Finite Group Databasebeta

← C73×#36732 #32946136

Subgroups — C73×#36732 #32946136

Order 18688.

1770 conjugacy classes of subgroups.

The subgroup lattice has 504 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2848C212yesmaximal
2C73×#2744C214yesmaximal, complemented
3C73×#2739C214yesmaximal, complemented
4C73×#2698C214yesmaximal, complemented
5C73×#2689C214yesmaximal, complemented
6C73×#2659C211yesmaximal, characteristic, complemented
7C73×#2646C211yesmaximal, characteristic, complemented
8C73×#2505C214yesmaximal, complemented
9C73×#2480C214yesmaximal
10C73×#2329C212yesmaximal, complemented
11C2×#381×C73C211yesmaximal, characteristic
12C24×C4×C73C2211yescharacteristic
13C2×#126×C73C2214yes—
14C2×C22⋊Q8×C73C2212yes—
15C2×C22⋊Q8×C73C2212yes—
16C2×C22⋊Q8×C73C2212yes—
17C22×C22⋊C4×C73C2212yes—
18#400×C73C2214yescomplemented
19#400×C73C2214yescomplemented
20#400×C73C2214yescomplemented
21#400×C73C2214yescomplemented
22#398×C73C2214yescomplemented
23#398×C73C2214yescomplemented
24#398×C73C2214yescomplemented
25#397×C73C2214yes—
26#397×C73C2214yes—
27#397×C73C2214yes—
28#396×C73C2214yes—
29#395×C73C2214yescomplemented
30#391×C73C2214yescomplemented
31#389×C73C2214yescomplemented
32#389×C73C2214yescomplemented
33#388×C73C2214yes—
34#388×C73C2214yes—
35#388×C73C2214yes—
36#387×C73C2214yescomplemented
37#387×C73C2214yescomplemented
38#387×C73C2214yescomplemented
39#387×C73C2214yescomplemented
40#385×C73C2214yes—
41#385×C73C2214yes—
42#385×C73C2214yes—
43#385×C73C2214yes—
44#385×C73C2214yes—
45#382×C73C2214yescomplemented
46#381×C73C2214yes—
47#381×C73C2214yes—
48#380×C73C2214yes—
49#380×C73C2212yes—
50#380×C73C2212yes—
51#380×C73C2212yes—
52#379×C73C2214yes—
53C4×C22⋊C4×C73C2214yes—
54C2×#95×C73C2212yes—
55C2×#95×C73C2211yescharacteristic
56C2×#95×C73C2211yescharacteristic
57C25×C73C2311yescharacteristic
58C22×Q8×C73C2312yes—
59C23×C4×C73—24no—
60C23×C4×C73—44no—
61C23×C4×C73C2312yes—
62C23×C4×C73C2312yes—
63C23×C4×C73C2312yes—
64C23×C4×C73C2312yes—
65C23×C4×C73C2311yescharacteristic
66C23×C4×C73C2311yescharacteristic
67#126×C73—48no—
68C22⋊Q8×C73—28no—
69C22⋊Q8×C73—44no—
70C22⋊Q8×C73—44no—
71C2×C4⋊C4×C73C2312yes—
72C2×C4⋊C4×C73C2314yes—
73C2×C4⋊C4×C73C2312yes—
74C2×C4⋊C4×C73C2312yes—
75C2×C4⋊C4×C73C2314yes—
76C2×C4⋊C4×C73C2314yes—
77C2×C4⋊C4×C73C2314yes—
78C2×C4⋊C4×C73C2314yes—
79C2×C4⋊C4×C73C2314yes—
80C2×C4⋊C4×C73C2314yes—
81C2×C4⋊C4×C73C2314yes—
82C2×C4⋊C4×C73C2314yes—
83C2×C22⋊C4×C73—44no—
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×C22⋊C4×C73C2314yes—
91C2×C22⋊C4×C73C2314yes—
92C2×C42×C73C2314yes—
93C2×C42×C73C2314yes—
94#95×C73C2314yes—
95#95×C73C2314yes—
96#95×C73C2314yes—
97#95×C73C2314yes—
98#95×C73C2314yes—
99#95×C73C2314yes—
100#95×C73C2314yes—
101#95×C73C2314yes—
102#95×C73C2314yes—
103#95×C73C2314yes—
104#95×C73C2314yes—
105#95×C73C2314yes—
106#95×C73C2314yes—
107#95×C73C2314yes—
108#95×C73C2314yes—
109C24×C73—22no—
110C24×C73—24no—
111C24×C73—24no—
112C24×C73—41no—
113C24×C73—41no—
114C24×C73C2412yes—
115C24×C73C2411yescharacteristic
116C2×Q8×C73—24no—
117C2×Q8×C73—42no—
118C2×Q8×C73—42no—
119C22×C4×C73—22no—
120C22×C4×C73—24no—
121C22×C4×C73—24no—
122C22×C4×C73—24no—
123C22×C4×C73—24no—
124C22×C4×C73—24no—
125C22×C4×C73—24no—
126C22×C4×C73—42no—
127C22×C4×C73—42no—
128C22×C4×C73—42no—
129C22×C4×C73—42no—
130C22×C4×C73—42no—
131C22×C4×C73—42no—
132C22×C4×C73—42no—
133C22×C4×C73—42no—
134C22×C4×C73—416no—
135C22×C4×C73#4114yes—
136C22×C4×C73C2414yes—
137C22×C4×C73C2414yes—
138C22×C4×C73C2411yescharacteristic
139C22×C4×C73C2411yescharacteristic
140C22×C4×C73C2414yes—
141C22×C4×C73C2414yes—
142C22×C4×C73C2414yes—
143C22×C4×C73C2414yes—
144C22×C4×C73C2412yes—
145C4⋊C4×C73—24no—
146C4⋊C4×C73—28no—
147C4⋊C4×C73—44no—
148C4⋊C4×C73—44no—
149C4⋊C4×C73—44no—
150C4⋊C4×C73—42no—
151C4⋊C4×C73—42no—
152C4⋊C4×C73—44no—
153C4⋊C4×C73—44no—
154C4⋊C4×C73—44no—
155C4⋊C4×C73—44no—
156C4⋊C4×C73—44no—
157C22⋊C4×C73—28no—
158C22⋊C4×C73—28no—
159C22⋊C4×C73—28no—
160C22⋊C4×C73—28no—
161C22⋊C4×C73—28no—
162C22⋊C4×C73—44no—
163C22⋊C4×C73—44no—
164C22⋊C4×C73—44no—
165C42×C73—44no—
166C42×C73—44no—
167C23×C73—22no—
168C23×C73—21no—
169C23×C73—21no—
170C23×C73—28no—
171C23×C73—22no—
172C23×C73—22no—
173C23×C73—22no—
174C23×C73—22no—
175C23×C73—22no—
176C23×C73—22no—
177C23×C73—48no—
178C23×C73—48no—
179C23×C73—44no—
180C23×C73—44no—
181C23×C73C2×#4112yes—
182C23×C73H(5,𝔽2)14yes—
183C23×C732−1+414yes—
184C23×C73C2511yescharacteristic
185Q8×C73—84no—
186C2×C4×C73—22no—
187C2×C4×C73—22no—
188C2×C4×C73—24no—
189C2×C4×C73—24no—
190C2×C4×C73—21no—
191C2×C4×C73—21no—
192C2×C4×C73—24no—
193C2×C4×C73—24no—
194C2×C4×C73—24no—
195C2×C4×C73—24no—
196C2×C4×C73—24no—
197C2×C4×C73—24no—
198C2×C4×C73—22no—
199C2×C4×C73—22no—
200C2×C4×C73—24no—
201C2×C4×C73—24no—
202C2×C4×C73—24no—
203C2×C4×C73—24no—
204C2×C4×C73—24no—
205C2×C4×C73—24no—
206C2×C4×C73—24no—
207C2×C4×C73—24no—
208C2×C4×C73—24no—
209C2×C4×C73—24no—
210C2×C4×C73—44no—
211C2×C4×C73—48no—
212C2×C4×C73—48no—
213C2×C4×C73—44no—
214C2×C4×C73—84no—
215C2×C4×C73—84no—
216C2×C4×C73C2×#4114yes—
217C22×C73—22no—
218C22×C73—22no—
219C22×C73—24no—
220C22×C73—24no—
221C22×C73—24no—
222C22×C73—24no—
223C22×C73—24no—
224C22×C73—416no—
225C22×C73—42no—
226C22×C73—42no—
227C22×C73—42no—
228C22×C73—42no—
229C22×C73#54114yes—
230C22×C73C22×#4111yescharacteristic
231C22×C73C2×H(5,𝔽2)12yes—
232C22×C73C2×2−1+412yes—
233C22×C73#58511yescharacteristic
234C22×C73#58511yescharacteristic
235C4×C73—24no—
236C4×C73—41no—
237C4×C73—41no—
238C4×C73—44no—
239C4×C73—44no—
240C4×C73—44no—
241C4×C73—44no—
242C4×C73—44no—
243C4×C73—44no—
244#36732C7311yesmaximal, characteristic, direct product factor, Sylow
245C2×C73—24no—
246C2×C73—44no—
247C2×C73C2×#54111yescharacteristic
248C2×C73#349011yescharacteristic
249C2×C73#349311yescharacteristic
250C2×C73#353512yes—
251C2×C73#353512yes—
252#2848C2×C7312yes—
253#2744C2×C7314yescomplemented
254#2739C2×C7314yescomplemented
255#2698C2×C7314yescomplemented
256#2689C2×C7314yescomplemented
257#2659C2×C7311yescharacteristic, complemented
258#2646C2×C7311yescharacteristic, complemented
259#2505C2×C7314yescomplemented
260#2480C2×C7314yes—
261#2329C2×C7312yescomplemented
262C2×#381C2×C7311yescharacteristic
263C73#3673211yescharacteristic, direct product factor, Sylow
264C24×C4C22×C7311yescharacteristic
265C2×#126C22×C7314yes—
266C2×C22⋊Q8C22×C7312yes—
267C2×C22⋊Q8C22×C7312yes—
268C2×C22⋊Q8C22×C7312yes—
269C22×C22⋊C4C22×C7312yes—
270#400C22×C7314yescomplemented
271#400C22×C7314yescomplemented
272#400C22×C7314yescomplemented
273#400C22×C7314yescomplemented
274#398C22×C7314yescomplemented
275#398C22×C7314yescomplemented
276#398C22×C7314yescomplemented
277#397C22×C7314yes—
278#397C22×C7314yes—
279#397C22×C7314yes—
280#396C22×C7314yes—
281#395C22×C7314yescomplemented
282#391C22×C7314yescomplemented
283#389C22×C7314yescomplemented
284#389C22×C7314yescomplemented
285#388C22×C7314yes—
286#388C22×C7314yes—
287#388C22×C7314yes—
288#387C22×C7314yescomplemented
289#387C22×C7314yescomplemented
290#387C22×C7314yescomplemented
291#387C22×C7314yescomplemented
292#385C22×C7314yes—
293#385C22×C7314yes—
294#385C22×C7314yes—
295#385C22×C7314yes—
296#385C22×C7314yes—
297#382C22×C7314yescomplemented
298#381C22×C7314yes—
299#381C22×C7314yes—
300#380C22×C7312yes—
301#380C22×C7312yes—
302#380C22×C7312yes—
303#380C22×C7314yes—
304#379C22×C7314yes—
305C4×C22⋊C4C22×C7314yes—
306C2×#95C22×C7311yescharacteristic
307C2×#95C22×C7311yescharacteristic
308C2×#95C22×C7312yes—
309C25C23×C7311yescharacteristic
310C22×Q8C23×C7312yes—
311C23×C4—24no—
312C23×C4—44no—
313C23×C4C23×C7312yes—
314C23×C4C23×C7312yes—
315C23×C4C23×C7312yes—
316C23×C4C23×C7312yes—
317C23×C4C23×C7311yescharacteristic
318C23×C4C23×C7311yescharacteristic
319#126—48no—
320C22⋊Q8—28no—
321C22⋊Q8—44no—
322C22⋊Q8—44no—
323C2×C4⋊C4C23×C7312yes—
324C2×C4⋊C4C23×C7314yes—
325C2×C4⋊C4C23×C7312yes—
326C2×C4⋊C4C23×C7312yes—
327C2×C4⋊C4C23×C7314yes—
328C2×C4⋊C4C23×C7314yes—
329C2×C4⋊C4C23×C7314yes—
330C2×C4⋊C4C23×C7314yes—
331C2×C4⋊C4C23×C7314yes—
332C2×C4⋊C4C23×C7314yes—
333C2×C4⋊C4C23×C7314yes—
334C2×C4⋊C4C23×C7314yes—
335C2×C22⋊C4—44no—
336C2×C22⋊C4C23×C7314yes—
337C2×C22⋊C4C23×C7314yes—
338C2×C22⋊C4C23×C7314yes—
339C2×C22⋊C4C23×C7314yes—
340C2×C22⋊C4C23×C7314yes—
341C2×C22⋊C4C23×C7314yes—
342C2×C22⋊C4C23×C7314yes—
343C2×C22⋊C4C23×C7314yes—
344C2×C42C23×C7314yes—
345C2×C42C23×C7314yes—
346#95C23×C7314yes—
347#95C23×C7314yes—
348#95C23×C7314yes—
349#95C23×C7314yes—
350#95C23×C7314yes—
351#95C23×C7314yes—
352#95C23×C7314yes—
353#95C23×C7314yes—
354#95C23×C7314yes—
355#95C23×C7314yes—
356#95C23×C7314yes—
357#95C23×C7314yes—
358#95C23×C7314yes—
359#95C23×C7314yes—
360#95C23×C7314yes—
361C24—22no—
362C24—24no—
363C24—24no—
364C24—41no—
365C24—41no—
366C24C24×C7312yes—
367C24C24×C7311yescharacteristic
368C2×Q8—24no—
369C2×Q8—42no—
370C2×Q8—42no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—24no—
374C22×C4—24no—
375C22×C4—24no—
376C22×C4—24no—
377C22×C4—24no—
378C22×C4—42no—
379C22×C4—42no—
380C22×C4—42no—
381C22×C4—42no—
382C22×C4—42no—
383C22×C4—42no—
384C22×C4—42no—
385C22×C4—42no—
386C22×C4—416no—
387C22×C4#41×C7314yes—
388C22×C4C24×C7314yes—
389C22×C4C24×C7314yes—
390C22×C4C24×C7311yescharacteristic
391C22×C4C24×C7311yescharacteristic
392C22×C4C24×C7314yes—
393C22×C4C24×C7314yes—
394C22×C4C24×C7314yes—
395C22×C4C24×C7314yes—
396C22×C4C24×C7312yes—
397C4⋊C4—24no—
398C4⋊C4—28no—
399C4⋊C4—44no—
400C4⋊C4—44no—
401C4⋊C4—44no—
402C4⋊C4—42no—
403C4⋊C4—42no—
404C4⋊C4—44no—
405C4⋊C4—44no—
406C4⋊C4—44no—
407C4⋊C4—44no—
408C4⋊C4—44no—
409C22⋊C4—28no—
410C22⋊C4—28no—
411C22⋊C4—28no—
412C22⋊C4—28no—
413C22⋊C4—28no—
414C22⋊C4—44no—
415C22⋊C4—44no—
416C22⋊C4—44no—
417C42—44no—
418C42—44no—
419C23—22no—
420C23—21no—
421C23—21no—
422C23—28no—
423C23—22no—
424C23—22no—
425C23—22no—
426C23—22no—
427C23—22no—
428C23—22no—
429C23—48no—
430C23—48no—
431C23—44no—
432C23—44no—
433C23C2×#41×C7312yes—
434C23H(5,𝔽2)×C7314yes—
435C232−1+4×C7314yes—
436C23C25×C7311yescharacteristic
437Q8—84no—
438C2×C4—22no—
439C2×C4—22no—
440C2×C4—24no—
441C2×C4—24no—
442C2×C4—21no—
443C2×C4—21no—
444C2×C4—24no—
445C2×C4—24no—
446C2×C4—24no—
447C2×C4—24no—
448C2×C4—24no—
449C2×C4—24no—
450C2×C4—22no—
451C2×C4—22no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—24no—
457C2×C4—24no—
458C2×C4—24no—
459C2×C4—24no—
460C2×C4—24no—
461C2×C4—24no—
462C2×C4—44no—
463C2×C4—48no—
464C2×C4—48no—
465C2×C4—44no—
466C2×C4—84no—
467C2×C4—84no—
468C2×C4C2×#41×C7314yes—
469C22—22no—
470C22—22no—
471C22—24no—
472C22—24no—
473C22—24no—
474C22—24no—
475C22—24no—
476C22—416no—
477C22—42no—
478C22—42no—
479C22—42no—
480C22—42no—
481C22#541×C7314yes—
482C22C22×#41×C7311yescharacteristic
483C22C2×H(5,𝔽2)×C7312yes—
484C22C2×2−1+4×C7312yes—
485C22#585×C7311yescharacteristic
486C22#585×C7311yescharacteristic
487C4—24no—
488C4—41no—
489C4—41no—
490C4—44no—
491C4—44no—
492C4—44no—
493C4—44no—
494C4—44no—
495C4—44no—
496C2—24no—
497C2—44no—
498C2C2×#541×C7311yescharacteristic
499C2C73×#349011yescharacteristic
500C2C73×#349311yescharacteristic
501C2C73×#353512yes—
502C2C73×#353512yes—
subgroupG/H
center, socleC23×C73C25
commutator, Frattini, cosocleC23C25×C73
prime radicalC25×C73C23
LCSG ▷ C23 ▷ C1
UCSC1 ◁ C23×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2744C2semidirect
3. C73×#2739C2semidirect
4. C73×#2698C2semidirect
5. C73×#2689C2semidirect
6. C73×#2659C2semidirect
7. C73×#2646C2semidirect
8. C73×#2505C2semidirect
10. C73×#2329C2semidirect
18. #400×C73C22semidirect
19. #400×C73C22semidirect
20. #400×C73C22semidirect
21. #400×C73C22semidirect
22. #398×C73C22semidirect
23. #398×C73C22semidirect
24. #398×C73C22semidirect
29. #395×C73C22semidirect
30. #391×C73C22semidirect
31. #389×C73C22semidirect
32. #389×C73C22semidirect
36. #387×C73C22semidirect
37. #387×C73C22semidirect
38. #387×C73C22semidirect
39. #387×C73C22semidirect
45. #382×C73C22semidirect
244. #36732C73direct (N × H)
253. #2744C2×C73semidirect
254. #2739C2×C73semidirect
255. #2698C2×C73semidirect
256. #2689C2×C73semidirect
257. #2659C2×C73semidirect
258. #2646C2×C73semidirect
259. #2505C2×C73semidirect
261. #2329C2×C73semidirect
263. C73#36732direct (N × H)
270. #400C22×C73semidirect
271. #400C22×C73semidirect
272. #400C22×C73semidirect
273. #400C22×C73semidirect
274. #398C22×C73semidirect
275. #398C22×C73semidirect
276. #398C22×C73semidirect
281. #395C22×C73semidirect
282. #391C22×C73semidirect
283. #389C22×C73semidirect
284. #389C22×C73semidirect
288. #387C22×C73semidirect
289. #387C22×C73semidirect
290. #387C22×C73semidirect
291. #387C22×C73semidirect
297. #382C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#28482
C73×#27442
C73×#27392
C73×#26982
C73×#26892
C73×#26592
C73×#26462
C73×#25052
C73×#24802
C73×#23292
C2×#381×C732
#3673273