Finite Group Databasebeta

← C73×#26600 #32936004

Subgroups — C73×#26600 #32936004

Order 18688.

1006 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
1C2×#463×C73C211yesmaximal, characteristic, complemented
2C2×#442×C73C211yesmaximal, characteristic, complemented
3C73×#2447C211yesmaximal, characteristic, complemented
4C73×#2366C211yesmaximal, characteristic, complemented
5C73×#2067C211yesmaximal, characteristic, complemented
6C73×#2014C211yesmaximal, characteristic, complemented
7C73×#2012C211yesmaximal, characteristic, complemented
8C73×#2011C211yesmaximal, characteristic
9C73×#1973C211yesmaximal, characteristic, complemented
10C73×#1927C211yesmaximal, characteristic, complemented
11C73×#1925C211yesmaximal, characteristic, complemented
12C73×#1917C211yesmaximal, characteristic, complemented
13C73×#1879C211yesmaximal, characteristic, complemented
14C73×#1877C211yesmaximal, characteristic, complemented
15C73×#1864C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C22×SD16×C73C2211yescharacteristic
18C22×D8×C73C2211yescharacteristic
19C22×D8×C73C2211yescharacteristic
20C2×#127×C73C2211yescharacteristic
21C2×#124×C73C2211yescharacteristic
22C2×C4×D4×C73—21no—
23C2×C4×D4×C73C2211yescharacteristic
24C2×C4×D4×C73C2211yescharacteristic
25C2×C4×D4×C73C2211yescharacteristic
26#463×C73—24no—
27#442×C73—24no—
28C2×#107×C73C2211yescharacteristic
29C2×#106×C73C2211yescharacteristic
30C2×C4⋊C8×C73C2211yescharacteristic
31C2×#103×C73C2211yescharacteristic
32C2×#103×C73C2211yescharacteristic
33C2×#102×C73C2211yescharacteristic
34C2×#102×C73C2211yescharacteristic
35C2×#102×C73C2211yescharacteristic
36C2×#102×C73C2211yescharacteristic
37C2×#102×C73C2211yescharacteristic
38C2×#102×C73C2211yescharacteristic
39C2×#97×C73C2211yescharacteristic
40#397×C73—21no—
41#397×C73—21no—
42#391×C73C2211yescharacteristic
43#391×C73C2211yescharacteristic
44#390×C73—21no—
45#390×C73C2211yescharacteristic
46#390×C73C2211yescharacteristic
47#390×C73C2211yescharacteristic
48#389×C73C2211yescharacteristic
49#386×C73—21no—
50#386×C73—21no—
51#385×C73—21no—
52#381×C73—21no—
53C4×C4⋊C4×C73C2211yescharacteristic
54C4×C4⋊C4×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59#336×C73C2211yescharacteristic
60#336×C73C2211yescharacteristic
61C22×Q8×C73C2311yescharacteristic
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73C2311yescharacteristic
65C22×D4×C73C2311yescharacteristic
66C22×D4×C73C2311yescharacteristic
67C23×C4×C73—21no—
68C23×C4×C73—21no—
69C23×C4×C73—21no—
70C2×SD16×C73—22no—
71C2×SD16×C73—22no—
72C2×SD16×C73—22no—
73C2×SD16×C73—41no—
74C2×SD16×C73—41no—
75C2×SD16×C73—41no—
76C2×D8×C73—22no—
77C2×D8×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—22no—
81C2×D8×C73—41no—
82C22×C8×C73C2311yescharacteristic
83C22×C8×C73C2311yescharacteristic
84C22×C8×C73C2311yescharacteristic
85C22×C8×C73C2311yescharacteristic
86#127×C73—22no—
87#127×C73—22no—
88#124×C73—22no—
89#124×C73—41no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—41no—
94C4×D4×C73—41no—
95C4×D4×C73—41no—
96C4×D4×C73—44no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73D411yescharacteristic
99C2×C4⋊C4×C73D411yescharacteristic
100C2×C4⋊C4×C73C2311yescharacteristic
101C2×C4⋊C4×C73C2311yescharacteristic
102C2×C4⋊C4×C73C2311yescharacteristic
103C2×C4⋊C4×C73C2311yescharacteristic
104C2×C22⋊C4×C73—21no—
105C2×C22⋊C4×C73—21no—
106C2×C22⋊C4×C73—21no—
107C2×C22⋊C4×C73—21no—
108C2×C22⋊C4×C73—21no—
109C2×C22⋊C4×C73—21no—
110C2×C22⋊C4×C73—21no—
111C2×C22⋊C4×C73—21no—
112C2×C22⋊C4×C73—21no—
113C2×C22⋊C4×C73—21no—
114C2×C22⋊C4×C73—21no—
115C2×C42×C73—21no—
116C2×C42×C73C2311yescharacteristic
117C2×C42×C73C2311yescharacteristic
118C2×C42×C73C2311yescharacteristic
119#107×C73—41no—
120#106×C73—22no—
121C4⋊C8×C73—22no—
122#103×C73—22no—
123#103×C73—22no—
124#102×C73—22no—
125#102×C73—22no—
126#102×C73—41no—
127#102×C73—41no—
128#102×C73—41no—
129#102×C73D414yescomplemented
130#97×C73—22no—
131#95×C73—21no—
132#95×C73—21no—
133#95×C73—21no—
134#95×C73—21no—
135#95×C73—21no—
136#95×C73—21no—
137#95×C73D411yescharacteristic
138#95×C73D411yescharacteristic
139C24×C73—21no—
140C24×C73—21no—
141C24×C73—21no—
142C2×Q8×C73—21no—
143C2×Q8×C73—21no—
144C2×Q8×C73—21no—
145C2×Q8×C73—21no—
146C2×Q8×C73—21no—
147C2×Q8×C73—21no—
148C2×D4×C73—24no—
149C2×D4×C73—24no—
150C2×D4×C73—21no—
151C2×D4×C73—21no—
152C2×D4×C73—21no—
153C2×D4×C73—21no—
154C2×D4×C73—21no—
155C2×D4×C73—21no—
156C2×D4×C73—21no—
157C2×D4×C73—21no—
158C2×D4×C73—21no—
159C2×D4×C73—21no—
160C2×D4×C73—21no—
161C2×D4×C73—21no—
162C2×D4×C73—21no—
163C2×D4×C73—21no—
164C2×D4×C73—21no—
165C2×D4×C73—42no—
166C2×D4×C73—42no—
167C2×D4×C73—81no—
168C2×D4×C73—81no—
169C2×D4×C73C2×D412yes—
170C2×D4×C73#4112yes—
171C2×D4×C73#4112yes—
172C22×C4×C73—21no—
173C22×C4×C73—21no—
174C22×C4×C73—21no—
175C22×C4×C73—21no—
176C22×C4×C73—21no—
177C22×C4×C73—42no—
178C22×C4×C73—42no—
179C22×C4×C73—42no—
180C22×C4×C73—42no—
181C22×C4×C73—42no—
182C22×C4×C73—42no—
183C22×C4×C73—81no—
184C22×C4×C73—81no—
185C22×C4×C73—81no—
186C22×C4×C73C2×D411yescharacteristic
187C22×C4×C73C2×D411yescharacteristic
188C22×C4×C73C2×D411yescharacteristic
189C22×C4×C73C2×D411yescharacteristic
190C22×C4×C73C2×D411yescharacteristic
191C22×C4×C73C2×D411yescharacteristic
192C22×C4×C73C2411yescharacteristic
193SD16×C73—44no—
194SD16×C73—44no—
195D8×C73—28no—
196D8×C73—44no—
197C2×C8×C73—21no—
198C2×C8×C73—21no—
199C2×C8×C73—21no—
200C2×C8×C73—21no—
201C2×C8×C73—21no—
202C2×C8×C73—21no—
203C2×C8×C73—21no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73C2×D412yes—
208C2×C8×C73#4112yes—
209C4⋊C4×C73—22no—
210C4⋊C4×C73—21no—
211C4⋊C4×C73—21no—
212C4⋊C4×C73—21no—
213C4⋊C4×C73—21no—
214C4⋊C4×C73—21no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—41no—
218C4⋊C4×C73—81no—
219C4⋊C4×C73C2×D412yes—
220C22⋊C4×C73—42no—
221C22⋊C4×C73—42no—
222C22⋊C4×C73—42no—
223C22⋊C4×C73—42no—
224C22⋊C4×C73—42no—
225C22⋊C4×C73—42no—
226C22⋊C4×C73—42no—
227C22⋊C4×C73—42no—
228C22⋊C4×C73—81no—
229C22⋊C4×C73—81no—
230C22⋊C4×C73—81no—
231C42×C73—21no—
232C42×C73—21no—
233C42×C73—21no—
234C42×C73—21no—
235C42×C73—21no—
236C42×C73—21no—
237C42×C73—42no—
238C23×C73—22no—
239C23×C73—22no—
240C23×C73—22no—
241C23×C73—41no—
242C23×C73—41no—
243C23×C73—41no—
244C23×C73—41no—
245C23×C73—41no—
246C23×C73—41no—
247C23×C73—41no—
248C23×C73—41no—
249C23×C73—41no—
250C23×C73—41no—
251C23×C73—41no—
252C23×C73—41no—
253C23×C73—41no—
254C23×C73—41no—
255C23×C73—41no—
256C23×C73—41no—
257C23×C73—41no—
258C23×C73—41no—
259C23×C73C22×D411yescharacteristic
260Q8×C73—41no—
261Q8×C73—41no—
262Q8×C73—41no—
263Q8×C73—41no—
264D4×C73—22no—
265D4×C73—22no—
266D4×C73—22no—
267D4×C73—22no—
268D4×C73—22no—
269D4×C73—22no—
270D4×C73—48no—
271D4×C73—41no—
272D4×C73—41no—
273D4×C73—41no—
274D4×C73—41no—
275D4×C73—41no—
276D4×C73—41no—
277D4×C73—84no—
278C2×C4×C73—21no—
279C2×C4×C73—21no—
280C2×C4×C73—21no—
281C2×C4×C73—21no—
282C2×C4×C73—21no—
283C2×C4×C73—21no—
284C2×C4×C73—21no—
285C2×C4×C73—22no—
286C2×C4×C73—21no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—21no—
295C2×C4×C73—21no—
296C2×C4×C73—41no—
297C2×C4×C73—41no—
298C2×C4×C73—41no—
299C2×C4×C73—41no—
300C2×C4×C73—41no—
301C2×C4×C73—41no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—41no—
309C2×C4×C73—41no—
310C2×C4×C73—84no—
311C2×C4×C73—84no—
312C2×C4×C73—84no—
313C2×C4×C73AGL(1,ℤ/8)12yes—
314C2×C4×C73C22×D411yescharacteristic
315C2×C4×C73C2×#4111yescharacteristic
316C2×C4×C73C2×#4111yescharacteristic
317C2×C4×C73C2×#4111yescharacteristic
318C2×C4×C73H(5,𝔽2)11yescharacteristic
319C2×C4×C73H(5,𝔽2)11yescharacteristic
320C8×C73—22no—
321C8×C73—22no—
322C8×C73—41no—
323C8×C73—41no—
324C22×C73—42no—
325C22×C73—42no—
326C22×C73—42no—
327C22×C73—42no—
328C22×C73—42no—
329C22×C73—42no—
330C22×C73—42no—
331C22×C73—42no—
332C22×C73—42no—
333C22×C73—81no—
334C22×C73—81no—
335C22×C73—81no—
336C22×C73—81no—
337C22×C73—81no—
338C22×C73—81no—
339C22×C73—81no—
340C22×C73—81no—
341C22×C73—81no—
342C22×C73—81no—
343C22×C73—81no—
344C22×C73—81no—
345C22×C73#52511yescharacteristic
346C22×C73D4211yescharacteristic
347C22×C73#55011yescharacteristic
348C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
349C22×C73#57511yescharacteristic
350C22×C73#57611yescharacteristic
351C22×C73#57711yescharacteristic
352C4×C73—22no—
353C4×C73—41no—
354C4×C73—41no—
355C4×C73—41no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73—42no—
359C4×C73—81no—
360C4×C73—81no—
361C4×C73—81no—
362C4×C73—81no—
363C4×C73#52511yescharacteristic
364C4×C73#53811yescharacteristic
365C4×C73#54611yescharacteristic
366C4×C73#55311yescharacteristic
367#26600C7311yesmaximal, characteristic, direct product factor, Sylow
368C2×C73—82no—
369C2×C73—82no—
370C2×C73—82no—
371C2×C73#245611yescharacteristic
372C2×C73#311411yescharacteristic
373C2×C73#311811yescharacteristic
374C2×C73#326811yescharacteristic
375C2×C73#327211yescharacteristic
376C2×C73#339911yescharacteristic
377C2×C73#340111yescharacteristic
378C2×#463C2×C7311yescharacteristic, complemented
379C2×#442C2×C7311yescharacteristic, complemented
380#2447C2×C7311yescharacteristic, complemented
381#2366C2×C7311yescharacteristic, complemented
382#2067C2×C7311yescharacteristic, complemented
383#2014C2×C7311yescharacteristic, complemented
384#2012C2×C7311yescharacteristic, complemented
385#2011C2×C7311yescharacteristic
386#1973C2×C7311yescharacteristic, complemented
387#1927C2×C7311yescharacteristic, complemented
388#1925C2×C7311yescharacteristic, complemented
389#1917C2×C7311yescharacteristic, complemented
390#1879C2×C7311yescharacteristic, complemented
391#1877C2×C7311yescharacteristic, complemented
392#1864C2×C7311yescharacteristic, complemented
393C73#2660011yescharacteristic, direct product factor, Sylow
394C22×SD16C22×C7311yescharacteristic
395C22×SD16C22×C7311yescharacteristic
396C22×D8C22×C7311yescharacteristic
397C22×D8C22×C7311yescharacteristic
398C2×#127C22×C7311yescharacteristic
399C2×#124C22×C7311yescharacteristic
400C2×C4×D4—21no—
401C2×C4×D4C22×C7311yescharacteristic
402C2×C4×D4C22×C7311yescharacteristic
403C2×C4×D4C22×C7311yescharacteristic
404#463—24no—
405#442—24no—
406C2×#107C22×C7311yescharacteristic
407C2×#106C22×C7311yescharacteristic
408C2×C4⋊C8C22×C7311yescharacteristic
409C2×#103C22×C7311yescharacteristic
410C2×#103C22×C7311yescharacteristic
411C2×#102C22×C7311yescharacteristic
412C2×#102C22×C7311yescharacteristic
413C2×#102C22×C7311yescharacteristic
414C2×#102C22×C7311yescharacteristic
415C2×#102C22×C7311yescharacteristic
416C2×#102C22×C7311yescharacteristic
417C2×#97C22×C7311yescharacteristic
418#397—21no—
419#397—21no—
420#391C22×C7311yescharacteristic
421#391C22×C7311yescharacteristic
422#390—21no—
423#390C22×C7311yescharacteristic
424#390C22×C7311yescharacteristic
425#390C22×C7311yescharacteristic
426#389C22×C7311yescharacteristic
427#386—21no—
428#386—21no—
429#385—21no—
430#381—21no—
431C4×C4⋊C4C22×C7311yescharacteristic
432C4×C4⋊C4C22×C7311yescharacteristic
433#340C22×C7311yescharacteristic
434#340C22×C7311yescharacteristic
435#336C22×C7311yescharacteristic
436#336C22×C7311yescharacteristic
437#336C22×C7311yescharacteristic
438#336C22×C7311yescharacteristic
439C22×Q8C23×C7311yescharacteristic
440C22×D4—21no—
441C22×D4—21no—
442C22×D4C23×C7311yescharacteristic
443C22×D4C23×C7311yescharacteristic
444C22×D4C23×C7311yescharacteristic
445C23×C4—21no—
446C23×C4—21no—
447C23×C4—21no—
448C2×SD16—22no—
449C2×SD16—22no—
450C2×SD16—22no—
451C2×SD16—41no—
452C2×SD16—41no—
453C2×SD16—41no—
454C2×D8—22no—
455C2×D8—22no—
456C2×D8—22no—
457C2×D8—22no—
458C2×D8—22no—
459C2×D8—41no—
460C22×C8C23×C7311yescharacteristic
461C22×C8C23×C7311yescharacteristic
462C22×C8C23×C7311yescharacteristic
463C22×C8C23×C7311yescharacteristic
464#127—22no—
465#127—22no—
466#124—22no—
467#124—41no—
468C4×D4—22no—
469C4×D4—22no—
470C4×D4—22no—
471C4×D4—41no—
472C4×D4—41no—
473C4×D4—41no—
474C4×D4—44no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4D4×C7311yescharacteristic
477C2×C4⋊C4D4×C7311yescharacteristic
478C2×C4⋊C4C23×C7311yescharacteristic
479C2×C4⋊C4C23×C7311yescharacteristic
480C2×C4⋊C4C23×C7311yescharacteristic
481C2×C4⋊C4C23×C7311yescharacteristic
482C2×C22⋊C4—21no—
483C2×C22⋊C4—21no—
484C2×C22⋊C4—21no—
485C2×C22⋊C4—21no—
486C2×C22⋊C4—21no—
487C2×C22⋊C4—21no—
488C2×C22⋊C4—21no—
489C2×C22⋊C4—21no—
490C2×C22⋊C4—21no—
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C42—21no—
494C2×C42C23×C7311yescharacteristic
495C2×C42C23×C7311yescharacteristic
496C2×C42C23×C7311yescharacteristic
497#107—41no—
498#106—22no—
499C4⋊C8—22no—
500#103—22no—
501#103—22no—
502#102—22no—
503#102—22no—
504#102—41no—
505#102—41no—
506#102—41no—
507#102D4×C7314yescomplemented
508#97—22no—
509#95—21no—
510#95—21no—
511#95—21no—
512#95—21no—
513#95—21no—
514#95—21no—
515#95D4×C7311yescharacteristic
516#95D4×C7311yescharacteristic
517C24—21no—
518C24—21no—
519C24—21no—
520C2×Q8—21no—
521C2×Q8—21no—
522C2×Q8—21no—
523C2×Q8—21no—
524C2×Q8—21no—
525C2×Q8—21no—
526C2×D4—24no—
527C2×D4—24no—
528C2×D4—21no—
529C2×D4—21no—
530C2×D4—21no—
531C2×D4—21no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—42no—
544C2×D4—42no—
545C2×D4—81no—
546C2×D4—81no—
547C2×D4C2×D4×C7312yes—
548C2×D4#41×C7312yes—
549C2×D4#41×C7312yes—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—42no—
556C22×C4—42no—
557C22×C4—42no—
558C22×C4—42no—
559C22×C4—42no—
560C22×C4—42no—
561C22×C4—81no—
562C22×C4—81no—
563C22×C4—81no—
564C22×C4C2×D4×C7311yescharacteristic
565C22×C4C2×D4×C7311yescharacteristic
566C22×C4C2×D4×C7311yescharacteristic
567C22×C4C2×D4×C7311yescharacteristic
568C22×C4C2×D4×C7311yescharacteristic
569C22×C4C2×D4×C7311yescharacteristic
570C22×C4C24×C7311yescharacteristic
571SD16—44no—
572SD16—44no—
573D8—28no—
574D8—44no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—21no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C2×C8C2×D4×C7312yes—
586C2×C8#41×C7312yes—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—41no—
596C4⋊C4—81no—
597C4⋊C4C2×D4×C7312yes—
598C22⋊C4—42no—
599C22⋊C4—42no—
600C22⋊C4—42no—
601C22⋊C4—42no—
602C22⋊C4—42no—
603C22⋊C4—42no—
604C22⋊C4—42no—
605C22⋊C4—42no—
606C22⋊C4—81no—
607C22⋊C4—81no—
608C22⋊C4—81no—
609C42—21no—
610C42—21no—
611C42—21no—
612C42—21no—
613C42—21no—
614C42—21no—
615C42—42no—
616C23—22no—
617C23—22no—
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23—41no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23C22×D4×C7311yescharacteristic
638Q8—41no—
639Q8—41no—
640Q8—41no—
641Q8—41no—
642D4—22no—
643D4—22no—
644D4—22no—
645D4—22no—
646D4—22no—
647D4—22no—
648D4—48no—
649D4—41no—
650D4—41no—
651D4—41no—
652D4—41no—
653D4—41no—
654D4—41no—
655D4—84no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—21no—
659C2×C4—21no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—22no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—84no—
689C2×C4—84no—
690C2×C4—84no—
691C2×C4AGL(1,ℤ/8)×C7312yes—
692C2×C4C22×D4×C7311yescharacteristic
693C2×C4C2×#41×C7311yescharacteristic
694C2×C4C2×#41×C7311yescharacteristic
695C2×C4C2×#41×C7311yescharacteristic
696C2×C4H(5,𝔽2)×C7311yescharacteristic
697C2×C4H(5,𝔽2)×C7311yescharacteristic
698C8—22no—
699C8—22no—
700C8—41no—
701C8—41no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—42no—
707C22—42no—
708C22—42no—
709C22—42no—
710C22—42no—
711C22—81no—
712C22—81no—
713C22—81no—
714C22—81no—
715C22—81no—
716C22—81no—
717C22—81no—
718C22—81no—
719C22—81no—
720C22—81no—
721C22—81no—
722C22—81no—
723C22#525×C7311yescharacteristic
724C22D42×C7311yescharacteristic
725C22#550×C7311yescharacteristic
726C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
727C22#575×C7311yescharacteristic
728C22#576×C7311yescharacteristic
729C22#577×C7311yescharacteristic
730C4—22no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—41no—
735C4—42no—
736C4—41no—
737C4—81no—
738C4—81no—
739C4—81no—
740C4—81no—
741C4#525×C7311yescharacteristic
742C4#538×C7311yescharacteristic
743C4#546×C7311yescharacteristic
744C4#553×C7311yescharacteristic
745C2—82no—
746C2—82no—
747C2—82no—
748C2C73×#245611yescharacteristic
749C2C73×#311411yescharacteristic
750C2C73×#311811yescharacteristic
751C2C73×#326811yescharacteristic
752C2C73×#327211yescharacteristic
753C2C73×#339911yescharacteristic
754C2C73×#340111yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#2011C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C4×C4⋊C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#463×C73C2semidirect
2. C2×#442×C73C2semidirect
3. C73×#2447C2semidirect
4. C73×#2366C2semidirect
5. C73×#2067C2semidirect
6. C73×#2014C2semidirect
7. C73×#2012C2semidirect
9. C73×#1973C2semidirect
10. C73×#1927C2semidirect
11. C73×#1925C2semidirect
12. C73×#1917C2semidirect
13. C73×#1879C2semidirect
14. C73×#1877C2semidirect
15. C73×#1864C2semidirect
129. #102×C73D4semidirect
367. #26600C73direct (N × H)
378. C2×#463C2×C73semidirect
379. C2×#442C2×C73semidirect
380. #2447C2×C73semidirect
381. #2366C2×C73semidirect
382. #2067C2×C73semidirect
383. #2014C2×C73semidirect
384. #2012C2×C73semidirect
386. #1973C2×C73semidirect
387. #1927C2×C73semidirect
388. #1925C2×C73semidirect
389. #1917C2×C73semidirect
390. #1879C2×C73semidirect
391. #1877C2×C73semidirect
392. #1864C2×C73semidirect
393. C73#26600direct (N × H)
507. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#463×C732
C2×#442×C732
C73×#24472
C73×#23662
C73×#20672
C73×#20142
C73×#20122
C73×#20112
C73×#19732
C73×#19272
C73×#19252
C73×#19172
C73×#18792
C73×#18772
C73×#18642
#2660073