Finite Group Databasebeta

← C47×#25962 #26065660

Subgroups — C47×#25962 #26065660

Order 12032.

994 conjugacy classes of subgroups.

The subgroup lattice has 706 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#476C211yesmaximal, characteristic, complemented
2C2×C47×#416C211yesmaximal, characteristic
3C47×#2439C211yesmaximal, characteristic, complemented
4C47×#2339C211yesmaximal, characteristic
5C47×#2097C211yesmaximal, characteristic, complemented
6C47×#2066C211yesmaximal, characteristic, complemented
7C47×#2066C211yesmaximal, characteristic, complemented
8C47×#2024C211yesmaximal, characteristic, complemented
9C47×#1864C211yesmaximal, characteristic, complemented
10C47×#1862C211yesmaximal, characteristic, complemented
11C47×#1854C211yesmaximal, characteristic, complemented
12C47×#1850C211yesmaximal, characteristic, complemented
13C47×#1807C211yesmaximal, characteristic, complemented
14C47×#1804C211yesmaximal, characteristic, complemented
15C47×#1788C211yesmaximal, characteristic
16C22×#41×C47C2211yescharacteristic
17C23×C8×C47C2211yescharacteristic
18C2×C4⋊Q8×C47C2211yescharacteristic
19C2×C4×D4×C47C2211yescharacteristic
20C2×C4×D4×C47C2211yescharacteristic
21C2×#117×C47C2211yescharacteristic
22C47×#476—24no—
23C2×#107×C47C2211yescharacteristic
24C2×#106×C47C2211yescharacteristic
25C2×#106×C47C2211yescharacteristic
26C2×#106×C47C2211yescharacteristic
27C2×C4⋊C8×C47C2211yescharacteristic
28C2×C4⋊C8×C47C2211yescharacteristic
29C47×#416—24no—
30C2×#103×C47C2211yescharacteristic
31C2×#103×C47C2211yescharacteristic
32C2×#103×C47C2211yescharacteristic
33C2×#103×C47C2211yescharacteristic
34C2×#102×C47C2211yescharacteristic
35C2×#102×C47C2211yescharacteristic
36C2×#102×C47C2211yescharacteristic
37C2×#102×C47C2211yescharacteristic
38C2×C22⋊C8×C47C2211yescharacteristic
39C47×#396—21no—
40C47×#393—21no—
41C47×#391—21no—
42C47×#391C2211yescharacteristic
43C47×#391C2211yescharacteristic
44C47×#389C2211yescharacteristic
45C47×#389C2211yescharacteristic
46C47×#387—21no—
47C47×#386—21no—
48C47×#386—21no—
49C47×#382C2211yescharacteristic
50C47×#381—21no—
51C47×#380C2211yescharacteristic
52C47×#380C2211yescharacteristic
53C4×C22⋊C4×C47C2211yescharacteristic
54C2×#95×C47—21no—
55C47×#340C2211yescharacteristic
56C47×#340C2211yescharacteristic
57C47×#340C2211yescharacteristic
58C47×#340C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C2×#41×C47—22no—
62C2×#41×C47—22no—
63C2×#41×C47—22no—
64C2×#41×C47—41no—
65C2×#41×C47—41no—
66C2×#41×C47Q814yescomplemented
67C22×Q8×C47—21no—
68C22×Q8×C47C2311yescharacteristic
69C22×D4×C47—21no—
70C22×D4×C47C2311yescharacteristic
71C23×C4×C47—21no—
72C23×C4×C47—21no—
73C23×C4×C47—21no—
74C23×C4×C47C2311yescharacteristic
75C22×C8×C47—22no—
76C22×C8×C47—22no—
77C22×C8×C47—41no—
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C4⋊Q8×C47—22no—
83C4⋊Q8×C47—41no—
84C4×D4×C47—22no—
85C4×D4×C47—22no—
86C4×D4×C47—41no—
87C4×D4×C47—41no—
88#117×C47—22no—
89#117×C47—41no—
90C2×C4⋊C4×C47—21no—
91C2×C4⋊C4×C47—21no—
92C2×C4⋊C4×C47—21no—
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×C47D411yescharacteristic
105C2×C22⋊C4×C47D411yescharacteristic
106C2×C42×C47—21no—
107C2×C42×C47C2311yescharacteristic
108C2×C42×C47C2311yescharacteristic
109#107×C47—41no—
110#106×C47—22no—
111#106×C47—22no—
112#106×C47—41no—
113C4⋊C8×C47—22no—
114C4⋊C8×C47—41no—
115#103×C47—22no—
116#103×C47—22no—
117#103×C47—41no—
118#103×C47—41no—
119#102×C47—22no—
120#102×C47—22no—
121#102×C47—22no—
122#102×C47D414yes—
123C22⋊C8×C47—22no—
124#95×C47—21no—
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—
132#95×C47—21no—
133#95×C47—21no—
134#95×C47D411yescharacteristic
135#95×C47D411yescharacteristic
136C24×C47—21no—
137C24×C47C2×D411yescharacteristic
138#41×C47—28no—
139#41×C47—44no—
140#41×C47—44no—
141#41×C47—44no—
142C2×Q8×C47—21no—
143C2×Q8×C47—21no—
144C2×Q8×C47—21no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—42no—
148C2×Q8×C47—42no—
149C2×Q8×C47—81no—
150C2×Q8×C47C2×Q812yes—
151C2×D4×C47—24no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47C2×D412yes—
158C2×D4×C47C2×Q812yes—
159C2×D4×C47#4112yes—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—24no—
167C22×C4×C47—21no—
168C22×C4×C47—21no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—42no—
173C22×C4×C47—42no—
174C22×C4×C47—42no—
175C22×C4×C47—42no—
176C22×C4×C47—42no—
177C22×C4×C47—42no—
178C22×C4×C47—81no—
179C22×C4×C47—81no—
180C22×C4×C47C2×D411yescharacteristic
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×Q812yes—
186C22×C4×C47#4112yes—
187C22×C4×C47C2411yescharacteristic
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47—21no—
191C2×C8×C47—21no—
192C2×C8×C47—21no—
193C2×C8×C47—21no—
194C2×C8×C47—21no—
195C2×C8×C47—21no—
196C2×C8×C47—21no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—44no—
200C2×C8×C47C2×D412yes—
201C4⋊C4×C47—21no—
202C4⋊C4×C47—21no—
203C4⋊C4×C47—21no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47—21no—
206C4⋊C4×C47—21no—
207C4⋊C4×C47—21no—
208C4⋊C4×C47—21no—
209C4⋊C4×C47—21no—
210C4⋊C4×C47—21no—
211C4⋊C4×C47—21no—
212C4⋊C4×C47—42no—
213C4⋊C4×C47—42no—
214C4⋊C4×C47—81no—
215C4⋊C4×C47C2×D412yes—
216C22⋊C4×C47—22no—
217C22⋊C4×C47—41no—
218C22⋊C4×C47—42no—
219C22⋊C4×C47—42no—
220C22⋊C4×C47—42no—
221C22⋊C4×C47—81no—
222C22⋊C4×C47—81no—
223C42×C47—21no—
224C42×C47—21no—
225C42×C47—21no—
226C42×C47—21no—
227C42×C47—42no—
228C23×C47—22no—
229C23×C47—21no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—21no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—41no—
238C23×C47—41no—
239C23×C47—41no—
240C23×C47—41no—
241C23×C47C22⋊Q812yes—
242C23×C47C22×D411yescharacteristic
243Q8×C47—22no—
244Q8×C47—22no—
245Q8×C47—41no—
246Q8×C47—41no—
247Q8×C47—84no—
248D4×C47—22no—
249D4×C47—22no—
250D4×C47—22no—
251D4×C47—48no—
252D4×C47C22⋊Q814yes—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—21no—
263C2×C4×C47—22no—
264C2×C4×C47—21no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—48no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—41no—
292C2×C4×C47—84no—
293C2×C4×C47—84no—
294C2×C4×C47C22⋊Q812yes—
295C2×C4×C47#13512yes—
296C2×C4×C47C22×D411yescharacteristic
297C2×C4×C47C22×Q811yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47C2×#4111yescharacteristic
300C2×C4×C47H(5,𝔽2)11yescharacteristic
301C2×C4×C47H(5,𝔽2)11yescharacteristic
302C8×C47—22no—
303C8×C47—41no—
304C8×C47—41no—
305C8×C47—41no—
306#25962C4711yesmaximal, characteristic, direct product factor, Sylow
307C22×C47—22no—
308C22×C47—22no—
309C22×C47—22no—
310C22×C47—24no—
311C22×C47—42no—
312C22×C47—42no—
313C22×C47—41no—
314C22×C47—42no—
315C22×C47—42no—
316C22×C47—41no—
317C22×C47—41no—
318C22×C47—42no—
319C22×C47—42no—
320C22×C47—41no—
321C22×C47C2×C22⋊Q811yescharacteristic
322C22×C47D4211yescharacteristic
323C22×C47#54611yescharacteristic
324C22×C47C2×#13511yescharacteristic
325C22×C47#57511yescharacteristic
326C22×C47#57711yescharacteristic
327C22×C47#57711yescharacteristic
328C4×C47—22no—
329C4×C47—22no—
330C4×C47—42no—
331C4×C47—41no—
332C4×C47—42no—
333C4×C47—41no—
334C4×C47—41no—
335C4×C47—81no—
336C4×C47—81no—
337C4×C47—81no—
338C4×C47—81no—
339C4×C47—81no—
340C4×C47C2×C22⋊Q811yescharacteristic
341C4×C47#54311yescharacteristic
342C4×C47#54611yescharacteristic
343C4×C47#55111yescharacteristic
344C2×#476C2×C4711yescharacteristic, complemented
345C2×#416C2×C4711yescharacteristic
346#2439C2×C4711yescharacteristic, complemented
347#2339C2×C4711yescharacteristic
348#2097C2×C4711yescharacteristic, complemented
349#2066C2×C4711yescharacteristic, complemented
350#2066C2×C4711yescharacteristic, complemented
351#2024C2×C4711yescharacteristic, complemented
352#1864C2×C4711yescharacteristic, complemented
353#1862C2×C4711yescharacteristic, complemented
354#1854C2×C4711yescharacteristic, complemented
355#1850C2×C4711yescharacteristic, complemented
356#1807C2×C4711yescharacteristic, complemented
357#1804C2×C4711yescharacteristic, complemented
358#1788C2×C4711yescharacteristic
359C2×C47—42no—
360C2×C47—44no—
361C2×C47#243711yescharacteristic
362C2×C47#307611yescharacteristic
363C2×C47#308411yescharacteristic
364C2×C47#326711yescharacteristic
365C2×C47#328211yescharacteristic
366C2×C47#330311yescharacteristic
367C2×C47#331111yescharacteristic
368C22×#41C22×C4711yescharacteristic
369C23×C8C22×C4711yescharacteristic
370C2×C4⋊Q8C22×C4711yescharacteristic
371C2×C4×D4C22×C4711yescharacteristic
372C2×C4×D4C22×C4711yescharacteristic
373C2×#117C22×C4711yescharacteristic
374#476—24no—
375C2×#107C22×C4711yescharacteristic
376C2×#106C22×C4711yescharacteristic
377C2×#106C22×C4711yescharacteristic
378C2×#106C22×C4711yescharacteristic
379C2×C4⋊C8C22×C4711yescharacteristic
380C2×C4⋊C8C22×C4711yescharacteristic
381#416—24no—
382C2×#103C22×C4711yescharacteristic
383C2×#103C22×C4711yescharacteristic
384C2×#103C22×C4711yescharacteristic
385C2×#103C22×C4711yescharacteristic
386C2×#102C22×C4711yescharacteristic
387C2×#102C22×C4711yescharacteristic
388C2×#102C22×C4711yescharacteristic
389C2×#102C22×C4711yescharacteristic
390C2×C22⋊C8C22×C4711yescharacteristic
391#396—21no—
392#393—21no—
393#391—21no—
394#391C22×C4711yescharacteristic
395#391C22×C4711yescharacteristic
396#389C22×C4711yescharacteristic
397#389C22×C4711yescharacteristic
398#387—21no—
399#386—21no—
400#386—21no—
401#382C22×C4711yescharacteristic
402#381—21no—
403#380C22×C4711yescharacteristic
404#380C22×C4711yescharacteristic
405C4×C22⋊C4C22×C4711yescharacteristic
406C2×#95—21no—
407#340C22×C4711yescharacteristic
408#340C22×C4711yescharacteristic
409#340C22×C4711yescharacteristic
410#340C22×C4711yescharacteristic
411#336C22×C4711yescharacteristic
412#336C22×C4711yescharacteristic
413C47#2596211yescharacteristic, direct product factor, Sylow
414C2×#41—22no—
415C2×#41—22no—
416C2×#41—22no—
417C2×#41—41no—
418C2×#41—41no—
419C2×#41Q8×C4714yescomplemented
420C22×Q8—21no—
421C22×Q8C23×C4711yescharacteristic
422C22×D4—21no—
423C22×D4C23×C4711yescharacteristic
424C23×C4—21no—
425C23×C4—21no—
426C23×C4—21no—
427C23×C4C23×C4711yescharacteristic
428C22×C8—22no—
429C22×C8—22no—
430C22×C8—41no—
431C22×C8C23×C4711yescharacteristic
432C22×C8C23×C4711yescharacteristic
433C22×C8C23×C4711yescharacteristic
434C22×C8C23×C4711yescharacteristic
435C4⋊Q8—22no—
436C4⋊Q8—41no—
437C4×D4—22no—
438C4×D4—22no—
439C4×D4—41no—
440C4×D4—41no—
441#117—22no—
442#117—41no—
443C2×C4⋊C4—21no—
444C2×C4⋊C4—21no—
445C2×C4⋊C4—21no—
446C2×C4⋊C4C23×C4711yescharacteristic
447C2×C4⋊C4C23×C4711yescharacteristic
448C2×C4⋊C4C23×C4711yescharacteristic
449C2×C4⋊C4C23×C4711yescharacteristic
450C2×C4⋊C4C23×C4711yescharacteristic
451C2×C4⋊C4C23×C4711yescharacteristic
452C2×C22⋊C4—21no—
453C2×C22⋊C4—21no—
454C2×C22⋊C4—21no—
455C2×C22⋊C4—21no—
456C2×C22⋊C4—21no—
457C2×C22⋊C4D4×C4711yescharacteristic
458C2×C22⋊C4D4×C4711yescharacteristic
459C2×C42—21no—
460C2×C42C23×C4711yescharacteristic
461C2×C42C23×C4711yescharacteristic
462#107—41no—
463#106—22no—
464#106—22no—
465#106—41no—
466C4⋊C8—22no—
467C4⋊C8—41no—
468#103—22no—
469#103—22no—
470#103—41no—
471#103—41no—
472#102—22no—
473#102—22no—
474#102—22no—
475#102D4×C4714yes—
476C22⋊C8—22no—
477#95—21no—
478#95—21no—
479#95—21no—
480#95—21no—
481#95—21no—
482#95—21no—
483#95—21no—
484#95—21no—
485#95—21no—
486#95—21no—
487#95D4×C4711yescharacteristic
488#95D4×C4711yescharacteristic
489C24—21no—
490C24C2×D4×C4711yescharacteristic
491#41—28no—
492#41—44no—
493#41—44no—
494#41—44no—
495C2×Q8—21no—
496C2×Q8—21no—
497C2×Q8—21no—
498C2×Q8—21no—
499C2×Q8—21no—
500C2×Q8—42no—
501C2×Q8—42no—
502C2×Q8—81no—
503C2×Q8C2×Q8×C4712yes—
504C2×D4—24no—
505C2×D4—21no—
506C2×D4—21no—
507C2×D4—21no—
508C2×D4—42no—
509C2×D4—42no—
510C2×D4C2×D4×C4712yes—
511C2×D4C2×Q8×C4712yes—
512C2×D4#41×C4712yes—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—21no—
519C22×C4—24no—
520C22×C4—21no—
521C22×C4—21no—
522C22×C4—21no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—42no—
526C22×C4—42no—
527C22×C4—42no—
528C22×C4—42no—
529C22×C4—42no—
530C22×C4—42no—
531C22×C4—81no—
532C22×C4—81no—
533C22×C4C2×D4×C4711yescharacteristic
534C22×C4C2×D4×C4711yescharacteristic
535C22×C4C2×D4×C4711yescharacteristic
536C22×C4C2×D4×C4711yescharacteristic
537C22×C4C2×D4×C4711yescharacteristic
538C22×C4C2×Q8×C4712yes—
539C22×C4#41×C4712yes—
540C22×C4C24×C4711yescharacteristic
541C2×C8—21no—
542C2×C8—21no—
543C2×C8—21no—
544C2×C8—21no—
545C2×C8—21no—
546C2×C8—21no—
547C2×C8—21no—
548C2×C8—21no—
549C2×C8—21no—
550C2×C8—21no—
551C2×C8—21no—
552C2×C8—44no—
553C2×C8C2×D4×C4712yes—
554C4⋊C4—21no—
555C4⋊C4—21no—
556C4⋊C4—21no—
557C4⋊C4—21no—
558C4⋊C4—21no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—42no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4C2×D4×C4712yes—
569C22⋊C4—22no—
570C22⋊C4—41no—
571C22⋊C4—42no—
572C22⋊C4—42no—
573C22⋊C4—42no—
574C22⋊C4—81no—
575C22⋊C4—81no—
576C42—21no—
577C42—21no—
578C42—21no—
579C42—21no—
580C42—42no—
581C23—22no—
582C23—21no—
583C23—22no—
584C23—22no—
585C23—21no—
586C23—21no—
587C23—21no—
588C23—21no—
589C23—21no—
590C23—41no—
591C23—41no—
592C23—41no—
593C23—41no—
594C23C22⋊Q8×C4712yes—
595C23C22×D4×C4711yescharacteristic
596Q8—22no—
597Q8—22no—
598Q8—41no—
599Q8—41no—
600Q8—84no—
601D4—22no—
602D4—22no—
603D4—22no—
604D4—48no—
605D4C22⋊Q8×C4714yes—
606C2×C4—21no—
607C2×C4—21no—
608C2×C4—21no—
609C2×C4—21no—
610C2×C4—22no—
611C2×C4—22no—
612C2×C4—22no—
613C2×C4—22no—
614C2×C4—22no—
615C2×C4—21no—
616C2×C4—22no—
617C2×C4—21no—
618C2×C4—21no—
619C2×C4—21no—
620C2×C4—21no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—48no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—41no—
633C2×C4—41no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—84no—
646C2×C4—84no—
647C2×C4C22⋊Q8×C4712yes—
648C2×C4#135×C4712yes—
649C2×C4C22×D4×C4711yescharacteristic
650C2×C4C22×Q8×C4711yescharacteristic
651C2×C4C2×#41×C4711yescharacteristic
652C2×C4C2×#41×C4711yescharacteristic
653C2×C4H(5,𝔽2)×C4711yescharacteristic
654C2×C4H(5,𝔽2)×C4711yescharacteristic
655C8—22no—
656C8—41no—
657C8—41no—
658C8—41no—
659C22—22no—
660C22—22no—
661C22—22no—
662C22—24no—
663C22—41no—
664C22—42no—
665C22—42no—
666C22—41no—
667C22—42no—
668C22—42no—
669C22—41no—
670C22—42no—
671C22—42no—
672C22—41no—
673C22C2×C22⋊Q8×C4711yescharacteristic
674C22D42×C4711yescharacteristic
675C22C47×#54611yescharacteristic
676C22C2×#135×C4711yescharacteristic
677C22C47×#57511yescharacteristic
678C22C47×#57711yescharacteristic
679C22C47×#57711yescharacteristic
680C4—22no—
681C4—22no—
682C4—41no—
683C4—41no—
684C4—42no—
685C4—41no—
686C4—42no—
687C4—81no—
688C4—81no—
689C4—81no—
690C4—81no—
691C4—81no—
692C4C2×C22⋊Q8×C4711yescharacteristic
693C4C47×#54311yescharacteristic
694C4C47×#54611yescharacteristic
695C4C47×#55111yescharacteristic
696C2—42no—
697C2—44no—
698C2C47×#243711yescharacteristic
699C2C47×#307611yescharacteristic
700C2C47×#308411yescharacteristic
701C2C47×#326711yescharacteristic
702C2C47×#328211yescharacteristic
703C2C47×#330311yescharacteristic
704C2C47×#331111yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×#41×C47C22
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C4×C22⋊C4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#476C2semidirect
3. C47×#2439C2semidirect
5. C47×#2097C2semidirect
6. C47×#2066C2semidirect
7. C47×#2066C2semidirect
8. C47×#2024C2semidirect
9. C47×#1864C2semidirect
10. C47×#1862C2semidirect
11. C47×#1854C2semidirect
12. C47×#1850C2semidirect
13. C47×#1807C2semidirect
14. C47×#1804C2semidirect
66. C2×#41×C47Q8semidirect
306. #25962C47direct (N × H)
344. C2×#476C2×C47semidirect
346. #2439C2×C47semidirect
348. #2097C2×C47semidirect
349. #2066C2×C47semidirect
350. #2066C2×C47semidirect
351. #2024C2×C47semidirect
352. #1864C2×C47semidirect
353. #1862C2×C47semidirect
354. #1854C2×C47semidirect
355. #1850C2×C47semidirect
356. #1807C2×C47semidirect
357. #1804C2×C47semidirect
413. C47#25962direct (N × H)
419. C2×#41Q8×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4762
C2×C47×#4162
C47×#24392
C47×#23392
C47×#20972
C47×#20662
C47×#20242
C47×#18642
C47×#18622
C47×#18542
C47×#18502
C47×#18072
C47×#18042
C47×#17882
#2596247