Finite Group Databasebeta

← C73×#33556 #32942960

Subgroups — C73×#33556 #32942960

Order 18688.

1134 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×#3540C211yesmaximal, characteristic, complemented
2C73×#3028C211yesmaximal, characteristic, complemented
3C73×#3025C211yesmaximal, characteristic, complemented
4C73×#3021C211yesmaximal, characteristic, complemented
5C73×#2200C214yesmaximal, complemented
6C73×#2198C214yesmaximal, complemented
7C73×#2128C211yesmaximal, characteristic, complemented
8C73×#2123C211yesmaximal, characteristic, complemented
9C73×#2120C211yesmaximal, characteristic, complemented
10#585×C73C2211yescharacteristic
11C2×AGL(1,ℤ/8)×C73—21no—
12H(3,𝔽4)×C73—21no—
13#560×C73C2212yescomplemented
14#559×C73C2212yescomplemented
15#556×C73—21no—
16#555×C73—21no—
17#551×C73—21no—
18#548×C73—21no—
19#546×C73—21no—
20#542×C73—22no—
21#542×C73—21no—
22#538×C73—22no—
23#536×C73—21no—
24#536×C73C2211yescharacteristic
25#535×C73C2211yescharacteristic
26#525×C73—21no—
27#525×C73—21no—
28#525×C73C2211yescharacteristic
29#458×C73—21no—
30#458×C73—22no—
31#458×C73C2212yescomplemented
32#458×C73C2214yescomplemented
33B(4,𝔽2)×C73—21no—
34B(4,𝔽2)×C73C2212yescomplemented
35#454×C73—22no—
36#453×C73C2214yes—
37#421×C73—21no—
38#413×C73C2211yescharacteristic
39#410×C73—21no—
40#410×C73—21no—
41#410×C73C2211yescharacteristic
42#410×C73C2211yescharacteristic
43#353×C73C2214yescomplemented
44#352×C73C2212yescomplemented
45#352×C73C2214yescomplemented
46AΣL(1,𝔽16)×C73C2212yescomplemented
472−1+4×C73—21no—
482−1+4×C73—41no—
49H(5,𝔽2)×C73—21no—
50H(5,𝔽2)×C73—21no—
51H(5,𝔽2)×C73—41no—
52H(5,𝔽2)×C73C2312yes—
53C2×#41×C73—21no—
54C2×#41×C73—21no—
55C2×#41×C73—21no—
56C2×#41×C73—21no—
57C2×#41×C73—42no—
58C2×#41×C73C2311yescharacteristic
59C22×Q8×C73D411yescharacteristic, complemented
60C22×D4×C73D411yescharacteristic, complemented
61C23×C4×C73D411yescharacteristic
62AGL(1,ℤ/8)×C73—24no—
63AGL(1,ℤ/8)×C73—42no—
64C2×SD16×C73—41no—
65C2×D8×C73—41no—
66C2×M16×C73—21no—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73—21no—
69C4⋊Q8×C73—41no—
70#127×C73C2312yes—
71#126×C73—22no—
72#126×C73—22no—
73#126×C73—22no—
74#124×C73—22no—
75#124×C73—21no—
76#124×C73—22no—
77#124×C73—22no—
78#124×C73—21no—
79#124×C73—22no—
80#124×C73—22no—
81#124×C73—41no—
82#124×C73D412yescomplemented
83#123×C73—22no—
84#123×C73—22no—
85#123×C73—22no—
86#123×C73—22no—
87#123×C73—24no—
88#123×C73D411yescharacteristic
89#123×C73D412yescomplemented
90#123×C73C2311yescharacteristic
91#123×C73C2312yes—
92C22⋊Q8×C73—21no—
93C22⋊Q8×C73—22no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—21no—
96C22⋊Q8×C73—21no—
97C22⋊Q8×C73—21no—
98C22⋊Q8×C73—42no—
99C22⋊Q8×C73—41no—
100#121×C73—21no—
101#121×C73—21no—
102#121×C73—22no—
103#121×C73—21no—
104#121×C73—21no—
105#121×C73—22no—
106#121×C73—22no—
107#121×C73—41no—
108#120×C73—22no—
109#120×C73—22no—
110#120×C73—21no—
111#120×C73—21no—
112#120×C73—22no—
113#120×C73D411yescharacteristic
114#120×C73C2311yescharacteristic
115C4×Q8×C73—21no—
116C4×Q8×C73—22no—
117C4×D4×C73—22no—
118C4×D4×C73—21no—
119C4×D4×C73—22no—
120C4×D4×C73—21no—
121C4×D4×C73—21no—
122C4×D4×C73—22no—
123C4×D4×C73—42no—
124#117×C73—21no—
125#117×C73—22no—
126#117×C73—21no—
127#117×C73—21no—
128#117×C73D411yescharacteristic
129#117×C73D411yescharacteristic, complemented
130#117×C73D411yescharacteristic, complemented
131C2×C22⋊C4×C73—22no—
132#104×C73—24no—
133#101×C73—21no—
134#100×C73C2312yes—
135#99×C73—21no—
136#99×C73—21no—
137#99×C73—22no—
138#99×C73—22no—
139#99×C73—24no—
140#99×C73C2312yes—
141#99×C73C2312yes—
142C24×C73—21no—
143C24×C73C2×D411yescharacteristic
144#41×C73—22no—
145#41×C73—22no—
146#41×C73—41no—
147#41×C73—41no—
148#41×C73—42no—
149#41×C73—41no—
150#41×C73—41no—
151#41×C73—41no—
152#41×C73—41no—
153#41×C73—41no—
154#41×C73—42no—
155#41×C73—42no—
156#41×C73—42no—
157#41×C73—41no—
158#41×C73—41no—
159#41×C73—41no—
160#41×C73—81no—
161#41×C73—81no—
162C2×Q8×C73—21no—
163C2×Q8×C73—21no—
164C2×Q8×C73—22no—
165C2×Q8×C73—21no—
166C2×Q8×C73—21no—
167C2×Q8×C73—21no—
168C2×Q8×C73—41no—
169C2×Q8×C73—41no—
170C2×Q8×C73—42no—
171C2×Q8×C73C2×D411yescharacteristic
172C2×D4×C73—21no—
173C2×D4×C73—21no—
174C2×D4×C73—21no—
175C2×D4×C73—22no—
176C2×D4×C73—22no—
177C2×D4×C73—22no—
178C2×D4×C73—22no—
179C2×D4×C73—21no—
180C2×D4×C73—22no—
181C2×D4×C73—22no—
182C2×D4×C73—21no—
183C2×D4×C73—21no—
184C2×D4×C73—41no—
185C2×D4×C73—41no—
186C2×D4×C73—42no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—41no—
190C2×D4×C73—42no—
191C2×D4×C73C2×D411yescharacteristic
192C2×D4×C73C2×D411yescharacteristic
193C2×D4×C73C2×D412yes—
194C2×D4×C73C2411yescharacteristic
195C22×C4×C73—22no—
196C22×C4×C73—22no—
197C22×C4×C73—22no—
198C22×C4×C73—22no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—41no—
202C22×C4×C73—41no—
203C22×C4×C73—41no—
204C22×C4×C73C2×D411yescharacteristic
205C22×C4×C73C2×D411yescharacteristic
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D412yes—
209SD16×C73—44no—
210D8×C73—44no—
211M16×C73—22no—
212M16×C73—41no—
213C2×C8×C73—41no—
214C4⋊C4×C73—22no—
215C4⋊C4×C73—22no—
216C4⋊C4×C73—22no—
217C4⋊C4×C73—21no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—22no—
224C4⋊C4×C73—41no—
225C4⋊C4×C73—41no—
226C4⋊C4×C73—42no—
227C4⋊C4×C73—44no—
228C22⋊C4×C73—22no—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—22no—
232C22⋊C4×C73—22no—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—21no—
235C22⋊C4×C73—22no—
236C22⋊C4×C73—21no—
237C22⋊C4×C73—21no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—22no—
240C22⋊C4×C73—22no—
241C22⋊C4×C73—21no—
242C22⋊C4×C73—21no—
243C22⋊C4×C73—22no—
244C22⋊C4×C73—22no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—42no—
247C22⋊C4×C73—44no—
248C22⋊C4×C73C2×D411yescharacteristic
249C22⋊C4×C73C2×D411yescharacteristic
250C22⋊C4×C73C2×D412yes—
251C42×C73—22no—
252C42×C73—22no—
253C42×C73—21no—
254C42×C73—21no—
255C42×C73—41no—
256C42×C73—41no—
257C42×C73C2×D412yes—
258C23×C73—22no—
259C23×C73—22no—
260C23×C73—21no—
261C23×C73—22no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—81no—
265C23×C73—81no—
266C23×C73—82no—
267C23×C73#12011yescharacteristic
268C23×C73C22×D411yescharacteristic
269C23×C73C22×D411yescharacteristic
270Q8×C73—22no—
271Q8×C73—41no—
272Q8×C73—41no—
273Q8×C73—41no—
274Q8×C73—41no—
275Q8×C73—41no—
276Q8×C73—41no—
277Q8×C73—81no—
278Q8×C73—82no—
279D4×C73—22no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—42no—
284D4×C73—41no—
285D4×C73—41no—
286D4×C73—42no—
287D4×C73—42no—
288D4×C73—42no—
289D4×C73—42no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—41no—
293D4×C73—81no—
294D4×C73—82no—
295D4×C73—82no—
296D4×C73—82no—
297D4×C73—81no—
298D4×C73—82no—
299D4×C73—84no—
300C2×C4×C73—21no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—22no—
307C2×C4×C73—22no—
308C2×C4×C73—21no—
309C2×C4×C73—22no—
310C2×C4×C73—22no—
311C2×C4×C73—21no—
312C2×C4×C73—22no—
313C2×C4×C73—21no—
314C2×C4×C73—42no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—41no—
318C2×C4×C73—42no—
319C2×C4×C73—41no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—42no—
323C2×C4×C73—42no—
324C2×C4×C73—42no—
325C2×C4×C73—81no—
326C2×C4×C73—82no—
327C2×C4×C73—82no—
328C2×C4×C73#12011yescharacteristic
329C2×C4×C73#12011yescharacteristic
330C2×C4×C73#12011yescharacteristic
331C2×C4×C73C22×D411yescharacteristic
332C8×C73—42no—
333C22×C73—21no—
334C22×C73—21no—
335C22×C73—21no—
336C22×C73—41no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—42no—
340C22×C73—41no—
341C22×C73—41no—
342C22×C73—42no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—41no—
346C22×C73—42no—
347C22×C73—82no—
348C22×C73—82no—
349C22×C73—81no—
350C22×C73—161no—
351C22×C73—162no—
352C22×C73C2×#12011yescharacteristic
353C4×C73—21no—
354C4×C73—21no—
355C4×C73—21no—
356C4×C73—41no—
357C4×C73—42no—
358C4×C73—42no—
359C4×C73—41no—
360C4×C73—42no—
361C4×C73—41no—
362C4×C73—42no—
363C4×C73—82no—
364C4×C73—82no—
365C4×C73B(4,𝔽2)11yescharacteristic
366C4×C73B(4,𝔽2)11yescharacteristic
367#33556C7311yesmaximal, characteristic, direct product factor, Sylow
368C2×C73—21no—
369C2×C73—41no—
370C2×C73—41no—
371C2×C73—41no—
372C2×C73—81no—
373C2×C73—82no—
374C2×C73—82no—
375C2×C73C2×B(4,𝔽2)11yescharacteristic
376#3540C2×C7311yescharacteristic, complemented
377#3028C2×C7311yescharacteristic, complemented
378#3025C2×C7311yescharacteristic, complemented
379#3021C2×C7311yescharacteristic, complemented
380#2200C2×C7314yescomplemented
381#2198C2×C7314yescomplemented
382#2128C2×C7311yescharacteristic, complemented
383#2123C2×C7311yescharacteristic, complemented
384#2120C2×C7311yescharacteristic, complemented
385C73#3355611yescharacteristic, direct product factor, Sylow
386#585C22×C7311yescharacteristic
387C2×AGL(1,ℤ/8)—21no—
388H(3,𝔽4)—21no—
389#560C22×C7312yescomplemented
390#559C22×C7312yescomplemented
391#556—21no—
392#555—21no—
393#551—21no—
394#548—21no—
395#546—21no—
396#542—22no—
397#542—21no—
398#538—22no—
399#536—21no—
400#536C22×C7311yescharacteristic
401#535C22×C7311yescharacteristic
402#525—21no—
403#525—21no—
404#525C22×C7311yescharacteristic
405#458—21no—
406#458—22no—
407#458C22×C7312yescomplemented
408#458C22×C7314yescomplemented
409B(4,𝔽2)—21no—
410B(4,𝔽2)C22×C7312yescomplemented
411#454—22no—
412#453C22×C7314yes—
413#421—21no—
414#413C22×C7311yescharacteristic
415#410—21no—
416#410—21no—
417#410C22×C7311yescharacteristic
418#410C22×C7311yescharacteristic
419#353C22×C7314yescomplemented
420#352C22×C7312yescomplemented
421#352C22×C7314yescomplemented
422AΣL(1,𝔽16)C22×C7312yescomplemented
4232−1+4—21no—
4242−1+4—41no—
425H(5,𝔽2)—21no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—41no—
428H(5,𝔽2)C23×C7312yes—
429C2×#41—21no—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—42no—
434C2×#41C23×C7311yescharacteristic
435C22×Q8D4×C7311yescharacteristic, complemented
436C22×D4D4×C7311yescharacteristic, complemented
437C23×C4D4×C7311yescharacteristic
438AGL(1,ℤ/8)—24no—
439AGL(1,ℤ/8)—42no—
440C2×SD16—41no—
441C2×D8—41no—
442C2×M16—21no—
443C4⋊Q8—21no—
444C4⋊Q8—21no—
445C4⋊Q8—41no—
446#127C23×C7312yes—
447#126—22no—
448#126—22no—
449#126—22no—
450#124—22no—
451#124—21no—
452#124—22no—
453#124—22no—
454#124—21no—
455#124—22no—
456#124—22no—
457#124—41no—
458#124D4×C7312yescomplemented
459#123—22no—
460#123—22no—
461#123—22no—
462#123—22no—
463#123—24no—
464#123D4×C7311yescharacteristic
465#123D4×C7312yescomplemented
466#123C23×C7311yescharacteristic
467#123C23×C7312yes—
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—22no—
471C22⋊Q8—21no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—42no—
475C22⋊Q8—41no—
476#121—21no—
477#121—21no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—22no—
482#121—22no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—21no—
487#120—21no—
488#120—22no—
489#120D4×C7311yescharacteristic
490#120C23×C7311yescharacteristic
491C4×Q8—21no—
492C4×Q8—22no—
493C4×D4—22no—
494C4×D4—21no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—21no—
498C4×D4—22no—
499C4×D4—42no—
500#117—21no—
501#117—22no—
502#117—21no—
503#117—21no—
504#117D4×C7311yescharacteristic
505#117D4×C7311yescharacteristic, complemented
506#117D4×C7311yescharacteristic, complemented
507C2×C22⋊C4—22no—
508#104—24no—
509#101—21no—
510#100C23×C7312yes—
511#99—21no—
512#99—21no—
513#99—22no—
514#99—22no—
515#99—24no—
516#99C23×C7312yes—
517#99C23×C7312yes—
518C24—21no—
519C24C2×D4×C7311yescharacteristic
520#41—22no—
521#41—22no—
522#41—41no—
523#41—41no—
524#41—42no—
525#41—41no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—42no—
531#41—42no—
532#41—42no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—81no—
537#41—81no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—22no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C7311yescharacteristic
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—41no—
561C2×D4—41no—
562C2×D4—42no—
563C2×D4—42no—
564C2×D4—42no—
565C2×D4—41no—
566C2×D4—42no—
567C2×D4C2×D4×C7311yescharacteristic
568C2×D4C2×D4×C7311yescharacteristic
569C2×D4C2×D4×C7312yes—
570C2×D4C24×C7311yescharacteristic
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—41no—
578C22×C4—41no—
579C22×C4—41no—
580C22×C4C2×D4×C7311yescharacteristic
581C22×C4C2×D4×C7311yescharacteristic
582C22×C4C2×D4×C7311yescharacteristic
583C22×C4C2×D4×C7311yescharacteristic
584C22×C4C2×D4×C7312yes—
585SD16—44no—
586D8—44no—
587M16—22no—
588M16—41no—
589C2×C8—41no—
590C4⋊C4—22no—
591C4⋊C4—22no—
592C4⋊C4—22no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—22no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—41no—
601C4⋊C4—41no—
602C4⋊C4—42no—
603C4⋊C4—44no—
604C22⋊C4—22no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—21no—
611C22⋊C4—22no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—22no—
617C22⋊C4—21no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—42no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4C2×D4×C7311yescharacteristic
625C22⋊C4C2×D4×C7311yescharacteristic
626C22⋊C4C2×D4×C7312yes—
627C42—22no—
628C42—22no—
629C42—21no—
630C42—21no—
631C42—41no—
632C42—41no—
633C42C2×D4×C7312yes—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—41no—
639C23—41no—
640C23—81no—
641C23—81no—
642C23—82no—
643C23#120×C7311yescharacteristic
644C23C22×D4×C7311yescharacteristic
645C23C22×D4×C7311yescharacteristic
646Q8—22no—
647Q8—41no—
648Q8—41no—
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—81no—
654Q8—82no—
655D4—22no—
656D4—41no—
657D4—41no—
658D4—41no—
659D4—42no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—82no—
670D4—81no—
671D4—82no—
672D4—82no—
673D4—82no—
674D4—81no—
675D4—84no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—22no—
683C2×C4—22no—
684C2×C4—21no—
685C2×C4—22no—
686C2×C4—22no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—21no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—41no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—42no—
699C2×C4—42no—
700C2×C4—42no—
701C2×C4—81no—
702C2×C4—82no—
703C2×C4—82no—
704C2×C4#120×C7311yescharacteristic
705C2×C4#120×C7311yescharacteristic
706C2×C4#120×C7311yescharacteristic
707C2×C4C22×D4×C7311yescharacteristic
708C8—42no—
709C22—21no—
710C22—21no—
711C22—21no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—42no—
716C22—41no—
717C22—41no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—41no—
722C22—42no—
723C22—82no—
724C22—82no—
725C22—81no—
726C22—161no—
727C22—162no—
728C22C2×#120×C7311yescharacteristic
729C4—21no—
730C4—21no—
731C4—21no—
732C4—41no—
733C4—42no—
734C4—42no—
735C4—41no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—82no—
740C4—82no—
741C4B(4,𝔽2)×C7311yescharacteristic
742C4B(4,𝔽2)×C7311yescharacteristic
743C2—21no—
744C2—41no—
745C2—41no—
746C2—41no—
747C2—81no—
748C2—82no—
749C2—82no—
750C2C2×B(4,𝔽2)×C7311yescharacteristic
subgroupG/H
center, socleC2×C73C2×B(4,𝔽2)
commutator, Frattini, cosocleC2×D4C24×C73
LCSG ▷ C2×D4 ▷ C22 ▷ C2 ▷ C1
UCSC1 ◁ C2×C73 ◁ C2×C4×C73 ◁ C2×#41×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3540C2semidirect
2. C73×#3028C2semidirect
3. C73×#3025C2semidirect
4. C73×#3021C2semidirect
5. C73×#2200C2semidirect
6. C73×#2198C2semidirect
7. C73×#2128C2semidirect
8. C73×#2123C2semidirect
9. C73×#2120C2semidirect
13. #560×C73C22semidirect
14. #559×C73C22semidirect
31. #458×C73C22semidirect
32. #458×C73C22semidirect
34. B(4,𝔽2)×C73C22semidirect
43. #353×C73C22semidirect
44. #352×C73C22semidirect
45. #352×C73C22semidirect
46. AΣL(1,𝔽16)×C73C22semidirect
59. C22×Q8×C73D4semidirect
60. C22×D4×C73D4semidirect
82. #124×C73D4semidirect
89. #123×C73D4semidirect
129. #117×C73D4semidirect
130. #117×C73D4semidirect
367. #33556C73direct (N × H)
376. #3540C2×C73semidirect
377. #3028C2×C73semidirect
378. #3025C2×C73semidirect
379. #3021C2×C73semidirect
380. #2200C2×C73semidirect
381. #2198C2×C73semidirect
382. #2128C2×C73semidirect
383. #2123C2×C73semidirect
384. #2120C2×C73semidirect
385. C73#33556direct (N × H)
389. #560C22×C73semidirect
390. #559C22×C73semidirect
407. #458C22×C73semidirect
408. #458C22×C73semidirect
410. B(4,𝔽2)C22×C73semidirect
419. #353C22×C73semidirect
420. #352C22×C73semidirect
421. #352C22×C73semidirect
422. AΣL(1,𝔽16)C22×C73semidirect
435. C22×Q8D4×C73semidirect
436. C22×D4D4×C73semidirect
458. #124D4×C73semidirect
465. #123D4×C73semidirect
505. #117D4×C73semidirect
506. #117D4×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#35402
C73×#30282
C73×#30252
C73×#30212
C73×#22002
C73×#21982
C73×#21282
C73×#21232
C73×#21202
#3355673