Finite Group Databasebeta

← C73×#18813 #32928217

Subgroups — C73×#18813 #32928217

Order 18688.

914 conjugacy classes of subgroups.

The subgroup lattice has 730 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3522C211yesmaximal, characteristic
2C73×#3252C211yesmaximal, characteristic, complemented
3C73×#3210C211yesmaximal, characteristic, complemented
4C73×#3078C211yesmaximal, characteristic, complemented
5C73×#1645C211yesmaximal, characteristic, complemented
6C73×#1643C211yesmaximal, characteristic, complemented
7C73×#1642C211yesmaximal, characteristic, complemented
8C73×#1640C211yesmaximal, characteristic, complemented
9C73×#1633C211yesmaximal, characteristic, complemented
10C73×#1632C211yesmaximal, characteristic, complemented
11C73×#1631C211yesmaximal, characteristic, complemented
12C73×#1630C211yesmaximal, characteristic, complemented
13C73×#1560C211yesmaximal, characteristic, complemented
14C73×#1495C211yesmaximal, characteristic, complemented
15C73×#1487C211yesmaximal, characteristic, complemented
16#559×C73—21no—
17#559×C73C2211yescharacteristic
18Q82×C73C2211yescharacteristic
19#554×C73—21no—
20#554×C73C2211yescharacteristic
21#550×C73C2211yescharacteristic
22#548×C73—21no—
23#547×C73—22no—
24#547×C73—21no—
25#542×C73—22no—
26#542×C73—21no—
27#533×C73C2211yescharacteristic
28#532×C73—21no—
29#532×C73C2211yescharacteristic
30#529×C73—21no—
31#529×C73C2211yescharacteristic
32#520×C73—21no—
33C2×C4×Q8×C73C2211yescharacteristic
34#494×C73C2211yescharacteristic
35#492×C73C2211yescharacteristic
36#487×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#479×C73—21no—
39#479×C73—21no—
40#479×C73—21no—
41#477×C73C2211yescharacteristic
42#477×C73C2211yescharacteristic
43#477×C73C2211yescharacteristic
44#476×C73C2211yescharacteristic
45#475×C73C2211yescharacteristic
46#475×C73C2211yescharacteristic
47#470×C73—21no—
48#468×C73—21no—
49#464×C73—22no—
50#464×C73—21no—
51#462×C73C2211yescharacteristic
52#461×C73C2211yescharacteristic
53#452×C73—22no—
54#431×C73C2211yescharacteristic
55#428×C73—21no—
56#423×C73C2211yescharacteristic
57#423×C73C2211yescharacteristic
58#419×C73—21no—
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#331×C73C2211yescharacteristic
62#331×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67Q8⋊C8×C73C2211yescharacteristic
68Q8⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73—22no—
72C2×#41×C73—21no—
73C2×#41×C73D412yes—
74C22×Q8×C73D411yescharacteristic
75C2×Q16×C73—22no—
76C2×Q16×C73—21no—
77C2×SD16×C73—22no—
78C2×SD16×C73—21no—
79C2×M16×C73—21no—
80C2×M16×C73—21no—
81C4⋊Q8×C73—22no—
82C4⋊Q8×C73—21no—
83C4⋊Q8×C73—21no—
84C4⋊Q8×C73C2311yescharacteristic
85C4⋊Q8×C73C2311yescharacteristic
86C4⋊Q8×C73C2311yescharacteristic
87#127×C73—21no—
88#127×C73C2311yescharacteristic
89#126×C73—22no—
90#126×C73—21no—
91#125×C73—21no—
92#125×C73—21no—
93#125×C73D411yescharacteristic
94#124×C73—22no—
95#124×C73—22no—
96#124×C73—21no—
97#124×C73—21no—
98#124×C73D411yescharacteristic
99#124×C73D412yes—
100#123×C73—22no—
101#123×C73—22no—
102#123×C73—22no—
103#123×C73—22no—
104#123×C73—21no—
105C22⋊Q8×C73—22no—
106C22⋊Q8×C73—22no—
107C22⋊Q8×C73—22no—
108C22⋊Q8×C73—22no—
109C22⋊Q8×C73—21no—
110C22⋊Q8×C73—21no—
111C22⋊Q8×C73—21no—
112C22⋊Q8×C73D411yescharacteristic
113#121×C73—22no—
114#121×C73—22no—
115#121×C73—21no—
116#121×C73—21no—
117#121×C73—21no—
118#121×C73D411yescharacteristic
119C4×Q8×C73—21no—
120C4×Q8×C73—21no—
121C4×Q8×C73—21no—
122C4×Q8×C73—21no—
123C4×Q8×C73—21no—
124C4×Q8×C73—21no—
125C4×Q8×C73D411yescharacteristic
126C4×Q8×C73D411yescharacteristic
127C4×Q8×C73C2311yescharacteristic
128C4×Q8×C73C2311yescharacteristic
129C4×Q8×C73C2311yescharacteristic
130C4×D4×C73—22no—
131C4×D4×C73—22no—
132C4×D4×C73—22no—
133C4×D4×C73—21no—
134C4×D4×C73—21no—
135C4×D4×C73—21no—
136C4×D4×C73—21no—
137C4×D4×C73—21no—
138C4×D4×C73—21no—
139C4×D4×C73—21no—
140C4×D4×C73C2311yescharacteristic
141#117×C73—22no—
142#117×C73—21no—
143#117×C73—21no—
144C2×C4⋊C4×C73—22no—
145C2×C4⋊C4×C73—21no—
146C2×C4⋊C4×C73—21no—
147C2×C4⋊C4×C73D411yescharacteristic
148C2×C42×C73—21no—
149C2×C42×C73C2311yescharacteristic
150#107×C73—21no—
151#107×C73—21no—
152#107×C73—21no—
153#106×C73—21no—
154#106×C73—21no—
155#106×C73—21no—
156C4⋊C8×C73—21no—
157C4⋊C8×C73—21no—
158C4⋊C8×C73—21no—
159C4⋊C8×C73C2311yescharacteristic
160C4⋊C8×C73C2311yescharacteristic
161C4⋊C8×C73C2311yescharacteristic
162C4⋊C8×C73C2311yescharacteristic
163#103×C73—21no—
164#103×C73—21no—
165#103×C73—21no—
166#103×C73—21no—
167#103×C73—22no—
168#103×C73—21no—
169#103×C73—21no—
170#103×C73—21no—
171#102×C73—22no—
172#102×C73—21no—
173C22⋊C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176#41×C73—42no—
177#41×C73—42no—
178#41×C73—84no—
179#41×C73—82no—
180C2×Q8×C73—22no—
181C2×Q8×C73—21no—
182C2×Q8×C73—22no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—41no—
186C2×Q8×C73C2×D411yescharacteristic
187C2×Q8×C73C2×D411yescharacteristic
188C2×Q8×C73C2×D411yescharacteristic
189C2×Q8×C73C2×D412yes—
190C2×D4×C73—22no—
191C2×D4×C73—22no—
192C2×D4×C73—21no—
193C2×D4×C73—22no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73C2×D411yescharacteristic
197C2×D4×C73C2×D412yes—
198C22×C4×C73—22no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—22no—
202C22×C4×C73—22no—
203C22×C4×C73—21no—
204C22×C4×C73—22no—
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208Q16×C73—81no—
209Q16×C73—82no—
210SD16×C73—81no—
211SD16×C73—82no—
212M16×C73—42no—
213M16×C73—81no—
214C2×C8×C73—21no—
215C2×C8×C73—21no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—22no—
223C4⋊C4×C73—22no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—21no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—21no—
232C4⋊C4×C73—21no—
233C4⋊C4×C73—21no—
234C4⋊C4×C73—21no—
235C4⋊C4×C73—21no—
236C4⋊C4×C73—21no—
237C4⋊C4×C73—21no—
238C4⋊C4×C73—21no—
239C4⋊C4×C73—41no—
240C4⋊C4×C73—41no—
241C4⋊C4×C73C2×D411yescharacteristic
242C4⋊C4×C73C2×D411yescharacteristic
243C4⋊C4×C73C2×D411yescharacteristic
244C4⋊C4×C73C2×D411yescharacteristic
245C22⋊C4×C73—22no—
246C22⋊C4×C73—22no—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—21no—
251C22⋊C4×C73—22no—
252C22⋊C4×C73—21no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—22no—
255C22⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—41no—
258C42×C73—22no—
259C42×C73—21no—
260C42×C73—21no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—41no—
265C42×C73C2×D411yescharacteristic
266C42×C73C2×D411yescharacteristic
267C42×C73C2×D411yescharacteristic
268C42×C73C2411yescharacteristic
269C23×C73—21no—
270C23×C73—22no—
271C23×C73#12011yescharacteristic
272Q8×C73—21no—
273Q8×C73—21no—
274Q8×C73—21no—
275Q8×C73—21no—
276Q8×C73—21no—
277Q8×C73—42no—
278Q8×C73—42no—
279Q8×C73—42no—
280Q8×C73—41no—
281Q8×C73—41no—
282Q8×C73—82no—
283Q8×C73#13712yes—
284D4×C73—21no—
285D4×C73—21no—
286D4×C73—42no—
287D4×C73—44no—
288D4×C73—44no—
289D4×C73—42no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—41no—
294D4×C73—82no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—21no—
298C2×C4×C73—21no—
299C2×C4×C73—21no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—22no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—41no—
308C2×C4×C73—42no—
309C2×C4×C73—44no—
310C2×C4×C73—42no—
311C2×C4×C73—41no—
312C2×C4×C73—41no—
313C2×C4×C73—41no—
314C2×C4×C73—41no—
315C2×C4×C73—82no—
316C2×C4×C73—82no—
317C2×C4×C73—82no—
318C2×C4×C73#12011yescharacteristic
319C2×C4×C73#12011yescharacteristic
320C2×C4×C73#12011yescharacteristic
321C2×C4×C73C22×D411yescharacteristic
322C2×C4×C73C22×D411yescharacteristic
323C2×C4×C73C22×D411yescharacteristic
324C8×C73—41no—
325C8×C73—41no—
326C8×C73—41no—
327C8×C73—41no—
328C8×C73—41no—
329C8×C73—41no—
330C22×C73—21no—
331C22×C73—21no—
332C22×C73—21no—
333C22×C73—42no—
334C22×C73—41no—
335C22×C73—41no—
336C22×C73—42no—
337C22×C73—42no—
338C22×C73—41no—
339C22×C73C2×#12011yescharacteristic
340C4×C73—21no—
341C4×C73—22no—
342C4×C73—21no—
343C4×C73—21no—
344C4×C73—21no—
345C4×C73—41no—
346C4×C73—41no—
347C4×C73—41no—
348C4×C73—41no—
349C4×C73—41no—
350C4×C73—42no—
351C4×C73—41no—
352C4×C73—81no—
353C4×C73—81no—
354C4×C73C2×#13711yescharacteristic
355C4×C73#57511yescharacteristic
356C4×C73#57711yescharacteristic
357C4×C73#57811yescharacteristic
358#18813C7311yesmaximal, characteristic, direct product factor, Sylow
359C2×C73—41no—
360C2×C73—81no—
361C2×C73—82no—
362C2×C73#300711yescharacteristic
363C2×C73#301311yescharacteristic
364C2×C73#301911yescharacteristic
365#3522C2×C7311yescharacteristic
366#3252C2×C7311yescharacteristic, complemented
367#3210C2×C7311yescharacteristic, complemented
368#3078C2×C7311yescharacteristic, complemented
369#1645C2×C7311yescharacteristic, complemented
370#1643C2×C7311yescharacteristic, complemented
371#1642C2×C7311yescharacteristic, complemented
372#1640C2×C7311yescharacteristic, complemented
373#1633C2×C7311yescharacteristic, complemented
374#1632C2×C7311yescharacteristic, complemented
375#1631C2×C7311yescharacteristic, complemented
376#1630C2×C7311yescharacteristic, complemented
377#1560C2×C7311yescharacteristic, complemented
378#1495C2×C7311yescharacteristic, complemented
379#1487C2×C7311yescharacteristic, complemented
380C73#1881311yescharacteristic, direct product factor, Sylow
381#559—21no—
382#559C22×C7311yescharacteristic
383Q82C22×C7311yescharacteristic
384#554—21no—
385#554C22×C7311yescharacteristic
386#550C22×C7311yescharacteristic
387#548—21no—
388#547—22no—
389#547—21no—
390#542—22no—
391#542—21no—
392#533C22×C7311yescharacteristic
393#532—21no—
394#532C22×C7311yescharacteristic
395#529—21no—
396#529C22×C7311yescharacteristic
397#520—21no—
398C2×C4×Q8C22×C7311yescharacteristic
399#494C22×C7311yescharacteristic
400#492C22×C7311yescharacteristic
401#487C22×C7311yescharacteristic
402#486C22×C7311yescharacteristic
403#479—21no—
404#479—21no—
405#479—21no—
406#477C22×C7311yescharacteristic
407#477C22×C7311yescharacteristic
408#477C22×C7311yescharacteristic
409#476C22×C7311yescharacteristic
410#475C22×C7311yescharacteristic
411#475C22×C7311yescharacteristic
412#470—21no—
413#468—21no—
414#464—22no—
415#464—21no—
416#462C22×C7311yescharacteristic
417#461C22×C7311yescharacteristic
418#452—22no—
419#431C22×C7311yescharacteristic
420#428—21no—
421#423C22×C7311yescharacteristic
422#423C22×C7311yescharacteristic
423#419—21no—
424#333C22×C7311yescharacteristic
425#333C22×C7311yescharacteristic
426#331C22×C7311yescharacteristic
427#331C22×C7311yescharacteristic
428Q8⋊C8C22×C7311yescharacteristic
429Q8⋊C8C22×C7311yescharacteristic
430Q8⋊C8C22×C7311yescharacteristic
431Q8⋊C8C22×C7311yescharacteristic
432Q8⋊C8C22×C7311yescharacteristic
433Q8⋊C8C22×C7311yescharacteristic
434D4⋊C8C22×C7311yescharacteristic
435D4⋊C8C22×C7311yescharacteristic
436C2×#41—22no—
437C2×#41—21no—
438C2×#41D4×C7312yes—
439C22×Q8D4×C7311yescharacteristic
440C2×Q16—22no—
441C2×Q16—21no—
442C2×SD16—22no—
443C2×SD16—21no—
444C2×M16—21no—
445C2×M16—21no—
446C4⋊Q8—22no—
447C4⋊Q8—21no—
448C4⋊Q8—21no—
449C4⋊Q8C23×C7311yescharacteristic
450C4⋊Q8C23×C7311yescharacteristic
451C4⋊Q8C23×C7311yescharacteristic
452#127—21no—
453#127C23×C7311yescharacteristic
454#126—22no—
455#126—21no—
456#125—21no—
457#125—21no—
458#125D4×C7311yescharacteristic
459#124—22no—
460#124—22no—
461#124—21no—
462#124—21no—
463#124D4×C7311yescharacteristic
464#124D4×C7312yes—
465#123—22no—
466#123—22no—
467#123—22no—
468#123—22no—
469#123—21no—
470C22⋊Q8—22no—
471C22⋊Q8—22no—
472C22⋊Q8—22no—
473C22⋊Q8—22no—
474C22⋊Q8—21no—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477C22⋊Q8D4×C7311yescharacteristic
478#121—22no—
479#121—22no—
480#121—21no—
481#121—21no—
482#121—21no—
483#121D4×C7311yescharacteristic
484C4×Q8—21no—
485C4×Q8—21no—
486C4×Q8—21no—
487C4×Q8—21no—
488C4×Q8—21no—
489C4×Q8—21no—
490C4×Q8D4×C7311yescharacteristic
491C4×Q8D4×C7311yescharacteristic
492C4×Q8C23×C7311yescharacteristic
493C4×Q8C23×C7311yescharacteristic
494C4×Q8C23×C7311yescharacteristic
495C4×D4—22no—
496C4×D4—22no—
497C4×D4—22no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—21no—
501C4×D4—21no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4C23×C7311yescharacteristic
506#117—22no—
507#117—21no—
508#117—21no—
509C2×C4⋊C4—22no—
510C2×C4⋊C4—21no—
511C2×C4⋊C4—21no—
512C2×C4⋊C4D4×C7311yescharacteristic
513C2×C42—21no—
514C2×C42C23×C7311yescharacteristic
515#107—21no—
516#107—21no—
517#107—21no—
518#106—21no—
519#106—21no—
520#106—21no—
521C4⋊C8—21no—
522C4⋊C8—21no—
523C4⋊C8—21no—
524C4⋊C8C23×C7311yescharacteristic
525C4⋊C8C23×C7311yescharacteristic
526C4⋊C8C23×C7311yescharacteristic
527C4⋊C8C23×C7311yescharacteristic
528#103—21no—
529#103—21no—
530#103—21no—
531#103—21no—
532#103—22no—
533#103—21no—
534#103—21no—
535#103—21no—
536#102—22no—
537#102—21no—
538C22⋊C8—21no—
539C4×C8C23×C7311yescharacteristic
540C4×C8C23×C7311yescharacteristic
541#41—42no—
542#41—42no—
543#41—84no—
544#41—82no—
545C2×Q8—22no—
546C2×Q8—21no—
547C2×Q8—22no—
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—41no—
551C2×Q8C2×D4×C7311yescharacteristic
552C2×Q8C2×D4×C7311yescharacteristic
553C2×Q8C2×D4×C7311yescharacteristic
554C2×Q8C2×D4×C7312yes—
555C2×D4—22no—
556C2×D4—22no—
557C2×D4—21no—
558C2×D4—22no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4C2×D4×C7311yescharacteristic
562C2×D4C2×D4×C7312yes—
563C22×C4—22no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4C2×D4×C7311yescharacteristic
571C22×C4C2×D4×C7311yescharacteristic
572C22×C4C2×D4×C7311yescharacteristic
573Q16—81no—
574Q16—82no—
575SD16—81no—
576SD16—82no—
577M16—42no—
578M16—81no—
579C2×C8—21no—
580C2×C8—21no—
581C2×C8—21no—
582C2×C8—21no—
583C2×C8—21no—
584C2×C8—21no—
585C4⋊C4—22no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—22no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—41no—
605C4⋊C4—41no—
606C4⋊C4C2×D4×C7311yescharacteristic
607C4⋊C4C2×D4×C7311yescharacteristic
608C4⋊C4C2×D4×C7311yescharacteristic
609C4⋊C4C2×D4×C7311yescharacteristic
610C22⋊C4—22no—
611C22⋊C4—22no—
612C22⋊C4—22no—
613C22⋊C4—22no—
614C22⋊C4—22no—
615C22⋊C4—21no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—21no—
621C22⋊C4—21no—
622C22⋊C4—41no—
623C42—22no—
624C42—21no—
625C42—21no—
626C42—21no—
627C42—21no—
628C42—21no—
629C42—41no—
630C42C2×D4×C7311yescharacteristic
631C42C2×D4×C7311yescharacteristic
632C42C2×D4×C7311yescharacteristic
633C42C24×C7311yescharacteristic
634C23—21no—
635C23—22no—
636C23#120×C7311yescharacteristic
637Q8—21no—
638Q8—21no—
639Q8—21no—
640Q8—21no—
641Q8—21no—
642Q8—42no—
643Q8—42no—
644Q8—42no—
645Q8—41no—
646Q8—41no—
647Q8—82no—
648Q8#137×C7312yes—
649D4—21no—
650D4—21no—
651D4—42no—
652D4—44no—
653D4—44no—
654D4—42no—
655D4—41no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—82no—
660C2×C4—21no—
661C2×C4—21no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—21no—
665C2×C4—21no—
666C2×C4—21no—
667C2×C4—21no—
668C2×C4—21no—
669C2×C4—22no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—41no—
673C2×C4—42no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—82no—
681C2×C4—82no—
682C2×C4—82no—
683C2×C4#120×C7311yescharacteristic
684C2×C4#120×C7311yescharacteristic
685C2×C4#120×C7311yescharacteristic
686C2×C4C22×D4×C7311yescharacteristic
687C2×C4C22×D4×C7311yescharacteristic
688C2×C4C22×D4×C7311yescharacteristic
689C8—41no—
690C8—41no—
691C8—41no—
692C8—41no—
693C8—41no—
694C8—41no—
695C22—21no—
696C22—21no—
697C22—21no—
698C22—42no—
699C22—41no—
700C22—41no—
701C22—42no—
702C22—42no—
703C22—41no—
704C22C2×#120×C7311yescharacteristic
705C4—21no—
706C4—22no—
707C4—21no—
708C4—21no—
709C4—21no—
710C4—41no—
711C4—41no—
712C4—41no—
713C4—41no—
714C4—41no—
715C4—42no—
716C4—41no—
717C4—81no—
718C4—81no—
719C4C2×#137×C7311yescharacteristic
720C4#575×C7311yescharacteristic
721C4#577×C7311yescharacteristic
722C4#578×C7311yescharacteristic
723C2—41no—
724C2—81no—
725C2—82no—
726C2C73×#300711yescharacteristic
727C2C73×#301311yescharacteristic
728C2C73×#301911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3522C2
LCSG ▷ C42 ▷ C22 ▷ C1
UCSC1 ◁ C22×C73 ◁ C2×C42×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3252C2semidirect
3. C73×#3210C2semidirect
4. C73×#3078C2semidirect
5. C73×#1645C2semidirect
6. C73×#1643C2semidirect
7. C73×#1642C2semidirect
8. C73×#1640C2semidirect
9. C73×#1633C2semidirect
10. C73×#1632C2semidirect
11. C73×#1631C2semidirect
12. C73×#1630C2semidirect
13. C73×#1560C2semidirect
14. C73×#1495C2semidirect
15. C73×#1487C2semidirect
358. #18813C73direct (N × H)
366. #3252C2×C73semidirect
367. #3210C2×C73semidirect
368. #3078C2×C73semidirect
369. #1645C2×C73semidirect
370. #1643C2×C73semidirect
371. #1642C2×C73semidirect
372. #1640C2×C73semidirect
373. #1633C2×C73semidirect
374. #1632C2×C73semidirect
375. #1631C2×C73semidirect
376. #1630C2×C73semidirect
377. #1560C2×C73semidirect
378. #1495C2×C73semidirect
379. #1487C2×C73semidirect
380. C73#18813direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35222
C73×#32522
C73×#32102
C73×#30782
C73×#16452
C73×#16432
C73×#16422
C73×#16402
C73×#16332
C73×#16322
C73×#16312
C73×#16302
C73×#15602
C73×#14952
C73×#14872
#1881373