Finite Group Databasebeta

← C73×#9083 #32918487

Subgroups — C73×#9083 #32918487

Order 18688.

1100 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#407×C73C211yesmaximal, characteristic, complemented
2C2×#386×C73C211yesmaximal, characteristic
3C73×#1779C211yesmaximal, characteristic, complemented
4C2×#323×C73C212yesmaximal, complemented
5C73×#1280C212yesmaximal, complemented
6C23×D4×C73C411yescharacteristic
7C24×C4×C73C2211yescharacteristic
8C22×M16×C73—21no—
9C22×C22⋊C4×C73C411yescharacteristic
10C22×C22⋊C4×C73C411yescharacteristic
11C22×C22⋊C4×C73C2211yescharacteristic
12#407×C73—24no—
13C2×C22⋊C8×C73—21no—
14C2×C22⋊C8×C73—21no—
15C2×C22⋊C8×C73—21no—
16C2×C22⋊C8×C73C2212yes—
17C2×C22⋊C8×C73C2212yes—
18#386×C73—21no—
19#386×C73—21no—
20#386×C73—21no—
21#386×C73—21no—
22C2×#95×C73C411yescharacteristic
23C2×#95×C73C2211yescharacteristic
24#323×C73—24no—
25C25×C73C2×C411yescharacteristic
26C25×C73C2×C411yescharacteristic
27C22×D4×C73—21no—
28C22×D4×C73—21no—
29C22×D4×C73—22no—
30C22×D4×C73—22no—
31C22×D4×C73—42no—
32C22×D4×C73—42no—
33C23×C4×C73—22no—
34C23×C4×C73—22no—
35C23×C4×C73—42no—
36C23×C4×C73—42no—
37C23×C4×C73C2×C411yescharacteristic
38C23×C4×C73C2×C411yescharacteristic
39C23×C4×C73C2×C411yescharacteristic
40C23×C4×C73C2×C411yescharacteristic
41C23×C4×C73D411yescharacteristic
42C23×C4×C73D411yescharacteristic
43C23×C4×C73D411yescharacteristic
44C23×C4×C73D411yescharacteristic
45C23×C4×C73C2311yescharacteristic
46C2×M16×C73—24no—
47C2×M16×C73—42no—
48C2×M16×C73—42no—
49C22×C8×C73—22no—
50C22×C8×C73—22no—
51C2×C22⋊C4×C73—21no—
52C2×C22⋊C4×C73—21no—
53C2×C22⋊C4×C73—21no—
54C2×C22⋊C4×C73—21no—
55C2×C22⋊C4×C73—21no—
56C2×C22⋊C4×C73—21no—
57C2×C22⋊C4×C73—22no—
58C2×C22⋊C4×C73—22no—
59C2×C22⋊C4×C73—42no—
60C2×C22⋊C4×C73—42no—
61C22⋊C8×C73—24no—
62C22⋊C8×C73—22no—
63C22⋊C8×C73—22no—
64C22⋊C8×C73—22no—
65C22⋊C8×C73—42no—
66C22⋊C8×C73—42no—
67C22⋊C8×C73D414yescomplemented
68#95×C73—21no—
69#95×C73—21no—
70#95×C73—21no—
71#95×C73—21no—
72C24×C73—22no—
73C24×C73—22no—
74C24×C73—21no—
75C24×C73—21no—
76C24×C73—21no—
77C24×C73—22no—
78C24×C73—21no—
79C24×C73—22no—
80C24×C73—22no—
81C24×C73—22no—
82C24×C73—41no—
83C24×C73—41no—
84C24×C73—41no—
85C24×C73—41no—
86C24×C73—41no—
87C24×C73—41no—
88C24×C73C22⋊C411yescharacteristic
89C24×C73C22⋊C411yescharacteristic
90C24×C73M1612yescomplemented
91C24×C73C22×C411yescharacteristic
92C2×D4×C73—24no—
93C2×D4×C73—24no—
94C2×D4×C73—48no—
95C2×D4×C73—42no—
96C2×D4×C73—42no—
97C2×D4×C73—48no—
98C2×D4×C73—42no—
99C2×D4×C73—42no—
100C22×C4×C73—22no—
101C22×C4×C73—22no—
102C22×C4×C73—21no—
103C22×C4×C73—21no—
104C22×C4×C73—22no—
105C22×C4×C73—21no—
106C22×C4×C73—22no—
107C22×C4×C73—21no—
108C22×C4×C73—22no—
109C22×C4×C73—22no—
110C22×C4×C73—21no—
111C22×C4×C73—22no—
112C22×C4×C73—22no—
113C22×C4×C73—21no—
114C22×C4×C73—21no—
115C22×C4×C73—21no—
116C22×C4×C73—22no—
117C22×C4×C73—22no—
118C22×C4×C73—41no—
119C22×C4×C73—41no—
120C22×C4×C73—41no—
121C22×C4×C73—41no—
122C22×C4×C73—41no—
123C22×C4×C73—41no—
124C22×C4×C73—41no—
125C22×C4×C73—48no—
126C22×C4×C73—48no—
127C22×C4×C73—41no—
128C22×C4×C73—41no—
129C22×C4×C73—41no—
130C22×C4×C73—41no—
131C22×C4×C73—41no—
132C22×C4×C73—41no—
133C22×C4×C73C22⋊C411yescharacteristic
134C22×C4×C73C22⋊C411yescharacteristic
135C22×C4×C73M1612yescomplemented
136C22×C4×C73C2×D411yescharacteristic
137C22×C4×C73C2×D411yescharacteristic
138C22×C4×C73C2×D412yes—
139C22×C4×C73#4112yes—
140M16×C73—48no—
141C2×C8×C73—24no—
142C2×C8×C73—42no—
143C2×C8×C73—42no—
144C2×C8×C73—42no—
145C2×C8×C73—42no—
146C2×C8×C73—42no—
147C22⋊C4×C73—42no—
148C22⋊C4×C73—42no—
149C22⋊C4×C73—42no—
150C22⋊C4×C73—42no—
151C22⋊C4×C73—41no—
152C22⋊C4×C73—42no—
153C22⋊C4×C73—41no—
154C23×C73—21no—
155C23×C73—21no—
156C23×C73—21no—
157C23×C73—21no—
158C23×C73—24no—
159C23×C73—24no—
160C23×C73—21no—
161C23×C73—21no—
162C23×C73—21no—
163C23×C73—21no—
164C23×C73—21no—
165C23×C73—21no—
166C23×C73—21no—
167C23×C73—21no—
168C23×C73—21no—
169C23×C73—21no—
170C23×C73—21no—
171C23×C73—21no—
172C23×C73—22no—
173C23×C73—24no—
174C23×C73—44no—
175C23×C73—44no—
176C23×C73—44no—
177C23×C73—44no—
178C23×C73—42no—
179C23×C73—42no—
180C23×C73—42no—
181C23×C73—42no—
182C23×C73—42no—
183C23×C73—42no—
184C23×C73—42no—
185C23×C73—42no—
186C23×C73—41no—
187C23×C73—41no—
188C23×C73—41no—
189C23×C73—41no—
190C23×C73—41no—
191C23×C73—41no—
192C23×C73—42no—
193C23×C73—82no—
194C23×C73—82no—
195C23×C73—82no—
196C23×C73—82no—
197C23×C73#9912yes—
198C23×C73#10012yes—
199C23×C73C2×C22⋊C411yescharacteristic
200C23×C73C4×D412yes—
201C23×C73C2×M1611yescharacteristic
202C23×C73C2×M1611yescharacteristic
203C23×C73#13112yes—
204D4×C73—48no—
205D4×C73—48no—
206C2×C4×C73—24no—
207C2×C4×C73—24no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—21no—
211C2×C4×C73—21no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—22no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—42no—
219C2×C4×C73—42no—
220C2×C4×C73—44no—
221C2×C4×C73—44no—
222C2×C4×C73—44no—
223C2×C4×C73—42no—
224C2×C4×C73—42no—
225C2×C4×C73—42no—
226C2×C4×C73—41no—
227C2×C4×C73—41no—
228C2×C4×C73—42no—
229C2×C4×C73—41no—
230C2×C4×C73—41no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—82no—
236C2×C4×C73—82no—
237C2×C4×C73#9912yes—
238C2×C4×C73#12011yescharacteristic
239C2×C4×C73#12112yes—
240C2×C4×C73#12311yescharacteristic
241C8×C73—44no—
242C8×C73—82no—
243C22×C73—22no—
244C22×C73—22no—
245C22×C73—21no—
246C22×C73—21no—
247C22×C73—21no—
248C22×C73—21no—
249C22×C73—22no—
250C22×C73—22no—
251C22×C73—22no—
252C22×C73—22no—
253C22×C73—22no—
254C22×C73—22no—
255C22×C73—22no—
256C22×C73—22no—
257C22×C73—48no—
258C22×C73—48no—
259C22×C73—41no—
260C22×C73—41no—
261C22×C73—41no—
262C22×C73—41no—
263C22×C73—41no—
264C22×C73—41no—
265C22×C73—41no—
266C22×C73—41no—
267C22×C73—42no—
268C22×C73—42no—
269C22×C73—42no—
270C22×C73—84no—
271C22×C73—84no—
272C22×C73—81no—
273C22×C73—81no—
274C22×C73—81no—
275C22×C73—81no—
276C22×C73#38611yescharacteristic
277C22×C73#40711yescharacteristic
278C22×C73#40811yescharacteristic
279C22×C73C2×#9911yescharacteristic
280C22×C73C2×#9911yescharacteristic
281C22×C73C2×#10011yescharacteristic
282C22×C73#41311yescharacteristic
283C22×C73#43512yes—
284C22×C73#43612yes—
285C4×C73—21no—
286C4×C73—22no—
287C4×C73—22no—
288C4×C73—21no—
289C4×C73—41no—
290C4×C73—42no—
291C4×C73—81no—
292C4×C73—81no—
293#9083C7311yesmaximal, characteristic, direct product factor, Sylow
294C2×C73—22no—
295C2×C73—22no—
296C2×C73—42no—
297C2×C73—42no—
298C2×C73—82no—
299C2×C73#146211yescharacteristic
300C2×C73#146511yescharacteristic
301C2×C73#146811yescharacteristic
302C2×C73#147111yescharacteristic
303C2×C73#187011yescharacteristic
304C2×C73#189811yescharacteristic
305C2×C73#190011yescharacteristic
306C2×#407C2×C7311yescharacteristic, complemented
307C2×#386C2×C7311yescharacteristic
308#1779C2×C7311yescharacteristic, complemented
309C2×#323C2×C7312yescomplemented
310#1280C2×C7312yescomplemented
311C73#908311yescharacteristic, direct product factor, Sylow
312C23×D4C4×C7311yescharacteristic
313C24×C4C22×C7311yescharacteristic
314C22×M16—21no—
315C22×C22⋊C4C4×C7311yescharacteristic
316C22×C22⋊C4C4×C7311yescharacteristic
317C22×C22⋊C4C22×C7311yescharacteristic
318#407—24no—
319C2×C22⋊C8—21no—
320C2×C22⋊C8—21no—
321C2×C22⋊C8—21no—
322C2×C22⋊C8C22×C7312yes—
323C2×C22⋊C8C22×C7312yes—
324#386—21no—
325#386—21no—
326#386—21no—
327#386—21no—
328C2×#95C4×C7311yescharacteristic
329C2×#95C22×C7311yescharacteristic
330#323—24no—
331C25C2×C4×C7311yescharacteristic
332C25C2×C4×C7311yescharacteristic
333C22×D4—21no—
334C22×D4—21no—
335C22×D4—22no—
336C22×D4—22no—
337C22×D4—42no—
338C22×D4—42no—
339C23×C4—22no—
340C23×C4—22no—
341C23×C4—42no—
342C23×C4—42no—
343C23×C4C2×C4×C7311yescharacteristic
344C23×C4C2×C4×C7311yescharacteristic
345C23×C4C2×C4×C7311yescharacteristic
346C23×C4C2×C4×C7311yescharacteristic
347C23×C4D4×C7311yescharacteristic
348C23×C4D4×C7311yescharacteristic
349C23×C4D4×C7311yescharacteristic
350C23×C4D4×C7311yescharacteristic
351C23×C4C23×C7311yescharacteristic
352C2×M16—24no—
353C2×M16—42no—
354C2×M16—42no—
355C22×C8—22no—
356C22×C8—22no—
357C2×C22⋊C4—21no—
358C2×C22⋊C4—21no—
359C2×C22⋊C4—21no—
360C2×C22⋊C4—21no—
361C2×C22⋊C4—22no—
362C2×C22⋊C4—21no—
363C2×C22⋊C4—21no—
364C2×C22⋊C4—22no—
365C2×C22⋊C4—42no—
366C2×C22⋊C4—42no—
367C22⋊C8—24no—
368C22⋊C8—22no—
369C22⋊C8—22no—
370C22⋊C8—22no—
371C22⋊C8—42no—
372C22⋊C8—42no—
373C22⋊C8D4×C7314yescomplemented
374#95—21no—
375#95—21no—
376#95—21no—
377#95—21no—
378C24—22no—
379C24—22no—
380C24—21no—
381C24—21no—
382C24—21no—
383C24—22no—
384C24—21no—
385C24—22no—
386C24—22no—
387C24—22no—
388C24—41no—
389C24—41no—
390C24—41no—
391C24—41no—
392C24—41no—
393C24—41no—
394C24C22⋊C4×C7311yescharacteristic
395C24C22⋊C4×C7311yescharacteristic
396C24M16×C7312yescomplemented
397C24C22×C4×C7311yescharacteristic
398C2×D4—24no—
399C2×D4—24no—
400C2×D4—48no—
401C2×D4—42no—
402C2×D4—42no—
403C2×D4—48no—
404C2×D4—42no—
405C2×D4—42no—
406C22×C4—22no—
407C22×C4—22no—
408C22×C4—21no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—22no—
413C22×C4—21no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—21no—
417C22×C4—22no—
418C22×C4—22no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—22no—
423C22×C4—22no—
424C22×C4—41no—
425C22×C4—41no—
426C22×C4—41no—
427C22×C4—41no—
428C22×C4—41no—
429C22×C4—41no—
430C22×C4—41no—
431C22×C4—48no—
432C22×C4—48no—
433C22×C4—41no—
434C22×C4—41no—
435C22×C4—41no—
436C22×C4—41no—
437C22×C4—41no—
438C22×C4—41no—
439C22×C4C22⋊C4×C7311yescharacteristic
440C22×C4C22⋊C4×C7311yescharacteristic
441C22×C4M16×C7312yescomplemented
442C22×C4C2×D4×C7311yescharacteristic
443C22×C4C2×D4×C7311yescharacteristic
444C22×C4C2×D4×C7312yes—
445C22×C4#41×C7312yes—
446M16—48no—
447C2×C8—24no—
448C2×C8—42no—
449C2×C8—42no—
450C2×C8—42no—
451C2×C8—42no—
452C2×C8—42no—
453C22⋊C4—42no—
454C22⋊C4—42no—
455C22⋊C4—42no—
456C22⋊C4—42no—
457C22⋊C4—41no—
458C22⋊C4—42no—
459C22⋊C4—41no—
460C23—21no—
461C23—21no—
462C23—21no—
463C23—21no—
464C23—24no—
465C23—24no—
466C23—21no—
467C23—21no—
468C23—21no—
469C23—21no—
470C23—21no—
471C23—21no—
472C23—21no—
473C23—21no—
474C23—21no—
475C23—21no—
476C23—21no—
477C23—21no—
478C23—22no—
479C23—24no—
480C23—44no—
481C23—44no—
482C23—44no—
483C23—44no—
484C23—42no—
485C23—42no—
486C23—42no—
487C23—42no—
488C23—42no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23—41no—
497C23—41no—
498C23—42no—
499C23—82no—
500C23—82no—
501C23—82no—
502C23—82no—
503C23#99×C7312yes—
504C23#100×C7312yes—
505C23C2×C22⋊C4×C7311yescharacteristic
506C23C4×D4×C7312yes—
507C23C2×M16×C7311yescharacteristic
508C23C2×M16×C7311yescharacteristic
509C23#131×C7312yes—
510D4—48no—
511D4—48no—
512C2×C4—24no—
513C2×C4—24no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—22no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—44no—
527C2×C4—44no—
528C2×C4—44no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—41no—
533C2×C4—41no—
534C2×C4—42no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—82no—
542C2×C4—82no—
543C2×C4#99×C7312yes—
544C2×C4#120×C7311yescharacteristic
545C2×C4#121×C7312yes—
546C2×C4#123×C7311yescharacteristic
547C8—44no—
548C8—82no—
549C22—21no—
550C22—21no—
551C22—21no—
552C22—21no—
553C22—22no—
554C22—22no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—22no—
560C22—22no—
561C22—22no—
562C22—22no—
563C22—48no—
564C22—48no—
565C22—41no—
566C22—41no—
567C22—41no—
568C22—41no—
569C22—41no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—42no—
574C22—42no—
575C22—42no—
576C22—84no—
577C22—84no—
578C22—81no—
579C22—81no—
580C22—81no—
581C22—81no—
582C22#386×C7311yescharacteristic
583C22#407×C7311yescharacteristic
584C22#408×C7311yescharacteristic
585C22C2×#99×C7311yescharacteristic
586C22C2×#99×C7311yescharacteristic
587C22C2×#100×C7311yescharacteristic
588C22#413×C7311yescharacteristic
589C22#435×C7312yes—
590C22#436×C7312yes—
591C4—21no—
592C4—22no—
593C4—22no—
594C4—21no—
595C4—42no—
596C4—41no—
597C4—81no—
598C4—81no—
599C2—22no—
600C2—22no—
601C2—42no—
602C2—42no—
603C2—82no—
604C2C73×#146211yescharacteristic
605C2C73×#146511yescharacteristic
606C2C73×#146811yescharacteristic
607C2C73×#147111yescharacteristic
608C2C73×#187011yescharacteristic
609C2C73×#189811yescharacteristic
610C2C73×#190011yescharacteristic
subgroupG/H
center, socleC23×C73C2×C22⋊C4
commutatorC24C22×C4×C73
Frattini, cosocleC23×C4C23×C73
prime radicalC23×D4×C73C4
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C24×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×#407×C73C2semidirect
3. C73×#1779C2semidirect
4. C2×#323×C73C2semidirect
5. C73×#1280C2semidirect
67. C22⋊C8×C73D4semidirect
90. C24×C73M16semidirect
135. C22×C4×C73M16semidirect
293. #9083C73direct (N × H)
306. C2×#407C2×C73semidirect
308. #1779C2×C73semidirect
309. C2×#323C2×C73semidirect
310. #1280C2×C73semidirect
311. C73#9083direct (N × H)
373. C22⋊C8D4×C73semidirect
396. C24M16×C73semidirect
441. C22×C4M16×C73semidirect

Maximal subgroups

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

subgroupindex
C2×#407×C732
C2×#386×C732
C73×#17792
C2×#323×C732
C73×#12802
#908373