Finite Group Databasebeta

← C73×#18775 #32928179

Subgroups — C73×#18775 #32928179

Order 18688.

968 conjugacy classes of subgroups.

The subgroup lattice has 754 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3483C211yesmaximal, characteristic
2C73×#3210C211yesmaximal, characteristic, complemented
3C73×#3116C211yesmaximal, characteristic, complemented
4C73×#3076C211yesmaximal, characteristic, complemented
5C73×#1646C211yesmaximal, characteristic, complemented
6C73×#1645C211yesmaximal, characteristic, complemented
7C73×#1642C211yesmaximal, characteristic, complemented
8C73×#1641C211yesmaximal, characteristic, complemented
9C73×#1634C211yesmaximal, characteristic, complemented
10C73×#1633C211yesmaximal, characteristic, complemented
11C73×#1631C211yesmaximal, characteristic, complemented
12C73×#1631C211yesmaximal, characteristic, complemented
13C73×#1551C211yesmaximal, characteristic, complemented
14C73×#1488C211yesmaximal, characteristic, complemented
15C73×#1477C211yesmaximal, characteristic, complemented
16Q82×C73C2211yescharacteristic
17#555×C73—22no—
18#555×C73—21no—
19#555×C73—21no—
20#555×C73C2211yescharacteristic
21#550×C73—21no—
22#550×C73—21no—
23#550×C73C2211yescharacteristic
24#550×C73C2211yescharacteristic
25#533×C73C2211yescharacteristic
26#532×C73—22no—
27#532×C73—21no—
28#532×C73—21no—
29#532×C73C2211yescharacteristic
30C4×#41×C73—21no—
31C4×#41×C73—21no—
32C4×#41×C73C2211yescharacteristic
33C4×#41×C73C2211yescharacteristic
34#494×C73C2211yescharacteristic
35#492×C73C2211yescharacteristic
36#487×C73C2211yescharacteristic
37#486×C73C2211yescharacteristic
38#485×C73—21no—
39#479×C73—21no—
40#478×C73—21no—
41#477×C73C2211yescharacteristic
42#477×C73C2211yescharacteristic
43#476×C73C2211yescharacteristic
44#476×C73C2211yescharacteristic
45#475×C73C2211yescharacteristic
46#474×C73C2211yescharacteristic
47#464×C73—22no—
48#462×C73C2211yescharacteristic
49#461×C73C2211yescharacteristic
50#452×C73—22no—
51#452×C73—21no—
52#441×C73—21no—
53#440×C73—21no—
54#432×C73C2211yescharacteristic
55#431×C73C2211yescharacteristic
56#427×C73—21no—
57C2×C4⋊C8×C73C2211yescharacteristic
58#416×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
67D4⋊C8×C73C2211yescharacteristic
68D4⋊C8×C73C2211yescharacteristic
69D4⋊C8×C73C2211yescharacteristic
70D4⋊C8×C73C2211yescharacteristic
71C2×#41×C73—22no—
72C2×#41×C73—21no—
73C2×#41×C73—21no—
74C2×#41×C73D411yescharacteristic
75C2×#41×C73D411yescharacteristic
76C2×#41×C73D412yes—
77C2×Q16×C73—21no—
78C2×Q16×C73—22no—
79C2×SD16×C73—21no—
80C2×SD16×C73—22no—
81C22×C8×C73—21no—
82C4⋊Q8×C73—22no—
83C4⋊Q8×C73—21no—
84C4⋊Q8×C73—21no—
85C4⋊Q8×C73C2311yescharacteristic
86C4⋊Q8×C73C2311yescharacteristic
87C4⋊Q8×C73C2311yescharacteristic
88#127×C73—22no—
89#127×C73—21no—
90#127×C73—21no—
91#127×C73C2311yescharacteristic
92#125×C73—21no—
93#124×C73—22no—
94#124×C73—22no—
95#124×C73—22no—
96#124×C73—22no—
97#124×C73D412yes—
98C22⋊Q8×C73—21no—
99C22⋊Q8×C73—21no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—22no—
103#121×C73—22no—
104#121×C73—21no—
105#121×C73—21no—
106#121×C73—22no—
107#121×C73—22no—
108#121×C73—21no—
109#121×C73—21no—
110#121×C73—21no—
111#121×C73—21no—
112C4×Q8×C73—21no—
113C4×Q8×C73—21no—
114C4×Q8×C73—21no—
115C4×Q8×C73—21no—
116C4×Q8×C73D411yescharacteristic
117C4×Q8×C73D411yescharacteristic
118C4×Q8×C73C2311yescharacteristic
119C4×Q8×C73C2311yescharacteristic
120C4×D4×C73—22no—
121C4×D4×C73—22no—
122C4×D4×C73—22no—
123C4×D4×C73—22no—
124C4×D4×C73—21no—
125C4×D4×C73—21no—
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×C73D411yescharacteristic
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×C73D411yescharacteristic
144#117×C73D411yescharacteristic
145C2×C42×C73—22no—
146C2×C42×C73—21no—
147C2×C42×C73—21no—
148C2×C42×C73C2311yescharacteristic
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×C73—21no—
156C4⋊C8×C73—21no—
157C4⋊C8×C73C2311yescharacteristic
158C4⋊C8×C73C2311yescharacteristic
159C4⋊C8×C73C2311yescharacteristic
160C4⋊C8×C73C2311yescharacteristic
161#103×C73—21no—
162#103×C73—21no—
163#103×C73—21no—
164#103×C73—22no—
165#103×C73—21no—
166#103×C73—21no—
167#102×C73—21no—
168#102×C73—21no—
169#102×C73—21no—
170#102×C73—22no—
171C22⋊C8×C73—21no—
172C22⋊C8×C73—21no—
173#97×C73—21no—
174C4×C8×C73C2311yescharacteristic
175C4×C8×C73C2311yescharacteristic
176#41×C73—22no—
177#41×C73—22no—
178#41×C73—41no—
179#41×C73—41no—
180#41×C73—42no—
181#41×C73—42no—
182#41×C73—42no—
183#41×C73—42no—
184#41×C73—82no—
185#41×C73—84no—
186C2×Q8×C73—22no—
187C2×Q8×C73—21no—
188C2×Q8×C73—21no—
189C2×Q8×C73C2×D411yescharacteristic
190C2×Q8×C73C2×D411yescharacteristic
191C2×Q8×C73C2×D412yes—
192C2×D4×C73—22no—
193C2×D4×C73—22no—
194C2×D4×C73—21no—
195C2×D4×C73—21no—
196C2×D4×C73—22no—
197C2×D4×C73—22no—
198C2×D4×C73—22no—
199C2×D4×C73—22no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73C2×D411yescharacteristic
203C2×D4×C73C2×D411yescharacteristic
204C2×D4×C73C2×D412yes—
205C22×C4×C73—22no—
206C22×C4×C73—22no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—22no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—21no—
213C22×C4×C73—21no—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217Q16×C73—42no—
218Q16×C73—82no—
219SD16×C73—42no—
220SD16×C73—82no—
221C2×C8×C73—21no—
222C2×C8×C73—21no—
223C2×C8×C73—21no—
224C2×C8×C73—21no—
225C2×C8×C73—21no—
226C2×C8×C73—21no—
227C2×C8×C73—42no—
228C4⋊C4×C73—22no—
229C4⋊C4×C73—22no—
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—21no—
240C4⋊C4×C73—41no—
241C4⋊C4×C73—41no—
242C4⋊C4×C73C2×D411yescharacteristic
243C4⋊C4×C73C2×D411yescharacteristic
244C4⋊C4×C73C2×D411yescharacteristic
245C4⋊C4×C73C2×D411yescharacteristic
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—22no—
253C22⋊C4×C73—22no—
254C22⋊C4×C73—21no—
255C22⋊C4×C73—21no—
256C22⋊C4×C73—21no—
257C22⋊C4×C73—21no—
258C22⋊C4×C73—41no—
259C42×C73—22no—
260C42×C73—22no—
261C42×C73—21no—
262C42×C73—21no—
263C42×C73—21no—
264C42×C73—21no—
265C42×C73—21no—
266C42×C73—21no—
267C42×C73—41no—
268C42×C73C2×D411yescharacteristic
269C42×C73C2×D411yescharacteristic
270C42×C73C2×D411yescharacteristic
271C42×C73C2411yescharacteristic
272C23×C73—21no—
273C23×C73—21no—
274C23×C73—22no—
275C23×C73#12011yescharacteristic
276Q8×C73—21no—
277Q8×C73—21no—
278Q8×C73—42no—
279Q8×C73—42no—
280Q8×C73—41no—
281Q8×C73—41no—
282Q8×C73—82no—
283Q8×C73#13512yes—
284Q8×C73#13712yes—
285D4×C73—21no—
286D4×C73—21no—
287D4×C73—21no—
288D4×C73—21no—
289D4×C73—42no—
290D4×C73—42no—
291D4×C73—42no—
292D4×C73—44no—
293D4×C73—44no—
294D4×C73—41no—
295D4×C73—41no—
296D4×C73—41no—
297D4×C73—41no—
298D4×C73—82no—
299D4×C73—82no—
300D4×C73—82no—
301D4×C73—82no—
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—22no—
311C2×C4×C73—21no—
312C2×C4×C73—21no—
313C2×C4×C73—41no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—44no—
317C2×C4×C73—44no—
318C2×C4×C73—44no—
319C2×C4×C73—42no—
320C2×C4×C73—42no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—41no—
324C2×C4×C73—41no—
325C2×C4×C73—41no—
326C2×C4×C73—41no—
327C2×C4×C73#12011yescharacteristic
328C2×C4×C73#12011yescharacteristic
329C2×C4×C73#12011yescharacteristic
330C2×C4×C73C22×D411yescharacteristic
331C2×C4×C73C22×D411yescharacteristic
332C2×C4×C73C22×D411yescharacteristic
333C8×C73—41no—
334C8×C73—41no—
335C8×C73—41no—
336C8×C73—41no—
337C8×C73—41no—
338C8×C73—41no—
339C22×C73—21no—
340C22×C73—21no—
341C22×C73—21no—
342C22×C73—41no—
343C22×C73—42no—
344C22×C73—41no—
345C22×C73—41no—
346C22×C73—42no—
347C22×C73—41no—
348C22×C73—42no—
349C22×C73—41no—
350C22×C73—41no—
351C22×C73C2×#12011yescharacteristic
352C4×C73—21no—
353C4×C73—22no—
354C4×C73—21no—
355C4×C73—22no—
356C4×C73—21no—
357C4×C73—21no—
358C4×C73—41no—
359C4×C73—41no—
360C4×C73—42no—
361C4×C73—41no—
362C4×C73—41no—
363C4×C73—81no—
364C4×C73—81no—
365C4×C73C2×#13511yescharacteristic
366C4×C73C2×#13711yescharacteristic
367C4×C73#57511yescharacteristic
368C4×C73#57511yescharacteristic
369#18775C7311yesmaximal, characteristic, direct product factor, Sylow
370C2×C73—41no—
371C2×C73—81no—
372C2×C73—81no—
373C2×C73—82no—
374C2×C73#300211yescharacteristic
375C2×C73#300711yescharacteristic
376C2×C73#301911yescharacteristic
377#3483C2×C7311yescharacteristic
378#3210C2×C7311yescharacteristic, complemented
379#3116C2×C7311yescharacteristic, complemented
380#3076C2×C7311yescharacteristic, complemented
381#1646C2×C7311yescharacteristic, complemented
382#1645C2×C7311yescharacteristic, complemented
383#1642C2×C7311yescharacteristic, complemented
384#1641C2×C7311yescharacteristic, complemented
385#1634C2×C7311yescharacteristic, complemented
386#1633C2×C7311yescharacteristic, complemented
387#1631C2×C7311yescharacteristic, complemented
388#1631C2×C7311yescharacteristic, complemented
389#1551C2×C7311yescharacteristic, complemented
390#1488C2×C7311yescharacteristic, complemented
391#1477C2×C7311yescharacteristic, complemented
392C73#1877511yescharacteristic, direct product factor, Sylow
393Q82C22×C7311yescharacteristic
394#555—22no—
395#555—21no—
396#555—21no—
397#555C22×C7311yescharacteristic
398#550—21no—
399#550—21no—
400#550C22×C7311yescharacteristic
401#550C22×C7311yescharacteristic
402#533C22×C7311yescharacteristic
403#532—22no—
404#532—21no—
405#532—21no—
406#532C22×C7311yescharacteristic
407C4×#41—21no—
408C4×#41—21no—
409C4×#41C22×C7311yescharacteristic
410C4×#41C22×C7311yescharacteristic
411#494C22×C7311yescharacteristic
412#492C22×C7311yescharacteristic
413#487C22×C7311yescharacteristic
414#486C22×C7311yescharacteristic
415#485—21no—
416#479—21no—
417#478—21no—
418#477C22×C7311yescharacteristic
419#477C22×C7311yescharacteristic
420#476C22×C7311yescharacteristic
421#476C22×C7311yescharacteristic
422#475C22×C7311yescharacteristic
423#474C22×C7311yescharacteristic
424#464—22no—
425#462C22×C7311yescharacteristic
426#461C22×C7311yescharacteristic
427#452—21no—
428#452—22no—
429#441—21no—
430#440—21no—
431#432C22×C7311yescharacteristic
432#431C22×C7311yescharacteristic
433#427—21no—
434C2×C4⋊C8C22×C7311yescharacteristic
435#416—21no—
436#333C22×C7311yescharacteristic
437#333C22×C7311yescharacteristic
438#331C22×C7311yescharacteristic
439#331C22×C7311yescharacteristic
440Q8⋊C8C22×C7311yescharacteristic
441Q8⋊C8C22×C7311yescharacteristic
442Q8⋊C8C22×C7311yescharacteristic
443Q8⋊C8C22×C7311yescharacteristic
444D4⋊C8C22×C7311yescharacteristic
445D4⋊C8C22×C7311yescharacteristic
446D4⋊C8C22×C7311yescharacteristic
447D4⋊C8C22×C7311yescharacteristic
448C2×#41—22no—
449C2×#41—21no—
450C2×#41—21no—
451C2×#41D4×C7311yescharacteristic
452C2×#41D4×C7311yescharacteristic
453C2×#41D4×C7312yes—
454C2×Q16—21no—
455C2×Q16—22no—
456C2×SD16—21no—
457C2×SD16—22no—
458C22×C8—21no—
459C4⋊Q8—22no—
460C4⋊Q8—21no—
461C4⋊Q8—21no—
462C4⋊Q8C23×C7311yescharacteristic
463C4⋊Q8C23×C7311yescharacteristic
464C4⋊Q8C23×C7311yescharacteristic
465#127—22no—
466#127—21no—
467#127—21no—
468#127C23×C7311yescharacteristic
469#125—21no—
470#124—22no—
471#124—22no—
472#124—22no—
473#124—22no—
474#124D4×C7312yes—
475C22⋊Q8—21no—
476C22⋊Q8—21no—
477#121—22no—
478#121—22no—
479#121—22no—
480#121—22no—
481#121—21no—
482#121—21no—
483#121—22no—
484#121—22no—
485#121—21no—
486#121—21no—
487#121—21no—
488#121—21no—
489C4×Q8—21no—
490C4×Q8—21no—
491C4×Q8—21no—
492C4×Q8—21no—
493C4×Q8D4×C7311yescharacteristic
494C4×Q8D4×C7311yescharacteristic
495C4×Q8C23×C7311yescharacteristic
496C4×Q8C23×C7311yescharacteristic
497C4×D4—22no—
498C4×D4—22no—
499C4×D4—22no—
500C4×D4—22no—
501C4×D4—21no—
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×C7311yescharacteristic
511C4×D4C23×C7311yescharacteristic
512C4×D4C23×C7311yescharacteristic
513#117—22no—
514#117—22no—
515#117—21no—
516#117—21no—
517#117—21no—
518#117—21no—
519#117—21no—
520#117D4×C7311yescharacteristic
521#117D4×C7311yescharacteristic
522C2×C42—22no—
523C2×C42—21no—
524C2×C42—21no—
525C2×C42C23×C7311yescharacteristic
526#107—21no—
527#107—21no—
528#107—21no—
529#106—21no—
530#106—21no—
531#106—21no—
532C4⋊C8—21no—
533C4⋊C8—21no—
534C4⋊C8C23×C7311yescharacteristic
535C4⋊C8C23×C7311yescharacteristic
536C4⋊C8C23×C7311yescharacteristic
537C4⋊C8C23×C7311yescharacteristic
538#103—21no—
539#103—21no—
540#103—21no—
541#103—22no—
542#103—21no—
543#103—21no—
544#102—21no—
545#102—21no—
546#102—21no—
547#102—22no—
548C22⋊C8—21no—
549C22⋊C8—21no—
550#97—21no—
551C4×C8C23×C7311yescharacteristic
552C4×C8C23×C7311yescharacteristic
553#41—22no—
554#41—22no—
555#41—41no—
556#41—41no—
557#41—42no—
558#41—42no—
559#41—42no—
560#41—42no—
561#41—82no—
562#41—84no—
563C2×Q8—22no—
564C2×Q8—21no—
565C2×Q8—21no—
566C2×Q8C2×D4×C7311yescharacteristic
567C2×Q8C2×D4×C7311yescharacteristic
568C2×Q8C2×D4×C7312yes—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—22no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—21no—
578C2×D4—21no—
579C2×D4C2×D4×C7311yescharacteristic
580C2×D4C2×D4×C7311yescharacteristic
581C2×D4C2×D4×C7312yes—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—22no—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—21no—
590C22×C4—21no—
591C22×C4C2×D4×C7311yescharacteristic
592C22×C4C2×D4×C7311yescharacteristic
593C22×C4C2×D4×C7311yescharacteristic
594Q16—42no—
595Q16—82no—
596SD16—42no—
597SD16—82no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—42no—
605C4⋊C4—22no—
606C4⋊C4—22no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—41no—
618C4⋊C4—41no—
619C4⋊C4C2×D4×C7311yescharacteristic
620C4⋊C4C2×D4×C7311yescharacteristic
621C4⋊C4C2×D4×C7311yescharacteristic
622C4⋊C4C2×D4×C7311yescharacteristic
623C22⋊C4—22no—
624C22⋊C4—22no—
625C22⋊C4—22no—
626C22⋊C4—22no—
627C22⋊C4—21no—
628C22⋊C4—21no—
629C22⋊C4—22no—
630C22⋊C4—22no—
631C22⋊C4—21no—
632C22⋊C4—21no—
633C22⋊C4—21no—
634C22⋊C4—21no—
635C22⋊C4—41no—
636C42—22no—
637C42—22no—
638C42—21no—
639C42—21no—
640C42—21no—
641C42—21no—
642C42—21no—
643C42—21no—
644C42—41no—
645C42C2×D4×C7311yescharacteristic
646C42C2×D4×C7311yescharacteristic
647C42C2×D4×C7311yescharacteristic
648C42C24×C7311yescharacteristic
649C23—21no—
650C23—21no—
651C23—22no—
652C23#120×C7311yescharacteristic
653Q8—21no—
654Q8—21no—
655Q8—42no—
656Q8—42no—
657Q8—41no—
658Q8—41no—
659Q8—82no—
660Q8#135×C7312yes—
661Q8#137×C7312yes—
662D4—21no—
663D4—21no—
664D4—21no—
665D4—21no—
666D4—42no—
667D4—42no—
668D4—42no—
669D4—44no—
670D4—44no—
671D4—41no—
672D4—41no—
673D4—41no—
674D4—41no—
675D4—82no—
676D4—82no—
677D4—82no—
678D4—82no—
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—22no—
688C2×C4—21no—
689C2×C4—21no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—44no—
694C2×C4—44no—
695C2×C4—44no—
696C2×C4—42no—
697C2×C4—42no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4#120×C7311yescharacteristic
705C2×C4#120×C7311yescharacteristic
706C2×C4#120×C7311yescharacteristic
707C2×C4C22×D4×C7311yescharacteristic
708C2×C4C22×D4×C7311yescharacteristic
709C2×C4C22×D4×C7311yescharacteristic
710C8—41no—
711C8—41no—
712C8—41no—
713C8—41no—
714C8—41no—
715C8—41no—
716C22—21no—
717C22—21no—
718C22—21no—
719C22—41no—
720C22—42no—
721C22—41no—
722C22—41no—
723C22—42no—
724C22—41no—
725C22—42no—
726C22—41no—
727C22—41no—
728C22C2×#120×C7311yescharacteristic
729C4—21no—
730C4—22no—
731C4—21no—
732C4—22no—
733C4—21no—
734C4—21no—
735C4—41no—
736C4—41no—
737C4—42no—
738C4—41no—
739C4—41no—
740C4—81no—
741C4—81no—
742C4C2×#135×C7311yescharacteristic
743C4C2×#137×C7311yescharacteristic
744C4#575×C7311yescharacteristic
745C4#575×C7311yescharacteristic
746C2—41no—
747C2—81no—
748C2—81no—
749C2—82no—
750C2C73×#300211yescharacteristic
751C2C73×#300711yescharacteristic
752C2C73×#301911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
prime radicalC73×#3483C2
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×#3210C2semidirect
3. C73×#3116C2semidirect
4. C73×#3076C2semidirect
5. C73×#1646C2semidirect
6. C73×#1645C2semidirect
7. C73×#1642C2semidirect
8. C73×#1641C2semidirect
9. C73×#1634C2semidirect
10. C73×#1633C2semidirect
11. C73×#1631C2semidirect
12. C73×#1631C2semidirect
13. C73×#1551C2semidirect
14. C73×#1488C2semidirect
15. C73×#1477C2semidirect
369. #18775C73direct (N × H)
378. #3210C2×C73semidirect
379. #3116C2×C73semidirect
380. #3076C2×C73semidirect
381. #1646C2×C73semidirect
382. #1645C2×C73semidirect
383. #1642C2×C73semidirect
384. #1641C2×C73semidirect
385. #1634C2×C73semidirect
386. #1633C2×C73semidirect
387. #1631C2×C73semidirect
388. #1631C2×C73semidirect
389. #1551C2×C73semidirect
390. #1488C2×C73semidirect
391. #1477C2×C73semidirect
392. C73#18775direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#34832
C73×#32102
C73×#31162
C73×#30762
C73×#16462
C73×#16452
C73×#16422
C73×#16412
C73×#16342
C73×#16332
C73×#16312
C73×#15512
C73×#14882
C73×#14772
#1877573