Finite Group Databasebeta

← #26369023

Subgroups — #26369023

Order 12032.

1236 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20256717C211yesmaximal, characteristic
2C2×#15689097C211yesmaximal, characteristic, complemented
3#20245043C212yesmaximal, complemented
4#20245039C212yesmaximal, complemented
5#20245035C214yesmaximal, complemented
6#20245030C214yesmaximal, complemented
7C2×C47×#413C211yesmaximal, characteristic, complemented
8C22×#10625350C411yescharacteristic, complemented
9#15689701—21no—
10#15689701—21no—
11#15689697—21no—
12#15689694C411yescharacteristic, complemented
13#15689694C2211yescharacteristic
14#15689690—21no—
15#15689687C411yescharacteristic, complemented
16#15689687C2211yescharacteristic
17#15689682C412yescomplemented
18#15689682C2212yes—
19#15689669—21no—
20#15689669—21no—
21#15689634—21no—
22#15689634—21no—
23#15689630C412yescomplemented
24#15689630C2212yes—
25C2×#13093983—21no—
26C2×#13093983C411yescharacteristic, complemented
27#15689097—21no—
28#15689097—21no—
29#15689097C2212yes—
30#15689097C2212yes—
31C2×#13093939—21no—
32C2×#13093939C2212yes—
33#15688914C2218yescomplemented
34#15688911C2218yescomplemented
35C22×#41×C47C2211yescharacteristic
36C22×M16×C47—21no—
37C47×#413—21no—
38C47×#413—21no—
39C47×#413C2212yes—
40C47×#413C2212yes—
41C2×#101×C47—21no—
42C2×#100×C47C2212yes—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—41no—
48C2×#10625350—41no—
49C2×#10625350—41no—
50C2×#10625350—41no—
51C22×Dic94C2×C411yescharacteristic, complemented
52C22×D188C2×C411yescharacteristic, complemented
53C22×C22⋊D47C2×C412yes—
54C22×C4×D47C2×C412yescomplemented
55#13094022—21no—
56#13094022—21no—
57#13094020—21no—
58#13094020—21no—
59#13094013—21no—
60#13094013—21no—
61#13094011—21no—
62#13094011—21no—
63#13094007—22no—
64#13094007—22no—
65#13094005C2×C412yes—
66#13094005C2×C412yescomplemented
67#13094005C2×C412yescomplemented
68#13094005C2312yes—
69#13094003—21no—
70#13094003—21no—
71#13094003—21no—
72#13094003—21no—
73#13094000—22no—
74#13094000—22no—
75#13093998—21no—
76#13093998—21no—
77#13093998—21no—
78#13093998—21no—
79#13093996—22no—
80#13093996—22no—
81#13093996—22no—
82#13093996—22no—
83#13093995—22no—
84#13093995—22no—
85#13093993—22no—
86#13093993—22no—
87#13093992C2×C412yes—
88#13093992C2×C412yescomplemented
89#13093992C2×C412yescomplemented
90#13093992C2312yes—
91C4×C22⋊D47—22no—
92C4×C22⋊D47—22no—
93C4×C22⋊D47—22no—
94C4×C22⋊D47—22no—
95#13093983—21no—
96#13093983—21no—
97#13093983—22no—
98#13093983—22no—
99#13093983—41no—
100#13093983—41no—
101#13093983C2×C412yescomplemented
102#13093983C2×C411yescharacteristic, complemented
103#13093983C2×C411yescharacteristic, complemented
104C2×C4⋊Dic47—21no—
105C2×C4⋊Dic47—41no—
106C2×C22⋊Dic47—22no—
107C2×C22⋊Dic47C2×C412yes—
108C2×C4×Dic47—21no—
109C2×C4×Dic47—41no—
110#13093939—22no—
111#13093939—22no—
112#13093939—22no—
113#13093939C2314yes—
114C2×#41×C47—41no—
115C2×#41×C47—41no—
116C2×#41×C47—41no—
117C2×#41×C47—41no—
118C2×#41×C47C2×C411yescharacteristic
119C2×#41×C47C2×C411yescharacteristic
120C2×#41×C47D411yescharacteristic
121C2×#41×C47D411yescharacteristic
122C2×#41×C47D411yescharacteristic
123C2×#41×C47D411yescharacteristic
124C2×#41×C47C2311yescharacteristic
125C2×#41×C47C2311yescharacteristic
126C22×Q8×C47D411yescharacteristic
127C22×D4×C47C2×C411yescharacteristic
128C22×D4×C47D411yescharacteristic
129C22×D4×C47C2311yescharacteristic
130C23×C4×C47C2×C411yescharacteristic
131C23×C4×C47D411yescharacteristic
132C23×C4×C47D411yescharacteristic
133C2×M16×C47—22no—
134C2×M16×C47—22no—
135C2×M16×C47—22no—
136C2×M16×C47—41no—
137C2×M16×C47—41no—
138C2×M16×C47—41no—
139C22×C8×C47—41no—
140#101×C47—22no—
141#101×C47—22no—
142#100×C47—22no—
143#100×C47C2314yes—
144C24×C47C22⋊C411yescharacteristic
145C24×C47C22×C411yescharacteristic
146C24×C47C2×D411yescharacteristic
147C23×D47C22×C412yes—
148#41×C47—41no—
149#41×C47—41no—
150#41×C47—41no—
151#41×C47—41no—
152#41×C47—41no—
153#41×C47—41no—
154#41×C47—41no—
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—
163#41×C47—41no—
164C2×Q8×C47—41no—
165C2×Q8×C47—41no—
166C2×Q8×C47C22⋊C411yescharacteristic
167C2×Q8×C47C22⋊C411yescharacteristic
168C2×Q8×C47C2×D411yescharacteristic
169C2×Q8×C47C2×D411yescharacteristic
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47C22⋊C411yescharacteristic
177C2×D4×C47C22⋊C411yescharacteristic
178C2×D4×C47C22⋊C411yescharacteristic
179C2×D4×C47C22⋊C411yescharacteristic
180C2×D4×C47C22×C411yescharacteristic
181C2×D4×C47C22×C411yescharacteristic
182C2×D4×C47C22×C411yescharacteristic
183C2×D4×C47C2×D411yescharacteristic
184C2×D4×C47C2×D411yescharacteristic
185C2×D4×C47C2×D411yescharacteristic
186C2×D4×C47C2×D411yescharacteristic
187C2×D4×C47C2411yescharacteristic
188C22×C4×C47—21no—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—21no—
197C22×C4×C47—21no—
198C22×C4×C47—21no—
199C22×C4×C47—21no—
200C22×C4×C47C22⋊C411yescharacteristic
201C22×C4×C47C22⋊C411yescharacteristic
202C22×C4×C47C22⋊C411yescharacteristic
203C22×C4×C47C22⋊C411yescharacteristic
204C22×C4×C47C22⋊C411yescharacteristic
205C22×C4×C47C22⋊C411yescharacteristic
206C22×C4×C47C22⋊C411yescharacteristic
207C22×C4×C47C22⋊C411yescharacteristic
208C22×C4×C47C22⋊C411yescharacteristic
209C22×C4×C47C22×C411yescharacteristic
210C22×C4×C47C22×C411yescharacteristic
211C22×C4×C47C2×D411yescharacteristic
212C22×C4×C47C2×D411yescharacteristic
213C22×C4×C47C2×D411yescharacteristic
214C22×C4×C47C2×D411yescharacteristic
215C22×C4×C47C2×D411yescharacteristic
216C2×C22⋊D47—22no—
217C2×C22⋊D47—22no—
218C2×C22⋊D47—22no—
219C2×C22⋊D47—22no—
220C2×C22⋊D47—22no—
221C2×C22⋊D47—22no—
222C2×C22⋊D47—42no—
223C2×C22⋊D47—42no—
224C22×Dic47—22no—
225C22×Dic47—42no—
226C22×Dic47C22×C412yes—
227#10625350—42no—
228#10625350—42no—
229#10625350—42no—
230#10625350—42no—
231#10625350—42no—
232#10625350—42no—
233#10625350—41no—
234#10625350—41no—
235#10625350—41no—
236#10625350—41no—
237C2×D188—21no—
238C2×D188—21no—
239C2×D188—41no—
240C2×D188—41no—
241C2×C4×D47—22no—
242C2×C4×D47—22no—
243C2×C4×D47—42no—
244C2×C4×D47—42no—
245C2×Dic94—21no—
246C2×Dic94—21no—
247C2×Dic94—41no—
248C2×Dic94—41no—
249M16×C47—24no—
250M16×C47—42no—
251M16×C47—42no—
252M16×C47—42no—
253C2×C8×C47—42no—
254C2×C8×C47—42no—
255C2×C8×C47—42no—
256C22⋊Dic47—22no—
257C22⋊Dic47—22no—
258C22⋊Dic47—22no—
259C22⋊Dic47—22no—
260C22⋊Dic47—22no—
261C22⋊Dic47—24no—
262C22⋊Dic47—42no—
263C22⋊Dic47C22×C412yes—
264C22⋊Dic47C22×C412yes—
265(C2×D47)⋊C4—22no—
266(C2×D47)⋊C4—22no—
267(C2×D47)⋊C4—22no—
268(C2×D47)⋊C4—22no—
269C4⋊Dic47—22no—
270C4⋊Dic47—21no—
271C4⋊Dic47—21no—
272C4⋊Dic47—42no—
273C4⋊Dic47—42no—
274Dic47⋊C4—22no—
275Dic47⋊C4—22no—
276Dic47⋊C4—22no—
277Dic47⋊C4—22no—
278C4×Dic47—22no—
279C4×Dic47—21no—
280C4×Dic47—21no—
281C4×Dic47—42no—
282C4×Dic47—42no—
283C23×C47—21no—
284C23×C47—21no—
285C23×C47—21no—
286C23×C47—21no—
287C23×C47—21no—
288C23×C47—21no—
289C23×C47—81no—
290C23×C47—81no—
291C23×C47—81no—
292C23×C47C2×C22⋊C411yescharacteristic
293C23×C47C2×C22⋊C411yescharacteristic
294C23×C47C2×C22⋊C411yescharacteristic
295C23×C47C2×C22⋊C411yescharacteristic
296C23×C47C2×C22⋊C411yescharacteristic
297C23×C47C23×C411yescharacteristic
298C23×C47C22×D411yescharacteristic
299C22×D47—22no—
300C22×D47—42no—
301C22×D47—82no—
302Q8×C47—41no—
303Q8×C47—41no—
304Q8×C47—41no—
305Q8×C47—41no—
306D4×C47—41no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311D4×C47—41no—
312D4×C47—41no—
313D4×C47—41no—
314D4×C47—41no—
315D4×C47—41no—
316D4×C47—41no—
317D4×C47—41no—
318C2×C4×C47—21no—
319C2×C4×C47—21no—
320C2×C4×C47—21no—
321C2×C4×C47—21no—
322C2×C4×C47—21no—
323C2×C4×C47—21no—
324C2×C4×C47—21no—
325C2×C4×C47—21no—
326C2×C4×C47—21no—
327C2×C4×C47—21no—
328C2×C4×C47—21no—
329C2×C4×C47—21no—
330C2×C4×C47—21no—
331C2×C4×C47—21no—
332C2×C4×C47—21no—
333C2×C4×C47—21no—
334C2×C4×C47—21no—
335C2×C4×C47—21no—
336C2×C4×C47—21no—
337C2×C4×C47—21no—
338C2×C4×C47—21no—
339C2×C4×C47—21no—
340C2×C4×C47—21no—
341C2×C4×C47—21no—
342C2×C4×C47—21no—
343C2×C4×C47—21no—
344C2×C4×C47—21no—
345C2×C4×C47—21no—
346C2×C4×C47—21no—
347C2×C4×C47—21no—
348C2×C4×C47#9911yescharacteristic
349C2×C4×C47#9911yescharacteristic
350C2×C4×C47#9911yescharacteristic
351C2×C4×C47#9911yescharacteristic
352C2×C4×C47C2×C22⋊C411yescharacteristic
353C2×C4×C47C2×C22⋊C411yescharacteristic
354C2×C4×C47C2×C22⋊C411yescharacteristic
355C2×C4×C47C2×C22⋊C411yescharacteristic
356C2×C4×C47C2×C22⋊C411yescharacteristic
357C2×C4×C47C2×C22⋊C411yescharacteristic
358C2×C4×C47C2×C22⋊C411yescharacteristic
359C2×C4×C47C22×D411yescharacteristic
360C22⋊D47—44no—
361C22⋊D47—42no—
362C22⋊D47—42no—
363C22⋊D47—82no—
364C22⋊D47—82no—
365C22⋊D47—82no—
366C22⋊D47—82no—
367C2×Dic47—22no—
368C2×Dic47—22no—
369C2×Dic47—22no—
370C2×Dic47—42no—
371C2×Dic47—44no—
372C2×Dic47—82no—
373C2×Dic47—84no—
374D188—42no—
375D188—41no—
376D188—41no—
377C4×D47—44no—
378C4×D47—42no—
379C4×D47—42no—
380Dic94—42no—
381Dic94—41no—
382Dic94—41no—
383C8×C47—44no—
384#33347—471nomaximal, Sylow
385C22×C47—21no—
386C22×C47—21no—
387C22×C47—21no—
388C22×C47—21no—
389C22×C47—21no—
390C22×C47—21no—
391C22×C47—41no—
392C22×C47—41no—
393C22×C47—41no—
394C22×C47—41no—
395C22×C47—41no—
396C22×C47—41no—
397C22×C47—41no—
398C22×C47—42no—
399C22×C47—42no—
400C22×C47—81no—
401C22×C47—81no—
402C22×C47—81no—
403C22×C47—81no—
404C22×C47C2×#9911yescharacteristic
405C22×C47C2×#9911yescharacteristic
406C22×C47C22×C22⋊C411yescharacteristic
407C2×D47—42no—
408C2×D47—42no—
409C2×D47—42no—
410C2×D47—84no—
411C4×C47—21no—
412C4×C47—21no—
413C4×C47—21no—
414C4×C47—21no—
415C4×C47—21no—
416C4×C47—21no—
417C4×C47C2×#9911yescharacteristic
418C4×C47C2×#9911yescharacteristic
419C4×C47C2×#9911yescharacteristic
420C4×C47C2×#9911yescharacteristic
421Dic47—42no—
422Dic47—42no—
423Dic47—42no—
424Dic47—84no—
425#3449—471no—
426C2×#413D4711yescharacteristic, complemented
427C2×#410—471no—
428#2123—472no—
429#2122—472no—
430#2121—474no—
431#2120—474no—
432C2×C47—21no—
433C2×C47—21no—
434C2×C47—21no—
435C2×C47—41no—
436C2×C47—41no—
437C2×C47—41no—
438C2×C47—41no—
439C2×C47—41no—
440C2×C47—41no—
441C2×C47C22×#9911yescharacteristic
442D47—82no—
443C22×#41—471no—
444C22×#41C2×D4711yescharacteristic
445C22×M16—21no—
446#537—941no—
447#537—941no—
448#536—471no—
449#536—471no—
450#536—941no—
451#535—471no—
452#535—471no—
453#535—941no—
454#534—472no—
455#534—472no—
456#532—941no—
457#532—941no—
458#525—472no—
459#525—472no—
460#525—941no—
461#525—941no—
462C2×#117—471no—
463C2×#117—941no—
464#413—21no—
465#413—21no—
466#413C2×D4712yes—
467#413C2×D4712yes—
468C2×#101—21no—
469C2×#100C2×D4712yes—
470#410—472no—
471#410—472no—
472#410—941no—
473#410—941no—
474C2×#99—472no—
475C2×#99—941no—
476#352—478no—
477AΣL(1,𝔽16)—478no—
478C47#3334711yescharacteristic, complemented, Sylow
479C2×#41—41no—
480C2×#41—41no—
481C2×#41—41no—
482C2×#41—41no—
483C2×#41—941no—
484C2×#41—941no—
485C2×#41—941no—
486C2×#41—941no—
487C2×#41—1881no—
488C2×#41—1881no—
489C2×#41—1881no—
490C2×#41—1881no—
491C2×#41C4×D4711yescharacteristic
492C2×#41C4×D4711yescharacteristic
493C2×#41D18811yescharacteristic
494C2×#41D18811yescharacteristic
495C2×#41C22⋊D4711yescharacteristic
496C2×#41C22⋊D4711yescharacteristic
497C2×#41C22×D4711yescharacteristic
498C2×#41C22×D4711yescharacteristic
499C22×Q8—471no—
500C22×Q8C22⋊D4711yescharacteristic
501C22×D4—472no—
502C22×D4—471no—
503C22×D4C4×D4711yescharacteristic
504C22×D4D18811yescharacteristic
505C22×D4C22×D4711yescharacteristic
506C23×C4—472no—
507C23×C4C4×D4711yescharacteristic
508C23×C4D18811yescharacteristic
509C23×C4C22⋊D4711yescharacteristic
510C2×M16—22no—
511C2×M16—22no—
512C2×M16—22no—
513C2×M16—41no—
514C2×M16—41no—
515C2×M16—41no—
516C22×C8—41no—
517C4⋊Q8—941no—
518C4⋊Q8—941no—
519#127—941no—
520#127—941no—
521#124—941no—
522#124—941no—
523#124—941no—
524#124—941no—
525#123—472no—
526#123—472no—
527#123—472no—
528#123—472no—
529#123—942no—
530#123—942no—
531C22⋊Q8—942no—
532C22⋊Q8—942no—
533C22⋊Q8—941no—
534C22⋊Q8—941no—
535C22⋊Q8—941no—
536C22⋊Q8—941no—
537#121—942no—
538#121—942no—
539#121—942no—
540#121—942no—
541#121—942no—
542#121—942no—
543#121—941no—
544#121—941no—
545#121—941no—
546#121—941no—
547#120—472no—
548#120—472no—
549#120—472no—
550#120—472no—
551#120—942no—
552#120—942no—
553C4×D4—942no—
554C4×D4—942no—
555C4×D4—942no—
556C4×D4—942no—
557#117—472no—
558#117—471no—
559#117—471no—
560#117—941no—
561#117—941no—
562#117—942no—
563#117—942no—
564#117—1881no—
565#117—1881no—
566C2×C4⋊C4—941no—
567C2×C4⋊C4—1881no—
568C2×C22⋊C4—472no—
569C2×C22⋊C4—942no—
570C2×C42—941no—
571C2×C42—1881no—
572#101—22no—
573#101—22no—
574#100—22no—
575#100C22×D4714yes—
576#99—474no—
577#99—942no—
578#99—942no—
579#99—942no—
580C24—472no—
581C24(C2×D47)⋊C411yescharacteristic
582C24C2×C4×D4711yescharacteristic
583C24C2×D18811yescharacteristic
584#41—41no—
585#41—41no—
586#41—41no—
587#41—41no—
588#41—41no—
589#41—41no—
590#41—41no—
591#41—41no—
592#41—41no—
593#41—41no—
594#41—41no—
595#41—41no—
596#41—41no—
597#41—41no—
598#41—41no—
599#41—41no—
600#41—1882no—
601#41—1882no—
602#41—1882no—
603#41—1882no—
604#41—1882no—
605#41—1882no—
606#41—1881no—
607#41—1881no—
608#41—1881no—
609#41—1881no—
610C2×Q8—41no—
611C2×Q8—41no—
612C2×Q8—941no—
613C2×Q8—941no—
614C2×Q8—1881no—
615C2×Q8—1881no—
616C2×Q8(C2×D47)⋊C411yescharacteristic
617C2×Q8(C2×D47)⋊C411yescharacteristic
618C2×Q8C2×C22⋊D4711yescharacteristic
619C2×Q8C2×C22⋊D4711yescharacteristic
620C2×D4—41no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—41no—
626C2×D4—942no—
627C2×D4—942no—
628C2×D4—942no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—942no—
632C2×D4—941no—
633C2×D4—941no—
634C2×D4—1881no—
635C2×D4—1881no—
636C2×D4—1882no—
637C2×D4—1882no—
638C2×D4(C2×D47)⋊C411yescharacteristic
639C2×D4(C2×D47)⋊C411yescharacteristic
640C2×D4(C2×D47)⋊C411yescharacteristic
641C2×D4(C2×D47)⋊C411yescharacteristic
642C2×D4C2×C4×D4711yescharacteristic
643C2×D4C2×C4×D4711yescharacteristic
644C2×D4C2×C4×D4711yescharacteristic
645C2×D4C2×D18811yescharacteristic
646C2×D4C2×D18811yescharacteristic
647C2×D4C2×D18811yescharacteristic
648C2×D4C2×C22⋊D4711yescharacteristic
649C2×D4C23×D4711yescharacteristic
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—21no—
662C22×C4—472no—
663C22×C4—942no—
664C22×C4—942no—
665C22×C4—942no—
666C22×C4—1882no—
667C22×C4—1882no—
668C22×C4—1882no—
669C22×C4(C2×D47)⋊C411yescharacteristic
670C22×C4(C2×D47)⋊C411yescharacteristic
671C22×C4(C2×D47)⋊C411yescharacteristic
672C22×C4(C2×D47)⋊C411yescharacteristic
673C22×C4(C2×D47)⋊C411yescharacteristic
674C22×C4(C2×D47)⋊C411yescharacteristic
675C22×C4(C2×D47)⋊C411yescharacteristic
676C22×C4(C2×D47)⋊C411yescharacteristic
677C22×C4(C2×D47)⋊C411yescharacteristic
678C22×C4C2×C4×D4711yescharacteristic
679C22×C4C2×C4×D4711yescharacteristic
680C22×C4C2×D18811yescharacteristic
681C22×C4C2×D18811yescharacteristic
682C22×C4C2×C22⋊D4711yescharacteristic
683C22×C4C2×C22⋊D4711yescharacteristic
684C22×C4C2×C22⋊D4711yescharacteristic
685M16—24no—
686M16—42no—
687M16—42no—
688M16—42no—
689C2×C8—42no—
690C2×C8—42no—
691C2×C8—42no—
692C4⋊C4—942no—
693C4⋊C4—942no—
694C4⋊C4—942no—
695C4⋊C4—942no—
696C4⋊C4—941no—
697C4⋊C4—941no—
698C4⋊C4—942no—
699C4⋊C4—1882no—
700C4⋊C4—1882no—
701C22⋊C4—472no—
702C22⋊C4—472no—
703C22⋊C4—942no—
704C22⋊C4—942no—
705C22⋊C4—942no—
706C22⋊C4—942no—
707C22⋊C4—942no—
708C22⋊C4—942no—
709C22⋊C4—942no—
710C22⋊C4—942no—
711C22⋊C4—942no—
712C22⋊C4—944no—
713C22⋊C4—1882no—
714C42—942no—
715C42—941no—
716C42—941no—
717C42—1882no—
718C42—1882no—
719C23—21no—
720C23—21no—
721C23—21no—
722C23—21no—
723C23—21no—
724C23—21no—
725C23—81no—
726C23—81no—
727C23—81no—
728C23—942no—
729C23—3762no—
730C23—1882no—
731C23C2×(C2×D47)⋊C411yescharacteristic
732C23C2×(C2×D47)⋊C411yescharacteristic
733C23C2×(C2×D47)⋊C411yescharacteristic
734C23C2×(C2×D47)⋊C411yescharacteristic
735C23C2×(C2×D47)⋊C411yescharacteristic
736C23C22×C4×D4711yescharacteristic
737C23C22×D18811yescharacteristic
738Q8—41no—
739Q8—41no—
740Q8—41no—
741Q8—41no—
742Q8—1882no—
743Q8—1881no—
744Q8—1881no—
745D4—41no—
746D4—41no—
747D4—41no—
748D4—41no—
749D4—41no—
750D4—41no—
751D4—41no—
752D4—41no—
753D4—41no—
754D4—41no—
755D4—41no—
756D4—41no—
757D4—3762no—
758D4—3762no—
759D4—3762no—
760D4—3762no—
761D4—1882no—
762D4—1884no—
763D4—1882no—
764D4—1882no—
765D4—1881no—
766D4—1881no—
767C2×C4—21no—
768C2×C4—21no—
769C2×C4—21no—
770C2×C4—21no—
771C2×C4—21no—
772C2×C4—21no—
773C2×C4—21no—
774C2×C4—21no—
775C2×C4—21no—
776C2×C4—21no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—21no—
795C2×C4—21no—
796C2×C4—21no—
797C2×C4—942no—
798C2×C4—942no—
799C2×C4—942no—
800C2×C4—3764no—
801C2×C4—3762no—
802C2×C4—1884no—
803C2×C4—1884no—
804C2×C4—1882no—
805C2×C4—1882no—
806C2×C4—1882no—
807C2×C4#1309393811yescharacteristic
808C2×C4#1309393811yescharacteristic
809C2×C4#1309393811yescharacteristic
810C2×C4#1309393811yescharacteristic
811C2×C4C2×(C2×D47)⋊C411yescharacteristic
812C2×C4C2×(C2×D47)⋊C411yescharacteristic
813C2×C4C2×(C2×D47)⋊C411yescharacteristic
814C2×C4C2×(C2×D47)⋊C411yescharacteristic
815C2×C4C2×(C2×D47)⋊C411yescharacteristic
816C2×C4C2×(C2×D47)⋊C411yescharacteristic
817C2×C4C2×(C2×D47)⋊C411yescharacteristic
818C2×C4C22×C22⋊D4711yescharacteristic
819C8—44no—
820C22—21no—
821C22—21no—
822C22—21no—
823C22—21no—
824C22—21no—
825C22—21no—
826C22—41no—
827C22—41no—
828C22—41no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—42no—
834C22—42no—
835C22—81no—
836C22—81no—
837C22—81no—
838C22—81no—
839C22—3764no—
840C22—1882no—
841C22—1882no—
842C22—1882no—
843C22C2×#1309393811yescharacteristic
844C22C2×#1309393811yescharacteristic
845C22C22×(C2×D47)⋊C411yescharacteristic
846C4—21no—
847C4—21no—
848C4—21no—
849C4—21no—
850C4—21no—
851C4—21no—
852C4—3764no—
853C4—1882no—
854C4—1882no—
855C4—1882no—
856C4C2×#1309393811yescharacteristic
857C4C2×#1309393811yescharacteristic
858C4C2×#1309393811yescharacteristic
859C4C2×#1309393811yescharacteristic
860C2—21no—
861C2—21no—
862C2—21no—
863C2—41no—
864C2—41no—
865C2—41no—
866C2—41no—
867C2—41no—
868C2—41no—
869C2—3762no—
870C2C22×#1309393811yescharacteristic
subgroupG/H
centerC4C2×#13093938
commutatorC23×C47C23×C4
FrattiniC2×D4C23×D47
FittingC2×C47×#413C2
socleC2×C47C22×#99
prime radical#20256717C2
cosocleC2×D4×C47C24
hypercenterC2×#413D47
hypocenterC47#33347
LCSG ▷ C23×C47 ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C22×C4 ◁ C22×#41 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
2. C2×#15689097C2semidirect
3. #20245043C2semidirect
4. #20245039C2semidirect
5. #20245035C2semidirect
6. #20245030C2semidirect
7. C2×C47×#413C2semidirect
8. C22×#10625350C4semidirect
12. #15689694C4semidirect
15. #15689687C4semidirect
17. #15689682C4semidirect
23. #15689630C4semidirect
26. C2×#13093983C4semidirect
33. #15688914C22semidirect
34. #15688911C22semidirect
51. C22×Dic94C2×C4semidirect
52. C22×D188C2×C4semidirect
54. C22×C4×D47C2×C4semidirect
66. #13094005C2×C4semidirect
67. #13094005C2×C4semidirect
88. #13093992C2×C4semidirect
89. #13093992C2×C4semidirect
101. #13093983C2×C4semidirect
102. #13093983C2×C4semidirect
103. #13093983C2×C4semidirect
426. C2×#413D47semidirect
478. C47#33347semidirect

Maximal subgroups

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

subgroupindex
#202567172
C2×#156890972
#202450432
#202450392
#202450352
#202450302
C2×C47×#4132
#3334747