Finite Group Databasebeta

← #26236606

Subgroups — #26236606

Order 12032.

1086 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689279C211yesmaximal, characteristic
2C2×#15689228C211yesmaximal, characteristic, complemented
3C22×#13093948C211yesmaximal, characteristic
4#20246391C211yesmaximal, characteristic
5#20244258C211yesmaximal, characteristic, complemented
6#20244081C211yesmaximal, characteristic, complemented
7#20244019C211yesmaximal, characteristic, complemented
8#20243809C211yesmaximal, characteristic
9#20243732C211yesmaximal, characteristic, complemented
10#20243729C211yesmaximal, characteristic, complemented
11#20243656C211yesmaximal, characteristic, complemented
12#20243580C211yesmaximal, characteristic
13#20243218C211yesmaximal, characteristic, complemented
14#20243166C211yesmaximal, characteristic
15Q8×C22⋊C4×C47C211yesmaximal, characteristic
16C22×#10625337C2211yescharacteristic
17C22×#10625337C2211yescharacteristic
18C23×C47⋊C8C2211yescharacteristic
19C2×#13094003C2211yescharacteristic
20C2×C4×Dic94C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22#15689279C418yescomplemented
23#15689228—24no—
24C2×#13093955C2211yescharacteristic
25C2×#13093955C2211yescharacteristic
26C2×#13093948—24no—
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093948C2211yescharacteristic
32C2×#13093948C2211yescharacteristic
33C2×#13093947C2211yescharacteristic
34C2×#13093947C2211yescharacteristic
35C2×C22⋊(C47⋊C8)C2211yescharacteristic
36C2×#13093935C2211yescharacteristic
37C2×#13093935C2211yescharacteristic
38#15689029C2211yescharacteristic
39#15689021C2211yescharacteristic
40#15689020—21no—
41#15689010—21no—
42#15688995—21no—
43C4×C4⋊Dic47C2211yescharacteristic
44C22⋊C4×Dic47—21no—
45#15688885C2211yescharacteristic
46#15688885C2211yescharacteristic
47#15688885C2211yescharacteristic
48#15688885C2211yescharacteristic
49#15688878C2211yescharacteristic
50#15688878C2211yescharacteristic
51C23×Q8×C47C2211yescharacteristic
52C2×C4×Q8×C47C2211yescharacteristic
53C2×C4×Q8×C47C2211yescharacteristic
54C47×#391—21no—
55C47×#391—21no—
56C47×#391C2211yescharacteristic
57C47×#391C2211yescharacteristic
58C47×#380—21no—
59C47×#380C2211yescharacteristic
60C4×C22⋊C4×C47—21no—
61C4×C22⋊C4×C47C2211yescharacteristic
62C22×Dic94C2311yescharacteristic
63C23×Dic47—21no—
64C2×#10625337—22no—
65C2×#10625337—22no—
66C2×#10625337—41no—
67C2×#10625337—41no—
68C2×#10625337C2×C414yescomplemented
69C2×#10625337C2×C414yescomplemented
70C22×C47⋊C8—22no—
71C22×C47⋊C8—22no—
72C22×C47⋊C8—41no—
73C22×C47⋊C8C2311yescharacteristic
74C22×C47⋊C8C2311yescharacteristic
75C22×C47⋊C8C2311yescharacteristic
76C22×C47⋊C8C2311yescharacteristic
77#13094003—22no—
78#13094003C2×C414yes—
79C4×Dic94—22no—
80C4×Dic94—41no—
81C2×C4⋊Dic47—22no—
82C2×C4⋊Dic47—21no—
83C2×C4⋊Dic47—41no—
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C4⋊Dic47C2311yescharacteristic
86C2×C4⋊Dic47C2311yescharacteristic
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4—21no—
89C2×Dic47⋊C4—21no—
90C2×C22⋊Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47—21no—
93#13093955—22no—
94#13093955—41no—
95#13093948—22no—
96#13093948—22no—
97#13093948—22no—
98#13093948C2×C414yescomplemented
99#13093948C2×C414yescomplemented
100#13093948D414yes—
101#13093947—22no—
102#13093947—41no—
103C22⋊(C47⋊C8)C2×C414yes—
104#13093935—22no—
105#13093935—41no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C22×Q8×C47—21no—
111C22×Q8×C47—22no—
112C22×Q8×C47—22no—
113C22×Q8×C47—22no—
114C22×Q8×C47—41no—
115C22×Q8×C47—41no—
116C22×Q8×C47C2×C414yes—
117C22×Q8×C47C2311yescharacteristic
118C22×Q8×C47C2311yescharacteristic
119C23×C4×C47—21no—
120C23×C4×C47C2311yescharacteristic
121C4×Q8×C47—22no—
122C4×Q8×C47—22no—
123C4×Q8×C47—41no—
124C4×Q8×C47—41no—
125C2×C4⋊C4×C47—21no—
126C2×C4⋊C4×C47—21no—
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C4⋊C4×C47C2311yescharacteristic
129C2×C22⋊C4×C47—21no—
130C2×C22⋊C4×C47D411yescharacteristic
131C2×C22⋊C4×C47D411yescharacteristic
132C2×C42×C47—21no—
133C2×C42×C47—21no—
134C2×C42×C47C2311yescharacteristic
135C2×C42×C47C2311yescharacteristic
136#95×C47—21no—
137#95×C47—21no—
138#95×C47—21no—
139#95×C47—21no—
140#95×C47—21no—
141#95×C47D411yescharacteristic
142#95×C47D411yescharacteristic
143C24×C47C2×D411yescharacteristic
144C2×Q8×C47—24no—
145C2×Q8×C47—21no—
146C2×Q8×C47—21no—
147C2×Q8×C47—21no—
148C2×Q8×C47—21no—
149C2×Q8×C47—28no—
150C2×Q8×C47—21no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—42no—
155C2×Q8×C47—42no—
156C2×Q8×C47—44no—
157C2×Q8×C47—44no—
158C2×Q8×C47—44no—
159C2×Q8×C47C22×C412yes—
160C2×Q8×C47C22×C412yes—
161C2×Q8×C47C2×D412yes—
162C2×Q8×C47#4112yes—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47—21no—
168C22×C4×C47—24no—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—42no—
173C22×C4×C47—42no—
174C22×C4×C47C22×C412yes—
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47C2×D411yescharacteristic
180C22×C4×C47#4112yes—
181C22×C4×C47C2411yescharacteristic
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—42no—
187C22×Dic47—42no—
188C22×Dic47—81no—
189C2×Dic94—21no—
190C2×Dic94—21no—
191C2×Dic94—21no—
192C2×Dic94—21no—
193C2×Dic94—21no—
194C2×Dic94C22×C412yes—
195C4⋊C4×C47—21no—
196C4⋊C4×C47—21no—
197C4⋊C4×C47—21no—
198C4⋊C4×C47—21no—
199C4⋊C4×C47—42no—
200C4⋊C4×C47—42no—
201C22⋊C4×C47—22no—
202C22⋊C4×C47—22no—
203C22⋊C4×C47—42no—
204C42×C47—21no—
205C42×C47—21no—
206C42×C47—21no—
207C42×C47—21no—
208C42×C47—42no—
209C42×C47—42no—
210C22⋊Dic47—24no—
211#10625337—28no—
212#10625337—44no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—42no—
218C4⋊Dic47C22×C412yes—
219C4⋊Dic47C2×D412yes—
220Dic47⋊C4—24no—
221Dic47⋊C4—42no—
222Dic47⋊C4—81no—
223C4×Dic47—42no—
224C4×Dic47—81no—
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—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—44no—
235C2×C47⋊C8C22×C412yes—
236C2×C47⋊C8C22×C412yes—
237C2×C47⋊C8C2×D412yes—
238C23×C47—21no—
239C23×C47—21no—
240C23×C47—21no—
241C23×C47—21no—
242C23×C47C4×D412yes—
243C23×C47#13712yes—
244C23×C47#13712yes—
245C23×C47C22×D411yescharacteristic
246Q8×C47—22no—
247Q8×C47—22no—
248Q8×C47—22no—
249Q8×C47—22no—
250Q8×C47—22no—
251Q8×C47—48no—
252Q8×C47—41no—
253Q8×C47—41no—
254Q8×C47C4×D414yes—
255C2×C4×C47—22no—
256C2×C4×C47—21no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—21no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—21no—
266C2×C4×C47—21no—
267C2×C4×C47—21no—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—21no—
271C2×C4×C47—21no—
272C2×C4×C47—21no—
273C2×C4×C47—21no—
274C2×C4×C47—21no—
275C2×C4×C47—21no—
276C2×C4×C47—21no—
277C2×C4×C47—48no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47C4×D412yes—
287C2×C4×C47C23×C411yescharacteristic
288C2×C4×C47C22×D411yescharacteristic
289C2×C4×C47C2×#4111yescharacteristic
290C2×C4×C47C2×#4111yescharacteristic
291C2×C4×C47H(5,𝔽2)11yescharacteristic
292C2×C4×C47H(5,𝔽2)11yescharacteristic
293C2×Dic47—22no—
294C2×Dic47—22no—
295C2×Dic47—22no—
296C2×Dic47—41no—
297C2×Dic47—41no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—84no—
306Dic94—22no—
307Dic94—22no—
308Dic94—41no—
309Dic94—41no—
310C47⋊C8—22no—
311C47⋊C8—22no—
312C47⋊C8—22no—
313C47⋊C8—41no—
314#22859—471nomaximal, Sylow
315C22×C47—22no—
316C22×C47—22no—
317C22×C47—22no—
318C22×C47—22no—
319C22×C47—22no—
320C22×C47—22no—
321C22×C47#44114yescomplemented
322C22×C47C2×C4×D411yescharacteristic
323C22×C47D4211yescharacteristic
324C22×C47#54611yescharacteristic
325C22×C47C2×#13711yescharacteristic
326C22×C47C2×#13711yescharacteristic
327C22×C47#57711yescharacteristic
328C22×C47#57811yescharacteristic
329C4×C47—22no—
330C4×C47—24no—
331C4×C47—42no—
332C4×C47—41no—
333C4×C47—41no—
334C4×C47—41no—
335C4×C47—41no—
336C4×C47—81no—
337C4×C47—81no—
338C4×C47C2×C4×D411yescharacteristic
339C4×C47#51811yescharacteristic
340C4×C47#54611yescharacteristic
341C4×C47#55111yescharacteristic
342Dic47—42no—
343Dic47—42no—
344Dic47—42no—
345Dic47—81no—
346C2×#451—471no—
347C2×#441—471no—
348C22×#103—471no—
349#2360—471no—
350Q8×C22⋊C4D4711yescharacteristic
351#1971—471no—
352#1935—471no—
353#1927—471no—
354#1892—471no—
355#1878—471no—
356#1878—471no—
357#1865—471no—
358#1853—471no—
359#1763—471no—
360#1752—471no—
361C2×C47—24no—
362C2×C47#235811yescharacteristic
363C2×C47C2×#44111yescharacteristic
364C2×C47#294711yescharacteristic
365C2×C47#326611yescharacteristic
366C2×C47#327011yescharacteristic
367C2×C47#331211yescharacteristic
368C2×C47#331611yescharacteristic
369C23×Q8C2×D4711yescharacteristic
370C22×Q16—471no—
371C22×Q16—471no—
372C23×C8—471no—
373C2×C22⋊Q8—471no—
374C2×C4×Q8—471no—
375C2×C4×Q8C2×D4711yescharacteristic
376C2×C4×Q8C2×D4711yescharacteristic
377C22×C4⋊C4—471no—
378#451—478no—
379#441—944no—
380C2×#106—471no—
381C2×#106—471no—
382C2×#103—471no—
383C2×#103—471no—
384C2×#103—471no—
385C2×#103—471no—
386C2×#103—471no—
387C2×#103—471no—
388C2×#103—471no—
389C2×#103—471no—
390C2×#103—944no—
391C2×C22⋊C8—471no—
392C2×#97—471no—
393C2×#97—471no—
394#391—21no—
395#391—21no—
396#391—471no—
397#391C2×D4711yescharacteristic
398#391C2×D4711yescharacteristic
399#389—471no—
400#389—941no—
401#387—941no—
402#385—941no—
403#380—21no—
404#380C2×D4711yescharacteristic
405C4×C4⋊C4—471no—
406C4×C22⋊C4—21no—
407C4×C22⋊C4—941no—
408C4×C22⋊C4C2×D4711yescharacteristic
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#336—471no—
414#336—471no—
415C47#2285911yescharacteristic, complemented, Sylow
416C22×Q8—22no—
417C22×Q8—21no—
418C22×Q8—22no—
419C22×Q8—22no—
420C22×Q8—41no—
421C22×Q8—41no—
422C22×Q8—471no—
423C22×Q8C4×D4714yes—
424C22×Q8C22×D4711yescharacteristic
425C22×Q8C22×D4711yescharacteristic
426C23×C4—21no—
427C23×C4—941no—
428C23×C4C22×D4711yescharacteristic
429C2×Q16—474no—
430C2×Q16—474no—
431C2×Q16—942no—
432C2×Q16—942no—
433C2×Q16—1881no—
434C2×Q16—1881no—
435C22×C8—471no—
436C22×C8—471no—
437C22×C8—471no—
438C22×C8—471no—
439C22×C8—942no—
440C22×C8—942no—
441C22×C8—1881no—
442C22⋊Q8—474no—
443C22⋊Q8—942no—
444C4×Q8—22no—
445C4×Q8—22no—
446C4×Q8—41no—
447C4×Q8—41no—
448C4×Q8—942no—
449C4×Q8—1881no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—21no—
452C2×C4⋊C4—471no—
453C2×C4⋊C4—471no—
454C2×C4⋊C4—471no—
455C2×C4⋊C4—942no—
456C2×C4⋊C4—941no—
457C2×C4⋊C4—941no—
458C2×C4⋊C4—941no—
459C2×C4⋊C4—941no—
460C2×C4⋊C4—1881no—
461C2×C4⋊C4C22×D4711yescharacteristic
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—941no—
465C2×C22⋊C4C22⋊D4711yescharacteristic
466C2×C22⋊C4C22⋊D4711yescharacteristic
467C2×C42—21no—
468C2×C42—21no—
469C2×C42—941no—
470C2×C42—941no—
471C2×C42C22×D4711yescharacteristic
472C2×C42C22×D4711yescharacteristic
473#106—942no—
474#106—1881no—
475#103—474no—
476#103—474no—
477#103—474no—
478#103—942no—
479#103—942no—
480#103—942no—
481#103—942no—
482#103—1881no—
483C22⋊C8—474no—
484#97—942no—
485#97—1881no—
486#95—21no—
487#95—21no—
488#95—21no—
489#95—21no—
490#95—21no—
491#95—941no—
492#95—941no—
493#95—941no—
494#95—941no—
495#95C22⋊D4711yescharacteristic
496#95C22⋊D4711yescharacteristic
497C24C2×C22⋊D4711yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—28no—
504C2×Q8—21no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—42no—
509C2×Q8—42no—
510C2×Q8—44no—
511C2×Q8—44no—
512C2×Q8—44no—
513C2×Q8—472no—
514C2×Q8—941no—
515C2×Q8—941no—
516C2×Q8—941no—
517C2×Q8—941no—
518C2×Q8—941no—
519C2×Q8C2×C4×D4712yes—
520C2×Q8C2×C4×D4712yes—
521C2×Q8D4×D4712yes—
522C2×Q8#1062535212yes—
523C22×C4—21no—
524C22×C4—21no—
525C22×C4—21no—
526C22×C4—21no—
527C22×C4—21no—
528C22×C4—24no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—42no—
533C22×C4—42no—
534C22×C4—941no—
535C22×C4—941no—
536C22×C4—941no—
537C22×C4—941no—
538C22×C4—3761no—
539C22×C4—1882no—
540C22×C4—1882no—
541C22×C4C2×C4×D4712yes—
542C22×C4#1062535012yes—
543C22×C4C2×C22⋊D4711yescharacteristic
544C22×C4C2×C22⋊D4711yescharacteristic
545C22×C4C2×C22⋊D4711yescharacteristic
546C22×C4C2×C22⋊D4711yescharacteristic
547C22×C4C2×C22⋊D4711yescharacteristic
548C22×C4C23×D4711yescharacteristic
549Q16—948no—
550Q16—1884no—
551C2×C8—472no—
552C2×C8—472no—
553C2×C8—472no—
554C2×C8—941no—
555C2×C8—941no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—941no—
563C2×C8—1884no—
564C4⋊C4—21no—
565C4⋊C4—21no—
566C4⋊C4—21no—
567C4⋊C4—21no—
568C4⋊C4—42no—
569C4⋊C4—42no—
570C4⋊C4—472no—
571C4⋊C4—472no—
572C4⋊C4—944no—
573C4⋊C4—941no—
574C4⋊C4—941no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—3761no—
578C4⋊C4—1882no—
579C4⋊C4—1882no—
580C22⋊C4—22no—
581C22⋊C4—22no—
582C22⋊C4—42no—
583C22⋊C4—944no—
584C42—21no—
585C42—21no—
586C42—21no—
587C42—21no—
588C42—42no—
589C42—42no—
590C42—3761no—
591C42—1882no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23C4×C22⋊D4712yes—
597C23#1309405412yes—
598C23#1309405512yes—
599C23C22×C22⋊D4711yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—48no—
606Q8—41no—
607Q8—41no—
608Q8—942no—
609Q8—942no—
610Q8—1881no—
611Q8—1881no—
612Q8(C22⋊D47)⋊C414yes—
613C2×C4—22no—
614C2×C4—21no—
615C2×C4—22no—
616C2×C4—21no—
617C2×C4—22no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—21no—
623C2×C4—21no—
624C2×C4—21no—
625C2×C4—21no—
626C2×C4—22no—
627C2×C4—21no—
628C2×C4—21no—
629C2×C4—21no—
630C2×C4—21no—
631C2×C4—21no—
632C2×C4—21no—
633C2×C4—21no—
634C2×C4—21no—
635C2×C4—48no—
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—942no—
645C2×C4—942no—
646C2×C4—942no—
647C2×C4—3764no—
648C2×C4—1881no—
649C2×C4—1881no—
650C2×C4—1881no—
651C2×C4—1881no—
652C2×C4—1881no—
653C2×C4—1881no—
654C2×C4—1881no—
655C2×C4—1881no—
656C2×C4—1881no—
657C2×C4C4×C22⋊D4712yes—
658C2×C4C22×C4×D4711yescharacteristic
659C2×C4C2×D4×D4711yescharacteristic
660C2×C4C2×#1062535211yescharacteristic
661C2×C4C2×#1062535011yescharacteristic
662C2×C4#1309406911yescharacteristic
663C2×C4#1309406911yescharacteristic
664C8—942no—
665C8—942no—
666C8—942no—
667C8—1881no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22#1568922814yescomplemented
675C22C2×C4×C22⋊D4711yescharacteristic
676C22D4×C22⋊D4711yescharacteristic
677C22#1568976711yescharacteristic
678C22C2×#1309405411yescharacteristic
679C22C2×#1309405511yescharacteristic
680C22#1568993111yescharacteristic
681C22#1568993811yescharacteristic
682C4—22no—
683C4—24no—
684C4—41no—
685C4—42no—
686C4—41no—
687C4—41no—
688C4—41no—
689C4—81no—
690C4—81no—
691C4—3761no—
692C4—1882no—
693C4—1882no—
694C4—1882no—
695C4C2×(C22⋊D47)⋊C411yescharacteristic
696C4#1568959611yescharacteristic
697C4#1568976311yescharacteristic
698C4#1568979911yescharacteristic
699C2—24no—
700C2#2024636711yescharacteristic
701C2C2×#1568922811yescharacteristic
702C2#2025223111yescharacteristic
703C2#2025489911yescharacteristic
704C2#2025495411yescharacteristic
705C2#2025543911yescharacteristic
706C2#2025549911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingQ8×C22⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterQ8×C22⋊C4D47
hypocenterC47#22859
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ Q8×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C2×#15689228C2semidirect
5. #20244258C2semidirect
6. #20244081C2semidirect
7. #20244019C2semidirect
9. #20243732C2semidirect
10. #20243729C2semidirect
11. #20243656C2semidirect
13. #20243218C2semidirect
22. #15689279C4semidirect
68. C2×#10625337C2×C4semidirect
69. C2×#10625337C2×C4semidirect
98. #13093948C2×C4semidirect
99. #13093948C2×C4semidirect
321. C22×C47#441semidirect
415. C47#22859semidirect
674. C22#15689228semidirect

Maximal subgroups

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

subgroupindex
C2×#156892792
C2×#156892282
C22×#130939482
#202463912
#202442582
#202440812
#202440192
#202438092
#202437322
#202437292
#202436562
#202435802
#202432182
#202431662
Q8×C22⋊C4×C472
#2285947