Finite Group Databasebeta

← C73×#29442 #32938846

Subgroups — C73×#29442 #32938846

Order 18688.

660 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#2644C211yesmaximal, characteristic
2C73×#2320C211yesmaximal, characteristic, complemented
3C73×#2088C211yesmaximal, characteristic, complemented
4C73×#2066C211yesmaximal, characteristic, complemented
5C73×#2065C211yesmaximal, characteristic
6C73×#2055C211yesmaximal, characteristic
7C73×#1968C211yesmaximal, characteristic
8C73×#1941C211yesmaximal, characteristic, complemented
9C73×#1936C211yesmaximal, characteristic
10C73×#1935C211yesmaximal, characteristic, complemented
11C73×#1926C211yesmaximal, characteristic
12C73×#1920C211yesmaximal, characteristic, complemented
13C73×#1880C211yesmaximal, characteristic
14C73×#1865C211yesmaximal, characteristic, complemented
15C73×#1768C211yesmaximal, characteristic, complemented
16C22×SD16×C73C2211yescharacteristic
17C2×C4×Q8×C73C2211yescharacteristic
18C2×#106×C73C2211yescharacteristic
19C2×#106×C73C2211yescharacteristic
20C2×#106×C73C2211yescharacteristic
21C2×C4⋊C8×C73C2211yescharacteristic
22C2×C4⋊C8×C73C2211yescharacteristic
23C2×#103×C73C2211yescharacteristic
24C2×#103×C73C2211yescharacteristic
25C2×#103×C73C2211yescharacteristic
26C2×#102×C73C2211yescharacteristic
27C2×#102×C73C2211yescharacteristic
28C2×#102×C73C2211yescharacteristic
29C2×#97×C73C2211yescharacteristic
30C2×C4×C8×C73C2211yescharacteristic
31#397×C73—21no—
32#397×C73—21no—
33#397×C73—21no—
34#396×C73—21no—
35#391×C73C2211yescharacteristic
36#391×C73C2211yescharacteristic
37#390×C73C2211yescharacteristic
38#390×C73C2211yescharacteristic
39#390×C73C2211yescharacteristic
40#389×C73C2211yescharacteristic
41#389×C73C2211yescharacteristic
42#389×C73C2211yescharacteristic
43#389×C73C2211yescharacteristic
44#389×C73C2211yescharacteristic
45#387×C73—21no—
46#387×C73—21no—
47#383×C73—21no—
48#382×C73—21no—
49C4×C4⋊C4×C73C2211yescharacteristic
50#376×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
61C2×SD16×C73—22no—
62C2×SD16×C73—22no—
63C2×SD16×C73—41no—
64C22×C8×C73C2311yescharacteristic
65C22×C8×C73C2311yescharacteristic
66C22×C8×C73C2311yescharacteristic
67C22×C8×C73C2311yescharacteristic
68C4×Q8×C73—22no—
69C4×Q8×C73—22no—
70C2×C4⋊C4×C73—21no—
71C2×C4⋊C4×C73—21no—
72C2×C4⋊C4×C73—21no—
73C2×C4⋊C4×C73—21no—
74C2×C4⋊C4×C73—21no—
75C2×C4⋊C4×C73—21no—
76C2×C4⋊C4×C73C2311yescharacteristic
77C2×C4⋊C4×C73C2311yescharacteristic
78C2×C4⋊C4×C73C2311yescharacteristic
79C2×C4⋊C4×C73C2311yescharacteristic
80C2×C4⋊C4×C73C2311yescharacteristic
81C2×C4⋊C4×C73C2311yescharacteristic
82C2×C22⋊C4×C73—21no—
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×C73—21no—
90C2×C42×C73C2311yescharacteristic
91C2×C42×C73C2311yescharacteristic
92C2×C42×C73C2311yescharacteristic
93#106×C73—22no—
94#106×C73—22no—
95#106×C73—41no—
96C4⋊C8×C73—22no—
97C4⋊C8×C73—22no—
98#103×C73—22no—
99#103×C73—22no—
100#103×C73—41no—
101#102×C73—22no—
102#102×C73—22no—
103#102×C73—41no—
104#97×C73—41no—
105C4×C8×C73—41no—
106#95×C73—21no—
107#95×C73—21no—
108#95×C73—21no—
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×C73D411yescharacteristic
117#95×C73D411yescharacteristic
118#95×C73D411yescharacteristic
119#95×C73D411yescharacteristic
120C24×C73—21no—
121C2×Q8×C73—21no—
122C2×Q8×C73—21no—
123C2×Q8×C73—21no—
124C2×Q8×C73—21no—
125C2×Q8×C73—21no—
126C2×Q8×C73#4112yes—
127C2×D4×C73—21no—
128C2×D4×C73—21no—
129C2×D4×C73—21no—
130C2×D4×C73—21no—
131C2×D4×C73—21no—
132C2×D4×C73—21no—
133C22×C4×C73—21no—
134C22×C4×C73—21no—
135C22×C4×C73—21no—
136C22×C4×C73—21no—
137C22×C4×C73—21no—
138C22×C4×C73—21no—
139C22×C4×C73—21no—
140C22×C4×C73C2×D411yescharacteristic
141C22×C4×C73C2×D411yescharacteristic
142C22×C4×C73C2×D411yescharacteristic
143C22×C4×C73C2×D411yescharacteristic
144C22×C4×C73C2×D411yescharacteristic
145C22×C4×C73C2×D411yescharacteristic
146C22×C4×C73C2411yescharacteristic
147SD16×C73—44no—
148C2×C8×C73—21no—
149C2×C8×C73—21no—
150C2×C8×C73—21no—
151C2×C8×C73—21no—
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#4112yes—
159C2×C8×C73#4112yes—
160C4⋊C4×C73—24no—
161C4⋊C4×C73—21no—
162C4⋊C4×C73—21no—
163C4⋊C4×C73—21no—
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—81no—
173C4⋊C4×C73—81no—
174C4⋊C4×C73—81no—
175C4⋊C4×C73—81no—
176C4⋊C4×C73—81no—
177C4⋊C4×C73#4112yes—
178C22⋊C4×C73—81no—
179C22⋊C4×C73—81no—
180C22⋊C4×C73—81no—
181C22⋊C4×C73—81no—
182C22⋊C4×C73—81no—
183C22⋊C4×C73—81no—
184C42×C73—24no—
185C42×C73—21no—
186C42×C73—21no—
187C42×C73—21no—
188C42×C73—21no—
189C42×C73—21no—
190C42×C73—21no—
191C42×C73—81no—
192C23×C73—41no—
193C23×C73—41no—
194C23×C73—41no—
195C23×C73—41no—
196C23×C73—41no—
197C23×C73—41no—
198C23×C73—41no—
199C23×C73C22×D411yescharacteristic
200Q8×C73—22no—
201Q8×C73—22no—
202Q8×C73—41no—
203Q8×C73—41no—
204D4×C73—41no—
205D4×C73—41no—
206D4×C73—41no—
207D4×C73—41no—
208C2×C4×C73—21no—
209C2×C4×C73—21no—
210C2×C4×C73—22no—
211C2×C4×C73—22no—
212C2×C4×C73—21no—
213C2×C4×C73—21no—
214C2×C4×C73—21no—
215C2×C4×C73—21no—
216C2×C4×C73—21no—
217C2×C4×C73—21no—
218C2×C4×C73—21no—
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—41no—
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—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×C73C2×#4111yescharacteristic
248C2×C4×C73C2×#4111yescharacteristic
249C2×C4×C73C2×#4111yescharacteristic
250C2×C4×C73C2×#4111yescharacteristic
251C2×C4×C73H(5,𝔽2)11yescharacteristic
252C2×C4×C732−1+411yescharacteristic
253C8×C73—22no—
254C8×C73—22no—
255C8×C73—41no—
256C8×C73—41no—
257C22×C73—81no—
258C22×C73—81no—
259C22×C73—81no—
260C22×C73—81no—
261C22×C73—81no—
262C22×C73—81no—
263C22×C73—81no—
264C22×C73#52511yescharacteristic
265C22×C73#53211yescharacteristic
266C22×C73#53711yescharacteristic
267C22×C73#57711yescharacteristic
268C22×C73#57711yescharacteristic
269C22×C73#57711yescharacteristic
270C22×C73#57711yescharacteristic
271C4×C73—42no—
272C4×C73—41no—
273C4×C73—42no—
274C4×C73—41no—
275C4×C73—41no—
276C4×C73—41no—
277C4×C73—41no—
278C4×C73—41no—
279C4×C73—81no—
280C4×C73—81no—
281C4×C73—81no—
282C4×C73—81no—
283C4×C73—81no—
284C4×C73#55111yescharacteristic
285C4×C73#55211yescharacteristic
286C4×C73#55311yescharacteristic
287C4×C73#55611yescharacteristic
288#29442C7311yesmaximal, characteristic, direct product factor, Sylow
289C2×C73—161no—
290C2×C73#260111yescharacteristic
291C2×C73#312511yescharacteristic
292C2×C73#312611yescharacteristic
293C2×C73#317311yescharacteristic
294C2×C73#317411yescharacteristic
295C2×C73#326011yescharacteristic
296C2×C73#326311yescharacteristic
297#2644C2×C7311yescharacteristic
298#2320C2×C7311yescharacteristic, complemented
299#2088C2×C7311yescharacteristic, complemented
300#2066C2×C7311yescharacteristic, complemented
301#2065C2×C7311yescharacteristic
302#2055C2×C7311yescharacteristic
303#1968C2×C7311yescharacteristic
304#1941C2×C7311yescharacteristic, complemented
305#1936C2×C7311yescharacteristic
306#1935C2×C7311yescharacteristic, complemented
307#1926C2×C7311yescharacteristic
308#1920C2×C7311yescharacteristic, complemented
309#1880C2×C7311yescharacteristic
310#1865C2×C7311yescharacteristic, complemented
311#1768C2×C7311yescharacteristic, complemented
312C73#2944211yescharacteristic, direct product factor, Sylow
313C22×SD16C22×C7311yescharacteristic
314C2×C4×Q8C22×C7311yescharacteristic
315C2×#106C22×C7311yescharacteristic
316C2×#106C22×C7311yescharacteristic
317C2×#106C22×C7311yescharacteristic
318C2×C4⋊C8C22×C7311yescharacteristic
319C2×C4⋊C8C22×C7311yescharacteristic
320C2×#103C22×C7311yescharacteristic
321C2×#103C22×C7311yescharacteristic
322C2×#103C22×C7311yescharacteristic
323C2×#102C22×C7311yescharacteristic
324C2×#102C22×C7311yescharacteristic
325C2×#102C22×C7311yescharacteristic
326C2×#97C22×C7311yescharacteristic
327C2×C4×C8C22×C7311yescharacteristic
328#397—21no—
329#397—21no—
330#397—21no—
331#396—21no—
332#391C22×C7311yescharacteristic
333#391C22×C7311yescharacteristic
334#390C22×C7311yescharacteristic
335#390C22×C7311yescharacteristic
336#390C22×C7311yescharacteristic
337#389C22×C7311yescharacteristic
338#389C22×C7311yescharacteristic
339#389C22×C7311yescharacteristic
340#389C22×C7311yescharacteristic
341#389C22×C7311yescharacteristic
342#387—21no—
343#387—21no—
344#383—21no—
345#382—21no—
346C4×C4⋊C4C22×C7311yescharacteristic
347#376C22×C7311yescharacteristic
348#340C22×C7311yescharacteristic
349#340C22×C7311yescharacteristic
350#340C22×C7311yescharacteristic
351#340C22×C7311yescharacteristic
352#340C22×C7311yescharacteristic
353#340C22×C7311yescharacteristic
354#336C22×C7311yescharacteristic
355#336C22×C7311yescharacteristic
356C22×Q8C23×C7311yescharacteristic
357C22×D4C23×C7311yescharacteristic
358C2×SD16—22no—
359C2×SD16—22no—
360C2×SD16—41no—
361C22×C8C23×C7311yescharacteristic
362C22×C8C23×C7311yescharacteristic
363C22×C8C23×C7311yescharacteristic
364C22×C8C23×C7311yescharacteristic
365C4×Q8—22no—
366C4×Q8—22no—
367C2×C4⋊C4—21no—
368C2×C4⋊C4—21no—
369C2×C4⋊C4—21no—
370C2×C4⋊C4—21no—
371C2×C4⋊C4—21no—
372C2×C4⋊C4—21no—
373C2×C4⋊C4C23×C7311yescharacteristic
374C2×C4⋊C4C23×C7311yescharacteristic
375C2×C4⋊C4C23×C7311yescharacteristic
376C2×C4⋊C4C23×C7311yescharacteristic
377C2×C4⋊C4C23×C7311yescharacteristic
378C2×C4⋊C4C23×C7311yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—21no—
381C2×C22⋊C4—21no—
382C2×C22⋊C4—21no—
383C2×C22⋊C4—21no—
384C2×C22⋊C4—21no—
385C2×C42—21no—
386C2×C42—21no—
387C2×C42C23×C7311yescharacteristic
388C2×C42C23×C7311yescharacteristic
389C2×C42C23×C7311yescharacteristic
390#106—22no—
391#106—22no—
392#106—41no—
393C4⋊C8—22no—
394C4⋊C8—22no—
395#103—22no—
396#103—22no—
397#103—41no—
398#102—22no—
399#102—22no—
400#102—41no—
401#97—41no—
402C4×C8—41no—
403#95—21no—
404#95—21no—
405#95—21no—
406#95—21no—
407#95—21no—
408#95—21no—
409#95—21no—
410#95—21no—
411#95—21no—
412#95—21no—
413#95D4×C7311yescharacteristic
414#95D4×C7311yescharacteristic
415#95D4×C7311yescharacteristic
416#95D4×C7311yescharacteristic
417C24—21no—
418C2×Q8—21no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8#41×C7312yes—
424C2×D4—21no—
425C2×D4—21no—
426C2×D4—21no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—21no—
435C22×C4—21no—
436C22×C4—21no—
437C22×C4C2×D4×C7311yescharacteristic
438C22×C4C2×D4×C7311yescharacteristic
439C22×C4C2×D4×C7311yescharacteristic
440C22×C4C2×D4×C7311yescharacteristic
441C22×C4C2×D4×C7311yescharacteristic
442C22×C4C2×D4×C7311yescharacteristic
443C22×C4C24×C7311yescharacteristic
444SD16—44no—
445C2×C8—21no—
446C2×C8—21no—
447C2×C8—21no—
448C2×C8—21no—
449C2×C8—21no—
450C2×C8—21no—
451C2×C8—21no—
452C2×C8—21no—
453C2×C8—21no—
454C2×C8—21no—
455C2×C8#41×C7312yes—
456C2×C8#41×C7312yes—
457C4⋊C4—24no—
458C4⋊C4—21no—
459C4⋊C4—21no—
460C4⋊C4—21no—
461C4⋊C4—21no—
462C4⋊C4—21no—
463C4⋊C4—21no—
464C4⋊C4—21no—
465C4⋊C4—21no—
466C4⋊C4—21no—
467C4⋊C4—21no—
468C4⋊C4—21no—
469C4⋊C4—81no—
470C4⋊C4—81no—
471C4⋊C4—81no—
472C4⋊C4—81no—
473C4⋊C4—81no—
474C4⋊C4#41×C7312yes—
475C22⋊C4—81no—
476C22⋊C4—81no—
477C22⋊C4—81no—
478C22⋊C4—81no—
479C22⋊C4—81no—
480C22⋊C4—81no—
481C42—24no—
482C42—21no—
483C42—21no—
484C42—21no—
485C42—21no—
486C42—21no—
487C42—21no—
488C42—81no—
489C23—41no—
490C23—41no—
491C23—41no—
492C23—41no—
493C23—41no—
494C23—41no—
495C23—41no—
496C23C22×D4×C7311yescharacteristic
497Q8—22no—
498Q8—22no—
499Q8—41no—
500Q8—41no—
501D4—41no—
502D4—41no—
503D4—41no—
504D4—41no—
505C2×C4—21no—
506C2×C4—21no—
507C2×C4—22no—
508C2×C4—22no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—21no—
513C2×C4—21no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—21no—
523C2×C4—21no—
524C2×C4—21no—
525C2×C4—41no—
526C2×C4—41no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—41no—
530C2×C4—41no—
531C2×C4—41no—
532C2×C4—41no—
533C2×C4—41no—
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×C4C2×#41×C7311yescharacteristic
545C2×C4C2×#41×C7311yescharacteristic
546C2×C4C2×#41×C7311yescharacteristic
547C2×C4C2×#41×C7311yescharacteristic
548C2×C4H(5,𝔽2)×C7311yescharacteristic
549C2×C42−1+4×C7311yescharacteristic
550C8—22no—
551C8—22no—
552C8—41no—
553C8—41no—
554C22—81no—
555C22—81no—
556C22—81no—
557C22—81no—
558C22—81no—
559C22—81no—
560C22—81no—
561C22#525×C7311yescharacteristic
562C22#532×C7311yescharacteristic
563C22#537×C7311yescharacteristic
564C22#577×C7311yescharacteristic
565C22#577×C7311yescharacteristic
566C22#577×C7311yescharacteristic
567C22#577×C7311yescharacteristic
568C4—41no—
569C4—41no—
570C4—42no—
571C4—41no—
572C4—42no—
573C4—41no—
574C4—41no—
575C4—41no—
576C4—81no—
577C4—81no—
578C4—81no—
579C4—81no—
580C4—81no—
581C4#551×C7311yescharacteristic
582C4#552×C7311yescharacteristic
583C4#553×C7311yescharacteristic
584C4#556×C7311yescharacteristic
585C2—161no—
586C2C73×#260111yescharacteristic
587C2C73×#312511yescharacteristic
588C2C73×#312611yescharacteristic
589C2C73×#317311yescharacteristic
590C2C73×#317411yescharacteristic
591C2C73×#326011yescharacteristic
592C2C73×#326311yescharacteristic
subgroupG/H
center, socleC23×C73C22×D4
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC22×D4×C73C23
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C73 ◁ #376×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#2320C2semidirect
3. C73×#2088C2semidirect
4. C73×#2066C2semidirect
8. C73×#1941C2semidirect
10. C73×#1935C2semidirect
12. C73×#1920C2semidirect
14. C73×#1865C2semidirect
15. C73×#1768C2semidirect
288. #29442C73direct (N × H)
298. #2320C2×C73semidirect
299. #2088C2×C73semidirect
300. #2066C2×C73semidirect
304. #1941C2×C73semidirect
306. #1935C2×C73semidirect
308. #1920C2×C73semidirect
310. #1865C2×C73semidirect
311. #1768C2×C73semidirect
312. C73#29442direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#26442
C73×#23202
C73×#20882
C73×#20662
C73×#20652
C73×#20552
C73×#19682
C73×#19412
C73×#19362
C73×#19352
C73×#19262
C73×#19202
C73×#18802
C73×#18652
C73×#17682
#2944273