Finite Group Databasebeta

← C73×#19068 #32928472

Subgroups — C73×#19068 #32928472

Order 18688.

920 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3545C211yesmaximal, characteristic, complemented
2C73×#3219C211yesmaximal, characteristic, complemented
3C73×#3213C211yesmaximal, characteristic, complemented
4C73×#3171C211yesmaximal, characteristic, complemented
5C73×#1664C211yesmaximal, characteristic, complemented
6C73×#1662C211yesmaximal, characteristic, complemented
7C73×#1661C211yesmaximal, characteristic, complemented
8C73×#1659C211yesmaximal, characteristic, complemented
9C73×#1657C211yesmaximal, characteristic, complemented
10C73×#1656C211yesmaximal, characteristic, complemented
11C73×#1656C211yesmaximal, characteristic, complemented
12C73×#1655C211yesmaximal, characteristic, complemented
13C73×#1535C211yesmaximal, characteristic, complemented
14C73×#1529C211yesmaximal, characteristic, complemented
15C73×#1527C211yesmaximal, characteristic, complemented
16#563×C73C2211yescharacteristic
17#562×C73C2211yescharacteristic
18#562×C73C2211yescharacteristic
19H(3,𝔽4)×C73C2211yescharacteristic
20#555×C73—21no—
21#551×C73—21no—
22#551×C73—21no—
23#551×C73—21no—
24#546×C73—21no—
25#546×C73—21no—
26#542×C73—21no—
27#542×C73—21no—
28#538×C73—21no—
29#538×C73—21no—
30#536×C73—21no—
31#534×C73—21no—
32#532×C73C2211yescharacteristic, complemented
33#529×C73C2211yescharacteristic
34#529×C73C2211yescharacteristic
35C2×#124×C73C2211yescharacteristic
36#501×C73C2211yescharacteristic, complemented
37#497×C73C2211yescharacteristic, complemented
38#496×C73C2211yescharacteristic
39#496×C73C2211yescharacteristic, complemented
40#496×C73C2211yescharacteristic, complemented
41#496×C73C2211yescharacteristic, complemented
42#491×C73C2211yescharacteristic, complemented
43#490×C73C2211yescharacteristic, complemented
44#490×C73C2211yescharacteristic, complemented
45#489×C73C2211yescharacteristic
46#489×C73C2211yescharacteristic, complemented
47#489×C73C2211yescharacteristic, complemented
48#469×C73—21no—
49#468×C73—21no—
50#464×C73—21no—
51#463×C73—21no—
52#463×C73—21no—
53#463×C73—21no—
54#452×C73—21no—
55#449×C73—21no—
56#448×C73—21no—
57#447×C73—21no—
58C4×SD16×C73—21no—
59C4×D8×C73—21no—
60#432×C73C2211yescharacteristic, complemented
61#432×C73C2211yescharacteristic, complemented
62C4×M16×C73C2211yescharacteristic, complemented
63#330×C73C2211yescharacteristic, complemented
64#330×C73C2211yescharacteristic, complemented
65#330×C73C2211yescharacteristic, complemented
66#330×C73C2211yescharacteristic, complemented
67#329×C73C2211yescharacteristic
68#329×C73C2211yescharacteristic
69#329×C73C2211yescharacteristic, complemented
70#329×C73C2211yescharacteristic, complemented
71#329×C73C2211yescharacteristic, complemented
72#329×C73C2211yescharacteristic, complemented
73#329×C73C2211yescharacteristic, complemented
74#329×C73C2211yescharacteristic, complemented
75C2×#41×C73—21no—
76C2×#41×C73—21no—
77C22×Q8×C73D411yescharacteristic
78C22×D4×C73—21no—
79C22×D4×C73D411yescharacteristic
80C2×Q16×C73—21no—
81C2×SD16×C73—21no—
82C2×SD16×C73—21no—
83C2×SD16×C73—21no—
84C2×SD16×C73—21no—
85C2×SD16×C73—21no—
86C2×D8×C73—21no—
87C2×D8×C73—21no—
88C2×D8×C73—21no—
89C2×D8×C73—21no—
90C2×M16×C73—21no—
91C4⋊Q8×C73—21no—
92C4⋊Q8×C73—21no—
93C4⋊Q8×C73C2311yescharacteristic
94#127×C73C2311yescharacteristic
95#126×C73—21no—
96#126×C73—21no—
97#126×C73—21no—
98#126×C73—21no—
99#126×C73—21no—
100#126×C73—21no—
101#125×C73C2311yescharacteristic
102#125×C73C2311yescharacteristic
103#124×C73—21no—
104#124×C73—21no—
105#124×C73—21no—
106#124×C73—21no—
107#124×C73—21no—
108#124×C73—21no—
109#124×C73—21no—
110#124×C73—21no—
111#124×C73—21no—
112#124×C73D411yescharacteristic
113#124×C73D411yescharacteristic
114#124×C73C2311yescharacteristic
115#124×C73C2311yescharacteristic
116#124×C73C2311yescharacteristic
117#124×C73C2311yescharacteristic
118#123×C73—21no—
119#123×C73—21no—
120#123×C73—21no—
121#123×C73—21no—
122#123×C73—21no—
123#123×C73—21no—
124#123×C73—21no—
125#123×C73—21no—
126#123×C73—21no—
127#123×C73—21no—
128#123×C73—21no—
129#123×C73—21no—
130C22⋊Q8×C73—21no—
131C22⋊Q8×C73—21no—
132C22⋊Q8×C73—21no—
133C22⋊Q8×C73—21no—
134C22⋊Q8×C73—21no—
135C22⋊Q8×C73—21no—
136C22⋊Q8×C73—21no—
137C22⋊Q8×C73—21no—
138C22⋊Q8×C73D411yescharacteristic
139C22⋊Q8×C73D411yescharacteristic
140#121×C73—21no—
141#121×C73—21no—
142#121×C73—21no—
143#121×C73—21no—
144#121×C73—21no—
145#121×C73—21no—
146#121×C73—21no—
147#121×C73—21no—
148#121×C73—21no—
149#121×C73—21no—
150#121×C73D411yescharacteristic
151#121×C73D411yescharacteristic
152#120×C73—21no—
153#120×C73—21no—
154#120×C73—21no—
155#120×C73—21no—
156#120×C73—21no—
157#120×C73—21no—
158C4×Q8×C73D411yescharacteristic
159C4×Q8×C73D411yescharacteristic
160C4×D4×C73—21no—
161C4×D4×C73—21no—
162C4×D4×C73—21no—
163C4×D4×C73—21no—
164C4×D4×C73—21no—
165C4×D4×C73—21no—
166C4×D4×C73—21no—
167C4×D4×C73—21no—
168C4×D4×C73D411yescharacteristic
169C4×D4×C73D411yescharacteristic
170#117×C73—21no—
171#117×C73—21no—
172#117×C73—21no—
173#117×C73—21no—
174#117×C73—21no—
175C2×C22⋊C4×C73—21no—
176C2×C22⋊C4×C73—21no—
177C2×C22⋊C4×C73—21no—
178C2×C22⋊C4×C73—21no—
179C2×C22⋊C4×C73—21no—
180C2×C42×C73C2311yescharacteristic
181#107×C73—21no—
182#106×C73—21no—
183C4⋊C8×C73—21no—
184C4⋊C8×C73—21no—
185#103×C73—21no—
186#103×C73—21no—
187#103×C73—21no—
188#103×C73—21no—
189#103×C73—21no—
190#102×C73—21no—
191#102×C73—21no—
192#102×C73—21no—
193#102×C73—21no—
194#102×C73—21no—
195#102×C73—21no—
196#102×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73—21no—
199#97×C73C2311yescharacteristic
200#97×C73C2311yescharacteristic
201#97×C73C2311yescharacteristic
202#97×C73C2311yescharacteristic
203#97×C73C2311yescharacteristic
204#97×C73C2311yescharacteristic
205C4×C8×C73—21no—
206C24×C73—21no—
207C24×C73—21no—
208#41×C73—82no—
209#41×C73—81no—
210#41×C73—81no—
211C2×Q8×C73—21no—
212C2×Q8×C73—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73—81no—
215C2×Q8×C73C2×D411yescharacteristic
216C2×Q8×C73C2×D411yescharacteristic
217C2×Q8×C73C2×D411yescharacteristic
218C2×Q8×C73C2×D411yescharacteristic
219C2×D4×C73—21no—
220C2×D4×C73—21no—
221C2×D4×C73—21no—
222C2×D4×C73—21no—
223C2×D4×C73—21no—
224C2×D4×C73—21no—
225C2×D4×C73—21no—
226C2×D4×C73—21no—
227C2×D4×C73—21no—
228C2×D4×C73—21no—
229C2×D4×C73—21no—
230C2×D4×C73—21no—
231C2×D4×C73—21no—
232C2×D4×C73—41no—
233C2×D4×C73—81no—
234C2×D4×C73—82no—
235C2×D4×C73C2×D411yescharacteristic
236C2×D4×C73C2×D411yescharacteristic
237C2×D4×C73C2×D411yescharacteristic
238C2×D4×C73C2×D411yescharacteristic
239C22×C4×C73—21no—
240C22×C4×C73—21no—
241C22×C4×C73—21no—
242C22×C4×C73—21no—
243C22×C4×C73—21no—
244C22×C4×C73—21no—
245C22×C4×C73—21no—
246C22×C4×C73—21no—
247C22×C4×C73—41no—
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2×D411yescharacteristic
251Q16×C73—81no—
252SD16×C73—42no—
253SD16×C73—81no—
254SD16×C73—81no—
255SD16×C73—81no—
256SD16×C73—81no—
257D8×C73—42no—
258D8×C73—81no—
259D8×C73—81no—
260D8×C73—81no—
261M16×C73—42no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—21no—
267C2×C8×C73—21no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73—21no—
283C4⋊C4×C73—21no—
284C4⋊C4×C73C2×D411yescharacteristic
285C4⋊C4×C73C2×D411yescharacteristic
286C4⋊C4×C73C2×D411yescharacteristic
287C4⋊C4×C73C2×D411yescharacteristic
288C22⋊C4×C73—21no—
289C22⋊C4×C73—21no—
290C22⋊C4×C73—21no—
291C22⋊C4×C73—21no—
292C22⋊C4×C73—21no—
293C22⋊C4×C73—21no—
294C22⋊C4×C73—21no—
295C22⋊C4×C73—21no—
296C22⋊C4×C73—21no—
297C22⋊C4×C73—21no—
298C22⋊C4×C73—21no—
299C22⋊C4×C73—21no—
300C22⋊C4×C73—21no—
301C22⋊C4×C73—21no—
302C22⋊C4×C73—21no—
303C22⋊C4×C73—21no—
304C22⋊C4×C73—21no—
305C22⋊C4×C73—21no—
306C22⋊C4×C73—21no—
307C22⋊C4×C73—21no—
308C22⋊C4×C73—21no—
309C22⋊C4×C73—21no—
310C22⋊C4×C73—21no—
311C22⋊C4×C73—21no—
312C22⋊C4×C73—21no—
313C22⋊C4×C73—21no—
314C22⋊C4×C73—21no—
315C22⋊C4×C73—21no—
316C22⋊C4×C73—41no—
317C22⋊C4×C73—41no—
318C42×C73—21no—
319C42×C73—21no—
320C42×C73—21no—
321C42×C73—21no—
322C42×C73C2×D411yescharacteristic
323C42×C73C2×D411yescharacteristic
324C42×C73C2×D411yescharacteristic
325C42×C73C2411yescharacteristic
326C23×C73—21no—
327C23×C73—21no—
328C23×C73—21no—
329C23×C73—21no—
330C23×C73—42no—
331C23×C73—41no—
332C23×C73—81no—
333C23×C73—81no—
334C23×C73—81no—
335C23×C73—81no—
336C23×C73—81no—
337C23×C73#12011yescharacteristic
338Q8×C73—41no—
339Q8×C73—41no—
340Q8×C73—41no—
341Q8×C73—41no—
342Q8×C73—41no—
343Q8×C73—41no—
344Q8×C73—81no—
345Q8×C73—81no—
346D4×C73—41no—
347D4×C73—41no—
348D4×C73—41no—
349D4×C73—41no—
350D4×C73—41no—
351D4×C73—41no—
352D4×C73—41no—
353D4×C73—41no—
354D4×C73—41no—
355D4×C73—41no—
356D4×C73—42no—
357D4×C73—42no—
358D4×C73—81no—
359D4×C73—81no—
360D4×C73—81no—
361D4×C73—81no—
362D4×C73—81no—
363D4×C73—81no—
364D4×C73—81no—
365D4×C73—81no—
366D4×C73—82no—
367C2×C4×C73—21no—
368C2×C4×C73—21no—
369C2×C4×C73—21no—
370C2×C4×C73—21no—
371C2×C4×C73—21no—
372C2×C4×C73—21no—
373C2×C4×C73—21no—
374C2×C4×C73—21no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—42no—
379C2×C4×C73—41no—
380C2×C4×C73—81no—
381C2×C4×C73—81no—
382C2×C4×C73—82no—
383C2×C4×C73—81no—
384C2×C4×C73—81no—
385C2×C4×C73—81no—
386C2×C4×C73—81no—
387C2×C4×C73—81no—
388C2×C4×C73#12011yescharacteristic
389C2×C4×C73#12011yescharacteristic
390C2×C4×C73#12011yescharacteristic
391C2×C4×C73C22×D411yescharacteristic
392C2×C4×C73C22×D411yescharacteristic
393C2×C4×C73C22×D411yescharacteristic
394C8×C73—22no—
395C8×C73—41no—
396C8×C73—41no—
397C8×C73—41no—
398C8×C73—41no—
399C8×C73—41no—
400C22×C73—21no—
401C22×C73—21no—
402C22×C73—21no—
403C22×C73—41no—
404C22×C73—41no—
405C22×C73—41no—
406C22×C73—41no—
407C22×C73—41no—
408C22×C73—41no—
409C22×C73—41no—
410C22×C73—41no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—41no—
414C22×C73—41no—
415C22×C73—81no—
416C22×C73—81no—
417C22×C73—81no—
418C22×C73—162no—
419C22×C73—162no—
420C22×C73C2×#12011yescharacteristic
421C4×C73—21no—
422C4×C73—21no—
423C4×C73—21no—
424C4×C73—21no—
425C4×C73—21no—
426C4×C73—21no—
427C4×C73—41no—
428C4×C73—41no—
429C4×C73—41no—
430C4×C73—41no—
431C4×C73—41no—
432C4×C73—41no—
433C4×C73—41no—
434C4×C73—41no—
435C4×C73—81no—
436#19068C7311yesmaximal, characteristic, direct product factor, Sylow
437C2×C73—41no—
438C2×C73—81no—
439C2×C73—81no—
440C2×C73—81no—
441C2×C73—81no—
442C2×C73—161no—
443C2×C73#301811yescharacteristic
444C2×C73#301911yescharacteristic
445C2×C73#302111yescharacteristic
446#3545C2×C7311yescharacteristic, complemented
447#3219C2×C7311yescharacteristic, complemented
448#3213C2×C7311yescharacteristic, complemented
449#3171C2×C7311yescharacteristic, complemented
450#1664C2×C7311yescharacteristic, complemented
451#1662C2×C7311yescharacteristic, complemented
452#1661C2×C7311yescharacteristic, complemented
453#1659C2×C7311yescharacteristic, complemented
454#1657C2×C7311yescharacteristic, complemented
455#1656C2×C7311yescharacteristic, complemented
456#1656C2×C7311yescharacteristic, complemented
457#1655C2×C7311yescharacteristic, complemented
458#1535C2×C7311yescharacteristic, complemented
459#1529C2×C7311yescharacteristic, complemented
460#1527C2×C7311yescharacteristic, complemented
461C73#1906811yescharacteristic, direct product factor, Sylow
462#563C22×C7311yescharacteristic
463#562C22×C7311yescharacteristic
464#562C22×C7311yescharacteristic
465H(3,𝔽4)C22×C7311yescharacteristic
466#555—21no—
467#551—21no—
468#551—21no—
469#551—21no—
470#546—21no—
471#546—21no—
472#542—21no—
473#542—21no—
474#538—21no—
475#538—21no—
476#536—21no—
477#534—21no—
478#532C22×C7311yescharacteristic, complemented
479#529C22×C7311yescharacteristic
480#529C22×C7311yescharacteristic
481C2×#124C22×C7311yescharacteristic
482#501C22×C7311yescharacteristic, complemented
483#497C22×C7311yescharacteristic, complemented
484#496C22×C7311yescharacteristic
485#496C22×C7311yescharacteristic, complemented
486#496C22×C7311yescharacteristic, complemented
487#496C22×C7311yescharacteristic, complemented
488#491C22×C7311yescharacteristic, complemented
489#490C22×C7311yescharacteristic, complemented
490#490C22×C7311yescharacteristic, complemented
491#489C22×C7311yescharacteristic
492#489C22×C7311yescharacteristic, complemented
493#489C22×C7311yescharacteristic, complemented
494#469—21no—
495#468—21no—
496#464—21no—
497#463—21no—
498#463—21no—
499#463—21no—
500#452—21no—
501#449—21no—
502#448—21no—
503#447—21no—
504C4×SD16—21no—
505C4×D8—21no—
506#432C22×C7311yescharacteristic, complemented
507#432C22×C7311yescharacteristic, complemented
508C4×M16C22×C7311yescharacteristic, complemented
509#330C22×C7311yescharacteristic, complemented
510#330C22×C7311yescharacteristic, complemented
511#330C22×C7311yescharacteristic, complemented
512#330C22×C7311yescharacteristic, complemented
513#329C22×C7311yescharacteristic
514#329C22×C7311yescharacteristic
515#329C22×C7311yescharacteristic, complemented
516#329C22×C7311yescharacteristic, complemented
517#329C22×C7311yescharacteristic, complemented
518#329C22×C7311yescharacteristic, complemented
519#329C22×C7311yescharacteristic, complemented
520#329C22×C7311yescharacteristic, complemented
521C2×#41—21no—
522C2×#41—21no—
523C22×Q8D4×C7311yescharacteristic
524C22×D4—21no—
525C22×D4D4×C7311yescharacteristic
526C2×Q16—21no—
527C2×SD16—21no—
528C2×SD16—21no—
529C2×SD16—21no—
530C2×SD16—21no—
531C2×SD16—21no—
532C2×D8—21no—
533C2×D8—21no—
534C2×D8—21no—
535C2×D8—21no—
536C2×M16—21no—
537C4⋊Q8—21no—
538C4⋊Q8—21no—
539C4⋊Q8C23×C7311yescharacteristic
540#127C23×C7311yescharacteristic
541#126—21no—
542#126—21no—
543#126—21no—
544#126—21no—
545#126—21no—
546#126—21no—
547#125C23×C7311yescharacteristic
548#125C23×C7311yescharacteristic
549#124—21no—
550#124—21no—
551#124—21no—
552#124—21no—
553#124—21no—
554#124—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#124D4×C7311yescharacteristic
559#124D4×C7311yescharacteristic
560#124C23×C7311yescharacteristic
561#124C23×C7311yescharacteristic
562#124C23×C7311yescharacteristic
563#124C23×C7311yescharacteristic
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572#123—21no—
573#123—21no—
574#123—21no—
575#123—21no—
576C22⋊Q8—21no—
577C22⋊Q8—21no—
578C22⋊Q8—21no—
579C22⋊Q8—21no—
580C22⋊Q8—21no—
581C22⋊Q8—21no—
582C22⋊Q8—21no—
583C22⋊Q8—21no—
584C22⋊Q8D4×C7311yescharacteristic
585C22⋊Q8D4×C7311yescharacteristic
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121—21no—
595#121—21no—
596#121D4×C7311yescharacteristic
597#121D4×C7311yescharacteristic
598#120—21no—
599#120—21no—
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604C4×Q8D4×C7311yescharacteristic
605C4×Q8D4×C7311yescharacteristic
606C4×D4—21no—
607C4×D4—21no—
608C4×D4—21no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4D4×C7311yescharacteristic
615C4×D4D4×C7311yescharacteristic
616#117—21no—
617#117—21no—
618#117—21no—
619#117—21no—
620#117—21no—
621C2×C22⋊C4—21no—
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C42C23×C7311yescharacteristic
627#107—21no—
628#106—21no—
629C4⋊C8—21no—
630C4⋊C8—21no—
631#103—21no—
632#103—21no—
633#103—21no—
634#103—21no—
635#103—21no—
636#102—21no—
637#102—21no—
638#102—21no—
639#102—21no—
640#102—21no—
641#102—21no—
642#102—21no—
643C22⋊C8—21no—
644C22⋊C8—21no—
645#97C23×C7311yescharacteristic
646#97C23×C7311yescharacteristic
647#97C23×C7311yescharacteristic
648#97C23×C7311yescharacteristic
649#97C23×C7311yescharacteristic
650#97C23×C7311yescharacteristic
651C4×C8—21no—
652C24—21no—
653C24—21no—
654#41—82no—
655#41—81no—
656#41—81no—
657C2×Q8—21no—
658C2×Q8—21no—
659C2×Q8—21no—
660C2×Q8—81no—
661C2×Q8C2×D4×C7311yescharacteristic
662C2×Q8C2×D4×C7311yescharacteristic
663C2×Q8C2×D4×C7311yescharacteristic
664C2×Q8C2×D4×C7311yescharacteristic
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—21no—
677C2×D4—21no—
678C2×D4—41no—
679C2×D4—81no—
680C2×D4—82no—
681C2×D4C2×D4×C7311yescharacteristic
682C2×D4C2×D4×C7311yescharacteristic
683C2×D4C2×D4×C7311yescharacteristic
684C2×D4C2×D4×C7311yescharacteristic
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—41no—
694C22×C4C2×D4×C7311yescharacteristic
695C22×C4C2×D4×C7311yescharacteristic
696C22×C4C2×D4×C7311yescharacteristic
697Q16—81no—
698SD16—42no—
699SD16—81no—
700SD16—81no—
701SD16—81no—
702SD16—81no—
703D8—42no—
704D8—81no—
705D8—81no—
706D8—81no—
707M16—42no—
708C2×C8—21no—
709C2×C8—21no—
710C2×C8—21no—
711C2×C8—21no—
712C2×C8—21no—
713C2×C8—21no—
714C4⋊C4—21no—
715C4⋊C4—21no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—21no—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4C2×D4×C7311yescharacteristic
731C4⋊C4C2×D4×C7311yescharacteristic
732C4⋊C4C2×D4×C7311yescharacteristic
733C4⋊C4C2×D4×C7311yescharacteristic
734C22⋊C4—21no—
735C22⋊C4—21no—
736C22⋊C4—21no—
737C22⋊C4—21no—
738C22⋊C4—21no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—41no—
763C22⋊C4—41no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—21no—
768C42C2×D4×C7311yescharacteristic
769C42C2×D4×C7311yescharacteristic
770C42C2×D4×C7311yescharacteristic
771C42C24×C7311yescharacteristic
772C23—21no—
773C23—21no—
774C23—21no—
775C23—21no—
776C23—42no—
777C23—41no—
778C23—81no—
779C23—81no—
780C23—81no—
781C23—81no—
782C23—81no—
783C23#120×C7311yescharacteristic
784Q8—41no—
785Q8—41no—
786Q8—41no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—81no—
791Q8—81no—
792D4—41no—
793D4—41no—
794D4—41no—
795D4—41no—
796D4—41no—
797D4—41no—
798D4—41no—
799D4—41no—
800D4—41no—
801D4—41no—
802D4—42no—
803D4—42no—
804D4—81no—
805D4—81no—
806D4—81no—
807D4—81no—
808D4—81no—
809D4—81no—
810D4—81no—
811D4—81no—
812D4—82no—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—21no—
816C2×C4—21no—
817C2×C4—21no—
818C2×C4—21no—
819C2×C4—21no—
820C2×C4—21no—
821C2×C4—41no—
822C2×C4—41no—
823C2×C4—41no—
824C2×C4—42no—
825C2×C4—41no—
826C2×C4—81no—
827C2×C4—81no—
828C2×C4—82no—
829C2×C4—81no—
830C2×C4—81no—
831C2×C4—81no—
832C2×C4—81no—
833C2×C4—81no—
834C2×C4#120×C7311yescharacteristic
835C2×C4#120×C7311yescharacteristic
836C2×C4#120×C7311yescharacteristic
837C2×C4C22×D4×C7311yescharacteristic
838C2×C4C22×D4×C7311yescharacteristic
839C2×C4C22×D4×C7311yescharacteristic
840C8—22no—
841C8—41no—
842C8—41no—
843C8—41no—
844C8—41no—
845C8—41no—
846C22—21no—
847C22—21no—
848C22—21no—
849C22—41no—
850C22—41no—
851C22—41no—
852C22—41no—
853C22—41no—
854C22—41no—
855C22—41no—
856C22—41no—
857C22—41no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—81no—
862C22—81no—
863C22—81no—
864C22—162no—
865C22—162no—
866C22C2×#120×C7311yescharacteristic
867C4—21no—
868C4—21no—
869C4—21no—
870C4—21no—
871C4—21no—
872C4—21no—
873C4—41no—
874C4—41no—
875C4—41no—
876C4—41no—
877C4—41no—
878C4—41no—
879C4—41no—
880C4—41no—
881C4—81no—
882C2—41no—
883C2—81no—
884C2—81no—
885C2—81no—
886C2—81no—
887C2—161no—
888C2C73×#301811yescharacteristic
889C2C73×#301911yescharacteristic
890C2C73×#302111yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3545C2semidirect
2. C73×#3219C2semidirect
3. C73×#3213C2semidirect
4. C73×#3171C2semidirect
5. C73×#1664C2semidirect
6. C73×#1662C2semidirect
7. C73×#1661C2semidirect
8. C73×#1659C2semidirect
9. C73×#1657C2semidirect
10. C73×#1656C2semidirect
11. C73×#1656C2semidirect
12. C73×#1655C2semidirect
13. C73×#1535C2semidirect
14. C73×#1529C2semidirect
15. C73×#1527C2semidirect
32. #532×C73C22semidirect
36. #501×C73C22semidirect
37. #497×C73C22semidirect
39. #496×C73C22semidirect
40. #496×C73C22semidirect
41. #496×C73C22semidirect
42. #491×C73C22semidirect
43. #490×C73C22semidirect
44. #490×C73C22semidirect
46. #489×C73C22semidirect
47. #489×C73C22semidirect
60. #432×C73C22semidirect
61. #432×C73C22semidirect
62. C4×M16×C73C22semidirect
63. #330×C73C22semidirect
64. #330×C73C22semidirect
65. #330×C73C22semidirect
66. #330×C73C22semidirect
69. #329×C73C22semidirect
70. #329×C73C22semidirect
71. #329×C73C22semidirect
72. #329×C73C22semidirect
73. #329×C73C22semidirect
74. #329×C73C22semidirect
436. #19068C73direct (N × H)
446. #3545C2×C73semidirect
447. #3219C2×C73semidirect
448. #3213C2×C73semidirect
449. #3171C2×C73semidirect
450. #1664C2×C73semidirect
451. #1662C2×C73semidirect
452. #1661C2×C73semidirect
453. #1659C2×C73semidirect
454. #1657C2×C73semidirect
455. #1656C2×C73semidirect
456. #1656C2×C73semidirect
457. #1655C2×C73semidirect
458. #1535C2×C73semidirect
459. #1529C2×C73semidirect
460. #1527C2×C73semidirect
461. C73#19068direct (N × H)
478. #532C22×C73semidirect
482. #501C22×C73semidirect
483. #497C22×C73semidirect
485. #496C22×C73semidirect
486. #496C22×C73semidirect
487. #496C22×C73semidirect
488. #491C22×C73semidirect
489. #490C22×C73semidirect
490. #490C22×C73semidirect
492. #489C22×C73semidirect
493. #489C22×C73semidirect
506. #432C22×C73semidirect
507. #432C22×C73semidirect
508. C4×M16C22×C73semidirect
509. #330C22×C73semidirect
510. #330C22×C73semidirect
511. #330C22×C73semidirect
512. #330C22×C73semidirect
515. #329C22×C73semidirect
516. #329C22×C73semidirect
517. #329C22×C73semidirect
518. #329C22×C73semidirect
519. #329C22×C73semidirect
520. #329C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35452
C73×#32192
C73×#32132
C73×#31712
C73×#16642
C73×#16622
C73×#16612
C73×#16592
C73×#16572
C73×#16562
C73×#16552
C73×#15352
C73×#15292
C73×#15272
#1906873