Finite Group Databasebeta

← C73×#25196 #32934600

Subgroups — C73×#25196 #32934600

Order 18688.

1032 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3068C211yesmaximal, characteristic, complemented
2C73×#3068C211yesmaximal, characteristic, complemented
3C73×#3019C211yesmaximal, characteristic, complemented
4C2×#453×C73C211yesmaximal, characteristic, complemented
5C73×#2956C211yesmaximal, characteristic, complemented
6C73×#2888C211yesmaximal, characteristic, complemented
7C73×#2069C211yesmaximal, characteristic, complemented
8C73×#2050C211yesmaximal, characteristic, complemented
9C73×#2048C211yesmaximal, characteristic, complemented
10C73×#2002C211yesmaximal, characteristic, complemented
11C73×#1965C211yesmaximal, characteristic, complemented
12C73×#1932C211yesmaximal, characteristic, complemented
13C73×#1914C211yesmaximal, characteristic, complemented
14C73×#1903C211yesmaximal, characteristic, complemented
15C73×#1861C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C73C2211yescharacteristic
17#575×C73C2211yescharacteristic
18#575×C73C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C73C2211yescharacteristic, complemented
22#568×C73C2211yescharacteristic
23#568×C73C2211yescharacteristic
24#568×C73C2211yescharacteristic, complemented
25#535×C73C2211yescharacteristic
26C2×#127×C73C2211yescharacteristic
27#472×C73—22no—
28#472×C73—22no—
29#471×C73—22no—
30#471×C73—22no—
31#455×C73—22no—
32#453×C73—22no—
33#453×C73—22no—
34#453×C73—22no—
35#444×C73—22no—
36#443×C73—22no—
37#430×C73C2211yescharacteristic, complemented
38#430×C73C2211yescharacteristic, complemented
39#430×C73C2211yescharacteristic, complemented
40#423×C73C2211yescharacteristic, complemented
41#421×C73C2211yescharacteristic
42#421×C73C2211yescharacteristic
43C2×#104×C73C2211yescharacteristic
44C2×#104×C73C2211yescharacteristic
45C2×#104×C73C2211yescharacteristic, complemented
46#418×C73C2211yescharacteristic, complemented
47#413×C73—22no—
48#413×C73C2211yescharacteristic
49#413×C73C2211yescharacteristic
50#413×C73C2211yescharacteristic, complemented
51C2×#100×C73—22no—
52C2×#100×C73C2211yescharacteristic
53C2×#100×C73C2211yescharacteristic
54C2×#100×C73C2211yescharacteristic
55C2×#100×C73C2211yescharacteristic
56C2×#100×C73C2211yescharacteristic, complemented
57C2×#100×C73C2211yescharacteristic, complemented
58C4×M16×C73C2211yescharacteristic, complemented
59#344×C73C2211yescharacteristic, complemented
60#344×C73C2211yescharacteristic, complemented
61#339×C73C2211yescharacteristic, complemented
62#338×C73C2211yescharacteristic, complemented
63H(5,𝔽2)×C73—22no—
64H(5,𝔽2)×C73—22no—
65H(5,𝔽2)×C73—41no—
66H(5,𝔽2)×C73—41no—
67C2×#41×C73—21no—
68C2×#41×C73—21no—
69C2×#41×C73C2311yescharacteristic
70C2×#41×C73C2311yescharacteristic
71C2×#41×C73C2311yescharacteristic
72C22×D4×C73—22no—
73C22×D4×C73—21no—
74C22×D4×C73—21no—
75C22×D4×C73—22no—
76C22×D4×C73C2311yescharacteristic
77C22×D4×C73C2311yescharacteristic
78#137×C73—21no—
79#137×C73—21no—
80#137×C73—21no—
81#137×C73D412yescomplemented
82AGL(1,ℤ/8)×C73—21no—
83AGL(1,ℤ/8)×C73—22no—
84AGL(1,ℤ/8)×C73—22no—
85AGL(1,ℤ/8)×C73—21no—
86AGL(1,ℤ/8)×C73—21no—
87AGL(1,ℤ/8)×C73—22no—
88AGL(1,ℤ/8)×C73—22no—
89AGL(1,ℤ/8)×C73—41no—
90AGL(1,ℤ/8)×C73—41no—
91AGL(1,ℤ/8)×C73D412yescomplemented
92#135×C73—22no—
93#135×C73—41no—
94C2×SD16×C73—21no—
95C2×SD16×C73—21no—
96C2×SD16×C73—21no—
97C2×D8×C73—21no—
98C2×D8×C73—21no—
99C2×D8×C73—21no—
100#131×C73—22no—
101#131×C73—22no—
102#131×C73—22no—
103#131×C73—22no—
104#131×C73—41no—
105#131×C73—41no—
106C2×M16×C73—22no—
107C2×M16×C73—22no—
108C2×M16×C73—41no—
109C2×M16×C73C2311yescharacteristic
110C2×M16×C73C2311yescharacteristic
111C2×M16×C73C2311yescharacteristic
112C2×M16×C73C2311yescharacteristic
113C2×M16×C73C2311yescharacteristic
114C2×M16×C73C2311yescharacteristic
115C2×M16×C73C2311yescharacteristic
116C2×M16×C73C2311yescharacteristic
117#127×C73—21no—
118#127×C73—21no—
119#127×C73—21no—
120#127×C73—41no—
121#124×C73—21no—
122#121×C73—41no—
123#120×C73—22no—
124#117×C73C2311yescharacteristic
125C2×C42×C73C2311yescharacteristic
126#108×C73—22no—
127#108×C73—22no—
128#108×C73—22no—
129C4⋊C8×C73—41no—
130#104×C73—22no—
131#104×C73—22no—
132#104×C73—21no—
133#104×C73—21no—
134#104×C73—21no—
135#104×C73—21no—
136#104×C73D412yescomplemented
137#104×C73D412yescomplemented
138#102×C73—41no—
139#101×C73—21no—
140#101×C73—21no—
141#101×C73D412yescomplemented
142#100×C73—21no—
143#100×C73—21no—
144#100×C73—22no—
145#100×C73—22no—
146#100×C73—22no—
147#100×C73—22no—
148#100×C73—22no—
149#100×C73—22no—
150#100×C73D412yescomplemented
151#97×C73—21no—
152C4×C8×C73—21no—
153C24×C73—22no—
154C24×C73—21no—
155C24×C73#4112yes—
156#41×C73—21no—
157#41×C73—21no—
158#41×C73—21no—
159#41×C73—21no—
160#41×C73—21no—
161#41×C73—21no—
162#41×C73—21no—
163#41×C73—21no—
164#41×C73—21no—
165#41×C73—21no—
166#41×C73—42no—
167#41×C73—42no—
168#41×C73—42no—
169#41×C73—42no—
170#41×C73C2×D412yes—
171#41×C73C2×D412yes—
172C2×Q8×C73C2×D411yescharacteristic
173C2×Q8×C73C2×D411yescharacteristic
174C2×Q8×C73#4111yescharacteristic
175C2×D4×C73—21no—
176C2×D4×C73—22no—
177C2×D4×C73—22no—
178C2×D4×C73—21no—
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—21no—
191C2×D4×C73—21no—
192C2×D4×C73—42no—
193C2×D4×C73—42no—
194C2×D4×C73—42no—
195C2×D4×C73—42no—
196C2×D4×C73—44no—
197C2×D4×C73—44no—
198C2×D4×C73—42no—
199C2×D4×C73—42no—
200C2×D4×C73—42no—
201C2×D4×C73—84no—
202C2×D4×C73C2×D411yescharacteristic
203C2×D4×C73C2×D411yescharacteristic
204C2×D4×C73#4111yescharacteristic
205C22×C4×C73—21no—
206C22×C4×C73—22no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73C2411yescharacteristic
211Q16×C73—22no—
212Q16×C73—41no—
213SD16×C73—22no—
214SD16×C73—22no—
215SD16×C73—42no—
216SD16×C73—42no—
217SD16×C73—41no—
218SD16×C73—41no—
219SD16×C73—42no—
220D8×C73—22no—
221D8×C73—42no—
222D8×C73—42no—
223D8×C73—41no—
224D8×C73—42no—
225M16×C73—21no—
226M16×C73—21no—
227M16×C73—21no—
228M16×C73—21no—
229M16×C73—21no—
230M16×C73—21no—
231M16×C73—21no—
232M16×C73—21no—
233M16×C73—21no—
234M16×C73—21no—
235M16×C73—21no—
236M16×C73—21no—
237M16×C73—42no—
238M16×C73—42no—
239M16×C73—42no—
240M16×C73C2×D412yes—
241M16×C73C2×D412yes—
242M16×C73C2×D412yes—
243M16×C73C2×D412yes—
244C2×C8×C73—21no—
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—42no—
253C2×C8×C73—42no—
254C2×C8×C73—42no—
255C4⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—42no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73C2×D411yescharacteristic
261C42×C73C2×D411yescharacteristic
262C23×C73—21no—
263C23×C73—22no—
264C23×C73—21no—
265C23×C73—22no—
266C23×C73—21no—
267C23×C73—22no—
268C23×C73—44no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—82no—
273C23×C73—82no—
274C23×C73—162no—
275C23×C73C2×#4111yescharacteristic
276Q8×C73—21no—
277Q8×C73—21no—
278Q8×C73—21no—
279Q8×C73—21no—
280Q8×C73—21no—
281Q8×C73#12112yes—
282D4×C73—22no—
283D4×C73—22no—
284D4×C73—21no—
285D4×C73—21no—
286D4×C73—21no—
287D4×C73—21no—
288D4×C73—21no—
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—41no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—84no—
304D4×C73—84no—
305D4×C73—162no—
306D4×C73#12112yes—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—44no—
315C2×C4×C73—42no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73C22×D411yescharacteristic
322C2×C4×C73C22×D411yescharacteristic
323C2×C4×C73C22×D411yescharacteristic
324C2×C4×C73C2×#4111yescharacteristic
325C2×C4×C73H(5,𝔽2)11yescharacteristic
326C2×C4×C73H(5,𝔽2)11yescharacteristic
327C8×C73—22no—
328C8×C73—22no—
329C8×C73—22no—
330C8×C73—22no—
331C8×C73—41no—
332C8×C73—41no—
333C8×C73—41no—
334C8×C73—41no—
335C22×C73—22no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—42no—
340C22×C73—81no—
341C22×C73—82no—
342C22×C73—81no—
343C22×C73—82no—
344C22×C73—82no—
345C22×C73—81no—
346C22×C73—82no—
347C22×C73—81no—
348C22×C73—161no—
349C22×C73—161no—
350C22×C73—164no—
351C22×C73#52511yescharacteristic
352C22×C73#54611yescharacteristic
353C22×C73#54611yescharacteristic
354C4×C73—22no—
355C4×C73—22no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73—41no—
359C4×C73—81no—
360C4×C73C2×#12111yescharacteristic
361C4×C73#53811yescharacteristic
362C4×C73D4211yescharacteristic
363C4×C73D4211yescharacteristic
364#25196C7311yesmaximal, characteristic, direct product factor, Sylow
365C2×C73—21no—
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—42no—
369C2×C73—81no—
370C2×C73—82no—
371C2×C73—81no—
372C2×C73—161no—
373C2×C73#242411yescharacteristic
374#3068C2×C7311yescharacteristic, complemented
375#3068C2×C7311yescharacteristic, complemented
376#3019C2×C7311yescharacteristic, complemented
377C2×#453C2×C7311yescharacteristic, complemented
378#2956C2×C7311yescharacteristic, complemented
379#2888C2×C7311yescharacteristic, complemented
380#2069C2×C7311yescharacteristic, complemented
381#2050C2×C7311yescharacteristic, complemented
382#2048C2×C7311yescharacteristic, complemented
383#2002C2×C7311yescharacteristic, complemented
384#1965C2×C7311yescharacteristic, complemented
385#1932C2×C7311yescharacteristic, complemented
386#1914C2×C7311yescharacteristic, complemented
387#1903C2×C7311yescharacteristic, complemented
388#1861C2×C7311yescharacteristic, complemented
389C73#2519611yescharacteristic, direct product factor, Sylow
390C2×H(5,𝔽2)C22×C7311yescharacteristic
391#575C22×C7311yescharacteristic
392#575C22×C7311yescharacteristic
393C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
394C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
395C2×AGL(1,ℤ/8)C22×C7311yescharacteristic, complemented
396#568C22×C7311yescharacteristic
397#568C22×C7311yescharacteristic
398#568C22×C7311yescharacteristic, complemented
399#535C22×C7311yescharacteristic
400C2×#127C22×C7311yescharacteristic
401#472—22no—
402#472—22no—
403#471—22no—
404#471—22no—
405#455—22no—
406#453—22no—
407#453—22no—
408#453—22no—
409#444—22no—
410#443—22no—
411#430C22×C7311yescharacteristic, complemented
412#430C22×C7311yescharacteristic, complemented
413#430C22×C7311yescharacteristic, complemented
414#423C22×C7311yescharacteristic, complemented
415#421C22×C7311yescharacteristic
416#421C22×C7311yescharacteristic
417C2×#104C22×C7311yescharacteristic
418C2×#104C22×C7311yescharacteristic
419C2×#104C22×C7311yescharacteristic, complemented
420#418C22×C7311yescharacteristic, complemented
421#413—22no—
422#413C22×C7311yescharacteristic
423#413C22×C7311yescharacteristic
424#413C22×C7311yescharacteristic, complemented
425C2×#100—22no—
426C2×#100C22×C7311yescharacteristic
427C2×#100C22×C7311yescharacteristic
428C2×#100C22×C7311yescharacteristic
429C2×#100C22×C7311yescharacteristic
430C2×#100C22×C7311yescharacteristic, complemented
431C2×#100C22×C7311yescharacteristic, complemented
432C4×M16C22×C7311yescharacteristic, complemented
433#344C22×C7311yescharacteristic, complemented
434#344C22×C7311yescharacteristic, complemented
435#339C22×C7311yescharacteristic, complemented
436#338C22×C7311yescharacteristic, complemented
437H(5,𝔽2)—22no—
438H(5,𝔽2)—22no—
439H(5,𝔽2)—41no—
440H(5,𝔽2)—41no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41C23×C7311yescharacteristic
444C2×#41C23×C7311yescharacteristic
445C2×#41C23×C7311yescharacteristic
446C22×D4—22no—
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—22no—
450C22×D4C23×C7311yescharacteristic
451C22×D4C23×C7311yescharacteristic
452#137—21no—
453#137—21no—
454#137—21no—
455#137D4×C7312yescomplemented
456AGL(1,ℤ/8)—21no—
457AGL(1,ℤ/8)—22no—
458AGL(1,ℤ/8)—22no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—22no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—41no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)D4×C7312yescomplemented
466#135—22no—
467#135—41no—
468C2×SD16—21no—
469C2×SD16—21no—
470C2×SD16—21no—
471C2×D8—21no—
472C2×D8—21no—
473C2×D8—21no—
474#131—22no—
475#131—22no—
476#131—22no—
477#131—22no—
478#131—41no—
479#131—41no—
480C2×M16—22no—
481C2×M16—22no—
482C2×M16—41no—
483C2×M16C23×C7311yescharacteristic
484C2×M16C23×C7311yescharacteristic
485C2×M16C23×C7311yescharacteristic
486C2×M16C23×C7311yescharacteristic
487C2×M16C23×C7311yescharacteristic
488C2×M16C23×C7311yescharacteristic
489C2×M16C23×C7311yescharacteristic
490C2×M16C23×C7311yescharacteristic
491#127—21no—
492#127—21no—
493#127—21no—
494#127—41no—
495#124—21no—
496#121—41no—
497#120—22no—
498#117C23×C7311yescharacteristic
499C2×C42C23×C7311yescharacteristic
500#108—22no—
501#108—22no—
502#108—22no—
503C4⋊C8—41no—
504#104—22no—
505#104—22no—
506#104—21no—
507#104—21no—
508#104—21no—
509#104—21no—
510#104D4×C7312yescomplemented
511#104D4×C7312yescomplemented
512#102—41no—
513#101—21no—
514#101—21no—
515#101D4×C7312yescomplemented
516#100—21no—
517#100—21no—
518#100—22no—
519#100—22no—
520#100—22no—
521#100—22no—
522#100—22no—
523#100—22no—
524#100D4×C7312yescomplemented
525#97—21no—
526C4×C8—21no—
527C24—22no—
528C24—21no—
529C24#41×C7312yes—
530#41—21no—
531#41—21no—
532#41—21no—
533#41—21no—
534#41—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—42no—
541#41—42no—
542#41—42no—
543#41—42no—
544#41C2×D4×C7312yes—
545#41C2×D4×C7312yes—
546C2×Q8C2×D4×C7311yescharacteristic
547C2×Q8C2×D4×C7311yescharacteristic
548C2×Q8#41×C7311yescharacteristic
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—22no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—42no—
567C2×D4—42no—
568C2×D4—42no—
569C2×D4—42no—
570C2×D4—44no—
571C2×D4—44no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—42no—
575C2×D4—84no—
576C2×D4C2×D4×C7311yescharacteristic
577C2×D4C2×D4×C7311yescharacteristic
578C2×D4#41×C7311yescharacteristic
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C7311yescharacteristic
585Q16—22no—
586Q16—41no—
587SD16—22no—
588SD16—22no—
589SD16—42no—
590SD16—42no—
591SD16—41no—
592SD16—41no—
593SD16—42no—
594D8—22no—
595D8—42no—
596D8—42no—
597D8—41no—
598D8—42no—
599M16—21no—
600M16—21no—
601M16—21no—
602M16—21no—
603M16—21no—
604M16—21no—
605M16—21no—
606M16—21no—
607M16—21no—
608M16—21no—
609M16—21no—
610M16—21no—
611M16—42no—
612M16—42no—
613M16—42no—
614M16C2×D4×C7312yes—
615M16C2×D4×C7312yes—
616M16C2×D4×C7312yes—
617M16C2×D4×C7312yes—
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—42no—
627C2×C8—42no—
628C2×C8—42no—
629C4⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—42no—
632C42—21no—
633C42—21no—
634C42C2×D4×C7311yescharacteristic
635C42C2×D4×C7311yescharacteristic
636C23—21no—
637C23—22no—
638C23—21no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—44no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—82no—
647C23—82no—
648C23—162no—
649C23C2×#41×C7311yescharacteristic
650Q8—21no—
651Q8—21no—
652Q8—21no—
653Q8—21no—
654Q8—21no—
655Q8#121×C7312yes—
656D4—22no—
657D4—22no—
658D4—21no—
659D4—21no—
660D4—21no—
661D4—21no—
662D4—21no—
663D4—44no—
664D4—44no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—41no—
676D4—41no—
677D4—84no—
678D4—84no—
679D4—162no—
680D4#121×C7312yes—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—22no—
684C2×C4—22no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—44no—
689C2×C4—42no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4C22×D4×C7311yescharacteristic
696C2×C4C22×D4×C7311yescharacteristic
697C2×C4C22×D4×C7311yescharacteristic
698C2×C4C2×#41×C7311yescharacteristic
699C2×C4H(5,𝔽2)×C7311yescharacteristic
700C2×C4H(5,𝔽2)×C7311yescharacteristic
701C8—22no—
702C8—22no—
703C8—22no—
704C8—22no—
705C8—41no—
706C8—41no—
707C8—41no—
708C8—41no—
709C22—22no—
710C22—41no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—81no—
715C22—82no—
716C22—81no—
717C22—82no—
718C22—82no—
719C22—81no—
720C22—82no—
721C22—81no—
722C22—161no—
723C22—161no—
724C22—164no—
725C22#525×C7311yescharacteristic
726C22#546×C7311yescharacteristic
727C22#546×C7311yescharacteristic
728C4—22no—
729C4—22no—
730C4—41no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4C2×#121×C7311yescharacteristic
735C4#538×C7311yescharacteristic
736C4D42×C7311yescharacteristic
737C4D42×C7311yescharacteristic
738C2—21no—
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—81no—
744C2—81no—
745C2—161no—
746C2C73×#242411yescharacteristic
subgroupG/H
center, socleC2×C73#2424
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C2×C73 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3068C2semidirect
2. C73×#3068C2semidirect
3. C73×#3019C2semidirect
4. C2×#453×C73C2semidirect
5. C73×#2956C2semidirect
6. C73×#2888C2semidirect
7. C73×#2069C2semidirect
8. C73×#2050C2semidirect
9. C73×#2048C2semidirect
10. C73×#2002C2semidirect
11. C73×#1965C2semidirect
12. C73×#1932C2semidirect
13. C73×#1914C2semidirect
14. C73×#1903C2semidirect
15. C73×#1861C2semidirect
21. C2×AGL(1,ℤ/8)×C73C22semidirect
24. #568×C73C22semidirect
37. #430×C73C22semidirect
38. #430×C73C22semidirect
39. #430×C73C22semidirect
40. #423×C73C22semidirect
45. C2×#104×C73C22semidirect
46. #418×C73C22semidirect
50. #413×C73C22semidirect
56. C2×#100×C73C22semidirect
57. C2×#100×C73C22semidirect
58. C4×M16×C73C22semidirect
59. #344×C73C22semidirect
60. #344×C73C22semidirect
61. #339×C73C22semidirect
62. #338×C73C22semidirect
81. #137×C73D4semidirect
91. AGL(1,ℤ/8)×C73D4semidirect
136. #104×C73D4semidirect
137. #104×C73D4semidirect
141. #101×C73D4semidirect
150. #100×C73D4semidirect
364. #25196C73direct (N × H)
374. #3068C2×C73semidirect
375. #3068C2×C73semidirect
376. #3019C2×C73semidirect
377. C2×#453C2×C73semidirect
378. #2956C2×C73semidirect
379. #2888C2×C73semidirect
380. #2069C2×C73semidirect
381. #2050C2×C73semidirect
382. #2048C2×C73semidirect
383. #2002C2×C73semidirect
384. #1965C2×C73semidirect
385. #1932C2×C73semidirect
386. #1914C2×C73semidirect
387. #1903C2×C73semidirect
388. #1861C2×C73semidirect
389. C73#25196direct (N × H)
395. C2×AGL(1,ℤ/8)C22×C73semidirect
398. #568C22×C73semidirect
411. #430C22×C73semidirect
412. #430C22×C73semidirect
413. #430C22×C73semidirect
414. #423C22×C73semidirect
419. C2×#104C22×C73semidirect
420. #418C22×C73semidirect
424. #413C22×C73semidirect
430. C2×#100C22×C73semidirect
431. C2×#100C22×C73semidirect
432. C4×M16C22×C73semidirect
433. #344C22×C73semidirect
434. #344C22×C73semidirect
435. #339C22×C73semidirect
436. #338C22×C73semidirect
455. #137D4×C73semidirect
465. AGL(1,ℤ/8)D4×C73semidirect
510. #104D4×C73semidirect
511. #104D4×C73semidirect
515. #101D4×C73semidirect
524. #100D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30682
C73×#30192
C2×#453×C732
C73×#29562
C73×#28882
C73×#20692
C73×#20502
C73×#20482
C73×#20022
C73×#19652
C73×#19322
C73×#19142
C73×#19032
C73×#18612
#2519673