Finite Group Databasebeta

← C47×#61634 #26101332

Subgroups — C47×#61634 #26101332

Order 12032.

2018 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C47×#3538C211yesmaximal, characteristic, complemented
2C47×#3486C211yesmaximal, characteristic
3C47×#3312C214yesmaximal, complemented
4C47×#3300C214yesmaximal, complemented
5D4×Q16×C47C214yesmaximal, complemented
6C47×#3270C214yesmaximal, complemented
7C47×#3223C212yesmaximal, complemented
8C47×#3202C212yesmaximal, complemented
9C47×#3190C212yesmaximal, complemented
10C47×#3127C212yesmaximal, complemented
11C47×#3011C212yesmaximal, complemented
12C2×C47×#451C212yesmaximal, complemented
13C47×#2977C211yesmaximal, characteristic, complemented
14C2×2−1+4×C47C2211yescharacteristic
15C23×Q8×C47C2211yescharacteristic
16C2×#137×C47C2212yescomplemented
17C22×Q16×C47C2214yes—
18C22×Q16×C47C2212yescomplemented
19C47×#563—22no—
20C47×#552C2214yes—
21C47×#551—22no—
22D4×Q8×C47—22no—
23D4×Q8×C47C2214yes—
24D4×Q8×C47C2214yes—
25C47×#548—22no—
26C47×#548C2214yes—
27C47×#544—22no—
28C47×#541C2212yes—
29C47×#539—22no—
30C47×#536—22no—
31C47×#536C2211yescharacteristic
32C47×#536C2211yescharacteristic
33C47×#536C2212yes—
34C47×#525—22no—
35C47×#525C2211yescharacteristic
36C47×#525C2211yescharacteristic
37C2×C22⋊Q8×C47C2212yes—
38C47×#519C2211yescharacteristic
39C47×#497C2212yescomplemented
40C47×#494C2212yescomplemented
41C47×#491C2212yescomplemented
42C47×#488C2212yescomplemented
43C47×#485C2214yes—
44C47×#485C2214yescomplemented
45C47×#483C2212yes—
46C47×#480C2212yes—
47C47×#479C2214yescomplemented
48C47×#470C2214yescomplemented
49C47×#467C2214yes—
50C47×#467C2214yescomplemented
51C47×#465C2214yes—
52C47×#464C2214yescomplemented
53C47×#462C2214yescomplemented
54C47×#462C2214yescomplemented
55C47×#452C2214yes—
56C47×#452C2214yescomplemented
57C47×#451C2212yes—
58C47×#451C2214yes—
59C47×#451C2214yes—
60C47×#451C2214yes—
61C47×#451C2214yes—
62C47×#451C2214yescomplemented
63C47×#451C2214yescomplemented
64C47×#448C2212yes—
65C47×#441C2214yescomplemented
66C4×Q16×C47C2214yescomplemented
67C47×#435C2214yes—
68C8×D4×C47C2214yes—
69C47×#433C2212yes—
70C47×#419C2212yescomplemented
71C47×#416C2212yescomplemented
72C2×#103×C47C2214yes—
73C47×#408C2212yes—
74C2×C22⋊C8×C47C2212yes—
752−1+4×C47—44no—
76C2×#41×C47—22no—
77C2×#41×C47—21no—
78C2×#41×C47C2312yes—
79C2×#41×C47C2311yescharacteristic
80C2×#41×C47C2311yescharacteristic
81C22×Q8×C47—21no—
82C22×Q8×C47—21no—
83C22×Q8×C47—22no—
84C22×Q8×C47—44no—
85C22×Q8×C47C2311yescharacteristic
86C22×Q8×C47C2314yes—
87C22×Q8×C47C2312yes—
88C22×Q8×C47C2311yescharacteristic
89C22×Q8×C47C2312yes—
90C22×Q8×C47C2312yes—
91C23×C4×C47—21no—
92C23×C4×C47C2311yescharacteristic
93#137×C47—44no—
94C2×Q16×C47—48no—
95C2×Q16×C47—44no—
96C2×Q16×C47C2314yes—
97C2×Q16×C47C2314yes—
98C2×Q16×C47C2314yes—
99C2×Q16×C47C2314yes—
100C2×Q16×C47C2314yes—
101C2×SD16×C47C2314yes—
102C2×M16×C47C2312yes—
103C22×C8×C47C2314yes—
104C22×C8×C47C2312yes—
105C4⋊Q8×C47—22no—
106C4⋊Q8×C47—21no—
107C4⋊Q8×C47—24no—
108C4⋊Q8×C47—24no—
109C4⋊Q8×C47C2312yes—
110C4⋊Q8×C47C2312yes—
111#126×C47—24no—
112#126×C47—24no—
113#125×C47—24no—
114#125×C47—24no—
115#125×C47C2312yes—
116#124×C47—21no—
117#124×C47—22no—
118#124×C47—24no—
119#124×C47C2312yes—
120#123×C47—22no—
121#123×C47—22no—
122#123×C47—22no—
123#123×C47—24no—
124#123×C47—21no—
125#123×C47—22no—
126#123×C47D412yes—
127C22⋊Q8×C47—22no—
128C22⋊Q8×C47—22no—
129C22⋊Q8×C47—24no—
130C22⋊Q8×C47—22no—
131C22⋊Q8×C47—24no—
132C22⋊Q8×C47—24no—
133C22⋊Q8×C47—24no—
134C22⋊Q8×C47—24no—
135C22⋊Q8×C47D412yes—
136C22⋊Q8×C47C2314yes—
137C22⋊Q8×C47C2314yes—
138C22⋊Q8×C47C2312yes—
139C22⋊Q8×C47C2314yes—
140C22⋊Q8×C47C2314yes—
141#121×C47—24no—
142#121×C47D412yes—
143#121×C47C2312yes—
144#120×C47—21no—
145#120×C47D412yes—
146C4×Q8×C47—22no—
147C4×Q8×C47C2314yes—
148C4×Q8×C47C2314yes—
149C4×D4×C47—24no—
150C4×D4×C47—24no—
151C4×D4×C47—22no—
152C4×D4×C47—24no—
153C4×D4×C47C2314yes—
154#117×C47—22no—
155#117×C47—24no—
156#117×C47C2311yescharacteristic
157#117×C47C2312yes—
158#117×C47C2311yescharacteristic
159C2×C4⋊C4×C47—22no—
160C2×C4⋊C4×C47C2312yes—
161C2×C22⋊C4×C47—22no—
162#107×C47C2314yes—
163#106×C47C2314yes—
164C4⋊C8×C47C2314yes—
165#103×C47C2314yes—
166#103×C47C2314yes—
167#103×C47C2314yes—
168#103×C47C2314yes—
169#103×C47C2314yes—
170#103×C47C2314yes—
171#103×C47C2314yes—
172#102×C47C2314yes—
173C22⋊C8×C47C2312yes—
174C22⋊C8×C47C2314yes—
175C22⋊C8×C47C2312yes—
176C22⋊C8×C47C2314yes—
177#97×C47C2312yes—
178C4×C8×C47C2312yes—
179C24×C47C2×D411yescharacteristic
180#41×C47—24no—
181#41×C47—42no—
182#41×C47—42no—
183#41×C47—42no—
184#41×C47—48no—
185#41×C47—44no—
186C2×Q8×C47—24no—
187C2×Q8×C47—21no—
188C2×Q8×C47—24no—
189C2×Q8×C47—21no—
190C2×Q8×C47—22no—
191C2×Q8×C47—22no—
192C2×Q8×C47—22no—
193C2×Q8×C47—28no—
194C2×Q8×C47—24no—
195C2×Q8×C47—44no—
196C2×Q8×C47—42no—
197C2×Q8×C47—42no—
198C2×Q8×C47—44no—
199C2×Q8×C47—44no—
200C2×Q8×C47—42no—
201C2×Q8×C47—42no—
202C2×Q8×C47—48no—
203C2×Q8×C47—44no—
204C2×Q8×C47C2×D411yescharacteristic
205C2×Q8×C47C2412yes—
206C2×Q8×C47C2411yescharacteristic
207C2×Q8×C47C2414yes—
208C2×Q8×C47C2412yes—
209C2×D4×C47—22no—
210C2×D4×C47—21no—
211C2×D4×C47—22no—
212C2×D4×C47C2×D414yes—
213C2×D4×C47C2×D412yes—
214C2×D4×C47C2×D411yescharacteristic
215C2×D4×C47C2411yescharacteristic
216C22×C4×C47—21no—
217C22×C4×C47—22no—
218C22×C4×C47—24no—
219C22×C4×C47—22no—
220C22×C4×C47—21no—
221C22×C4×C47—22no—
222C22×C4×C47—22no—
223C22×C4×C47—22no—
224C22×C4×C47—21no—
225C22×C4×C47—42no—
226C22×C4×C47—44no—
227C22×C4×C47C2×D412yes—
228C22×C4×C47C2×D411yescharacteristic
229C22×C4×C47C2412yes—
230C22×C4×C47C2411yescharacteristic
231C22×C4×C47C2412yes—
232Q16×C47—28no—
233Q16×C47—28no—
234Q16×C47—44no—
235Q16×C47—44no—
236Q16×C47—44no—
237SD16×C47—44no—
238M16×C47—42no—
239C2×C8×C47—42no—
240C2×C8×C47—44no—
241C2×C8×C47C2414yes—
242C2×C8×C47C2414yes—
243C4⋊C4×C47—24no—
244C4⋊C4×C47—24no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—24no—
247C4⋊C4×C47—24no—
248C4⋊C4×C47—24no—
249C4⋊C4×C47—24no—
250C4⋊C4×C47—24no—
251C4⋊C4×C47—22no—
252C4⋊C4×C47—24no—
253C4⋊C4×C47—24no—
254C4⋊C4×C47C2×D412yes—
255C4⋊C4×C47C2×D414yes—
256C4⋊C4×C47C2414yes—
257C4⋊C4×C47C2412yes—
258C22⋊C4×C47—24no—
259C22⋊C4×C47—24no—
260C22⋊C4×C47—21no—
261C22⋊C4×C47—22no—
262C22⋊C4×C47—22no—
263C22⋊C4×C47—24no—
264C22⋊C4×C47—24no—
265C22⋊C4×C47—24no—
266C22⋊C4×C47—22no—
267C22⋊C4×C47C2×D412yes—
268C22⋊C4×C47C2×D414yes—
269C22⋊C4×C47C2×D414yes—
270C42×C47—22no—
271C42×C47—24no—
272C42×C47—24no—
273C42×C47—21no—
274C42×C47C2412yes—
275C23×C47—24no—
276C23×C47—21no—
277C23×C47—41no—
278C23×C47C22×D411yescharacteristic
279C23×C47C22×D412yes—
280C23×C47C22×D412yes—
281Q8×C47—24no—
282Q8×C47—22no—
283Q8×C47—24no—
284Q8×C47—24no—
285Q8×C47—24no—
286Q8×C47—22no—
287Q8×C47—41no—
288Q8×C47—48no—
289Q8×C47—44no—
290Q8×C47—42no—
291Q8×C47—82no—
292Q8×C47—82no—
293Q8×C47H(5,𝔽2)14yes—
294D4×C47—28no—
295D4×C47—22no—
296D4×C47—41no—
297D4×C47—42no—
298D4×C47—44no—
299D4×C47—42no—
300D4×C47—44no—
301C2×C4×C47—24no—
302C2×C4×C47—22no—
303C2×C4×C47—24no—
304C2×C4×C47—22no—
305C2×C4×C47—22no—
306C2×C4×C47—22no—
307C2×C4×C47—22no—
308C2×C4×C47—24no—
309C2×C4×C47—24no—
310C2×C4×C47—22no—
311C2×C4×C47—21no—
312C2×C4×C47—42no—
313C2×C4×C47—41no—
314C2×C4×C47—44no—
315C2×C4×C47—48no—
316C2×C4×C47—44no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—44no—
320C2×C4×C47—82no—
321C2×C4×C47—82no—
322C2×C4×C47C22×D414yes—
323C2×C4×C47C22×D412yes—
324C2×C4×C47C22×D411yescharacteristic
325C2×C4×C47C22×D412yes—
326C2×C4×C47C2511yescharacteristic
327C8×C47—24no—
328C8×C47—24no—
329#61634C4711yesmaximal, characteristic, direct product factor, Sylow
330C22×C47—22no—
331C22×C47—22no—
332C22×C47—21no—
333C22×C47—22no—
334C22×C47—24no—
335C22×C47—22no—
336C22×C47—44no—
337C22×C47—41no—
338C22×C47—42no—
339C22×C47#57814yes—
340C22×C47C23×D411yescharacteristic
341C4×C47—24no—
342C4×C47—21no—
343C4×C47—22no—
344C4×C47—22no—
345C4×C47—24no—
346C4×C47—41no—
347C4×C47—42no—
348C4×C47—44no—
349C4×C47—44no—
350C4×C47—42no—
351C4×C47C2×H(5,𝔽2)12yes—
352#3538C2×C4711yescharacteristic, complemented
353#3486C2×C4711yescharacteristic
354#3312C2×C4714yescomplemented
355#3300C2×C4714yescomplemented
356D4×Q16C2×C4714yescomplemented
357#3270C2×C4714yescomplemented
358#3223C2×C4712yescomplemented
359#3202C2×C4712yescomplemented
360#3190C2×C4712yescomplemented
361#3127C2×C4712yescomplemented
362#3011C2×C4712yescomplemented
363C2×#451C2×C4712yescomplemented
364#2977C2×C4711yescharacteristic, complemented
365C2×C47—24no—
366C2×C47—42no—
367C2×C47—41no—
368C2×C47—81no—
369C2×C47#348411yescharacteristic
370C2×C47C2×#57812yes—
371C2×2−1+4C22×C4711yescharacteristic
372C23×Q8C22×C4711yescharacteristic
373C2×#137C22×C4712yescomplemented
374C22×Q16C22×C4714yes—
375C22×Q16C22×C4712yescomplemented
376#563—22no—
377#552C22×C4714yes—
378#551—22no—
379D4×Q8—22no—
380D4×Q8C22×C4714yes—
381D4×Q8C22×C4714yes—
382#548—22no—
383#548C22×C4714yes—
384#544—22no—
385#541C22×C4712yes—
386#539—22no—
387#536—22no—
388#536C22×C4711yescharacteristic
389#536C22×C4711yescharacteristic
390#536C22×C4712yes—
391#525—22no—
392#525C22×C4711yescharacteristic
393#525C22×C4711yescharacteristic
394C2×C22⋊Q8C22×C4712yes—
395#519C22×C4711yescharacteristic
396#497C22×C4712yescomplemented
397#494C22×C4712yescomplemented
398#491C22×C4712yescomplemented
399#488C22×C4712yescomplemented
400#485C22×C4714yes—
401#485C22×C4714yescomplemented
402#483C22×C4712yes—
403#480C22×C4712yes—
404#479C22×C4714yescomplemented
405#470C22×C4714yescomplemented
406#467C22×C4714yes—
407#467C22×C4714yescomplemented
408#465C22×C4714yes—
409#464C22×C4714yescomplemented
410#462C22×C4714yescomplemented
411#462C22×C4714yescomplemented
412#452C22×C4714yes—
413#452C22×C4714yescomplemented
414#451C22×C4714yes—
415#451C22×C4712yes—
416#451C22×C4714yes—
417#451C22×C4714yes—
418#451C22×C4714yes—
419#451C22×C4714yescomplemented
420#451C22×C4714yescomplemented
421#448C22×C4712yes—
422#441C22×C4714yescomplemented
423C4×Q16C22×C4714yescomplemented
424#435C22×C4714yes—
425C8×D4C22×C4714yes—
426#433C22×C4712yes—
427#419C22×C4712yescomplemented
428#416C22×C4712yescomplemented
429C2×#103C22×C4714yes—
430#408C22×C4712yes—
431C2×C22⋊C8C22×C4712yes—
432C47#6163411yescharacteristic, direct product factor, Sylow
4332−1+4—44no—
434C2×#41—22no—
435C2×#41—21no—
436C2×#41C23×C4712yes—
437C2×#41C23×C4711yescharacteristic
438C2×#41C23×C4711yescharacteristic
439C22×Q8—21no—
440C22×Q8—21no—
441C22×Q8—22no—
442C22×Q8—44no—
443C22×Q8C23×C4711yescharacteristic
444C22×Q8C23×C4714yes—
445C22×Q8C23×C4712yes—
446C22×Q8C23×C4712yes—
447C22×Q8C23×C4711yescharacteristic
448C22×Q8C23×C4712yes—
449C23×C4—21no—
450C23×C4C23×C4711yescharacteristic
451#137—44no—
452C2×Q16—48no—
453C2×Q16—44no—
454C2×Q16C23×C4714yes—
455C2×Q16C23×C4714yes—
456C2×Q16C23×C4714yes—
457C2×Q16C23×C4714yes—
458C2×Q16C23×C4714yes—
459C2×SD16C23×C4714yes—
460C2×M16C23×C4712yes—
461C22×C8C23×C4714yes—
462C22×C8C23×C4712yes—
463C4⋊Q8—22no—
464C4⋊Q8—21no—
465C4⋊Q8—24no—
466C4⋊Q8—24no—
467C4⋊Q8C23×C4712yes—
468C4⋊Q8C23×C4712yes—
469#126—24no—
470#126—24no—
471#125—24no—
472#125—24no—
473#125C23×C4712yes—
474#124—21no—
475#124—22no—
476#124—24no—
477#124C23×C4712yes—
478#123—22no—
479#123—22no—
480#123—22no—
481#123—24no—
482#123—21no—
483#123—22no—
484#123D4×C4712yes—
485C22⋊Q8—22no—
486C22⋊Q8—22no—
487C22⋊Q8—24no—
488C22⋊Q8—22no—
489C22⋊Q8—24no—
490C22⋊Q8—24no—
491C22⋊Q8—24no—
492C22⋊Q8—24no—
493C22⋊Q8D4×C4712yes—
494C22⋊Q8C23×C4714yes—
495C22⋊Q8C23×C4714yes—
496C22⋊Q8C23×C4712yes—
497C22⋊Q8C23×C4714yes—
498C22⋊Q8C23×C4714yes—
499#121—24no—
500#121D4×C4712yes—
501#121C23×C4712yes—
502#120—21no—
503#120D4×C4712yes—
504C4×Q8—22no—
505C4×Q8C23×C4714yes—
506C4×Q8C23×C4714yes—
507C4×D4—24no—
508C4×D4—24no—
509C4×D4—22no—
510C4×D4—24no—
511C4×D4C23×C4714yes—
512#117—22no—
513#117—24no—
514#117C23×C4711yescharacteristic
515#117C23×C4712yes—
516#117C23×C4711yescharacteristic
517C2×C4⋊C4—22no—
518C2×C4⋊C4C23×C4712yes—
519C2×C22⋊C4—22no—
520#107C23×C4714yes—
521#106C23×C4714yes—
522C4⋊C8C23×C4714yes—
523#103C23×C4714yes—
524#103C23×C4714yes—
525#103C23×C4714yes—
526#103C23×C4714yes—
527#103C23×C4714yes—
528#103C23×C4714yes—
529#103C23×C4714yes—
530#102C23×C4714yes—
531C22⋊C8C23×C4714yes—
532C22⋊C8C23×C4712yes—
533C22⋊C8C23×C4712yes—
534C22⋊C8C23×C4714yes—
535#97C23×C4712yes—
536C4×C8C23×C4712yes—
537C24C2×D4×C4711yescharacteristic
538#41—24no—
539#41—42no—
540#41—42no—
541#41—42no—
542#41—48no—
543#41—44no—
544C2×Q8—24no—
545C2×Q8—21no—
546C2×Q8—24no—
547C2×Q8—21no—
548C2×Q8—22no—
549C2×Q8—22no—
550C2×Q8—22no—
551C2×Q8—28no—
552C2×Q8—24no—
553C2×Q8—44no—
554C2×Q8—42no—
555C2×Q8—42no—
556C2×Q8—44no—
557C2×Q8—44no—
558C2×Q8—42no—
559C2×Q8—42no—
560C2×Q8—48no—
561C2×Q8—44no—
562C2×Q8C2×D4×C4711yescharacteristic
563C2×Q8C24×C4712yes—
564C2×Q8C24×C4711yescharacteristic
565C2×Q8C24×C4714yes—
566C2×Q8C24×C4712yes—
567C2×D4—22no—
568C2×D4—21no—
569C2×D4—22no—
570C2×D4C2×D4×C4714yes—
571C2×D4C2×D4×C4712yes—
572C2×D4C2×D4×C4711yescharacteristic
573C2×D4C24×C4711yescharacteristic
574C22×C4—21no—
575C22×C4—22no—
576C22×C4—24no—
577C22×C4—22no—
578C22×C4—21no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—21no—
583C22×C4—42no—
584C22×C4—44no—
585C22×C4C2×D4×C4712yes—
586C22×C4C2×D4×C4711yescharacteristic
587C22×C4C24×C4711yescharacteristic
588C22×C4C24×C4712yes—
589C22×C4C24×C4712yes—
590Q16—28no—
591Q16—28no—
592Q16—44no—
593Q16—44no—
594Q16—44no—
595SD16—44no—
596M16—42no—
597C2×C8—42no—
598C2×C8—44no—
599C2×C8C24×C4714yes—
600C2×C8C24×C4714yes—
601C4⋊C4—24no—
602C4⋊C4—24no—
603C4⋊C4—22no—
604C4⋊C4—24no—
605C4⋊C4—24no—
606C4⋊C4—24no—
607C4⋊C4—24no—
608C4⋊C4—24no—
609C4⋊C4—22no—
610C4⋊C4—24no—
611C4⋊C4—24no—
612C4⋊C4C2×D4×C4712yes—
613C4⋊C4C2×D4×C4714yes—
614C4⋊C4C24×C4714yes—
615C4⋊C4C24×C4712yes—
616C22⋊C4—24no—
617C22⋊C4—24no—
618C22⋊C4—21no—
619C22⋊C4—22no—
620C22⋊C4—22no—
621C22⋊C4—24no—
622C22⋊C4—24no—
623C22⋊C4—24no—
624C22⋊C4—22no—
625C22⋊C4C2×D4×C4712yes—
626C22⋊C4C2×D4×C4714yes—
627C22⋊C4C2×D4×C4714yes—
628C42—22no—
629C42—24no—
630C42—24no—
631C42—21no—
632C42C24×C4712yes—
633C23—24no—
634C23—21no—
635C23—41no—
636C23C22×D4×C4711yescharacteristic
637C23C22×D4×C4712yes—
638C23C22×D4×C4712yes—
639Q8—24no—
640Q8—22no—
641Q8—24no—
642Q8—24no—
643Q8—24no—
644Q8—22no—
645Q8—41no—
646Q8—48no—
647Q8—44no—
648Q8—42no—
649Q8—82no—
650Q8—82no—
651Q8H(5,𝔽2)×C4714yes—
652D4—28no—
653D4—22no—
654D4—41no—
655D4—42no—
656D4—44no—
657D4—42no—
658D4—44no—
659C2×C4—24no—
660C2×C4—22no—
661C2×C4—24no—
662C2×C4—22no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—24no—
667C2×C4—24no—
668C2×C4—22no—
669C2×C4—21no—
670C2×C4—42no—
671C2×C4—41no—
672C2×C4—44no—
673C2×C4—48no—
674C2×C4—44no—
675C2×C4—42no—
676C2×C4—42no—
677C2×C4—44no—
678C2×C4—82no—
679C2×C4—82no—
680C2×C4C22×D4×C4714yes—
681C2×C4C22×D4×C4712yes—
682C2×C4C22×D4×C4711yescharacteristic
683C2×C4C22×D4×C4712yes—
684C2×C4C25×C4711yescharacteristic
685C8—24no—
686C8—24no—
687C22—22no—
688C22—22no—
689C22—24no—
690C22—22no—
691C22—21no—
692C22—22no—
693C22—44no—
694C22—42no—
695C22—41no—
696C22C47×#57814yes—
697C22C23×D4×C4711yescharacteristic
698C4—24no—
699C4—24no—
700C4—21no—
701C4—22no—
702C4—22no—
703C4—44no—
704C4—42no—
705C4—41no—
706C4—42no—
707C4—44no—
708C4C2×H(5,𝔽2)×C4712yes—
709C2—24no—
710C2—41no—
711C2—42no—
712C2—81no—
713C2C47×#348411yescharacteristic
714C2C2×C47×#57812yes—
subgroupG/H
center, socleC22×C47C23×D4
commutator, Frattini, cosocleC2×C4C25×C47
prime radicalC47×#3486C2
LCSG ▷ C2×C4 ▷ C2 ▷ C1
UCSC1 ◁ C22×C47 ◁ C47×#525 ◁ G

Complements

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

NH ≅ G/Ntype
1. C47×#3538C2semidirect
3. C47×#3312C2semidirect
4. C47×#3300C2semidirect
5. D4×Q16×C47C2semidirect
6. C47×#3270C2semidirect
7. C47×#3223C2semidirect
8. C47×#3202C2semidirect
9. C47×#3190C2semidirect
10. C47×#3127C2semidirect
11. C47×#3011C2semidirect
12. C2×C47×#451C2semidirect
13. C47×#2977C2semidirect
16. C2×#137×C47C22semidirect
18. C22×Q16×C47C22semidirect
39. C47×#497C22semidirect
40. C47×#494C22semidirect
41. C47×#491C22semidirect
42. C47×#488C22semidirect
44. C47×#485C22semidirect
47. C47×#479C22semidirect
48. C47×#470C22semidirect
50. C47×#467C22semidirect
52. C47×#464C22semidirect
53. C47×#462C22semidirect
54. C47×#462C22semidirect
56. C47×#452C22semidirect
62. C47×#451C22semidirect
63. C47×#451C22semidirect
65. C47×#441C22semidirect
66. C4×Q16×C47C22semidirect
70. C47×#419C22semidirect
71. C47×#416C22semidirect
329. #61634C47direct (N × H)
352. #3538C2×C47semidirect
354. #3312C2×C47semidirect
355. #3300C2×C47semidirect
356. D4×Q16C2×C47semidirect
357. #3270C2×C47semidirect
358. #3223C2×C47semidirect
359. #3202C2×C47semidirect
360. #3190C2×C47semidirect
361. #3127C2×C47semidirect
362. #3011C2×C47semidirect
363. C2×#451C2×C47semidirect
364. #2977C2×C47semidirect
373. C2×#137C22×C47semidirect
375. C22×Q16C22×C47semidirect
396. #497C22×C47semidirect
397. #494C22×C47semidirect
398. #491C22×C47semidirect
399. #488C22×C47semidirect
401. #485C22×C47semidirect
404. #479C22×C47semidirect
405. #470C22×C47semidirect
407. #467C22×C47semidirect
409. #464C22×C47semidirect
410. #462C22×C47semidirect
411. #462C22×C47semidirect
413. #452C22×C47semidirect
419. #451C22×C47semidirect
420. #451C22×C47semidirect
422. #441C22×C47semidirect
423. C4×Q16C22×C47semidirect
427. #419C22×C47semidirect
428. #416C22×C47semidirect
432. C47#61634direct (N × H)

Maximal subgroups

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

subgroupindex
C47×#35382
C47×#34862
C47×#33122
C47×#33002
D4×Q16×C472
C47×#32702
C47×#32232
C47×#32022
C47×#31902
C47×#31272
C47×#30112
C2×C47×#4512
C47×#29772
#6163447