Finite Group Databasebeta

← C73×#33555 #32942959

Subgroups — C73×#33555 #32942959

Order 18688.

1146 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×#3540C211yesmaximal, characteristic, complemented
2C73×#3027C211yesmaximal, characteristic, complemented
3C73×#3025C211yesmaximal, characteristic, complemented
4C73×#3022C211yesmaximal, characteristic, complemented
5C73×#2199C214yesmaximal, complemented
6C73×#2197C214yesmaximal, complemented
7C73×#2129C211yesmaximal, characteristic, complemented
8C73×#2122C211yesmaximal, characteristic, complemented
9C73×#2120C211yesmaximal, characteristic, complemented
10#585×C73C2211yescharacteristic
11C2×#137×C73—21no—
12H(3,𝔽4)×C73C2212yescomplemented
13#560×C73—21no—
14#559×C73—21no—
15#556×C73—21no—
16#555×C73—21no—
17#551×C73C2212yescomplemented
18#548×C73—21no—
19#546×C73—21no—
20#542×C73—22no—
21#542×C73—21no—
22#538×C73—22no—
23#536×C73C2211yescharacteristic
24#535×C73—21no—
25#535×C73C2211yescharacteristic
26#525×C73—21no—
27#525×C73—21no—
28#525×C73C2211yescharacteristic
29#458×C73—21no—
30#458×C73C2212yes—
31B(4,𝔽2)×C73—21no—
32B(4,𝔽2)×C73—22no—
33B(4,𝔽2)×C73C2214yes—
34B(4,𝔽2)×C73C2212yes—
35#456×C73—22no—
36#455×C73C2214yes—
37#421×C73—21no—
38#413×C73C2211yescharacteristic
39#410×C73—21no—
40#410×C73—21no—
41#410×C73C2211yescharacteristic
42#410×C73C2211yescharacteristic
43#354×C73C2214yescomplemented
44#352×C73C2212yescomplemented
45AΣL(1,𝔽16)×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, complemented
62#137×C73—24no—
63#137×C73—42no—
64C2×Q16×C73—41no—
65C2×SD16×C73—41no—
66C2×M16×C73—21no—
67C4⋊Q8×C73—21no—
68C4⋊Q8×C73D412yescomplemented
69#127×C73—21no—
70#127×C73—41no—
71#126×C73—22no—
72#126×C73—22no—
73#126×C73—22no—
74#124×C73—22no—
75#124×C73—21no—
76#124×C73—21no—
77#124×C73—22no—
78#124×C73—22no—
79#124×C73—22no—
80#124×C73—22no—
81#124×C73—41no—
82#124×C73C2312yes—
83#123×C73—22no—
84#123×C73—22no—
85#123×C73—21no—
86#123×C73—21no—
87#123×C73—22no—
88#123×C73—22no—
89#123×C73D411yescharacteristic, complemented
90#123×C73C2311yescharacteristic
91C22⋊Q8×C73—21no—
92C22⋊Q8×C73—22no—
93C22⋊Q8×C73—21no—
94C22⋊Q8×C73—22no—
95C22⋊Q8×C73—21no—
96C22⋊Q8×C73—21no—
97C22⋊Q8×C73—41no—
98#121×C73—21no—
99#121×C73—22no—
100#121×C73—22no—
101#121×C73—22no—
102#121×C73—21no—
103#121×C73—21no—
104#121×C73—21no—
105#121×C73—42no—
106#121×C73—41no—
107#120×C73—22no—
108#120×C73—22no—
109#120×C73—22no—
110#120×C73—24no—
111#120×C73D411yescharacteristic, complemented
112#120×C73D412yescomplemented
113#120×C73C2311yescharacteristic
114#120×C73C2312yes—
115C4×Q8×C73—21no—
116C4×Q8×C73—22no—
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—42no—
124#117×C73—21no—
125#117×C73—22no—
126#117×C73—21no—
127#117×C73—21no—
128#117×C73D411yescharacteristic, complemented
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—24no—
138#99×C73—22no—
139#99×C73—22no—
140#99×C73C2312yes—
141#99×C73C2312yes—
142C24×C73C2×D412yes—
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—41no—
168C2×Q8×C73—41no—
169C2×Q8×C73—42no—
170C2×Q8×C73C2×D412yes—
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—21no—
182C2×D4×C73—22no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—41no—
186C2×D4×C73—41no—
187C2×D4×C73—42no—
188C2×D4×C73—42no—
189C2×D4×C73—42no—
190C2×D4×C73—41no—
191C2×D4×C73—42no—
192C2×D4×C73—44no—
193C2×D4×C73C2×D411yescharacteristic
194C2×D4×C73C2×D411yescharacteristic
195C2×D4×C73C2411yescharacteristic
196C22×C4×C73—22no—
197C22×C4×C73—22no—
198C22×C4×C73—22no—
199C22×C4×C73—22no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—41no—
204C22×C4×C73—41no—
205C22×C4×C73—41no—
206C22×C4×C73C2×D411yescharacteristic
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D411yescharacteristic
209C22×C4×C73C2×D411yescharacteristic
210Q16×C73—44no—
211SD16×C73—44no—
212M16×C73—22no—
213M16×C73—41no—
214C2×C8×C73—41no—
215C4⋊C4×C73—22no—
216C4⋊C4×C73—22no—
217C4⋊C4×C73—22no—
218C4⋊C4×C73—21no—
219C4⋊C4×C73—21no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—21no—
225C4⋊C4×C73—41no—
226C4⋊C4×C73—41no—
227C4⋊C4×C73—42no—
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—21no—
236C22⋊C4×C73—21no—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—21no—
240C22⋊C4×C73—22no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—21no—
243C22⋊C4×C73—22no—
244C22⋊C4×C73—22no—
245C22⋊C4×C73—42no—
246C22⋊C4×C73—44no—
247C22⋊C4×C73—42no—
248C22⋊C4×C73C2×D412yes—
249C22⋊C4×C73C2×D411yescharacteristic
250C22⋊C4×C73C2×D411yescharacteristic
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—22no—
261C23×C73—21no—
262C23×C73—41no—
263C23×C73—41no—
264C23×C73—42no—
265C23×C73—81no—
266C23×C73—82no—
267C23×C73#12011yescharacteristic
268C23×C73C22×D411yescharacteristic
269C23×C73C22×D411yescharacteristic
270Q8×C73—22no—
271Q8×C73—41no—
272Q8×C73—42no—
273Q8×C73—41no—
274Q8×C73—41no—
275Q8×C73—41no—
276Q8×C73—41no—
277Q8×C73—41no—
278Q8×C73—82no—
279D4×C73—22no—
280D4×C73—41no—
281D4×C73—41no—
282D4×C73—41no—
283D4×C73—41no—
284D4×C73—41no—
285D4×C73—42no—
286D4×C73—42no—
287D4×C73—42no—
288D4×C73—42no—
289D4×C73—41no—
290D4×C73—41no—
291D4×C73—41no—
292D4×C73—81no—
293D4×C73—81no—
294D4×C73—82no—
295D4×C73—82no—
296D4×C73—82no—
297D4×C73—81no—
298D4×C73—82no—
299D4×C73—84no—
300D4×C73—164no—
301C2×C4×C73—21no—
302C2×C4×C73—21no—
303C2×C4×C73—21no—
304C2×C4×C73—21no—
305C2×C4×C73—21no—
306C2×C4×C73—21no—
307C2×C4×C73—22no—
308C2×C4×C73—22no—
309C2×C4×C73—21no—
310C2×C4×C73—22no—
311C2×C4×C73—21no—
312C2×C4×C73—22no—
313C2×C4×C73—22no—
314C2×C4×C73—21no—
315C2×C4×C73—42no—
316C2×C4×C73—42no—
317C2×C4×C73—42no—
318C2×C4×C73—41no—
319C2×C4×C73—42no—
320C2×C4×C73—41no—
321C2×C4×C73—41no—
322C2×C4×C73—41no—
323C2×C4×C73—42no—
324C2×C4×C73—42no—
325C2×C4×C73—81no—
326C2×C4×C73—81no—
327C2×C4×C73—82no—
328C2×C4×C73—82no—
329C2×C4×C73#12011yescharacteristic
330C2×C4×C73#12011yescharacteristic
331C2×C4×C73#12011yescharacteristic
332C2×C4×C73C22×D411yescharacteristic
333C8×C73—42no—
334C22×C73—21no—
335C22×C73—21no—
336C22×C73—21no—
337C22×C73—41no—
338C22×C73—41no—
339C22×C73—41no—
340C22×C73—42no—
341C22×C73—41no—
342C22×C73—41no—
343C22×C73—42no—
344C22×C73—42no—
345C22×C73—42no—
346C22×C73—41no—
347C22×C73—42no—
348C22×C73—82no—
349C22×C73—82no—
350C22×C73—84no—
351C22×C73—81no—
352C22×C73—161no—
353C22×C73C2×#12011yescharacteristic
354C4×C73—21no—
355C4×C73—21no—
356C4×C73—21no—
357C4×C73—41no—
358C4×C73—42no—
359C4×C73—42no—
360C4×C73—41no—
361C4×C73—42no—
362C4×C73—41no—
363C4×C73—42no—
364C4×C73—82no—
365C4×C73—82no—
366C4×C73B(4,𝔽2)11yescharacteristic
367C4×C73B(4,𝔽2)11yescharacteristic
368#33555C7311yesmaximal, characteristic, direct product factor, Sylow
369C2×C73—21no—
370C2×C73—41no—
371C2×C73—41no—
372C2×C73—41no—
373C2×C73—81no—
374C2×C73—82no—
375C2×C73—82no—
376C2×C73C2×B(4,𝔽2)11yescharacteristic
377#3540C2×C7311yescharacteristic, complemented
378#3027C2×C7311yescharacteristic, complemented
379#3025C2×C7311yescharacteristic, complemented
380#3022C2×C7311yescharacteristic, complemented
381#2199C2×C7314yescomplemented
382#2197C2×C7314yescomplemented
383#2129C2×C7311yescharacteristic, complemented
384#2122C2×C7311yescharacteristic, complemented
385#2120C2×C7311yescharacteristic, complemented
386C73#3355511yescharacteristic, direct product factor, Sylow
387#585C22×C7311yescharacteristic
388C2×#137—21no—
389H(3,𝔽4)C22×C7312yescomplemented
390#560—21no—
391#559—21no—
392#556—21no—
393#555—21no—
394#551C22×C7312yescomplemented
395#548—21no—
396#546—21no—
397#542—22no—
398#542—21no—
399#538—22no—
400#536C22×C7311yescharacteristic
401#535—21no—
402#535C22×C7311yescharacteristic
403#525—21no—
404#525—21no—
405#525C22×C7311yescharacteristic
406#458—21no—
407#458C22×C7312yes—
408B(4,𝔽2)—21no—
409B(4,𝔽2)—22no—
410B(4,𝔽2)C22×C7314yes—
411B(4,𝔽2)C22×C7312yes—
412#456—22no—
413#455C22×C7314yes—
414#421—21no—
415#413C22×C7311yescharacteristic
416#410—21no—
417#410—21no—
418#410C22×C7311yescharacteristic
419#410C22×C7311yescharacteristic
420#354C22×C7314yescomplemented
421#352C22×C7312yescomplemented
422AΣL(1,𝔽16)C22×C7312yescomplemented
423AΣL(1,𝔽16)C22×C7314yescomplemented
4242−1+4—21no—
4252−1+4—41no—
426H(5,𝔽2)—21no—
427H(5,𝔽2)—21no—
428H(5,𝔽2)—41no—
429H(5,𝔽2)C23×C7312yes—
430C2×#41—21no—
431C2×#41—21no—
432C2×#41—21no—
433C2×#41—21no—
434C2×#41—42no—
435C2×#41C23×C7311yescharacteristic
436C22×Q8D4×C7311yescharacteristic, complemented
437C22×D4D4×C7311yescharacteristic, complemented
438C23×C4D4×C7311yescharacteristic, complemented
439#137—24no—
440#137—42no—
441C2×Q16—41no—
442C2×SD16—41no—
443C2×M16—21no—
444C4⋊Q8—21no—
445C4⋊Q8D4×C7312yescomplemented
446#127—21no—
447#127—41no—
448#126—22no—
449#126—22no—
450#126—22no—
451#124—22no—
452#124—21no—
453#124—21no—
454#124—22no—
455#124—22no—
456#124—22no—
457#124—22no—
458#124—41no—
459#124C23×C7312yes—
460#123—22no—
461#123—22no—
462#123—21no—
463#123—21no—
464#123—22no—
465#123—22no—
466#123D4×C7311yescharacteristic, complemented
467#123C23×C7311yescharacteristic
468C22⋊Q8—21no—
469C22⋊Q8—22no—
470C22⋊Q8—21no—
471C22⋊Q8—22no—
472C22⋊Q8—21no—
473C22⋊Q8—21no—
474C22⋊Q8—41no—
475#121—21no—
476#121—22no—
477#121—22no—
478#121—22no—
479#121—21no—
480#121—21no—
481#121—21no—
482#121—42no—
483#121—41no—
484#120—22no—
485#120—22no—
486#120—22no—
487#120—24no—
488#120D4×C7311yescharacteristic, complemented
489#120D4×C7312yescomplemented
490#120C23×C7311yescharacteristic
491#120C23×C7312yes—
492C4×Q8—21no—
493C4×Q8—22no—
494C4×D4—22no—
495C4×D4—22no—
496C4×D4—21no—
497C4×D4—22no—
498C4×D4—21no—
499C4×D4—21no—
500C4×D4—42no—
501#117—21no—
502#117—22no—
503#117—21no—
504#117—21no—
505#117D4×C7311yescharacteristic, complemented
506#117D4×C7311yescharacteristic, complemented
507#117D4×C7311yescharacteristic, complemented
508C2×C22⋊C4—22no—
509#104—24no—
510#101—21no—
511#100C23×C7312yes—
512#99—21no—
513#99—21no—
514#99—24no—
515#99—22no—
516#99—22no—
517#99C23×C7312yes—
518#99C23×C7312yes—
519C24C2×D4×C7312yes—
520C24C2×D4×C7311yescharacteristic
521#41—22no—
522#41—22no—
523#41—41no—
524#41—41no—
525#41—42no—
526#41—41no—
527#41—41no—
528#41—41no—
529#41—41no—
530#41—41no—
531#41—42no—
532#41—42no—
533#41—42no—
534#41—41no—
535#41—41no—
536#41—41no—
537#41—81no—
538#41—81no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—22no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—41no—
545C2×Q8—41no—
546C2×Q8—42no—
547C2×Q8C2×D4×C7312yes—
548C2×Q8C2×D4×C7311yescharacteristic
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—22no—
555C2×D4—22no—
556C2×D4—21no—
557C2×D4—22no—
558C2×D4—21no—
559C2×D4—22no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—41no—
563C2×D4—41no—
564C2×D4—42no—
565C2×D4—42no—
566C2×D4—42no—
567C2×D4—41no—
568C2×D4—42no—
569C2×D4—44no—
570C2×D4C2×D4×C7311yescharacteristic
571C2×D4C2×D4×C7311yescharacteristic
572C2×D4C24×C7311yescharacteristic
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—41no—
581C22×C4—41no—
582C22×C4—41no—
583C22×C4C2×D4×C7311yescharacteristic
584C22×C4C2×D4×C7311yescharacteristic
585C22×C4C2×D4×C7311yescharacteristic
586C22×C4C2×D4×C7311yescharacteristic
587Q16—44no—
588SD16—44no—
589M16—22no—
590M16—41no—
591C2×C8—41no—
592C4⋊C4—22no—
593C4⋊C4—22no—
594C4⋊C4—22no—
595C4⋊C4—21no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—21no—
599C4⋊C4—22no—
600C4⋊C4—22no—
601C4⋊C4—21no—
602C4⋊C4—41no—
603C4⋊C4—41no—
604C4⋊C4—42no—
605C22⋊C4—22no—
606C22⋊C4—22no—
607C22⋊C4—22no—
608C22⋊C4—22no—
609C22⋊C4—22no—
610C22⋊C4—22no—
611C22⋊C4—21no—
612C22⋊C4—21no—
613C22⋊C4—21no—
614C22⋊C4—22no—
615C22⋊C4—22no—
616C22⋊C4—21no—
617C22⋊C4—22no—
618C22⋊C4—22no—
619C22⋊C4—21no—
620C22⋊C4—22no—
621C22⋊C4—22no—
622C22⋊C4—42no—
623C22⋊C4—44no—
624C22⋊C4—42no—
625C22⋊C4C2×D4×C7312yes—
626C22⋊C4C2×D4×C7311yescharacteristic
627C22⋊C4C2×D4×C7311yescharacteristic
628C42—22no—
629C42—22no—
630C42—21no—
631C42—21no—
632C42—41no—
633C42—41no—
634C42C2×D4×C7312yes—
635C23—22no—
636C23—22no—
637C23—22no—
638C23—21no—
639C23—41no—
640C23—41no—
641C23—42no—
642C23—81no—
643C23—82no—
644C23#120×C7311yescharacteristic
645C23C22×D4×C7311yescharacteristic
646C23C22×D4×C7311yescharacteristic
647Q8—22no—
648Q8—41no—
649Q8—42no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653Q8—41no—
654Q8—41no—
655Q8—82no—
656D4—22no—
657D4—41no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662D4—42no—
663D4—42no—
664D4—42no—
665D4—42no—
666D4—41no—
667D4—41no—
668D4—41no—
669D4—81no—
670D4—82no—
671D4—81no—
672D4—82no—
673D4—82no—
674D4—82no—
675D4—81no—
676D4—84no—
677D4—164no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—21no—
683C2×C4—21no—
684C2×C4—22no—
685C2×C4—22no—
686C2×C4—21no—
687C2×C4—22no—
688C2×C4—21no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—21no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—41no—
696C2×C4—42no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—42no—
701C2×C4—42no—
702C2×C4—81no—
703C2×C4—81no—
704C2×C4—82no—
705C2×C4—82no—
706C2×C4#120×C7311yescharacteristic
707C2×C4#120×C7311yescharacteristic
708C2×C4#120×C7311yescharacteristic
709C2×C4C22×D4×C7311yescharacteristic
710C8—42no—
711C22—21no—
712C22—21no—
713C22—21no—
714C22—41no—
715C22—41no—
716C22—41no—
717C22—42no—
718C22—41no—
719C22—41no—
720C22—42no—
721C22—42no—
722C22—42no—
723C22—41no—
724C22—42no—
725C22—82no—
726C22—82no—
727C22—84no—
728C22—81no—
729C22—161no—
730C22C2×#120×C7311yescharacteristic
731C4—21no—
732C4—21no—
733C4—21no—
734C4—41no—
735C4—42no—
736C4—42no—
737C4—41no—
738C4—42no—
739C4—41no—
740C4—42no—
741C4—82no—
742C4—82no—
743C4B(4,𝔽2)×C7311yescharacteristic
744C4B(4,𝔽2)×C7311yescharacteristic
745C2—21no—
746C2—41no—
747C2—41no—
748C2—41no—
749C2—81no—
750C2—82no—
751C2—82no—
752C2C2×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×#3027C2semidirect
3. C73×#3025C2semidirect
4. C73×#3022C2semidirect
5. C73×#2199C2semidirect
6. C73×#2197C2semidirect
7. C73×#2129C2semidirect
8. C73×#2122C2semidirect
9. C73×#2120C2semidirect
12. H(3,𝔽4)×C73C22semidirect
17. #551×C73C22semidirect
43. #354×C73C22semidirect
44. #352×C73C22semidirect
45. AΣL(1,𝔽16)×C73C22semidirect
46. AΣL(1,𝔽16)×C73C22semidirect
59. C22×Q8×C73D4semidirect
60. C22×D4×C73D4semidirect
61. C23×C4×C73D4semidirect
68. C4⋊Q8×C73D4semidirect
89. #123×C73D4semidirect
111. #120×C73D4semidirect
112. #120×C73D4semidirect
128. #117×C73D4semidirect
129. #117×C73D4semidirect
130. #117×C73D4semidirect
368. #33555C73direct (N × H)
377. #3540C2×C73semidirect
378. #3027C2×C73semidirect
379. #3025C2×C73semidirect
380. #3022C2×C73semidirect
381. #2199C2×C73semidirect
382. #2197C2×C73semidirect
383. #2129C2×C73semidirect
384. #2122C2×C73semidirect
385. #2120C2×C73semidirect
386. C73#33555direct (N × H)
389. H(3,𝔽4)C22×C73semidirect
394. #551C22×C73semidirect
420. #354C22×C73semidirect
421. #352C22×C73semidirect
422. AΣL(1,𝔽16)C22×C73semidirect
423. AΣL(1,𝔽16)C22×C73semidirect
436. C22×Q8D4×C73semidirect
437. C22×D4D4×C73semidirect
438. C23×C4D4×C73semidirect
445. C4⋊Q8D4×C73semidirect
466. #123D4×C73semidirect
488. #120D4×C73semidirect
489. #120D4×C73semidirect
505. #117D4×C73semidirect
506. #117D4×C73semidirect
507. #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×#30272
C73×#30252
C73×#30222
C73×#21992
C73×#21972
C73×#21292
C73×#21222
C73×#21202
#3355573