Finite Group Databasebeta

← C73×#24461 #32933865

Subgroups — C73×#24461 #32933865

Order 18688.

1318 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#578×C73C211yesmaximal, characteristic, complemented
2C2×#471×C73C211yesmaximal, characteristic, complemented
3C73×#3045C211yesmaximal, characteristic, complemented
4C2×#454×C73C211yesmaximal, characteristic, complemented
5C73×#3010C211yesmaximal, characteristic, complemented
6C73×#2898C211yesmaximal, characteristic, complemented
7C73×#2052C211yesmaximal, characteristic, complemented
8C73×#2047C211yesmaximal, characteristic, complemented
9C73×#2015C211yesmaximal, characteristic, complemented
10C73×#2004C211yesmaximal, characteristic, complemented
11C73×#1907C211yesmaximal, characteristic, complemented
12C73×#1882C211yesmaximal, characteristic, complemented
13C73×#1876C211yesmaximal, characteristic, complemented
14C73×#1866C211yesmaximal, characteristic, complemented
15C73×#1793C211yesmaximal, characteristic, complemented
16C2×2−1+4×C73C2211yescharacteristic
17C2×2−1+4×C73C2211yescharacteristic
18#578×C73—24no—
19#578×C73—24no—
20C2×#137×C73—21no—
21C2×#137×C73—21no—
22C2×#137×C73C2211yescharacteristic
23C2×#137×C73C2211yescharacteristic
24C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
25C2×AGL(1,ℤ/8)×C73C2211yescharacteristic
26C2×#135×C73—21no—
27C2×#135×C73C2211yescharacteristic
28C22×Q16×C73—21no—
29C22×Q16×C73C2211yescharacteristic
30C22×SD16×C73C2211yescharacteristic
31C2×#131×C73C2211yescharacteristic
32C2×#131×C73C2211yescharacteristic
33#535×C73C2211yescharacteristic
34C2×#124×C73C2211yescharacteristic
35#520×C73C2211yescharacteristic
36#471×C73—24no—
37#464×C73—21no—
38#463×C73—21no—
39#460×C73—21no—
40#459×C73—21no—
41#454×C73—24no—
42#449×C73—21no—
43#449×C73—21no—
44#448×C73—21no—
45#448×C73—21no—
46C2×#108×C73C2211yescharacteristic
47#424×C73C2211yescharacteristic
48C2×#104×C73C2211yescharacteristic
49C2×#104×C73C2211yescharacteristic
50C2×#104×C73C2211yescharacteristic
51#419×C73—21no—
52#419×C73C2211yescharacteristic
53#419×C73C2211yescharacteristic
54#417×C73—21no—
55#417×C73C2211yescharacteristic
56#417×C73C2211yescharacteristic
57#416×C73—21no—
58#416×C73C2211yescharacteristic
59C2×#103×C73—21no—
60C2×#103×C73C2211yescharacteristic
61C2×#102×C73C2211yescharacteristic
62C2×#101×C73C2211yescharacteristic
63C2×#101×C73C2211yescharacteristic
64C2×#100×C73C2211yescharacteristic
65#408×C73C2211yescharacteristic
66#391×C73C2211yescharacteristic
67#343×C73C2211yescharacteristic
68#341×C73C2211yescharacteristic
69#339×C73C2211yescharacteristic
70#336×C73C2211yescharacteristic
712−1+4×C73—22no—
722−1+4×C73—22no—
732−1+4×C73—22no—
742−1+4×C73—22no—
752−1+4×C73—22no—
762−1+4×C73—41no—
772−1+4×C73—41no—
782−1+4×C73D414yescomplemented
79C2×#41×C73—21no—
80C2×#41×C73—21no—
81C2×#41×C73—21no—
82C2×#41×C73—21no—
83C2×#41×C73—41no—
84C2×#41×C73—41no—
85C2×#41×C73C2311yescharacteristic
86C2×#41×C73C2311yescharacteristic
87C2×#41×C73C2311yescharacteristic
88C22×Q8×C73—21no—
89C22×Q8×C73—21no—
90C22×Q8×C73—21no—
91C22×Q8×C73—21no—
92C22×Q8×C73C2311yescharacteristic
93C22×Q8×C73C2311yescharacteristic
94C22×D4×C73C2311yescharacteristic
95#137×C73—28no—
96#137×C73—28no—
97#137×C73—22no—
98#137×C73—22no—
99#137×C73—22no—
100#137×C73D414yescomplemented
101AGL(1,ℤ/8)×C73—22no—
102AGL(1,ℤ/8)×C73—22no—
103AGL(1,ℤ/8)×C73—22no—
104AGL(1,ℤ/8)×C73—22no—
105#135×C73—28no—
106#135×C73—22no—
107#135×C73—22no—
108C2×Q16×C73—28no—
109C2×Q16×C73—21no—
110C2×Q16×C73—21no—
111C2×Q16×C73—22no—
112C2×Q16×C73—22no—
113C2×Q16×C73—21no—
114C2×Q16×C73—21no—
115C2×Q16×C73D411yescharacteristic
116C2×SD16×C73—21no—
117C2×SD16×C73—21no—
118C2×SD16×C73—21no—
119C2×SD16×C73—21no—
120C2×SD16×C73—22no—
121C2×SD16×C73—21no—
122C2×SD16×C73—21no—
123C2×SD16×C73—41no—
124C2×SD16×C73D411yescharacteristic
125C2×SD16×C73D411yescharacteristic
126C2×D8×C73—21no—
127C2×D8×C73—21no—
128C2×D8×C73D411yescharacteristic
129#131×C73—22no—
130#131×C73—22no—
131#131×C73—22no—
132#131×C73—41no—
133C2×M16×C73—21no—
134C2×M16×C73—21no—
135C2×M16×C73C2311yescharacteristic
136C2×M16×C73C2311yescharacteristic
137C2×M16×C73C2311yescharacteristic
138C2×M16×C73C2311yescharacteristic
139C22×C8×C73—21no—
140C22×C8×C73—21no—
141C22×C8×C73C2311yescharacteristic
142C22×C8×C73C2311yescharacteristic
143#127×C73—21no—
144#124×C73—22no—
145#124×C73—21no—
146#124×C73—41no—
147#121×C73—21no—
148#121×C73—21no—
149#120×C73—41no—
150C4×Q8×C73—21no—
151C4×D4×C73—21no—
152C4×D4×C73—41no—
153#117×C73—21no—
154#117×C73C2311yescharacteristic
155C2×C4⋊C4×C73—21no—
156C2×C4⋊C4×C73C2311yescharacteristic
157C2×C22⋊C4×C73—41no—
158C2×C42×C73C2311yescharacteristic
159#108×C73—22no—
160C4⋊C8×C73—21no—
161C4⋊C8×C73—21no—
162#104×C73—22no—
163#104×C73—22no—
164#104×C73—41no—
165#103×C73—21no—
166#103×C73—21no—
167#103×C73—21no—
168#103×C73—21no—
169#103×C73—21no—
170#103×C73—21no—
171#103×C73—21no—
172#103×C73—21no—
173#103×C73D411yescharacteristic
174#103×C73D411yescharacteristic
175#102×C73—21no—
176#102×C73—21no—
177#102×C73—21no—
178#102×C73—21no—
179#102×C73D411yescharacteristic
180#102×C73D411yescharacteristic
181#101×C73—22no—
182#101×C73—22no—
183#100×C73—22no—
184C22⋊C8×C73—21no—
185C22⋊C8×C73—21no—
186#95×C73—41no—
187C24×C73—21no—
188#41×C73—21no—
189#41×C73—21no—
190#41×C73—21no—
191#41×C73—21no—
192#41×C73—24no—
193#41×C73—24no—
194#41×C73—24no—
195#41×C73—21no—
196#41×C73—21no—
197#41×C73—21no—
198#41×C73—21no—
199#41×C73—44no—
200#41×C73—42no—
201#41×C73—42no—
202#41×C73—42no—
203#41×C73—44no—
204#41×C73—44no—
205#41×C73—42no—
206#41×C73—44no—
207#41×C73—42no—
208#41×C73C2×D412yes—
209#41×C73C2×D412yes—
210#41×C73C2×D412yes—
211#41×C73#4112yes—
212C2×Q8×C73—21no—
213C2×Q8×C73—21no—
214C2×Q8×C73—24no—
215C2×Q8×C73—24no—
216C2×Q8×C73—24no—
217C2×Q8×C73—21no—
218C2×Q8×C73—21no—
219C2×Q8×C73—21no—
220C2×Q8×C73—21no—
221C2×Q8×C73—21no—
222C2×Q8×C73—21no—
223C2×Q8×C73—21no—
224C2×Q8×C73—21no—
225C2×Q8×C73—41no—
226C2×Q8×C73—41no—
227C2×Q8×C73—42no—
228C2×Q8×C73—42no—
229C2×Q8×C73—42no—
230C2×Q8×C73—42no—
231C2×Q8×C73—42no—
232C2×Q8×C73C2×D412yes—
233C2×Q8×C73C2×D412yes—
234C2×Q8×C73C2×D411yescharacteristic
235C2×Q8×C73C2×D411yescharacteristic
236C2×Q8×C73C2×D411yescharacteristic
237C2×D4×C73—21no—
238C2×D4×C73—21no—
239C2×D4×C73—21no—
240C2×D4×C73—21no—
241C2×D4×C73—21no—
242C2×D4×C73—21no—
243C2×D4×C73—21no—
244C2×D4×C73—21no—
245C2×D4×C73—21no—
246C2×D4×C73—41no—
247C2×D4×C73—41no—
248C2×D4×C73—41no—
249C2×D4×C73—41no—
250C2×D4×C73C2×D411yescharacteristic
251C2×D4×C73C2×D411yescharacteristic
252C2×D4×C73C2×D411yescharacteristic
253C22×C4×C73—21no—
254C22×C4×C73—21no—
255C22×C4×C73—21no—
256C22×C4×C73—21no—
257C22×C4×C73—21no—
258C22×C4×C73—21no—
259C22×C4×C73—21no—
260C22×C4×C73—41no—
261C22×C4×C73—41no—
262C22×C4×C73—41no—
263C22×C4×C73—41no—
264C22×C4×C73—41no—
265C22×C4×C73C2411yescharacteristic
266Q16×C73—24no—
267Q16×C73—24no—
268Q16×C73—24no—
269Q16×C73—22no—
270Q16×C73—24no—
271SD16×C73—24no—
272SD16×C73—22no—
273SD16×C73—24no—
274SD16×C73—22no—
275SD16×C73—42no—
276SD16×C73—42no—
277SD16×C73—42no—
278SD16×C73—42no—
279D8×C73—22no—
280D8×C73—42no—
281D8×C73—42no—
282M16×C73—24no—
283M16×C73—21no—
284M16×C73—21no—
285M16×C73—21no—
286M16×C73—21no—
287M16×C73—21no—
288M16×C73—21no—
289M16×C73—21no—
290M16×C73—42no—
291M16×C73C2×D412yes—
292C2×C8×C73—24no—
293C2×C8×C73—21no—
294C2×C8×C73—21no—
295C2×C8×C73—21no—
296C2×C8×C73—21no—
297C2×C8×C73—21no—
298C2×C8×C73—21no—
299C2×C8×C73—21no—
300C2×C8×C73—21no—
301C2×C8×C73—42no—
302C2×C8×C73C2×D411yescharacteristic
303C2×C8×C73C2×D411yescharacteristic
304C2×C8×C73C2×D411yescharacteristic
305C2×C8×C73C2×D411yescharacteristic
306C4⋊C4×C73—21no—
307C4⋊C4×C73—21no—
308C4⋊C4×C73—41no—
309C4⋊C4×C73C2×D411yescharacteristic
310C4⋊C4×C73C2×D411yescharacteristic
311C22⋊C4×C73—21no—
312C22⋊C4×C73—41no—
313C22⋊C4×C73—41no—
314C22⋊C4×C73—41no—
315C22⋊C4×C73—44no—
316C42×C73—21no—
317C42×C73—21no—
318C42×C73—21no—
319C42×C73—41no—
320C23×C73—21no—
321C23×C73—21no—
322C23×C73—21no—
323C23×C73—41no—
324C23×C73—41no—
325C23×C73—41no—
326C23×C73—81no—
327C23×C73—81no—
328C23×C73H(5,𝔽2)11yescharacteristic
329Q8×C73—21no—
330Q8×C73—21no—
331Q8×C73—22no—
332Q8×C73—22no—
333Q8×C73—21no—
334Q8×C73—22no—
335Q8×C73—22no—
336Q8×C73—21no—
337Q8×C73—44no—
338Q8×C73—44no—
339Q8×C73—41no—
340Q8×C73—41no—
341Q8×C73—41no—
342Q8×C73—41no—
343Q8×C73#12012yes—
344Q8×C73#12112yes—
345D4×C73—22no—
346D4×C73—22no—
347D4×C73—22no—
348D4×C73—22no—
349D4×C73—21no—
350D4×C73—21no—
351D4×C73—21no—
352D4×C73—21no—
353D4×C73—44no—
354D4×C73—44no—
355D4×C73—41no—
356D4×C73—41no—
357D4×C73—41no—
358D4×C73—41no—
359D4×C73—41no—
360D4×C73—41no—
361D4×C73—161no—
362D4×C73—161no—
363D4×C73#12012yes—
364D4×C73#12112yes—
365C2×C4×C73—21no—
366C2×C4×C73—21no—
367C2×C4×C73—22no—
368C2×C4×C73—22no—
369C2×C4×C73—22no—
370C2×C4×C73—22no—
371C2×C4×C73—22no—
372C2×C4×C73—21no—
373C2×C4×C73—21no—
374C2×C4×C73—21no—
375C2×C4×C73—22no—
376C2×C4×C73—44no—
377C2×C4×C73—44no—
378C2×C4×C73—44no—
379C2×C4×C73—44no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—41no—
384C2×C4×C73—41no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—41no—
388C2×C4×C73—41no—
389C2×C4×C73—41no—
390C2×C4×C73—81no—
391C2×C4×C73—161no—
392C2×C4×C73C22×D411yescharacteristic
393C2×C4×C73C22×D411yescharacteristic
394C2×C4×C73C22×D411yescharacteristic
395C2×C4×C73C22×D411yescharacteristic
396C2×C4×C73C2×#4111yescharacteristic
397C2×C4×C73H(5,𝔽2)11yescharacteristic
398C8×C73—21no—
399C8×C73—22no—
400C8×C73—21no—
401C8×C73—21no—
402C8×C73—21no—
403C8×C73—41no—
404C8×C73—41no—
405C8×C73—41no—
406C22×C73—21no—
407C22×C73—21no—
408C22×C73—22no—
409C22×C73—22no—
410C22×C73—41no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—41no—
414C22×C73—41no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—82no—
418C22×C73—81no—
419C22×C73—81no—
420C22×C73—81no—
421C22×C73—161no—
422C22×C73#53411yescharacteristic
423C22×C73D4211yescharacteristic
424C22×C73#54611yescharacteristic
425C4×C73—22no—
426C4×C73—22no—
427C4×C73—42no—
428C4×C73—41no—
429C4×C73—42no—
430C4×C73—41no—
431C4×C73—41no—
432C4×C73—81no—
433C4×C73—81no—
434C4×C73C2×#12011yescharacteristic
435C4×C73C2×#12111yescharacteristic
436C4×C73D4211yescharacteristic
437C4×C73#54611yescharacteristic
438#24461C7311yesmaximal, characteristic, direct product factor, Sylow
439C2×C73—21no—
440C2×C73—21no—
441C2×C73—42no—
442C2×C73—42no—
443C2×C73—81no—
444C2×C73—161no—
445C2×C73#241011yescharacteristic
446C2×C73#328911yescharacteristic
447C2×C73#329011yescharacteristic
448C2×#578C2×C7311yescharacteristic, complemented
449C2×#471C2×C7311yescharacteristic, complemented
450#3045C2×C7311yescharacteristic, complemented
451C2×#454C2×C7311yescharacteristic, complemented
452#3010C2×C7311yescharacteristic, complemented
453#2898C2×C7311yescharacteristic, complemented
454#2052C2×C7311yescharacteristic, complemented
455#2047C2×C7311yescharacteristic, complemented
456#2015C2×C7311yescharacteristic, complemented
457#2004C2×C7311yescharacteristic, complemented
458#1907C2×C7311yescharacteristic, complemented
459#1882C2×C7311yescharacteristic, complemented
460#1876C2×C7311yescharacteristic, complemented
461#1866C2×C7311yescharacteristic, complemented
462#1793C2×C7311yescharacteristic, complemented
463C73#2446111yescharacteristic, direct product factor, Sylow
464C2×2−1+4C22×C7311yescharacteristic
465C2×2−1+4C22×C7311yescharacteristic
466#578—24no—
467#578—24no—
468C2×#137—21no—
469C2×#137—21no—
470C2×#137C22×C7311yescharacteristic
471C2×#137C22×C7311yescharacteristic
472C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
473C2×AGL(1,ℤ/8)C22×C7311yescharacteristic
474C2×#135—21no—
475C2×#135C22×C7311yescharacteristic
476C22×Q16—21no—
477C22×Q16C22×C7311yescharacteristic
478C22×SD16C22×C7311yescharacteristic
479C2×#131C22×C7311yescharacteristic
480C2×#131C22×C7311yescharacteristic
481#535C22×C7311yescharacteristic
482C2×#124C22×C7311yescharacteristic
483#520C22×C7311yescharacteristic
484#471—24no—
485#464—21no—
486#463—21no—
487#460—21no—
488#459—21no—
489#454—24no—
490#449—21no—
491#449—21no—
492#448—21no—
493#448—21no—
494C2×#108C22×C7311yescharacteristic
495#424C22×C7311yescharacteristic
496C2×#104C22×C7311yescharacteristic
497C2×#104C22×C7311yescharacteristic
498C2×#104C22×C7311yescharacteristic
499#419—21no—
500#419C22×C7311yescharacteristic
501#419C22×C7311yescharacteristic
502#417—21no—
503#417C22×C7311yescharacteristic
504#417C22×C7311yescharacteristic
505#416—21no—
506#416C22×C7311yescharacteristic
507C2×#103—21no—
508C2×#103C22×C7311yescharacteristic
509C2×#102C22×C7311yescharacteristic
510C2×#101C22×C7311yescharacteristic
511C2×#101C22×C7311yescharacteristic
512C2×#100C22×C7311yescharacteristic
513#408C22×C7311yescharacteristic
514#391C22×C7311yescharacteristic
515#343C22×C7311yescharacteristic
516#341C22×C7311yescharacteristic
517#339C22×C7311yescharacteristic
518#336C22×C7311yescharacteristic
5192−1+4—22no—
5202−1+4—22no—
5212−1+4—22no—
5222−1+4—22no—
5232−1+4—22no—
5242−1+4—41no—
5252−1+4—41no—
5262−1+4D4×C7314yescomplemented
527C2×#41—21no—
528C2×#41—21no—
529C2×#41—21no—
530C2×#41—21no—
531C2×#41—41no—
532C2×#41—41no—
533C2×#41C23×C7311yescharacteristic
534C2×#41C23×C7311yescharacteristic
535C2×#41C23×C7311yescharacteristic
536C22×Q8—21no—
537C22×Q8—21no—
538C22×Q8—21no—
539C22×Q8—21no—
540C22×Q8C23×C7311yescharacteristic
541C22×Q8C23×C7311yescharacteristic
542C22×D4C23×C7311yescharacteristic
543#137—28no—
544#137—28no—
545#137—22no—
546#137—22no—
547#137—22no—
548#137D4×C7314yescomplemented
549AGL(1,ℤ/8)—22no—
550AGL(1,ℤ/8)—22no—
551AGL(1,ℤ/8)—22no—
552AGL(1,ℤ/8)—22no—
553#135—28no—
554#135—22no—
555#135—22no—
556C2×Q16—28no—
557C2×Q16—21no—
558C2×Q16—21no—
559C2×Q16—22no—
560C2×Q16—22no—
561C2×Q16—21no—
562C2×Q16—21no—
563C2×Q16D4×C7311yescharacteristic
564C2×SD16—21no—
565C2×SD16—21no—
566C2×SD16—22no—
567C2×SD16—21no—
568C2×SD16—21no—
569C2×SD16—21no—
570C2×SD16—21no—
571C2×SD16—41no—
572C2×SD16D4×C7311yescharacteristic
573C2×SD16D4×C7311yescharacteristic
574C2×D8—21no—
575C2×D8—21no—
576C2×D8D4×C7311yescharacteristic
577#131—22no—
578#131—22no—
579#131—22no—
580#131—41no—
581C2×M16—21no—
582C2×M16—21no—
583C2×M16C23×C7311yescharacteristic
584C2×M16C23×C7311yescharacteristic
585C2×M16C23×C7311yescharacteristic
586C2×M16C23×C7311yescharacteristic
587C22×C8—21no—
588C22×C8—21no—
589C22×C8C23×C7311yescharacteristic
590C22×C8C23×C7311yescharacteristic
591#127—21no—
592#124—22no—
593#124—21no—
594#124—41no—
595#121—21no—
596#121—21no—
597#120—41no—
598C4×Q8—21no—
599C4×D4—21no—
600C4×D4—41no—
601#117—21no—
602#117C23×C7311yescharacteristic
603C2×C4⋊C4—21no—
604C2×C4⋊C4C23×C7311yescharacteristic
605C2×C22⋊C4—41no—
606C2×C42C23×C7311yescharacteristic
607#108—22no—
608C4⋊C8—21no—
609C4⋊C8—21no—
610#104—22no—
611#104—22no—
612#104—41no—
613#103—21no—
614#103—21no—
615#103—21no—
616#103—21no—
617#103—21no—
618#103—21no—
619#103—21no—
620#103—21no—
621#103D4×C7311yescharacteristic
622#103D4×C7311yescharacteristic
623#102—21no—
624#102—21no—
625#102—21no—
626#102—21no—
627#102D4×C7311yescharacteristic
628#102D4×C7311yescharacteristic
629#101—22no—
630#101—22no—
631#100—22no—
632C22⋊C8—21no—
633C22⋊C8—21no—
634#95—41no—
635C24—21no—
636#41—21no—
637#41—21no—
638#41—21no—
639#41—21no—
640#41—24no—
641#41—24no—
642#41—24no—
643#41—21no—
644#41—21no—
645#41—21no—
646#41—21no—
647#41—44no—
648#41—42no—
649#41—42no—
650#41—42no—
651#41—44no—
652#41—44no—
653#41—42no—
654#41—44no—
655#41—42no—
656#41C2×D4×C7312yes—
657#41C2×D4×C7312yes—
658#41C2×D4×C7312yes—
659#41#41×C7312yes—
660C2×Q8—21no—
661C2×Q8—21no—
662C2×Q8—24no—
663C2×Q8—24no—
664C2×Q8—24no—
665C2×Q8—21no—
666C2×Q8—21no—
667C2×Q8—21no—
668C2×Q8—21no—
669C2×Q8—21no—
670C2×Q8—21no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—41no—
674C2×Q8—41no—
675C2×Q8—42no—
676C2×Q8—42no—
677C2×Q8—42no—
678C2×Q8—42no—
679C2×Q8—42no—
680C2×Q8C2×D4×C7312yes—
681C2×Q8C2×D4×C7312yes—
682C2×Q8C2×D4×C7311yescharacteristic
683C2×Q8C2×D4×C7311yescharacteristic
684C2×Q8C2×D4×C7311yescharacteristic
685C2×D4—21no—
686C2×D4—21no—
687C2×D4—21no—
688C2×D4—21no—
689C2×D4—21no—
690C2×D4—21no—
691C2×D4—21no—
692C2×D4—21no—
693C2×D4—21no—
694C2×D4—41no—
695C2×D4—41no—
696C2×D4—41no—
697C2×D4—41no—
698C2×D4C2×D4×C7311yescharacteristic
699C2×D4C2×D4×C7311yescharacteristic
700C2×D4C2×D4×C7311yescharacteristic
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—41no—
709C22×C4—41no—
710C22×C4—41no—
711C22×C4—41no—
712C22×C4—41no—
713C22×C4C24×C7311yescharacteristic
714Q16—24no—
715Q16—24no—
716Q16—24no—
717Q16—22no—
718Q16—24no—
719SD16—24no—
720SD16—22no—
721SD16—24no—
722SD16—22no—
723SD16—42no—
724SD16—42no—
725SD16—42no—
726SD16—42no—
727D8—22no—
728D8—42no—
729D8—42no—
730M16—24no—
731M16—21no—
732M16—21no—
733M16—21no—
734M16—21no—
735M16—21no—
736M16—21no—
737M16—21no—
738M16—42no—
739M16C2×D4×C7312yes—
740C2×C8—24no—
741C2×C8—21no—
742C2×C8—21no—
743C2×C8—21no—
744C2×C8—21no—
745C2×C8—21no—
746C2×C8—21no—
747C2×C8—21no—
748C2×C8—21no—
749C2×C8—42no—
750C2×C8C2×D4×C7311yescharacteristic
751C2×C8C2×D4×C7311yescharacteristic
752C2×C8C2×D4×C7311yescharacteristic
753C2×C8C2×D4×C7311yescharacteristic
754C4⋊C4—21no—
755C4⋊C4—21no—
756C4⋊C4—41no—
757C4⋊C4C2×D4×C7311yescharacteristic
758C4⋊C4C2×D4×C7311yescharacteristic
759C22⋊C4—21no—
760C22⋊C4—41no—
761C22⋊C4—41no—
762C22⋊C4—41no—
763C22⋊C4—44no—
764C42—21no—
765C42—21no—
766C42—21no—
767C42—41no—
768C23—21no—
769C23—21no—
770C23—21no—
771C23—41no—
772C23—41no—
773C23—41no—
774C23—81no—
775C23—81no—
776C23H(5,𝔽2)×C7311yescharacteristic
777Q8—21no—
778Q8—21no—
779Q8—22no—
780Q8—22no—
781Q8—21no—
782Q8—22no—
783Q8—22no—
784Q8—21no—
785Q8—44no—
786Q8—44no—
787Q8—41no—
788Q8—41no—
789Q8—41no—
790Q8—41no—
791Q8#120×C7312yes—
792Q8#121×C7312yes—
793D4—22no—
794D4—22no—
795D4—22no—
796D4—22no—
797D4—21no—
798D4—21no—
799D4—21no—
800D4—21no—
801D4—44no—
802D4—44no—
803D4—41no—
804D4—41no—
805D4—41no—
806D4—41no—
807D4—41no—
808D4—41no—
809D4—161no—
810D4—161no—
811D4#120×C7312yes—
812D4#121×C7312yes—
813C2×C4—21no—
814C2×C4—21no—
815C2×C4—22no—
816C2×C4—22no—
817C2×C4—22no—
818C2×C4—22no—
819C2×C4—22no—
820C2×C4—21no—
821C2×C4—21no—
822C2×C4—21no—
823C2×C4—22no—
824C2×C4—44no—
825C2×C4—44no—
826C2×C4—44no—
827C2×C4—44no—
828C2×C4—41no—
829C2×C4—41no—
830C2×C4—41no—
831C2×C4—41no—
832C2×C4—41no—
833C2×C4—41no—
834C2×C4—41no—
835C2×C4—41no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—81no—
839C2×C4—161no—
840C2×C4C22×D4×C7311yescharacteristic
841C2×C4C22×D4×C7311yescharacteristic
842C2×C4C22×D4×C7311yescharacteristic
843C2×C4C22×D4×C7311yescharacteristic
844C2×C4C2×#41×C7311yescharacteristic
845C2×C4H(5,𝔽2)×C7311yescharacteristic
846C8—21no—
847C8—22no—
848C8—21no—
849C8—21no—
850C8—21no—
851C8—41no—
852C8—41no—
853C8—41no—
854C22—21no—
855C22—21no—
856C22—22no—
857C22—22no—
858C22—41no—
859C22—41no—
860C22—41no—
861C22—41no—
862C22—41no—
863C22—41no—
864C22—41no—
865C22—82no—
866C22—81no—
867C22—81no—
868C22—81no—
869C22—161no—
870C22#534×C7311yescharacteristic
871C22D42×C7311yescharacteristic
872C22#546×C7311yescharacteristic
873C4—22no—
874C4—22no—
875C4—41no—
876C4—41no—
877C4—42no—
878C4—41no—
879C4—42no—
880C4—81no—
881C4—81no—
882C4C2×#120×C7311yescharacteristic
883C4C2×#121×C7311yescharacteristic
884C4D42×C7311yescharacteristic
885C4#546×C7311yescharacteristic
886C2—21no—
887C2—21no—
888C2—42no—
889C2—42no—
890C2—81no—
891C2—161no—
892C2C73×#241011yescharacteristic
893C2C73×#328911yescharacteristic
894C2C73×#329011yescharacteristic
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. C2×#578×C73C2semidirect
2. C2×#471×C73C2semidirect
3. C73×#3045C2semidirect
4. C2×#454×C73C2semidirect
5. C73×#3010C2semidirect
6. C73×#2898C2semidirect
7. C73×#2052C2semidirect
8. C73×#2047C2semidirect
9. C73×#2015C2semidirect
10. C73×#2004C2semidirect
11. C73×#1907C2semidirect
12. C73×#1882C2semidirect
13. C73×#1876C2semidirect
14. C73×#1866C2semidirect
15. C73×#1793C2semidirect
78. 2−1+4×C73D4semidirect
100. #137×C73D4semidirect
438. #24461C73direct (N × H)
448. C2×#578C2×C73semidirect
449. C2×#471C2×C73semidirect
450. #3045C2×C73semidirect
451. C2×#454C2×C73semidirect
452. #3010C2×C73semidirect
453. #2898C2×C73semidirect
454. #2052C2×C73semidirect
455. #2047C2×C73semidirect
456. #2015C2×C73semidirect
457. #2004C2×C73semidirect
458. #1907C2×C73semidirect
459. #1882C2×C73semidirect
460. #1876C2×C73semidirect
461. #1866C2×C73semidirect
462. #1793C2×C73semidirect
463. C73#24461direct (N × H)
526. 2−1+4D4×C73semidirect
548. #137D4×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#578×C732
C2×#471×C732
C73×#30452
C2×#454×C732
C73×#30102
C73×#28982
C73×#20522
C73×#20472
C73×#20152
C73×#20042
C73×#19072
C73×#18822
C73×#18762
C73×#18662
C73×#17932
#2446173