Finite Group Databasebeta

← C73×#25188 #32934592

Subgroups — C73×#25188 #32934592

Order 18688.

1066 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3062C211yesmaximal, characteristic, complemented
2C73×#3045C211yesmaximal, characteristic, complemented
3C2×#453×C73C211yesmaximal, characteristic, complemented
4C73×#3012C211yesmaximal, characteristic, complemented
5C2×#443×C73C211yesmaximal, characteristic, complemented
6C73×#2897C211yesmaximal, characteristic, complemented
7C73×#2063C211yesmaximal, characteristic, complemented
8C73×#2051C211yesmaximal, characteristic, complemented
9C73×#2039C211yesmaximal, characteristic, complemented
10C73×#2002C211yesmaximal, characteristic, complemented
11C73×#1957C211yesmaximal, characteristic, complemented
12C73×#1937C211yesmaximal, characteristic, complemented
13C73×#1907C211yesmaximal, characteristic, complemented
14C73×#1907C211yesmaximal, characteristic, complemented
15C73×#1859C211yesmaximal, characteristic, complemented
16C2×H(5,𝔽2)×C73C2211yescharacteristic
17C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
18C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
19C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
20C2×#135×C73C2211yescharacteristic
21C2×#131×C73C2211yescharacteristic
22C2×#131×C73C2211yescharacteristic, complemented
23#537×C73C2211yescharacteristic
24#535×C73C2211yescharacteristic, complemented
25C2×#127×C73C2211yescharacteristic
26#520×C73C2211yescharacteristic
27#469×C73—21no—
28#468×C73—21no—
29#466×C73—21no—
30#465×C73—21no—
31#464×C73—21no—
32#463×C73—21no—
33#460×C73—21no—
34#459×C73—21no—
35#453×C73—24no—
36#452×C73—21no—
37#450×C73—21no—
38#449×C73—21no—
39#447×C73—21no—
40#443×C73—24no—
41C2×#108×C73C2211yescharacteristic, complemented
42#428×C73C2211yescharacteristic, complemented
43#424×C73C2211yescharacteristic, complemented
44C2×#104×C73C2211yescharacteristic
45C2×#104×C73C2211yescharacteristic
46C2×#104×C73C2211yescharacteristic, complemented
47#418×C73—21no—
48#418×C73C2211yescharacteristic
49#417×C73—21no—
50#417×C73C2211yescharacteristic
51#417×C73C2211yescharacteristic
52#417×C73C2211yescharacteristic, complemented
53#416×C73—21no—
54#416×C73C2211yescharacteristic
55C2×#102×C73—21no—
56C2×#102×C73C2211yescharacteristic
57C2×#102×C73C2211yescharacteristic
58C2×#102×C73C2211yescharacteristic, complemented
59C2×#102×C73C2211yescharacteristic, complemented
60C2×#100×C73C2211yescharacteristic
61C2×#100×C73C2211yescharacteristic, complemented
62#408×C73C2211yescharacteristic
63C2×C4×C8×C73C2211yescharacteristic, complemented
64#384×C73C2211yescharacteristic, complemented
65#343×C73C2211yescharacteristic, complemented
66#343×C73C2211yescharacteristic, complemented
67#341×C73C2211yescharacteristic, complemented
68#339×C73C2211yescharacteristic, complemented
69H(5,𝔽2)×C73—22no—
70H(5,𝔽2)×C73—22no—
71H(5,𝔽2)×C73—22no—
72H(5,𝔽2)×C73—41no—
73C2×#41×C73—21no—
74C2×#41×C73—21no—
75C2×#41×C73C2311yescharacteristic
76C2×#41×C73C2311yescharacteristic
77C2×#41×C73C2311yescharacteristic
78C22×D4×C73—21no—
79C22×D4×C73—21no—
80C22×D4×C73—41no—
81C22×D4×C73—41no—
82C22×D4×C73C2311yescharacteristic
83C22×D4×C73C2311yescharacteristic
84AGL(1,ℤ/8)×C73—22no—
85AGL(1,ℤ/8)×C73—22no—
86AGL(1,ℤ/8)×C73—22no—
87AGL(1,ℤ/8)×C73—22no—
88AGL(1,ℤ/8)×C73—41no—
89AGL(1,ℤ/8)×C73—41no—
90#135×C73—22no—
91#135×C73—22no—
92C2×Q16×C73D411yescharacteristic, complemented
93C2×SD16×C73—21no—
94C2×SD16×C73—21no—
95C2×SD16×C73—21no—
96C2×SD16×C73D411yescharacteristic, complemented
97C2×SD16×C73D411yescharacteristic, complemented
98C2×D8×C73—21no—
99C2×D8×C73—21no—
100C2×D8×C73—21no—
101C2×D8×C73D411yescharacteristic, complemented
102#131×C73—22no—
103#131×C73—22no—
104#131×C73—41no—
105#131×C73—41no—
106C2×M16×C73—21no—
107C2×M16×C73—21no—
108C2×M16×C73C2311yescharacteristic
109C2×M16×C73C2311yescharacteristic
110C2×M16×C73C2311yescharacteristic
111C2×M16×C73C2311yescharacteristic
112C22×C8×C73—21no—
113C22×C8×C73—21no—
114C22×C8×C73C2311yescharacteristic
115C22×C8×C73C2311yescharacteristic
116#127×C73—21no—
117#127×C73—22no—
118#127×C73—22no—
119#124×C73—21no—
120C22⋊Q8×C73—21no—
121C22⋊Q8×C73—21no—
122#121×C73—21no—
123#121×C73—21no—
124#121×C73—21no—
125#121×C73—21no—
126#121×C73—41no—
127#120×C73—41no—
128C4×Q8×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73—41no—
131#117×C73—21no—
132#117×C73C2311yescharacteristic
133C2×C4⋊C4×C73—21no—
134C2×C4⋊C4×C73—41no—
135C2×C4⋊C4×C73C2311yescharacteristic
136C2×C4⋊C4×C73C2311yescharacteristic
137C2×C42×C73C2311yescharacteristic
138#108×C73—22no—
139#107×C73—21no—
140#106×C73—21no—
141C4⋊C8×C73—21no—
142C4⋊C8×C73—21no—
143#104×C73—22no—
144#104×C73—22no—
145#104×C73D414yescomplemented
146#103×C73—21no—
147#103×C73—21no—
148#103×C73—21no—
149#103×C73D411yescharacteristic, complemented
150#103×C73D411yescharacteristic, complemented
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#102×C73—21no—
159#102×C73—21no—
160#102×C73—21no—
161#102×C73—21no—
162#102×C73—21no—
163#102×C73—21no—
164#102×C73D411yescharacteristic, complemented
165#102×C73D411yescharacteristic, complemented
166#100×C73—22no—
167#100×C73—41no—
168C22⋊C8×C73—21no—
169C22⋊C8×C73—21no—
170C4×C8×C73—22no—
171C24×C73—21no—
172C24×C73—21no—
173C24×C73—41no—
174#41×C73—21no—
175#41×C73—21no—
176#41×C73—24no—
177#41×C73—21no—
178#41×C73—21no—
179#41×C73—21no—
180#41×C73—21no—
181#41×C73—21no—
182#41×C73—21no—
183#41×C73—21no—
184#41×C73—21no—
185#41×C73—42no—
186#41×C73—42no—
187#41×C73—42no—
188#41×C73C2×D412yes—
189#41×C73#4112yes—
190C2×Q8×C73C2×D411yescharacteristic
191C2×Q8×C73C2×D411yescharacteristic
192C2×Q8×C73C2×D411yescharacteristic
193C2×D4×C73—21no—
194C2×D4×C73—24no—
195C2×D4×C73—21no—
196C2×D4×C73—21no—
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—42no—
209C2×D4×C73—41no—
210C2×D4×C73—41no—
211C2×D4×C73—44no—
212C2×D4×C73—41no—
213C2×D4×C73—41no—
214C2×D4×C73—42no—
215C2×D4×C73—44no—
216C2×D4×C73—44no—
217C2×D4×C73—42no—
218C2×D4×C73—41no—
219C2×D4×C73—82no—
220C2×D4×C73—82no—
221C2×D4×C73C2×D411yescharacteristic
222C2×D4×C73C2×D411yescharacteristic
223C2×D4×C73C2×D411yescharacteristic
224C2×D4×C73#4112yes—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—41no—
232C22×C4×C73—41no—
233C22×C4×C73C2411yescharacteristic
234Q16×C73—22no—
235SD16×C73—22no—
236SD16×C73—22no—
237SD16×C73—42no—
238SD16×C73—42no—
239SD16×C73—42no—
240D8×C73—22no—
241D8×C73—42no—
242D8×C73—42no—
243D8×C73—42no—
244M16×C73—21no—
245M16×C73—21no—
246M16×C73—21no—
247M16×C73—21no—
248M16×C73—21no—
249M16×C73—21no—
250M16×C73—21no—
251M16×C73—42no—
252M16×C73—42no—
253M16×C73C2×D412yes—
254C2×C8×C73—21no—
255C2×C8×C73—21no—
256C2×C8×C73—21no—
257C2×C8×C73—21no—
258C2×C8×C73—21no—
259C2×C8×C73—21no—
260C2×C8×C73—21no—
261C2×C8×C73—21no—
262C2×C8×C73—42no—
263C2×C8×C73—42no—
264C2×C8×C73C2×D411yescharacteristic
265C2×C8×C73C2×D411yescharacteristic
266C2×C8×C73C2×D411yescharacteristic
267C2×C8×C73C2×D411yescharacteristic
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—41no—
273C4⋊C4×C73—41no—
274C4⋊C4×C73—82no—
275C4⋊C4×C73C2×D411yescharacteristic
276C4⋊C4×C73C2×D411yescharacteristic
277C22⋊C4×C73—21no—
278C22⋊C4×C73—41no—
279C22⋊C4×C73—41no—
280C22⋊C4×C73—41no—
281C22⋊C4×C73—41no—
282C22⋊C4×C73—41no—
283C42×C73—21no—
284C42×C73—21no—
285C42×C73—41no—
286C42×C73C2×D412yes—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—21no—
290C23×C73—22no—
291C23×C73—44no—
292C23×C73—41no—
293C23×C73—41no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—81no—
298C23×C73—81no—
299C23×C73—81no—
300C23×C73—81no—
301C23×C73—161no—
302C23×C73—161no—
303C23×C73H(5,𝔽2)11yescharacteristic
304Q8×C73—21no—
305Q8×C73—21no—
306Q8×C73—21no—
307Q8×C73—21no—
308Q8×C73—21no—
309Q8×C73#12112yes—
310D4×C73—22no—
311D4×C73—22no—
312D4×C73—21no—
313D4×C73—21no—
314D4×C73—22no—
315D4×C73—21no—
316D4×C73—21no—
317D4×C73—21no—
318D4×C73—22no—
319D4×C73—44no—
320D4×C73—44no—
321D4×C73—41no—
322D4×C73—41no—
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—88no—
332D4×C73—161no—
333D4×C73—161no—
334D4×C73—161no—
335D4×C73#12112yes—
336C2×C4×C73—22no—
337C2×C4×C73—22no—
338C2×C4×C73—21no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—22no—
342C2×C4×C73—21no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—21no—
346C2×C4×C73—44no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—81no—
354C2×C4×C73—81no—
355C2×C4×C73—161no—
356C2×C4×C73C22×D411yescharacteristic
357C2×C4×C73C22×D411yescharacteristic
358C2×C4×C73C22×D411yescharacteristic
359C2×C4×C73C2×#4111yescharacteristic
360C2×C4×C73C2×#4111yescharacteristic
361C2×C4×C73H(5,𝔽2)11yescharacteristic
362C8×C73—21no—
363C8×C73—21no—
364C8×C73—21no—
365C8×C73—21no—
366C8×C73—22no—
367C8×C73—41no—
368C8×C73—41no—
369C8×C73—41no—
370C22×C73—21no—
371C22×C73—21no—
372C22×C73—22no—
373C22×C73—41no—
374C22×C73—41no—
375C22×C73—41no—
376C22×C73—42no—
377C22×C73—41no—
378C22×C73—41no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—82no—
383C22×C73—82no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—161no—
390C22×C73—161no—
391C22×C73—164no—
392C22×C73#53811yescharacteristic
393C22×C73D4211yescharacteristic
394C22×C73#54611yescharacteristic
395C4×C73—24no—
396C4×C73—22no—
397C4×C73—41no—
398C4×C73—41no—
399C4×C73—41no—
400C4×C73—41no—
401C4×C73—81no—
402C4×C73—81no—
403C4×C73C2×#12111yescharacteristic
404C4×C73#52511yescharacteristic
405C4×C73D4211yescharacteristic
406C4×C73#54611yescharacteristic
407#25188C7311yesmaximal, characteristic, direct product factor, Sylow
408C2×C73—21no—
409C2×C73—21no—
410C2×C73—42no—
411C2×C73—81no—
412C2×C73—81no—
413C2×C73—82no—
414C2×C73—161no—
415C2×C73#242411yescharacteristic
416C2×C73#329111yescharacteristic
417C2×C73#329211yescharacteristic
418#3062C2×C7311yescharacteristic, complemented
419#3045C2×C7311yescharacteristic, complemented
420C2×#453C2×C7311yescharacteristic, complemented
421#3012C2×C7311yescharacteristic, complemented
422C2×#443C2×C7311yescharacteristic, complemented
423#2897C2×C7311yescharacteristic, complemented
424#2063C2×C7311yescharacteristic, complemented
425#2051C2×C7311yescharacteristic, complemented
426#2039C2×C7311yescharacteristic, complemented
427#2002C2×C7311yescharacteristic, complemented
428#1957C2×C7311yescharacteristic, complemented
429#1937C2×C7311yescharacteristic, complemented
430#1907C2×C7311yescharacteristic, complemented
431#1907C2×C7311yescharacteristic, complemented
432#1859C2×C7311yescharacteristic, complemented
433C73#2518811yescharacteristic, direct product factor, Sylow
434C2×H(5,𝔽2)C22×C7311yescharacteristic
435C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
436C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
437C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
438C2×#135C22×C7311yescharacteristic
439C2×#131C22×C7311yescharacteristic
440C2×#131C22×C7311yescharacteristic, complemented
441#537C22×C7311yescharacteristic
442#535C22×C7311yescharacteristic, complemented
443C2×#127C22×C7311yescharacteristic
444#520C22×C7311yescharacteristic
445#469—21no—
446#468—21no—
447#466—21no—
448#465—21no—
449#464—21no—
450#463—21no—
451#460—21no—
452#459—21no—
453#453—24no—
454#452—21no—
455#450—21no—
456#449—21no—
457#447—21no—
458#443—24no—
459C2×#108C22×C7311yescharacteristic, complemented
460#428C22×C7311yescharacteristic, complemented
461#424C22×C7311yescharacteristic, complemented
462C2×#104C22×C7311yescharacteristic
463C2×#104C22×C7311yescharacteristic
464C2×#104C22×C7311yescharacteristic, complemented
465#418—21no—
466#418C22×C7311yescharacteristic
467#417—21no—
468#417C22×C7311yescharacteristic
469#417C22×C7311yescharacteristic
470#417C22×C7311yescharacteristic, complemented
471#416—21no—
472#416C22×C7311yescharacteristic
473C2×#102—21no—
474C2×#102C22×C7311yescharacteristic
475C2×#102C22×C7311yescharacteristic
476C2×#102C22×C7311yescharacteristic, complemented
477C2×#102C22×C7311yescharacteristic, complemented
478C2×#100C22×C7311yescharacteristic
479C2×#100C22×C7311yescharacteristic, complemented
480#408C22×C7311yescharacteristic
481C2×C4×C8C22×C7311yescharacteristic, complemented
482#384C22×C7311yescharacteristic, complemented
483#343C22×C7311yescharacteristic, complemented
484#343C22×C7311yescharacteristic, complemented
485#341C22×C7311yescharacteristic, complemented
486#339C22×C7311yescharacteristic, complemented
487H(5,𝔽2)—22no—
488H(5,𝔽2)—22no—
489H(5,𝔽2)—22no—
490H(5,𝔽2)—41no—
491C2×#41—21no—
492C2×#41—21no—
493C2×#41C23×C7311yescharacteristic
494C2×#41C23×C7311yescharacteristic
495C2×#41C23×C7311yescharacteristic
496C22×D4—21no—
497C22×D4—21no—
498C22×D4—41no—
499C22×D4—41no—
500C22×D4C23×C7311yescharacteristic
501C22×D4C23×C7311yescharacteristic
502AGL(1,ℤ/8)—22no—
503AGL(1,ℤ/8)—22no—
504AGL(1,ℤ/8)—22no—
505AGL(1,ℤ/8)—22no—
506AGL(1,ℤ/8)—41no—
507AGL(1,ℤ/8)—41no—
508#135—22no—
509#135—22no—
510C2×Q16D4×C7311yescharacteristic, complemented
511C2×SD16—21no—
512C2×SD16—21no—
513C2×SD16—21no—
514C2×SD16D4×C7311yescharacteristic, complemented
515C2×SD16D4×C7311yescharacteristic, complemented
516C2×D8—21no—
517C2×D8—21no—
518C2×D8—21no—
519C2×D8D4×C7311yescharacteristic, complemented
520#131—22no—
521#131—22no—
522#131—41no—
523#131—41no—
524C2×M16—21no—
525C2×M16—21no—
526C2×M16C23×C7311yescharacteristic
527C2×M16C23×C7311yescharacteristic
528C2×M16C23×C7311yescharacteristic
529C2×M16C23×C7311yescharacteristic
530C22×C8—21no—
531C22×C8—21no—
532C22×C8C23×C7311yescharacteristic
533C22×C8C23×C7311yescharacteristic
534#127—21no—
535#127—22no—
536#127—22no—
537#124—21no—
538C22⋊Q8—21no—
539C22⋊Q8—21no—
540#121—21no—
541#121—21no—
542#121—21no—
543#121—21no—
544#121—41no—
545#120—41no—
546C4×Q8—21no—
547C4×D4—21no—
548C4×D4—41no—
549#117—21no—
550#117C23×C7311yescharacteristic
551C2×C4⋊C4—21no—
552C2×C4⋊C4—41no—
553C2×C4⋊C4C23×C7311yescharacteristic
554C2×C4⋊C4C23×C7311yescharacteristic
555C2×C42C23×C7311yescharacteristic
556#108—22no—
557#107—21no—
558#106—21no—
559C4⋊C8—21no—
560C4⋊C8—21no—
561#104—22no—
562#104—22no—
563#104D4×C7314yescomplemented
564#103—21no—
565#103—21no—
566#103—21no—
567#103D4×C7311yescharacteristic, complemented
568#103D4×C7311yescharacteristic, complemented
569#102—21no—
570#102—21no—
571#102—21no—
572#102—21no—
573#102—21no—
574#102—21no—
575#102—21no—
576#102—21no—
577#102—21no—
578#102—21no—
579#102—21no—
580#102—21no—
581#102—21no—
582#102D4×C7311yescharacteristic, complemented
583#102D4×C7311yescharacteristic, complemented
584#100—22no—
585#100—41no—
586C22⋊C8—21no—
587C22⋊C8—21no—
588C4×C8—22no—
589C24—21no—
590C24—21no—
591C24—41no—
592#41—21no—
593#41—21no—
594#41—24no—
595#41—21no—
596#41—21no—
597#41—21no—
598#41—21no—
599#41—21no—
600#41—21no—
601#41—21no—
602#41—21no—
603#41—42no—
604#41—42no—
605#41—42no—
606#41C2×D4×C7312yes—
607#41#41×C7312yes—
608C2×Q8C2×D4×C7311yescharacteristic
609C2×Q8C2×D4×C7311yescharacteristic
610C2×Q8C2×D4×C7311yescharacteristic
611C2×D4—21no—
612C2×D4—24no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—42no—
627C2×D4—41no—
628C2×D4—41no—
629C2×D4—44no—
630C2×D4—41no—
631C2×D4—41no—
632C2×D4—42no—
633C2×D4—44no—
634C2×D4—44no—
635C2×D4—42no—
636C2×D4—41no—
637C2×D4—82no—
638C2×D4—82no—
639C2×D4C2×D4×C7311yescharacteristic
640C2×D4C2×D4×C7311yescharacteristic
641C2×D4C2×D4×C7311yescharacteristic
642C2×D4#41×C7312yes—
643C22×C4—21no—
644C22×C4—21no—
645C22×C4—21no—
646C22×C4—21no—
647C22×C4—21no—
648C22×C4—21no—
649C22×C4—41no—
650C22×C4—41no—
651C22×C4C24×C7311yescharacteristic
652Q16—22no—
653SD16—22no—
654SD16—22no—
655SD16—42no—
656SD16—42no—
657SD16—42no—
658D8—22no—
659D8—42no—
660D8—42no—
661D8—42no—
662M16—21no—
663M16—21no—
664M16—21no—
665M16—21no—
666M16—21no—
667M16—21no—
668M16—21no—
669M16—42no—
670M16—42no—
671M16C2×D4×C7312yes—
672C2×C8—21no—
673C2×C8—21no—
674C2×C8—21no—
675C2×C8—21no—
676C2×C8—21no—
677C2×C8—21no—
678C2×C8—21no—
679C2×C8—21no—
680C2×C8—42no—
681C2×C8—42no—
682C2×C8C2×D4×C7311yescharacteristic
683C2×C8C2×D4×C7311yescharacteristic
684C2×C8C2×D4×C7311yescharacteristic
685C2×C8C2×D4×C7311yescharacteristic
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—41no—
691C4⋊C4—41no—
692C4⋊C4—82no—
693C4⋊C4C2×D4×C7311yescharacteristic
694C4⋊C4C2×D4×C7311yescharacteristic
695C22⋊C4—21no—
696C22⋊C4—41no—
697C22⋊C4—41no—
698C22⋊C4—41no—
699C22⋊C4—41no—
700C22⋊C4—41no—
701C42—21no—
702C42—21no—
703C42—41no—
704C42C2×D4×C7312yes—
705C23—21no—
706C23—21no—
707C23—21no—
708C23—22no—
709C23—44no—
710C23—41no—
711C23—41no—
712C23—41no—
713C23—41no—
714C23—41no—
715C23—81no—
716C23—81no—
717C23—81no—
718C23—81no—
719C23—161no—
720C23—161no—
721C23H(5,𝔽2)×C7311yescharacteristic
722Q8—21no—
723Q8—21no—
724Q8—21no—
725Q8—21no—
726Q8—21no—
727Q8#121×C7312yes—
728D4—22no—
729D4—22no—
730D4—21no—
731D4—21no—
732D4—22no—
733D4—21no—
734D4—21no—
735D4—21no—
736D4—22no—
737D4—44no—
738D4—44no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—88no—
750D4—161no—
751D4—161no—
752D4—161no—
753D4#121×C7312yes—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—22no—
759C2×C4—22no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—44no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—41no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—161no—
774C2×C4C22×D4×C7311yescharacteristic
775C2×C4C22×D4×C7311yescharacteristic
776C2×C4C22×D4×C7311yescharacteristic
777C2×C4C2×#41×C7311yescharacteristic
778C2×C4C2×#41×C7311yescharacteristic
779C2×C4H(5,𝔽2)×C7311yescharacteristic
780C8—21no—
781C8—21no—
782C8—21no—
783C8—21no—
784C8—22no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—22no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—41no—
798C22—42no—
799C22—41no—
800C22—82no—
801C22—82no—
802C22—81no—
803C22—81no—
804C22—81no—
805C22—81no—
806C22—81no—
807C22—161no—
808C22—161no—
809C22—164no—
810C22#538×C7311yescharacteristic
811C22D42×C7311yescharacteristic
812C22#546×C7311yescharacteristic
813C4—24no—
814C4—22no—
815C4—41no—
816C4—41no—
817C4—41no—
818C4—41no—
819C4—81no—
820C4—81no—
821C4C2×#121×C7311yescharacteristic
822C4#525×C7311yescharacteristic
823C4D42×C7311yescharacteristic
824C4#546×C7311yescharacteristic
825C2—21no—
826C2—21no—
827C2—42no—
828C2—81no—
829C2—81no—
830C2—82no—
831C2—161no—
832C2C73×#242411yescharacteristic
833C2C73×#329111yescharacteristic
834C2C73×#329211yescharacteristic
subgroupG/H
center, socleC22×C73D42
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C22×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3062C2semidirect
2. C73×#3045C2semidirect
3. C2×#453×C73C2semidirect
4. C73×#3012C2semidirect
5. C2×#443×C73C2semidirect
6. C73×#2897C2semidirect
7. C73×#2063C2semidirect
8. C73×#2051C2semidirect
9. C73×#2039C2semidirect
10. C73×#2002C2semidirect
11. C73×#1957C2semidirect
12. C73×#1937C2semidirect
13. C73×#1907C2semidirect
14. C73×#1907C2semidirect
15. C73×#1859C2semidirect
22. C2×#131×C73C22semidirect
24. #535×C73C22semidirect
41. C2×#108×C73C22semidirect
42. #428×C73C22semidirect
43. #424×C73C22semidirect
46. C2×#104×C73C22semidirect
52. #417×C73C22semidirect
58. C2×#102×C73C22semidirect
59. C2×#102×C73C22semidirect
61. C2×#100×C73C22semidirect
63. C2×C4×C8×C73C22semidirect
64. #384×C73C22semidirect
65. #343×C73C22semidirect
66. #343×C73C22semidirect
67. #341×C73C22semidirect
68. #339×C73C22semidirect
92. C2×Q16×C73D4semidirect
96. C2×SD16×C73D4semidirect
97. C2×SD16×C73D4semidirect
101. C2×D8×C73D4semidirect
145. #104×C73D4semidirect
149. #103×C73D4semidirect
150. #103×C73D4semidirect
164. #102×C73D4semidirect
165. #102×C73D4semidirect
407. #25188C73direct (N × H)
418. #3062C2×C73semidirect
419. #3045C2×C73semidirect
420. C2×#453C2×C73semidirect
421. #3012C2×C73semidirect
422. C2×#443C2×C73semidirect
423. #2897C2×C73semidirect
424. #2063C2×C73semidirect
425. #2051C2×C73semidirect
426. #2039C2×C73semidirect
427. #2002C2×C73semidirect
428. #1957C2×C73semidirect
429. #1937C2×C73semidirect
430. #1907C2×C73semidirect
431. #1907C2×C73semidirect
432. #1859C2×C73semidirect
433. C73#25188direct (N × H)
440. C2×#131C22×C73semidirect
442. #535C22×C73semidirect
459. C2×#108C22×C73semidirect
460. #428C22×C73semidirect
461. #424C22×C73semidirect
464. C2×#104C22×C73semidirect
470. #417C22×C73semidirect
476. C2×#102C22×C73semidirect
477. C2×#102C22×C73semidirect
479. C2×#100C22×C73semidirect
481. C2×C4×C8C22×C73semidirect
482. #384C22×C73semidirect
483. #343C22×C73semidirect
484. #343C22×C73semidirect
485. #341C22×C73semidirect
486. #339C22×C73semidirect
510. C2×Q16D4×C73semidirect
514. C2×SD16D4×C73semidirect
515. C2×SD16D4×C73semidirect
519. C2×D8D4×C73semidirect
563. #104D4×C73semidirect
567. #103D4×C73semidirect
568. #103D4×C73semidirect
582. #102D4×C73semidirect
583. #102D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#30622
C73×#30452
C2×#453×C732
C73×#30122
C2×#443×C732
C73×#28972
C73×#20632
C73×#20512
C73×#20392
C73×#20022
C73×#19572
C73×#19372
C73×#19072
C73×#18592
#2518873