Finite Group Databasebeta

← C2×#20255913 #27094900

Subgroups — C2×#20255913 #27094900

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×#15689844C211yesmaximal, characteristic
2C2×#15689815C211yesmaximal, characteristic
3#20255913C2116yesmaximal, direct product factor
4C2×#15689530C211yesmaximal, characteristic, complemented
5C2×#15689456C211yesmaximal, characteristic, complemented
6C2×#15689463C211yesmaximal, characteristic, complemented
7C2×#15689462C211yesmaximal, characteristic, complemented
8C2×#15689461C211yesmaximal, characteristic, complemented
9C2×#15689428C211yesmaximal, characteristic, complemented
10C2×#15689416C211yesmaximal, characteristic, complemented
11C2×#15689361C211yesmaximal, characteristic, complemented
12C2×#15689230C211yesmaximal, characteristic, complemented
13C2×#15689192C211yesmaximal, characteristic
14C2×#15689165C211yesmaximal, characteristic, complemented
15C2×#15689158C211yesmaximal, characteristic, complemented
16C2×C47×#470C211yesmaximal, characteristic, complemented
17C22×C8×D47C2211yescharacteristic
18#15689844—24no—
19#15689844C2218yes—
20#15689815—24no—
21#15689815C2218yes—
22C2×#13094023C2211yescharacteristic
23C2×#13094019—21no—
24C2×#13094019—21no—
25C2×#13094017—21no—
26C2×#13094015—21no—
27C2×#13094015C2211yescharacteristic
28C2×#13094010—21no—
29C2×#13094008—21no—
30C2×#13094000C2211yescharacteristic
31C2×#13094000C2211yescharacteristic
32C2×Q8×Dic47C2211yescharacteristic
33C2×Q8×Dic47C2211yescharacteristic
34C2×#13093989—21no—
35C2×C4×C22⋊D47C2211yescharacteristic
36C2×#13093983C2211yescharacteristic
37C2×#13093982C2211yescharacteristic
38C2×#13093982C2211yescharacteristic
39C2×#13093980—21no—
40C22×C4⋊Dic47C2211yescharacteristic
41#15689530C2218yescomplemented
42#15689463C2218yescomplemented
43#15689462C2218yescomplemented
44#15689461C2218yescomplemented
45#15689456C2218yescomplemented
46#15689428C2218yescomplemented
47#15689416C2218yescomplemented
48#15689361C2218yescomplemented
49#15689230C2218yescomplemented
50#15689192C2218yes—
51#15689165C2218yescomplemented
52#15689158C2218yescomplemented
53C2×#13093958C2211yescharacteristic
54C2×#13093958C2211yescharacteristic
55C2×#13093957C2211yescharacteristic
56C2×#13093957C2211yescharacteristic
57C2×#13093957C2211yescharacteristic
58C2×#13093956C2211yescharacteristic
59C2×#13093956C2211yescharacteristic
60C2×#13093955C2211yescharacteristic
61C2×Dic47⋊C8C2211yescharacteristic
62C2×#13093948C2211yescharacteristic
63C2×#13093948C2211yescharacteristic
64C2×#13093948C2211yescharacteristic
65C2×#13093948C2211yescharacteristic
66C2×C22⋊(C47⋊C8)C2211yescharacteristic
67C2×(C2×D47)⋊C8C2211yescharacteristic
68C2×#13093934C2211yescharacteristic
69C22×Q16×C47C2211yescharacteristic
70C22×M16×C47C2211yescharacteristic
71C2×C22⋊Q8×C47C2211yescharacteristic
72C2×C22⋊Q8×C47C2211yescharacteristic
73C47×#470C2218yescomplemented
74C2×#106×C47C2211yescharacteristic
75C2×#103×C47C2211yescharacteristic
76C2×#103×C47C2211yescharacteristic
77C22×Dic94—21no—
78C22×C22⋊D47D411yescharacteristic
79C23×Dic47—21no—
80C22×C4×D47C2311yescharacteristic
81C22×C47⋊C8C2311yescharacteristic
82C22×C47⋊C8C2311yescharacteristic
83C2×C8×D47—24no—
84C2×C8×D47C2314yes—
85#13094023—22no—
86#13094023C2314yes—
87#13094019—28no—
88#13094019—28no—
89#13094017—28no—
90#13094015—28no—
91#13094015—22no—
92#13094015C2314yes—
93#13094010—28no—
94#13094008—28no—
95#13094000—22no—
96#13094000—22no—
97#13094000C2314yes—
98#13094000C2314yes—
99Q8×Dic47—22no—
100Q8×Dic47—22no—
101Q8×Dic47C2314yes—
102Q8×Dic47C2314yes—
103#13093989—28no—
104C4×C22⋊D47D414yes—
105C4×C22⋊D47C2314yes—
106#13093983—22no—
107#13093983C2314yes—
108#13093982—22no—
109#13093982—22no—
110#13093982C2314yes—
111#13093982C2314yes—
112#13093980—28no—
113C2×C4⋊Dic47—22no—
114C2×C4⋊Dic47—21no—
115C2×C4⋊Dic47—21no—
116C2×C4⋊Dic47—21no—
117C2×C4⋊Dic47—21no—
118C2×C4⋊Dic47C2314yes—
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⋊C4D411yescharacteristic
128C2×C22⋊Dic47—21no—
129C2×C22⋊Dic47D411yescharacteristic
130C2×(C2×D47)⋊C4—21no—
131C2×(C2×D47)⋊C4—21no—
132C2×(C2×D47)⋊C4—21no—
133C2×(C2×D47)⋊C4—21no—
134C2×(C2×D47)⋊C4D411yescharacteristic
135C2×C4×Dic47—21no—
136C2×C4×Dic47—21no—
137C2×C4×Dic47—21no—
138C2×C4×Dic47—21no—
139C2×C4×Dic47—21no—
140C2×C4×Dic47C2311yescharacteristic
141#13093958C2314yes—
142#13093958C2314yes—
143#13093957C2314yes—
144#13093957C2314yes—
145#13093957C2314yes—
146#13093956C2314yes—
147#13093956C2314yes—
148#13093955C2314yes—
149Dic47⋊C8C2314yes—
150#13093948C2314yes—
151#13093948C2314yes—
152#13093948C2314yes—
153#13093948C2314yes—
154C22⋊(C47⋊C8)C2314yes—
155(C2×D47)⋊C8C2314yes—
156#13093934C2314yes—
157C22×Q8×C47C2311yescharacteristic
158C22×Q8×C47C2311yescharacteristic
159C23×C4×C47C2311yescharacteristic
160C2×Q16×C47—24no—
161C2×Q16×C47C2314yes—
162C2×M16×C47—24no—
163C2×M16×C47C2314yes—
164C22×C8×C47C2311yescharacteristic
165C22×C8×C47C2311yescharacteristic
166C22⋊Q8×C47—22no—
167C22⋊Q8×C47—22no—
168C22⋊Q8×C47C2314yes—
169C22⋊Q8×C47C2314yes—
170C2×C4⋊C4×C47—21no—
171C2×C4⋊C4×C47—21no—
172C2×C4⋊C4×C47C2311yescharacteristic
173C2×C4⋊C4×C47C2311yescharacteristic
174C2×C22⋊C4×C47—21no—
175C2×C22⋊C4×C47—21no—
176#106×C47C2314yes—
177#103×C47C2314yes—
178#103×C47C2314yes—
179C24×C47C2×D411yescharacteristic
180C23×D47C2×D411yescharacteristic
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—
189C22×C4×C47—22no—
190C22×C4×C47—22no—
191C22×C4×C47—21no—
192C22×C4×C47—21no—
193C22×C4×C47—21no—
194C22×C4×C47—21no—
195C22×C4×C47C2×D411yescharacteristic
196C22×C4×C47C2×D412yes—
197C22×C4×C47C2412yes—
198C22×C4×C47C2411yescharacteristic
199C2×C22⋊D47—42no—
200C2×C22⋊D47C2×D414yes—
201C22×Dic47—21no—
202C22×Dic47—21no—
203C22×Dic47—21no—
204C22×Dic47—21no—
205C22×Dic47—24no—
206C22×Dic47—44no—
207C22×Dic47C2×D411yescharacteristic
208C22×Dic47C2×D411yescharacteristic
209C22×Dic47C2×D411yescharacteristic
210C2×C4×D47—22no—
211C2×C4×D47—22no—
212C2×C4×D47C2×D412yes—
213C2×C4×D47C2412yes—
214C2×Dic94—24no—
215C2×Dic94—44no—
216Q16×C47—28no—
217M16×C47—28no—
218C2×C8×C47—22no—
219C2×C8×C47#4114yes—
220C2×C8×C47C2412yes—
221C2×C8×C47C2412yes—
222C4⋊C4×C47—24no—
223C4⋊C4×C47—24no—
224C4⋊C4×C47—21no—
225C4⋊C4×C47—21no—
226C4⋊C4×C47C2412yes—
227C4⋊C4×C47C2412yes—
228C22⋊C4×C47—24no—
229C22⋊C4×C47—24no—
230C22⋊Dic47—24no—
231C22⋊Dic47C2×D414yes—
232(C2×D47)⋊C4—24no—
233(C2×D47)⋊C4—24no—
234(C2×D47)⋊C4—24no—
235(C2×D47)⋊C4—24no—
236(C2×D47)⋊C4C2×D414yes—
237C4⋊Dic47—21no—
238C4⋊Dic47—21no—
239C4⋊Dic47—24no—
240C4⋊Dic47—21no—
241C4⋊Dic47—21no—
242C4⋊Dic47—24no—
243C4⋊Dic47—24no—
244C4⋊Dic47—24no—
245C4⋊Dic47C2412yes—
246C4⋊Dic47C2412yes—
247C4⋊Dic47C2412yes—
248C4⋊Dic47C2412yes—
249Dic47⋊C4—24no—
250Dic47⋊C4—24no—
251Dic47⋊C4—24no—
252Dic47⋊C4—24no—
253Dic47⋊C4C2×D414yes—
254C4×Dic47—24no—
255C4×Dic47—24no—
256C4×Dic47—24no—
257C4×Dic47—24no—
258C4×Dic47—24no—
259C4×Dic47C2×D412yes—
260C4×Dic47C2412yes—
261C2×C47⋊C8—22no—
262C2×C47⋊C8—22no—
263C2×C47⋊C8C2412yes—
264C2×C47⋊C8C2412yes—
265C8×D47—28no—
266C23×C47—22no—
267C23×C47—22no—
268C23×C47—22no—
269C23×C47C22×D412yes—
270C23×C47C22×D411yescharacteristic
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—22no—
274C22×D47C22×D412yes—
275Q8×C47—22no—
276Q8×C47—22no—
277Q8×C47—22no—
278Q8×C47—22no—
279Q8×C47—42no—
280Q8×C47—42no—
281C2×C4×C47—22no—
282C2×C4×C47—24no—
283C2×C4×C47—22no—
284C2×C4×C47—22no—
285C2×C4×C47—22no—
286C2×C4×C47—22no—
287C2×C4×C47—22no—
288C2×C4×C47—22no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47C22×D412yes—
294C2×C4×C47C22×D411yescharacteristic
295C2×C4×C47C2×#4112yes—
296C2×C4×C472−1+412yes—
297C2×C4×C47C2511yescharacteristic
298C22⋊D47—44no—
299C2×Dic47—22no—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—48no—
307C2×Dic47—42no—
308C2×Dic47—42no—
309C2×Dic47—42no—
310C2×Dic47—42no—
311C2×Dic47C22×D412yes—
312C2×Dic47C22×D412yes—
313C2×Dic47C22×D412yes—
314C4×D47—24no—
315C4×D47—22no—
316C4×D47—22no—
317Dic94—48no—
318C8×C47—22no—
319C8×C47C2×#4114yes—
320C47⋊C8—22no—
321C47⋊C8—22no—
322C2×#3349—471nomaximal, Sylow
323C22×C47—22no—
324C22×C47—22no—
325C22×C47—22no—
326C22×C47—44no—
327C22×C47#54712yes—
328C22×C47#57512yes—
329C22×C47#57812yes—
330C22×C47C23×D411yescharacteristic
331C2×D47—22no—
332C2×D47—22no—
333C2×D47—22no—
334C2×D47—44no—
335C4×C47—22no—
336C4×C47—42no—
337C4×C47—42no—
338C4×C47—42no—
339C4×C47—42no—
340C4×C47#54712yes—
341C4×C47C22×#4111yescharacteristic
342C4×C47C2×2−1+411yescharacteristic
343Dic47—22no—
344Dic47—22no—
345Dic47—22no—
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×#470D4711yescharacteristic, complemented
361C2×#467—471no—
362C2×#441—471no—
363C2×#435—471no—
364C2×#428—471no—
365C2×#427—471no—
366C2×C47—42no—
367C2×C47#334914yescomplemented
368C2×C47C2×#54711yescharacteristic
369C2×C47C2×#57511yescharacteristic
370C2×C47C2×#57811yescharacteristic
371D47—42no—
372C22×Q16C2×D4711yescharacteristic
373C22×M16C2×D4711yescharacteristic
374C23×C8—471no—
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⋊Q8C2×D4711yescharacteristic
390C2×C22⋊Q8C2×D4711yescharacteristic
391C2×C4×Q8—471no—
392C2×C4×Q8—471no—
393C2×C4×Q8—941no—
394C2×C4×D4—471no—
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#470C2×D4718yescomplemented
408#467—478no—
409#441—478no—
410#435—478no—
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×#106C2×D4711yescharacteristic
422C2×C4⋊C8—471no—
423C2×#103—471no—
424C2×#103—471no—
425C2×#103—471no—
426C2×#103—471no—
427C2×#103C2×D4711yescharacteristic
428C2×#103C2×D4711yescharacteristic
429C2×C22⋊C8—471no—
430C2×C22⋊C8—471no—
431C2×#97—471no—
432C47C2×#334911yescharacteristic, complemented, Sylow
433C22×Q8—941no—
434C22×Q8C22×D4711yescharacteristic
435C22×Q8C22×D4711yescharacteristic
436C22×D4—471no—
437C23×C4—471no—
438C23×C4—941no—
439C23×C4C22×D4711yescharacteristic
440C2×Q16—24no—
441C2×Q16C22×D4714yes—
442C2×M16—24no—
443C2×M16C22×D4714yes—
444C22×C8—471no—
445C22×C8—471no—
446C22×C8—474no—
447C22×C8—944no—
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—942no—
457#125—948no—
458#124—948no—
459#123—948no—
460C22⋊Q8—22no—
461C22⋊Q8—22no—
462C22⋊Q8—474no—
463C22⋊Q8—474no—
464C22⋊Q8—942no—
465C22⋊Q8—942no—
466C22⋊Q8C22×D4714yes—
467C22⋊Q8C22×D4714yes—
468C4×Q8—474no—
469C4×Q8—474no—
470C4×Q8—942no—
471C4×Q8—942no—
472C4×Q8—948no—
473C4×D4—474no—
474C4×D4—474no—
475#117—474no—
476#117—474no—
477#117—474no—
478#117—948no—
479#117—942no—
480#117—942no—
481#117—942no—
482C2×C4⋊C4—21no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—471no—
485C2×C4⋊C4—471no—
486C2×C4⋊C4—471no—
487C2×C4⋊C4—474no—
488C2×C4⋊C4—471no—
489C2×C4⋊C4—471no—
490C2×C4⋊C4—941no—
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—942no—
499C2×C4⋊C4C22×D4711yescharacteristic
500C2×C4⋊C4C22×D4711yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—471no—
504C2×C22⋊C4—471no—
505C2×C22⋊C4—941no—
506C2×C22⋊C4—941no—
507C2×C22⋊C4—941no—
508C2×C22⋊C4—941no—
509C2×C22⋊C4—941no—
510C2×C42—471no—
511C2×C42—941no—
512C2×C42—941no—
513C2×C42—941no—
514C2×C42—941no—
515C2×C42—941no—
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#106C22×D4714yes—
525C4⋊C8—474no—
526#103—474no—
527#103—474no—
528#103—474no—
529#103—474no—
530#103C22×D4714yes—
531#103C22×D4714yes—
532C22⋊C8—474no—
533C22⋊C8—474no—
534#97—474no—
535C24—471no—
536C24D4×D4711yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—22no—
540C2×Q8—22no—
541C2×Q8—22no—
542C2×Q8—22no—
543C2×Q8—944no—
544C2×Q8—1884no—
545C2×Q8C23×D4712yes—
546C2×Q8C23×D4712yes—
547C2×D4—474no—
548C2×D4—1882no—
549C22×C4—22no—
550C22×C4—22no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—471no—
556C22×C4—471no—
557C22×C4—471no—
558C22×C4—472no—
559C22×C4—472no—
560C22×C4—942no—
561C22×C4—942no—
562C22×C4—944no—
563C22×C4—941no—
564C22×C4—941no—
565C22×C4—941no—
566C22×C4—941no—
567C22×C4—1884no—
568C22×C4D4×D4712yes—
569C22×C4D4×D4711yescharacteristic
570C22×C4C23×D4712yes—
571C22×C4C23×D4711yescharacteristic
572Q16—28no—
573M16—28no—
574C2×C8—22no—
575C2×C8—472no—
576C2×C8—472no—
577C2×C8—942no—
578C2×C8—942no—
579C2×C8—948no—
580C2×C8#1062535214yes—
581C2×C8C23×D4712yes—
582C2×C8C23×D4712yes—
583C4⋊C4—24no—
584C4⋊C4—24no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—474no—
588C4⋊C4—472no—
589C4⋊C4—472no—
590C4⋊C4—472no—
591C4⋊C4—472no—
592C4⋊C4—944no—
593C4⋊C4—944no—
594C4⋊C4—944no—
595C4⋊C4—944no—
596C4⋊C4—944no—
597C4⋊C4—944no—
598C4⋊C4—944no—
599C4⋊C4—941no—
600C4⋊C4—941no—
601C4⋊C4—944no—
602C4⋊C4—941no—
603C4⋊C4—941no—
604C4⋊C4C23×D4712yes—
605C4⋊C4C23×D4712yes—
606C22⋊C4—24no—
607C22⋊C4—24no—
608C22⋊C4—474no—
609C22⋊C4—474no—
610C22⋊C4—944no—
611C22⋊C4—944no—
612C22⋊C4—944no—
613C22⋊C4—944no—
614C22⋊C4—944no—
615C42—472no—
616C42—472no—
617C42—944no—
618C42—944no—
619C42—944no—
620C42—944no—
621C42—944no—
622C23—22no—
623C23—22no—
624C23—22no—
625C23—472no—
626C23—942no—
627C23—942no—
628C23—942no—
629C23C2×D4×D4712yes—
630C23C2×D4×D4711yescharacteristic
631Q8—22no—
632Q8—22no—
633Q8—22no—
634Q8—22no—
635Q8—42no—
636Q8—42no—
637Q8—1888no—
638D4—1884no—
639C2×C4—22no—
640C2×C4—24no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—42no—
650C2×C4—42no—
651C2×C4—472no—
652C2×C4—472no—
653C2×C4—472no—
654C2×C4—942no—
655C2×C4—942no—
656C2×C4—942no—
657C2×C4—944no—
658C2×C4—942no—
659C2×C4—942no—
660C2×C4—942no—
661C2×C4—942no—
662C2×C4—942no—
663C2×C4—942no—
664C2×C4—1888no—
665C2×C4—1882no—
666C2×C4—1882no—
667C2×C4—1882no—
668C2×C4—1882no—
669C2×C4C2×D4×D4712yes—
670C2×C4C2×D4×D4711yescharacteristic
671C2×C4C2×#1062535212yes—
672C2×C4#1309407112yes—
673C2×C4C24×D4711yescharacteristic
674C8—22no—
675C8—942no—
676C8—942no—
677C8C2×#1062535214yes—
678C22—22no—
679C22—22no—
680C22—22no—
681C22—44no—
682C22—942no—
683C22—942no—
684C22—942no—
685C22—1884no—
686C22#1568977312yes—
687C22#1568992212yes—
688C22#1568993912yes—
689C22C22×D4×D4711yescharacteristic
690C4—22no—
691C4—42no—
692C4—42no—
693C4—42no—
694C4—42no—
695C4—942no—
696C4—942no—
697C4—942no—
698C4—1882no—
699C4—1882no—
700C4—1882no—
701C4—1882no—
702C4#1568977312yes—
703C4C22×#1062535211yescharacteristic
704C4C2×#1309407111yescharacteristic
705C2—42no—
706C2—1882no—
707C2#2025591314yesdirect product factor
708C2C2×#1568977311yescharacteristic
709C2C2×#1568992211yescharacteristic
710C2C2×#1568993911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutator, cosocleC2×C4×C47C25
FrattiniC2×C4C24×D47
FittingC2×C47×#470C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
hypercenterC2×#470D47
hypocenterC47C2×#3349
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#470

Complements

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

NH ≅ G/Ntype
3. #20255913C2direct (N × H)
4. C2×#15689530C2semidirect
5. C2×#15689456C2semidirect
6. C2×#15689463C2semidirect
7. C2×#15689462C2semidirect
8. C2×#15689461C2semidirect
9. C2×#15689428C2semidirect
10. C2×#15689416C2semidirect
11. C2×#15689361C2semidirect
12. C2×#15689230C2semidirect
14. C2×#15689165C2semidirect
15. C2×#15689158C2semidirect
16. C2×C47×#470C2semidirect
41. #15689530C22semidirect
42. #15689463C22semidirect
43. #15689462C22semidirect
44. #15689461C22semidirect
45. #15689456C22semidirect
46. #15689428C22semidirect
47. #15689416C22semidirect
48. #15689361C22semidirect
49. #15689230C22semidirect
51. #15689165C22semidirect
52. #15689158C22semidirect
73. C47×#470C22semidirect
360. C2×#470D47semidirect
367. C2×C47#3349semidirect
407. #470C2×D47semidirect
432. C47C2×#3349semidirect
707. C2#20255913direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156898442
C2×#156898152
#202559132
C2×#156895302
C2×#156894562
C2×#156894632
C2×#156894622
C2×#156894612
C2×#156894282
C2×#156894162
C2×#156893612
C2×#156892302
C2×#156891922
C2×#156891652
C2×#156891582
C2×C47×#4702
C2×#334947