Finite Group Databasebeta

← C73×#24674 #32934078

Subgroups — C73×#24674 #32934078

Order 18688.

796 conjugacy classes of subgroups.

The subgroup lattice has 728 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3040C211yesmaximal, characteristic, complemented
2C2×#463×C73C211yesmaximal, characteristic, complemented
3C4×AGL(1,ℤ/8)×C73C211yesmaximal, characteristic, complemented
4C73×#2925C211yesmaximal, characteristic, complemented
5C73×#2052C211yesmaximal, characteristic, complemented
6C73×#2051C211yesmaximal, characteristic, complemented
7C73×#2019C211yesmaximal, characteristic, complemented
8C73×#2018C211yesmaximal, characteristic
9C73×#1978C211yesmaximal, characteristic, complemented
10C73×#1977C211yesmaximal, characteristic, complemented
11C73×#1967C211yesmaximal, characteristic, complemented
12C73×#1950C211yesmaximal, characteristic, complemented
13C73×#1931C211yesmaximal, characteristic, complemented
14C73×#1930C211yesmaximal, 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×#124×C73C2211yescharacteristic
22C4×#41×C73C2211yescharacteristic
23C2×C4×D4×C73C2211yescharacteristic
24#464×C73—21no—
25#464×C73—21no—
26#463×C73—21no—
27#463×C73—21no—
28#463×C73—21no—
29#463×C73—21no—
30#463×C73—21no—
31#463×C73—21no—
32#442×C73—21no—
33#440×C73—21no—
34C4×SD16×C73—21no—
35C4×D8×C73—21no—
36#433×C73—21no—
37#433×C73—21no—
38#432×C73—21no—
39#431×C73—21no—
40C2×#108×C73C2211yescharacteristic
41C2×#108×C73C2211yescharacteristic
42#428×C73C2211yescharacteristic
43#423×C73C2211yescharacteristic
44#423×C73C2211yescharacteristic
45C2×C4⋊C8×C73C2211yescharacteristic
46#419×C73C2211yescharacteristic
47#418×C73C2211yescharacteristic
48#418×C73C2211yescharacteristic
49#417×C73C2211yescharacteristic
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#408×C73C2211yescharacteristic
59#408×C73C2211yescharacteristic
60#405×C73C2211yescharacteristic
61#405×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#343×C73C2211yescharacteristic
64#343×C73C2211yescharacteristic
65#341×C73C2211yescharacteristic
66#341×C73C2211yescharacteristic
67C2×#41×C73C2311yescharacteristic
68C22×Q8×C73C2311yescharacteristic
69C22×D4×C73C2311yescharacteristic
70C22×D4×C73C2311yescharacteristic
71C23×C4×C73—21no—
72#137×C73—41no—
73#137×C73—41no—
74AGL(1,ℤ/8)×C73—22no—
75AGL(1,ℤ/8)×C73—22no—
76AGL(1,ℤ/8)×C73—41no—
77AGL(1,ℤ/8)×C73—41no—
78C2×Q16×C73—21no—
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×SD16×C73—21no—
82C2×SD16×C73—22no—
83C2×SD16×C73—21no—
84C2×SD16×C73—21no—
85C2×SD16×C73—41no—
86C2×D8×C73—21no—
87C2×D8×C73—21no—
88C2×D8×C73—22no—
89C2×D8×C73—21no—
90C2×D8×C73—21no—
91C2×D8×C73—41no—
92C2×M16×C73C2311yescharacteristic
93C2×M16×C73C2311yescharacteristic
94C2×M16×C73C2311yescharacteristic
95C2×M16×C73C2311yescharacteristic
96C2×M16×C73C2311yescharacteristic
97C2×M16×C73C2311yescharacteristic
98C22×C8×C73C2311yescharacteristic
99C22×C8×C73C2311yescharacteristic
100#124×C73—21no—
101#124×C73—21no—
102#124×C73—21no—
103#124×C73—21no—
104C4×Q8×C73D411yescharacteristic
105C4×Q8×C73D411yescharacteristic
106C4×D4×C73—21no—
107C4×D4×C73—21no—
108C4×D4×C73—21no—
109C4×D4×C73—21no—
110C4×D4×C73—21no—
111C4×D4×C73—21no—
112C4×D4×C73D411yescharacteristic
113C4×D4×C73D411yescharacteristic
114#117×C73—21no—
115#117×C73C2311yescharacteristic
116C2×C4⋊C4×C73C2311yescharacteristic
117C2×C22⋊C4×C73—21no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C42×C73—21no—
121C2×C42×C73C2311yescharacteristic
122#108×C73—41no—
123#108×C73—41no—
124#107×C73—21no—
125#106×C73—21no—
126C4⋊C8×C73—21no—
127C4⋊C8×C73—21no—
128C4⋊C8×C73—21no—
129C4⋊C8×C73—21no—
130C4⋊C8×C73D411yescharacteristic
131C4⋊C8×C73D411yescharacteristic
132C4⋊C8×C73D411yescharacteristic
133C4⋊C8×C73D411yescharacteristic
134#103×C73—21no—
135#103×C73—21no—
136#103×C73—21no—
137#103×C73—21no—
138#103×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#101×C73—22no—
147#101×C73—41no—
148#100×C73—22no—
149#100×C73—41no—
150#100×C73—41no—
151#100×C73—41no—
152C22⋊C8×C73—21no—
153C22⋊C8×C73—21no—
154C22⋊C8×C73—21no—
155C22⋊C8×C73—21no—
156#97×C73—21no—
157#97×C73—21no—
158#97×C73—21no—
159C4×C8×C73—21no—
160C4×C8×C73—21no—
161C4×C8×C73—21no—
162C24×C73—21no—
163C24×C73—21no—
164#41×C73—21no—
165#41×C73—21no—
166#41×C73—21no—
167#41×C73—21no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—21no—
171C2×Q8×C73—21no—
172C2×Q8×C73—21no—
173C2×Q8×C73—21no—
174C2×Q8×C73C2×D411yescharacteristic
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—21no—
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×C73C2×D411yescharacteristic
188C2×D4×C73#4112yes—
189C22×C4×C73—21no—
190C22×C4×C73—21no—
191C22×C4×C73—21no—
192C22×C4×C73—21no—
193C22×C4×C73—21no—
194C22×C4×C73—41no—
195C22×C4×C73—41no—
196C22×C4×C73—82no—
197C22×C4×C73#4111yescharacteristic
198C22×C4×C73#4111yescharacteristic
199C22×C4×C73C2411yescharacteristic
200Q16×C73—42no—
201SD16×C73—24no—
202SD16×C73—42no—
203SD16×C73—42no—
204SD16×C73—42no—
205SD16×C73—42no—
206D8×C73—24no—
207D8×C73—42no—
208D8×C73—42no—
209D8×C73—42no—
210M16×C73—21no—
211M16×C73—21no—
212M16×C73—21no—
213M16×C73—21no—
214M16×C73—21no—
215M16×C73—21no—
216M16×C73—21no—
217M16×C73—21no—
218M16×C73—21no—
219M16×C73—21no—
220M16×C73—21no—
221M16×C73#4112yes—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C2×C8×C73—21no—
232C2×C8×C73C2×D411yescharacteristic
233C2×C8×C73C2×D411yescharacteristic
234C2×C8×C73C2×D411yescharacteristic
235C2×C8×C73C2×D411yescharacteristic
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73C2×D411yescharacteristic
241C4⋊C4×C73C2×D411yescharacteristic
242C22⋊C4×C73—21no—
243C22⋊C4×C73—21no—
244C22⋊C4×C73—21no—
245C22⋊C4×C73—41no—
246C22⋊C4×C73—41no—
247C22⋊C4×C73—41no—
248C22⋊C4×C73—41no—
249C22⋊C4×C73—41no—
250C22⋊C4×C73—41no—
251C42×C73—21no—
252C42×C73—21no—
253C42×C73—21no—
254C42×C73C2×D411yescharacteristic
255C42×C73C2×D411yescharacteristic
256C42×C73C2×D411yescharacteristic
257C42×C73C2×D411yescharacteristic
258C23×C73—21no—
259C23×C73—22no—
260C23×C73—41no—
261C23×C73—41no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—81no—
266C23×C73—81no—
267C23×C73—81no—
268C23×C73—81no—
269C23×C73C2×#4111yescharacteristic
270Q8×C73—21no—
271Q8×C73—21no—
272Q8×C73—41no—
273Q8×C73—41no—
274Q8×C73—41no—
275Q8×C73—41no—
276D4×C73—21no—
277D4×C73—22no—
278D4×C73—21no—
279D4×C73—22no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—41no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—41no—
292C2×C4×C73—41no—
293C2×C4×C73—42no—
294C2×C4×C73—41no—
295C2×C4×C73—41no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—81no—
301C2×C4×C73—82no—
302C2×C4×C73—82no—
303C2×C4×C73—81no—
304C2×C4×C73#12111yescharacteristic
305C2×C4×C73#12111yescharacteristic
306C2×C4×C73#12111yescharacteristic
307C2×C4×C73#12111yescharacteristic
308C2×C4×C73C22×D411yescharacteristic
309C2×C4×C73C22×D411yescharacteristic
310C2×C4×C73C2×#4111yescharacteristic
311C2×C4×C73C2×#4111yescharacteristic
312C2×C4×C73H(5,𝔽2)11yescharacteristic
313C2×C4×C73H(5,𝔽2)11yescharacteristic
314C8×C73—22no—
315C8×C73—21no—
316C8×C73—21no—
317C8×C73—21no—
318C8×C73—21no—
319C8×C73—41no—
320C8×C73—41no—
321C8×C73—41no—
322C8×C73—41no—
323C8×C73—41no—
324C22×C73—21no—
325C22×C73—21no—
326C22×C73—41no—
327C22×C73—42no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73—82no—
331C22×C73—82no—
332C22×C73—81no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—161no—
338C22×C73—161no—
339C22×C73C2×#12111yescharacteristic
340C22×C73#55311yescharacteristic
341C22×C73#55511yescharacteristic
342C4×C73—21no—
343C4×C73—21no—
344C4×C73—21no—
345C4×C73—21no—
346C4×C73—41no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—81no—
350C4×C73—81no—
351C4×C73#52511yescharacteristic
352C4×C73#53511yescharacteristic
353C4×C73#54611yescharacteristic
354C4×C73#55011yescharacteristic
355#24674C7311yesmaximal, characteristic, direct product factor, Sylow
356C2×C73—21no—
357C2×C73—21no—
358C2×C73—81no—
359C2×C73—82no—
360C2×C73—161no—
361C2×C73#241411yescharacteristic
362C2×C73#306711yescharacteristic
363C2×C73#306811yescharacteristic
364#3040C2×C7311yescharacteristic, complemented
365C2×#463C2×C7311yescharacteristic, complemented
366C4×AGL(1,ℤ/8)C2×C7311yescharacteristic, complemented
367#2925C2×C7311yescharacteristic, complemented
368#2052C2×C7311yescharacteristic, complemented
369#2051C2×C7311yescharacteristic, complemented
370#2019C2×C7311yescharacteristic, complemented
371#2018C2×C7311yescharacteristic
372#1978C2×C7311yescharacteristic, complemented
373#1977C2×C7311yescharacteristic, complemented
374#1967C2×C7311yescharacteristic, complemented
375#1950C2×C7311yescharacteristic, complemented
376#1931C2×C7311yescharacteristic, complemented
377#1930C2×C7311yescharacteristic, complemented
378#1800C2×C7311yescharacteristic, complemented
379C73#2467411yescharacteristic, direct product factor, Sylow
380C2×#137C22×C7311yescharacteristic
381C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
382C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
383C22×SD16C22×C7311yescharacteristic
384C22×D8C22×C7311yescharacteristic
385C2×#124C22×C7311yescharacteristic
386C4×#41C22×C7311yescharacteristic
387C2×C4×D4C22×C7311yescharacteristic
388#464—21no—
389#464—21no—
390#463—21no—
391#463—21no—
392#463—21no—
393#463—21no—
394#463—21no—
395#463—21no—
396#442—21no—
397#440—21no—
398C4×SD16—21no—
399C4×D8—21no—
400#433—21no—
401#433—21no—
402#432—21no—
403#431—21no—
404C2×#108C22×C7311yescharacteristic
405C2×#108C22×C7311yescharacteristic
406#428C22×C7311yescharacteristic
407#423C22×C7311yescharacteristic
408#423C22×C7311yescharacteristic
409C2×C4⋊C8C22×C7311yescharacteristic
410#419C22×C7311yescharacteristic
411#418C22×C7311yescharacteristic
412#418C22×C7311yescharacteristic
413#417C22×C7311yescharacteristic
414C2×#103C22×C7311yescharacteristic
415C2×#102C22×C7311yescharacteristic
416C2×#101C22×C7311yescharacteristic
417C2×#101C22×C7311yescharacteristic
418C2×#100C22×C7311yescharacteristic
419C2×#100C22×C7311yescharacteristic
420C2×#100C22×C7311yescharacteristic
421C2×#100C22×C7311yescharacteristic
422#408C22×C7311yescharacteristic
423#408C22×C7311yescharacteristic
424#405C22×C7311yescharacteristic
425#405C22×C7311yescharacteristic
426C4×M16C22×C7311yescharacteristic
427#343C22×C7311yescharacteristic
428#343C22×C7311yescharacteristic
429#341C22×C7311yescharacteristic
430#341C22×C7311yescharacteristic
431C2×#41C23×C7311yescharacteristic
432C22×Q8C23×C7311yescharacteristic
433C22×D4C23×C7311yescharacteristic
434C22×D4C23×C7311yescharacteristic
435C23×C4—21no—
436#137—41no—
437#137—41no—
438AGL(1,ℤ/8)—22no—
439AGL(1,ℤ/8)—22no—
440AGL(1,ℤ/8)—41no—
441AGL(1,ℤ/8)—41no—
442C2×Q16—21no—
443C2×SD16—21no—
444C2×SD16—21no—
445C2×SD16—21no—
446C2×SD16—22no—
447C2×SD16—21no—
448C2×SD16—21no—
449C2×SD16—41no—
450C2×D8—21no—
451C2×D8—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×D8—21no—
455C2×D8—41no—
456C2×M16C23×C7311yescharacteristic
457C2×M16C23×C7311yescharacteristic
458C2×M16C23×C7311yescharacteristic
459C2×M16C23×C7311yescharacteristic
460C2×M16C23×C7311yescharacteristic
461C2×M16C23×C7311yescharacteristic
462C22×C8C23×C7311yescharacteristic
463C22×C8C23×C7311yescharacteristic
464#124—21no—
465#124—21no—
466#124—21no—
467#124—21no—
468C4×Q8D4×C7311yescharacteristic
469C4×Q8D4×C7311yescharacteristic
470C4×D4—21no—
471C4×D4—21no—
472C4×D4—21no—
473C4×D4—21no—
474C4×D4—21no—
475C4×D4—21no—
476C4×D4D4×C7311yescharacteristic
477C4×D4D4×C7311yescharacteristic
478#117—21no—
479#117C23×C7311yescharacteristic
480C2×C4⋊C4C23×C7311yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C42—21no—
485C2×C42C23×C7311yescharacteristic
486#108—41no—
487#108—41no—
488#107—21no—
489#106—21no—
490C4⋊C8—21no—
491C4⋊C8—21no—
492C4⋊C8—21no—
493C4⋊C8—21no—
494C4⋊C8D4×C7311yescharacteristic
495C4⋊C8D4×C7311yescharacteristic
496C4⋊C8D4×C7311yescharacteristic
497C4⋊C8D4×C7311yescharacteristic
498#103—21no—
499#103—21no—
500#103—21no—
501#103—21no—
502#103—21no—
503#102—21no—
504#102—21no—
505#102—21no—
506#102—21no—
507#102—21no—
508#102—21no—
509#102—21no—
510#101—22no—
511#101—41no—
512#100—22no—
513#100—41no—
514#100—41no—
515#100—41no—
516C22⋊C8—21no—
517C22⋊C8—21no—
518C22⋊C8—21no—
519C22⋊C8—21no—
520#97—21no—
521#97—21no—
522#97—21no—
523C4×C8—21no—
524C4×C8—21no—
525C4×C8—21no—
526C24—21no—
527C24—21no—
528#41—21no—
529#41—21no—
530#41—21no—
531#41—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8C2×D4×C7311yescharacteristic
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4C2×D4×C7311yescharacteristic
552C2×D4#41×C7312yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—41no—
559C22×C4—41no—
560C22×C4—82no—
561C22×C4#41×C7311yescharacteristic
562C22×C4#41×C7311yescharacteristic
563C22×C4C24×C7311yescharacteristic
564Q16—42no—
565SD16—24no—
566SD16—42no—
567SD16—42no—
568SD16—42no—
569SD16—42no—
570D8—24no—
571D8—42no—
572D8—42no—
573D8—42no—
574M16—21no—
575M16—21no—
576M16—21no—
577M16—21no—
578M16—21no—
579M16—21no—
580M16—21no—
581M16—21no—
582M16—21no—
583M16—21no—
584M16—21no—
585M16#41×C7312yes—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8C2×D4×C7311yescharacteristic
597C2×C8C2×D4×C7311yescharacteristic
598C2×C8C2×D4×C7311yescharacteristic
599C2×C8C2×D4×C7311yescharacteristic
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4C2×D4×C7311yescharacteristic
605C4⋊C4C2×D4×C7311yescharacteristic
606C22⋊C4—21no—
607C22⋊C4—21no—
608C22⋊C4—21no—
609C22⋊C4—41no—
610C22⋊C4—41no—
611C22⋊C4—41no—
612C22⋊C4—41no—
613C22⋊C4—41no—
614C22⋊C4—41no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42C2×D4×C7311yescharacteristic
619C42C2×D4×C7311yescharacteristic
620C42C2×D4×C7311yescharacteristic
621C42C2×D4×C7311yescharacteristic
622C23—21no—
623C23—22no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—81no—
630C23—81no—
631C23—81no—
632C23—81no—
633C23C2×#41×C7311yescharacteristic
634Q8—21no—
635Q8—21no—
636Q8—41no—
637Q8—41no—
638Q8—41no—
639Q8—41no—
640D4—21no—
641D4—22no—
642D4—21no—
643D4—22no—
644D4—41no—
645D4—41no—
646D4—41no—
647D4—41no—
648D4—41no—
649D4—41no—
650D4—41no—
651D4—41no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—42no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—81no—
665C2×C4—82no—
666C2×C4—82no—
667C2×C4—81no—
668C2×C4#121×C7311yescharacteristic
669C2×C4#121×C7311yescharacteristic
670C2×C4#121×C7311yescharacteristic
671C2×C4#121×C7311yescharacteristic
672C2×C4C22×D4×C7311yescharacteristic
673C2×C4C22×D4×C7311yescharacteristic
674C2×C4C2×#41×C7311yescharacteristic
675C2×C4C2×#41×C7311yescharacteristic
676C2×C4H(5,𝔽2)×C7311yescharacteristic
677C2×C4H(5,𝔽2)×C7311yescharacteristic
678C8—22no—
679C8—21no—
680C8—21no—
681C8—21no—
682C8—21no—
683C8—41no—
684C8—41no—
685C8—41no—
686C8—41no—
687C8—41no—
688C22—21no—
689C22—21no—
690C22—41no—
691C22—41no—
692C22—41no—
693C22—42no—
694C22—82no—
695C22—82no—
696C22—81no—
697C22—81no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—161no—
702C22—161no—
703C22C2×#121×C7311yescharacteristic
704C22#553×C7311yescharacteristic
705C22#555×C7311yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—81no—
714C4—81no—
715C4#525×C7311yescharacteristic
716C4#535×C7311yescharacteristic
717C4#546×C7311yescharacteristic
718C4#550×C7311yescharacteristic
719C2—21no—
720C2—21no—
721C2—81no—
722C2—82no—
723C2—161no—
724C2C73×#241411yescharacteristic
725C2C73×#306711yescharacteristic
726C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2018C2
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
1. C73×#3040C2semidirect
2. C2×#463×C73C2semidirect
3. C4×AGL(1,ℤ/8)×C73C2semidirect
4. C73×#2925C2semidirect
5. C73×#2052C2semidirect
6. C73×#2051C2semidirect
7. C73×#2019C2semidirect
9. C73×#1978C2semidirect
10. C73×#1977C2semidirect
11. C73×#1967C2semidirect
12. C73×#1950C2semidirect
13. C73×#1931C2semidirect
14. C73×#1930C2semidirect
15. C73×#1800C2semidirect
355. #24674C73direct (N × H)
364. #3040C2×C73semidirect
365. C2×#463C2×C73semidirect
366. C4×AGL(1,ℤ/8)C2×C73semidirect
367. #2925C2×C73semidirect
368. #2052C2×C73semidirect
369. #2051C2×C73semidirect
370. #2019C2×C73semidirect
372. #1978C2×C73semidirect
373. #1977C2×C73semidirect
374. #1967C2×C73semidirect
375. #1950C2×C73semidirect
376. #1931C2×C73semidirect
377. #1930C2×C73semidirect
378. #1800C2×C73semidirect
379. C73#24674direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#30402
C2×#463×C732
C4×AGL(1,ℤ/8)×C732
C73×#29252
C73×#20522
C73×#20512
C73×#20192
C73×#20182
C73×#19782
C73×#19772
C73×#19672
C73×#19502
C73×#19312
C73×#19302
C73×#18002
#2467473