Finite Group Databasebeta

← C73×#25147 #32934551

Subgroups — C73×#25147 #32934551

Order 18688.

1022 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#471×C73C211yesmaximal, characteristic, complemented
2C73×#3055C211yesmaximal, characteristic, complemented
3C73×#3005C211yesmaximal, characteristic, complemented
4C2×#449×C73C211yesmaximal, characteristic, complemented
5C73×#2933C211yesmaximal, characteristic, complemented
6C2×#413×C73C211yesmaximal, characteristic, complemented
7C73×#2063C211yesmaximal, characteristic, complemented
8C73×#2052C211yesmaximal, characteristic, complemented
9C73×#2046C211yesmaximal, characteristic, complemented
10C73×#2018C211yesmaximal, characteristic, complemented
11C73×#1978C211yesmaximal, characteristic, complemented
12C73×#1930C211yesmaximal, characteristic, complemented
13C73×#1907C211yesmaximal, characteristic, complemented
14C73×#1900C211yesmaximal, characteristic, complemented
15C73×#1855C211yesmaximal, characteristic, complemented
16C22×#41×C73C2211yescharacteristic
17C2×#137×C73C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
20C22×SD16×C73C2211yescharacteristic
21C22×D8×C73C2211yescharacteristic
22C2×#131×C73C2211yescharacteristic
23C22×M16×C73C2211yescharacteristic
24C22×M16×C73C2211yescharacteristic
25#525×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27#471×C73—24no—
28#469×C73—21no—
29#468×C73—21no—
30#466×C73—21no—
31#465×C73—21no—
32#452×C73—21no—
33#452×C73—21no—
34#449×C73—21no—
35#449×C73—21no—
36#449×C73—21no—
37#449×C73—21no—
38#449×C73—21no—
39#449×C73—21no—
40#436×C73—21no—
41#435×C73—21no—
42#435×C73—21no—
43C8×D4×C73—21no—
44C2×#108×C73C2211yescharacteristic
45C2×#108×C73C2211yescharacteristic
46#428×C73C2211yescharacteristic
47#424×C73C2211yescharacteristic
48#419×C73C2211yescharacteristic
49#418×C73C2211yescharacteristic
50#418×C73C2211yescharacteristic
51#417×C73C2211yescharacteristic
52C2×#103×C73C2211yescharacteristic
53C2×#102×C73C2211yescharacteristic
54#413×C73—24no—
55C2×#101×C73C2211yescharacteristic
56C2×#101×C73C2211yescharacteristic
57C2×#100×C73C2211yescharacteristic
58C2×#100×C73C2211yescharacteristic
59C2×#100×C73C2211yescharacteristic
60C2×#100×C73C2211yescharacteristic
61#408×C73C2211yescharacteristic
62#407×C73C2211yescharacteristic
63C2×C22⋊C8×C73C2211yescharacteristic
64#405×C73C2211yescharacteristic
65#343×C73C2211yescharacteristic
66#343×C73C2211yescharacteristic
67#341×C73C2211yescharacteristic
68#341×C73C2211yescharacteristic
69C2×#41×C73—22no—
70C2×#41×C73—22no—
71C2×#41×C73—21no—
72C2×#41×C73—21no—
73C2×#41×C73—21no—
74C2×#41×C73—21no—
75C2×#41×C73—41no—
76C2×#41×C73—41no—
77C2×#41×C73C2311yescharacteristic
78C22×Q8×C73C2311yescharacteristic
79C22×D4×C73—21no—
80C22×D4×C73—21no—
81C22×D4×C73C2311yescharacteristic
82C22×D4×C73C2311yescharacteristic
83C23×C4×C73—21no—
84C23×C4×C73C2311yescharacteristic
85#137×C73—22no—
86#137×C73—41no—
87AGL(1,ℤ/8)×C73—22no—
88AGL(1,ℤ/8)×C73—22no—
89AGL(1,ℤ/8)×C73—41no—
90AGL(1,ℤ/8)×C73—41no—
91C2×Q16×C73—21no—
92C2×SD16×C73—21no—
93C2×SD16×C73—21no—
94C2×SD16×C73—22no—
95C2×SD16×C73—21no—
96C2×SD16×C73—21no—
97C2×SD16×C73—21no—
98C2×SD16×C73—41no—
99C2×D8×C73—21no—
100C2×D8×C73—21no—
101C2×D8×C73—22no—
102C2×D8×C73—21no—
103C2×D8×C73—21no—
104C2×D8×C73—41no—
105#131×C73—22no—
106#131×C73—41no—
107C2×M16×C73—21no—
108C2×M16×C73—21no—
109C2×M16×C73—21no—
110C2×M16×C73—22no—
111C2×M16×C73—22no—
112C2×M16×C73—41no—
113C2×M16×C73—41no—
114C2×M16×C73C2311yescharacteristic
115C2×M16×C73C2311yescharacteristic
116C2×M16×C73C2311yescharacteristic
117C2×M16×C73C2311yescharacteristic
118C2×M16×C73C2311yescharacteristic
119C2×M16×C73C2311yescharacteristic
120C22×C8×C73—21no—
121C22×C8×C73—21no—
122C22×C8×C73—21no—
123C22×C8×C73C2311yescharacteristic
124C22×C8×C73C2311yescharacteristic
125#123×C73—21no—
126C22⋊Q8×C73D411yescharacteristic
127C22⋊Q8×C73D411yescharacteristic
128#121×C73—21no—
129#121×C73—21no—
130#121×C73—21no—
131#121×C73—21no—
132#121×C73D411yescharacteristic
133#121×C73D411yescharacteristic
134#120×C73—21no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137#117×C73C2311yescharacteristic
138C2×C4⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73—21no—
140#108×C73—22no—
141#108×C73—41no—
142#107×C73—21no—
143#106×C73—21no—
144C4⋊C8×C73—21no—
145C4⋊C8×C73—21no—
146#103×C73—21no—
147#103×C73—21no—
148#103×C73—21no—
149#103×C73—21no—
150#103×C73—21no—
151#102×C73—21no—
152#102×C73—21no—
153#102×C73—21no—
154#102×C73—21no—
155#102×C73—21no—
156#102×C73—21no—
157#102×C73—21no—
158#101×C73—22no—
159#101×C73D414yescomplemented
160#100×C73—22no—
161#100×C73—22no—
162#100×C73—22no—
163#100×C73—41no—
164C22⋊C8×C73—21no—
165C22⋊C8×C73—21no—
166C22⋊C8×C73—21no—
167C22⋊C8×C73—21no—
168C22⋊C8×C73D411yescharacteristic
169C22⋊C8×C73D411yescharacteristic
170C22⋊C8×C73D411yescharacteristic
171C22⋊C8×C73D411yescharacteristic
172#97×C73—21no—
173C4×C8×C73—21no—
174C24×C73—21no—
175C24×C73—21no—
176C24×C73#4111yescharacteristic
177#41×C73—21no—
178#41×C73—21no—
179#41×C73—21no—
180#41×C73—21no—
181#41×C73—42no—
182#41×C73—42no—
183#41×C73—42no—
184#41×C73—42no—
185#41×C73—42no—
186#41×C73—42no—
187#41×C73—42no—
188#41×C73—42no—
189C2×Q8×C73—21no—
190C2×Q8×C73—21no—
191C2×Q8×C73—21no—
192C2×Q8×C73—21no—
193C2×Q8×C73—21no—
194C2×Q8×C73C2×D412yes—
195C2×Q8×C73C2×D411yescharacteristic
196C2×D4×C73—24no—
197C2×D4×C73—21no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—21no—
205C2×D4×C73—21no—
206C2×D4×C73—21no—
207C2×D4×C73—21no—
208C2×D4×C73—21no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—42no—
212C2×D4×C73—41no—
213C2×D4×C73—41no—
214C2×D4×C73—41no—
215C2×D4×C73—41no—
216C2×D4×C73—82no—
217C2×D4×C73C2×D411yescharacteristic
218C2×D4×C73#4112yes—
219C22×C4×C73—21no—
220C22×C4×C73—21no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—24no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—42no—
228C22×C4×C73—41no—
229C22×C4×C73—41no—
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73#4111yescharacteristic
235C22×C4×C73C2411yescharacteristic
236Q16×C73—42no—
237SD16×C73—42no—
238SD16×C73—42no—
239SD16×C73—42no—
240SD16×C73—42no—
241SD16×C73—42no—
242D8×C73—42no—
243D8×C73—42no—
244D8×C73—42no—
245D8×C73—42no—
246M16×C73—21no—
247M16×C73—21no—
248M16×C73—21no—
249M16×C73—21no—
250M16×C73—21no—
251M16×C73—21no—
252M16×C73—21no—
253M16×C73—21no—
254M16×C73—21no—
255M16×C73—21no—
256M16×C73—42no—
257M16×C73—42no—
258M16×C73—42no—
259M16×C73C2×D412yes—
260M16×C73C2×D412yes—
261C2×C8×C73—21no—
262C2×C8×C73—21no—
263C2×C8×C73—21no—
264C2×C8×C73—21no—
265C2×C8×C73—21no—
266C2×C8×C73—21no—
267C2×C8×C73—21no—
268C2×C8×C73—21no—
269C2×C8×C73—21no—
270C2×C8×C73—21no—
271C2×C8×C73—42no—
272C2×C8×C73—42no—
273C2×C8×C73—42no—
274C2×C8×C73C2×D411yescharacteristic
275C2×C8×C73C2×D411yescharacteristic
276C2×C8×C73C2×D411yescharacteristic
277C2×C8×C73C2×D411yescharacteristic
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73—21no—
281C4⋊C4×C73—21no—
282C4⋊C4×C73C2×D411yescharacteristic
283C4⋊C4×C73C2×D411yescharacteristic
284C22⋊C4×C73—21no—
285C22⋊C4×C73—21no—
286C22⋊C4×C73—21no—
287C22⋊C4×C73—21no—
288C22⋊C4×C73—21no—
289C22⋊C4×C73—41no—
290C22⋊C4×C73—41no—
291C42×C73—21no—
292C23×C73—21no—
293C23×C73—21no—
294C23×C73—21no—
295C23×C73—22no—
296C23×C73—41no—
297C23×C73—41no—
298C23×C73—41no—
299C23×C73—41no—
300C23×C73—41no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—81no—
304C23×C73—81no—
305C23×C73—81no—
306C23×C73—81no—
307C23×C73#12111yescharacteristic
308C23×C73#12111yescharacteristic
309C23×C73C2×#4111yescharacteristic
310Q8×C73—21no—
311Q8×C73—22no—
312Q8×C73—22no—
313Q8×C73—21no—
314Q8×C73—41no—
315Q8×C73—41no—
316D4×C73—21no—
317D4×C73—22no—
318D4×C73—21no—
319D4×C73—22no—
320D4×C73—42no—
321D4×C73—44no—
322D4×C73—44no—
323D4×C73—41no—
324D4×C73—41no—
325D4×C73—41no—
326D4×C73—41no—
327D4×C73—41no—
328D4×C73—41no—
329D4×C73—41no—
330D4×C73—41no—
331D4×C73—81no—
332D4×C73—82no—
333D4×C73—82no—
334C2×C4×C73—21no—
335C2×C4×C73—21no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—21no—
346C2×C4×C73—21no—
347C2×C4×C73—22no—
348C2×C4×C73—44no—
349C2×C4×C73—44no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—81no—
356C2×C4×C73#12111yescharacteristic
357C2×C4×C73#12111yescharacteristic
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C22×D411yescharacteristic
360C2×C4×C73C22×D411yescharacteristic
361C2×C4×C73C2×#4111yescharacteristic
362C2×C4×C73H(5,𝔽2)11yescharacteristic
363C2×C4×C73H(5,𝔽2)11yescharacteristic
364C8×C73—21no—
365C8×C73—21no—
366C8×C73—22no—
367C8×C73—22no—
368C8×C73—21no—
369C8×C73—21no—
370C8×C73—41no—
371C8×C73—41no—
372C8×C73—41no—
373C8×C73—41no—
374C22×C73—21no—
375C22×C73—21no—
376C22×C73—21no—
377C22×C73—21no—
378C22×C73—21no—
379C22×C73—21no—
380C22×C73—21no—
381C22×C73—21no—
382C22×C73—42no—
383C22×C73—41no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—81no—
387C22×C73—81no—
388C22×C73—82no—
389C22×C73—82no—
390C22×C73—81no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73—81no—
395C22×C73—161no—
396C22×C73—161no—
397C22×C73C2×#12111yescharacteristic
398C22×C73#52511yescharacteristic
399C22×C73#53811yescharacteristic
400C4×C73—21no—
401C4×C73—21no—
402C4×C73—42no—
403C4×C73—41no—
404C4×C73—41no—
405C4×C73—41no—
406C4×C73—81no—
407C4×C73D4211yescharacteristic
408C4×C73D4211yescharacteristic
409C4×C73#54611yescharacteristic
410C4×C73#54611yescharacteristic
411#25147C7311yesmaximal, characteristic, direct product factor, Sylow
412C2×C73—21no—
413C2×C73—21no—
414C2×C73—41no—
415C2×C73—41no—
416C2×C73—81no—
417C2×C73—82no—
418C2×C73—161no—
419C2×C73#242411yescharacteristic
420C2×C73#306711yescharacteristic
421C2×C73#306811yescharacteristic
422C2×#471C2×C7311yescharacteristic, complemented
423#3055C2×C7311yescharacteristic, complemented
424#3005C2×C7311yescharacteristic, complemented
425C2×#449C2×C7311yescharacteristic, complemented
426#2933C2×C7311yescharacteristic, complemented
427C2×#413C2×C7311yescharacteristic, complemented
428#2063C2×C7311yescharacteristic, complemented
429#2052C2×C7311yescharacteristic, complemented
430#2046C2×C7311yescharacteristic, complemented
431#2018C2×C7311yescharacteristic, complemented
432#1978C2×C7311yescharacteristic, complemented
433#1930C2×C7311yescharacteristic, complemented
434#1907C2×C7311yescharacteristic, complemented
435#1900C2×C7311yescharacteristic, complemented
436#1855C2×C7311yescharacteristic, complemented
437C73#2514711yescharacteristic, direct product factor, Sylow
438C22×#41C22×C7311yescharacteristic
439C2×#137C22×C7311yescharacteristic
440C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
441C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
442C22×SD16C22×C7311yescharacteristic
443C22×D8C22×C7311yescharacteristic
444C2×#131C22×C7311yescharacteristic
445C22×M16C22×C7311yescharacteristic
446C22×M16C22×C7311yescharacteristic
447#525C22×C7311yescharacteristic
448C2×#121C22×C7311yescharacteristic
449#471—24no—
450#469—21no—
451#468—21no—
452#466—21no—
453#465—21no—
454#452—21no—
455#452—21no—
456#449—21no—
457#449—21no—
458#449—21no—
459#449—21no—
460#449—21no—
461#449—21no—
462#436—21no—
463#435—21no—
464#435—21no—
465C8×D4—21no—
466C2×#108C22×C7311yescharacteristic
467C2×#108C22×C7311yescharacteristic
468#428C22×C7311yescharacteristic
469#424C22×C7311yescharacteristic
470#419C22×C7311yescharacteristic
471#418C22×C7311yescharacteristic
472#418C22×C7311yescharacteristic
473#417C22×C7311yescharacteristic
474C2×#103C22×C7311yescharacteristic
475C2×#102C22×C7311yescharacteristic
476#413—24no—
477C2×#101C22×C7311yescharacteristic
478C2×#101C22×C7311yescharacteristic
479C2×#100C22×C7311yescharacteristic
480C2×#100C22×C7311yescharacteristic
481C2×#100C22×C7311yescharacteristic
482C2×#100C22×C7311yescharacteristic
483#408C22×C7311yescharacteristic
484#407C22×C7311yescharacteristic
485C2×C22⋊C8C22×C7311yescharacteristic
486#405C22×C7311yescharacteristic
487#343C22×C7311yescharacteristic
488#343C22×C7311yescharacteristic
489#341C22×C7311yescharacteristic
490#341C22×C7311yescharacteristic
491C2×#41—22no—
492C2×#41—22no—
493C2×#41—21no—
494C2×#41—21no—
495C2×#41—21no—
496C2×#41—21no—
497C2×#41—41no—
498C2×#41—41no—
499C2×#41C23×C7311yescharacteristic
500C22×Q8C23×C7311yescharacteristic
501C22×D4—21no—
502C22×D4—21no—
503C22×D4C23×C7311yescharacteristic
504C22×D4C23×C7311yescharacteristic
505C23×C4—21no—
506C23×C4C23×C7311yescharacteristic
507#137—22no—
508#137—41no—
509AGL(1,ℤ/8)—22no—
510AGL(1,ℤ/8)—22no—
511AGL(1,ℤ/8)—41no—
512AGL(1,ℤ/8)—41no—
513C2×Q16—21no—
514C2×SD16—22no—
515C2×SD16—21no—
516C2×SD16—21no—
517C2×SD16—21no—
518C2×SD16—21no—
519C2×SD16—21no—
520C2×SD16—41no—
521C2×D8—21no—
522C2×D8—21no—
523C2×D8—22no—
524C2×D8—21no—
525C2×D8—21no—
526C2×D8—41no—
527#131—22no—
528#131—41no—
529C2×M16—21no—
530C2×M16—21no—
531C2×M16—21no—
532C2×M16—22no—
533C2×M16—22no—
534C2×M16—41no—
535C2×M16—41no—
536C2×M16C23×C7311yescharacteristic
537C2×M16C23×C7311yescharacteristic
538C2×M16C23×C7311yescharacteristic
539C2×M16C23×C7311yescharacteristic
540C2×M16C23×C7311yescharacteristic
541C2×M16C23×C7311yescharacteristic
542C22×C8—21no—
543C22×C8—21no—
544C22×C8—21no—
545C22×C8C23×C7311yescharacteristic
546C22×C8C23×C7311yescharacteristic
547#123—21no—
548C22⋊Q8D4×C7311yescharacteristic
549C22⋊Q8D4×C7311yescharacteristic
550#121—21no—
551#121—21no—
552#121—21no—
553#121—21no—
554#121D4×C7311yescharacteristic
555#121D4×C7311yescharacteristic
556#120—21no—
557C4×D4—21no—
558C4×D4—21no—
559#117C23×C7311yescharacteristic
560C2×C4⋊C4C23×C7311yescharacteristic
561C2×C22⋊C4—21no—
562#108—22no—
563#108—41no—
564#107—21no—
565#106—21no—
566C4⋊C8—21no—
567C4⋊C8—21no—
568#103—21no—
569#103—21no—
570#103—21no—
571#103—21no—
572#103—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#101—22no—
581#101D4×C7314yescomplemented
582#100—22no—
583#100—22no—
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C22⋊C8—21no—
589C22⋊C8—21no—
590C22⋊C8D4×C7311yescharacteristic
591C22⋊C8D4×C7311yescharacteristic
592C22⋊C8D4×C7311yescharacteristic
593C22⋊C8D4×C7311yescharacteristic
594#97—21no—
595C4×C8—21no—
596C24—21no—
597C24—21no—
598C24#41×C7311yescharacteristic
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41—42no—
607#41—42no—
608#41—42no—
609#41—42no—
610#41—42no—
611C2×Q8—21no—
612C2×Q8—21no—
613C2×Q8—21no—
614C2×Q8—21no—
615C2×Q8—21no—
616C2×Q8C2×D4×C7312yes—
617C2×Q8C2×D4×C7311yescharacteristic
618C2×D4—24no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—42no—
634C2×D4—41no—
635C2×D4—41no—
636C2×D4—41no—
637C2×D4—41no—
638C2×D4—82no—
639C2×D4C2×D4×C7311yescharacteristic
640C2×D4#41×C7312yes—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—24no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—42no—
650C22×C4—41no—
651C22×C4—41no—
652C22×C4C2×D4×C7311yescharacteristic
653C22×C4C2×D4×C7311yescharacteristic
654C22×C4C2×D4×C7311yescharacteristic
655C22×C4C2×D4×C7311yescharacteristic
656C22×C4#41×C7311yescharacteristic
657C22×C4C24×C7311yescharacteristic
658Q16—42no—
659SD16—42no—
660SD16—42no—
661SD16—42no—
662SD16—42no—
663SD16—42no—
664D8—42no—
665D8—42no—
666D8—42no—
667D8—42no—
668M16—21no—
669M16—21no—
670M16—21no—
671M16—21no—
672M16—21no—
673M16—21no—
674M16—21no—
675M16—21no—
676M16—21no—
677M16—21no—
678M16—42no—
679M16—42no—
680M16—42no—
681M16C2×D4×C7312yes—
682M16C2×D4×C7312yes—
683C2×C8—21no—
684C2×C8—21no—
685C2×C8—21no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—42no—
694C2×C8—42no—
695C2×C8—42no—
696C2×C8C2×D4×C7311yescharacteristic
697C2×C8C2×D4×C7311yescharacteristic
698C2×C8C2×D4×C7311yescharacteristic
699C2×C8C2×D4×C7311yescharacteristic
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4C2×D4×C7311yescharacteristic
705C4⋊C4C2×D4×C7311yescharacteristic
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—41no—
712C22⋊C4—41no—
713C42—21no—
714C23—21no—
715C23—21no—
716C23—21no—
717C23—22no—
718C23—41no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—41no—
723C23—41no—
724C23—41no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—81no—
729C23#121×C7311yescharacteristic
730C23#121×C7311yescharacteristic
731C23C2×#41×C7311yescharacteristic
732Q8—21no—
733Q8—22no—
734Q8—22no—
735Q8—21no—
736Q8—41no—
737Q8—41no—
738D4—21no—
739D4—22no—
740D4—21no—
741D4—22no—
742D4—44no—
743D4—44no—
744D4—42no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—81no—
754D4—82no—
755D4—82no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—21no—
766C2×C4—21no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—22no—
770C2×C4—44no—
771C2×C4—44no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—81no—
778C2×C4#121×C7311yescharacteristic
779C2×C4#121×C7311yescharacteristic
780C2×C4C22×D4×C7311yescharacteristic
781C2×C4C22×D4×C7311yescharacteristic
782C2×C4C22×D4×C7311yescharacteristic
783C2×C4C2×#41×C7311yescharacteristic
784C2×C4H(5,𝔽2)×C7311yescharacteristic
785C2×C4H(5,𝔽2)×C7311yescharacteristic
786C8—21no—
787C8—21no—
788C8—22no—
789C8—22no—
790C8—21no—
791C8—21no—
792C8—41no—
793C8—41no—
794C8—41no—
795C8—41no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—21no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—81no—
809C22—81no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—81no—
814C22—81no—
815C22—81no—
816C22—81no—
817C22—161no—
818C22—161no—
819C22C2×#121×C7311yescharacteristic
820C22#525×C7311yescharacteristic
821C22#538×C7311yescharacteristic
822C4—21no—
823C4—21no—
824C4—41no—
825C4—41no—
826C4—42no—
827C4—41no—
828C4—81no—
829C4D42×C7311yescharacteristic
830C4D42×C7311yescharacteristic
831C4#546×C7311yescharacteristic
832C4#546×C7311yescharacteristic
833C2—21no—
834C2—21no—
835C2—41no—
836C2—41no—
837C2—81no—
838C2—82no—
839C2—161no—
840C2C73×#242411yescharacteristic
841C2C73×#306711yescharacteristic
842C2C73×#306811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#121
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#471×C73C2semidirect
2. C73×#3055C2semidirect
3. C73×#3005C2semidirect
4. C2×#449×C73C2semidirect
5. C73×#2933C2semidirect
6. C2×#413×C73C2semidirect
7. C73×#2063C2semidirect
8. C73×#2052C2semidirect
9. C73×#2046C2semidirect
10. C73×#2018C2semidirect
11. C73×#1978C2semidirect
12. C73×#1930C2semidirect
13. C73×#1907C2semidirect
14. C73×#1900C2semidirect
15. C73×#1855C2semidirect
159. #101×C73D4semidirect
411. #25147C73direct (N × H)
422. C2×#471C2×C73semidirect
423. #3055C2×C73semidirect
424. #3005C2×C73semidirect
425. C2×#449C2×C73semidirect
426. #2933C2×C73semidirect
427. C2×#413C2×C73semidirect
428. #2063C2×C73semidirect
429. #2052C2×C73semidirect
430. #2046C2×C73semidirect
431. #2018C2×C73semidirect
432. #1978C2×C73semidirect
433. #1930C2×C73semidirect
434. #1907C2×C73semidirect
435. #1900C2×C73semidirect
436. #1855C2×C73semidirect
437. C73#25147direct (N × H)
581. #101D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#471×C732
C73×#30552
C73×#30052
C2×#449×C732
C73×#29332
C2×#413×C732
C73×#20632
C73×#20522
C73×#20462
C73×#20182
C73×#19782
C73×#19302
C73×#19072
C73×#19002
C73×#18552
#2514773