Finite Group Databasebeta

← #27084171

Subgroups — #27084171

Order 12032.

2298 conjugacy classes of subgroups.

The subgroup lattice has 936 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689689C211yesmaximal, characteristic
2#20256589C211yesmaximal, characteristic, complemented
3#20253345C214yesmaximal, complemented
4#20253343C214yesmaximal, complemented
5#20253341C214yesmaximal, complemented
6#20253339C214yesmaximal, complemented
7#20253330C212yesmaximal, complemented
8#20253329C211yesmaximal, characteristic, complemented
9#20253328C211yesmaximal, characteristic, complemented
10#20253326C212yesmaximal, complemented
11#20253324C211yesmaximal, characteristic, complemented
12#20251975C212yesmaximal, complemented
13#418×D47C212yesmaximal, complemented
14#20251831C211yesmaximal, characteristic, complemented
15C47×#3094C211yesmaximal, characteristic, complemented
16C22×#10625350C2211yescharacteristic
17C22×D4×D47C2211yescharacteristic
18C2×M16×D47C2212yes—
19#15689689—22no—
20#15689689—22no—
21#15689689C2214yes—
22#15689689C2214yes—
23C2×#13094020—21no—
24C2×#13094010—21no—
25C2×#13093999C2211yescharacteristic
26C2×#13093998C2211yescharacteristic
27C2×#13093995C2211yescharacteristic
28C2×#13093994—21no—
29C2×#13093992—21no—
30#15689604C2212yescomplemented
31#15689604C2212yescomplemented
32#15689603C2212yescomplemented
33#15689603C2212yescomplemented
34#15689600—21no—
35#15689597—21no—
36#15689596—21no—
37#15689596—21no—
38C4×#10625350—22no—
39#15689591—22no—
40C2×#13093983C2211yescharacteristic, complemented
41C2×#13093982C2211yescharacteristic
42#117×D47C2212yes—
43#117×D47C2212yescomplemented
44#15689450C2214yescomplemented
45#15689449C2214yescomplemented
46#15689448C2214yescomplemented
47#15689447C2214yescomplemented
48#15689446C2214yescomplemented
49#15689445C2214yescomplemented
50#15689444C2214yescomplemented
51#15689443C2214yescomplemented
52#15689442C2212yescomplemented
53#15689441C2212yescomplemented
54#15689440C2214yescomplemented
55#15689439C2212yescomplemented
56#15689438C2214yescomplemented
57#15689437C2212yescomplemented
58#15689436C2212yescomplemented
59#15689435C2214yescomplemented
60#15689434C2212yescomplemented
61#15689166C2212yescomplemented
62#15689165C2212yescomplemented
63#15689164C2214yescomplemented
64#15689163C2212yescomplemented
65#15689162C2214yescomplemented
66#15689160C2214yescomplemented
67#15689158C2214yescomplemented
68#15689129C2212yes—
69#15689128C2212yes—
70#15689127C2212yes—
71#15689126C2214yescomplemented
72#15689126C2214yescomplemented
73#102×D47C2214yescomplemented
74#102×D47C2214yescomplemented
75#15689088C2214yescomplemented
76#15689088C2214yescomplemented
77#15689087C2211yescharacteristic, complemented
78#15689086C2212yescomplemented
79C2×#121×C47C2211yescharacteristic
80C2×#117×C47C2211yescharacteristic, complemented
81C47×#482C2214yescomplemented
82C47×#481C2212yescomplemented
83C47×#480C2212yescomplemented
84C47×#428C2212yescomplemented
85C47×#418C2212yes—
86C47×#407C2211yescharacteristic, complemented
87C24×D47—21no—
88C2×#10625350—28no—
89C2×#10625350D412yes—
90C2×#10625350D412yes—
91C2×#10625350C2312yes—
92C2×#10625350C2312yes—
93C22×Dic94D411yescharacteristic
94C22×D188—21no—
95C22×D188D411yescharacteristic
96C22×D188C2311yescharacteristic
97C22×C22⋊D47—21no—
98C22×C22⋊D47—21no—
99C22×C22⋊D47—21no—
100C22×C22⋊D47D411yescharacteristic
101C22×C22⋊D47D411yescharacteristic
102C2×D4×D47—22no—
103C2×D4×D47—28no—
104C2×D4×D47C2314yes—
105C22×C4×D47C2311yescharacteristic
106C22×C4×D47C2311yescharacteristic
107C2×#10625329C2312yes—
108C2×#10625324C2314yes—
109M16×D47—28no—
110C2×C8×D47C2314yes—
111#13094020—24no—
112#13094020—24no—
113#13094010—24no—
114#13094010—24no—
115#13093999—22no—
116#13093999C2314yes—
117#13093998—21no—
118#13093998—21no—
119#13093998C2312yes—
120#13093998C2312yes—
121#13093995—22no—
122#13093995C2314yes—
123#13093994—24no—
124#13093994—24no—
125#13093992—24no—
126#13093992—24no—
127C4×Dic94—22no—
128C4×Dic94—22no—
129#13093989—22no—
130#13093989—22no—
131C4×D188—22no—
132C4×D188—22no—
133#13093986—22no—
134#13093986—22no—
135C4×C22⋊D47—22no—
136C4×C22⋊D47—22no—
137C4×C22⋊D47—22no—
138C4×C22⋊D47—22no—
139(C22⋊D47)⋊C4—22no—
140(C22⋊D47)⋊C4—22no—
141(C22⋊D47)⋊C4—22no—
142(C22⋊D47)⋊C4—22no—
143#13093983—21no—
144#13093983—21no—
145#13093983C2312yes—
146#13093983C2312yescomplemented
147#13093982—22no—
148#13093982C2312yes—
149#13093982C2312yes—
150#13093982C2314yes—
151#13093982C2312yescomplemented
152#13093982C2312yescomplemented
153#13093981—22no—
154#13093981—22no—
155#13093980—22no—
156#13093980—22no—
157C2×C4⋊Dic47C2311yescharacteristic
158C2×C4⋊Dic47C2311yescharacteristic, complemented
159C2×C4⋊Dic47C2311yescharacteristic, complemented
160C4⋊C4×D47C2312yes—
161C4⋊C4×D47C2312yes—
162C4⋊C4×D47C2312yescomplemented
163C4⋊C4×D47C2312yescomplemented
164C2×C22⋊Dic47—21no—
165C2×C22⋊Dic47—21no—
166C2×(C2×D47)⋊C4—21no—
167C2×(C2×D47)⋊C4—21no—
168C2×(C2×D47)⋊C4—21no—
169C22⋊C4×D47—22no—
170C22⋊C4×D47—22no—
171C2×C4×Dic47—21no—
172C2×C4×Dic47—21no—
173C42×D47—22no—
174C42×D47—22no—
175#13093958C2314yescomplemented
176#13093957C2314yescomplemented
177#13093957C2314yescomplemented
178#13093956C2314yescomplemented
179#13093955C2314yescomplemented
180#13093955C2314yescomplemented
181#13093946C2314yes—
182#13093946C2314yes—
183#13093945C2314yes—
184#13093945C2314yes—
185#13093944C2314yes—
186#13093944C2314yes—
187C22⋊(C47⋊C8)C2312yescomplemented
188C22⋊(C47⋊C8)C2312yescomplemented
189(C2×D47)⋊C8C2314yescomplemented
190(C2×D47)⋊C8C2314yescomplemented
191C22×D4×C47—21no—
192C22×D4×C47C2311yescharacteristic
193C23×C4×C47C2311yescharacteristic
194C2×M16×C47C2312yes—
195#121×C47—21no—
196#121×C47—21no—
197#121×C47C2312yes—
198#121×C47C2312yes—
199#117×C47—21no—
200#117×C47—21no—
201#117×C47C2312yes—
202#117×C47C2312yescomplemented
203C2×C4⋊C4×C47C2311yescharacteristic
204C2×C4⋊C4×C47C2311yescharacteristic, complemented
205C2×C4⋊C4×C47C2311yescharacteristic, complemented
206C2×C22⋊C4×C47—21no—
207C2×C22⋊C4×C47—21no—
208C2×C42×C47—21no—
209#107×C47C2314yescomplemented
210#106×C47C2314yescomplemented
211#102×C47C2314yes—
212#102×C47C2314yes—
213C22⋊C8×C47C2312yescomplemented
214C22⋊C8×C47C2312yescomplemented
215C24×C47—21no—
216C24×C47C2×D411yescharacteristic
217C23×D47—21no—
218C23×D47—24no—
219C23×D47—44no—
220C23×D47—82no—
221C23×D47—82no—
222C23×D47C2×D411yescharacteristic
223C23×D47C2×D411yescharacteristic
224C2×D4×C47—22no—
225C2×D4×C47—22no—
226C2×D4×C47—21no—
227C2×D4×C47—24no—
228C2×D4×C47—82no—
229C2×D4×C47C2412yes—
230C22×C4×C47—24no—
231C22×C4×C47—21no—
232C22×C4×C47—21no—
233C22×C4×C47—21no—
234C22×C4×C47C2×D411yescharacteristic
235C22×C4×C47C2×D411yescharacteristic
236C22×C4×C47C2×D411yescharacteristic
237C22×C4×C47C2411yescharacteristic
238C22×C4×C47C2411yescharacteristic
239C22×C4×C47C2411yescharacteristic
240C2×C22⋊D47—24no—
241C2×C22⋊D47—22no—
242C2×C22⋊D47—22no—
243C2×C22⋊D47—24no—
244C2×C22⋊D47—24no—
245C2×C22⋊D47—24no—
246C2×C22⋊D47—44no—
247C2×C22⋊D47—82no—
248C2×C22⋊D47—82no—
249C2×C22⋊D47C2×D412yes—
250C2×C22⋊D47C2×D412yes—
251C2×C22⋊D47C2×D412yes—
252C2×C22⋊D47C2×D412yes—
253C22×Dic47—21no—
254C22×Dic47—21no—
255C22×Dic47—21no—
256C22×Dic47C2×D411yescharacteristic
257C22×Dic47C2×D411yescharacteristic
258D4×D47—28no—
259D4×D47—28no—
260D4×D47—48no—
261#10625350—28no—
262#10625350—28no—
263#10625350—24no—
264#10625350—24no—
265#10625350—24no—
266#10625350—24no—
267C2×D188—24no—
268C2×D188—24no—
269C2×D188—21no—
270C2×D188—24no—
271C2×D188—82no—
272C2×D188C2×D412yes—
273C2×D188C2×D412yes—
274C2×D188C2412yes—
275C2×C4×D47—24no—
276C2×C4×D47—22no—
277C2×C4×D47—22no—
278C2×C4×D47—22no—
279C2×C4×D47—22no—
280C2×C4×D47C2×D412yes—
281C2×C4×D47C2×D412yes—
282C2×C4×D47#4118yes—
283C2×C4×D47C2412yes—
284C2×C4×D47C2412yes—
285C2×Dic94—24no—
286C2×Dic94C2×D412yes—
287C2×Dic94C2×D412yes—
288M16×C47—24no—
289C2×C8×C47C2414yes—
290C4⋊C4×C47—21no—
291C4⋊C4×C47—21no—
292C4⋊C4×C47—21no—
293C4⋊C4×C47C2412yes—
294C4⋊C4×C47C2412yes—
295C4⋊C4×C47C2412yes—
296C22⋊C4×C47—22no—
297C22⋊C4×C47—22no—
298C22⋊C4×C47—22no—
299C22⋊C4×C47—22no—
300C42×C47—22no—
301C42×C47—22no—
302C22⋊Dic47—22no—
303C22⋊Dic47—22no—
304C22⋊Dic47—24no—
305(C2×D47)⋊C4—22no—
306(C2×D47)⋊C4—22no—
307(C2×D47)⋊C4—22no—
308(C2×D47)⋊C4—22no—
309(C2×D47)⋊C4—24no—
310(C2×D47)⋊C4—22no—
311(C2×D47)⋊C4—22no—
312(C2×D47)⋊C4—24no—
313C4⋊Dic47—21no—
314C4⋊Dic47—21no—
315C4⋊Dic47—21no—
316C4⋊Dic47C2412yes—
317C4⋊Dic47C2412yes—
318C4⋊Dic47C2412yes—
319Dic47⋊C4—22no—
320Dic47⋊C4—22no—
321Dic47⋊C4—22no—
322Dic47⋊C4—22no—
323C4×Dic47—22no—
324C4×Dic47—22no—
325C4×Dic47—22no—
326C4×Dic47—22no—
327C4×Dic47—22no—
328C4×Dic47—22no—
329C4×Dic47—24no—
330#10625329—24no—
331C2×C47⋊C8C2414yes—
332#10625324—28no—
333C8×D47—28no—
334C23×C47—22no—
335C23×C47—22no—
336C23×C47—41no—
337C23×C47—41no—
338C23×C47—42no—
339C23×C47—42no—
340C23×C47—42no—
341C23×C47C22×D411yescharacteristic
342C23×C47C22×D411yescharacteristic
343C23×C47C22×D411yescharacteristic
344C22×D47—22no—
345C22×D47—22no—
346C22×D47—41no—
347C22×D47—41no—
348C22×D47—41no—
349C22×D47—41no—
350C22×D47—42no—
351C22×D47—42no—
352C22×D47—42no—
353C22×D47—48no—
354C22×D47—84no—
355C22×D47—84no—
356C22×D47—816no—
357C22×D47#12314yes—
358C22×D47C22×D412yes—
359C22×D47C22×D412yes—
360D4×C47—24no—
361D4×C47—42no—
362D4×C47—82no—
363D4×C47—82no—
364C2×C4×C47—22no—
365C2×C4×C47—22no—
366C2×C4×C47—22no—
367C2×C4×C47—22no—
368C2×C4×C47—22no—
369C2×C4×C47—22no—
370C2×C4×C47—22no—
371C2×C4×C47—22no—
372C2×C4×C47—42no—
373C2×C4×C47—81no—
374C2×C4×C47—81no—
375C2×C4×C47C22×D411yescharacteristic
376C2×C4×C47C22×D411yescharacteristic
377C2×C4×C47C22×D411yescharacteristic
378C2×C4×C47C2×#4114yes—
379C2×C4×C47C2511yescharacteristic
380C22⋊D47—24no—
381C22⋊D47—24no—
382C22⋊D47—24no—
383C22⋊D47—24no—
384C22⋊D47—48no—
385C22⋊D47—84no—
386C22⋊D47—82no—
387C22⋊D47—82no—
388C2×Dic47—22no—
389C2×Dic47—22no—
390C2×Dic47—22no—
391C2×Dic47—22no—
392C2×Dic47—42no—
393C2×Dic47—81no—
394C2×Dic47—81no—
395C2×Dic47#12314yes—
396C2×Dic47C22×D412yes—
397C2×Dic47C22×D412yes—
398D188—24no—
399D188—24no—
400D188—24no—
401D188—42no—
402D188—84no—
403C4×D47—24no—
404C4×D47—22no—
405C4×D47—22no—
406C4×D47—82no—
407C4×D47—82no—
408C4×D47—82no—
409C4×D47—82no—
410C4×D47#12318yes—
411C4×D47C2×#4114yes—
412C4×D47C2×#4114yes—
413Dic94—24no—
414Dic94—24no—
415C8×C47—24no—
416C47⋊C8—24no—
417#60518—471nomaximal, Sylow
418C22×C47—21no—
419C22×C47—21no—
420C22×C47—21no—
421C22×C47—21no—
422C22×C47—21no—
423C22×C47—21no—
424C22×C47—21no—
425C22×C47—21no—
426C22×C47—42no—
427C22×C47—42no—
428C22×C47—42no—
429C22×C47—82no—
430C22×C47—84no—
431C22×C47C2×#12312yes—
432C22×C47C23×D411yescharacteristic
433C2×D47—22no—
434C2×D47—22no—
435C2×D47—22no—
436C2×D47—22no—
437C2×D47—22no—
438C2×D47—44no—
439C2×D47—42no—
440C2×D47—42no—
441C2×D47—42no—
442C2×D47—816no—
443C2×D47—82no—
444C2×D47—84no—
445C2×D47C2×#12314yes—
446C4×C47—21no—
447C4×C47—21no—
448C4×C47—42no—
449C4×C47—42no—
450C4×C47—42no—
451C4×C47C2×#12312yes—
452C4×C47C22×#4112yes—
453Dic47—22no—
454Dic47—42no—
455Dic47—42no—
456Dic47—42no—
457Dic47C2×#12314yes—
458C2×#535—471no—
459#3428—471no—
460#3096—474no—
461#3096—474no—
462#3096—474no—
463#3096—474no—
464#3094—472no—
465#3094—472no—
466#3094—471no—
467#3094—471no—
468#3094—471no—
469#3094D4711yescharacteristic, complemented
470#2911—472no—
471C2×#418—472no—
472#2879—471no—
473C2×C47—22no—
474C2×C47—41no—
475C2×C47—41no—
476C2×C47—82no—
477C2×C47C22×#12311yescharacteristic
478C2×C47#358511yescharacteristic
479C2×C47#358511yescharacteristic
480D47—24no—
481D47—42no—
482D47—82no—
483C22×#41—471no—
484C23×D4—471no—
485C22×M16—472no—
486#535—474no—
487#535—474no—
488#535—942no—
489#535—942no—
490C2×#127—941no—
491C2×#124—941no—
492C2×#121—471no—
493C2×#121—471no—
494C2×#121—471no—
495C2×#121C2×D4711yescharacteristic
496C2×#120—941no—
497C2×#120—941no—
498#520—472no—
499#520—472no—
500#520—472no—
501#520—472no—
502#519—941no—
503#518—941no—
504#518—941no—
505#518—941no—
506C4×#41—942no—
507C4×#41—942no—
508C2×#117—471no—
509C2×#117—472no—
510C2×#117—472no—
511C2×#117—471no—
512C2×#117C2×D4711yescharacteristic, complemented
513#482—474no—
514#482—474no—
515#482—474no—
516#482—474no—
517#482—474no—
518#482—474no—
519#482—474no—
520#482C2×D4714yescomplemented
521#481—472no—
522#481—472no—
523#481—474no—
524#481—474no—
525#481—472no—
526#481C2×D4712yescomplemented
527#480—472no—
528#480—472no—
529#480—474no—
530#480—474no—
531#480—472no—
532#480C2×D4712yescomplemented
533#428—472no—
534#428—472no—
535#428—472no—
536#428—474no—
537#428—474no—
538#428C2×D4712yescomplemented
539#427—474no—
540#427—474no—
541#418—472no—
542#418—472no—
543#418—472no—
544#418—474no—
545#418—474no—
546#418C2×D4712yes—
547C2×#102—474no—
548C2×#102—474no—
549#408—474no—
550#408—474no—
551#407—471no—
552#407—472no—
553#407C2×D4711yescharacteristic, complemented
554C47#6051811yescharacteristic, complemented, Sylow
555C25—941no—
556C2×#41—472no—
557C2×#41—472no—
558C2×#41—472no—
559C2×#41—472no—
560C2×#41—948no—
561C22×Q8—471no—
562C22×D4—21no—
563C22×D4—471no—
564C22×D4—471no—
565C22×D4—474no—
566C22×D4—471no—
567C22×D4—471no—
568C22×D4—941no—
569C22×D4—948no—
570C22×D4—942no—
571C22×D4—941no—
572C22×D4—941no—
573C22×D4—941no—
574C22×D4C22×D4711yescharacteristic
575C23×C4—471no—
576C23×C4—471no—
577C23×C4C22×D4711yescharacteristic
578C2×M16—472no—
579C2×M16—474no—
580C2×M16—948no—
581C2×M16C22×D4712yes—
582C22×C8—474no—
583#127—944no—
584#127—944no—
585#124—944no—
586#124—944no—
587#121—21no—
588#121—21no—
589#121—474no—
590#121—472no—
591#121—472no—
592#121—474no—
593#121—942no—
594#121—942no—
595#121—941no—
596#121—941no—
597#121C22×D4712yes—
598#121C22×D4712yes—
599#120—944no—
600#120—944no—
601#120—944no—
602#120—944no—
603C4×Q8—942no—
604C4×Q8—942no—
605C4×Q8—942no—
606C4×Q8—942no—
607C4×D4—942no—
608C4×D4—942no—
609C4×D4—942no—
610C4×D4—942no—
611C4×D4—942no—
612C4×D4—942no—
613C4×D4—942no—
614C4×D4—942no—
615C4×D4—942no—
616C4×D4—942no—
617C4×D4—942no—
618C4×D4—942no—
619#117—21no—
620#117—21no—
621#117—472no—
622#117—472no—
623#117—472no—
624#117—472no—
625#117—472no—
626#117—472no—
627#117—474no—
628#117—942no—
629#117—942no—
630#117—942no—
631#117—942no—
632#117—942no—
633#117—941no—
634#117—941no—
635#117C22×D4712yes—
636#117C22×D4712yescomplemented
637C2×C4⋊C4—471no—
638C2×C4⋊C4—471no—
639C2×C4⋊C4—471no—
640C2×C4⋊C4—472no—
641C2×C4⋊C4—472no—
642C2×C4⋊C4—472no—
643C2×C4⋊C4—472no—
644C2×C4⋊C4C22×D4711yescharacteristic
645C2×C4⋊C4C22×D4711yescharacteristic, complemented
646C2×C4⋊C4C22×D4711yescharacteristic, complemented
647C2×C22⋊C4—21no—
648C2×C22⋊C4—21no—
649C2×C22⋊C4—942no—
650C2×C22⋊C4—942no—
651C2×C22⋊C4—941no—
652C2×C22⋊C4—941no—
653C2×C22⋊C4—941no—
654C2×C22⋊C4—941no—
655C2×C22⋊C4—941no—
656C2×C42—21no—
657C2×C42—942no—
658C2×C42—942no—
659C2×C42—941no—
660C2×C42—941no—
661#107—474no—
662#107—474no—
663#107—474no—
664#107C22×D4714yescomplemented
665#106—474no—
666#106—474no—
667#106—474no—
668#106C22×D4714yescomplemented
669#102—474no—
670#102—474no—
671#102—474no—
672#102—474no—
673#102—474no—
674#102—474no—
675#102C22×D4714yes—
676#102C22×D4714yes—
677C22⋊C8—472no—
678C22⋊C8—472no—
679C22⋊C8—474no—
680C22⋊C8—474no—
681C22⋊C8C22×D4712yescomplemented
682C22⋊C8C22×D4712yescomplemented
683C24—21no—
684C24—471no—
685C24—471no—
686C24—944no—
687C24—941no—
688C24—3762no—
689C24—3762no—
690C24—1884no—
691C24D4×D4711yescharacteristic
692#41—948no—
693#41—948no—
694#41—944no—
695#41—944no—
696#41—944no—
697#41—944no—
698C2×Q8—472no—
699C2×Q8—472no—
700C2×Q8—944no—
701C2×D4—22no—
702C2×D4—22no—
703C2×D4—21no—
704C2×D4—24no—
705C2×D4—82no—
706C2×D4—472no—
707C2×D4—472no—
708C2×D4—472no—
709C2×D4—472no—
710C2×D4—472no—
711C2×D4—472no—
712C2×D4—472no—
713C2×D4—944no—
714C2×D4—944no—
715C2×D4—948no—
716C2×D4—948no—
717C2×D4—944no—
718C2×D4—944no—
719C2×D4—944no—
720C2×D4—944no—
721C2×D4—942no—
722C2×D4—942no—
723C2×D4—941no—
724C2×D4—944no—
725C2×D4—3762no—
726C2×D4—3762no—
727C2×D4—3762no—
728C2×D4—1888no—
729C2×D4—1884no—
730C2×D4C23×D4712yes—
731C22×C4—24no—
732C22×C4—21no—
733C22×C4—21no—
734C22×C4—21no—
735C22×C4—471no—
736C22×C4—472no—
737C22×C4—478no—
738C22×C4—472no—
739C22×C4—471no—
740C22×C4—472no—
741C22×C4—472no—
742C22×C4—942no—
743C22×C4—942no—
744C22×C4—942no—
745C22×C4—942no—
746C22×C4—944no—
747C22×C4—941no—
748C22×C4—941no—
749C22×C4—941no—
750C22×C4D4×D4711yescharacteristic
751C22×C4D4×D4711yescharacteristic
752C22×C4D4×D4711yescharacteristic
753C22×C4C23×D4711yescharacteristic
754C22×C4C23×D4711yescharacteristic
755C22×C4C23×D4711yescharacteristic
756M16—24no—
757M16—948no—
758M16—944no—
759C2×C8—474no—
760C2×C8—948no—
761C2×C8C23×D4714yes—
762C4⋊C4—21no—
763C4⋊C4—21no—
764C4⋊C4—21no—
765C4⋊C4—472no—
766C4⋊C4—472no—
767C4⋊C4—472no—
768C4⋊C4—942no—
769C4⋊C4—942no—
770C4⋊C4—942no—
771C4⋊C4—942no—
772C4⋊C4—941no—
773C4⋊C4—941no—
774C4⋊C4—941no—
775C4⋊C4C23×D4712yes—
776C4⋊C4C23×D4712yes—
777C4⋊C4C23×D4712yes—
778C22⋊C4—22no—
779C22⋊C4—22no—
780C22⋊C4—22no—
781C22⋊C4—22no—
782C22⋊C4—944no—
783C22⋊C4—942no—
784C22⋊C4—942no—
785C22⋊C4—942no—
786C22⋊C4—942no—
787C22⋊C4—944no—
788C22⋊C4—944no—
789C22⋊C4—942no—
790C22⋊C4—942no—
791C22⋊C4—942no—
792C22⋊C4—942no—
793C42—22no—
794C42—22no—
795C42—942no—
796C42—942no—
797C42—942no—
798C42—942no—
799C42—944no—
800C42—942no—
801C42—942no—
802C23—22no—
803C23—22no—
804C23—41no—
805C23—41no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—472no—
810C23—474no—
811C23—472no—
812C23—942no—
813C23—942no—
814C23—3764no—
815C23—3764no—
816C23—37616no—
817C23—1881no—
818C23—1881no—
819C23—1881no—
820C23—1881no—
821C23—1882no—
822C23—1882no—
823C23—1888no—
824C23—1882no—
825C23C2×D4×D4711yescharacteristic
826C23C2×D4×D4711yescharacteristic
827C23C2×D4×D4711yescharacteristic
828Q8—944no—
829Q8—944no—
830D4—24no—
831D4—42no—
832D4—82no—
833D4—82no—
834D4—944no—
835D4—944no—
836D4—944no—
837D4—944no—
838D4—944no—
839D4—944no—
840D4—944no—
841D4—3764no—
842D4—3762no—
843D4—3762no—
844D4—3764no—
845D4—1888no—
846D4—1882no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—22no—
851C2×C4—22no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—42no—
856C2×C4—81no—
857C2×C4—81no—
858C2×C4—474no—
859C2×C4—472no—
860C2×C4—478no—
861C2×C4—474no—
862C2×C4—474no—
863C2×C4—472no—
864C2×C4—942no—
865C2×C4—944no—
866C2×C4—942no—
867C2×C4—942no—
868C2×C4—942no—
869C2×C4—942no—
870C2×C4—942no—
871C2×C4—3762no—
872C2×C4—3762no—
873C2×C4—3762no—
874C2×C4—3762no—
875C2×C4—3761no—
876C2×C4—3761no—
877C2×C4—1882no—
878C2×C4C2×D4×D4711yescharacteristic
879C2×C4C2×D4×D4711yescharacteristic
880C2×C4C2×D4×D4711yescharacteristic
881C2×C4#41×D4714yes—
882C2×C4C24×D4711yescharacteristic
883C8—24no—
884C8—944no—
885C22—21no—
886C22—21no—
887C22—21no—
888C22—21no—
889C22—21no—
890C22—21no—
891C22—21no—
892C22—21no—
893C22—42no—
894C22—42no—
895C22—42no—
896C22—82no—
897C22—84no—
898C22—474no—
899C22—942no—
900C22—942no—
901C22—942no—
902C22—942no—
903C22—942no—
904C22—3764no—
905C22—3762no—
906C22—37616no—
907C22—1884no—
908C22—1882no—
909C22—1882no—
910C22—1882no—
911C22#123×D4712yes—
912C22C22×D4×D4711yescharacteristic
913C4—21no—
914C4—21no—
915C4—42no—
916C4—42no—
917C4—42no—
918C4—474no—
919C4—942no—
920C4—1882no—
921C4—1882no—
922C4—1882no—
923C4#123×D4712yes—
924C4C2×#41×D4712yes—
925C2—22no—
926C2—41no—
927C2—41no—
928C2—82no—
929C2—944no—
930C2—3762no—
931C2—1882no—
932C2C2×#123×D4711yescharacteristic
933C2#2025816411yescharacteristic
934C2#2025816511yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC47×#3094C2
socleC22×C47C23×D4
prime radicalC2×#15689689C2
hypercenter#3094D47
hypocenterC47#60518
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3094

Complements

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

NH ≅ G/Ntype
2. #20256589C2semidirect
3. #20253345C2semidirect
4. #20253343C2semidirect
5. #20253341C2semidirect
6. #20253339C2semidirect
7. #20253330C2semidirect
8. #20253329C2semidirect
9. #20253328C2semidirect
10. #20253326C2semidirect
11. #20253324C2semidirect
12. #20251975C2semidirect
13. #418×D47C2semidirect
14. #20251831C2semidirect
15. C47×#3094C2semidirect
30. #15689604C22semidirect
31. #15689604C22semidirect
32. #15689603C22semidirect
33. #15689603C22semidirect
40. C2×#13093983C22semidirect
43. #117×D47C22semidirect
44. #15689450C22semidirect
45. #15689449C22semidirect
46. #15689448C22semidirect
47. #15689447C22semidirect
48. #15689446C22semidirect
49. #15689445C22semidirect
50. #15689444C22semidirect
51. #15689443C22semidirect
52. #15689442C22semidirect
53. #15689441C22semidirect
54. #15689440C22semidirect
55. #15689439C22semidirect
56. #15689438C22semidirect
57. #15689437C22semidirect
58. #15689436C22semidirect
59. #15689435C22semidirect
60. #15689434C22semidirect
61. #15689166C22semidirect
62. #15689165C22semidirect
63. #15689164C22semidirect
64. #15689163C22semidirect
65. #15689162C22semidirect
66. #15689160C22semidirect
67. #15689158C22semidirect
71. #15689126C22semidirect
72. #15689126C22semidirect
73. #102×D47C22semidirect
74. #102×D47C22semidirect
75. #15689088C22semidirect
76. #15689088C22semidirect
77. #15689087C22semidirect
78. #15689086C22semidirect
80. C2×#117×C47C22semidirect
81. C47×#482C22semidirect
82. C47×#481C22semidirect
83. C47×#480C22semidirect
84. C47×#428C22semidirect
86. C47×#407C22semidirect
146. #13093983C23semidirect
151. #13093982C23semidirect
152. #13093982C23semidirect
158. C2×C4⋊Dic47C23semidirect
159. C2×C4⋊Dic47C23semidirect
162. C4⋊C4×D47C23semidirect
163. C4⋊C4×D47C23semidirect
175. #13093958C23semidirect
176. #13093957C23semidirect
177. #13093957C23semidirect
178. #13093956C23semidirect
179. #13093955C23semidirect
180. #13093955C23semidirect
187. C22⋊(C47⋊C8)C23semidirect
188. C22⋊(C47⋊C8)C23semidirect
189. (C2×D47)⋊C8C23semidirect
190. (C2×D47)⋊C8C23semidirect
202. #117×C47C23semidirect
204. C2×C4⋊C4×C47C23semidirect
205. C2×C4⋊C4×C47C23semidirect
209. #107×C47C23semidirect
210. #106×C47C23semidirect
213. C22⋊C8×C47C23semidirect
214. C22⋊C8×C47C23semidirect
469. #3094D47semidirect
512. C2×#117C2×D47semidirect
520. #482C2×D47semidirect
526. #481C2×D47semidirect
532. #480C2×D47semidirect
538. #428C2×D47semidirect
553. #407C2×D47semidirect
554. C47#60518semidirect
636. #117C22×D47semidirect
645. C2×C4⋊C4C22×D47semidirect
646. C2×C4⋊C4C22×D47semidirect
664. #107C22×D47semidirect
668. #106C22×D47semidirect
681. C22⋊C8C22×D47semidirect
682. C22⋊C8C22×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896892
#202565892
#202533452
#202533432
#202533412
#202533392
#202533302
#202533292
#202533282
#202533262
#202533242
#202519752
#418×D472
#202518312
C47×#30942
#6051847