Finite Group Databasebeta

← C73×#19380 #32928784

Subgroups — C73×#19380 #32928784

Order 18688.

636 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3252C211yesmaximal, characteristic, complemented
2C73×#3217C211yesmaximal, characteristic
3C73×#3138C211yesmaximal, characteristic, complemented
4C73×#2969C211yesmaximal, characteristic, complemented
5C73×#1702C211yesmaximal, characteristic, complemented
6C73×#1701C211yesmaximal, characteristic, complemented
7C73×#1698C211yesmaximal, characteristic, complemented
8C73×#1697C211yesmaximal, characteristic, complemented
9C73×#1682C211yesmaximal, characteristic, complemented
10C73×#1681C211yesmaximal, characteristic, complemented
11C73×#1678C211yesmaximal, characteristic, complemented
12C73×#1677C211yesmaximal, characteristic, complemented
13C73×#1569C211yesmaximal, characteristic, complemented
14C73×#1554C211yesmaximal, characteristic, complemented
15C73×#1545C211yesmaximal, characteristic, complemented
16#533×C73C2211yescharacteristic
17C2×#127×C73C2211yescharacteristic
18#529×C73C2211yescharacteristic
19#496×C73—21no—
20#490×C73—21no—
21#490×C73—21no—
22#490×C73—21no—
23#486×C73C2211yescharacteristic
24#486×C73C2211yescharacteristic
25#486×C73C2211yescharacteristic
26#486×C73C2211yescharacteristic
27#479×C73—21no—
28#477×C73C2211yescharacteristic, complemented
29#476×C73C2211yescharacteristic, complemented
30#470×C73—21no—
31#468×C73—21no—
32#464×C73—21no—
33#462×C73C2211yescharacteristic, complemented
34#461×C73C2211yescharacteristic, complemented
35#460×C73C2211yescharacteristic
36#460×C73C2211yescharacteristic
37#459×C73C2211yescharacteristic
38#459×C73C2211yescharacteristic
39#450×C73—21no—
40#447×C73—21no—
41#446×C73C2211yescharacteristic, complemented
42C8×Q8×C73C2211yescharacteristic, complemented
43#436×C73—21no—
44#436×C73C2211yescharacteristic, complemented
45#435×C73—21no—
46C8×D4×C73C2211yescharacteristic, complemented
47#433×C73—21no—
48#432×C73C2211yescharacteristic
49#431×C73C2211yescharacteristic
50#423×C73C2211yescharacteristic
51#418×C73—21no—
52#418×C73—21no—
53#405×C73—21no—
54C4×M16×C73C2211yescharacteristic
55#335×C73C2211yescharacteristic, complemented
56#335×C73C2211yescharacteristic, complemented
57#334×C73C2211yescharacteristic, complemented
58#334×C73C2211yescharacteristic, complemented
59#333×C73C2211yescharacteristic, complemented
60#333×C73C2211yescharacteristic, complemented
61#332×C73C2211yescharacteristic, complemented
62#332×C73C2211yescharacteristic, complemented
63#331×C73C2211yescharacteristic
64#331×C73C2211yescharacteristic
65#331×C73C2211yescharacteristic
66#331×C73C2211yescharacteristic
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C2×Q16×C73—21no—
71C2×SD16×C73—21no—
72C2×SD16×C73—21no—
73C2×SD16×C73—21no—
74C2×D8×C73—21no—
75C2×D8×C73—21no—
76C2×M16×C73—21no—
77C2×M16×C73—21no—
78C2×M16×C73D411yescharacteristic
79C2×M16×C73D411yescharacteristic
80C22×C8×C73—21no—
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83#127×C73—21no—
84#127×C73—21no—
85#127×C73—21no—
86#127×C73C2311yescharacteristic
87#127×C73C2311yescharacteristic
88#126×C73—21no—
89#125×C73—21no—
90#125×C73D411yescharacteristic
91#124×C73D411yescharacteristic
92#123×C73—21no—
93C22⋊Q8×C73—21no—
94C22⋊Q8×C73—21no—
95C22⋊Q8×C73D411yescharacteristic
96#121×C73D411yescharacteristic
97C4×Q8×C73—21no—
98C4×Q8×C73—21no—
99C4×Q8×C73C2311yescharacteristic
100C4×D4×C73—21no—
101C4×D4×C73C2311yescharacteristic
102#117×C73—21no—
103#117×C73—21no—
104C2×C42×C73C2311yescharacteristic
105#107×C73—21no—
106#106×C73—21no—
107C4⋊C8×C73—21no—
108C4⋊C8×C73—21no—
109C4⋊C8×C73—21no—
110C4⋊C8×C73C2311yescharacteristic
111C4⋊C8×C73C2311yescharacteristic
112C4⋊C8×C73C2311yescharacteristic
113C4⋊C8×C73C2311yescharacteristic
114C4⋊C8×C73C2311yescharacteristic
115C4⋊C8×C73C2311yescharacteristic
116#103×C73—21no—
117#103×C73—21no—
118#103×C73—21no—
119#102×C73—21no—
120#102×C73—21no—
121#102×C73—21no—
122#102×C73—21no—
123#102×C73—21no—
124#102×C73—21no—
125#102×C73—21no—
126#102×C73—21no—
127#102×C73—21no—
128#102×C73—21no—
129#102×C73—21no—
130#102×C73—21no—
131#102×C73—21no—
132C22⋊C8×C73—21no—
133C22⋊C8×C73—21no—
134C22⋊C8×C73—21no—
135C22⋊C8×C73—21no—
136#97×C73—21no—
137#97×C73—21no—
138#97×C73D411yescharacteristic
139#97×C73D411yescharacteristic
140C4×C8×C73—21no—
141C4×C8×C73—21no—
142C4×C8×C73C2311yescharacteristic
143C4×C8×C73C2311yescharacteristic
144C24×C73—41no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73C2×D411yescharacteristic
148C2×D4×C73—21no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—42no—
156C2×D4×C73—42no—
157C2×D4×C73—41no—
158C2×D4×C73—41no—
159C2×D4×C73—41no—
160C2×D4×C73—81no—
161C2×D4×C73—81no—
162C2×D4×C73—82no—
163C2×D4×C73C2×D411yescharacteristic
164C22×C4×C73—21no—
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D411yescharacteristic
167C22×C4×C73#4111yescharacteristic
168Q16×C73—81no—
169SD16×C73—81no—
170SD16×C73—81no—
171SD16×C73—81no—
172D8×C73—81no—
173D8×C73—81no—
174M16×C73—41no—
175M16×C73—41no—
176M16×C73—42no—
177M16×C73—81no—
178C2×C8×C73—21no—
179C2×C8×C73—21no—
180C2×C8×C73—21no—
181C2×C8×C73—21no—
182C2×C8×C73—21no—
183C2×C8×C73—21no—
184C2×C8×C73—42no—
185C2×C8×C73C2×D411yescharacteristic
186C2×C8×C73C2×D411yescharacteristic
187C2×C8×C73C2×D411yescharacteristic
188C2×C8×C73C2×D411yescharacteristic
189C4⋊C4×C73—21no—
190C4⋊C4×C73—21no—
191C4⋊C4×C73—21no—
192C4⋊C4×C73—21no—
193C4⋊C4×C73—21no—
194C4⋊C4×C73—21no—
195C4⋊C4×C73—21no—
196C4⋊C4×C73—21no—
197C4⋊C4×C73—41no—
198C4⋊C4×C73—41no—
199C4⋊C4×C73C2×D411yescharacteristic
200C4⋊C4×C73C2×D411yescharacteristic
201C22⋊C4×C73—21no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—21no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—21no—
206C22⋊C4×C73—41no—
207C42×C73—21no—
208C42×C73—41no—
209C42×C73C2×D411yescharacteristic
210C42×C73C2×D411yescharacteristic
211C42×C73#4111yescharacteristic
212C42×C73C2411yescharacteristic
213C23×C73—21no—
214C23×C73—41no—
215C23×C73—41no—
216C23×C73—82no—
217C23×C73—82no—
218C23×C73—82no—
219C23×C73#12111yescharacteristic
220Q8×C73—21no—
221Q8×C73—21no—
222Q8×C73—41no—
223Q8×C73—41no—
224Q8×C73—81no—
225D4×C73—21no—
226D4×C73—21no—
227D4×C73—41no—
228D4×C73—41no—
229D4×C73—41no—
230D4×C73—41no—
231D4×C73—41no—
232D4×C73—41no—
233D4×C73—41no—
234D4×C73—41no—
235D4×C73—81no—
236D4×C73—81no—
237D4×C73—82no—
238D4×C73—82no—
239D4×C73—82no—
240D4×C73—81no—
241C2×C4×C73—21no—
242C2×C4×C73—21no—
243C2×C4×C73—21no—
244C2×C4×C73—21no—
245C2×C4×C73—21no—
246C2×C4×C73—21no—
247C2×C4×C73—21no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73—41no—
252C2×C4×C73—41no—
253C2×C4×C73#12111yescharacteristic
254C2×C4×C73#12111yescharacteristic
255C2×C4×C73#12111yescharacteristic
256C2×C4×C73C22×D411yescharacteristic
257C2×C4×C73C22×D411yescharacteristic
258C2×C4×C73C2×#4111yescharacteristic
259C8×C73—21no—
260C8×C73—21no—
261C8×C73—21no—
262C8×C73—21no—
263C8×C73—41no—
264C8×C73—41no—
265C8×C73—41no—
266C8×C73—41no—
267C8×C73—41no—
268C8×C73—41no—
269C22×C73—21no—
270C22×C73—21no—
271C22×C73—21no—
272C22×C73—41no—
273C22×C73—41no—
274C22×C73—41no—
275C22×C73—81no—
276C22×C73—81no—
277C22×C73—81no—
278C22×C73—81no—
279C22×C73—81no—
280C22×C73—81no—
281C22×C73—164no—
282C22×C73C2×#12111yescharacteristic
283C4×C73—21no—
284C4×C73—21no—
285C4×C73—21no—
286C4×C73—21no—
287C4×C73—41no—
288C4×C73—41no—
289C4×C73—41no—
290C4×C73—81no—
291C4×C73—81no—
292C4×C73#57511yescharacteristic
293C4×C73#57511yescharacteristic
294C4×C73#57611yescharacteristic
295C4×C73#57711yescharacteristic
296#19380C7311yesmaximal, characteristic, direct product factor, Sylow
297C2×C73—41no—
298C2×C73—81no—
299C2×C73—161no—
300C2×C73—161no—
301C2×C73#304011yescharacteristic
302C2×C73#306211yescharacteristic
303C2×C73#306811yescharacteristic
304#3252C2×C7311yescharacteristic, complemented
305#3217C2×C7311yescharacteristic
306#3138C2×C7311yescharacteristic, complemented
307#2969C2×C7311yescharacteristic, complemented
308#1702C2×C7311yescharacteristic, complemented
309#1701C2×C7311yescharacteristic, complemented
310#1698C2×C7311yescharacteristic, complemented
311#1697C2×C7311yescharacteristic, complemented
312#1682C2×C7311yescharacteristic, complemented
313#1681C2×C7311yescharacteristic, complemented
314#1678C2×C7311yescharacteristic, complemented
315#1677C2×C7311yescharacteristic, complemented
316#1569C2×C7311yescharacteristic, complemented
317#1554C2×C7311yescharacteristic, complemented
318#1545C2×C7311yescharacteristic, complemented
319C73#1938011yescharacteristic, direct product factor, Sylow
320#533C22×C7311yescharacteristic
321C2×#127C22×C7311yescharacteristic
322#529C22×C7311yescharacteristic
323#496—21no—
324#490—21no—
325#490—21no—
326#490—21no—
327#486C22×C7311yescharacteristic
328#486C22×C7311yescharacteristic
329#486C22×C7311yescharacteristic
330#486C22×C7311yescharacteristic
331#479—21no—
332#477C22×C7311yescharacteristic, complemented
333#476C22×C7311yescharacteristic, complemented
334#470—21no—
335#468—21no—
336#464—21no—
337#462C22×C7311yescharacteristic, complemented
338#461C22×C7311yescharacteristic, complemented
339#460C22×C7311yescharacteristic
340#460C22×C7311yescharacteristic
341#459C22×C7311yescharacteristic
342#459C22×C7311yescharacteristic
343#450—21no—
344#447—21no—
345#446C22×C7311yescharacteristic, complemented
346C8×Q8C22×C7311yescharacteristic, complemented
347#436—21no—
348#436C22×C7311yescharacteristic, complemented
349#435—21no—
350C8×D4C22×C7311yescharacteristic, complemented
351#433—21no—
352#432C22×C7311yescharacteristic
353#431C22×C7311yescharacteristic
354#423C22×C7311yescharacteristic
355#418—21no—
356#418—21no—
357#405—21no—
358C4×M16C22×C7311yescharacteristic
359#335C22×C7311yescharacteristic, complemented
360#335C22×C7311yescharacteristic, complemented
361#334C22×C7311yescharacteristic, complemented
362#334C22×C7311yescharacteristic, complemented
363#333C22×C7311yescharacteristic, complemented
364#333C22×C7311yescharacteristic, complemented
365#332C22×C7311yescharacteristic, complemented
366#332C22×C7311yescharacteristic, complemented
367#331C22×C7311yescharacteristic
368#331C22×C7311yescharacteristic
369#331C22×C7311yescharacteristic
370#331C22×C7311yescharacteristic
371C22×D4—21no—
372C22×D4—21no—
373C22×D4—21no—
374C2×Q16—21no—
375C2×SD16—21no—
376C2×SD16—21no—
377C2×SD16—21no—
378C2×D8—21no—
379C2×D8—21no—
380C2×M16—21no—
381C2×M16—21no—
382C2×M16D4×C7311yescharacteristic
383C2×M16D4×C7311yescharacteristic
384C22×C8—21no—
385C4⋊Q8C23×C7311yescharacteristic
386C4⋊Q8C23×C7311yescharacteristic
387#127—21no—
388#127—21no—
389#127—21no—
390#127C23×C7311yescharacteristic
391#127C23×C7311yescharacteristic
392#126—21no—
393#125—21no—
394#125D4×C7311yescharacteristic
395#124D4×C7311yescharacteristic
396#123—21no—
397C22⋊Q8—21no—
398C22⋊Q8—21no—
399C22⋊Q8D4×C7311yescharacteristic
400#121D4×C7311yescharacteristic
401C4×Q8—21no—
402C4×Q8—21no—
403C4×Q8C23×C7311yescharacteristic
404C4×D4—21no—
405C4×D4C23×C7311yescharacteristic
406#117—21no—
407#117—21no—
408C2×C42C23×C7311yescharacteristic
409#107—21no—
410#106—21no—
411C4⋊C8—21no—
412C4⋊C8—21no—
413C4⋊C8—21no—
414C4⋊C8C23×C7311yescharacteristic
415C4⋊C8C23×C7311yescharacteristic
416C4⋊C8C23×C7311yescharacteristic
417C4⋊C8C23×C7311yescharacteristic
418C4⋊C8C23×C7311yescharacteristic
419C4⋊C8C23×C7311yescharacteristic
420#103—21no—
421#103—21no—
422#103—21no—
423#102—21no—
424#102—21no—
425#102—21no—
426#102—21no—
427#102—21no—
428#102—21no—
429#102—21no—
430#102—21no—
431#102—21no—
432#102—21no—
433#102—21no—
434#102—21no—
435#102—21no—
436C22⋊C8—21no—
437C22⋊C8—21no—
438C22⋊C8—21no—
439C22⋊C8—21no—
440#97—21no—
441#97—21no—
442#97D4×C7311yescharacteristic
443#97D4×C7311yescharacteristic
444C4×C8—21no—
445C4×C8—21no—
446C4×C8C23×C7311yescharacteristic
447C4×C8C23×C7311yescharacteristic
448C24—41no—
449C2×Q8—21no—
450C2×Q8—21no—
451C2×Q8C2×D4×C7311yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4—21no—
458C2×D4—21no—
459C2×D4—42no—
460C2×D4—42no—
461C2×D4—41no—
462C2×D4—41no—
463C2×D4—41no—
464C2×D4—81no—
465C2×D4—81no—
466C2×D4—82no—
467C2×D4C2×D4×C7311yescharacteristic
468C22×C4—21no—
469C22×C4C2×D4×C7311yescharacteristic
470C22×C4C2×D4×C7311yescharacteristic
471C22×C4#41×C7311yescharacteristic
472Q16—81no—
473SD16—81no—
474SD16—81no—
475SD16—81no—
476D8—81no—
477D8—81no—
478M16—41no—
479M16—41no—
480M16—42no—
481M16—81no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—21no—
485C2×C8—21no—
486C2×C8—21no—
487C2×C8—21no—
488C2×C8—42no—
489C2×C8C2×D4×C7311yescharacteristic
490C2×C8C2×D4×C7311yescharacteristic
491C2×C8C2×D4×C7311yescharacteristic
492C2×C8C2×D4×C7311yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4—21no—
497C4⋊C4—21no—
498C4⋊C4—21no—
499C4⋊C4—21no—
500C4⋊C4—21no—
501C4⋊C4—41no—
502C4⋊C4—41no—
503C4⋊C4C2×D4×C7311yescharacteristic
504C4⋊C4C2×D4×C7311yescharacteristic
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—21no—
508C22⋊C4—21no—
509C22⋊C4—21no—
510C22⋊C4—41no—
511C42—21no—
512C42—41no—
513C42C2×D4×C7311yescharacteristic
514C42C2×D4×C7311yescharacteristic
515C42#41×C7311yescharacteristic
516C42C24×C7311yescharacteristic
517C23—21no—
518C23—41no—
519C23—41no—
520C23—82no—
521C23—82no—
522C23—82no—
523C23#121×C7311yescharacteristic
524Q8—21no—
525Q8—21no—
526Q8—41no—
527Q8—41no—
528Q8—81no—
529D4—21no—
530D4—21no—
531D4—41no—
532D4—41no—
533D4—41no—
534D4—41no—
535D4—41no—
536D4—41no—
537D4—41no—
538D4—41no—
539D4—81no—
540D4—81no—
541D4—82no—
542D4—82no—
543D4—82no—
544D4—81no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—21no—
549C2×C4—21no—
550C2×C4—21no—
551C2×C4—21no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4—41no—
555C2×C4—41no—
556C2×C4—41no—
557C2×C4#121×C7311yescharacteristic
558C2×C4#121×C7311yescharacteristic
559C2×C4#121×C7311yescharacteristic
560C2×C4C22×D4×C7311yescharacteristic
561C2×C4C22×D4×C7311yescharacteristic
562C2×C4C2×#41×C7311yescharacteristic
563C8—21no—
564C8—21no—
565C8—21no—
566C8—21no—
567C8—41no—
568C8—41no—
569C8—41no—
570C8—41no—
571C8—41no—
572C8—41no—
573C22—21no—
574C22—21no—
575C22—21no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22—81no—
583C22—81no—
584C22—81no—
585C22—164no—
586C22C2×#121×C7311yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—41no—
594C4—81no—
595C4—81no—
596C4#575×C7311yescharacteristic
597C4#575×C7311yescharacteristic
598C4#576×C7311yescharacteristic
599C4#577×C7311yescharacteristic
600C2—41no—
601C2—81no—
602C2—161no—
603C2—161no—
604C2C73×#304011yescharacteristic
605C2C73×#306211yescharacteristic
606C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3217C2
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×#3138C2semidirect
4. C73×#2969C2semidirect
5. C73×#1702C2semidirect
6. C73×#1701C2semidirect
7. C73×#1698C2semidirect
8. C73×#1697C2semidirect
9. C73×#1682C2semidirect
10. C73×#1681C2semidirect
11. C73×#1678C2semidirect
12. C73×#1677C2semidirect
13. C73×#1569C2semidirect
14. C73×#1554C2semidirect
15. C73×#1545C2semidirect
28. #477×C73C22semidirect
29. #476×C73C22semidirect
33. #462×C73C22semidirect
34. #461×C73C22semidirect
41. #446×C73C22semidirect
42. C8×Q8×C73C22semidirect
44. #436×C73C22semidirect
46. C8×D4×C73C22semidirect
55. #335×C73C22semidirect
56. #335×C73C22semidirect
57. #334×C73C22semidirect
58. #334×C73C22semidirect
59. #333×C73C22semidirect
60. #333×C73C22semidirect
61. #332×C73C22semidirect
62. #332×C73C22semidirect
296. #19380C73direct (N × H)
304. #3252C2×C73semidirect
306. #3138C2×C73semidirect
307. #2969C2×C73semidirect
308. #1702C2×C73semidirect
309. #1701C2×C73semidirect
310. #1698C2×C73semidirect
311. #1697C2×C73semidirect
312. #1682C2×C73semidirect
313. #1681C2×C73semidirect
314. #1678C2×C73semidirect
315. #1677C2×C73semidirect
316. #1569C2×C73semidirect
317. #1554C2×C73semidirect
318. #1545C2×C73semidirect
319. C73#19380direct (N × H)
332. #477C22×C73semidirect
333. #476C22×C73semidirect
337. #462C22×C73semidirect
338. #461C22×C73semidirect
345. #446C22×C73semidirect
346. C8×Q8C22×C73semidirect
348. #436C22×C73semidirect
350. C8×D4C22×C73semidirect
359. #335C22×C73semidirect
360. #335C22×C73semidirect
361. #334C22×C73semidirect
362. #334C22×C73semidirect
363. #333C22×C73semidirect
364. #333C22×C73semidirect
365. #332C22×C73semidirect
366. #332C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#32522
C73×#32172
C73×#31382
C73×#29692
C73×#17022
C73×#17012
C73×#16982
C73×#16972
C73×#16822
C73×#16812
C73×#16782
C73×#16772
C73×#15692
C73×#15542
C73×#15452
#1938073