Finite Group Databasebeta

← C73×#24084 #32933488

Subgroups — C73×#24084 #32933488

Order 18688.

1060 conjugacy classes of subgroups.

The subgroup lattice has 844 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3494C211yesmaximal, characteristic
2C73×#3093C211yesmaximal, characteristic, complemented
3C73×#2911C211yesmaximal, characteristic, complemented
4C73×#2500C211yesmaximal, characteristic, complemented
5C73×#2061C211yesmaximal, characteristic, complemented
6C73×#2060C211yesmaximal, characteristic, complemented
7C73×#2037C211yesmaximal, characteristic, complemented
8C73×#2037C211yesmaximal, characteristic, complemented
9C73×#1900C211yesmaximal, characteristic, complemented
10C73×#1871C211yesmaximal, characteristic, complemented
11C73×#1860C211yesmaximal, characteristic, complemented
12C73×#1859C211yesmaximal, characteristic, complemented
13C73×#1856C211yesmaximal, characteristic, complemented
14C73×#1856C211yesmaximal, characteristic, complemented
15C73×#1826C211yesmaximal, characteristic, complemented
16C22×M16×C73C2211yescharacteristic
17#555×C73—21no—
18#553×C73—21no—
19#553×C73—21no—
20#551×C73—22no—
21#547×C73—21no—
22#546×C73—22no—
23#544×C73C2211yescharacteristic
24#542×C73—21no—
25#540×C73—21no—
26#535×C73C2211yescharacteristic
27#532×C73—21no—
28#529×C73—21no—
29#525×C73C2211yescharacteristic
30C2×#121×C73C2211yescharacteristic
31#520×C73C2211yescharacteristic
32#518×C73C2211yescharacteristic
33C2×#117×C73C2211yescharacteristic
34C2×#117×C73C2211yescharacteristic
35#485×C73—21no—
36#485×C73—21no—
37#482×C73—21no—
38#482×C73—21no—
39#428×C73—21no—
40#428×C73—21no—
41#428×C73C2211yescharacteristic
42#428×C73C2211yescharacteristic
43#428×C73C2211yescharacteristic
44#428×C73C2211yescharacteristic
45#428×C73C2211yescharacteristic
46#428×C73C2211yescharacteristic
47#427×C73—21no—
48#427×C73—21no—
49C2×#104×C73C2211yescharacteristic
50C2×#104×C73C2211yescharacteristic
51#417×C73C2211yescharacteristic
52#417×C73C2211yescharacteristic
53C2×#100×C73C2211yescharacteristic
54C2×#100×C73C2211yescharacteristic
55#407×C73C2211yescharacteristic
56#394×C73—22no—
57#390×C73C2211yescharacteristic
58#390×C73C2211yescharacteristic
59#388×C73—22no—
60#384×C73C2211yescharacteristic
61#382×C73C2211yescharacteristic
62C4×C22⋊C4×C73C2211yescharacteristic
63#343×C73C2211yescharacteristic
64#343×C73C2211yescharacteristic
65#339×C73C2211yescharacteristic
66#339×C73C2211yescharacteristic
67#339×C73C2211yescharacteristic
68#339×C73C2211yescharacteristic
69#339×C73C2211yescharacteristic
70#339×C73C2211yescharacteristic
71C2×#41×C73—22no—
72C2×#41×C73C2311yescharacteristic
73C22×D4×C73D412yes—
74C22×D4×C73C2311yescharacteristic
75C23×C4×C73C2311yescharacteristic
76C2×M16×C73—21no—
77C2×M16×C73—22no—
78C2×M16×C73—22no—
79C2×M16×C73C2311yescharacteristic
80C2×M16×C73C2311yescharacteristic
81C2×M16×C73C2311yescharacteristic
82C2×M16×C73C2311yescharacteristic
83C22×C8×C73—21no—
84C4⋊Q8×C73—21no—
85C4⋊Q8×C73—21no—
86#127×C73—21no—
87#126×C73—22no—
88#126×C73—22no—
89#125×C73—21no—
90#125×C73—21no—
91#124×C73—22no—
92#124×C73—22no—
93#124×C73—21no—
94#123×C73—22no—
95#123×C73—22no—
96#123×C73—22no—
97#123×C73—22no—
98#123×C73—21no—
99C22⋊Q8×C73—22no—
100C22⋊Q8×C73—22no—
101C22⋊Q8×C73D411yescharacteristic
102C22⋊Q8×C73D411yescharacteristic
103#121×C73—22no—
104#121×C73—22no—
105#121×C73—22no—
106#121×C73—21no—
107#121×C73—21no—
108#121×C73—21no—
109#121×C73—21no—
110#121×C73—21no—
111#121×C73—21no—
112#121×C73D411yescharacteristic
113#121×C73D411yescharacteristic
114#120×C73—21no—
115#120×C73—22no—
116C4×Q8×C73—21no—
117C4×D4×C73—22no—
118C4×D4×C73—22no—
119C4×D4×C73—21no—
120C4×D4×C73—22no—
121C4×D4×C73—21no—
122C4×D4×C73—21no—
123C4×D4×C73—21no—
124C4×D4×C73—21no—
125C4×D4×C73—21no—
126C4×D4×C73—21no—
127#117×C73—22no—
128#117×C73—21no—
129#117×C73—21no—
130#117×C73—21no—
131#117×C73—21no—
132#117×C73—21no—
133#117×C73—21no—
134#117×C73—21no—
135#117×C73D411yescharacteristic
136#117×C73D411yescharacteristic
137#117×C73C2311yescharacteristic
138#117×C73C2311yescharacteristic
139#117×C73C2311yescharacteristic
140C2×C4⋊C4×C73—21no—
141C2×C4⋊C4×C73—22no—
142C2×C4⋊C4×C73D411yescharacteristic
143C2×C4⋊C4×C73D411yescharacteristic
144C2×C4⋊C4×C73C2311yescharacteristic
145C2×C4⋊C4×C73C2311yescharacteristic
146C2×C4⋊C4×C73C2311yescharacteristic
147C2×C22⋊C4×C73—21no—
148C2×C22⋊C4×C73—22no—
149C2×C22⋊C4×C73—21no—
150C2×C22⋊C4×C73—22no—
151C2×C22⋊C4×C73—21no—
152C2×C22⋊C4×C73—22no—
153C2×C22⋊C4×C73D412yes—
154C2×C42×C73—21no—
155C2×C42×C73—21no—
156C2×C42×C73C2311yescharacteristic
157C2×C42×C73C2311yescharacteristic
158#107×C73—21no—
159#107×C73—21no—
160#107×C73—21no—
161#107×C73—21no—
162#107×C73—21no—
163#107×C73—21no—
164#106×C73—21no—
165#106×C73—21no—
166#106×C73—21no—
167#106×C73—21no—
168#106×C73—21no—
169#106×C73—21no—
170#104×C73—22no—
171#104×C73—22no—
172#103×C73—21no—
173#103×C73—21no—
174#102×C73—21no—
175#102×C73—21no—
176#100×C73—22no—
177#100×C73—22no—
178C22⋊C8×C73—21no—
179C22⋊C8×C73—21no—
180#95×C73—21no—
181#95×C73—22no—
182C24×C73C2×D412yes—
183C24×C73C2×D411yescharacteristic
184#41×C73—21no—
185#41×C73—21no—
186#41×C73—21no—
187#41×C73—21no—
188#41×C73—84no—
189C2×Q8×C73—22no—
190C2×Q8×C73C2×D411yescharacteristic
191C2×D4×C73—21no—
192C2×D4×C73—22no—
193C2×D4×C73—21no—
194C2×D4×C73—22no—
195C2×D4×C73—22no—
196C2×D4×C73—21no—
197C2×D4×C73—22no—
198C2×D4×C73—21no—
199C2×D4×C73—21no—
200C2×D4×C73—21no—
201C2×D4×C73—21no—
202C2×D4×C73—21no—
203C2×D4×C73—21no—
204C2×D4×C73—82no—
205C2×D4×C73C2×D411yescharacteristic
206C22×C4×C73—21no—
207C22×C4×C73—21no—
208C22×C4×C73—21no—
209C22×C4×C73—21no—
210C22×C4×C73—21no—
211C22×C4×C73—21no—
212C22×C4×C73—22no—
213C22×C4×C73—22no—
214C22×C4×C73—22no—
215C22×C4×C73—21no—
216C22×C4×C73—21no—
217C22×C4×C73—21no—
218C22×C4×C73—21no—
219C22×C4×C73—21no—
220C22×C4×C73C2×D411yescharacteristic
221C22×C4×C73C2×D411yescharacteristic
222C22×C4×C73C2×D411yescharacteristic
223C22×C4×C73C2×D411yescharacteristic
224C22×C4×C73C2×D411yescharacteristic
225C22×C4×C73C2×D412yes—
226C22×C4×C73C2411yescharacteristic
227M16×C73—24no—
228M16×C73—21no—
229M16×C73—21no—
230M16×C73—21no—
231M16×C73—21no—
232M16×C73—21no—
233M16×C73—21no—
234M16×C73#4112yescomplemented
235M16×C73#4112yescomplemented
236C2×C8×C73—24no—
237C2×C8×C73—21no—
238C2×C8×C73—21no—
239C2×C8×C73—21no—
240C2×C8×C73—21no—
241C4⋊C4×C73—22no—
242C4⋊C4×C73—22no—
243C4⋊C4×C73—22no—
244C4⋊C4×C73—22no—
245C4⋊C4×C73—21no—
246C4⋊C4×C73—21no—
247C4⋊C4×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—82no—
256C4⋊C4×C73C2×D411yescharacteristic
257C4⋊C4×C73C2×D411yescharacteristic
258C4⋊C4×C73C2×D411yescharacteristic
259C4⋊C4×C73C2×D411yescharacteristic
260C4⋊C4×C73C2×D411yescharacteristic
261C4⋊C4×C73C2×D411yescharacteristic
262C22⋊C4×C73—22no—
263C22⋊C4×C73—22no—
264C22⋊C4×C73—22no—
265C22⋊C4×C73—22no—
266C22⋊C4×C73—22no—
267C22⋊C4×C73—21no—
268C22⋊C4×C73—21no—
269C22⋊C4×C73—21no—
270C22⋊C4×C73—21no—
271C22⋊C4×C73—21no—
272C22⋊C4×C73—21no—
273C22⋊C4×C73—21no—
274C22⋊C4×C73—22no—
275C22⋊C4×C73—22no—
276C22⋊C4×C73—21no—
277C22⋊C4×C73—21no—
278C22⋊C4×C73—42no—
279C22⋊C4×C73—44no—
280C22⋊C4×C73—41no—
281C22⋊C4×C73—41no—
282C22⋊C4×C73—82no—
283C42×C73—22no—
284C42×C73—21no—
285C42×C73—21no—
286C42×C73—21no—
287C42×C73—21no—
288C42×C73—21no—
289C42×C73—21no—
290C42×C73—21no—
291C42×C73—21no—
292C42×C73—21no—
293C42×C73—41no—
294C42×C73—41no—
295C23×C73—21no—
296C23×C73—21no—
297C23×C73—22no—
298C23×C73—21no—
299C23×C73—22no—
300C23×C73—22no—
301C23×C73—41no—
302C23×C73—41no—
303C23×C73—42no—
304C23×C73—42no—
305C23×C73#12011yescharacteristic
306C23×C73#12011yescharacteristic
307C23×C73C22×D411yescharacteristic
308Q8×C73—21no—
309Q8×C73—21no—
310Q8×C73—82no—
311D4×C73—21no—
312D4×C73—21no—
313D4×C73—44no—
314D4×C73—42no—
315D4×C73—41no—
316D4×C73—41no—
317D4×C73—41no—
318D4×C73—41no—
319D4×C73—41no—
320D4×C73—41no—
321D4×C73—81no—
322D4×C73—82no—
323D4×C73—82no—
324D4×C73—82no—
325C2×C4×C73—21no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—21no—
329C2×C4×C73—21no—
330C2×C4×C73—21no—
331C2×C4×C73—21no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—21no—
335C2×C4×C73—22no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—21no—
339C2×C4×C73—21no—
340C2×C4×C73—21no—
341C2×C4×C73—21no—
342C2×C4×C73—21no—
343C2×C4×C73—22no—
344C2×C4×C73—41no—
345C2×C4×C73—42no—
346C2×C4×C73—41no—
347C2×C4×C73—41no—
348C2×C4×C73—41no—
349C2×C4×C73—42no—
350C2×C4×C73—41no—
351C2×C4×C73—42no—
352C2×C4×C73—41no—
353C2×C4×C73—42no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—41no—
357C2×C4×C73—81no—
358C2×C4×C73—82no—
359C2×C4×C73—82no—
360C2×C4×C73—82no—
361C2×C4×C73#12011yescharacteristic
362C2×C4×C73#12011yescharacteristic
363C2×C4×C73C22×D411yescharacteristic
364C2×C4×C73C22×D411yescharacteristic
365C2×C4×C73C2×#4111yescharacteristic
366C2×C4×C73C2×#4111yescharacteristic
367C2×C4×C732−1+411yescharacteristic
368C2×C4×C732−1+411yescharacteristic
369C8×C73—22no—
370C8×C73—22no—
371C8×C73—41no—
372C8×C73—41no—
373C22×C73—21no—
374C22×C73—21no—
375C22×C73—21no—
376C22×C73—21no—
377C22×C73—21no—
378C22×C73—21no—
379C22×C73—21no—
380C22×C73—21no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—42no—
384C22×C73—41no—
385C22×C73—41no—
386C22×C73—42no—
387C22×C73—81no—
388C22×C73—81no—
389C22×C73—82no—
390C22×C73—82no—
391C22×C73C2×#12011yescharacteristic
392C22×C73#54711yescharacteristic
393C22×C73#54711yescharacteristic
394C4×C73—21no—
395C4×C73—21no—
396C4×C73—42no—
397C4×C73—41no—
398C4×C73—41no—
399C4×C73—41no—
400C4×C73—41no—
401C4×C73—41no—
402C4×C73—41no—
403C4×C73—42no—
404C4×C73—41no—
405C4×C73—81no—
406C4×C73—81no—
407C4×C73—81no—
408C4×C73#52511yescharacteristic
409C4×C73#53611yescharacteristic
410C4×C73#54711yescharacteristic
411C4×C73#54711yescharacteristic
412#24084C7311yesmaximal, characteristic, direct product factor, Sylow
413C2×C73—21no—
414C2×C73—21no—
415C2×C73—41no—
416C2×C73—41no—
417C2×C73—81no—
418C2×C73—82no—
419C2×C73#240611yescharacteristic
420C2×C73#301811yescharacteristic
421C2×C73#301911yescharacteristic
422#3494C2×C7311yescharacteristic
423#3093C2×C7311yescharacteristic, complemented
424#2911C2×C7311yescharacteristic, complemented
425#2500C2×C7311yescharacteristic, complemented
426#2061C2×C7311yescharacteristic, complemented
427#2060C2×C7311yescharacteristic, complemented
428#2037C2×C7311yescharacteristic, complemented
429#2037C2×C7311yescharacteristic, complemented
430#1900C2×C7311yescharacteristic, complemented
431#1871C2×C7311yescharacteristic, complemented
432#1860C2×C7311yescharacteristic, complemented
433#1859C2×C7311yescharacteristic, complemented
434#1856C2×C7311yescharacteristic, complemented
435#1856C2×C7311yescharacteristic, complemented
436#1826C2×C7311yescharacteristic, complemented
437C73#2408411yescharacteristic, direct product factor, Sylow
438C22×M16C22×C7311yescharacteristic
439#555—21no—
440#553—21no—
441#553—21no—
442#551—22no—
443#547—21no—
444#546—22no—
445#544C22×C7311yescharacteristic
446#542—21no—
447#540—21no—
448#535C22×C7311yescharacteristic
449#532—21no—
450#529—21no—
451#525C22×C7311yescharacteristic
452C2×#121C22×C7311yescharacteristic
453#520C22×C7311yescharacteristic
454#518C22×C7311yescharacteristic
455C2×#117C22×C7311yescharacteristic
456C2×#117C22×C7311yescharacteristic
457#485—21no—
458#485—21no—
459#482—21no—
460#482—21no—
461#428—21no—
462#428—21no—
463#428C22×C7311yescharacteristic
464#428C22×C7311yescharacteristic
465#428C22×C7311yescharacteristic
466#428C22×C7311yescharacteristic
467#428C22×C7311yescharacteristic
468#428C22×C7311yescharacteristic
469#427—21no—
470#427—21no—
471C2×#104C22×C7311yescharacteristic
472C2×#104C22×C7311yescharacteristic
473#417C22×C7311yescharacteristic
474#417C22×C7311yescharacteristic
475C2×#100C22×C7311yescharacteristic
476C2×#100C22×C7311yescharacteristic
477#407C22×C7311yescharacteristic
478#394—22no—
479#390C22×C7311yescharacteristic
480#390C22×C7311yescharacteristic
481#388—22no—
482#384C22×C7311yescharacteristic
483#382C22×C7311yescharacteristic
484C4×C22⋊C4C22×C7311yescharacteristic
485#343C22×C7311yescharacteristic
486#343C22×C7311yescharacteristic
487#339C22×C7311yescharacteristic
488#339C22×C7311yescharacteristic
489#339C22×C7311yescharacteristic
490#339C22×C7311yescharacteristic
491#339C22×C7311yescharacteristic
492#339C22×C7311yescharacteristic
493C2×#41—22no—
494C2×#41C23×C7311yescharacteristic
495C22×D4D4×C7312yes—
496C22×D4C23×C7311yescharacteristic
497C23×C4C23×C7311yescharacteristic
498C2×M16—21no—
499C2×M16—22no—
500C2×M16—22no—
501C2×M16C23×C7311yescharacteristic
502C2×M16C23×C7311yescharacteristic
503C2×M16C23×C7311yescharacteristic
504C2×M16C23×C7311yescharacteristic
505C22×C8—21no—
506C4⋊Q8—21no—
507C4⋊Q8—21no—
508#127—21no—
509#126—22no—
510#126—22no—
511#125—21no—
512#125—21no—
513#124—22no—
514#124—22no—
515#124—21no—
516#123—22no—
517#123—22no—
518#123—22no—
519#123—22no—
520#123—21no—
521C22⋊Q8—22no—
522C22⋊Q8—22no—
523C22⋊Q8D4×C7311yescharacteristic
524C22⋊Q8D4×C7311yescharacteristic
525#121—22no—
526#121—22no—
527#121—22no—
528#121—21no—
529#121—21no—
530#121—21no—
531#121—21no—
532#121—21no—
533#121—21no—
534#121D4×C7311yescharacteristic
535#121D4×C7311yescharacteristic
536#120—21no—
537#120—22no—
538C4×Q8—21no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—21no—
542C4×D4—22no—
543C4×D4—21no—
544C4×D4—21no—
545C4×D4—21no—
546C4×D4—21no—
547C4×D4—21no—
548C4×D4—21no—
549#117—22no—
550#117—21no—
551#117—21no—
552#117—21no—
553#117—21no—
554#117—21no—
555#117—21no—
556#117—21no—
557#117D4×C7311yescharacteristic
558#117D4×C7311yescharacteristic
559#117C23×C7311yescharacteristic
560#117C23×C7311yescharacteristic
561#117C23×C7311yescharacteristic
562C2×C4⋊C4—21no—
563C2×C4⋊C4—22no—
564C2×C4⋊C4D4×C7311yescharacteristic
565C2×C4⋊C4D4×C7311yescharacteristic
566C2×C4⋊C4C23×C7311yescharacteristic
567C2×C4⋊C4C23×C7311yescharacteristic
568C2×C4⋊C4C23×C7311yescharacteristic
569C2×C22⋊C4—21no—
570C2×C22⋊C4—22no—
571C2×C22⋊C4—21no—
572C2×C22⋊C4—21no—
573C2×C22⋊C4—22no—
574C2×C22⋊C4—22no—
575C2×C22⋊C4D4×C7312yes—
576C2×C42—21no—
577C2×C42—21no—
578C2×C42C23×C7311yescharacteristic
579C2×C42C23×C7311yescharacteristic
580#107—21no—
581#107—21no—
582#107—21no—
583#107—21no—
584#107—21no—
585#107—21no—
586#106—21no—
587#106—21no—
588#106—21no—
589#106—21no—
590#106—21no—
591#106—21no—
592#104—22no—
593#104—22no—
594#103—21no—
595#103—21no—
596#102—21no—
597#102—21no—
598#100—22no—
599#100—22no—
600C22⋊C8—21no—
601C22⋊C8—21no—
602#95—21no—
603#95—22no—
604C24C2×D4×C7312yes—
605C24C2×D4×C7311yescharacteristic
606#41—21no—
607#41—21no—
608#41—21no—
609#41—21no—
610#41—84no—
611C2×Q8—22no—
612C2×Q8C2×D4×C7311yescharacteristic
613C2×D4—21no—
614C2×D4—22no—
615C2×D4—21no—
616C2×D4—22no—
617C2×D4—22no—
618C2×D4—21no—
619C2×D4—22no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—21no—
623C2×D4—21no—
624C2×D4—21no—
625C2×D4—21no—
626C2×D4—82no—
627C2×D4C2×D4×C7311yescharacteristic
628C22×C4—21no—
629C22×C4—21no—
630C22×C4—21no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—21no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—21no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4C2×D4×C7311yescharacteristic
643C22×C4C2×D4×C7311yescharacteristic
644C22×C4C2×D4×C7311yescharacteristic
645C22×C4C2×D4×C7311yescharacteristic
646C22×C4C2×D4×C7311yescharacteristic
647C22×C4C2×D4×C7312yes—
648C22×C4C24×C7311yescharacteristic
649M16—24no—
650M16—21no—
651M16—21no—
652M16—21no—
653M16—21no—
654M16—21no—
655M16—21no—
656M16#41×C7312yescomplemented
657M16#41×C7312yescomplemented
658C2×C8—24no—
659C2×C8—21no—
660C2×C8—21no—
661C2×C8—21no—
662C2×C8—21no—
663C4⋊C4—22no—
664C4⋊C4—22no—
665C4⋊C4—22no—
666C4⋊C4—22no—
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—82no—
678C4⋊C4C2×D4×C7311yescharacteristic
679C4⋊C4C2×D4×C7311yescharacteristic
680C4⋊C4C2×D4×C7311yescharacteristic
681C4⋊C4C2×D4×C7311yescharacteristic
682C4⋊C4C2×D4×C7311yescharacteristic
683C4⋊C4C2×D4×C7311yescharacteristic
684C22⋊C4—22no—
685C22⋊C4—22no—
686C22⋊C4—22no—
687C22⋊C4—22no—
688C22⋊C4—22no—
689C22⋊C4—21no—
690C22⋊C4—21no—
691C22⋊C4—21no—
692C22⋊C4—21no—
693C22⋊C4—21no—
694C22⋊C4—21no—
695C22⋊C4—21no—
696C22⋊C4—22no—
697C22⋊C4—22no—
698C22⋊C4—21no—
699C22⋊C4—21no—
700C22⋊C4—42no—
701C22⋊C4—44no—
702C22⋊C4—41no—
703C22⋊C4—41no—
704C22⋊C4—82no—
705C42—22no—
706C42—21no—
707C42—21no—
708C42—21no—
709C42—21no—
710C42—21no—
711C42—21no—
712C42—21no—
713C42—21no—
714C42—21no—
715C42—41no—
716C42—41no—
717C23—21no—
718C23—21no—
719C23—22no—
720C23—21no—
721C23—22no—
722C23—22no—
723C23—41no—
724C23—41no—
725C23—42no—
726C23—42no—
727C23#120×C7311yescharacteristic
728C23#120×C7311yescharacteristic
729C23C22×D4×C7311yescharacteristic
730Q8—21no—
731Q8—21no—
732Q8—82no—
733D4—21no—
734D4—21no—
735D4—44no—
736D4—42no—
737D4—41no—
738D4—41no—
739D4—41no—
740D4—41no—
741D4—41no—
742D4—41no—
743D4—82no—
744D4—81no—
745D4—82no—
746D4—82no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—21no—
750C2×C4—21no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—21no—
754C2×C4—21no—
755C2×C4—21no—
756C2×C4—21no—
757C2×C4—22no—
758C2×C4—21no—
759C2×C4—21no—
760C2×C4—21no—
761C2×C4—21no—
762C2×C4—21no—
763C2×C4—21no—
764C2×C4—21no—
765C2×C4—22no—
766C2×C4—41no—
767C2×C4—42no—
768C2×C4—41no—
769C2×C4—41no—
770C2×C4—41no—
771C2×C4—42no—
772C2×C4—41no—
773C2×C4—42no—
774C2×C4—41no—
775C2×C4—42no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—81no—
780C2×C4—82no—
781C2×C4—82no—
782C2×C4—82no—
783C2×C4#120×C7311yescharacteristic
784C2×C4#120×C7311yescharacteristic
785C2×C4C22×D4×C7311yescharacteristic
786C2×C4C22×D4×C7311yescharacteristic
787C2×C4C2×#41×C7311yescharacteristic
788C2×C4C2×#41×C7311yescharacteristic
789C2×C42−1+4×C7311yescharacteristic
790C2×C42−1+4×C7311yescharacteristic
791C8—22no—
792C8—22no—
793C8—41no—
794C8—41no—
795C22—21no—
796C22—21no—
797C22—21no—
798C22—21no—
799C22—21no—
800C22—21no—
801C22—21no—
802C22—21no—
803C22—42no—
804C22—41no—
805C22—41no—
806C22—42no—
807C22—41no—
808C22—42no—
809C22—81no—
810C22—81no—
811C22—82no—
812C22—82no—
813C22C2×#120×C7311yescharacteristic
814C22#547×C7311yescharacteristic
815C22#547×C7311yescharacteristic
816C4—21no—
817C4—21no—
818C4—42no—
819C4—41no—
820C4—41no—
821C4—41no—
822C4—41no—
823C4—41no—
824C4—42no—
825C4—41no—
826C4—41no—
827C4—81no—
828C4—81no—
829C4—81no—
830C4#525×C7311yescharacteristic
831C4#536×C7311yescharacteristic
832C4#547×C7311yescharacteristic
833C4#547×C7311yescharacteristic
834C2—21no—
835C2—21no—
836C2—41no—
837C2—41no—
838C2—82no—
839C2—81no—
840C2C73×#240611yescharacteristic
841C2C73×#301811yescharacteristic
842C2C73×#301911yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC22×C4C24×C73
prime radicalC73×#3494C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
2. C73×#3093C2semidirect
3. C73×#2911C2semidirect
4. C73×#2500C2semidirect
5. C73×#2061C2semidirect
6. C73×#2060C2semidirect
7. C73×#2037C2semidirect
8. C73×#2037C2semidirect
9. C73×#1900C2semidirect
10. C73×#1871C2semidirect
11. C73×#1860C2semidirect
12. C73×#1859C2semidirect
13. C73×#1856C2semidirect
14. C73×#1856C2semidirect
15. C73×#1826C2semidirect
234. M16×C73#41semidirect
235. M16×C73#41semidirect
412. #24084C73direct (N × H)
423. #3093C2×C73semidirect
424. #2911C2×C73semidirect
425. #2500C2×C73semidirect
426. #2061C2×C73semidirect
427. #2060C2×C73semidirect
428. #2037C2×C73semidirect
429. #2037C2×C73semidirect
430. #1900C2×C73semidirect
431. #1871C2×C73semidirect
432. #1860C2×C73semidirect
433. #1859C2×C73semidirect
434. #1856C2×C73semidirect
435. #1856C2×C73semidirect
436. #1826C2×C73semidirect
437. C73#24084direct (N × H)
656. M16#41×C73semidirect
657. M16#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34942
C73×#30932
C73×#29112
C73×#25002
C73×#20612
C73×#20602
C73×#20372
C73×#19002
C73×#18712
C73×#18602
C73×#18592
C73×#18562
C73×#18262
#2408473