Finite Group Databasebeta

← C73×#25440 #32934844

Subgroups — C73×#25440 #32934844

Order 18688.

914 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3154C211yesmaximal, characteristic, complemented
2C2×#471×C73C211yesmaximal, characteristic, complemented
3C73×#3063C211yesmaximal, characteristic, complemented
4C73×#3062C211yesmaximal, characteristic, complemented
5C73×#3060C211yesmaximal, characteristic, complemented
6C2×#443×C73C211yesmaximal, characteristic, complemented
7C73×#2038C211yesmaximal, characteristic, complemented
8C73×#2037C211yesmaximal, characteristic, complemented
9C73×#2007C211yesmaximal, characteristic, complemented
10C73×#2006C211yesmaximal, characteristic, complemented
11C73×#1968C211yesmaximal, characteristic, complemented
12C73×#1951C211yesmaximal, characteristic, complemented
13C73×#1908C211yesmaximal, characteristic, complemented
14C73×#1907C211yesmaximal, characteristic, complemented
15C73×#1764C211yesmaximal, characteristic, complemented
16C2×#137×C73C2211yescharacteristic
17C2×#137×C73C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
20C2×#135×C73C2211yescharacteristic
21C22×SD16×C73C2211yescharacteristic
22C2×#131×C73C2211yescharacteristic
23C2×#131×C73C2211yescharacteristic
24C2×#131×C73C2211yescharacteristic
25#537×C73C2211yescharacteristic
26#537×C73C2211yescharacteristic
27#536×C73C2211yescharacteristic
28#535×C73C2211yescharacteristic
29#497×C73—21no—
30#496×C73—21no—
31#495×C73—21no—
32#492×C73—21no—
33#471×C73—24no—
34#470×C73—21no—
35#470×C73—21no—
36#469×C73—21no—
37#469×C73—21no—
38#468×C73—21no—
39#468×C73—21no—
40#467×C73—21no—
41#466×C73—21no—
42#465×C73—21no—
43#465×C73—21no—
44#465×C73—21no—
45#465×C73—21no—
46#443×C73—24no—
47C2×#108×C73C2211yescharacteristic
48#428×C73C2211yescharacteristic
49#428×C73C2211yescharacteristic
50C2×#106×C73C2211yescharacteristic
51C2×#104×C73C2211yescharacteristic
52C2×#104×C73C2211yescharacteristic
53C2×#104×C73C2211yescharacteristic
54#417×C73C2211yescharacteristic
55#417×C73C2211yescharacteristic
56#416×C73C2211yescharacteristic
57C2×#103×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic
59C2×#101×C73C2211yescharacteristic
60C2×#100×C73C2211yescharacteristic
61#405×C73C2211yescharacteristic
62C2×C4×C8×C73C2211yescharacteristic
63#391×C73C2211yescharacteristic
64#390×C73C2211yescharacteristic
65#343×C73C2211yescharacteristic
66#343×C73C2211yescharacteristic
67#341×C73C2211yescharacteristic
68#339×C73C2211yescharacteristic
69C2×#41×C73C2311yescharacteristic
70C2×#41×C73C2311yescharacteristic
71C2×#41×C73C2311yescharacteristic
72C22×Q8×C73C2311yescharacteristic
73C22×D4×C73C2311yescharacteristic
74#137×C73—22no—
75#137×C73—22no—
76#137×C73—41no—
77#137×C73—41no—
78AGL(1,ℤ/8)×C73—22no—
79AGL(1,ℤ/8)×C73—22no—
80AGL(1,ℤ/8)×C73—41no—
81AGL(1,ℤ/8)×C73—41no—
82#135×C73—22no—
83#135×C73—22no—
84C2×Q16×C73—21no—
85C2×Q16×C73—21no—
86C2×Q16×C73D411yescharacteristic
87C2×SD16×C73—21no—
88C2×SD16×C73—21no—
89C2×SD16×C73—21no—
90C2×SD16×C73—21no—
91C2×SD16×C73—22no—
92C2×SD16×C73—21no—
93C2×SD16×C73—21no—
94C2×SD16×C73—22no—
95C2×SD16×C73D411yescharacteristic
96C2×SD16×C73D411yescharacteristic
97C2×D8×C73—21no—
98C2×D8×C73—21no—
99C2×D8×C73D411yescharacteristic
100#131×C73—22no—
101#131×C73—22no—
102#131×C73—22no—
103#131×C73—22no—
104#131×C73—41no—
105#131×C73—41no—
106C2×M16×C73—21no—
107C2×M16×C73—21no—
108C2×M16×C73—21no—
109C2×M16×C73C2311yescharacteristic
110C2×M16×C73C2311yescharacteristic
111C2×M16×C73C2311yescharacteristic
112C2×M16×C73C2311yescharacteristic
113C22×C8×C73—21no—
114C22×C8×C73—21no—
115C22×C8×C73—21no—
116C22×C8×C73C2311yescharacteristic
117C22×C8×C73C2311yescharacteristic
118C4⋊Q8×C73—21no—
119#127×C73—21no—
120#124×C73—21no—
121#124×C73—21no—
122#123×C73—41no—
123C22⋊Q8×C73—21no—
124C22⋊Q8×C73—21no—
125C22⋊Q8×C73—21no—
126C22⋊Q8×C73—21no—
127C22⋊Q8×C73—21no—
128C22⋊Q8×C73—21no—
129#121×C73—21no—
130#121×C73—21no—
131#121×C73—21no—
132#121×C73—21no—
133#121×C73—21no—
134#121×C73—21no—
135#121×C73—41no—
136#121×C73—41no—
137#120×C73—41no—
138#117×C73C2311yescharacteristic
139C2×C4⋊C4×C73C2311yescharacteristic
140C2×C4⋊C4×C73C2311yescharacteristic
141C2×C22⋊C4×C73—41no—
142C2×C42×C73C2311yescharacteristic
143#108×C73D414yescomplemented
144#107×C73—21no—
145#107×C73—21no—
146#106×C73—21no—
147#106×C73—21no—
148#106×C73—21no—
149#106×C73—21no—
150#104×C73—22no—
151#104×C73—22no—
152#104×C73—22no—
153#103×C73—21no—
154#103×C73—21no—
155#103×C73—21no—
156#103×C73—21no—
157#103×C73D411yescharacteristic
158#103×C73D411yescharacteristic
159#102×C73—21no—
160#102×C73—21no—
161#102×C73—21no—
162#102×C73—21no—
163#102×C73D411yescharacteristic
164#102×C73D411yescharacteristic
165#101×C73—22no—
166#100×C73—22no—
167#97×C73—21no—
168C4×C8×C73—22no—
169C4×C8×C73—21no—
170#95×C73—41no—
171C24×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—
180#41×C73—21no—
181#41×C73—21no—
182#41×C73—21no—
183#41×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—21no—
186C2×Q8×C73—21no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73—21no—
190C2×Q8×C73C2×D411yescharacteristic
191C2×Q8×C73C2×D411yescharacteristic
192C2×Q8×C73C2×D411yescharacteristic
193C2×D4×C73—21no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—41no—
203C2×D4×C73—41no—
204C2×D4×C73—41no—
205C2×D4×C73—41no—
206C2×D4×C73C2×D411yescharacteristic
207C2×D4×C73C2×D411yescharacteristic
208C2×D4×C73C2×D411yescharacteristic
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73—21no—
215C22×C4×C73—21no—
216C22×C4×C73C2411yescharacteristic
217Q16×C73—22no—
218Q16×C73—42no—
219Q16×C73—42no—
220SD16×C73—22no—
221SD16×C73—22no—
222SD16×C73—42no—
223SD16×C73—42no—
224SD16×C73—42no—
225SD16×C73—42no—
226SD16×C73—42no—
227SD16×C73—42no—
228D8×C73—22no—
229D8×C73—42no—
230D8×C73—42no—
231M16×C73—21no—
232M16×C73—21no—
233M16×C73—21no—
234M16×C73—21no—
235M16×C73—21no—
236M16×C73—42no—
237M16×C73—42no—
238M16×C73—42no—
239M16×C73C2×D412yes—
240M16×C73C2×D412yes—
241M16×C73#4112yes—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C2×C8×C73—42no—
249C2×C8×C73—42no—
250C2×C8×C73—42no—
251C2×C8×C73C2×D411yescharacteristic
252C2×C8×C73C2×D411yescharacteristic
253C2×C8×C73C2×D411yescharacteristic
254C2×C8×C73C2×D412yes—
255C2×C8×C73C2×D411yescharacteristic
256C2×C8×C73#4112yes—
257C4⋊C4×C73—21no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—41no—
262C4⋊C4×C73—41no—
263C4⋊C4×C73—41no—
264C4⋊C4×C73—41no—
265C4⋊C4×C73C2×D411yescharacteristic
266C4⋊C4×C73C2×D411yescharacteristic
267C22⋊C4×C73—21no—
268C22⋊C4×C73—41no—
269C22⋊C4×C73—41no—
270C22⋊C4×C73—41no—
271C22⋊C4×C73—41no—
272C22⋊C4×C73—41no—
273C22⋊C4×C73—41no—
274C22⋊C4×C73—41no—
275C22⋊C4×C73—41no—
276C22⋊C4×C73—82no—
277C42×C73—21no—
278C42×C73—21no—
279C42×C73—21no—
280C23×C73—21no—
281C23×C73—21no—
282C23×C73—21no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—41no—
286C23×C73—81no—
287C23×C73—81no—
288C23×C73H(5,𝔽2)11yescharacteristic
289Q8×C73—21no—
290Q8×C73—21no—
291Q8×C73—21no—
292Q8×C73—21no—
293Q8×C73—21no—
294Q8×C73—21no—
295Q8×C73—41no—
296Q8×C73—41no—
297Q8×C73—41no—
298Q8×C73—41no—
299D4×C73—21no—
300D4×C73—21no—
301D4×C73—21no—
302D4×C73—21no—
303D4×C73—21no—
304D4×C73—21no—
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—41no—
314D4×C73—41no—
315D4×C73—161no—
316D4×C73—161no—
317D4×C73—161no—
318D4×C73—161no—
319C2×C4×C73—22no—
320C2×C4×C73—21no—
321C2×C4×C73—21no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—21no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—41no—
328C2×C4×C73—41no—
329C2×C4×C73—41no—
330C2×C4×C73—41no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—41no—
338C2×C4×C73—81no—
339C2×C4×C73—81no—
340C2×C4×C73C22×D411yescharacteristic
341C2×C4×C73C22×D411yescharacteristic
342C2×C4×C73C22×D411yescharacteristic
343C2×C4×C73C2×#4111yescharacteristic
344C2×C4×C73C2×#4111yescharacteristic
345C2×C4×C73H(5,𝔽2)11yescharacteristic
346C8×C73—21no—
347C8×C73—21no—
348C8×C73—22no—
349C8×C73—22no—
350C8×C73—22no—
351C8×C73—41no—
352C8×C73#12112yes—
353C8×C73#12112yes—
354C22×C73—21no—
355C22×C73—21no—
356C22×C73—41no—
357C22×C73—41no—
358C22×C73—41no—
359C22×C73—41no—
360C22×C73—41no—
361C22×C73—41no—
362C22×C73—41no—
363C22×C73—41no—
364C22×C73—41no—
365C22×C73—82no—
366C22×C73—81no—
367C22×C73—81no—
368C22×C73—81no—
369C22×C73—161no—
370C22×C73#54011yescharacteristic
371C22×C73D4211yescharacteristic
372C22×C73#55011yescharacteristic
373C4×C73—42no—
374C4×C73—41no—
375C4×C73—41no—
376C4×C73—41no—
377C4×C73—41no—
378C4×C73—41no—
379C4×C73—81no—
380C4×C73—81no—
381C4×C73—81no—
382C4×C73C2×#12111yescharacteristic
383C4×C73#53211yescharacteristic
384C4×C73D4211yescharacteristic
385C4×C73#54611yescharacteristic
386#25440C7311yesmaximal, characteristic, direct product factor, Sylow
387C2×C73—21no—
388C2×C73—21no—
389C2×C73—81no—
390C2×C73—81no—
391C2×C73—81no—
392C2×C73—161no—
393C2×C73#242811yescharacteristic
394C2×C73#329011yescharacteristic
395C2×C73#329111yescharacteristic
396#3154C2×C7311yescharacteristic, complemented
397C2×#471C2×C7311yescharacteristic, complemented
398#3063C2×C7311yescharacteristic, complemented
399#3062C2×C7311yescharacteristic, complemented
400#3060C2×C7311yescharacteristic, complemented
401C2×#443C2×C7311yescharacteristic, complemented
402#2038C2×C7311yescharacteristic, complemented
403#2037C2×C7311yescharacteristic, complemented
404#2007C2×C7311yescharacteristic, complemented
405#2006C2×C7311yescharacteristic, complemented
406#1968C2×C7311yescharacteristic, complemented
407#1951C2×C7311yescharacteristic, complemented
408#1908C2×C7311yescharacteristic, complemented
409#1907C2×C7311yescharacteristic, complemented
410#1764C2×C7311yescharacteristic, complemented
411C73#2544011yescharacteristic, direct product factor, Sylow
412C2×#137C22×C7311yescharacteristic
413C2×#137C22×C7311yescharacteristic
414C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
415C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
416C2×#135C22×C7311yescharacteristic
417C22×SD16C22×C7311yescharacteristic
418C2×#131C22×C7311yescharacteristic
419C2×#131C22×C7311yescharacteristic
420C2×#131C22×C7311yescharacteristic
421#537C22×C7311yescharacteristic
422#537C22×C7311yescharacteristic
423#536C22×C7311yescharacteristic
424#535C22×C7311yescharacteristic
425#497—21no—
426#496—21no—
427#495—21no—
428#492—21no—
429#471—24no—
430#470—21no—
431#470—21no—
432#469—21no—
433#469—21no—
434#468—21no—
435#468—21no—
436#467—21no—
437#466—21no—
438#465—21no—
439#465—21no—
440#465—21no—
441#465—21no—
442#443—24no—
443C2×#108C22×C7311yescharacteristic
444#428C22×C7311yescharacteristic
445#428C22×C7311yescharacteristic
446C2×#106C22×C7311yescharacteristic
447C2×#104C22×C7311yescharacteristic
448C2×#104C22×C7311yescharacteristic
449C2×#104C22×C7311yescharacteristic
450#417C22×C7311yescharacteristic
451#417C22×C7311yescharacteristic
452#416C22×C7311yescharacteristic
453C2×#103C22×C7311yescharacteristic
454C2×#102C22×C7311yescharacteristic
455C2×#101C22×C7311yescharacteristic
456C2×#100C22×C7311yescharacteristic
457#405C22×C7311yescharacteristic
458C2×C4×C8C22×C7311yescharacteristic
459#391C22×C7311yescharacteristic
460#390C22×C7311yescharacteristic
461#343C22×C7311yescharacteristic
462#343C22×C7311yescharacteristic
463#341C22×C7311yescharacteristic
464#339C22×C7311yescharacteristic
465C2×#41C23×C7311yescharacteristic
466C2×#41C23×C7311yescharacteristic
467C2×#41C23×C7311yescharacteristic
468C22×Q8C23×C7311yescharacteristic
469C22×D4C23×C7311yescharacteristic
470#137—22no—
471#137—22no—
472#137—41no—
473#137—41no—
474AGL(1,ℤ/8)—22no—
475AGL(1,ℤ/8)—22no—
476AGL(1,ℤ/8)—41no—
477AGL(1,ℤ/8)—41no—
478#135—22no—
479#135—22no—
480C2×Q16—21no—
481C2×Q16—21no—
482C2×Q16D4×C7311yescharacteristic
483C2×SD16—21no—
484C2×SD16—21no—
485C2×SD16—21no—
486C2×SD16—21no—
487C2×SD16—22no—
488C2×SD16—21no—
489C2×SD16—21no—
490C2×SD16—22no—
491C2×SD16D4×C7311yescharacteristic
492C2×SD16D4×C7311yescharacteristic
493C2×D8—21no—
494C2×D8—21no—
495C2×D8D4×C7311yescharacteristic
496#131—22no—
497#131—22no—
498#131—22no—
499#131—22no—
500#131—41no—
501#131—41no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16C23×C7311yescharacteristic
506C2×M16C23×C7311yescharacteristic
507C2×M16C23×C7311yescharacteristic
508C2×M16C23×C7311yescharacteristic
509C22×C8—21no—
510C22×C8—21no—
511C22×C8—21no—
512C22×C8C23×C7311yescharacteristic
513C22×C8C23×C7311yescharacteristic
514C4⋊Q8—21no—
515#127—21no—
516#124—21no—
517#124—21no—
518#123—41no—
519C22⋊Q8—21no—
520C22⋊Q8—21no—
521C22⋊Q8—21no—
522C22⋊Q8—21no—
523C22⋊Q8—21no—
524C22⋊Q8—21no—
525#121—21no—
526#121—21no—
527#121—21no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—41no—
532#121—41no—
533#120—41no—
534#117C23×C7311yescharacteristic
535C2×C4⋊C4C23×C7311yescharacteristic
536C2×C4⋊C4C23×C7311yescharacteristic
537C2×C22⋊C4—41no—
538C2×C42C23×C7311yescharacteristic
539#108D4×C7314yescomplemented
540#107—21no—
541#107—21no—
542#106—21no—
543#106—21no—
544#106—21no—
545#106—21no—
546#104—22no—
547#104—22no—
548#104—22no—
549#103—21no—
550#103—21no—
551#103—21no—
552#103—21no—
553#103D4×C7311yescharacteristic
554#103D4×C7311yescharacteristic
555#102—21no—
556#102—21no—
557#102—21no—
558#102—21no—
559#102D4×C7311yescharacteristic
560#102D4×C7311yescharacteristic
561#101—22no—
562#100—22no—
563#97—21no—
564C4×C8—22no—
565C4×C8—21no—
566#95—41no—
567C24—21no—
568#41—21no—
569#41—21no—
570#41—21no—
571#41—21no—
572#41—21no—
573#41—21no—
574#41—21no—
575#41—21no—
576#41—21no—
577#41—21no—
578#41—21no—
579#41—21no—
580C2×Q8—21no—
581C2×Q8—21no—
582C2×Q8—21no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8C2×D4×C7311yescharacteristic
587C2×Q8C2×D4×C7311yescharacteristic
588C2×Q8C2×D4×C7311yescharacteristic
589C2×D4—21no—
590C2×D4—21no—
591C2×D4—21no—
592C2×D4—21no—
593C2×D4—21no—
594C2×D4—21no—
595C2×D4—21no—
596C2×D4—21no—
597C2×D4—21no—
598C2×D4—41no—
599C2×D4—41no—
600C2×D4—41no—
601C2×D4—41no—
602C2×D4C2×D4×C7311yescharacteristic
603C2×D4C2×D4×C7311yescharacteristic
604C2×D4C2×D4×C7311yescharacteristic
605C22×C4—21no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—21no—
609C22×C4—21no—
610C22×C4—21no—
611C22×C4—21no—
612C22×C4C24×C7311yescharacteristic
613Q16—22no—
614Q16—42no—
615Q16—42no—
616SD16—22no—
617SD16—22no—
618SD16—42no—
619SD16—42no—
620SD16—42no—
621SD16—42no—
622SD16—42no—
623SD16—42no—
624D8—22no—
625D8—42no—
626D8—42no—
627M16—21no—
628M16—21no—
629M16—21no—
630M16—21no—
631M16—21no—
632M16—42no—
633M16—42no—
634M16—42no—
635M16C2×D4×C7312yes—
636M16C2×D4×C7312yes—
637M16#41×C7312yes—
638C2×C8—21no—
639C2×C8—21no—
640C2×C8—21no—
641C2×C8—21no—
642C2×C8—21no—
643C2×C8—21no—
644C2×C8—42no—
645C2×C8—42no—
646C2×C8—42no—
647C2×C8C2×D4×C7311yescharacteristic
648C2×C8C2×D4×C7311yescharacteristic
649C2×C8C2×D4×C7311yescharacteristic
650C2×C8C2×D4×C7312yes—
651C2×C8C2×D4×C7311yescharacteristic
652C2×C8#41×C7312yes—
653C4⋊C4—21no—
654C4⋊C4—21no—
655C4⋊C4—21no—
656C4⋊C4—21no—
657C4⋊C4—41no—
658C4⋊C4—41no—
659C4⋊C4—41no—
660C4⋊C4—41no—
661C4⋊C4C2×D4×C7311yescharacteristic
662C4⋊C4C2×D4×C7311yescharacteristic
663C22⋊C4—21no—
664C22⋊C4—41no—
665C22⋊C4—41no—
666C22⋊C4—41no—
667C22⋊C4—41no—
668C22⋊C4—41no—
669C22⋊C4—41no—
670C22⋊C4—41no—
671C22⋊C4—41no—
672C22⋊C4—82no—
673C42—21no—
674C42—21no—
675C42—21no—
676C23—21no—
677C23—21no—
678C23—21no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—81no—
683C23—81no—
684C23H(5,𝔽2)×C7311yescharacteristic
685Q8—21no—
686Q8—21no—
687Q8—21no—
688Q8—21no—
689Q8—21no—
690Q8—21no—
691Q8—41no—
692Q8—41no—
693Q8—41no—
694Q8—41no—
695D4—21no—
696D4—21no—
697D4—21no—
698D4—21no—
699D4—21no—
700D4—21no—
701D4—41no—
702D4—41no—
703D4—41no—
704D4—41no—
705D4—41no—
706D4—41no—
707D4—41no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—161no—
712D4—161no—
713D4—161no—
714D4—161no—
715C2×C4—22no—
716C2×C4—21no—
717C2×C4—21no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—41no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—41no—
732C2×C4—41no—
733C2×C4—41no—
734C2×C4—81no—
735C2×C4—81no—
736C2×C4C22×D4×C7311yescharacteristic
737C2×C4C22×D4×C7311yescharacteristic
738C2×C4C22×D4×C7311yescharacteristic
739C2×C4C2×#41×C7311yescharacteristic
740C2×C4C2×#41×C7311yescharacteristic
741C2×C4H(5,𝔽2)×C7311yescharacteristic
742C8—21no—
743C8—21no—
744C8—22no—
745C8—22no—
746C8—22no—
747C8—41no—
748C8#121×C7312yes—
749C8#121×C7312yes—
750C22—21no—
751C22—21no—
752C22—41no—
753C22—41no—
754C22—41no—
755C22—41no—
756C22—41no—
757C22—41no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—82no—
762C22—81no—
763C22—81no—
764C22—81no—
765C22—161no—
766C22#540×C7311yescharacteristic
767C22D42×C7311yescharacteristic
768C22#550×C7311yescharacteristic
769C4—42no—
770C4—41no—
771C4—41no—
772C4—41no—
773C4—41no—
774C4—41no—
775C4—81no—
776C4—81no—
777C4—81no—
778C4C2×#121×C7311yescharacteristic
779C4#532×C7311yescharacteristic
780C4D42×C7311yescharacteristic
781C4#546×C7311yescharacteristic
782C2—21no—
783C2—21no—
784C2—81no—
785C2—81no—
786C2—81no—
787C2—161no—
788C2C73×#242811yescharacteristic
789C2C73×#329011yescharacteristic
790C2C73×#329111yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
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. C73×#3154C2semidirect
2. C2×#471×C73C2semidirect
3. C73×#3063C2semidirect
4. C73×#3062C2semidirect
5. C73×#3060C2semidirect
6. C2×#443×C73C2semidirect
7. C73×#2038C2semidirect
8. C73×#2037C2semidirect
9. C73×#2007C2semidirect
10. C73×#2006C2semidirect
11. C73×#1968C2semidirect
12. C73×#1951C2semidirect
13. C73×#1908C2semidirect
14. C73×#1907C2semidirect
15. C73×#1764C2semidirect
143. #108×C73D4semidirect
386. #25440C73direct (N × H)
396. #3154C2×C73semidirect
397. C2×#471C2×C73semidirect
398. #3063C2×C73semidirect
399. #3062C2×C73semidirect
400. #3060C2×C73semidirect
401. C2×#443C2×C73semidirect
402. #2038C2×C73semidirect
403. #2037C2×C73semidirect
404. #2007C2×C73semidirect
405. #2006C2×C73semidirect
406. #1968C2×C73semidirect
407. #1951C2×C73semidirect
408. #1908C2×C73semidirect
409. #1907C2×C73semidirect
410. #1764C2×C73semidirect
411. C73#25440direct (N × H)
539. #108D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#31542
C2×#471×C732
C73×#30632
C73×#30622
C73×#30602
C2×#443×C732
C73×#20382
C73×#20372
C73×#20072
C73×#20062
C73×#19682
C73×#19512
C73×#19082
C73×#19072
C73×#17642
#2544073