Finite Group Databasebeta

← C73×#24775 #32934179

Subgroups — C73×#24775 #32934179

Order 18688.

850 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
1C2×#473×C73C211yesmaximal, characteristic, complemented
2C2×#471×C73C211yesmaximal, characteristic
3C73×#3040C211yesmaximal, characteristic
4C2×#464×C73C211yesmaximal, characteristic, complemented
5C4×#137×C73C211yesmaximal, characteristic, complemented
6C73×#2906C211yesmaximal, characteristic, complemented
7C73×#2064C211yesmaximal, characteristic, complemented
8C73×#2063C211yesmaximal, characteristic, complemented
9C73×#2047C211yesmaximal, characteristic, complemented
10C73×#2046C211yesmaximal, characteristic, complemented
11C73×#1967C211yesmaximal, characteristic, complemented
12C73×#1950C211yesmaximal, characteristic, complemented
13C73×#1908C211yesmaximal, characteristic, complemented
14C73×#1907C211yesmaximal, characteristic
15C73×#1801C211yesmaximal, characteristic, complemented
16C2×#137×C73C2211yescharacteristic
17C2×#137×C73C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C22×Q16×C73C2211yescharacteristic
20C22×SD16×C73C2211yescharacteristic
21C2×#131×C73C2211yescharacteristic
22C2×#131×C73C2211yescharacteristic
23C2×#124×C73C2211yescharacteristic
24C4×#41×C73C2211yescharacteristic
25C2×C4×Q8×C73C2211yescharacteristic
26#473×C73—24no—
27#471×C73—24no—
28#464×C73—21no—
29#464×C73—21no—
30#464×C73—21no—
31#464×C73—21no—
32#464×C73—21no—
33#464×C73—21no—
34#463×C73—21no—
35#463×C73—21no—
36#441×C73—21no—
37#440×C73—21no—
38C4×Q16×C73—21no—
39C4×SD16×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#419×C73C2211yescharacteristic
54#418×C73C2211yescharacteristic
55#417×C73C2211yescharacteristic
56C2×#103×C73C2211yescharacteristic
57C2×#102×C73C2211yescharacteristic
58C2×#101×C73C2211yescharacteristic
59C2×#101×C73C2211yescharacteristic
60C2×#101×C73C2211yescharacteristic
61C2×#101×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×Q8×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73#137×C73—22no—
74#137×C73—22no—
75#137×C73—22no—
76#137×C73D414yes—
77AGL(1,ℤ/8)×C73—22no—
78AGL(1,ℤ/8)×C73—22no—
79C2×Q16×C73—21no—
80C2×Q16×C73—21no—
81C2×Q16×C73—22no—
82C2×Q16×C73—21no—
83C2×Q16×C73—21no—
84C2×Q16×C73—41no—
85C2×SD16×C73—21no—
86C2×SD16×C73—21no—
87C2×SD16×C73—22no—
88C2×SD16×C73—21no—
89C2×SD16×C73—21no—
90C2×SD16×C73—21no—
91C2×SD16×C73—41no—
92C2×D8×C73—21no—
93#131×C73—22no—
94#131×C73—22no—
95#131×C73—41no—
96#131×C73—41no—
97C2×M16×C73—21no—
98C2×M16×C73—21no—
99C2×M16×C73C2311yescharacteristic
100C2×M16×C73C2311yescharacteristic
101C2×M16×C73C2311yescharacteristic
102C2×M16×C73C2311yescharacteristic
103C2×M16×C73C2311yescharacteristic
104C2×M16×C73C2311yescharacteristic
105C22×C8×C73—21no—
106C22×C8×C73—21no—
107C22×C8×C73C2311yescharacteristic
108C22×C8×C73C2311yescharacteristic
109#124×C73—21no—
110#124×C73—21no—
111#124×C73—21no—
112#124×C73—21no—
113C4×Q8×C73—21no—
114C4×Q8×C73—21no—
115C4×Q8×C73—21no—
116C4×Q8×C73—21no—
117C4×Q8×C73D411yescharacteristic
118C4×Q8×C73D411yescharacteristic
119C4×D4×C73—21no—
120C4×D4×C73—21no—
121C4×D4×C73D411yescharacteristic
122C4×D4×C73D411yescharacteristic
123#117×C73—21no—
124#117×C73C2311yescharacteristic
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73C2311yescharacteristic
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C42×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#103×C73—21no—
154#103×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—22no—
162#101×C73—22no—
163#101×C73—41no—
164#100×C73—22no—
165#100×C73—41no—
166#97×C73—21no—
167C4×C8×C73—21no—
168C24×C73—21no—
169#41×C73—21no—
170#41×C73—21no—
171#41×C73C2×D412yes—
172#41×C73#4112yes—
173C2×Q8×C73—21no—
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×C73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73C2×D412yes—
185C2×Q8×C73C2×D411yescharacteristic
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×D411yescharacteristic
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—21no—
199C22×C4×C73—21no—
200C22×C4×C73#4111yescharacteristic
201C22×C4×C73#4111yescharacteristic
202C22×C4×C73C2411yescharacteristic
203Q16×C73—24no—
204Q16×C73—42no—
205Q16×C73—42no—
206Q16×C73—42no—
207SD16×C73—24no—
208SD16×C73—42no—
209SD16×C73—42no—
210SD16×C73—42no—
211SD16×C73—42no—
212D8×C73—42no—
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—21no—
222M16×C73—21no—
223M16×C73—21no—
224M16×C73—42no—
225M16×C73—42no—
226M16×C73C2×D412yes—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
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—42no—
238C2×C8×C73—42no—
239C2×C8×C73C2×D411yescharacteristic
240C2×C8×C73C2×D411yescharacteristic
241C2×C8×C73C2×D411yescharacteristic
242C2×C8×C73C2×D411yescharacteristic
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—41no—
248C4⋊C4×C73—41no—
249C4⋊C4×C73C2×D411yescharacteristic
250C4⋊C4×C73C2×D411yescharacteristic
251C22⋊C4×C73—21no—
252C22⋊C4×C73—21no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—41no—
255C22⋊C4×C73—41no—
256C22⋊C4×C73—41no—
257C22⋊C4×C73—41no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—41no—
262C42×C73—41no—
263C42×C73C2×D411yescharacteristic
264C42×C73C2×D411yescharacteristic
265C42×C73C2×D411yescharacteristic
266C42×C73C2×D411yescharacteristic
267C23×C73—21no—
268C23×C73—41no—
269C23×C73—41no—
270C23×C73—41no—
271C23×C73—81no—
272C23×C73—81no—
273C23×C73C2×#4111yescharacteristic
274Q8×C73—21no—
275Q8×C73—22no—
276Q8×C73—22no—
277Q8×C73—41no—
278Q8×C73—41no—
279Q8×C73—41no—
280Q8×C73—41no—
281Q8×C73—41no—
282Q8×C73—41no—
283Q8×C73#12112yes—
284D4×C73—22no—
285D4×C73—22no—
286D4×C73—21no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73#12112yes—
292C2×C4×C73—21no—
293C2×C4×C73—22no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—22no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—42no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—81no—
308C2×C4×C73—81no—
309C2×C4×C73#12111yescharacteristic
310C2×C4×C73#12111yescharacteristic
311C2×C4×C73#12111yescharacteristic
312C2×C4×C73#12111yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C22×D411yescharacteristic
315C2×C4×C73C22×D411yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×C4×C73H(5,𝔽2)11yescharacteristic
318C2×C4×C732−1+411yescharacteristic
319C8×C73—22no—
320C8×C73—21no—
321C8×C73—21no—
322C8×C73—21no—
323C8×C73—21no—
324C8×C73—41no—
325C8×C73—41no—
326C8×C73—41no—
327C8×C73—41no—
328C8×C73—41no—
329C22×C73—21no—
330C22×C73—21no—
331C22×C73—22no—
332C22×C73—41no—
333C22×C73—41no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—161no—
338C22×C73—161no—
339C22×C73C2×#12111yescharacteristic
340C22×C73#54711yescharacteristic
341C22×C73#55311yescharacteristic
342C4×C73—22no—
343C4×C73—21no—
344C4×C73—21no—
345C4×C73—21no—
346C4×C73—21no—
347C4×C73—42no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—81no—
351C4×C73—81no—
352C4×C73C2×#12111yescharacteristic
353C4×C73#53711yescharacteristic
354C4×C73D4211yescharacteristic
355C4×C73#54811yescharacteristic
356#24775C7311yesmaximal, characteristic, direct product factor, Sylow
357C2×C73—21no—
358C2×C73—21no—
359C2×C73—42no—
360C2×C73—161no—
361C2×C73#241611yescharacteristic
362C2×C73#306711yescharacteristic
363C2×C73#306911yescharacteristic
364C2×#473C2×C7311yescharacteristic, complemented
365C2×#471C2×C7311yescharacteristic
366#3040C2×C7311yescharacteristic
367C2×#464C2×C7311yescharacteristic, complemented
368C4×#137C2×C7311yescharacteristic, complemented
369#2906C2×C7311yescharacteristic, complemented
370#2064C2×C7311yescharacteristic, complemented
371#2063C2×C7311yescharacteristic, complemented
372#2047C2×C7311yescharacteristic, complemented
373#2046C2×C7311yescharacteristic, complemented
374#1967C2×C7311yescharacteristic, complemented
375#1950C2×C7311yescharacteristic, complemented
376#1908C2×C7311yescharacteristic, complemented
377#1907C2×C7311yescharacteristic
378#1801C2×C7311yescharacteristic, complemented
379C73#2477511yescharacteristic, direct product factor, Sylow
380C2×#137C22×C7311yescharacteristic
381C2×#137C22×C7311yescharacteristic
382C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
383C22×Q16C22×C7311yescharacteristic
384C22×SD16C22×C7311yescharacteristic
385C2×#131C22×C7311yescharacteristic
386C2×#131C22×C7311yescharacteristic
387C2×#124C22×C7311yescharacteristic
388C4×#41C22×C7311yescharacteristic
389C2×C4×Q8C22×C7311yescharacteristic
390#473—24no—
391#471—24no—
392#464—21no—
393#464—21no—
394#464—21no—
395#464—21no—
396#464—21no—
397#464—21no—
398#463—21no—
399#463—21no—
400#441—21no—
401#440—21no—
402C4×Q16—21no—
403C4×SD16—21no—
404C2×#108C22×C7311yescharacteristic
405C2×#108C22×C7311yescharacteristic
406#428C22×C7311yescharacteristic
407#424—21no—
408#424—21no—
409#424C22×C7311yescharacteristic
410#424C22×C7311yescharacteristic
411#423—21no—
412#423C22×C7311yescharacteristic
413#423C22×C7311yescharacteristic
414C2×C4⋊C8—21no—
415C2×C4⋊C8C22×C7311yescharacteristic
416#419C22×C7311yescharacteristic
417#419C22×C7311yescharacteristic
418#418C22×C7311yescharacteristic
419#417C22×C7311yescharacteristic
420C2×#103C22×C7311yescharacteristic
421C2×#102C22×C7311yescharacteristic
422C2×#101C22×C7311yescharacteristic
423C2×#101C22×C7311yescharacteristic
424C2×#101C22×C7311yescharacteristic
425C2×#101C22×C7311yescharacteristic
426C2×#100C22×C7311yescharacteristic
427C2×#100C22×C7311yescharacteristic
428C4×M16C22×C7311yescharacteristic
429#343C22×C7311yescharacteristic
430#343C22×C7311yescharacteristic
431#341C22×C7311yescharacteristic
432#341C22×C7311yescharacteristic
433C2×#41C23×C7311yescharacteristic
434C22×Q8C23×C7311yescharacteristic
435C22×Q8C23×C7311yescharacteristic
436C22×D4C23×C7311yescharacteristic
437#137—22no—
438#137—22no—
439#137—22no—
440#137D4×C7314yes—
441AGL(1,ℤ/8)—22no—
442AGL(1,ℤ/8)—22no—
443C2×Q16—21no—
444C2×Q16—22no—
445C2×Q16—21no—
446C2×Q16—21no—
447C2×Q16—21no—
448C2×Q16—41no—
449C2×SD16—21no—
450C2×SD16—22no—
451C2×SD16—21no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—21no—
455C2×SD16—41no—
456C2×D8—21no—
457#131—22no—
458#131—22no—
459#131—41no—
460#131—41no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16C23×C7311yescharacteristic
464C2×M16C23×C7311yescharacteristic
465C2×M16C23×C7311yescharacteristic
466C2×M16C23×C7311yescharacteristic
467C2×M16C23×C7311yescharacteristic
468C2×M16C23×C7311yescharacteristic
469C22×C8—21no—
470C22×C8—21no—
471C22×C8C23×C7311yescharacteristic
472C22×C8C23×C7311yescharacteristic
473#124—21no—
474#124—21no—
475#124—21no—
476#124—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8—21no—
481C4×Q8D4×C7311yescharacteristic
482C4×Q8D4×C7311yescharacteristic
483C4×D4—21no—
484C4×D4—21no—
485C4×D4D4×C7311yescharacteristic
486C4×D4D4×C7311yescharacteristic
487#117—21no—
488#117C23×C7311yescharacteristic
489C2×C4⋊C4—21no—
490C2×C4⋊C4C23×C7311yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C42—21no—
494C2×C42—21no—
495C2×C42C23×C7311yescharacteristic
496#108—22no—
497#108—22no—
498#107—21no—
499#106—21no—
500C4⋊C8—21no—
501C4⋊C8—21no—
502C4⋊C8—21no—
503C4⋊C8—21no—
504C4⋊C8—21no—
505C4⋊C8—21no—
506C4⋊C8—21no—
507C4⋊C8—21no—
508C4⋊C8D4×C7311yescharacteristic
509C4⋊C8D4×C7311yescharacteristic
510C4⋊C8D4×C7311yescharacteristic
511C4⋊C8D4×C7311yescharacteristic
512#103—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#101—22no—
525#101—22no—
526#101—22no—
527#101—41no—
528#100—22no—
529#100—41no—
530#97—21no—
531C4×C8—21no—
532C24—21no—
533#41—21no—
534#41—21no—
535#41C2×D4×C7312yes—
536#41#41×C7312yes—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8C2×D4×C7312yes—
549C2×Q8C2×D4×C7311yescharacteristic
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4C2×D4×C7311yescharacteristic
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4#41×C7311yescharacteristic
565C22×C4#41×C7311yescharacteristic
566C22×C4C24×C7311yescharacteristic
567Q16—24no—
568Q16—42no—
569Q16—42no—
570Q16—42no—
571SD16—24no—
572SD16—42no—
573SD16—42no—
574SD16—42no—
575SD16—42no—
576D8—42no—
577M16—21no—
578M16—21no—
579M16—21no—
580M16—21no—
581M16—21no—
582M16—21no—
583M16—21no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—42no—
589M16—42no—
590M16C2×D4×C7312yes—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—42no—
602C2×C8—42no—
603C2×C8C2×D4×C7311yescharacteristic
604C2×C8C2×D4×C7311yescharacteristic
605C2×C8C2×D4×C7311yescharacteristic
606C2×C8C2×D4×C7311yescharacteristic
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4C2×D4×C7311yescharacteristic
614C4⋊C4C2×D4×C7311yescharacteristic
615C22⋊C4—21no—
616C22⋊C4—21no—
617C22⋊C4—21no—
618C22⋊C4—41no—
619C22⋊C4—41no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C42—21no—
623C42—21no—
624C42—21no—
625C42—41no—
626C42—41no—
627C42C2×D4×C7311yescharacteristic
628C42C2×D4×C7311yescharacteristic
629C42C2×D4×C7311yescharacteristic
630C42C2×D4×C7311yescharacteristic
631C23—21no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—81no—
636C23—81no—
637C23C2×#41×C7311yescharacteristic
638Q8—21no—
639Q8—22no—
640Q8—22no—
641Q8—41no—
642Q8—41no—
643Q8—41no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8#121×C7312yes—
648D4—22no—
649D4—22no—
650D4—21no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4#121×C7312yes—
656C2×C4—21no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—42no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—81no—
672C2×C4—81no—
673C2×C4#121×C7311yescharacteristic
674C2×C4#121×C7311yescharacteristic
675C2×C4#121×C7311yescharacteristic
676C2×C4#121×C7311yescharacteristic
677C2×C4C22×D4×C7311yescharacteristic
678C2×C4C22×D4×C7311yescharacteristic
679C2×C4C22×D4×C7311yescharacteristic
680C2×C4C2×#41×C7311yescharacteristic
681C2×C4H(5,𝔽2)×C7311yescharacteristic
682C2×C42−1+4×C7311yescharacteristic
683C8—22no—
684C8—21no—
685C8—21no—
686C8—21no—
687C8—21no—
688C8—41no—
689C8—41no—
690C8—41no—
691C8—41no—
692C8—41no—
693C22—21no—
694C22—21no—
695C22—22no—
696C22—41no—
697C22—41no—
698C22—81no—
699C22—81no—
700C22—81no—
701C22—161no—
702C22—161no—
703C22C2×#121×C7311yescharacteristic
704C22#547×C7311yescharacteristic
705C22#553×C7311yescharacteristic
706C4—21no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—22no—
711C4—41no—
712C4—41no—
713C4—42no—
714C4—81no—
715C4—81no—
716C4C2×#121×C7311yescharacteristic
717C4#537×C7311yescharacteristic
718C4D42×C7311yescharacteristic
719C4#548×C7311yescharacteristic
720C2—21no—
721C2—21no—
722C2—42no—
723C2—161no—
724C2C73×#241611yescharacteristic
725C2C73×#306711yescharacteristic
726C2C73×#306911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC2×AGL(1,ℤ/8)×C73C22
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. C2×#473×C73C2semidirect
4. C2×#464×C73C2semidirect
5. C4×#137×C73C2semidirect
6. C73×#2906C2semidirect
7. C73×#2064C2semidirect
8. C73×#2063C2semidirect
9. C73×#2047C2semidirect
10. C73×#2046C2semidirect
11. C73×#1967C2semidirect
12. C73×#1950C2semidirect
13. C73×#1908C2semidirect
15. C73×#1801C2semidirect
356. #24775C73direct (N × H)
364. C2×#473C2×C73semidirect
367. C2×#464C2×C73semidirect
368. C4×#137C2×C73semidirect
369. #2906C2×C73semidirect
370. #2064C2×C73semidirect
371. #2063C2×C73semidirect
372. #2047C2×C73semidirect
373. #2046C2×C73semidirect
374. #1967C2×C73semidirect
375. #1950C2×C73semidirect
376. #1908C2×C73semidirect
378. #1801C2×C73semidirect
379. C73#24775direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#473×C732
C2×#471×C732
C73×#30402
C2×#464×C732
C4×#137×C732
C73×#29062
C73×#20642
C73×#20632
C73×#20472
C73×#20462
C73×#19672
C73×#19502
C73×#19082
C73×#19072
C73×#18012
#2477573