Finite Group Databasebeta

← C2×#20256208 #27096036

Subgroups — C2×#20256208 #27096036

Order 12032.

1886 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×#15689847C211yesmaximal, characteristic, complemented
2C2×#15689832C211yesmaximal, characteristic, complemented
3#20256208C2116yesmaximal, direct product factor
4C2×#15689491C211yesmaximal, characteristic, complemented
5C2×#15689484C211yesmaximal, characteristic, complemented
6C2×#15689479C211yesmaximal, characteristic, complemented
7C2×#15689432C211yesmaximal, characteristic, complemented
8C2×#15689406C211yesmaximal, characteristic, complemented
9C2×#15689424C211yesmaximal, characteristic, complemented
10C2×#15689340C211yesmaximal, characteristic
11C2×#15689340C211yesmaximal, characteristic
12C2×#15689252C211yesmaximal, characteristic, complemented
13C2×#15689233C211yesmaximal, characteristic
14C2×#15689224C211yesmaximal, characteristic, complemented
15C2×SD16×Dic47C211yesmaximal, characteristic, complemented
16C2×C47×#461C211yesmaximal, characteristic, complemented
17C22×#10625334C2211yescharacteristic
18#15689847—24no—
19#15689847C2218yescomplemented
20#15689832—24no—
21#15689832C2218yescomplemented
22C2×#13094023C2211yescharacteristic
23C2×#13094019—21no—
24C2×#13094019—21no—
25C2×#13094016C2211yescharacteristic
26C2×#13094015C2211yescharacteristic
27C2×#13094013C2211yescharacteristic
28C2×#13094013C2211yescharacteristic
29C2×#13094004—21no—
30C2×#13094003—21no—
31C2×#13094001—21no—
32C2×#13094001—21no—
33C2×Q8×Dic47C2211yescharacteristic
34C2×Q8×Dic47C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×C4×D188C2211yescharacteristic
37C2×D4×Dic47C2211yescharacteristic
38C2×D4×Dic47C2211yescharacteristic
39C2×#13093982—21no—
40C22×Dic47⋊C4—21no—
41#15689491C2218yescomplemented
42#15689484C2218yescomplemented
43#15689479C2218yescomplemented
44#15689432C2218yescomplemented
45#15689424C2218yescomplemented
46#15689406C2218yescomplemented
47#15689340C2218yes—
48#15689340C2218yes—
49#15689252C2218yescomplemented
50#15689233C2218yes—
51#15689224C2218yescomplemented
52SD16×Dic47C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093956C2211yescharacteristic
55C2×#13093955C2211yescharacteristic
56C2×Dic47⋊C8C2211yescharacteristic
57C2×Dic47⋊C8C2211yescharacteristic
58C2×#13093948C2211yescharacteristic
59C2×#13093948C2211yescharacteristic
60C2×#13093948C2211yescharacteristic
61C2×#13093948C2211yescharacteristic
62C2×#13093946C2211yescharacteristic
63C2×#13093946C2211yescharacteristic
64C2×#13093945C2211yescharacteristic
65C2×#13093944C2211yescharacteristic
66C2×#13093935C2211yescharacteristic
67C2×#13093934C2211yescharacteristic
68C2×C8×Dic47C2211yescharacteristic
69C22×SD16×C47C2211yescharacteristic
70C22×SD16×C47C2211yescharacteristic
71C2×C4⋊Q8×C47C2211yescharacteristic
72C2×C4×D4×C47C2211yescharacteristic
73C47×#461C2218yescomplemented
74C2×C4⋊C8×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94D411yescharacteristic
79C22×D188C2311yescharacteristic
80C23×Dic47—21no—
81C23×Dic47—21no—
82C22×C4×D47—21no—
83C2×#10625334—24no—
84C2×#10625334C2314yes—
85C22×C47⋊C8C2311yescharacteristic
86C22×C47⋊C8C2311yescharacteristic
87#13094023—22no—
88#13094023C2314yes—
89#13094019—28no—
90#13094019—28no—
91#13094016—22no—
92#13094016C2314yes—
93#13094015—22no—
94#13094015C2314yes—
95#13094013—22no—
96#13094013—22no—
97#13094013C2314yes—
98#13094013C2314yes—
99#13094004—28no—
100#13094003—28no—
101#13094001—28no—
102#13094001—28no—
103Q8×Dic47—22no—
104Q8×Dic47—22no—
105Q8×Dic47C2314yes—
106Q8×Dic47C2314yes—
107C4×Dic94D414yes—
108C4×Dic94C2314yes—
109C4×D188—22no—
110C4×D188C2314yes—
111D4×Dic47—22no—
112D4×Dic47—22no—
113D4×Dic47C2314yes—
114D4×Dic47C2314yes—
115#13093982—28no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47—21no—
119C2×C4⋊Dic47D411yescharacteristic
120C2×C4⋊Dic47C2311yescharacteristic
121C2×C4⋊Dic47C2311yescharacteristic
122C2×C4⋊Dic47C2311yescharacteristic
123C2×Dic47⋊C4—21no—
124C2×Dic47⋊C4—21no—
125C2×Dic47⋊C4—21no—
126C2×Dic47⋊C4—21no—
127C2×Dic47⋊C4—28no—
128C2×Dic47⋊C4D411yescharacteristic
129C2×Dic47⋊C4D411yescharacteristic
130C2×C22⋊Dic47—21no—
131C2×C22⋊Dic47—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4—21no—
135C2×(C2×D47)⋊C4—21no—
136C2×(C2×D47)⋊C4—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47C2311yescharacteristic
140C2×C4×Dic47C2311yescharacteristic
141#13093958C2314yes—
142#13093956C2314yes—
143#13093955C2314yes—
144Dic47⋊C8C2314yes—
145Dic47⋊C8C2314yes—
146#13093948C2314yes—
147#13093948C2314yes—
148#13093948C2314yes—
149#13093948C2314yes—
150#13093946C2314yes—
151#13093946C2314yes—
152#13093945C2314yes—
153#13093944C2314yes—
154#13093935C2314yes—
155#13093934C2314yes—
156C8×Dic47C2314yes—
157C22×Q8×C47C2311yescharacteristic
158C22×Q8×C47C2311yescharacteristic
159C22×D4×C47C2311yescharacteristic
160C23×C4×C47—21no—
161C2×SD16×C47—24no—
162C2×SD16×C47—24no—
163C2×SD16×C47C2314yes—
164C2×SD16×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C4⋊Q8×C47—22no—
168C4⋊Q8×C47C2314yes—
169C4×D4×C47—22no—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47—21no—
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C42×C47C2311yescharacteristic
176C4⋊C8×C47C2314yes—
177#103×C47C2314yes—
178#103×C47C2314yes—
179C24×C47—21no—
180C23×D47—21no—
181C2×Q8×C47—21no—
182C2×Q8×C47—21no—
183C2×Q8×C47—22no—
184C2×Q8×C47—22no—
185C2×Q8×C47—22no—
186C2×Q8×C47—22no—
187C2×Q8×C47C2412yes—
188C2×Q8×C47C2412yes—
189C2×D4×C47—21no—
190C2×D4×C47—22no—
191C2×D4×C47#4114yes—
192C2×D4×C47C2412yes—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47—21no—
196C22×C4×C47—24no—
197C22×C4×C47—82no—
198C22×C4×C47C2×D411yescharacteristic
199C22×C4×C47C2×D411yescharacteristic
200C22×C4×C47C2411yescharacteristic
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—24no—
206C22×Dic47—44no—
207C22×Dic47—82no—
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C22×Dic47C2×D411yescharacteristic
211C22×Dic47C2×D411yescharacteristic
212C2×D188—22no—
213C2×D188—22no—
214C2×D188—21no—
215C2×D188C2412yes—
216C2×C4×D47—24no—
217C2×C4×D47—44no—
218C2×Dic94—24no—
219C2×Dic94—42no—
220C2×Dic94—82no—
221C2×Dic94C2×D414yes—
222SD16×C47—28no—
223SD16×C47—28no—
224C2×C8×C47—22no—
225C2×C8×C47—22no—
226C2×C8×C47C2412yes—
227C2×C8×C47C2412yes—
228C4⋊C4×C47—24no—
229C4⋊C4×C47—24no—
230C4⋊C4×C47—21no—
231C4⋊C4×C47C2412yes—
232C22⋊C4×C47—24no—
233C42×C47C2×D412yes—
234C42×C47C2412yes—
235C22⋊Dic47—24no—
236C22⋊Dic47—24no—
237#10625334—28no—
238(C2×D47)⋊C4—24no—
239(C2×D47)⋊C4—24no—
240(C2×D47)⋊C4—24no—
241(C2×D47)⋊C4—24no—
242(C2×D47)⋊C4—24no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47—24no—
247C4⋊Dic47—24no—
248C4⋊Dic47—24no—
249C4⋊Dic47C2×D414yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252C4⋊Dic47C2412yes—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4C2×D414yes—
258Dic47⋊C4C2×D414yes—
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—24no—
270C23×C47—22no—
271C23×C47—42no—
272C23×C47—42no—
273C23×C47C22×D411yescharacteristic
274C22×D47—22no—
275C22×D47—42no—
276C22×D47—42no—
277C22×D47—42no—
278Q8×C47—22no—
279Q8×C47—22no—
280Q8×C47—22no—
281Q8×C47—22no—
282Q8×C47—42no—
283Q8×C47—42no—
284D4×C47—24no—
285D4×C47—22no—
286D4×C47C2×#4114yes—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—22no—
291C2×C4×C47—22no—
292C2×C4×C47—42no—
293C2×C4×C47—42no—
294C2×C4×C47—42no—
295C2×C4×C47—84no—
296C2×C4×C47C22×D412yes—
297C2×C4×C47C22×D412yes—
298C2×C4×C47C22×D411yescharacteristic
299C2×C4×C47C2×#4112yes—
300C2×C4×C472−1+412yes—
301C2×C4×C47C2511yescharacteristic
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—22no—
308C2×Dic47—22no—
309C2×Dic47—48no—
310C2×Dic47—42no—
311C2×Dic47—42no—
312C2×Dic47—42no—
313C2×Dic47—84no—
314C2×Dic47C22×D412yes—
315C2×Dic47C22×D412yes—
316C2×Dic47C22×D412yes—
317C2×Dic47C22×D412yes—
318D188—22no—
319D188—22no—
320D188—42no—
321C4×D47—48no—
322Dic94—44no—
323Dic94—84no—
324C8×C47—22no—
325C8×C47—22no—
326C47⋊C8—22no—
327C47⋊C8—22no—
328C2×#3376—471nomaximal, Sylow
329C22×C47—24no—
330C22×C47—48no—
331C22×C47—42no—
332C22×C47—42no—
333C22×C47#54812yes—
334C22×C47#57512yes—
335C22×C47#57712yes—
336C22×C47C23×D411yescharacteristic
337C2×D47—42no—
338C2×D47—42no—
339C2×D47—42no—
340C2×D47—84no—
341C4×C47—22no—
342C4×C47—22no—
343C4×C47—42no—
344C4×C47—42no—
345C4×C47—42no—
346C4×C47#54812yes—
347C4×C47C22×#4111yescharacteristic
348C4×C47C2×2−1+411yescharacteristic
349Dic47—22no—
350Dic47—22no—
351Dic47—22no—
352Dic47—22no—
353Dic47—42no—
354Dic47—42no—
355Dic47—42no—
356C2×#556—471no—
357C2×#554—471no—
358#3376—4716no—
359C2×#491—471no—
360C2×#489—471no—
361C2×#488—471no—
362C2×#479—471no—
363C2×#475—471no—
364C2×#478—471no—
365C2×#463—471no—
366C2×#463—471no—
367C2×#461D4711yescharacteristic, complemented
368C2×#446—471no—
369C2×#442—471no—
370C2×#440—471no—
371C2×C4×SD16—471no—
372C2×C47—44no—
373C2×C47#337614yescomplemented
374C2×C47C2×#54811yescharacteristic
375C2×C47C2×#57511yescharacteristic
376C2×C47C2×#57711yescharacteristic
377D47—82no—
378C22×SD16C2×D4711yescharacteristic
379C22×SD16C2×D4711yescharacteristic
380C22×D8—471no—
381#556—478no—
382#556—944no—
383#554—478no—
384#554—944no—
385C2×C4⋊Q8—471no—
386C2×C4⋊Q8C2×D4711yescharacteristic
387C2×#126—941no—
388C2×#126—941no—
389C2×#125—471no—
390C2×#125—471no—
391C2×#124—471no—
392C2×#124—471no—
393C2×C22⋊Q8—941no—
394C2×C22⋊Q8—941no—
395C2×C22⋊Q8—941no—
396C2×C22⋊Q8—941no—
397C2×C4×Q8—471no—
398C2×C4×Q8—471no—
399C2×C4×Q8—471no—
400C2×C4×D4—471no—
401C2×C4×D4—471no—
402C2×C4×D4—471no—
403C2×C4×D4C2×D4711yescharacteristic
404C2×#117—941no—
405C22×C4⋊C4—941no—
406#491—478no—
407#489—478no—
408#488—478no—
409#479—478no—
410#478—478no—
411#475—478no—
412#463—478no—
413#463—478no—
414#461C2×D4718yescomplemented
415#446—478no—
416#442—478no—
417#440—478no—
418C4×SD16—478no—
419C2×#107—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8—471no—
423C2×C4⋊C8—471no—
424C2×C4⋊C8C2×D4711yescharacteristic
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×#103C2×D4711yescharacteristic
430C2×#103C2×D4711yescharacteristic
431C2×#102—471no—
432C2×#102—471no—
433C2×#102—471no—
434C2×#102—471no—
435C2×#97—471no—
436C2×#97—471no—
437C2×C4×C8—471no—
438C47C2×#337611yescharacteristic, complemented, Sylow
439C22×Q8—471no—
440C22×Q8—941no—
441C22×Q8C22×D4711yescharacteristic
442C22×Q8C22×D4711yescharacteristic
443C22×D4—471no—
444C22×D4C22×D4711yescharacteristic
445C23×C4—21no—
446C23×C4—941no—
447C23×C4—941no—
448C23×C4—941no—
449C2×SD16—24no—
450C2×SD16—24no—
451C2×SD16C22×D4714yes—
452C2×SD16C22×D4714yes—
453C2×D8—474no—
454C2×D8—944no—
455C22×C8—471no—
456C22×C8—471no—
457C22×C8C22×D4711yescharacteristic
458C22×C8C22×D4711yescharacteristic
459C4⋊Q8—22no—
460C4⋊Q8—474no—
461C4⋊Q8—942no—
462C4⋊Q8C22×D4714yes—
463#126—948no—
464#126—948no—
465#125—474no—
466#125—474no—
467#125—942no—
468#125—942no—
469#124—474no—
470#124—474no—
471#124—942no—
472#124—942no—
473C22⋊Q8—948no—
474C22⋊Q8—948no—
475C22⋊Q8—948no—
476C22⋊Q8—948no—
477C4×Q8—474no—
478C4×Q8—474no—
479C4×Q8—474no—
480C4×Q8—474no—
481C4×Q8—942no—
482C4×Q8—942no—
483C4×D4—22no—
484C4×D4—474no—
485C4×D4—474no—
486C4×D4—474no—
487C4×D4—942no—
488C4×D4—942no—
489C4×D4—942no—
490C4×D4C22×D4714yes—
491#117—948no—
492C2×C4⋊C4—21no—
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—471no—
500C2×C4⋊C4—948no—
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⋊C4—941no—
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×C22⋊C4—941no—
516C2×C22⋊C4—941no—
517C2×C42—471no—
518C2×C42—471no—
519C2×C42—941no—
520C2×C42—941no—
521C2×C42C22×D4711yescharacteristic
522#107—474no—
523#106—474no—
524#106—474no—
525C4⋊C8—474no—
526C4⋊C8—474no—
527C4⋊C8C22×D4714yes—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532#103C22×D4714yes—
533#103C22×D4714yes—
534#102—474no—
535#102—474no—
536#102—474no—
537#102—474no—
538#97—474no—
539#97—474no—
540C4×C8—474no—
541C24—21no—
542C24—941no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—22no—
546C2×Q8—22no—
547C2×Q8—22no—
548C2×Q8—22no—
549C2×Q8—474no—
550C2×Q8—944no—
551C2×Q8—3762no—
552C2×Q8—1882no—
553C2×Q8C23×D4712yes—
554C2×Q8C23×D4712yes—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—472no—
558C2×D4—941no—
559C2×D4—942no—
560C2×D4—942no—
561C2×D4#1062535214yes—
562C2×D4C23×D4712yes—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—24no—
567C22×C4—82no—
568C22×C4—471no—
569C22×C4—471no—
570C22×C4—471no—
571C22×C4—471no—
572C22×C4—944no—
573C22×C4—944no—
574C22×C4—941no—
575C22×C4—941no—
576C22×C4—941no—
577C22×C4—944no—
578C22×C4—3762no—
579C22×C4—1884no—
580C22×C4—1884no—
581C22×C4D4×D4711yescharacteristic
582C22×C4D4×D4711yescharacteristic
583C22×C4C23×D4711yescharacteristic
584SD16—28no—
585SD16—28no—
586D8—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—24no—
597C4⋊C4—21no—
598C4⋊C4—474no—
599C4⋊C4—474no—
600C4⋊C4—474no—
601C4⋊C4—472no—
602C4⋊C4—472no—
603C4⋊C4—472no—
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⋊C4—941no—
614C4⋊C4C23×D4712yes—
615C22⋊C4—24no—
616C22⋊C4—944no—
617C22⋊C4—944no—
618C22⋊C4—944no—
619C22⋊C4—944no—
620C22⋊C4—944no—
621C22⋊C4—944no—
622C22⋊C4—944no—
623C42—472no—
624C42—472no—
625C42—472no—
626C42—472no—
627C42—944no—
628C42—944no—
629C42D4×D4712yes—
630C42C23×D4712yes—
631C23—24no—
632C23—22no—
633C23—42no—
634C23—42no—
635C23—942no—
636C23—1882no—
637C23—1882no—
638C23—1882no—
639C23C2×D4×D4711yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—22no—
644Q8—42no—
645Q8—42no—
646Q8—3764no—
647Q8—1884no—
648D4—24no—
649D4—22no—
650D4—942no—
651D4—942no—
652D4—1882no—
653D4C2×#1062535214yes—
654C2×C4—22no—
655C2×C4—22no—
656C2×C4—22no—
657C2×C4—22no—
658C2×C4—22no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—84no—
663C2×C4—472no—
664C2×C4—472no—
665C2×C4—472no—
666C2×C4—472no—
667C2×C4—942no—
668C2×C4—942no—
669C2×C4—942no—
670C2×C4—942no—
671C2×C4—942no—
672C2×C4—942no—
673C2×C4—942no—
674C2×C4—3764no—
675C2×C4—1888no—
676C2×C4—1888no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4C2×D4×D4712yes—
681C2×C4C2×D4×D4712yes—
682C2×C4C2×D4×D4711yescharacteristic
683C2×C4C2×#1062535212yes—
684C2×C4#1309407112yes—
685C2×C4C24×D4711yescharacteristic
686C8—22no—
687C8—22no—
688C8—942no—
689C8—942no—
690C22—24no—
691C22—42no—
692C22—42no—
693C22—48no—
694C22—3764no—
695C22—1882no—
696C22—1882no—
697C22—1882no—
698C22#1568977912yes—
699C22#1568992212yes—
700C22#1568992912yes—
701C22C22×D4×D4711yescharacteristic
702C4—22no—
703C4—22no—
704C4—42no—
705C4—42no—
706C4—42no—
707C4—942no—
708C4—942no—
709C4—942no—
710C4—942no—
711C4—1882no—
712C4—1882no—
713C4—1882no—
714C4#1568977912yes—
715C4C22×#1062535211yescharacteristic
716C4C2×#1309407111yescharacteristic
717C2—44no—
718C2—3762no—
719C2#2025620814yesdirect product factor
720C2C2×#1568977911yescharacteristic
721C2C2×#1568992211yescharacteristic
722C2C2×#1568992911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#461C2
socleC23×C47C22×D4
prime radicalC22×#10625334C22
hypercenterC2×#461D47
hypocenterC47C2×#3376
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#461

Complements

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

NH ≅ G/Ntype
1. C2×#15689847C2semidirect
2. C2×#15689832C2semidirect
3. #20256208C2direct (N × H)
4. C2×#15689491C2semidirect
5. C2×#15689484C2semidirect
6. C2×#15689479C2semidirect
7. C2×#15689432C2semidirect
8. C2×#15689406C2semidirect
9. C2×#15689424C2semidirect
12. C2×#15689252C2semidirect
14. C2×#15689224C2semidirect
15. C2×SD16×Dic47C2semidirect
16. C2×C47×#461C2semidirect
19. #15689847C22semidirect
21. #15689832C22semidirect
41. #15689491C22semidirect
42. #15689484C22semidirect
43. #15689479C22semidirect
44. #15689432C22semidirect
45. #15689424C22semidirect
46. #15689406C22semidirect
49. #15689252C22semidirect
51. #15689224C22semidirect
52. SD16×Dic47C22semidirect
73. C47×#461C22semidirect
367. C2×#461D47semidirect
373. C2×C47#3376semidirect
414. #461C2×D47semidirect
438. C47C2×#3376semidirect
719. C2#20256208direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898472
C2×#156898322
#202562082
C2×#156894912
C2×#156894842
C2×#156894792
C2×#156894322
C2×#156894062
C2×#156894242
C2×#156893402
C2×#156892522
C2×#156892332
C2×#156892242
C2×SD16×Dic472
C2×C47×#4612
C2×#337647