Finite Group Databasebeta

← C73×#25563 #32934967

Subgroups — C73×#25563 #32934967

Order 18688.

1608 conjugacy classes of subgroups.

The subgroup lattice has 876 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3490C211yesmaximal, characteristic, complemented
2C73×#2410C212yesmaximal, complemented
3C73×#2405C211yesmaximal, characteristic, complemented
4C73×#2062C211yesmaximal, characteristic, complemented
5C73×#2044C211yesmaximal, characteristic, complemented
6C73×#2029C211yesmaximal, characteristic, complemented
7C73×#2021C211yesmaximal, characteristic, complemented
8C73×#1898C212yesmaximal, complemented
9C73×#1889C212yesmaximal, complemented
10C73×#1867C212yesmaximal, complemented
11C2×#342×C73C211yesmaximal, characteristic, complemented
12C23×D4×C73C2211yescharacteristic
13#551×C73—22no—
14#551×C73—22no—
15#546×C73—22no—
16#546×C73—22no—
17#543×C73C2211yescharacteristic
18#538×C73—21no—
19#538×C73—21no—
20#534×C73C2211yescharacteristic
21#525×C73—21no—
22#525×C73—21no—
23C2×#123×C73—21no—
24C2×#121×C73—22no—
25C2×#120×C73C2212yes—
26C2×#120×C73C2212yes—
27#518×C73C2212yes—
28C22×C22⋊C4×C73C2211yescharacteristic
29C22×C22⋊C4×C73C2212yes—
30C2×#99×C73C2212yes—
31C2×#99×C73C2212yes—
32#394×C73—21no—
33#394×C73—21no—
34#394×C73—22no—
35#392×C73—22no—
36#386×C73—21no—
37#386×C73—22no—
38#386×C73C2212yes—
39#385×C73C2211yescharacteristic
40#385×C73C2212yes—
41#385×C73C2211yescharacteristic
42#379×C73C2211yescharacteristic
43#379×C73C2212yes—
44#379×C73C2211yescharacteristic
45#379×C73C2211yescharacteristic
46#342×C73C2211yescharacteristic
47#342×C73C2211yescharacteristic
48#342×C73C2212yes—
49#342×C73C2212yes—
50#342×C73C2212yes—
51C25×C73C2311yescharacteristic
52C25×C73C2311yescharacteristic
53C2×#41×C73—21no—
54C2×#41×C73—21no—
55C22×D4×C73—22no—
56C22×D4×C73—21no—
57C22×D4×C73—22no—
58C22×D4×C73—21no—
59C22×D4×C73—22no—
60C22×D4×C73—44no—
61C22×D4×C73D412yescomplemented
62C22×D4×C73D412yescomplemented
63C22×D4×C73C2312yes—
64C23×C4×C73—22no—
65C23×C4×C73D411yescharacteristic, complemented
66C23×C4×C73D411yescharacteristic, complemented
67C23×C4×C73C2311yescharacteristic
68#126×C73—22no—
69#126×C73—22no—
70#124×C73—22no—
71#124×C73—22no—
72#123×C73—22no—
73#123×C73—22no—
74#123×C73—22no—
75#123×C73—22no—
76#123×C73—22no—
77#123×C73—44no—
78C22⋊Q8×C73—21no—
79C22⋊Q8×C73—21no—
80C22⋊Q8×C73—21no—
81C22⋊Q8×C73—21no—
82C22⋊Q8×C73—22no—
83C22⋊Q8×C73—22no—
84#121×C73—21no—
85#121×C73—21no—
86#121×C73—22no—
87#121×C73—22no—
88#121×C73—21no—
89#121×C73—21no—
90#121×C73—48no—
91#120×C73—22no—
92#120×C73—22no—
93#120×C73—22no—
94#120×C73—22no—
95#120×C73—22no—
96#120×C73—24no—
97#120×C73—42no—
98C4×D4×C73—22no—
99C4×D4×C73—22no—
100C4×D4×C73—22no—
101C4×D4×C73—22no—
102C4×D4×C73—22no—
103C4×D4×C73—22no—
104#117×C73—21no—
105#117×C73—21no—
106#117×C73—22no—
107C2×C4⋊C4×C73—22no—
108C2×C4⋊C4×C73—21no—
109C2×C4⋊C4×C73—21no—
110C2×C22⋊C4×C73—22no—
111C2×C22⋊C4×C73—22no—
112C2×C22⋊C4×C73—22no—
113C2×C22⋊C4×C73—24no—
114C2×C22⋊C4×C73—21no—
115C2×C22⋊C4×C73—22no—
116C2×C22⋊C4×C73—22no—
117C2×C22⋊C4×C73—22no—
118C2×C22⋊C4×C73—21no—
119C2×C22⋊C4×C73—21no—
120C2×C22⋊C4×C73—22no—
121C2×C22⋊C4×C73—21no—
122C2×C22⋊C4×C73—22no—
123C2×C22⋊C4×C73—21no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—42no—
126C2×C22⋊C4×C73D412yescomplemented
127C2×C22⋊C4×C73D411yescharacteristic, complemented
128C2×C22⋊C4×C73D411yescharacteristic, complemented
129C2×C22⋊C4×C73D412yescomplemented
130C2×C22⋊C4×C73C2311yescharacteristic
131C2×C22⋊C4×C73C2311yescharacteristic
132C2×C22⋊C4×C73C2312yes—
133C2×C22⋊C4×C73C2311yescharacteristic
134C2×C22⋊C4×C73C2311yescharacteristic
135C2×C22⋊C4×C73C2312yes—
136C2×C22⋊C4×C73C2312yes—
137#99×C73—24no—
138#99×C73—42no—
139#95×C73—22no—
140#95×C73—21no—
141#95×C73—21no—
142#95×C73—22no—
143C24×C73—22no—
144C24×C73—21no—
145C24×C73—21no—
146C24×C73—21no—
147C24×C73—22no—
148C24×C73—22no—
149C24×C73—21no—
150C24×C73—21no—
151C24×C73—42no—
152C24×C73—42no—
153C24×C73—81no—
154C24×C73—81no—
155C24×C73C2×D412yes—
156C24×C73C2×D411yescharacteristic
157C24×C73C2×D412yes—
158C24×C73C2×D412yes—
159C24×C73C2×D411yescharacteristic
160C24×C73C2411yescharacteristic
161#41×C73—82no—
162#41×C73—82no—
163C2×Q8×C73—21no—
164C2×Q8×C73—21no—
165C2×D4×C73—28no—
166C2×D4×C73—24no—
167C2×D4×C73—22no—
168C2×D4×C73—22no—
169C2×D4×C73—22no—
170C2×D4×C73—22no—
171C2×D4×C73—22no—
172C2×D4×C73—22no—
173C2×D4×C73—22no—
174C2×D4×C73—22no—
175C2×D4×C73—21no—
176C2×D4×C73—21no—
177C2×D4×C73—22no—
178C2×D4×C73—22no—
179C2×D4×C73—44no—
180C2×D4×C73—42no—
181C2×D4×C73—44no—
182C2×D4×C73—42no—
183C2×D4×C73—44no—
184C2×D4×C73—42no—
185C2×D4×C73—44no—
186C2×D4×C73—42no—
187C2×D4×C73—41no—
188C2×D4×C73—41no—
189C2×D4×C73—44no—
190C2×D4×C73—44no—
191C2×D4×C73—82no—
192C2×D4×C73—82no—
193C22×C4×C73—21no—
194C22×C4×C73—21no—
195C22×C4×C73—22no—
196C22×C4×C73—21no—
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—21no—
204C22×C4×C73—22no—
205C22×C4×C73—42no—
206C22×C4×C73—44no—
207C22×C4×C73—42no—
208C22×C4×C73—44no—
209C22×C4×C73—81no—
210C22×C4×C73—82no—
211C22×C4×C73C2×D412yes—
212C22×C4×C73C2×D411yescharacteristic
213C22×C4×C73C2×D412yes—
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D412yes—
217C22×C4×C73C2×D411yescharacteristic
218C4⋊C4×C73—22no—
219C4⋊C4×C73—22no—
220C4⋊C4×C73—21no—
221C4⋊C4×C73—21no—
222C4⋊C4×C73—21no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—22no—
225C4⋊C4×C73—22no—
226C4⋊C4×C73—44no—
227C4⋊C4×C73—42no—
228C4⋊C4×C73—42no—
229C22⋊C4×C73—22no—
230C22⋊C4×C73—22no—
231C22⋊C4×C73—22no—
232C22⋊C4×C73—22no—
233C22⋊C4×C73—22no—
234C22⋊C4×C73—22no—
235C22⋊C4×C73—22no—
236C22⋊C4×C73—22no—
237C22⋊C4×C73—22no—
238C22⋊C4×C73—22no—
239C22⋊C4×C73—22no—
240C22⋊C4×C73—22no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—22no—
243C22⋊C4×C73—22no—
244C22⋊C4×C73—22no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—21no—
247C22⋊C4×C73—22no—
248C22⋊C4×C73—21no—
249C22⋊C4×C73—44no—
250C22⋊C4×C73—44no—
251C22⋊C4×C73—44no—
252C22⋊C4×C73—44no—
253C22⋊C4×C73—42no—
254C22⋊C4×C73—42no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—81no—
257C22⋊C4×C73—81no—
258C22⋊C4×C73—82no—
259C22⋊C4×C73—81no—
260C22⋊C4×C73#4114yescomplemented
261C42×C73—22no—
262C42×C73—22no—
263C23×C73—21no—
264C23×C73—21no—
265C23×C73—22no—
266C23×C73—22no—
267C23×C73—22no—
268C23×C73—24no—
269C23×C73—21no—
270C23×C73—21no—
271C23×C73—22no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—24no—
275C23×C73—22no—
276C23×C73—22no—
277C23×C73—22no—
278C23×C73—41no—
279C23×C73—41no—
280C23×C73—42no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—42no—
285C23×C73—42no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—42no—
289C23×C73—41no—
290C23×C73—42no—
291C23×C73—42no—
292C23×C73—42no—
293C23×C73—42no—
294C23×C73—41no—
295C23×C73—41no—
296C23×C73—41no—
297C23×C73—42no—
298C23×C73—42no—
299C23×C73—84no—
300C23×C73—84no—
301C23×C73—82no—
302C23×C73—82no—
303C23×C73—82no—
304C23×C73—82no—
305C23×C73#12012yes—
306C23×C73#12011yescharacteristic
307C23×C73#12011yescharacteristic
308C23×C73C22×D411yescharacteristic
309C23×C73C22×D412yes—
310C23×C73C2×#4112yes—
311C23×C73H(5,𝔽2)11yescharacteristic
312C23×C732−1+411yescharacteristic
313Q8×C73—81no—
314Q8×C73—81no—
315D4×C73—44no—
316D4×C73—48no—
317D4×C73—44no—
318D4×C73—42no—
319D4×C73—42no—
320D4×C73—42no—
321D4×C73—42no—
322D4×C73—44no—
323D4×C73—44no—
324D4×C73—82no—
325D4×C73—82no—
326D4×C73—81no—
327D4×C73—81no—
328D4×C73—88no—
329C2×C4×C73—24no—
330C2×C4×C73—22no—
331C2×C4×C73—22no—
332C2×C4×C73—21no—
333C2×C4×C73—21no—
334C2×C4×C73—22no—
335C2×C4×C73—22no—
336C2×C4×C73—21no—
337C2×C4×C73—21no—
338C2×C4×C73—24no—
339C2×C4×C73—22no—
340C2×C4×C73—22no—
341C2×C4×C73—42no—
342C2×C4×C73—41no—
343C2×C4×C73—42no—
344C2×C4×C73—42no—
345C2×C4×C73—42no—
346C2×C4×C73—41no—
347C2×C4×C73—42no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—42no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—42no—
354C2×C4×C73—41no—
355C2×C4×C73—41no—
356C2×C4×C73—42no—
357C2×C4×C73—41no—
358C2×C4×C73—41no—
359C2×C4×C73—42no—
360C2×C4×C73—41no—
361C2×C4×C73—41no—
362C2×C4×C73—42no—
363C2×C4×C73—81no—
364C2×C4×C73—81no—
365C2×C4×C73—82no—
366C2×C4×C73—82no—
367C2×C4×C73—88no—
368C22×C73—21no—
369C22×C73—21no—
370C22×C73—22no—
371C22×C73—21no—
372C22×C73—22no—
373C22×C73—21no—
374C22×C73—21no—
375C22×C73—22no—
376C22×C73—21no—
377C22×C73—22no—
378C22×C73—21no—
379C22×C73—22no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—41no—
383C22×C73—44no—
384C22×C73—42no—
385C22×C73—42no—
386C22×C73—44no—
387C22×C73—44no—
388C22×C73—42no—
389C22×C73—42no—
390C22×C73—44no—
391C22×C73—42no—
392C22×C73—42no—
393C22×C73—42no—
394C22×C73—42no—
395C22×C73—82no—
396C22×C73—81no—
397C22×C73—81no—
398C22×C73—82no—
399C22×C73—82no—
400C22×C73—82no—
401C22×C73—82no—
402C22×C73—81no—
403C22×C73—81no—
404C22×C73—82no—
405C22×C73—81no—
406C22×C73—81no—
407C22×C73B(4,𝔽2)12yes—
408C22×C73C2×#12011yescharacteristic
409C22×C73#53211yescharacteristic
410C22×C73#53711yescharacteristic
411C22×C73#54612yes—
412C22×C73#54712yes—
413C4×C73—44no—
414C4×C73—42no—
415C4×C73—42no—
416C4×C73—41no—
417C4×C73—41no—
418C4×C73—42no—
419C4×C73—41no—
420C4×C73—41no—
421C4×C73—42no—
422C4×C73—81no—
423C4×C73—81no—
424C4×C73—82no—
425#25563C7311yesmaximal, characteristic, direct product factor, Sylow
426C2×C73—22no—
427C2×C73—21no—
428C2×C73—21no—
429C2×C73—22no—
430C2×C73—22no—
431C2×C73—41no—
432C2×C73—42no—
433C2×C73—82no—
434C2×C73—82no—
435C2×C73#243011yescharacteristic
436C2×C73C2×B(4,𝔽2)11yescharacteristic
437C2×C73#302611yescharacteristic
438#3490C2×C7311yescharacteristic, complemented
439#2410C2×C7312yescomplemented
440#2405C2×C7311yescharacteristic, complemented
441#2062C2×C7311yescharacteristic, complemented
442#2044C2×C7311yescharacteristic, complemented
443#2029C2×C7311yescharacteristic, complemented
444#2021C2×C7311yescharacteristic, complemented
445#1898C2×C7312yescomplemented
446#1889C2×C7312yescomplemented
447#1867C2×C7312yescomplemented
448C2×#342C2×C7311yescharacteristic, complemented
449C73#2556311yescharacteristic, direct product factor, Sylow
450C23×D4C22×C7311yescharacteristic
451#551—22no—
452#551—22no—
453#546—22no—
454#546—22no—
455#543C22×C7311yescharacteristic
456#538—21no—
457#538—21no—
458#534C22×C7311yescharacteristic
459#525—21no—
460#525—21no—
461C2×#123—21no—
462C2×#121—22no—
463C2×#120C22×C7312yes—
464C2×#120C22×C7312yes—
465#518C22×C7312yes—
466C22×C22⋊C4C22×C7311yescharacteristic
467C22×C22⋊C4C22×C7312yes—
468C2×#99C22×C7312yes—
469C2×#99C22×C7312yes—
470#394—21no—
471#394—21no—
472#394—22no—
473#392—22no—
474#386—21no—
475#386—22no—
476#386C22×C7312yes—
477#385C22×C7312yes—
478#385C22×C7311yescharacteristic
479#385C22×C7311yescharacteristic
480#379C22×C7311yescharacteristic
481#379C22×C7312yes—
482#379C22×C7311yescharacteristic
483#379C22×C7311yescharacteristic
484#342C22×C7312yes—
485#342C22×C7311yescharacteristic
486#342C22×C7312yes—
487#342C22×C7312yes—
488#342C22×C7311yescharacteristic
489C25C23×C7311yescharacteristic
490C25C23×C7311yescharacteristic
491C2×#41—21no—
492C2×#41—21no—
493C22×D4—22no—
494C22×D4—21no—
495C22×D4—22no—
496C22×D4—21no—
497C22×D4—22no—
498C22×D4—44no—
499C22×D4D4×C7312yescomplemented
500C22×D4D4×C7312yescomplemented
501C22×D4C23×C7312yes—
502C23×C4—22no—
503C23×C4D4×C7311yescharacteristic, complemented
504C23×C4D4×C7311yescharacteristic, complemented
505C23×C4C23×C7311yescharacteristic
506#126—22no—
507#126—22no—
508#124—22no—
509#124—22no—
510#123—22no—
511#123—22no—
512#123—22no—
513#123—22no—
514#123—22no—
515#123—44no—
516C22⋊Q8—21no—
517C22⋊Q8—21no—
518C22⋊Q8—21no—
519C22⋊Q8—21no—
520C22⋊Q8—22no—
521C22⋊Q8—22no—
522#121—21no—
523#121—21no—
524#121—22no—
525#121—22no—
526#121—21no—
527#121—21no—
528#121—48no—
529#120—22no—
530#120—22no—
531#120—22no—
532#120—22no—
533#120—22no—
534#120—24no—
535#120—42no—
536C4×D4—22no—
537C4×D4—22no—
538C4×D4—22no—
539C4×D4—22no—
540C4×D4—22no—
541C4×D4—22no—
542#117—21no—
543#117—21no—
544#117—22no—
545C2×C4⋊C4—22no—
546C2×C4⋊C4—21no—
547C2×C4⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—22no—
550C2×C22⋊C4—22no—
551C2×C22⋊C4—24no—
552C2×C22⋊C4—22no—
553C2×C22⋊C4—22no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—22no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—21no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4—21no—
562C2×C22⋊C4—21no—
563C2×C22⋊C4—42no—
564C2×C22⋊C4D4×C7311yescharacteristic, complemented
565C2×C22⋊C4D4×C7311yescharacteristic, complemented
566C2×C22⋊C4D4×C7312yescomplemented
567C2×C22⋊C4D4×C7312yescomplemented
568C2×C22⋊C4C23×C7312yes—
569C2×C22⋊C4C23×C7311yescharacteristic
570C2×C22⋊C4C23×C7311yescharacteristic
571C2×C22⋊C4C23×C7311yescharacteristic
572C2×C22⋊C4C23×C7311yescharacteristic
573C2×C22⋊C4C23×C7312yes—
574C2×C22⋊C4C23×C7312yes—
575#99—24no—
576#99—42no—
577#95—22no—
578#95—21no—
579#95—21no—
580#95—22no—
581C24—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—21no—
588C24—21no—
589C24—42no—
590C24—42no—
591C24—81no—
592C24—81no—
593C24C2×D4×C7312yes—
594C24C2×D4×C7311yescharacteristic
595C24C2×D4×C7312yes—
596C24C2×D4×C7312yes—
597C24C2×D4×C7311yescharacteristic
598C24C24×C7311yescharacteristic
599#41—82no—
600#41—82no—
601C2×Q8—21no—
602C2×Q8—21no—
603C2×D4—28no—
604C2×D4—24no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—22no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—44no—
618C2×D4—42no—
619C2×D4—44no—
620C2×D4—42no—
621C2×D4—44no—
622C2×D4—42no—
623C2×D4—44no—
624C2×D4—42no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—44no—
628C2×D4—44no—
629C2×D4—82no—
630C2×D4—82no—
631C22×C4—21no—
632C22×C4—21no—
633C22×C4—22no—
634C22×C4—21no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—22no—
638C22×C4—21no—
639C22×C4—21no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—42no—
644C22×C4—44no—
645C22×C4—42no—
646C22×C4—44no—
647C22×C4—81no—
648C22×C4—82no—
649C22×C4C2×D4×C7312yes—
650C22×C4C2×D4×C7311yescharacteristic
651C22×C4C2×D4×C7312yes—
652C22×C4C2×D4×C7311yescharacteristic
653C22×C4C2×D4×C7311yescharacteristic
654C22×C4C2×D4×C7312yes—
655C22×C4C2×D4×C7311yescharacteristic
656C4⋊C4—22no—
657C4⋊C4—22no—
658C4⋊C4—21no—
659C4⋊C4—21no—
660C4⋊C4—21no—
661C4⋊C4—21no—
662C4⋊C4—22no—
663C4⋊C4—22no—
664C4⋊C4—44no—
665C4⋊C4—42no—
666C4⋊C4—42no—
667C22⋊C4—22no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—22no—
672C22⋊C4—22no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—22no—
679C22⋊C4—22no—
680C22⋊C4—22no—
681C22⋊C4—22no—
682C22⋊C4—22no—
683C22⋊C4—22no—
684C22⋊C4—21no—
685C22⋊C4—22no—
686C22⋊C4—21no—
687C22⋊C4—44no—
688C22⋊C4—44no—
689C22⋊C4—44no—
690C22⋊C4—44no—
691C22⋊C4—42no—
692C22⋊C4—42no—
693C22⋊C4—42no—
694C22⋊C4—81no—
695C22⋊C4—81no—
696C22⋊C4—82no—
697C22⋊C4—81no—
698C22⋊C4#41×C7314yescomplemented
699C42—22no—
700C42—22no—
701C23—22no—
702C23—24no—
703C23—21no—
704C23—21no—
705C23—22no—
706C23—22no—
707C23—21no—
708C23—21no—
709C23—22no—
710C23—22no—
711C23—22no—
712C23—24no—
713C23—22no—
714C23—22no—
715C23—22no—
716C23—41no—
717C23—41no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—41no—
725C23—41no—
726C23—42no—
727C23—41no—
728C23—42no—
729C23—42no—
730C23—42no—
731C23—42no—
732C23—41no—
733C23—41no—
734C23—41no—
735C23—42no—
736C23—42no—
737C23—84no—
738C23—84no—
739C23—82no—
740C23—82no—
741C23—82no—
742C23—82no—
743C23#120×C7312yes—
744C23#120×C7311yescharacteristic
745C23#120×C7311yescharacteristic
746C23C22×D4×C7311yescharacteristic
747C23C22×D4×C7312yes—
748C23C2×#41×C7312yes—
749C23H(5,𝔽2)×C7311yescharacteristic
750C232−1+4×C7311yescharacteristic
751Q8—81no—
752Q8—81no—
753D4—44no—
754D4—48no—
755D4—44no—
756D4—44no—
757D4—44no—
758D4—42no—
759D4—42no—
760D4—42no—
761D4—42no—
762D4—82no—
763D4—82no—
764D4—81no—
765D4—81no—
766D4—88no—
767C2×C4—24no—
768C2×C4—22no—
769C2×C4—22no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—22no—
773C2×C4—22no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—24no—
777C2×C4—22no—
778C2×C4—22no—
779C2×C4—42no—
780C2×C4—41no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—42no—
784C2×C4—42no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—42no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—42no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—42no—
795C2×C4—41no—
796C2×C4—41no—
797C2×C4—42no—
798C2×C4—41no—
799C2×C4—41no—
800C2×C4—42no—
801C2×C4—81no—
802C2×C4—81no—
803C2×C4—82no—
804C2×C4—82no—
805C2×C4—88no—
806C22—21no—
807C22—22no—
808C22—21no—
809C22—22no—
810C22—21no—
811C22—21no—
812C22—21no—
813C22—22no—
814C22—21no—
815C22—22no—
816C22—21no—
817C22—22no—
818C22—42no—
819C22—41no—
820C22—41no—
821C22—44no—
822C22—42no—
823C22—42no—
824C22—44no—
825C22—44no—
826C22—42no—
827C22—42no—
828C22—44no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—42no—
833C22—82no—
834C22—81no—
835C22—81no—
836C22—82no—
837C22—82no—
838C22—82no—
839C22—82no—
840C22—81no—
841C22—81no—
842C22—82no—
843C22—81no—
844C22—81no—
845C22B(4,𝔽2)×C7312yes—
846C22C2×#120×C7311yescharacteristic
847C22#532×C7311yescharacteristic
848C22#537×C7311yescharacteristic
849C22#546×C7312yes—
850C22#547×C7312yes—
851C4—44no—
852C4—42no—
853C4—41no—
854C4—41no—
855C4—42no—
856C4—41no—
857C4—41no—
858C4—42no—
859C4—42no—
860C4—82no—
861C4—81no—
862C4—81no—
863C2—22no—
864C2—21no—
865C2—21no—
866C2—22no—
867C2—22no—
868C2—41no—
869C2—42no—
870C2—82no—
871C2—82no—
872C2C73×#243011yescharacteristic
873C2C2×B(4,𝔽2)×C7311yescharacteristic
874C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC24C24×C73
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C25×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3490C2semidirect
2. C73×#2410C2semidirect
3. C73×#2405C2semidirect
4. C73×#2062C2semidirect
5. C73×#2044C2semidirect
6. C73×#2029C2semidirect
7. C73×#2021C2semidirect
8. C73×#1898C2semidirect
9. C73×#1889C2semidirect
10. C73×#1867C2semidirect
11. C2×#342×C73C2semidirect
61. C22×D4×C73D4semidirect
62. C22×D4×C73D4semidirect
65. C23×C4×C73D4semidirect
66. C23×C4×C73D4semidirect
126. C2×C22⋊C4×C73D4semidirect
127. C2×C22⋊C4×C73D4semidirect
128. C2×C22⋊C4×C73D4semidirect
129. C2×C22⋊C4×C73D4semidirect
260. C22⋊C4×C73#41semidirect
425. #25563C73direct (N × H)
438. #3490C2×C73semidirect
439. #2410C2×C73semidirect
440. #2405C2×C73semidirect
441. #2062C2×C73semidirect
442. #2044C2×C73semidirect
443. #2029C2×C73semidirect
444. #2021C2×C73semidirect
445. #1898C2×C73semidirect
446. #1889C2×C73semidirect
447. #1867C2×C73semidirect
448. C2×#342C2×C73semidirect
449. C73#25563direct (N × H)
499. C22×D4D4×C73semidirect
500. C22×D4D4×C73semidirect
503. C23×C4D4×C73semidirect
504. C23×C4D4×C73semidirect
564. C2×C22⋊C4D4×C73semidirect
565. C2×C22⋊C4D4×C73semidirect
566. C2×C22⋊C4D4×C73semidirect
567. C2×C22⋊C4D4×C73semidirect
698. C22⋊C4#41×C73semidirect

Maximal subgroups

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

subgroupindex
C73×#34902
C73×#24102
C73×#24052
C73×#20622
C73×#20442
C73×#20292
C73×#20212
C73×#18982
C73×#18892
C73×#18672
C2×#342×C732
#2556373