Finite Group Databasebeta

← C73×#18418 #32927822

Subgroups — C73×#18418 #32927822

Order 18688.

1176 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3537C211yesmaximal, characteristic, complemented
2C73×#3192C211yesmaximal, characteristic, complemented
3C73×#3188C211yesmaximal, characteristic, complemented
4C73×#2656C211yesmaximal, characteristic, complemented
5C73×#1618C212yesmaximal, complemented
6C73×#1613C212yesmaximal, complemented
7C73×#1600C212yesmaximal, complemented
8C73×#1595C212yesmaximal, complemented
9C73×#1504C211yesmaximal, characteristic, complemented
10C2×#327×C73C211yesmaximal, characteristic, complemented
11C73×#1471C211yesmaximal, characteristic, complemented
12#560×C73—22no—
13#553×C73—21no—
14#553×C73—21no—
15D42×C73—22no—
16D42×C73—21no—
17D42×C73—21no—
18#540×C73—21no—
19#538×C73—21no—
20#538×C73C2212yes—
21#535×C73—21no—
22#534×C73—21no—
23#534×C73C2212yes—
24#525×C73C2211yescharacteristic
25C2×#121×C73—22no—
26C2×#121×C73C2211yescharacteristic
27C2×#121×C73C2211yescharacteristic
28C2×#121×C73C2211yescharacteristic, complemented
29#484×C73C2211yescharacteristic, complemented
30#482×C73—21no—
31#481×C73—21no—
32#481×C73C2211yescharacteristic, complemented
33#481×C73C2212yescomplemented
34#469×C73—22no—
35#466×C73—21no—
36#465×C73—21no—
37#450×C73C2211yescharacteristic, complemented
38#449×C73—21no—
39#447×C73—21no—
40#447×C73C2211yescharacteristic, complemented
41#447×C73C2212yescomplemented
42#407×C73C2211yescharacteristic, complemented
43C2×C22⋊C8×C73C2211yescharacteristic, complemented
44#399×C73—21no—
45#399×C73C2212yescomplemented
46#392×C73—21no—
47#392×C73C2212yescomplemented
48C2×#95×C73C2211yescharacteristic, complemented
49#328×C73C2212yescomplemented
50#327×C73C2212yescomplemented
51#327×C73C2212yescomplemented
52#327×C73C2212yescomplemented
53#323×C73C2212yescomplemented
54#323×C73C2212yescomplemented
55C2×#41×C73D411yescharacteristic, complemented
56C22×D4×C73—22no—
57C22×D4×C73—21no—
58C22×D4×C73—21no—
59C22×D4×C73—22no—
60C22×D4×C73—21no—
61C22×D4×C73—22no—
62C22×D4×C73D412yes—
63C22×D4×C73D411yescharacteristic
64C22×D4×C73D411yescharacteristic, complemented
65C22×D4×C73C2311yescharacteristic
66C23×C4×C73—21no—
67C23×C4×C73C2311yescharacteristic
68C2×SD16×C73—21no—
69C2×D8×C73—22no—
70C2×D8×C73—21no—
71C2×M16×C73—21no—
72C22×C8×C73—21no—
73#127×C73—22no—
74#127×C73—21no—
75#126×C73—22no—
76#126×C73—22no—
77#125×C73—21no—
78#124×C73—22no—
79#123×C73—22no—
80#123×C73—21no—
81#123×C73—22no—
82#123×C73—22no—
83#123×C73—22no—
84C22⋊Q8×C73D411yescharacteristic, complemented
85C22⋊Q8×C73C2311yescharacteristic
86#121×C73—22no—
87#121×C73—21no—
88#121×C73—21no—
89#121×C73—22no—
90#121×C73—22no—
91#121×C73—22no—
92#121×C73—22no—
93#121×C73—21no—
94#121×C73—21no—
95#121×C73—21no—
96#121×C73—21no—
97#121×C73—21no—
98#121×C73—21no—
99#121×C73—22no—
100#121×C73—21no—
101#121×C73—21no—
102#121×C73—21no—
103#121×C73—21no—
104#121×C73—48no—
105#121×C73D411yescharacteristic, complemented
106#121×C73D412yescomplemented
107#121×C73C2312yes—
108#121×C73C2311yescharacteristic
109#120×C73—22no—
110#120×C73—22no—
111#120×C73—22no—
112#120×C73—21no—
113#120×C73—22no—
114#120×C73—22no—
115#120×C73—22no—
116C4×D4×C73—22no—
117C4×D4×C73—21no—
118C4×D4×C73—21no—
119C4×D4×C73—21no—
120C4×D4×C73—21no—
121C4×D4×C73—22no—
122#117×C73—21no—
123#117×C73D411yescharacteristic, complemented
124C2×C4⋊C4×C73—22no—
125C2×C4⋊C4×C73D411yescharacteristic
126C2×C4⋊C4×C73D411yescharacteristic, complemented
127C2×C4⋊C4×C73C2311yescharacteristic
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—21no—
131C2×C22⋊C4×C73—22no—
132C2×C22⋊C4×C73C2312yes—
133#107×C73—21no—
134#106×C73—21no—
135#106×C73—22no—
136#103×C73—21no—
137#102×C73—22no—
138#102×C73—21no—
139#102×C73—21no—
140#102×C73—22no—
141#102×C73—21no—
142C22⋊C8×C73—21no—
143C22⋊C8×C73—21no—
144C22⋊C8×C73C2311yescharacteristic
145C22⋊C8×C73C2311yescharacteristic
146C22⋊C8×C73C2312yes—
147#95×C73—21no—
148#95×C73C2312yes—
149C24×C73—22no—
150C24×C73—21no—
151C24×C73—21no—
152C24×C73C2×D411yescharacteristic
153C24×C73C2×D412yes—
154#41×C73—81no—
155C2×Q8×C73C2×D411yescharacteristic
156C2×D4×C73—22no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—22no—
160C2×D4×C73—22no—
161C2×D4×C73—22no—
162C2×D4×C73—22no—
163C2×D4×C73—22no—
164C2×D4×C73—22no—
165C2×D4×C73—21no—
166C2×D4×C73—22no—
167C2×D4×C73—22no—
168C2×D4×C73—21no—
169C2×D4×C73—21no—
170C2×D4×C73—21no—
171C2×D4×C73—21no—
172C2×D4×C73—21no—
173C2×D4×C73—44no—
174C2×D4×C73—44no—
175C2×D4×C73—44no—
176C2×D4×C73—41no—
177C2×D4×C73—41no—
178C2×D4×C73—81no—
179C2×D4×C73—81no—
180C2×D4×C73—82no—
181C2×D4×C73—81no—
182C2×D4×C73—82no—
183C2×D4×C73—82no—
184C2×D4×C73—81no—
185C2×D4×C73—81no—
186C2×D4×C73—82no—
187C2×D4×C73—82no—
188C2×D4×C73—84no—
189C2×D4×C73C2×D411yescharacteristic
190C2×D4×C73C2×D412yes—
191C22×C4×C73—22no—
192C22×C4×C73—22no—
193C22×C4×C73—22no—
194C22×C4×C73—24no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—81no—
199C22×C4×C73—81no—
200C22×C4×C73—81no—
201C22×C4×C73C2×D412yes—
202C22×C4×C73C2×D411yescharacteristic
203C22×C4×C73C2×D411yescharacteristic
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2411yescharacteristic
208SD16×C73—81no—
209D8×C73—81no—
210D8×C73—82no—
211M16×C73—81no—
212C2×C8×C73—21no—
213C2×C8×C73—22no—
214C2×C8×C73—21no—
215C2×C8×C73—81no—
216C4⋊C4×C73—22no—
217C4⋊C4×C73—22no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—44no—
226C4⋊C4×C73C2×D412yes—
227C4⋊C4×C73C2×D411yescharacteristic
228C4⋊C4×C73C2×D411yescharacteristic
229C22⋊C4×C73—22no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—22no—
232C22⋊C4×C73—22no—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—21no—
235C22⋊C4×C73—21no—
236C22⋊C4×C73—21no—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—21no—
239C22⋊C4×C73—22no—
240C22⋊C4×C73—22no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—21no—
243C22⋊C4×C73—44no—
244C22⋊C4×C73—44no—
245C22⋊C4×C73—41no—
246C22⋊C4×C73—41no—
247C42×C73—22no—
248C42×C73—21no—
249C23×C73—21no—
250C23×C73—21no—
251C23×C73—22no—
252C23×C73—22no—
253C23×C73—22no—
254C23×C73—21no—
255C23×C73—22no—
256C23×C73—22no—
257C23×C73—41no—
258C23×C73—42no—
259C23×C73—42no—
260C23×C73—42no—
261C23×C73—42no—
262C23×C73—42no—
263C23×C73—41no—
264C23×C73—41no—
265C23×C73—41no—
266C23×C73—81no—
267C23×C73—81no—
268C23×C73—82no—
269C23×C73—82no—
270C23×C73—82no—
271C23×C73#12011yescharacteristic
272C23×C73#12011yescharacteristic
273C23×C73C22×D411yescharacteristic
274Q8×C73—41no—
275D4×C73—42no—
276D4×C73—41no—
277D4×C73—42no—
278D4×C73—42no—
279D4×C73—42no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—42no—
283D4×C73—41no—
284D4×C73—42no—
285D4×C73—41no—
286D4×C73—44no—
287D4×C73—42no—
288D4×C73—81no—
289D4×C73—82no—
290D4×C73—82no—
291D4×C73—81no—
292D4×C73—82no—
293D4×C73—82no—
294D4×C73—82no—
295D4×C73—82no—
296D4×C73—82no—
297D4×C73—88no—
298D4×C73—82no—
299D4×C73—82no—
300C2×C4×C73—24no—
301C2×C4×C73—21no—
302C2×C4×C73—22no—
303C2×C4×C73—22no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
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—42no—
313C2×C4×C73—42no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—41no—
318C2×C4×C73—81no—
319C2×C4×C73—84no—
320C2×C4×C73—82no—
321C2×C4×C73—82no—
322C2×C4×C73#12011yescharacteristic
323C2×C4×C73#12011yescharacteristic
324C2×C4×C73C22×D411yescharacteristic
325C2×C4×C73C22×D411yescharacteristic
326C8×C73—41no—
327C8×C73—41no—
328C8×C73—42no—
329C22×C73—21no—
330C22×C73—21no—
331C22×C73—21no—
332C22×C73—21no—
333C22×C73—21no—
334C22×C73—21no—
335C22×C73—21no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—42no—
339C22×C73—42no—
340C22×C73—41no—
341C22×C73—42no—
342C22×C73—42no—
343C22×C73—41no—
344C22×C73—41no—
345C22×C73—42no—
346C22×C73—42no—
347C22×C73—82no—
348C22×C73—82no—
349C22×C73—82no—
350C22×C73—82no—
351C22×C73—81no—
352C22×C73—81no—
353C22×C73—81no—
354C22×C73—162no—
355C22×C73—164no—
356C22×C73#45312yes—
357C22×C73C2×#12011yescharacteristic
358C22×C73#57611yescharacteristic
359C22×C73#57711yescharacteristic
360C4×C73—21no—
361C4×C73—21no—
362C4×C73—21no—
363C4×C73—21no—
364C4×C73—44no—
365C4×C73—42no—
366C4×C73—41no—
367C4×C73—42no—
368C4×C73—41no—
369C4×C73—41no—
370C4×C73—81no—
371#18418C7311yesmaximal, characteristic, direct product factor, Sylow
372C2×C73—21no—
373C2×C73—21no—
374C2×C73—22no—
375C2×C73—41no—
376C2×C73—82no—
377C2×C73—82no—
378C2×C73—81no—
379C2×C73—161no—
380C2×C73#301211yescharacteristic
381C2×C73C2×#45311yescharacteristic
382C2×C73#302611yescharacteristic
383#3537C2×C7311yescharacteristic, complemented
384#3192C2×C7311yescharacteristic, complemented
385#3188C2×C7311yescharacteristic, complemented
386#2656C2×C7311yescharacteristic, complemented
387#1618C2×C7312yescomplemented
388#1613C2×C7312yescomplemented
389#1600C2×C7312yescomplemented
390#1595C2×C7312yescomplemented
391#1504C2×C7311yescharacteristic, complemented
392C2×#327C2×C7311yescharacteristic, complemented
393#1471C2×C7311yescharacteristic, complemented
394C73#1841811yescharacteristic, direct product factor, Sylow
395#560—22no—
396#553—21no—
397#553—21no—
398D42—22no—
399D42—21no—
400D42—21no—
401#540—21no—
402#538—21no—
403#538C22×C7312yes—
404#535—21no—
405#534—21no—
406#534C22×C7312yes—
407#525C22×C7311yescharacteristic
408C2×#121—22no—
409C2×#121C22×C7311yescharacteristic
410C2×#121C22×C7311yescharacteristic
411C2×#121C22×C7311yescharacteristic, complemented
412#484C22×C7311yescharacteristic, complemented
413#482—21no—
414#481—21no—
415#481C22×C7311yescharacteristic, complemented
416#481C22×C7312yescomplemented
417#469—22no—
418#466—21no—
419#465—21no—
420#450C22×C7311yescharacteristic, complemented
421#449—21no—
422#447—21no—
423#447C22×C7311yescharacteristic, complemented
424#447C22×C7312yescomplemented
425#407C22×C7311yescharacteristic, complemented
426C2×C22⋊C8C22×C7311yescharacteristic, complemented
427#399—21no—
428#399C22×C7312yescomplemented
429#392—21no—
430#392C22×C7312yescomplemented
431C2×#95C22×C7311yescharacteristic, complemented
432#328C22×C7312yescomplemented
433#327C22×C7312yescomplemented
434#327C22×C7312yescomplemented
435#327C22×C7312yescomplemented
436#323C22×C7312yescomplemented
437#323C22×C7312yescomplemented
438C2×#41D4×C7311yescharacteristic, complemented
439C22×D4—22no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—22no—
445C22×D4D4×C7312yes—
446C22×D4D4×C7311yescharacteristic
447C22×D4D4×C7311yescharacteristic, complemented
448C22×D4C23×C7311yescharacteristic
449C23×C4—21no—
450C23×C4C23×C7311yescharacteristic
451C2×SD16—21no—
452C2×D8—22no—
453C2×D8—21no—
454C2×M16—21no—
455C22×C8—21no—
456#127—22no—
457#127—21no—
458#126—22no—
459#126—22no—
460#125—21no—
461#124—22no—
462#123—22no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123—22no—
467C22⋊Q8D4×C7311yescharacteristic, complemented
468C22⋊Q8C23×C7311yescharacteristic
469#121—22no—
470#121—21no—
471#121—21no—
472#121—22no—
473#121—22no—
474#121—22no—
475#121—22no—
476#121—21no—
477#121—21no—
478#121—21no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—22no—
483#121—21no—
484#121—21no—
485#121—21no—
486#121—21no—
487#121—48no—
488#121D4×C7312yescomplemented
489#121D4×C7311yescharacteristic, complemented
490#121C23×C7312yes—
491#121C23×C7311yescharacteristic
492#120—22no—
493#120—22no—
494#120—22no—
495#120—21no—
496#120—22no—
497#120—22no—
498#120—22no—
499C4×D4—22no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—22no—
505#117—21no—
506#117D4×C7311yescharacteristic, complemented
507C2×C4⋊C4—22no—
508C2×C4⋊C4D4×C7311yescharacteristic
509C2×C4⋊C4D4×C7311yescharacteristic, complemented
510C2×C4⋊C4C23×C7311yescharacteristic
511C2×C22⋊C4—21no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—21no—
515C2×C22⋊C4C23×C7312yes—
516#107—21no—
517#106—21no—
518#106—22no—
519#103—21no—
520#102—22no—
521#102—21no—
522#102—21no—
523#102—22no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527C22⋊C8C23×C7311yescharacteristic
528C22⋊C8C23×C7311yescharacteristic
529C22⋊C8C23×C7312yes—
530#95—21no—
531#95C23×C7312yes—
532C24—22no—
533C24—21no—
534C24—21no—
535C24C2×D4×C7311yescharacteristic
536C24C2×D4×C7312yes—
537#41—81no—
538C2×Q8C2×D4×C7311yescharacteristic
539C2×D4—22no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—22no—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—21no—
549C2×D4—22no—
550C2×D4—22no—
551C2×D4—21no—
552C2×D4—21no—
553C2×D4—21no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4—44no—
559C2×D4—41no—
560C2×D4—41no—
561C2×D4—81no—
562C2×D4—81no—
563C2×D4—82no—
564C2×D4—81no—
565C2×D4—82no—
566C2×D4—82no—
567C2×D4—81no—
568C2×D4—81no—
569C2×D4—82no—
570C2×D4—82no—
571C2×D4—84no—
572C2×D4C2×D4×C7311yescharacteristic
573C2×D4C2×D4×C7312yes—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—24no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—81no—
582C22×C4—81no—
583C22×C4—81no—
584C22×C4C2×D4×C7312yes—
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C2×D4×C7311yescharacteristic
587C22×C4C2×D4×C7311yescharacteristic
588C22×C4C2×D4×C7311yescharacteristic
589C22×C4C2×D4×C7311yescharacteristic
590C22×C4C24×C7311yescharacteristic
591SD16—81no—
592D8—81no—
593D8—82no—
594M16—81no—
595C2×C8—21no—
596C2×C8—22no—
597C2×C8—21no—
598C2×C8—81no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—44no—
609C4⋊C4C2×D4×C7312yes—
610C4⋊C4C2×D4×C7311yescharacteristic
611C4⋊C4C2×D4×C7311yescharacteristic
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—21no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—21no—
626C22⋊C4—44no—
627C22⋊C4—44no—
628C22⋊C4—41no—
629C22⋊C4—41no—
630C42—22no—
631C42—21no—
632C23—22no—
633C23—21no—
634C23—21no—
635C23—22no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—41no—
641C23—42no—
642C23—42no—
643C23—42no—
644C23—42no—
645C23—42no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—81no—
650C23—81no—
651C23—82no—
652C23—82no—
653C23—82no—
654C23#120×C7311yescharacteristic
655C23#120×C7311yescharacteristic
656C23C22×D4×C7311yescharacteristic
657Q8—41no—
658D4—42no—
659D4—41no—
660D4—42no—
661D4—42no—
662D4—42no—
663D4—41no—
664D4—41no—
665D4—44no—
666D4—42no—
667D4—42no—
668D4—41no—
669D4—42no—
670D4—41no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
679D4—82no—
680D4—88no—
681D4—82no—
682D4—82no—
683C2×C4—24no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—21no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—81no—
702C2×C4—84no—
703C2×C4—82no—
704C2×C4—82no—
705C2×C4#120×C7311yescharacteristic
706C2×C4#120×C7311yescharacteristic
707C2×C4C22×D4×C7311yescharacteristic
708C2×C4C22×D4×C7311yescharacteristic
709C8—41no—
710C8—41no—
711C8—42no—
712C22—21no—
713C22—21no—
714C22—21no—
715C22—21no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—82no—
731C22—82no—
732C22—82no—
733C22—82no—
734C22—81no—
735C22—81no—
736C22—81no—
737C22—162no—
738C22—164no—
739C22#453×C7312yes—
740C22C2×#120×C7311yescharacteristic
741C22#576×C7311yescharacteristic
742C22#577×C7311yescharacteristic
743C4—21no—
744C4—21no—
745C4—21no—
746C4—21no—
747C4—44no—
748C4—42no—
749C4—41no—
750C4—42no—
751C4—41no—
752C4—41no—
753C4—81no—
754C2—21no—
755C2—21no—
756C2—22no—
757C2—41no—
758C2—82no—
759C2—82no—
760C2—81no—
761C2—161no—
762C2C73×#301211yescharacteristic
763C2C2×#453×C7311yescharacteristic
764C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3537C2semidirect
2. C73×#3192C2semidirect
3. C73×#3188C2semidirect
4. C73×#2656C2semidirect
5. C73×#1618C2semidirect
6. C73×#1613C2semidirect
7. C73×#1600C2semidirect
8. C73×#1595C2semidirect
9. C73×#1504C2semidirect
10. C2×#327×C73C2semidirect
11. C73×#1471C2semidirect
28. C2×#121×C73C22semidirect
29. #484×C73C22semidirect
32. #481×C73C22semidirect
33. #481×C73C22semidirect
37. #450×C73C22semidirect
40. #447×C73C22semidirect
41. #447×C73C22semidirect
42. #407×C73C22semidirect
43. C2×C22⋊C8×C73C22semidirect
45. #399×C73C22semidirect
47. #392×C73C22semidirect
48. C2×#95×C73C22semidirect
49. #328×C73C22semidirect
50. #327×C73C22semidirect
51. #327×C73C22semidirect
52. #327×C73C22semidirect
53. #323×C73C22semidirect
54. #323×C73C22semidirect
55. C2×#41×C73D4semidirect
64. C22×D4×C73D4semidirect
84. C22⋊Q8×C73D4semidirect
105. #121×C73D4semidirect
106. #121×C73D4semidirect
123. #117×C73D4semidirect
126. C2×C4⋊C4×C73D4semidirect
371. #18418C73direct (N × H)
383. #3537C2×C73semidirect
384. #3192C2×C73semidirect
385. #3188C2×C73semidirect
386. #2656C2×C73semidirect
387. #1618C2×C73semidirect
388. #1613C2×C73semidirect
389. #1600C2×C73semidirect
390. #1595C2×C73semidirect
391. #1504C2×C73semidirect
392. C2×#327C2×C73semidirect
393. #1471C2×C73semidirect
394. C73#18418direct (N × H)
411. C2×#121C22×C73semidirect
412. #484C22×C73semidirect
415. #481C22×C73semidirect
416. #481C22×C73semidirect
420. #450C22×C73semidirect
423. #447C22×C73semidirect
424. #447C22×C73semidirect
425. #407C22×C73semidirect
426. C2×C22⋊C8C22×C73semidirect
428. #399C22×C73semidirect
430. #392C22×C73semidirect
431. C2×#95C22×C73semidirect
432. #328C22×C73semidirect
433. #327C22×C73semidirect
434. #327C22×C73semidirect
435. #327C22×C73semidirect
436. #323C22×C73semidirect
437. #323C22×C73semidirect
438. C2×#41D4×C73semidirect
447. C22×D4D4×C73semidirect
467. C22⋊Q8D4×C73semidirect
488. #121D4×C73semidirect
489. #121D4×C73semidirect
506. #117D4×C73semidirect
509. C2×C4⋊C4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35372
C73×#31922
C73×#31882
C73×#26562
C73×#16182
C73×#16132
C73×#16002
C73×#15952
C73×#15042
C2×#327×C732
C73×#14712
#1841873