Finite Group Databasebeta

← C73×#19997 #32929401

Subgroups — C73×#19997 #32929401

Order 18688.

602 conjugacy classes of subgroups.

The subgroup lattice has 574 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3360C211yesmaximal, characteristic, complemented
2C73×#3340C211yesmaximal, characteristic, complemented
3C73×#3335C211yesmaximal, characteristic, complemented
4C73×#3303C211yesmaximal, characteristic
5C73×#1707C211yesmaximal, characteristic, complemented
6C73×#1684C211yesmaximal, characteristic, complemented
7C73×#1683C211yesmaximal, characteristic, complemented
8C73×#1671C211yesmaximal, characteristic, complemented
9C73×#1671C211yesmaximal, characteristic, complemented
10C73×#1650C211yesmaximal, characteristic, complemented
11C73×#1647C211yesmaximal, characteristic, complemented
12C73×#1634C211yesmaximal, characteristic, complemented
13C73×#1632C211yesmaximal, characteristic, complemented
14C8×SD16×C73C211yesmaximal, characteristic, complemented
15C8×D8×C73C211yesmaximal, characteristic, complemented
16#556×C73C2211yescharacteristic
17#555×C73C2211yescharacteristic
18#554×C73C2211yescharacteristic
19#547×C73C2211yescharacteristic
20#500×C73C2211yescharacteristic
21#498×C73C2211yescharacteristic
22#498×C73C2211yescharacteristic
23#494×C73C2211yescharacteristic
24#488×C73—21no—
25#487×C73C2211yescharacteristic
26#487×C73C2211yescharacteristic
27#485×C73—21no—
28#485×C73—21no—
29#483×C73—21no—
30#482×C73—21no—
31#481×C73—21no—
32#479×C73—21no—
33#477×C73C2211yescharacteristic
34#476×C73C2211yescharacteristic
35#476×C73C2211yescharacteristic
36#476×C73C2211yescharacteristic
37#475×C73C2211yescharacteristic
38#474×C73C2211yescharacteristic
39#465×C73—21no—
40#465×C73—21no—
41#465×C73—21no—
42#463×C73—21no—
43#461×C73C2211yescharacteristic
44#461×C73C2211yescharacteristic
45#449×C73—21no—
46C8×Q8×C73C2211yescharacteristic
47C4×SD16×C73—21no—
48C4×SD16×C73C2211yescharacteristic
49C4×D8×C73C2211yescharacteristic
50C8×D4×C73C2211yescharacteristic
51C8×D4×C73C2211yescharacteristic
52C8×D4×C73C2211yescharacteristic
53#427×C73—21no—
54C2×#106×C73—21no—
55#416×C73—21no—
56#335×C73C2211yescharacteristic
57#334×C73C2211yescharacteristic
58#333×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic
60#332×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62Q8⋊C8×C73C2211yescharacteristic
63D4⋊C8×C73C2211yescharacteristic
64D4⋊C8×C73C2211yescharacteristic
65D4⋊C8×C73C2211yescharacteristic
66C82×C73C2211yescharacteristic
67C2×#41×C73—21no—
68C2×Q16×C73—41no—
69C2×SD16×C73—21no—
70C2×SD16×C73—21no—
71C2×SD16×C73D411yescharacteristic
72C2×D8×C73D411yescharacteristic
73C22×C8×C73—21no—
74C22×C8×C73—21no—
75C22×C8×C73—21no—
76C4⋊Q8×C73C2311yescharacteristic
77C4⋊Q8×C73C2311yescharacteristic
78C4⋊Q8×C73C2311yescharacteristic
79C4⋊Q8×C73C2311yescharacteristic
80#126×C73—41no—
81#125×C73—21no—
82#124×C73—21no—
83#124×C73—41no—
84#123×C73—41no—
85C22⋊Q8×C73—21no—
86C22⋊Q8×C73—21no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—41no—
89#121×C73—21no—
90#121×C73—21no—
91#121×C73—21no—
92C4×Q8×C73—21no—
93C4×Q8×C73C2311yescharacteristic
94C4×D4×C73—21no—
95C4×D4×C73C2311yescharacteristic
96C4×D4×C73C2311yescharacteristic
97C4×D4×C73C2311yescharacteristic
98#117×C73—21no—
99#117×C73—21no—
100#117×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103#107×C73—21no—
104#107×C73—21no—
105#107×C73—41no—
106#107×C73D411yescharacteristic
107#106×C73—21no—
108#106×C73—21no—
109#106×C73—21no—
110#106×C73—21no—
111#106×C73—21no—
112#106×C73—21no—
113#106×C73—21no—
114#106×C73—21no—
115#106×C73D411yescharacteristic
116C4⋊C8×C73—21no—
117C4⋊C8×C73C2311yescharacteristic
118C4⋊C8×C73C2311yescharacteristic
119C4⋊C8×C73C2311yescharacteristic
120C4⋊C8×C73C2311yescharacteristic
121#103×C73—21no—
122#103×C73—21no—
123#103×C73—21no—
124#103×C73—21no—
125#103×C73—21no—
126#103×C73—21no—
127#103×C73—21no—
128#103×C73—21no—
129#103×C73D411yescharacteristic
130#102×C73—21no—
131#102×C73—21no—
132#102×C73—21no—
133#102×C73—21no—
134#102×C73D411yescharacteristic
135#102×C73D411yescharacteristic
136#102×C73D411yescharacteristic
137C22⋊C8×C73—21no—
138C22⋊C8×C73—21no—
139C22⋊C8×C73—21no—
140C4×C8×C73—21no—
141C4×C8×C73C2311yescharacteristic
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144#41×C73—42no—
145#41×C73—81no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×Q8×C73—21no—
149C2×Q8×C73—21no—
150C2×Q8×C73C2×D411yescharacteristic
151C2×D4×C73—41no—
152C2×D4×C73—41no—
153C2×D4×C73C2×D411yescharacteristic
154C2×D4×C73C2×D411yescharacteristic
155C2×D4×C73C2×D411yescharacteristic
156C22×C4×C73—21no—
157C22×C4×C73—21no—
158C22×C4×C73—21no—
159C22×C4×C73—41no—
160C22×C4×C73—41no—
161Q16×C73—82no—
162SD16×C73—22no—
163SD16×C73—42no—
164SD16×C73—81no—
165D8×C73—22no—
166C2×C8×C73—21no—
167C2×C8×C73—21no—
168C2×C8×C73—21no—
169C2×C8×C73—21no—
170C2×C8×C73—21no—
171C2×C8×C73—42no—
172C2×C8×C73—42no—
173C2×C8×C73—81no—
174C2×C8×C73C2×D411yescharacteristic
175C2×C8×C73C2×D411yescharacteristic
176C2×C8×C73C2×D411yescharacteristic
177C2×C8×C73C2×D411yescharacteristic
178C4⋊C4×C73—21no—
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—41no—
188C4⋊C4×C73—41no—
189C4⋊C4×C73—41no—
190C4⋊C4×C73—41no—
191C4⋊C4×C73C2×D411yescharacteristic
192C4⋊C4×C73C2×D411yescharacteristic
193C4⋊C4×C73C2×D411yescharacteristic
194C4⋊C4×C73C2×D411yescharacteristic
195C22⋊C4×C73—21no—
196C22⋊C4×C73—21no—
197C22⋊C4×C73—21no—
198C22⋊C4×C73—41no—
199C22⋊C4×C73—41no—
200C22⋊C4×C73—41no—
201C22⋊C4×C73—41no—
202C22⋊C4×C73—41no—
203C22⋊C4×C73—41no—
204C42×C73—21no—
205C42×C73—41no—
206C42×C73—41no—
207C42×C73C2411yescharacteristic
208C23×C73—21no—
209C23×C73—21no—
210C23×C73—21no—
211Q8×C73—21no—
212Q8×C73—21no—
213Q8×C73—41no—
214Q8×C73—41no—
215Q8×C73—41no—
216Q8×C73—41no—
217Q8×C73—81no—
218Q8×C73—81no—
219D4×C73—21no—
220D4×C73—21no—
221D4×C73—21no—
222D4×C73—21no—
223D4×C73—21no—
224D4×C73—82no—
225D4×C73—161no—
226D4×C73#13512yes—
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—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—82no—
243C2×C4×C73—161no—
244C2×C4×C73C22×D411yescharacteristic
245C2×C4×C73C22×D411yescharacteristic
246C2×C4×C73H(5,𝔽2)11yescharacteristic
247C8×C73—22no—
248C8×C73—21no—
249C8×C73—21no—
250C8×C73—21no—
251C8×C73—41no—
252C8×C73—41no—
253C8×C73—41no—
254C8×C73—41no—
255C8×C73#13512yes—
256C22×C73—22no—
257C22×C73—41no—
258C22×C73—41no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73D4211yescharacteristic
266C4×C73—21no—
267C4×C73—41no—
268C4×C73—41no—
269C4×C73—41no—
270C4×C73—41no—
271C4×C73—41no—
272C4×C73—81no—
273C4×C73—81no—
274C4×C73—81no—
275C4×C73—81no—
276C4×C73C2×#13511yescharacteristic
277C4×C73C2×#13511yescharacteristic
278C4×C73#57711yescharacteristic
279C4×C73#57811yescharacteristic
280#19997C7311yesmaximal, characteristic, direct product factor, Sylow
281C2×C73—42no—
282C2×C73—81no—
283C2×C73—81no—
284C2×C73#328211yescharacteristic
285C2×C73#328311yescharacteristic
286C2×C73#329111yescharacteristic
287#3360C2×C7311yescharacteristic, complemented
288#3340C2×C7311yescharacteristic, complemented
289#3335C2×C7311yescharacteristic, complemented
290#3303C2×C7311yescharacteristic
291#1707C2×C7311yescharacteristic, complemented
292#1684C2×C7311yescharacteristic, complemented
293#1683C2×C7311yescharacteristic, complemented
294#1671C2×C7311yescharacteristic, complemented
295#1671C2×C7311yescharacteristic, complemented
296#1650C2×C7311yescharacteristic, complemented
297#1647C2×C7311yescharacteristic, complemented
298#1634C2×C7311yescharacteristic, complemented
299#1632C2×C7311yescharacteristic, complemented
300C8×SD16C2×C7311yescharacteristic, complemented
301C8×D8C2×C7311yescharacteristic, complemented
302C73#1999711yescharacteristic, direct product factor, Sylow
303#556C22×C7311yescharacteristic
304#555C22×C7311yescharacteristic
305#554C22×C7311yescharacteristic
306#547C22×C7311yescharacteristic
307#500C22×C7311yescharacteristic
308#498C22×C7311yescharacteristic
309#498C22×C7311yescharacteristic
310#494C22×C7311yescharacteristic
311#488—21no—
312#487C22×C7311yescharacteristic
313#487C22×C7311yescharacteristic
314#485—21no—
315#485—21no—
316#483—21no—
317#482—21no—
318#481—21no—
319#479—21no—
320#477C22×C7311yescharacteristic
321#476C22×C7311yescharacteristic
322#476C22×C7311yescharacteristic
323#476C22×C7311yescharacteristic
324#475C22×C7311yescharacteristic
325#474C22×C7311yescharacteristic
326#465—21no—
327#465—21no—
328#465—21no—
329#463—21no—
330#461C22×C7311yescharacteristic
331#461C22×C7311yescharacteristic
332#449—21no—
333C8×Q8C22×C7311yescharacteristic
334C4×SD16—21no—
335C4×SD16C22×C7311yescharacteristic
336C4×D8C22×C7311yescharacteristic
337C8×D4C22×C7311yescharacteristic
338C8×D4C22×C7311yescharacteristic
339C8×D4C22×C7311yescharacteristic
340#427—21no—
341C2×#106—21no—
342#416—21no—
343#335C22×C7311yescharacteristic
344#334C22×C7311yescharacteristic
345#333C22×C7311yescharacteristic
346#333C22×C7311yescharacteristic
347#332C22×C7311yescharacteristic
348#332C22×C7311yescharacteristic
349Q8⋊C8C22×C7311yescharacteristic
350D4⋊C8C22×C7311yescharacteristic
351D4⋊C8C22×C7311yescharacteristic
352D4⋊C8C22×C7311yescharacteristic
353C82C22×C7311yescharacteristic
354C2×#41—21no—
355C2×Q16—41no—
356C2×SD16—21no—
357C2×SD16—21no—
358C2×SD16D4×C7311yescharacteristic
359C2×D8D4×C7311yescharacteristic
360C22×C8—21no—
361C22×C8—21no—
362C22×C8—21no—
363C4⋊Q8C23×C7311yescharacteristic
364C4⋊Q8C23×C7311yescharacteristic
365C4⋊Q8C23×C7311yescharacteristic
366C4⋊Q8C23×C7311yescharacteristic
367#126—41no—
368#125—21no—
369#124—21no—
370#124—41no—
371#123—41no—
372C22⋊Q8—21no—
373C22⋊Q8—21no—
374C22⋊Q8—21no—
375C22⋊Q8—41no—
376#121—21no—
377#121—21no—
378#121—21no—
379C4×Q8—21no—
380C4×Q8C23×C7311yescharacteristic
381C4×D4—21no—
382C4×D4C23×C7311yescharacteristic
383C4×D4C23×C7311yescharacteristic
384C4×D4C23×C7311yescharacteristic
385#117—21no—
386#117—21no—
387#117—21no—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390#107—21no—
391#107—21no—
392#107—41no—
393#107D4×C7311yescharacteristic
394#106—21no—
395#106—21no—
396#106—21no—
397#106—21no—
398#106—21no—
399#106—21no—
400#106—21no—
401#106—21no—
402#106D4×C7311yescharacteristic
403C4⋊C8—21no—
404C4⋊C8C23×C7311yescharacteristic
405C4⋊C8C23×C7311yescharacteristic
406C4⋊C8C23×C7311yescharacteristic
407C4⋊C8C23×C7311yescharacteristic
408#103—21no—
409#103—21no—
410#103—21no—
411#103—21no—
412#103—21no—
413#103—21no—
414#103—21no—
415#103—21no—
416#103D4×C7311yescharacteristic
417#102—21no—
418#102—21no—
419#102—21no—
420#102—21no—
421#102D4×C7311yescharacteristic
422#102D4×C7311yescharacteristic
423#102D4×C7311yescharacteristic
424C22⋊C8—21no—
425C22⋊C8—21no—
426C22⋊C8—21no—
427C4×C8—21no—
428C4×C8C23×C7311yescharacteristic
429C4×C8C23×C7311yescharacteristic
430C4×C8C23×C7311yescharacteristic
431#41—42no—
432#41—81no—
433C2×Q8—21no—
434C2×Q8—21no—
435C2×Q8—21no—
436C2×Q8—21no—
437C2×Q8C2×D4×C7311yescharacteristic
438C2×D4—41no—
439C2×D4—41no—
440C2×D4C2×D4×C7311yescharacteristic
441C2×D4C2×D4×C7311yescharacteristic
442C2×D4C2×D4×C7311yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—41no—
447C22×C4—41no—
448Q16—82no—
449SD16—22no—
450SD16—42no—
451SD16—81no—
452D8—22no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—42no—
459C2×C8—42no—
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—41no—
475C4⋊C4—41no—
476C4⋊C4—41no—
477C4⋊C4—41no—
478C4⋊C4C2×D4×C7311yescharacteristic
479C4⋊C4C2×D4×C7311yescharacteristic
480C4⋊C4C2×D4×C7311yescharacteristic
481C4⋊C4C2×D4×C7311yescharacteristic
482C22⋊C4—21no—
483C22⋊C4—21no—
484C22⋊C4—21no—
485C22⋊C4—41no—
486C22⋊C4—41no—
487C22⋊C4—41no—
488C22⋊C4—41no—
489C22⋊C4—41no—
490C22⋊C4—41no—
491C42—21no—
492C42—41no—
493C42—41no—
494C42C24×C7311yescharacteristic
495C23—21no—
496C23—21no—
497C23—21no—
498Q8—21no—
499Q8—21no—
500Q8—41no—
501Q8—41no—
502Q8—41no—
503Q8—41no—
504Q8—81no—
505Q8—81no—
506D4—21no—
507D4—21no—
508D4—21no—
509D4—21no—
510D4—21no—
511D4—82no—
512D4—161no—
513D4#135×C7312yes—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—82no—
530C2×C4—161no—
531C2×C4C22×D4×C7311yescharacteristic
532C2×C4C22×D4×C7311yescharacteristic
533C2×C4H(5,𝔽2)×C7311yescharacteristic
534C8—22no—
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8#135×C7312yes—
543C22—22no—
544C22—41no—
545C22—41no—
546C22—41no—
547C22—41no—
548C22—41no—
549C22—41no—
550C22—41no—
551C22—41no—
552C22D42×C7311yescharacteristic
553C4—21no—
554C4—41no—
555C4—41no—
556C4—41no—
557C4—41no—
558C4—41no—
559C4—81no—
560C4—81no—
561C4—81no—
562C4—81no—
563C4C2×#135×C7311yescharacteristic
564C4C2×#135×C7311yescharacteristic
565C4#577×C7311yescharacteristic
566C4#578×C7311yescharacteristic
567C2—42no—
568C2—81no—
569C2—81no—
570C2C73×#328211yescharacteristic
571C2C73×#328311yescharacteristic
572C2C73×#329111yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3303C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3360C2semidirect
2. C73×#3340C2semidirect
3. C73×#3335C2semidirect
5. C73×#1707C2semidirect
6. C73×#1684C2semidirect
7. C73×#1683C2semidirect
8. C73×#1671C2semidirect
9. C73×#1671C2semidirect
10. C73×#1650C2semidirect
11. C73×#1647C2semidirect
12. C73×#1634C2semidirect
13. C73×#1632C2semidirect
14. C8×SD16×C73C2semidirect
15. C8×D8×C73C2semidirect
280. #19997C73direct (N × H)
287. #3360C2×C73semidirect
288. #3340C2×C73semidirect
289. #3335C2×C73semidirect
291. #1707C2×C73semidirect
292. #1684C2×C73semidirect
293. #1683C2×C73semidirect
294. #1671C2×C73semidirect
295. #1671C2×C73semidirect
296. #1650C2×C73semidirect
297. #1647C2×C73semidirect
298. #1634C2×C73semidirect
299. #1632C2×C73semidirect
300. C8×SD16C2×C73semidirect
301. C8×D8C2×C73semidirect
302. C73#19997direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#33602
C73×#33402
C73×#33352
C73×#33032
C73×#17072
C73×#16842
C73×#16832
C73×#16712
C73×#16502
C73×#16472
C73×#16342
C73×#16322
C8×SD16×C732
C8×D8×C732
#1999773