Finite Group Databasebeta

← C73×#24801 #32934205

Subgroups — C73×#24801 #32934205

Order 18688.

866 conjugacy classes of subgroups.

The subgroup lattice has 738 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C73C211yesmaximal, characteristic, complemented
2C73×#3057C211yesmaximal, characteristic, complemented
3C73×#3046C211yesmaximal, characteristic, complemented
4C73×#3045C211yesmaximal, characteristic
5C2×#444×C73C211yesmaximal, characteristic, complemented
6C73×#2913C211yesmaximal, characteristic, complemented
7C73×#2064C211yesmaximal, characteristic, complemented
8C73×#2063C211yesmaximal, characteristic, complemented
9C73×#2038C211yesmaximal, characteristic, complemented
10C73×#2037C211yesmaximal, characteristic, complemented
11C73×#1973C211yesmaximal, characteristic, complemented
12C73×#1946C211yesmaximal, characteristic, complemented
13C73×#1883C211yesmaximal, characteristic, complemented
14C73×#1882C211yesmaximal, characteristic, complemented
15C73×#1816C211yesmaximal, characteristic, complemented
16C2×#137×C73C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
18C2×#135×C73C2211yescharacteristic
19C22×SD16×C73C2211yescharacteristic
20C2×#131×C73C2211yescharacteristic
21C2×#131×C73C2211yescharacteristic
22#536×C73C2211yescharacteristic
23#535×C73C2211yescharacteristic
24#520×C73C2211yescharacteristic
25#520×C73C2211yescharacteristic
26#471×C73—24no—
27#468×C73—21no—
28#468×C73—21no—
29#465×C73—21no—
30#465×C73—21no—
31#464×C73—21no—
32#464×C73—21no—
33#463×C73—21no—
34#463×C73—21no—
35#462×C73—21no—
36#461×C73—21no—
37#460×C73—21no—
38#459×C73—21no—
39#444×C73—24no—
40C2×#108×C73C2211yescharacteristic
41C2×#108×C73C2211yescharacteristic
42#428×C73—21no—
43#428×C73—21no—
44#428×C73C2211yescharacteristic
45#428×C73C2211yescharacteristic
46#427×C73—21no—
47#427×C73C2211yescharacteristic
48C2×#107×C73—21no—
49C2×#107×C73C2211yescharacteristic
50#424×C73C2211yescharacteristic
51#424×C73C2211yescharacteristic
52C2×#104×C73C2211yescharacteristic
53C2×#104×C73C2211yescharacteristic
54#419×C73C2211yescharacteristic
55#418×C73C2211yescharacteristic
56#417×C73C2211yescharacteristic
57#417×C73C2211yescharacteristic
58C2×#103×C73C2211yescharacteristic
59C2×#102×C73C2211yescharacteristic
60C2×#101×C73C2211yescharacteristic
61C2×#100×C73C2211yescharacteristic
62C2×#97×C73C2211yescharacteristic
63#391×C73C2211yescharacteristic
64#390×C73C2211yescharacteristic
65#343×C73C2211yescharacteristic
66#343×C73C2211yescharacteristic
67#339×C73C2211yescharacteristic
68#339×C73C2211yescharacteristic
69C2×#41×C73C2311yescharacteristic
70C2×#41×C73C2311yescharacteristic
71C22×Q8×C73C2311yescharacteristic
72C22×D4×C73C2311yescharacteristic
73#137×C73—22no—
74#137×C73—22no—
75AGL(1,ℤ/8)×C73—22no—
76AGL(1,ℤ/8)×C73—22no—
77#135×C73—22no—
78#135×C73—22no—
79C2×Q16×C73—21no—
80C2×Q16×C73D411yescharacteristic
81C2×SD16×C73—21no—
82C2×SD16×C73—21no—
83C2×SD16×C73—21no—
84C2×SD16×C73—21no—
85C2×SD16×C73—22no—
86C2×SD16×C73—22no—
87C2×SD16×C73D411yescharacteristic
88C2×SD16×C73D411yescharacteristic
89C2×D8×C73—21no—
90C2×D8×C73D411yescharacteristic
91#131×C73—22no—
92#131×C73—22no—
93#131×C73—22no—
94#131×C73D414yescomplemented
95C2×M16×C73—21no—
96C2×M16×C73—21no—
97C2×M16×C73C2311yescharacteristic
98C2×M16×C73C2311yescharacteristic
99C2×M16×C73C2311yescharacteristic
100C2×M16×C73C2311yescharacteristic
101C22×C8×C73—21no—
102C22×C8×C73—21no—
103C22×C8×C73C2311yescharacteristic
104C22×C8×C73C2311yescharacteristic
105C4⋊Q8×C73—21no—
106#127×C73—21no—
107#124×C73—21no—
108#124×C73—21no—
109#123×C73—41no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112#121×C73—21no—
113#121×C73—21no—
114#120×C73—41no—
115C4×Q8×C73—21no—
116C4×Q8×C73—21no—
117C4×D4×C73—21no—
118C4×D4×C73—21no—
119C4×D4×C73—41no—
120C4×D4×C73—41no—
121#117×C73—21no—
122#117×C73—21no—
123#117×C73C2311yescharacteristic
124#117×C73C2311yescharacteristic
125C2×C4⋊C4×C73—21no—
126C2×C4⋊C4×C73—21no—
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C4⋊C4×C73C2311yescharacteristic
129C2×C22⋊C4×C73—41no—
130C2×C42×C73C2311yescharacteristic
131#108×C73—22no—
132#108×C73—22no—
133#107×C73—21no—
134#107×C73—21no—
135#107×C73—21no—
136#107×C73—21no—
137#107×C73D411yescharacteristic
138#107×C73D411yescharacteristic
139#106×C73—21no—
140#106×C73—21no—
141#106×C73D411yescharacteristic
142#106×C73D411yescharacteristic
143C4⋊C8×C73—21no—
144C4⋊C8×C73—21no—
145C4⋊C8×C73—21no—
146C4⋊C8×C73—21no—
147#104×C73—22no—
148#104×C73—22no—
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#102×C73—21no—
161#101×C73—22no—
162#100×C73—22no—
163#97×C73—22no—
164#95×C73—41no—
165C24×C73—21no—
166#41×C73—21no—
167#41×C73—21no—
168#41×C73—21no—
169#41×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×Q8×C73C2×D411yescharacteristic
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—41no—
191C2×D4×C73—41no—
192C2×D4×C73C2×D411yescharacteristic
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—41no—
201C22×C4×C73—41no—
202C22×C4×C73C2411yescharacteristic
203Q16×C73—22no—
204Q16×C73—42no—
205SD16×C73—22no—
206SD16×C73—22no—
207SD16×C73—42no—
208SD16×C73—42no—
209SD16×C73—42no—
210SD16×C73—42no—
211D8×C73—22no—
212D8×C73—42no—
213M16×C73—21no—
214M16×C73—24no—
215M16×C73—21no—
216M16×C73—21no—
217M16×C73—21no—
218M16×C73—21no—
219M16×C73—21no—
220M16×C73—21no—
221M16×C73—42no—
222M16×C73C2×D412yes—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—24no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—42no—
231C2×C8×C73C2×D411yescharacteristic
232C2×C8×C73C2×D411yescharacteristic
233C2×C8×C73C2×D412yes—
234C2×C8×C73C2×D411yescharacteristic
235C2×C8×C73C2×D411yescharacteristic
236C2×C8×C73#4112yes—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—41no—
242C4⋊C4×C73—41no—
243C4⋊C4×C73—41no—
244C4⋊C4×C73—41no—
245C4⋊C4×C73C2×D411yescharacteristic
246C4⋊C4×C73C2×D411yescharacteristic
247C4⋊C4×C73C2×D411yescharacteristic
248C4⋊C4×C73C2×D411yescharacteristic
249C22⋊C4×C73—21no—
250C22⋊C4×C73—21no—
251C22⋊C4×C73—41no—
252C22⋊C4×C73—41no—
253C22⋊C4×C73—41no—
254C22⋊C4×C73—41no—
255C22⋊C4×C73—41no—
256C22⋊C4×C73—41no—
257C22⋊C4×C73—82no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—21no—
262C42×C73—41no—
263C42×C73—41no—
264C23×C73—21no—
265C23×C73—21no—
266C23×C73—41no—
267C23×C73—41no—
268C23×C73—41no—
269C23×C73—81no—
270C23×C73—81no—
271C23×C73H(5,𝔽2)11yescharacteristic
272Q8×C73—21no—
273Q8×C73—21no—
274Q8×C73—21no—
275Q8×C73—41no—
276Q8×C73—41no—
277Q8×C73—41no—
278Q8×C73—41no—
279Q8×C73#12112yes—
280D4×C73—22no—
281D4×C73—22no—
282D4×C73—21no—
283D4×C73—21no—
284D4×C73—21no—
285D4×C73—41no—
286D4×C73—41no—
287D4×C73—41no—
288D4×C73—41no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—161no—
292D4×C73—161no—
293D4×C73#12112yes—
294C2×C4×C73—21no—
295C2×C4×C73—22no—
296C2×C4×C73—22no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—41no—
311C2×C4×C73—41no—
312C2×C4×C73—81no—
313C2×C4×C73—81no—
314C2×C4×C73—161no—
315C2×C4×C73—161no—
316C2×C4×C73C22×D411yescharacteristic
317C2×C4×C73C22×D411yescharacteristic
318C2×C4×C73C22×D411yescharacteristic
319C2×C4×C73C2×#4111yescharacteristic
320C2×C4×C73C2×#4111yescharacteristic
321C2×C4×C732−1+411yescharacteristic
322C8×C73—22no—
323C8×C73—21no—
324C8×C73—21no—
325C8×C73—41no—
326C8×C73—41no—
327C8×C73—41no—
328C8×C73#12112yes—
329C8×C73#12112yes—
330C22×C73—21no—
331C22×C73—21no—
332C22×C73—22no—
333C22×C73—41no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—82no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—161no—
343C22×C73#53711yescharacteristic
344C22×C73D4211yescharacteristic
345C22×C73#55311yescharacteristic
346C4×C73—22no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—41no—
351C4×C73—41no—
352C4×C73—81no—
353C4×C73—81no—
354C4×C73—81no—
355C4×C73—81no—
356C4×C73C2×#12111yescharacteristic
357C4×C73C2×#12111yescharacteristic
358C4×C73#54711yescharacteristic
359C4×C73#54811yescharacteristic
360#24801C7311yesmaximal, characteristic, direct product factor, Sylow
361C2×C73—21no—
362C2×C73—21no—
363C2×C73—42no—
364C2×C73—81no—
365C2×C73—161no—
366C2×C73#241611yescharacteristic
367C2×C73#328811yescharacteristic
368C2×C73#328911yescharacteristic
369C2×#471C2×C7311yescharacteristic, complemented
370#3057C2×C7311yescharacteristic, complemented
371#3046C2×C7311yescharacteristic, complemented
372#3045C2×C7311yescharacteristic
373C2×#444C2×C7311yescharacteristic, complemented
374#2913C2×C7311yescharacteristic, complemented
375#2064C2×C7311yescharacteristic, complemented
376#2063C2×C7311yescharacteristic, complemented
377#2038C2×C7311yescharacteristic, complemented
378#2037C2×C7311yescharacteristic, complemented
379#1973C2×C7311yescharacteristic, complemented
380#1946C2×C7311yescharacteristic, complemented
381#1883C2×C7311yescharacteristic, complemented
382#1882C2×C7311yescharacteristic, complemented
383#1816C2×C7311yescharacteristic, complemented
384C73#2480111yescharacteristic, direct product factor, Sylow
385C2×#137C22×C7311yescharacteristic
386C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
387C2×#135C22×C7311yescharacteristic
388C22×SD16C22×C7311yescharacteristic
389C2×#131C22×C7311yescharacteristic
390C2×#131C22×C7311yescharacteristic
391#536C22×C7311yescharacteristic
392#535C22×C7311yescharacteristic
393#520C22×C7311yescharacteristic
394#520C22×C7311yescharacteristic
395#471—24no—
396#468—21no—
397#468—21no—
398#465—21no—
399#465—21no—
400#464—21no—
401#464—21no—
402#463—21no—
403#463—21no—
404#462—21no—
405#461—21no—
406#460—21no—
407#459—21no—
408#444—24no—
409C2×#108C22×C7311yescharacteristic
410C2×#108C22×C7311yescharacteristic
411#428—21no—
412#428—21no—
413#428C22×C7311yescharacteristic
414#428C22×C7311yescharacteristic
415#427—21no—
416#427C22×C7311yescharacteristic
417C2×#107—21no—
418C2×#107C22×C7311yescharacteristic
419#424C22×C7311yescharacteristic
420#424C22×C7311yescharacteristic
421C2×#104C22×C7311yescharacteristic
422C2×#104C22×C7311yescharacteristic
423#419C22×C7311yescharacteristic
424#418C22×C7311yescharacteristic
425#417C22×C7311yescharacteristic
426#417C22×C7311yescharacteristic
427C2×#103C22×C7311yescharacteristic
428C2×#102C22×C7311yescharacteristic
429C2×#101C22×C7311yescharacteristic
430C2×#100C22×C7311yescharacteristic
431C2×#97C22×C7311yescharacteristic
432#391C22×C7311yescharacteristic
433#390C22×C7311yescharacteristic
434#343C22×C7311yescharacteristic
435#343C22×C7311yescharacteristic
436#339C22×C7311yescharacteristic
437#339C22×C7311yescharacteristic
438C2×#41C23×C7311yescharacteristic
439C2×#41C23×C7311yescharacteristic
440C22×Q8C23×C7311yescharacteristic
441C22×D4C23×C7311yescharacteristic
442#137—22no—
443#137—22no—
444AGL(1,ℤ/8)—22no—
445AGL(1,ℤ/8)—22no—
446#135—22no—
447#135—22no—
448C2×Q16—21no—
449C2×Q16D4×C7311yescharacteristic
450C2×SD16—21no—
451C2×SD16—21no—
452C2×SD16—21no—
453C2×SD16—21no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16D4×C7311yescharacteristic
457C2×SD16D4×C7311yescharacteristic
458C2×D8—21no—
459C2×D8D4×C7311yescharacteristic
460#131—22no—
461#131—22no—
462#131—22no—
463#131D4×C7314yescomplemented
464C2×M16—21no—
465C2×M16—21no—
466C2×M16C23×C7311yescharacteristic
467C2×M16C23×C7311yescharacteristic
468C2×M16C23×C7311yescharacteristic
469C2×M16C23×C7311yescharacteristic
470C22×C8—21no—
471C22×C8—21no—
472C22×C8C23×C7311yescharacteristic
473C22×C8C23×C7311yescharacteristic
474C4⋊Q8—21no—
475#127—21no—
476#124—21no—
477#124—21no—
478#123—41no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481#121—21no—
482#121—21no—
483#120—41no—
484C4×Q8—21no—
485C4×Q8—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—41no—
489C4×D4—41no—
490#117—21no—
491#117—21no—
492#117C23×C7311yescharacteristic
493#117C23×C7311yescharacteristic
494C2×C4⋊C4—21no—
495C2×C4⋊C4—21no—
496C2×C4⋊C4C23×C7311yescharacteristic
497C2×C4⋊C4C23×C7311yescharacteristic
498C2×C22⋊C4—41no—
499C2×C42C23×C7311yescharacteristic
500#108—22no—
501#108—22no—
502#107—21no—
503#107—21no—
504#107—21no—
505#107—21no—
506#107D4×C7311yescharacteristic
507#107D4×C7311yescharacteristic
508#106—21no—
509#106—21no—
510#106D4×C7311yescharacteristic
511#106D4×C7311yescharacteristic
512C4⋊C8—21no—
513C4⋊C8—21no—
514C4⋊C8—21no—
515C4⋊C8—21no—
516#104—22no—
517#104—22no—
518#103—21no—
519#103—21no—
520#103—21no—
521#103—21no—
522#103—21no—
523#103—21no—
524#102—21no—
525#102—21no—
526#102—21no—
527#102—21no—
528#102—21no—
529#102—21no—
530#101—22no—
531#100—22no—
532#97—22no—
533#95—41no—
534C24—21no—
535#41—21no—
536#41—21no—
537#41—21no—
538#41—21no—
539#41—21no—
540#41—21no—
541#41C2×D4×C7312yes—
542#41#41×C7312yes—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—21no—
548C2×Q8—21no—
549C2×Q8C2×D4×C7311yescharacteristic
550C2×Q8C2×D4×C7311yescharacteristic
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—21no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4C2×D4×C7311yescharacteristic
562C2×D4C2×D4×C7311yescharacteristic
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—41no—
570C22×C4—41no—
571C22×C4C24×C7311yescharacteristic
572Q16—22no—
573Q16—42no—
574SD16—22no—
575SD16—22no—
576SD16—42no—
577SD16—42no—
578SD16—42no—
579SD16—42no—
580D8—22no—
581D8—42no—
582M16—21no—
583M16—24no—
584M16—21no—
585M16—21no—
586M16—21no—
587M16—21no—
588M16—21no—
589M16—21no—
590M16—42no—
591M16C2×D4×C7312yes—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—24no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—42no—
600C2×C8C2×D4×C7311yescharacteristic
601C2×C8C2×D4×C7311yescharacteristic
602C2×C8C2×D4×C7312yes—
603C2×C8C2×D4×C7311yescharacteristic
604C2×C8C2×D4×C7311yescharacteristic
605C2×C8#41×C7312yes—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—41no—
611C4⋊C4—41no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4C2×D4×C7311yescharacteristic
615C4⋊C4C2×D4×C7311yescharacteristic
616C4⋊C4C2×D4×C7311yescharacteristic
617C4⋊C4C2×D4×C7311yescharacteristic
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—41no—
621C22⋊C4—41no—
622C22⋊C4—41no—
623C22⋊C4—41no—
624C22⋊C4—41no—
625C22⋊C4—41no—
626C22⋊C4—82no—
627C42—21no—
628C42—21no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C23—21no—
634C23—21no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—81no—
639C23—81no—
640C23H(5,𝔽2)×C7311yescharacteristic
641Q8—21no—
642Q8—21no—
643Q8—21no—
644Q8—41no—
645Q8—41no—
646Q8—41no—
647Q8—41no—
648Q8#121×C7312yes—
649D4—22no—
650D4—22no—
651D4—21no—
652D4—21no—
653D4—21no—
654D4—41no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—161no—
661D4—161no—
662D4#121×C7312yes—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—81no—
682C2×C4—81no—
683C2×C4—161no—
684C2×C4—161no—
685C2×C4C22×D4×C7311yescharacteristic
686C2×C4C22×D4×C7311yescharacteristic
687C2×C4C22×D4×C7311yescharacteristic
688C2×C4C2×#41×C7311yescharacteristic
689C2×C4C2×#41×C7311yescharacteristic
690C2×C42−1+4×C7311yescharacteristic
691C8—22no—
692C8—21no—
693C8—21no—
694C8—41no—
695C8—41no—
696C8—41no—
697C8#121×C7312yes—
698C8#121×C7312yes—
699C22—21no—
700C22—21no—
701C22—22no—
702C22—41no—
703C22—41no—
704C22—41no—
705C22—41no—
706C22—41no—
707C22—82no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22—161no—
712C22#537×C7311yescharacteristic
713C22D42×C7311yescharacteristic
714C22#553×C7311yescharacteristic
715C4—22no—
716C4—41no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—41no—
721C4—81no—
722C4—81no—
723C4—81no—
724C4—81no—
725C4C2×#121×C7311yescharacteristic
726C4C2×#121×C7311yescharacteristic
727C4#547×C7311yescharacteristic
728C4#548×C7311yescharacteristic
729C2—21no—
730C2—21no—
731C2—42no—
732C2—81no—
733C2—161no—
734C2C73×#241611yescharacteristic
735C2C73×#328811yescharacteristic
736C2C73×#328911yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3045C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#471×C73C2semidirect
2. C73×#3057C2semidirect
3. C73×#3046C2semidirect
5. C2×#444×C73C2semidirect
6. C73×#2913C2semidirect
7. C73×#2064C2semidirect
8. C73×#2063C2semidirect
9. C73×#2038C2semidirect
10. C73×#2037C2semidirect
11. C73×#1973C2semidirect
12. C73×#1946C2semidirect
13. C73×#1883C2semidirect
14. C73×#1882C2semidirect
15. C73×#1816C2semidirect
94. #131×C73D4semidirect
360. #24801C73direct (N × H)
369. C2×#471C2×C73semidirect
370. #3057C2×C73semidirect
371. #3046C2×C73semidirect
373. C2×#444C2×C73semidirect
374. #2913C2×C73semidirect
375. #2064C2×C73semidirect
376. #2063C2×C73semidirect
377. #2038C2×C73semidirect
378. #2037C2×C73semidirect
379. #1973C2×C73semidirect
380. #1946C2×C73semidirect
381. #1883C2×C73semidirect
382. #1882C2×C73semidirect
383. #1816C2×C73semidirect
384. C73#24801direct (N × H)
463. #131D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C732
C73×#30572
C73×#30462
C73×#30452
C2×#444×C732
C73×#29132
C73×#20642
C73×#20632
C73×#20382
C73×#20372
C73×#19732
C73×#19462
C73×#18832
C73×#18822
C73×#18162
#2480173