Finite Group Databasebeta

← C73×#19070 #32928474

Subgroups — C73×#19070 #32928474

Order 18688.

844 conjugacy classes of subgroups.

The subgroup lattice has 826 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3553C211yesmaximal, characteristic, complemented
2C73×#3234C211yesmaximal, characteristic, complemented
3C73×#3219C211yesmaximal, characteristic, complemented
4C73×#3171C211yesmaximal, characteristic, complemented
5C73×#1664C211yesmaximal, characteristic, complemented
6C73×#1663C211yesmaximal, characteristic, complemented
7C73×#1661C211yesmaximal, characteristic, complemented
8C73×#1660C211yesmaximal, characteristic, complemented
9C73×#1658C211yesmaximal, characteristic, complemented
10C73×#1657C211yesmaximal, characteristic, complemented
11C73×#1657C211yesmaximal, characteristic, complemented
12C73×#1656C211yesmaximal, characteristic, complemented
13C73×#1535C211yesmaximal, characteristic, complemented
14C73×#1529C211yesmaximal, characteristic, complemented
15C73×#1528C211yesmaximal, characteristic, complemented
16#564×C73C2211yescharacteristic
17#563×C73C2211yescharacteristic
18#563×C73C2211yescharacteristic
19#562×C73C2211yescharacteristic
20#554×C73—21no—
21#554×C73—21no—
22#553×C73—21no—
23#553×C73—21no—
24#552×C73—21no—
25#552×C73—21no—
26#541×C73—21no—
27#541×C73—21no—
28#539×C73—21no—
29#539×C73—21no—
30#539×C73—21no—
31#539×C73—21no—
32#532×C73C2211yescharacteristic
33#529×C73C2211yescharacteristic
34#529×C73C2211yescharacteristic
35C2×#125×C73C2211yescharacteristic
36#501×C73C2211yescharacteristic
37#501×C73C2211yescharacteristic
38#501×C73C2211yescharacteristic
39#497×C73C2211yescharacteristic
40#496×C73C2211yescharacteristic
41#496×C73C2211yescharacteristic
42#491×C73C2211yescharacteristic
43#490×C73C2211yescharacteristic
44#490×C73C2211yescharacteristic
45#490×C73C2211yescharacteristic
46#490×C73C2211yescharacteristic
47#489×C73C2211yescharacteristic
48#481×C73—21no—
49#480×C73—21no—
50#478×C73—21no—
51#478×C73—21no—
52#469×C73—21no—
53#468×C73—21no—
54#464×C73—21no—
55#463×C73—21no—
56#452×C73—21no—
57#449×C73—21no—
58C4×SD16×C73—21no—
59C4×D8×C73—21no—
60#432×C73C2211yescharacteristic
61#432×C73C2211yescharacteristic
62C4×M16×C73C2211yescharacteristic
63#330×C73C2211yescharacteristic
64#330×C73C2211yescharacteristic
65#330×C73C2211yescharacteristic
66#330×C73C2211yescharacteristic
67#330×C73C2211yescharacteristic
68#330×C73C2211yescharacteristic
69#330×C73C2211yescharacteristic
70#330×C73C2211yescharacteristic
71#329×C73C2211yescharacteristic
72#329×C73C2211yescharacteristic
73#329×C73C2211yescharacteristic
74#329×C73C2211yescharacteristic
75C2×#41×C73—21no—
76C2×Q16×C73—21no—
77C2×SD16×C73—21no—
78C2×SD16×C73—21no—
79C2×SD16×C73—21no—
80C2×D8×C73—21no—
81C2×D8×C73—21no—
82C2×M16×C73—21no—
83C4⋊Q8×C73—21no—
84C4⋊Q8×C73—21no—
85C4⋊Q8×C73C2311yescharacteristic
86#127×C73C2311yescharacteristic
87#126×C73—21no—
88#126×C73—21no—
89#126×C73—21no—
90#126×C73—21no—
91#126×C73—21no—
92#126×C73—21no—
93#126×C73—21no—
94#126×C73—21no—
95#126×C73—21no—
96#126×C73—21no—
97#125×C73—21no—
98#125×C73—21no—
99#125×C73—21no—
100#125×C73—21no—
101#125×C73—21no—
102#125×C73—21no—
103#125×C73—21no—
104#125×C73—21no—
105#125×C73—21no—
106#125×C73—21no—
107#125×C73—21no—
108#125×C73—21no—
109#125×C73D411yescharacteristic
110#125×C73D411yescharacteristic
111#125×C73C2311yescharacteristic
112#125×C73C2311yescharacteristic
113#125×C73C2311yescharacteristic
114#125×C73C2311yescharacteristic
115#124×C73—21no—
116#124×C73C2311yescharacteristic
117#124×C73C2311yescharacteristic
118#123×C73—21no—
119#123×C73—21no—
120#123×C73—21no—
121#123×C73—21no—
122#123×C73—21no—
123#123×C73—21no—
124#123×C73—21no—
125#123×C73—21no—
126#123×C73—21no—
127#123×C73—21no—
128C22⋊Q8×C73—21no—
129C22⋊Q8×C73—21no—
130C22⋊Q8×C73—21no—
131C22⋊Q8×C73—21no—
132C22⋊Q8×C73—21no—
133C22⋊Q8×C73—21no—
134C22⋊Q8×C73—21no—
135C22⋊Q8×C73—21no—
136C22⋊Q8×C73—21no—
137C22⋊Q8×C73—21no—
138C22⋊Q8×C73—21no—
139C22⋊Q8×C73—21no—
140C22⋊Q8×C73D411yescharacteristic
141C22⋊Q8×C73D411yescharacteristic
142#121×C73—21no—
143#121×C73—21no—
144#121×C73—21no—
145#121×C73—21no—
146#121×C73—21no—
147#121×C73—21no—
148#121×C73D411yescharacteristic
149#121×C73D411yescharacteristic
150C4×Q8×C73—21no—
151C4×Q8×C73—21no—
152C4×Q8×C73D411yescharacteristic
153C4×Q8×C73D411yescharacteristic
154C4×D4×C73—21no—
155C4×D4×C73—21no—
156C4×D4×C73—21no—
157C4×D4×C73—21no—
158C4×D4×C73—21no—
159C4×D4×C73—21no—
160C4×D4×C73—21no—
161C4×D4×C73—21no—
162C4×D4×C73—21no—
163C4×D4×C73—21no—
164C4×D4×C73D411yescharacteristic
165C4×D4×C73D411yescharacteristic
166#117×C73—21no—
167#117×C73—21no—
168#117×C73—21no—
169#117×C73—21no—
170C2×C4⋊C4×C73—21no—
171C2×C4⋊C4×C73—21no—
172C2×C4⋊C4×C73—21no—
173C2×C4⋊C4×C73—21no—
174C2×C4⋊C4×C73D411yescharacteristic
175C2×C4⋊C4×C73D411yescharacteristic
176C2×C42×C73C2311yescharacteristic
177#107×C73—21no—
178#107×C73—21no—
179#107×C73—21no—
180#106×C73—21no—
181#106×C73—21no—
182#106×C73—21no—
183C4⋊C8×C73—21no—
184C4⋊C8×C73—21no—
185#103×C73—21no—
186#103×C73—21no—
187#103×C73—21no—
188#102×C73—21no—
189#102×C73—21no—
190#102×C73—21no—
191#102×C73—21no—
192#102×C73—21no—
193#102×C73—21no—
194#102×C73—21no—
195#102×C73—21no—
196#102×C73—21no—
197C22⋊C8×C73—21no—
198C22⋊C8×C73—21no—
199#97×C73C2311yescharacteristic
200#97×C73C2311yescharacteristic
201#97×C73C2311yescharacteristic
202#97×C73C2311yescharacteristic
203#97×C73C2311yescharacteristic
204#97×C73C2311yescharacteristic
205C4×C8×C73—21no—
206#41×C73—81no—
207#41×C73—81no—
208C2×Q8×C73—21no—
209C2×Q8×C73—21no—
210C2×Q8×C73—21no—
211C2×Q8×C73C2×D411yescharacteristic
212C2×Q8×C73C2×D411yescharacteristic
213C2×D4×C73—21no—
214C2×D4×C73—21no—
215C2×D4×C73—21no—
216C2×D4×C73—21no—
217C2×D4×C73—21no—
218C2×D4×C73—21no—
219C2×D4×C73—21no—
220C2×D4×C73—41no—
221C2×D4×C73C2×D411yescharacteristic
222C2×D4×C73C2×D411yescharacteristic
223C22×C4×C73—21no—
224C22×C4×C73—21no—
225C22×C4×C73—21no—
226C22×C4×C73—21no—
227C22×C4×C73—21no—
228C22×C4×C73—21no—
229C22×C4×C73—21no—
230C22×C4×C73—21no—
231C22×C4×C73—41no—
232C22×C4×C73C2×D411yescharacteristic
233C22×C4×C73C2×D411yescharacteristic
234C22×C4×C73C2×D411yescharacteristic
235Q16×C73—81no—
236SD16×C73—42no—
237SD16×C73—81no—
238SD16×C73—81no—
239D8×C73—42no—
240D8×C73—81no—
241M16×C73—42no—
242C2×C8×C73—21no—
243C2×C8×C73—21no—
244C2×C8×C73—21no—
245C2×C8×C73—21no—
246C2×C8×C73—21no—
247C2×C8×C73—21no—
248C4⋊C4×C73—21no—
249C4⋊C4×C73—21no—
250C4⋊C4×C73—21no—
251C4⋊C4×C73—21no—
252C4⋊C4×C73—21no—
253C4⋊C4×C73—21no—
254C4⋊C4×C73—21no—
255C4⋊C4×C73—21no—
256C4⋊C4×C73—21no—
257C4⋊C4×C73—21no—
258C4⋊C4×C73—21no—
259C4⋊C4×C73—21no—
260C4⋊C4×C73—21no—
261C4⋊C4×C73—21no—
262C4⋊C4×C73—21no—
263C4⋊C4×C73—21no—
264C4⋊C4×C73—21no—
265C4⋊C4×C73—21no—
266C4⋊C4×C73—21no—
267C4⋊C4×C73—21no—
268C4⋊C4×C73—21no—
269C4⋊C4×C73—21no—
270C4⋊C4×C73—21no—
271C4⋊C4×C73—21no—
272C4⋊C4×C73—21no—
273C4⋊C4×C73—21no—
274C4⋊C4×C73—21no—
275C4⋊C4×C73—21no—
276C4⋊C4×C73—21no—
277C4⋊C4×C73—21no—
278C4⋊C4×C73—21no—
279C4⋊C4×C73—21no—
280C4⋊C4×C73C2×D411yescharacteristic
281C4⋊C4×C73C2×D411yescharacteristic
282C4⋊C4×C73C2×D411yescharacteristic
283C4⋊C4×C73C2×D411yescharacteristic
284C4⋊C4×C73C2×D411yescharacteristic
285C4⋊C4×C73C2×D411yescharacteristic
286C4⋊C4×C73C2×D411yescharacteristic
287C4⋊C4×C73C2×D411yescharacteristic
288C22⋊C4×C73—21no—
289C22⋊C4×C73—21no—
290C22⋊C4×C73—21no—
291C22⋊C4×C73—21no—
292C22⋊C4×C73—21no—
293C22⋊C4×C73—21no—
294C22⋊C4×C73—21no—
295C22⋊C4×C73—21no—
296C22⋊C4×C73—21no—
297C22⋊C4×C73—21no—
298C22⋊C4×C73—21no—
299C22⋊C4×C73—21no—
300C22⋊C4×C73—21no—
301C22⋊C4×C73—21no—
302C22⋊C4×C73—21no—
303C22⋊C4×C73—21no—
304C22⋊C4×C73—21no—
305C22⋊C4×C73—21no—
306C22⋊C4×C73—41no—
307C22⋊C4×C73—41no—
308C42×C73—21no—
309C42×C73—21no—
310C42×C73—21no—
311C42×C73—21no—
312C42×C73—21no—
313C42×C73—21no—
314C42×C73C2×D411yescharacteristic
315C42×C73C2×D411yescharacteristic
316C42×C73C2×D411yescharacteristic
317C42×C73C2411yescharacteristic
318C23×C73—21no—
319C23×C73—21no—
320C23×C73—41no—
321C23×C73#12011yescharacteristic
322Q8×C73—41no—
323Q8×C73—41no—
324Q8×C73—41no—
325Q8×C73—41no—
326Q8×C73—81no—
327Q8×C73—81no—
328D4×C73—41no—
329D4×C73—41no—
330D4×C73—41no—
331D4×C73—41no—
332D4×C73—41no—
333D4×C73—41no—
334D4×C73—42no—
335D4×C73—42no—
336D4×C73—42no—
337D4×C73—81no—
338D4×C73—81no—
339D4×C73—82no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—21no—
344C2×C4×C73—21no—
345C2×C4×C73—21no—
346C2×C4×C73—21no—
347C2×C4×C73—21no—
348C2×C4×C73—21no—
349C2×C4×C73—21no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—81no—
355C2×C4×C73—81no—
356C2×C4×C73—82no—
357C2×C4×C73—81no—
358C2×C4×C73—81no—
359C2×C4×C73—81no—
360C2×C4×C73—81no—
361C2×C4×C73—81no—
362C2×C4×C73—81no—
363C2×C4×C73#12011yescharacteristic
364C2×C4×C73#12011yescharacteristic
365C2×C4×C73#12011yescharacteristic
366C2×C4×C73C22×D411yescharacteristic
367C2×C4×C73C22×D411yescharacteristic
368C2×C4×C73C22×D411yescharacteristic
369C8×C73—22no—
370C8×C73—41no—
371C8×C73—41no—
372C8×C73—41no—
373C8×C73—41no—
374C8×C73—41no—
375C22×C73—21no—
376C22×C73—21no—
377C22×C73—21no—
378C22×C73—41no—
379C22×C73—41no—
380C22×C73—41no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—41no—
384C22×C73—81no—
385C22×C73—81no—
386C22×C73—81no—
387C22×C73C2×#12011yescharacteristic
388C4×C73—21no—
389C4×C73—21no—
390C4×C73—21no—
391C4×C73—21no—
392C4×C73—21no—
393C4×C73—21no—
394C4×C73—41no—
395C4×C73—41no—
396C4×C73—41no—
397C4×C73—41no—
398C4×C73—41no—
399C4×C73—41no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73—41no—
403C4×C73—41no—
404C4×C73—81no—
405#19070C7311yesmaximal, characteristic, direct product factor, Sylow
406C2×C73—41no—
407C2×C73—81no—
408C2×C73—81no—
409C2×C73—161no—
410C2×C73#301811yescharacteristic
411C2×C73#302011yescharacteristic
412C2×C73#302111yescharacteristic
413#3553C2×C7311yescharacteristic, complemented
414#3234C2×C7311yescharacteristic, complemented
415#3219C2×C7311yescharacteristic, complemented
416#3171C2×C7311yescharacteristic, complemented
417#1664C2×C7311yescharacteristic, complemented
418#1663C2×C7311yescharacteristic, complemented
419#1661C2×C7311yescharacteristic, complemented
420#1660C2×C7311yescharacteristic, complemented
421#1658C2×C7311yescharacteristic, complemented
422#1657C2×C7311yescharacteristic, complemented
423#1657C2×C7311yescharacteristic, complemented
424#1656C2×C7311yescharacteristic, complemented
425#1535C2×C7311yescharacteristic, complemented
426#1529C2×C7311yescharacteristic, complemented
427#1528C2×C7311yescharacteristic, complemented
428C73#1907011yescharacteristic, direct product factor, Sylow
429#564C22×C7311yescharacteristic
430#563C22×C7311yescharacteristic
431#563C22×C7311yescharacteristic
432#562C22×C7311yescharacteristic
433#554—21no—
434#554—21no—
435#553—21no—
436#553—21no—
437#552—21no—
438#552—21no—
439#541—21no—
440#541—21no—
441#539—21no—
442#539—21no—
443#539—21no—
444#539—21no—
445#532C22×C7311yescharacteristic
446#529C22×C7311yescharacteristic
447#529C22×C7311yescharacteristic
448C2×#125C22×C7311yescharacteristic
449#501C22×C7311yescharacteristic
450#501C22×C7311yescharacteristic
451#501C22×C7311yescharacteristic
452#497C22×C7311yescharacteristic
453#496C22×C7311yescharacteristic
454#496C22×C7311yescharacteristic
455#491C22×C7311yescharacteristic
456#490C22×C7311yescharacteristic
457#490C22×C7311yescharacteristic
458#490C22×C7311yescharacteristic
459#490C22×C7311yescharacteristic
460#489C22×C7311yescharacteristic
461#481—21no—
462#480—21no—
463#478—21no—
464#478—21no—
465#469—21no—
466#468—21no—
467#464—21no—
468#463—21no—
469#452—21no—
470#449—21no—
471C4×SD16—21no—
472C4×D8—21no—
473#432C22×C7311yescharacteristic
474#432C22×C7311yescharacteristic
475C4×M16C22×C7311yescharacteristic
476#330C22×C7311yescharacteristic
477#330C22×C7311yescharacteristic
478#330C22×C7311yescharacteristic
479#330C22×C7311yescharacteristic
480#330C22×C7311yescharacteristic
481#330C22×C7311yescharacteristic
482#330C22×C7311yescharacteristic
483#330C22×C7311yescharacteristic
484#329C22×C7311yescharacteristic
485#329C22×C7311yescharacteristic
486#329C22×C7311yescharacteristic
487#329C22×C7311yescharacteristic
488C2×#41—21no—
489C2×Q16—21no—
490C2×SD16—21no—
491C2×SD16—21no—
492C2×SD16—21no—
493C2×D8—21no—
494C2×D8—21no—
495C2×M16—21no—
496C4⋊Q8—21no—
497C4⋊Q8—21no—
498C4⋊Q8C23×C7311yescharacteristic
499#127C23×C7311yescharacteristic
500#126—21no—
501#126—21no—
502#126—21no—
503#126—21no—
504#126—21no—
505#126—21no—
506#126—21no—
507#126—21no—
508#126—21no—
509#126—21no—
510#125—21no—
511#125—21no—
512#125—21no—
513#125—21no—
514#125—21no—
515#125—21no—
516#125—21no—
517#125—21no—
518#125—21no—
519#125—21no—
520#125—21no—
521#125—21no—
522#125D4×C7311yescharacteristic
523#125D4×C7311yescharacteristic
524#125C23×C7311yescharacteristic
525#125C23×C7311yescharacteristic
526#125C23×C7311yescharacteristic
527#125C23×C7311yescharacteristic
528#124—21no—
529#124C23×C7311yescharacteristic
530#124C23×C7311yescharacteristic
531#123—21no—
532#123—21no—
533#123—21no—
534#123—21no—
535#123—21no—
536#123—21no—
537#123—21no—
538#123—21no—
539#123—21no—
540#123—21no—
541C22⋊Q8—21no—
542C22⋊Q8—21no—
543C22⋊Q8—21no—
544C22⋊Q8—21no—
545C22⋊Q8—21no—
546C22⋊Q8—21no—
547C22⋊Q8—21no—
548C22⋊Q8—21no—
549C22⋊Q8—21no—
550C22⋊Q8—21no—
551C22⋊Q8—21no—
552C22⋊Q8—21no—
553C22⋊Q8D4×C7311yescharacteristic
554C22⋊Q8D4×C7311yescharacteristic
555#121—21no—
556#121—21no—
557#121—21no—
558#121—21no—
559#121—21no—
560#121—21no—
561#121D4×C7311yescharacteristic
562#121D4×C7311yescharacteristic
563C4×Q8—21no—
564C4×Q8—21no—
565C4×Q8D4×C7311yescharacteristic
566C4×Q8D4×C7311yescharacteristic
567C4×D4—21no—
568C4×D4—21no—
569C4×D4—21no—
570C4×D4—21no—
571C4×D4—21no—
572C4×D4—21no—
573C4×D4—21no—
574C4×D4—21no—
575C4×D4—21no—
576C4×D4—21no—
577C4×D4D4×C7311yescharacteristic
578C4×D4D4×C7311yescharacteristic
579#117—21no—
580#117—21no—
581#117—21no—
582#117—21no—
583C2×C4⋊C4—21no—
584C2×C4⋊C4—21no—
585C2×C4⋊C4—21no—
586C2×C4⋊C4—21no—
587C2×C4⋊C4D4×C7311yescharacteristic
588C2×C4⋊C4D4×C7311yescharacteristic
589C2×C42C23×C7311yescharacteristic
590#107—21no—
591#107—21no—
592#107—21no—
593#106—21no—
594#106—21no—
595#106—21no—
596C4⋊C8—21no—
597C4⋊C8—21no—
598#103—21no—
599#103—21no—
600#103—21no—
601#102—21no—
602#102—21no—
603#102—21no—
604#102—21no—
605#102—21no—
606#102—21no—
607#102—21no—
608#102—21no—
609#102—21no—
610C22⋊C8—21no—
611C22⋊C8—21no—
612#97C23×C7311yescharacteristic
613#97C23×C7311yescharacteristic
614#97C23×C7311yescharacteristic
615#97C23×C7311yescharacteristic
616#97C23×C7311yescharacteristic
617#97C23×C7311yescharacteristic
618C4×C8—21no—
619#41—81no—
620#41—81no—
621C2×Q8—21no—
622C2×Q8—21no—
623C2×Q8—21no—
624C2×Q8C2×D4×C7311yescharacteristic
625C2×Q8C2×D4×C7311yescharacteristic
626C2×D4—21no—
627C2×D4—21no—
628C2×D4—21no—
629C2×D4—21no—
630C2×D4—21no—
631C2×D4—21no—
632C2×D4—21no—
633C2×D4—41no—
634C2×D4C2×D4×C7311yescharacteristic
635C2×D4C2×D4×C7311yescharacteristic
636C22×C4—21no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—21no—
643C22×C4—21no—
644C22×C4—41no—
645C22×C4C2×D4×C7311yescharacteristic
646C22×C4C2×D4×C7311yescharacteristic
647C22×C4C2×D4×C7311yescharacteristic
648Q16—81no—
649SD16—42no—
650SD16—81no—
651SD16—81no—
652D8—42no—
653D8—81no—
654M16—42no—
655C2×C8—21no—
656C2×C8—21no—
657C2×C8—21no—
658C2×C8—21no—
659C2×C8—21no—
660C2×C8—21no—
661C4⋊C4—21no—
662C4⋊C4—21no—
663C4⋊C4—21no—
664C4⋊C4—21no—
665C4⋊C4—21no—
666C4⋊C4—21no—
667C4⋊C4—21no—
668C4⋊C4—21no—
669C4⋊C4—21no—
670C4⋊C4—21no—
671C4⋊C4—21no—
672C4⋊C4—21no—
673C4⋊C4—21no—
674C4⋊C4—21no—
675C4⋊C4—21no—
676C4⋊C4—21no—
677C4⋊C4—21no—
678C4⋊C4—21no—
679C4⋊C4—21no—
680C4⋊C4—21no—
681C4⋊C4—21no—
682C4⋊C4—21no—
683C4⋊C4—21no—
684C4⋊C4—21no—
685C4⋊C4—21no—
686C4⋊C4—21no—
687C4⋊C4—21no—
688C4⋊C4—21no—
689C4⋊C4—21no—
690C4⋊C4—21no—
691C4⋊C4—21no—
692C4⋊C4—21no—
693C4⋊C4C2×D4×C7311yescharacteristic
694C4⋊C4C2×D4×C7311yescharacteristic
695C4⋊C4C2×D4×C7311yescharacteristic
696C4⋊C4C2×D4×C7311yescharacteristic
697C4⋊C4C2×D4×C7311yescharacteristic
698C4⋊C4C2×D4×C7311yescharacteristic
699C4⋊C4C2×D4×C7311yescharacteristic
700C4⋊C4C2×D4×C7311yescharacteristic
701C22⋊C4—21no—
702C22⋊C4—21no—
703C22⋊C4—21no—
704C22⋊C4—21no—
705C22⋊C4—21no—
706C22⋊C4—21no—
707C22⋊C4—21no—
708C22⋊C4—21no—
709C22⋊C4—21no—
710C22⋊C4—21no—
711C22⋊C4—21no—
712C22⋊C4—21no—
713C22⋊C4—21no—
714C22⋊C4—21no—
715C22⋊C4—21no—
716C22⋊C4—21no—
717C22⋊C4—21no—
718C22⋊C4—21no—
719C22⋊C4—41no—
720C22⋊C4—41no—
721C42—21no—
722C42—21no—
723C42—21no—
724C42—21no—
725C42—21no—
726C42—21no—
727C42C2×D4×C7311yescharacteristic
728C42C2×D4×C7311yescharacteristic
729C42C2×D4×C7311yescharacteristic
730C42C24×C7311yescharacteristic
731C23—21no—
732C23—21no—
733C23—41no—
734C23#120×C7311yescharacteristic
735Q8—41no—
736Q8—41no—
737Q8—41no—
738Q8—41no—
739Q8—81no—
740Q8—81no—
741D4—41no—
742D4—41no—
743D4—41no—
744D4—41no—
745D4—41no—
746D4—41no—
747D4—42no—
748D4—42no—
749D4—42no—
750D4—81no—
751D4—81no—
752D4—82no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—21no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—41no—
764C2×C4—41no—
765C2×C4—41no—
766C2×C4—41no—
767C2×C4—81no—
768C2×C4—81no—
769C2×C4—82no—
770C2×C4—81no—
771C2×C4—81no—
772C2×C4—81no—
773C2×C4—81no—
774C2×C4—81no—
775C2×C4—81no—
776C2×C4#120×C7311yescharacteristic
777C2×C4#120×C7311yescharacteristic
778C2×C4#120×C7311yescharacteristic
779C2×C4C22×D4×C7311yescharacteristic
780C2×C4C22×D4×C7311yescharacteristic
781C2×C4C22×D4×C7311yescharacteristic
782C8—22no—
783C8—41no—
784C8—41no—
785C8—41no—
786C8—41no—
787C8—41no—
788C22—21no—
789C22—21no—
790C22—21no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—41no—
796C22—41no—
797C22—81no—
798C22—81no—
799C22—81no—
800C22C2×#120×C7311yescharacteristic
801C4—21no—
802C4—21no—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—21no—
807C4—41no—
808C4—41no—
809C4—41no—
810C4—41no—
811C4—41no—
812C4—41no—
813C4—41no—
814C4—41no—
815C4—41no—
816C4—41no—
817C4—81no—
818C2—41no—
819C2—81no—
820C2—81no—
821C2—161no—
822C2C73×#301811yescharacteristic
823C2C73×#302011yescharacteristic
824C2C73×#302111yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC42C24×C73
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
1. C73×#3553C2semidirect
2. C73×#3234C2semidirect
3. C73×#3219C2semidirect
4. C73×#3171C2semidirect
5. C73×#1664C2semidirect
6. C73×#1663C2semidirect
7. C73×#1661C2semidirect
8. C73×#1660C2semidirect
9. C73×#1658C2semidirect
10. C73×#1657C2semidirect
11. C73×#1657C2semidirect
12. C73×#1656C2semidirect
13. C73×#1535C2semidirect
14. C73×#1529C2semidirect
15. C73×#1528C2semidirect
405. #19070C73direct (N × H)
413. #3553C2×C73semidirect
414. #3234C2×C73semidirect
415. #3219C2×C73semidirect
416. #3171C2×C73semidirect
417. #1664C2×C73semidirect
418. #1663C2×C73semidirect
419. #1661C2×C73semidirect
420. #1660C2×C73semidirect
421. #1658C2×C73semidirect
422. #1657C2×C73semidirect
423. #1657C2×C73semidirect
424. #1656C2×C73semidirect
425. #1535C2×C73semidirect
426. #1529C2×C73semidirect
427. #1528C2×C73semidirect
428. C73#19070direct (N × H)

Maximal subgroups

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

subgroupindex
C73×#35532
C73×#32342
C73×#32192
C73×#31712
C73×#16642
C73×#16632
C73×#16612
C73×#16602
C73×#16582
C73×#16572
C73×#16562
C73×#15352
C73×#15292
C73×#15282
#1907073