Finite Group Databasebeta

← C47×#24793 #26064491

Subgroups — C47×#24793 #26064491

Order 12032.

956 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C47×#470C211yesmaximal, characteristic, complemented
2C2×C47×#470C211yesmaximal, characteristic, complemented
3C2×C47×#436C211yesmaximal, characteristic
4C2×C47×#428C211yesmaximal, characteristic, complemented
5C47×#2417C211yesmaximal, characteristic
6C47×#2415C211yesmaximal, characteristic
7C47×#2068C211yesmaximal, characteristic, complemented
8C47×#2066C211yesmaximal, characteristic, complemented
9C47×#2036C211yesmaximal, characteristic, complemented
10C47×#2035C211yesmaximal, characteristic, complemented
11C47×#1969C211yesmaximal, characteristic, complemented
12C47×#1941C211yesmaximal, characteristic, complemented
13C47×#1873C211yesmaximal, characteristic, complemented
14C47×#1872C211yesmaximal, characteristic, complemented
15C47×#1809C211yesmaximal, characteristic, complemented
16C22×Q16×C47C2211yescharacteristic
17C22×M16×C47C2211yescharacteristic
18C22×M16×C47C2211yescharacteristic
19C2×C22⋊Q8×C47C2211yescharacteristic
20C2×C22⋊Q8×C47C2211yescharacteristic
21C2×C22⋊Q8×C47C2211yescharacteristic
22C2×C22⋊Q8×C47C2211yescharacteristic
23C2×C4×D4×C47C2211yescharacteristic
24C2×#117×C47C2211yescharacteristic
25C22×C4⋊C4×C47C2211yescharacteristic
26C47×#470—24no—
27C47×#470—24no—
28C47×#436—24no—
29C47×#428—24no—
30C2×#107×C47C2211yescharacteristic
31C2×#107×C47C2211yescharacteristic
32C2×#106×C47C2211yescharacteristic
33C2×#106×C47C2211yescharacteristic
34C2×#106×C47C2211yescharacteristic
35C2×C4⋊C8×C47C2211yescharacteristic
36C2×#103×C47C2211yescharacteristic
37C2×#103×C47C2211yescharacteristic
38C2×#103×C47C2211yescharacteristic
39C2×#103×C47C2211yescharacteristic
40C2×#103×C47C2211yescharacteristic
41C2×#103×C47C2211yescharacteristic
42C2×C22⋊C8×C47C2211yescharacteristic
43C2×C22⋊C8×C47C2211yescharacteristic
44C2×C4×C8×C47C2211yescharacteristic
45C47×#398—21no—
46C47×#397—21no—
47C47×#396—21no—
48C47×#394—21no—
49C47×#391C2211yescharacteristic
50C47×#391C2211yescharacteristic
51C47×#389—21no—
52C47×#389C2211yescharacteristic
53C47×#389C2211yescharacteristic
54C47×#388—21no—
55C47×#386—21no—
56C47×#380—21no—
57C47×#380C2211yescharacteristic
58C47×#380C2211yescharacteristic
59C47×#340C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C47×#340C2211yescharacteristic
63C22×Q8×C47C2311yescharacteristic
64C22×Q8×C47C2311yescharacteristic
65C22×D4×C47D411yescharacteristic
66C23×C4×C47—21no—
67C23×C4×C47C2311yescharacteristic
68C23×C4×C47C2311yescharacteristic
69C2×Q16×C47—22no—
70C2×Q16×C47—22no—
71C2×Q16×C47—22no—
72C2×M16×C47—22no—
73C2×M16×C47—22no—
74C2×M16×C47—22no—
75C2×M16×C47—22no—
76C2×M16×C47—22no—
77C2×M16×C47D414yes—
78C22×C8×C47C2311yescharacteristic
79C22×C8×C47C2311yescharacteristic
80C22×C8×C47C2311yescharacteristic
81C22×C8×C47C2311yescharacteristic
82C22⋊Q8×C47—22no—
83C22⋊Q8×C47—22no—
84C22⋊Q8×C47—22no—
85C22⋊Q8×C47—22no—
86C22⋊Q8×C47—22no—
87C22⋊Q8×C47—22no—
88C22⋊Q8×C47—41no—
89C22⋊Q8×C47—41no—
90C4×D4×C47—22no—
91C4×D4×C47—22no—
92#117×C47—22no—
93#117×C47—41no—
94C2×C4⋊C4×C47—22no—
95C2×C4⋊C4×C47—21no—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47—21no—
98C2×C4⋊C4×C47—21no—
99C2×C4⋊C4×C47—21no—
100C2×C4⋊C4×C47—21no—
101C2×C4⋊C4×C47—21no—
102C2×C4⋊C4×C47—41no—
103C2×C4⋊C4×C47D411yescharacteristic
104C2×C4⋊C4×C47C2311yescharacteristic
105C2×C4⋊C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47C2311yescharacteristic
107C2×C4⋊C4×C47C2311yescharacteristic
108C2×C4⋊C4×C47C2311yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C22⋊C4×C47—21no—
111C2×C22⋊C4×C47—21no—
112C2×C22⋊C4×C47—21no—
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47—21no—
116C2×C22⋊C4×C47—21no—
117C2×C22⋊C4×C47D411yescharacteristic
118C2×C22⋊C4×C47D411yescharacteristic
119C2×C42×C47—21no—
120C2×C42×C47C2311yescharacteristic
121#107×C47—22no—
122#107×C47—22no—
123#106×C47—22no—
124#106×C47—22no—
125#106×C47D414yescomplemented
126C4⋊C8×C47—22no—
127#103×C47—22no—
128#103×C47—22no—
129#103×C47—22no—
130#103×C47—22no—
131#103×C47—41no—
132#103×C47—41no—
133C22⋊C8×C47—22no—
134C22⋊C8×C47—22no—
135C4×C8×C47—22no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47—21no—
142#95×C47—21no—
143#95×C47—21no—
144C24×C47C2×D411yescharacteristic
145C24×C47C2×D411yescharacteristic
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—21no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×D4×C47—22no—
159C2×D4×C47—22no—
160C2×D4×C47—41no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
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—42no—
180C22×C4×C47—42no—
181C22×C4×C47—81no—
182C22×C4×C47C2×D411yescharacteristic
183C22×C4×C47C2×D411yescharacteristic
184C22×C4×C47C2×D411yescharacteristic
185C22×C4×C47C2×D412yes—
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47#4112yes—
188C22×C4×C47C2411yescharacteristic
189Q16×C47—44no—
190M16×C47—28no—
191M16×C47—44no—
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—21no—
200C2×C8×C47C2×D412yes—
201C2×C8×C47C2×D412yes—
202C2×C8×C47C2×D412yes—
203C2×C8×C47#4112yes—
204C4⋊C4×C47—22no—
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—21no—
213C4⋊C4×C47—21no—
214C4⋊C4×C47—21no—
215C4⋊C4×C47—42no—
216C4⋊C4×C47—42no—
217C4⋊C4×C47—42no—
218C4⋊C4×C47—42no—
219C4⋊C4×C47—42no—
220C4⋊C4×C47—42no—
221C4⋊C4×C47—81no—
222C4⋊C4×C47C2×D412yes—
223C4⋊C4×C47C2×D412yes—
224C22⋊C4×C47—22no—
225C22⋊C4×C47—22no—
226C22⋊C4×C47—42no—
227C22⋊C4×C47—42no—
228C22⋊C4×C47—42no—
229C22⋊C4×C47—42no—
230C22⋊C4×C47—42no—
231C22⋊C4×C47—42no—
232C22⋊C4×C47—81no—
233C42×C47—21no—
234C42×C47—21no—
235C42×C47—42no—
236C23×C47—21no—
237C23×C47—21no—
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#12112yes—
250C23×C47C22×D411yescharacteristic
251Q8×C47—41no—
252Q8×C47—41no—
253Q8×C47—41no—
254Q8×C47—41no—
255Q8×C47—41no—
256Q8×C47—41no—
257Q8×C47—41no—
258Q8×C47—41no—
259D4×C47—44no—
260C2×C4×C47—21no—
261C2×C4×C47—21no—
262C2×C4×C47—21no—
263C2×C4×C47—21no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
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—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—84no—
303C2×C4×C47#12112yes—
304C2×C4×C47#13712yes—
305C2×C4×C47C22×D411yescharacteristic
306C2×C4×C47C22×D411yescharacteristic
307C2×C4×C47C2×#4111yescharacteristic
308C2×C4×C47C2×#4111yescharacteristic
309C2×C4×C47H(5,𝔽2)11yescharacteristic
310C2×C4×C472−1+411yescharacteristic
311C8×C47—22no—
312C8×C47—41no—
313C8×C47—41no—
314C8×C47#12114yes—
315#24793C4711yesmaximal, characteristic, direct product factor, Sylow
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—41no—
320C22×C47—41no—
321C22×C47—41no—
322C22×C47—41no—
323C22×C47—41no—
324C22×C47—41no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—41no—
330C22×C47C2×#12111yescharacteristic
331C22×C47D4211yescharacteristic
332C22×C47#54711yescharacteristic
333C22×C47C2×#13711yescharacteristic
334C22×C47#57511yescharacteristic
335C22×C47#57711yescharacteristic
336C22×C47#57811yescharacteristic
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—41no—
340C4×C47—42no—
341C4×C47—42no—
342C4×C47—41no—
343C4×C47—81no—
344C4×C47—81no—
345C4×C47—81no—
346C4×C47—81no—
347C4×C47—81no—
348C4×C47—81no—
349C4×C47C2×#12111yescharacteristic
350C4×C47#53711yescharacteristic
351C4×C47#54811yescharacteristic
352C4×C47#55311yescharacteristic
353C2×#470C2×C4711yescharacteristic, complemented
354C2×#470C2×C4711yescharacteristic, complemented
355C2×#436C2×C4711yescharacteristic
356C2×#428C2×C4711yescharacteristic, complemented
357#2417C2×C4711yescharacteristic
358#2415C2×C4711yescharacteristic
359#2068C2×C4711yescharacteristic, complemented
360#2066C2×C4711yescharacteristic, complemented
361#2036C2×C4711yescharacteristic, complemented
362#2035C2×C4711yescharacteristic, complemented
363#1969C2×C4711yescharacteristic, complemented
364#1941C2×C4711yescharacteristic, complemented
365#1873C2×C4711yescharacteristic, complemented
366#1872C2×C4711yescharacteristic, complemented
367#1809C2×C4711yescharacteristic, complemented
368C2×C47—42no—
369C2×C47—81no—
370C2×C47#241611yescharacteristic
371C2×C47#305611yescharacteristic
372C2×C47#306311yescharacteristic
373C2×C47#327511yescharacteristic
374C2×C47#327611yescharacteristic
375C2×C47#335211yescharacteristic
376C2×C47#335611yescharacteristic
377C22×Q16C22×C4711yescharacteristic
378C22×M16C22×C4711yescharacteristic
379C22×M16C22×C4711yescharacteristic
380C2×C22⋊Q8C22×C4711yescharacteristic
381C2×C22⋊Q8C22×C4711yescharacteristic
382C2×C22⋊Q8C22×C4711yescharacteristic
383C2×C22⋊Q8C22×C4711yescharacteristic
384C2×C4×D4C22×C4711yescharacteristic
385C2×#117C22×C4711yescharacteristic
386C22×C4⋊C4C22×C4711yescharacteristic
387#470—24no—
388#470—24no—
389#436—24no—
390#428—24no—
391C2×#107C22×C4711yescharacteristic
392C2×#107C22×C4711yescharacteristic
393C2×#106C22×C4711yescharacteristic
394C2×#106C22×C4711yescharacteristic
395C2×#106C22×C4711yescharacteristic
396C2×C4⋊C8C22×C4711yescharacteristic
397C2×#103C22×C4711yescharacteristic
398C2×#103C22×C4711yescharacteristic
399C2×#103C22×C4711yescharacteristic
400C2×#103C22×C4711yescharacteristic
401C2×#103C22×C4711yescharacteristic
402C2×#103C22×C4711yescharacteristic
403C2×C22⋊C8C22×C4711yescharacteristic
404C2×C22⋊C8C22×C4711yescharacteristic
405C2×C4×C8C22×C4711yescharacteristic
406#398—21no—
407#397—21no—
408#396—21no—
409#394—21no—
410#391C22×C4711yescharacteristic
411#391C22×C4711yescharacteristic
412#389—21no—
413#389C22×C4711yescharacteristic
414#389C22×C4711yescharacteristic
415#388—21no—
416#386—21no—
417#380—21no—
418#380C22×C4711yescharacteristic
419#380C22×C4711yescharacteristic
420#340C22×C4711yescharacteristic
421#340C22×C4711yescharacteristic
422#340C22×C4711yescharacteristic
423#340C22×C4711yescharacteristic
424C47#2479311yescharacteristic, direct product factor, Sylow
425C22×Q8C23×C4711yescharacteristic
426C22×Q8C23×C4711yescharacteristic
427C22×D4D4×C4711yescharacteristic
428C23×C4—21no—
429C23×C4C23×C4711yescharacteristic
430C23×C4C23×C4711yescharacteristic
431C2×Q16—22no—
432C2×Q16—22no—
433C2×Q16—22no—
434C2×M16—22no—
435C2×M16—22no—
436C2×M16—22no—
437C2×M16—22no—
438C2×M16—22no—
439C2×M16D4×C4714yes—
440C22×C8C23×C4711yescharacteristic
441C22×C8C23×C4711yescharacteristic
442C22×C8C23×C4711yescharacteristic
443C22×C8C23×C4711yescharacteristic
444C22⋊Q8—22no—
445C22⋊Q8—22no—
446C22⋊Q8—22no—
447C22⋊Q8—22no—
448C22⋊Q8—22no—
449C22⋊Q8—22no—
450C22⋊Q8—41no—
451C22⋊Q8—41no—
452C4×D4—22no—
453C4×D4—22no—
454#117—22no—
455#117—41no—
456C2×C4⋊C4—22no—
457C2×C4⋊C4—21no—
458C2×C4⋊C4—21no—
459C2×C4⋊C4—21no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—41no—
465C2×C4⋊C4D4×C4711yescharacteristic
466C2×C4⋊C4C23×C4711yescharacteristic
467C2×C4⋊C4C23×C4711yescharacteristic
468C2×C4⋊C4C23×C4711yescharacteristic
469C2×C4⋊C4C23×C4711yescharacteristic
470C2×C4⋊C4C23×C4711yescharacteristic
471C2×C4⋊C4C23×C4711yescharacteristic
472C2×C22⋊C4—21no—
473C2×C22⋊C4—21no—
474C2×C22⋊C4—21no—
475C2×C22⋊C4—21no—
476C2×C22⋊C4—21no—
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4D4×C4711yescharacteristic
480C2×C22⋊C4D4×C4711yescharacteristic
481C2×C42—21no—
482C2×C42C23×C4711yescharacteristic
483#107—22no—
484#107—22no—
485#106—22no—
486#106—22no—
487#106D4×C4714yescomplemented
488C4⋊C8—22no—
489#103—22no—
490#103—22no—
491#103—22no—
492#103—22no—
493#103—41no—
494#103—41no—
495C22⋊C8—22no—
496C22⋊C8—22no—
497C4×C8—22no—
498#95—21no—
499#95—21no—
500#95—21no—
501#95—21no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506C24C2×D4×C4711yescharacteristic
507C24C2×D4×C4711yescharacteristic
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—21no—
514C2×Q8—21no—
515C2×Q8—21no—
516C2×Q8—21no—
517C2×Q8—21no—
518C2×Q8—21no—
519C2×Q8—21no—
520C2×D4—22no—
521C2×D4—22no—
522C2×D4—41no—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—21no—
540C22×C4—21no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4C2×D4×C4711yescharacteristic
545C22×C4C2×D4×C4711yescharacteristic
546C22×C4C2×D4×C4711yescharacteristic
547C22×C4C2×D4×C4712yes—
548C22×C4C2×D4×C4711yescharacteristic
549C22×C4#41×C4712yes—
550C22×C4C24×C4711yescharacteristic
551Q16—44no—
552M16—28no—
553M16—44no—
554C2×C8—21no—
555C2×C8—21no—
556C2×C8—21no—
557C2×C8—21no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8C2×D4×C4712yes—
563C2×C8C2×D4×C4712yes—
564C2×C8C2×D4×C4712yes—
565C2×C8#41×C4712yes—
566C4⋊C4—22no—
567C4⋊C4—21no—
568C4⋊C4—21no—
569C4⋊C4—21no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—21no—
575C4⋊C4—21no—
576C4⋊C4—21no—
577C4⋊C4—42no—
578C4⋊C4—42no—
579C4⋊C4—42no—
580C4⋊C4—42no—
581C4⋊C4—42no—
582C4⋊C4—42no—
583C4⋊C4—81no—
584C4⋊C4C2×D4×C4712yes—
585C4⋊C4C2×D4×C4712yes—
586C22⋊C4—22no—
587C22⋊C4—22no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—42no—
592C22⋊C4—42no—
593C22⋊C4—42no—
594C22⋊C4—81no—
595C42—21no—
596C42—21no—
597C42—42no—
598C23—21no—
599C23—21no—
600C23—21no—
601C23—21no—
602C23—21no—
603C23—21no—
604C23—21no—
605C23—21no—
606C23—21no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23#121×C4712yes—
612C23C22×D4×C4711yescharacteristic
613Q8—41no—
614Q8—41no—
615Q8—41no—
616Q8—41no—
617Q8—41no—
618Q8—41no—
619Q8—41no—
620Q8—41no—
621D4—44no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—22no—
629C2×C4—22no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—21no—
635C2×C4—21no—
636C2×C4—21no—
637C2×C4—21no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—41no—
646C2×C4—41no—
647C2×C4—41no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—41no—
653C2×C4—41no—
654C2×C4—41no—
655C2×C4—41no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—84no—
665C2×C4#121×C4712yes—
666C2×C4#137×C4712yes—
667C2×C4C22×D4×C4711yescharacteristic
668C2×C4C22×D4×C4711yescharacteristic
669C2×C4C2×#41×C4711yescharacteristic
670C2×C4C2×#41×C4711yescharacteristic
671C2×C4H(5,𝔽2)×C4711yescharacteristic
672C2×C42−1+4×C4711yescharacteristic
673C8—22no—
674C8—41no—
675C8—41no—
676C8#121×C4714yes—
677C22—22no—
678C22—22no—
679C22—22no—
680C22—41no—
681C22—41no—
682C22—41no—
683C22—41no—
684C22—41no—
685C22—41no—
686C22—41no—
687C22—41no—
688C22—41no—
689C22—41no—
690C22—41no—
691C22C2×#121×C4711yescharacteristic
692C22D42×C4711yescharacteristic
693C22C47×#54711yescharacteristic
694C22C2×#137×C4711yescharacteristic
695C22C47×#57511yescharacteristic
696C22C47×#57711yescharacteristic
697C22C47×#57811yescharacteristic
698C4—22no—
699C4—22no—
700C4—41no—
701C4—41no—
702C4—42no—
703C4—42no—
704C4—81no—
705C4—81no—
706C4—81no—
707C4—81no—
708C4—81no—
709C4—81no—
710C4C2×#121×C4711yescharacteristic
711C4C47×#53711yescharacteristic
712C4C47×#54811yescharacteristic
713C4C47×#55311yescharacteristic
714C2—42no—
715C2—81no—
716C2C47×#241611yescharacteristic
717C2C47×#305611yescharacteristic
718C2C47×#306311yescharacteristic
719C2C47×#327511yescharacteristic
720C2C47×#327611yescharacteristic
721C2C47×#335211yescharacteristic
722C2C47×#335611yescharacteristic
subgroupG/H
center, socleC23×C47C22×D4
commutator, Frattini, cosocleC22×C4C24×C47
prime radicalC22×D4×C47D4
LCSG ▷ C22×C4 ▷ C2 ▷ C1
UCSC1 ◁ C23×C47 ◁ C2×C4×D4×C47 ◁ G

Complements

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

NH ≅ G/Ntype
1. C2×C47×#470C2semidirect
2. C2×C47×#470C2semidirect
4. C2×C47×#428C2semidirect
7. C47×#2068C2semidirect
8. C47×#2066C2semidirect
9. C47×#2036C2semidirect
10. C47×#2035C2semidirect
11. C47×#1969C2semidirect
12. C47×#1941C2semidirect
13. C47×#1873C2semidirect
14. C47×#1872C2semidirect
15. C47×#1809C2semidirect
125. #106×C47D4semidirect
315. #24793C47direct (N × H)
353. C2×#470C2×C47semidirect
354. C2×#470C2×C47semidirect
356. C2×#428C2×C47semidirect
359. #2068C2×C47semidirect
360. #2066C2×C47semidirect
361. #2036C2×C47semidirect
362. #2035C2×C47semidirect
363. #1969C2×C47semidirect
364. #1941C2×C47semidirect
365. #1873C2×C47semidirect
366. #1872C2×C47semidirect
367. #1809C2×C47semidirect
424. C47#24793direct (N × H)
487. #106D4×C47semidirect

Maximal subgroups

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

subgroupindex
C2×C47×#4702
C2×C47×#4362
C2×C47×#4282
C47×#24172
C47×#24152
C47×#20682
C47×#20662
C47×#20362
C47×#20352
C47×#19692
C47×#19412
C47×#18732
C47×#18722
C47×#18092
#2479347