Finite Group Databasebeta

← C73×#24405 #32933809

Subgroups — C73×#24405 #32933809

Order 18688.

1698 conjugacy classes of subgroups.

The subgroup lattice has 948 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3484C211yesmaximal, characteristic
2C2×#458×C73C211yesmaximal, characteristic, complemented
3C22×#99×C73C211yesmaximal, characteristic, complemented
4C73×#2412C212yesmaximal, complemented
5C73×#2405C211yesmaximal, characteristic, complemented
6C73×#2044C212yesmaximal, complemented
7C73×#2022C212yesmaximal, complemented
8C73×#1898C212yesmaximal, complemented
9C73×#1890C211yesmaximal, characteristic, complemented
10C73×#1867C211yesmaximal, characteristic, complemented
11C73×#1790C211yesmaximal, characteristic, complemented
12C2×H(5,𝔽2)×C73C2211yescharacteristic
13C23×D4×C73C2211yescharacteristic
14#546×C73—22no—
15#546×C73—22no—
16D42×C73—22no—
17D42×C73—22no—
18#535×C73—21no—
19#534×C73—21no—
20#534×C73C2212yes—
21#525×C73—21no—
22C2×#123×C73C2211yescharacteristic
23C2×#123×C73C2212yescomplemented
24C2×#123×C73C2211yescharacteristic, complemented
25C2×#120×C73—21no—
26C2×#120×C73C2212yes—
27#518×C73C2211yescharacteristic
28C22×C22⋊C4×C73C2211yescharacteristic, complemented
29C22×C22⋊C4×C73C2212yescomplemented
30#458×C73—24no—
31C2×#99×C73—24no—
32C2×#99×C73C2211yescharacteristic
33C2×#99×C73C2211yescharacteristic
34C2×#99×C73C2212yescomplemented
35C2×#99×C73C2212yescomplemented
36C2×#99×C73C2212yescomplemented
37#397×C73—22no—
38#394×C73—21no—
39#394×C73—21no—
40#394×C73—22no—
41#386×C73—22no—
42#386×C73C2211yescharacteristic
43#386×C73C2211yescharacteristic, complemented
44#386×C73C2212yescomplemented
45#385×C73—21no—
46#385×C73C2212yescomplemented
47#381×C73C2212yescomplemented
48#380×C73—22no—
49#379×C73—21no—
50#379×C73C2211yescharacteristic, complemented
51#342×C73C2212yescomplemented
52#342×C73C2212yescomplemented
53C25×C73D411yescharacteristic
54C25×C73C2311yescharacteristic
55H(5,𝔽2)×C73—22no—
56H(5,𝔽2)×C73—22no—
57H(5,𝔽2)×C73—42no—
58C2×#41×C73—21no—
59C2×#41×C73—22no—
60C22×D4×C73—21no—
61C22×D4×C73—22no—
62C22×D4×C73—22no—
63C22×D4×C73—22no—
64C22×D4×C73—21no—
65C22×D4×C73—21no—
66C22×D4×C73—22no—
67C22×D4×C73—22no—
68C22×D4×C73—42no—
69C22×D4×C73D411yescharacteristic
70C22×D4×C73D411yescharacteristic
71C22×D4×C73D412yes—
72C22×D4×C73D412yes—
73C22×D4×C73C2312yes—
74C22×D4×C73C2311yescharacteristic
75C22×D4×C73C2311yescharacteristic
76C23×C4×C73—22no—
77C23×C4×C73D411yescharacteristic
78C23×C4×C73C2311yescharacteristic
79C23×C4×C73C2311yescharacteristic
80#127×C73—22no—
81#124×C73—22no—
82#123×C73—22no—
83#123×C73—22no—
84#123×C73—22no—
85#123×C73—22no—
86#123×C73—22no—
87#123×C73—24no—
88#123×C73—42no—
89#123×C73—42no—
90C22⋊Q8×C73—21no—
91C22⋊Q8×C73—21no—
92#121×C73—21no—
93#121×C73—21no—
94#121×C73—22no—
95#121×C73—22no—
96#121×C73—22no—
97#121×C73—22no—
98#121×C73—22no—
99#121×C73—22no—
100#120×C73—22no—
101#120×C73—22no—
102#120×C73—22no—
103#120×C73—22no—
104#120×C73—22no—
105#120×C73—22no—
106#120×C73—22no—
107#120×C73—22no—
108#120×C73—22no—
109C4×D4×C73—22no—
110C4×D4×C73—22no—
111C4×D4×C73—22no—
112C4×D4×C73—22no—
113#117×C73—21no—
114C2×C4⋊C4×C73—22no—
115C2×C4⋊C4×C73—21no—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73—22no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—21no—
121C2×C22⋊C4×C73—24no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—21no—
126C2×C22⋊C4×C73—22no—
127C2×C22⋊C4×C73—22no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—22no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—22no—
135C2×C22⋊C4×C73—42no—
136C2×C22⋊C4×C73D412yes—
137C2×C22⋊C4×C73D412yes—
138C2×C22⋊C4×C73C2311yescharacteristic
139C2×C22⋊C4×C73C2311yescharacteristic
140C2×C22⋊C4×C73C2312yes—
141C2×C22⋊C4×C73C2312yes—
142C2×C22⋊C4×C73C2312yes—
143#99×C73—22no—
144#99×C73—24no—
145#99×C73—24no—
146#99×C73—42no—
147#99×C73D414yescomplemented
148#95×C73—22no—
149#95×C73—22no—
150#95×C73—22no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—22no—
154C24×C73—21no—
155C24×C73—21no—
156C24×C73—22no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73—21no—
160C24×C73—22no—
161C24×C73—41no—
162C24×C73—42no—
163C24×C73—42no—
164C24×C73—81no—
165C24×C73—81no—
166C24×C73C2×D411yescharacteristic
167C24×C73C2×D412yes—
168C24×C73C2×D411yescharacteristic
169C24×C73C2×D412yes—
170C24×C73C2×D412yes—
171C24×C73C2×D411yescharacteristic
172C24×C73C2×D411yescharacteristic
173C24×C73C2411yescharacteristic
174#41×C73—44no—
175#41×C73—44no—
176#41×C73—42no—
177#41×C73—42no—
178C2×Q8×C73—21no—
179C2×D4×C73—22no—
180C2×D4×C73—22no—
181C2×D4×C73—22no—
182C2×D4×C73—21no—
183C2×D4×C73—22no—
184C2×D4×C73—22no—
185C2×D4×C73—22no—
186C2×D4×C73—22no—
187C2×D4×C73—22no—
188C2×D4×C73—21no—
189C2×D4×C73—22no—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—22no—
193C2×D4×C73—21no—
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—22no—
197C2×D4×C73—22no—
198C2×D4×C73—22no—
199C2×D4×C73—22no—
200C2×D4×C73—22no—
201C2×D4×C73—22no—
202C2×D4×C73—22no—
203C2×D4×C73—41no—
204C2×D4×C73—41no—
205C2×D4×C73—44no—
206C2×D4×C73—44no—
207C2×D4×C73—44no—
208C2×D4×C73—44no—
209C2×D4×C73—44no—
210C2×D4×C73—44no—
211C2×D4×C73—42no—
212C2×D4×C73—42no—
213C2×D4×C73—44no—
214C2×D4×C73—82no—
215C2×D4×C73—82no—
216C2×D4×C73—82no—
217C2×D4×C73C2×D412yes—
218C2×D4×C73#4112yes—
219C22×C4×C73—21no—
220C22×C4×C73—22no—
221C22×C4×C73—21no—
222C22×C4×C73—21no—
223C22×C4×C73—22no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—22no—
227C22×C4×C73—22no—
228C22×C4×C73—21no—
229C22×C4×C73—22no—
230C22×C4×C73—22no—
231C22×C4×C73—21no—
232C22×C4×C73—21no—
233C22×C4×C73—21no—
234C22×C4×C73—21no—
235C22×C4×C73—21no—
236C22×C4×C73—22no—
237C22×C4×C73—41no—
238C22×C4×C73—44no—
239C22×C4×C73—44no—
240C22×C4×C73—81no—
241C22×C4×C73—82no—
242C22×C4×C73C2×D412yes—
243C22×C4×C73C2×D411yescharacteristic
244C22×C4×C73C2×D411yescharacteristic
245C22×C4×C73C2×D412yes—
246C22×C4×C73C2×D412yes—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—22no—
250C4⋊C4×C73—22no—
251C4⋊C4×C73—44no—
252C4⋊C4×C73—42no—
253C4⋊C4×C73—42no—
254C4⋊C4×C73—82no—
255C22⋊C4×C73—22no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—22no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—22no—
261C22⋊C4×C73—22no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—22no—
264C22⋊C4×C73—22no—
265C22⋊C4×C73—22no—
266C22⋊C4×C73—22no—
267C22⋊C4×C73—22no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—22no—
271C22⋊C4×C73—22no—
272C22⋊C4×C73—44no—
273C22⋊C4×C73—44no—
274C22⋊C4×C73—42no—
275C22⋊C4×C73—42no—
276C22⋊C4×C73—41no—
277C22⋊C4×C73—42no—
278C22⋊C4×C73—41no—
279C22⋊C4×C73—42no—
280C22⋊C4×C73—81no—
281C22⋊C4×C73—81no—
282C22⋊C4×C73—81no—
283C22⋊C4×C73—82no—
284C22⋊C4×C73C2×D414yescomplemented
285C42×C73—22no—
286C23×C73—21no—
287C23×C73—21no—
288C23×C73—21no—
289C23×C73—22no—
290C23×C73—22no—
291C23×C73—22no—
292C23×C73—24no—
293C23×C73—21no—
294C23×C73—21no—
295C23×C73—21no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—21no—
299C23×C73—22no—
300C23×C73—21no—
301C23×C73—21no—
302C23×C73—22no—
303C23×C73—22no—
304C23×C73—42no—
305C23×C73—41no—
306C23×C73—41no—
307C23×C73—41no—
308C23×C73—41no—
309C23×C73—42no—
310C23×C73—42no—
311C23×C73—41no—
312C23×C73—42no—
313C23×C73—42no—
314C23×C73—41no—
315C23×C73—41no—
316C23×C73—41no—
317C23×C73—41no—
318C23×C73—42no—
319C23×C73—42no—
320C23×C73—42no—
321C23×C73—42no—
322C23×C73—42no—
323C23×C73—81no—
324C23×C73—81no—
325C23×C73—82no—
326C23×C73—82no—
327C23×C73—84no—
328C23×C73—81no—
329C23×C73—81no—
330C23×C73—84no—
331C23×C73—84no—
332C23×C73#12011yescharacteristic
333C23×C73#12012yes—
334C23×C73#12011yescharacteristic
335C23×C73#12112yes—
336C23×C73C22×D411yescharacteristic
337C23×C73C22×D412yes—
338C23×C73C22×D411yescharacteristic
339C23×C73C2×#4111yescharacteristic
340C23×C73H(5,𝔽2)12yes—
341Q8×C73—42no—
342D4×C73—24no—
343D4×C73—24no—
344D4×C73—44no—
345D4×C73—42no—
346D4×C73—44no—
347D4×C73—44no—
348D4×C73—44no—
349D4×C73—42no—
350D4×C73—42no—
351D4×C73—42no—
352D4×C73—42no—
353D4×C73—42no—
354D4×C73—42no—
355D4×C73—44no—
356D4×C73—82no—
357D4×C73—82no—
358D4×C73—82no—
359D4×C73—82no—
360C2×C4×C73—21no—
361C2×C4×C73—21no—
362C2×C4×C73—22no—
363C2×C4×C73—22no—
364C2×C4×C73—22no—
365C2×C4×C73—21no—
366C2×C4×C73—21no—
367C2×C4×C73—21no—
368C2×C4×C73—24no—
369C2×C4×C73—22no—
370C2×C4×C73—22no—
371C2×C4×C73—42no—
372C2×C4×C73—42no—
373C2×C4×C73—44no—
374C2×C4×C73—42no—
375C2×C4×C73—42no—
376C2×C4×C73—42no—
377C2×C4×C73—42no—
378C2×C4×C73—42no—
379C2×C4×C73—41no—
380C2×C4×C73—41no—
381C2×C4×C73—41no—
382C2×C4×C73—41no—
383C2×C4×C73—42no—
384C2×C4×C73—42no—
385C2×C4×C73—41no—
386C2×C4×C73—41no—
387C2×C4×C73—42no—
388C2×C4×C73—42no—
389C2×C4×C73—41no—
390C2×C4×C73—41no—
391C2×C4×C73—41no—
392C2×C4×C73—41no—
393C2×C4×C73—41no—
394C2×C4×C73—41no—
395C2×C4×C73—42no—
396C2×C4×C73—42no—
397C2×C4×C73—42no—
398C2×C4×C73—81no—
399C2×C4×C73—81no—
400C2×C4×C73—88no—
401C2×C4×C73#12112yes—
402C22×C73—21no—
403C22×C73—22no—
404C22×C73—21no—
405C22×C73—22no—
406C22×C73—21no—
407C22×C73—21no—
408C22×C73—21no—
409C22×C73—22no—
410C22×C73—22no—
411C22×C73—22no—
412C22×C73—21no—
413C22×C73—21no—
414C22×C73—22no—
415C22×C73—41no—
416C22×C73—41no—
417C22×C73—42no—
418C22×C73—44no—
419C22×C73—44no—
420C22×C73—42no—
421C22×C73—42no—
422C22×C73—42no—
423C22×C73—42no—
424C22×C73—41no—
425C22×C73—41no—
426C22×C73—42no—
427C22×C73—41no—
428C22×C73—42no—
429C22×C73—41no—
430C22×C73—42no—
431C22×C73—41no—
432C22×C73—82no—
433C22×C73—81no—
434C22×C73—81no—
435C22×C73—81no—
436C22×C73—82no—
437C22×C73—84no—
438C22×C73—82no—
439C22×C73—82no—
440C22×C73—81no—
441C22×C73—84no—
442C22×C73—162no—
443C22×C73#45812yescomplemented
444C22×C73C2×#12011yescharacteristic
445C22×C73C2×#12111yescharacteristic
446C22×C73#53411yescharacteristic
447C22×C73D4212yes—
448C22×C73#54612yes—
449C4×C73—22no—
450C4×C73—44no—
451C4×C73—41no—
452C4×C73—42no—
453C4×C73—42no—
454C4×C73—42no—
455C4×C73—81no—
456C4×C73—81no—
457C4×C73—82no—
458C4×C73—81no—
459C4×C73—81no—
460#24405C7311yesmaximal, characteristic, direct product factor, Sylow
461C2×C73—22no—
462C2×C73—21no—
463C2×C73—21no—
464C2×C73—22no—
465C2×C73—22no—
466C2×C73—42no—
467C2×C73—41no—
468C2×C73—42no—
469C2×C73—81no—
470C2×C73—82no—
471C2×C73#241011yescharacteristic
472C2×C73C2×#45811yescharacteristic
473C2×C73#302611yescharacteristic
474#3484C2×C7311yescharacteristic
475C2×#458C2×C7311yescharacteristic, complemented
476C22×#99C2×C7311yescharacteristic, complemented
477#2412C2×C7312yescomplemented
478#2405C2×C7311yescharacteristic, complemented
479#2044C2×C7312yescomplemented
480#2022C2×C7312yescomplemented
481#1898C2×C7312yescomplemented
482#1890C2×C7311yescharacteristic, complemented
483#1867C2×C7311yescharacteristic, complemented
484#1790C2×C7311yescharacteristic, complemented
485C73#2440511yescharacteristic, direct product factor, Sylow
486C2×H(5,𝔽2)C22×C7311yescharacteristic
487C23×D4C22×C7311yescharacteristic
488#546—22no—
489#546—22no—
490D42—22no—
491D42—22no—
492#535—21no—
493#534—21no—
494#534C22×C7312yes—
495#525—21no—
496C2×#123C22×C7311yescharacteristic
497C2×#123C22×C7312yescomplemented
498C2×#123C22×C7311yescharacteristic, complemented
499C2×#120—21no—
500C2×#120C22×C7312yes—
501#518C22×C7311yescharacteristic
502C22×C22⋊C4C22×C7311yescharacteristic, complemented
503C22×C22⋊C4C22×C7312yescomplemented
504#458—24no—
505C2×#99—24no—
506C2×#99C22×C7311yescharacteristic
507C2×#99C22×C7311yescharacteristic
508C2×#99C22×C7312yescomplemented
509C2×#99C22×C7312yescomplemented
510C2×#99C22×C7312yescomplemented
511#397—22no—
512#394—21no—
513#394—21no—
514#394—22no—
515#386—22no—
516#386C22×C7311yescharacteristic
517#386C22×C7311yescharacteristic, complemented
518#386C22×C7312yescomplemented
519#385—21no—
520#385C22×C7312yescomplemented
521#381C22×C7312yescomplemented
522#380—22no—
523#379—21no—
524#379C22×C7311yescharacteristic, complemented
525#342C22×C7312yescomplemented
526#342C22×C7312yescomplemented
527C25D4×C7311yescharacteristic
528C25C23×C7311yescharacteristic
529H(5,𝔽2)—22no—
530H(5,𝔽2)—22no—
531H(5,𝔽2)—42no—
532C2×#41—21no—
533C2×#41—22no—
534C22×D4—21no—
535C22×D4—22no—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—21no—
539C22×D4—21no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—42no—
543C22×D4D4×C7311yescharacteristic
544C22×D4D4×C7311yescharacteristic
545C22×D4D4×C7312yes—
546C22×D4D4×C7312yes—
547C22×D4C23×C7312yes—
548C22×D4C23×C7311yescharacteristic
549C22×D4C23×C7311yescharacteristic
550C23×C4—22no—
551C23×C4D4×C7311yescharacteristic
552C23×C4C23×C7311yescharacteristic
553C23×C4C23×C7311yescharacteristic
554#127—22no—
555#124—22no—
556#123—22no—
557#123—22no—
558#123—22no—
559#123—22no—
560#123—22no—
561#123—24no—
562#123—42no—
563#123—42no—
564C22⋊Q8—21no—
565C22⋊Q8—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—22no—
571#121—22no—
572#121—22no—
573#121—22no—
574#120—22no—
575#120—22no—
576#120—22no—
577#120—22no—
578#120—22no—
579#120—22no—
580#120—22no—
581#120—22no—
582#120—22no—
583C4×D4—22no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587#117—21no—
588C2×C4⋊C4—21no—
589C2×C4⋊C4—22no—
590C2×C4⋊C4—21no—
591C2×C4⋊C4—22no—
592C2×C22⋊C4—21no—
593C2×C22⋊C4—21no—
594C2×C22⋊C4—21no—
595C2×C22⋊C4—24no—
596C2×C22⋊C4—21no—
597C2×C22⋊C4—22no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—22no—
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4—42no—
610C2×C22⋊C4D4×C7312yes—
611C2×C22⋊C4D4×C7312yes—
612C2×C22⋊C4C23×C7312yes—
613C2×C22⋊C4C23×C7311yescharacteristic
614C2×C22⋊C4C23×C7311yescharacteristic
615C2×C22⋊C4C23×C7312yes—
616C2×C22⋊C4C23×C7312yes—
617#99—22no—
618#99—24no—
619#99—24no—
620#99—42no—
621#99D4×C7314yescomplemented
622#95—22no—
623#95—22no—
624#95—22no—
625#95—21no—
626#95—21no—
627#95—22no—
628C24—21no—
629C24—21no—
630C24—22no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—22no—
635C24—41no—
636C24—42no—
637C24—42no—
638C24—81no—
639C24—81no—
640C24C2×D4×C7311yescharacteristic
641C24C2×D4×C7312yes—
642C24C2×D4×C7311yescharacteristic
643C24C2×D4×C7312yes—
644C24C2×D4×C7312yes—
645C24C2×D4×C7311yescharacteristic
646C24C2×D4×C7311yescharacteristic
647C24C24×C7311yescharacteristic
648#41—44no—
649#41—44no—
650#41—42no—
651#41—42no—
652C2×Q8—21no—
653C2×D4—22no—
654C2×D4—22no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—22no—
661C2×D4—22no—
662C2×D4—21no—
663C2×D4—22no—
664C2×D4—22no—
665C2×D4—22no—
666C2×D4—22no—
667C2×D4—21no—
668C2×D4—22no—
669C2×D4—22no—
670C2×D4—22no—
671C2×D4—22no—
672C2×D4—22no—
673C2×D4—22no—
674C2×D4—22no—
675C2×D4—22no—
676C2×D4—22no—
677C2×D4—41no—
678C2×D4—41no—
679C2×D4—44no—
680C2×D4—44no—
681C2×D4—44no—
682C2×D4—44no—
683C2×D4—44no—
684C2×D4—44no—
685C2×D4—42no—
686C2×D4—42no—
687C2×D4—44no—
688C2×D4—82no—
689C2×D4—82no—
690C2×D4—82no—
691C2×D4C2×D4×C7312yes—
692C2×D4#41×C7312yes—
693C22×C4—21no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—22no—
698C22×C4—21no—
699C22×C4—21no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—22no—
705C22×C4—21no—
706C22×C4—21no—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—22no—
711C22×C4—41no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—81no—
715C22×C4—82no—
716C22×C4C2×D4×C7312yes—
717C22×C4C2×D4×C7311yescharacteristic
718C22×C4C2×D4×C7311yescharacteristic
719C22×C4C2×D4×C7312yes—
720C22×C4C2×D4×C7312yes—
721C4⋊C4—21no—
722C4⋊C4—21no—
723C4⋊C4—22no—
724C4⋊C4—22no—
725C4⋊C4—44no—
726C4⋊C4—42no—
727C4⋊C4—42no—
728C4⋊C4—82no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—22no—
734C22⋊C4—22no—
735C22⋊C4—22no—
736C22⋊C4—22no—
737C22⋊C4—22no—
738C22⋊C4—22no—
739C22⋊C4—22no—
740C22⋊C4—22no—
741C22⋊C4—22no—
742C22⋊C4—21no—
743C22⋊C4—21no—
744C22⋊C4—22no—
745C22⋊C4—22no—
746C22⋊C4—44no—
747C22⋊C4—44no—
748C22⋊C4—42no—
749C22⋊C4—42no—
750C22⋊C4—41no—
751C22⋊C4—42no—
752C22⋊C4—41no—
753C22⋊C4—42no—
754C22⋊C4—81no—
755C22⋊C4—81no—
756C22⋊C4—81no—
757C22⋊C4—82no—
758C22⋊C4C2×D4×C7314yescomplemented
759C42—22no—
760C23—22no—
761C23—24no—
762C23—21no—
763C23—21no—
764C23—21no—
765C23—22no—
766C23—22no—
767C23—21no—
768C23—21no—
769C23—21no—
770C23—22no—
771C23—22no—
772C23—21no—
773C23—22no—
774C23—21no—
775C23—21no—
776C23—22no—
777C23—22no—
778C23—42no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—42no—
784C23—42no—
785C23—41no—
786C23—42no—
787C23—42no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—81no—
798C23—81no—
799C23—82no—
800C23—82no—
801C23—84no—
802C23—81no—
803C23—81no—
804C23—84no—
805C23—84no—
806C23#120×C7311yescharacteristic
807C23#120×C7312yes—
808C23#120×C7311yescharacteristic
809C23#121×C7312yes—
810C23C22×D4×C7311yescharacteristic
811C23C22×D4×C7312yes—
812C23C22×D4×C7311yescharacteristic
813C23C2×#41×C7311yescharacteristic
814C23H(5,𝔽2)×C7312yes—
815Q8—42no—
816D4—24no—
817D4—24no—
818D4—44no—
819D4—42no—
820D4—44no—
821D4—44no—
822D4—44no—
823D4—44no—
824D4—42no—
825D4—42no—
826D4—42no—
827D4—42no—
828D4—42no—
829D4—42no—
830D4—82no—
831D4—82no—
832D4—82no—
833D4—82no—
834C2×C4—21no—
835C2×C4—21no—
836C2×C4—22no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—21no—
840C2×C4—21no—
841C2×C4—21no—
842C2×C4—24no—
843C2×C4—22no—
844C2×C4—22no—
845C2×C4—42no—
846C2×C4—42no—
847C2×C4—44no—
848C2×C4—42no—
849C2×C4—42no—
850C2×C4—42no—
851C2×C4—42no—
852C2×C4—42no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—42no—
858C2×C4—42no—
859C2×C4—41no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—81no—
873C2×C4—81no—
874C2×C4—88no—
875C2×C4#121×C7312yes—
876C22—22no—
877C22—21no—
878C22—22no—
879C22—21no—
880C22—21no—
881C22—21no—
882C22—22no—
883C22—21no—
884C22—21no—
885C22—22no—
886C22—21no—
887C22—22no—
888C22—22no—
889C22—41no—
890C22—41no—
891C22—42no—
892C22—44no—
893C22—42no—
894C22—42no—
895C22—44no—
896C22—42no—
897C22—42no—
898C22—41no—
899C22—41no—
900C22—42no—
901C22—41no—
902C22—42no—
903C22—41no—
904C22—42no—
905C22—41no—
906C22—82no—
907C22—81no—
908C22—81no—
909C22—81no—
910C22—82no—
911C22—84no—
912C22—81no—
913C22—82no—
914C22—82no—
915C22—84no—
916C22—162no—
917C22#458×C7312yescomplemented
918C22C2×#120×C7311yescharacteristic
919C22C2×#121×C7311yescharacteristic
920C22#534×C7311yescharacteristic
921C22D42×C7312yes—
922C22#546×C7312yes—
923C4—22no—
924C4—44no—
925C4—42no—
926C4—42no—
927C4—41no—
928C4—42no—
929C4—82no—
930C4—81no—
931C4—81no—
932C4—81no—
933C4—81no—
934C2—22no—
935C2—21no—
936C2—21no—
937C2—22no—
938C2—22no—
939C2—41no—
940C2—42no—
941C2—42no—
942C2—81no—
943C2—82no—
944C2C73×#241011yescharacteristic
945C2C2×#458×C7311yescharacteristic
946C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC24C24×C73
prime radicalC73×#3484C2
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C25×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C2×#458×C73C2semidirect
3. C22×#99×C73C2semidirect
4. C73×#2412C2semidirect
5. C73×#2405C2semidirect
6. C73×#2044C2semidirect
7. C73×#2022C2semidirect
8. C73×#1898C2semidirect
9. C73×#1890C2semidirect
10. C73×#1867C2semidirect
11. C73×#1790C2semidirect
23. C2×#123×C73C22semidirect
24. C2×#123×C73C22semidirect
28. C22×C22⋊C4×C73C22semidirect
29. C22×C22⋊C4×C73C22semidirect
34. C2×#99×C73C22semidirect
35. C2×#99×C73C22semidirect
36. C2×#99×C73C22semidirect
43. #386×C73C22semidirect
44. #386×C73C22semidirect
46. #385×C73C22semidirect
47. #381×C73C22semidirect
50. #379×C73C22semidirect
51. #342×C73C22semidirect
52. #342×C73C22semidirect
147. #99×C73D4semidirect
284. C22⋊C4×C73C2×D4semidirect
443. C22×C73#458semidirect
460. #24405C73direct (N × H)
475. C2×#458C2×C73semidirect
476. C22×#99C2×C73semidirect
477. #2412C2×C73semidirect
478. #2405C2×C73semidirect
479. #2044C2×C73semidirect
480. #2022C2×C73semidirect
481. #1898C2×C73semidirect
482. #1890C2×C73semidirect
483. #1867C2×C73semidirect
484. #1790C2×C73semidirect
485. C73#24405direct (N × H)
497. C2×#123C22×C73semidirect
498. C2×#123C22×C73semidirect
502. C22×C22⋊C4C22×C73semidirect
503. C22×C22⋊C4C22×C73semidirect
508. C2×#99C22×C73semidirect
509. C2×#99C22×C73semidirect
510. C2×#99C22×C73semidirect
517. #386C22×C73semidirect
518. #386C22×C73semidirect
520. #385C22×C73semidirect
521. #381C22×C73semidirect
524. #379C22×C73semidirect
525. #342C22×C73semidirect
526. #342C22×C73semidirect
621. #99D4×C73semidirect
758. C22⋊C4C2×D4×C73semidirect
917. C22#458×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34842
C2×#458×C732
C22×#99×C732
C73×#24122
C73×#24052
C73×#20442
C73×#20222
C73×#18982
C73×#18902
C73×#18672
C73×#17902
#2440573