Finite Group Databasebeta

← C2×#20243768 #26217815

Subgroups — C2×#20243768 #26217815

Order 12032.

1794 conjugacy classes of subgroups.

The subgroup lattice has 854 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689889C211yesmaximal, characteristic, complemented
2C2×#15689669C211yesmaximal, characteristic
3C2×#15689140C211yesmaximal, characteristic, complemented
4C2×#15689096C211yesmaximal, characteristic, complemented
5#20243768C218yesmaximal, direct product factor
6C2×#15688884C211yesmaximal, characteristic, complemented
7C2×#15688882C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689889—22no—
11#15689889—22no—
12#15689889—22no—
13#15689889C2214yescomplemented
14C2×#13094032—22no—
15C2×#13094030—22no—
16C22×#10625329C2211yescharacteristic
17C2×M16×D47—22no—
18#15689669—22no—
19#15689669—22no—
20#15689669C414yescomplemented
21#15689669C2214yes—
22C2×#13094022C411yescharacteristic, complemented
23C2×#13094020C411yescharacteristic, complemented
24C2×#13094013C411yescharacteristic, complemented
25C2×#13094011C411yescharacteristic, complemented
26C2×#13093996—22no—
27C2×C4×C22⋊D47—22no—
28C2×#13093983C2211yescharacteristic
29C22×C4×Dic47C2211yescharacteristic
30#15689140—22no—
31#15689140C2214yescomplemented
32C2×#13093951—22no—
33#15689096—22no—
34#15689096C2214yescomplemented
35C2×#13093938—22no—
36#15688884C2214yescomplemented
37#15688882C2214yescomplemented
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×#10625350—21no—
51C2×#10625350—21no—
52C2×#10625350C2×C412yes—
53C2×#10625350D412yes—
54C2×#10625350D412yes—
55C2×#10625350C2312yes—
56C22×Dic94C2×C411yescharacteristic
57C22×D188C2×C411yescharacteristic
58C22×C22⋊D47—22no—
59C22×C22⋊D47D412yes—
60C23×Dic47—21no—
61C22×C4×D47D412yes—
62#13094032—28no—
63#13094032—28no—
64#13094030—28no—
65#13094030—28no—
66C2×#10625329—21no—
67C2×#10625329—21no—
68C2×#10625329—21no—
69C2×#10625329D412yescomplemented
70C2×#10625329D412yescomplemented
71C2×#10625329C2312yes—
72C2×#10625324—24no—
73M16×D47—28no—
74M16×D47—28no—
75C22×C47⋊C8—21no—
76C2×C8×D47—24no—
77#13094022—22no—
78#13094022C2×C414yescomplemented
79#13094020—22no—
80#13094020C2×C414yescomplemented
81#13094013—22no—
82#13094013C2×C414yescomplemented
83#13094011—22no—
84#13094011C2×C414yescomplemented
85#13093996—28no—
86#13093996—28no—
87C4×C22⋊D47—28no—
88C4×C22⋊D47—28no—
89#13093983—21no—
90#13093983—21no—
91#13093983—21no—
92#13093983C2312yes—
93C2×C4⋊Dic47—21no—
94C2×Dic47⋊C4—22no—
95C2×C22⋊Dic47—22no—
96C2×C22⋊Dic47—21no—
97C2×(C2×D47)⋊C4—22no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47C2×C411yescharacteristic
103C2×C4×Dic47C2×C411yescharacteristic
104C2×C4×Dic47C2×C412yes—
105C2×C4×Dic47C2312yes—
106#13093951—28no—
107#13093938—28no—
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×C47—21no—
117C2×#41×C47—21no—
118C2×#41×C47C2×C412yes—
119C2×#41×C47C2312yes—
120C22×Q8×C47C2×C411yescharacteristic
121C22×D4×C47—21no—
122C22×D4×C47C2×C411yescharacteristic
123C23×C4×C47—21no—
124C23×C4×C47C2311yescharacteristic
125C2×M16×C47—21no—
126C2×M16×C47—21no—
127C2×M16×C47—21no—
128C2×M16×C47D412yescomplemented
129C2×M16×C47D412yescomplemented
130C2×M16×C47C2312yes—
131C22×C8×C47—21no—
132#117×C47—21no—
133#117×C47—21no—
134#117×C47—21no—
135#117×C47C2312yes—
136C2×C4⋊C4×C47—21no—
137C2×C22⋊C4×C47—21no—
138C2×C42×C47—21no—
139#104×C47—28no—
140C24×C47—21no—
141C24×C47C2×D411yescharacteristic
142C23×D47C22⋊C412yes—
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—22no—
150#41×C47—22no—
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—
159C2×Q8×C47—21no—
160C2×Q8×C47—21no—
161C2×Q8×C47—21no—
162C2×Q8×C47—21no—
163C2×Q8×C47—21no—
164C2×Q8×C47C22×C412yes—
165C2×D4×C47—22no—
166C2×D4×C47—22no—
167C2×D4×C47—21no—
168C2×D4×C47—21no—
169C2×D4×C47—21no—
170C2×D4×C47—21no—
171C2×D4×C47—21no—
172C2×D4×C47—41no—
173C2×D4×C47—41no—
174C2×D4×C47—41no—
175C2×D4×C47—41no—
176C2×D4×C47C22×C412yes—
177C22×C4×C47—21no—
178C22×C4×C47—22no—
179C22×C4×C47—22no—
180C22×C4×C47—41no—
181C22×C4×C47—41no—
182C22×C4×C47—41no—
183C22×C4×C47—41no—
184C22×C4×C47—41no—
185C22×C4×C47C22×C411yescharacteristic
186C22×C4×C47C22×C411yescharacteristic
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×C47C2×D411yescharacteristic
194C22×C4×C47#4111yescharacteristic
195C22×C4×C47#4111yescharacteristic
196C22×C4×C47#4111yescharacteristic
197C22×C4×C47#4111yescharacteristic
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—22no—
200C2×C22⋊D47—22no—
201C2×C22⋊D47—22no—
202C2×C22⋊D47—22no—
203C2×C22⋊D47—28no—
204C2×C22⋊D47—48no—
205C2×C22⋊D47C22⋊C414yes—
206C2×C22⋊D47C2×D414yes—
207C22×Dic47—21no—
208C22×Dic47—21no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47—44no—
212C22×Dic47—41no—
213C22×Dic47C22⋊C412yes—
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—
226#10625350—22no—
227#10625350—22no—
228#10625350—22no—
229#10625350—22no—
230C2×D188—21no—
231C2×D188—21no—
232C2×D188—21no—
233C2×D188—21no—
234C2×D188C22⋊C412yes—
235C2×D188C22×C412yes—
236C2×C4×D47—22no—
237C2×C4×D47—22no—
238C2×C4×D47—22no—
239C2×C4×D47—22no—
240C2×C4×D47C22⋊C414yes—
241C2×C4×D47C2×D414yes—
242C2×Dic94—21no—
243C2×Dic94—21no—
244C2×Dic94—21no—
245C2×Dic94—21no—
246C2×Dic94C22⋊C412yes—
247C2×Dic94C22×C412yes—
248M16×C47—22no—
249M16×C47—22no—
250M16×C47—22no—
251M16×C47C2×D414yescomplemented
252C2×C8×C47—22no—
253C2×C8×C47—22no—
254C2×C8×C47—22no—
255C4⋊C4×C47—22no—
256C4⋊C4×C47—41no—
257C22⋊C4×C47—22no—
258C22⋊C4×C47—41no—
259C42×C47—22no—
260C42×C47—41no—
261C22⋊Dic47—28no—
262C22⋊Dic47—22no—
263C22⋊Dic47—41no—
264(C2×D47)⋊C4—28no—
265C4⋊Dic47—22no—
266C4⋊Dic47—41no—
267Dic47⋊C4—28no—
268C4×Dic47—22no—
269C4×Dic47—21no—
270C4×Dic47—21no—
271C4×Dic47—22no—
272C4×Dic47—22no—
273C4×Dic47—41no—
274C4×Dic47C22×C412yes—
275C4×Dic47C22×C412yes—
276#10625329—22no—
277#10625329—22no—
278#10625329—22no—
279#10625329C2×D414yescomplemented
280C2×C47⋊C8—22no—
281C2×C47⋊C8—22no—
282C2×C47⋊C8—22no—
283#10625324—216no—
284C8×D47—216no—
285C23×C47—22no—
286C23×C47—42no—
287C23×C47—44no—
288C23×C47—41no—
289C23×C47—41no—
290C23×C47C2×C22⋊C411yescharacteristic
291C23×C47C2×C22⋊C411yescharacteristic
292C23×C47#12111yescharacteristic
293C23×C47#12111yescharacteristic
294C23×C47#12111yescharacteristic
295C23×C47#12111yescharacteristic
296C23×C47C22×D411yescharacteristic
297C22×D47—22no—
298C22×D47—22no—
299C22×D47—44no—
300C22×D47C2×C22⋊C414yes—
301Q8×C47—22no—
302Q8×C47—22no—
303Q8×C47—41no—
304Q8×C47—41no—
305D4×C47—22no—
306D4×C47—22no—
307D4×C47—42no—
308D4×C47—42no—
309D4×C47—42no—
310D4×C47—42no—
311D4×C47—41no—
312D4×C47—41no—
313C2×C4×C47—22no—
314C2×C4×C47—41no—
315C2×C4×C47—41no—
316C2×C4×C47—42no—
317C2×C4×C47—42no—
318C2×C4×C47—42no—
319C2×C4×C47—42no—
320C2×C4×C47—42no—
321C2×C4×C47—82no—
322C2×C4×C47C2×C22⋊C411yescharacteristic
323C2×C4×C47C2×C22⋊C411yescharacteristic
324C2×C4×C47C4×D411yescharacteristic
325C2×C4×C47C4×D411yescharacteristic
326C2×C4×C47C4×D411yescharacteristic
327C2×C4×C47C4×D411yescharacteristic
328C2×C4×C47C4×D411yescharacteristic
329C2×C4×C47C4×D411yescharacteristic
330C2×C4×C47C4×D411yescharacteristic
331C2×C4×C47C4×D411yescharacteristic
332C2×C4×C47#12011yescharacteristic
333C2×C4×C47#12011yescharacteristic
334C2×C4×C47#12011yescharacteristic
335C2×C4×C47#12011yescharacteristic
336C2×C4×C47#12111yescharacteristic
337C2×C4×C47#12111yescharacteristic
338C2×C4×C47#12111yescharacteristic
339C2×C4×C47#12111yescharacteristic
340C2×C4×C47#12311yescharacteristic
341C2×C4×C47#12311yescharacteristic
342C2×C4×C47#12311yescharacteristic
343C2×C4×C47#12311yescharacteristic
344C2×C4×C47C23×C411yescharacteristic
345C2×C4×C47C22×D411yescharacteristic
346C2×C4×C47C22×D411yescharacteristic
347C2×C4×C47C22×D411yescharacteristic
348C2×C4×C47C2×#4111yescharacteristic
349C2×C4×C47C2×#4111yescharacteristic
350C22⋊D47—24no—
351C22⋊D47—24no—
352C22⋊D47—24no—
353C22⋊D47—24no—
354C22⋊D47—416no—
355C2×Dic47—24no—
356C2×Dic47—22no—
357C2×Dic47—22no—
358C2×Dic47—22no—
359C2×Dic47—22no—
360C2×Dic47—44no—
361C2×Dic47—44no—
362C2×Dic47—42no—
363C2×Dic47—42no—
364C2×Dic47—82no—
365C2×Dic47C2×C22⋊C414yes—
366D188—22no—
367D188—22no—
368D188—22no—
369D188—22no—
370C4×D47—24no—
371C4×D47—24no—
372C4×D47—24no—
373C4×D47—24no—
374Dic94—22no—
375Dic94—22no—
376Dic94—22no—
377Dic94—22no—
378C8×C47—24no—
379C47⋊C8—24no—
380C2×#1884—471nomaximal, Sylow
381C22×C47—22no—
382C22×C47—22no—
383C22×C47—22no—
384C22×C47—41no—
385C22×C47—41no—
386C22×C47—41no—
387C22×C47—41no—
388C22×C47—44no—
389C22×C47—42no—
390C22×C47—82no—
391C22×C47—82no—
392C22×C47#38611yescharacteristic
393C22×C47#38611yescharacteristic
394C22×C47#38611yescharacteristic
395C22×C47#38611yescharacteristic
396C22×C47C22×C22⋊C411yescharacteristic
397C22×C47C2×#12111yescharacteristic
398C22×C47C2×#12111yescharacteristic
399C2×D47—24no—
400C2×D47—44no—
401C2×D47—44no—
402C2×D47—82no—
403C4×C47—42no—
404C4×C47—82no—
405C4×C47#38611yescharacteristic
406C4×C47#38611yescharacteristic
407C4×C47#38611yescharacteristic
408C4×C47#38611yescharacteristic
409C4×C47C2×C4×D411yescharacteristic
410C4×C47C2×C4×D411yescharacteristic
411C4×C47C2×#12011yescharacteristic
412C4×C47C2×#12311yescharacteristic
413Dic47—24no—
414Dic47—24no—
415Dic47—42no—
416Dic47—82no—
417C2×#568—471no—
418C2×#532—471no—
419C2×#421—471no—
420C2×#421D4711yescharacteristic, complemented
421C2×#410—471no—
422#1884—478no—
423C2×#339—471no—
424C2×#339—471no—
425C2×C47—21no—
426C2×C47—21no—
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—21no—
430C2×C47—21no—
431C2×C47—82no—
432C2×C47#188412yescomplemented
433C2×C47C2×#38611yescharacteristic
434D47—44no—
435C22×#41—471no—
436C22×#41C2×D4711yescharacteristic
437#568—474no—
438#568—942no—
439#568—942no—
440#568—942no—
441C2×#131—942no—
442C2×#131—942no—
443C22×M16—471no—
444C22×M16—942no—
445C22×M16C2×D4711yescharacteristic
446#532—474no—
447#532—474no—
448#532—942no—
449#532—942no—
450C2×C4⋊Q8—471no—
451C2×#127—471no—
452C2×#124—471no—
453C2×#124—471no—
454C2×#121—942no—
455C2×C4×D4—942no—
456C2×#117—471no—
457C2×#117C2×D4711yescharacteristic
458C22×C42—471no—
459#421—22no—
460#421—474no—
461#421—942no—
462#421C2×D4714yescomplemented
463C2×#104—22no—
464C2×#104—942no—
465#410—474no—
466#410—942no—
467C2×#99—942no—
468#339—474no—
469#339—474no—
470C47C2×#188411yescharacteristic, complemented, Sylow
471C2×#41—21no—
472C2×#41—21no—
473C2×#41—21no—
474C2×#41—21no—
475C2×#41—21no—
476C2×#41—21no—
477C2×#41—21no—
478C2×#41—21no—
479C2×#41—21no—
480C2×#41—21no—
481C2×#41—472no—
482C2×#41—472no—
483C2×#41—472no—
484C2×#41—472no—
485C2×#41—941no—
486C2×#41—941no—
487C2×#41—941no—
488C2×#41—941no—
489C2×#41—941no—
490C2×#41—941no—
491C2×#41—941no—
492C2×#41—941no—
493C2×#41C4×D4712yes—
494C2×#41C22×D4712yes—
495C22×Q8—471no—
496C22×Q8C4×D4711yescharacteristic
497C22×D4—21no—
498C22×D4—472no—
499C22×D4—471no—
500C22×D4—942no—
501C22×D4C4×D4711yescharacteristic
502C23×C4—21no—
503C23×C4—472no—
504C23×C4—941no—
505C23×C4C22×D4711yescharacteristic
506#131—948no—
507#131—948no—
508#131—948no—
509#131—948no—
510C2×M16—21no—
511C2×M16—21no—
512C2×M16—21no—
513C2×M16—472no—
514C2×M16—472no—
515C2×M16—472no—
516C2×M16—944no—
517C2×M16—948no—
518C2×M16—948no—
519C2×M16—941no—
520C2×M16—941no—
521C2×M16—941no—
522C2×M16C22⋊D4712yescomplemented
523C2×M16C22⋊D4712yescomplemented
524C2×M16C22×D4712yes—
525C22×C8—21no—
526C22×C8—944no—
527C22×C8—941no—
528C4⋊Q8—474no—
529C4⋊Q8—942no—
530#127—474no—
531#127—942no—
532#124—474no—
533#124—474no—
534#124—942no—
535#124—942no—
536#121—948no—
537#121—948no—
538C4×D4—948no—
539C4×D4—948no—
540#117—21no—
541#117—21no—
542#117—21no—
543#117—472no—
544#117—941no—
545#117—941no—
546#117—941no—
547#117C22×D4712yes—
548C2×C4⋊C4—21no—
549C2×C4⋊C4—942no—
550C2×C4⋊C4—941no—
551C2×C22⋊C4—21no—
552C2×C22⋊C4—942no—
553C2×C22⋊C4—942no—
554C2×C22⋊C4—941no—
555C2×C42—21no—
556C2×C42—471no—
557C2×C42—471no—
558C2×C42—472no—
559C2×C42—472no—
560C2×C42—941no—
561C2×C42—941no—
562C2×C42—941no—
563C2×C42—941no—
564#104—28no—
565#104—948no—
566#99—948no—
567C24—21no—
568C24—472no—
569C24D4×D4711yescharacteristic
570#41—22no—
571#41—22no—
572#41—22no—
573#41—22no—
574#41—22no—
575#41—22no—
576#41—22no—
577#41—22no—
578#41—41no—
579#41—41no—
580#41—41no—
581#41—41no—
582#41—41no—
583#41—41no—
584#41—41no—
585#41—41no—
586#41—942no—
587#41—942no—
588#41—942no—
589#41—942no—
590#41—942no—
591#41—942no—
592#41—942no—
593#41—942no—
594#41—942no—
595#41—942no—
596#41—942no—
597#41—942no—
598#41—942no—
599#41—942no—
600#41—942no—
601#41—942no—
602C2×Q8—21no—
603C2×Q8—21no—
604C2×Q8—21no—
605C2×Q8—21no—
606C2×Q8—21no—
607C2×Q8—472no—
608C2×Q8—472no—
609C2×Q8—941no—
610C2×Q8—941no—
611C2×Q8—941no—
612C2×Q8—941no—
613C2×Q8C2×C4×D4712yes—
614C2×D4—22no—
615C2×D4—22no—
616C2×D4—21no—
617C2×D4—21no—
618C2×D4—21no—
619C2×D4—21no—
620C2×D4—21no—
621C2×D4—41no—
622C2×D4—41no—
623C2×D4—41no—
624C2×D4—41no—
625C2×D4—474no—
626C2×D4—474no—
627C2×D4—472no—
628C2×D4—472no—
629C2×D4—942no—
630C2×D4—942no—
631C2×D4—942no—
632C2×D4—942no—
633C2×D4—948no—
634C2×D4—941no—
635C2×D4—941no—
636C2×D4—941no—
637C2×D4—941no—
638C2×D4—1888no—
639C2×D4C2×C4×D4712yes—
640C22×C4—21no—
641C22×C4—22no—
642C22×C4—22no—
643C22×C4—41no—
644C22×C4—41no—
645C22×C4—41no—
646C22×C4—41no—
647C22×C4—41no—
648C22×C4—472no—
649C22×C4—474no—
650C22×C4—474no—
651C22×C4—941no—
652C22×C4—942no—
653C22×C4—942no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—941no—
657C22×C4—942no—
658C22×C4—942no—
659C22×C4—1884no—
660C22×C4—1881no—
661C22×C4C2×C4×D4711yescharacteristic
662C22×C4C2×C4×D4711yescharacteristic
663C22×C4#1062535011yescharacteristic
664C22×C4#1062535011yescharacteristic
665C22×C4D4×D4711yescharacteristic
666C22×C4D4×D4711yescharacteristic
667C22×C4D4×D4711yescharacteristic
668C22×C4D4×D4711yescharacteristic
669C22×C4D4×D4711yescharacteristic
670C22×C4#1062535211yescharacteristic
671C22×C4#1062535211yescharacteristic
672C22×C4C2×C22⋊D4711yescharacteristic
673C22×C4C2×C22⋊D4711yescharacteristic
674C22×C4C23×D4711yescharacteristic
675M16—22no—
676M16—22no—
677M16—22no—
678M16—474no—
679M16—9416no—
680M16—942no—
681M16—942no—
682M16—942no—
683M16C2×C22⋊D4714yescomplemented
684C2×C8—22no—
685C2×C8—22no—
686C2×C8—22no—
687C2×C8—9416no—
688C2×C8—942no—
689C2×C8—942no—
690C2×C8—942no—
691C4⋊C4—22no—
692C4⋊C4—41no—
693C4⋊C4—948no—
694C4⋊C4—942no—
695C4⋊C4—1881no—
696C22⋊C4—22no—
697C22⋊C4—41no—
698C22⋊C4—948no—
699C22⋊C4—948no—
700C22⋊C4—942no—
701C22⋊C4—1881no—
702C42—22no—
703C42—41no—
704C42—472no—
705C42—472no—
706C42—942no—
707C42—941no—
708C42—941no—
709C42—942no—
710C42—942no—
711C42—1881no—
712C23—22no—
713C23—42no—
714C23—44no—
715C23—41no—
716C23—41no—
717C23—474no—
718C23—942no—
719C23—942no—
720C23—1884no—
721C23C22⋊C4×D4711yescharacteristic
722C23C22⋊C4×D4711yescharacteristic
723C23#1309399511yescharacteristic
724C23#1309399511yescharacteristic
725C23#1309399711yescharacteristic
726C23#1309399711yescharacteristic
727C23C2×D4×D4711yescharacteristic
728Q8—22no—
729Q8—22no—
730Q8—41no—
731Q8—41no—
732Q8—942no—
733Q8—942no—
734Q8—942no—
735Q8—942no—
736D4—22no—
737D4—22no—
738D4—42no—
739D4—42no—
740D4—42no—
741D4—42no—
742D4—41no—
743D4—41no—
744D4—944no—
745D4—944no—
746D4—944no—
747D4—944no—
748D4—942no—
749D4—942no—
750D4—942no—
751D4—942no—
752D4—18816no—
753C2×C4—22no—
754C2×C4—41no—
755C2×C4—41no—
756C2×C4—42no—
757C2×C4—42no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—42no—
761C2×C4—82no—
762C2×C4—474no—
763C2×C4—944no—
764C2×C4—942no—
765C2×C4—942no—
766C2×C4—942no—
767C2×C4—944no—
768C2×C4—944no—
769C2×C4—944no—
770C2×C4—944no—
771C2×C4—942no—
772C2×C4—3762no—
773C2×C4—1884no—
774C2×C4—1884no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4C22⋊C4×D4711yescharacteristic
778C2×C4C22⋊C4×D4711yescharacteristic
779C2×C4(C22⋊D47)⋊C411yescharacteristic
780C2×C4(C22⋊D47)⋊C411yescharacteristic
781C2×C4(C22⋊D47)⋊C411yescharacteristic
782C2×C4(C22⋊D47)⋊C411yescharacteristic
783C2×C4C4×C22⋊D4711yescharacteristic
784C2×C4C4×C22⋊D4711yescharacteristic
785C2×C4C4×C22⋊D4711yescharacteristic
786C2×C4C4×C22⋊D4711yescharacteristic
787C2×C4#1309399211yescharacteristic
788C2×C4#1309399211yescharacteristic
789C2×C4#1309399211yescharacteristic
790C2×C4#1309399211yescharacteristic
791C2×C4#1309399511yescharacteristic
792C2×C4#1309399511yescharacteristic
793C2×C4#1309399711yescharacteristic
794C2×C4#1309399711yescharacteristic
795C2×C4#1309400611yescharacteristic
796C2×C4#1309400611yescharacteristic
797C2×C4#1309400611yescharacteristic
798C2×C4#1309400611yescharacteristic
799C2×C4C22×C4×D4711yescharacteristic
800C2×C4C2×D4×D4711yescharacteristic
801C2×C4C2×D4×D4711yescharacteristic
802C2×C4C22×C22⋊D4711yescharacteristic
803C2×C4C2×#1062535211yescharacteristic
804C2×C4C2×#1062535011yescharacteristic
805C8—24no—
806C8—944no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—44no—
815C22—42no—
816C22—82no—
817C22—82no—
818C22—944no—
819C22—3762no—
820C22—1884no—
821C22—1884no—
822C22#1568899911yescharacteristic
823C22#1568899911yescharacteristic
824C22#1568899911yescharacteristic
825C22#1568899911yescharacteristic
826C22C2×C22⋊C4×D4711yescharacteristic
827C22C2×#1309399511yescharacteristic
828C22C2×#1309399711yescharacteristic
829C4—42no—
830C4—82no—
831C4—944no—
832C4—944no—
833C4—3762no—
834C4—1882no—
835C4#1568899911yescharacteristic
836C4#1568899911yescharacteristic
837C4#1568899911yescharacteristic
838C4#1568899911yescharacteristic
839C4C2×(C22⋊D47)⋊C411yescharacteristic
840C4C2×C4×C22⋊D4711yescharacteristic
841C4C2×#1309399211yescharacteristic
842C4C2×#1309400611yescharacteristic
843C2—21no—
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—82no—
850C2—1884no—
851C2#2024376812yesdirect product factor
852C2C2×#1568899911yescharacteristic
subgroupG/H
centerC2×C4#13093992
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47#386
prime radicalC2×#15689669C2
cosocleC22×C4×C47C24
hypercenterC2×#421D47
hypocenterC47C2×#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#15689889C2semidirect
3. C2×#15689140C2semidirect
4. C2×#15689096C2semidirect
5. #20243768C2direct (N × H)
6. C2×#15688884C2semidirect
7. C2×#15688882C2semidirect
8. C2×C47×#421C2semidirect
13. #15689889C22semidirect
20. #15689669C4semidirect
22. C2×#13094022C4semidirect
23. C2×#13094020C4semidirect
24. C2×#13094013C4semidirect
25. C2×#13094011C4semidirect
31. #15689140C22semidirect
34. #15689096C22semidirect
36. #15688884C22semidirect
37. #15688882C22semidirect
42. C47×#421C22semidirect
69. C2×#10625329D4semidirect
70. C2×#10625329D4semidirect
78. #13094022C2×C4semidirect
80. #13094020C2×C4semidirect
82. #13094013C2×C4semidirect
84. #13094011C2×C4semidirect
128. C2×M16×C47D4semidirect
129. C2×M16×C47D4semidirect
251. M16×C47C2×D4semidirect
279. #10625329C2×D4semidirect
420. C2×#421D47semidirect
432. C2×C47#1884semidirect
462. #421C2×D47semidirect
470. C47C2×#1884semidirect
522. C2×M16C22⋊D47semidirect
523. C2×M16C22⋊D47semidirect
683. M16C2×C22⋊D47semidirect
851. C2#20243768direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898892
C2×#156896692
C2×#156891402
C2×#156890962
#202437682
C2×#156888842
C2×#156888822
C2×C47×#4212
C2×#188447