Finite Group Databasebeta

← C73×#25446 #32934850

Subgroups — C73×#25446 #32934850

Order 18688.

876 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3154C211yesmaximal, characteristic, complemented
2C73×#3069C211yesmaximal, characteristic, complemented
3C73×#3068C211yesmaximal, characteristic, complemented
4C73×#3067C211yesmaximal, characteristic, complemented
5C2×#471×C73C211yesmaximal, characteristic, complemented
6C73×#2957C211yesmaximal, characteristic, complemented
7C73×#2049C211yesmaximal, characteristic, complemented
8C73×#2048C211yesmaximal, characteristic, complemented
9C73×#2009C211yesmaximal, characteristic, complemented
10C73×#2008C211yesmaximal, characteristic, complemented
11C73×#1977C211yesmaximal, characteristic, complemented
12C73×#1953C211yesmaximal, characteristic, complemented
13C73×#1915C211yesmaximal, characteristic, complemented
14C73×#1914C211yesmaximal, characteristic, complemented
15C73×#1757C211yesmaximal, characteristic, complemented
16#575×C73C2211yescharacteristic
17#575×C73C2211yescharacteristic
18C2×#137×C73C2211yescharacteristic
19C2×#137×C73C2211yescharacteristic
20C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
21C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
22C2×#135×C73C2211yescharacteristic
23C22×SD16×C73C2211yescharacteristic
24#568×C73C2211yescharacteristic
25#568×C73C2211yescharacteristic
26C2×#131×C73C2211yescharacteristic
27#536×C73C2211yescharacteristic
28#535×C73C2211yescharacteristic
29#497×C73—21no—
30#496×C73—21no—
31#495×C73—21no—
32#492×C73—21no—
33#473×C73—21no—
34#473×C73—22no—
35#472×C73—21no—
36#472×C73—22no—
37#471×C73—21no—
38#471×C73—21no—
39#471×C73—22no—
40#471×C73—22no—
41#471×C73—22no—
42#471×C73—22no—
43#444×C73—22no—
44#443×C73—22no—
45#430×C73C2211yescharacteristic
46#430×C73C2211yescharacteristic
47C2×#108×C73C2211yescharacteristic
48C2×#108×C73C2211yescharacteristic
49#421×C73C2211yescharacteristic
50#421×C73C2211yescharacteristic
51#419×C73C2211yescharacteristic
52#418×C73C2211yescharacteristic
53#413×C73C2211yescharacteristic
54#413×C73C2211yescharacteristic
55#413×C73C2211yescharacteristic
56C2×#101×C73C2211yescharacteristic
57C2×#101×C73C2211yescharacteristic
58C2×#100×C73C2211yescharacteristic
59C2×#100×C73C2211yescharacteristic
60#410×C73C2211yescharacteristic
61#405×C73C2211yescharacteristic
62#405×C73C2211yescharacteristic
63#344×C73C2211yescharacteristic
64#344×C73C2211yescharacteristic
65#344×C73C2211yescharacteristic
66#344×C73C2211yescharacteristic
67C2×#41×C73C2311yescharacteristic
68C2×#41×C73C2311yescharacteristic
69C2×#41×C73C2311yescharacteristic
70C22×Q8×C73C2311yescharacteristic
71C22×D4×C73C2311yescharacteristic
72#137×C73—21no—
73#137×C73—21no—
74#137×C73—21no—
75#137×C73—21no—
76#137×C73—22no—
77#137×C73—22no—
78#137×C73—41no—
79#137×C73—41no—
80AGL(1,ℤ/8)×C73—21no—
81AGL(1,ℤ/8)×C73—21no—
82AGL(1,ℤ/8)×C73—21no—
83AGL(1,ℤ/8)×C73—21no—
84AGL(1,ℤ/8)×C73—22no—
85AGL(1,ℤ/8)×C73—22no—
86AGL(1,ℤ/8)×C73—41no—
87AGL(1,ℤ/8)×C73—41no—
88#135×C73—21no—
89#135×C73—21no—
90#135×C73—21no—
91#135×C73—21no—
92#135×C73—41no—
93#135×C73—41no—
94C2×Q16×C73—21no—
95C2×Q16×C73—21no—
96C2×Q16×C73D411yescharacteristic
97C2×SD16×C73—21no—
98C2×SD16×C73—21no—
99C2×SD16×C73—21no—
100C2×SD16×C73—21no—
101C2×SD16×C73—21no—
102C2×SD16×C73—21no—
103C2×SD16×C73—21no—
104C2×SD16×C73—21no—
105C2×SD16×C73—21no—
106C2×SD16×C73—21no—
107C2×SD16×C73D411yescharacteristic
108C2×SD16×C73D411yescharacteristic
109C2×D8×C73—21no—
110C2×D8×C73—21no—
111C2×D8×C73D411yescharacteristic
112#131×C73—22no—
113#131×C73—22no—
114#131×C73—22no—
115#131×C73—22no—
116#131×C73—21no—
117#131×C73—21no—
118#131×C73—21no—
119#131×C73—21no—
120C2×M16×C73—21no—
121C2×M16×C73—41no—
122C2×M16×C73—41no—
123C2×M16×C73C2311yescharacteristic
124C2×M16×C73C2311yescharacteristic
125C2×M16×C73C2311yescharacteristic
126C2×M16×C73C2311yescharacteristic
127C2×M16×C73C2311yescharacteristic
128C2×M16×C73C2311yescharacteristic
129C2×M16×C73C2311yescharacteristic
130C22×C8×C73—21no—
131C22×C8×C73C2311yescharacteristic
132C4⋊Q8×C73—21no—
133#127×C73—21no—
134#124×C73—21no—
135#124×C73—21no—
136#123×C73—22no—
137C22⋊Q8×C73—41no—
138#121×C73—41no—
139#120×C73—22no—
140#117×C73C2311yescharacteristic
141#117×C73C2311yescharacteristic
142#108×C73—22no—
143#108×C73—22no—
144#108×C73—21no—
145#108×C73—21no—
146#108×C73D412yescomplemented
147#108×C73D412yescomplemented
148#104×C73—22no—
149#104×C73—22no—
150#103×C73—41no—
151#102×C73—41no—
152#101×C73—21no—
153#101×C73—21no—
154#101×C73—22no—
155#101×C73—22no—
156#101×C73D412yescomplemented
157#100×C73—21no—
158#100×C73—21no—
159#100×C73—22no—
160#100×C73—22no—
161#100×C73D412yescomplemented
162#99×C73—22no—
163#97×C73—21no—
164#97×C73—21no—
165C4×C8×C73—21no—
166C4×C8×C73—21no—
167C24×C73—21no—
168#41×C73—21no—
169#41×C73—21no—
170#41×C73—21no—
171#41×C73—21no—
172#41×C73—21no—
173#41×C73—21no—
174#41×C73—21no—
175#41×C73—21no—
176#41×C73—21no—
177#41×C73—21no—
178#41×C73—21no—
179#41×C73—21no—
180C2×Q8×C73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73C2×D411yescharacteristic
187C2×Q8×C73C2×D411yescharacteristic
188C2×Q8×C73C2×D411yescharacteristic
189C2×D4×C73—21no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—21no—
193C2×D4×C73—21no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—42no—
199C2×D4×C73C2×D411yescharacteristic
200C2×D4×C73C2×D411yescharacteristic
201C2×D4×C73C2×D411yescharacteristic
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—21no—
206C22×C4×C73C2411yescharacteristic
207Q16×C73—21no—
208Q16×C73—21no—
209Q16×C73—42no—
210Q16×C73—42no—
211Q16×C73—41no—
212Q16×C73—41no—
213SD16×C73—21no—
214SD16×C73—21no—
215SD16×C73—21no—
216SD16×C73—21no—
217SD16×C73—42no—
218SD16×C73—42no—
219SD16×C73—42no—
220SD16×C73—42no—
221SD16×C73—41no—
222SD16×C73—41no—
223SD16×C73—41no—
224SD16×C73—41no—
225SD16×C73—41no—
226SD16×C73—41no—
227SD16×C73—41no—
228SD16×C73—41no—
229D8×C73—21no—
230D8×C73—21no—
231D8×C73—42no—
232D8×C73—42no—
233D8×C73—41no—
234D8×C73—41no—
235M16×C73—21no—
236M16×C73—21no—
237M16×C73—21no—
238M16×C73—21no—
239M16×C73—21no—
240M16×C73—21no—
241M16×C73—21no—
242M16×C73—21no—
243M16×C73—21no—
244M16×C73—21no—
245M16×C73—42no—
246M16×C73—42no—
247M16×C73—41no—
248M16×C73—41no—
249M16×C73C2×D412yes—
250M16×C73C2×D412yes—
251M16×C73C2×D412yes—
252M16×C73C2×D412yes—
253C2×C8×C73—21no—
254C2×C8×C73—21no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—42no—
261C2×C8×C73—42no—
262C2×C8×C73—41no—
263C2×C8×C73—41no—
264C2×C8×C73C2×D411yescharacteristic
265C2×C8×C73C2×D411yescharacteristic
266C2×C8×C73C2×D411yescharacteristic
267C2×C8×C73C2×D411yescharacteristic
268C2×C8×C73#4111yescharacteristic
269C2×C8×C73#4111yescharacteristic
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—42no—
273C22⋊C4×C73—21no—
274C22⋊C4×C73—42no—
275C22⋊C4×C73—42no—
276C22⋊C4×C73#4112yes—
277C42×C73—21no—
278C42×C73—21no—
279C23×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—161no—
286C23×C73C2×#4111yescharacteristic
287Q8×C73—21no—
288Q8×C73—21no—
289Q8×C73—21no—
290Q8×C73—21no—
291Q8×C73—21no—
292Q8×C73—21no—
293Q8×C73—41no—
294Q8×C73—41no—
295Q8×C73—41no—
296Q8×C73—41no—
297D4×C73—21no—
298D4×C73—21no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—21no—
302D4×C73—21no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—41no—
307D4×C73—41no—
308D4×C73—41no—
309D4×C73—41no—
310D4×C73—41no—
311D4×C73—41no—
312D4×C73—41no—
313D4×C73—162no—
314C2×C4×C73—21no—
315C2×C4×C73—22no—
316C2×C4×C73—21no—
317C2×C4×C73—21no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73C22×D411yescharacteristic
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C2×#4111yescharacteristic
332C2×C4×C73H(5,𝔽2)11yescharacteristic
333C2×C4×C73H(5,𝔽2)11yescharacteristic
334C8×C73—22no—
335C8×C73—22no—
336C8×C73—22no—
337C8×C73—22no—
338C8×C73—41no—
339C8×C73—41no—
340C8×C73—41no—
341C8×C73#12111yescharacteristic
342C8×C73#12111yescharacteristic
343C8×C73#12111yescharacteristic
344C8×C73#12111yescharacteristic
345C22×C73—41no—
346C22×C73—41no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—81no—
350C22×C73—81no—
351C22×C73—81no—
352C22×C73—82no—
353C22×C73—81no—
354C22×C73—161no—
355C22×C73—161no—
356C22×C73#53211yescharacteristic
357C22×C73#54611yescharacteristic
358C22×C73#55011yescharacteristic
359C4×C73—42no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73C2×#12111yescharacteristic
366C4×C73#54011yescharacteristic
367C4×C73D4211yescharacteristic
368C4×C73D4211yescharacteristic
369#25446C7311yesmaximal, characteristic, direct product factor, Sylow
370C2×C73—21no—
371C2×C73—21no—
372C2×C73—21no—
373C2×C73—81no—
374C2×C73—81no—
375C2×C73—81no—
376C2×C73—161no—
377C2×C73#242811yescharacteristic
378#3154C2×C7311yescharacteristic, complemented
379#3069C2×C7311yescharacteristic, complemented
380#3068C2×C7311yescharacteristic, complemented
381#3067C2×C7311yescharacteristic, complemented
382C2×#471C2×C7311yescharacteristic, complemented
383#2957C2×C7311yescharacteristic, complemented
384#2049C2×C7311yescharacteristic, complemented
385#2048C2×C7311yescharacteristic, complemented
386#2009C2×C7311yescharacteristic, complemented
387#2008C2×C7311yescharacteristic, complemented
388#1977C2×C7311yescharacteristic, complemented
389#1953C2×C7311yescharacteristic, complemented
390#1915C2×C7311yescharacteristic, complemented
391#1914C2×C7311yescharacteristic, complemented
392#1757C2×C7311yescharacteristic, complemented
393C73#2544611yescharacteristic, direct product factor, Sylow
394#575C22×C7311yescharacteristic
395#575C22×C7311yescharacteristic
396C2×#137C22×C7311yescharacteristic
397C2×#137C22×C7311yescharacteristic
398C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
399C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
400C2×#135C22×C7311yescharacteristic
401C22×SD16C22×C7311yescharacteristic
402#568C22×C7311yescharacteristic
403#568C22×C7311yescharacteristic
404C2×#131C22×C7311yescharacteristic
405#536C22×C7311yescharacteristic
406#535C22×C7311yescharacteristic
407#497—21no—
408#496—21no—
409#495—21no—
410#492—21no—
411#473—21no—
412#473—22no—
413#472—21no—
414#472—22no—
415#471—21no—
416#471—21no—
417#471—22no—
418#471—22no—
419#471—22no—
420#471—22no—
421#444—22no—
422#443—22no—
423#430C22×C7311yescharacteristic
424#430C22×C7311yescharacteristic
425C2×#108C22×C7311yescharacteristic
426C2×#108C22×C7311yescharacteristic
427#421C22×C7311yescharacteristic
428#421C22×C7311yescharacteristic
429#419C22×C7311yescharacteristic
430#418C22×C7311yescharacteristic
431#413C22×C7311yescharacteristic
432#413C22×C7311yescharacteristic
433#413C22×C7311yescharacteristic
434C2×#101C22×C7311yescharacteristic
435C2×#101C22×C7311yescharacteristic
436C2×#100C22×C7311yescharacteristic
437C2×#100C22×C7311yescharacteristic
438#410C22×C7311yescharacteristic
439#405C22×C7311yescharacteristic
440#405C22×C7311yescharacteristic
441#344C22×C7311yescharacteristic
442#344C22×C7311yescharacteristic
443#344C22×C7311yescharacteristic
444#344C22×C7311yescharacteristic
445C2×#41C23×C7311yescharacteristic
446C2×#41C23×C7311yescharacteristic
447C2×#41C23×C7311yescharacteristic
448C22×Q8C23×C7311yescharacteristic
449C22×D4C23×C7311yescharacteristic
450#137—21no—
451#137—21no—
452#137—21no—
453#137—21no—
454#137—22no—
455#137—22no—
456#137—41no—
457#137—41no—
458AGL(1,ℤ/8)—21no—
459AGL(1,ℤ/8)—21no—
460AGL(1,ℤ/8)—21no—
461AGL(1,ℤ/8)—21no—
462AGL(1,ℤ/8)—22no—
463AGL(1,ℤ/8)—22no—
464AGL(1,ℤ/8)—41no—
465AGL(1,ℤ/8)—41no—
466#135—21no—
467#135—21no—
468#135—21no—
469#135—21no—
470#135—41no—
471#135—41no—
472C2×Q16—21no—
473C2×Q16—21no—
474C2×Q16D4×C7311yescharacteristic
475C2×SD16—21no—
476C2×SD16—21no—
477C2×SD16—21no—
478C2×SD16—21no—
479C2×SD16—21no—
480C2×SD16—21no—
481C2×SD16—21no—
482C2×SD16—21no—
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16D4×C7311yescharacteristic
486C2×SD16D4×C7311yescharacteristic
487C2×D8—21no—
488C2×D8—21no—
489C2×D8D4×C7311yescharacteristic
490#131—22no—
491#131—22no—
492#131—22no—
493#131—22no—
494#131—21no—
495#131—21no—
496#131—21no—
497#131—21no—
498C2×M16—21no—
499C2×M16—41no—
500C2×M16—41no—
501C2×M16C23×C7311yescharacteristic
502C2×M16C23×C7311yescharacteristic
503C2×M16C23×C7311yescharacteristic
504C2×M16C23×C7311yescharacteristic
505C2×M16C23×C7311yescharacteristic
506C2×M16C23×C7311yescharacteristic
507C2×M16C23×C7311yescharacteristic
508C22×C8—21no—
509C22×C8C23×C7311yescharacteristic
510C4⋊Q8—21no—
511#127—21no—
512#124—21no—
513#124—21no—
514#123—22no—
515C22⋊Q8—41no—
516#121—41no—
517#120—22no—
518#117C23×C7311yescharacteristic
519#117C23×C7311yescharacteristic
520#108—22no—
521#108—22no—
522#108—21no—
523#108—21no—
524#108D4×C7312yescomplemented
525#108D4×C7312yescomplemented
526#104—22no—
527#104—22no—
528#103—41no—
529#102—41no—
530#101—21no—
531#101—21no—
532#101—22no—
533#101—22no—
534#101D4×C7312yescomplemented
535#100—21no—
536#100—21no—
537#100—22no—
538#100—22no—
539#100D4×C7312yescomplemented
540#99—22no—
541#97—21no—
542#97—21no—
543C4×C8—21no—
544C4×C8—21no—
545C24—21no—
546#41—21no—
547#41—21no—
548#41—21no—
549#41—21no—
550#41—21no—
551#41—21no—
552#41—21no—
553#41—21no—
554#41—21no—
555#41—21no—
556#41—21no—
557#41—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8—21no—
563C2×Q8—21no—
564C2×Q8C2×D4×C7311yescharacteristic
565C2×Q8C2×D4×C7311yescharacteristic
566C2×Q8C2×D4×C7311yescharacteristic
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—21no—
575C2×D4—21no—
576C2×D4—42no—
577C2×D4C2×D4×C7311yescharacteristic
578C2×D4C2×D4×C7311yescharacteristic
579C2×D4C2×D4×C7311yescharacteristic
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4C24×C7311yescharacteristic
585Q16—21no—
586Q16—21no—
587Q16—42no—
588Q16—42no—
589Q16—41no—
590Q16—41no—
591SD16—21no—
592SD16—21no—
593SD16—21no—
594SD16—21no—
595SD16—42no—
596SD16—42no—
597SD16—42no—
598SD16—42no—
599SD16—41no—
600SD16—41no—
601SD16—41no—
602SD16—41no—
603SD16—41no—
604SD16—41no—
605SD16—41no—
606SD16—41no—
607D8—21no—
608D8—21no—
609D8—42no—
610D8—42no—
611D8—41no—
612D8—41no—
613M16—21no—
614M16—21no—
615M16—21no—
616M16—21no—
617M16—21no—
618M16—21no—
619M16—21no—
620M16—21no—
621M16—21no—
622M16—21no—
623M16—42no—
624M16—42no—
625M16—41no—
626M16—41no—
627M16C2×D4×C7312yes—
628M16C2×D4×C7312yes—
629M16C2×D4×C7312yes—
630M16C2×D4×C7312yes—
631C2×C8—21no—
632C2×C8—21no—
633C2×C8—21no—
634C2×C8—21no—
635C2×C8—21no—
636C2×C8—21no—
637C2×C8—21no—
638C2×C8—42no—
639C2×C8—42no—
640C2×C8—41no—
641C2×C8—41no—
642C2×C8C2×D4×C7311yescharacteristic
643C2×C8C2×D4×C7311yescharacteristic
644C2×C8C2×D4×C7311yescharacteristic
645C2×C8C2×D4×C7311yescharacteristic
646C2×C8#41×C7311yescharacteristic
647C2×C8#41×C7311yescharacteristic
648C4⋊C4—21no—
649C4⋊C4—21no—
650C4⋊C4—42no—
651C22⋊C4—21no—
652C22⋊C4—42no—
653C22⋊C4—42no—
654C22⋊C4#41×C7312yes—
655C42—21no—
656C42—21no—
657C23—21no—
658C23—21no—
659C23—21no—
660C23—41no—
661C23—41no—
662C23—41no—
663C23—161no—
664C23C2×#41×C7311yescharacteristic
665Q8—21no—
666Q8—21no—
667Q8—21no—
668Q8—21no—
669Q8—21no—
670Q8—21no—
671Q8—41no—
672Q8—41no—
673Q8—41no—
674Q8—41no—
675D4—21no—
676D4—21no—
677D4—21no—
678D4—21no—
679D4—21no—
680D4—21no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—41no—
688D4—41no—
689D4—41no—
690D4—41no—
691D4—162no—
692C2×C4—21no—
693C2×C4—22no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4C22×D4×C7311yescharacteristic
707C2×C4C22×D4×C7311yescharacteristic
708C2×C4C22×D4×C7311yescharacteristic
709C2×C4C2×#41×C7311yescharacteristic
710C2×C4H(5,𝔽2)×C7311yescharacteristic
711C2×C4H(5,𝔽2)×C7311yescharacteristic
712C8—22no—
713C8—22no—
714C8—22no—
715C8—22no—
716C8—41no—
717C8—41no—
718C8—41no—
719C8#121×C7311yescharacteristic
720C8#121×C7311yescharacteristic
721C8#121×C7311yescharacteristic
722C8#121×C7311yescharacteristic
723C22—41no—
724C22—41no—
725C22—41no—
726C22—41no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—82no—
731C22—81no—
732C22—161no—
733C22—161no—
734C22#532×C7311yescharacteristic
735C22#546×C7311yescharacteristic
736C22#550×C7311yescharacteristic
737C4—42no—
738C4—41no—
739C4—41no—
740C4—41no—
741C4—81no—
742C4—81no—
743C4C2×#121×C7311yescharacteristic
744C4#540×C7311yescharacteristic
745C4D42×C7311yescharacteristic
746C4D42×C7311yescharacteristic
747C2—21no—
748C2—21no—
749C2—21no—
750C2—81no—
751C2—81no—
752C2—81no—
753C2—161no—
754C2C73×#242811yescharacteristic
subgroupG/H
center, socleC2×C73#2428
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×#3154C2semidirect
2. C73×#3069C2semidirect
3. C73×#3068C2semidirect
4. C73×#3067C2semidirect
5. C2×#471×C73C2semidirect
6. C73×#2957C2semidirect
7. C73×#2049C2semidirect
8. C73×#2048C2semidirect
9. C73×#2009C2semidirect
10. C73×#2008C2semidirect
11. C73×#1977C2semidirect
12. C73×#1953C2semidirect
13. C73×#1915C2semidirect
14. C73×#1914C2semidirect
15. C73×#1757C2semidirect
146. #108×C73D4semidirect
147. #108×C73D4semidirect
156. #101×C73D4semidirect
161. #100×C73D4semidirect
369. #25446C73direct (N × H)
378. #3154C2×C73semidirect
379. #3069C2×C73semidirect
380. #3068C2×C73semidirect
381. #3067C2×C73semidirect
382. C2×#471C2×C73semidirect
383. #2957C2×C73semidirect
384. #2049C2×C73semidirect
385. #2048C2×C73semidirect
386. #2009C2×C73semidirect
387. #2008C2×C73semidirect
388. #1977C2×C73semidirect
389. #1953C2×C73semidirect
390. #1915C2×C73semidirect
391. #1914C2×C73semidirect
392. #1757C2×C73semidirect
393. C73#25446direct (N × H)
524. #108D4×C73semidirect
525. #108D4×C73semidirect
534. #101D4×C73semidirect
539. #100D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#31542
C73×#30692
C73×#30682
C73×#30672
C2×#471×C732
C73×#29572
C73×#20492
C73×#20482
C73×#20092
C73×#20082
C73×#19772
C73×#19532
C73×#19152
C73×#19142
C73×#17572
#2544673