Finite Group Databasebeta

← C73×#25664 #32935068

Subgroups — C73×#25664 #32935068

Order 18688.

1136 conjugacy classes of subgroups.

The subgroup lattice has 674 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3505C211yesmaximal, characteristic
2C73×#2504C211yesmaximal, characteristic, complemented
3C73×#2502C211yesmaximal, characteristic, complemented
4C73×#2487C211yesmaximal, characteristic, complemented
5C73×#2044C214yesmaximal, complemented
6C73×#1996C211yesmaximal, characteristic, complemented
7C73×#1964C211yesmaximal, characteristic, complemented
8C73×#1867C214yesmaximal, complemented
9C4×#99×C73C211yesmaximal, characteristic, complemented
10#553×C73—21no—
11#553×C73—22no—
12#552×C73—21no—
13#551×C73—22no—
14#548×C73—21no—
15#546×C73—21no—
16#539×C73—21no—
17#538×C73—21no—
18#534×C73C2212yes—
19#529×C73—21no—
20#525×C73—21no—
21C2×C22⋊Q8×C73C2211yescharacteristic
22C2×#121×C73C2211yescharacteristic
23#518×C73C2212yes—
24C2×C4×D4×C73C2211yescharacteristic
25C22×C4⋊C4×C73C2211yescharacteristic
26C2×#99×C73C2214yes—
27C2×#99×C73C2212yes—
28#400×C73—21no—
29#399×C73—21no—
30#398×C73—22no—
31#397×C73—22no—
32#391×C73—21no—
33#390×C73—21no—
34#389×C73—21no—
35#386×C73C2212yes—
36#386×C73C2214yes—
37#385×C73C2212yes—
38#385×C73C2214yes—
39#384×C73—21no—
40#382×C73—21no—
41#380×C73—21no—
42#380×C73C2211yescharacteristic
43C4×C22⋊C4×C73C2211yescharacteristic
44C4×C22⋊C4×C73C2211yescharacteristic
45#342×C73C2214yes—
46#342×C73C2212yes—
47C2×#41×C73—21no—
48C22×Q8×C73D411yescharacteristic
49C22×D4×C73D411yescharacteristic
50C22×D4×C73C2311yescharacteristic
51C22×D4×C73C2312yes—
52C23×C4×C73D411yescharacteristic
53C23×C4×C73C2312yes—
54C23×C4×C73C2311yescharacteristic
55#126×C73—22no—
56#126×C73—22no—
57#126×C73—22no—
58#125×C73—21no—
59#125×C73—22no—
60#124×C73—21no—
61#124×C73—22no—
62#123×C73—22no—
63#123×C73—22no—
64#123×C73—22no—
65#123×C73—22no—
66#123×C73—22no—
67C22⋊Q8×C73—21no—
68C22⋊Q8×C73—22no—
69C22⋊Q8×C73—21no—
70C22⋊Q8×C73—21no—
71C22⋊Q8×C73—21no—
72C22⋊Q8×C73—21no—
73#121×C73—21no—
74#121×C73—22no—
75#121×C73—21no—
76#121×C73—21no—
77#121×C73—21no—
78#121×C73—21no—
79#121×C73—22no—
80#121×C73—22no—
81#120×C73—22no—
82#120×C73—22no—
83C4×Q8×C73—21no—
84C4×D4×C73—22no—
85C4×D4×C73—21no—
86C4×D4×C73—21no—
87C4×D4×C73—21no—
88C4×D4×C73—21no—
89C4×D4×C73—21no—
90C4×D4×C73—22no—
91C4×D4×C73—22no—
92C4×D4×C73—22no—
93C4×D4×C73—22no—
94#117×C73—21no—
95#117×C73—22no—
96#117×C73—22no—
97C2×C4⋊C4×C73—21no—
98C2×C4⋊C4×C73—21no—
99C2×C4⋊C4×C73—21no—
100C2×C4⋊C4×C73—21no—
101C2×C4⋊C4×C73—21no—
102C2×C4⋊C4×C73—21no—
103C2×C4⋊C4×C73—21no—
104C2×C4⋊C4×C73—24no—
105C2×C4⋊C4×C73—22no—
106C2×C4⋊C4×C73D411yescharacteristic
107C2×C4⋊C4×C73D411yescharacteristic
108C2×C4⋊C4×C73D412yes—
109C2×C4⋊C4×C73D411yescharacteristic
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—24no—
113C2×C22⋊C4×C73D412yes—
114C2×C22⋊C4×C73D411yescharacteristic
115C2×C22⋊C4×C73C2312yes—
116C2×C22⋊C4×C73C2312yes—
117C2×C22⋊C4×C73C2311yescharacteristic
118C2×C22⋊C4×C73C2312yes—
119C2×C22⋊C4×C73C2312yes—
120C2×C42×C73—21no—
121C2×C42×C73—21no—
122C2×C42×C73D411yescharacteristic
123#99×C73—28no—
124#99×C73—24no—
125#95×C73—21no—
126#95×C73—21no—
127#95×C73—22no—
128#95×C73—21no—
129#95×C73—24no—
130#95×C73—24no—
131#95×C73—22no—
132C24×C73C2×D412yes—
133C24×C73C2×D411yescharacteristic
134C24×C73C2411yescharacteristic
135#41×C73—82no—
136C2×Q8×C73—21no—
137C2×Q8×C73—21no—
138C2×Q8×C73—42no—
139C2×D4×C73—21no—
140C2×D4×C73—22no—
141C2×D4×C73—21no—
142C2×D4×C73—22no—
143C2×D4×C73—22no—
144C2×D4×C73—24no—
145C2×D4×C73—22no—
146C2×D4×C73—24no—
147C2×D4×C73—22no—
148C2×D4×C73—22no—
149C2×D4×C73—21no—
150C2×D4×C73—21no—
151C2×D4×C73—42no—
152C22×C4×C73—22no—
153C22×C4×C73—22no—
154C22×C4×C73—22no—
155C22×C4×C73—21no—
156C22×C4×C73—21no—
157C22×C4×C73—22no—
158C22×C4×C73—22no—
159C22×C4×C73—22no—
160C22×C4×C73—22no—
161C22×C4×C73—22no—
162C22×C4×C73—42no—
163C22×C4×C73—42no—
164C22×C4×C73—82no—
165C22×C4×C73C2×D411yescharacteristic
166C22×C4×C73C2×D412yes—
167C22×C4×C73C2×D411yescharacteristic
168C22×C4×C73C2×D411yescharacteristic
169C22×C4×C73C2×D411yescharacteristic
170C22×C4×C73C2×D411yescharacteristic
171C22×C4×C73C2×D412yes—
172C22×C4×C73C2×D411yescharacteristic
173C22×C4×C73C2×D412yes—
174C22×C4×C73C2×D411yescharacteristic
175C22×C4×C73C2×D411yescharacteristic
176C22×C4×C73C2×D411yescharacteristic
177C4⋊C4×C73—22no—
178C4⋊C4×C73—22no—
179C4⋊C4×C73—22no—
180C4⋊C4×C73—22no—
181C4⋊C4×C73—21no—
182C4⋊C4×C73—22no—
183C4⋊C4×C73—21no—
184C4⋊C4×C73—21no—
185C4⋊C4×C73—21no—
186C4⋊C4×C73—21no—
187C4⋊C4×C73—22no—
188C4⋊C4×C73—21no—
189C4⋊C4×C73—42no—
190C4⋊C4×C73—41no—
191C4⋊C4×C73—41no—
192C4⋊C4×C73—41no—
193C4⋊C4×C73—41no—
194C4⋊C4×C73—84no—
195C4⋊C4×C73—82no—
196C22⋊C4×C73—22no—
197C22⋊C4×C73—22no—
198C22⋊C4×C73—22no—
199C22⋊C4×C73—22no—
200C22⋊C4×C73—22no—
201C22⋊C4×C73—22no—
202C22⋊C4×C73—21no—
203C22⋊C4×C73—22no—
204C22⋊C4×C73—21no—
205C22⋊C4×C73—22no—
206C22⋊C4×C73—22no—
207C22⋊C4×C73—22no—
208C22⋊C4×C73—21no—
209C22⋊C4×C73—21no—
210C22⋊C4×C73—22no—
211C22⋊C4×C73—24no—
212C22⋊C4×C73—22no—
213C22⋊C4×C73—22no—
214C22⋊C4×C73—84no—
215C22⋊C4×C73—82no—
216C22⋊C4×C73#4114yescomplemented
217C42×C73—22no—
218C42×C73—22no—
219C42×C73—21no—
220C42×C73—21no—
221C42×C73—42no—
222C42×C73—42no—
223C23×C73—21no—
224C23×C73—22no—
225C23×C73—21no—
226C23×C73—21no—
227C23×C73—24no—
228C23×C73—41no—
229C23×C73—41no—
230C23×C73—41no—
231C23×C73—41no—
232C23×C73—42no—
233C23×C73—42no—
234C23×C73C22×D411yescharacteristic
235C23×C73C22×D411yescharacteristic
236C23×C73C22×D411yescharacteristic
237C23×C73C2×#4112yes—
238C23×C732−1+412yes—
239Q8×C73—42no—
240Q8×C73—81no—
241D4×C73—42no—
242D4×C73—42no—
243D4×C73—42no—
244D4×C73—42no—
245D4×C73—44no—
246D4×C73—42no—
247D4×C73—81no—
248D4×C73—82no—
249D4×C73—82no—
250C2×C4×C73—22no—
251C2×C4×C73—22no—
252C2×C4×C73—22no—
253C2×C4×C73—21no—
254C2×C4×C73—22no—
255C2×C4×C73—21no—
256C2×C4×C73—21no—
257C2×C4×C73—22no—
258C2×C4×C73—22no—
259C2×C4×C73—21no—
260C2×C4×C73—21no—
261C2×C4×C73—24no—
262C2×C4×C73—24no—
263C2×C4×C73—41no—
264C2×C4×C73—41no—
265C2×C4×C73—41no—
266C2×C4×C73—42no—
267C2×C4×C73—42no—
268C2×C4×C73—42no—
269C2×C4×C73—41no—
270C2×C4×C73—42no—
271C2×C4×C73—41no—
272C2×C4×C73—42no—
273C2×C4×C73—42no—
274C2×C4×C73—42no—
275C2×C4×C73—42no—
276C2×C4×C73—42no—
277C2×C4×C73—44no—
278C2×C4×C73—42no—
279C2×C4×C73—44no—
280C2×C4×C73—42no—
281C2×C4×C73—42no—
282C2×C4×C73—42no—
283C2×C4×C73—42no—
284C2×C4×C73—81no—
285C2×C4×C73—82no—
286C2×C4×C73—82no—
287C2×C4×C73#12011yescharacteristic
288C2×C4×C73#12011yescharacteristic
289C2×C4×C73#12011yescharacteristic
290C2×C4×C73#12011yescharacteristic
291C22×C73—21no—
292C22×C73—21no—
293C22×C73—21no—
294C22×C73—21no—
295C22×C73—21no—
296C22×C73—21no—
297C22×C73—42no—
298C22×C73—42no—
299C22×C73—42no—
300C22×C73—41no—
301C22×C73—42no—
302C22×C73—41no—
303C22×C73—42no—
304C22×C73—42no—
305C22×C73—41no—
306C22×C73—81no—
307C22×C73—84no—
308C22×C73C2×#12011yescharacteristic
309C22×C73#53211yescharacteristic
310C22×C73#53611yescharacteristic
311C22×C73#54712yes—
312C22×C73#54812yes—
313C4×C73—21no—
314C4×C73—21no—
315C4×C73—21no—
316C4×C73—44no—
317C4×C73—41no—
318C4×C73—42no—
319C4×C73—41no—
320C4×C73—42no—
321C4×C73—41no—
322C4×C73—42no—
323C4×C73—82no—
324C4×C73—82no—
325C4×C73—82no—
326C4×C73#45812yes—
327#25664C7311yesmaximal, characteristic, direct product factor, Sylow
328C2×C73—22no—
329C2×C73—21no—
330C2×C73—22no—
331C2×C73—21no—
332C2×C73—81no—
333C2×C73—82no—
334C2×C73#243211yescharacteristic
335C2×C73C2×#45811yescharacteristic
336C2×C73#302711yescharacteristic
337#3505C2×C7311yescharacteristic
338#2504C2×C7311yescharacteristic, complemented
339#2502C2×C7311yescharacteristic, complemented
340#2487C2×C7311yescharacteristic, complemented
341#2044C2×C7314yescomplemented
342#1996C2×C7311yescharacteristic, complemented
343#1964C2×C7311yescharacteristic, complemented
344#1867C2×C7314yescomplemented
345C4×#99C2×C7311yescharacteristic, complemented
346C73#2566411yescharacteristic, direct product factor, Sylow
347#553—21no—
348#553—22no—
349#552—21no—
350#551—22no—
351#548—21no—
352#546—21no—
353#539—21no—
354#538—21no—
355#534C22×C7312yes—
356#529—21no—
357#525—21no—
358C2×C22⋊Q8C22×C7311yescharacteristic
359C2×#121C22×C7311yescharacteristic
360#518C22×C7312yes—
361C2×C4×D4C22×C7311yescharacteristic
362C22×C4⋊C4C22×C7311yescharacteristic
363C2×#99C22×C7314yes—
364C2×#99C22×C7312yes—
365#400—21no—
366#399—21no—
367#398—22no—
368#397—22no—
369#391—21no—
370#390—21no—
371#389—21no—
372#386C22×C7314yes—
373#386C22×C7312yes—
374#385C22×C7312yes—
375#385C22×C7314yes—
376#384—21no—
377#382—21no—
378#380—21no—
379#380C22×C7311yescharacteristic
380C4×C22⋊C4C22×C7311yescharacteristic
381C4×C22⋊C4C22×C7311yescharacteristic
382#342C22×C7312yes—
383#342C22×C7314yes—
384C2×#41—21no—
385C22×Q8D4×C7311yescharacteristic
386C22×D4D4×C7311yescharacteristic
387C22×D4C23×C7311yescharacteristic
388C22×D4C23×C7312yes—
389C23×C4D4×C7311yescharacteristic
390C23×C4C23×C7312yes—
391C23×C4C23×C7311yescharacteristic
392#126—22no—
393#126—22no—
394#126—22no—
395#125—21no—
396#125—22no—
397#124—21no—
398#124—22no—
399#123—22no—
400#123—22no—
401#123—22no—
402#123—22no—
403#123—22no—
404C22⋊Q8—21no—
405C22⋊Q8—22no—
406C22⋊Q8—21no—
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C22⋊Q8—21no—
410#121—21no—
411#121—22no—
412#121—21no—
413#121—21no—
414#121—21no—
415#121—21no—
416#121—22no—
417#121—22no—
418#120—22no—
419#120—22no—
420C4×Q8—21no—
421C4×D4—22no—
422C4×D4—21no—
423C4×D4—21no—
424C4×D4—21no—
425C4×D4—21no—
426C4×D4—21no—
427C4×D4—22no—
428C4×D4—22no—
429C4×D4—22no—
430C4×D4—22no—
431#117—21no—
432#117—22no—
433#117—22no—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—21no—
436C2×C4⋊C4—21no—
437C2×C4⋊C4—21no—
438C2×C4⋊C4—21no—
439C2×C4⋊C4—21no—
440C2×C4⋊C4—21no—
441C2×C4⋊C4—24no—
442C2×C4⋊C4—22no—
443C2×C4⋊C4D4×C7311yescharacteristic
444C2×C4⋊C4D4×C7311yescharacteristic
445C2×C4⋊C4D4×C7311yescharacteristic
446C2×C4⋊C4D4×C7312yes—
447C2×C22⋊C4—22no—
448C2×C22⋊C4—22no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4D4×C7311yescharacteristic
451C2×C22⋊C4D4×C7312yes—
452C2×C22⋊C4C23×C7312yes—
453C2×C22⋊C4C23×C7312yes—
454C2×C22⋊C4C23×C7311yescharacteristic
455C2×C22⋊C4C23×C7312yes—
456C2×C22⋊C4C23×C7312yes—
457C2×C42—21no—
458C2×C42—21no—
459C2×C42D4×C7311yescharacteristic
460#99—28no—
461#99—24no—
462#95—21no—
463#95—21no—
464#95—22no—
465#95—21no—
466#95—24no—
467#95—24no—
468#95—22no—
469C24C2×D4×C7312yes—
470C24C2×D4×C7311yescharacteristic
471C24C24×C7311yescharacteristic
472#41—82no—
473C2×Q8—21no—
474C2×Q8—21no—
475C2×Q8—42no—
476C2×D4—21no—
477C2×D4—22no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—24no—
482C2×D4—22no—
483C2×D4—24no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—21no—
487C2×D4—21no—
488C2×D4—42no—
489C22×C4—22no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—22no—
495C22×C4—22no—
496C22×C4—22no—
497C22×C4—22no—
498C22×C4—22no—
499C22×C4—42no—
500C22×C4—42no—
501C22×C4—82no—
502C22×C4C2×D4×C7311yescharacteristic
503C22×C4C2×D4×C7312yes—
504C22×C4C2×D4×C7311yescharacteristic
505C22×C4C2×D4×C7311yescharacteristic
506C22×C4C2×D4×C7311yescharacteristic
507C22×C4C2×D4×C7311yescharacteristic
508C22×C4C2×D4×C7312yes—
509C22×C4C2×D4×C7311yescharacteristic
510C22×C4C2×D4×C7312yes—
511C22×C4C2×D4×C7311yescharacteristic
512C22×C4C2×D4×C7311yescharacteristic
513C22×C4C2×D4×C7311yescharacteristic
514C4⋊C4—22no—
515C4⋊C4—22no—
516C4⋊C4—22no—
517C4⋊C4—22no—
518C4⋊C4—21no—
519C4⋊C4—22no—
520C4⋊C4—21no—
521C4⋊C4—21no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—22no—
525C4⋊C4—21no—
526C4⋊C4—42no—
527C4⋊C4—41no—
528C4⋊C4—41no—
529C4⋊C4—41no—
530C4⋊C4—41no—
531C4⋊C4—84no—
532C4⋊C4—82no—
533C22⋊C4—22no—
534C22⋊C4—22no—
535C22⋊C4—22no—
536C22⋊C4—22no—
537C22⋊C4—22no—
538C22⋊C4—22no—
539C22⋊C4—21no—
540C22⋊C4—22no—
541C22⋊C4—21no—
542C22⋊C4—22no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—21no—
546C22⋊C4—21no—
547C22⋊C4—22no—
548C22⋊C4—24no—
549C22⋊C4—22no—
550C22⋊C4—22no—
551C22⋊C4—84no—
552C22⋊C4—82no—
553C22⋊C4#41×C7314yescomplemented
554C42—22no—
555C42—22no—
556C42—21no—
557C42—21no—
558C42—42no—
559C42—42no—
560C23—21no—
561C23—22no—
562C23—21no—
563C23—21no—
564C23—24no—
565C23—41no—
566C23—41no—
567C23—41no—
568C23—41no—
569C23—42no—
570C23—42no—
571C23C22×D4×C7311yescharacteristic
572C23C22×D4×C7311yescharacteristic
573C23C22×D4×C7311yescharacteristic
574C23C2×#41×C7312yes—
575C232−1+4×C7312yes—
576Q8—42no—
577Q8—81no—
578D4—42no—
579D4—42no—
580D4—42no—
581D4—42no—
582D4—44no—
583D4—42no—
584D4—81no—
585D4—82no—
586D4—82no—
587C2×C4—22no—
588C2×C4—22no—
589C2×C4—22no—
590C2×C4—21no—
591C2×C4—22no—
592C2×C4—21no—
593C2×C4—21no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—21no—
597C2×C4—21no—
598C2×C4—24no—
599C2×C4—24no—
600C2×C4—41no—
601C2×C4—41no—
602C2×C4—41no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—42no—
606C2×C4—41no—
607C2×C4—42no—
608C2×C4—41no—
609C2×C4—42no—
610C2×C4—42no—
611C2×C4—42no—
612C2×C4—42no—
613C2×C4—42no—
614C2×C4—44no—
615C2×C4—42no—
616C2×C4—44no—
617C2×C4—42no—
618C2×C4—42no—
619C2×C4—42no—
620C2×C4—42no—
621C2×C4—81no—
622C2×C4—82no—
623C2×C4—82no—
624C2×C4#120×C7311yescharacteristic
625C2×C4#120×C7311yescharacteristic
626C2×C4#120×C7311yescharacteristic
627C2×C4#120×C7311yescharacteristic
628C22—21no—
629C22—21no—
630C22—21no—
631C22—21no—
632C22—21no—
633C22—21no—
634C22—42no—
635C22—42no—
636C22—42no—
637C22—41no—
638C22—42no—
639C22—42no—
640C22—41no—
641C22—41no—
642C22—42no—
643C22—81no—
644C22—84no—
645C22C2×#120×C7311yescharacteristic
646C22#532×C7311yescharacteristic
647C22#536×C7311yescharacteristic
648C22#547×C7312yes—
649C22#548×C7312yes—
650C4—21no—
651C4—21no—
652C4—21no—
653C4—44no—
654C4—41no—
655C4—42no—
656C4—41no—
657C4—42no—
658C4—41no—
659C4—42no—
660C4—82no—
661C4—82no—
662C4—82no—
663C4#458×C7312yes—
664C2—22no—
665C2—21no—
666C2—22no—
667C2—21no—
668C2—81no—
669C2—82no—
670C2C73×#243211yescharacteristic
671C2C2×#458×C7311yescharacteristic
672C2C73×#302711yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC24C24×C73
prime radicalC73×#3505C2
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
2. C73×#2504C2semidirect
3. C73×#2502C2semidirect
4. C73×#2487C2semidirect
5. C73×#2044C2semidirect
6. C73×#1996C2semidirect
7. C73×#1964C2semidirect
8. C73×#1867C2semidirect
9. C4×#99×C73C2semidirect
216. C22⋊C4×C73#41semidirect
327. #25664C73direct (N × H)
338. #2504C2×C73semidirect
339. #2502C2×C73semidirect
340. #2487C2×C73semidirect
341. #2044C2×C73semidirect
342. #1996C2×C73semidirect
343. #1964C2×C73semidirect
344. #1867C2×C73semidirect
345. C4×#99C2×C73semidirect
346. C73#25664direct (N × H)
553. 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×#25042
C73×#25022
C73×#24872
C73×#20442
C73×#19962
C73×#19642
C73×#18672
C4×#99×C732
#2566473