Finite Group Databasebeta

← C73×#24524 #32933928

Subgroups — C73×#24524 #32933928

Order 18688.

884 conjugacy classes of subgroups.

The subgroup lattice has 770 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3094C211yesmaximal, characteristic, complemented
2C2×#449×C73C211yesmaximal, characteristic
3C73×#2924C211yesmaximal, characteristic, complemented
4C73×#2896C211yesmaximal, characteristic, complemented
5C73×#2064C211yesmaximal, characteristic, complemented
6C73×#2063C211yesmaximal, characteristic, complemented
7C73×#2046C211yesmaximal, characteristic, complemented
8C73×#2045C211yesmaximal, characteristic, complemented
9C73×#1978C211yesmaximal, characteristic, complemented
10C73×#1977C211yesmaximal, characteristic, complemented
11C73×#1931C211yesmaximal, characteristic, complemented
12C73×#1930C211yesmaximal, characteristic, complemented
13C73×#1900C211yesmaximal, characteristic, complemented
14C73×#1855C211yesmaximal, characteristic, complemented
15C73×#1785C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×M16×C73C2211yescharacteristic
20C2×#121×C73C2211yescharacteristic
21C2×#117×C73C2211yescharacteristic
22#482×C73—21no—
23#482×C73—21no—
24#481×C73—21no—
25#480×C73—21no—
26#449×C73—21no—
27#449×C73—21no—
28#449×C73—21no—
29#449×C73—21no—
30#433×C73—21no—
31#433×C73—21no—
32#432×C73—21no—
33#431×C73—21no—
34C2×#108×C73C2211yescharacteristic
35C2×#108×C73C2211yescharacteristic
36#428×C73C2211yescharacteristic
37#428×C73C2211yescharacteristic
38#424×C73C2211yescharacteristic
39#424×C73C2211yescharacteristic
40#419×C73C2211yescharacteristic
41#419×C73C2211yescharacteristic
42#418×C73C2211yescharacteristic
43#418×C73C2211yescharacteristic
44#418×C73C2211yescharacteristic
45#418×C73C2211yescharacteristic
46#417×C73—21no—
47#417×C73—21no—
48#416×C73—21no—
49#416×C73—21no—
50C2×#103×C73C2211yescharacteristic
51C2×#102×C73C2211yescharacteristic
52C2×#101×C73C2211yescharacteristic
53C2×#101×C73C2211yescharacteristic
54C2×#100×C73C2211yescharacteristic
55C2×#100×C73C2211yescharacteristic
56C2×#100×C73C2211yescharacteristic
57C2×#100×C73C2211yescharacteristic
58#407×C73C2211yescharacteristic
59#407×C73C2211yescharacteristic
60C2×C22⋊C8×C73C2211yescharacteristic
61#405×C73C2211yescharacteristic
62#405×C73C2211yescharacteristic
63#343×C73C2211yescharacteristic
64#343×C73C2211yescharacteristic
65#341×C73C2211yescharacteristic
66#341×C73C2211yescharacteristic
67C2×#41×C73—22no—
68C2×#41×C73—22no—
69C2×#41×C73—21no—
70C2×#41×C73—21no—
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73—41no—
74C2×#41×C73—41no—
75C22×Q8×C73C2311yescharacteristic
76C22×D4×C73—21no—
77C22×D4×C73—21no—
78C22×D4×C73C2311yescharacteristic
79C22×D4×C73C2311yescharacteristic
80C23×C4×C73—21no—
81C23×C4×C73C2311yescharacteristic
82C2×SD16×C73—22no—
83C2×SD16×C73—21no—
84C2×SD16×C73—21no—
85C2×SD16×C73—41no—
86C2×D8×C73—22no—
87C2×D8×C73—21no—
88C2×D8×C73—21no—
89C2×D8×C73—41no—
90C2×M16×C73—21no—
91C2×M16×C73—41no—
92C2×M16×C73—41no—
93C2×M16×C73C2311yescharacteristic
94C2×M16×C73C2311yescharacteristic
95C2×M16×C73C2311yescharacteristic
96C2×M16×C73C2311yescharacteristic
97C2×M16×C73C2311yescharacteristic
98C2×M16×C73C2311yescharacteristic
99C22×C8×C73—21no—
100C22×C8×C73C2311yescharacteristic
101C22×C8×C73C2311yescharacteristic
102#121×C73—21no—
103#121×C73—21no—
104#121×C73—21no—
105#121×C73—21no—
106#117×C73—21no—
107#117×C73—21no—
108#117×C73D411yescharacteristic
109#117×C73D411yescharacteristic
110#117×C73C2311yescharacteristic
111#117×C73C2311yescharacteristic
112C2×C4⋊C4×C73D411yescharacteristic
113C2×C4⋊C4×C73D411yescharacteristic
114C2×C4⋊C4×C73C2311yescharacteristic
115C2×C22⋊C4×C73—21no—
116C2×C22⋊C4×C73—21no—
117C2×C42×C73—21no—
118#108×C73—41no—
119#108×C73—41no—
120#107×C73—21no—
121#107×C73—21no—
122#106×C73—21no—
123#106×C73—21no—
124C4⋊C8×C73—21no—
125C4⋊C8×C73—21no—
126C4⋊C8×C73—21no—
127C4⋊C8×C73—21no—
128#103×C73—21no—
129#103×C73—21no—
130#103×C73—21no—
131#103×C73—21no—
132#103×C73—21no—
133#103×C73—21no—
134#102×C73—21no—
135#102×C73—21no—
136#102×C73—21no—
137#102×C73—21no—
138#102×C73—21no—
139#102×C73—21no—
140#102×C73—21no—
141#102×C73—21no—
142#102×C73—21no—
143#102×C73—21no—
144#101×C73—22no—
145#101×C73—41no—
146#100×C73—22no—
147#100×C73—41no—
148#100×C73—41no—
149#100×C73—41no—
150C22⋊C8×C73—21no—
151C22⋊C8×C73—21no—
152C22⋊C8×C73—21no—
153C22⋊C8×C73—21no—
154C22⋊C8×C73D411yescharacteristic
155C22⋊C8×C73D411yescharacteristic
156C22⋊C8×C73D411yescharacteristic
157C22⋊C8×C73D411yescharacteristic
158#97×C73—21no—
159#97×C73—21no—
160C4×C8×C73—21no—
161C4×C8×C73—21no—
162C24×C73—21no—
163C24×C73—21no—
164C24×C73#4111yescharacteristic
165#41×C73—24no—
166#41×C73—24no—
167#41×C73—42no—
168#41×C73—42no—
169#41×C73—42no—
170#41×C73—42no—
171#41×C73—42no—
172#41×C73—42no—
173C2×Q8×C73—21no—
174C2×Q8×C73—21no—
175C2×Q8×C73—21no—
176C2×Q8×C73—21no—
177C2×Q8×C73—21no—
178C2×Q8×C73#4112yes—
179C2×D4×C73—21no—
180C2×D4×C73—21no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—21no—
186C2×D4×C73—21no—
187C2×D4×C73—21no—
188C2×D4×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—42no—
191C2×D4×C73—42no—
192C2×D4×C73—41no—
193C2×D4×C73—41no—
194C2×D4×C73—41no—
195C2×D4×C73—41no—
196C2×D4×C73—82no—
197C2×D4×C73#4112yes—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73—42no—
207C22×C4×C73—42no—
208C22×C4×C73—41no—
209C22×C4×C73—41no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73#4111yescharacteristic
215C22×C4×C73C2411yescharacteristic
216SD16×C73—42no—
217SD16×C73—42no—
218D8×C73—42no—
219D8×C73—42no—
220M16×C73—21no—
221M16×C73—21no—
222M16×C73—21no—
223M16×C73—21no—
224M16×C73—21no—
225M16×C73—21no—
226M16×C73—21no—
227M16×C73—21no—
228M16×C73—21no—
229M16×C73—21no—
230M16×C73—21no—
231M16×C73—21no—
232M16×C73—42no—
233C2×C8×C73—21no—
234C2×C8×C73—21no—
235C2×C8×C73—21no—
236C2×C8×C73—21no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C2×C8×C73—21no—
242C2×C8×C73—21no—
243C2×C8×C73—42no—
244C2×C8×C73C2×D411yescharacteristic
245C2×C8×C73C2×D411yescharacteristic
246C2×C8×C73C2×D411yescharacteristic
247C2×C8×C73C2×D411yescharacteristic
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73C2×D411yescharacteristic
253C4⋊C4×C73C2×D411yescharacteristic
254C4⋊C4×C73C2×D411yescharacteristic
255C4⋊C4×C73C2×D411yescharacteristic
256C22⋊C4×C73—21no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—21no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—41no—
261C22⋊C4×C73—41no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—21no—
265C42×C73—21no—
266C23×C73—21no—
267C23×C73—21no—
268C23×C73—22no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—41no—
276C23×C73—81no—
277C23×C73—81no—
278C23×C73—81no—
279C23×C73—81no—
280C23×C73#12111yescharacteristic
281C23×C73#12111yescharacteristic
282C23×C73C2×#4111yescharacteristic
283Q8×C73—22no—
284Q8×C73—22no—
285Q8×C73—41no—
286Q8×C73—41no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—44no—
290D4×C73—44no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—82no—
298D4×C73—82no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—22no—
314C2×C4×C73—44no—
315C2×C4×C73—44no—
316C2×C4×C73—42no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—81no—
321C2×C4×C73—81no—
322C2×C4×C73#12111yescharacteristic
323C2×C4×C73#12111yescharacteristic
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C22×D411yescharacteristic
326C2×C4×C73C2×#4111yescharacteristic
327C2×C4×C73C2×#4111yescharacteristic
328C2×C4×C73H(5,𝔽2)11yescharacteristic
329C2×C4×C73H(5,𝔽2)11yescharacteristic
330C8×C73—21no—
331C8×C73—21no—
332C8×C73—21no—
333C8×C73—21no—
334C8×C73—41no—
335C8×C73—41no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340C22×C73—21no—
341C22×C73—21no—
342C22×C73—21no—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—21no—
346C22×C73—21no—
347C22×C73—21no—
348C22×C73—42no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—82no—
352C22×C73—82no—
353C22×C73—81no—
354C22×C73—81no—
355C22×C73—81no—
356C22×C73—81no—
357C22×C73—81no—
358C22×C73—161no—
359C22×C73—161no—
360C22×C73C2×#12111yescharacteristic
361C22×C73#55111yescharacteristic
362C22×C73#55111yescharacteristic
363C4×C73—21no—
364C4×C73—21no—
365C4×C73—42no—
366C4×C73—41no—
367C4×C73—41no—
368C4×C73—41no—
369C4×C73—41no—
370C4×C73—81no—
371C4×C73#52511yescharacteristic
372C4×C73#53511yescharacteristic
373C4×C73#54611yescharacteristic
374C4×C73#54611yescharacteristic
375#24524C7311yesmaximal, characteristic, direct product factor, Sylow
376C2×C73—21no—
377C2×C73—21no—
378C2×C73—41no—
379C2×C73—41no—
380C2×C73—82no—
381C2×C73—161no—
382C2×C73#241111yescharacteristic
383C2×C73#306711yescharacteristic
384C2×C73#306811yescharacteristic
385#3094C2×C7311yescharacteristic, complemented
386C2×#449C2×C7311yescharacteristic
387#2924C2×C7311yescharacteristic, complemented
388#2896C2×C7311yescharacteristic, complemented
389#2064C2×C7311yescharacteristic, complemented
390#2063C2×C7311yescharacteristic, complemented
391#2046C2×C7311yescharacteristic, complemented
392#2045C2×C7311yescharacteristic, complemented
393#1978C2×C7311yescharacteristic, complemented
394#1977C2×C7311yescharacteristic, complemented
395#1931C2×C7311yescharacteristic, complemented
396#1930C2×C7311yescharacteristic, complemented
397#1900C2×C7311yescharacteristic, complemented
398#1855C2×C7311yescharacteristic, complemented
399#1785C2×C7311yescharacteristic, complemented
400C73#2452411yescharacteristic, direct product factor, Sylow
401C22×#41C22×C7311yescharacteristic
402C22×SD16C22×C7311yescharacteristic
403C22×D8C22×C7311yescharacteristic
404C22×M16C22×C7311yescharacteristic
405C2×#121C22×C7311yescharacteristic
406C2×#117C22×C7311yescharacteristic
407#482—21no—
408#482—21no—
409#481—21no—
410#480—21no—
411#449—21no—
412#449—21no—
413#449—21no—
414#449—21no—
415#433—21no—
416#433—21no—
417#432—21no—
418#431—21no—
419C2×#108C22×C7311yescharacteristic
420C2×#108C22×C7311yescharacteristic
421#428C22×C7311yescharacteristic
422#428C22×C7311yescharacteristic
423#424C22×C7311yescharacteristic
424#424C22×C7311yescharacteristic
425#419C22×C7311yescharacteristic
426#419C22×C7311yescharacteristic
427#418C22×C7311yescharacteristic
428#418C22×C7311yescharacteristic
429#418C22×C7311yescharacteristic
430#418C22×C7311yescharacteristic
431#417—21no—
432#417—21no—
433#416—21no—
434#416—21no—
435C2×#103C22×C7311yescharacteristic
436C2×#102C22×C7311yescharacteristic
437C2×#101C22×C7311yescharacteristic
438C2×#101C22×C7311yescharacteristic
439C2×#100C22×C7311yescharacteristic
440C2×#100C22×C7311yescharacteristic
441C2×#100C22×C7311yescharacteristic
442C2×#100C22×C7311yescharacteristic
443#407C22×C7311yescharacteristic
444#407C22×C7311yescharacteristic
445C2×C22⋊C8C22×C7311yescharacteristic
446#405C22×C7311yescharacteristic
447#405C22×C7311yescharacteristic
448#343C22×C7311yescharacteristic
449#343C22×C7311yescharacteristic
450#341C22×C7311yescharacteristic
451#341C22×C7311yescharacteristic
452C2×#41—22no—
453C2×#41—22no—
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—41no—
459C2×#41—41no—
460C22×Q8C23×C7311yescharacteristic
461C22×D4—21no—
462C22×D4—21no—
463C22×D4C23×C7311yescharacteristic
464C22×D4C23×C7311yescharacteristic
465C23×C4—21no—
466C23×C4C23×C7311yescharacteristic
467C2×SD16—22no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—41no—
471C2×D8—22no—
472C2×D8—21no—
473C2×D8—21no—
474C2×D8—41no—
475C2×M16—21no—
476C2×M16—41no—
477C2×M16—41no—
478C2×M16C23×C7311yescharacteristic
479C2×M16C23×C7311yescharacteristic
480C2×M16C23×C7311yescharacteristic
481C2×M16C23×C7311yescharacteristic
482C2×M16C23×C7311yescharacteristic
483C2×M16C23×C7311yescharacteristic
484C22×C8—21no—
485C22×C8C23×C7311yescharacteristic
486C22×C8C23×C7311yescharacteristic
487#121—21no—
488#121—21no—
489#121—21no—
490#121—21no—
491#117—21no—
492#117—21no—
493#117D4×C7311yescharacteristic
494#117D4×C7311yescharacteristic
495#117C23×C7311yescharacteristic
496#117C23×C7311yescharacteristic
497C2×C4⋊C4D4×C7311yescharacteristic
498C2×C4⋊C4D4×C7311yescharacteristic
499C2×C4⋊C4C23×C7311yescharacteristic
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#108—41no—
504#108—41no—
505#107—21no—
506#107—21no—
507#106—21no—
508#106—21no—
509C4⋊C8—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513#103—21no—
514#103—21no—
515#103—21no—
516#103—21no—
517#103—21no—
518#103—21no—
519#102—21no—
520#102—21no—
521#102—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#101—22no—
530#101—41no—
531#100—22no—
532#100—41no—
533#100—41no—
534#100—41no—
535C22⋊C8—21no—
536C22⋊C8—21no—
537C22⋊C8—21no—
538C22⋊C8—21no—
539C22⋊C8D4×C7311yescharacteristic
540C22⋊C8D4×C7311yescharacteristic
541C22⋊C8D4×C7311yescharacteristic
542C22⋊C8D4×C7311yescharacteristic
543#97—21no—
544#97—21no—
545C4×C8—21no—
546C4×C8—21no—
547C24—21no—
548C24—21no—
549C24#41×C7311yescharacteristic
550#41—24no—
551#41—24no—
552#41—42no—
553#41—42no—
554#41—42no—
555#41—42no—
556#41—42no—
557#41—42no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8#41×C7312yes—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—42no—
576C2×D4—42no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4—82no—
582C2×D4#41×C7312yes—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4—42no—
592C22×C4—42no—
593C22×C4—41no—
594C22×C4—41no—
595C22×C4C2×D4×C7311yescharacteristic
596C22×C4C2×D4×C7311yescharacteristic
597C22×C4C2×D4×C7311yescharacteristic
598C22×C4C2×D4×C7311yescharacteristic
599C22×C4#41×C7311yescharacteristic
600C22×C4C24×C7311yescharacteristic
601SD16—42no—
602SD16—42no—
603D8—42no—
604D8—42no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—21no—
612M16—21no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—42no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—21no—
621C2×C8—21no—
622C2×C8—21no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—42no—
629C2×C8C2×D4×C7311yescharacteristic
630C2×C8C2×D4×C7311yescharacteristic
631C2×C8C2×D4×C7311yescharacteristic
632C2×C8C2×D4×C7311yescharacteristic
633C4⋊C4—21no—
634C4⋊C4—21no—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4C2×D4×C7311yescharacteristic
638C4⋊C4C2×D4×C7311yescharacteristic
639C4⋊C4C2×D4×C7311yescharacteristic
640C4⋊C4C2×D4×C7311yescharacteristic
641C22⋊C4—21no—
642C22⋊C4—21no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—21no—
648C42—21no—
649C42—21no—
650C42—21no—
651C23—21no—
652C23—21no—
653C23—22no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23—41no—
658C23—41no—
659C23—41no—
660C23—41no—
661C23—81no—
662C23—81no—
663C23—81no—
664C23—81no—
665C23#121×C7311yescharacteristic
666C23#121×C7311yescharacteristic
667C23C2×#41×C7311yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—22no—
673D4—22no—
674D4—44no—
675D4—44no—
676D4—41no—
677D4—41no—
678D4—41no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—82no—
683D4—82no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—44no—
700C2×C4—44no—
701C2×C4—42no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—81no—
706C2×C4—81no—
707C2×C4#121×C7311yescharacteristic
708C2×C4#121×C7311yescharacteristic
709C2×C4C22×D4×C7311yescharacteristic
710C2×C4C22×D4×C7311yescharacteristic
711C2×C4C2×#41×C7311yescharacteristic
712C2×C4C2×#41×C7311yescharacteristic
713C2×C4H(5,𝔽2)×C7311yescharacteristic
714C2×C4H(5,𝔽2)×C7311yescharacteristic
715C8—21no—
716C8—21no—
717C8—21no—
718C8—21no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C8—41no—
725C22—21no—
726C22—21no—
727C22—21no—
728C22—21no—
729C22—21no—
730C22—21no—
731C22—21no—
732C22—21no—
733C22—42no—
734C22—81no—
735C22—81no—
736C22—82no—
737C22—82no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22—81no—
742C22—81no—
743C22—161no—
744C22—161no—
745C22C2×#121×C7311yescharacteristic
746C22#551×C7311yescharacteristic
747C22#551×C7311yescharacteristic
748C4—21no—
749C4—21no—
750C4—41no—
751C4—41no—
752C4—41no—
753C4—41no—
754C4—42no—
755C4—81no—
756C4#525×C7311yescharacteristic
757C4#535×C7311yescharacteristic
758C4#546×C7311yescharacteristic
759C4#546×C7311yescharacteristic
760C2—21no—
761C2—21no—
762C2—41no—
763C2—41no—
764C2—82no—
765C2—161no—
766C2C73×#241111yescharacteristic
767C2C73×#306711yescharacteristic
768C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#449×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3094C2semidirect
3. C73×#2924C2semidirect
4. C73×#2896C2semidirect
5. C73×#2064C2semidirect
6. C73×#2063C2semidirect
7. C73×#2046C2semidirect
8. C73×#2045C2semidirect
9. C73×#1978C2semidirect
10. C73×#1977C2semidirect
11. C73×#1931C2semidirect
12. C73×#1930C2semidirect
13. C73×#1900C2semidirect
14. C73×#1855C2semidirect
15. C73×#1785C2semidirect
375. #24524C73direct (N × H)
385. #3094C2×C73semidirect
387. #2924C2×C73semidirect
388. #2896C2×C73semidirect
389. #2064C2×C73semidirect
390. #2063C2×C73semidirect
391. #2046C2×C73semidirect
392. #2045C2×C73semidirect
393. #1978C2×C73semidirect
394. #1977C2×C73semidirect
395. #1931C2×C73semidirect
396. #1930C2×C73semidirect
397. #1900C2×C73semidirect
398. #1855C2×C73semidirect
399. #1785C2×C73semidirect
400. C73#24524direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#30942
C2×#449×C732
C73×#29242
C73×#28962
C73×#20642
C73×#20632
C73×#20462
C73×#20452
C73×#19782
C73×#19772
C73×#19312
C73×#19302
C73×#19002
C73×#18552
C73×#17852
#2452473