Finite Group Databasebeta

← C73×#33791 #32943195

Subgroups — C73×#33791 #32943195

Order 18688.

574 conjugacy classes of subgroups.

The subgroup lattice has 534 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3175C211yesmaximal, characteristic, complemented
2C73×#3156C211yesmaximal, characteristic, complemented
3C73×#2251C211yesmaximal, characteristic, complemented
4C73×#2249C211yesmaximal, characteristic, complemented
5C73×#2243C211yesmaximal, characteristic, complemented
6C73×#2241C211yesmaximal, characteristic, complemented
7C73×#2211C211yesmaximal, characteristic, complemented
8C73×#2210C211yesmaximal, characteristic, complemented
9C73×#2209C211yesmaximal, characteristic, complemented
10C73×#2208C211yesmaximal, characteristic, complemented
11C73×#2189C211yesmaximal, characteristic, complemented
12C73×#2188C211yesmaximal, characteristic, complemented
13C73×#2186C211yesmaximal, characteristic
14C73×#2185C211yesmaximal, characteristic, complemented
15C73×#2164C211yesmaximal, characteristic, complemented
16C2×#137×C73—21no—
17C2×#135×C73C2211yescharacteristic
18C22×Q16×C73C2211yescharacteristic
19#542×C73—21no—
20#536×C73—21no—
21C2×Q32×C73C2211yescharacteristic
22C2×Q32×C73C2211yescharacteristic
23C2×Q32×C73C2211yescharacteristic
24C2×SD32×C73C2211yescharacteristic
25C2×SD32×C73C2211yescharacteristic
26C2×SD32×C73C2211yescharacteristic
27C2×SD32×C73C2211yescharacteristic
28C2×D16×C73C2211yescharacteristic
29#500×C73C2211yescharacteristic
30#497×C73—21no—
31#497×C73—21no—
32#495×C73C2211yescharacteristic
33#495×C73C2211yescharacteristic
34#495×C73C2211yescharacteristic
35#494×C73C2211yescharacteristic
36#494×C73C2211yescharacteristic
37#489×C73—21no—
38#468×C73—21no—
39#467×C73C2211yescharacteristic
40#466×C73C2211yescharacteristic
41#440×C73—21no—
42C4×Q16×C73C2211yescharacteristic
43C4×D8×C73C2211yescharacteristic
44#405×C73C2211yescharacteristic
45C4⋊C16×C73C2211yescharacteristic
46C4⋊C16×C73C2211yescharacteristic
47#358×C73C2211yescharacteristic
48#358×C73C2211yescharacteristic
49#358×C73C2211yescharacteristic
50#358×C73C2211yescharacteristic
51#358×C73C2211yescharacteristic
52#358×C73C2211yescharacteristic
53#357×C73C2211yescharacteristic
54#357×C73C2211yescharacteristic
55C22⋊C16×C73C2211yescharacteristic
56C22⋊C16×C73C2211yescharacteristic
57#346×C73C2211yescharacteristic
58C4×C16×C73C2211yescharacteristic
59C2×#41×C73—21no—
60C22×Q8×C73—21no—
61#137×C73—44no—
62#135×C73—41no—
63#135×C73—41no—
64C2×Q16×C73—21no—
65C2×Q16×C73—21no—
66C2×Q16×C73—21no—
67C2×Q16×C73—41no—
68C2×Q16×C73—41no—
69C2×Q16×C73C2311yescharacteristic
70C2×Q16×C73C2311yescharacteristic
71C2×Q16×C73C2311yescharacteristic
72C2×Q16×C73C2311yescharacteristic
73C2×SD16×C73—21no—
74C2×SD16×C73—21no—
75C2×SD16×C73—21no—
76C2×SD16×C73—21no—
77C2×D8×C73C2311yescharacteristic
78C2×D8×C73C2311yescharacteristic
79C2×M16×C73D411yescharacteristic
80C22×C8×C73C2311yescharacteristic
81C4⋊Q8×C73—21no—
82C4⋊Q8×C73—21no—
83C4⋊Q8×C73—21no—
84#126×C73—41no—
85#124×C73—21no—
86#124×C73—21no—
87#124×C73—21no—
88#124×C73—41no—
89#123×C73—41no—
90#123×C73—41no—
91#123×C73—41no—
92C22⋊Q8×C73—21no—
93C22⋊Q8×C73—41no—
94C22⋊Q8×C73—41no—
95C22⋊Q8×C73—41no—
96#121×C73—21no—
97C4×Q8×C73—21no—
98C4×D4×C73—21no—
99#117×C73D411yescharacteristic
100Q32×C73—41no—
101Q32×C73—41no—
102Q32×C73—41no—
103SD32×C73—41no—
104SD32×C73—41no—
105SD32×C73—41no—
106SD32×C73—41no—
107D16×C73—41no—
108C2×C16×C73C2311yescharacteristic
109C2×C16×C73C2311yescharacteristic
110C2×C16×C73C2311yescharacteristic
111C2×C16×C73C2311yescharacteristic
112#107×C73—21no—
113#107×C73C2311yescharacteristic
114#107×C73C2311yescharacteristic
115#103×C73—21no—
116#103×C73—21no—
117#102×C73—21no—
118#102×C73—21no—
119#97×C73D411yescharacteristic
120#97×C73D411yescharacteristic
121C4×C8×C73C2311yescharacteristic
122C4×C8×C73C2311yescharacteristic
123#41×C73—42no—
124#41×C73—42no—
125C2×Q8×C73—21no—
126C2×Q8×C73—21no—
127C2×Q8×C73—21no—
128C2×Q8×C73—21no—
129C2×Q8×C73—42no—
130C2×Q8×C73—42no—
131C2×Q8×C73—41no—
132C2×Q8×C73—41no—
133C2×D4×C73—21no—
134C2×D4×C73—21no—
135C2×D4×C73—41no—
136C2×D4×C73—41no—
137C22×C4×C73—41no—
138C22×C4×C73—41no—
139C22×C4×C73—41no—
140C22×C4×C73C2×D411yescharacteristic
141Q16×C73—21no—
142Q16×C73—21no—
143Q16×C73—21no—
144Q16×C73—21no—
145Q16×C73—21no—
146Q16×C73—21no—
147Q16×C73—21no—
148Q16×C73—21no—
149Q16×C73—42no—
150Q16×C73—42no—
151Q16×C73—42no—
152SD16×C73—42no—
153SD16×C73—42no—
154SD16×C73—42no—
155SD16×C73—42no—
156D8×C73—21no—
157D8×C73—21no—
158D8×C73—21no—
159D8×C73—21no—
160M16×C73—22no—
161C2×C8×C73—21no—
162C2×C8×C73—21no—
163C2×C8×C73C2×D411yescharacteristic
164C2×C8×C73C2×D411yescharacteristic
165C2×C8×C73C2×D411yescharacteristic
166C2×C8×C73C2411yescharacteristic
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—41no—
170C4⋊C4×C73—41no—
171C4⋊C4×C73—41no—
172C4⋊C4×C73—41no—
173C4⋊C4×C73—41no—
174C4⋊C4×C73—41no—
175C4⋊C4×C73—41no—
176C4⋊C4×C73D811yescharacteristic
177C4⋊C4×C73D811yescharacteristic
178C22⋊C4×C73—41no—
179C22⋊C4×C73—41no—
180C22⋊C4×C73—41no—
181C22⋊C4×C73—41no—
182C22⋊C4×C73—41no—
183C22⋊C4×C73—41no—
184C22⋊C4×C73—41no—
185C22⋊C4×C73—41no—
186C22⋊C4×C73—41no—
187C22⋊C4×C73D811yescharacteristic
188C22⋊C4×C73D811yescharacteristic
189C42×C73—41no—
190C42×C73C2×D411yescharacteristic
191C42×C73C2×D411yescharacteristic
192C16×C73—21no—
193C16×C73—21no—
194C16×C73—21no—
195C16×C73—21no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73C2×D811yescharacteristic
199Q8×C73—41no—
200Q8×C73—41no—
201Q8×C73—41no—
202Q8×C73—41no—
203Q8×C73—41no—
204Q8×C73—41no—
205Q8×C73—41no—
206Q8×C73—41no—
207Q8×C73—82no—
208Q8×C73—161no—
209D4×C73—41no—
210D4×C73—41no—
211D4×C73—41no—
212D4×C73—41no—
213D4×C73—82no—
214D4×C73—161no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—41no—
218C2×C4×C73—41no—
219C2×C4×C73—41no—
220C2×C4×C73—41no—
221C2×C4×C73—41no—
222C2×C4×C73—41no—
223C2×C4×C73—82no—
224C2×C4×C73—82no—
225C2×C4×C73—161no—
226C2×C4×C73C2×D811yescharacteristic
227C2×C4×C73C2×D811yescharacteristic
228C2×C4×C73C2×D811yescharacteristic
229C2×C4×C73C2×D811yescharacteristic
230C2×C4×C73C2×D811yescharacteristic
231C2×C4×C73C22×D411yescharacteristic
232C8×C73—21no—
233C8×C73—21no—
234C8×C73AGL(1,ℤ/8)12yes—
235C8×C73H(5,𝔽2)11yescharacteristic
236C8×C73H(5,𝔽2)11yescharacteristic
237C22×C73—21no—
238C22×C73—21no—
239C22×C73—21no—
240C22×C73—81no—
241C22×C73—81no—
242C22×C73—81no—
243C22×C73—81no—
244C22×C73—81no—
245C22×C73—81no—
246C22×C73C22×D811yescharacteristic
247C4×C73—21no—
248C4×C73—21no—
249C4×C73—21no—
250C4×C73—21no—
251C4×C73—21no—
252C4×C73—81no—
253C4×C73—81no—
254C4×C73—81no—
255C4×C73—81no—
256C4×C73—81no—
257C4×C73—81no—
258C4×C73#53511yescharacteristic
259C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
260#33791C7311yesmaximal, characteristic, direct product factor, Sylow
261C2×C73—41no—
262C2×C73—161no—
263C2×C73—161no—
264C2×C73#320511yescharacteristic
265C2×C73#341611yescharacteristic
266C2×C73#341711yescharacteristic
267#3175C2×C7311yescharacteristic, complemented
268#3156C2×C7311yescharacteristic, complemented
269#2251C2×C7311yescharacteristic, complemented
270#2249C2×C7311yescharacteristic, complemented
271#2243C2×C7311yescharacteristic, complemented
272#2241C2×C7311yescharacteristic, complemented
273#2211C2×C7311yescharacteristic, complemented
274#2210C2×C7311yescharacteristic, complemented
275#2209C2×C7311yescharacteristic, complemented
276#2208C2×C7311yescharacteristic, complemented
277#2189C2×C7311yescharacteristic, complemented
278#2188C2×C7311yescharacteristic, complemented
279#2186C2×C7311yescharacteristic
280#2185C2×C7311yescharacteristic, complemented
281#2164C2×C7311yescharacteristic, complemented
282C73#3379111yescharacteristic, direct product factor, Sylow
283C2×#137—21no—
284C2×#135C22×C7311yescharacteristic
285C22×Q16C22×C7311yescharacteristic
286#542—21no—
287#536—21no—
288C2×Q32C22×C7311yescharacteristic
289C2×Q32C22×C7311yescharacteristic
290C2×Q32C22×C7311yescharacteristic
291C2×SD32C22×C7311yescharacteristic
292C2×SD32C22×C7311yescharacteristic
293C2×SD32C22×C7311yescharacteristic
294C2×SD32C22×C7311yescharacteristic
295C2×D16C22×C7311yescharacteristic
296#500C22×C7311yescharacteristic
297#497—21no—
298#497—21no—
299#495C22×C7311yescharacteristic
300#495C22×C7311yescharacteristic
301#495C22×C7311yescharacteristic
302#494C22×C7311yescharacteristic
303#494C22×C7311yescharacteristic
304#489—21no—
305#468—21no—
306#467C22×C7311yescharacteristic
307#466C22×C7311yescharacteristic
308#440—21no—
309C4×Q16C22×C7311yescharacteristic
310C4×D8C22×C7311yescharacteristic
311#405C22×C7311yescharacteristic
312C4⋊C16C22×C7311yescharacteristic
313C4⋊C16C22×C7311yescharacteristic
314#358C22×C7311yescharacteristic
315#358C22×C7311yescharacteristic
316#358C22×C7311yescharacteristic
317#358C22×C7311yescharacteristic
318#358C22×C7311yescharacteristic
319#358C22×C7311yescharacteristic
320#357C22×C7311yescharacteristic
321#357C22×C7311yescharacteristic
322C22⋊C16C22×C7311yescharacteristic
323C22⋊C16C22×C7311yescharacteristic
324#346C22×C7311yescharacteristic
325C4×C16C22×C7311yescharacteristic
326C2×#41—21no—
327C22×Q8—21no—
328#137—44no—
329#135—41no—
330#135—41no—
331C2×Q16—21no—
332C2×Q16—21no—
333C2×Q16—21no—
334C2×Q16—41no—
335C2×Q16—41no—
336C2×Q16C23×C7311yescharacteristic
337C2×Q16C23×C7311yescharacteristic
338C2×Q16C23×C7311yescharacteristic
339C2×Q16C23×C7311yescharacteristic
340C2×SD16—21no—
341C2×SD16—21no—
342C2×SD16—21no—
343C2×SD16—21no—
344C2×D8C23×C7311yescharacteristic
345C2×D8C23×C7311yescharacteristic
346C2×M16D4×C7311yescharacteristic
347C22×C8C23×C7311yescharacteristic
348C4⋊Q8—21no—
349C4⋊Q8—21no—
350C4⋊Q8—21no—
351#126—41no—
352#124—21no—
353#124—21no—
354#124—21no—
355#124—41no—
356#123—41no—
357#123—41no—
358#123—41no—
359C22⋊Q8—21no—
360C22⋊Q8—41no—
361C22⋊Q8—41no—
362C22⋊Q8—41no—
363#121—21no—
364C4×Q8—21no—
365C4×D4—21no—
366#117D4×C7311yescharacteristic
367Q32—41no—
368Q32—41no—
369Q32—41no—
370SD32—41no—
371SD32—41no—
372SD32—41no—
373SD32—41no—
374D16—41no—
375C2×C16C23×C7311yescharacteristic
376C2×C16C23×C7311yescharacteristic
377C2×C16C23×C7311yescharacteristic
378C2×C16C23×C7311yescharacteristic
379#107—21no—
380#107C23×C7311yescharacteristic
381#107C23×C7311yescharacteristic
382#103—21no—
383#103—21no—
384#102—21no—
385#102—21no—
386#97D4×C7311yescharacteristic
387#97D4×C7311yescharacteristic
388C4×C8C23×C7311yescharacteristic
389C4×C8C23×C7311yescharacteristic
390#41—42no—
391#41—42no—
392C2×Q8—21no—
393C2×Q8—21no—
394C2×Q8—21no—
395C2×Q8—21no—
396C2×Q8—42no—
397C2×Q8—42no—
398C2×Q8—41no—
399C2×Q8—41no—
400C2×D4—21no—
401C2×D4—21no—
402C2×D4—41no—
403C2×D4—41no—
404C22×C4—41no—
405C22×C4—41no—
406C22×C4—41no—
407C22×C4C2×D4×C7311yescharacteristic
408Q16—21no—
409Q16—21no—
410Q16—21no—
411Q16—21no—
412Q16—21no—
413Q16—21no—
414Q16—21no—
415Q16—21no—
416Q16—42no—
417Q16—42no—
418Q16—42no—
419SD16—42no—
420SD16—42no—
421SD16—42no—
422SD16—42no—
423D8—21no—
424D8—21no—
425D8—21no—
426D8—21no—
427M16—22no—
428C2×C8—21no—
429C2×C8—21no—
430C2×C8C2×D4×C7311yescharacteristic
431C2×C8C2×D4×C7311yescharacteristic
432C2×C8C2×D4×C7311yescharacteristic
433C2×C8C24×C7311yescharacteristic
434C4⋊C4—21no—
435C4⋊C4—21no—
436C4⋊C4—41no—
437C4⋊C4—41no—
438C4⋊C4—41no—
439C4⋊C4—41no—
440C4⋊C4—41no—
441C4⋊C4—41no—
442C4⋊C4—41no—
443C4⋊C4D8×C7311yescharacteristic
444C4⋊C4D8×C7311yescharacteristic
445C22⋊C4—41no—
446C22⋊C4—41no—
447C22⋊C4—41no—
448C22⋊C4—41no—
449C22⋊C4—41no—
450C22⋊C4—41no—
451C22⋊C4—41no—
452C22⋊C4—41no—
453C22⋊C4—41no—
454C22⋊C4D8×C7311yescharacteristic
455C22⋊C4D8×C7311yescharacteristic
456C42—41no—
457C42C2×D4×C7311yescharacteristic
458C42C2×D4×C7311yescharacteristic
459C16—21no—
460C16—21no—
461C16—21no—
462C16—21no—
463C23—41no—
464C23—41no—
465C23C2×D8×C7311yescharacteristic
466Q8—41no—
467Q8—41no—
468Q8—41no—
469Q8—41no—
470Q8—41no—
471Q8—41no—
472Q8—41no—
473Q8—41no—
474Q8—82no—
475Q8—161no—
476D4—41no—
477D4—41no—
478D4—41no—
479D4—41no—
480D4—82no—
481D4—161no—
482C2×C4—21no—
483C2×C4—21no—
484C2×C4—41no—
485C2×C4—41no—
486C2×C4—41no—
487C2×C4—41no—
488C2×C4—41no—
489C2×C4—41no—
490C2×C4—82no—
491C2×C4—82no—
492C2×C4—161no—
493C2×C4C2×D8×C7311yescharacteristic
494C2×C4C2×D8×C7311yescharacteristic
495C2×C4C2×D8×C7311yescharacteristic
496C2×C4C2×D8×C7311yescharacteristic
497C2×C4C2×D8×C7311yescharacteristic
498C2×C4C22×D4×C7311yescharacteristic
499C8—21no—
500C8—21no—
501C8AGL(1,ℤ/8)×C7312yes—
502C8H(5,𝔽2)×C7311yescharacteristic
503C8H(5,𝔽2)×C7311yescharacteristic
504C22—21no—
505C22—21no—
506C22—21no—
507C22—81no—
508C22—81no—
509C22—81no—
510C22—81no—
511C22—81no—
512C22—81no—
513C22C22×D8×C7311yescharacteristic
514C4—21no—
515C4—21no—
516C4—21no—
517C4—21no—
518C4—21no—
519C4—81no—
520C4—81no—
521C4—81no—
522C4—81no—
523C4—81no—
524C4—81no—
525C4#535×C7311yescharacteristic
526C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
527C2—41no—
528C2—161no—
529C2—161no—
530C2C73×#320511yescharacteristic
531C2C73×#341611yescharacteristic
532C2C73×#341711yescharacteristic
subgroupG/H
center, socleC22×C73C22×D8
commutator, Frattini, cosocleC2×C8C24×C73
prime radicalC73×#2186C2
LCSG ▷ C2×C8 ▷ C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ #117×C73 ◁ #405×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3175C2semidirect
2. C73×#3156C2semidirect
3. C73×#2251C2semidirect
4. C73×#2249C2semidirect
5. C73×#2243C2semidirect
6. C73×#2241C2semidirect
7. C73×#2211C2semidirect
8. C73×#2210C2semidirect
9. C73×#2209C2semidirect
10. C73×#2208C2semidirect
11. C73×#2189C2semidirect
12. C73×#2188C2semidirect
14. C73×#2185C2semidirect
15. C73×#2164C2semidirect
260. #33791C73direct (N × H)
267. #3175C2×C73semidirect
268. #3156C2×C73semidirect
269. #2251C2×C73semidirect
270. #2249C2×C73semidirect
271. #2243C2×C73semidirect
272. #2241C2×C73semidirect
273. #2211C2×C73semidirect
274. #2210C2×C73semidirect
275. #2209C2×C73semidirect
276. #2208C2×C73semidirect
277. #2189C2×C73semidirect
278. #2188C2×C73semidirect
280. #2185C2×C73semidirect
281. #2164C2×C73semidirect
282. C73#33791direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#31752
C73×#31562
C73×#22512
C73×#22492
C73×#22432
C73×#22412
C73×#22112
C73×#22102
C73×#22092
C73×#22082
C73×#21892
C73×#21882
C73×#21862
C73×#21852
C73×#21642
#3379173