Finite Group Databasebeta

← C73×#18224 #32927628

Subgroups — C73×#18224 #32927628

Order 18688.

1370 conjugacy classes of subgroups.

The subgroup lattice has 928 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3534C211yesmaximal, characteristic, complemented
2C73×#3003C211yesmaximal, characteristic, complemented
3C2×#447×C73C211yesmaximal, characteristic, complemented
4C73×#2613C211yesmaximal, characteristic, complemented
5C73×#1600C212yesmaximal, complemented
6C73×#1598C212yesmaximal, complemented
7C73×#1597C212yesmaximal, complemented
8C73×#1595C212yesmaximal, complemented
9C73×#1516C211yesmaximal, characteristic, complemented
10C73×#1510C211yesmaximal, characteristic, complemented
11C73×#1468C211yesmaximal, characteristic, complemented
12C23×D4×C73C2211yescharacteristic, complemented
13C2×AGL(1,ℤ/8)×C73—21no—
14C22×D8×C73—21no—
15#562×C73—21no—
16#560×C73—21no—
17#553×C73—21no—
18#551×C73—21no—
19#546×C73—21no—
20#546×C73—21no—
21#546×C73—21no—
22D42×C73—21no—
23#540×C73—21no—
24#539×C73—21no—
25#539×C73C2211yescharacteristic, complemented
26#538×C73—21no—
27#538×C73C2211yescharacteristic, complemented
28#537×C73C2211yescharacteristic, complemented
29#534×C73—21no—
30#534×C73C2211yescharacteristic, complemented
31#525×C73C2211yescharacteristic
32C2×#123×C73C2211yescharacteristic
33C2×#121×C73C2211yescharacteristic
34C2×#120×C73—21no—
35#450×C73—21no—
36#450×C73C2212yescomplemented
37#447×C73—21no—
38#447×C73—21no—
39#447×C73—21no—
40#447×C73C2212yes—
41#447×C73C2212yescomplemented
42#447×C73C2212yescomplemented
43#418×C73—21no—
44C2×#102×C73—21no—
45#407×C73C2211yescharacteristic, complemented
46C2×C22⋊C8×C73C2211yescharacteristic, complemented
47#394×C73—21no—
48#394×C73C2212yescomplemented
49#392×C73—21no—
50#392×C73C2212yescomplemented
51#381×C73C2211yescharacteristic, complemented
52#379×C73—21no—
53#328×C73C2212yescomplemented
54#327×C73C2212yescomplemented
55#327×C73C2212yescomplemented
56#327×C73C2212yescomplemented
57#324×C73C2212yescomplemented
58#323×C73C2212yescomplemented
59C25×C73—21no—
60C2×#41×C73—21no—
61C2×#41×C73D411yescharacteristic, complemented
62C22×D4×C73—21no—
63C22×D4×C73—21no—
64C22×D4×C73—21no—
65C22×D4×C73—22no—
66C22×D4×C73—21no—
67C22×D4×C73—21no—
68C22×D4×C73—21no—
69C22×D4×C73—21no—
70C22×D4×C73—21no—
71C22×D4×C73—44no—
72C22×D4×C73D411yescharacteristic
73C22×D4×C73D411yescharacteristic, complemented
74C22×D4×C73C2312yes—
75C23×C4×C73C2311yescharacteristic
76AGL(1,ℤ/8)×C73—44no—
77C2×SD16×C73—22no—
78C2×D8×C73—22no—
79C2×D8×C73—22no—
80C2×D8×C73—22no—
81C2×D8×C73—44no—
82C2×M16×C73—21no—
83C22×C8×C73—21no—
84#127×C73—21no—
85#126×C73—21no—
86#126×C73—21no—
87#126×C73—21no—
88#126×C73—21no—
89#125×C73—21no—
90#125×C73—21no—
91#124×C73—21no—
92#124×C73—21no—
93#124×C73—21no—
94#123×C73—21no—
95#123×C73—21no—
96#123×C73—21no—
97#123×C73—21no—
98#123×C73—21no—
99#123×C73—21no—
100#123×C73—21no—
101#123×C73—21no—
102#123×C73—21no—
103#123×C73—21no—
104#123×C73—21no—
105#123×C73—21no—
106#123×C73—21no—
107#123×C73—21no—
108C22⋊Q8×C73—21no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112C22⋊Q8×C73—21no—
113C22⋊Q8×C73D411yescharacteristic, complemented
114C22⋊Q8×C73C2311yescharacteristic
115#121×C73—21no—
116#121×C73—21no—
117#121×C73—21no—
118#121×C73—21no—
119#121×C73—21no—
120#121×C73—21no—
121#121×C73—21no—
122#121×C73—21no—
123#121×C73—21no—
124#121×C73—21no—
125#121×C73—21no—
126#121×C73—21no—
127#121×C73—21no—
128#121×C73—21no—
129#121×C73—21no—
130#121×C73D411yescharacteristic, complemented
131#121×C73D411yescharacteristic, complemented
132#121×C73D411yescharacteristic, complemented
133#121×C73C2311yescharacteristic
134#121×C73C2311yescharacteristic
135#121×C73C2311yescharacteristic
136#120×C73—21no—
137#120×C73—21no—
138#120×C73—21no—
139#120×C73—21no—
140#120×C73—21no—
141#120×C73—21no—
142#120×C73—21no—
143#120×C73—21no—
144#120×C73—44no—
145C4×D4×C73—21no—
146C4×D4×C73—21no—
147C4×D4×C73—21no—
148C4×D4×C73—21no—
149C4×D4×C73—21no—
150C4×D4×C73—21no—
151C4×D4×C73—21no—
152C4×D4×C73—21no—
153#117×C73—21no—
154#117×C73D411yescharacteristic, complemented
155C2×C4⋊C4×C73D411yescharacteristic
156C2×C4⋊C4×C73D411yescharacteristic, complemented
157C2×C4⋊C4×C73C2311yescharacteristic
158C2×C22⋊C4×C73—21no—
159C2×C22⋊C4×C73—21no—
160C2×C22⋊C4×C73—21no—
161C2×C22⋊C4×C73—21no—
162C2×C22⋊C4×C73—22no—
163C2×C22⋊C4×C73—22no—
164C2×C22⋊C4×C73—22no—
165C2×C22⋊C4×C73D411yescharacteristic
166C2×C22⋊C4×C73D411yescharacteristic
167C2×C22⋊C4×C73C2311yescharacteristic
168#102×C73—22no—
169#102×C73—22no—
170#102×C73—22no—
171#102×C73—22no—
172C22⋊C8×C73—21no—
173C22⋊C8×C73—21no—
174C22⋊C8×C73C2312yes—
175C22⋊C8×C73C2312yes—
176#95×C73—21no—
177#95×C73C2312yes—
178C24×C73—24no—
179C24×C73—21no—
180C24×C73—22no—
181C24×C73—21no—
182C24×C73—42no—
183C24×C73—41no—
184C24×C73—41no—
185C24×C73—82no—
186C24×C73—82no—
187C24×C73C2×D411yescharacteristic
188C24×C73C2×D411yescharacteristic
189#41×C73—42no—
190#41×C73—82no—
191C2×Q8×C73—21no—
192C2×Q8×C73C2×D411yescharacteristic
193C2×D4×C73—24no—
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—21no—
209C2×D4×C73—21no—
210C2×D4×C73—21no—
211C2×D4×C73—21no—
212C2×D4×C73—22no—
213C2×D4×C73—22no—
214C2×D4×C73—42no—
215C2×D4×C73—42no—
216C2×D4×C73—42no—
217C2×D4×C73—44no—
218C2×D4×C73—44no—
219C2×D4×C73—44no—
220C2×D4×C73—44no—
221C2×D4×C73—42no—
222C2×D4×C73—44no—
223C2×D4×C73—41no—
224C2×D4×C73—41no—
225C2×D4×C73—82no—
226C2×D4×C73—82no—
227C2×D4×C73—82no—
228C2×D4×C73—82no—
229C2×D4×C73—82no—
230C2×D4×C73C2×D411yescharacteristic
231C2×D4×C73C2×D411yescharacteristic
232C2×D4×C73C2×D411yescharacteristic
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—21no—
237C22×C4×C73—21no—
238C22×C4×C73—21no—
239C22×C4×C73—21no—
240C22×C4×C73—22no—
241C22×C4×C73—42no—
242C22×C4×C73C2×D411yescharacteristic
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73C2×D411yescharacteristic
246C22×C4×C73C2×D411yescharacteristic
247C22×C4×C73C2×D411yescharacteristic
248C22×C4×C73C2×D411yescharacteristic
249C22×C4×C73C2×D411yescharacteristic
250C22×C4×C73C2411yescharacteristic
251SD16×C73—44no—
252D8×C73—44no—
253D8×C73—44no—
254D8×C73—44no—
255M16×C73—42no—
256C2×C8×C73—22no—
257C2×C8×C73—22no—
258C2×C8×C73—42no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73C2×D411yescharacteristic
273C4⋊C4×C73C2×D411yescharacteristic
274C4⋊C4×C73C2×D411yescharacteristic
275C4⋊C4×C73C2×D411yescharacteristic
276C22⋊C4×C73—21no—
277C22⋊C4×C73—21no—
278C22⋊C4×C73—21no—
279C22⋊C4×C73—21no—
280C22⋊C4×C73—21no—
281C22⋊C4×C73—21no—
282C22⋊C4×C73—21no—
283C22⋊C4×C73—21no—
284C22⋊C4×C73—21no—
285C22⋊C4×C73—21no—
286C22⋊C4×C73—21no—
287C22⋊C4×C73—21no—
288C22⋊C4×C73—21no—
289C22⋊C4×C73—21no—
290C22⋊C4×C73—21no—
291C22⋊C4×C73—21no—
292C22⋊C4×C73—21no—
293C22⋊C4×C73—21no—
294C22⋊C4×C73—21no—
295C22⋊C4×C73—21no—
296C22⋊C4×C73—21no—
297C22⋊C4×C73—21no—
298C22⋊C4×C73—21no—
299C22⋊C4×C73—21no—
300C22⋊C4×C73—21no—
301C22⋊C4×C73—44no—
302C22⋊C4×C73—42no—
303C22⋊C4×C73—82no—
304C22⋊C4×C73—82no—
305C42×C73—21no—
306C42×C73—21no—
307C42×C73—21no—
308C23×C73—22no—
309C23×C73—22no—
310C23×C73—24no—
311C23×C73—21no—
312C23×C73—21no—
313C23×C73—21no—
314C23×C73—21no—
315C23×C73—22no—
316C23×C73—41no—
317C23×C73—42no—
318C23×C73—42no—
319C23×C73—44no—
320C23×C73—42no—
321C23×C73—41no—
322C23×C73—41no—
323C23×C73—42no—
324C23×C73—42no—
325C23×C73—42no—
326C23×C73—44no—
327C23×C73—42no—
328C23×C73—81no—
329C23×C73—81no—
330C23×C73—82no—
331C23×C73—82no—
332C23×C73—82no—
333C23×C73—82no—
334C23×C73—88no—
335C23×C73—81no—
336C23×C73—81no—
337C23×C73—81no—
338C23×C73—88no—
339C23×C73#12011yescharacteristic
340C23×C73#12011yescharacteristic
341C23×C73C22×D411yescharacteristic
342Q8×C73—41no—
343Q8×C73—81no—
344D4×C73—24no—
345D4×C73—24no—
346D4×C73—41no—
347D4×C73—41no—
348D4×C73—41no—
349D4×C73—42no—
350D4×C73—42no—
351D4×C73—44no—
352D4×C73—44no—
353D4×C73—42no—
354D4×C73—42no—
355D4×C73—42no—
356D4×C73—42no—
357D4×C73—42no—
358D4×C73—81no—
359D4×C73—81no—
360D4×C73—81no—
361D4×C73—81no—
362D4×C73—81no—
363D4×C73—81no—
364D4×C73—81no—
365D4×C73—81no—
366D4×C73—81no—
367D4×C73—81no—
368D4×C73—81no—
369D4×C73—81no—
370D4×C73—88no—
371C2×C4×C73—22no—
372C2×C4×C73—22no—
373C2×C4×C73—21no—
374C2×C4×C73—21no—
375C2×C4×C73—21no—
376C2×C4×C73—21no—
377C2×C4×C73—21no—
378C2×C4×C73—21no—
379C2×C4×C73—21no—
380C2×C4×C73—21no—
381C2×C4×C73—22no—
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—42no—
389C2×C4×C73—42no—
390C2×C4×C73—42no—
391C2×C4×C73—81no—
392C2×C4×C73—81no—
393C2×C4×C73—81no—
394C2×C4×C73—81no—
395C2×C4×C73—81no—
396C2×C4×C73—81no—
397C2×C4×C73—81no—
398C2×C4×C73#12011yescharacteristic
399C2×C4×C73#12011yescharacteristic
400C2×C4×C73C22×D411yescharacteristic
401C2×C4×C73C22×D411yescharacteristic
402C8×C73—42no—
403C8×C73—42no—
404C22×C73—21no—
405C22×C73—21no—
406C22×C73—21no—
407C22×C73—21no—
408C22×C73—21no—
409C22×C73—21no—
410C22×C73—21no—
411C22×C73—44no—
412C22×C73—44no—
413C22×C73—44no—
414C22×C73—41no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—41no—
418C22×C73—41no—
419C22×C73—41no—
420C22×C73—41no—
421C22×C73—41no—
422C22×C73—41no—
423C22×C73—41no—
424C22×C73—44no—
425C22×C73—41no—
426C22×C73—41no—
427C22×C73—82no—
428C22×C73—82no—
429C22×C73—82no—
430C22×C73—88no—
431C22×C73—88no—
432C22×C73—82no—
433C22×C73—82no—
434C22×C73—162no—
435C22×C73—162no—
436C22×C73B(4,𝔽2)12yes—
437C22×C73C2×#12011yescharacteristic
438C22×C73#57612yes—
439C4×C73—21no—
440C4×C73—21no—
441C4×C73—21no—
442C4×C73—21no—
443C4×C73—41no—
444C4×C73—41no—
445C4×C73—41no—
446C4×C73—41no—
447C4×C73—41no—
448C4×C73—41no—
449C4×C73—41no—
450C4×C73—41no—
451C4×C73—82no—
452#18224C7311yesmaximal, characteristic, direct product factor, Sylow
453C2×C73—22no—
454C2×C73—22no—
455C2×C73—41no—
456C2×C73—84no—
457C2×C73—81no—
458C2×C73—81no—
459C2×C73—81no—
460C2×C73—81no—
461C2×C73#300811yescharacteristic
462C2×C73#302111yescharacteristic
463C2×C73C2×B(4,𝔽2)11yescharacteristic
464#3534C2×C7311yescharacteristic, complemented
465#3003C2×C7311yescharacteristic, complemented
466C2×#447C2×C7311yescharacteristic, complemented
467#2613C2×C7311yescharacteristic, complemented
468#1600C2×C7312yescomplemented
469#1598C2×C7312yescomplemented
470#1597C2×C7312yescomplemented
471#1595C2×C7312yescomplemented
472#1516C2×C7311yescharacteristic, complemented
473#1510C2×C7311yescharacteristic, complemented
474#1468C2×C7311yescharacteristic, complemented
475C73#1822411yescharacteristic, direct product factor, Sylow
476C23×D4C22×C7311yescharacteristic, complemented
477C2×AGL(1,ℤ/8)—21no—
478C22×D8—21no—
479#562—21no—
480#560—21no—
481#553—21no—
482#551—21no—
483#546—21no—
484#546—21no—
485#546—21no—
486D42—21no—
487#540—21no—
488#539—21no—
489#539C22×C7311yescharacteristic, complemented
490#538—21no—
491#538C22×C7311yescharacteristic, complemented
492#537C22×C7311yescharacteristic, complemented
493#534—21no—
494#534C22×C7311yescharacteristic, complemented
495#525C22×C7311yescharacteristic
496C2×#123C22×C7311yescharacteristic
497C2×#121C22×C7311yescharacteristic
498C2×#120—21no—
499#450—21no—
500#450C22×C7312yescomplemented
501#447—21no—
502#447—21no—
503#447—21no—
504#447C22×C7312yes—
505#447C22×C7312yescomplemented
506#447C22×C7312yescomplemented
507#418—21no—
508C2×#102—21no—
509#407C22×C7311yescharacteristic, complemented
510C2×C22⋊C8C22×C7311yescharacteristic, complemented
511#394—21no—
512#394C22×C7312yescomplemented
513#392—21no—
514#392C22×C7312yescomplemented
515#381C22×C7311yescharacteristic, complemented
516#379—21no—
517#328C22×C7312yescomplemented
518#327C22×C7312yescomplemented
519#327C22×C7312yescomplemented
520#327C22×C7312yescomplemented
521#324C22×C7312yescomplemented
522#323C22×C7312yescomplemented
523C25—21no—
524C2×#41—21no—
525C2×#41D4×C7311yescharacteristic, complemented
526C22×D4—21no—
527C22×D4—21no—
528C22×D4—21no—
529C22×D4—22no—
530C22×D4—21no—
531C22×D4—21no—
532C22×D4—21no—
533C22×D4—21no—
534C22×D4—21no—
535C22×D4—44no—
536C22×D4D4×C7311yescharacteristic
537C22×D4D4×C7311yescharacteristic, complemented
538C22×D4C23×C7312yes—
539C23×C4C23×C7311yescharacteristic
540AGL(1,ℤ/8)—44no—
541C2×SD16—22no—
542C2×D8—22no—
543C2×D8—22no—
544C2×D8—22no—
545C2×D8—44no—
546C2×M16—21no—
547C22×C8—21no—
548#127—21no—
549#126—21no—
550#126—21no—
551#126—21no—
552#126—21no—
553#125—21no—
554#125—21no—
555#124—21no—
556#124—21no—
557#124—21no—
558#123—21no—
559#123—21no—
560#123—21no—
561#123—21no—
562#123—21no—
563#123—21no—
564#123—21no—
565#123—21no—
566#123—21no—
567#123—21no—
568#123—21no—
569#123—21no—
570#123—21no—
571#123—21no—
572C22⋊Q8—21no—
573C22⋊Q8—21no—
574C22⋊Q8—21no—
575C22⋊Q8—21no—
576C22⋊Q8—21no—
577C22⋊Q8D4×C7311yescharacteristic, complemented
578C22⋊Q8C23×C7311yescharacteristic
579#121—21no—
580#121—21no—
581#121—21no—
582#121—21no—
583#121—21no—
584#121—21no—
585#121—21no—
586#121—21no—
587#121—21no—
588#121—21no—
589#121—21no—
590#121—21no—
591#121—21no—
592#121—21no—
593#121—21no—
594#121D4×C7311yescharacteristic, complemented
595#121D4×C7311yescharacteristic, complemented
596#121D4×C7311yescharacteristic, complemented
597#121C23×C7311yescharacteristic
598#121C23×C7311yescharacteristic
599#121C23×C7311yescharacteristic
600#120—21no—
601#120—21no—
602#120—21no—
603#120—21no—
604#120—21no—
605#120—21no—
606#120—21no—
607#120—21no—
608#120—44no—
609C4×D4—21no—
610C4×D4—21no—
611C4×D4—21no—
612C4×D4—21no—
613C4×D4—21no—
614C4×D4—21no—
615C4×D4—21no—
616C4×D4—21no—
617#117—21no—
618#117D4×C7311yescharacteristic, complemented
619C2×C4⋊C4D4×C7311yescharacteristic
620C2×C4⋊C4D4×C7311yescharacteristic, complemented
621C2×C4⋊C4C23×C7311yescharacteristic
622C2×C22⋊C4—21no—
623C2×C22⋊C4—21no—
624C2×C22⋊C4—21no—
625C2×C22⋊C4—21no—
626C2×C22⋊C4—22no—
627C2×C22⋊C4—22no—
628C2×C22⋊C4—22no—
629C2×C22⋊C4D4×C7311yescharacteristic
630C2×C22⋊C4D4×C7311yescharacteristic
631C2×C22⋊C4C23×C7311yescharacteristic
632#102—22no—
633#102—22no—
634#102—22no—
635#102—22no—
636C22⋊C8—21no—
637C22⋊C8—21no—
638C22⋊C8C23×C7312yes—
639C22⋊C8C23×C7312yes—
640#95—21no—
641#95C23×C7312yes—
642C24—24no—
643C24—21no—
644C24—22no—
645C24—21no—
646C24—42no—
647C24—41no—
648C24—41no—
649C24—82no—
650C24—82no—
651C24C2×D4×C7311yescharacteristic
652C24C2×D4×C7311yescharacteristic
653#41—42no—
654#41—82no—
655C2×Q8—21no—
656C2×Q8C2×D4×C7311yescharacteristic
657C2×D4—24no—
658C2×D4—24no—
659C2×D4—21no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—21no—
666C2×D4—21no—
667C2×D4—21no—
668C2×D4—21no—
669C2×D4—21no—
670C2×D4—21no—
671C2×D4—21no—
672C2×D4—21no—
673C2×D4—21no—
674C2×D4—21no—
675C2×D4—21no—
676C2×D4—22no—
677C2×D4—22no—
678C2×D4—42no—
679C2×D4—42no—
680C2×D4—42no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—44no—
687C2×D4—41no—
688C2×D4—41no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4—82no—
692C2×D4—82no—
693C2×D4—82no—
694C2×D4C2×D4×C7311yescharacteristic
695C2×D4C2×D4×C7311yescharacteristic
696C2×D4C2×D4×C7311yescharacteristic
697C22×C4—21no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—21no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—22no—
705C22×C4—42no—
706C22×C4C2×D4×C7311yescharacteristic
707C22×C4C2×D4×C7311yescharacteristic
708C22×C4C2×D4×C7311yescharacteristic
709C22×C4C2×D4×C7311yescharacteristic
710C22×C4C2×D4×C7311yescharacteristic
711C22×C4C2×D4×C7311yescharacteristic
712C22×C4C2×D4×C7311yescharacteristic
713C22×C4C2×D4×C7311yescharacteristic
714C22×C4C24×C7311yescharacteristic
715SD16—44no—
716D8—44no—
717D8—44no—
718D8—44no—
719M16—42no—
720C2×C8—22no—
721C2×C8—22no—
722C2×C8—42no—
723C4⋊C4—21no—
724C4⋊C4—21no—
725C4⋊C4—21no—
726C4⋊C4—21no—
727C4⋊C4—21no—
728C4⋊C4—21no—
729C4⋊C4—21no—
730C4⋊C4—21no—
731C4⋊C4—21no—
732C4⋊C4—21no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—21no—
736C4⋊C4C2×D4×C7311yescharacteristic
737C4⋊C4C2×D4×C7311yescharacteristic
738C4⋊C4C2×D4×C7311yescharacteristic
739C4⋊C4C2×D4×C7311yescharacteristic
740C22⋊C4—21no—
741C22⋊C4—21no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—21no—
745C22⋊C4—21no—
746C22⋊C4—21no—
747C22⋊C4—21no—
748C22⋊C4—21no—
749C22⋊C4—21no—
750C22⋊C4—21no—
751C22⋊C4—21no—
752C22⋊C4—21no—
753C22⋊C4—21no—
754C22⋊C4—21no—
755C22⋊C4—21no—
756C22⋊C4—21no—
757C22⋊C4—21no—
758C22⋊C4—21no—
759C22⋊C4—21no—
760C22⋊C4—21no—
761C22⋊C4—21no—
762C22⋊C4—21no—
763C22⋊C4—21no—
764C22⋊C4—21no—
765C22⋊C4—44no—
766C22⋊C4—42no—
767C22⋊C4—82no—
768C22⋊C4—82no—
769C42—21no—
770C42—21no—
771C42—21no—
772C23—22no—
773C23—22no—
774C23—24no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—21no—
779C23—22no—
780C23—41no—
781C23—42no—
782C23—42no—
783C23—44no—
784C23—42no—
785C23—41no—
786C23—41no—
787C23—44no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—81no—
793C23—81no—
794C23—82no—
795C23—82no—
796C23—82no—
797C23—82no—
798C23—88no—
799C23—81no—
800C23—81no—
801C23—81no—
802C23—88no—
803C23#120×C7311yescharacteristic
804C23#120×C7311yescharacteristic
805C23C22×D4×C7311yescharacteristic
806Q8—41no—
807Q8—81no—
808D4—24no—
809D4—24no—
810D4—41no—
811D4—41no—
812D4—41no—
813D4—42no—
814D4—42no—
815D4—44no—
816D4—44no—
817D4—42no—
818D4—42no—
819D4—42no—
820D4—42no—
821D4—42no—
822D4—81no—
823D4—81no—
824D4—81no—
825D4—81no—
826D4—81no—
827D4—81no—
828D4—81no—
829D4—81no—
830D4—81no—
831D4—81no—
832D4—81no—
833D4—81no—
834D4—88no—
835C2×C4—22no—
836C2×C4—22no—
837C2×C4—21no—
838C2×C4—21no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—21no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—41no—
849C2×C4—41no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—42no—
853C2×C4—42no—
854C2×C4—42no—
855C2×C4—81no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—81no—
859C2×C4—81no—
860C2×C4—81no—
861C2×C4—81no—
862C2×C4#120×C7311yescharacteristic
863C2×C4#120×C7311yescharacteristic
864C2×C4C22×D4×C7311yescharacteristic
865C2×C4C22×D4×C7311yescharacteristic
866C8—42no—
867C8—42no—
868C22—21no—
869C22—21no—
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—44no—
876C22—44no—
877C22—44no—
878C22—41no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—41no—
884C22—41no—
885C22—41no—
886C22—41no—
887C22—41no—
888C22—44no—
889C22—41no—
890C22—41no—
891C22—82no—
892C22—82no—
893C22—82no—
894C22—88no—
895C22—88no—
896C22—82no—
897C22—82no—
898C22—162no—
899C22—162no—
900C22B(4,𝔽2)×C7312yes—
901C22C2×#120×C7311yescharacteristic
902C22#576×C7312yes—
903C4—21no—
904C4—21no—
905C4—21no—
906C4—21no—
907C4—41no—
908C4—41no—
909C4—41no—
910C4—41no—
911C4—41no—
912C4—41no—
913C4—41no—
914C4—41no—
915C4—82no—
916C2—22no—
917C2—22no—
918C2—41no—
919C2—84no—
920C2—81no—
921C2—81no—
922C2—81no—
923C2—81no—
924C2C73×#300811yescharacteristic
925C2C73×#302111yescharacteristic
926C2C2×B(4,𝔽2)×C7311yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
LCSG ▷ C22×C4 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3534C2semidirect
2. C73×#3003C2semidirect
3. C2×#447×C73C2semidirect
4. C73×#2613C2semidirect
5. C73×#1600C2semidirect
6. C73×#1598C2semidirect
7. C73×#1597C2semidirect
8. C73×#1595C2semidirect
9. C73×#1516C2semidirect
10. C73×#1510C2semidirect
11. C73×#1468C2semidirect
12. C23×D4×C73C22semidirect
25. #539×C73C22semidirect
27. #538×C73C22semidirect
28. #537×C73C22semidirect
30. #534×C73C22semidirect
36. #450×C73C22semidirect
41. #447×C73C22semidirect
42. #447×C73C22semidirect
45. #407×C73C22semidirect
46. C2×C22⋊C8×C73C22semidirect
48. #394×C73C22semidirect
50. #392×C73C22semidirect
51. #381×C73C22semidirect
53. #328×C73C22semidirect
54. #327×C73C22semidirect
55. #327×C73C22semidirect
56. #327×C73C22semidirect
57. #324×C73C22semidirect
58. #323×C73C22semidirect
61. C2×#41×C73D4semidirect
73. C22×D4×C73D4semidirect
113. C22⋊Q8×C73D4semidirect
130. #121×C73D4semidirect
131. #121×C73D4semidirect
132. #121×C73D4semidirect
154. #117×C73D4semidirect
156. C2×C4⋊C4×C73D4semidirect
452. #18224C73direct (N × H)
464. #3534C2×C73semidirect
465. #3003C2×C73semidirect
466. C2×#447C2×C73semidirect
467. #2613C2×C73semidirect
468. #1600C2×C73semidirect
469. #1598C2×C73semidirect
470. #1597C2×C73semidirect
471. #1595C2×C73semidirect
472. #1516C2×C73semidirect
473. #1510C2×C73semidirect
474. #1468C2×C73semidirect
475. C73#18224direct (N × H)
476. C23×D4C22×C73semidirect
489. #539C22×C73semidirect
491. #538C22×C73semidirect
492. #537C22×C73semidirect
494. #534C22×C73semidirect
500. #450C22×C73semidirect
505. #447C22×C73semidirect
506. #447C22×C73semidirect
509. #407C22×C73semidirect
510. C2×C22⋊C8C22×C73semidirect
512. #394C22×C73semidirect
514. #392C22×C73semidirect
515. #381C22×C73semidirect
517. #328C22×C73semidirect
518. #327C22×C73semidirect
519. #327C22×C73semidirect
520. #327C22×C73semidirect
521. #324C22×C73semidirect
522. #323C22×C73semidirect
525. C2×#41D4×C73semidirect
537. C22×D4D4×C73semidirect
577. C22⋊Q8D4×C73semidirect
594. #121D4×C73semidirect
595. #121D4×C73semidirect
596. #121D4×C73semidirect
618. #117D4×C73semidirect
620. C2×C4⋊C4D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35342
C73×#30032
C2×#447×C732
C73×#26132
C73×#16002
C73×#15982
C73×#15972
C73×#15952
C73×#15162
C73×#15102
C73×#14682
#1822473