Finite Group Databasebeta

← #26218310

Subgroups — #26218310

Order 12032.

1692 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic, complemented
2#20256717C211yesmaximal, characteristic
3C2×#15689107C211yesmaximal, characteristic, complemented
4C2×#15689105C211yesmaximal, characteristic, complemented
5#20243937C214yesmaximal, complemented
6#20243932C214yesmaximal, complemented
7C2×#15688895C211yesmaximal, characteristic, complemented
8C2×#15688894C211yesmaximal, characteristic, complemented
9C2×C47×#413C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11#15689889—22no—
12#15689889—22no—
13#15689889—22no—
14#15689889C2214yes—
15C2×#13094032—22no—
16C2×#13094030—22no—
17C22×#10625329C2211yescharacteristic
18C22×#10625329C2211yescharacteristic
19C2×M16×D47—22no—
20#15689701—22no—
21#15689697C2212yes—
22#15689694—21no—
23#15689690C2212yes—
24#15689687—21no—
25#15689682C414yes—
26#15689669—22no—
27#15689634C414yes—
28#15689630—22no—
29C2×#13093983C2211yescharacteristic
30#15689107—22no—
31#15689107—22no—
32#15689105—22no—
33#15689105C2214yes—
34C2×#13093943C2212yescomplemented
35C2×#13093942—21no—
36C2×#13093941C2212yescomplemented
37C2×#13093940—21no—
38#15688895C2214yescomplemented
39#15688894C2214yescomplemented
40C22×#41×C47C2211yescharacteristic
41C22×M16×C47C2211yescharacteristic
42C22×M16×C47C2211yescharacteristic
43C47×#413—22no—
44C47×#413—22no—
45C2×#101×C47C2212yescomplemented
46C2×#100×C47C2212yescomplemented
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350—21no—
53C2×#10625350—21no—
54C2×#10625350—21no—
55C2×#10625350C2×C412yes—
56C2×#10625350D412yes—
57C2×#10625350D412yes—
58C2×#10625350C2312yes—
59C22×Dic94D411yescharacteristic
60C22×D188D411yescharacteristic
61C22×C22⋊D47C2×C412yes—
62C22×C4×D47D412yes—
63#13094032—28no—
64#13094032—28no—
65#13094030—28no—
66#13094030—28no—
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329—21no—
70C2×#10625329—21no—
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625329—21no—
74C2×#10625329—21no—
75C2×#10625329D412yescomplemented
76C2×#10625329D412yescomplemented
77C2×#10625329C2312yes—
78C2×#10625329C2312yes—
79C2×#10625324—24no—
80M16×D47—28no—
81M16×D47—28no—
82C22×C47⋊C8—21no—
83C22×C47⋊C8—21no—
84C2×C8×D47—24no—
85#13094022—22no—
86#13094020—22no—
87#13094013—22no—
88#13094011—22no—
89#13094007C2×C418yes—
90#13094005—24no—
91#13094003—24no—
92#13094000—24no—
93#13093998—24no—
94#13093996—28no—
95#13093995—24no—
96#13093993C2×C418yes—
97#13093992—24no—
98C4×C22⋊D47—28no—
99#13093983—21no—
100#13093983—21no—
101#13093983C2×C412yes—
102#13093983C2312yes—
103C2×C4⋊Dic47—21no—
104C2×C22⋊Dic47C2×C412yes—
105C2×C4×Dic47—21no—
106#13093943—24no—
107#13093942—24no—
108#13093941—24no—
109#13093940—24no—
110C2×#41×C47—21no—
111C2×#41×C47—21no—
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—
122C22×Q8×C47C2311yescharacteristic
123C22×D4×C47C2×C412yes—
124C22×D4×C47C2311yescharacteristic
125C23×C4×C47C2×C412yes—
126C23×C4×C47C2311yescharacteristic
127C2×M16×C47—21no—
128C2×M16×C47—21no—
129C2×M16×C47—21no—
130C2×M16×C47—21no—
131C2×M16×C47—21no—
132C2×M16×C47—21no—
133C2×M16×C47—21no—
134C2×M16×C47—21no—
135C2×M16×C47D412yescomplemented
136C2×M16×C47D412yescomplemented
137C2×M16×C47C2312yes—
138C2×M16×C47C2312yes—
139C22×C8×C47—21no—
140C22×C8×C47—21no—
141#101×C47—24no—
142#100×C47—24no—
143C24×C47C22×C412yes—
144C24×C47C22×C411yescharacteristic
145C23×D47C22⋊C412yes—
146#41×C47—41no—
147#41×C47—41no—
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—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47—21no—
165C2×Q8×C47—21no—
166C2×Q8×C47—21no—
167C2×Q8×C47—21no—
168C2×D4×C47—22no—
169C2×D4×C47—22no—
170C2×D4×C47—22no—
171C2×D4×C47—22no—
172C2×D4×C47—22no—
173C2×D4×C47—22no—
174C2×D4×C47—21no—
175C2×D4×C47—21no—
176C2×D4×C47—21no—
177C2×D4×C47—21no—
178C2×D4×C47—21no—
179C2×D4×C47—21no—
180C22×C4×C47—22no—
181C22×C4×C47—22no—
182C22×C4×C47—22no—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47C22×C412yes—
187C22×C4×C47C22×C411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47C2×D411yescharacteristic
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47#4111yescharacteristic
197C22×C4×C47#4111yescharacteristic
198C22×C4×C47#4111yescharacteristic
199C22×C4×C47#4111yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C2×C22⋊D47—22no—
202C2×C22⋊D47—22no—
203C2×C22⋊D47—22no—
204C2×C22⋊D47—22no—
205C2×C22⋊D47—28no—
206C2×C22⋊D47C22⋊C414yes—
207C2×C22⋊D47C22×C414yes—
208C22×Dic47—22no—
209C22×Dic47C22⋊C412yes—
210#10625350—22no—
211#10625350—22no—
212#10625350—22no—
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—
226C2×D188—21no—
227C2×D188—21no—
228C2×D188—21no—
229C2×D188—21no—
230C2×D188C22⋊C412yes—
231C2×D188C2×D412yes—
232C2×C4×D47—22no—
233C2×C4×D47—22no—
234C2×C4×D47—22no—
235C2×C4×D47—22no—
236C2×C4×D47C22⋊C414yes—
237C2×C4×D47C2×D414yes—
238C2×Dic94—21no—
239C2×Dic94—21no—
240C2×Dic94—21no—
241C2×Dic94—21no—
242C2×Dic94C22⋊C412yes—
243C2×Dic94C2×D412yes—
244M16×C47—22no—
245M16×C47—22no—
246M16×C47—22no—
247M16×C47—22no—
248M16×C47—22no—
249M16×C47—41no—
250M16×C47—41no—
251M16×C47C2×D414yes—
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47—22no—
255C2×C8×C47—22no—
256C2×C8×C47—41no—
257C2×C8×C47—41no—
258C22⋊Dic47—22no—
259C22⋊Dic47—28no—
260C22⋊Dic47C22×C414yes—
261(C2×D47)⋊C4—28no—
262C4⋊Dic47—22no—
263C4⋊Dic47—22no—
264Dic47⋊C4—28no—
265C4×Dic47—22no—
266C4×Dic47—22no—
267#10625329—22no—
268#10625329—22no—
269#10625329—22no—
270#10625329—22no—
271#10625329—22no—
272#10625329—41no—
273#10625329—41no—
274#10625329C2×D414yes—
275C2×C47⋊C8—22no—
276C2×C47⋊C8—22no—
277C2×C47⋊C8—22no—
278C2×C47⋊C8—22no—
279C2×C47⋊C8—41no—
280C2×C47⋊C8—41no—
281#10625324—216no—
282C8×D47—216no—
283C23×C47—22no—
284C23×C47—22no—
285C23×C47—22no—
286C23×C47—81no—
287C23×C47—82no—
288C23×C47C2×C22⋊C411yescharacteristic
289C23×C47C2×C22⋊C411yescharacteristic
290C23×C47C4×D411yescharacteristic
291C23×C47C4×D411yescharacteristic
292C23×C47C4×D411yescharacteristic
293C23×C47C4×D411yescharacteristic
294C23×C47C23×C411yescharacteristic
295C22×D47—22no—
296C22×D47—22no—
297C22×D47—82no—
298C22×D47C2×C22⋊C414yes—
299Q8×C47—41no—
300Q8×C47—41no—
301Q8×C47—41no—
302Q8×C47—41no—
303D4×C47—42no—
304D4×C47—42no—
305D4×C47—42no—
306D4×C47—42no—
307D4×C47—41no—
308D4×C47—41no—
309D4×C47—41no—
310D4×C47—41no—
311C2×C4×C47—22no—
312C2×C4×C47—22no—
313C2×C4×C47—22no—
314C2×C4×C47—42no—
315C2×C4×C47—42no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47C2×C22⋊C411yescharacteristic
319C2×C4×C47C2×C22⋊C411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C4×D411yescharacteristic
322C2×C4×C47C4×D411yescharacteristic
323C2×C4×C47C4×D411yescharacteristic
324C2×C4×C47#12011yescharacteristic
325C2×C4×C47#12011yescharacteristic
326C2×C4×C47#12011yescharacteristic
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47#12111yescharacteristic
329C2×C4×C47#12111yescharacteristic
330C2×C4×C47#12111yescharacteristic
331C2×C4×C47#12111yescharacteristic
332C2×C4×C47#12111yescharacteristic
333C2×C4×C47#12111yescharacteristic
334C2×C4×C47#12111yescharacteristic
335C2×C4×C47#12111yescharacteristic
336C2×C4×C47#12311yescharacteristic
337C2×C4×C47#12311yescharacteristic
338C2×C4×C47#12311yescharacteristic
339C2×C4×C47#12311yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C22×D411yescharacteristic
343C2×C4×C47C22×D411yescharacteristic
344C2×C4×C47C2×#4111yescharacteristic
345C2×C4×C47C2×#4111yescharacteristic
346C22⋊D47—24no—
347C22⋊D47—24no—
348C22⋊D47—24no—
349C22⋊D47—24no—
350C22⋊D47—88no—
351C2×Dic47—22no—
352C2×Dic47—22no—
353C2×Dic47—24no—
354C2×Dic47—82no—
355C2×Dic47C2×C22⋊C414yes—
356D188—22no—
357D188—22no—
358D188—22no—
359D188—22no—
360C4×D47—24no—
361C4×D47—24no—
362C4×D47—24no—
363C4×D47—24no—
364Dic94—22no—
365Dic94—22no—
366Dic94—22no—
367Dic94—22no—
368C8×C47—24no—
369C8×C47—42no—
370C47⋊C8—24no—
371C47⋊C8—42no—
372#21017—471nomaximal, Sylow
373C22×C47—41no—
374C22×C47—41no—
375C22×C47—41no—
376C22×C47—41no—
377C22×C47—41no—
378C22×C47—41no—
379C22×C47—41no—
380C22×C47—44no—
381C22×C47—42no—
382C22×C47—82no—
383C22×C47—82no—
384C22×C47#38611yescharacteristic
385C22×C47#38611yescharacteristic
386C22×C47#38611yescharacteristic
387C22×C47#38611yescharacteristic
388C22×C47C22×C22⋊C411yescharacteristic
389C22×C47C2×C4×D411yescharacteristic
390C22×C47C2×C4×D411yescharacteristic
391C2×D47—24no—
392C2×D47—44no—
393C2×D47—44no—
394C2×D47—82no—
395C4×C47—42no—
396C4×C47#38611yescharacteristic
397C4×C47#38611yescharacteristic
398C4×C47#38611yescharacteristic
399C4×C47#38611yescharacteristic
400C4×C47C2×#12011yescharacteristic
401C4×C47C2×#12111yescharacteristic
402C4×C47C2×#12111yescharacteristic
403C4×C47C2×#12311yescharacteristic
404Dic47—24no—
405Dic47—44no—
406C2×#568—471no—
407#3449—471no—
408C2×#413—471no—
409C2×#413—471no—
410C2×#413D4711yescharacteristic, complemented
411#1915—474no—
412#1914—474no—
413C2×#344—471no—
414C2×#344—471no—
415C2×C47—21no—
416C2×C47—21no—
417C2×C47—21no—
418C2×C47—21no—
419C2×C47—21no—
420C2×C47—21no—
421C2×C47—21no—
422C2×C47—82no—
423C2×C47C2×#38611yescharacteristic
424D47—44no—
425C22×#41—471no—
426C22×#41C2×D4711yescharacteristic
427#568—474no—
428#568—942no—
429#568—942no—
430#568—942no—
431C2×#131—942no—
432C2×#131—942no—
433C22×M16—471no—
434C22×M16—471no—
435C22×M16—942no—
436C22×M16C2×D4711yescharacteristic
437C22×M16C2×D4711yescharacteristic
438#537—942no—
439#536—472no—
440#536—941no—
441#535—472no—
442#535—941no—
443#534—474no—
444#532—942no—
445#525—474no—
446#525—942no—
447C2×#117—471no—
448#413—22no—
449#413—22no—
450#413—474no—
451#413—942no—
452#413—942no—
453#413—942no—
454C2×#101—472no—
455C2×#101—941no—
456C2×#101C2×D4712yescomplemented
457C2×#100—472no—
458C2×#100—941no—
459C2×#100C2×D4712yescomplemented
460#344—474no—
461#344—474no—
462C47#2101711yescharacteristic, complemented, Sylow
463C2×#41—21no—
464C2×#41—21no—
465C2×#41—21no—
466C2×#41—21no—
467C2×#41—21no—
468C2×#41—21no—
469C2×#41—21no—
470C2×#41—21no—
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—472no—
476C2×#41—472no—
477C2×#41—472no—
478C2×#41—472no—
479C2×#41—941no—
480C2×#41—941no—
481C2×#41—941no—
482C2×#41—941no—
483C2×#41—941no—
484C2×#41—941no—
485C2×#41—941no—
486C2×#41—941no—
487C22×Q8—471no—
488C22×Q8C22×D4711yescharacteristic
489C22×D4—472no—
490C22×D4—471no—
491C22×D4C4×D4712yes—
492C22×D4C22×D4711yescharacteristic
493C23×C4—472no—
494C23×C4C4×D4712yes—
495C23×C4C22×D4711yescharacteristic
496#131—948no—
497#131—948no—
498#131—948no—
499#131—948no—
500C2×M16—21no—
501C2×M16—21no—
502C2×M16—21no—
503C2×M16—21no—
504C2×M16—21no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—472no—
509C2×M16—472no—
510C2×M16—472no—
511C2×M16—472no—
512C2×M16—944no—
513C2×M16—948no—
514C2×M16—948no—
515C2×M16—941no—
516C2×M16—941no—
517C2×M16—941no—
518C2×M16—941no—
519C2×M16—941no—
520C2×M16—941no—
521C2×M16—941no—
522C2×M16—941no—
523C2×M16C22⋊D4712yescomplemented
524C2×M16C22⋊D4712yescomplemented
525C2×M16C22×D4712yes—
526C2×M16C22×D4712yes—
527C22×C8—21no—
528C22×C8—21no—
529C22×C8—944no—
530C22×C8—941no—
531C22×C8—941no—
532C4⋊Q8—942no—
533#127—942no—
534#124—942no—
535#124—942no—
536#123—478no—
537#123—944no—
538C22⋊Q8—944no—
539C22⋊Q8—944no—
540#121—944no—
541#121—944no—
542#121—948no—
543#120—478no—
544#120—944no—
545C4×D4—948no—
546#117—472no—
547#117—472no—
548#117—941no—
549#117—941no—
550C2×C4⋊C4—941no—
551C2×C22⋊C4—472no—
552C2×C42—941no—
553#101—24no—
554#101—944no—
555#101—944no—
556#100—24no—
557#100—944no—
558#100—944no—
559C24—472no—
560C24C2×C4×D4712yes—
561C24C2×C4×D4711yescharacteristic
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—41no—
568#41—41no—
569#41—41no—
570#41—41no—
571#41—41no—
572#41—41no—
573#41—41no—
574#41—41no—
575#41—41no—
576#41—41no—
577#41—41no—
578#41—942no—
579#41—942no—
580#41—942no—
581#41—942no—
582#41—942no—
583#41—942no—
584#41—942no—
585#41—942no—
586#41—942no—
587#41—942no—
588#41—942no—
589#41—942no—
590#41—942no—
591#41—942no—
592#41—942no—
593#41—942no—
594C2×Q8—21no—
595C2×Q8—21no—
596C2×Q8—21no—
597C2×Q8—21no—
598C2×Q8—21no—
599C2×Q8—21no—
600C2×Q8—472no—
601C2×Q8—472no—
602C2×Q8—941no—
603C2×Q8—941no—
604C2×Q8—941no—
605C2×Q8—941no—
606C2×D4—22no—
607C2×D4—22no—
608C2×D4—22no—
609C2×D4—22no—
610C2×D4—22no—
611C2×D4—22no—
612C2×D4—21no—
613C2×D4—21no—
614C2×D4—21no—
615C2×D4—21no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—474no—
619C2×D4—474no—
620C2×D4—472no—
621C2×D4—472no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—942no—
625C2×D4—942no—
626C2×D4—948no—
627C2×D4—941no—
628C2×D4—941no—
629C2×D4—941no—
630C2×D4—941no—
631C22×C4—22no—
632C22×C4—22no—
633C22×C4—22no—
634C22×C4—22no—
635C22×C4—22no—
636C22×C4—22no—
637C22×C4—472no—
638C22×C4—474no—
639C22×C4—474no—
640C22×C4—942no—
641C22×C4—942no—
642C22×C4—942no—
643C22×C4—942no—
644C22×C4—942no—
645C22×C4C2×C4×D4712yes—
646C22×C4C2×C4×D4711yescharacteristic
647C22×C4#1062535011yescharacteristic
648C22×C4#1062535011yescharacteristic
649C22×C4D4×D4711yescharacteristic
650C22×C4D4×D4711yescharacteristic
651C22×C4D4×D4711yescharacteristic
652C22×C4D4×D4711yescharacteristic
653C22×C4D4×D4711yescharacteristic
654C22×C4D4×D4711yescharacteristic
655C22×C4#1062535211yescharacteristic
656C22×C4#1062535211yescharacteristic
657C22×C4C2×C22⋊D4711yescharacteristic
658C22×C4C2×C22⋊D4711yescharacteristic
659C22×C4C23×D4711yescharacteristic
660M16—22no—
661M16—22no—
662M16—22no—
663M16—22no—
664M16—22no—
665M16—41no—
666M16—41no—
667M16—474no—
668M16—9416no—
669M16—942no—
670M16—942no—
671M16—942no—
672M16—942no—
673M16—942no—
674M16—1881no—
675M16—1881no—
676M16C2×C22⋊D4714yes—
677C2×C8—22no—
678C2×C8—22no—
679C2×C8—22no—
680C2×C8—22no—
681C2×C8—41no—
682C2×C8—41no—
683C2×C8—9416no—
684C2×C8—942no—
685C2×C8—942no—
686C2×C8—942no—
687C2×C8—942no—
688C2×C8—1881no—
689C2×C8—1881no—
690C4⋊C4—948no—
691C4⋊C4—942no—
692C4⋊C4—942no—
693C22⋊C4—474no—
694C22⋊C4—948no—
695C22⋊C4—948no—
696C22⋊C4—942no—
697C42—942no—
698C42—942no—
699C23—22no—
700C23—22no—
701C23—22no—
702C23—81no—
703C23—82no—
704C23—474no—
705C23—942no—
706C23—942no—
707C23—3762no—
708C23C22⋊C4×D4711yescharacteristic
709C23C22⋊C4×D4711yescharacteristic
710C23(C22⋊D47)⋊C411yescharacteristic
711C23(C22⋊D47)⋊C411yescharacteristic
712C23C4×C22⋊D4711yescharacteristic
713C23C4×C22⋊D4711yescharacteristic
714C23C22×C4×D4711yescharacteristic
715Q8—41no—
716Q8—41no—
717Q8—41no—
718Q8—41no—
719Q8—942no—
720Q8—942no—
721Q8—942no—
722Q8—942no—
723D4—42no—
724D4—42no—
725D4—42no—
726D4—42no—
727D4—41no—
728D4—41no—
729D4—41no—
730D4—41no—
731D4—944no—
732D4—944no—
733D4—944no—
734D4—944no—
735D4—942no—
736D4—942no—
737D4—942no—
738D4—942no—
739D4—3768no—
740C2×C4—22no—
741C2×C4—22no—
742C2×C4—22no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—42no—
747C2×C4—474no—
748C2×C4—942no—
749C2×C4—942no—
750C2×C4—944no—
751C2×C4—944no—
752C2×C4—944no—
753C2×C4—944no—
754C2×C4—944no—
755C2×C4—3762no—
756C2×C4C22⋊C4×D4711yescharacteristic
757C2×C4C22⋊C4×D4711yescharacteristic
758C2×C4(C22⋊D47)⋊C411yescharacteristic
759C2×C4(C22⋊D47)⋊C411yescharacteristic
760C2×C4C4×C22⋊D4711yescharacteristic
761C2×C4C4×C22⋊D4711yescharacteristic
762C2×C4#1309399211yescharacteristic
763C2×C4#1309399211yescharacteristic
764C2×C4#1309399211yescharacteristic
765C2×C4#1309399211yescharacteristic
766C2×C4#1309399511yescharacteristic
767C2×C4#1309399511yescharacteristic
768C2×C4#1309399511yescharacteristic
769C2×C4#1309399511yescharacteristic
770C2×C4#1309399711yescharacteristic
771C2×C4#1309399711yescharacteristic
772C2×C4#1309399711yescharacteristic
773C2×C4#1309399711yescharacteristic
774C2×C4#1309400611yescharacteristic
775C2×C4#1309400611yescharacteristic
776C2×C4#1309400611yescharacteristic
777C2×C4#1309400611yescharacteristic
778C2×C4C2×D4×D4711yescharacteristic
779C2×C4C2×D4×D4711yescharacteristic
780C2×C4C2×D4×D4711yescharacteristic
781C2×C4C22×C22⋊D4711yescharacteristic
782C2×C4C2×#1062535211yescharacteristic
783C2×C4C2×#1062535011yescharacteristic
784C8—24no—
785C8—42no—
786C8—944no—
787C8—1882no—
788C22—41no—
789C22—41no—
790C22—41no—
791C22—41no—
792C22—41no—
793C22—41no—
794C22—41no—
795C22—44no—
796C22—42no—
797C22—82no—
798C22—82no—
799C22—944no—
800C22—3762no—
801C22—1884no—
802C22—1884no—
803C22#1568899911yescharacteristic
804C22#1568899911yescharacteristic
805C22#1568899911yescharacteristic
806C22#1568899911yescharacteristic
807C22C2×C22⋊C4×D4711yescharacteristic
808C22C2×(C22⋊D47)⋊C411yescharacteristic
809C22C2×C4×C22⋊D4711yescharacteristic
810C4—42no—
811C4—944no—
812C4—1884no—
813C4#1568899911yescharacteristic
814C4#1568899911yescharacteristic
815C4#1568899911yescharacteristic
816C4#1568899911yescharacteristic
817C4C2×#1309399211yescharacteristic
818C4C2×#1309399511yescharacteristic
819C4C2×#1309399711yescharacteristic
820C4C2×#1309400611yescharacteristic
821C2—21no—
822C2—21no—
823C2—21no—
824C2—21no—
825C2—21no—
826C2—21no—
827C2—21no—
828C2—82no—
829C2—1884no—
830C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4#15688999
commutatorC23×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#413C2
socleC2×C47C2×#386
prime radical#20256717C2
cosocleC22×C4×C47C24
hypercenterC2×#413D47
hypocenterC47#21017
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#413

Complements

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

NH ≅ G/Ntype
1. C2×#15689889C2semidirect
3. C2×#15689107C2semidirect
4. C2×#15689105C2semidirect
5. #20243937C2semidirect
6. #20243932C2semidirect
7. C2×#15688895C2semidirect
8. C2×#15688894C2semidirect
9. C2×C47×#413C2semidirect
34. C2×#13093943C22semidirect
36. C2×#13093941C22semidirect
38. #15688895C22semidirect
39. #15688894C22semidirect
45. C2×#101×C47C22semidirect
46. C2×#100×C47C22semidirect
75. C2×#10625329D4semidirect
76. C2×#10625329D4semidirect
135. C2×M16×C47D4semidirect
136. C2×M16×C47D4semidirect
410. C2×#413D47semidirect
456. C2×#101C2×D47semidirect
459. C2×#100C2×D47semidirect
462. C47#21017semidirect
523. C2×M16C22⋊D47semidirect
524. C2×M16C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156898892
#202567172
C2×#156891072
C2×#156891052
#202439372
#202439322
C2×#156888952
C2×#156888942
C2×C47×#4132
#2101747