Finite Group Databasebeta

← #26233158

Subgroups — #26233158

Order 12032.

1118 conjugacy classes of subgroups.

The subgroup lattice has 716 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689858C211yesmaximal, characteristic
2C2×#15689254C211yesmaximal, characteristic, complemented
3#20244320C211yesmaximal, characteristic, complemented
4#20244320C211yesmaximal, characteristic, complemented
5#20244315C211yesmaximal, characteristic
6#20244211C211yesmaximal, characteristic
7#20244202C211yesmaximal, characteristic, complemented
8#20244197C211yesmaximal, characteristic, complemented
9#20243400C211yesmaximal, characteristic, complemented
10#20243395C211yesmaximal, characteristic, complemented
11#20243385C211yesmaximal, characteristic, complemented
12#20243221C211yesmaximal, characteristic, complemented
13#20243216C211yesmaximal, characteristic, complemented
14C4×#13093944C211yesmaximal, characteristic, complemented
15C47×#2355C211yesmaximal, characteristic, complemented
16#15689858—24no—
17#15689858C418yescomplemented
18C2×#13094021C2211yescharacteristic
19C2×#13094013—21no—
20C2×#13094012C2211yescharacteristic
21C2×#13094012C2211yescharacteristic
22C2×#13094009—21no—
23C2×#13094009—21no—
24C2×C4×Dic94C2211yescharacteristic
25C2×C4×D188C2211yescharacteristic
26C2×C4×D188C2211yescharacteristic
27C2×#13093986—21no—
28#15689254—24no—
29C2×C4⋊(C47⋊C8)C2211yescharacteristic
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×#13093947C2211yescharacteristic
33C2×#13093947C2211yescharacteristic
34C2×#13093947C2211yescharacteristic
35C2×#13093947C2211yescharacteristic
36C2×#13093944C2211yescharacteristic
37C2×#13093944C2211yescharacteristic
38C2×#13093944C2211yescharacteristic
39C2×#13093944C2211yescharacteristic
40C2×#13093944C2211yescharacteristic
41C2×#13093944C2211yescharacteristic
42C2×#13093944C2211yescharacteristic
43C2×#13093944C2211yescharacteristic
44C2×#13093935C2211yescharacteristic
45C2×#13093935C2211yescharacteristic
46C2×C4×C47⋊C8C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688885C2211yescharacteristic
50#15688885C2211yescharacteristic
51C2×C4×Q8×C47C2211yescharacteristic
52C47×#391—21no—
53C47×#387—21no—
54C47×#387—21no—
55C47×#384C2211yescharacteristic
56C47×#382C2211yescharacteristic
57C47×#382C2211yescharacteristic
58C4×C4⋊C4×C47—21no—
59C4×C4⋊C4×C47C2211yescharacteristic
60C4×C4⋊C4×C47C2211yescharacteristic
61C4×C4⋊C4×C47C2211yescharacteristic
62C22×Dic94C2311yescharacteristic
63C22×D188—21no—
64C22×D188—21no—
65C22×D188C2311yescharacteristic
66C22×D188C2311yescharacteristic
67C22×C4×D47—21no—
68C22×C4×D47—21no—
69C22×C47⋊C8C2311yescharacteristic
70C22×C47⋊C8C2311yescharacteristic
71C22×C47⋊C8C2311yescharacteristic
72C22×C47⋊C8C2311yescharacteristic
73#13094021—22no—
74#13094021C2×C414yes—
75#13094013—28no—
76#13094012—22no—
77#13094012—22no—
78#13094012C2×C414yes—
79#13094012C2×C414yes—
80#13094009—28no—
81#13094009—28no—
82C4×Dic94—22no—
83C4×Dic94C2×C414yes—
84C4×D188—22no—
85C4×D188—22no—
86C4×D188C2×C414yes—
87C4×D188C2×C414yes—
88#13093986—28no—
89C2×C4⋊Dic47C2311yescharacteristic
90C2×Dic47⋊C4—21no—
91C2×(C2×D47)⋊C4—21no—
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×(C2×D47)⋊C4—21no—
96C2×(C2×D47)⋊C4—21no—
97C2×C4×Dic47—21no—
98C4⋊(C47⋊C8)—22no—
99C4⋊(C47⋊C8)—22no—
100C4⋊(C47⋊C8)—22no—
101#13093947—22no—
102#13093947—22no—
103#13093947—41no—
104#13093947—41no—
105#13093944—22no—
106#13093944—22no—
107#13093944—22no—
108#13093944—22no—
109#13093944—41no—
110#13093944—41no—
111#13093944—41no—
112#13093944—41no—
113#13093935—22no—
114#13093935—22no—
115C4×C47⋊C8—22no—
116C22×Q8×C47D411yescharacteristic
117C4×Q8×C47C2×C414yes—
118C4×Q8×C47D414yes—
119C2×C4⋊C4×C47—21no—
120C2×C4⋊C4×C47—21no—
121C2×C4⋊C4×C47D411yescharacteristic
122C2×C4⋊C4×C47D411yescharacteristic
123C2×C4⋊C4×C47D411yescharacteristic
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C42×C47—21no—
129C2×C42×C47—21no—
130C2×C42×C47—21no—
131C2×C42×C47C2311yescharacteristic
132C2×C42×C47C2311yescharacteristic
133C2×C42×C47C2311yescharacteristic
134#95×C47—21no—
135#95×C47—21no—
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141C23×D47—21no—
142C23×D47—21no—
143C2×Q8×C47—41no—
144C2×Q8×C47—41no—
145C2×Q8×C47C22⋊C414yes—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D411yescharacteristic
152C22×C4×C47C2×D411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47C2×D411yescharacteristic
155C22×C4×C47C2×D411yescharacteristic
156C22×C4×C47C2411yescharacteristic
157C22×Dic47—21no—
158C22×Dic47—21no—
159C2×D188—21no—
160C2×D188—21no—
161C2×D188—21no—
162C2×D188—21no—
163C2×D188—21no—
164C2×D188—21no—
165C2×D188—21no—
166C2×D188—21no—
167C2×D188—24no—
168C2×D188—21no—
169C2×D188—21no—
170C2×D188—24no—
171C2×D188—42no—
172C2×D188—42no—
173C2×D188—81no—
174C2×D188—81no—
175C2×D188C22×C412yes—
176C2×D188C22×C412yes—
177C2×C4×D47—24no—
178C2×C4×D47—24no—
179C2×C4×D47—81no—
180C2×C4×D47—81no—
181C2×C4×D47—81no—
182C2×C4×D47—81no—
183C2×Dic94—21no—
184C2×Dic94—21no—
185C2×Dic94—21no—
186C2×Dic94—21no—
187C2×Dic94—21no—
188C2×Dic94C22×C412yes—
189C4⋊C4×C47—21no—
190C4⋊C4×C47—21no—
191C4⋊C4×C47—21no—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47—21no—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—42no—
197C4⋊C4×C47—81no—
198C4⋊C4×C47C22⋊C414yes—
199C4⋊C4×C47C22⋊C414yes—
200C4⋊C4×C47C22⋊C414yes—
201C4⋊C4×C47#4112yes—
202C42×C47—42no—
203C42×C47—81no—
204C42×C47—81no—
205C42×C47C22×C412yes—
206C42×C47C22×C412yes—
207C42×C47C22×C412yes—
208C42×C47C2×D412yes—
209C42×C47C2×D412yes—
210C42×C47C2×D412yes—
211(C2×D47)⋊C4—24no—
212(C2×D47)⋊C4—24no—
213(C2×D47)⋊C4—24no—
214(C2×D47)⋊C4—24no—
215(C2×D47)⋊C4—24no—
216(C2×D47)⋊C4—24no—
217C4⋊Dic47—21no—
218C4⋊Dic47C22×C412yes—
219Dic47⋊C4—24no—
220C4×Dic47—24no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8—21no—
223C2×C47⋊C8—21no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C2×C47⋊C8—21no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8#4112yes—
233C23×C47C22×D411yescharacteristic
234C22×D47—22no—
235C22×D47—22no—
236C22×D47—41no—
237C22×D47—41no—
238C22×D47—41no—
239C22×D47—41no—
240C22×D47—41no—
241C22×D47—41no—
242C22×D47—41no—
243C22×D47—41no—
244C22×D47—41no—
245C22×D47—41no—
246C22×D47—41no—
247C22×D47—41no—
248Q8×C47—44no—
249C2×C4×C47—21no—
250C2×C4×C47—21no—
251C2×C4×C47—21no—
252C2×C4×C47—21no—
253C2×C4×C47—21no—
254C2×C4×C47—21no—
255C2×C4×C47—21no—
256C2×C4×C47—21no—
257C2×C4×C47—21no—
258C2×C4×C47—21no—
259C2×C4×C47—21no—
260C2×C4×C47—21no—
261C2×C4×C47—22no—
262C2×C4×C47—41no—
263C2×C4×C47—41no—
264C2×C4×C47—41no—
265C2×C4×C47—41no—
266C2×C4×C47—41no—
267C2×C4×C47—41no—
268C2×C4×C47—41no—
269C2×C4×C47—41no—
270C2×C4×C47—41no—
271C2×C4×C47—41no—
272C2×C4×C47—41no—
273C2×C4×C47C2×C22⋊C412yes—
274C2×C4×C47C2×C22⋊C412yes—
275C2×C4×C47C2×C22⋊C412yes—
276C2×C4×C47C2×C22⋊C412yes—
277C2×C4×C47C2×C22⋊C412yes—
278C2×C4×C47C2×C22⋊C412yes—
279C2×C4×C47C23×C411yescharacteristic
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C2×#4111yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47H(5,𝔽2)11yescharacteristic
284C2×C4×C472−1+411yescharacteristic
285C2×Dic47—22no—
286C2×Dic47—22no—
287C2×Dic47—41no—
288C2×Dic47—41no—
289C2×Dic47—41no—
290C2×Dic47—41no—
291D188—22no—
292D188—22no—
293D188—22no—
294D188—22no—
295D188—48no—
296D188—41no—
297D188—41no—
298D188—41no—
299D188—41no—
300D188—84no—
301C4×D47—84no—
302C4×D47—84no—
303Dic94—22no—
304Dic94—22no—
305Dic94—41no—
306Dic94—41no—
307C47⋊C8—22no—
308C47⋊C8—41no—
309C47⋊C8—41no—
310C47⋊C8—41no—
311#22549—471nomaximal, Sylow
312C22×C47C22×C22⋊C411yescharacteristic
313C22×C47#54811yescharacteristic
314C22×C47#55011yescharacteristic
315C22×C47#57511yescharacteristic
316C22×C47#57511yescharacteristic
317C22×C47#57611yescharacteristic
318C22×C47#57711yescharacteristic
319C2×D47—42no—
320C2×D47—42no—
321C2×D47—42no—
322C2×D47—42no—
323C2×D47—42no—
324C2×D47—42no—
325C2×D47—81no—
326C2×D47—81no—
327C2×D47—81no—
328C2×D47—81no—
329C2×D47—81no—
330C2×D47—81no—
331C2×D47—81no—
332C2×D47—81no—
333C4×C47—22no—
334C4×C47—22no—
335C4×C47—22no—
336C4×C47—22no—
337C4×C47—22no—
338C4×C47—22no—
339C4×C47—42no—
340C4×C47—81no—
341C4×C47—81no—
342C4×C47—81no—
343C4×C47C4×#4111yescharacteristic
344C4×C47#52011yescharacteristic
345C4×C47#54811yescharacteristic
346C4×C47#55011yescharacteristic
347Dic47—42no—
348Dic47—42no—
349C2×#559—471no—
350C2×#446—471no—
351#2355D4711yescharacteristic, complemented
352#1983—471no—
353#1983—471no—
354#1982—471no—
355#1961—471no—
356#1959—471no—
357#1958—471no—
358#1805—471no—
359#1804—471no—
360#1802—471no—
361#1763—471no—
362#1762—471no—
363C4×#102—471no—
364C2×C47#234111yescharacteristic
365C2×C47#289611yescharacteristic
366C2×C47#289711yescharacteristic
367C2×C47#337011yescharacteristic
368C2×C47#337111yescharacteristic
369C2×C47#340111yescharacteristic
370C2×C47#340311yescharacteristic
371D47—82no—
372D47—82no—
373#559—478no—
374#559—944no—
375C2×#127—471no—
376C2×#124—471no—
377C2×#124—471no—
378C2×#124—941no—
379C2×#123—941no—
380C2×#123—941no—
381C2×C4×Q8—471no—
382C2×C4×Q8C2×D4711yescharacteristic
383C2×C4×D4—471no—
384C2×C4×D4—471no—
385C2×C4×D4—941no—
386#446—944no—
387C2×C4⋊C8—471no—
388C2×C4⋊C8—471no—
389C2×C4⋊C8—471no—
390C2×#103—471no—
391C2×#103—471no—
392C2×#103—471no—
393C2×#103—471no—
394C2×#102—471no—
395C2×#102—471no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102—471no—
401C2×#102—471no—
402C2×#97—471no—
403C2×#97—471no—
404C2×C4×C8—471no—
405#391—21no—
406#387—21no—
407#387—21no—
408#384C2×D4711yescharacteristic
409#382C2×D4711yescharacteristic
410#382C2×D4711yescharacteristic
411C4×C4⋊C4—21no—
412C4×C4⋊C4C2×D4711yescharacteristic
413C4×C4⋊C4C2×D4711yescharacteristic
414C4×C4⋊C4C2×D4711yescharacteristic
415#340—471no—
416#340—471no—
417#340—471no—
418#340—471no—
419C47#2254911yescharacteristic, complemented, Sylow
420C22×Q8—471no—
421C22×Q8C22⋊D4711yescharacteristic
422C22×D4—471no—
423C22×D4—471no—
424C22×D4—941no—
425C22×D4—941no—
426C23×C4—941no—
427C23×C4—941no—
428C22×C8—471no—
429C22×C8—471no—
430C22×C8—471no—
431C22×C8—471no—
432#127—474no—
433#127—942no—
434#124—474no—
435#124—474no—
436#124—948no—
437#124—942no—
438#124—942no—
439#123—948no—
440#123—948no—
441C4×Q8—474no—
442C4×Q8—942no—
443C4×Q8C4×D4714yes—
444C4×Q8D18814yes—
445C4×D4—474no—
446C4×D4—474no—
447C4×D4—948no—
448C4×D4—942no—
449C4×D4—942no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—471no—
453C2×C4⋊C4—941no—
454C2×C4⋊C4C22⋊D4711yescharacteristic
455C2×C4⋊C4C22⋊D4711yescharacteristic
456C2×C4⋊C4C22⋊D4711yescharacteristic
457C2×C4⋊C4C22×D4711yescharacteristic
458C2×C4⋊C4C22×D4711yescharacteristic
459C2×C4⋊C4C22×D4711yescharacteristic
460C2×C4⋊C4C22×D4711yescharacteristic
461C2×C22⋊C4—941no—
462C2×C22⋊C4—941no—
463C2×C22⋊C4—941no—
464C2×C22⋊C4—941no—
465C2×C22⋊C4—941no—
466C2×C22⋊C4—941no—
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—21no—
470C2×C42—941no—
471C2×C42C22×D4711yescharacteristic
472C2×C42C22×D4711yescharacteristic
473C2×C42C22×D4711yescharacteristic
474C4⋊C8—942no—
475C4⋊C8—942no—
476C4⋊C8—942no—
477#103—942no—
478#103—942no—
479#103—1881no—
480#103—1881no—
481#102—942no—
482#102—942no—
483#102—942no—
484#102—942no—
485#102—1881no—
486#102—1881no—
487#102—1881no—
488#102—1881no—
489#97—942no—
490#97—942no—
491C4×C8—942no—
492#95—21no—
493#95—21no—
494#95—21no—
495#95—21no—
496#95—21no—
497#95—21no—
498#95—21no—
499C24—941no—
500C24—941no—
501C2×Q8—41no—
502C2×Q8—41no—
503C2×Q8—472no—
504C2×Q8—941no—
505C2×Q8—941no—
506C2×Q8—941no—
507C2×Q8—941no—
508C2×Q8—941no—
509C2×Q8(C2×D47)⋊C414yes—
510C2×D4—472no—
511C2×D4—472no—
512C2×D4—944no—
513C2×D4—944no—
514C2×D4—941no—
515C2×D4—941no—
516C2×D4—941no—
517C2×D4—941no—
518C2×D4—941no—
519C2×D4—941no—
520C2×D4—941no—
521C2×D4—941no—
522C2×D4—941no—
523C2×D4—941no—
524C2×D4—3761no—
525C2×D4—3761no—
526C2×D4—1882no—
527C2×D4—1882no—
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—941no—
533C22×C4—941no—
534C22×C4—944no—
535C22×C4—944no—
536C22×C4—3761no—
537C22×C4—3761no—
538C22×C4—3761no—
539C22×C4—3761no—
540C22×C4C2×C22⋊D4711yescharacteristic
541C22×C4C2×C22⋊D4711yescharacteristic
542C22×C4C2×C22⋊D4711yescharacteristic
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C2×C22⋊D4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C23×D4711yescharacteristic
547C2×C8—472no—
548C2×C8—941no—
549C2×C8—941no—
550C2×C8—941no—
551C2×C8—941no—
552C2×C8—941no—
553C2×C8—941no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C4⋊C4—21no—
560C4⋊C4—21no—
561C4⋊C4—21no—
562C4⋊C4—21no—
563C4⋊C4—21no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—42no—
567C4⋊C4—81no—
568C4⋊C4—472no—
569C4⋊C4—944no—
570C4⋊C4—941no—
571C4⋊C4(C2×D47)⋊C414yes—
572C4⋊C4(C2×D47)⋊C414yes—
573C4⋊C4(C2×D47)⋊C414yes—
574C4⋊C4#1062535412yes—
575C22⋊C4—944no—
576C22⋊C4—944no—
577C22⋊C4—944no—
578C22⋊C4—944no—
579C22⋊C4—944no—
580C22⋊C4—944no—
581C42—42no—
582C42—81no—
583C42—81no—
584C42—944no—
585C42C2×C4×D4712yes—
586C42C2×C4×D4712yes—
587C42C2×C4×D4712yes—
588C42C2×D18812yes—
589C42C2×D18812yes—
590C42C2×D18812yes—
591C23—942no—
592C23—942no—
593C23—1881no—
594C23—1881no—
595C23—1881no—
596C23—1881no—
597C23—1881no—
598C23—1881no—
599C23—1881no—
600C23—1881no—
601C23—1881no—
602C23—1881no—
603C23—1881no—
604C23—1881no—
605C23C22×C22⋊D4711yescharacteristic
606Q8—44no—
607Q8—942no—
608Q8—942no—
609Q8—1881no—
610Q8—1881no—
611D4—942no—
612D4—942no—
613D4—942no—
614D4—942no—
615D4—3764no—
616D4—1888no—
617D4—1881no—
618D4—1881no—
619D4—1881no—
620D4—1881no—
621C2×C4—21no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—21no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—22no—
634C2×C4—41no—
635C2×C4—41no—
636C2×C4—41no—
637C2×C4—41no—
638C2×C4—41no—
639C2×C4—41no—
640C2×C4—41no—
641C2×C4—41no—
642C2×C4—41no—
643C2×C4—41no—
644C2×C4—41no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—3764no—
648C2×C4—3764no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4C2×(C2×D47)⋊C412yes—
654C2×C4C2×(C2×D47)⋊C412yes—
655C2×C4C2×(C2×D47)⋊C412yes—
656C2×C4C2×(C2×D47)⋊C412yes—
657C2×C4C2×(C2×D47)⋊C412yes—
658C2×C4C2×(C2×D47)⋊C412yes—
659C2×C4C22×C4×D4711yescharacteristic
660C2×C4C22×D18811yescharacteristic
661C2×C4#41×D4711yescharacteristic
662C2×C4C2×#1062535411yescharacteristic
663C2×C4#1309407011yescharacteristic
664C2×C4#1309407211yescharacteristic
665C8—942no—
666C8—1881no—
667C8—1881no—
668C8—1881no—
669C22—3761no—
670C22—3761no—
671C22—3761no—
672C22—3761no—
673C22—3761no—
674C22—3761no—
675C22—3761no—
676C22—3761no—
677C22—1882no—
678C22—1882no—
679C22—1882no—
680C22—1882no—
681C22—1882no—
682C22—1882no—
683C22C22×(C2×D47)⋊C411yescharacteristic
684C22#1568978411yescharacteristic
685C22#1568979211yescharacteristic
686C22#1568992111yescharacteristic
687C22#1568992111yescharacteristic
688C22#1568992611yescharacteristic
689C22#1568993111yescharacteristic
690C4—22no—
691C4—22no—
692C4—22no—
693C4—22no—
694C4—22no—
695C4—22no—
696C4—42no—
697C4—81no—
698C4—81no—
699C4—81no—
700C4—1882no—
701C4—1882no—
702C4C4×#1062535411yescharacteristic
703C4#1568960511yescharacteristic
704C4#1568978511yescharacteristic
705C4#1568979511yescharacteristic
706C2—3762no—
707C2—3762no—
708C2#2024622611yescharacteristic
709C2#2025190511yescharacteristic
710C2#2025191111yescharacteristic
711C2#2025614111yescharacteristic
712C2#2025615611yescharacteristic
713C2#2025645411yescharacteristic
714C2#2025647211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#2355C2
socleC23×C47C22×D4
prime radicalC2×#13094021C22
cosocleC22×C4×C47C24
hypercenter#2355D47
hypocenterC47#22549
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ #2355

Complements

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

NH ≅ G/Ntype
2. C2×#15689254C2semidirect
3. #20244320C2semidirect
4. #20244320C2semidirect
7. #20244202C2semidirect
8. #20244197C2semidirect
9. #20243400C2semidirect
10. #20243395C2semidirect
11. #20243385C2semidirect
12. #20243221C2semidirect
13. #20243216C2semidirect
14. C4×#13093944C2semidirect
15. C47×#2355C2semidirect
17. #15689858C4semidirect
351. #2355D47semidirect
419. C47#22549semidirect

Maximal subgroups

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

subgroupindex
C2×#156898582
C2×#156892542
#202443202
#202443152
#202442112
#202442022
#202441972
#202434002
#202433952
#202433852
#202432212
#202432162
C4×#130939442
C47×#23552
#2254947