Finite Group Databasebeta

← C47×#29898 #26069596

Subgroups — C47×#29898 #26069596

Order 12032.

922 conjugacy classes of subgroups.

The subgroup lattice has 784 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#2615C211yesmaximal, characteristic
2C47×#2311C211yesmaximal, characteristic, complemented
3C47×#2077C211yesmaximal, characteristic, complemented
4C47×#2076C211yesmaximal, characteristic, complemented
5C47×#2076C211yesmaximal, characteristic, complemented
6C47×#2075C211yesmaximal, characteristic, complemented
7C47×#2034C211yesmaximal, characteristic, complemented
8C47×#2033C211yesmaximal, characteristic, complemented
9C47×#2033C211yesmaximal, characteristic, complemented
10C47×#2033C211yesmaximal, characteristic, complemented
11C47×#1875C211yesmaximal, characteristic, complemented
12C47×#1874C211yesmaximal, characteristic, complemented
13C47×#1854C211yesmaximal, characteristic, complemented
14C47×#1852C211yesmaximal, characteristic, complemented
15C47×#1780C211yesmaximal, characteristic, complemented
16C22×#41×C47C2211yescharacteristic
17C2×#121×C47C2211yescharacteristic
18C2×#121×C47C2211yescharacteristic
19C2×#121×C47C2211yescharacteristic
20C2×#117×C47C2211yescharacteristic
21C22×C4⋊C4×C47C2211yescharacteristic
22C2×#107×C47C2211yescharacteristic
23C2×#107×C47C2211yescharacteristic
24C2×#107×C47C2211yescharacteristic
25C2×#106×C47C2211yescharacteristic
26C2×#102×C47C2211yescharacteristic
27C2×#102×C47C2211yescharacteristic
28C2×#102×C47C2211yescharacteristic
29C2×#102×C47C2211yescharacteristic
30C2×C22⋊C8×C47C2211yescharacteristic
31C2×C22⋊C8×C47C2211yescharacteristic
32C2×C22⋊C8×C47C2211yescharacteristic
33C2×C22⋊C8×C47C2211yescharacteristic
34C2×C22⋊C8×C47C2211yescharacteristic
35C2×C22⋊C8×C47C2211yescharacteristic
36C47×#393—21no—
37C47×#392—21no—
38C47×#392—21no—
39C47×#392—21no—
40C47×#391—21no—
41C47×#390—21no—
42C47×#386—21no—
43C47×#386—21no—
44C47×#380C2211yescharacteristic
45C47×#380C2211yescharacteristic
46C47×#380C2211yescharacteristic
47C47×#380C2211yescharacteristic
48C47×#380C2211yescharacteristic
49C47×#380C2211yescharacteristic
50C47×#380C2211yescharacteristic
51C47×#340C2211yescharacteristic
52C47×#340C2211yescharacteristic
53C47×#340C2211yescharacteristic
54C47×#340C2211yescharacteristic
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C2×#41×C47—22no—
60C2×#41×C47—22no—
61C2×#41×C47—41no—
62C2×#41×C47—41no—
63C2×#41×C47—41no—
64C2×#41×C47—41no—
65C22×Q8×C47D411yescharacteristic
66C22×D4×C47—21no—
67C22×D4×C47—21no—
68C22×D4×C47—21no—
69C22×D4×C47D411yescharacteristic
70C22×D4×C47D411yescharacteristic
71C22×D4×C47D411yescharacteristic
72C22×D4×C47C2311yescharacteristic
73C23×C4×C47—21no—
74C23×C4×C47C2311yescharacteristic
75C23×C4×C47C2311yescharacteristic
76C23×C4×C47C2311yescharacteristic
77C22×C8×C47C2311yescharacteristic
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81#121×C47—22no—
82#121×C47—22no—
83#121×C47—41no—
84#121×C47—41no—
85#121×C47—41no—
86#121×C47—41no—
87#117×C47—41no—
88#117×C47—41no—
89C2×C4⋊C4×C47—21no—
90C2×C4⋊C4×C47—41no—
91C2×C4⋊C4×C47—41no—
92C2×C4⋊C4×C47C2311yescharacteristic
93C2×C4⋊C4×C47C2311yescharacteristic
94C2×C4⋊C4×C47C2311yescharacteristic
95C2×C4⋊C4×C47C2311yescharacteristic
96C2×C4⋊C4×C47C2311yescharacteristic
97C2×C4⋊C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47C2311yescharacteristic
99C2×C22⋊C4×C47—21no—
100C2×C22⋊C4×C47—21no—
101C2×C22⋊C4×C47—21no—
102C2×C22⋊C4×C47—21no—
103C2×C22⋊C4×C47—21no—
104C2×C22⋊C4×C47—21no—
105C2×C22⋊C4×C47—21no—
106C2×C22⋊C4×C47—21no—
107C2×C22⋊C4×C47—21no—
108C2×C22⋊C4×C47—21no—
109C2×C22⋊C4×C47—21no—
110C2×C42×C47—21no—
111#107×C47—41no—
112#107×C47—41no—
113#107×C47—41no—
114#106×C47—41no—
115#102×C47—41no—
116#102×C47—41no—
117#102×C47—41no—
118#102×C47—41no—
119C22⋊C8×C47—22no—
120C22⋊C8×C47—22no—
121C22⋊C8×C47—41no—
122C22⋊C8×C47—41no—
123C22⋊C8×C47—41no—
124C22⋊C8×C47—41no—
125#95×C47—21no—
126#95×C47—21no—
127#95×C47—21no—
128#95×C47—21no—
129#95×C47—21no—
130#95×C47—21no—
131#95×C47—21no—
132C24×C47—21no—
133C24×C47C2×D411yescharacteristic
134C24×C47C2×D411yescharacteristic
135C24×C47C2×D411yescharacteristic
136#41×C47—44no—
137#41×C47—44no—
138#41×C47—44no—
139#41×C47—44no—
140C2×Q8×C47—22no—
141C2×Q8×C47—41no—
142C2×Q8×C47—41no—
143C2×D4×C47—22no—
144C2×D4×C47—22no—
145C2×D4×C47—22no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—41no—
153C2×D4×C47—41no—
154C2×D4×C47—41no—
155C2×D4×C47—41no—
156C2×D4×C47—41no—
157C2×D4×C47—41no—
158C2×D4×C47—42no—
159C2×D4×C47—42no—
160C2×D4×C47—42no—
161C2×D4×C47—81no—
162C2×D4×C47—81no—
163C2×D4×C47—81no—
164C2×D4×C47—81no—
165C2×D4×C47—81no—
166C2×D4×C47—81no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—21no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—21no—
179C22×C4×C47—21no—
180C22×C4×C47—21no—
181C22×C4×C47—21no—
182C22×C4×C47—21no—
183C22×C4×C47—21no—
184C22×C4×C47—21no—
185C22×C4×C47—21no—
186C22×C4×C47—21no—
187C22×C4×C47—21no—
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—42no—
191C22×C4×C47—81no—
192C22×C4×C47—81no—
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47#4112yes—
197C22×C4×C47#4112yes—
198C22×C4×C47C2411yescharacteristic
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47—21no—
202C2×C8×C47—21no—
203C2×C8×C47—21no—
204C2×C8×C47—21no—
205C2×C8×C47—21no—
206C2×C8×C47—21no—
207C2×C8×C47—21no—
208C2×C8×C47—21no—
209C2×C8×C47—21no—
210C2×C8×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—21no—
216C4⋊C4×C47—21no—
217C4⋊C4×C47—21no—
218C4⋊C4×C47—21no—
219C4⋊C4×C47—21no—
220C4⋊C4×C47—21no—
221C4⋊C4×C47—21no—
222C4⋊C4×C47—21no—
223C4⋊C4×C47—21no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—42no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—81no—
231C22⋊C4×C47—81no—
232C22⋊C4×C47—81no—
233C22⋊C4×C47—81no—
234C22⋊C4×C47—81no—
235C22⋊C4×C47—81no—
236C22⋊C4×C47—81no—
237C42×C47—42no—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47—21no—
243C23×C47—21no—
244C23×C47—21no—
245C23×C47—21no—
246C23×C47—21no—
247C23×C47—21no—
248C23×C47—21no—
249C23×C47—21no—
250C23×C47—21no—
251C23×C47—21no—
252C23×C47—21no—
253C23×C47—21no—
254C23×C47—21no—
255C23×C47—21no—
256C23×C47—21no—
257C23×C47—21no—
258C23×C47—41no—
259C23×C47—41no—
260C23×C47—41no—
261C23×C47—41no—
262C23×C47—41no—
263C23×C47—41no—
264C23×C47—41no—
265C23×C47#12312yes—
266C23×C47C22×D411yescharacteristic
267Q8×C47—44no—
268D4×C47—44no—
269D4×C47—44no—
270D4×C47—44no—
271D4×C47—41no—
272D4×C47—41no—
273D4×C47—41no—
274D4×C47—41no—
275D4×C47—84no—
276D4×C47—84no—
277D4×C47—84no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—22no—
281C2×C4×C47—22no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—21no—
285C2×C4×C47—21no—
286C2×C4×C47—21no—
287C2×C4×C47—21no—
288C2×C4×C47—21no—
289C2×C4×C47—21no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—41no—
293C2×C4×C47—41no—
294C2×C4×C47—41no—
295C2×C4×C47—41no—
296C2×C4×C47—41no—
297C2×C4×C47—41no—
298C2×C4×C47—41no—
299C2×C4×C47—41no—
300C2×C4×C47—41no—
301C2×C4×C47—41no—
302C2×C4×C47—41no—
303C2×C4×C47—41no—
304C2×C4×C47—41no—
305C2×C4×C47—41no—
306C2×C4×C47—41no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—41no—
310C2×C4×C47—41no—
311C2×C4×C47—41no—
312C2×C4×C47—41no—
313C2×C4×C47—41no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—41no—
319C2×C4×C47—84no—
320C2×C4×C47#12312yes—
321C2×C4×C47C2×#4111yescharacteristic
322C2×C4×C47C2×#4111yescharacteristic
323C2×C4×C47H(5,𝔽2)11yescharacteristic
324C2×C4×C47H(5,𝔽2)11yescharacteristic
325C2×C4×C47H(5,𝔽2)11yescharacteristic
326C2×C4×C47H(5,𝔽2)11yescharacteristic
327C8×C47—41no—
328C8×C47—41no—
329C8×C47—41no—
330C8×C47—41no—
331#29898C4711yesmaximal, characteristic, direct product factor, Sylow
332C22×C47—22no—
333C22×C47—22no—
334C22×C47—22no—
335C22×C47—41no—
336C22×C47—41no—
337C22×C47—41no—
338C22×C47—41no—
339C22×C47—41no—
340C22×C47—41no—
341C22×C47—41no—
342C22×C47—41no—
343C22×C47—41no—
344C22×C47—41no—
345C22×C47—41no—
346C22×C47—41no—
347C22×C47—41no—
348C22×C47—41no—
349C22×C47—41no—
350C22×C47—41no—
351C22×C47—41no—
352C22×C47—41no—
353C22×C47—81no—
354C22×C47—81no—
355C22×C47—81no—
356C22×C47—81no—
357C22×C47—81no—
358C22×C47—81no—
359C22×C47—81no—
360C22×C47C2×#12311yescharacteristic
361C22×C47#53411yescharacteristic
362C22×C47#53411yescharacteristic
363C22×C47#57611yescharacteristic
364C22×C47#57611yescharacteristic
365C22×C47#57711yescharacteristic
366C22×C47#57811yescharacteristic
367C4×C47—22no—
368C4×C47—41no—
369C4×C47—41no—
370C4×C47—81no—
371C4×C47—81no—
372C4×C47—81no—
373C4×C47—81no—
374C4×C47—81no—
375C4×C47—81no—
376C4×C47—81no—
377C4×C47#53811yescharacteristic
378C4×C47#53811yescharacteristic
379C4×C47#53811yescharacteristic
380C4×C47#53811yescharacteristic
381#2615C2×C4711yescharacteristic
382#2311C2×C4711yescharacteristic, complemented
383#2077C2×C4711yescharacteristic, complemented
384#2076C2×C4711yescharacteristic, complemented
385#2076C2×C4711yescharacteristic, complemented
386#2075C2×C4711yescharacteristic, complemented
387#2034C2×C4711yescharacteristic, complemented
388#2033C2×C4711yescharacteristic, complemented
389#2033C2×C4711yescharacteristic, complemented
390#2033C2×C4711yescharacteristic, complemented
391#1875C2×C4711yescharacteristic, complemented
392#1874C2×C4711yescharacteristic, complemented
393#1854C2×C4711yescharacteristic, complemented
394#1852C2×C4711yescharacteristic, complemented
395#1780C2×C4711yescharacteristic, complemented
396C2×C47—42no—
397C2×C47—81no—
398C2×C47—81no—
399C2×C47—161no—
400C2×C47#262211yescharacteristic
401C2×C47#309611yescharacteristic
402C2×C47#309811yescharacteristic
403C2×C47#319811yescharacteristic
404C2×C47#319911yescharacteristic
405C2×C47#320111yescharacteristic
406C2×C47#320311yescharacteristic
407C22×#41C22×C4711yescharacteristic
408C2×#121C22×C4711yescharacteristic
409C2×#121C22×C4711yescharacteristic
410C2×#121C22×C4711yescharacteristic
411C2×#117C22×C4711yescharacteristic
412C22×C4⋊C4C22×C4711yescharacteristic
413C2×#107C22×C4711yescharacteristic
414C2×#107C22×C4711yescharacteristic
415C2×#107C22×C4711yescharacteristic
416C2×#106C22×C4711yescharacteristic
417C2×#102C22×C4711yescharacteristic
418C2×#102C22×C4711yescharacteristic
419C2×#102C22×C4711yescharacteristic
420C2×#102C22×C4711yescharacteristic
421C2×C22⋊C8C22×C4711yescharacteristic
422C2×C22⋊C8C22×C4711yescharacteristic
423C2×C22⋊C8C22×C4711yescharacteristic
424C2×C22⋊C8C22×C4711yescharacteristic
425C2×C22⋊C8C22×C4711yescharacteristic
426C2×C22⋊C8C22×C4711yescharacteristic
427#393—21no—
428#392—21no—
429#392—21no—
430#392—21no—
431#391—21no—
432#390—21no—
433#386—21no—
434#386—21no—
435#380C22×C4711yescharacteristic
436#380C22×C4711yescharacteristic
437#380C22×C4711yescharacteristic
438#380C22×C4711yescharacteristic
439#380C22×C4711yescharacteristic
440#380C22×C4711yescharacteristic
441#380C22×C4711yescharacteristic
442#340C22×C4711yescharacteristic
443#340C22×C4711yescharacteristic
444#340C22×C4711yescharacteristic
445#340C22×C4711yescharacteristic
446#340C22×C4711yescharacteristic
447#340C22×C4711yescharacteristic
448#340C22×C4711yescharacteristic
449#340C22×C4711yescharacteristic
450C47#2989811yescharacteristic, direct product factor, Sylow
451C2×#41—22no—
452C2×#41—22no—
453C2×#41—41no—
454C2×#41—41no—
455C2×#41—41no—
456C2×#41—41no—
457C22×Q8D4×C4711yescharacteristic
458C22×D4—21no—
459C22×D4—21no—
460C22×D4—21no—
461C22×D4D4×C4711yescharacteristic
462C22×D4D4×C4711yescharacteristic
463C22×D4D4×C4711yescharacteristic
464C22×D4C23×C4711yescharacteristic
465C23×C4—21no—
466C23×C4C23×C4711yescharacteristic
467C23×C4C23×C4711yescharacteristic
468C23×C4C23×C4711yescharacteristic
469C22×C8C23×C4711yescharacteristic
470C22×C8C23×C4711yescharacteristic
471C22×C8C23×C4711yescharacteristic
472C22×C8C23×C4711yescharacteristic
473#121—22no—
474#121—22no—
475#121—41no—
476#121—41no—
477#121—41no—
478#121—41no—
479#117—41no—
480#117—41no—
481C2×C4⋊C4—21no—
482C2×C4⋊C4—41no—
483C2×C4⋊C4—41no—
484C2×C4⋊C4C23×C4711yescharacteristic
485C2×C4⋊C4C23×C4711yescharacteristic
486C2×C4⋊C4C23×C4711yescharacteristic
487C2×C4⋊C4C23×C4711yescharacteristic
488C2×C4⋊C4C23×C4711yescharacteristic
489C2×C4⋊C4C23×C4711yescharacteristic
490C2×C4⋊C4C23×C4711yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—21no—
500C2×C22⋊C4—21no—
501C2×C22⋊C4—21no—
502C2×C42—21no—
503#107—41no—
504#107—41no—
505#107—41no—
506#106—41no—
507#102—41no—
508#102—41no—
509#102—41no—
510#102—41no—
511C22⋊C8—22no—
512C22⋊C8—22no—
513C22⋊C8—41no—
514C22⋊C8—41no—
515C22⋊C8—41no—
516C22⋊C8—41no—
517#95—21no—
518#95—21no—
519#95—21no—
520#95—21no—
521#95—21no—
522#95—21no—
523#95—21no—
524C24—21no—
525C24C2×D4×C4711yescharacteristic
526C24C2×D4×C4711yescharacteristic
527C24C2×D4×C4711yescharacteristic
528#41—44no—
529#41—44no—
530#41—44no—
531#41—44no—
532C2×Q8—22no—
533C2×Q8—41no—
534C2×Q8—41no—
535C2×D4—22no—
536C2×D4—22no—
537C2×D4—22no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—41no—
545C2×D4—41no—
546C2×D4—41no—
547C2×D4—41no—
548C2×D4—41no—
549C2×D4—41no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—81no—
554C2×D4—81no—
555C2×D4—81no—
556C2×D4—81no—
557C2×D4—81no—
558C2×D4—81no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—21no—
582C22×C4—42no—
583C22×C4—81no—
584C22×C4—81no—
585C22×C4C2×D4×C4711yescharacteristic
586C22×C4C2×D4×C4711yescharacteristic
587C22×C4C2×D4×C4711yescharacteristic
588C22×C4#41×C4712yes—
589C22×C4#41×C4712yes—
590C22×C4C24×C4711yescharacteristic
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—21no—
595C2×C8—21no—
596C2×C8—21no—
597C2×C8—21no—
598C2×C8—21no—
599C2×C8—21no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C4⋊C4—21no—
604C4⋊C4—21no—
605C4⋊C4—21no—
606C4⋊C4—21no—
607C4⋊C4—21no—
608C4⋊C4—21no—
609C4⋊C4—21no—
610C4⋊C4—21no—
611C4⋊C4—21no—
612C4⋊C4—21no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—42no—
618C22⋊C4—42no—
619C22⋊C4—42no—
620C22⋊C4—42no—
621C22⋊C4—42no—
622C22⋊C4—81no—
623C22⋊C4—81no—
624C22⋊C4—81no—
625C22⋊C4—81no—
626C22⋊C4—81no—
627C22⋊C4—81no—
628C22⋊C4—81no—
629C42—42no—
630C23—21no—
631C23—21no—
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—21no—
637C23—21no—
638C23—21no—
639C23—21no—
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—41no—
657C23#123×C4712yes—
658C23C22×D4×C4711yescharacteristic
659Q8—44no—
660D4—44no—
661D4—44no—
662D4—44no—
663D4—41no—
664D4—41no—
665D4—41no—
666D4—41no—
667D4—84no—
668D4—84no—
669D4—84no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
680C2×C4—21no—
681C2×C4—21no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—41no—
693C2×C4—41no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—41no—
710C2×C4—41no—
711C2×C4—84no—
712C2×C4#123×C4712yes—
713C2×C4C2×#41×C4711yescharacteristic
714C2×C4C2×#41×C4711yescharacteristic
715C2×C4H(5,𝔽2)×C4711yescharacteristic
716C2×C4H(5,𝔽2)×C4711yescharacteristic
717C2×C4H(5,𝔽2)×C4711yescharacteristic
718C2×C4H(5,𝔽2)×C4711yescharacteristic
719C8—41no—
720C8—41no—
721C8—41no—
722C8—41no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—41no—
727C22—41no—
728C22—41no—
729C22—41no—
730C22—41no—
731C22—41no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—41no—
737C22—41no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—41no—
743C22—41no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22C2×#123×C4711yescharacteristic
752C22C47×#53411yescharacteristic
753C22C47×#53411yescharacteristic
754C22C47×#57611yescharacteristic
755C22C47×#57611yescharacteristic
756C22C47×#57711yescharacteristic
757C22C47×#57811yescharacteristic
758C4—22no—
759C4—41no—
760C4—41no—
761C4—81no—
762C4—81no—
763C4—81no—
764C4—81no—
765C4—81no—
766C4—81no—
767C4—81no—
768C4C47×#53811yescharacteristic
769C4C47×#53811yescharacteristic
770C4C47×#53811yescharacteristic
771C4C47×#53811yescharacteristic
772C2—42no—
773C2—81no—
774C2—81no—
775C2—161no—
776C2C47×#262211yescharacteristic
777C2C47×#309611yescharacteristic
778C2C47×#309811yescharacteristic
779C2C47×#319811yescharacteristic
780C2C47×#319911yescharacteristic
781C2C47×#320111yescharacteristic
782C2C47×#320311yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC47×#2615C2
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C22×#41×C47 ◁ G

Complements

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

NH ≅ G/Ntype
2. C47×#2311C2semidirect
3. C47×#2077C2semidirect
4. C47×#2076C2semidirect
5. C47×#2076C2semidirect
6. C47×#2075C2semidirect
7. C47×#2034C2semidirect
8. C47×#2033C2semidirect
9. C47×#2033C2semidirect
10. C47×#2033C2semidirect
11. C47×#1875C2semidirect
12. C47×#1874C2semidirect
13. C47×#1854C2semidirect
14. C47×#1852C2semidirect
15. C47×#1780C2semidirect
331. #29898C47direct (N × H)
382. #2311C2×C47semidirect
383. #2077C2×C47semidirect
384. #2076C2×C47semidirect
385. #2076C2×C47semidirect
386. #2075C2×C47semidirect
387. #2034C2×C47semidirect
388. #2033C2×C47semidirect
389. #2033C2×C47semidirect
390. #2033C2×C47semidirect
391. #1875C2×C47semidirect
392. #1874C2×C47semidirect
393. #1854C2×C47semidirect
394. #1852C2×C47semidirect
395. #1780C2×C47semidirect
450. C47#29898direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#26152
C47×#23112
C47×#20772
C47×#20762
C47×#20752
C47×#20342
C47×#20332
C47×#18752
C47×#18742
C47×#18542
C47×#18522
C47×#17802
#2989847