Finite Group Databasebeta

← #26218279

Subgroups — #26218279

Order 12032.

1732 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256717C211yesmaximal, characteristic
2#20256589C211yesmaximal, characteristic, complemented
3C2×#15689140C211yesmaximal, characteristic, complemented
4C2×#15689105C211yesmaximal, characteristic, complemented
5#20243922C214yesmaximal, complemented
6#20243917C214yesmaximal, complemented
7C2×#15688880C211yesmaximal, characteristic, complemented
8C2×#15688879C211yesmaximal, characteristic, complemented
9C2×C47×#421C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689701—22no—
13#15689697C412yescomplemented
14#15689694C2212yes—
15#15689690C412yescomplemented
16#15689687C2212yes—
17#15689682—22no—
18#15689669C414yescomplemented
19#15689634—22no—
20#15689630—22no—
21#15689604—22no—
22#15689603—22no—
23#15689600C2212yescomplemented
24#15689597C2212yescomplemented
25#15689596—22no—
26C4×#10625350—22no—
27#15689591—22no—
28C2×#13093983C2211yescharacteristic
29C2×#13093983C2211yescharacteristic
30#117×D47—22no—
31#15689140—22no—
32#15689140C2214yes—
33C2×#13093951—22no—
34#15689105—22no—
35#15689105—22no—
36C2×#13093942C2212yescomplemented
37C2×#13093940C2212yescomplemented
38#15688880C2214yescomplemented
39#15688879C2214yescomplemented
40C22×#41×C47C2211yescharacteristic
41C22×M16×C47C2211yescharacteristic
42C2×#117×C47C2211yescharacteristic
43C47×#421—22no—
44C47×#421C2214yes—
45C2×#104×C47—22no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350—21no—
54C2×#10625350C2×C412yes—
55C2×#10625350C2×C412yes—
56C2×#10625350D412yes—
57C2×#10625350D412yes—
58C22×Dic94C2311yescharacteristic
59C22×D188C2311yescharacteristic
60C22×C22⋊D47D412yes—
61C22×C4×D47D412yes—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329C2312yes—
68C22×C47⋊C8—21no—
69#13094022C2×C414yescomplemented
70#13094020C2×C414yescomplemented
71#13094013C2×C414yescomplemented
72#13094011C2×C414yescomplemented
73#13094007—24no—
74#13094005—24no—
75#13094003—24no—
76#13094000—24no—
77#13093998—24no—
78#13093996—28no—
79#13093995—24no—
80#13093993—24no—
81#13093992—24no—
82C4×Dic94—24no—
83#13093989—24no—
84C4×D188—24no—
85#13093986—24no—
86C4×C22⋊D47—28no—
87C4×C22⋊D47—28no—
88(C22⋊D47)⋊C4—28no—
89#13093983—21no—
90#13093983—21no—
91#13093983—21no—
92#13093983—21no—
93#13093983C2×C412yescomplemented
94#13093983D412yescomplemented
95#13093983C2312yes—
96#13093983C2312yes—
97#13093982—24no—
98#13093981—24no—
99#13093980—24no—
100C2×C4⋊Dic47—21no—
101C2×C4⋊Dic47—21no—
102C4⋊C4×D47—24no—
103C2×C22⋊Dic47—21no—
104C2×C22⋊Dic47—21no—
105C22⋊C4×D47—24no—
106C2×C4×Dic47C2×C412yescomplemented
107C2×C4×Dic47D412yescomplemented
108C42×D47—24no—
109#13093951—28no—
110#13093942—24no—
111#13093940—24no—
112C2×#41×C47—21no—
113C2×#41×C47—21no—
114C2×#41×C47—21no—
115C2×#41×C47—21no—
116C2×#41×C47—21no—
117C2×#41×C47—21no—
118C2×#41×C47—21no—
119C2×#41×C47—21no—
120C2×#41×C47—21no—
121C2×#41×C47—21no—
122C2×#41×C47C2×C412yescomplemented
123C2×#41×C47C2312yes—
124C22×Q8×C47C2×C411yescharacteristic, complemented
125C22×D4×C47—21no—
126C22×D4×C47C2×C411yescharacteristic, complemented
127C23×C4×C47—21no—
128C23×C4×C47C2311yescharacteristic
129C2×M16×C47—21no—
130C2×M16×C47—21no—
131C2×M16×C47—21no—
132C2×M16×C47—21no—
133C2×M16×C47—21no—
134C2×M16×C47C2312yes—
135C22×C8×C47—21no—
136#117×C47—21no—
137#117×C47—21no—
138#117×C47D412yescomplemented
139#117×C47C2312yes—
140C2×C4⋊C4×C47—21no—
141C2×C22⋊C4×C47—21no—
142C2×C42×C47D412yescomplemented
143#104×C47—28no—
144C24×C47—21no—
145C24×C47C2×D411yescharacteristic
146C23×D47C2×D412yes—
147#41×C47—22no—
148#41×C47—22no—
149#41×C47—22no—
150#41×C47—22no—
151#41×C47—22no—
152#41×C47—22no—
153#41×C47—22no—
154#41×C47—22no—
155#41×C47—41no—
156#41×C47—41no—
157#41×C47—41no—
158#41×C47—41no—
159#41×C47—41no—
160#41×C47—41no—
161#41×C47—41no—
162#41×C47—41no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×Q8×C47C22×C412yes—
169C2×D4×C47—22no—
170C2×D4×C47—22no—
171C2×D4×C47—21no—
172C2×D4×C47—21no—
173C2×D4×C47—21no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—41no—
177C2×D4×C47—41no—
178C2×D4×C47—41no—
179C2×D4×C47—41no—
180C2×D4×C47C22×C412yes—
181C22×C4×C47—21no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—41no—
186C22×C4×C47—41no—
187C22×C4×C47—41no—
188C22×C4×C47—41no—
189C22×C4×C47C22×C411yescharacteristic
190C22×C4×C47C22×C411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D411yescharacteristic
197C22×C4×C47C2×D411yescharacteristic
198C22×C4×C47#4111yescharacteristic
199C22×C4×C47#4111yescharacteristic
200C22×C4×C47#4111yescharacteristic
201C22×C4×C47#4111yescharacteristic
202C22×C4×C47C2411yescharacteristic
203C2×C22⋊D47—22no—
204C2×C22⋊D47—22no—
205C2×C22⋊D47—22no—
206C2×C22⋊D47—22no—
207C2×C22⋊D47—28no—
208C2×C22⋊D47C22⋊C414yes—
209C2×C22⋊D47C22⋊C414yes—
210C22×Dic47—22no—
211C22×Dic47—22no—
212C22×Dic47C2×D412yes—
213#10625350—22no—
214#10625350—22no—
215#10625350—22no—
216#10625350—22no—
217#10625350—22no—
218#10625350—22no—
219#10625350—22no—
220#10625350—22no—
221#10625350—22no—
222#10625350—22no—
223#10625350—22no—
224#10625350—22no—
225#10625350—22no—
226#10625350—22no—
227#10625350—22no—
228#10625350—22no—
229C2×D188—21no—
230C2×D188—21no—
231C2×D188—21no—
232C2×D188—21no—
233C2×D188C22×C412yes—
234C2×D188C2×D412yes—
235C2×C4×D47—22no—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—22no—
239C2×C4×D47—28no—
240C2×C4×D47C22⋊C414yes—
241C2×C4×D47C22⋊C414yes—
242C2×Dic94—21no—
243C2×Dic94—21no—
244C2×Dic94—21no—
245C2×Dic94—21no—
246C2×Dic94C22×C412yes—
247C2×Dic94C2×D412yes—
248M16×C47—22no—
249M16×C47—22no—
250M16×C47—41no—
251M16×C47—41no—
252C2×C8×C47—22no—
253C2×C8×C47—41no—
254C2×C8×C47—41no—
255C4⋊C4×C47—22no—
256C4⋊C4×C47—22no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—22no—
259C42×C47—22no—
260C42×C47C2×D414yes—
261C22⋊Dic47—22no—
262C22⋊Dic47—22no—
263C22⋊Dic47—22no—
264C22⋊Dic47—22no—
265C22⋊Dic47—28no—
266(C2×D47)⋊C4—28no—
267(C2×D47)⋊C4—28no—
268C4⋊Dic47—22no—
269C4⋊Dic47—22no—
270C4⋊Dic47—22no—
271C4⋊Dic47—22no—
272Dic47⋊C4—28no—
273Dic47⋊C4—28no—
274C4×Dic47—28no—
275C4×Dic47—22no—
276C4×Dic47—22no—
277C4×Dic47C22×C414yes—
278C4×Dic47C2×D414yes—
279#10625329—22no—
280#10625329—22no—
281#10625329—41no—
282#10625329—41no—
283C2×C47⋊C8—22no—
284C2×C47⋊C8—41no—
285C2×C47⋊C8—41no—
286C23×C47—22no—
287C23×C47—41no—
288C23×C47—41no—
289C23×C47—81no—
290C23×C47—82no—
291C23×C47C2×C22⋊C411yescharacteristic
292C23×C47C2×C22⋊C411yescharacteristic
293C23×C47#12011yescharacteristic
294C23×C47#12011yescharacteristic
295C23×C47#12311yescharacteristic
296C23×C47#12311yescharacteristic
297C23×C47C22×D411yescharacteristic
298C22×D47—22no—
299C22×D47—22no—
300C22×D47—82no—
301C22×D47C2×C22⋊C414yes—
302Q8×C47—22no—
303Q8×C47—22no—
304Q8×C47—41no—
305Q8×C47—41no—
306D4×C47—22no—
307D4×C47—22no—
308D4×C47—42no—
309D4×C47—42no—
310D4×C47—42no—
311D4×C47—42no—
312D4×C47—41no—
313D4×C47—41no—
314C2×C4×C47—22no—
315C2×C4×C47—24no—
316C2×C4×C47—41no—
317C2×C4×C47—41no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—42no—
322C2×C4×C47—82no—
323C2×C4×C47C2×C22⋊C411yescharacteristic
324C2×C4×C47C2×C22⋊C411yescharacteristic
325C2×C4×C47C4×D411yescharacteristic
326C2×C4×C47C4×D411yescharacteristic
327C2×C4×C47C4×D411yescharacteristic
328C2×C4×C47C4×D411yescharacteristic
329C2×C4×C47C4×D411yescharacteristic
330C2×C4×C47C4×D411yescharacteristic
331C2×C4×C47C4×D411yescharacteristic
332C2×C4×C47C4×D411yescharacteristic
333C2×C4×C47#12011yescharacteristic
334C2×C4×C47#12011yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47#12111yescharacteristic
338C2×C4×C47#12111yescharacteristic
339C2×C4×C47#12111yescharacteristic
340C2×C4×C47#12111yescharacteristic
341C2×C4×C47#12111yescharacteristic
342C2×C4×C47#12111yescharacteristic
343C2×C4×C47#12311yescharacteristic
344C2×C4×C47#12311yescharacteristic
345C2×C4×C47C23×C411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C22×D411yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C2×C4×C47C2×#4111yescharacteristic
351C22⋊D47—24no—
352C22⋊D47—24no—
353C22⋊D47—24no—
354C22⋊D47—24no—
355C22⋊D47—88no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—24no—
359C2×Dic47—24no—
360C2×Dic47—82no—
361C2×Dic47—82no—
362C2×Dic47C2×C22⋊C414yes—
363D188—22no—
364D188—22no—
365D188—22no—
366D188—22no—
367C4×D47—24no—
368C4×D47—24no—
369C4×D47—24no—
370C4×D47—24no—
371C4×D47—88no—
372Dic94—22no—
373Dic94—22no—
374Dic94—22no—
375Dic94—22no—
376C8×C47—42no—
377C47⋊C8—42no—
378#21012—471nomaximal, Sylow
379C22×C47—41no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47—41no—
383C22×C47—41no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—44no—
387C22×C47—42no—
388C22×C47—82no—
389C22×C47—82no—
390C22×C47#38611yescharacteristic
391C22×C47#38611yescharacteristic
392C22×C47#38611yescharacteristic
393C22×C47#38611yescharacteristic
394C22×C47C22×C22⋊C411yescharacteristic
395C22×C47C2×#12011yescharacteristic
396C22×C47C2×#12311yescharacteristic
397C2×D47—24no—
398C2×D47—44no—
399C2×D47—44no—
400C2×D47—82no—
401C4×C47—44no—
402C4×C47—42no—
403C4×C47#38611yescharacteristic
404C4×C47#38611yescharacteristic
405C4×C47#38611yescharacteristic
406C4×C47#38611yescharacteristic
407C4×C47C2×C4×D411yescharacteristic
408C4×C47C2×C4×D411yescharacteristic
409C4×C47C2×#12111yescharacteristic
410C4×C47C2×#12111yescharacteristic
411Dic47—24no—
412Dic47—44no—
413Dic47—44no—
414#3449—471no—
415#3428—471no—
416C2×#421—471no—
417C2×#421D4711yescharacteristic, complemented
418C2×#413—471no—
419#1912—474no—
420#1911—474no—
421C2×H(3,ℤ/4)—471no—
422C2×H(3,ℤ/4)—471no—
423C2×C47—21no—
424C2×C47—21no—
425C2×C47—21no—
426C2×C47—21no—
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—21no—
430C2×C47—82no—
431C2×C47C2×#38611yescharacteristic
432D47—44no—
433C22×#41—471no—
434C22×#41C2×D4711yescharacteristic
435C22×M16—471no—
436C22×M16C2×D4711yescharacteristic
437#537—942no—
438#536—472no—
439#536—472no—
440#535—472no—
441#535—472no—
442#534—942no—
443#532—474no—
444#525—942no—
445#525—942no—
446#520—942no—
447#520—942no—
448#519—472no—
449#518—472no—
450#518—942no—
451C4×#41—942no—
452C4×#41—942no—
453C2×#117—471no—
454C2×#117—471no—
455C2×#117—942no—
456C2×#117C2×D4711yescharacteristic
457#421—22no—
458#421—474no—
459#421—942no—
460#421C2×D4714yes—
461C2×#104—22no—
462C2×#104—942no—
463#413—942no—
464#413—942no—
465C2×#101—472no—
466C2×#100—472no—
467H(3,ℤ/4)—474no—
468H(3,ℤ/4)—474no—
469C47#2101211yescharacteristic, complemented, Sylow
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—472no—
481C2×#41—472no—
482C2×#41—472no—
483C2×#41—472no—
484C2×#41—941no—
485C2×#41—941no—
486C2×#41—941no—
487C2×#41—941no—
488C2×#41—941no—
489C2×#41—941no—
490C2×#41—941no—
491C2×#41—941no—
492C2×#41C4×D4712yescomplemented
493C2×#41C22×D4712yes—
494C22×Q8—471no—
495C22×Q8C4×D4711yescharacteristic, complemented
496C22×D4—21no—
497C22×D4—472no—
498C22×D4—471no—
499C22×D4C4×D4711yescharacteristic, complemented
500C23×C4—21no—
501C23×C4—472no—
502C23×C4C22×D4711yescharacteristic
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—472no—
509C2×M16—941no—
510C2×M16—941no—
511C2×M16—941no—
512C2×M16—941no—
513C2×M16—941no—
514C2×M16C22×D4712yes—
515C22×C8—21no—
516C22×C8—941no—
517C4⋊Q8—474no—
518#127—474no—
519#124—474no—
520#124—474no—
521#123—944no—
522#123—944no—
523C22⋊Q8—944no—
524C22⋊Q8—944no—
525#121—944no—
526#121—944no—
527#121—948no—
528#120—944no—
529#120—944no—
530C4×Q8—944no—
531C4×Q8—944no—
532C4×D4—944no—
533C4×D4—948no—
534C4×D4—948no—
535C4×D4—948no—
536C4×D4—944no—
537#117—21no—
538#117—21no—
539#117—472no—
540#117—472no—
541#117—472no—
542#117—472no—
543#117—944no—
544#117—944no—
545#117—944no—
546#117—941no—
547#117—941no—
548#117—941no—
549#117—941no—
550#117C22⋊D4712yescomplemented
551#117C22×D4712yes—
552C2×C4⋊C4—21no—
553C2×C4⋊C4—944no—
554C2×C4⋊C4—941no—
555C2×C4⋊C4—941no—
556C2×C22⋊C4—21no—
557C2×C22⋊C4—944no—
558C2×C22⋊C4—941no—
559C2×C22⋊C4—941no—
560C2×C42—472no—
561C2×C42—472no—
562C2×C42—944no—
563C2×C42C22⋊D4712yescomplemented
564#104—28no—
565#104—948no—
566#101—944no—
567#100—944no—
568C24—21no—
569C24—472no—
570C24D4×D4711yescharacteristic
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—22no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—41no—
587#41—942no—
588#41—942no—
589#41—942no—
590#41—942no—
591#41—942no—
592#41—942no—
593#41—942no—
594#41—942no—
595#41—942no—
596#41—942no—
597#41—942no—
598#41—942no—
599#41—942no—
600#41—942no—
601#41—942no—
602#41—942no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—21no—
608C2×Q8—472no—
609C2×Q8—472no—
610C2×Q8—941no—
611C2×Q8—941no—
612C2×Q8—941no—
613C2×Q8—941no—
614C2×Q8C2×C4×D4712yes—
615C2×D4—22no—
616C2×D4—22no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—21no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—474no—
627C2×D4—474no—
628C2×D4—472no—
629C2×D4—472no—
630C2×D4—942no—
631C2×D4—942no—
632C2×D4—942no—
633C2×D4—942no—
634C2×D4—948no—
635C2×D4—941no—
636C2×D4—941no—
637C2×D4—941no—
638C2×D4—941no—
639C2×D4C2×C4×D4712yes—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—472no—
649C22×C4—474no—
650C22×C4—474no—
651C22×C4—948no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—942no—
657C22×C4—942no—
658C22×C4C2×C4×D4711yescharacteristic
659C22×C4C2×C4×D4711yescharacteristic
660C22×C4#1062535011yescharacteristic
661C22×C4#1062535011yescharacteristic
662C22×C4D4×D4711yescharacteristic
663C22×C4D4×D4711yescharacteristic
664C22×C4D4×D4711yescharacteristic
665C22×C4D4×D4711yescharacteristic
666C22×C4D4×D4711yescharacteristic
667C22×C4#1062535211yescharacteristic
668C22×C4#1062535211yescharacteristic
669C22×C4C2×C22⋊D4711yescharacteristic
670C22×C4C2×C22⋊D4711yescharacteristic
671C22×C4C23×D4711yescharacteristic
672M16—22no—
673M16—22no—
674M16—41no—
675M16—41no—
676M16—942no—
677M16—942no—
678M16—1881no—
679M16—1881no—
680C2×C8—22no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—942no—
684C2×C8—1881no—
685C2×C8—1881no—
686C4⋊C4—22no—
687C4⋊C4—22no—
688C4⋊C4—948no—
689C4⋊C4—948no—
690C4⋊C4—942no—
691C4⋊C4—942no—
692C4⋊C4—942no—
693C4⋊C4—942no—
694C22⋊C4—22no—
695C22⋊C4—22no—
696C22⋊C4—948no—
697C22⋊C4—948no—
698C22⋊C4—948no—
699C22⋊C4—942no—
700C22⋊C4—942no—
701C22⋊C4—942no—
702C22⋊C4—942no—
703C42—22no—
704C42—474no—
705C42—474no—
706C42—948no—
707C42—942no—
708C42—942no—
709C42C2×C22⋊D4714yes—
710C23—22no—
711C23—41no—
712C23—41no—
713C23—81no—
714C23—82no—
715C23—474no—
716C23—942no—
717C23—942no—
718C23—3762no—
719C23C22⋊C4×D4711yescharacteristic
720C23C22⋊C4×D4711yescharacteristic
721C23#1309399211yescharacteristic
722C23#1309399211yescharacteristic
723C23#1309400611yescharacteristic
724C23#1309400611yescharacteristic
725C23C2×D4×D4711yescharacteristic
726Q8—22no—
727Q8—22no—
728Q8—41no—
729Q8—41no—
730Q8—942no—
731Q8—942no—
732Q8—942no—
733Q8—942no—
734D4—22no—
735D4—22no—
736D4—42no—
737D4—42no—
738D4—42no—
739D4—42no—
740D4—41no—
741D4—41no—
742D4—944no—
743D4—944no—
744D4—944no—
745D4—944no—
746D4—942no—
747D4—942no—
748D4—942no—
749D4—942no—
750D4—3768no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—41no—
754C2×C4—41no—
755C2×C4—42no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—82no—
760C2×C4—474no—
761C2×C4—942no—
762C2×C4—942no—
763C2×C4—944no—
764C2×C4—944no—
765C2×C4—944no—
766C2×C4—944no—
767C2×C4—944no—
768C2×C4—944no—
769C2×C4—3768no—
770C2×C4—3762no—
771C2×C4—3762no—
772C2×C4C22⋊C4×D4711yescharacteristic
773C2×C4C22⋊C4×D4711yescharacteristic
774C2×C4(C22⋊D47)⋊C411yescharacteristic
775C2×C4(C22⋊D47)⋊C411yescharacteristic
776C2×C4(C22⋊D47)⋊C411yescharacteristic
777C2×C4(C22⋊D47)⋊C411yescharacteristic
778C2×C4C4×C22⋊D4711yescharacteristic
779C2×C4C4×C22⋊D4711yescharacteristic
780C2×C4C4×C22⋊D4711yescharacteristic
781C2×C4C4×C22⋊D4711yescharacteristic
782C2×C4#1309399211yescharacteristic
783C2×C4#1309399211yescharacteristic
784C2×C4#1309399511yescharacteristic
785C2×C4#1309399511yescharacteristic
786C2×C4#1309399511yescharacteristic
787C2×C4#1309399511yescharacteristic
788C2×C4#1309399711yescharacteristic
789C2×C4#1309399711yescharacteristic
790C2×C4#1309399711yescharacteristic
791C2×C4#1309399711yescharacteristic
792C2×C4#1309400611yescharacteristic
793C2×C4#1309400611yescharacteristic
794C2×C4C22×C4×D4711yescharacteristic
795C2×C4C2×D4×D4711yescharacteristic
796C2×C4C2×D4×D4711yescharacteristic
797C2×C4C22×C22⋊D4711yescharacteristic
798C2×C4C2×#1062535211yescharacteristic
799C2×C4C2×#1062535011yescharacteristic
800C8—42no—
801C8—1882no—
802C22—41no—
803C22—41no—
804C22—41no—
805C22—41no—
806C22—41no—
807C22—41no—
808C22—41no—
809C22—44no—
810C22—42no—
811C22—82no—
812C22—82no—
813C22—944no—
814C22—3762no—
815C22—1884no—
816C22—1884no—
817C22#1568899911yescharacteristic
818C22#1568899911yescharacteristic
819C22#1568899911yescharacteristic
820C22#1568899911yescharacteristic
821C22C2×C22⋊C4×D4711yescharacteristic
822C22C2×#1309399211yescharacteristic
823C22C2×#1309400611yescharacteristic
824C4—44no—
825C4—42no—
826C4—944no—
827C4—1884no—
828C4—1884no—
829C4#1568899911yescharacteristic
830C4#1568899911yescharacteristic
831C4#1568899911yescharacteristic
832C4#1568899911yescharacteristic
833C4C2×(C22⋊D47)⋊C411yescharacteristic
834C4C2×C4×C22⋊D4711yescharacteristic
835C4C2×#1309399511yescharacteristic
836C4C2×#1309399711yescharacteristic
837C2—21no—
838C2—21no—
839C2—21no—
840C2—21no—
841C2—21no—
842C2—21no—
843C2—21no—
844C2—82no—
845C2—1884no—
846C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4#15688999
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC2×C47C2×#386
prime radical#20256717C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47#21012
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. #20256589C2semidirect
3. C2×#15689140C2semidirect
4. C2×#15689105C2semidirect
5. #20243922C2semidirect
6. #20243917C2semidirect
7. C2×#15688880C2semidirect
8. C2×#15688879C2semidirect
9. C2×C47×#421C2semidirect
13. #15689697C4semidirect
15. #15689690C4semidirect
18. #15689669C4semidirect
23. #15689600C22semidirect
24. #15689597C22semidirect
36. C2×#13093942C22semidirect
37. C2×#13093940C22semidirect
38. #15688880C22semidirect
39. #15688879C22semidirect
69. #13094022C2×C4semidirect
70. #13094020C2×C4semidirect
71. #13094013C2×C4semidirect
72. #13094011C2×C4semidirect
93. #13093983C2×C4semidirect
94. #13093983D4semidirect
106. C2×C4×Dic47C2×C4semidirect
107. C2×C4×Dic47D4semidirect
122. C2×#41×C47C2×C4semidirect
124. C22×Q8×C47C2×C4semidirect
126. C22×D4×C47C2×C4semidirect
138. #117×C47D4semidirect
142. C2×C42×C47D4semidirect
417. C2×#421D47semidirect
469. C47#21012semidirect
492. C2×#41C4×D47semidirect
495. C22×Q8C4×D47semidirect
499. C22×D4C4×D47semidirect
550. #117C22⋊D47semidirect
563. C2×C42C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
#202567172
#202565892
C2×#156891402
C2×#156891052
#202439222
#202439172
C2×#156888802
C2×#156888792
C2×C47×#4212
#2101247