Finite Group Databasebeta

← C73×#18673 #32928077

Subgroups — C73×#18673 #32928077

Order 18688.

872 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3518C211yesmaximal, characteristic
2C73×#3233C211yesmaximal, characteristic, complemented
3C73×#3170C211yesmaximal, characteristic, complemented
4C73×#3116C211yesmaximal, characteristic, complemented
5C73×#1650C211yesmaximal, characteristic, complemented
6C73×#1649C211yesmaximal, characteristic, complemented
7C73×#1646C211yesmaximal, characteristic, complemented
8C73×#1645C211yesmaximal, characteristic, complemented
9C73×#1638C211yesmaximal, characteristic, complemented
10C73×#1637C211yesmaximal, characteristic, complemented
11C73×#1634C211yesmaximal, characteristic, complemented
12C73×#1633C211yesmaximal, characteristic, complemented
13C73×#1554C211yesmaximal, characteristic, complemented
14C73×#1494C211yesmaximal, characteristic, complemented
15C73×#1476C211yesmaximal, characteristic, complemented
16Q82×C73C2211yescharacteristic
17#556×C73—21no—
18#556×C73—22no—
19#556×C73—21no—
20#556×C73C2211yescharacteristic
21#555×C73—21no—
22#555×C73C2211yescharacteristic
23D4×Q8×C73C2211yescharacteristic
24#548×C73—21no—
25#542×C73—22no—
26#542×C73—21no—
27#533×C73—21no—
28#533×C73C2211yescharacteristic
29#533×C73C2211yescharacteristic
30#529×C73—21no—
31#529×C73C2211yescharacteristic
32#519×C73—21no—
33C4×#41×C73C2211yescharacteristic
34#500×C73C2211yescharacteristic
35#499×C73—21no—
36#494×C73C2211yescharacteristic
37#488×C73—21no—
38#487×C73C2211yescharacteristic
39#487×C73C2211yescharacteristic
40#485×C73—21no—
41#485×C73—21no—
42#482×C73—21no—
43#477×C73C2211yescharacteristic
44#477×C73C2211yescharacteristic
45#476×C73C2211yescharacteristic
46#476×C73C2211yescharacteristic
47#475×C73C2211yescharacteristic
48#474×C73C2211yescharacteristic
49#467×C73—22no—
50#462×C73C2211yescharacteristic
51#461×C73C2211yescharacteristic
52#452×C73—21no—
53#441×C73—21no—
54#440×C73—21no—
55C4×Q16×C73—22no—
56#432×C73C2211yescharacteristic
57#431×C73C2211yescharacteristic
58C2×C4×C8×C73C2211yescharacteristic
59#333×C73C2211yescharacteristic
60#333×C73C2211yescharacteristic
61#332×C73C2211yescharacteristic
62#332×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic
64Q8⋊C8×C73C2211yescharacteristic
65Q8⋊C8×C73C2211yescharacteristic
66Q8⋊C8×C73C2211yescharacteristic
67D4⋊C8×C73C2211yescharacteristic
68D4⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73D411yescharacteristic
72C22×Q8×C73—21no—
73C2×Q16×C73—22no—
74C2×Q16×C73—21no—
75C2×SD16×C73—21no—
76C22×C8×C73—21no—
77C4⋊Q8×C73—22no—
78C4⋊Q8×C73—21no—
79C4⋊Q8×C73—21no—
80C4⋊Q8×C73—21no—
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84C4⋊Q8×C73C2311yescharacteristic
85#126×C73—22no—
86#126×C73—22no—
87#126×C73—22no—
88#126×C73—22no—
89#126×C73—21no—
90#125×C73—21no—
91#125×C73—21no—
92#125×C73D411yescharacteristic
93#124×C73—22no—
94#124×C73—22no—
95#124×C73—22no—
96#124×C73—22no—
97#124×C73—21no—
98#124×C73D411yescharacteristic
99#123×C73—22no—
100#123×C73—21no—
101C22⋊Q8×C73—22no—
102C22⋊Q8×C73—22no—
103C22⋊Q8×C73—21no—
104C22⋊Q8×C73—21no—
105C22⋊Q8×C73—21no—
106C22⋊Q8×C73—22no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73—21no—
109C22⋊Q8×C73D412yes—
110C22⋊Q8×C73D411yescharacteristic
111#121×C73—22no—
112#121×C73—21no—
113#121×C73—21no—
114#121×C73D411yescharacteristic
115C4×Q8×C73—22no—
116C4×Q8×C73—22no—
117C4×Q8×C73—22no—
118C4×Q8×C73—21no—
119C4×Q8×C73—21no—
120C4×Q8×C73—21no—
121C4×Q8×C73—21no—
122C4×Q8×C73—21no—
123C4×Q8×C73—21no—
124C4×Q8×C73D412yes—
125C4×Q8×C73D411yescharacteristic
126C4×Q8×C73C2311yescharacteristic
127C4×Q8×C73C2311yescharacteristic
128C4×D4×C73—22no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73—21no—
132C4×D4×C73—21no—
133C4×D4×C73D411yescharacteristic
134C4×D4×C73C2311yescharacteristic
135C4×D4×C73C2311yescharacteristic
136#117×C73—22no—
137#117×C73—22no—
138#117×C73—21no—
139#117×C73—21no—
140#117×C73—21no—
141#117×C73—21no—
142#117×C73—21no—
143#117×C73—21no—
144#117×C73—21no—
145#117×C73D411yescharacteristic
146C2×C42×C73—21no—
147C2×C42×C73C2311yescharacteristic
148#107×C73—22no—
149#107×C73—21no—
150#107×C73—21no—
151#107×C73—21no—
152#106×C73—21no—
153#106×C73—21no—
154#106×C73—21no—
155C4⋊C8×C73C2311yescharacteristic
156C4⋊C8×C73C2311yescharacteristic
157C4⋊C8×C73C2311yescharacteristic
158C4⋊C8×C73C2311yescharacteristic
159#103×C73—22no—
160#103×C73—21no—
161#103×C73—21no—
162#103×C73—21no—
163#103×C73—22no—
164#103×C73—21no—
165#103×C73—21no—
166#102×C73—21no—
167#102×C73—21no—
168#102×C73—21no—
169C22⋊C8×C73—21no—
170C22⋊C8×C73—21no—
171#97×C73—21no—
172C4×C8×C73—21no—
173C4×C8×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176#41×C73—22no—
177#41×C73—41no—
178C2×Q8×C73—22no—
179C2×Q8×C73—22no—
180C2×Q8×C73—21no—
181C2×Q8×C73—21no—
182C2×Q8×C73—21no—
183C2×Q8×C73—42no—
184C2×Q8×C73—42no—
185C2×Q8×C73C2×D411yescharacteristic
186C2×Q8×C73C2×D411yescharacteristic
187C2×Q8×C73C2×D412yes—
188C2×D4×C73—21no—
189C2×D4×C73—22no—
190C2×D4×C73—21no—
191C2×D4×C73C2×D411yescharacteristic
192C2×D4×C73C2×D411yescharacteristic
193C22×C4×C73—22no—
194C22×C4×C73—21no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73C2×D411yescharacteristic
199C22×C4×C73C2×D411yescharacteristic
200C22×C4×C73C2×D411yescharacteristic
201Q16×C73—44no—
202Q16×C73—42no—
203SD16×C73—42no—
204C2×C8×C73—21no—
205C2×C8×C73—21no—
206C2×C8×C73—21no—
207C2×C8×C73—21no—
208C2×C8×C73—21no—
209C2×C8×C73—21no—
210C2×C8×C73—42no—
211C4⋊C4×C73—22no—
212C4⋊C4×C73—22no—
213C4⋊C4×C73—22no—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—21no—
216C4⋊C4×C73—21no—
217C4⋊C4×C73—22no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
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—41no—
231C4⋊C4×C73—41no—
232C4⋊C4×C73C2×D411yescharacteristic
233C4⋊C4×C73C2×D411yescharacteristic
234C4⋊C4×C73C2×D412yes—
235C4⋊C4×C73C2×D411yescharacteristic
236C4⋊C4×C73C2×D411yescharacteristic
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—22no—
240C22⋊C4×C73—22no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—22no—
243C22⋊C4×C73—21no—
244C22⋊C4×C73—21no—
245C22⋊C4×C73—21no—
246C22⋊C4×C73—21no—
247C22⋊C4×C73—21no—
248C22⋊C4×C73—21no—
249C22⋊C4×C73—21no—
250C22⋊C4×C73—21no—
251C22⋊C4×C73—41no—
252C42×C73—22no—
253C42×C73—22no—
254C42×C73—22no—
255C42×C73—21no—
256C42×C73—21no—
257C42×C73—22no—
258C42×C73—21no—
259C42×C73—21no—
260C42×C73—41no—
261C42×C73C2×D411yescharacteristic
262C42×C73C2×D411yescharacteristic
263C42×C73C2×D411yescharacteristic
264C42×C73C2411yescharacteristic
265C23×C73—21no—
266C23×C73—21no—
267C23×C73#12011yescharacteristic
268Q8×C73—21no—
269Q8×C73—21no—
270Q8×C73—21no—
271Q8×C73—42no—
272Q8×C73—44no—
273Q8×C73—42no—
274Q8×C73—41no—
275Q8×C73—41no—
276Q8×C73—41no—
277Q8×C73—41no—
278Q8×C73—82no—
279Q8×C73#13512yes—
280D4×C73—21no—
281D4×C73—21no—
282D4×C73—21no—
283D4×C73—21no—
284D4×C73—42no—
285D4×C73—81no—
286D4×C73—82no—
287C2×C4×C73—21no—
288C2×C4×C73—21no—
289C2×C4×C73—21no—
290C2×C4×C73—21no—
291C2×C4×C73—21no—
292C2×C4×C73—21no—
293C2×C4×C73—21no—
294C2×C4×C73—22no—
295C2×C4×C73—21no—
296C2×C4×C73—21no—
297C2×C4×C73—22no—
298C2×C4×C73—21no—
299C2×C4×C73—41no—
300C2×C4×C73—42no—
301C2×C4×C73—44no—
302C2×C4×C73—41no—
303C2×C4×C73—41no—
304C2×C4×C73—41no—
305C2×C4×C73—41no—
306C2×C4×C73—41no—
307C2×C4×C73—41no—
308C2×C4×C73—81no—
309C2×C4×C73#12011yescharacteristic
310C2×C4×C73#12011yescharacteristic
311C2×C4×C73#12011yescharacteristic
312C2×C4×C73C22×D411yescharacteristic
313C2×C4×C73C22×D411yescharacteristic
314C2×C4×C73C22×D411yescharacteristic
315C8×C73—22no—
316C8×C73—41no—
317C8×C73—41no—
318C8×C73—41no—
319C8×C73—41no—
320C8×C73—41no—
321C22×C73—21no—
322C22×C73—21no—
323C22×C73—21no—
324C22×C73—41no—
325C22×C73—41no—
326C22×C73—41no—
327C22×C73—41no—
328C22×C73—41no—
329C22×C73—41no—
330C22×C73C2×#12011yescharacteristic
331C4×C73—21no—
332C4×C73—22no—
333C4×C73—21no—
334C4×C73—21no—
335C4×C73—21no—
336C4×C73—42no—
337C4×C73—41no—
338C4×C73—41no—
339C4×C73—41no—
340C4×C73—41no—
341C4×C73—42no—
342C4×C73—41no—
343C4×C73—81no—
344C4×C73—81no—
345C4×C73C2×#13511yescharacteristic
346C4×C73#57511yescharacteristic
347C4×C73#57811yescharacteristic
348C4×C73#57811yescharacteristic
349#18673C7311yesmaximal, characteristic, direct product factor, Sylow
350C2×C73—41no—
351C2×C73—81no—
352C2×C73—81no—
353C2×C73#300211yescharacteristic
354C2×C73#301111yescharacteristic
355C2×C73#301811yescharacteristic
356#3518C2×C7311yescharacteristic
357#3233C2×C7311yescharacteristic, complemented
358#3170C2×C7311yescharacteristic, complemented
359#3116C2×C7311yescharacteristic, complemented
360#1650C2×C7311yescharacteristic, complemented
361#1649C2×C7311yescharacteristic, complemented
362#1646C2×C7311yescharacteristic, complemented
363#1645C2×C7311yescharacteristic, complemented
364#1638C2×C7311yescharacteristic, complemented
365#1637C2×C7311yescharacteristic, complemented
366#1634C2×C7311yescharacteristic, complemented
367#1633C2×C7311yescharacteristic, complemented
368#1554C2×C7311yescharacteristic, complemented
369#1494C2×C7311yescharacteristic, complemented
370#1476C2×C7311yescharacteristic, complemented
371C73#1867311yescharacteristic, direct product factor, Sylow
372Q82C22×C7311yescharacteristic
373#556—21no—
374#556—22no—
375#556—21no—
376#556C22×C7311yescharacteristic
377#555—21no—
378#555C22×C7311yescharacteristic
379D4×Q8C22×C7311yescharacteristic
380#548—21no—
381#542—22no—
382#542—21no—
383#533—21no—
384#533C22×C7311yescharacteristic
385#533C22×C7311yescharacteristic
386#529—21no—
387#529C22×C7311yescharacteristic
388#519—21no—
389C4×#41C22×C7311yescharacteristic
390#500C22×C7311yescharacteristic
391#499—21no—
392#494C22×C7311yescharacteristic
393#488—21no—
394#487C22×C7311yescharacteristic
395#487C22×C7311yescharacteristic
396#485—21no—
397#485—21no—
398#482—21no—
399#477C22×C7311yescharacteristic
400#477C22×C7311yescharacteristic
401#476C22×C7311yescharacteristic
402#476C22×C7311yescharacteristic
403#475C22×C7311yescharacteristic
404#474C22×C7311yescharacteristic
405#467—22no—
406#462C22×C7311yescharacteristic
407#461C22×C7311yescharacteristic
408#452—21no—
409#441—21no—
410#440—21no—
411C4×Q16—22no—
412#432C22×C7311yescharacteristic
413#431C22×C7311yescharacteristic
414C2×C4×C8C22×C7311yescharacteristic
415#333C22×C7311yescharacteristic
416#333C22×C7311yescharacteristic
417#332C22×C7311yescharacteristic
418#332C22×C7311yescharacteristic
419Q8⋊C8C22×C7311yescharacteristic
420Q8⋊C8C22×C7311yescharacteristic
421Q8⋊C8C22×C7311yescharacteristic
422Q8⋊C8C22×C7311yescharacteristic
423D4⋊C8C22×C7311yescharacteristic
424D4⋊C8C22×C7311yescharacteristic
425D4⋊C8C22×C7311yescharacteristic
426D4⋊C8C22×C7311yescharacteristic
427C2×#41D4×C7311yescharacteristic
428C22×Q8—21no—
429C2×Q16—22no—
430C2×Q16—21no—
431C2×SD16—21no—
432C22×C8—21no—
433C4⋊Q8—22no—
434C4⋊Q8—21no—
435C4⋊Q8—21no—
436C4⋊Q8—21no—
437C4⋊Q8C23×C7311yescharacteristic
438C4⋊Q8C23×C7311yescharacteristic
439C4⋊Q8C23×C7311yescharacteristic
440C4⋊Q8C23×C7311yescharacteristic
441#126—22no—
442#126—22no—
443#126—22no—
444#126—22no—
445#126—21no—
446#125—21no—
447#125—21no—
448#125D4×C7311yescharacteristic
449#124—22no—
450#124—22no—
451#124—22no—
452#124—22no—
453#124—21no—
454#124D4×C7311yescharacteristic
455#123—22no—
456#123—21no—
457C22⋊Q8—22no—
458C22⋊Q8—22no—
459C22⋊Q8—21no—
460C22⋊Q8—21no—
461C22⋊Q8—21no—
462C22⋊Q8—22no—
463C22⋊Q8—21no—
464C22⋊Q8—21no—
465C22⋊Q8D4×C7311yescharacteristic
466C22⋊Q8D4×C7312yes—
467#121—22no—
468#121—21no—
469#121—21no—
470#121D4×C7311yescharacteristic
471C4×Q8—22no—
472C4×Q8—22no—
473C4×Q8—22no—
474C4×Q8—21no—
475C4×Q8—21no—
476C4×Q8—21no—
477C4×Q8—21no—
478C4×Q8—21no—
479C4×Q8—21no—
480C4×Q8D4×C7311yescharacteristic
481C4×Q8D4×C7312yes—
482C4×Q8C23×C7311yescharacteristic
483C4×Q8C23×C7311yescharacteristic
484C4×D4—22no—
485C4×D4—21no—
486C4×D4—21no—
487C4×D4—21no—
488C4×D4—21no—
489C4×D4D4×C7311yescharacteristic
490C4×D4C23×C7311yescharacteristic
491C4×D4C23×C7311yescharacteristic
492#117—22no—
493#117—22no—
494#117—21no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—21no—
500#117—21no—
501#117D4×C7311yescharacteristic
502C2×C42—21no—
503C2×C42C23×C7311yescharacteristic
504#107—22no—
505#107—21no—
506#107—21no—
507#107—21no—
508#106—21no—
509#106—21no—
510#106—21no—
511C4⋊C8C23×C7311yescharacteristic
512C4⋊C8C23×C7311yescharacteristic
513C4⋊C8C23×C7311yescharacteristic
514C4⋊C8C23×C7311yescharacteristic
515#103—22no—
516#103—21no—
517#103—21no—
518#103—21no—
519#103—22no—
520#103—21no—
521#103—21no—
522#102—21no—
523#102—21no—
524#102—21no—
525C22⋊C8—21no—
526C22⋊C8—21no—
527#97—21no—
528C4×C8—21no—
529C4×C8—21no—
530C4×C8C23×C7311yescharacteristic
531C4×C8C23×C7311yescharacteristic
532#41—22no—
533#41—41no—
534C2×Q8—22no—
535C2×Q8—22no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—42no—
540C2×Q8—42no—
541C2×Q8C2×D4×C7311yescharacteristic
542C2×Q8C2×D4×C7311yescharacteristic
543C2×Q8C2×D4×C7312yes—
544C2×D4—21no—
545C2×D4—22no—
546C2×D4—21no—
547C2×D4C2×D4×C7311yescharacteristic
548C2×D4C2×D4×C7311yescharacteristic
549C22×C4—22no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4C2×D4×C7311yescharacteristic
555C22×C4C2×D4×C7311yescharacteristic
556C22×C4C2×D4×C7311yescharacteristic
557Q16—44no—
558Q16—42no—
559SD16—42no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—21no—
563C2×C8—21no—
564C2×C8—21no—
565C2×C8—21no—
566C2×C8—42no—
567C4⋊C4—22no—
568C4⋊C4—22no—
569C4⋊C4—22no—
570C4⋊C4—22no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—22no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—22no—
577C4⋊C4—21no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—21no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—41no—
587C4⋊C4—41no—
588C4⋊C4C2×D4×C7311yescharacteristic
589C4⋊C4C2×D4×C7311yescharacteristic
590C4⋊C4C2×D4×C7312yes—
591C4⋊C4C2×D4×C7311yescharacteristic
592C4⋊C4C2×D4×C7311yescharacteristic
593C22⋊C4—22no—
594C22⋊C4—22no—
595C22⋊C4—22no—
596C22⋊C4—22no—
597C22⋊C4—22no—
598C22⋊C4—22no—
599C22⋊C4—21no—
600C22⋊C4—21no—
601C22⋊C4—21no—
602C22⋊C4—21no—
603C22⋊C4—21no—
604C22⋊C4—21no—
605C22⋊C4—21no—
606C22⋊C4—21no—
607C22⋊C4—41no—
608C42—22no—
609C42—22no—
610C42—22no—
611C42—21no—
612C42—21no—
613C42—22no—
614C42—21no—
615C42—21no—
616C42—41no—
617C42C2×D4×C7311yescharacteristic
618C42C2×D4×C7311yescharacteristic
619C42C2×D4×C7311yescharacteristic
620C42C24×C7311yescharacteristic
621C23—21no—
622C23—21no—
623C23#120×C7311yescharacteristic
624Q8—21no—
625Q8—21no—
626Q8—21no—
627Q8—42no—
628Q8—44no—
629Q8—42no—
630Q8—41no—
631Q8—41no—
632Q8—41no—
633Q8—41no—
634Q8—82no—
635Q8#135×C7312yes—
636D4—21no—
637D4—21no—
638D4—21no—
639D4—21no—
640D4—42no—
641D4—81no—
642D4—82no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—21no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—22no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—41no—
656C2×C4—42no—
657C2×C4—44no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—81no—
665C2×C4#120×C7311yescharacteristic
666C2×C4#120×C7311yescharacteristic
667C2×C4#120×C7311yescharacteristic
668C2×C4C22×D4×C7311yescharacteristic
669C2×C4C22×D4×C7311yescharacteristic
670C2×C4C22×D4×C7311yescharacteristic
671C8—22no—
672C8—41no—
673C8—41no—
674C8—41no—
675C8—41no—
676C8—41no—
677C22—21no—
678C22—21no—
679C22—21no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22C2×#120×C7311yescharacteristic
687C4—21no—
688C4—22no—
689C4—21no—
690C4—21no—
691C4—21no—
692C4—42no—
693C4—41no—
694C4—41no—
695C4—41no—
696C4—41no—
697C4—42no—
698C4—41no—
699C4—81no—
700C4—81no—
701C4C2×#135×C7311yescharacteristic
702C4#575×C7311yescharacteristic
703C4#578×C7311yescharacteristic
704C4#578×C7311yescharacteristic
705C2—41no—
706C2—81no—
707C2—81no—
708C2C73×#300211yescharacteristic
709C2C73×#301111yescharacteristic
710C2C73×#301811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3518C2
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×#3233C2semidirect
3. C73×#3170C2semidirect
4. C73×#3116C2semidirect
5. C73×#1650C2semidirect
6. C73×#1649C2semidirect
7. C73×#1646C2semidirect
8. C73×#1645C2semidirect
9. C73×#1638C2semidirect
10. C73×#1637C2semidirect
11. C73×#1634C2semidirect
12. C73×#1633C2semidirect
13. C73×#1554C2semidirect
14. C73×#1494C2semidirect
15. C73×#1476C2semidirect
349. #18673C73direct (N × H)
357. #3233C2×C73semidirect
358. #3170C2×C73semidirect
359. #3116C2×C73semidirect
360. #1650C2×C73semidirect
361. #1649C2×C73semidirect
362. #1646C2×C73semidirect
363. #1645C2×C73semidirect
364. #1638C2×C73semidirect
365. #1637C2×C73semidirect
366. #1634C2×C73semidirect
367. #1633C2×C73semidirect
368. #1554C2×C73semidirect
369. #1494C2×C73semidirect
370. #1476C2×C73semidirect
371. C73#18673direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35182
C73×#32332
C73×#31702
C73×#31162
C73×#16502
C73×#16492
C73×#16462
C73×#16452
C73×#16382
C73×#16372
C73×#16342
C73×#16332
C73×#15542
C73×#14942
C73×#14762
#1867373