Finite Group Databasebeta

← C2×#20255920 #27094907

Subgroups — C2×#20255920 #27094907

Order 12032.

1834 conjugacy classes of subgroups.

The subgroup lattice has 712 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689843C211yesmaximal, characteristic
2C2×#15689813C211yesmaximal, characteristic
3#20255920C2116yesmaximal, direct product factor
4C2×#15689532C211yesmaximal, characteristic, complemented
5C2×#15689459C211yesmaximal, characteristic, complemented
6C2×#15689465C211yesmaximal, characteristic, complemented
7C2×#15689465C211yesmaximal, characteristic, complemented
8C2×#15689465C211yesmaximal, characteristic, complemented
9C2×#15689431C211yesmaximal, characteristic, complemented
10C2×#15689419C211yesmaximal, characteristic, complemented
11C2×#15689381C211yesmaximal, characteristic, complemented
12C2×#15689364C211yesmaximal, characteristic, complemented
13C2×#15689231C211yesmaximal, characteristic, complemented
14C2×#15689165C211yesmaximal, characteristic, complemented
15C2×#15689161C211yesmaximal, characteristic, complemented
16C2×C47×#435C211yesmaximal, characteristic
17C22×Dic188C2211yescharacteristic
18#15689843—24no—
19#15689843C2218yes—
20#15689813—24no—
21#15689813C2218yes—
22C2×#13094024C2211yescharacteristic
23C2×#13094017—21no—
24C2×#13094017—21no—
25C2×#13094017—21no—
26C2×#13094016C2211yescharacteristic
27C2×#13094014—21no—
28C2×#13094011—21no—
29C2×#13094005—21no—
30C2×#13094003C2211yescharacteristic
31C2×#13094003C2211yescharacteristic
32C2×#13094003C2211yescharacteristic
33C2×#13094003C2211yescharacteristic
34C2×C4×Dic94C2211yescharacteristic
35C2×C4×Dic94C2211yescharacteristic
36C2×#13093989—21no—
37C2×#13093983C2211yescharacteristic
38C2×#13093983C2211yescharacteristic
39C2×#13093983C2211yescharacteristic
40C2×#13093980—21no—
41C22×C4⋊Dic47C2211yescharacteristic
42#15689532C2218yescomplemented
43#15689465C2218yescomplemented
44#15689465C2218yescomplemented
45#15689465C2218yescomplemented
46#15689459C2218yescomplemented
47#15689431C2218yescomplemented
48#15689419C2218yescomplemented
49#15689381C2218yescomplemented
50#15689364C2218yescomplemented
51#15689231C2218yescomplemented
52#15689165C2218yescomplemented
53#15689161C2218yescomplemented
54C2×#13093958C2211yescharacteristic
55C2×#13093958C2211yescharacteristic
56C2×#13093958C2211yescharacteristic
57C2×#13093958C2211yescharacteristic
58C2×#13093958C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093956C2211yescharacteristic
61C2×#13093956C2211yescharacteristic
62C2×#13093956C2211yescharacteristic
63C2×#13093949C2211yescharacteristic
64C2×#13093949C2211yescharacteristic
65C2×#13093949C2211yescharacteristic
66C2×#13093949C2211yescharacteristic
67C2×#13093949C2211yescharacteristic
68C2×#13093949C2211yescharacteristic
69C22×M16×C47C2211yescharacteristic
70C23×C8×C47C2211yescharacteristic
71C2×C4×D4×C47C2211yescharacteristic
72C47×#435C2218yes—
73C2×C4⋊C8×C47C2211yescharacteristic
74C2×C22⋊C8×C47C2211yescharacteristic
75C2×C22⋊C8×C47C2211yescharacteristic
76C2×#97×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×Dic94C2311yescharacteristic
79C22×Dic94C2311yescharacteristic
80C23×Dic47—21no—
81C2×Dic188—24no—
82C2×Dic188C2314yes—
83#13094024—22no—
84#13094024C2314yes—
85#13094017—28no—
86#13094017—28no—
87#13094017—28no—
88#13094016—22no—
89#13094016C2314yes—
90#13094014—28no—
91#13094011—28no—
92#13094005—28no—
93#13094003—22no—
94#13094003—22no—
95#13094003—22no—
96#13094003—22no—
97#13094003C2314yes—
98#13094003C2314yes—
99#13094003C2314yes—
100#13094003C2314yes—
101C4×Dic94—22no—
102C4×Dic94—22no—
103C4×Dic94C2314yes—
104C4×Dic94C2314yes—
105#13093989—28no—
106#13093983—22no—
107#13093983—22no—
108#13093983—22no—
109#13093983C2314yes—
110#13093983C2314yes—
111#13093983C2314yes—
112#13093980—28no—
113C2×C4⋊Dic47—22no—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47C2314yes—
117C2×C4⋊Dic47C2311yescharacteristic
118C2×C4⋊Dic47C2311yescharacteristic
119C2×C4⋊Dic47C2311yescharacteristic
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—21no—
128C2×Dic47⋊C4—21no—
129C2×Dic47⋊C4—21no—
130C2×Dic47⋊C4—21no—
131C2×C22⋊Dic47—21no—
132C2×C22⋊Dic47—21no—
133C2×C22⋊Dic47—21no—
134C2×C22⋊Dic47—21no—
135C2×C22⋊Dic47—21no—
136C2×C22⋊Dic47—21no—
137C2×C22⋊Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47—21no—
141C2×C4×Dic47—21no—
142C2×C4×Dic47—21no—
143#13093958C2314yes—
144#13093958C2314yes—
145#13093958C2314yes—
146#13093958C2314yes—
147#13093958C2314yes—
148#13093956C2314yes—
149#13093956C2314yes—
150#13093956C2314yes—
151#13093956C2314yes—
152#13093949C2314yes—
153#13093949C2314yes—
154#13093949C2314yes—
155#13093949C2314yes—
156#13093949C2314yes—
157#13093949C2314yes—
158C22×D4×C47D411yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C23×C4×C47C2311yescharacteristic
161C2×M16×C47—24no—
162C2×M16×C47C2314yes—
163C22×C8×C47—24no—
164C22×C8×C47C2314yes—
165C22×C8×C47C2311yescharacteristic
166C22×C8×C47C2311yescharacteristic
167C22×C8×C47C2311yescharacteristic
168C22×C8×C47C2311yescharacteristic
169C4×D4×C47D414yes—
170C4×D4×C47C2314yes—
171C2×C4⋊C4×C47D411yescharacteristic
172C2×C22⋊C4×C47D411yescharacteristic
173C2×C22⋊C4×C47D411yescharacteristic
174C2×C42×C47C2311yescharacteristic
175C4⋊C8×C47C2314yes—
176C22⋊C8×C47C2314yes—
177C22⋊C8×C47C2314yes—
178#97×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C24×C47C2×D411yescharacteristic
181C2×D4×C47—42no—
182C2×D4×C47C2×D414yes—
183C22×C4×C47—22no—
184C22×C4×C47—22no—
185C22×C4×C47—22no—
186C22×C4×C47—22no—
187C22×C4×C47C2×D411yescharacteristic
188C22×C4×C47C2×D411yescharacteristic
189C22×C4×C47C2×D411yescharacteristic
190C22×C4×C47C2×D411yescharacteristic
191C22×C4×C47C2×D412yes—
192C22×C4×C47C2×D412yes—
193C22×C4×C47C2412yes—
194C22×C4×C47C2412yes—
195C22×C4×C47C2411yescharacteristic
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47—21no—
200C22×Dic47—21no—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—24no—
205C22×Dic47—44no—
206C2×Dic94—22no—
207C2×Dic94—22no—
208C2×Dic94—22no—
209C2×Dic94—22no—
210C2×Dic94—24no—
211C2×Dic94—21no—
212C2×Dic94—21no—
213C2×Dic94—44no—
214C2×Dic94C2412yes—
215C2×Dic94C2412yes—
216M16×C47—28no—
217C2×C8×C47—22no—
218C2×C8×C47—22no—
219C2×C8×C47—22no—
220C2×C8×C47—28no—
221C2×C8×C47#4114yes—
222C2×C8×C47C2412yes—
223C2×C8×C47C2412yes—
224C2×C8×C47C2412yes—
225C2×C8×C47C2412yes—
226C4⋊C4×C47C2×D414yes—
227C22⋊C4×C47C2×D414yes—
228C22⋊C4×C47C2×D414yes—
229C42×C47C2×D412yes—
230C42×C47C2412yes—
231C22⋊Dic47—24no—
232C22⋊Dic47—24no—
233C22⋊Dic47—24no—
234C22⋊Dic47—24no—
235C22⋊Dic47—24no—
236C22⋊Dic47—24no—
237C22⋊Dic47—24no—
238C4⋊Dic47—21no—
239C4⋊Dic47—21no—
240C4⋊Dic47—24no—
241C4⋊Dic47—24no—
242C4⋊Dic47—21no—
243C4⋊Dic47—21no—
244C4⋊Dic47—21no—
245C4⋊Dic47—21no—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249C4⋊Dic47C2412yes—
250C4⋊Dic47C2412yes—
251C4⋊Dic47C2412yes—
252Dic47⋊C4—24no—
253Dic47⋊C4—24no—
254Dic47⋊C4—24no—
255Dic47⋊C4—24no—
256Dic47⋊C4—24no—
257Dic47⋊C4—24no—
258Dic47⋊C4—24no—
259Dic47⋊C4—24no—
260C4×Dic47—24no—
261C4×Dic47—24no—
262C4×Dic47—24no—
263C4×Dic47—24no—
264C4×Dic47—24no—
265Dic188—28no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47—22no—
270C23×C47—22no—
271C23×C47—22no—
272C23×C47C22×D412yes—
273C23×C47C22×D412yes—
274C23×C47C22×D411yescharacteristic
275D4×C47—44no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—22no—
279C2×C4×C47—22no—
280C2×C4×C47—24no—
281C2×C4×C47—24no—
282C2×C4×C47—22no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47C22×D412yes—
287C2×C4×C47C22×D412yes—
288C2×C4×C47C22×D412yes—
289C2×C4×C47C22×D412yes—
290C2×C4×C47C22×D411yescharacteristic
291C2×C4×C47C2×#4112yes—
292C2×C4×C472−1+412yes—
293C2×C4×C47C2511yescharacteristic
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—22no—
297C2×Dic47—22no—
298C2×Dic47—22no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—48no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305C2×Dic47—42no—
306C2×Dic47—42no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311Dic94—22no—
312Dic94—22no—
313Dic94—22no—
314Dic94—22no—
315Dic94—48no—
316Dic94—42no—
317Dic94—42no—
318C8×C47—22no—
319C8×C47—22no—
320C8×C47—22no—
321C8×C47C2×#4114yes—
322C2×#3349—471nomaximal, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—22no—
327C22×C47—22no—
328C22×C47—22no—
329C22×C47—44no—
330C22×C47—44no—
331C22×C47#54712yes—
332C22×C47#57512yes—
333C22×C47#57812yes—
334C22×C47C23×D411yescharacteristic
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47#54712yes—
340C4×C47C22×#4111yescharacteristic
341C4×C47C2×2−1+411yescharacteristic
342Dic47—42no—
343Dic47—42no—
344Dic47—42no—
345Dic47—42no—
346Dic47—42no—
347Dic47—42no—
348Dic47—42no—
349Dic47—42no—
350C2×#556—471no—
351C2×#552—471no—
352#3349—4716no—
353C2×#501—471no—
354C2×#484—471no—
355C2×#485—471no—
356C2×#485—471no—
357C2×#485—471no—
358C2×#479—471no—
359C2×#477—471no—
360C2×#470—471no—
361C2×#467—471no—
362C2×#441—471no—
363C2×#435D4711yescharacteristic
364C2×#428—471no—
365C2×#427—471no—
366C2×C47—42no—
367C2×C47—42no—
368C2×C47#334914yescomplemented
369C2×C47C2×#54711yescharacteristic
370C2×C47C2×#57511yescharacteristic
371C2×C47C2×#57811yescharacteristic
372C22×Q16—471no—
373C22×M16C2×D4711yescharacteristic
374C23×C8C2×D4711yescharacteristic
375#556—478no—
376#556—944no—
377#552—478no—
378#552—944no—
379C2×C4⋊Q8—471no—
380C2×#126—941no—
381C2×#126—941no—
382C2×#126—941no—
383C2×#125—471no—
384C2×#125—941no—
385C2×#124—941no—
386C2×#123—941no—
387C2×C22⋊Q8—471no—
388C2×C22⋊Q8—471no—
389C2×C22⋊Q8—471no—
390C2×C22⋊Q8—471no—
391C2×C4×Q8—471no—
392C2×C4×Q8—471no—
393C2×C4×Q8—941no—
394C2×C4×D4C2×D4711yescharacteristic
395C2×#117—471no—
396C2×#117—471no—
397C2×#117—471no—
398C2×#117—941no—
399C22×C4⋊C4—471no—
400#501—478no—
401#485—478no—
402#485—478no—
403#485—478no—
404#484—478no—
405#479—478no—
406#477—478no—
407#470—478no—
408#467—478no—
409#441—478no—
410#435C2×D4718yes—
411#428—478no—
412#427—478no—
413C2×#107—471no—
414C2×#107—471no—
415C2×#107—471no—
416C2×#107—471no—
417C2×#107—471no—
418C2×#106—471no—
419C2×#106—471no—
420C2×#106—471no—
421C2×#106—471no—
422C2×C4⋊C8C2×D4711yescharacteristic
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103—471no—
428C2×#103—471no—
429C2×C22⋊C8C2×D4711yescharacteristic
430C2×C22⋊C8C2×D4711yescharacteristic
431C2×#97C2×D4711yescharacteristic
432C47C2×#334911yescharacteristic, complemented, Sylow
433C22×Q8—471no—
434C22×Q8—471no—
435C22×Q8—941no—
436C22×D4D18811yescharacteristic
437C23×C4—941no—
438C23×C4C22×D4711yescharacteristic
439C23×C4C22×D4711yescharacteristic
440C2×Q16—474no—
441C2×Q16—944no—
442C2×M16—24no—
443C2×M16C22×D4714yes—
444C22×C8—24no—
445C22×C8C22×D4711yescharacteristic
446C22×C8C22×D4714yes—
447C22×C8C22×D4711yescharacteristic
448C22×C8C22×D4711yescharacteristic
449C22×C8C22×D4711yescharacteristic
450C4⋊Q8—474no—
451C4⋊Q8—942no—
452#126—948no—
453#126—948no—
454#126—948no—
455#125—474no—
456#125—948no—
457#125—942no—
458#124—948no—
459#123—948no—
460C22⋊Q8—474no—
461C22⋊Q8—474no—
462C22⋊Q8—474no—
463C22⋊Q8—474no—
464C22⋊Q8—942no—
465C22⋊Q8—942no—
466C22⋊Q8—942no—
467C22⋊Q8—942no—
468C4×Q8—474no—
469C4×Q8—474no—
470C4×Q8—948no—
471C4×Q8—942no—
472C4×Q8—942no—
473C4×D4D18814yes—
474C4×D4C22×D4714yes—
475#117—474no—
476#117—474no—
477#117—474no—
478#117—942no—
479#117—942no—
480#117—942no—
481#117—948no—
482C2×C4⋊C4—471no—
483C2×C4⋊C4—471no—
484C2×C4⋊C4—474no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—471no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—941no—
490C2×C4⋊C4—942no—
491C2×C4⋊C4—941no—
492C2×C4⋊C4—941no—
493C2×C4⋊C4—941no—
494C2×C4⋊C4—941no—
495C2×C4⋊C4—941no—
496C2×C4⋊C4—941no—
497C2×C4⋊C4—941no—
498C2×C4⋊C4—941no—
499C2×C4⋊C4—941no—
500C2×C4⋊C4D18811yescharacteristic
501C2×C22⋊C4—941no—
502C2×C22⋊C4—941no—
503C2×C22⋊C4—941no—
504C2×C22⋊C4—941no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4D18811yescharacteristic
509C2×C22⋊C4D18811yescharacteristic
510C2×C42—941no—
511C2×C42—941no—
512C2×C42—941no—
513C2×C42—941no—
514C2×C42—941no—
515C2×C42C22×D4711yescharacteristic
516#107—474no—
517#107—474no—
518#107—474no—
519#107—474no—
520#107—474no—
521#106—474no—
522#106—474no—
523#106—474no—
524#106—474no—
525C4⋊C8C22×D4714yes—
526#103—474no—
527#103—474no—
528#103—474no—
529#103—474no—
530#103—474no—
531#103—474no—
532C22⋊C8C22×D4714yes—
533C22⋊C8C22×D4714yes—
534#97C22×D4714yes—
535C24C2×D18811yescharacteristic
536C24C2×D18811yescharacteristic
537C2×Q8—472no—
538C2×Q8—472no—
539C2×Q8—941no—
540C2×Q8—941no—
541C2×Q8—944no—
542C2×Q8—942no—
543C2×Q8—942no—
544C2×Q8—942no—
545C2×Q8—942no—
546C2×Q8—1884no—
547C2×D4—42no—
548C2×D4C2×D18814yes—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—944no—
554C22×C4—941no—
555C22×C4—941no—
556C22×C4—941no—
557C22×C4—941no—
558C22×C4—941no—
559C22×C4—941no—
560C22×C4—941no—
561C22×C4—941no—
562C22×C4—1884no—
563C22×C4C2×D18812yes—
564C22×C4C2×D18812yes—
565C22×C4C2×D18811yescharacteristic
566C22×C4C2×D18811yescharacteristic
567C22×C4C2×D18811yescharacteristic
568C22×C4C2×D18811yescharacteristic
569C22×C4C23×D4712yes—
570C22×C4C23×D4712yes—
571C22×C4C23×D4711yescharacteristic
572Q16—948no—
573M16—28no—
574C2×C8—22no—
575C2×C8—22no—
576C2×C8—22no—
577C2×C8—28no—
578C2×C8#1062535214yes—
579C2×C8C23×D4712yes—
580C2×C8C23×D4712yes—
581C2×C8C23×D4712yes—
582C2×C8C23×D4712yes—
583C4⋊C4—472no—
584C4⋊C4—472no—
585C4⋊C4—472no—
586C4⋊C4—472no—
587C4⋊C4—472no—
588C4⋊C4—472no—
589C4⋊C4—944no—
590C4⋊C4—944no—
591C4⋊C4—944no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—944no—
597C4⋊C4—941no—
598C4⋊C4—941no—
599C4⋊C4—944no—
600C4⋊C4—941no—
601C4⋊C4—941no—
602C4⋊C4—941no—
603C4⋊C4—941no—
604C4⋊C4—944no—
605C4⋊C4C2×D18814yes—
606C22⋊C4—944no—
607C22⋊C4—944no—
608C22⋊C4—944no—
609C22⋊C4—944no—
610C22⋊C4—944no—
611C22⋊C4—944no—
612C22⋊C4—944no—
613C22⋊C4C2×D18814yes—
614C22⋊C4C2×D18814yes—
615C42—944no—
616C42—944no—
617C42—944no—
618C42—944no—
619C42—944no—
620C42C2×D18812yes—
621C42C23×D4712yes—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—22no—
626C23—22no—
627C23—22no—
628C23C22×D18812yes—
629C23C22×D18812yes—
630C23C22×D18811yescharacteristic
631Q8—942no—
632Q8—942no—
633Q8—942no—
634Q8—942no—
635Q8—1888no—
636Q8—1882no—
637Q8—1882no—
638D4—44no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—24no—
644C2×C4—24no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—942no—
650C2×C4—942no—
651C2×C4—942no—
652C2×C4—942no—
653C2×C4—942no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—1888no—
658C2×C4—1882no—
659C2×C4—1882no—
660C2×C4—1882no—
661C2×C4—1882no—
662C2×C4—1882no—
663C2×C4—1882no—
664C2×C4—1882no—
665C2×C4—1882no—
666C2×C4C22×D18812yes—
667C2×C4C22×D18812yes—
668C2×C4C22×D18812yes—
669C2×C4C22×D18812yes—
670C2×C4C22×D18811yescharacteristic
671C2×C4C2×#1062535212yes—
672C2×C4#1309407112yes—
673C2×C4C24×D4711yescharacteristic
674C8—22no—
675C8—22no—
676C8—22no—
677C8C2×#1062535214yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—44no—
685C22—44no—
686C22#1568977712yes—
687C22#1568992312yes—
688C22#1568994012yes—
689C22C23×D18811yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—1882no—
695C4—1882no—
696C4—1882no—
697C4—1882no—
698C4—1882no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4#1568977712yes—
703C4C22×#1062535211yescharacteristic
704C4C2×#1309407111yescharacteristic
705C2—42no—
706C2—42no—
707C2#2025592014yesdirect product factor
708C2C2×#1568977711yescharacteristic
709C2C2×#1568992311yescharacteristic
710C2C2×#1568994011yescharacteristic
subgroupG/H
centerC23C22×D188
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#435C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
hypercenterC2×#435D47
hypocenterC47C2×#3349
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
3. #20255920C2direct (N × H)
4. C2×#15689532C2semidirect
5. C2×#15689459C2semidirect
6. C2×#15689465C2semidirect
7. C2×#15689465C2semidirect
8. C2×#15689465C2semidirect
9. C2×#15689431C2semidirect
10. C2×#15689419C2semidirect
11. C2×#15689381C2semidirect
12. C2×#15689364C2semidirect
13. C2×#15689231C2semidirect
14. C2×#15689165C2semidirect
15. C2×#15689161C2semidirect
42. #15689532C22semidirect
43. #15689465C22semidirect
44. #15689465C22semidirect
45. #15689465C22semidirect
46. #15689459C22semidirect
47. #15689431C22semidirect
48. #15689419C22semidirect
49. #15689381C22semidirect
50. #15689364C22semidirect
51. #15689231C22semidirect
52. #15689165C22semidirect
53. #15689161C22semidirect
368. C2×C47#3349semidirect
432. C47C2×#3349semidirect
707. C2#20255920direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898432
C2×#156898132
#202559202
C2×#156895322
C2×#156894592
C2×#156894652
C2×#156894312
C2×#156894192
C2×#156893812
C2×#156893642
C2×#156892312
C2×#156891652
C2×#156891612
C2×C47×#4352
C2×#334947