Finite Group Databasebeta

← C73×#18812 #32928216

Subgroups — C73×#18812 #32928216

Order 18688.

968 conjugacy classes of subgroups.

The subgroup lattice has 762 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3522C211yesmaximal, characteristic, complemented
2C73×#3251C211yesmaximal, characteristic, complemented
3C73×#3207C211yesmaximal, characteristic, complemented
4C73×#3037C211yesmaximal, characteristic, complemented
5C73×#1645C211yesmaximal, characteristic, complemented
6C73×#1644C211yesmaximal, characteristic, complemented
7C73×#1641C211yesmaximal, characteristic, complemented
8C73×#1640C211yesmaximal, characteristic, complemented
9C73×#1623C211yesmaximal, characteristic, complemented
10C73×#1622C211yesmaximal, characteristic, complemented
11C73×#1621C211yesmaximal, characteristic, complemented
12C73×#1620C211yesmaximal, characteristic, complemented
13C73×#1560C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1487C211yesmaximal, characteristic, complemented
16C2×#137×C73—21no—
17#559×C73—21no—
18#559×C73C2211yescharacteristic
19Q82×C73C2211yescharacteristic
20#554×C73—21no—
21#554×C73C2211yescharacteristic
22#550×C73C2211yescharacteristic
23#548×C73—21no—
24#547×C73—22no—
25#547×C73—21no—
26#542×C73—22no—
27#542×C73—21no—
28#532×C73—21no—
29#532×C73C2211yescharacteristic
30#532×C73C2211yescharacteristic
31#529×C73—21no—
32#529×C73C2211yescharacteristic
33#520×C73—21no—
34C2×C4×Q8×C73C2211yescharacteristic
35#493×C73C2211yescharacteristic
36#492×C73C2211yescharacteristic
37#487×C73C2211yescharacteristic
38#486×C73C2211yescharacteristic
39#478×C73—21no—
40#475×C73C2211yescharacteristic
41#474×C73C2211yescharacteristic
42#469×C73—21no—
43#468×C73—21no—
44#464×C73—21no—
45#464×C73—21no—
46#463×C73—22no—
47#463×C73—21no—
48#462×C73C2211yescharacteristic
49#462×C73C2211yescharacteristic
50#460×C73C2211yescharacteristic
51#460×C73C2211yescharacteristic
52#460×C73C2211yescharacteristic
53#459×C73C2211yescharacteristic
54#449×C73—22no—
55#431×C73C2211yescharacteristic
56#423×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58#417×C73—21no—
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62#331×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67Q8⋊C8×C73C2211yescharacteristic
68Q8⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73—22no—
72C2×#41×C73—21no—
73C2×#41×C73—21no—
74C2×#41×C73D412yes—
75C22×Q8×C73D411yescharacteristic
76#137×C73—44no—
77C2×Q16×C73—21no—
78C2×Q16×C73—21no—
79C2×SD16×C73—21no—
80C2×SD16×C73—21no—
81C2×SD16×C73—22no—
82C2×SD16×C73—21no—
83C2×D8×C73—22no—
84C2×D8×C73—21no—
85C2×M16×C73—21no—
86C2×M16×C73—21no—
87C4⋊Q8×C73—22no—
88C4⋊Q8×C73—21no—
89C4⋊Q8×C73—21no—
90C4⋊Q8×C73C2311yescharacteristic
91C4⋊Q8×C73C2311yescharacteristic
92#127×C73—21no—
93#127×C73C2311yescharacteristic
94#127×C73C2311yescharacteristic
95#126×C73—22no—
96#126×C73—21no—
97#125×C73—21no—
98#125×C73D411yescharacteristic
99#124×C73—22no—
100#124×C73—22no—
101#124×C73—21no—
102#124×C73—21no—
103#124×C73—21no—
104#124×C73D411yescharacteristic
105#124×C73D412yes—
106#123×C73—22no—
107#123×C73—22no—
108#123×C73—22no—
109#123×C73—22no—
110#123×C73—21no—
111C22⋊Q8×C73—22no—
112C22⋊Q8×C73—22no—
113C22⋊Q8×C73—22no—
114C22⋊Q8×C73—22no—
115C22⋊Q8×C73—21no—
116C22⋊Q8×C73D411yescharacteristic
117#121×C73—22no—
118#121×C73—22no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
123#121×C73—21no—
124#121×C73D411yescharacteristic
125C4×Q8×C73—21no—
126C4×Q8×C73—21no—
127C4×Q8×C73—21no—
128C4×Q8×C73—21no—
129C4×Q8×C73D411yescharacteristic
130C4×Q8×C73D411yescharacteristic
131C4×Q8×C73C2311yescharacteristic
132C4×Q8×C73C2311yescharacteristic
133C4×Q8×C73C2311yescharacteristic
134C4×D4×C73—22no—
135C4×D4×C73—22no—
136C4×D4×C73—22no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73—21no—
141C4×D4×C73—21no—
142C4×D4×C73—21no—
143C4×D4×C73—21no—
144C4×D4×C73—21no—
145C4×D4×C73—21no—
146C4×D4×C73C2311yescharacteristic
147#117×C73—22no—
148#117×C73—21no—
149C2×C4⋊C4×C73—22no—
150C2×C4⋊C4×C73—21no—
151C2×C4⋊C4×C73—21no—
152C2×C4⋊C4×C73D411yescharacteristic
153C2×C42×C73—21no—
154C2×C42×C73C2311yescharacteristic
155#107×C73—21no—
156#106×C73—21no—
157C4⋊C8×C73—21no—
158C4⋊C8×C73—21no—
159C4⋊C8×C73—21no—
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162C4⋊C8×C73C2311yescharacteristic
163C4⋊C8×C73C2311yescharacteristic
164#103×C73—22no—
165#103×C73—21no—
166#103×C73—21no—
167#103×C73—21no—
168#102×C73—22no—
169#102×C73—21no—
170#102×C73—21no—
171#102×C73—21no—
172#102×C73—21no—
173#102×C73—21no—
174C22⋊C8×C73—21no—
175C4×C8×C73C2311yescharacteristic
176C4×C8×C73C2311yescharacteristic
177#41×C73—42no—
178#41×C73—42no—
179#41×C73—42no—
180#41×C73—42no—
181#41×C73—84no—
182#41×C73—82no—
183C2×Q8×C73—22no—
184C2×Q8×C73—21no—
185C2×Q8×C73—22no—
186C2×Q8×C73—21no—
187C2×Q8×C73—41no—
188C2×Q8×C73C2×D411yescharacteristic
189C2×Q8×C73C2×D411yescharacteristic
190C2×Q8×C73C2×D411yescharacteristic
191C2×Q8×C73C2×D412yes—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—21no—
195C2×D4×C73—22no—
196C2×D4×C73—21no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—41no—
202C2×D4×C73C2×D411yescharacteristic
203C2×D4×C73C2×D412yes—
204C22×C4×C73—22no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—22no—
208C22×C4×C73—22no—
209C22×C4×C73—21no—
210C22×C4×C73—22no—
211C22×C4×C73—41no—
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215Q16×C73—42no—
216Q16×C73—42no—
217SD16×C73—42no—
218SD16×C73—42no—
219SD16×C73—81no—
220SD16×C73—82no—
221D8×C73—81no—
222D8×C73—82no—
223M16×C73—42no—
224M16×C73—81no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—21no—
228C2×C8×C73—21no—
229C2×C8×C73—21no—
230C2×C8×C73—21no—
231C4⋊C4×C73—22no—
232C4⋊C4×C73—22no—
233C4⋊C4×C73—22no—
234C4⋊C4×C73—22no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—21no—
240C4⋊C4×C73—21no—
241C4⋊C4×C73—21no—
242C4⋊C4×C73—21no—
243C4⋊C4×C73—21no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73C2×D411yescharacteristic
249C4⋊C4×C73C2×D411yescharacteristic
250C4⋊C4×C73C2×D411yescharacteristic
251C4⋊C4×C73C2×D411yescharacteristic
252C22⋊C4×C73—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—22no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—21no—
261C22⋊C4×C73—22no—
262C22⋊C4×C73—21no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—41no—
265C22⋊C4×C73—41no—
266C42×C73—22no—
267C42×C73—21no—
268C42×C73—21no—
269C42×C73—21no—
270C42×C73—21no—
271C42×C73—21no—
272C42×C73C2×D411yescharacteristic
273C42×C73C2×D411yescharacteristic
274C42×C73C2×D411yescharacteristic
275C42×C73C2411yescharacteristic
276C23×C73—21no—
277C23×C73—22no—
278C23×C73—41no—
279C23×C73#12011yescharacteristic
280Q8×C73—21no—
281Q8×C73—21no—
282Q8×C73—21no—
283Q8×C73—21no—
284Q8×C73—21no—
285Q8×C73—42no—
286Q8×C73—42no—
287Q8×C73—41no—
288Q8×C73—41no—
289Q8×C73—82no—
290Q8×C73AGL(1,ℤ/8)12yes—
291D4×C73—21no—
292D4×C73—21no—
293D4×C73—42no—
294D4×C73—44no—
295D4×C73—42no—
296D4×C73—44no—
297D4×C73—42no—
298D4×C73—41no—
299D4×C73—41no—
300D4×C73—41no—
301D4×C73—41no—
302D4×C73—41no—
303D4×C73—41no—
304D4×C73—41no—
305D4×C73—41no—
306D4×C73—82no—
307D4×C73—82no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—21no—
314C2×C4×C73—21no—
315C2×C4×C73—21no—
316C2×C4×C73—21no—
317C2×C4×C73—22no—
318C2×C4×C73—21no—
319C2×C4×C73—21no—
320C2×C4×C73—41no—
321C2×C4×C73—42no—
322C2×C4×C73—44no—
323C2×C4×C73—42no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73—82no—
328C2×C4×C73—82no—
329C2×C4×C73—82no—
330C2×C4×C73—82no—
331C2×C4×C73#12011yescharacteristic
332C2×C4×C73#12011yescharacteristic
333C2×C4×C73#12011yescharacteristic
334C2×C4×C73C22×D411yescharacteristic
335C2×C4×C73C22×D411yescharacteristic
336C2×C4×C73C22×D411yescharacteristic
337C8×C73—41no—
338C8×C73—41no—
339C8×C73—41no—
340C8×C73—41no—
341C8×C73—41no—
342C8×C73—41no—
343C22×C73—21no—
344C22×C73—21no—
345C22×C73—21no—
346C22×C73—42no—
347C22×C73—41no—
348C22×C73—41no—
349C22×C73—42no—
350C22×C73—42no—
351C22×C73—41no—
352C22×C73—81no—
353C22×C73—81no—
354C22×C73—81no—
355C22×C73C2×#12011yescharacteristic
356C4×C73—21no—
357C4×C73—22no—
358C4×C73—21no—
359C4×C73—21no—
360C4×C73—21no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—41no—
364C4×C73—41no—
365C4×C73—41no—
366C4×C73—42no—
367C4×C73—41no—
368C4×C73—81no—
369C4×C73C2×AGL(1,ℤ/8)11yescharacteristic
370C4×C73#57511yescharacteristic
371C4×C73#57711yescharacteristic
372C4×C73#57811yescharacteristic
373#18812C7311yesmaximal, characteristic, direct product factor, Sylow
374C2×C73—41no—
375C2×C73—81no—
376C2×C73—82no—
377C2×C73—161no—
378C2×C73#300611yescharacteristic
379C2×C73#301311yescharacteristic
380C2×C73#301911yescharacteristic
381#3522C2×C7311yescharacteristic, complemented
382#3251C2×C7311yescharacteristic, complemented
383#3207C2×C7311yescharacteristic, complemented
384#3037C2×C7311yescharacteristic, complemented
385#1645C2×C7311yescharacteristic, complemented
386#1644C2×C7311yescharacteristic, complemented
387#1641C2×C7311yescharacteristic, complemented
388#1640C2×C7311yescharacteristic, complemented
389#1623C2×C7311yescharacteristic, complemented
390#1622C2×C7311yescharacteristic, complemented
391#1621C2×C7311yescharacteristic, complemented
392#1620C2×C7311yescharacteristic, complemented
393#1560C2×C7311yescharacteristic, complemented
394#1495C2×C7311yescharacteristic, complemented
395#1487C2×C7311yescharacteristic, complemented
396C73#1881211yescharacteristic, direct product factor, Sylow
397C2×#137—21no—
398#559—21no—
399#559C22×C7311yescharacteristic
400Q82C22×C7311yescharacteristic
401#554—21no—
402#554C22×C7311yescharacteristic
403#550C22×C7311yescharacteristic
404#548—21no—
405#547—22no—
406#547—21no—
407#542—22no—
408#542—21no—
409#532—21no—
410#532C22×C7311yescharacteristic
411#532C22×C7311yescharacteristic
412#529—21no—
413#529C22×C7311yescharacteristic
414#520—21no—
415C2×C4×Q8C22×C7311yescharacteristic
416#493C22×C7311yescharacteristic
417#492C22×C7311yescharacteristic
418#487C22×C7311yescharacteristic
419#486C22×C7311yescharacteristic
420#478—21no—
421#475C22×C7311yescharacteristic
422#474C22×C7311yescharacteristic
423#469—21no—
424#468—21no—
425#464—21no—
426#464—21no—
427#463—22no—
428#463—21no—
429#462C22×C7311yescharacteristic
430#462C22×C7311yescharacteristic
431#460C22×C7311yescharacteristic
432#460C22×C7311yescharacteristic
433#460C22×C7311yescharacteristic
434#459C22×C7311yescharacteristic
435#449—22no—
436#431C22×C7311yescharacteristic
437#423C22×C7311yescharacteristic
438#423C22×C7311yescharacteristic
439#417—21no—
440#333C22×C7311yescharacteristic
441#333C22×C7311yescharacteristic
442#331C22×C7311yescharacteristic
443#331C22×C7311yescharacteristic
444Q8⋊C8C22×C7311yescharacteristic
445Q8⋊C8C22×C7311yescharacteristic
446Q8⋊C8C22×C7311yescharacteristic
447Q8⋊C8C22×C7311yescharacteristic
448Q8⋊C8C22×C7311yescharacteristic
449Q8⋊C8C22×C7311yescharacteristic
450D4⋊C8C22×C7311yescharacteristic
451D4⋊C8C22×C7311yescharacteristic
452C2×#41—22no—
453C2×#41—21no—
454C2×#41—21no—
455C2×#41D4×C7312yes—
456C22×Q8D4×C7311yescharacteristic
457#137—44no—
458C2×Q16—21no—
459C2×Q16—21no—
460C2×SD16—21no—
461C2×SD16—21no—
462C2×SD16—22no—
463C2×SD16—21no—
464C2×D8—22no—
465C2×D8—21no—
466C2×M16—21no—
467C2×M16—21no—
468C4⋊Q8—22no—
469C4⋊Q8—21no—
470C4⋊Q8—21no—
471C4⋊Q8C23×C7311yescharacteristic
472C4⋊Q8C23×C7311yescharacteristic
473#127—21no—
474#127C23×C7311yescharacteristic
475#127C23×C7311yescharacteristic
476#126—22no—
477#126—21no—
478#125—21no—
479#125D4×C7311yescharacteristic
480#124—22no—
481#124—22no—
482#124—21no—
483#124—21no—
484#124—21no—
485#124D4×C7311yescharacteristic
486#124D4×C7312yes—
487#123—22no—
488#123—22no—
489#123—22no—
490#123—22no—
491#123—21no—
492C22⋊Q8—22no—
493C22⋊Q8—22no—
494C22⋊Q8—22no—
495C22⋊Q8—22no—
496C22⋊Q8—21no—
497C22⋊Q8D4×C7311yescharacteristic
498#121—22no—
499#121—22no—
500#121—21no—
501#121—21no—
502#121—21no—
503#121—21no—
504#121—21no—
505#121D4×C7311yescharacteristic
506C4×Q8—21no—
507C4×Q8—21no—
508C4×Q8—21no—
509C4×Q8—21no—
510C4×Q8D4×C7311yescharacteristic
511C4×Q8D4×C7311yescharacteristic
512C4×Q8C23×C7311yescharacteristic
513C4×Q8C23×C7311yescharacteristic
514C4×Q8C23×C7311yescharacteristic
515C4×D4—22no—
516C4×D4—22no—
517C4×D4—22no—
518C4×D4—21no—
519C4×D4—21no—
520C4×D4—21no—
521C4×D4—21no—
522C4×D4—21no—
523C4×D4—21no—
524C4×D4—21no—
525C4×D4—21no—
526C4×D4—21no—
527C4×D4C23×C7311yescharacteristic
528#117—22no—
529#117—21no—
530C2×C4⋊C4—22no—
531C2×C4⋊C4—21no—
532C2×C4⋊C4—21no—
533C2×C4⋊C4D4×C7311yescharacteristic
534C2×C42—21no—
535C2×C42C23×C7311yescharacteristic
536#107—21no—
537#106—21no—
538C4⋊C8—21no—
539C4⋊C8—21no—
540C4⋊C8—21no—
541C4⋊C8C23×C7311yescharacteristic
542C4⋊C8C23×C7311yescharacteristic
543C4⋊C8C23×C7311yescharacteristic
544C4⋊C8C23×C7311yescharacteristic
545#103—22no—
546#103—21no—
547#103—21no—
548#103—21no—
549#102—22no—
550#102—21no—
551#102—21no—
552#102—21no—
553#102—21no—
554#102—21no—
555C22⋊C8—21no—
556C4×C8C23×C7311yescharacteristic
557C4×C8C23×C7311yescharacteristic
558#41—42no—
559#41—42no—
560#41—42no—
561#41—42no—
562#41—84no—
563#41—82no—
564C2×Q8—22no—
565C2×Q8—21no—
566C2×Q8—22no—
567C2×Q8—21no—
568C2×Q8—41no—
569C2×Q8C2×D4×C7311yescharacteristic
570C2×Q8C2×D4×C7311yescharacteristic
571C2×Q8C2×D4×C7311yescharacteristic
572C2×Q8C2×D4×C7312yes—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—21no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4—21no—
580C2×D4—21no—
581C2×D4—21no—
582C2×D4—41no—
583C2×D4C2×D4×C7311yescharacteristic
584C2×D4C2×D4×C7312yes—
585C22×C4—22no—
586C22×C4—21no—
587C22×C4—21no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—21no—
591C22×C4—22no—
592C22×C4—41no—
593C22×C4C2×D4×C7311yescharacteristic
594C22×C4C2×D4×C7311yescharacteristic
595C22×C4C2×D4×C7311yescharacteristic
596Q16—42no—
597Q16—42no—
598SD16—42no—
599SD16—42no—
600SD16—81no—
601SD16—82no—
602D8—81no—
603D8—82no—
604M16—42no—
605M16—81no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C4⋊C4—22no—
613C4⋊C4—22no—
614C4⋊C4—22no—
615C4⋊C4—22no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—21no—
625C4⋊C4—21no—
626C4⋊C4—21no—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4C2×D4×C7311yescharacteristic
630C4⋊C4C2×D4×C7311yescharacteristic
631C4⋊C4C2×D4×C7311yescharacteristic
632C4⋊C4C2×D4×C7311yescharacteristic
633C22⋊C4—22no—
634C22⋊C4—22no—
635C22⋊C4—22no—
636C22⋊C4—22no—
637C22⋊C4—22no—
638C22⋊C4—21no—
639C22⋊C4—22no—
640C22⋊C4—21no—
641C22⋊C4—21no—
642C22⋊C4—22no—
643C22⋊C4—21no—
644C22⋊C4—21no—
645C22⋊C4—41no—
646C22⋊C4—41no—
647C42—22no—
648C42—21no—
649C42—21no—
650C42—21no—
651C42—21no—
652C42—21no—
653C42C2×D4×C7311yescharacteristic
654C42C2×D4×C7311yescharacteristic
655C42C2×D4×C7311yescharacteristic
656C42C24×C7311yescharacteristic
657C23—21no—
658C23—22no—
659C23—41no—
660C23#120×C7311yescharacteristic
661Q8—21no—
662Q8—21no—
663Q8—21no—
664Q8—21no—
665Q8—21no—
666Q8—42no—
667Q8—42no—
668Q8—41no—
669Q8—41no—
670Q8—82no—
671Q8AGL(1,ℤ/8)×C7312yes—
672D4—21no—
673D4—21no—
674D4—42no—
675D4—44no—
676D4—42no—
677D4—44no—
678D4—42no—
679D4—41no—
680D4—41no—
681D4—41no—
682D4—41no—
683D4—41no—
684D4—41no—
685D4—41no—
686D4—41no—
687D4—82no—
688D4—82no—
689C2×C4—21no—
690C2×C4—21no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—21no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—22no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—41no—
702C2×C4—42no—
703C2×C4—44no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—82no—
709C2×C4—82no—
710C2×C4—82no—
711C2×C4—82no—
712C2×C4#120×C7311yescharacteristic
713C2×C4#120×C7311yescharacteristic
714C2×C4#120×C7311yescharacteristic
715C2×C4C22×D4×C7311yescharacteristic
716C2×C4C22×D4×C7311yescharacteristic
717C2×C4C22×D4×C7311yescharacteristic
718C8—41no—
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C8—41no—
724C22—21no—
725C22—21no—
726C22—21no—
727C22—42no—
728C22—41no—
729C22—41no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—81no—
734C22—81no—
735C22—81no—
736C22C2×#120×C7311yescharacteristic
737C4—21no—
738C4—22no—
739C4—21no—
740C4—21no—
741C4—21no—
742C4—41no—
743C4—41no—
744C4—41no—
745C4—41no—
746C4—41no—
747C4—42no—
748C4—41no—
749C4—81no—
750C4C2×AGL(1,ℤ/8)×C7311yescharacteristic
751C4#575×C7311yescharacteristic
752C4#577×C7311yescharacteristic
753C4#578×C7311yescharacteristic
754C2—41no—
755C2—81no—
756C2—82no—
757C2—161no—
758C2C73×#300611yescharacteristic
759C2C73×#301311yescharacteristic
760C2C73×#301911yescharacteristic
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×#3522C2semidirect
2. C73×#3251C2semidirect
3. C73×#3207C2semidirect
4. C73×#3037C2semidirect
5. C73×#1645C2semidirect
6. C73×#1644C2semidirect
7. C73×#1641C2semidirect
8. C73×#1640C2semidirect
9. C73×#1623C2semidirect
10. C73×#1622C2semidirect
11. C73×#1621C2semidirect
12. C73×#1620C2semidirect
13. C73×#1560C2semidirect
14. C73×#1495C2semidirect
15. C73×#1487C2semidirect
373. #18812C73direct (N × H)
381. #3522C2×C73semidirect
382. #3251C2×C73semidirect
383. #3207C2×C73semidirect
384. #3037C2×C73semidirect
385. #1645C2×C73semidirect
386. #1644C2×C73semidirect
387. #1641C2×C73semidirect
388. #1640C2×C73semidirect
389. #1623C2×C73semidirect
390. #1622C2×C73semidirect
391. #1621C2×C73semidirect
392. #1620C2×C73semidirect
393. #1560C2×C73semidirect
394. #1495C2×C73semidirect
395. #1487C2×C73semidirect
396. C73#18812direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35222
C73×#32512
C73×#32072
C73×#30372
C73×#16452
C73×#16442
C73×#16412
C73×#16402
C73×#16232
C73×#16222
C73×#16212
C73×#16202
C73×#15602
C73×#14952
C73×#14872
#1881273