Finite Group Databasebeta

← D47×#3499 #27124686

Subgroups — D47×#3499 #27124686

Order 12032.

11126 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×2−1+4×D47C212yesmaximal, complemented
2#20257173C211yesmaximal, characteristic, complemented
3#20257172C214yesmaximal, complemented
4#20257171C213yesmaximal, complemented
5#20257170C216yesmaximal, complemented
6#20257169C212yesmaximal, complemented
7#20257168C213yesmaximal, complemented
8#20257167C2112yesmaximal, complemented
9D4×Q8×D47C214yesmaximal, complemented
10#547×D47C2112yesmaximal, complemented
11#536×D47C216yesmaximal, complemented
12#532×D47C213yesmaximal, complemented
13C2×C4⋊Q8×D47C213yesmaximal, complemented
14C4×#41×D47C211yesmaximal, characteristic, complemented
15C47×#3499C211yesmaximal, characteristic, complemented
16C2×#13094072C2216yescomplemented
17C2×#13094072C2214yescomplemented
18C2×#13094071C22112yescomplemented
19C2×#13094071C2216yescomplemented
20C2×#13094071C2212yescomplemented
212−1+4×D47—232no—
22C2×#41×D47C22112yes—
23C2×#41×D47C2216yes—
24C2×#41×D47C2211yescharacteristic
25C22×Q8×D47C2214yes—
26C22×Q8×D47C2216yes—
27Q8×D188C2214yescomplemented
28D4×Dic94C22112yescomplemented
29#15689788C22112yescomplemented
30Q8×C22⋊D47C2218yescomplemented
31#15689786C22124yescomplemented
32#15689778C22112yescomplemented
33#15689777C22112yescomplemented
34#15689776C22112yescomplemented
35#15689775C22124yescomplemented
36#15689774C22124yescomplemented
37#15689773C22124yescomplemented
38#15689772C22124yescomplemented
39#15689771C22148yescomplemented
40#15689699C2216yescomplemented
41#15689698C22112yescomplemented
42#15689697C2216yescomplemented
43#15689696C22124yescomplemented
44#15689695C22124yescomplemented
45#15689694C2216yescomplemented
46#15689693C22112yescomplemented
47#15689674C2213yescomplemented
48#15689673C2213yescomplemented
49#15689672C2216yescomplemented
50#15689671C2213yescomplemented
51#15689670C22112yescomplemented
52#15689669C2216yescomplemented
53#15689668C22112yescomplemented
54C2×#13094024C2213yescomplemented
55C2×#13094023C22112yescomplemented
56C2×#13094022C2216yescomplemented
57C4⋊Q8×D47C22112yes—
58C4⋊Q8×D47C2213yes—
59C4⋊Q8×D47C2216yes—
60C4⋊Q8×D47C22112yescomplemented
61C4⋊Q8×D47C2216yescomplemented
62C4⋊Q8×D47C2216yescomplemented
63#127×D47C2211yescharacteristic
64#124×D47C2216yes—
65#123×D47C22124yes—
66C22⋊Q8×D47C22124yes—
67#121×D47C22112yes—
68#41×Dic47C2211yescharacteristic, complemented
69C4×#10625354C2212yescomplemented
70C4×#10625350C2213yescomplemented
71#15689591C2213yescomplemented
72C4×#10625352C2216yescomplemented
73C4×Q8×D47C2212yes—
74C4×D4×D47C2216yes—
75C4×D4×D47C22112yes—
76#117×D47C2213yes—
77C2×C4⋊C4×D47C22112yes—
78C2×C42×D47C2213yes—
79C2×2−1+4×C47C2212yescomplemented
80D4×Q8×C47C2214yescomplemented
81C47×#547C22112yescomplemented
82C47×#536C2216yescomplemented
83C47×#532C2213yescomplemented
84C2×C4⋊Q8×C47C2213yescomplemented
85C4×#41×C47C2211yescharacteristic, complemented
86#13094072—232no—
87#13094072—248no—
88#13094071—216no—
89#13094071—296no—
90#13094071—248no—
91C2×#10625354C23112yes—
92C2×#10625354C2316yes—
93C2×#10625354C2311yescharacteristic
94C2×#10625350C23124yes—
95C2×#10625350C23112yes—
96C2×#10625350C2316yes—
97C2×#10625350C23112yes—
98C2×#10625350C2313yes—
99C2×#10625352C23124yes—
100C2×#10625352C23112yes—
101C2×#10625352C23112yes—
102C2×#10625352C2316yes—
103C2×#10625352C2313yes—
104#41×D47—296no—
105#41×D47—248no—
106#41×D47D4116yescomplemented
107C22×Dic94C23112yes—
108C22×Dic94C2316yes—
109C22×Dic94C23112yes—
110C2×Q8×D47—232no—
111C2×Q8×D47—248no—
112C2×Q8×D47C23112yes—
113C2×Q8×D47C2314yes—
114C2×Q8×D47C23112yes—
115C2×Q8×D47C2316yes—
116C2×Q8×D47C23112yes—
117C2×Q8×D47C23112yes—
118C2×Q8×D47C2311yescharacteristic
119C2×D4×D47C2314yes—
120C2×D4×D47C23112yes—
121C2×D4×D47C2312yes—
122C2×D4×D47C2313yes—
123C22×C4×D47C2316yes—
124C22×C4×D47C23112yes—
125C22×C4×D47C23112yes—
126C22×C4×D47C2313yes—
127#13094024C23112yes—
128#13094024C2313yes—
129#13094024C2316yes—
130#13094023C23124yes—
131#13094023C23124yes—
132#13094023C23112yes—
133#13094023C23124yes—
134#13094022C23124yes—
135#13094022C2316yes—
136#13094022C23112yes—
137#13094021C2311yescharacteristic
138#13094020C2314yes—
139#13094020C2312yes—
140#13094013C2316yes—
141#13094012C2316yes—
142#13094011C2316yes—
143#13094010C23124yes—
144#13094009C23148yes—
145#13094008C23124yes—
146#13094007C23124yes—
147#13094006C23148yes—
148#13094005C23124yes—
149#13094004C23124yes—
150#13094003C23124yes—
151#13094002C23148yes—
152#13094001C23148yes—
153#13094000C23124yes—
154#13093999C23112yes—
155#13093998C23112yes—
156#13093997C23124yes—
157#13093996C23124yes—
158#13093995C23112yes—
159Q8×Dic47C2312yes—
160C4×Dic94C2316yes—
161#13093989C2316yes—
162C4×D188C2316yes—
163C4×D188C23112yes—
164D4×Dic47C2316yes—
165D4×Dic47C23112yes—
166#13093986C23112yes—
167#13093986C2316yes—
168C4×C22⋊D47C23124yes—
169C4×C22⋊D47C23112yes—
170(C22⋊D47)⋊C4C23112yes—
171(C22⋊D47)⋊C4C23124yes—
172#13093983C2313yes—
173#13093982C2316yes—
174#13093981C2316yes—
175#13093980C2316yes—
176C2×C4⋊Dic47C23112yes—
177C2×Dic47⋊C4C23124yes—
178C4⋊C4×D47C23124yes—
179C4⋊C4×D47C23124yes—
180C4⋊C4×D47C23112yes—
181C4⋊C4×D47C23124yes—
182C4⋊C4×D47C2316yes—
183C22⋊C4×D47C2316yes—
184C22⋊C4×D47C23124yes—
185C2×C4×Dic47C2316yes—
186C2×C4×Dic47C2313yes—
187C42×D47C2311yescharacteristic
188C42×D47C2313yes—
189C42×D47C2316yes—
190C42×D47C2316yes—
191C42×D47C2313yes—
192C42×D47C2313yes—
1932−1+4×C47—216no—
194C2×#41×C47C23112yes—
195C2×#41×C47C2316yes—
196C2×#41×C47C2311yescharacteristic
197C22×Q8×C47C2314yes—
198C22×Q8×C47C2316yes—
199C4⋊Q8×C47C23112yes—
200C4⋊Q8×C47C2313yes—
201C4⋊Q8×C47C2316yes—
202#127×C47C2311yescharacteristic
203#124×C47C2316yes—
204#123×C47C23124yes—
205C22⋊Q8×C47C23124yes—
206#121×C47C23112yes—
207C4×Q8×C47C2312yes—
208C4×D4×C47C2316yes—
209C4×D4×C47C23112yes—
210#117×C47C2313yes—
211C2×C4⋊C4×C47C23112yes—
212C2×C42×C47C2313yes—
213C23×D47C2414yes—
214C23×D47C2413yes—
215#41×C47—248no—
216#41×C47—224no—
217#41×C47C2×D418yescomplemented
218C2×Q8×C47—216no—
219C2×Q8×C47—224no—
220C2×Q8×C47C24112yes—
221C2×Q8×C47C2416yes—
222C2×Q8×C47C2411yescharacteristic
223C2×D4×C47C2414yes—
224C2×D4×C47C24112yes—
225C2×D4×C47C2412yes—
226C2×D4×C47C2413yes—
227C22×C4×C47C2416yes—
228C22×C4×C47C24112yes—
229C22×C4×C47C24112yes—
230C22×C4×C47C2413yes—
231C2×C22⋊D47C2418yes—
232C2×C22⋊D47C24112yes—
233C2×C22⋊D47C24112yes—
234C2×C22⋊D47C2414yes—
235C2×C22⋊D47C2416yes—
236C22×Dic47C2416yes—
237C22×Dic47C24112yes—
238C22×Dic47C24112yes—
239C22×Dic47C2413yes—
240#10625354—248no—
241#10625354—224no—
242#10625354C2×D418yescomplemented
243Q8×D47—216no—
244Q8×D47—248no—
245Q8×D47—224no—
246Q8×D47—248no—
247Q8×D47—248no—
248Q8×D47—248no—
249Q8×D47C2×D418yes—
250#10625352—248no—
251#10625352—296no—
252#10625352—248no—
253#10625352—224no—
254#10625352C2×D4124yescomplemented
255D4×D47—248no—
256D4×D47—28no—
257D4×D47—216no—
258D4×D47C2×D4124yes—
259#10625350—224no—
260#10625350—296no—
261#10625350—248no—
262#10625350—248no—
263#10625350C2×D4124yescomplemented
264C2×D188C2414yes—
265C2×D188C24112yes—
266C2×D188C2412yes—
267C2×D188C2413yes—
268C2×C4×D47—248no—
269C2×C4×D47—248no—
270C2×C4×D47—224no—
271C2×C4×D47C2×D4124yes—
272C2×C4×D47C2416yes—
273C2×C4×D47C2416yes—
274C2×C4×D47C2416yes—
275C2×C4×D47C24112yes—
276C2×C4×D47C24124yes—
277C2×C4×D47C24112yes—
278C2×C4×D47C24112yes—
279C2×C4×D47C2411yescharacteristic
280C2×C4×D47C2413yes—
281C2×C4×D47C2413yes—
282C2×C4×D47C2413yes—
283C2×C4×D47C2412yes—
284C2×Dic94—224no—
285C2×Dic94—248no—
286C2×Dic94—248no—
287C2×Dic94C24124yes—
288C2×Dic94C24112yes—
289C2×Dic94C24112yes—
290C2×Dic94C2416yes—
291C2×Dic94C2413yes—
292C4⋊C4×C47C24112yes—
293C4⋊C4×C47C24124yes—
294C4⋊C4×C47C2416yes—
295C22⋊C4×C47C2416yes—
296C22⋊C4×C47C24124yes—
297C42×C47C2411yescharacteristic
298C42×C47C2413yes—
299C42×C47C2416yes—
300C22⋊Dic47C2416yes—
301C22⋊Dic47C24124yes—
302(C2×D47)⋊C4C24112yes—
303(C2×D47)⋊C4C24124yes—
304(C2×D47)⋊C4C24124yes—
305C4⋊Dic47C24112yes—
306C4⋊Dic47C24124yes—
307C4⋊Dic47C2416yes—
308Dic47⋊C4C24124yes—
309Dic47⋊C4C24148yes—
310Dic47⋊C4C24112yes—
311C4×Dic47C2411yescharacteristic
312C4×Dic47C2412yes—
313C4×Dic47C2416yes—
314C4×Dic47C2413yes—
315C4×Dic47C2416yes—
316C4×Dic47C2416yes—
317C4×Dic47C2416yes—
318C23×C47C2514yes—
319C23×C47C2513yes—
320C22×D47—212no—
321C22×D47—28no—
322C22×D47—216no—
323C22×D47C22×D4112yes—
324C22×D47C2514yes—
325C22×D47C2513yes—
326C22×D47C2511yescharacteristic
327Q8×C47—212no—
328Q8×C47—224no—
329Q8×C47C22×D414yes—
330D4×C47—224no—
331D4×C47—24no—
332D4×C47—28no—
333D4×C47C22×D4112yes—
334C2×C4×C47—224no—
335C2×C4×C47—224no—
336C2×C4×C47—212no—
337C2×C4×C47C22×D4112yes—
338C2×C4×C47C2516yes—
339C2×C4×C47C25112yes—
340C2×C4×C47C2511yescharacteristic
341C2×C4×C47C2513yes—
342C2×C4×C47C2512yes—
343C22⋊D47—224no—
344C22⋊D47—224no—
345C22⋊D47—28no—
346C22⋊D47—216no—
347C22⋊D47C22×D4124yes—
348C2×Dic47—224no—
349C2×Dic47—224no—
350C2×Dic47—212no—
351C2×Dic47C22×D4112yes—
352C2×Dic47C2516yes—
353C2×Dic47C25112yes—
354C2×Dic47C2511yescharacteristic
355C2×Dic47C2513yes—
356C2×Dic47C2512yes—
357D188—224no—
358D188—24no—
359D188—28no—
360D188C22×D4112yes—
361C4×D47—224no—
362C4×D47—248no—
363C4×D47—212no—
364C4×D47—224no—
365C4×D47—212no—
366C4×D47—224no—
367C4×D47—212no—
368C4×D47C22×D4112yes—
369C4×D47C22×D414yes—
370C4×D47C22×D4112yes—
371C4×D47C22×D4112yes—
372C4×D472−1+418yescomplemented
373Dic94—212no—
374Dic94—224no—
375Dic94—224no—
376Dic94—248no—
377Dic94C22×D4112yes—
378C2×#3499—471nomaximal, Sylow
379C22×C47—26no—
380C22×C47—24no—
381C22×C47—28no—
382C22×C47C23×D416yes—
383C22×C47C2611yescharacteristic
384C2×D47—26no—
385C2×D47—224no—
386C2×D47—24no—
387C2×D47—28no—
388C2×D47—416no—
389C2×D47C23×D416yes—
390C2×D47C23×D412yes—
391C2×D47C2×2−1+414yes—
392C4×C47—212no—
393C4×C47—26no—
394C4×C47C23×D412yes—
395C4×C47C23×D416yes—
396C4×C47C2×2−1+414yescomplemented
397Dic47—212no—
398Dic47—26no—
399Dic47C23×D412yes—
400Dic47C23×D416yes—
401Dic47C2×2−1+414yescomplemented
402C22×2−1+4—472no—
403#3499—472no—
404#3499—474no—
405#3499—4712no—
406#3499—476no—
407#3499—473no—
408#3499—473no—
409#3499—471no—
410#3499D4711yescharacteristic, direct product factor
411C2×D4×Q8—474no—
412C2×#547—4712no—
413C2×#536—476no—
414C2×#532—473no—
415C22×C4⋊Q8—473no—
416C2×C4×#41—471no—
417C2×C47—26no—
418C2×C47—44no—
419C2×C47C24×D411yescharacteristic
420C2×C47C22×2−1+412yes—
421D47—26no—
422D47—44no—
423D47#349914yesdirect product factor
424C2×2−1+4—476no—
425C2×2−1+4—4712no—
426C2×2−1+4—472no—
427C2×2−1+4—474no—
428C2×2−1+4—476no—
429C2×2−1+4—9432no—
430C2×2−1+4C2×D4712yescomplemented
431C22×#41—471no—
432C22×#41—476no—
433C22×#41—4712no—
434C23×Q8—476no—
435C23×Q8—474no—
436D4×Q8—478no—
437D4×Q8—4712no—
438D4×Q8—4724no—
439D4×Q8—474no—
440D4×Q8—4712no—
441D4×Q8C2×D4714yescomplemented
442#547—4724no—
443#547—4712no—
444#547—4748no—
445#547—4724no—
446#547—4724no—
447#547—4712no—
448#547—4712no—
449#547—4724no—
450#547C2×D47112yescomplemented
451#536—476no—
452#536—476no—
453#536—4712no—
454#536—4712no—
455#536—4724no—
456#536—4724no—
457#536—476no—
458#536C2×D4716yescomplemented
459#532—476no—
460#532—473no—
461#532—473no—
462#532—476no—
463#532—4712no—
464#532—4712no—
465#532—473no—
466#532C2×D4713yescomplemented
467C2×C4⋊Q8—476no—
468C2×C4⋊Q8—473no—
469C2×C4⋊Q8—476no—
470C2×C4⋊Q8—4712no—
471C2×C4⋊Q8—476no—
472C2×C4⋊Q8—476no—
473C2×C4⋊Q8—4712no—
474C2×C4⋊Q8—4712no—
475C2×C4⋊Q8—473no—
476C2×C4⋊Q8C2×D4713yescomplemented
477C2×#127—471no—
478C2×#124—476no—
479C2×#123—4724no—
480C2×C22⋊Q8—4724no—
481C2×#121—4712no—
482C4×#41—471no—
483C4×#41—472no—
484C4×#41—476no—
485C4×#41—473no—
486C4×#41—473no—
487C4×#41C2×D4711yescharacteristic, complemented
488C2×C4×Q8—472no—
489C2×C4×D4—476no—
490C2×C4×D4—4712no—
491C2×#117—473no—
492C22×C4⋊C4—4712no—
493C22×C42—473no—
494C47C2×#349911yescharacteristic, complemented, Sylow
4952−1+4—216no—
4962−1+4—9432no—
4972−1+4—9448no—
4982−1+4—9496no—
4992−1+4—9448no—
5002−1+4—9416no—
501C2×#41—4716no—
502C2×#41—471no—
503C2×#41—476no—
504C2×#41—4712no—
505C2×#41—473no—
506C2×#41—4712no—
507C2×#41—476no—
508C2×#41—4712no—
509C2×#41—4724no—
510C2×#41—473no—
511C2×#41—4712no—
512C2×#41—476no—
513C2×#41—4712no—
514C2×#41—4724no—
515C2×#41—9448no—
516C2×#41—9496no—
517C2×#41C22×D4716yes—
518C2×#41C22×D47112yes—
519C2×#41C22×D4711yescharacteristic
520C22×Q8—471no—
521C22×Q8—4712no—
522C22×Q8—476no—
523C22×Q8—4712no—
524C22×Q8—4712no—
525C22×Q8—4712no—
526C22×Q8—474no—
527C22×Q8—4712no—
528C22×Q8—476no—
529C22×Q8—4712no—
530C22×Q8—9448no—
531C22×Q8—9432no—
532C22×Q8C22×D4716yes—
533C22×Q8C22×D4714yes—
534C22×D4—473no—
535C22×D4—474no—
536C22×D4—4712no—
537C22×D4—472no—
538C23×C4—473no—
539C23×C4—476no—
540C23×C4—4712no—
541C23×C4—4712no—
542C4⋊Q8—476no—
543C4⋊Q8—4712no—
544C4⋊Q8—4724no—
545C4⋊Q8—4712no—
546C4⋊Q8—4724no—
547C4⋊Q8—4724no—
548C4⋊Q8—4724no—
549C4⋊Q8—473no—
550C4⋊Q8—476no—
551C4⋊Q8—4712no—
552C4⋊Q8C22×D4713yes—
553C4⋊Q8C22×D4716yes—
554C4⋊Q8C22×D47112yes—
555#127—472no—
556#127—474no—
557#127—471no—
558#127C22×D4711yescharacteristic
559#124—476no—
560#124—476no—
561#124—4724no—
562#124—476no—
563#124C22×D4716yes—
564#123—4724no—
565#123—4724no—
566#123—4748no—
567#123—4748no—
568#123—4724no—
569#123C22×D47124yes—
570C22⋊Q8—4724no—
571C22⋊Q8—4724no—
572C22⋊Q8—4748no—
573C22⋊Q8—4724no—
574C22⋊Q8—4748no—
575C22⋊Q8C22×D47124yes—
576#121—4712no—
577#121—4724no—
578#121—4712no—
579#121—4712no—
580#121—4724no—
581#121C22×D47112yes—
582C4×Q8—472no—
583C4×Q8—476no—
584C4×Q8—476no—
585C4×Q8C22×D4712yes—
586C4×D4—476no—
587C4×D4—4712no—
588C4×D4—4712no—
589C4×D4—4724no—
590C4×D4—476no—
591C4×D4—4712no—
592C4×D4—4712no—
593C4×D4—4724no—
594C4×D4—476no—
595C4×D4—4712no—
596C4×D4C22×D4716yes—
597C4×D4C22×D47112yes—
598#117—473no—
599#117—476no—
600#117—476no—
601#117—476no—
602#117C22×D4713yes—
603C2×C4⋊C4—4724no—
604C2×C4⋊C4—4712no—
605C2×C4⋊C4—4712no—
606C2×C4⋊C4—4724no—
607C2×C4⋊C4—4724no—
608C2×C4⋊C4—4724no—
609C2×C4⋊C4—476no—
610C2×C4⋊C4C22×D47112yes—
611C2×C22⋊C4—476no—
612C2×C22⋊C4—4724no—
613C2×C42—476no—
614C2×C42—473no—
615C2×C42—473no—
616C2×C42—476no—
617C2×C42—476no—
618C2×C42—473no—
619C2×C42—473no—
620C2×C42—471no—
621C2×C42C22×D4713yes—
622C24—473no—
623C24—474no—
624#41—248no—
625#41—224no—
626#41—478no—
627#41—4724no—
628#41—4724no—
629#41—9448no—
630#41—9496no—
631#41—9448no—
632#41—9448no—
633#41—9424no—
634#41—9424no—
635#41—9496no—
636#41—9448no—
637#41—9448no—
638#41—9424no—
639#41D4×D4718yescomplemented
640C2×Q8—216no—
641C2×Q8—224no—
642C2×Q8—478no—
643C2×Q8—473no—
644C2×Q8—4724no—
645C2×Q8—4712no—
646C2×Q8—4712no—
647C2×Q8—476no—
648C2×Q8—9448no—
649C2×Q8—9448no—
650C2×Q8—9424no—
651C2×Q8—9448no—
652C2×Q8—9448no—
653C2×Q8—9448no—
654C2×Q8—9448no—
655C2×Q8—9416no—
656C2×Q8—9424no—
657C2×Q8C23×D47112yes—
658C2×Q8C23×D4716yes—
659C2×Q8C23×D4711yescharacteristic
660C2×D4—476no—
661C2×D4—4724no—
662C2×D4—478no—
663C2×D4—4712no—
664C2×D4—4712no—
665C2×D4—474no—
666C2×D4—473no—
667C2×D4—474no—
668C2×D4—4712no—
669C2×D4—472no—
670C2×D4—9416no—
671C2×D4—948no—
672C2×D4—9448no—
673C2×D4C23×D4714yes—
674C2×D4C23×D47112yes—
675C2×D4C23×D4712yes—
676C2×D4C23×D4713yes—
677C22×C4—473no—
678C22×C4—4724no—
679C22×C4—472no—
680C22×C4—471no—
681C22×C4—473no—
682C22×C4—473no—
683C22×C4—473no—
684C22×C4—476no—
685C22×C4—4712no—
686C22×C4—4712no—
687C22×C4—476no—
688C22×C4—476no—
689C22×C4—476no—
690C22×C4—4712no—
691C22×C4—4724no—
692C22×C4—4712no—
693C22×C4—4712no—
694C22×C4—9424no—
695C22×C4—9448no—
696C22×C4—9448no—
697C22×C4C23×D4716yes—
698C22×C4C23×D47112yes—
699C22×C4C23×D47112yes—
700C22×C4C23×D4713yes—
701C4⋊C4—4724no—
702C4⋊C4—4748no—
703C4⋊C4—4712no—
704C4⋊C4—4712no—
705C4⋊C4—4724no—
706C4⋊C4—476no—
707C4⋊C4C23×D47112yes—
708C4⋊C4C23×D47124yes—
709C4⋊C4C23×D4716yes—
710C22⋊C4—476no—
711C22⋊C4—4724no—
712C22⋊C4—4712no—
713C22⋊C4—4724no—
714C22⋊C4—4724no—
715C22⋊C4C23×D4716yes—
716C22⋊C4C23×D47124yes—
717C42—471no—
718C42—472no—
719C42—476no—
720C42—473no—
721C42—476no—
722C42—476no—
723C42—476no—
724C42C23×D4711yescharacteristic
725C42C23×D4713yes—
726C42C23×D4716yes—
727C23—471no—
728C23—4712no—
729C23—473no—
730C23—474no—
731C23—9412no—
732C23—948no—
733C23—9416no—
734C23C24×D4714yes—
735C23C24×D4713yes—
736Q8—224no—
737Q8—212no—
738Q8—4712no—
739Q8—9424no—
740Q8—9448no—
741Q8—9424no—
742Q8—9412no—
743Q8C2×D4×D4714yes—
744D4—224no—
745D4—24no—
746D4—28no—
747D4—4724no—
748D4—4712no—
749D4—9424no—
750D4—9416no—
751D4—948no—
752D4—9424no—
753D4—9424no—
754D4—944no—
755D4—948no—
756D4C2×D4×D47112yes—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—212no—
760C2×C4—4712no—
761C2×C4—472no—
762C2×C4—471no—
763C2×C4—473no—
764C2×C4—474no—
765C2×C4—4712no—
766C2×C4—4712no—
767C2×C4—4712no—
768C2×C4—478no—
769C2×C4—476no—
770C2×C4—4712no—
771C2×C4—9412no—
772C2×C4—9424no—
773C2×C4—9412no—
774C2×C4—9424no—
775C2×C4—9448no—
776C2×C4—9412no—
777C2×C4—9424no—
778C2×C4—9424no—
779C2×C4—9424no—
780C2×C4—9412no—
781C2×C4C2×D4×D47112yes—
782C2×C4C24×D4716yes—
783C2×C4C24×D47112yes—
784C2×C4C24×D4711yescharacteristic
785C2×C4C24×D4713yes—
786C2×C4C24×D4712yes—
787C22—26no—
788C22—24no—
789C22—28no—
790C22—472no—
791C22—474no—
792C22—476no—
793C22—9424no—
794C22—946no—
795C22—944no—
796C22—948no—
797C22—18816no—
798C22C22×D4×D4716yes—
799C22C25×D4711yescharacteristic
800C4—212no—
801C4—26no—
802C4—472no—
803C4—476no—
804C4—474no—
805C4—9412no—
806C4—946no—
807C4C22×D4×D4716yes—
808C4C22×D4×D4712yes—
809C42−1+4×D4714yescomplemented
810C2—26no—
811C2—44no—
812C2—474no—
813C2—946no—
814C2—1884no—
815C2C23×D4×D4711yescharacteristic
816C2C2×2−1+4×D4712yes—
subgroupG/H
center, FrattiniC22C25×D47
commutator, socle, cosocleC22×C47C26
FittingC47×#3499C2
hypercenter#3499D47
hypocenterC47C2×#3499
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C22 ◁ #3499

Complements

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

NH ≅ G/Ntype
1. C2×2−1+4×D47C2semidirect
2. #20257173C2semidirect
3. #20257172C2semidirect
4. #20257171C2semidirect
5. #20257170C2semidirect
6. #20257169C2semidirect
7. #20257168C2semidirect
8. #20257167C2semidirect
9. D4×Q8×D47C2semidirect
10. #547×D47C2semidirect
11. #536×D47C2semidirect
12. #532×D47C2semidirect
13. C2×C4⋊Q8×D47C2semidirect
14. C4×#41×D47C2semidirect
15. C47×#3499C2semidirect
16. C2×#13094072C22semidirect
17. C2×#13094072C22semidirect
18. C2×#13094071C22semidirect
19. C2×#13094071C22semidirect
20. C2×#13094071C22semidirect
27. Q8×D188C22semidirect
28. D4×Dic94C22semidirect
29. #15689788C22semidirect
30. Q8×C22⋊D47C22semidirect
31. #15689786C22semidirect
32. #15689778C22semidirect
33. #15689777C22semidirect
34. #15689776C22semidirect
35. #15689775C22semidirect
36. #15689774C22semidirect
37. #15689773C22semidirect
38. #15689772C22semidirect
39. #15689771C22semidirect
40. #15689699C22semidirect
41. #15689698C22semidirect
42. #15689697C22semidirect
43. #15689696C22semidirect
44. #15689695C22semidirect
45. #15689694C22semidirect
46. #15689693C22semidirect
47. #15689674C22semidirect
48. #15689673C22semidirect
49. #15689672C22semidirect
50. #15689671C22semidirect
51. #15689670C22semidirect
52. #15689669C22semidirect
53. #15689668C22semidirect
54. C2×#13094024C22semidirect
55. C2×#13094023C22semidirect
56. C2×#13094022C22semidirect
60. C4⋊Q8×D47C22semidirect
61. C4⋊Q8×D47C22semidirect
62. C4⋊Q8×D47C22semidirect
68. #41×Dic47C22semidirect
69. C4×#10625354C22semidirect
70. C4×#10625350C22semidirect
71. #15689591C22semidirect
72. C4×#10625352C22semidirect
79. C2×2−1+4×C47C22semidirect
80. D4×Q8×C47C22semidirect
81. C47×#547C22semidirect
82. C47×#536C22semidirect
83. C47×#532C22semidirect
84. C2×C4⋊Q8×C47C22semidirect
85. C4×#41×C47C22semidirect
106. #41×D47D4semidirect
217. #41×C47C2×D4semidirect
242. #10625354C2×D4semidirect
254. #10625352C2×D4semidirect
263. #10625350C2×D4semidirect
372. C4×D472−1+4semidirect
396. C4×C47C2×2−1+4semidirect
401. Dic47C2×2−1+4semidirect
410. #3499D47direct (N × H)
423. D47#3499direct (N × H)
430. C2×2−1+4C2×D47semidirect
441. D4×Q8C2×D47semidirect
450. #547C2×D47semidirect
458. #536C2×D47semidirect
466. #532C2×D47semidirect
476. C2×C4⋊Q8C2×D47semidirect
487. C4×#41C2×D47semidirect
494. C47C2×#3499semidirect
639. #41D4×D47semidirect
809. C42−1+4×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
#202571732
#202571722
#202571712
#202571702
#202571692
#202571682
#202571672
D4×Q8×D472
#547×D472
#536×D472
#532×D472
C2×C4⋊Q8×D472
C4×#41×D472
C47×#34992
C2×#349947