Finite Group Databasebeta

← C2×#20243770 #26217817

Subgroups — C2×#20243770 #26217817

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×#15689673C211yesmaximal, characteristic
3C2×#15689141C211yesmaximal, characteristic, complemented
4C2×#15689139C211yesmaximal, characteristic, complemented
5C2×#15689096C211yesmaximal, characteristic, complemented
6#20243770C218yesmaximal, direct product factor
7C2×#15688883C211yesmaximal, characteristic, complemented
8C2×C47×#339C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C22×#10625350C2211yescharacteristic
11#15689889—22no—
12#15689889—22no—
13#15689889—22no—
14#15689889C2214yescomplemented
15C2×#13094032—22no—
16C2×#13094030—22no—
17C22×#10625329C2211yescharacteristic
18C2×M16×D47—22no—
19#15689673—22no—
20#15689673—22no—
21#15689673C414yescomplemented
22#15689673C2214yes—
23C2×#13094024C411yescharacteristic, complemented
24C2×#13094021C411yescharacteristic, complemented
25C2×#13094012C411yescharacteristic, complemented
26C2×#13094012C411yescharacteristic, complemented
27C2×#13093998—22no—
28C2×C4×D188—22no—
29C2×#13093983C2211yescharacteristic
30#15689141—22no—
31#15689141C2214yescomplemented
32#15689139—22no—
33#15689139C2214yescomplemented
34C2×#13093952—22no—
35C2×#13093950—22no—
36#15689096—22no—
37#15689096C2214yescomplemented
38C2×#13093938—22no—
39#15688883C2214yescomplemented
40C22×M16×C47C2211yescharacteristic
41C2×#117×C47C2211yescharacteristic
42C22×C42×C47C2211yescharacteristic
43C47×#339C2214yescomplemented
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×#10625350—21no—
53C2×#10625350—21no—
54C2×#10625350—21no—
55C2×#10625350—21no—
56C2×#10625350—21no—
57C2×#10625350—21no—
58C2×#10625350—21no—
59C2×#10625350—21no—
60C2×#10625350—21no—
61C2×#10625350—21no—
62C2×#10625350C2×C412yes—
63C2×#10625350C2×C412yes—
64C2×#10625350D412yes—
65C2×#10625350D412yes—
66C2×#10625350C2312yes—
67C2×#10625350C2312yes—
68C22×Dic94C2×C411yescharacteristic
69C22×Dic94C2×C411yescharacteristic
70C22×D188—22no—
71C22×D188C2×C411yescharacteristic
72C22×D188C2×C411yescharacteristic
73C22×C22⋊D47—21no—
74C22×C22⋊D47D412yes—
75C22×C4×D47—21no—
76C22×C4×D47D412yes—
77#13094032—28no—
78#13094032—28no—
79#13094030—28no—
80#13094030—28no—
81C2×#10625329—21no—
82C2×#10625329—21no—
83C2×#10625329—21no—
84C2×#10625329D412yescomplemented
85C2×#10625329D412yescomplemented
86C2×#10625329C2312yes—
87C2×#10625324—24no—
88M16×D47—28no—
89M16×D47—28no—
90C22×C47⋊C8—21no—
91C2×C8×D47—24no—
92#13094024—22no—
93#13094024C2×C414yescomplemented
94#13094021—22no—
95#13094021C2×C414yescomplemented
96#13094012—22no—
97#13094012—22no—
98#13094012C2×C414yescomplemented
99#13094012C2×C414yescomplemented
100#13093998—28no—
101#13093998—28no—
102C4×D188—28no—
103C4×D188—28no—
104#13093983—21no—
105#13093983—21no—
106#13093983—21no—
107#13093983C2312yes—
108C2×C4⋊Dic47—22no—
109C2×C4⋊Dic47—21no—
110C2×C22⋊Dic47—21no—
111C2×(C2×D47)⋊C4—22no—
112C2×(C2×D47)⋊C4—22no—
113C2×C4×Dic47—21no—
114#13093952—28no—
115#13093950—28no—
116#13093938—28no—
117C23×C4×C47—21no—
118C23×C4×C47C2311yescharacteristic
119C2×M16×C47—21no—
120C2×M16×C47—21no—
121C2×M16×C47—21no—
122C2×M16×C47D412yescomplemented
123C2×M16×C47D412yescomplemented
124C2×M16×C47C2312yes—
125C22×C8×C47—21no—
126#117×C47—21no—
127#117×C47—21no—
128#117×C47—21no—
129#117×C47C2312yes—
130C2×C4⋊C4×C47—21no—
131C2×C22⋊C4×C47—21no—
132C2×C42×C47—21no—
133C2×C42×C47—21no—
134C2×C42×C47—21no—
135C2×C42×C47—21no—
136C2×C42×C47C2×C411yescharacteristic
137C2×C42×C47C2×C411yescharacteristic
138C2×C42×C47C2×C412yes—
139C2×C42×C47C2312yes—
140C24×C47C2×D411yescharacteristic
141C23×D47—21no—
142C23×D47C22⋊C412yes—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—44no—
148C22×C4×C47—41no—
149C22×C4×C47C22×C411yescharacteristic
150C22×C4×C47C22×C411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2×D411yescharacteristic
157C22×C4×C47C2×D411yescharacteristic
158C22×C4×C47#4111yescharacteristic
159C22×C4×C47#4111yescharacteristic
160C22×C4×C47#4111yescharacteristic
161C22×C4×C47#4111yescharacteristic
162C22×C4×C47C2411yescharacteristic
163C2×C22⋊D47—22no—
164C2×C22⋊D47—22no—
165C2×C22⋊D47—22no—
166C2×C22⋊D47—22no—
167C2×C22⋊D47—22no—
168C2×C22⋊D47—22no—
169C2×C22⋊D47—41no—
170C2×C22⋊D47—41no—
171C2×C22⋊D47—41no—
172C2×C22⋊D47—41no—
173C2×C22⋊D47C22⋊C414yes—
174C2×C22⋊D47C2×D414yes—
175C22×Dic47—21no—
176C22×Dic47—41no—
177C22×Dic47C22⋊C412yes—
178#10625350—22no—
179#10625350—22no—
180#10625350—22no—
181#10625350—22no—
182#10625350—22no—
183#10625350—22no—
184#10625350—22no—
185#10625350—22no—
186#10625350—22no—
187#10625350—22no—
188#10625350—22no—
189#10625350—22no—
190#10625350—22no—
191#10625350—22no—
192#10625350—22no—
193#10625350—22no—
194#10625350—22no—
195#10625350—22no—
196#10625350—22no—
197#10625350—22no—
198#10625350—22no—
199#10625350—22no—
200#10625350—22no—
201#10625350—22no—
202#10625350—41no—
203#10625350—41no—
204#10625350—41no—
205#10625350—41no—
206#10625350—41no—
207#10625350—41no—
208#10625350—41no—
209#10625350—41no—
210C2×D188—21no—
211C2×D188—21no—
212C2×D188—21no—
213C2×D188—21no—
214C2×D188—21no—
215C2×D188—21no—
216C2×D188—21no—
217C2×D188—21no—
218C2×D188—28no—
219C2×D188—21no—
220C2×D188—48no—
221C2×D188C22⋊C412yes—
222C2×D188C22×C412yes—
223C2×D188C22×C412yes—
224C2×C4×D47—22no—
225C2×C4×D47—22no—
226C2×C4×D47—22no—
227C2×C4×D47—22no—
228C2×C4×D47—22no—
229C2×C4×D47—22no—
230C2×C4×D47—41no—
231C2×C4×D47—41no—
232C2×C4×D47—41no—
233C2×C4×D47—41no—
234C2×C4×D47C22⋊C414yes—
235C2×C4×D47C2×D414yes—
236C2×Dic94—21no—
237C2×Dic94—21no—
238C2×Dic94—21no—
239C2×Dic94—21no—
240C2×Dic94—21no—
241C2×Dic94—21no—
242C2×Dic94—21no—
243C2×Dic94—21no—
244C2×Dic94—21no—
245C2×Dic94C22⋊C412yes—
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—21no—
261C42×C47—21no—
262C42×C47—22no—
263C42×C47—22no—
264C42×C47—41no—
265C42×C47C22×C412yes—
266C42×C47C22×C412yes—
267C22⋊Dic47—22no—
268C22⋊Dic47—41no—
269(C2×D47)⋊C4—28no—
270(C2×D47)⋊C4—28no—
271C4⋊Dic47—28no—
272C4⋊Dic47—22no—
273C4⋊Dic47—41no—
274C4×Dic47—22no—
275C4×Dic47—41no—
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—42no—
286C23×C47C2×C22⋊C411yescharacteristic
287C23×C47C2×C22⋊C411yescharacteristic
288C23×C47#12111yescharacteristic
289C23×C47#12111yescharacteristic
290C23×C47#12111yescharacteristic
291C23×C47#12111yescharacteristic
292C23×C47C22×D411yescharacteristic
293C22×D47—22no—
294C22×D47—22no—
295C22×D47—22no—
296C22×D47—44no—
297C22×D47—44no—
298C22×D47—41no—
299C22×D47—41no—
300C22×D47C2×C22⋊C414yes—
301C2×C4×C47—24no—
302C2×C4×C47—22no—
303C2×C4×C47—22no—
304C2×C4×C47—44no—
305C2×C4×C47—44no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—82no—
309C2×C4×C47C2×C22⋊C411yescharacteristic
310C2×C4×C47C2×C22⋊C411yescharacteristic
311C2×C4×C47C4×D411yescharacteristic
312C2×C4×C47C4×D411yescharacteristic
313C2×C4×C47C4×D411yescharacteristic
314C2×C4×C47C4×D411yescharacteristic
315C2×C4×C47C4×D411yescharacteristic
316C2×C4×C47C4×D411yescharacteristic
317C2×C4×C47C4×D411yescharacteristic
318C2×C4×C47C4×D411yescharacteristic
319C2×C4×C47#12011yescharacteristic
320C2×C4×C47#12011yescharacteristic
321C2×C4×C47#12011yescharacteristic
322C2×C4×C47#12011yescharacteristic
323C2×C4×C47#12111yescharacteristic
324C2×C4×C47#12111yescharacteristic
325C2×C4×C47#12111yescharacteristic
326C2×C4×C47#12111yescharacteristic
327C2×C4×C47#12311yescharacteristic
328C2×C4×C47#12311yescharacteristic
329C2×C4×C47#12311yescharacteristic
330C2×C4×C47#12311yescharacteristic
331C2×C4×C47C23×C411yescharacteristic
332C2×C4×C47C22×D411yescharacteristic
333C2×C4×C47C22×D411yescharacteristic
334C2×C4×C47C22×D411yescharacteristic
335C2×C4×C47C2×#4111yescharacteristic
336C2×C4×C47C2×#4111yescharacteristic
337C22⋊D47—24no—
338C22⋊D47—24no—
339C22⋊D47—24no—
340C22⋊D47—24no—
341C22⋊D47—42no—
342C22⋊D47—42no—
343C22⋊D47—42no—
344C22⋊D47—42no—
345C2×Dic47—22no—
346C2×Dic47—22no—
347C2×Dic47—22no—
348C2×Dic47—41no—
349C2×Dic47—41no—
350C2×Dic47—42no—
351C2×Dic47—82no—
352C2×Dic47C2×C22⋊C414yes—
353D188—22no—
354D188—22no—
355D188—22no—
356D188—22no—
357D188—22no—
358D188—22no—
359D188—416no—
360D188—41no—
361D188—41no—
362C4×D47—24no—
363C4×D47—24no—
364C4×D47—24no—
365C4×D47—24no—
366C4×D47—42no—
367C4×D47—42no—
368C4×D47—42no—
369C4×D47—42no—
370Dic94—22no—
371Dic94—22no—
372Dic94—22no—
373Dic94—22no—
374Dic94—22no—
375Dic94—22no—
376Dic94—41no—
377Dic94—41no—
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#38611yescharacteristic
389C22×C47#38611yescharacteristic
390C22×C47#38611yescharacteristic
391C22×C47#38611yescharacteristic
392C22×C47C22×C22⋊C411yescharacteristic
393C22×C47C2×#12111yescharacteristic
394C22×C47C2×#12111yescharacteristic
395C2×D47—24no—
396C2×D47—44no—
397C2×D47—44no—
398C2×D47—44no—
399C2×D47—42no—
400C2×D47—82no—
401C2×D47—82no—
402C2×D47—82no—
403C4×C47—24no—
404C4×C47—42no—
405C4×C47—82no—
406C4×C47#38611yescharacteristic
407C4×C47#38611yescharacteristic
408C4×C47#38611yescharacteristic
409C4×C47#38611yescharacteristic
410C4×C47C2×C4×D411yescharacteristic
411C4×C47C2×C4×D411yescharacteristic
412C4×C47C2×#12011yescharacteristic
413C4×C47C2×#12311yescharacteristic
414Dic47—24no—
415Dic47—42no—
416Dic47—82no—
417C2×#568—471no—
418C2×#532—471no—
419C2×#421—471no—
420C2×#421—471no—
421C2×#410—471no—
422#1884—478no—
423C2×#339—471no—
424C2×#339D4711yescharacteristic, complemented
425C2×C47—21no—
426C2×C47—21no—
427C2×C47—21no—
428C2×C47—21no—
429C2×C47—21no—
430C2×C47—21no—
431C2×C47#188412yescomplemented
432C2×C47C2×#38611yescharacteristic
433D47—44no—
434D47—82no—
435C22×#41—471no—
436C22×#41—471no—
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×C42C2×D4711yescharacteristic
459#421—474no—
460#421—474no—
461#421—942no—
462#421—942no—
463C2×#104—942no—
464C2×#104—942no—
465#410—474no—
466#410—942no—
467C2×#99—942no—
468#339—474no—
469#339C2×D4714yescomplemented
470C47C2×#188411yescharacteristic, complemented, Sylow
471C2×#41—472no—
472C2×#41—472no—
473C2×#41—472no—
474C2×#41—472no—
475C2×#41—472no—
476C2×#41—472no—
477C2×#41—941no—
478C2×#41—941no—
479C2×#41—941no—
480C2×#41—941no—
481C2×#41—941no—
482C2×#41—941no—
483C2×#41—941no—
484C2×#41—941no—
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×#41—941no—
494C2×#41—941no—
495C22×Q8—471no—
496C22×Q8—471no—
497C22×D4—472no—
498C22×D4—471no—
499C22×D4—471no—
500C22×D4—942no—
501C22×D4—941no—
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×M16D18812yescomplemented
523C2×M16D18812yescomplemented
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—21no—
557C2×C42—21no—
558C2×C42—21no—
559C2×C42—941no—
560C2×C42C4×D4711yescharacteristic
561C2×C42C4×D4711yescharacteristic
562C2×C42C4×D4712yes—
563C2×C42C22×D4712yes—
564#104—948no—
565#104—948no—
566#99—948no—
567C24—472no—
568C24—941no—
569C24D4×D4711yescharacteristic
570#41—942no—
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—
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—
594#41—1881no—
595#41—1881no—
596#41—1881no—
597#41—1881no—
598#41—1881no—
599#41—1881no—
600#41—1881no—
601#41—1881no—
602C2×Q8—472no—
603C2×Q8—472no—
604C2×Q8—472no—
605C2×Q8—941no—
606C2×Q8—941no—
607C2×Q8—941no—
608C2×Q8—941no—
609C2×Q8—941no—
610C2×Q8—941no—
611C2×Q8—941no—
612C2×Q8—941no—
613C2×Q8—941no—
614C2×D4—474no—
615C2×D4—474no—
616C2×D4—472no—
617C2×D4—472no—
618C2×D4—472no—
619C2×D4—948no—
620C2×D4—942no—
621C2×D4—942no—
622C2×D4—942no—
623C2×D4—942no—
624C2×D4—942no—
625C2×D4—942no—
626C2×D4—941no—
627C2×D4—941no—
628C2×D4—941no—
629C2×D4—941no—
630C2×D4—941no—
631C2×D4—941no—
632C2×D4—941no—
633C2×D4—941no—
634C2×D4—941no—
635C2×D4—1888no—
636C2×D4—1881no—
637C2×D4—1881no—
638C2×D4—1881no—
639C2×D4—1881no—
640C22×C4—21no—
641C22×C4—21no—
642C22×C4—22no—
643C22×C4—22no—
644C22×C4—44no—
645C22×C4—41no—
646C22×C4—472no—
647C22×C4—474no—
648C22×C4—474no—
649C22×C4—942no—
650C22×C4—942no—
651C22×C4—942no—
652C22×C4—942no—
653C22×C4—941no—
654C22×C4—942no—
655C22×C4—942no—
656C22×C4—1881no—
657C22×C4—1881no—
658C22×C4—1881no—
659C22×C4—1881no—
660C22×C4—1881no—
661C22×C4C2×C4×D4711yescharacteristic
662C22×C4C2×C4×D4711yescharacteristic
663C22×C4C2×D18811yescharacteristic
664C22×C4C2×D18811yescharacteristic
665C22×C4#1062535011yescharacteristic
666C22×C4#1062535011yescharacteristic
667C22×C4D4×D4711yescharacteristic
668C22×C4D4×D4711yescharacteristic
669C22×C4D4×D4711yescharacteristic
670C22×C4D4×D4711yescharacteristic
671C22×C4D4×D4711yescharacteristic
672C22×C4#1062535411yescharacteristic
673C22×C4#1062535411yescharacteristic
674C22×C4C23×D4711yescharacteristic
675M16—22no—
676M16—22no—
677M16—22no—
678M16—474no—
679M16—9416no—
680M16—942no—
681M16—942no—
682M16—942no—
683M16C2×D18814yescomplemented
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—21no—
704C42—21no—
705C42—22no—
706C42—22no—
707C42—41no—
708C42—942no—
709C42—1881no—
710C42C2×C4×D4712yes—
711C42C2×C4×D4712yes—
712C23—42no—
713C23—474no—
714C23—942no—
715C23—942no—
716C23—942no—
717C23—1884no—
718C23—1884no—
719C23—1881no—
720C23—1881no—
721C23C22⋊C4×D4711yescharacteristic
722C23C22⋊C4×D4711yescharacteristic
723C23#1309399711yescharacteristic
724C23#1309399711yescharacteristic
725C23#1309399911yescharacteristic
726C23#1309399911yescharacteristic
727C23C2×D4×D4711yescharacteristic
728Q8—942no—
729Q8—942no—
730Q8—942no—
731Q8—942no—
732Q8—942no—
733Q8—942no—
734Q8—1881no—
735Q8—1881no—
736D4—944no—
737D4—944no—
738D4—944no—
739D4—944no—
740D4—942no—
741D4—942no—
742D4—942no—
743D4—942no—
744D4—942no—
745D4—942no—
746D4—18816no—
747D4—1882no—
748D4—1882no—
749D4—1882no—
750D4—1882no—
751D4—1881no—
752D4—1881no—
753C2×C4—24no—
754C2×C4—22no—
755C2×C4—22no—
756C2×C4—44no—
757C2×C4—44no—
758C2×C4—42no—
759C2×C4—42no—
760C2×C4—82no—
761C2×C4—474no—
762C2×C4—942no—
763C2×C4—942no—
764C2×C4—944no—
765C2×C4—944no—
766C2×C4—944no—
767C2×C4—944no—
768C2×C4—942no—
769C2×C4—3762no—
770C2×C4—1882no—
771C2×C4—1881no—
772C2×C4—1881no—
773C2×C4—1882no—
774C2×C4—1882no—
775C2×C4—1882no—
776C2×C4—1882no—
777C2×C4C22⋊C4×D4711yescharacteristic
778C2×C4C22⋊C4×D4711yescharacteristic
779C2×C4#1309398611yescharacteristic
780C2×C4#1309398611yescharacteristic
781C2×C4#1309398611yescharacteristic
782C2×C4#1309398611yescharacteristic
783C2×C4C4×D18811yescharacteristic
784C2×C4C4×D18811yescharacteristic
785C2×C4C4×D18811yescharacteristic
786C2×C4C4×D18811yescharacteristic
787C2×C4#1309399411yescharacteristic
788C2×C4#1309399411yescharacteristic
789C2×C4#1309399411yescharacteristic
790C2×C4#1309399411yescharacteristic
791C2×C4#1309399711yescharacteristic
792C2×C4#1309399711yescharacteristic
793C2×C4#1309399911yescharacteristic
794C2×C4#1309399911yescharacteristic
795C2×C4#1309400911yescharacteristic
796C2×C4#1309400911yescharacteristic
797C2×C4#1309400911yescharacteristic
798C2×C4#1309400911yescharacteristic
799C2×C4C22×C4×D4711yescharacteristic
800C2×C4C2×D4×D4711yescharacteristic
801C2×C4C2×D4×D4711yescharacteristic
802C2×C4C22×D18811yescharacteristic
803C2×C4C2×#1062535011yescharacteristic
804C2×C4C2×#1062535411yescharacteristic
805C8—24no—
806C8—944no—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—41no—
811C22—41no—
812C22—41no—
813C22—41no—
814C22—944no—
815C22—3762no—
816C22—3762no—
817C22—3762no—
818C22—1884no—
819C22—1884no—
820C22—1882no—
821C22—1884no—
822C22#1568900111yescharacteristic
823C22#1568900111yescharacteristic
824C22#1568900111yescharacteristic
825C22#1568900111yescharacteristic
826C22C2×C22⋊C4×D4711yescharacteristic
827C22C2×#1309399711yescharacteristic
828C22C2×#1309399911yescharacteristic
829C4—24no—
830C4—42no—
831C4—82no—
832C4—944no—
833C4—3762no—
834C4—1882no—
835C4#1568900111yescharacteristic
836C4#1568900111yescharacteristic
837C4#1568900111yescharacteristic
838C4#1568900111yescharacteristic
839C4C2×#1309398611yescharacteristic
840C4C2×C4×D18811yescharacteristic
841C4C2×#1309399411yescharacteristic
842C4C2×#1309400911yescharacteristic
843C2—21no—
844C2—21no—
845C2—21no—
846C2—21no—
847C2—21no—
848C2—21no—
849C2—3762no—
850C2—1884no—
851C2#2024377012yesdirect product factor
852C2C2×#1568900111yescharacteristic
subgroupG/H
centerC2×C4#13093994
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#339C2
socleC22×C47#386
prime radicalC2×#15689673C2
cosocleC22×C4×C47C24
hypercenterC2×#339D47
hypocenterC47C2×#1884
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#339

Complements

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

NH ≅ G/Ntype
1. C2×#15689889C2semidirect
3. C2×#15689141C2semidirect
4. C2×#15689139C2semidirect
5. C2×#15689096C2semidirect
6. #20243770C2direct (N × H)
7. C2×#15688883C2semidirect
8. C2×C47×#339C2semidirect
14. #15689889C22semidirect
21. #15689673C4semidirect
23. C2×#13094024C4semidirect
24. C2×#13094021C4semidirect
25. C2×#13094012C4semidirect
26. C2×#13094012C4semidirect
31. #15689141C22semidirect
33. #15689139C22semidirect
37. #15689096C22semidirect
39. #15688883C22semidirect
43. C47×#339C22semidirect
84. C2×#10625329D4semidirect
85. C2×#10625329D4semidirect
93. #13094024C2×C4semidirect
95. #13094021C2×C4semidirect
98. #13094012C2×C4semidirect
99. #13094012C2×C4semidirect
122. C2×M16×C47D4semidirect
123. C2×M16×C47D4semidirect
251. M16×C47C2×D4semidirect
279. #10625329C2×D4semidirect
424. C2×#339D47semidirect
431. C2×C47#1884semidirect
469. #339C2×D47semidirect
470. C47C2×#1884semidirect
522. C2×M16D188semidirect
523. C2×M16D188semidirect
683. M16C2×D188semidirect
851. C2#20243770direct (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×#156896732
C2×#156891412
C2×#156891392
C2×#156890962
#202437702
C2×#156888832
C2×C47×#3392
C2×#188447