Finite Group Databasebeta

← #26217757

Subgroups — #26217757

Order 12032.

1668 conjugacy classes of subgroups.

The subgroup lattice has 820 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689921C211yesmaximal, characteristic
2C2×#15689889C211yesmaximal, characteristic, complemented
3#20251905C211yesmaximal, characteristic, complemented
4#20251833C211yesmaximal, characteristic, complemented
5#20243747C218yesmaximal, complemented
6C2×#15688893C211yesmaximal, characteristic, complemented
7#20243114C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689921—22no—
11#15689921—22no—
12#15689921C414yescomplemented
13#15689921C2214yes—
14C2×#13094055C412yescomplemented
15C2×#13094054—21no—
16C2×#13094050C412yescomplemented
17C2×#13094049—21no—
18C2×#13094044—22no—
19#15689889—22no—
20#15689889—22no—
21#15689889—22no—
22#15689889C2214yescomplemented
23C2×#13094032—22no—
24C2×#13094030—22no—
25C22×#10625329C2211yescharacteristic
26C22×#10625329C2211yescharacteristic
27C22×#10625329C2211yescharacteristic
28C2×M16×D47—22no—
29#15689131—21no—
30#15689127—21no—
31#15689122—22no—
32#15689117C2214yescomplemented
33#15689090—22no—
34#15689090C2214yescomplemented
35#15689087—22no—
36#15688893C2214yescomplemented
37#15688887C2214yescomplemented
38C22×#41×C47C2211yescharacteristic
39C22×M16×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C47×#421—22no—
42C47×#421C2214yescomplemented
43C2×#104×C47—22no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350C2×C412yes—
51C2×#10625350C2×C412yes—
52C2×#10625350D412yes—
53C2×#10625350D412yes—
54C2×#10625350D412yes—
55C2×#10625350C2312yes—
56C22×Dic94D411yescharacteristic
57C22×D188D411yescharacteristic
58C22×C22⋊D47—21no—
59C22×C4×D47—21no—
60#13094055—24no—
61#13094055C2×C418yescomplemented
62#13094054—24no—
63#13094054—24no—
64#13094050—24no—
65#13094050C2×C418yescomplemented
66#13094049—24no—
67#13094049—24no—
68#13094044—28no—
69#13094044—28no—
70C2×#10625337—22no—
71C2×#10625335—22no—
72C2×#10625336—22no—
73C2×#10625334—22no—
74#13094032—28no—
75#13094032—28no—
76#13094030—28no—
77#13094030—28no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329—21no—
81C2×#10625329—21no—
82C2×#10625329—21no—
83C2×#10625329—21no—
84C2×#10625329—21no—
85C2×#10625329—21no—
86C2×#10625329—21no—
87C2×#10625329—21no—
88C2×#10625329—21no—
89C2×#10625329—21no—
90C2×#10625329—21no—
91C2×#10625329C2×C412yes—
92C2×#10625329C2×C412yes—
93C2×#10625329D412yes—
94C2×#10625329C2312yes—
95C2×#10625329C2312yes—
96C2×#10625324—24no—
97M16×D47—28no—
98M16×D47—28no—
99C22×C47⋊C8—21no—
100C22×C47⋊C8D412yes—
101C22×C47⋊C8C2312yes—
102C2×C8×D47—24no—
103#13093947—24no—
104#13093944—24no—
105C22⋊(C47⋊C8)—28no—
106C2×#41×C47—21no—
107C2×#41×C47—21no—
108C2×#41×C47—21no—
109C2×#41×C47—21no—
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×C47C2×C412yes—
117C2×#41×C47C2312yes—
118C22×Q8×C47C2×C411yescharacteristic
119C22×D4×C47—21no—
120C22×D4×C47C2×C411yescharacteristic
121C23×C4×C47—21no—
122C23×C4×C47C2311yescharacteristic
123C2×M16×C47—21no—
124C2×M16×C47—21no—
125C2×M16×C47—21no—
126C2×M16×C47D412yes—
127C2×M16×C47D412yes—
128C2×M16×C47C2312yes—
129C22×C8×C47—21no—
130#117×C47—21no—
131#117×C47—21no—
132#117×C47—21no—
133#117×C47C2312yes—
134C2×C4⋊C4×C47—21no—
135C2×C22⋊C4×C47—21no—
136C2×C42×C47—21no—
137#104×C47—28no—
138C24×C47—21no—
139C24×C47#4111yescharacteristic
140C23×D47—21no—
141#41×C47—22no—
142#41×C47—22no—
143#41×C47—22no—
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—22no—
147#41×C47—22no—
148#41×C47—22no—
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—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47C22×C412yes—
163C2×D4×C47—22no—
164C2×D4×C47—22no—
165C2×D4×C47—21no—
166C2×D4×C47—21no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—41no—
171C2×D4×C47—41no—
172C2×D4×C47—41no—
173C2×D4×C47—41no—
174C2×D4×C47C22×C412yes—
175C22×C4×C47—21no—
176C22×C4×C47—22no—
177C22×C4×C47—22no—
178C22×C4×C47—41no—
179C22×C4×C47—41no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47—41no—
183C22×C4×C47C22×C411yescharacteristic
184C22×C4×C47C22×C411yescharacteristic
185C22×C4×C47C2×D411yescharacteristic
186C22×C4×C47C2×D411yescharacteristic
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D411yescharacteristic
192C22×C4×C47C2×D411yescharacteristic
193C22×C4×C47#4111yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47#4111yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—22no—
198C2×C22⋊D47—22no—
199C2×C22⋊D47—22no—
200C2×C22⋊D47—22no—
201C2×C22⋊D47—22no—
202C2×C22⋊D47—22no—
203C22×Dic47—21no—
204#10625350—22no—
205#10625350—22no—
206#10625350—22no—
207#10625350—22no—
208#10625350—22no—
209#10625350—22no—
210#10625350—22no—
211#10625350—22no—
212#10625350—22no—
213#10625350—22no—
214#10625350—22no—
215#10625350—22no—
216#10625350C22⋊C414yes—
217#10625350C22⋊C414yes—
218#10625350C22×C414yes—
219#10625350C2×D414yes—
220C2×D188—21no—
221C2×D188—21no—
222C2×D188—21no—
223C2×D188C22⋊C412yes—
224C2×D188C22⋊C412yes—
225C2×D188C2×D412yes—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—22no—
231C2×C4×D47—22no—
232C2×Dic94—21no—
233C2×Dic94—21no—
234C2×Dic94—21no—
235C2×Dic94C22⋊C412yes—
236C2×Dic94C22⋊C412yes—
237C2×Dic94C2×D412yes—
238M16×C47—22no—
239M16×C47—22no—
240M16×C47—22no—
241M16×C47C2×D414yes—
242C2×C8×C47—22no—
243C2×C8×C47—22no—
244C2×C8×C47—22no—
245C4⋊C4×C47—22no—
246C4⋊C4×C47—41no—
247C22⋊C4×C47—22no—
248C22⋊C4×C47—41no—
249C42×C47—22no—
250C42×C47—41no—
251#10625337—28no—
252#10625336—28no—
253#10625335—28no—
254#10625334—28no—
255#10625329—22no—
256#10625329—22no—
257#10625329—22no—
258#10625329—22no—
259#10625329—22no—
260#10625329—22no—
261#10625329—22no—
262#10625329—41no—
263#10625329—41no—
264#10625329—41no—
265#10625329—41no—
266#10625329C22×C414yes—
267C2×C47⋊C8—22no—
268C2×C47⋊C8—22no—
269C2×C47⋊C8—22no—
270C2×C47⋊C8—22no—
271C2×C47⋊C8—22no—
272C2×C47⋊C8—22no—
273C2×C47⋊C8—22no—
274C2×C47⋊C8—22no—
275C2×C47⋊C8C2×D414yes—
276#10625324—216no—
277C8×D47—216no—
278C23×C47—22no—
279C23×C47—41no—
280C23×C47—41no—
281C23×C47—81no—
282C23×C47—82no—
283C23×C47C4×D411yescharacteristic
284C23×C47C4×D411yescharacteristic
285C23×C47#12111yescharacteristic
286C23×C47#12111yescharacteristic
287C23×C47#12311yescharacteristic
288C23×C47#12311yescharacteristic
289C23×C47C2×#4111yescharacteristic
290C22×D47—22no—
291C22×D47—22no—
292C22×D47—22no—
293C22×D47—82no—
294Q8×C47—22no—
295Q8×C47—22no—
296Q8×C47—41no—
297Q8×C47—41no—
298D4×C47—22no—
299D4×C47—22no—
300D4×C47—42no—
301D4×C47—42no—
302D4×C47—42no—
303D4×C47—42no—
304D4×C47—41no—
305D4×C47—41no—
306C2×C4×C47—22no—
307C2×C4×C47—41no—
308C2×C4×C47—41no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47—82no—
315C2×C4×C47C2×C22⋊C411yescharacteristic
316C2×C4×C47C2×C22⋊C411yescharacteristic
317C2×C4×C47C2×C22⋊C411yescharacteristic
318C2×C4×C47C2×C22⋊C411yescharacteristic
319C2×C4×C47C4×D411yescharacteristic
320C2×C4×C47C4×D411yescharacteristic
321C2×C4×C47C4×D411yescharacteristic
322C2×C4×C47C4×D411yescharacteristic
323C2×C4×C47C4×D411yescharacteristic
324C2×C4×C47C4×D411yescharacteristic
325C2×C4×C47#12011yescharacteristic
326C2×C4×C47#12011yescharacteristic
327C2×C4×C47#12011yescharacteristic
328C2×C4×C47#12011yescharacteristic
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#12311yescharacteristic
336C2×C4×C47#12311yescharacteristic
337C2×C4×C47C23×C411yescharacteristic
338C2×C4×C47C22×D411yescharacteristic
339C2×C4×C47C22×D411yescharacteristic
340C2×C4×C47C22×D411yescharacteristic
341C2×C4×C47C22×D411yescharacteristic
342C2×C4×C47C2×#4111yescharacteristic
343C22⋊D47—24no—
344C22⋊D47—24no—
345C22⋊D47—24no—
346C22⋊D47—24no—
347C2×Dic47—22no—
348C2×Dic47—22no—
349C2×Dic47—22no—
350D188—22no—
351D188—22no—
352D188—22no—
353D188C2×C22⋊C414yes—
354C4×D47—24no—
355C4×D47—24no—
356C4×D47—24no—
357C4×D47—24no—
358Dic94—22no—
359Dic94—22no—
360Dic94—22no—
361Dic94C2×C22⋊C414yes—
362C8×C47—24no—
363C47⋊C8—24no—
364C47⋊C8—24no—
365C47⋊C8—42no—
366#20939—471nomaximal, Sylow
367C22×C47—41no—
368C22×C47—41no—
369C22×C47—41no—
370C22×C47—41no—
371C22×C47—41no—
372C22×C47—41no—
373C22×C47—41no—
374C22×C47—44no—
375C22×C47—42no—
376C22×C47—82no—
377C22×C47—82no—
378C22×C47#38611yescharacteristic
379C22×C47#38611yescharacteristic
380C22×C47#38611yescharacteristic
381C22×C47#38611yescharacteristic
382C22×C47C2×C4×D411yescharacteristic
383C22×C47C2×#12111yescharacteristic
384C22×C47C2×#12311yescharacteristic
385C2×D47—24no—
386C2×D47—44no—
387C2×D47—82no—
388C2×D47—82no—
389C4×C47—42no—
390C4×C47—82no—
391C4×C47#38611yescharacteristic
392C4×C47#38611yescharacteristic
393C4×C47#38611yescharacteristic
394C4×C47#38611yescharacteristic
395C4×C47C22×C22⋊C411yescharacteristic
396C4×C47C2×C4×D411yescharacteristic
397C4×C47C2×#12011yescharacteristic
398C4×C47C2×#12111yescharacteristic
399Dic47—24no—
400C2×#575—471no—
401C2×#568—471no—
402C2×#421D4711yescharacteristic, complemented
403#2896—471no—
404#2879—471no—
405#1881—478no—
406C2×#344—471no—
407#1738—471no—
408C2×C47—21no—
409C2×C47—21no—
410C2×C47—21no—
411C2×C47—21no—
412C2×C47—21no—
413C2×C47—21no—
414C2×C47—21no—
415C2×C47—82no—
416C2×C47C2×#38611yescharacteristic
417D47—44no—
418C22×#41—471no—
419C22×#41C2×D4711yescharacteristic
420#575—474no—
421#575—474no—
422#575—942no—
423#575—942no—
424C2×#137—472no—
425C2×#137—941no—
426C2×AGL(1,ℤ/8)—472no—
427C2×AGL(1,ℤ/8)—941no—
428C2×#135—942no—
429#568—474no—
430#568—942no—
431#568—942no—
432#568—942no—
433C2×#131—942no—
434C2×#131—942no—
435C22×M16—471no—
436C22×M16—471no—
437C22×M16—471no—
438C22×M16—942no—
439C22×M16C2×D4711yescharacteristic
440C2×#117C2×D4711yescharacteristic
441#421—22no—
442#421C2×D4714yescomplemented
443C2×#104—22no—
444#419—941no—
445#418—941no—
446#417—942no—
447#416—474no—
448#408—474no—
449#408—942no—
450#407—942no—
451#344—474no—
452#341—474no—
453C47#2093911yescharacteristic, complemented, Sylow
454C2×#41—21no—
455C2×#41—21no—
456C2×#41—21no—
457C2×#41—21no—
458C2×#41—21no—
459C2×#41—21no—
460C2×#41—21no—
461C2×#41—21no—
462C2×#41—21no—
463C2×#41—21no—
464C2×#41—472no—
465C2×#41—472no—
466C2×#41—472no—
467C2×#41—472no—
468C2×#41—472no—
469C2×#41—472no—
470C2×#41—941no—
471C2×#41—941no—
472C2×#41—941no—
473C2×#41—941no—
474C2×#41—941no—
475C2×#41—941no—
476C2×#41C4×D4712yes—
477C2×#41C22×D4712yes—
478C22×Q8—471no—
479C22×Q8C4×D4711yescharacteristic
480C22×D4—21no—
481C22×D4—471no—
482C22×D4—941no—
483C22×D4C4×D4711yescharacteristic
484C23×C4—21no—
485C23×C4—941no—
486C23×C4C22×D4711yescharacteristic
487#137—478no—
488#137—944no—
489#137—944no—
490#137—944no—
491AGL(1,ℤ/8)—478no—
492AGL(1,ℤ/8)—944no—
493AGL(1,ℤ/8)—944no—
494AGL(1,ℤ/8)—944no—
495#135—948no—
496#135—948no—
497C2×Q16—942no—
498C2×SD16—942no—
499C2×SD16—942no—
500C2×D8—942no—
501#131—948no—
502#131—948no—
503#131—948no—
504#131—948no—
505C2×M16—21no—
506C2×M16—21no—
507C2×M16—21no—
508C2×M16—472no—
509C2×M16—472no—
510C2×M16—472no—
511C2×M16—472no—
512C2×M16—472no—
513C2×M16—944no—
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—948no—
523C2×M16—941no—
524C2×M16—941no—
525C2×M16—941no—
526C2×M16—941no—
527C2×M16—941no—
528C2×M16—941no—
529C2×M16C22⋊D4712yes—
530C2×M16C22⋊D4712yes—
531C2×M16C22×D4712yes—
532C22×C8—21no—
533C22×C8—472no—
534C22×C8—472no—
535C22×C8—944no—
536C22×C8—941no—
537#117—21no—
538#117—21no—
539#117—21no—
540#117C22×D4712yes—
541C2×C4⋊C4—21no—
542C2×C22⋊C4—21no—
543C2×C42—21no—
544#104—28no—
545#103—944no—
546#102—944no—
547C22⋊C8—948no—
548C24—21no—
549C24—941no—
550C24#1062535211yescharacteristic
551#41—22no—
552#41—22no—
553#41—22no—
554#41—22no—
555#41—22no—
556#41—22no—
557#41—22no—
558#41—22no—
559#41—41no—
560#41—41no—
561#41—41no—
562#41—41no—
563#41—41no—
564#41—41no—
565#41—41no—
566#41—41no—
567#41—474no—
568#41—474no—
569#41—474no—
570#41—474no—
571#41—942no—
572#41—942no—
573#41—942no—
574#41—942no—
575#41—942no—
576#41—942no—
577#41—942no—
578#41—942no—
579#41—942no—
580#41—942no—
581#41—942no—
582#41—942no—
583C2×Q8—21no—
584C2×Q8—21no—
585C2×Q8—21no—
586C2×Q8—21no—
587C2×Q8—21no—
588C2×Q8—472no—
589C2×Q8—472no—
590C2×Q8—472no—
591C2×Q8—941no—
592C2×Q8—941no—
593C2×Q8—941no—
594C2×Q8C2×C4×D4712yes—
595C2×D4—22no—
596C2×D4—22no—
597C2×D4—21no—
598C2×D4—21no—
599C2×D4—21no—
600C2×D4—21no—
601C2×D4—21no—
602C2×D4—41no—
603C2×D4—41no—
604C2×D4—41no—
605C2×D4—41no—
606C2×D4—472no—
607C2×D4—472no—
608C2×D4—472no—
609C2×D4—942no—
610C2×D4—942no—
611C2×D4—942no—
612C2×D4—942no—
613C2×D4—942no—
614C2×D4—942no—
615C2×D4—941no—
616C2×D4—941no—
617C2×D4—941no—
618C2×D4C2×C4×D4712yes—
619C22×C4—21no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—41no—
623C22×C4—41no—
624C22×C4—41no—
625C22×C4—41no—
626C22×C4—41no—
627C22×C4—941no—
628C22×C4—942no—
629C22×C4—942no—
630C22×C4—942no—
631C22×C4—942no—
632C22×C4—942no—
633C22×C4—942no—
634C22×C4C2×C4×D4711yescharacteristic
635C22×C4C2×C4×D4711yescharacteristic
636C22×C4#1062535011yescharacteristic
637C22×C4#1062535011yescharacteristic
638C22×C4D4×D4711yescharacteristic
639C22×C4D4×D4711yescharacteristic
640C22×C4D4×D4711yescharacteristic
641C22×C4D4×D4711yescharacteristic
642C22×C4D4×D4711yescharacteristic
643C22×C4D4×D4711yescharacteristic
644C22×C4#1062535211yescharacteristic
645C22×C4C2×C22⋊D4711yescharacteristic
646C22×C4C2×C22⋊D4711yescharacteristic
647C22×C4C23×D4711yescharacteristic
648Q16—948no—
649SD16—948no—
650SD16—948no—
651D8—948no—
652M16—22no—
653M16—22no—
654M16—22no—
655M16—474no—
656M16—9416no—
657M16—942no—
658M16—942no—
659M16—942no—
660M16—942no—
661M16—942no—
662M16—942no—
663M16—942no—
664M16—1881no—
665M16—1881no—
666M16—1881no—
667M16—1881no—
668M16C2×C22⋊D4714yes—
669C2×C8—22no—
670C2×C8—22no—
671C2×C8—22no—
672C2×C8—474no—
673C2×C8—9416no—
674C2×C8—942no—
675C2×C8—942no—
676C2×C8—942no—
677C2×C8—942no—
678C2×C8—942no—
679C2×C8—942no—
680C2×C8—942no—
681C2×C8—942no—
682C4⋊C4—22no—
683C4⋊C4—41no—
684C22⋊C4—22no—
685C22⋊C4—41no—
686C42—22no—
687C42—41no—
688C23—22no—
689C23—41no—
690C23—41no—
691C23—81no—
692C23—82no—
693C23—942no—
694C23—942no—
695C23—942no—
696C23—3762no—
697C23(C22⋊D47)⋊C411yescharacteristic
698C23(C22⋊D47)⋊C411yescharacteristic
699C23#1309399511yescharacteristic
700C23#1309399511yescharacteristic
701C23#1309400611yescharacteristic
702C23#1309400611yescharacteristic
703C23C2×#1062535211yescharacteristic
704Q8—22no—
705Q8—22no—
706Q8—41no—
707Q8—41no—
708Q8—474no—
709Q8—942no—
710Q8—942no—
711Q8—942no—
712D4—22no—
713D4—22no—
714D4—42no—
715D4—42no—
716D4—42no—
717D4—42no—
718D4—41no—
719D4—41no—
720D4—474no—
721D4—944no—
722D4—944no—
723D4—944no—
724D4—944no—
725D4—942no—
726D4—942no—
727D4—942no—
728C2×C4—22no—
729C2×C4—41no—
730C2×C4—41no—
731C2×C4—42no—
732C2×C4—42no—
733C2×C4—42no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—82no—
737C2×C4—942no—
738C2×C4—942no—
739C2×C4—942no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—944no—
744C2×C4C22⋊C4×D4711yescharacteristic
745C2×C4C22⋊C4×D4711yescharacteristic
746C2×C4C22⋊C4×D4711yescharacteristic
747C2×C4C22⋊C4×D4711yescharacteristic
748C2×C4(C22⋊D47)⋊C411yescharacteristic
749C2×C4(C22⋊D47)⋊C411yescharacteristic
750C2×C4C4×C22⋊D4711yescharacteristic
751C2×C4C4×C22⋊D4711yescharacteristic
752C2×C4C4×C22⋊D4711yescharacteristic
753C2×C4C4×C22⋊D4711yescharacteristic
754C2×C4#1309399211yescharacteristic
755C2×C4#1309399211yescharacteristic
756C2×C4#1309399211yescharacteristic
757C2×C4#1309399211yescharacteristic
758C2×C4#1309399511yescharacteristic
759C2×C4#1309399511yescharacteristic
760C2×C4#1309399711yescharacteristic
761C2×C4#1309399711yescharacteristic
762C2×C4#1309399711yescharacteristic
763C2×C4#1309399711yescharacteristic
764C2×C4#1309400611yescharacteristic
765C2×C4#1309400611yescharacteristic
766C2×C4C22×C4×D4711yescharacteristic
767C2×C4C2×D4×D4711yescharacteristic
768C2×C4C2×D4×D4711yescharacteristic
769C2×C4C2×D4×D4711yescharacteristic
770C2×C4C22×C22⋊D4711yescharacteristic
771C2×C4C2×#1062535011yescharacteristic
772C8—24no—
773C8—944no—
774C8—944no—
775C8—1882no—
776C22—41no—
777C22—41no—
778C22—41no—
779C22—41no—
780C22—41no—
781C22—41no—
782C22—41no—
783C22—44no—
784C22—42no—
785C22—82no—
786C22—82no—
787C22—944no—
788C22—3762no—
789C22—3762no—
790C22—1884no—
791C22#1568899911yescharacteristic
792C22#1568899911yescharacteristic
793C22#1568899911yescharacteristic
794C22#1568899911yescharacteristic
795C22C2×(C22⋊D47)⋊C411yescharacteristic
796C22C2×#1309399511yescharacteristic
797C22C2×#1309400611yescharacteristic
798C4—42no—
799C4—82no—
800C4—944no—
801C4#1568899911yescharacteristic
802C4#1568899911yescharacteristic
803C4#1568899911yescharacteristic
804C4#1568899911yescharacteristic
805C4C2×C22⋊C4×D4711yescharacteristic
806C4C2×C4×C22⋊D4711yescharacteristic
807C4C2×#1309399211yescharacteristic
808C4C2×#1309399711yescharacteristic
809C2—21no—
810C2—21no—
811C2—21no—
812C2—21no—
813C2—21no—
814C2—21no—
815C2—21no—
816C2—82no—
817C2—1884no—
818C2C2×#1568899911yescharacteristic
subgroupG/H
centerC4C2×#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC2×C47C2×#386
prime radicalC2×#15689921C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47#20939
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
2. C2×#15689889C2semidirect
3. #20251905C2semidirect
4. #20251833C2semidirect
5. #20243747C2semidirect
6. C2×#15688893C2semidirect
7. #20243114C2semidirect
8. C2×C47×#421C2semidirect
12. #15689921C4semidirect
14. C2×#13094055C4semidirect
16. C2×#13094050C4semidirect
22. #15689889C22semidirect
32. #15689117C22semidirect
34. #15689090C22semidirect
36. #15688893C22semidirect
37. #15688887C22semidirect
42. C47×#421C22semidirect
61. #13094055C2×C4semidirect
65. #13094050C2×C4semidirect
402. C2×#421D47semidirect
442. #421C2×D47semidirect
453. C47#20939semidirect

Maximal subgroups

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

subgroupindex
C2×#156899212
C2×#156898892
#202519052
#202518332
#202437472
C2×#156888932
#202431142
C2×C47×#4212
#2093947