Finite Group Databasebeta

← C73×#25587 #32934991

Subgroups — C73×#25587 #32934991

Order 18688.

1332 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C73×#3505C211yesmaximal, characteristic, complemented
2C73×#2561C211yesmaximal, characteristic, complemented
3C73×#2539C211yesmaximal, characteristic, complemented
4C73×#2534C211yesmaximal, characteristic, complemented
5C73×#2022C212yesmaximal, complemented
6C73×#2021C212yesmaximal, complemented
7C73×#1996C211yesmaximal, characteristic, complemented
8C73×#1964C211yesmaximal, characteristic, complemented
9C73×#1890C212yesmaximal, complemented
10C73×#1889C212yesmaximal, complemented
11C4×#99×C73C211yesmaximal, characteristic, complemented
12#553×C73—22no—
13#553×C73—21no—
14#552×C73—21no—
15#551×C73—22no—
16#548×C73—21no—
17#546×C73—21no—
18#539×C73—21no—
19#538×C73—21no—
20#534×C73C2212yes—
21#529×C73—21no—
22#525×C73—21no—
23C2×#123×C73C2212yes—
24C2×#123×C73C2211yescharacteristic
25C2×C22⋊Q8×C73C2211yescharacteristic
26C2×#121×C73C2211yescharacteristic
27C2×#120×C73C2212yes—
28C2×#120×C73C2211yescharacteristic
29#518×C73C2212yes—
30C2×C4×D4×C73C2211yescharacteristic
31C22×C22⋊C4×C73C2211yescharacteristic
32C2×#99×C73C2212yes—
33C2×#99×C73C2212yes—
34C2×#99×C73C2212yes—
35#399×C73—21no—
36#397×C73—21no—
37#396×C73—21no—
38#394×C73—21no—
39#393×C73—21no—
40#392×C73—21no—
41#390×C73—22no—
42#388×C73—22no—
43#388×C73—21no—
44#386×C73—21no—
45#381×C73C2212yes—
46#381×C73C2211yescharacteristic
47#380×C73C2211yescharacteristic
48#379×C73C2212yes—
49#379×C73C2211yescharacteristic
50C4×C22⋊C4×C73C2211yescharacteristic
51C4×C22⋊C4×C73C2211yescharacteristic
52#342×C73C2212yes—
53#342×C73C2212yes—
54#342×C73C2212yes—
55C25×C73C2311yescharacteristic
56C2×#41×C73—21no—
57C22×Q8×C73D411yescharacteristic, complemented
58C22×D4×C73—21no—
59C22×D4×C73—22no—
60C22×D4×C73D411yescharacteristic, complemented
61C22×D4×C73C2311yescharacteristic
62C22×D4×C73C2312yes—
63C23×C4×C73D411yescharacteristic, complemented
64C23×C4×C73C2311yescharacteristic
65C23×C4×C73C2311yescharacteristic
66#126×C73—22no—
67#126×C73—22no—
68#126×C73—22no—
69#125×C73—21no—
70#125×C73—22no—
71#124×C73—21no—
72#124×C73—22no—
73#123×C73—22no—
74#123×C73—22no—
75#123×C73—22no—
76#123×C73—22no—
77#123×C73—22no—
78#123×C73—24no—
79#123×C73—42no—
80#123×C73—42no—
81C22⋊Q8×C73—21no—
82C22⋊Q8×C73—22no—
83C22⋊Q8×C73—21no—
84C22⋊Q8×C73—21no—
85C22⋊Q8×C73—21no—
86C22⋊Q8×C73—21no—
87#121×C73—21no—
88#121×C73—22no—
89#121×C73—21no—
90#121×C73—21no—
91#121×C73—21no—
92#121×C73—21no—
93#121×C73—22no—
94#121×C73—22no—
95#120×C73—22no—
96#120×C73—22no—
97#120×C73—24no—
98#120×C73—42no—
99#120×C73—42no—
100C4×Q8×C73—21no—
101C4×D4×C73—22no—
102C4×D4×C73—21no—
103C4×D4×C73—21no—
104C4×D4×C73—21no—
105C4×D4×C73—21no—
106C4×D4×C73—21no—
107C4×D4×C73—22no—
108C4×D4×C73—22no—
109C4×D4×C73—22no—
110C4×D4×C73—22no—
111#117×C73—21no—
112#117×C73—22no—
113#117×C73—22no—
114C2×C4⋊C4×C73—21no—
115C2×C4⋊C4×C73—22no—
116C2×C4⋊C4×C73—21no—
117C2×C4⋊C4×C73D412yescomplemented
118C2×C4⋊C4×C73D411yescharacteristic, complemented
119C2×C4⋊C4×C73D411yescharacteristic, complemented
120C2×C4⋊C4×C73D411yescharacteristic, complemented
121C2×C22⋊C4×C73—22no—
122C2×C22⋊C4×C73—21no—
123C2×C22⋊C4×C73—22no—
124C2×C22⋊C4×C73—21no—
125C2×C22⋊C4×C73—22no—
126C2×C22⋊C4×C73—21no—
127C2×C22⋊C4×C73—21no—
128C2×C22⋊C4×C73—21no—
129C2×C22⋊C4×C73—21no—
130C2×C22⋊C4×C73—22no—
131C2×C22⋊C4×C73—21no—
132C2×C22⋊C4×C73—21no—
133C2×C22⋊C4×C73—21no—
134C2×C22⋊C4×C73—21no—
135C2×C22⋊C4×C73—22no—
136C2×C22⋊C4×C73D412yescomplemented
137C2×C22⋊C4×C73D411yescharacteristic, complemented
138C2×C22⋊C4×C73C2312yes—
139C2×C22⋊C4×C73C2311yescharacteristic
140C2×C22⋊C4×C73C2311yescharacteristic
141C2×C22⋊C4×C73C2311yescharacteristic
142C2×C22⋊C4×C73C2312yes—
143C2×C22⋊C4×C73C2312yes—
144C2×C42×C73—21no—
145C2×C42×C73—21no—
146C2×C42×C73D411yescharacteristic, complemented
147#99×C73—24no—
148#99×C73—42no—
149#99×C73—42no—
150#95×C73—21no—
151#95×C73—21no—
152#95×C73—21no—
153#95×C73—21no—
154#95×C73—22no—
155#95×C73—21no—
156#95×C73—22no—
157C24×C73—21no—
158C24×C73—21no—
159C24×C73—21no—
160C24×C73—22no—
161C24×C73—22no—
162C24×C73—42no—
163C24×C73—81no—
164C24×C73C2×D412yes—
165C24×C73C2×D411yescharacteristic
166C24×C73C2411yescharacteristic
167#41×C73—82no—
168C2×Q8×C73—21no—
169C2×Q8×C73—21no—
170C2×Q8×C73—81no—
171C2×D4×C73—21no—
172C2×D4×C73—22no—
173C2×D4×C73—21no—
174C2×D4×C73—22no—
175C2×D4×C73—22no—
176C2×D4×C73—22no—
177C2×D4×C73—22no—
178C2×D4×C73—22no—
179C2×D4×C73—22no—
180C2×D4×C73—22no—
181C2×D4×C73—22no—
182C2×D4×C73—22no—
183C2×D4×C73—21no—
184C2×D4×C73—21no—
185C2×D4×C73—44no—
186C2×D4×C73—42no—
187C2×D4×C73—44no—
188C2×D4×C73—42no—
189C2×D4×C73—81no—
190C2×D4×C73—82no—
191C2×D4×C73—81no—
192C22×C4×C73—22no—
193C22×C4×C73—22no—
194C22×C4×C73—22no—
195C22×C4×C73—21no—
196C22×C4×C73—21no—
197C22×C4×C73—21no—
198C22×C4×C73—22no—
199C22×C4×C73—21no—
200C22×C4×C73—21no—
201C22×C4×C73—21no—
202C22×C4×C73—21no—
203C22×C4×C73—22no—
204C22×C4×C73—22no—
205C22×C4×C73—81no—
206C22×C4×C73—81no—
207C22×C4×C73C2×D411yescharacteristic
208C22×C4×C73C2×D412yes—
209C22×C4×C73C2×D411yescharacteristic
210C22×C4×C73C2×D412yes—
211C22×C4×C73C2×D411yescharacteristic
212C22×C4×C73C2×D412yes—
213C22×C4×C73C2×D411yescharacteristic
214C22×C4×C73C2×D411yescharacteristic
215C22×C4×C73C2×D411yescharacteristic
216C22×C4×C73C2×D411yescharacteristic
217C22×C4×C73C2×D411yescharacteristic
218C22×C4×C73C2×D411yescharacteristic
219C4⋊C4×C73—22no—
220C4⋊C4×C73—22no—
221C4⋊C4×C73—22no—
222C4⋊C4×C73—22no—
223C4⋊C4×C73—21no—
224C4⋊C4×C73—22no—
225C4⋊C4×C73—21no—
226C4⋊C4×C73—21no—
227C4⋊C4×C73—21no—
228C4⋊C4×C73—21no—
229C4⋊C4×C73—22no—
230C4⋊C4×C73—21no—
231C4⋊C4×C73—44no—
232C4⋊C4×C73—42no—
233C4⋊C4×C73—81no—
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—21no—
241C22⋊C4×C73—22no—
242C22⋊C4×C73—21no—
243C22⋊C4×C73—22no—
244C22⋊C4×C73—22no—
245C22⋊C4×C73—22no—
246C22⋊C4×C73—21no—
247C22⋊C4×C73—21no—
248C22⋊C4×C73—22no—
249C22⋊C4×C73—22no—
250C22⋊C4×C73—22no—
251C22⋊C4×C73—22no—
252C22⋊C4×C73—22no—
253C22⋊C4×C73—44no—
254C22⋊C4×C73—44no—
255C22⋊C4×C73—42no—
256C22⋊C4×C73—44no—
257C22⋊C4×C73—42no—
258C22⋊C4×C73—42no—
259C22⋊C4×C73—41no—
260C22⋊C4×C73—41no—
261C22⋊C4×C73—41no—
262C22⋊C4×C73—41no—
263C22⋊C4×C73—81no—
264C22⋊C4×C73—82no—
265C22⋊C4×C73#4114yescomplemented
266C42×C73—22no—
267C42×C73—22no—
268C42×C73—21no—
269C42×C73—21no—
270C42×C73—81no—
271C42×C73—81no—
272C23×C73—22no—
273C23×C73—22no—
274C23×C73—22no—
275C23×C73—22no—
276C23×C73—21no—
277C23×C73—21no—
278C23×C73—21no—
279C23×C73—22no—
280C23×C73—22no—
281C23×C73—41no—
282C23×C73—41no—
283C23×C73—41no—
284C23×C73—41no—
285C23×C73—42no—
286C23×C73—41no—
287C23×C73—41no—
288C23×C73—42no—
289C23×C73—41no—
290C23×C73—41no—
291C23×C73—41no—
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×C73C22×D411yescharacteristic
302C23×C73C22×D411yescharacteristic
303C23×C73C22×D411yescharacteristic
304C23×C73C2×#4112yes—
305C23×C73H(5,𝔽2)12yes—
306Q8×C73—42no—
307Q8×C73—81no—
308D4×C73—42no—
309D4×C73—42no—
310D4×C73—42no—
311D4×C73—42no—
312D4×C73—42no—
313D4×C73—42no—
314D4×C73—42no—
315D4×C73—81no—
316D4×C73—82no—
317D4×C73—82no—
318D4×C73—88no—
319D4×C73—84no—
320C2×C4×C73—21no—
321C2×C4×C73—22no—
322C2×C4×C73—21no—
323C2×C4×C73—21no—
324C2×C4×C73—22no—
325C2×C4×C73—22no—
326C2×C4×C73—21no—
327C2×C4×C73—21no—
328C2×C4×C73—24no—
329C2×C4×C73—22no—
330C2×C4×C73—22no—
331C2×C4×C73—41no—
332C2×C4×C73—41no—
333C2×C4×C73—41no—
334C2×C4×C73—41no—
335C2×C4×C73—41no—
336C2×C4×C73—41no—
337C2×C4×C73—42no—
338C2×C4×C73—42no—
339C2×C4×C73—42no—
340C2×C4×C73—41no—
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—41no—
348C2×C4×C73—41no—
349C2×C4×C73—41no—
350C2×C4×C73—41no—
351C2×C4×C73—41no—
352C2×C4×C73—41no—
353C2×C4×C73—41no—
354C2×C4×C73—41no—
355C2×C4×C73—42no—
356C2×C4×C73—42no—
357C2×C4×C73—42no—
358C2×C4×C73—81no—
359C2×C4×C73—82no—
360C2×C4×C73—82no—
361C2×C4×C73#12011yescharacteristic
362C2×C4×C73#12011yescharacteristic
363C2×C4×C73#12011yescharacteristic
364C2×C4×C73#12011yescharacteristic
365C22×C73—21no—
366C22×C73—21no—
367C22×C73—21no—
368C22×C73—21no—
369C22×C73—21no—
370C22×C73—21no—
371C22×C73—42no—
372C22×C73—42no—
373C22×C73—42no—
374C22×C73—44no—
375C22×C73—42no—
376C22×C73—44no—
377C22×C73—42no—
378C22×C73—41no—
379C22×C73—42no—
380C22×C73—42no—
381C22×C73—41no—
382C22×C73—42no—
383C22×C73—41no—
384C22×C73—42no—
385C22×C73—82no—
386C22×C73—82no—
387C22×C73—81no—
388C22×C73—82no—
389C22×C73—81no—
390C22×C73—82no—
391C22×C73—81no—
392C22×C73—81no—
393C22×C73—81no—
394C22×C73C2×#12011yescharacteristic
395C22×C73#53211yescharacteristic
396C22×C73#53511yescharacteristic
397C22×C73#54612yes—
398C22×C73#55012yes—
399C4×C73—21no—
400C4×C73—21no—
401C4×C73—21no—
402C4×C73—21no—
403C4×C73—44no—
404C4×C73—41no—
405C4×C73—42no—
406C4×C73—41no—
407C4×C73—42no—
408C4×C73—41no—
409C4×C73—42no—
410C4×C73—81no—
411C4×C73—82no—
412C4×C73—81no—
413C4×C73—81no—
414#25587C7311yesmaximal, characteristic, direct product factor, Sylow
415C2×C73—22no—
416C2×C73—21no—
417C2×C73—22no—
418C2×C73—21no—
419C2×C73—82no—
420C2×C73—81no—
421C2×C73—82no—
422C2×C73#243111yescharacteristic
423C2×C73#302511yescharacteristic
424C2×C73#302611yescharacteristic
425#3505C2×C7311yescharacteristic, complemented
426#2561C2×C7311yescharacteristic, complemented
427#2539C2×C7311yescharacteristic, complemented
428#2534C2×C7311yescharacteristic, complemented
429#2022C2×C7312yescomplemented
430#2021C2×C7312yescomplemented
431#1996C2×C7311yescharacteristic, complemented
432#1964C2×C7311yescharacteristic, complemented
433#1890C2×C7312yescomplemented
434#1889C2×C7312yescomplemented
435C4×#99C2×C7311yescharacteristic, complemented
436C73#2558711yescharacteristic, direct product factor, Sylow
437#553—22no—
438#553—21no—
439#552—21no—
440#551—22no—
441#548—21no—
442#546—21no—
443#539—21no—
444#538—21no—
445#534C22×C7312yes—
446#529—21no—
447#525—21no—
448C2×#123C22×C7312yes—
449C2×#123C22×C7311yescharacteristic
450C2×C22⋊Q8C22×C7311yescharacteristic
451C2×#121C22×C7311yescharacteristic
452C2×#120C22×C7312yes—
453C2×#120C22×C7311yescharacteristic
454#518C22×C7312yes—
455C2×C4×D4C22×C7311yescharacteristic
456C22×C22⋊C4C22×C7311yescharacteristic
457C2×#99C22×C7312yes—
458C2×#99C22×C7312yes—
459C2×#99C22×C7312yes—
460#399—21no—
461#397—21no—
462#396—21no—
463#394—21no—
464#393—21no—
465#392—21no—
466#390—22no—
467#388—22no—
468#388—21no—
469#386—21no—
470#381C22×C7312yes—
471#381C22×C7311yescharacteristic
472#380C22×C7311yescharacteristic
473#379C22×C7312yes—
474#379C22×C7311yescharacteristic
475C4×C22⋊C4C22×C7311yescharacteristic
476C4×C22⋊C4C22×C7311yescharacteristic
477#342C22×C7312yes—
478#342C22×C7312yes—
479#342C22×C7312yes—
480C25C23×C7311yescharacteristic
481C2×#41—21no—
482C22×Q8D4×C7311yescharacteristic, complemented
483C22×D4—21no—
484C22×D4—22no—
485C22×D4D4×C7311yescharacteristic, complemented
486C22×D4C23×C7311yescharacteristic
487C22×D4C23×C7312yes—
488C23×C4D4×C7311yescharacteristic, complemented
489C23×C4C23×C7311yescharacteristic
490C23×C4C23×C7311yescharacteristic
491#126—22no—
492#126—22no—
493#126—22no—
494#125—21no—
495#125—22no—
496#124—21no—
497#124—22no—
498#123—22no—
499#123—22no—
500#123—22no—
501#123—22no—
502#123—22no—
503#123—24no—
504#123—42no—
505#123—42no—
506C22⋊Q8—21no—
507C22⋊Q8—22no—
508C22⋊Q8—21no—
509C22⋊Q8—21no—
510C22⋊Q8—21no—
511C22⋊Q8—21no—
512#121—21no—
513#121—22no—
514#121—21no—
515#121—21no—
516#121—21no—
517#121—21no—
518#121—22no—
519#121—22no—
520#120—22no—
521#120—22no—
522#120—24no—
523#120—42no—
524#120—42no—
525C4×Q8—21no—
526C4×D4—22no—
527C4×D4—21no—
528C4×D4—21no—
529C4×D4—21no—
530C4×D4—21no—
531C4×D4—21no—
532C4×D4—22no—
533C4×D4—22no—
534C4×D4—22no—
535C4×D4—22no—
536#117—21no—
537#117—22no—
538#117—22no—
539C2×C4⋊C4—21no—
540C2×C4⋊C4—22no—
541C2×C4⋊C4—21no—
542C2×C4⋊C4D4×C7311yescharacteristic, complemented
543C2×C4⋊C4D4×C7311yescharacteristic, complemented
544C2×C4⋊C4D4×C7312yescomplemented
545C2×C4⋊C4D4×C7311yescharacteristic, complemented
546C2×C22⋊C4—22no—
547C2×C22⋊C4—21no—
548C2×C22⋊C4—22no—
549C2×C22⋊C4—21no—
550C2×C22⋊C4—21no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—21no—
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—21no—
556C2×C22⋊C4—22no—
557C2×C22⋊C4—21no—
558C2×C22⋊C4—22no—
559C2×C22⋊C4—21no—
560C2×C22⋊C4—22no—
561C2×C22⋊C4D4×C7311yescharacteristic, complemented
562C2×C22⋊C4D4×C7312yescomplemented
563C2×C22⋊C4C23×C7311yescharacteristic
564C2×C22⋊C4C23×C7311yescharacteristic
565C2×C22⋊C4C23×C7312yes—
566C2×C22⋊C4C23×C7311yescharacteristic
567C2×C22⋊C4C23×C7312yes—
568C2×C22⋊C4C23×C7312yes—
569C2×C42—21no—
570C2×C42—21no—
571C2×C42D4×C7311yescharacteristic, complemented
572#99—24no—
573#99—42no—
574#99—42no—
575#95—21no—
576#95—21no—
577#95—21no—
578#95—21no—
579#95—22no—
580#95—21no—
581#95—22no—
582C24—21no—
583C24—21no—
584C24—21no—
585C24—22no—
586C24—22no—
587C24—42no—
588C24—81no—
589C24C2×D4×C7312yes—
590C24C2×D4×C7311yescharacteristic
591C24C24×C7311yescharacteristic
592#41—82no—
593C2×Q8—21no—
594C2×Q8—21no—
595C2×Q8—81no—
596C2×D4—21no—
597C2×D4—22no—
598C2×D4—21no—
599C2×D4—22no—
600C2×D4—22no—
601C2×D4—22no—
602C2×D4—22no—
603C2×D4—22no—
604C2×D4—22no—
605C2×D4—22no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—21no—
609C2×D4—21no—
610C2×D4—44no—
611C2×D4—42no—
612C2×D4—44no—
613C2×D4—42no—
614C2×D4—81no—
615C2×D4—82no—
616C2×D4—81no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—21no—
621C22×C4—21no—
622C22×C4—21no—
623C22×C4—22no—
624C22×C4—21no—
625C22×C4—21no—
626C22×C4—21no—
627C22×C4—21no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—81no—
631C22×C4—81no—
632C22×C4C2×D4×C7311yescharacteristic
633C22×C4C2×D4×C7312yes—
634C22×C4C2×D4×C7311yescharacteristic
635C22×C4C2×D4×C7312yes—
636C22×C4C2×D4×C7311yescharacteristic
637C22×C4C2×D4×C7312yes—
638C22×C4C2×D4×C7311yescharacteristic
639C22×C4C2×D4×C7311yescharacteristic
640C22×C4C2×D4×C7311yescharacteristic
641C22×C4C2×D4×C7311yescharacteristic
642C22×C4C2×D4×C7311yescharacteristic
643C22×C4C2×D4×C7311yescharacteristic
644C4⋊C4—22no—
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—21no—
649C4⋊C4—22no—
650C4⋊C4—21no—
651C4⋊C4—21no—
652C4⋊C4—21no—
653C4⋊C4—21no—
654C4⋊C4—22no—
655C4⋊C4—21no—
656C4⋊C4—44no—
657C4⋊C4—42no—
658C4⋊C4—81no—
659C22⋊C4—22no—
660C22⋊C4—22no—
661C22⋊C4—22no—
662C22⋊C4—22no—
663C22⋊C4—22no—
664C22⋊C4—22no—
665C22⋊C4—21no—
666C22⋊C4—22no—
667C22⋊C4—21no—
668C22⋊C4—22no—
669C22⋊C4—22no—
670C22⋊C4—22no—
671C22⋊C4—21no—
672C22⋊C4—21no—
673C22⋊C4—22no—
674C22⋊C4—22no—
675C22⋊C4—22no—
676C22⋊C4—22no—
677C22⋊C4—22no—
678C22⋊C4—44no—
679C22⋊C4—44no—
680C22⋊C4—42no—
681C22⋊C4—44no—
682C22⋊C4—42no—
683C22⋊C4—42no—
684C22⋊C4—41no—
685C22⋊C4—41no—
686C22⋊C4—41no—
687C22⋊C4—41no—
688C22⋊C4—81no—
689C22⋊C4—82no—
690C22⋊C4#41×C7314yescomplemented
691C42—22no—
692C42—22no—
693C42—21no—
694C42—21no—
695C42—81no—
696C42—81no—
697C23—22no—
698C23—22no—
699C23—22no—
700C23—22no—
701C23—21no—
702C23—21no—
703C23—21no—
704C23—22no—
705C23—22no—
706C23—41no—
707C23—41no—
708C23—41no—
709C23—41no—
710C23—42no—
711C23—41no—
712C23—41no—
713C23—42no—
714C23—41no—
715C23—41no—
716C23—41no—
717C23—42no—
718C23—42no—
719C23—41no—
720C23—41no—
721C23—41no—
722C23—42no—
723C23—42no—
724C23—84no—
725C23—84no—
726C23C22×D4×C7311yescharacteristic
727C23C22×D4×C7311yescharacteristic
728C23C22×D4×C7311yescharacteristic
729C23C2×#41×C7312yes—
730C23H(5,𝔽2)×C7312yes—
731Q8—42no—
732Q8—81no—
733D4—42no—
734D4—42no—
735D4—42no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—81no—
741D4—82no—
742D4—82no—
743D4—88no—
744D4—84no—
745C2×C4—21no—
746C2×C4—22no—
747C2×C4—21no—
748C2×C4—21no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—21no—
752C2×C4—21no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—41no—
757C2×C4—41no—
758C2×C4—41no—
759C2×C4—41no—
760C2×C4—41no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—41no—
766C2×C4—42no—
767C2×C4—41no—
768C2×C4—42no—
769C2×C4—42no—
770C2×C4—42no—
771C2×C4—41no—
772C2×C4—41no—
773C2×C4—41no—
774C2×C4—41no—
775C2×C4—41no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—41no—
779C2×C4—41no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—81no—
784C2×C4—82no—
785C2×C4—82no—
786C2×C4#120×C7311yescharacteristic
787C2×C4#120×C7311yescharacteristic
788C2×C4#120×C7311yescharacteristic
789C2×C4#120×C7311yescharacteristic
790C22—21no—
791C22—21no—
792C22—21no—
793C22—21no—
794C22—21no—
795C22—21no—
796C22—42no—
797C22—42no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—44no—
802C22—42no—
803C22—42no—
804C22—41no—
805C22—42no—
806C22—41no—
807C22—42no—
808C22—41no—
809C22—42no—
810C22—82no—
811C22—82no—
812C22—81no—
813C22—82no—
814C22—81no—
815C22—82no—
816C22—81no—
817C22—81no—
818C22—81no—
819C22C2×#120×C7311yescharacteristic
820C22#532×C7311yescharacteristic
821C22#535×C7311yescharacteristic
822C22#546×C7312yes—
823C22#550×C7312yes—
824C4—21no—
825C4—21no—
826C4—21no—
827C4—21no—
828C4—44no—
829C4—41no—
830C4—42no—
831C4—41no—
832C4—42no—
833C4—41no—
834C4—42no—
835C4—81no—
836C4—81no—
837C4—82no—
838C4—81no—
839C2—22no—
840C2—21no—
841C2—22no—
842C2—21no—
843C2—82no—
844C2—81no—
845C2—82no—
846C2C73×#243111yescharacteristic
847C2C73×#302511yescharacteristic
848C2C73×#302611yescharacteristic
subgroupG/H
center, socleC22×C73C2×#120
commutator, Frattini, cosocleC24C24×C73
LCSG ▷ C24 ▷ C2 ▷ C1
UCSC1 ◁ C22×C73 ◁ C23×C4×C73 ◁ G

Complements

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

NH ≅ G/Ntype
1. C73×#3505C2semidirect
2. C73×#2561C2semidirect
3. C73×#2539C2semidirect
4. C73×#2534C2semidirect
5. C73×#2022C2semidirect
6. C73×#2021C2semidirect
7. C73×#1996C2semidirect
8. C73×#1964C2semidirect
9. C73×#1890C2semidirect
10. C73×#1889C2semidirect
11. C4×#99×C73C2semidirect
57. C22×Q8×C73D4semidirect
60. C22×D4×C73D4semidirect
63. C23×C4×C73D4semidirect
117. C2×C4⋊C4×C73D4semidirect
118. C2×C4⋊C4×C73D4semidirect
119. C2×C4⋊C4×C73D4semidirect
120. C2×C4⋊C4×C73D4semidirect
136. C2×C22⋊C4×C73D4semidirect
137. C2×C22⋊C4×C73D4semidirect
146. C2×C42×C73D4semidirect
265. C22⋊C4×C73#41semidirect
414. #25587C73direct (N × H)
425. #3505C2×C73semidirect
426. #2561C2×C73semidirect
427. #2539C2×C73semidirect
428. #2534C2×C73semidirect
429. #2022C2×C73semidirect
430. #2021C2×C73semidirect
431. #1996C2×C73semidirect
432. #1964C2×C73semidirect
433. #1890C2×C73semidirect
434. #1889C2×C73semidirect
435. C4×#99C2×C73semidirect
436. C73#25587direct (N × H)
482. C22×Q8D4×C73semidirect
485. C22×D4D4×C73semidirect
488. C23×C4D4×C73semidirect
542. C2×C4⋊C4D4×C73semidirect
543. C2×C4⋊C4D4×C73semidirect
544. C2×C4⋊C4D4×C73semidirect
545. C2×C4⋊C4D4×C73semidirect
561. C2×C22⋊C4D4×C73semidirect
562. C2×C22⋊C4D4×C73semidirect
571. C2×C42D4×C73semidirect
690. 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×#35052
C73×#25612
C73×#25392
C73×#25342
C73×#20222
C73×#20212
C73×#19962
C73×#19642
C73×#18902
C73×#18892
C4×#99×C732
#2558773