Finite Group Databasebeta

← C73×#24575 #32933979

Subgroups — C73×#24575 #32933979

Order 18688.

914 conjugacy classes of subgroups.

The subgroup lattice has 806 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#482×C73C211yesmaximal, characteristic, complemented
2C73×#3006C211yesmaximal, characteristic
3C73×#2896C211yesmaximal, characteristic, complemented
4C73×#2880C211yesmaximal, characteristic, complemented
5C73×#2079C211yesmaximal, characteristic, complemented
6C73×#2078C211yesmaximal, characteristic, complemented
7C73×#2051C211yesmaximal, characteristic, complemented
8C73×#2051C211yesmaximal, characteristic, complemented
9C73×#1907C211yesmaximal, characteristic, complemented
10C73×#1907C211yesmaximal, characteristic, complemented
11C73×#1900C211yesmaximal, characteristic, complemented
12C73×#1855C211yesmaximal, characteristic, complemented
13C73×#1822C211yesmaximal, characteristic, complemented
14C73×#1816C211yesmaximal, characteristic, complemented
15C73×#1815C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C2×#131×C73C2211yescharacteristic
20C2×#131×C73C2211yescharacteristic
21C22×M16×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23C2×#117×C73C2211yescharacteristic
24#482×C73—21no—
25#482×C73—21no—
26#482×C73—21no—
27#482×C73—21no—
28#449×C73—21no—
29#449×C73—21no—
30#448×C73—21no—
31#447×C73—21no—
32C2×#108×C73C2211yescharacteristic, complemented
33C2×#108×C73C2211yescharacteristic, complemented
34C2×#107×C73C2211yescharacteristic, complemented
35C2×#106×C73C2211yescharacteristic, complemented
36#419×C73—21no—
37#418×C73—21no—
38#417×C73C2211yescharacteristic
39#417×C73C2211yescharacteristic
40#417×C73C2211yescharacteristic
41#417×C73C2211yescharacteristic
42#417×C73C2211yescharacteristic
43#417×C73C2211yescharacteristic
44#416×C73—21no—
45#416×C73—21no—
46C2×#102×C73C2211yescharacteristic, complemented
47C2×#102×C73C2211yescharacteristic, complemented
48C2×#100×C73C2211yescharacteristic, complemented
49C2×#100×C73C2211yescharacteristic, complemented
50#408×C73—21no—
51#408×C73—21no—
52#408×C73C2211yescharacteristic
53#408×C73C2211yescharacteristic
54#407×C73—21no—
55#407×C73C2211yescharacteristic
56#407×C73C2211yescharacteristic
57C2×C22⋊C8×C73—21no—
58C2×C22⋊C8×C73C2211yescharacteristic
59#343×C73C2211yescharacteristic, complemented
60#343×C73C2211yescharacteristic, complemented
61#343×C73C2211yescharacteristic, complemented
62#343×C73C2211yescharacteristic, complemented
63#343×C73C2211yescharacteristic, complemented
64#343×C73C2211yescharacteristic, complemented
65#341×C73C2211yescharacteristic, complemented
66#341×C73C2211yescharacteristic, complemented
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C2×#41×C73—22no—
70C2×#41×C73—22no—
71C2×#41×C73—41no—
72C2×#41×C73—41no—
73C2×#41×C73D411yescharacteristic
74C2×#41×C73D411yescharacteristic
75C2×#41×C73C2311yescharacteristic
76C2×#41×C73C2311yescharacteristic
77C22×Q8×C73D411yescharacteristic
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73D411yescharacteristic
81C22×D4×C73C2311yescharacteristic
82C23×C4×C73—21no—
83C23×C4×C73C2311yescharacteristic
84AGL(1,ℤ/8)×C73—22no—
85AGL(1,ℤ/8)×C73—22no—
86AGL(1,ℤ/8)×C73—41no—
87AGL(1,ℤ/8)×C73—41no—
88C2×SD16×C73—21no—
89C2×SD16×C73—21no—
90C2×D8×C73—21no—
91C2×D8×C73—21no—
92#131×C73—22no—
93#131×C73—22no—
94#131×C73—41no—
95#131×C73—41no—
96C2×M16×C73—21no—
97C2×M16×C73—21no—
98C2×M16×C73—21no—
99C2×M16×C73—41no—
100C2×M16×C73—41no—
101C2×M16×C73C2311yescharacteristic
102C2×M16×C73C2311yescharacteristic
103C2×M16×C73C2311yescharacteristic
104C2×M16×C73C2311yescharacteristic
105C2×M16×C73C2311yescharacteristic
106C2×M16×C73C2311yescharacteristic
107C22×C8×C73—21no—
108C22×C8×C73—21no—
109C22×C8×C73—21no—
110C22×C8×C73C2311yescharacteristic
111C22×C8×C73C2311yescharacteristic
112#121×C73—21no—
113#121×C73—21no—
114#121×C73—21no—
115#121×C73—21no—
116#117×C73—21no—
117#117×C73—21no—
118#117×C73—21no—
119#117×C73—21no—
120C2×C4⋊C4×C73C2311yescharacteristic
121C2×C4⋊C4×C73C2311yescharacteristic
122C2×C4⋊C4×C73C2311yescharacteristic
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C42×C73—21no—
126#108×C73—41no—
127#108×C73—41no—
128#107×C73—21no—
129#107×C73—21no—
130#106×C73—21no—
131#106×C73—21no—
132#103×C73—21no—
133#103×C73—21no—
134#103×C73—21no—
135#103×C73—21no—
136#103×C73—21no—
137#103×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#102×C73—21no—
145#102×C73—21no—
146#102×C73—21no—
147#102×C73—21no—
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×C73—21no—
155C22⋊C8×C73—21no—
156C22⋊C8×C73—21no—
157C22⋊C8×C73—21no—
158C22⋊C8×C73D411yescharacteristic
159C22⋊C8×C73D411yescharacteristic
160C22⋊C8×C73D411yescharacteristic
161C22⋊C8×C73D411yescharacteristic
162C24×C73—21no—
163C24×C73—21no—
164C24×C73#4111yescharacteristic
165#41×C73—21no—
166#41×C73—21no—
167#41×C73—22no—
168#41×C73—22no—
169#41×C73—21no—
170#41×C73—21no—
171#41×C73—21no—
172#41×C73—21no—
173#41×C73—42no—
174#41×C73—42no—
175#41×C73—41no—
176#41×C73—41no—
177#41×C73—42no—
178#41×C73—42no—
179#41×C73#4112yes—
180#41×C73#4112yes—
181C2×Q8×C73—21no—
182C2×Q8×C73—22no—
183C2×Q8×C73—41no—
184C2×Q8×C73C2×D411yescharacteristic
185C2×Q8×C73C2×D411yescharacteristic
186C2×D4×C73—21no—
187C2×D4×C73—22no—
188C2×D4×C73—21no—
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—41no—
199C2×D4×C73—42no—
200C2×D4×C73—42no—
201C2×D4×C73—41no—
202C2×D4×C73—41no—
203C2×D4×C73—82no—
204C2×D4×C73C2×D411yescharacteristic
205C2×D4×C73C2×D411yescharacteristic
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—42no—
219C22×C4×C73—42no—
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73#4111yescharacteristic
225C22×C4×C73C2411yescharacteristic
226SD16×C73—42no—
227SD16×C73—42no—
228D8×C73—42no—
229D8×C73—42no—
230M16×C73—21no—
231M16×C73—21no—
232M16×C73—21no—
233M16×C73—21no—
234M16×C73—21no—
235M16×C73—21no—
236M16×C73—21no—
237M16×C73—21no—
238M16×C73—21no—
239M16×C73—21no—
240M16×C73—21no—
241M16×C73—21no—
242M16×C73—42no—
243M16×C73—42no—
244M16×C73—42no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—21no—
249C2×C8×C73—21no—
250C2×C8×C73—21no—
251C2×C8×C73—21no—
252C2×C8×C73—21no—
253C2×C8×C73—21no—
254C2×C8×C73—21no—
255C2×C8×C73—42no—
256C2×C8×C73—42no—
257C2×C8×C73—42no—
258C2×C8×C73C2×D411yescharacteristic
259C2×C8×C73C2×D411yescharacteristic
260C2×C8×C73C2×D411yescharacteristic
261C2×C8×C73C2×D411yescharacteristic
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—21no—
268C22⋊C4×C73—41no—
269C22⋊C4×C73—41no—
270C22⋊C4×C73—41no—
271C22⋊C4×C73—41no—
272C42×C73—41no—
273C42×C73—41no—
274C23×C73—21no—
275C23×C73—21no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—42no—
281C23×C73—42no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—81no—
286C23×C73—81no—
287C23×C73—81no—
288C23×C73#12111yescharacteristic
289C23×C73#12111yescharacteristic
290C23×C73C2×#4111yescharacteristic
291Q8×C73—21no—
292Q8×C73—21no—
293Q8×C73—21no—
294Q8×C73—42no—
295Q8×C73#12312yes—
296D4×C73—22no—
297D4×C73—22no—
298D4×C73—21no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—42no—
302D4×C73—42no—
303D4×C73—42no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—82no—
311D4×C73—82no—
312D4×C73#12312yes—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—22no—
321C2×C4×C73—22no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—42no—
328C2×C4×C73—42no—
329C2×C4×C73—42no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—81no—
336C2×C4×C73—81no—
337C2×C4×C73—81no—
338C2×C4×C73#12111yescharacteristic
339C2×C4×C73#12111yescharacteristic
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C22×D411yescharacteristic
342C2×C4×C73C2×#4111yescharacteristic
343C2×C4×C73C2×#4111yescharacteristic
344C2×C4×C73H(5,𝔽2)11yescharacteristic
345C2×C4×C73H(5,𝔽2)11yescharacteristic
346C8×C73—21no—
347C8×C73—21no—
348C8×C73—21no—
349C8×C73—21no—
350C8×C73—41no—
351C8×C73—41no—
352C8×C73—41no—
353C8×C73—41no—
354C8×C73—41no—
355C8×C73—41no—
356C22×C73—21no—
357C22×C73—21no—
358C22×C73—21no—
359C22×C73—21no—
360C22×C73—22no—
361C22×C73—21no—
362C22×C73—21no—
363C22×C73—21no—
364C22×C73—21no—
365C22×C73—41no—
366C22×C73—41no—
367C22×C73—41no—
368C22×C73—41no—
369C22×C73—41no—
370C22×C73—81no—
371C22×C73—81no—
372C22×C73—84no—
373C22×C73—81no—
374C22×C73—81no—
375C22×C73—81no—
376C22×C73—161no—
377C22×C73—161no—
378C22×C73C2×#12111yescharacteristic
379C22×C73#55111yescharacteristic
380C22×C73#55111yescharacteristic
381C4×C73—21no—
382C4×C73—21no—
383C4×C73—22no—
384C4×C73—41no—
385C4×C73—81no—
386C4×C73—81no—
387C4×C73—81no—
388C4×C73C2×#12311yescharacteristic
389C4×C73#53411yescharacteristic
390C4×C73#54611yescharacteristic
391C4×C73#54611yescharacteristic
392#24575C7311yesmaximal, characteristic, direct product factor, Sylow
393C2×C73—21no—
394C2×C73—21no—
395C2×C73—41no—
396C2×C73—41no—
397C2×C73—42no—
398C2×C73—81no—
399C2×C73—161no—
400C2×C73#241211yescharacteristic
401C2×C73#306711yescharacteristic
402C2×C73#306811yescharacteristic
403C2×#482C2×C7311yescharacteristic, complemented
404#3006C2×C7311yescharacteristic
405#2896C2×C7311yescharacteristic, complemented
406#2880C2×C7311yescharacteristic, complemented
407#2079C2×C7311yescharacteristic, complemented
408#2078C2×C7311yescharacteristic, complemented
409#2051C2×C7311yescharacteristic, complemented
410#2051C2×C7311yescharacteristic, complemented
411#1907C2×C7311yescharacteristic, complemented
412#1907C2×C7311yescharacteristic, complemented
413#1900C2×C7311yescharacteristic, complemented
414#1855C2×C7311yescharacteristic, complemented
415#1822C2×C7311yescharacteristic, complemented
416#1816C2×C7311yescharacteristic, complemented
417#1815C2×C7311yescharacteristic, complemented
418C73#2457511yescharacteristic, direct product factor, Sylow
419C22×#41C22×C7311yescharacteristic
420C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
421C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
422C2×#131C22×C7311yescharacteristic
423C2×#131C22×C7311yescharacteristic
424C22×M16C22×C7311yescharacteristic
425C2×#121C22×C7311yescharacteristic
426C2×#117C22×C7311yescharacteristic
427#482—21no—
428#482—21no—
429#482—21no—
430#482—21no—
431#449—21no—
432#449—21no—
433#448—21no—
434#447—21no—
435C2×#108C22×C7311yescharacteristic, complemented
436C2×#108C22×C7311yescharacteristic, complemented
437C2×#107C22×C7311yescharacteristic, complemented
438C2×#106C22×C7311yescharacteristic, complemented
439#419—21no—
440#418—21no—
441#417C22×C7311yescharacteristic
442#417C22×C7311yescharacteristic
443#417C22×C7311yescharacteristic
444#417C22×C7311yescharacteristic
445#417C22×C7311yescharacteristic
446#417C22×C7311yescharacteristic
447#416—21no—
448#416—21no—
449C2×#102C22×C7311yescharacteristic, complemented
450C2×#102C22×C7311yescharacteristic, complemented
451C2×#100C22×C7311yescharacteristic, complemented
452C2×#100C22×C7311yescharacteristic, complemented
453#408—21no—
454#408—21no—
455#408C22×C7311yescharacteristic
456#408C22×C7311yescharacteristic
457#407—21no—
458#407C22×C7311yescharacteristic
459#407C22×C7311yescharacteristic
460C2×C22⋊C8—21no—
461C2×C22⋊C8C22×C7311yescharacteristic
462#343C22×C7311yescharacteristic, complemented
463#343C22×C7311yescharacteristic, complemented
464#343C22×C7311yescharacteristic, complemented
465#343C22×C7311yescharacteristic, complemented
466#343C22×C7311yescharacteristic, complemented
467#343C22×C7311yescharacteristic, complemented
468#341C22×C7311yescharacteristic, complemented
469#341C22×C7311yescharacteristic, complemented
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—22no—
473C2×#41—22no—
474C2×#41—41no—
475C2×#41—41no—
476C2×#41D4×C7311yescharacteristic
477C2×#41D4×C7311yescharacteristic
478C2×#41C23×C7311yescharacteristic
479C2×#41C23×C7311yescharacteristic
480C22×Q8D4×C7311yescharacteristic
481C22×D4—21no—
482C22×D4—21no—
483C22×D4D4×C7311yescharacteristic
484C22×D4C23×C7311yescharacteristic
485C23×C4—21no—
486C23×C4C23×C7311yescharacteristic
487AGL(1,ℤ/8)—22no—
488AGL(1,ℤ/8)—22no—
489AGL(1,ℤ/8)—41no—
490AGL(1,ℤ/8)—41no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—21no—
494C2×D8—21no—
495#131—22no—
496#131—22no—
497#131—41no—
498#131—41no—
499C2×M16—21no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—41no—
503C2×M16—41no—
504C2×M16C23×C7311yescharacteristic
505C2×M16C23×C7311yescharacteristic
506C2×M16C23×C7311yescharacteristic
507C2×M16C23×C7311yescharacteristic
508C2×M16C23×C7311yescharacteristic
509C2×M16C23×C7311yescharacteristic
510C22×C8—21no—
511C22×C8—21no—
512C22×C8—21no—
513C22×C8C23×C7311yescharacteristic
514C22×C8C23×C7311yescharacteristic
515#121—21no—
516#121—21no—
517#121—21no—
518#121—21no—
519#117—21no—
520#117—21no—
521#117—21no—
522#117—21no—
523C2×C4⋊C4C23×C7311yescharacteristic
524C2×C4⋊C4C23×C7311yescharacteristic
525C2×C4⋊C4C23×C7311yescharacteristic
526C2×C22⋊C4—21no—
527C2×C22⋊C4—21no—
528C2×C42—21no—
529#108—41no—
530#108—41no—
531#107—21no—
532#107—21no—
533#106—21no—
534#106—21no—
535#103—21no—
536#103—21no—
537#103—21no—
538#103—21no—
539#103—21no—
540#103—21no—
541#102—21no—
542#102—21no—
543#102—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—21no—
548#102—21no—
549#102—21no—
550#102—21no—
551#100—41no—
552#100—41no—
553C22⋊C8—21no—
554C22⋊C8—21no—
555C22⋊C8—21no—
556C22⋊C8—21no—
557C22⋊C8—21no—
558C22⋊C8—21no—
559C22⋊C8—21no—
560C22⋊C8—21no—
561C22⋊C8D4×C7311yescharacteristic
562C22⋊C8D4×C7311yescharacteristic
563C22⋊C8D4×C7311yescharacteristic
564C22⋊C8D4×C7311yescharacteristic
565C24—21no—
566C24—21no—
567C24#41×C7311yescharacteristic
568#41—21no—
569#41—21no—
570#41—22no—
571#41—22no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—42no—
577#41—42no—
578#41—41no—
579#41—41no—
580#41—42no—
581#41—42no—
582#41#41×C7312yes—
583#41#41×C7312yes—
584C2×Q8—21no—
585C2×Q8—22no—
586C2×Q8—41no—
587C2×Q8C2×D4×C7311yescharacteristic
588C2×Q8C2×D4×C7311yescharacteristic
589C2×D4—21no—
590C2×D4—22no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—41no—
602C2×D4—42no—
603C2×D4—42no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—82no—
607C2×D4C2×D4×C7311yescharacteristic
608C2×D4C2×D4×C7311yescharacteristic
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—21no—
617C22×C4—21no—
618C22×C4—21no—
619C22×C4—21no—
620C22×C4—21no—
621C22×C4—42no—
622C22×C4—42no—
623C22×C4C2×D4×C7311yescharacteristic
624C22×C4C2×D4×C7311yescharacteristic
625C22×C4C2×D4×C7311yescharacteristic
626C22×C4C2×D4×C7311yescharacteristic
627C22×C4#41×C7311yescharacteristic
628C22×C4C24×C7311yescharacteristic
629SD16—42no—
630SD16—42no—
631D8—42no—
632D8—42no—
633M16—21no—
634M16—21no—
635M16—21no—
636M16—21no—
637M16—21no—
638M16—21no—
639M16—21no—
640M16—21no—
641M16—21no—
642M16—21no—
643M16—21no—
644M16—21no—
645M16—42no—
646M16—42no—
647M16—42no—
648C2×C8—21no—
649C2×C8—21no—
650C2×C8—21no—
651C2×C8—21no—
652C2×C8—21no—
653C2×C8—21no—
654C2×C8—21no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—42no—
659C2×C8—42no—
660C2×C8—42no—
661C2×C8C2×D4×C7311yescharacteristic
662C2×C8C2×D4×C7311yescharacteristic
663C2×C8C2×D4×C7311yescharacteristic
664C2×C8C2×D4×C7311yescharacteristic
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C22⋊C4—41no—
672C22⋊C4—41no—
673C22⋊C4—41no—
674C22⋊C4—41no—
675C42—41no—
676C42—41no—
677C23—21no—
678C23—21no—
679C23—21no—
680C23—21no—
681C23—41no—
682C23—41no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—41no—
687C23—41no—
688C23—81no—
689C23—81no—
690C23—81no—
691C23#121×C7311yescharacteristic
692C23#121×C7311yescharacteristic
693C23C2×#41×C7311yescharacteristic
694Q8—21no—
695Q8—21no—
696Q8—21no—
697Q8—42no—
698Q8#123×C7312yes—
699D4—22no—
700D4—22no—
701D4—21no—
702D4—21no—
703D4—21no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—41no—
713D4—82no—
714D4—82no—
715D4#123×C7312yes—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—21no—
726C2×C4—21no—
727C2×C4—21no—
728C2×C4—21no—
729C2×C4—21no—
730C2×C4—42no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—41no—
734C2×C4—41no—
735C2×C4—41no—
736C2×C4—41no—
737C2×C4—41no—
738C2×C4—81no—
739C2×C4—81no—
740C2×C4—81no—
741C2×C4#121×C7311yescharacteristic
742C2×C4#121×C7311yescharacteristic
743C2×C4C22×D4×C7311yescharacteristic
744C2×C4C22×D4×C7311yescharacteristic
745C2×C4C2×#41×C7311yescharacteristic
746C2×C4C2×#41×C7311yescharacteristic
747C2×C4H(5,𝔽2)×C7311yescharacteristic
748C2×C4H(5,𝔽2)×C7311yescharacteristic
749C8—21no—
750C8—21no—
751C8—21no—
752C8—21no—
753C8—41no—
754C8—41no—
755C8—41no—
756C8—41no—
757C8—41no—
758C8—41no—
759C22—21no—
760C22—21no—
761C22—21no—
762C22—21no—
763C22—21no—
764C22—21no—
765C22—21no—
766C22—21no—
767C22—22no—
768C22—41no—
769C22—41no—
770C22—41no—
771C22—41no—
772C22—41no—
773C22—81no—
774C22—81no—
775C22—84no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—161no—
780C22—161no—
781C22C2×#121×C7311yescharacteristic
782C22#551×C7311yescharacteristic
783C22#551×C7311yescharacteristic
784C4—21no—
785C4—21no—
786C4—22no—
787C4—41no—
788C4—81no—
789C4—81no—
790C4—81no—
791C4C2×#123×C7311yescharacteristic
792C4#534×C7311yescharacteristic
793C4#546×C7311yescharacteristic
794C4#546×C7311yescharacteristic
795C2—21no—
796C2—21no—
797C2—41no—
798C2—41no—
799C2—42no—
800C2—81no—
801C2—161no—
802C2C73×#241211yescharacteristic
803C2C73×#306711yescharacteristic
804C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3006C2
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. C2×#482×C73C2semidirect
3. C73×#2896C2semidirect
4. C73×#2880C2semidirect
5. C73×#2079C2semidirect
6. C73×#2078C2semidirect
7. C73×#2051C2semidirect
8. C73×#2051C2semidirect
9. C73×#1907C2semidirect
10. C73×#1907C2semidirect
11. C73×#1900C2semidirect
12. C73×#1855C2semidirect
13. C73×#1822C2semidirect
14. C73×#1816C2semidirect
15. C73×#1815C2semidirect
32. C2×#108×C73C22semidirect
33. C2×#108×C73C22semidirect
34. C2×#107×C73C22semidirect
35. C2×#106×C73C22semidirect
46. C2×#102×C73C22semidirect
47. C2×#102×C73C22semidirect
48. C2×#100×C73C22semidirect
49. C2×#100×C73C22semidirect
59. #343×C73C22semidirect
60. #343×C73C22semidirect
61. #343×C73C22semidirect
62. #343×C73C22semidirect
63. #343×C73C22semidirect
64. #343×C73C22semidirect
65. #341×C73C22semidirect
66. #341×C73C22semidirect
392. #24575C73direct (N × H)
403. C2×#482C2×C73semidirect
405. #2896C2×C73semidirect
406. #2880C2×C73semidirect
407. #2079C2×C73semidirect
408. #2078C2×C73semidirect
409. #2051C2×C73semidirect
410. #2051C2×C73semidirect
411. #1907C2×C73semidirect
412. #1907C2×C73semidirect
413. #1900C2×C73semidirect
414. #1855C2×C73semidirect
415. #1822C2×C73semidirect
416. #1816C2×C73semidirect
417. #1815C2×C73semidirect
418. C73#24575direct (N × H)
435. C2×#108C22×C73semidirect
436. C2×#108C22×C73semidirect
437. C2×#107C22×C73semidirect
438. C2×#106C22×C73semidirect
449. C2×#102C22×C73semidirect
450. C2×#102C22×C73semidirect
451. C2×#100C22×C73semidirect
452. C2×#100C22×C73semidirect
462. #343C22×C73semidirect
463. #343C22×C73semidirect
464. #343C22×C73semidirect
465. #343C22×C73semidirect
466. #343C22×C73semidirect
467. #343C22×C73semidirect
468. #341C22×C73semidirect
469. #341C22×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#482×C732
C73×#30062
C73×#28962
C73×#28802
C73×#20792
C73×#20782
C73×#20512
C73×#19072
C73×#19002
C73×#18552
C73×#18222
C73×#18162
C73×#18152
#2457573