Finite Group Databasebeta

← C73×#24140 #32933544

Subgroups — C73×#24140 #32933544

Order 18688.

1556 conjugacy classes of subgroups.

The subgroup lattice has 940 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3505C211yesmaximal, characteristic, complemented
2C73×#2848C211yesmaximal, characteristic, complemented
3C73×#2847C211yesmaximal, characteristic, complemented
4C4×#120×C73C211yesmaximal, characteristic, complemented
5C73×#2044C212yesmaximal, complemented
6C73×#2021C212yesmaximal, complemented
7C73×#1996C211yesmaximal, characteristic, complemented
8C73×#1964C211yesmaximal, characteristic, complemented
9C73×#1889C212yesmaximal, complemented
10C73×#1867C212yesmaximal, complemented
11C73×#1799C211yesmaximal, characteristic, complemented
12C24×C4×C73C2211yescharacteristic
13#553×C73—21no—
14#553×C73—22no—
15#552×C73—21no—
16#551×C73—22no—
17#548×C73—21no—
18#546×C73—21no—
19#539×C73—21no—
20#538×C73—21no—
21#534×C73C2212yes—
22#529×C73—21no—
23#525×C73—21no—
24C2×C22⋊Q8×C73—21no—
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×#121×C73—21no—
27C2×#121×C73C2211yescharacteristic
28C2×#120×C73C2211yescharacteristic
29C2×#120×C73C2212yes—
30#518×C73C2212yes—
31C2×C4×D4×C73—21no—
32C2×C4×D4×C73C2211yescharacteristic
33C2×#99×C73C2212yes—
34C2×#99×C73C2212yes—
35C2×#99×C73C2212yes—
36#386×C73—21no—
37#386×C73—22no—
38#386×C73C2211yescharacteristic
39#386×C73C2212yes—
40#385×C73—21no—
41#385×C73—22no—
42#385×C73C2211yescharacteristic
43#385×C73C2212yes—
44#380×C73—21no—
45#380×C73—21no—
46#380×C73C2211yescharacteristic
47#380×C73C2211yescharacteristic
48#379×C73C2212yes—
49#379×C73C2211yescharacteristic
50C4×C22⋊C4×C73—21no—
51C4×C22⋊C4×C73C2211yescharacteristic
52#342×C73C2212yes—
53#342×C73C2212yes—
54#342×C73C2212yes—
55C25×C73C2311yescharacteristic
56C2×#41×C73—21no—
57C22×Q8×C73D411yescharacteristic, complemented
58C22×D4×C73—21no—
59C22×D4×C73—22no—
60C22×D4×C73D411yescharacteristic, complemented
61C22×D4×C73C2311yescharacteristic
62C22×D4×C73C2312yes—
63C23×C4×C73—21no—
64C23×C4×C73—21no—
65C23×C4×C73—21no—
66C23×C4×C73—21no—
67C23×C4×C73—21no—
68C23×C4×C73—21no—
69C23×C4×C73—44no—
70C23×C4×C73D411yescharacteristic, complemented
71C23×C4×C73C2311yescharacteristic
72C23×C4×C73C2311yescharacteristic
73#126×C73—22no—
74#126×C73—22no—
75#126×C73—22no—
76#125×C73—21no—
77#125×C73—22no—
78#124×C73—21no—
79#124×C73—22no—
80#123×C73—22no—
81#123×C73—22no—
82#123×C73—22no—
83#123×C73—22no—
84#123×C73—22no—
85C22⋊Q8×C73—21no—
86C22⋊Q8×C73—22no—
87C22⋊Q8×C73—21no—
88C22⋊Q8×C73—21no—
89C22⋊Q8×C73—21no—
90C22⋊Q8×C73—21no—
91C22⋊Q8×C73—44no—
92#121×C73—21no—
93#121×C73—22no—
94#121×C73—21no—
95#121×C73—21no—
96#121×C73—21no—
97#121×C73—21no—
98#121×C73—22no—
99#121×C73—22no—
100#121×C73—44no—
101#120×C73—22no—
102#120×C73—22no—
103#120×C73—22no—
104#120×C73—22no—
105#120×C73—24no—
106#120×C73—42no—
107C4×Q8×C73—21no—
108C4×D4×C73—22no—
109C4×D4×C73—21no—
110C4×D4×C73—21no—
111C4×D4×C73—21no—
112C4×D4×C73—21no—
113C4×D4×C73—21no—
114C4×D4×C73—22no—
115C4×D4×C73—22no—
116C4×D4×C73—22no—
117C4×D4×C73—22no—
118C4×D4×C73—44no—
119#117×C73—21no—
120#117×C73—22no—
121#117×C73—22no—
122C2×C4⋊C4×C73—21no—
123C2×C4⋊C4×C73—21no—
124C2×C4⋊C4×C73—21no—
125C2×C4⋊C4×C73—22no—
126C2×C4⋊C4×C73D411yescharacteristic, complemented
127C2×C4⋊C4×C73D411yescharacteristic, complemented
128C2×C4⋊C4×C73D411yescharacteristic, complemented
129C2×C4⋊C4×C73D412yescomplemented
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—22no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—22no—
136C2×C22⋊C4×C73—21no—
137C2×C22⋊C4×C73—22no—
138C2×C22⋊C4×C73—22no—
139C2×C22⋊C4×C73D411yescharacteristic, complemented
140C2×C22⋊C4×C73D412yescomplemented
141C2×C22⋊C4×C73C2311yescharacteristic
142C2×C22⋊C4×C73C2312yes—
143C2×C22⋊C4×C73C2312yes—
144C2×C22⋊C4×C73C2311yescharacteristic
145C2×C22⋊C4×C73C2312yes—
146C2×C22⋊C4×C73C2311yescharacteristic
147C2×C42×C73—21no—
148C2×C42×C73D411yescharacteristic, complemented
149#99×C73—24no—
150#99×C73—42no—
151#99×C73—42no—
152#95×C73—21no—
153#95×C73—21no—
154#95×C73—21no—
155#95×C73—22no—
156#95×C73—22no—
157#95×C73—21no—
158#95×C73—21no—
159C24×C73—21no—
160C24×C73—21no—
161C24×C73—21no—
162C24×C73—21no—
163C24×C73—21no—
164C24×C73—21no—
165C24×C73—42no—
166C24×C73—42no—
167C24×C73C2×D412yes—
168C24×C73C2×D411yescharacteristic
169C24×C73#4112yescomplemented
170C24×C73C2411yescharacteristic
171#41×C73—82no—
172C2×Q8×C73—21no—
173C2×Q8×C73—21no—
174C2×Q8×C73—42no—
175C2×D4×C73—24no—
176C2×D4×C73—21no—
177C2×D4×C73—22no—
178C2×D4×C73—21no—
179C2×D4×C73—22no—
180C2×D4×C73—22no—
181C2×D4×C73—21no—
182C2×D4×C73—21no—
183C2×D4×C73—22no—
184C2×D4×C73—21no—
185C2×D4×C73—22no—
186C2×D4×C73—21no—
187C2×D4×C73—22no—
188C2×D4×C73—22no—
189C2×D4×C73—22no—
190C2×D4×C73—21no—
191C2×D4×C73—21no—
192C2×D4×C73—42no—
193C2×D4×C73—42no—
194C2×D4×C73—42no—
195C2×D4×C73—44no—
196C2×D4×C73—44no—
197C2×D4×C73—44no—
198C22×C4×C73—24no—
199C22×C4×C73—24no—
200C22×C4×C73—24no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—21no—
204C22×C4×C73—21no—
205C22×C4×C73—22no—
206C22×C4×C73—22no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—22no—
211C22×C4×C73—22no—
212C22×C4×C73—42no—
213C22×C4×C73—42no—
214C22×C4×C73—42no—
215C22×C4×C73—42no—
216C22×C4×C73—42no—
217C22×C4×C73—42no—
218C22×C4×C73—42no—
219C22×C4×C73—42no—
220C22×C4×C73—42no—
221C22×C4×C73—42no—
222C22×C4×C73—42no—
223C22×C4×C73—42no—
224C22×C4×C73—41no—
225C22×C4×C73—41no—
226C22×C4×C73—41no—
227C22×C4×C73—41no—
228C22×C4×C73C2×D411yescharacteristic
229C22×C4×C73C2×D412yes—
230C22×C4×C73C2×D411yescharacteristic
231C22×C4×C73C2×D411yescharacteristic
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73C2×D412yes—
235C22×C4×C73C2×D411yescharacteristic
236C22×C4×C73C2×D412yes—
237C22×C4×C73C2×D411yescharacteristic
238C22×C4×C73C2×D411yescharacteristic
239C22×C4×C73C2×D411yescharacteristic
240C4⋊C4×C73—22no—
241C4⋊C4×C73—22no—
242C4⋊C4×C73—22no—
243C4⋊C4×C73—22no—
244C4⋊C4×C73—21no—
245C4⋊C4×C73—22no—
246C4⋊C4×C73—21no—
247C4⋊C4×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—22no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—42no—
253C4⋊C4×C73—42no—
254C4⋊C4×C73—42no—
255C4⋊C4×C73—44no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—24no—
259C22⋊C4×C73—22no—
260C22⋊C4×C73—22no—
261C22⋊C4×C73—22no—
262C22⋊C4×C73—22no—
263C22⋊C4×C73—21no—
264C22⋊C4×C73—22no—
265C22⋊C4×C73—21no—
266C22⋊C4×C73—22no—
267C22⋊C4×C73—21no—
268C22⋊C4×C73—22no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—21no—
271C22⋊C4×C73—22no—
272C22⋊C4×C73—22no—
273C22⋊C4×C73—22no—
274C22⋊C4×C73—21no—
275C22⋊C4×C73—22no—
276C22⋊C4×C73—22no—
277C22⋊C4×C73—21no—
278C22⋊C4×C73—44no—
279C22⋊C4×C73—42no—
280C22⋊C4×C73—44no—
281C22⋊C4×C73—44no—
282C22⋊C4×C73—42no—
283C22⋊C4×C73—42no—
284C22⋊C4×C73—44no—
285C22⋊C4×C73#4112yescomplemented
286C42×C73—22no—
287C42×C73—22no—
288C42×C73—21no—
289C42×C73—21no—
290C42×C73—42no—
291C23×C73—22no—
292C23×C73—22no—
293C23×C73—22no—
294C23×C73—22no—
295C23×C73—22no—
296C23×C73—22no—
297C23×C73—22no—
298C23×C73—22no—
299C23×C73—22no—
300C23×C73—21no—
301C23×C73—22no—
302C23×C73—21no—
303C23×C73—21no—
304C23×C73—22no—
305C23×C73—22no—
306C23×C73—41no—
307C23×C73—44no—
308C23×C73—41no—
309C23×C73—41no—
310C23×C73—41no—
311C23×C73—41no—
312C23×C73—41no—
313C23×C73—41no—
314C23×C73—41no—
315C23×C73—44no—
316C23×C73—44no—
317C23×C73—44no—
318C23×C73—41no—
319C23×C73—41no—
320C23×C73—42no—
321C23×C73—42no—
322C23×C73—41no—
323C23×C73—41no—
324C23×C73—41no—
325C23×C73—41no—
326C23×C73C22×D411yescharacteristic
327C23×C73C22×D411yescharacteristic
328C23×C73C22×D411yescharacteristic
329C23×C73C2×#4111yescharacteristic
330C23×C73C2×#4111yescharacteristic
331C23×C73H(5,𝔽2)11yescharacteristic
332C23×C732−1+411yescharacteristic
333Q8×C73—42no—
334Q8×C73—81no—
335D4×C73—48no—
336D4×C73—42no—
337D4×C73—42no—
338D4×C73—41no—
339D4×C73—41no—
340D4×C73—41no—
341D4×C73—42no—
342D4×C73—42no—
343D4×C73—41no—
344D4×C73—42no—
345D4×C73—81no—
346D4×C73—82no—
347D4×C73—82no—
348D4×C73—88no—
349C2×C4×C73—22no—
350C2×C4×C73—22no—
351C2×C4×C73—22no—
352C2×C4×C73—22no—
353C2×C4×C73—22no—
354C2×C4×C73—22no—
355C2×C4×C73—21no—
356C2×C4×C73—22no—
357C2×C4×C73—21no—
358C2×C4×C73—21no—
359C2×C4×C73—22no—
360C2×C4×C73—22no—
361C2×C4×C73—21no—
362C2×C4×C73—22no—
363C2×C4×C73—21no—
364C2×C4×C73—22no—
365C2×C4×C73—22no—
366C2×C4×C73—41no—
367C2×C4×C73—41no—
368C2×C4×C73—41no—
369C2×C4×C73—44no—
370C2×C4×C73—44no—
371C2×C4×C73—44no—
372C2×C4×C73—41no—
373C2×C4×C73—41no—
374C2×C4×C73—41no—
375C2×C4×C73—41no—
376C2×C4×C73—41no—
377C2×C4×C73—41no—
378C2×C4×C73—44no—
379C2×C4×C73—42no—
380C2×C4×C73—41no—
381C2×C4×C73—42no—
382C2×C4×C73—41no—
383C2×C4×C73—42no—
384C2×C4×C73—41no—
385C2×C4×C73—42no—
386C2×C4×C73—42no—
387C2×C4×C73—42no—
388C2×C4×C73—41no—
389C2×C4×C73—42no—
390C2×C4×C73—41no—
391C2×C4×C73—42no—
392C2×C4×C73—42no—
393C2×C4×C73—81no—
394C2×C4×C73—82no—
395C2×C4×C73—82no—
396C2×C4×C73#12011yescharacteristic
397C2×C4×C73#12011yescharacteristic
398C2×C4×C73#12011yescharacteristic
399C2×C4×C73#12011yescharacteristic
400C22×C73—21no—
401C22×C73—21no—
402C22×C73—21no—
403C22×C73—21no—
404C22×C73—21no—
405C22×C73—21no—
406C22×C73—24no—
407C22×C73—24no—
408C22×C73—24no—
409C22×C73—41no—
410C22×C73—41no—
411C22×C73—41no—
412C22×C73—41no—
413C22×C73—42no—
414C22×C73—42no—
415C22×C73—42no—
416C22×C73—42no—
417C22×C73—42no—
418C22×C73—42no—
419C22×C73—42no—
420C22×C73—42no—
421C22×C73—42no—
422C22×C73—42no—
423C22×C73—42no—
424C22×C73—42no—
425C22×C73—42no—
426C22×C73—41no—
427C22×C73—42no—
428C22×C73—41no—
429C22×C73—42no—
430C22×C73—42no—
431C22×C73—41no—
432C22×C73—82no—
433C22×C73—81no—
434C22×C73—82no—
435C22×C73C2×#12011yescharacteristic
436C22×C73#52511yescharacteristic
437C22×C73#53711yescharacteristic
438C22×C73#54611yescharacteristic
439C22×C73#54711yescharacteristic
440C22×C73#54811yescharacteristic
441C22×C73#55011yescharacteristic
442C4×C73—21no—
443C4×C73—21no—
444C4×C73—21no—
445C4×C73—42no—
446C4×C73—41no—
447C4×C73—42no—
448C4×C73—42no—
449C4×C73—41no—
450C4×C73—42no—
451C4×C73—41no—
452C4×C73—42no—
453C4×C73—82no—
454C4×C73—81no—
455C4×C73—82no—
456C4×C73B(4,𝔽2)12yes—
457#24140C7311yesmaximal, characteristic, direct product factor, Sylow
458C2×C73—21no—
459C2×C73—21no—
460C2×C73—21no—
461C2×C73—21no—
462C2×C73—21no—
463C2×C73—21no—
464C2×C73—44no—
465C2×C73—81no—
466C2×C73—82no—
467C2×C73#240711yescharacteristic
468C2×C73C2×B(4,𝔽2)11yescharacteristic
469C2×C73#302511yescharacteristic
470#3505C2×C7311yescharacteristic, complemented
471#2848C2×C7311yescharacteristic, complemented
472#2847C2×C7311yescharacteristic, complemented
473C4×#120C2×C7311yescharacteristic, complemented
474#2044C2×C7312yescomplemented
475#2021C2×C7312yescomplemented
476#1996C2×C7311yescharacteristic, complemented
477#1964C2×C7311yescharacteristic, complemented
478#1889C2×C7312yescomplemented
479#1867C2×C7312yescomplemented
480#1799C2×C7311yescharacteristic, complemented
481C73#2414011yescharacteristic, direct product factor, Sylow
482C24×C4C22×C7311yescharacteristic
483#553—21no—
484#553—22no—
485#552—21no—
486#551—22no—
487#548—21no—
488#546—21no—
489#539—21no—
490#538—21no—
491#534C22×C7312yes—
492#529—21no—
493#525—21no—
494C2×C22⋊Q8—21no—
495C2×C22⋊Q8C22×C7311yescharacteristic
496C2×#121—21no—
497C2×#121C22×C7311yescharacteristic
498C2×#120C22×C7311yescharacteristic
499C2×#120C22×C7312yes—
500#518C22×C7312yes—
501C2×C4×D4—21no—
502C2×C4×D4C22×C7311yescharacteristic
503C2×#99C22×C7312yes—
504C2×#99C22×C7312yes—
505C2×#99C22×C7312yes—
506#386—22no—
507#386—21no—
508#386C22×C7312yes—
509#386C22×C7311yescharacteristic
510#385—22no—
511#385—21no—
512#385C22×C7312yes—
513#385C22×C7311yescharacteristic
514#380—21no—
515#380—21no—
516#380C22×C7311yescharacteristic
517#380C22×C7311yescharacteristic
518#379C22×C7312yes—
519#379C22×C7311yescharacteristic
520C4×C22⋊C4—21no—
521C4×C22⋊C4C22×C7311yescharacteristic
522#342C22×C7312yes—
523#342C22×C7312yes—
524#342C22×C7312yes—
525C25C23×C7311yescharacteristic
526C2×#41—21no—
527C22×Q8D4×C7311yescharacteristic, complemented
528C22×D4—21no—
529C22×D4—22no—
530C22×D4D4×C7311yescharacteristic, complemented
531C22×D4C23×C7311yescharacteristic
532C22×D4C23×C7312yes—
533C23×C4—21no—
534C23×C4—21no—
535C23×C4—21no—
536C23×C4—21no—
537C23×C4—21no—
538C23×C4—21no—
539C23×C4—44no—
540C23×C4D4×C7311yescharacteristic, complemented
541C23×C4C23×C7311yescharacteristic
542C23×C4C23×C7311yescharacteristic
543#126—22no—
544#126—22no—
545#126—22no—
546#125—21no—
547#125—22no—
548#124—21no—
549#124—22no—
550#123—22no—
551#123—22no—
552#123—22no—
553#123—22no—
554#123—22no—
555C22⋊Q8—21no—
556C22⋊Q8—22no—
557C22⋊Q8—21no—
558C22⋊Q8—21no—
559C22⋊Q8—21no—
560C22⋊Q8—21no—
561C22⋊Q8—44no—
562#121—21no—
563#121—22no—
564#121—21no—
565#121—21no—
566#121—21no—
567#121—21no—
568#121—22no—
569#121—22no—
570#121—44no—
571#120—22no—
572#120—22no—
573#120—22no—
574#120—22no—
575#120—24no—
576#120—42no—
577C4×Q8—21no—
578C4×D4—22no—
579C4×D4—21no—
580C4×D4—21no—
581C4×D4—21no—
582C4×D4—21no—
583C4×D4—21no—
584C4×D4—22no—
585C4×D4—22no—
586C4×D4—22no—
587C4×D4—22no—
588C4×D4—44no—
589#117—21no—
590#117—22no—
591#117—22no—
592C2×C4⋊C4—21no—
593C2×C4⋊C4—21no—
594C2×C4⋊C4—21no—
595C2×C4⋊C4—22no—
596C2×C4⋊C4D4×C7311yescharacteristic, complemented
597C2×C4⋊C4D4×C7311yescharacteristic, complemented
598C2×C4⋊C4D4×C7311yescharacteristic, complemented
599C2×C4⋊C4D4×C7312yescomplemented
600C2×C22⋊C4—22no—
601C2×C22⋊C4—21no—
602C2×C22⋊C4—21no—
603C2×C22⋊C4—22no—
604C2×C22⋊C4—21no—
605C2×C22⋊C4—22no—
606C2×C22⋊C4—22no—
607C2×C22⋊C4—21no—
608C2×C22⋊C4—22no—
609C2×C22⋊C4D4×C7311yescharacteristic, complemented
610C2×C22⋊C4D4×C7312yescomplemented
611C2×C22⋊C4C23×C7312yes—
612C2×C22⋊C4C23×C7311yescharacteristic
613C2×C22⋊C4C23×C7312yes—
614C2×C22⋊C4C23×C7311yescharacteristic
615C2×C22⋊C4C23×C7312yes—
616C2×C22⋊C4C23×C7311yescharacteristic
617C2×C42—21no—
618C2×C42D4×C7311yescharacteristic, complemented
619#99—24no—
620#99—42no—
621#99—42no—
622#95—21no—
623#95—21no—
624#95—21no—
625#95—22no—
626#95—22no—
627#95—21no—
628#95—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—42no—
636C24—42no—
637C24C2×D4×C7312yes—
638C24C2×D4×C7311yescharacteristic
639C24#41×C7312yescomplemented
640C24C24×C7311yescharacteristic
641#41—82no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—42no—
645C2×D4—24no—
646C2×D4—21no—
647C2×D4—22no—
648C2×D4—21no—
649C2×D4—22no—
650C2×D4—22no—
651C2×D4—21no—
652C2×D4—21no—
653C2×D4—22no—
654C2×D4—21no—
655C2×D4—22no—
656C2×D4—21no—
657C2×D4—22no—
658C2×D4—22no—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—42no—
663C2×D4—42no—
664C2×D4—42no—
665C2×D4—44no—
666C2×D4—44no—
667C2×D4—44no—
668C22×C4—24no—
669C22×C4—24no—
670C22×C4—24no—
671C22×C4—21no—
672C22×C4—21no—
673C22×C4—21no—
674C22×C4—21no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—22no—
681C22×C4—22no—
682C22×C4—42no—
683C22×C4—42no—
684C22×C4—42no—
685C22×C4—42no—
686C22×C4—42no—
687C22×C4—42no—
688C22×C4—42no—
689C22×C4—42no—
690C22×C4—42no—
691C22×C4—42no—
692C22×C4—42no—
693C22×C4—42no—
694C22×C4—41no—
695C22×C4—41no—
696C22×C4—41no—
697C22×C4—41no—
698C22×C4C2×D4×C7311yescharacteristic
699C22×C4C2×D4×C7312yes—
700C22×C4C2×D4×C7311yescharacteristic
701C22×C4C2×D4×C7311yescharacteristic
702C22×C4C2×D4×C7311yescharacteristic
703C22×C4C2×D4×C7311yescharacteristic
704C22×C4C2×D4×C7312yes—
705C22×C4C2×D4×C7311yescharacteristic
706C22×C4C2×D4×C7312yes—
707C22×C4C2×D4×C7311yescharacteristic
708C22×C4C2×D4×C7311yescharacteristic
709C22×C4C2×D4×C7311yescharacteristic
710C4⋊C4—22no—
711C4⋊C4—22no—
712C4⋊C4—22no—
713C4⋊C4—22no—
714C4⋊C4—21no—
715C4⋊C4—22no—
716C4⋊C4—21no—
717C4⋊C4—21no—
718C4⋊C4—21no—
719C4⋊C4—21no—
720C4⋊C4—22no—
721C4⋊C4—21no—
722C4⋊C4—42no—
723C4⋊C4—42no—
724C4⋊C4—42no—
725C4⋊C4—44no—
726C22⋊C4—22no—
727C22⋊C4—22no—
728C22⋊C4—24no—
729C22⋊C4—22no—
730C22⋊C4—22no—
731C22⋊C4—22no—
732C22⋊C4—22no—
733C22⋊C4—21no—
734C22⋊C4—22no—
735C22⋊C4—21no—
736C22⋊C4—22no—
737C22⋊C4—21no—
738C22⋊C4—22no—
739C22⋊C4—21no—
740C22⋊C4—21no—
741C22⋊C4—22no—
742C22⋊C4—22no—
743C22⋊C4—22no—
744C22⋊C4—21no—
745C22⋊C4—22no—
746C22⋊C4—22no—
747C22⋊C4—21no—
748C22⋊C4—44no—
749C22⋊C4—42no—
750C22⋊C4—44no—
751C22⋊C4—44no—
752C22⋊C4—42no—
753C22⋊C4—42no—
754C22⋊C4—44no—
755C22⋊C4#41×C7312yescomplemented
756C42—22no—
757C42—22no—
758C42—21no—
759C42—21no—
760C42—42no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—21no—
771C23—22no—
772C23—21no—
773C23—21no—
774C23—22no—
775C23—22no—
776C23—41no—
777C23—44no—
778C23—41no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—44no—
786C23—44no—
787C23—44no—
788C23—41no—
789C23—41no—
790C23—42no—
791C23—42no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23C22×D4×C7311yescharacteristic
797C23C22×D4×C7311yescharacteristic
798C23C22×D4×C7311yescharacteristic
799C23C2×#41×C7311yescharacteristic
800C23C2×#41×C7311yescharacteristic
801C23H(5,𝔽2)×C7311yescharacteristic
802C232−1+4×C7311yescharacteristic
803Q8—42no—
804Q8—81no—
805D4—48no—
806D4—42no—
807D4—42no—
808D4—41no—
809D4—41no—
810D4—41no—
811D4—42no—
812D4—42no—
813D4—41no—
814D4—42no—
815D4—81no—
816D4—82no—
817D4—82no—
818D4—88no—
819C2×C4—22no—
820C2×C4—22no—
821C2×C4—22no—
822C2×C4—22no—
823C2×C4—22no—
824C2×C4—22no—
825C2×C4—21no—
826C2×C4—22no—
827C2×C4—21no—
828C2×C4—21no—
829C2×C4—22no—
830C2×C4—22no—
831C2×C4—21no—
832C2×C4—22no—
833C2×C4—21no—
834C2×C4—22no—
835C2×C4—22no—
836C2×C4—41no—
837C2×C4—41no—
838C2×C4—41no—
839C2×C4—44no—
840C2×C4—44no—
841C2×C4—44no—
842C2×C4—41no—
843C2×C4—41no—
844C2×C4—41no—
845C2×C4—41no—
846C2×C4—41no—
847C2×C4—41no—
848C2×C4—44no—
849C2×C4—42no—
850C2×C4—41no—
851C2×C4—42no—
852C2×C4—41no—
853C2×C4—42no—
854C2×C4—41no—
855C2×C4—42no—
856C2×C4—42no—
857C2×C4—42no—
858C2×C4—41no—
859C2×C4—42no—
860C2×C4—41no—
861C2×C4—42no—
862C2×C4—42no—
863C2×C4—81no—
864C2×C4—82no—
865C2×C4—82no—
866C2×C4#120×C7311yescharacteristic
867C2×C4#120×C7311yescharacteristic
868C2×C4#120×C7311yescharacteristic
869C2×C4#120×C7311yescharacteristic
870C22—21no—
871C22—21no—
872C22—21no—
873C22—21no—
874C22—21no—
875C22—21no—
876C22—24no—
877C22—24no—
878C22—24no—
879C22—41no—
880C22—41no—
881C22—41no—
882C22—41no—
883C22—42no—
884C22—42no—
885C22—42no—
886C22—42no—
887C22—42no—
888C22—42no—
889C22—42no—
890C22—42no—
891C22—42no—
892C22—42no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—41no—
897C22—42no—
898C22—42no—
899C22—41no—
900C22—41no—
901C22—42no—
902C22—82no—
903C22—81no—
904C22—82no—
905C22C2×#120×C7311yescharacteristic
906C22#525×C7311yescharacteristic
907C22#537×C7311yescharacteristic
908C22#546×C7311yescharacteristic
909C22#547×C7311yescharacteristic
910C22#548×C7311yescharacteristic
911C22#550×C7311yescharacteristic
912C4—21no—
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—41no—
918C4—42no—
919C4—41no—
920C4—42no—
921C4—41no—
922C4—42no—
923C4—82no—
924C4—82no—
925C4—81no—
926C4B(4,𝔽2)×C7312yes—
927C2—21no—
928C2—21no—
929C2—21no—
930C2—21no—
931C2—21no—
932C2—21no—
933C2—44no—
934C2—81no—
935C2—82no—
936C2C73×#240711yescharacteristic
937C2C2×B(4,𝔽2)×C7311yescharacteristic
938C2C73×#302511yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC24C24×C73
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3505C2semidirect
2. C73×#2848C2semidirect
3. C73×#2847C2semidirect
4. C4×#120×C73C2semidirect
5. C73×#2044C2semidirect
6. C73×#2021C2semidirect
7. C73×#1996C2semidirect
8. C73×#1964C2semidirect
9. C73×#1889C2semidirect
10. C73×#1867C2semidirect
11. C73×#1799C2semidirect
57. C22×Q8×C73D4semidirect
60. C22×D4×C73D4semidirect
70. C23×C4×C73D4semidirect
126. C2×C4⋊C4×C73D4semidirect
127. C2×C4⋊C4×C73D4semidirect
128. C2×C4⋊C4×C73D4semidirect
129. C2×C4⋊C4×C73D4semidirect
139. C2×C22⋊C4×C73D4semidirect
140. C2×C22⋊C4×C73D4semidirect
148. C2×C42×C73D4semidirect
169. C24×C73#41semidirect
285. C22⋊C4×C73#41semidirect
457. #24140C73direct (N × H)
470. #3505C2×C73semidirect
471. #2848C2×C73semidirect
472. #2847C2×C73semidirect
473. C4×#120C2×C73semidirect
474. #2044C2×C73semidirect
475. #2021C2×C73semidirect
476. #1996C2×C73semidirect
477. #1964C2×C73semidirect
478. #1889C2×C73semidirect
479. #1867C2×C73semidirect
480. #1799C2×C73semidirect
481. C73#24140direct (N × H)
527. C22×Q8D4×C73semidirect
530. C22×D4D4×C73semidirect
540. C23×C4D4×C73semidirect
596. C2×C4⋊C4D4×C73semidirect
597. C2×C4⋊C4D4×C73semidirect
598. C2×C4⋊C4D4×C73semidirect
599. C2×C4⋊C4D4×C73semidirect
609. C2×C22⋊C4D4×C73semidirect
610. C2×C22⋊C4D4×C73semidirect
618. C2×C42D4×C73semidirect
639. C24#41×C73semidirect
755. C22⋊C4#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35052
C73×#28482
C73×#28472
C4×#120×C732
C73×#20442
C73×#20212
C73×#19962
C73×#19642
C73×#18892
C73×#18672
C73×#17992
#2414073