Finite Group Databasebeta

← C2×#20243919 #26218269

Subgroups — C2×#20243919 #26218269

Order 12032.

1974 conjugacy classes of subgroups.

The subgroup lattice has 808 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689692C211yesmaximal, characteristic
2C2×#15689597C211yesmaximal, characteristic, complemented
3C2×#15689141C211yesmaximal, characteristic, complemented
4C2×#15689139C211yesmaximal, characteristic, complemented
5C22×#13093940C211yesmaximal, characteristic, complemented
6#20243919C218yesmaximal, direct product factor
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10C23×D188C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12#15689692—22no—
13#15689692—22no—
14#15689692C414yescomplemented
15#15689692C2214yes—
16C2×#13094021C412yescomplemented
17C2×#13094012C412yescomplemented
18C2×#13093999—22no—
19C2×#13093994—22no—
20#15689597—22no—
21#15689597—22no—
22#15689597—22no—
23#15689597C2214yescomplemented
24C2×C4×D188—22no—
25C2×#13093986—22no—
26C2×#13093983C2211yescharacteristic
27C2×C22⋊C4×D47—22no—
28#15689141—22no—
29#15689141C2214yescomplemented
30#15689139—22no—
31#15689139C2214yescomplemented
32C2×#13093952—22no—
33C2×#13093950—22no—
34C2×#13093940—22no—
35C2×#13093940—22no—
36C2×#13093940C2214yescomplemented
37#15688879C2214yescomplemented
38C22×M16×C47C2211yescharacteristic
39C2×#117×C47C2211yescharacteristic
40C2×#117×C47C2211yescharacteristic
41C47×H(3,ℤ/4)C2214yescomplemented
42C24×D47D412yes—
43C2×#10625350—21no—
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×#10625350C2×C412yescomplemented
54C2×#10625350C2312yes—
55C22×Dic94C2×C411yescharacteristic, complemented
56C22×D188—21no—
57C22×D188—21no—
58C22×D188—21no—
59C22×D188—21no—
60C22×D188—21no—
61C22×D188—21no—
62C22×D188—21no—
63C22×D188—21no—
64C22×D188—24no—
65C22×D188C2×C412yes—
66C22×D188C2×C412yes—
67C22×D188C2×C411yescharacteristic, complemented
68C22×D188D412yes—
69C22×D188D412yes—
70C22×D188D412yes—
71C22×D188C2312yes—
72C22×C22⋊D47—21no—
73C22×C4×D47—21no—
74C22×C4×D47—24no—
75C2×#10625329—21no—
76C2×#10625329—21no—
77C2×#10625329—21no—
78C2×#10625329—21no—
79C2×#10625329—21no—
80C2×#10625329C2312yes—
81C22×C47⋊C8—21no—
82#13094021—24no—
83#13094021C2×C418yescomplemented
84#13094012—24no—
85#13094012C2×C418yescomplemented
86#13093999—28no—
87#13093999—28no—
88#13093994—28no—
89#13093994—28no—
90C4×D188—28no—
91C4×D188—28no—
92#13093986—28no—
93#13093986—28no—
94#13093983—21no—
95#13093983—21no—
96#13093983D412yescomplemented
97#13093983C2312yes—
98C2×C4⋊Dic47—21no—
99C2×C22⋊Dic47—21no—
100C2×(C2×D47)⋊C4—24no—
101C2×(C2×D47)⋊C4—24no—
102C22⋊C4×D47—28no—
103C22⋊C4×D47—28no—
104C2×C4×Dic47D412yescomplemented
105#13093952—28no—
106#13093950—28no—
107#13093940—28no—
108C23×C4×C47C2311yescharacteristic
109C2×M16×C47—21no—
110C2×M16×C47—21no—
111C2×M16×C47—21no—
112C2×M16×C47—21no—
113C2×M16×C47—21no—
114C2×M16×C47C2312yes—
115C22×C8×C47—21no—
116#117×C47—21no—
117#117×C47—21no—
118#117×C47—21no—
119#117×C47—21no—
120#117×C47C2×C412yescomplemented
121#117×C47D412yescomplemented
122#117×C47C2312yes—
123#117×C47C2312yes—
124C2×C4⋊C4×C47—21no—
125C2×C4⋊C4×C47—21no—
126C2×C22⋊C4×C47—21no—
127C2×C22⋊C4×C47—21no—
128C2×C42×C47C2×C412yescomplemented
129C2×C42×C47D412yescomplemented
130C24×C47C2×D411yescharacteristic
131C23×D47—22no—
132C23×D47—22no—
133C23×D47—22no—
134C23×D47—22no—
135C23×D47—21no—
136C23×D47—84no—
137C23×D47C22⋊C414yes—
138C23×D47C22⋊C414yes—
139C23×D47C2×D414yes—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47C22×C411yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×C4×C47C2411yescharacteristic
156C2×C22⋊D47—22no—
157C2×C22⋊D47—22no—
158C2×C22⋊D47—41no—
159C2×C22⋊D47—41no—
160C2×C22⋊D47—41no—
161C2×C22⋊D47—41no—
162C22×Dic47—21no—
163C22×Dic47—22no—
164#10625350—22no—
165#10625350—22no—
166#10625350—22no—
167#10625350—22no—
168#10625350—22no—
169#10625350—22no—
170#10625350—22no—
171#10625350—22no—
172#10625350—41no—
173#10625350—41no—
174#10625350—41no—
175#10625350—41no—
176#10625350—41no—
177#10625350—41no—
178#10625350—41no—
179#10625350—41no—
180C2×D188—22no—
181C2×D188—22no—
182C2×D188—22no—
183C2×D188—22no—
184C2×D188—22no—
185C2×D188—22no—
186C2×D188—22no—
187C2×D188—22no—
188C2×D188—22no—
189C2×D188—22no—
190C2×D188—22no—
191C2×D188—22no—
192C2×D188—22no—
193C2×D188—22no—
194C2×D188—22no—
195C2×D188—22no—
196C2×D188—22no—
197C2×D188—22no—
198C2×D188—22no—
199C2×D188—22no—
200C2×D188—22no—
201C2×D188—22no—
202C2×D188—22no—
203C2×D188—22no—
204C2×D188—21no—
205C2×D188—21no—
206C2×D188—21no—
207C2×D188—21no—
208C2×D188—21no—
209C2×D188—216no—
210C2×D188—88no—
211C2×D188C22⋊C414yes—
212C2×D188C22⋊C414yes—
213C2×D188C22×C414yes—
214C2×D188C22×C412yescomplemented
215C2×D188C2×D414yes—
216C2×C4×D47—22no—
217C2×C4×D47—22no—
218C2×C4×D47—216no—
219C2×C4×D47—41no—
220C2×C4×D47—41no—
221C2×C4×D47—41no—
222C2×C4×D47—41no—
223C2×C4×D47—88no—
224C2×Dic94—21no—
225C2×Dic94—21no—
226C2×Dic94—21no—
227C2×Dic94—21no—
228C2×Dic94—21no—
229C2×Dic94C22×C412yescomplemented
230M16×C47—22no—
231M16×C47—22no—
232M16×C47—41no—
233M16×C47—41no—
234C2×C8×C47—22no—
235C2×C8×C47—41no—
236C2×C8×C47—41no—
237C4⋊C4×C47—22no—
238C4⋊C4×C47—22no—
239C4⋊C4×C47—22no—
240C4⋊C4×C47—22no—
241C22⋊C4×C47—22no—
242C22⋊C4×C47—22no—
243C22⋊C4×C47—22no—
244C22⋊C4×C47—22no—
245C42×C47—22no—
246C42×C47—22no—
247C42×C47C22×C414yescomplemented
248C42×C47C2×D414yescomplemented
249C22⋊Dic47—22no—
250C22⋊Dic47—22no—
251(C2×D47)⋊C4—216no—
252(C2×D47)⋊C4—216no—
253C4⋊Dic47—22no—
254C4⋊Dic47—22no—
255C4×Dic47—22no—
256C4×Dic47C2×D414yescomplemented
257#10625329—22no—
258#10625329—22no—
259#10625329—41no—
260#10625329—41no—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—41no—
263C2×C47⋊C8—41no—
264C23×C47—42no—
265C23×C47C2×C22⋊C411yescharacteristic
266C23×C47C2×C22⋊C411yescharacteristic
267C23×C47#12011yescharacteristic
268C23×C47#12011yescharacteristic
269C23×C47#12311yescharacteristic
270C23×C47#12311yescharacteristic
271C23×C47C22×D411yescharacteristic
272C22×D47—24no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—24no—
278C22×D47—22no—
279C22×D47—48no—
280C22×D47—48no—
281C22×D47—44no—
282C22×D47—41no—
283C22×D47—41no—
284C22×D47—84no—
285C22×D47—84no—
286C22×D47—84no—
287C22×D47—84no—
288C22×D47—84no—
289C22×D47C2×C22⋊C418yes—
290C2×C4×C47—24no—
291C2×C4×C47—24no—
292C2×C4×C47—44no—
293C2×C4×C47—44no—
294C2×C4×C47C2×C22⋊C411yescharacteristic
295C2×C4×C47C2×C22⋊C411yescharacteristic
296C2×C4×C47C4×D411yescharacteristic
297C2×C4×C47C4×D411yescharacteristic
298C2×C4×C47C4×D411yescharacteristic
299C2×C4×C47C4×D411yescharacteristic
300C2×C4×C47C4×D411yescharacteristic
301C2×C4×C47C4×D411yescharacteristic
302C2×C4×C47C4×D411yescharacteristic
303C2×C4×C47C4×D411yescharacteristic
304C2×C4×C47#12011yescharacteristic
305C2×C4×C47#12011yescharacteristic
306C2×C4×C47#12111yescharacteristic
307C2×C4×C47#12111yescharacteristic
308C2×C4×C47#12111yescharacteristic
309C2×C4×C47#12111yescharacteristic
310C2×C4×C47#12111yescharacteristic
311C2×C4×C47#12111yescharacteristic
312C2×C4×C47#12111yescharacteristic
313C2×C4×C47#12111yescharacteristic
314C2×C4×C47#12311yescharacteristic
315C2×C4×C47#12311yescharacteristic
316C2×C4×C47C23×C411yescharacteristic
317C2×C4×C47C22×D411yescharacteristic
318C2×C4×C47C22×D411yescharacteristic
319C2×C4×C47C22×D411yescharacteristic
320C2×C4×C47C2×#4111yescharacteristic
321C2×C4×C47C2×#4111yescharacteristic
322C22⋊D47—42no—
323C22⋊D47—42no—
324C22⋊D47—42no—
325C22⋊D47—42no—
326C2×Dic47—22no—
327C2×Dic47—24no—
328C2×Dic47—44no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331D188—24no—
332D188—24no—
333D188—22no—
334D188—22no—
335D188—24no—
336D188—24no—
337D188—24no—
338D188—24no—
339D188—24no—
340D188—24no—
341D188—41no—
342D188—41no—
343D188—816no—
344C4×D47—42no—
345C4×D47—42no—
346C4×D47—42no—
347C4×D47—42no—
348C4×D47—816no—
349Dic94—22no—
350Dic94—22no—
351Dic94—41no—
352Dic94—41no—
353C8×C47—42no—
354C47⋊C8—42no—
355C2×#1911—471nomaximal, Sylow
356C22×C47—22no—
357C22×C47—22no—
358C22×C47—22no—
359C22×C47—41no—
360C22×C47—41no—
361C22×C47—41no—
362C22×C47—41no—
363C22×C47#38611yescharacteristic
364C22×C47#38611yescharacteristic
365C22×C47#38611yescharacteristic
366C22×C47#38611yescharacteristic
367C22×C47C22×C22⋊C411yescharacteristic
368C22×C47C2×#12011yescharacteristic
369C22×C47C2×#12311yescharacteristic
370C2×D47—28no—
371C2×D47—48no—
372C2×D47—48no—
373C2×D47—48no—
374C2×D47—48no—
375C2×D47—44no—
376C2×D47—42no—
377C2×D47—84no—
378C2×D47—84no—
379C2×D47—84no—
380C2×D47—82no—
381C2×D47—82no—
382C4×C47—44no—
383C4×C47—44no—
384C4×C47#38611yescharacteristic
385C4×C47#38611yescharacteristic
386C4×C47#38611yescharacteristic
387C4×C47#38611yescharacteristic
388C4×C47C2×C4×D411yescharacteristic
389C4×C47C2×C4×D411yescharacteristic
390C4×C47C2×#12111yescharacteristic
391C4×C47C2×#12111yescharacteristic
392Dic47—44no—
393Dic47—42no—
394C2×#535—471no—
395C2×#518—471no—
396C2×#421—471no—
397C2×#421—471no—
398C22×#100—471no—
399#1911—478no—
400C2×H(3,ℤ/4)—471no—
401C2×H(3,ℤ/4)D4711yescharacteristic, complemented
402C2×C47—21no—
403C2×C47—21no—
404C2×C47—21no—
405C2×C47—21no—
406C2×C47—21no—
407C2×C47—21no—
408C2×C47#191112yescomplemented
409C2×C47C2×#38611yescharacteristic
410D47—48no—
411D47—82no—
412C22×#41—471no—
413C23×D4—471no—
414C22×M16—471no—
415C22×M16C2×D4711yescharacteristic
416#535—474no—
417#535—474no—
418#535—942no—
419#535—942no—
420C2×#127—472no—
421C2×#124—472no—
422C2×#121—942no—
423C2×#120—942no—
424#518—474no—
425#518—942no—
426#518—942no—
427#518—942no—
428C2×C4×D4—942no—
429C2×C4×D4—942no—
430C2×#117—471no—
431C2×#117C2×D4711yescharacteristic
432C2×#117C2×D4711yescharacteristic
433C22×C22⋊C4—942no—
434#421—474no—
435#421—474no—
436#421—942no—
437#421—942no—
438C2×#104—942no—
439C2×#104—942no—
440C2×#100—474no—
441C2×#100—942no—
442C2×#100—942no—
443H(3,ℤ/4)—474no—
444H(3,ℤ/4)C2×D4714yescomplemented
445C47C2×#191111yescharacteristic, complemented, Sylow
446C25—472no—
447C2×#41—472no—
448C2×#41—472no—
449C2×#41—941no—
450C2×#41—941no—
451C2×#41—941no—
452C2×#41—941no—
453C2×#41—941no—
454C2×#41—941no—
455C2×#41—941no—
456C2×#41—941no—
457C2×#41—941no—
458C2×#41—941no—
459C22×Q8—471no—
460C22×D4—472no—
461C22×D4—472no—
462C22×D4—471no—
463C22×D4—472no—
464C22×D4—472no—
465C22×D4—472no—
466C22×D4—472no—
467C22×D4—944no—
468C22×D4—941no—
469C22×D4—941no—
470C22×D4—941no—
471C22×D4—941no—
472C22×D4—941no—
473C22×D4—941no—
474C22×D4—941no—
475C22×D4—941no—
476C22×D4—941no—
477C23×C4—944no—
478C23×C4—941no—
479C23×C4C22×D4711yescharacteristic
480C2×M16—21no—
481C2×M16—21no—
482C2×M16—21no—
483C2×M16—21no—
484C2×M16—21no—
485C2×M16—472no—
486C2×M16—941no—
487C2×M16—941no—
488C2×M16—941no—
489C2×M16—941no—
490C2×M16—941no—
491C2×M16C22×D4712yes—
492C22×C8—21no—
493C22×C8—941no—
494#127—478no—
495#127—944no—
496#124—478no—
497#124—944no—
498#121—948no—
499#121—948no—
500#120—948no—
501#120—948no—
502C4×D4—948no—
503C4×D4—948no—
504C4×D4—948no—
505C4×D4—948no—
506#117—21no—
507#117—21no—
508#117—21no—
509#117—21no—
510#117—472no—
511#117—472no—
512#117—941no—
513#117—941no—
514#117C4×D4712yescomplemented
515#117D18812yescomplemented
516#117C22×D4712yes—
517#117C22×D4712yes—
518C2×C4⋊C4—21no—
519C2×C4⋊C4—21no—
520C2×C4⋊C4—941no—
521C2×C22⋊C4—21no—
522C2×C22⋊C4—21no—
523C2×C22⋊C4—948no—
524C2×C22⋊C4—948no—
525C2×C22⋊C4—944no—
526C2×C22⋊C4—944no—
527C2×C22⋊C4—941no—
528C2×C42—472no—
529C2×C42C4×D4712yescomplemented
530C2×C42D18812yescomplemented
531#104—948no—
532#104—948no—
533#100—948no—
534C24—474no—
535C24—474no—
536C24—474no—
537C24—942no—
538C24—942no—
539C24—942no—
540C24—942no—
541C24—941no—
542C24—3764no—
543C24D4×D4711yescharacteristic
544#41—942no—
545#41—942no—
546#41—942no—
547#41—942no—
548#41—942no—
549#41—942no—
550#41—942no—
551#41—942no—
552#41—1881no—
553#41—1881no—
554#41—1881no—
555#41—1881no—
556#41—1881no—
557#41—1881no—
558#41—1881no—
559#41—1881no—
560C2×Q8—472no—
561C2×Q8—941no—
562C2×Q8—941no—
563C2×Q8—941no—
564C2×Q8—941no—
565C2×Q8—941no—
566C2×D4—474no—
567C2×D4—474no—
568C2×D4—474no—
569C2×D4—472no—
570C2×D4—474no—
571C2×D4—9416no—
572C2×D4—942no—
573C2×D4—942no—
574C2×D4—941no—
575C2×D4—942no—
576C2×D4—942no—
577C2×D4—942no—
578C2×D4—942no—
579C2×D4—941no—
580C2×D4—941no—
581C2×D4—942no—
582C2×D4—942no—
583C2×D4—942no—
584C2×D4—942no—
585C2×D4—941no—
586C2×D4—941no—
587C2×D4—942no—
588C2×D4—942no—
589C2×D4—942no—
590C2×D4—942no—
591C2×D4—942no—
592C2×D4—942no—
593C2×D4—942no—
594C2×D4—942no—
595C2×D4—942no—
596C2×D4—942no—
597C2×D4—942no—
598C2×D4—942no—
599C2×D4—942no—
600C2×D4—942no—
601C2×D4—942no—
602C2×D4—942no—
603C2×D4—3768no—
604C2×D4—1881no—
605C2×D4—1881no—
606C2×D4—1881no—
607C2×D4—1881no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—9416no—
611C22×C4—941no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—3768no—
616C22×C4—1881no—
617C22×C4—1881no—
618C22×C4—1881no—
619C22×C4—1881no—
620C22×C4C2×C4×D4711yescharacteristic
621C22×C4C2×C4×D4711yescharacteristic
622C22×C4C2×D18811yescharacteristic
623C22×C4C2×D18811yescharacteristic
624C22×C4#1062535011yescharacteristic
625C22×C4#1062535011yescharacteristic
626C22×C4D4×D4711yescharacteristic
627C22×C4D4×D4711yescharacteristic
628C22×C4D4×D4711yescharacteristic
629C22×C4D4×D4711yescharacteristic
630C22×C4D4×D4711yescharacteristic
631C22×C4#1062535411yescharacteristic
632C22×C4#1062535411yescharacteristic
633C22×C4C23×D4711yescharacteristic
634M16—22no—
635M16—22no—
636M16—41no—
637M16—41no—
638M16—942no—
639M16—942no—
640M16—1881no—
641M16—1881no—
642C2×C8—22no—
643C2×C8—41no—
644C2×C8—41no—
645C2×C8—942no—
646C2×C8—1881no—
647C2×C8—1881no—
648C4⋊C4—22no—
649C4⋊C4—22no—
650C4⋊C4—22no—
651C4⋊C4—22no—
652C4⋊C4—942no—
653C4⋊C4—942no—
654C22⋊C4—22no—
655C22⋊C4—22no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—9416no—
659C22⋊C4—9416no—
660C22⋊C4—942no—
661C22⋊C4—942no—
662C42—22no—
663C42—22no—
664C42—474no—
665C42—942no—
666C42C2×C4×D4714yescomplemented
667C42C2×D18814yescomplemented
668C23—42no—
669C23—478no—
670C23—944no—
671C23—944no—
672C23—944no—
673C23—944no—
674C23—944no—
675C23—944no—
676C23—942no—
677C23—3764no—
678C23—3764no—
679C23—3764no—
680C23—3764no—
681C23—3764no—
682C23—1884no—
683C23—1888no—
684C23—1888no—
685C23—1881no—
686C23—1881no—
687C23C22⋊C4×D4711yescharacteristic
688C23C22⋊C4×D4711yescharacteristic
689C23#1309399411yescharacteristic
690C23#1309399411yescharacteristic
691C23#1309400911yescharacteristic
692C23#1309400911yescharacteristic
693C23C2×D4×D4711yescharacteristic
694Q8—942no—
695Q8—942no—
696Q8—1881no—
697Q8—1881no—
698D4—944no—
699D4—944no—
700D4—944no—
701D4—944no—
702D4—944no—
703D4—942no—
704D4—944no—
705D4—942no—
706D4—944no—
707D4—944no—
708D4—37616no—
709D4—1882no—
710D4—1882no—
711D4—1882no—
712D4—1882no—
713D4—1881no—
714D4—1881no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—44no—
718C2×C4—44no—
719C2×C4—942no—
720C2×C4—944no—
721C2×C4—37616no—
722C2×C4—1884no—
723C2×C4—1881no—
724C2×C4—1881no—
725C2×C4—1882no—
726C2×C4—1882no—
727C2×C4—1882no—
728C2×C4—1882no—
729C2×C4C22⋊C4×D4711yescharacteristic
730C2×C4C22⋊C4×D4711yescharacteristic
731C2×C4#1309398611yescharacteristic
732C2×C4#1309398611yescharacteristic
733C2×C4#1309398611yescharacteristic
734C2×C4#1309398611yescharacteristic
735C2×C4C4×D18811yescharacteristic
736C2×C4C4×D18811yescharacteristic
737C2×C4C4×D18811yescharacteristic
738C2×C4C4×D18811yescharacteristic
739C2×C4#1309399411yescharacteristic
740C2×C4#1309399411yescharacteristic
741C2×C4#1309399711yescharacteristic
742C2×C4#1309399711yescharacteristic
743C2×C4#1309399711yescharacteristic
744C2×C4#1309399711yescharacteristic
745C2×C4#1309399911yescharacteristic
746C2×C4#1309399911yescharacteristic
747C2×C4#1309399911yescharacteristic
748C2×C4#1309399911yescharacteristic
749C2×C4#1309400911yescharacteristic
750C2×C4#1309400911yescharacteristic
751C2×C4C22×C4×D4711yescharacteristic
752C2×C4C2×D4×D4711yescharacteristic
753C2×C4C2×D4×D4711yescharacteristic
754C2×C4C22×D18811yescharacteristic
755C2×C4C2×#1062535011yescharacteristic
756C2×C4C2×#1062535411yescharacteristic
757C8—42no—
758C8—1882no—
759C22—22no—
760C22—22no—
761C22—22no—
762C22—41no—
763C22—41no—
764C22—41no—
765C22—41no—
766C22—948no—
767C22—3762no—
768C22—3764no—
769C22—3764no—
770C22—3764no—
771C22—3762no—
772C22—1884no—
773C22—1888no—
774C22—1888no—
775C22—1888no—
776C22—1882no—
777C22—1888no—
778C22#1568900111yescharacteristic
779C22#1568900111yescharacteristic
780C22#1568900111yescharacteristic
781C22#1568900111yescharacteristic
782C22C2×C22⋊C4×D4711yescharacteristic
783C22C2×#1309399411yescharacteristic
784C22C2×#1309400911yescharacteristic
785C4—44no—
786C4—44no—
787C4—1884no—
788C4—1882no—
789C4#1568900111yescharacteristic
790C4#1568900111yescharacteristic
791C4#1568900111yescharacteristic
792C4#1568900111yescharacteristic
793C4C2×#1309398611yescharacteristic
794C4C2×C4×D18811yescharacteristic
795C4C2×#1309399711yescharacteristic
796C4C2×#1309399911yescharacteristic
797C2—21no—
798C2—21no—
799C2—21no—
800C2—21no—
801C2—21no—
802C2—21no—
803C2—3762no—
804C2—1888no—
805C2#2024391912yesdirect product factor
806C2C2×#1568900111yescharacteristic
subgroupG/H
centerC22#15689001
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×H(3,ℤ/4)C2
socleC22×C47#386
prime radicalC2×#15689692C2
cosocleC22×C4×C47C24
hypercenterC2×H(3,ℤ/4)D47
hypocenterC47C2×#1911
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. C2×#15689597C2semidirect
3. C2×#15689141C2semidirect
4. C2×#15689139C2semidirect
5. C22×#13093940C2semidirect
6. #20243919C2direct (N × H)
7. C2×#15688879C2semidirect
8. C2×C47×H(3,ℤ/4)C2semidirect
14. #15689692C4semidirect
16. C2×#13094021C4semidirect
17. C2×#13094012C4semidirect
23. #15689597C22semidirect
29. #15689141C22semidirect
31. #15689139C22semidirect
36. C2×#13093940C22semidirect
37. #15688879C22semidirect
41. C47×H(3,ℤ/4)C22semidirect
53. C2×#10625350C2×C4semidirect
55. C22×Dic94C2×C4semidirect
67. C22×D188C2×C4semidirect
83. #13094021C2×C4semidirect
85. #13094012C2×C4semidirect
96. #13093983D4semidirect
104. C2×C4×Dic47D4semidirect
120. #117×C47C2×C4semidirect
121. #117×C47D4semidirect
128. C2×C42×C47C2×C4semidirect
129. C2×C42×C47D4semidirect
214. C2×D188C22×C4semidirect
229. C2×Dic94C22×C4semidirect
247. C42×C47C22×C4semidirect
248. C42×C47C2×D4semidirect
256. C4×Dic47C2×D4semidirect
401. C2×H(3,ℤ/4)D47semidirect
408. C2×C47#1911semidirect
444. H(3,ℤ/4)C2×D47semidirect
445. C47C2×#1911semidirect
514. #117C4×D47semidirect
515. #117D188semidirect
529. C2×C42C4×D47semidirect
530. C2×C42D188semidirect
666. C42C2×C4×D47semidirect
667. C42C2×D188semidirect
805. C2#20243919direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156896922
C2×#156895972
C2×#156891412
C2×#156891392
C22×#130939402
#202439192
C2×#156888792
C2×C47×H(3,ℤ/4)2
C2×#191147