214yes—
14C2×C4×D4×C73C2214yes—
15C2×#117×C73C2211yescharacteristic
16C2×#117×C73C2214yes—
17#400×C73C2214yes—
18#400×C73C2214yes—
19#399×C73C2214yes—
20#399×C73C2214yes—
21#398×C73C2214yes—
22#398×C73C2214yes—
23#398×C73C2212yes—
24#398×C73C2214yes—
25#397×C73C2214yes—
26#397×C73C2214yes—
27#397×C73C2214yes—
28#397×C73C2214yes—
29#397×C73C2212yes—
30#396×C73C2214yes—
31#396×C73C2214yes—
32#396×C73C2214yes—
33#394×C73C2214yes—
34#394×C73C2214yes—
35#394×C73C2214yes—
36#394×C73C2214yes—
37#394×C73C2214yes—
38#394×C73C2214yes—
39#394×C73C2212yes—
40#392×C73C2212yes—
41#392×C73C2214yes—
42#392×C73C2214yes—
43#390×C73C2214yes—
44#389×C73C2214yes—
45#388×C73C2214yes—
46#388×C73C2214yes—
47#388×C73C2214yes—
48#387×C73C2214yes—
49C4×C4⋊C4×C73C2212yes—
50C4×C4⋊C4×C73C2212yes—
51C4×C4⋊C4×C73C2214yes—
52C4×C22⋊C4×C73C2214yes—
53C4×C22⋊C4×C73C2212yes—
54C4×C22⋊C4×C73C2214yes—
55#376×C73C2211yescharacteristic
56C43×C73C2211yescharacteristic
57C22×D4×C73C2312yes—
58C22×D4×C73C2314yes—
59C22×D4×C73C2314yes—
60C23×C4×C73C2311yescharacteristic
61C23×C4×C73C2314yes—
62C4×D4×C73—28no—
63C4×D4×C73—48no—
64C4×D4×C73—48no—
65#117×C73—24no—
66#117×C73—48no—
67C2×C4⋊C4×C73C2312yes—
68C2×C4⋊C4×C73C2312yes—
69C2×C4⋊C4×C73C2314yes—
70C2×C4⋊C4×C73C2314yes—
71C2×C4⋊C4×C73C2314yes—
72C2×C4⋊C4×C73C2314yes—
73C2×C4⋊C4×C73C2314yes—
74C2×C4⋊C4×C73C2314yes—
75C2×C4⋊C4×C73C2314yes—
76C2×C4⋊C4×C73C2314yes—
77C2×C22⋊C4×C73C2312yes—
78C2×C22⋊C4×C73C2314yes—
79C2×C22⋊C4×C73C2314yes—
80C2×C22⋊C4×C73C2314yes—
81C2×C22⋊C4×C73C2314yes—
82C2×C22⋊C4×C73C2314yes—
83C2×C22⋊C4×C73C2314yes—
84C2×C22⋊C4×C73C2314yes—
85C2×C22⋊C4×C73C2314yes—
86C2×C22⋊C4×C73C2314yes—
87C2×C22⋊C4×C73C2314yes—
88C2×C22⋊C4×C73C2314yes—
89C2×C22⋊C4×C73C2314yes—
90C2×C42×C73C2311yescharacteristic
91C2×C42×C73C2312yes—
92C2×C42×C73C2314yes—
93C2×C42×C73C2312yes—
94C2×C42×C73C2314yes—
95C2×C42×C73C2311yescharacteristic
96#95×C73C2314yes—
97#95×C73C2314yes—
98#95×C73C2314yes—
99#95×C73C2314yes—
100#95×C73C2314yes—
101#95×C73C2314yes—
102#95×C73C2312yes—
103#95×C73C2312yes—
104#95×C73C2314yes—
105#95×C73C2314yes—
106#95×C73C2314yes—
107C24×C73C2411yescharacteristic
108C24×C73C2414yes—
109C2×D4×C73—24no—
110C2×D4×C73—44no—
111C2×D4×C73—44no—
112C2×D4×C73—44no—
113C2×D4×C73—44no—
114C2×D4×C73—44no—
115C2×D4×C73—44no—
116C2×D4×C73—44no—
117C22×C4×C73—22no—
118C22×C4×C73—28no—
119C22×C4×C73—28no—
120C22×C4×C73—24no—
121C22×C4×C73—28no—
122C22×C4×C73C2412yes—
123C22×C4×C73C2414yes—
124C22×C4×C73C2414yes—
125C22×C4×C73C2414yes—
126C22×C4×C73C2414yes—
127C22×C4×C73C2414yes—
128C22×C4×C73C2411yescharacteristic
129C22×C4×C73C2412yes—
130C22×C4×C73C2411yescharacteristic
131C4⋊C4×C73—24no—
132C4⋊C4×C73—24no—
133C4⋊C4×C73—44no—
134C4⋊C4×C73—44no—
135C4⋊C4×C73—44no—
136C4⋊C4×C73—44no—
137C4⋊C4×C73—44no—
138C4⋊C4×C73—44no—
139C4⋊C4×C73—44no—
140C4⋊C4×C73—44no—
141C22⋊C4×C73—24no—
142C22⋊C4×C73—28no—
143C22⋊C4×C73—44no—
144C22⋊C4×C73—44no—
145C22⋊C4×C73—44no—
146C22⋊C4×C73—44no—
147C22⋊C4×C73—44no—
148C22⋊C4×C73—44no—
149C22⋊C4×C73—44no—
150C22⋊C4×C73—44no—
151C22⋊C4×C73—44no—
152C22⋊C4×C73—44no—
153C22⋊C4×C73—44no—
154C42×C73—22no—
155C42×C73—24no—
156C42×C73—28no—
157C42×C73—24no—
158C42×C73—44no—
159C42×C73#4114yes—
160C23×C73—21no—
161C23×C73—24no—
162C23×C73—24no—
163C23×C73—22no—
164C23×C73—24no—
165C23×C73—24no—
166C23×C73—24no—
167C23×C73—24no—
168C23×C73—24no—
169C23×C73—24no—
170C23×C73C2511yescharacteristic
171D4×C73—48no—
172D4×C73—416no—
173D4×C73—416no—
174C2×C4×C73—24no—
175C2×C4×C73—22no—
176C2×C4×C73—24no—
177C2×C4×C73—21no—
178C2×C4×C73—24no—
179C2×C4×C73—24no—
180C2×C4×C73—24no—
181C2×C4×C73—24no—
182C2×C4×C73—24no—
183C2×C4×C73—22no—
184C2×C4×C73—24no—
185C2×C4×C73—24no—
186C2×C4×C73—24no—
187C2×C4×C73—24no—
188C2×C4×C73—24no—
189C2×C4×C73—24no—
190C2×C4×C73—24no—
191C2×C4×C73—24no—
192C2×C4×C73—24no—
193C2×C4×C73—24no—
194C2×C4×C73—44no—
195C2×C4×C73—416no—
196C2×C4×C73C2×#4114yes—
197C2×C4×C73C2×#4112yes—
198C2×C4×C73H(5,𝔽2)14yes—
199C22×C73—41no—
200C22×C73—44no—
201C22×C73—44no—
202C22×C73—42no—
203C22×C73—44no—
204C22×C73—44no—
205C22×C73—44no—
206C22×C73—44no—
207C22×C73—44no—
208C22×C73—44no—
209C22×C73C22×#4111yescharacteristic
210C22×C73C2×H(5,𝔽2)12yes—
211C22×C73#58514yes—
212C4×C73—24no—
213C4×C73—44no—
214C4×C73—41no—
215C4×C73—42no—
216C4×C73—44no—
217C4×C73—44no—
218C4×C73—44no—
219C4×C73—44no—
220C4×C73#54014yes—
221#36692C7311yesmaximal, characteristic, direct product factor, Sylow
222C2×C73—84no—
223C2×C73—81no—
224C2×C73C2×#54011yescharacteristic
225C2×C73#345512yes—
226C2×C73#352914yes—
227#2837C2×C7314yescomplemented
228#2836C2×C7314yescomplemented
229#2829C2×C7314yescomplemented
230#2828C2×C7314yescomplemented
231#2402C2×C7311yescharacteristic, complemented
232#2397C2×C7311yescharacteristic, complemented
233#2395C2×C7314yescomplemented
234#2392C2×C7312yescomplemented
235#2392C2×C7314yescomplemented
236#2298C2×C7311yescharacteristic, complemented
237#2293C2×C7312yescomplemented
238C73#3669211yescharacteristic, direct product factor, Sylow
239C2×C4×D4C22×C7312yes—
240C2×C4×D4C22×C7314yes—
241C2×C4×D4C22×C7314yes—
242C2×#117C22×C7311yescharacteristic
243C2×#117C22×C7314yes—
244#400C22×C7314yes—
245#400C22×C7314yes—
246#399C22×C7314yes—
247#399C22×C7314yes—
248#398C22×C7314yes—
249#398C22×C7314yes—
250#398C22×C7312yes—
251#398C22×C7314yes—
252#397C22×C7314yes—
253#397C22×C7314yes—
254#397C22×C7314yes—
255#397C22×C7314yes—
256#397C22×C7312yes—
257#396C22×C7314yes—
258#396C22×C7314yes—
259#396C22×C7314yes—
260#394C22×C7314yes—
261#394C22×C7314yes—
262#394C22×C7314yes—
263#394C22×C7314yes—
264#394C22×C7314yes—
265#394C22×C7314yes—
266#394C22×C7312yes—
267#392C22×C7312yes—
268#392C22×C7314yes—
269#392C22×C7314yes—
270#390C22×C7314yes—
271#389C22×C7314yes—
272#388C22×C7314yes—
273#388C22×C7314yes—
274#388C22×C7314yes—
275#387C22×C7314yes—
276C4×C4⋊C4C22×C7314yes—
277C4×C4⋊C4C22×C7312yes—
278C4×C4⋊C4C22×C7312yes—
279C4×C22⋊C4C22×C7312yes—
280C4×C22⋊C4C22×C7314yes—
281C4×C22⋊C4C22×C7314yes—
282#376C22×C7311yescharacteristic
283C43C22×C7311yescharacteristic
284C22×D4C23×C7312yes—
285C22×D4C23×C7314yes—
286C22×D4C23×C7314yes—
287C23×C4C23×C7311yescharacteristic
288C23×C4C23×C7314yes—
289C4×D4—28no—
290C4×D4—48no—
291C4×D4—48no—
292#117—24no—
293#117—48no—
294C2×C4⋊C4C23×C7312yes—
295C2×C4⋊C4C23×C7312yes—
296C2×C4⋊C4C23×C7314yes—
297C2×C4⋊C4C23×C7314yes—
298C2×C4⋊C4C23×C7314yes—
299C2×C4⋊C4C23×C7314yes—
300C2×C4⋊C4C23×C7314yes—
301C2×C4⋊C4C23×C7314yes—
302C2×C4⋊C4C23×C7314yes—
303C2×C4⋊C4C23×C7314yes—
304C2×C22⋊C4C23×C7312yes—
305C2×C22⋊C4C23×C7314yes—
306C2×C22⋊C4C23×C7314yes—
307C2×C22⋊C4C23×C7314yes—
308C2×C22⋊C4C23×C7314yes—
309C2×C22⋊C4C23×C7314yes—
310C2×C22⋊C4C23×C7314yes—
311C2×C22⋊C4C23×C7314yes—
312C2×C22⋊C4C23×C7314yes—
313C2×C22⋊C4C23×C7314yes—
314C2×C22⋊C4C23×C7314yes—
315C2×C22⋊C4C23×C7314yes—
316C2×C22⋊C4C23×C7314yes—
317C2×C42C23×C7312yes—
318C2×C42C23×C7314yes—
319C2×C42C23×C7311yescharacteristic
320C2×C42C23×C7312yes—
321C2×C42C23×C7314yes—
322C2×C42C23×C7311yescharacteristic
323#95C23×C7314yes—
324#95C23×C7314yes—
325#95C23×C7314yes—
326#95C23×C7314yes—
327#95C23×C7314yes—
328#95C23×C7314yes—
329#95C23×C7314yes—
330#95C23×C7312yes—
331#95C23×C7312yes—
332#95C23×C7314yes—
333#95C23×C7314yes—
334C24C24×C7311yescharacteristic
335C24C24×C7314yes—
336C2×D4—24no—
337C2×D4—44no—
338C2×D4—44no—
339C2×D4—44no—
340C2×D4—44no—
341C2×D4—44no—
342C2×D4—44no—
343C2×D4—44no—
344C22×C4—22no—
345C22×C4—28no—
346C22×C4—28no—
347C22×C4—24no—
348C22×C4—28no—
349C22×C4C24×C7312yes—
350C22×C4C24×C7314yes—
351C22×C4C24×C7314yes—
352C22×C4C24×C7314yes—
353C22×C4C24×C7314yes—
354C22×C4C24×C7314yes—
355C22×C4C24×C7311yescharacteristic
356C22×C4C24×C7312yes—
357C22×C4C24×C7311yescharacteristic
358C4⋊C4—24no—
359C4⋊C4—24no—
360C4⋊C4—44no—
361C4⋊C4—44no—
362C4⋊C4—44no—
363C4⋊C4—44no—
364C4⋊C4—44no—
365C4⋊C4—44no—
366C4⋊C4—44no—
367C4⋊C4—44no—
368C22⋊C4—24no—
369C22⋊C4—28no—
370C22⋊C4—44no—
371C22⋊C4—44no—
372C22⋊C4—44no—
373C22⋊C4—44no—
374C22⋊C4—44no—
375C22⋊C4—44no—
376C22⋊C4—44no—
377C22⋊C4—44no—
378C22⋊C4—44no—
379C22⋊C4—44no—
380C22⋊C4—44no—
381C42—22no—
382C42—24no—
383C42—28no—
384C42—24no—
385C42—44no—
386C42#41×C7314yes—
387C23—21no—
388C23—24no—
389C23—24no—
390C23—24no—
391C23—22no—
392C23—24no—
393C23—24no—
394C23—24no—
395C23—24no—
396C23—24no—
397C23C25×C7311yescharacteristic
398D4—48no—
399D4—416no—
400D4—416no—
401C2×C4—24no—
402C2×C4—22no—
403C2×C4—24no—
404C2×C4—21no—
405C2×C4—24no—
406C2×C4—24no—
407C2×C4—24no—
408C2×C4—24no—
409C2×C4—24no—
410C2×C4—22no—
411C2×C4—24no—
412C2×C4—24no—
413C2×C4—24no—
414C2×C4—24no—
415C2×C4—24no—
416C2×C4—24no—
417C2×C4—24no—
418C2×C4—24no—
419C2×C4—24no—
420C2×C4—24no—
421C2×C4—44no—
422C2×C4—416no—
423C2×C4C2×#41×C7314yes—
424C2×C4C2×#41×C7312yes—
425C2×C4H(5,𝔽2)×C7314yes—
426C22—44no—
427C22—44no—
428C22—44no—
429C22—44no—
430C22—44no—
431C22—41no—
432C22—44no—
433C22—44no—
434C22—42no—
435C22—44no—
436C22C22×#41×C7311yescharacteristic
437C22C2×H(5,𝔽2)×C7312yes—
438C22#585×C7314yes—
439C4—24no—
440C4—44no—
441C4—44no—
442C4—44no—
443C4—44no—
444C4—44no—
445C4—41no—
446C4—42no—
447C4#540×C7314yes—
448C2—81no—
449C2—84no—
450C2C2×#540×C7311yescharacteristic
451C2C73×#345512yes—
452C2C73×#352914yes—
subgroupG/H
centerC22×C4×C73C24
commutator, Frattini, cosocleC23C25×C73
socleC23×C73C25
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2837C2semidirect
2. C73×#2836C2semidirect
3. C73×#2829C2semidirect
4. C73×#2828C2semidirect
5. C73×#2402C2semidirect
6. C73×#2397C2semidirect
7. C73×#2395C2semidirect
8. C73×#2392C2semidirect
9. C73×#2392C2semidirect
10. C73×#2298C2semidirect
11. C73×#2293C2semidirect
221. #36692C73direct (N × H)
227. #2837C2×C73semidirect
228. #2836C2×C73semidirect
229. #2829C2×C73semidirect
230. #2828C2×C73semidirect
231. #2402C2×C73semidirect
232. #2397C2×C73semidirect
233. #2395C2×C73semidirect
234. #2392C2×C73semidirect
235. #2392C2×C73semidirect
236. #2298C2×C73semidirect
237. #2293C2×C73semidirect
238. C73#36692direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#28372
C73×#28362
C73×#28292
C73×#28282
C73×#24022
C73×#23972
C73×#23952
C73×#23922
C73×#22982
C73×#22932
#3669273