Finite Group Databasebeta

← C73×#18659 #32928063

Subgroups — C73×#18659 #32928063

Order 18688.

938 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3514C211yesmaximal, characteristic
2C73×#3233C211yesmaximal, characteristic, complemented
3C73×#3167C211yesmaximal, characteristic, complemented
4C73×#3116C211yesmaximal, characteristic, complemented
5C73×#1652C211yesmaximal, characteristic, complemented
6C73×#1651C211yesmaximal, characteristic, complemented
7C73×#1640C211yesmaximal, characteristic, complemented
8C73×#1639C211yesmaximal, characteristic, complemented
9C73×#1638C211yesmaximal, characteristic, complemented
10C73×#1637C211yesmaximal, characteristic, complemented
11C73×#1630C211yesmaximal, characteristic, complemented
12C73×#1629C211yesmaximal, characteristic, complemented
13C73×#1553C211yesmaximal, characteristic, complemented
14C73×#1494C211yesmaximal, characteristic, complemented
15C73×#1476C211yesmaximal, characteristic, complemented
16#559×C73C2211yescharacteristic
17#556×C73C2211yescharacteristic
18#555×C73—21no—
19#551×C73—22no—
20D4×Q8×C73C2211yescharacteristic
21#548×C73—21no—
22#546×C73—21no—
23#546×C73—21no—
24D42×C73C2211yescharacteristic
25#542×C73—21no—
26#538×C73—22no—
27#533×C73C2211yescharacteristic, complemented
28#532×C73C2211yescharacteristic
29#529×C73—21no—
30#529×C73C2211yescharacteristic
31C2×#124×C73—21no—
32#518×C73—21no—
33C4×#41×C73C2211yescharacteristic
34#499×C73—21no—
35#498×C73C2211yescharacteristic, complemented
36#492×C73C2211yescharacteristic
37#488×C73—21no—
38#487×C73C2211yescharacteristic, complemented
39#486×C73C2211yescharacteristic
40#485×C73—21no—
41#485×C73—21no—
42#482×C73—21no—
43#477×C73C2211yescharacteristic, complemented
44#477×C73C2211yescharacteristic, complemented
45#476×C73C2211yescharacteristic
46#476×C73C2211yescharacteristic
47#475×C73C2211yescharacteristic, complemented
48#474×C73C2211yescharacteristic
49#465×C73—22no—
50#462×C73C2211yescharacteristic, complemented
51#461×C73C2211yescharacteristic
52#452×C73—21no—
53#441×C73—21no—
54#440×C73—21no—
55C4×SD16×C73—22no—
56#432×C73C2211yescharacteristic, complemented
57#431×C73C2211yescharacteristic, complemented
58C2×C4×C8×C73C2211yescharacteristic, complemented
59#332×C73C2211yescharacteristic, complemented
60#332×C73C2211yescharacteristic, complemented
61#331×C73C2211yescharacteristic
62#331×C73C2211yescharacteristic
63Q8⋊C8×C73C2211yescharacteristic, complemented
64Q8⋊C8×C73C2211yescharacteristic, complemented
65Q8⋊C8×C73C2211yescharacteristic, complemented
66Q8⋊C8×C73C2211yescharacteristic, complemented
67D4⋊C8×C73C2211yescharacteristic
68D4⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73—21no—
72C2×#41×C73D411yescharacteristic
73C22×Q8×C73—21no—
74C22×D4×C73—21no—
75C22×D4×C73—21no—
76C2×Q16×C73—21no—
77C2×SD16×C73—22no—
78C2×SD16×C73—21no—
79C22×C8×C73—21no—
80C4⋊Q8×C73—21no—
81C4⋊Q8×C73C2311yescharacteristic
82C4⋊Q8×C73C2311yescharacteristic
83C4⋊Q8×C73C2311yescharacteristic
84#127×C73C2311yescharacteristic
85#126×C73—22no—
86#126×C73—22no—
87#126×C73—21no—
88#125×C73—21no—
89#125×C73D411yescharacteristic
90#124×C73—22no—
91#124×C73—22no—
92#124×C73—22no—
93#124×C73—21no—
94#124×C73—21no—
95#124×C73—21no—
96#124×C73—21no—
97#124×C73D411yescharacteristic
98#123×C73—22no—
99#123×C73—22no—
100#123×C73—22no—
101#123×C73—21no—
102C22⋊Q8×C73—22no—
103C22⋊Q8×C73—21no—
104C22⋊Q8×C73—21no—
105C22⋊Q8×C73—22no—
106C22⋊Q8×C73—21no—
107C22⋊Q8×C73—21no—
108C22⋊Q8×C73D411yescharacteristic
109#121×C73—22no—
110#121×C73—22no—
111#121×C73—21no—
112#121×C73—21no—
113#121×C73—21no—
114#121×C73D412yes—
115#121×C73D411yescharacteristic
116#120×C73—22no—
117#120×C73—22no—
118C4×Q8×C73—21no—
119C4×Q8×C73—21no—
120C4×Q8×C73—21no—
121C4×Q8×C73D411yescharacteristic
122C4×Q8×C73C2311yescharacteristic
123C4×Q8×C73C2311yescharacteristic
124C4×D4×C73—22no—
125C4×D4×C73—22no—
126C4×D4×C73—21no—
127C4×D4×C73—21no—
128C4×D4×C73—21no—
129C4×D4×C73—21no—
130C4×D4×C73—21no—
131C4×D4×C73—21no—
132C4×D4×C73—21no—
133C4×D4×C73D412yes—
134C4×D4×C73D411yescharacteristic
135C4×D4×C73C2311yescharacteristic
136C4×D4×C73C2311yescharacteristic
137#117×C73—22no—
138#117×C73—21no—
139#117×C73—21no—
140#117×C73—21no—
141#117×C73—21no—
142#117×C73D411yescharacteristic
143C2×C22⋊C4×C73—22no—
144C2×C22⋊C4×C73—22no—
145C2×C22⋊C4×C73—22no—
146C2×C42×C73—21no—
147C2×C42×C73C2311yescharacteristic
148#107×C73—21no—
149#107×C73—21no—
150#107×C73—21no—
151#106×C73—22no—
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—21no—
160#103×C73—21no—
161#103×C73—21no—
162#103×C73—22no—
163#103×C73—21no—
164#103×C73—21no—
165#102×C73—22no—
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
176C24×C73—22no—
177#41×C73—22no—
178#41×C73—41no—
179#41×C73—81no—
180#41×C73—81no—
181C2×Q8×C73—22no—
182C2×Q8×C73—21no—
183C2×Q8×C73—21no—
184C2×Q8×C73—21no—
185C2×Q8×C73—81no—
186C2×Q8×C73—81no—
187C2×Q8×C73C2×D411yescharacteristic
188C2×Q8×C73C2×D411yescharacteristic
189C2×D4×C73—22no—
190C2×D4×C73—21no—
191C2×D4×C73—22no—
192C2×D4×C73—21no—
193C2×D4×C73—22no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—42no—
197C2×D4×C73—42no—
198C2×D4×C73—81no—
199C2×D4×C73—81no—
200C2×D4×C73C2×D411yescharacteristic
201C2×D4×C73C2×D411yescharacteristic
202C2×D4×C73C2×D412yes—
203C22×C4×C73—22no—
204C22×C4×C73—22no—
205C22×C4×C73—21no—
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—22no—
210C22×C4×C73C2×D411yescharacteristic
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D411yescharacteristic
213Q16×C73—42no—
214SD16×C73—44no—
215SD16×C73—42no—
216C2×C8×C73—21no—
217C2×C8×C73—21no—
218C2×C8×C73—21no—
219C2×C8×C73—21no—
220C2×C8×C73—21no—
221C2×C8×C73—21no—
222C2×C8×C73—42no—
223C4⋊C4×C73—22no—
224C4⋊C4×C73—22no—
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—41no—
237C4⋊C4×C73—41no—
238C4⋊C4×C73C2×D411yescharacteristic
239C4⋊C4×C73C2×D412yes—
240C4⋊C4×C73C2×D411yescharacteristic
241C4⋊C4×C73C2×D411yescharacteristic
242C4⋊C4×C73C2×D411yescharacteristic
243C22⋊C4×C73—22no—
244C22⋊C4×C73—22no—
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—21no—
252C22⋊C4×C73—21no—
253C22⋊C4×C73—21no—
254C22⋊C4×C73—21no—
255C22⋊C4×C73—21no—
256C22⋊C4×C73—22no—
257C22⋊C4×C73—22no—
258C22⋊C4×C73—21no—
259C22⋊C4×C73—21no—
260C22⋊C4×C73—41no—
261C42×C73—22no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—21no—
265C42×C73—21no—
266C42×C73—41no—
267C42×C73C2×D411yescharacteristic
268C42×C73C2×D411yescharacteristic
269C42×C73C2×D411yescharacteristic
270C42×C73C2411yescharacteristic
271C23×C73—21no—
272C23×C73—21no—
273C23×C73—22no—
274C23×C73—44no—
275C23×C73—82no—
276C23×C73—82no—
277C23×C73#12011yescharacteristic
278Q8×C73—21no—
279Q8×C73—21no—
280Q8×C73—21no—
281Q8×C73—21no—
282Q8×C73—42no—
283Q8×C73—41no—
284Q8×C73—41no—
285Q8×C73—41no—
286Q8×C73—41no—
287Q8×C73—82no—
288D4×C73—21no—
289D4×C73—21no—
290D4×C73—21no—
291D4×C73—42no—
292D4×C73—42no—
293D4×C73—44no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—81no—
299D4×C73—82no—
300D4×C73—82no—
301D4×C73#13512yes—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—21no—
308C2×C4×C73—21no—
309C2×C4×C73—21no—
310C2×C4×C73—21no—
311C2×C4×C73—21no—
312C2×C4×C73—22no—
313C2×C4×C73—41no—
314C2×C4×C73—42no—
315C2×C4×C73—41no—
316C2×C4×C73—41no—
317C2×C4×C73—41no—
318C2×C4×C73—41no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—81no—
322C2×C4×C73—82no—
323C2×C4×C73—82no—
324C2×C4×C73—82no—
325C2×C4×C73#12011yescharacteristic
326C2×C4×C73#12011yescharacteristic
327C2×C4×C73#12011yescharacteristic
328C2×C4×C73C22×D411yescharacteristic
329C2×C4×C73C22×D411yescharacteristic
330C2×C4×C73C22×D411yescharacteristic
331C8×C73—22no—
332C8×C73—41no—
333C8×C73—41no—
334C8×C73—41no—
335C8×C73—41no—
336C8×C73—41no—
337C22×C73—21no—
338C22×C73—22no—
339C22×C73—21no—
340C22×C73—21no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—41no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—41no—
347C22×C73—42no—
348C22×C73—41no—
349C22×C73—164no—
350C22×C73C2×#12011yescharacteristic
351C4×C73—21no—
352C4×C73—21no—
353C4×C73—21no—
354C4×C73—21no—
355C4×C73—41no—
356C4×C73—41no—
357C4×C73—41no—
358C4×C73—42no—
359C4×C73—41no—
360C4×C73—41no—
361C4×C73—41no—
362C4×C73—81no—
363C4×C73—81no—
364C4×C73C2×#13511yescharacteristic
365C4×C73#57511yescharacteristic
366C4×C73#57711yescharacteristic
367C4×C73#57711yescharacteristic
368#18659C7311yesmaximal, characteristic, direct product factor, Sylow
369C2×C73—41no—
370C2×C73—42no—
371C2×C73—82no—
372C2×C73—81no—
373C2×C73#300211yescharacteristic
374C2×C73#300911yescharacteristic
375C2×C73#301811yescharacteristic
376#3514C2×C7311yescharacteristic
377#3233C2×C7311yescharacteristic, complemented
378#3167C2×C7311yescharacteristic, complemented
379#3116C2×C7311yescharacteristic, complemented
380#1652C2×C7311yescharacteristic, complemented
381#1651C2×C7311yescharacteristic, complemented
382#1640C2×C7311yescharacteristic, complemented
383#1639C2×C7311yescharacteristic, complemented
384#1638C2×C7311yescharacteristic, complemented
385#1637C2×C7311yescharacteristic, complemented
386#1630C2×C7311yescharacteristic, complemented
387#1629C2×C7311yescharacteristic, complemented
388#1553C2×C7311yescharacteristic, complemented
389#1494C2×C7311yescharacteristic, complemented
390#1476C2×C7311yescharacteristic, complemented
391C73#1865911yescharacteristic, direct product factor, Sylow
392#559C22×C7311yescharacteristic
393#556C22×C7311yescharacteristic
394#555—21no—
395#551—22no—
396D4×Q8C22×C7311yescharacteristic
397#548—21no—
398#546—21no—
399#546—21no—
400D42C22×C7311yescharacteristic
401#542—21no—
402#538—22no—
403#533C22×C7311yescharacteristic, complemented
404#532C22×C7311yescharacteristic
405#529—21no—
406#529C22×C7311yescharacteristic
407C2×#124—21no—
408#518—21no—
409C4×#41C22×C7311yescharacteristic
410#499—21no—
411#498C22×C7311yescharacteristic, complemented
412#492C22×C7311yescharacteristic
413#488—21no—
414#487C22×C7311yescharacteristic, complemented
415#486C22×C7311yescharacteristic
416#485—21no—
417#485—21no—
418#482—21no—
419#477C22×C7311yescharacteristic, complemented
420#477C22×C7311yescharacteristic, complemented
421#476C22×C7311yescharacteristic
422#476C22×C7311yescharacteristic
423#475C22×C7311yescharacteristic, complemented
424#474C22×C7311yescharacteristic
425#465—22no—
426#462C22×C7311yescharacteristic, complemented
427#461C22×C7311yescharacteristic
428#452—21no—
429#441—21no—
430#440—21no—
431C4×SD16—22no—
432#432C22×C7311yescharacteristic, complemented
433#431C22×C7311yescharacteristic, complemented
434C2×C4×C8C22×C7311yescharacteristic, complemented
435#332C22×C7311yescharacteristic, complemented
436#332C22×C7311yescharacteristic, complemented
437#331C22×C7311yescharacteristic
438#331C22×C7311yescharacteristic
439Q8⋊C8C22×C7311yescharacteristic, complemented
440Q8⋊C8C22×C7311yescharacteristic, complemented
441Q8⋊C8C22×C7311yescharacteristic, complemented
442Q8⋊C8C22×C7311yescharacteristic, complemented
443D4⋊C8C22×C7311yescharacteristic
444D4⋊C8C22×C7311yescharacteristic
445D4⋊C8C22×C7311yescharacteristic
446D4⋊C8C22×C7311yescharacteristic
447C2×#41—21no—
448C2×#41D4×C7311yescharacteristic
449C22×Q8—21no—
450C22×D4—21no—
451C22×D4—21no—
452C2×Q16—21no—
453C2×SD16—22no—
454C2×SD16—21no—
455C22×C8—21no—
456C4⋊Q8—21no—
457C4⋊Q8C23×C7311yescharacteristic
458C4⋊Q8C23×C7311yescharacteristic
459C4⋊Q8C23×C7311yescharacteristic
460#127C23×C7311yescharacteristic
461#126—22no—
462#126—22no—
463#126—21no—
464#125—21no—
465#125D4×C7311yescharacteristic
466#124—22no—
467#124—22no—
468#124—22no—
469#124—21no—
470#124—21no—
471#124—21no—
472#124—21no—
473#124D4×C7311yescharacteristic
474#123—22no—
475#123—22no—
476#123—22no—
477#123—21no—
478C22⋊Q8—22no—
479C22⋊Q8—21no—
480C22⋊Q8—21no—
481C22⋊Q8—22no—
482C22⋊Q8—21no—
483C22⋊Q8—21no—
484C22⋊Q8D4×C7311yescharacteristic
485#121—22no—
486#121—22no—
487#121—21no—
488#121—21no—
489#121—21no—
490#121D4×C7311yescharacteristic
491#121D4×C7312yes—
492#120—22no—
493#120—22no—
494C4×Q8—21no—
495C4×Q8—21no—
496C4×Q8—21no—
497C4×Q8D4×C7311yescharacteristic
498C4×Q8C23×C7311yescharacteristic
499C4×Q8C23×C7311yescharacteristic
500C4×D4—22no—
501C4×D4—22no—
502C4×D4—21no—
503C4×D4—21no—
504C4×D4—21no—
505C4×D4—21no—
506C4×D4—21no—
507C4×D4—21no—
508C4×D4—21no—
509C4×D4D4×C7311yescharacteristic
510C4×D4D4×C7312yes—
511C4×D4C23×C7311yescharacteristic
512C4×D4C23×C7311yescharacteristic
513#117—22no—
514#117—21no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117D4×C7311yescharacteristic
519C2×C22⋊C4—22no—
520C2×C22⋊C4—22no—
521C2×C22⋊C4—22no—
522C2×C42—21no—
523C2×C42C23×C7311yescharacteristic
524#107—21no—
525#107—21no—
526#107—21no—
527#106—22no—
528#106—21no—
529#106—21no—
530#106—21no—
531C4⋊C8C23×C7311yescharacteristic
532C4⋊C8C23×C7311yescharacteristic
533C4⋊C8C23×C7311yescharacteristic
534C4⋊C8C23×C7311yescharacteristic
535#103—21no—
536#103—21no—
537#103—21no—
538#103—22no—
539#103—21no—
540#103—21no—
541#102—22no—
542#102—21no—
543#102—21no—
544#102—21no—
545C22⋊C8—21no—
546C22⋊C8—21no—
547#97—21no—
548C4×C8—21no—
549C4×C8—21no—
550C4×C8C23×C7311yescharacteristic
551C4×C8C23×C7311yescharacteristic
552C24—22no—
553#41—22no—
554#41—41no—
555#41—81no—
556#41—81no—
557C2×Q8—22no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—81no—
562C2×Q8—81no—
563C2×Q8C2×D4×C7311yescharacteristic
564C2×Q8C2×D4×C7311yescharacteristic
565C2×D4—22no—
566C2×D4—21no—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—42no—
573C2×D4—42no—
574C2×D4—81no—
575C2×D4—81no—
576C2×D4C2×D4×C7311yescharacteristic
577C2×D4C2×D4×C7311yescharacteristic
578C2×D4C2×D4×C7312yes—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—22no—
586C22×C4C2×D4×C7311yescharacteristic
587C22×C4C2×D4×C7311yescharacteristic
588C22×C4C2×D4×C7311yescharacteristic
589Q16—42no—
590SD16—44no—
591SD16—42no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—42no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—41no—
613C4⋊C4—41no—
614C4⋊C4C2×D4×C7311yescharacteristic
615C4⋊C4C2×D4×C7312yes—
616C4⋊C4C2×D4×C7311yescharacteristic
617C4⋊C4C2×D4×C7311yescharacteristic
618C4⋊C4C2×D4×C7311yescharacteristic
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—22no—
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—21no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—21no—
630C22⋊C4—21no—
631C22⋊C4—21no—
632C22⋊C4—22no—
633C22⋊C4—22no—
634C22⋊C4—21no—
635C22⋊C4—21no—
636C22⋊C4—41no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—41no—
643C42C2×D4×C7311yescharacteristic
644C42C2×D4×C7311yescharacteristic
645C42C2×D4×C7311yescharacteristic
646C42C24×C7311yescharacteristic
647C23—21no—
648C23—21no—
649C23—22no—
650C23—44no—
651C23—82no—
652C23—82no—
653C23#120×C7311yescharacteristic
654Q8—21no—
655Q8—21no—
656Q8—21no—
657Q8—21no—
658Q8—42no—
659Q8—41no—
660Q8—41no—
661Q8—41no—
662Q8—41no—
663Q8—82no—
664D4—21no—
665D4—21no—
666D4—21no—
667D4—42no—
668D4—42no—
669D4—44no—
670D4—41no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—82no—
675D4—81no—
676D4—82no—
677D4#135×C7312yes—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—21no—
685C2×C4—21no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—42no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—82no—
698C2×C4—81no—
699C2×C4—82no—
700C2×C4—82no—
701C2×C4#120×C7311yescharacteristic
702C2×C4#120×C7311yescharacteristic
703C2×C4#120×C7311yescharacteristic
704C2×C4C22×D4×C7311yescharacteristic
705C2×C4C22×D4×C7311yescharacteristic
706C2×C4C22×D4×C7311yescharacteristic
707C8—22no—
708C8—41no—
709C8—41no—
710C8—41no—
711C8—41no—
712C8—41no—
713C22—21no—
714C22—22no—
715C22—21no—
716C22—21no—
717C22—41no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—41no—
723C22—42no—
724C22—41no—
725C22—164no—
726C22C2×#120×C7311yescharacteristic
727C4—21no—
728C4—21no—
729C4—21no—
730C4—21no—
731C4—41no—
732C4—41no—
733C4—41no—
734C4—42no—
735C4—41no—
736C4—41no—
737C4—41no—
738C4—81no—
739C4—81no—
740C4C2×#135×C7311yescharacteristic
741C4#575×C7311yescharacteristic
742C4#577×C7311yescharacteristic
743C4#577×C7311yescharacteristic
744C2—41no—
745C2—42no—
746C2—81no—
747C2—82no—
748C2C73×#300211yescharacteristic
749C2C73×#300911yescharacteristic
750C2C73×#301811yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3514C2
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×#3167C2semidirect
4. C73×#3116C2semidirect
5. C73×#1652C2semidirect
6. C73×#1651C2semidirect
7. C73×#1640C2semidirect
8. C73×#1639C2semidirect
9. C73×#1638C2semidirect
10. C73×#1637C2semidirect
11. C73×#1630C2semidirect
12. C73×#1629C2semidirect
13. C73×#1553C2semidirect
14. C73×#1494C2semidirect
15. C73×#1476C2semidirect
27. #533×C73C22semidirect
35. #498×C73C22semidirect
38. #487×C73C22semidirect
43. #477×C73C22semidirect
44. #477×C73C22semidirect
47. #475×C73C22semidirect
50. #462×C73C22semidirect
56. #432×C73C22semidirect
57. #431×C73C22semidirect
58. C2×C4×C8×C73C22semidirect
59. #332×C73C22semidirect
60. #332×C73C22semidirect
63. Q8⋊C8×C73C22semidirect
64. Q8⋊C8×C73C22semidirect
65. Q8⋊C8×C73C22semidirect
66. Q8⋊C8×C73C22semidirect
368. #18659C73direct (N × H)
377. #3233C2×C73semidirect
378. #3167C2×C73semidirect
379. #3116C2×C73semidirect
380. #1652C2×C73semidirect
381. #1651C2×C73semidirect
382. #1640C2×C73semidirect
383. #1639C2×C73semidirect
384. #1638C2×C73semidirect
385. #1637C2×C73semidirect
386. #1630C2×C73semidirect
387. #1629C2×C73semidirect
388. #1553C2×C73semidirect
389. #1494C2×C73semidirect
390. #1476C2×C73semidirect
391. C73#18659direct (N × H)
403. #533C22×C73semidirect
411. #498C22×C73semidirect
414. #487C22×C73semidirect
419. #477C22×C73semidirect
420. #477C22×C73semidirect
423. #475C22×C73semidirect
426. #462C22×C73semidirect
432. #432C22×C73semidirect
433. #431C22×C73semidirect
434. C2×C4×C8C22×C73semidirect
435. #332C22×C73semidirect
436. #332C22×C73semidirect
439. Q8⋊C8C22×C73semidirect
440. Q8⋊C8C22×C73semidirect
441. Q8⋊C8C22×C73semidirect
442. Q8⋊C8C22×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35142
C73×#32332
C73×#31672
C73×#31162
C73×#16522
C73×#16512
C73×#16402
C73×#16392
C73×#16382
C73×#16372
C73×#16302
C73×#16292
C73×#15532
C73×#14942
C73×#14762
#1865973