Finite Group Databasebeta

← C73×#19551 #32928955

Subgroups — C73×#19551 #32928955

Order 18688.

578 conjugacy classes of subgroups.

The subgroup lattice has 572 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3252C211yesmaximal, characteristic, complemented
2C73×#3247C211yesmaximal, characteristic
3C73×#3228C211yesmaximal, characteristic, complemented
4C73×#2993C211yesmaximal, characteristic, complemented
5C73×#1698C211yesmaximal, characteristic, complemented
6C73×#1697C211yesmaximal, characteristic, complemented
7C73×#1692C211yesmaximal, characteristic, complemented
8C73×#1691C211yesmaximal, characteristic, complemented
9C73×#1682C211yesmaximal, characteristic, complemented
10C73×#1681C211yesmaximal, characteristic, complemented
11C73×#1676C211yesmaximal, characteristic, complemented
12C73×#1675C211yesmaximal, characteristic, complemented
13C73×#1571C211yesmaximal, characteristic, complemented
14C73×#1560C211yesmaximal, characteristic, complemented
15C73×#1550C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17#532×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#500×C73C2211yescharacteristic
20#498×C73C2211yescharacteristic
21#486×C73C2211yescharacteristic
22#486×C73C2211yescharacteristic
23#482×C73—21no—
24#482×C73—21no—
25#479×C73—21no—
26#478×C73—21no—
27#478×C73—21no—
28#478×C73—21no—
29#477×C73C2211yescharacteristic
30#477×C73C2211yescharacteristic
31#476×C73C2211yescharacteristic
32#476×C73C2211yescharacteristic
33#470×C73—21no—
34#468×C73—21no—
35#466×C73—21no—
36#465×C73—21no—
37#464×C73—21no—
38#463×C73—21no—
39#462×C73C2211yescharacteristic
40#461×C73C2211yescharacteristic
41#460×C73C2211yescharacteristic
42#459×C73C2211yescharacteristic
43#446×C73C2211yescharacteristic
44C8×Q8×C73C2211yescharacteristic
45#436×C73—21no—
46#436×C73C2211yescharacteristic
47#435×C73—21no—
48C8×D4×C73C2211yescharacteristic
49#433×C73—21no—
50#431×C73C2211yescharacteristic
51#424×C73—21no—
52#423×C73C2211yescharacteristic
53#423×C73C2211yescharacteristic
54C2×C4⋊C8×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic
56#335×C73C2211yescharacteristic
57#335×C73C2211yescharacteristic
58#335×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#333×C73C2211yescharacteristic
62#333×C73C2211yescharacteristic
63#332×C73C2211yescharacteristic
64#332×C73C2211yescharacteristic
65#331×C73C2211yescharacteristic
66#331×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×Q16×C73—21no—
69C2×SD16×C73—21no—
70C2×SD16×C73—21no—
71C2×D8×C73—21no—
72C2×M16×C73—21no—
73C2×M16×C73—21no—
74C2×M16×C73—21no—
75C22×C8×C73—21no—
76C22×C8×C73—21no—
77C4⋊Q8×C73C2311yescharacteristic
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80#127×C73C2311yescharacteristic
81#126×C73—21no—
82#125×C73—21no—
83#125×C73D411yescharacteristic
84#124×C73—21no—
85#124×C73D411yescharacteristic
86#123×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73D411yescharacteristic
90#121×C73—21no—
91#121×C73—21no—
92#121×C73D411yescharacteristic
93C4×Q8×C73—21no—
94C4×Q8×C73—21no—
95C4×Q8×C73C2311yescharacteristic
96C4×D4×C73—21no—
97C4×D4×C73—21no—
98C4×D4×C73—21no—
99C4×D4×C73C2311yescharacteristic
100#117×C73—21no—
101#117×C73—21no—
102C2×C42×C73C2311yescharacteristic
103#107×C73—21no—
104#107×C73—21no—
105#107×C73—21no—
106#107×C73—21no—
107#106×C73—21no—
108#106×C73—21no—
109#106×C73—21no—
110#106×C73—21no—
111C4⋊C8×C73—21no—
112C4⋊C8×C73—21no—
113C4⋊C8×C73—21no—
114C4⋊C8×C73—21no—
115C4⋊C8×C73—21no—
116C4⋊C8×C73D411yescharacteristic
117C4⋊C8×C73D411yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120C4⋊C8×C73C2311yescharacteristic
121C4⋊C8×C73C2311yescharacteristic
122C4⋊C8×C73C2311yescharacteristic
123C4⋊C8×C73C2311yescharacteristic
124#103×C73—21no—
125#103×C73—21no—
126#103×C73—21no—
127#103×C73—21no—
128#102×C73—21no—
129#102×C73—21no—
130#102×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134#102×C73—21no—
135#102×C73—21no—
136C22⋊C8×C73—21no—
137C22⋊C8×C73—21no—
138C22⋊C8×C73D411yescharacteristic
139C22⋊C8×C73D411yescharacteristic
140#97×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#41×C73—82no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73C2×D411yescharacteristic
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—41no—
154C2×D4×C73C2×D411yescharacteristic
155C22×C4×C73—21no—
156C22×C4×C73—41no—
157C22×C4×C73C2×D411yescharacteristic
158C22×C4×C73C2×D411yescharacteristic
159C22×C4×C73#4111yescharacteristic
160Q16×C73—81no—
161SD16×C73—81no—
162SD16×C73—81no—
163D8×C73—81no—
164M16×C73—81no—
165M16×C73—81no—
166M16×C73—81no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—21no—
172C2×C8×C73—21no—
173C2×C8×C73—81no—
174C2×C8×C73—81no—
175C2×C8×C73C2×D411yescharacteristic
176C2×C8×C73C2×D411yescharacteristic
177C2×C8×C73C2×D411yescharacteristic
178C2×C8×C73C2×D411yescharacteristic
179C4⋊C4×C73—21no—
180C4⋊C4×C73—21no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—21no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—21no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—41no—
190C4⋊C4×C73—41no—
191C4⋊C4×C73C2×D411yescharacteristic
192C4⋊C4×C73C2×D411yescharacteristic
193C22⋊C4×C73—21no—
194C22⋊C4×C73—21no—
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—41no—
199C22⋊C4×C73—41no—
200C22⋊C4×C73—41no—
201C42×C73—21no—
202C42×C73—41no—
203C42×C73C2×D411yescharacteristic
204C42×C73C2×D411yescharacteristic
205C42×C73#4111yescharacteristic
206C42×C73C2411yescharacteristic
207C23×C73—21no—
208C23×C73—41no—
209C23×C73#12111yescharacteristic
210Q8×C73—21no—
211Q8×C73—21no—
212Q8×C73—41no—
213Q8×C73—41no—
214Q8×C73—81no—
215Q8×C73—81no—
216D4×C73—21no—
217D4×C73—21no—
218D4×C73—41no—
219D4×C73—41no—
220D4×C73—41no—
221D4×C73—41no—
222D4×C73—81no—
223D4×C73—81no—
224D4×C73—82no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—21no—
231C2×C4×C73—21no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—82no—
239C2×C4×C73#12111yescharacteristic
240C2×C4×C73#12111yescharacteristic
241C2×C4×C73#12111yescharacteristic
242C2×C4×C73C22×D411yescharacteristic
243C2×C4×C73C22×D411yescharacteristic
244C2×C4×C73C2×#4111yescharacteristic
245C8×C73—21no—
246C8×C73—21no—
247C8×C73—21no—
248C8×C73—21no—
249C8×C73—41no—
250C8×C73—41no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C22×C73—21no—
256C22×C73—21no—
257C22×C73—21no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—81no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73C2×#12111yescharacteristic
265C4×C73—21no—
266C4×C73—21no—
267C4×C73—21no—
268C4×C73—21no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—81no—
273C4×C73—81no—
274C4×C73—81no—
275C4×C73#57611yescharacteristic
276C4×C73#57711yescharacteristic
277C4×C73#57811yescharacteristic
278C4×C73#57811yescharacteristic
279#19551C7311yesmaximal, characteristic, direct product factor, Sylow
280C2×C73—41no—
281C2×C73—81no—
282C2×C73—161no—
283C2×C73#304611yescharacteristic
284C2×C73#306111yescharacteristic
285C2×C73#306811yescharacteristic
286#3252C2×C7311yescharacteristic, complemented
287#3247C2×C7311yescharacteristic
288#3228C2×C7311yescharacteristic, complemented
289#2993C2×C7311yescharacteristic, complemented
290#1698C2×C7311yescharacteristic, complemented
291#1697C2×C7311yescharacteristic, complemented
292#1692C2×C7311yescharacteristic, complemented
293#1691C2×C7311yescharacteristic, complemented
294#1682C2×C7311yescharacteristic, complemented
295#1681C2×C7311yescharacteristic, complemented
296#1676C2×C7311yescharacteristic, complemented
297#1675C2×C7311yescharacteristic, complemented
298#1571C2×C7311yescharacteristic, complemented
299#1560C2×C7311yescharacteristic, complemented
300#1550C2×C7311yescharacteristic, complemented
301C73#1955111yescharacteristic, direct product factor, Sylow
302#533C22×C7311yescharacteristic
303#532C22×C7311yescharacteristic
304#529C22×C7311yescharacteristic
305#500C22×C7311yescharacteristic
306#498C22×C7311yescharacteristic
307#486C22×C7311yescharacteristic
308#486C22×C7311yescharacteristic
309#482—21no—
310#482—21no—
311#479—21no—
312#478—21no—
313#478—21no—
314#478—21no—
315#477C22×C7311yescharacteristic
316#477C22×C7311yescharacteristic
317#476C22×C7311yescharacteristic
318#476C22×C7311yescharacteristic
319#470—21no—
320#468—21no—
321#466—21no—
322#465—21no—
323#464—21no—
324#463—21no—
325#462C22×C7311yescharacteristic
326#461C22×C7311yescharacteristic
327#460C22×C7311yescharacteristic
328#459C22×C7311yescharacteristic
329#446C22×C7311yescharacteristic
330C8×Q8C22×C7311yescharacteristic
331#436—21no—
332#436C22×C7311yescharacteristic
333#435—21no—
334C8×D4C22×C7311yescharacteristic
335#433—21no—
336#431C22×C7311yescharacteristic
337#424—21no—
338#423C22×C7311yescharacteristic
339#423C22×C7311yescharacteristic
340C2×C4⋊C8C22×C7311yescharacteristic
341#335C22×C7311yescharacteristic
342#335C22×C7311yescharacteristic
343#335C22×C7311yescharacteristic
344#335C22×C7311yescharacteristic
345#333C22×C7311yescharacteristic
346#333C22×C7311yescharacteristic
347#333C22×C7311yescharacteristic
348#333C22×C7311yescharacteristic
349#332C22×C7311yescharacteristic
350#332C22×C7311yescharacteristic
351#331C22×C7311yescharacteristic
352#331C22×C7311yescharacteristic
353C2×#41—21no—
354C2×Q16—21no—
355C2×SD16—21no—
356C2×SD16—21no—
357C2×D8—21no—
358C2×M16—21no—
359C2×M16—21no—
360C2×M16—21no—
361C22×C8—21no—
362C22×C8—21no—
363C4⋊Q8C23×C7311yescharacteristic
364C4⋊Q8C23×C7311yescharacteristic
365C4⋊Q8C23×C7311yescharacteristic
366#127C23×C7311yescharacteristic
367#126—21no—
368#125—21no—
369#125D4×C7311yescharacteristic
370#124—21no—
371#124D4×C7311yescharacteristic
372#123—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8D4×C7311yescharacteristic
376#121—21no—
377#121—21no—
378#121D4×C7311yescharacteristic
379C4×Q8—21no—
380C4×Q8—21no—
381C4×Q8C23×C7311yescharacteristic
382C4×D4—21no—
383C4×D4—21no—
384C4×D4—21no—
385C4×D4C23×C7311yescharacteristic
386#117—21no—
387#117—21no—
388C2×C42C23×C7311yescharacteristic
389#107—21no—
390#107—21no—
391#107—21no—
392#107—21no—
393#106—21no—
394#106—21no—
395#106—21no—
396#106—21no—
397C4⋊C8—21no—
398C4⋊C8—21no—
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—21no—
402C4⋊C8D4×C7311yescharacteristic
403C4⋊C8D4×C7311yescharacteristic
404C4⋊C8C23×C7311yescharacteristic
405C4⋊C8C23×C7311yescharacteristic
406C4⋊C8C23×C7311yescharacteristic
407C4⋊C8C23×C7311yescharacteristic
408C4⋊C8C23×C7311yescharacteristic
409C4⋊C8C23×C7311yescharacteristic
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#102—21no—
415#102—21no—
416#102—21no—
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102—21no—
422C22⋊C8—21no—
423C22⋊C8—21no—
424C22⋊C8D4×C7311yescharacteristic
425C22⋊C8D4×C7311yescharacteristic
426#97—21no—
427C4×C8—21no—
428C4×C8C23×C7311yescharacteristic
429C4×C8C23×C7311yescharacteristic
430#41—82no—
431C2×Q8—21no—
432C2×Q8—21no—
433C2×Q8—21no—
434C2×Q8C2×D4×C7311yescharacteristic
435C2×D4—21no—
436C2×D4—21no—
437C2×D4—21no—
438C2×D4—21no—
439C2×D4—41no—
440C2×D4C2×D4×C7311yescharacteristic
441C22×C4—21no—
442C22×C4—41no—
443C22×C4C2×D4×C7311yescharacteristic
444C22×C4C2×D4×C7311yescharacteristic
445C22×C4#41×C7311yescharacteristic
446Q16—81no—
447SD16—81no—
448SD16—81no—
449D8—81no—
450M16—81no—
451M16—81no—
452M16—81no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—81no—
461C2×C8C2×D4×C7311yescharacteristic
462C2×C8C2×D4×C7311yescharacteristic
463C2×C8C2×D4×C7311yescharacteristic
464C2×C8C2×D4×C7311yescharacteristic
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4C2×D4×C7311yescharacteristic
478C4⋊C4C2×D4×C7311yescharacteristic
479C22⋊C4—21no—
480C22⋊C4—21no—
481C22⋊C4—21no—
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—41no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C42—21no—
488C42—41no—
489C42C2×D4×C7311yescharacteristic
490C42C2×D4×C7311yescharacteristic
491C42#41×C7311yescharacteristic
492C42C24×C7311yescharacteristic
493C23—21no—
494C23—41no—
495C23#121×C7311yescharacteristic
496Q8—21no—
497Q8—21no—
498Q8—41no—
499Q8—41no—
500Q8—81no—
501Q8—81no—
502D4—21no—
503D4—21no—
504D4—41no—
505D4—41no—
506D4—41no—
507D4—41no—
508D4—81no—
509D4—81no—
510D4—82no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—82no—
525C2×C4#121×C7311yescharacteristic
526C2×C4#121×C7311yescharacteristic
527C2×C4#121×C7311yescharacteristic
528C2×C4C22×D4×C7311yescharacteristic
529C2×C4C22×D4×C7311yescharacteristic
530C2×C4C2×#41×C7311yescharacteristic
531C8—21no—
532C8—21no—
533C8—21no—
534C8—21no—
535C8—41no—
536C8—41no—
537C8—41no—
538C8—41no—
539C8—41no—
540C8—41no—
541C22—21no—
542C22—21no—
543C22—21no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—81no—
548C22—81no—
549C22—81no—
550C22C2×#121×C7311yescharacteristic
551C4—21no—
552C4—21no—
553C4—21no—
554C4—21no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—81no—
559C4—81no—
560C4—81no—
561C4#576×C7311yescharacteristic
562C4#577×C7311yescharacteristic
563C4#578×C7311yescharacteristic
564C4#578×C7311yescharacteristic
565C2—41no—
566C2—81no—
567C2—161no—
568C2C73×#304611yescharacteristic
569C2C73×#306111yescharacteristic
570C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3247C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3252C2semidirect
3. C73×#3228C2semidirect
4. C73×#2993C2semidirect
5. C73×#1698C2semidirect
6. C73×#1697C2semidirect
7. C73×#1692C2semidirect
8. C73×#1691C2semidirect
9. C73×#1682C2semidirect
10. C73×#1681C2semidirect
11. C73×#1676C2semidirect
12. C73×#1675C2semidirect
13. C73×#1571C2semidirect
14. C73×#1560C2semidirect
15. C73×#1550C2semidirect
279. #19551C73direct (N × H)
286. #3252C2×C73semidirect
288. #3228C2×C73semidirect
289. #2993C2×C73semidirect
290. #1698C2×C73semidirect
291. #1697C2×C73semidirect
292. #1692C2×C73semidirect
293. #1691C2×C73semidirect
294. #1682C2×C73semidirect
295. #1681C2×C73semidirect
296. #1676C2×C73semidirect
297. #1675C2×C73semidirect
298. #1571C2×C73semidirect
299. #1560C2×C73semidirect
300. #1550C2×C73semidirect
301. C73#19551direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#32522
C73×#32472
C73×#32282
C73×#29932
C73×#16982
C73×#16972
C73×#16922
C73×#16912
C73×#16822
C73×#16812
C73×#16762
C73×#16752
C73×#15712
C73×#15602
C73×#15502
#1955173