Finite Group Databasebeta

← C73×#24774 #32934178

Subgroups — C73×#24774 #32934178

Order 18688.

882 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
1C2×#472×C73C211yesmaximal, characteristic
2C2×#471×C73C211yesmaximal, characteristic, complemented
3C73×#3040C211yesmaximal, characteristic, complemented
4C2×#463×C73C211yesmaximal, characteristic, complemented
5C4×AGL(1,ℤ/8)×C73C211yesmaximal, characteristic, complemented
6C73×#2906C211yesmaximal, characteristic, complemented
7C73×#2064C211yesmaximal, characteristic, complemented
8C73×#2063C211yesmaximal, characteristic, complemented
9C73×#2046C211yesmaximal, characteristic, complemented
10C73×#2045C211yesmaximal, characteristic, complemented
11C73×#1967C211yesmaximal, characteristic, complemented
12C73×#1950C211yesmaximal, characteristic, complemented
13C73×#1908C211yesmaximal, characteristic, complemented
14C73×#1907C211yesmaximal, characteristic, complemented
15C73×#1800C211yesmaximal, characteristic, complemented
16C2×#137×C73C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C22×D8×C73C2211yescharacteristic
21C2×#131×C73C2211yescharacteristic
22C2×#131×C73C2211yescharacteristic
23C2×#124×C73C2211yescharacteristic
24C4×#41×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26#472×C73—24no—
27#471×C73—24no—
28#464×C73—21no—
29#464×C73—21no—
30#463×C73—21no—
31#463×C73—21no—
32#463×C73—21no—
33#463×C73—21no—
34#463×C73—21no—
35#463×C73—21no—
36#442×C73—21no—
37#440×C73—21no—
38C4×SD16×C73—21no—
39C4×D8×C73—21no—
40C2×#108×C73C2211yescharacteristic
41C2×#108×C73C2211yescharacteristic
42#428×C73C2211yescharacteristic
43#424×C73—21no—
44#424×C73—21no—
45#424×C73C2211yescharacteristic
46#424×C73C2211yescharacteristic
47#423×C73—21no—
48#423×C73C2211yescharacteristic
49#423×C73C2211yescharacteristic
50C2×C4⋊C8×C73—21no—
51C2×C4⋊C8×C73C2211yescharacteristic
52#419×C73C2211yescharacteristic
53#418×C73C2211yescharacteristic
54#418×C73C2211yescharacteristic
55#417×C73C2211yescharacteristic
56C2×#103×C73C2211yescharacteristic
57C2×#102×C73C2211yescharacteristic
58C2×#101×C73C2211yescharacteristic
59C2×#101×C73C2211yescharacteristic
60C2×#100×C73C2211yescharacteristic
61C2×#100×C73C2211yescharacteristic
62C2×#100×C73C2211yescharacteristic
63C2×#100×C73C2211yescharacteristic
64C4×M16×C73C2211yescharacteristic
65#343×C73C2211yescharacteristic
66#343×C73C2211yescharacteristic
67#341×C73C2211yescharacteristic
68#341×C73C2211yescharacteristic
69C2×#41×C73C2311yescharacteristic
70C22×Q8×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73C23×C4×C73—21no—
74#137×C73—22no—
75#137×C73—22no—
76AGL(1,ℤ/8)×C73—22no—
77AGL(1,ℤ/8)×C73—22no—
78AGL(1,ℤ/8)×C73—22no—
79AGL(1,ℤ/8)×C73D414yes—
80C2×Q16×C73—21no—
81C2×SD16×C73—21no—
82C2×SD16×C73—21no—
83C2×SD16×C73—21no—
84C2×SD16×C73—22no—
85C2×SD16×C73—21no—
86C2×SD16×C73—21no—
87C2×SD16×C73—41no—
88C2×D8×C73—21no—
89C2×D8×C73—21no—
90C2×D8×C73—22no—
91C2×D8×C73—21no—
92C2×D8×C73—21no—
93C2×D8×C73—41no—
94#131×C73—22no—
95#131×C73—22no—
96#131×C73—41no—
97#131×C73—41no—
98C2×M16×C73—21no—
99C2×M16×C73—21no—
100C2×M16×C73C2311yescharacteristic
101C2×M16×C73C2311yescharacteristic
102C2×M16×C73C2311yescharacteristic
103C2×M16×C73C2311yescharacteristic
104C2×M16×C73C2311yescharacteristic
105C2×M16×C73C2311yescharacteristic
106C22×C8×C73—21no—
107C22×C8×C73—21no—
108C22×C8×C73C2311yescharacteristic
109C22×C8×C73C2311yescharacteristic
110#124×C73—21no—
111#124×C73—21no—
112#124×C73—21no—
113#124×C73—21no—
114C4×Q8×C73D411yescharacteristic
115C4×Q8×C73D411yescharacteristic
116C4×D4×C73—21no—
117C4×D4×C73—21no—
118C4×D4×C73—21no—
119C4×D4×C73—21no—
120C4×D4×C73—21no—
121C4×D4×C73—21no—
122C4×D4×C73D411yescharacteristic
123C4×D4×C73D411yescharacteristic
124#117×C73—21no—
125#117×C73C2311yescharacteristic
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C42×C73—21no—
131C2×C42×C73C2311yescharacteristic
132#108×C73—22no—
133#108×C73—22no—
134#107×C73—21no—
135#106×C73—21no—
136C4⋊C8×C73—21no—
137C4⋊C8×C73—21no—
138C4⋊C8×C73—21no—
139C4⋊C8×C73—21no—
140C4⋊C8×C73—21no—
141C4⋊C8×C73—21no—
142C4⋊C8×C73—21no—
143C4⋊C8×C73—21no—
144C4⋊C8×C73D411yescharacteristic
145C4⋊C8×C73D411yescharacteristic
146C4⋊C8×C73D411yescharacteristic
147C4⋊C8×C73D411yescharacteristic
148#103×C73—21no—
149#103×C73—21no—
150#103×C73—21no—
151#103×C73—21no—
152#103×C73—21no—
153#102×C73—21no—
154#102×C73—21no—
155#102×C73—21no—
156#102×C73—21no—
157#102×C73—21no—
158#102×C73—21no—
159#102×C73—21no—
160#101×C73—22no—
161#101×C73—41no—
162#100×C73—22no—
163#100×C73—22no—
164#100×C73—22no—
165#100×C73—41no—
166#97×C73—21no—
167C4×C8×C73—21no—
168C24×C73—21no—
169C24×C73—21no—
170#41×C73—21no—
171#41×C73—21no—
172#41×C73C2×D412yes—
173#41×C73#4112yes—
174C2×Q8×C73—21no—
175C2×Q8×C73—21no—
176C2×Q8×C73—21no—
177C2×Q8×C73—21no—
178C2×Q8×C73—21no—
179C2×Q8×C73—21no—
180C2×Q8×C73C2×D411yescharacteristic
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—21no—
193C2×D4×C73C2×D412yes—
194C2×D4×C73C2×D411yescharacteristic
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73—41no—
201C22×C4×C73—41no—
202C22×C4×C73—82no—
203C22×C4×C73#4111yescharacteristic
204C22×C4×C73#4111yescharacteristic
205C22×C4×C73C2411yescharacteristic
206Q16×C73—42no—
207SD16×C73—24no—
208SD16×C73—42no—
209SD16×C73—42no—
210SD16×C73—42no—
211SD16×C73—42no—
212D8×C73—24no—
213D8×C73—42no—
214D8×C73—42no—
215D8×C73—42no—
216M16×C73—21no—
217M16×C73—21no—
218M16×C73—21no—
219M16×C73—21no—
220M16×C73—21no—
221M16×C73—21no—
222M16×C73—21no—
223M16×C73—21no—
224M16×C73—21no—
225M16×C73—21no—
226M16×C73—21no—
227M16×C73—42no—
228M16×C73—42no—
229M16×C73C2×D412yes—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73—21no—
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—42no—
241C2×C8×C73—42no—
242C2×C8×C73C2×D411yescharacteristic
243C2×C8×C73C2×D411yescharacteristic
244C2×C8×C73C2×D411yescharacteristic
245C2×C8×C73C2×D411yescharacteristic
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73C2×D411yescharacteristic
251C4⋊C4×C73C2×D411yescharacteristic
252C22⋊C4×C73—21no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—21no—
255C22⋊C4×C73—41no—
256C22⋊C4×C73—41no—
257C22⋊C4×C73—41no—
258C22⋊C4×C73—41no—
259C22⋊C4×C73—41no—
260C22⋊C4×C73—41no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73C2×D411yescharacteristic
265C42×C73C2×D411yescharacteristic
266C42×C73C2×D411yescharacteristic
267C42×C73C2×D411yescharacteristic
268C23×C73—21no—
269C23×C73—22no—
270C23×C73—41no—
271C23×C73—41no—
272C23×C73—41no—
273C23×C73—41no—
274C23×C73—41no—
275C23×C73—81no—
276C23×C73—81no—
277C23×C73—81no—
278C23×C73—81no—
279C23×C73C2×#4111yescharacteristic
280Q8×C73—21no—
281Q8×C73—41no—
282Q8×C73—41no—
283Q8×C73—41no—
284Q8×C73—41no—
285Q8×C73#12112yes—
286D4×C73—22no—
287D4×C73—22no—
288D4×C73—22no—
289D4×C73—21no—
290D4×C73—22no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73#12112yes—
298C2×C4×C73—21no—
299C2×C4×C73—22no—
300C2×C4×C73—22no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—42no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—81no—
311C2×C4×C73—82no—
312C2×C4×C73—82no—
313C2×C4×C73—81no—
314C2×C4×C73#12111yescharacteristic
315C2×C4×C73#12111yescharacteristic
316C2×C4×C73#12111yescharacteristic
317C2×C4×C73#12111yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C22×D411yescharacteristic
320C2×C4×C73C22×D411yescharacteristic
321C2×C4×C73C2×#4111yescharacteristic
322C2×C4×C73H(5,𝔽2)11yescharacteristic
323C2×C4×C732−1+411yescharacteristic
324C8×C73—22no—
325C8×C73—21no—
326C8×C73—21no—
327C8×C73—21no—
328C8×C73—21no—
329C8×C73—41no—
330C8×C73—41no—
331C8×C73—41no—
332C8×C73—41no—
333C8×C73—41no—
334C22×C73—21no—
335C22×C73—21no—
336C22×C73—22no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—42no—
340C22×C73—82no—
341C22×C73—82no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73—81no—
346C22×C73—81no—
347C22×C73—161no—
348C22×C73—161no—
349C22×C73C2×#12111yescharacteristic
350C22×C73#54711yescharacteristic
351C22×C73#55311yescharacteristic
352C4×C73—22no—
353C4×C73—21no—
354C4×C73—21no—
355C4×C73—21no—
356C4×C73—21no—
357C4×C73—41no—
358C4×C73—41no—
359C4×C73—81no—
360C4×C73—81no—
361C4×C73C2×#12111yescharacteristic
362C4×C73#53711yescharacteristic
363C4×C73D4211yescharacteristic
364C4×C73#54811yescharacteristic
365#24774C7311yesmaximal, characteristic, direct product factor, Sylow
366C2×C73—21no—
367C2×C73—21no—
368C2×C73—42no—
369C2×C73—82no—
370C2×C73—161no—
371C2×C73#241611yescharacteristic
372C2×C73#306711yescharacteristic
373C2×C73#306811yescharacteristic
374C2×#472C2×C7311yescharacteristic
375C2×#471C2×C7311yescharacteristic, complemented
376#3040C2×C7311yescharacteristic, complemented
377C2×#463C2×C7311yescharacteristic, complemented
378C4×AGL(1,ℤ/8)C2×C7311yescharacteristic, complemented
379#2906C2×C7311yescharacteristic, complemented
380#2064C2×C7311yescharacteristic, complemented
381#2063C2×C7311yescharacteristic, complemented
382#2046C2×C7311yescharacteristic, complemented
383#2045C2×C7311yescharacteristic, complemented
384#1967C2×C7311yescharacteristic, complemented
385#1950C2×C7311yescharacteristic, complemented
386#1908C2×C7311yescharacteristic, complemented
387#1907C2×C7311yescharacteristic, complemented
388#1800C2×C7311yescharacteristic, complemented
389C73#2477411yescharacteristic, direct product factor, Sylow
390C2×#137C22×C7311yescharacteristic
391C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
392C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
393C22×SD16C22×C7311yescharacteristic
394C22×D8C22×C7311yescharacteristic
395C2×#131C22×C7311yescharacteristic
396C2×#131C22×C7311yescharacteristic
397C2×#124C22×C7311yescharacteristic
398C4×#41C22×C7311yescharacteristic
399C2×C4×D4C22×C7311yescharacteristic
400#472—24no—
401#471—24no—
402#464—21no—
403#464—21no—
404#463—21no—
405#463—21no—
406#463—21no—
407#463—21no—
408#463—21no—
409#463—21no—
410#442—21no—
411#440—21no—
412C4×SD16—21no—
413C4×D8—21no—
414C2×#108C22×C7311yescharacteristic
415C2×#108C22×C7311yescharacteristic
416#428C22×C7311yescharacteristic
417#424—21no—
418#424—21no—
419#424C22×C7311yescharacteristic
420#424C22×C7311yescharacteristic
421#423—21no—
422#423C22×C7311yescharacteristic
423#423C22×C7311yescharacteristic
424C2×C4⋊C8—21no—
425C2×C4⋊C8C22×C7311yescharacteristic
426#419C22×C7311yescharacteristic
427#418C22×C7311yescharacteristic
428#418C22×C7311yescharacteristic
429#417C22×C7311yescharacteristic
430C2×#103C22×C7311yescharacteristic
431C2×#102C22×C7311yescharacteristic
432C2×#101C22×C7311yescharacteristic
433C2×#101C22×C7311yescharacteristic
434C2×#100C22×C7311yescharacteristic
435C2×#100C22×C7311yescharacteristic
436C2×#100C22×C7311yescharacteristic
437C2×#100C22×C7311yescharacteristic
438C4×M16C22×C7311yescharacteristic
439#343C22×C7311yescharacteristic
440#343C22×C7311yescharacteristic
441#341C22×C7311yescharacteristic
442#341C22×C7311yescharacteristic
443C2×#41C23×C7311yescharacteristic
444C22×Q8C23×C7311yescharacteristic
445C22×D4C23×C7311yescharacteristic
446C22×D4C23×C7311yescharacteristic
447C23×C4—21no—
448#137—22no—
449#137—22no—
450AGL(1,ℤ/8)—22no—
451AGL(1,ℤ/8)—22no—
452AGL(1,ℤ/8)—22no—
453AGL(1,ℤ/8)D4×C7314yes—
454C2×Q16—21no—
455C2×SD16—21no—
456C2×SD16—21no—
457C2×SD16—22no—
458C2×SD16—21no—
459C2×SD16—21no—
460C2×SD16—21no—
461C2×SD16—41no—
462C2×D8—21no—
463C2×D8—22no—
464C2×D8—21no—
465C2×D8—21no—
466C2×D8—21no—
467C2×D8—41no—
468#131—22no—
469#131—22no—
470#131—41no—
471#131—41no—
472C2×M16—21no—
473C2×M16—21no—
474C2×M16C23×C7311yescharacteristic
475C2×M16C23×C7311yescharacteristic
476C2×M16C23×C7311yescharacteristic
477C2×M16C23×C7311yescharacteristic
478C2×M16C23×C7311yescharacteristic
479C2×M16C23×C7311yescharacteristic
480C22×C8—21no—
481C22×C8—21no—
482C22×C8C23×C7311yescharacteristic
483C22×C8C23×C7311yescharacteristic
484#124—21no—
485#124—21no—
486#124—21no—
487#124—21no—
488C4×Q8D4×C7311yescharacteristic
489C4×Q8D4×C7311yescharacteristic
490C4×D4—21no—
491C4×D4—21no—
492C4×D4—21no—
493C4×D4—21no—
494C4×D4—21no—
495C4×D4—21no—
496C4×D4D4×C7311yescharacteristic
497C4×D4D4×C7311yescharacteristic
498#117—21no—
499#117C23×C7311yescharacteristic
500C2×C4⋊C4C23×C7311yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C42—21no—
505C2×C42C23×C7311yescharacteristic
506#108—22no—
507#108—22no—
508#107—21no—
509#106—21no—
510C4⋊C8—21no—
511C4⋊C8—21no—
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516C4⋊C8—21no—
517C4⋊C8—21no—
518C4⋊C8D4×C7311yescharacteristic
519C4⋊C8D4×C7311yescharacteristic
520C4⋊C8D4×C7311yescharacteristic
521C4⋊C8D4×C7311yescharacteristic
522#103—21no—
523#103—21no—
524#103—21no—
525#103—21no—
526#103—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530#102—21no—
531#102—21no—
532#102—21no—
533#102—21no—
534#101—22no—
535#101—41no—
536#100—22no—
537#100—22no—
538#100—22no—
539#100—41no—
540#97—21no—
541C4×C8—21no—
542C24—21no—
543C24—21no—
544#41—21no—
545#41—21no—
546#41C2×D4×C7312yes—
547#41#41×C7312yes—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8—21no—
554C2×Q8C2×D4×C7311yescharacteristic
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—21no—
567C2×D4C2×D4×C7312yes—
568C2×D4C2×D4×C7311yescharacteristic
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—41no—
575C22×C4—41no—
576C22×C4—82no—
577C22×C4#41×C7311yescharacteristic
578C22×C4#41×C7311yescharacteristic
579C22×C4C24×C7311yescharacteristic
580Q16—42no—
581SD16—24no—
582SD16—42no—
583SD16—42no—
584SD16—42no—
585SD16—42no—
586D8—24no—
587D8—42no—
588D8—42no—
589D8—42no—
590M16—21no—
591M16—21no—
592M16—21no—
593M16—21no—
594M16—21no—
595M16—21no—
596M16—21no—
597M16—21no—
598M16—21no—
599M16—21no—
600M16—21no—
601M16—42no—
602M16—42no—
603M16C2×D4×C7312yes—
604C2×C8—21no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—21no—
613C2×C8—21no—
614C2×C8—42no—
615C2×C8—42no—
616C2×C8C2×D4×C7311yescharacteristic
617C2×C8C2×D4×C7311yescharacteristic
618C2×C8C2×D4×C7311yescharacteristic
619C2×C8C2×D4×C7311yescharacteristic
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4C2×D4×C7311yescharacteristic
625C4⋊C4C2×D4×C7311yescharacteristic
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—41no—
630C22⋊C4—41no—
631C22⋊C4—41no—
632C22⋊C4—41no—
633C22⋊C4—41no—
634C22⋊C4—41no—
635C42—21no—
636C42—21no—
637C42—21no—
638C42C2×D4×C7311yescharacteristic
639C42C2×D4×C7311yescharacteristic
640C42C2×D4×C7311yescharacteristic
641C42C2×D4×C7311yescharacteristic
642C23—21no—
643C23—22no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—81no—
652C23—81no—
653C23C2×#41×C7311yescharacteristic
654Q8—21no—
655Q8—41no—
656Q8—41no—
657Q8—41no—
658Q8—41no—
659Q8#121×C7312yes—
660D4—22no—
661D4—22no—
662D4—22no—
663D4—21no—
664D4—22no—
665D4—41no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—41no—
670D4—41no—
671D4#121×C7312yes—
672C2×C4—21no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—42no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—81no—
685C2×C4—82no—
686C2×C4—82no—
687C2×C4—81no—
688C2×C4#121×C7311yescharacteristic
689C2×C4#121×C7311yescharacteristic
690C2×C4#121×C7311yescharacteristic
691C2×C4#121×C7311yescharacteristic
692C2×C4C22×D4×C7311yescharacteristic
693C2×C4C22×D4×C7311yescharacteristic
694C2×C4C22×D4×C7311yescharacteristic
695C2×C4C2×#41×C7311yescharacteristic
696C2×C4H(5,𝔽2)×C7311yescharacteristic
697C2×C42−1+4×C7311yescharacteristic
698C8—22no—
699C8—21no—
700C8—21no—
701C8—21no—
702C8—21no—
703C8—41no—
704C8—41no—
705C8—41no—
706C8—41no—
707C8—41no—
708C22—21no—
709C22—21no—
710C22—22no—
711C22—41no—
712C22—41no—
713C22—42no—
714C22—82no—
715C22—82no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—161no—
722C22—161no—
723C22C2×#121×C7311yescharacteristic
724C22#547×C7311yescharacteristic
725C22#553×C7311yescharacteristic
726C4—21no—
727C4—21no—
728C4—21no—
729C4—21no—
730C4—22no—
731C4—41no—
732C4—41no—
733C4—81no—
734C4—81no—
735C4C2×#121×C7311yescharacteristic
736C4#537×C7311yescharacteristic
737C4D42×C7311yescharacteristic
738C4#548×C7311yescharacteristic
739C2—21no—
740C2—21no—
741C2—42no—
742C2—82no—
743C2—161no—
744C2C73×#241611yescharacteristic
745C2C73×#306711yescharacteristic
746C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×#472×C73C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#471×C73C2semidirect
3. C73×#3040C2semidirect
4. C2×#463×C73C2semidirect
5. C4×AGL(1,ℤ/8)×C73C2semidirect
6. C73×#2906C2semidirect
7. C73×#2064C2semidirect
8. C73×#2063C2semidirect
9. C73×#2046C2semidirect
10. C73×#2045C2semidirect
11. C73×#1967C2semidirect
12. C73×#1950C2semidirect
13. C73×#1908C2semidirect
14. C73×#1907C2semidirect
15. C73×#1800C2semidirect
365. #24774C73direct (N × H)
375. C2×#471C2×C73semidirect
376. #3040C2×C73semidirect
377. C2×#463C2×C73semidirect
378. C4×AGL(1,ℤ/8)C2×C73semidirect
379. #2906C2×C73semidirect
380. #2064C2×C73semidirect
381. #2063C2×C73semidirect
382. #2046C2×C73semidirect
383. #2045C2×C73semidirect
384. #1967C2×C73semidirect
385. #1950C2×C73semidirect
386. #1908C2×C73semidirect
387. #1907C2×C73semidirect
388. #1800C2×C73semidirect
389. C73#24774direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#472×C732
C2×#471×C732
C73×#30402
C2×#463×C732
C4×AGL(1,ℤ/8)×C732
C73×#29062
C73×#20642
C73×#20632
C73×#20462
C73×#20452
C73×#19672
C73×#19502
C73×#19082
C73×#19072
C73×#18002
#2477473