Finite Group Databasebeta

← C73×#29448 #32938852

Subgroups — C73×#29448 #32938852

Order 18688.

734 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2863C211yesmaximal, characteristic, complemented
2C73×#2293C211yesmaximal, characteristic
3C73×#2086C211yesmaximal, characteristic, complemented
4C73×#2067C211yesmaximal, characteristic
5C73×#2066C211yesmaximal, characteristic, complemented
6C73×#2055C211yesmaximal, characteristic
7C73×#1973C211yesmaximal, characteristic
8C73×#1944C211yesmaximal, characteristic, complemented
9C73×#1936C211yesmaximal, characteristic
10C73×#1935C211yesmaximal, characteristic, complemented
11C73×#1928C211yesmaximal, characteristic, complemented
12C73×#1921C211yesmaximal, characteristic, complemented
13C73×#1877C211yesmaximal, characteristic
14C73×#1864C211yesmaximal, characteristic
15C73×#1767C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C2×C4×D4×C73C2211yescharacteristic
18C2×#117×C73—21no—
19C2×#107×C73C2211yescharacteristic
20C2×#107×C73C2211yescharacteristic
21C2×#106×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×C4⋊C8×C73C2211yescharacteristic
24C2×#103×C73C2211yescharacteristic
25C2×#103×C73C2211yescharacteristic
26C2×#103×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#102×C73C2211yescharacteristic
30C2×#97×C73C2211yescharacteristic
31C2×#97×C73C2211yescharacteristic
32#391×C73C2211yescharacteristic
33#391×C73C2211yescharacteristic
34#391×C73C2211yescharacteristic
35#390×C73C2211yescharacteristic
36#390×C73C2211yescharacteristic
37#389×C73C2211yescharacteristic
38#389×C73C2211yescharacteristic
39#389×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#388×C73—21no—
43#388×C73—21no—
44#387×C73—21no—
45#387×C73—21no—
46#387×C73—21no—
47#383×C73—21no—
48C4×C4⋊C4×C73C2211yescharacteristic
49C4×C22⋊C4×C73—21no—
50C43×C73C2211yescharacteristic
51#340×C73C2211yescharacteristic
52#340×C73C2211yescharacteristic
53#340×C73C2211yescharacteristic
54#340×C73C2211yescharacteristic
55#340×C73C2211yescharacteristic
56#340×C73C2211yescharacteristic
57#336×C73C2211yescharacteristic
58#336×C73C2211yescharacteristic
59C22×Q8×C73C2311yescharacteristic
60C22×D4×C73C2311yescharacteristic
61C23×C4×C73—21no—
62C2×SD16×C73—22no—
63C2×SD16×C73—22no—
64C2×SD16×C73—41no—
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C22×C8×C73C2311yescharacteristic
69C4×D4×C73—22no—
70C4×D4×C73—22no—
71#117×C73—44no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73—21no—
77C2×C4⋊C4×C73C2311yescharacteristic
78C2×C4⋊C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73C2311yescharacteristic
82C2×C4⋊C4×C73C2311yescharacteristic
83C2×C22⋊C4×C73—21no—
84C2×C22⋊C4×C73—21no—
85C2×C22⋊C4×C73—21no—
86C2×C22⋊C4×C73—21no—
87C2×C22⋊C4×C73—21no—
88C2×C42×C73—21no—
89C2×C42×C73D411yescharacteristic
90C2×C42×C73D411yescharacteristic
91C2×C42×C73D411yescharacteristic
92C2×C42×C73D411yescharacteristic
93C2×C42×C73C2311yescharacteristic
94C2×C42×C73C2311yescharacteristic
95C2×C42×C73C2311yescharacteristic
96#107×C73—22no—
97#107×C73—41no—
98#106×C73—22no—
99C4⋊C8×C73—22no—
100C4⋊C8×C73—22no—
101#103×C73—22no—
102#103×C73—22no—
103#103×C73—41no—
104#102×C73—22no—
105#102×C73—22no—
106#102×C73—41no—
107#97×C73—41no—
108#97×C73—41no—
109#95×C73—21no—
110#95×C73—21no—
111#95×C73—21no—
112#95×C73—21no—
113#95×C73—21no—
114#95×C73—21no—
115#95×C73—21no—
116#95×C73—21no—
117#95×C73—21no—
118#95×C73—21no—
119#95×C73—21no—
120#95×C73—21no—
121C24×C73—21no—
122C2×Q8×C73—21no—
123C2×Q8×C73—21no—
124C2×Q8×C73—21no—
125C2×Q8×C73—21no—
126C2×Q8×C73—21no—
127C2×Q8×C73—21no—
128C2×D4×C73—21no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C2×D4×C73#4112yes—
134C22×C4×C73—24no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73—21no—
141C22×C4×C73—21no—
142C22×C4×C73—42no—
143C22×C4×C73—42no—
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146C22×C4×C73C2×D411yescharacteristic
147C22×C4×C73C2×D411yescharacteristic
148C22×C4×C73C2×D411yescharacteristic
149C22×C4×C73C2×D411yescharacteristic
150C22×C4×C73C2411yescharacteristic
151SD16×C73—44no—
152C2×C8×C73—21no—
153C2×C8×C73—21no—
154C2×C8×C73—21no—
155C2×C8×C73—21no—
156C2×C8×C73—21no—
157C2×C8×C73—21no—
158C2×C8×C73—21no—
159C2×C8×C73—21no—
160C2×C8×C73—21no—
161C2×C8×C73—21no—
162C2×C8×C73#4112yes—
163C2×C8×C73#4112yes—
164C4⋊C4×C73—21no—
165C4⋊C4×C73—21no—
166C4⋊C4×C73—21no—
167C4⋊C4×C73—21no—
168C4⋊C4×C73—21no—
169C4⋊C4×C73—21no—
170C4⋊C4×C73—21no—
171C4⋊C4×C73—21no—
172C4⋊C4×C73—21no—
173C4⋊C4×C73—21no—
174C4⋊C4×C73—21no—
175C4⋊C4×C73—42no—
176C4⋊C4×C73—42no—
177C4⋊C4×C73—42no—
178C4⋊C4×C73—42no—
179C4⋊C4×C73—42no—
180C4⋊C4×C73#4112yes—
181C22⋊C4×C73—24no—
182C22⋊C4×C73—42no—
183C22⋊C4×C73—42no—
184C22⋊C4×C73—42no—
185C22⋊C4×C73—42no—
186C42×C73—22no—
187C42×C73—22no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—21no—
192C42×C73—21no—
193C42×C73—21no—
194C42×C73—41no—
195C42×C73—41no—
196C42×C73—42no—
197C23×C73—22no—
198C23×C73—41no—
199C23×C73—41no—
200C23×C73—41no—
201C23×C73—41no—
202C23×C73—41no—
203C23×C73—41no—
204C23×C73C22×D411yescharacteristic
205Q8×C73—41no—
206Q8×C73—41no—
207Q8×C73—41no—
208Q8×C73—41no—
209D4×C73—22no—
210D4×C73—22no—
211D4×C73—41no—
212D4×C73—41no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—22no—
219C2×C4×C73—21no—
220C2×C4×C73—21no—
221C2×C4×C73—21no—
222C2×C4×C73—21no—
223C2×C4×C73—21no—
224C2×C4×C73—21no—
225C2×C4×C73—21no—
226C2×C4×C73—21no—
227C2×C4×C73—21no—
228C2×C4×C73—21no—
229C2×C4×C73—21no—
230C2×C4×C73—48no—
231C2×C4×C73—41no—
232C2×C4×C73—41no—
233C2×C4×C73—41no—
234C2×C4×C73—41no—
235C2×C4×C73—41no—
236C2×C4×C73—41no—
237C2×C4×C73—41no—
238C2×C4×C73—41no—
239C2×C4×C73—41no—
240C2×C4×C73—41no—
241C2×C4×C73—41no—
242C2×C4×C73—41no—
243C2×C4×C73—41no—
244C2×C4×C73—41no—
245C2×C4×C73—41no—
246C2×C4×C73—41no—
247C2×C4×C73—41no—
248C2×C4×C73—41no—
249C2×C4×C73—41no—
250C2×C4×C73—41no—
251C2×C4×C73AGL(1,ℤ/8)12yes—
252C2×C4×C73#13712yes—
253C2×C4×C73C2×#4111yescharacteristic
254C2×C4×C73C2×#4111yescharacteristic
255C2×C4×C73C2×#4111yescharacteristic
256C2×C4×C73C2×#4111yescharacteristic
257C2×C4×C73H(5,𝔽2)11yescharacteristic
258C2×C4×C732−1+411yescharacteristic
259C8×C73—22no—
260C8×C73—22no—
261C8×C73—41no—
262C8×C73—41no—
263C22×C73—42no—
264C22×C73—42no—
265C22×C73—42no—
266C22×C73—81no—
267C22×C73—81no—
268C22×C73—81no—
269C22×C73—81no—
270C22×C73#52511yescharacteristic
271C22×C73#53211yescharacteristic
272C22×C73#53711yescharacteristic
273C22×C73C2×AGL(1,ℤ/8)11yescharacteristic
274C22×C73C2×#13711yescharacteristic
275C22×C73#57511yescharacteristic
276C22×C73#57511yescharacteristic
277C4×C73—22no—
278C4×C73—22no—
279C4×C73—42no—
280C4×C73—41no—
281C4×C73—41no—
282C4×C73—41no—
283C4×C73—41no—
284C4×C73—81no—
285C4×C73—81no—
286C4×C73—81no—
287C4×C73—81no—
288C4×C73—81no—
289C4×C73—81no—
290C4×C73#55111yescharacteristic
291C4×C73#55211yescharacteristic
292C4×C73#55311yescharacteristic
293C4×C73#55611yescharacteristic
294#29448C7311yesmaximal, characteristic, direct product factor, Sylow
295C2×C73—82no—
296C2×C73#260111yescharacteristic
297C2×C73#311011yescharacteristic
298C2×C73#311111yescharacteristic
299C2×C73#317211yescharacteristic
300C2×C73#318011yescharacteristic
301C2×C73#325111yescharacteristic
302C2×C73#325211yescharacteristic
303#2863C2×C7311yescharacteristic, complemented
304#2293C2×C7311yescharacteristic
305#2086C2×C7311yescharacteristic, complemented
306#2067C2×C7311yescharacteristic
307#2066C2×C7311yescharacteristic, complemented
308#2055C2×C7311yescharacteristic
309#1973C2×C7311yescharacteristic
310#1944C2×C7311yescharacteristic, complemented
311#1936C2×C7311yescharacteristic
312#1935C2×C7311yescharacteristic, complemented
313#1928C2×C7311yescharacteristic, complemented
314#1921C2×C7311yescharacteristic, complemented
315#1877C2×C7311yescharacteristic
316#1864C2×C7311yescharacteristic
317#1767C2×C7311yescharacteristic, complemented
318C73#2944811yescharacteristic, direct product factor, Sylow
319C22×SD16C22×C7311yescharacteristic
320C2×C4×D4C22×C7311yescharacteristic
321C2×#117—21no—
322C2×#107C22×C7311yescharacteristic
323C2×#107C22×C7311yescharacteristic
324C2×#106C22×C7311yescharacteristic
325C2×C4⋊C8C22×C7311yescharacteristic
326C2×C4⋊C8C22×C7311yescharacteristic
327C2×#103C22×C7311yescharacteristic
328C2×#103C22×C7311yescharacteristic
329C2×#103C22×C7311yescharacteristic
330C2×#102C22×C7311yescharacteristic
331C2×#102C22×C7311yescharacteristic
332C2×#102C22×C7311yescharacteristic
333C2×#97C22×C7311yescharacteristic
334C2×#97C22×C7311yescharacteristic
335#391C22×C7311yescharacteristic
336#391C22×C7311yescharacteristic
337#391C22×C7311yescharacteristic
338#390C22×C7311yescharacteristic
339#390C22×C7311yescharacteristic
340#389C22×C7311yescharacteristic
341#389C22×C7311yescharacteristic
342#389C22×C7311yescharacteristic
343#389C22×C7311yescharacteristic
344#389C22×C7311yescharacteristic
345#388—21no—
346#388—21no—
347#387—21no—
348#387—21no—
349#387—21no—
350#383—21no—
351C4×C4⋊C4C22×C7311yescharacteristic
352C4×C22⋊C4—21no—
353C43C22×C7311yescharacteristic
354#340C22×C7311yescharacteristic
355#340C22×C7311yescharacteristic
356#340C22×C7311yescharacteristic
357#340C22×C7311yescharacteristic
358#340C22×C7311yescharacteristic
359#340C22×C7311yescharacteristic
360#336C22×C7311yescharacteristic
361#336C22×C7311yescharacteristic
362C22×Q8C23×C7311yescharacteristic
363C22×D4C23×C7311yescharacteristic
364C23×C4—21no—
365C2×SD16—22no—
366C2×SD16—22no—
367C2×SD16—41no—
368C22×C8C23×C7311yescharacteristic
369C22×C8C23×C7311yescharacteristic
370C22×C8C23×C7311yescharacteristic
371C22×C8C23×C7311yescharacteristic
372C4×D4—22no—
373C4×D4—22no—
374#117—44no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4C23×C7311yescharacteristic
381C2×C4⋊C4C23×C7311yescharacteristic
382C2×C4⋊C4C23×C7311yescharacteristic
383C2×C4⋊C4C23×C7311yescharacteristic
384C2×C4⋊C4C23×C7311yescharacteristic
385C2×C4⋊C4C23×C7311yescharacteristic
386C2×C22⋊C4—21no—
387C2×C22⋊C4—21no—
388C2×C22⋊C4—21no—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C42—21no—
392C2×C42D4×C7311yescharacteristic
393C2×C42D4×C7311yescharacteristic
394C2×C42D4×C7311yescharacteristic
395C2×C42D4×C7311yescharacteristic
396C2×C42C23×C7311yescharacteristic
397C2×C42C23×C7311yescharacteristic
398C2×C42C23×C7311yescharacteristic
399#107—22no—
400#107—41no—
401#106—22no—
402C4⋊C8—22no—
403C4⋊C8—22no—
404#103—22no—
405#103—22no—
406#103—41no—
407#102—22no—
408#102—22no—
409#102—41no—
410#97—41no—
411#97—41no—
412#95—21no—
413#95—21no—
414#95—21no—
415#95—21no—
416#95—21no—
417#95—21no—
418#95—21no—
419#95—21no—
420#95—21no—
421#95—21no—
422#95—21no—
423#95—21no—
424C24—21no—
425C2×Q8—21no—
426C2×Q8—21no—
427C2×Q8—21no—
428C2×Q8—21no—
429C2×Q8—21no—
430C2×Q8—21no—
431C2×D4—21no—
432C2×D4—21no—
433C2×D4—21no—
434C2×D4—21no—
435C2×D4—21no—
436C2×D4#41×C7312yes—
437C22×C4—24no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—42no—
446C22×C4—42no—
447C22×C4C2×D4×C7311yescharacteristic
448C22×C4C2×D4×C7311yescharacteristic
449C22×C4C2×D4×C7311yescharacteristic
450C22×C4C2×D4×C7311yescharacteristic
451C22×C4C2×D4×C7311yescharacteristic
452C22×C4C2×D4×C7311yescharacteristic
453C22×C4C24×C7311yescharacteristic
454SD16—44no—
455C2×C8—21no—
456C2×C8—21no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—21no—
462C2×C8—21no—
463C2×C8—21no—
464C2×C8—21no—
465C2×C8#41×C7312yes—
466C2×C8#41×C7312yes—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—21no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—21no—
473C4⋊C4—21no—
474C4⋊C4—21no—
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—21no—
478C4⋊C4—42no—
479C4⋊C4—42no—
480C4⋊C4—42no—
481C4⋊C4—42no—
482C4⋊C4—42no—
483C4⋊C4#41×C7312yes—
484C22⋊C4—24no—
485C22⋊C4—42no—
486C22⋊C4—42no—
487C22⋊C4—42no—
488C22⋊C4—42no—
489C42—22no—
490C42—22no—
491C42—21no—
492C42—21no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—21no—
497C42—41no—
498C42—41no—
499C42—42no—
500C23—22no—
501C23—41no—
502C23—41no—
503C23—41no—
504C23—41no—
505C23—41no—
506C23—41no—
507C23C22×D4×C7311yescharacteristic
508Q8—41no—
509Q8—41no—
510Q8—41no—
511Q8—41no—
512D4—22no—
513D4—22no—
514D4—41no—
515D4—41no—
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—21no—
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—48no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—41no—
553C2×C4—41no—
554C2×C4AGL(1,ℤ/8)×C7312yes—
555C2×C4#137×C7312yes—
556C2×C4C2×#41×C7311yescharacteristic
557C2×C4C2×#41×C7311yescharacteristic
558C2×C4C2×#41×C7311yescharacteristic
559C2×C4C2×#41×C7311yescharacteristic
560C2×C4H(5,𝔽2)×C7311yescharacteristic
561C2×C42−1+4×C7311yescharacteristic
562C8—22no—
563C8—22no—
564C8—41no—
565C8—41no—
566C22—42no—
567C22—42no—
568C22—42no—
569C22—81no—
570C22—81no—
571C22—81no—
572C22—81no—
573C22#525×C7311yescharacteristic
574C22#532×C7311yescharacteristic
575C22#537×C7311yescharacteristic
576C22C2×AGL(1,ℤ/8)×C7311yescharacteristic
577C22C2×#137×C7311yescharacteristic
578C22#575×C7311yescharacteristic
579C22#575×C7311yescharacteristic
580C4—22no—
581C4—22no—
582C4—41no—
583C4—41no—
584C4—42no—
585C4—41no—
586C4—41no—
587C4—81no—
588C4—81no—
589C4—81no—
590C4—81no—
591C4—81no—
592C4—81no—
593C4#551×C7311yescharacteristic
594C4#552×C7311yescharacteristic
595C4#553×C7311yescharacteristic
596C4#556×C7311yescharacteristic
597C2—82no—
598C2C73×#260111yescharacteristic
599C2C73×#311011yescharacteristic
600C2C73×#311111yescharacteristic
601C2C73×#317211yescharacteristic
602C2C73×#318011yescharacteristic
603C2C73×#325111yescharacteristic
604C2C73×#325211yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ C43×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#2863C2semidirect
3. C73×#2086C2semidirect
5. C73×#2066C2semidirect
8. C73×#1944C2semidirect
10. C73×#1935C2semidirect
11. C73×#1928C2semidirect
12. C73×#1921C2semidirect
15. C73×#1767C2semidirect
294. #29448C73direct (N × H)
303. #2863C2×C73semidirect
305. #2086C2×C73semidirect
307. #2066C2×C73semidirect
310. #1944C2×C73semidirect
312. #1935C2×C73semidirect
313. #1928C2×C73semidirect
314. #1921C2×C73semidirect
317. #1767C2×C73semidirect
318. C73#29448direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#28632
C73×#22932
C73×#20862
C73×#20672
C73×#20662
C73×#20552
C73×#19732
C73×#19442
C73×#19362
C73×#19352
C73×#19282
C73×#19212
C73×#18772
C73×#18642
C73×#17672
#2944873