Finite Group Databasebeta

← C2×#20256085 #27095903

Subgroups — C2×#20256085 #27095903

Order 12032.

1894 conjugacy classes of subgroups.

The subgroup lattice has 724 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689856C211yesmaximal, characteristic
2C2×#15689849C211yesmaximal, characteristic, complemented
3#20256085C2116yesmaximal, direct product factor
4C2×#15689478C211yesmaximal, characteristic, complemented
5C2×#15689476C211yesmaximal, characteristic, complemented
6C2×#15689468C211yesmaximal, characteristic
7C2×#15689407C211yesmaximal, characteristic, complemented
8C2×#15689423C211yesmaximal, characteristic, complemented
9C2×#15689422C211yesmaximal, characteristic, complemented
10C2×#15689345C211yesmaximal, characteristic, complemented
11C2×#15689343C211yesmaximal, characteristic, complemented
12C2×#15689321C211yesmaximal, characteristic
13C2×C8×Dic94C211yesmaximal, characteristic, complemented
14C2×#15689215C211yesmaximal, characteristic, complemented
15C2×#15689208C211yesmaximal, characteristic, complemented
16C2×C4×SD16×C47C211yesmaximal, characteristic, complemented
17C22×#10625337C2211yescharacteristic
18C22×#10625336C2211yescharacteristic
19#15689856—24no—
20#15689856C2218yes—
21#15689849—24no—
22#15689849C2218yescomplemented
23C2×#13094023—21no—
24C2×#13094023C2211yescharacteristic
25C2×#13094020C2211yescharacteristic
26C2×#13094016—21no—
27C2×#13094016C2211yescharacteristic
28C2×#13094015—21no—
29C2×#13094015C2211yescharacteristic
30C2×#13094012C2211yescharacteristic
31C2×#13094011C2211yescharacteristic
32C2×#13094010—21no—
33C2×#13094007—21no—
34C2×#13094006—21no—
35C2×Q8×Dic47C2211yescharacteristic
36C2×Q8×Dic47C2211yescharacteristic
37C2×C4×Dic94—21no—
38C2×C4×Dic94C2211yescharacteristic
39C2×#13093989C2211yescharacteristic
40C2×#13093986C2211yescharacteristic
41C2×C4×C22⋊D47—21no—
42#15689478C2218yescomplemented
43#15689476C2218yescomplemented
44#15689468C2218yes—
45#15689423C2218yescomplemented
46#15689422C2218yescomplemented
47#15689407C2218yescomplemented
48#15689345C2218yescomplemented
49#15689343C2218yescomplemented
50#15689321C2218yes—
51C8×Dic94C2218yescomplemented
52#15689215C2218yescomplemented
53#15689208C2218yescomplemented
54C2×#13093957C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×C4⋊(C47⋊C8)C2211yescharacteristic
57C2×Dic47⋊C8C2211yescharacteristic
58C2×Dic47⋊C8C2211yescharacteristic
59C2×#13093949C2211yescharacteristic
60C2×#13093949C2211yescharacteristic
61C2×#13093947C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093945C2211yescharacteristic
66C2×#13093944C2211yescharacteristic
67C2×C8×Dic47C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C2×C4×Q8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C4×SD16×C47C2218yescomplemented
73C2×#106×C47C2211yescharacteristic
74C2×#103×C47C2211yescharacteristic
75C2×#102×C47C2211yescharacteristic
76C2×C4×C8×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94D411yescharacteristic
79C22×Dic94C2311yescharacteristic
80C22×D188C2311yescharacteristic
81C22×C22⋊D47—21no—
82C22×C22⋊D47—21no—
83C22×C4×D47—21no—
84C2×#10625337—24no—
85C2×#10625337C2314yes—
86C2×#10625336—24no—
87C2×#10625336C2314yes—
88C22×C47⋊C8C2311yescharacteristic
89C22×C47⋊C8C2311yescharacteristic
90#13094023—28no—
91#13094023—22no—
92#13094023C2314yes—
93#13094020—22no—
94#13094020C2314yes—
95#13094016—22no—
96#13094016—28no—
97#13094016C2314yes—
98#13094015—28no—
99#13094015—22no—
100#13094015C2314yes—
101#13094012—22no—
102#13094012C2314yes—
103#13094011—22no—
104#13094011C2314yes—
105#13094010—28no—
106#13094007—28no—
107#13094006—28no—
108Q8×Dic47—22no—
109Q8×Dic47—22no—
110Q8×Dic47C2314yes—
111Q8×Dic47C2314yes—
112C4×Dic94—28no—
113C4×Dic94D414yes—
114C4×Dic94C2314yes—
115#13093989—22no—
116#13093989C2314yes—
117#13093986—22no—
118#13093986C2314yes—
119C4×C22⋊D47—28no—
120C2×C4⋊Dic47—21no—
121C2×C4⋊Dic47—21no—
122C2×C4⋊Dic47—21no—
123C2×C4⋊Dic47D411yescharacteristic
124C2×C4⋊Dic47C2311yescharacteristic
125C2×C4⋊Dic47C2311yescharacteristic
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×Dic47⋊C4D411yescharacteristic
132C2×Dic47⋊C4D411yescharacteristic
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×(C2×D47)⋊C4—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47C2311yescharacteristic
142C2×C4×Dic47C2311yescharacteristic
143#13093957C2314yes—
144#13093955C2314yes—
145C4⋊(C47⋊C8)C2314yes—
146Dic47⋊C8C2314yes—
147Dic47⋊C8C2314yes—
148#13093949C2314yes—
149#13093949C2314yes—
150#13093947C2314yes—
151#13093946C2314yes—
152#13093946C2314yes—
153#13093945C2314yes—
154#13093945C2314yes—
155#13093944C2314yes—
156C8×Dic47C2314yes—
157C8×Dic47C2314yes—
158C22×Q8×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C2×SD16×C47—24no—
162C2×SD16×C47C2314yes—
163C22×C8×C47C2311yescharacteristic
164C22×C8×C47C2311yescharacteristic
165C4×Q8×C47—22no—
166C4×Q8×C47C2314yes—
167C4×D4×C47—22no—
168C4×D4×C47C2314yes—
169C2×C4⋊C4×C47—21no—
170C2×C4⋊C4×C47C2311yescharacteristic
171C2×C4⋊C4×C47C2311yescharacteristic
172C2×C22⋊C4×C47—21no—
173C2×C42×C47—21no—
174C2×C42×C47C2311yescharacteristic
175#106×C47C2314yes—
176#103×C47C2314yes—
177#102×C47C2314yes—
178C4×C8×C47C2314yes—
179C24×C47—21no—
180C23×D47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—22no—
183C2×Q8×C47#4114yes—
184C2×Q8×C47C2412yes—
185C2×D4×C47—21no—
186C2×D4×C47—22no—
187C2×D4×C47—22no—
188C2×D4×C47C2412yes—
189C22×C4×C47—21no—
190C22×C4×C47—21no—
191C22×C4×C47—21no—
192C22×C4×C47—24no—
193C22×C4×C47—82no—
194C22×C4×C47C2×D411yescharacteristic
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2411yescharacteristic
197C2×C22⋊D47—24no—
198C2×C22⋊D47—24no—
199C2×C22⋊D47—44no—
200C2×C22⋊D47—82no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47C2×D411yescharacteristic
205C22×Dic47C2×D411yescharacteristic
206C22×Dic47C2×D411yescharacteristic
207C22×Dic47C2×D411yescharacteristic
208C2×D188—22no—
209C2×D188—22no—
210C2×D188—21no—
211C2×D188C2412yes—
212C2×C4×D47—24no—
213C2×C4×D47—82no—
214C2×Dic94—24no—
215C2×Dic94—22no—
216C2×Dic94—22no—
217C2×Dic94—21no—
218C2×Dic94—24no—
219C2×Dic94—44no—
220C2×Dic94C2×D414yes—
221C2×Dic94C2412yes—
222SD16×C47—28no—
223C2×C8×C47—22no—
224C2×C8×C47—22no—
225C2×C8×C47C2412yes—
226C2×C8×C47C2412yes—
227C4⋊C4×C47—24no—
228C4⋊C4×C47—21no—
229C4⋊C4×C47—21no—
230C4⋊C4×C47C2412yes—
231C4⋊C4×C47C2412yes—
232C22⋊C4×C47—24no—
233C42×C47—24no—
234C42×C47C2×D412yes—
235C42×C47C2412yes—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238#10625337—28no—
239#10625336—28no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—24no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47C2×D414yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4C2×D414yes—
257Dic47⋊C4C2×D414yes—
258C4×Dic47—24no—
259C4×Dic47—24no—
260C4×Dic47—24no—
261C4×Dic47C2×D412yes—
262C4×Dic47C2×D412yes—
263C4×Dic47C2412yes—
264C4×Dic47C2412yes—
265C2×C47⋊C8—22no—
266C2×C47⋊C8—22no—
267C2×C47⋊C8C2412yes—
268C2×C47⋊C8C2412yes—
269C23×C47—22no—
270C23×C47—42no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47C22×D411yescharacteristic
274C22×D47—22no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278Q8×C47—24no—
279Q8×C47—22no—
280Q8×C47C2×#4114yes—
281D4×C47—22no—
282D4×C47—22no—
283D4×C47—42no—
284C2×C4×C47—24no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—84no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D412yes—
295C2×C4×C47C22×D411yescharacteristic
296C2×C4×C47C2×#4112yes—
297C2×C4×C472−1+412yes—
298C2×C4×C47C2511yescharacteristic
299C22⋊D47—48no—
300C22⋊D47—84no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47#13514yes—
311C2×Dic47C22×D412yes—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314C2×Dic47C22×D412yes—
315D188—22no—
316D188—22no—
317D188—42no—
318C4×D47—84no—
319Dic94—28no—
320Dic94—22no—
321Dic94—22no—
322Dic94—42no—
323Dic94—48no—
324C8×C47—22no—
325C8×C47—22no—
326C47⋊C8—22no—
327C47⋊C8—22no—
328C2×#3365—471nomaximal, Sylow
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—42no—
332C22×C47—84no—
333C22×C47#54812yes—
334C22×C47C2×#13512yes—
335C22×C47#57712yes—
336C22×C47C23×D411yescharacteristic
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—84no—
341C4×C47—24no—
342C4×C47—22no—
343C4×C47—22no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47#54812yes—
347C4×C47C22×#4111yescharacteristic
348C4×C47C2×2−1+411yescharacteristic
349Dic47—22no—
350Dic47—22no—
351Dic47—22no—
352Dic47—42no—
353Dic47—42no—
354Dic47—42no—
355Dic47C2×#13514yes—
356C2×#559—471no—
357C2×#557—471no—
358#3365—4716no—
359C2×#488—471no—
360C2×#488—471no—
361C2×#486—471no—
362C2×#475—471no—
363C2×#478—471no—
364C2×#478—471no—
365C2×#464—471no—
366C2×#464—471no—
367C2×#460—471no—
368C2×C8×Q8—471no—
369C2×C4×Q16—471no—
370C2×C4×SD16—471no—
371C2×C4×SD16D4711yescharacteristic, complemented
372C2×C47—82no—
373C2×C47#336514yescomplemented
374C2×C47C2×#54811yescharacteristic
375C2×C47C22×#13511yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—82no—
378C22×Q16—471no—
379C22×SD16—471no—
380C22×SD16C2×D4711yescharacteristic
381#559—478no—
382#559—944no—
383#557—478no—
384#557—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8—941no—
387C2×#127—471no—
388C2×#125—471no—
389C2×#125—471no—
390C2×#125—941no—
391C2×#125—941no—
392C2×#124—471no—
393C2×#124—471no—
394C2×#124—941no—
395C2×#123—941no—
396C2×#123—941no—
397C2×C4×Q8—471no—
398C2×C4×Q8—471no—
399C2×C4×Q8—471no—
400C2×C4×Q8—471no—
401C2×C4×Q8—941no—
402C2×C4×Q8C2×D4711yescharacteristic
403C2×C4×D4—471no—
404C2×C4×D4—941no—
405C2×C4×D4C2×D4711yescharacteristic
406#488—478no—
407#488—478no—
408#486—478no—
409#478—478no—
410#478—478no—
411#475—478no—
412#464—478no—
413#464—478no—
414#460—478no—
415C8×Q8—478no—
416C4×Q16—478no—
417C4×SD16—478no—
418C4×SD16C2×D4718yescomplemented
419C2×#107—471no—
420C2×#106—471no—
421C2×#106C2×D4711yescharacteristic
422C2×C4⋊C8—471no—
423C2×C4⋊C8—471no—
424C2×C4⋊C8—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103C2×D4711yescharacteristic
429C2×#102—471no—
430C2×#102—471no—
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102C2×D4711yescharacteristic
435C2×C4×C8—471no—
436C2×C4×C8—471no—
437C2×C4×C8C2×D4711yescharacteristic
438C47C2×#336511yescharacteristic, complemented, Sylow
439C22×Q8—471no—
440C22×Q8—471no—
441C22×Q8—941no—
442C22×Q8C22×D4711yescharacteristic
443C22×D4—471no—
444C22×D4—941no—
445C22×D4—941no—
446C22×D4C22×D4711yescharacteristic
447C23×C4—21no—
448C23×C4—941no—
449C2×Q16—474no—
450C2×Q16—944no—
451C2×SD16—24no—
452C2×SD16—474no—
453C2×SD16—944no—
454C2×SD16C22×D4714yes—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8C22×D4711yescharacteristic
458C22×C8C22×D4711yescharacteristic
459C4⋊Q8—474no—
460C4⋊Q8—942no—
461C4⋊Q8—948no—
462#127—474no—
463#127—942no—
464#125—474no—
465#125—474no—
466#125—948no—
467#125—942no—
468#125—948no—
469#125—942no—
470#124—474no—
471#124—474no—
472#124—942no—
473#124—948no—
474#124—942no—
475#123—948no—
476#123—948no—
477C4×Q8—22no—
478C4×Q8—474no—
479C4×Q8—474no—
480C4×Q8—474no—
481C4×Q8—474no—
482C4×Q8—474no—
483C4×Q8—948no—
484C4×Q8—942no—
485C4×Q8—942no—
486C4×Q8—942no—
487C4×Q8C22×D4714yes—
488C4×D4—22no—
489C4×D4—474no—
490C4×D4—942no—
491C4×D4—948no—
492C4×D4C22×D4714yes—
493C2×C4⋊C4—21no—
494C2×C4⋊C4—471no—
495C2×C4⋊C4—471no—
496C2×C4⋊C4—471no—
497C2×C4⋊C4—471no—
498C2×C4⋊C4—471no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4—941no—
501C2×C4⋊C4—941no—
502C2×C4⋊C4—941no—
503C2×C4⋊C4—941no—
504C2×C4⋊C4—941no—
505C2×C4⋊C4—941no—
506C2×C4⋊C4—941no—
507C2×C4⋊C4C22×D4711yescharacteristic
508C2×C4⋊C4C22×D4711yescharacteristic
509C2×C22⋊C4—21no—
510C2×C22⋊C4—941no—
511C2×C22⋊C4—941no—
512C2×C22⋊C4—941no—
513C2×C22⋊C4—941no—
514C2×C22⋊C4—941no—
515C2×C42—21no—
516C2×C42—471no—
517C2×C42—471no—
518C2×C42—941no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42C22×D4711yescharacteristic
522#107—474no—
523#106—474no—
524#106C22×D4714yes—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8—474no—
528#103—474no—
529#103—474no—
530#103—474no—
531#103C22×D4714yes—
532#102—474no—
533#102—474no—
534#102—474no—
535#102—474no—
536#102—474no—
537#102C22×D4714yes—
538C4×C8—474no—
539C4×C8—474no—
540C4×C8C22×D4714yes—
541C24—21no—
542C24—941no—
543C2×Q8—21no—
544C2×Q8—22no—
545C2×Q8—474no—
546C2×Q8—472no—
547C2×Q8—944no—
548C2×Q8—944no—
549C2×Q8—941no—
550C2×Q8—942no—
551C2×Q8—942no—
552C2×Q8—1884no—
553C2×Q8#1062535014yes—
554C2×Q8C23×D4712yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—472no—
559C2×D4—944no—
560C2×D4—944no—
561C2×D4—941no—
562C2×D4—942no—
563C2×D4—942no—
564C2×D4—3762no—
565C2×D4—1884no—
566C2×D4C23×D4712yes—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—24no—
571C22×C4—82no—
572C22×C4—471no—
573C22×C4—471no—
574C22×C4—471no—
575C22×C4—471no—
576C22×C4—944no—
577C22×C4—941no—
578C22×C4—941no—
579C22×C4—941no—
580C22×C4—3762no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584Q16—948no—
585SD16—28no—
586SD16—948no—
587C2×C8—22no—
588C2×C8—22no—
589C2×C8—472no—
590C2×C8—472no—
591C2×C8—942no—
592C2×C8—942no—
593C2×C8C23×D4712yes—
594C2×C8C23×D4712yes—
595C4⋊C4—24no—
596C4⋊C4—21no—
597C4⋊C4—21no—
598C4⋊C4—474no—
599C4⋊C4—474no—
600C4⋊C4—474no—
601C4⋊C4—472no—
602C4⋊C4—472no—
603C4⋊C4—944no—
604C4⋊C4—944no—
605C4⋊C4—944no—
606C4⋊C4—944no—
607C4⋊C4—944no—
608C4⋊C4—944no—
609C4⋊C4—944no—
610C4⋊C4—944no—
611C4⋊C4—941no—
612C4⋊C4—941no—
613C4⋊C4C23×D4712yes—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C42—24no—
622C42—472no—
623C42—472no—
624C42—472no—
625C42—472no—
626C42—944no—
627C42—944no—
628C42—944no—
629C42D4×D4712yes—
630C42C23×D4712yes—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—942no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C2×D4×D4711yescharacteristic
640Q8—24no—
641Q8—22no—
642Q8—948no—
643Q8—942no—
644Q8—942no—
645Q8—1888no—
646Q8—1882no—
647Q8C2×#1062535014yes—
648D4—22no—
649D4—22no—
650D4—42no—
651D4—942no—
652D4—942no—
653D4—3764no—
654D4—1888no—
655D4—1882no—
656C2×C4—24no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—84no—
665C2×C4—474no—
666C2×C4—472no—
667C2×C4—472no—
668C2×C4—472no—
669C2×C4—472no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—942no—
675C2×C4—942no—
676C2×C4—3764no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4C2×D4×D4712yes—
681C2×C4C2×D4×D4712yes—
682C2×C4C2×D4×D4711yescharacteristic
683C2×C4C2×#1062535012yes—
684C2×C4#1309407112yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—942no—
689C8—942no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—84no—
694C22—3764no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22#1568978212yes—
699C22#135×D4712yes—
700C22#1568992912yes—
701C22C22×D4×D4711yescharacteristic
702C4—22no—
703C4—24no—
704C4—22no—
705C4—42no—
706C4—42no—
707C4—474no—
708C4—942no—
709C4—942no—
710C4—942no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4#1568978212yes—
715C4C22×#1062535011yescharacteristic
716C4C2×#1309407111yescharacteristic
717C2—82no—
718C2—3762no—
719C2#2025608514yesdirect product factor
720C2C2×#1568978211yescharacteristic
721C2C2×#135×D4711yescharacteristic
722C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C4×SD16×C47C2
socleC23×C47C22×D4
prime radicalC2×#13094020C22
hypercenterC2×C4×SD16D47
hypocenterC47C2×#3365
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×C4×SD16

Complements

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

NH ≅ G/Ntype
2. C2×#15689849C2semidirect
3. #20256085C2direct (N × H)
4. C2×#15689478C2semidirect
5. C2×#15689476C2semidirect
7. C2×#15689407C2semidirect
8. C2×#15689423C2semidirect
9. C2×#15689422C2semidirect
10. C2×#15689345C2semidirect
11. C2×#15689343C2semidirect
13. C2×C8×Dic94C2semidirect
14. C2×#15689215C2semidirect
15. C2×#15689208C2semidirect
16. C2×C4×SD16×C47C2semidirect
22. #15689849C22semidirect
42. #15689478C22semidirect
43. #15689476C22semidirect
45. #15689423C22semidirect
46. #15689422C22semidirect
47. #15689407C22semidirect
48. #15689345C22semidirect
49. #15689343C22semidirect
51. C8×Dic94C22semidirect
52. #15689215C22semidirect
53. #15689208C22semidirect
72. C4×SD16×C47C22semidirect
371. C2×C4×SD16D47semidirect
373. C2×C47#3365semidirect
418. C4×SD16C2×D47semidirect
438. C47C2×#3365semidirect
719. C2#20256085direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898562
C2×#156898492
#202560852
C2×#156894782
C2×#156894762
C2×#156894682
C2×#156894072
C2×#156894232
C2×#156894222
C2×#156893452
C2×#156893432
C2×#156893212
C2×C8×Dic942
C2×#156892152
C2×#156892082
C2×C4×SD16×C472
C2×#336547