Finite Group Databasebeta

← D47×#2898 #27079830

Subgroups — D47×#2898 #27079830

Order 12032.

4882 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D47C211yesmaximal, characteristic
2C2×#131×D47C211yesmaximal, characteristic, complemented
3#520×D47C211yesmaximal, characteristic, complemented
4#20251922C211yesmaximal, characteristic, complemented
5#20251921C211yesmaximal, characteristic, complemented
6#20251920C213yesmaximal, complemented
7#20251919C213yesmaximal, complemented
8#20251918C211yesmaximal, characteristic, complemented
9#20251917C213yesmaximal, complemented
10#20251916C213yesmaximal, complemented
11#417×D47C213yesmaximal, complemented
12#419×D47C213yesmaximal, complemented
13#416×D47C213yesmaximal, complemented
14C2×#103×D47C213yesmaximal, complemented
15C47×#2898C211yesmaximal, characteristic, complemented
16C2×#13094072—21no—
17C2×#13094072C2213yes—
18C2×#13094071—23no—
19C2×#13094071C2211yescharacteristic
20C2×#13094071C2213yes—
212−1+4×D47—28no—
222−1+4×D47C4116yescomplemented
23C2×#41×D47—23no—
24C2×#41×D47C2213yes—
25C2×#41×D47C2211yescharacteristic
26C22×Q8×D47—21no—
27C22×Q8×D47C2213yes—
28C2×#13094032C2213yescomplemented
29C2×#13094031C2211yescharacteristic, complemented
30C2×#13094030C2213yescomplemented
31#131×D47—28no—
32C2×M16×D47C2213yes—
33C22×C8×D47C2213yes—
34#15689606C2211yescharacteristic, complemented
35#15689605—21no—
36#15689604C2213yescomplemented
37#15689603C2213yescomplemented
38#15689602—23no—
39C4×Q8×D47—21no—
40C4×D4×D47—23no—
41#117×D47C2213yes—
42C2×C4⋊C4×D47C2213yes—
43#15689133C2213yescomplemented
44#15689132C2213yescomplemented
45#15689131C2213yescomplemented
46#15689130C2216yescomplemented
47#15689130C2216yescomplemented
48#15689125C2213yescomplemented
49#15689124C2213yescomplemented
50#15689123C2216yescomplemented
51#15689122C2213yescomplemented
52#15689121C2216yescomplemented
53#15689120C2213yescomplemented
54#15689119C2213yescomplemented
55#15689118C2213yescomplemented
56#15689118C2213yescomplemented
57#15689117C2213yescomplemented
58#15689116C2213yescomplemented
59#15689116C2213yescomplemented
60C2×#13093949C2213yescomplemented
61C2×#13093948C2213yescomplemented
62C2×#13093947C2213yescomplemented
63#103×D47C2213yes—
64#103×D47C2216yes—
65#103×D47C2213yes—
66#103×D47C2216yescomplemented
67#103×D47C2216yescomplemented
68#102×D47C2211yescharacteristic
69#102×D47C2213yes—
70C2×2−1+4×C47C2211yescharacteristic
71C2×#131×C47C2211yescharacteristic, complemented
72C47×#520C2211yescharacteristic, complemented
73C47×#419C2213yescomplemented
74C47×#417C2213yescomplemented
75C47×#416C2213yescomplemented
76C2×#103×C47C2213yescomplemented
77#13094072—216no—
78#13094072—212no—
79#13094072C2×C4124yescomplemented
80#13094071—24no—
81#13094071—248no—
82#13094071—212no—
83#13094071C2×C4124yescomplemented
84#13094071C2×C418yescomplemented
85C2×#10625354—23no—
86C2×#10625354D411yescharacteristic
87C2×#10625354C2313yes—
88C2×#10625350—26no—
89C2×#10625350—23no—
90C2×#10625350—23no—
91C2×#10625350C2313yes—
92C2×#10625350C2313yes—
93C2×#10625352—23no—
94C2×#10625352—26no—
95C2×#10625352—23no—
96C2×#10625352D413yes—
97C2×#10625352C2313yes—
98#41×D47—248no—
99#41×D47—212no—
100#41×D47C2×C418yes—
101#41×D47C2×C4124yescomplemented
102#41×D47D418yes—
103C22×Dic94—23no—
104C22×Dic94—23no—
105C22×Dic94C2313yes—
106C2×Q8×D47—21no—
107C2×Q8×D47—216no—
108C2×Q8×D47—23no—
109C2×Q8×D47—212no—
110C2×Q8×D47—23no—
111C2×Q8×D47—23no—
112C2×Q8×D47C2×C4124yescomplemented
113C2×Q8×D47D411yescharacteristic
114C2×Q8×D47C2313yes—
115C2×Q8×D47C2316yes—
116C2×D4×D47—23no—
117C2×D4×D47D413yes—
118C2×D4×D47C2311yescharacteristic
119C22×C4×D47—23no—
120C22×C4×D47—23no—
121C22×C4×D47—23no—
122C22×C4×D47C2313yes—
123#13094032—212no—
124#13094031—24no—
125#13094030—212no—
126C2×#10625329C2313yes—
127C2×#10625324C2316yes—
128M16×D47—212no—
129C22×C47⋊C8C2313yes—
130C2×C8×D47—212no—
131C2×C8×D47C2311yescharacteristic
132C2×C8×D47C2313yes—
133C2×C8×D47C2313yes—
134C2×C8×D47C2313yes—
135Q8×Dic47—21no—
136C4×Dic94—23no—
137#13093989—23no—
138C4×D188—23no—
139D4×Dic47—23no—
140#13093986—23no—
141C4×C22⋊D47—26no—
142(C22⋊D47)⋊C4—26no—
143#13093983C2313yes—
144#13093982C2313yes—
145#13093982C2313yes—
146#13093981—23no—
147#13093980—23no—
148C2×C4⋊Dic47C2313yes—
149C2×Dic47⋊C4—23no—
150C4⋊C4×D47—23no—
151C4⋊C4×D47—23no—
152C4⋊C4×D47C2313yes—
153C4⋊C4×D47C2316yes—
154C4⋊C4×D47C2311yescharacteristic
155C22⋊C4×D47—23no—
156C42×D47—23no—
157#13093949C2313yes—
158#13093949C2316yes—
159#13093949C2313yes—
160#13093948C2313yes—
161#13093948C2316yes—
162#13093948C2313yes—
163#13093947C2313yes—
164#13093947C2316yes—
165#13093947C2313yes—
166#13093946C2311yescharacteristic
167#13093946C2313yes—
168#13093945C2311yescharacteristic
169#13093945C2313yes—
170#13093944C2311yescharacteristic
171#13093944C2313yes—
1722−1+4×C47—24no—
1732−1+4×C47C2×C418yescomplemented
174C2×#41×C47—23no—
175C2×#41×C47C2313yes—
176C2×#41×C47C2311yescharacteristic
177C22×Q8×C47—21no—
178C22×Q8×C47C2313yes—
179#131×C47—24no—
180C2×M16×C47C2313yes—
181C22×C8×C47C2313yes—
182C4×Q8×C47—21no—
183C4×D4×C47—23no—
184#117×C47C2313yes—
185C2×C4⋊C4×C47C2313yes—
186#103×C47C2313yes—
187#103×C47C2316yes—
188#103×C47C2313yes—
189#102×C47C2311yescharacteristic
190#102×C47C2313yes—
191C23×D47—21no—
192C23×D47C2×D413yes—
193#41×C47—224no—
194#41×C47—26no—
195#41×C47C22×C414yes—
196#41×C47C22×C4112yescomplemented
197#41×C47C2×D414yes—
198C2×Q8×C47—28no—
199C2×Q8×C47—23no—
200C2×Q8×C47—26no—
201C2×Q8×C47C22×C4112yescomplemented
202C2×Q8×C47C2×D411yescharacteristic
203C2×Q8×C47C2413yes—
204C2×D4×C47—23no—
205C2×D4×C47C2×D413yes—
206C2×D4×C47C2411yescharacteristic
207C22×C4×C47—23no—
208C22×C4×C47—23no—
209C22×C4×C47—23no—
210C22×C4×C47C2413yes—
211C2×C22⋊D47—23no—
212C2×C22⋊D47—23no—
213C2×C22⋊D47—21no—
214C2×C22⋊D47C2×D416yes—
215C22×Dic47—23no—
216C22×Dic47—23no—
217C22×Dic47—23no—
218C22×Dic47C2×D413yes—
219#10625354—224no—
220#10625354—26no—
221#10625354C22⋊C418yes—
222#10625354C22×C4112yescomplemented
223Q8×D47—28no—
224Q8×D47—224no—
225Q8×D47—224no—
226Q8×D47—26no—
227Q8×D47—212no—
228Q8×D47—224no—
229Q8×D47C22⋊C418yes—
230Q8×D47C22×C4112yes—
231Q8×D47C22×C4124yescomplemented
232#10625352—224no—
233#10625352—248no—
234#10625352—224no—
235#10625352—26no—
236#10625352C22⋊C4124yes—
237#10625352C22×C4112yescomplemented
238D4×D47—224no—
239D4×D47—22no—
240D4×D47C22⋊C4124yes—
241D4×D47C22×C414yes—
242#10625350—26no—
243#10625350—248no—
244#10625350—224no—
245#10625350—224no—
246#10625350C22×C4112yes—
247#10625350C22×C4112yescomplemented
248#10625350C2×D4112yes—
249C2×D188—23no—
250C2×D188C2×D413yes—
251C2×D188C2411yescharacteristic
252C2×C4×D47—224no—
253C2×C4×D47—23no—
254C2×C4×D47—26no—
255C2×C4×D47—23no—
256C2×C4×D47—23no—
257C2×C4×D47—224no—
258C2×C4×D47—21no—
259C2×C4×D47—23no—
260C2×C4×D47—26no—
261C2×C4×D47—86no—
262C2×C4×D47C22×C4112yes—
263C2×C4×D47C2×D413yes—
264C2×C4×D47C2×D413yes—
265C2×C4×D47C2×D4112yes—
266C2×C4×D47C2411yescharacteristic
267C2×C4×D47C2413yes—
268C2×Dic94—23no—
269C2×Dic94—26no—
270C2×Dic94—224no—
271C2×Dic94—23no—
272C2×Dic94—26no—
273C2×Dic94—224no—
274C2×Dic94C22×C4112yescomplemented
275C2×Dic94C2×D413yes—
276C2×Dic94C2413yes—
277M16×C47—26no—
278C2×C8×C47—26no—
279C2×C8×C47C2411yescharacteristic
280C2×C8×C47C2413yes—
281C4⋊C4×C47—23no—
282C4⋊C4×C47C2413yes—
283C4⋊C4×C47C2411yescharacteristic
284C22⋊C4×C47—23no—
285C42×C47—23no—
286C22⋊Dic47—23no—
287(C2×D47)⋊C4—23no—
288(C2×D47)⋊C4—23no—
289C4⋊Dic47—23no—
290C4⋊Dic47C2413yes—
291C4⋊Dic47C2411yescharacteristic
292Dic47⋊C4—23no—
293Dic47⋊C4—26no—
294Dic47⋊C4—21no—
295C4×Dic47—23no—
296C4×Dic47—23no—
297C4×Dic47—23no—
298#10625329—26no—
299C2×C47⋊C8—26no—
300C2×C47⋊C8C2411yescharacteristic
301C2×C47⋊C8C2413yes—
302#10625324—212no—
303C8×D47—22no—
304C8×D47—26no—
305C8×D47—26no—
306C8×D47—26no—
307C23×C47—21no—
308C23×C47C22×D413yes—
309C22×D47—26no—
310C22×D47—26no—
311C22×D47—21no—
312C22×D47—24no—
313C22×D47—42no—
314C22×D47—42no—
315C22×D47C2×C22⋊C4112yes—
316C22×D47C22×D413yes—
317C22×D47C22×D411yescharacteristic
318Q8×C47—212no—
319Q8×C47—23no—
320Q8×C47C2×C22⋊C414yes—
321Q8×C47C23×C416yes—
322D4×C47—212no—
323D4×C47—21no—
324D4×C47C2×C22⋊C4112yes—
325D4×C47C23×C412yes—
326C2×C4×C47—212no—
327C2×C4×C47—23no—
328C2×C4×C47—212no—
329C2×C4×C47—21no—
330C2×C4×C47—23no—
331C2×C4×C47—83no—
332C2×C4×C47C23×C416yes—
333C2×C4×C47C22×D413yes—
334C2×C4×C47C22×D416yes—
335C2×C4×C47C2511yescharacteristic
336C22⋊D47—212no—
337C22⋊D47—212no—
338C22⋊D47—24no—
339C22⋊D47C2×C22⋊C4124yes—
340C2×Dic47—212no—
341C2×Dic47—23no—
342C2×Dic47—212no—
343C2×Dic47—21no—
344C2×Dic47—23no—
345C2×Dic47—83no—
346C2×Dic47C2×C22⋊C4112yes—
347C2×Dic47C22×D413yes—
348C2×Dic47C22×D411yescharacteristic
349D188—212no—
350D188—21no—
351D188C2×C22⋊C4112yes—
352D188C23×C412yes—
353C4×D47—212no—
354C4×D47—224no—
355C4×D47—212no—
356C4×D47—212no—
357C4×D47—46no—
358C4×D47—42no—
359C4×D47—86no—
360C4×D47C2×C22⋊C4112yes—
361C4×D47C2×C22⋊C4112yes—
362C4×D47C23×C412yes—
363C4×D47C23×C416yes—
364C4×D47C22×D412yes—
365C4×D47C22×D416yes—
366Dic94—212no—
367Dic94—23no—
368Dic94—212no—
369Dic94—224no—
370Dic94C2×C22⋊C4112yes—
371Dic94C23×C416yes—
372C8×C47—21no—
373C8×C47—23no—
374C47⋊C8—21no—
375C47⋊C8—23no—
376C2×#2898—471nomaximal, Sylow
377C22×C47—23no—
378C22×C47—23no—
379C22×C47—22no—
380C22×C47—41no—
381C22×C47—41no—
382C22×C47C22×C22⋊C416yes—
383C22×C47C23×D411yescharacteristic
384C2×D47—23no—
385C2×D47—23no—
386C2×D47—224no—
387C2×D47—22no—
388C2×D47—41no—
389C2×D47—41no—
390C2×D47—48no—
391C2×D47C22×C22⋊C416yes—
392C2×D47C22×C22⋊C412yes—
393C2×D47#57712yes—
394C2×D47#57812yes—
395C4×C47—26no—
396C4×C47—43no—
397C4×C47—41no—
398C4×C47C22×C22⋊C416yes—
399C4×C47C24×C411yescharacteristic
400C4×C47C23×D411yescharacteristic
401Dic47—26no—
402Dic47—43no—
403Dic47—41no—
404Dic47C22×C22⋊C412yes—
405Dic47C22×C22⋊C416yes—
406C22×2−1+4—471no—
407C22×#131—471no—
408C2×#520—471no—
409#2898—473no—
410#2898—473no—
411#2898—473no—
412#2898—473no—
413#2898—471no—
414#2898—471no—
415#2898—471no—
416#2898D4711yescharacteristic, direct product factor
417C2×#417—473no—
418C2×#419—473no—
419C2×#416—473no—
420C22×#103—473no—
421C2×C47—26no—
422C2×C47—42no—
423C2×C47C23×C22⋊C411yescharacteristic
424C2×C47C2×#57711yescharacteristic
425C2×C47C2×#57811yescharacteristic
426D47—26no—
427D47—42no—
428D47#289814yesdirect product factor
429C2×2−1+4—4716no—
430C2×2−1+4—473no—
431C2×2−1+4—471no—
432C2×2−1+4—473no—
433C2×2−1+4—941no—
434C2×2−1+4—943no—
435C2×2−1+4—948no—
436C2×2−1+4C2×D4711yescharacteristic
437C22×#41—471no—
438C22×#41—473no—
439C22×#41—943no—
440C23×Q8—473no—
441C23×Q8—941no—
442C2×#131—471no—
443C2×#131—473no—
444C2×#131—473no—
445C2×#131—948no—
446C2×#131C2×D4711yescharacteristic, complemented
447C22×M16—473no—
448C23×C8—473no—
449#520—471no—
450#520—473no—
451#520—473no—
452#520—943no—
453#520—941no—
454#520C2×D4711yescharacteristic, complemented
455C2×C4×Q8—941no—
456C2×C4×D4—943no—
457C2×#117—473no—
458C22×C4⋊C4—473no—
459#419—473no—
460#419—473no—
461#419—473no—
462#419—476no—
463#419—476no—
464#419C2×D4713yescomplemented
465#417—473no—
466#417—473no—
467#417—473no—
468#417—476no—
469#417—476no—
470#417C2×D4713yescomplemented
471#416—473no—
472#416—473no—
473#416—473no—
474#416—473no—
475#416—473no—
476#416—473no—
477#416—473no—
478#416C2×D4713yescomplemented
479C2×#103—473no—
480C2×#103—473no—
481C2×#103—473no—
482C2×#103—473no—
483C2×#103—476no—
484C2×#103—476no—
485C2×#103—476no—
486C2×#103—473no—
487C2×#103C2×D4713yescomplemented
488C2×#102—471no—
489C2×#102—473no—
490C47C2×#289811yescharacteristic, complemented, Sylow
4912−1+4—24no—
4922−1+4—478no—
4932−1+4—4724no—
4942−1+4—4724no—
4952−1+4—9416no—
4962−1+4—9412no—
4972−1+4—9448no—
4982−1+4—9412no—
4992−1+4—944no—
5002−1+4C4×D4718yescomplemented
501C2×#41—23no—
502C2×#41—478no—
503C2×#41—478no—
504C2×#41—471no—
505C2×#41—473no—
506C2×#41—473no—
507C2×#41—4724no—
508C2×#41—473no—
509C2×#41—473no—
510C2×#41—473no—
511C2×#41—943no—
512C2×#41—946no—
513C2×#41—943no—
514C2×#41—943no—
515C2×#41—9412no—
516C2×#41—946no—
517C2×#41—943no—
518C2×#41—9448no—
519C2×#41—943no—
520C2×#41C22×D4713yes—
521C2×#41C22×D4711yescharacteristic
522C22×Q8—21no—
523C22×Q8—471no—
524C22×Q8—4724no—
525C22×Q8—473no—
526C22×Q8—476no—
527C22×Q8—473no—
528C22×Q8—943no—
529C22×Q8—943no—
530C22×Q8—943no—
531C22×Q8—943no—
532C22×Q8—9412no—
533C22×Q8—9416no—
534C22×Q8—943no—
535C22×Q8—941no—
536C22×Q8C22×D4713yes—
537C22×D4—473no—
538C22×D4—471no—
539C22×D4—943no—
540C23×C4—473no—
541C23×C4—943no—
542C23×C4—943no—
543C23×C4—943no—
544#131—24no—
545#131—9412no—
546#131—9412no—
547#131—944no—
548C2×M16—473no—
549C2×M16—476no—
550C2×M16—9412no—
551C2×M16C22×D4713yes—
552C22×C8—473no—
553C22×C8—471no—
554C22×C8—473no—
555C22×C8—473no—
556C22×C8—473no—
557C22×C8—9412no—
558C22×C8C22×D4713yes—
559C4×Q8—21no—
560C4×Q8—943no—
561C4×Q8—943no—
562C4×Q8—941no—
563C4×D4—23no—
564C4×D4—943no—
565C4×D4—946no—
566C4×D4—943no—
567C4×D4—946no—
568C4×D4—943no—
569#117—473no—
570#117—473no—
571#117—473no—
572#117—943no—
573#117—943no—
574#117C22×D4713yes—
575C2×C4⋊C4—473no—
576C2×C4⋊C4—473no—
577C2×C4⋊C4—476no—
578C2×C4⋊C4—471no—
579C2×C4⋊C4—943no—
580C2×C4⋊C4—943no—
581C2×C4⋊C4—943no—
582C2×C4⋊C4C22×D4713yes—
583C2×C22⋊C4—943no—
584C2×C42—943no—
585#103—473no—
586#103—476no—
587#103—473no—
588#103—473no—
589#103—476no—
590#103—473no—
591#103—473no—
592#103—476no—
593#103—473no—
594#103C22×D4713yes—
595#103C22×D4716yes—
596#103C22×D4713yes—
597#102—471no—
598#102—473no—
599#102—471no—
600#102—473no—
601#102—471no—
602#102—473no—
603#102C22×D4711yescharacteristic
604#102C22×D4713yes—
605C24—473no—
606C24—941no—
607#41—224no—
608#41—26no—
609#41—478no—
610#41—4724no—
611#41—4712no—
612#41—4712no—
613#41—4712no—
614#41—4712no—
615#41—4712no—
616#41—9424no—
617#41—9448no—
618#41—9424no—
619#41—9424no—
620#41—946no—
621#41—946no—
622#41—9448no—
623#41—9424no—
624#41—9424no—
625#41—946no—
626#41C2×C4×D4714yes—
627#41C2×C4×D47112yescomplemented
628#41D4×D4714yes—
629C2×Q8—28no—
630C2×Q8—23no—
631C2×Q8—26no—
632C2×Q8—478no—
633C2×Q8—473no—
634C2×Q8—4712no—
635C2×Q8—4724no—
636C2×Q8—4712no—
637C2×Q8—473no—
638C2×Q8—946no—
639C2×Q8—943no—
640C2×Q8—9424no—
641C2×Q8—9424no—
642C2×Q8—9424no—
643C2×Q8—946no—
644C2×Q8—9424no—
645C2×Q8—9412no—
646C2×Q8—9424no—
647C2×Q8—948no—
648C2×Q8—943no—
649C2×Q8—946no—
650C2×Q8C2×C4×D47112yescomplemented
651C2×Q8D4×D4711yescharacteristic
652C2×Q8C23×D4713yes—
653C2×D4—23no—
654C2×D4—476no—
655C2×D4—4724no—
656C2×D4—474no—
657C2×D4—473no—
658C2×D4—471no—
659C2×D4—943no—
660C2×D4—942no—
661C2×D4—941no—
662C2×D4—9424no—
663C2×D4—943no—
664C2×D4—943no—
665C2×D4D4×D4713yes—
666C2×D4C23×D4711yescharacteristic
667C22×C4—23no—
668C22×C4—23no—
669C22×C4—23no—
670C22×C4—473no—
671C22×C4—4712no—
672C22×C4—473no—
673C22×C4—473no—
674C22×C4—4712no—
675C22×C4—471no—
676C22×C4—473no—
677C22×C4—943no—
678C22×C4—9424no—
679C22×C4—943no—
680C22×C4—9424no—
681C22×C4—946no—
682C22×C4—946no—
683C22×C4—941no—
684C22×C4—943no—
685C22×C4—943no—
686C22×C4—943no—
687C22×C4—943no—
688C22×C4—943no—
689C22×C4—3766no—
690C22×C4C23×D4713yes—
691M16—26no—
692M16—9412no—
693M16—946no—
694C2×C8—26no—
695C2×C8—471no—
696C2×C8—473no—
697C2×C8—942no—
698C2×C8—946no—
699C2×C8—946no—
700C2×C8—946no—
701C2×C8—946no—
702C2×C8C23×D4711yescharacteristic
703C2×C8C23×D4713yes—
704C4⋊C4—23no—
705C4⋊C4—473no—
706C4⋊C4—471no—
707C4⋊C4—943no—
708C4⋊C4—946no—
709C4⋊C4—941no—
710C4⋊C4—943no—
711C4⋊C4C23×D4713yes—
712C4⋊C4C23×D4711yescharacteristic
713C22⋊C4—23no—
714C22⋊C4—943no—
715C22⋊C4—943no—
716C22⋊C4—943no—
717C42—23no—
718C42—943no—
719C42—943no—
720C42—943no—
721C23—21no—
722C23—471no—
723C23—4712no—
724C23—473no—
725C23—946no—
726C23—946no—
727C23—944no—
728C23—941no—
729C23—1882no—
730C23—1882no—
731C23C2×D4×D4713yes—
732Q8—212no—
733Q8—23no—
734Q8—4712no—
735Q8—476no—
736Q8—9412no—
737Q8—9424no—
738Q8—9412no—
739Q8—943no—
740Q8C22⋊C4×D4714yes—
741Q8C22×C4×D4716yes—
742D4—212no—
743D4—21no—
744D4—4724no—
745D4—4712no—
746D4—472no—
747D4—9412no—
748D4—944no—
749D4—9412no—
750D4—9412no—
751D4—941no—
752D4C22⋊C4×D47112yes—
753D4C22×C4×D4712yes—
754C2×C4—212no—
755C2×C4—23no—
756C2×C4—212no—
757C2×C4—21no—
758C2×C4—23no—
759C2×C4—83no—
760C2×C4—4712no—
761C2×C4—473no—
762C2×C4—471no—
763C2×C4—4712no—
764C2×C4—4712no—
765C2×C4—472no—
766C2×C4—476no—
767C2×C4—472no—
768C2×C4—476no—
769C2×C4—9412no—
770C2×C4—9412no—
771C2×C4—9424no—
772C2×C4—9412no—
773C2×C4—9412no—
774C2×C4—943no—
775C2×C4—9412no—
776C2×C4—941no—
777C2×C4—943no—
778C2×C4—3766no—
779C2×C4—3763no—
780C2×C4—1882no—
781C2×C4—1886no—
782C2×C4C22×C4×D4716yes—
783C2×C4C2×D4×D4713yes—
784C2×C4C2×D4×D4716yes—
785C2×C4C24×D4711yescharacteristic
786C8—21no—
787C8—23no—
788C8—941no—
789C8—943no—
790C22—23no—
791C22—23no—
792C22—22no—
793C22—41no—
794C22—41no—
795C22—472no—
796C22—472no—
797C22—472no—
798C22—476no—
799C22—9424no—
800C22—943no—
801C22—943no—
802C22—942no—
803C22—1888no—
804C22—1881no—
805C22—1881no—
806C22C2×C22⋊C4×D4716yes—
807C22C22×D4×D4711yescharacteristic
808C4—26no—
809C4—43no—
810C4—41no—
811C4—472no—
812C4—476no—
813C4—946no—
814C4—1883no—
815C4—1881no—
816C4C2×C22⋊C4×D4716yes—
817C4C23×C4×D4711yescharacteristic
818C4C22×D4×D4711yescharacteristic
819C2—26no—
820C2—42no—
821C2—474no—
822C2—946no—
823C2—1882no—
824C2C22×C22⋊C4×D4711yescharacteristic
825C2#577×D4711yescharacteristic
826C2#578×D4711yescharacteristic
subgroupG/H
centerC22C22×D4×D47
commutatorC4×C47C24×C4
FrattiniC2×C4C24×D47
FittingC47×#2898C2
socleC22×C47C23×D4
prime radicalC2×2−1+4×D47C2
cosocleC2×C4×C47C25
hypercenter#2898D47
hypocenterC47C2×#2898
LCSG ▷ C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C2×#41 ◁ #2898

Complements

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

NH ≅ G/Ntype
2. C2×#131×D47C2semidirect
3. #520×D47C2semidirect
4. #20251922C2semidirect
5. #20251921C2semidirect
6. #20251920C2semidirect
7. #20251919C2semidirect
8. #20251918C2semidirect
9. #20251917C2semidirect
10. #20251916C2semidirect
11. #417×D47C2semidirect
12. #419×D47C2semidirect
13. #416×D47C2semidirect
14. C2×#103×D47C2semidirect
15. C47×#2898C2semidirect
22. 2−1+4×D47C4semidirect
28. C2×#13094032C22semidirect
29. C2×#13094031C22semidirect
30. C2×#13094030C22semidirect
34. #15689606C22semidirect
36. #15689604C22semidirect
37. #15689603C22semidirect
43. #15689133C22semidirect
44. #15689132C22semidirect
45. #15689131C22semidirect
46. #15689130C22semidirect
47. #15689130C22semidirect
48. #15689125C22semidirect
49. #15689124C22semidirect
50. #15689123C22semidirect
51. #15689122C22semidirect
52. #15689121C22semidirect
53. #15689120C22semidirect
54. #15689119C22semidirect
55. #15689118C22semidirect
56. #15689118C22semidirect
57. #15689117C22semidirect
58. #15689116C22semidirect
59. #15689116C22semidirect
60. C2×#13093949C22semidirect
61. C2×#13093948C22semidirect
62. C2×#13093947C22semidirect
66. #103×D47C22semidirect
67. #103×D47C22semidirect
71. C2×#131×C47C22semidirect
72. C47×#520C22semidirect
73. C47×#419C22semidirect
74. C47×#417C22semidirect
75. C47×#416C22semidirect
76. C2×#103×C47C22semidirect
79. #13094072C2×C4semidirect
83. #13094071C2×C4semidirect
84. #13094071C2×C4semidirect
101. #41×D47C2×C4semidirect
112. C2×Q8×D47C2×C4semidirect
173. 2−1+4×C47C2×C4semidirect
196. #41×C47C22×C4semidirect
201. C2×Q8×C47C22×C4semidirect
222. #10625354C22×C4semidirect
231. Q8×D47C22×C4semidirect
237. #10625352C22×C4semidirect
247. #10625350C22×C4semidirect
274. C2×Dic94C22×C4semidirect
416. #2898D47direct (N × H)
428. D47#2898direct (N × H)
446. C2×#131C2×D47semidirect
454. #520C2×D47semidirect
464. #419C2×D47semidirect
470. #417C2×D47semidirect
478. #416C2×D47semidirect
487. C2×#103C2×D47semidirect
490. C47C2×#2898semidirect
500. 2−1+4C4×D47semidirect
627. #41C2×C4×D47semidirect
650. C2×Q8C2×C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×2−1+4×D472
C2×#131×D472
#520×D472
#202519222
#202519212
#202519202
#202519192
#202519182
#202519172
#202519162
#417×D472
#419×D472
#416×D472
C2×#103×D472
C47×#28982
C2×#289847