Finite Group Databasebeta

← #26236614

Subgroups — #26236614

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×#15689230C211yesmaximal, characteristic, complemented
2C22×#13093948C211yesmaximal, characteristic
3#20246397C211yesmaximal, characteristic
4Q8×C22⋊Dic47C211yesmaximal, characteristic
5#20244260C211yesmaximal, characteristic, complemented
6#20244080C211yesmaximal, characteristic, complemented
7#20244024C211yesmaximal, characteristic, complemented
8#20243812C211yesmaximal, characteristic
9#20243731C211yesmaximal, characteristic, complemented
10#20243731C211yesmaximal, characteristic, complemented
11#20243658C211yesmaximal, characteristic, complemented
12#20243583C211yesmaximal, characteristic
13#20243220C211yesmaximal, characteristic, complemented
14#20243167C211yesmaximal, characteristic
15C2×C47×#451C211yesmaximal, characteristic
16C23×C47⋊C8C2211yescharacteristic
17C2×Q8×Dic47C2211yescharacteristic
18C2×Q8×Dic47C2211yescharacteristic
19C2×Q8×Dic47C2211yescharacteristic
20C22×C4⋊Dic47C2211yescharacteristic
21#15689230—24no—
22C2×#13093956C2211yescharacteristic
23C2×#13093956C2211yescharacteristic
24C2×#13093948—24no—
25C2×#13093948C2211yescharacteristic
26C2×#13093948C2211yescharacteristic
27C2×#13093948C2211yescharacteristic
28C2×#13093948C2211yescharacteristic
29C2×#13093948C2211yescharacteristic
30C2×#13093948C2211yescharacteristic
31C2×#13093934C2211yescharacteristic
32C2×#13093934C2211yescharacteristic
33#15689030—21no—
34#15689030—21no—
35#15689030C2211yescharacteristic
36#15689030C2211yescharacteristic
37#15689030C2211yescharacteristic
38#15689022—21no—
39#15689022C2211yescharacteristic
40#15689009—21no—
41#15688998—21no—
42#15688983—21no—
43#15688983C2211yescharacteristic
44C4⋊C4×Dic47C2211yescharacteristic
45C22⋊C4×Dic47—21no—
46C4×C22⋊Dic47—21no—
47C4×C22⋊Dic47C2211yescharacteristic
48#15688886C2211yescharacteristic
49#15688886C2211yescharacteristic
50#15688885C2211yescharacteristic
51#15688885C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C23×Q8×C47C2211yescharacteristic
55C22×Q16×C47C2211yescharacteristic
56C22×Q16×C47C2211yescharacteristic
57C2×C22⋊Q8×C47C2211yescharacteristic
58C47×#451C418yescomplemented
59C2×#103×C47C2211yescharacteristic
60C2×#103×C47C2211yescharacteristic
61C2×C22⋊C8×C47C2211yescharacteristic
62C23×Dic47—21no—
63C22×C47⋊C8—22no—
64C22×C47⋊C8—22no—
65C22×C47⋊C8—41no—
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68Q8×Dic47—22no—
69Q8×Dic47—22no—
70Q8×Dic47—22no—
71Q8×Dic47—41no—
72Q8×Dic47—41no—
73Q8×Dic47—41no—
74C2×C4⋊Dic47—22no—
75C2×C4⋊Dic47—21no—
76C2×C4⋊Dic47—21no—
77C2×C4⋊Dic47—21no—
78C2×C4⋊Dic47—21no—
79C2×C4⋊Dic47—21no—
80C2×C4⋊Dic47—41no—
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×C4⋊Dic47C2311yescharacteristic
85C2×C22⋊Dic47—21no—
86C2×C22⋊Dic47D411yescharacteristic
87C2×C22⋊Dic47D411yescharacteristic
88C2×C4×Dic47—21no—
89C2×C4×Dic47—21no—
90C2×C4×Dic47—21no—
91C2×C4×Dic47—21no—
92C2×C4×Dic47C2311yescharacteristic
93C2×C4×Dic47C2311yescharacteristic
94#13093956—22no—
95#13093956—41no—
96#13093948—22no—
97#13093948—22no—
98#13093948—22no—
99#13093948—22no—
100#13093948—41no—
101#13093948D414yes—
102#13093934—22no—
103#13093934—41no—
104C47⋊#95—21no—
105C47⋊#95—21no—
106C47⋊#95—21no—
107C47⋊#95—21no—
108C47⋊#95—21no—
109C47⋊#95—21no—
110C47⋊#95—21no—
111C47⋊#95—21no—
112C47⋊#95—21no—
113C47⋊#95D411yescharacteristic
114C47⋊#95D411yescharacteristic
115C22×Q8×C47—21no—
116C22×Q8×C47—22no—
117C22×Q8×C47—22no—
118C22×Q8×C47—22no—
119C22×Q8×C47—41no—
120C22×Q8×C47—41no—
121C22×Q8×C47C2×C414yes—
122C22×Q8×C47C2311yescharacteristic
123C22×Q8×C47C2311yescharacteristic
124C22×Q8×C47C2311yescharacteristic
125C23×C4×C47—21no—
126C23×C4×C47C2311yescharacteristic
127C2×Q16×C47—22no—
128C2×Q16×C47—22no—
129C2×Q16×C47—41no—
130C2×Q16×C47—41no—
131C2×Q16×C47C2×C414yescomplemented
132C2×Q16×C47C2×C414yescomplemented
133C22×C8×C47C2311yescharacteristic
134C22×C8×C47C2311yescharacteristic
135C22⋊Q8×C47—22no—
136C22⋊Q8×C47C2×C414yes—
137C2×C4⋊C4×C47—21no—
138C2×C4⋊C4×C47C2311yescharacteristic
139C2×C22⋊C4×C47—21no—
140#103×C47C2×C414yescomplemented
141#103×C47C2×C414yescomplemented
142C22⋊C8×C47C2×C414yes—
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—21no—
150C2×Q8×C47—28no—
151C2×Q8×C47—21no—
152C2×Q8×C47—21no—
153C2×Q8×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C2×Q8×C47—21no—
157C2×Q8×C47—21no—
158C2×Q8×C47—21no—
159C2×Q8×C47—42no—
160C2×Q8×C47—42no—
161C2×Q8×C47—44no—
162C2×Q8×C47—44no—
163C2×Q8×C47—44no—
164C2×Q8×C47C22×C412yes—
165C2×Q8×C47C22×C412yes—
166C2×Q8×C47C22×C412yes—
167C2×Q8×C47C2×D412yes—
168C2×Q8×C47#4112yes—
169C22×C4×C47—21no—
170C22×C4×C47—21no—
171C22×C4×C47—21no—
172C22×C4×C47—21no—
173C22×C4×C47—21no—
174C22×C4×C47—24no—
175C22×C4×C47—21no—
176C22×C4×C47—21no—
177C22×C4×C47—21no—
178C22×C4×C47—42no—
179C22×C4×C47—42no—
180C22×C4×C47C22×C412yes—
181C22×C4×C47C2×D411yescharacteristic
182C22×C4×C47#4112yes—
183C22×C4×C47C2411yescharacteristic
184C22×Dic47—21no—
185C22×Dic47—21no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—42no—
189C22×Dic47—42no—
190C22×Dic47—81no—
191C22×Dic47C2×D411yescharacteristic
192C22×Dic47C2×D411yescharacteristic
193C22×Dic47C2×D411yescharacteristic
194C22×Dic47C2×D411yescharacteristic
195Q16×C47—28no—
196Q16×C47—44no—
197C2×C8×C47—21no—
198C2×C8×C47—21no—
199C2×C8×C47—21no—
200C2×C8×C47—21no—
201C2×C8×C47C22×C412yes—
202C2×C8×C47C22×C412yes—
203C4⋊C4×C47—24no—
204C4⋊C4×C47—21no—
205C4⋊C4×C47C22×C412yes—
206C22⋊C4×C47—24no—
207C22⋊Dic47—22no—
208C22⋊Dic47—22no—
209C22⋊Dic47—42no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—21no—
217C4⋊Dic47—42no—
218C4⋊Dic47—42no—
219C4⋊Dic47—42no—
220C4⋊Dic47—42no—
221C4⋊Dic47—81no—
222C4⋊Dic47C2×D412yes—
223C4×Dic47—21no—
224C4×Dic47—21no—
225C4×Dic47—21no—
226C4×Dic47—21no—
227C4×Dic47—42no—
228C4×Dic47—42no—
229C4×Dic47—42no—
230C4×Dic47—81no—
231C2×C47⋊C8—21no—
232C2×C47⋊C8—21no—
233C2×C47⋊C8—21no—
234C2×C47⋊C8—21no—
235C2×C47⋊C8—21no—
236C2×C47⋊C8—44no—
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—22no—
252Q8×C47—22no—
253Q8×C47—48no—
254Q8×C47—41no—
255Q8×C47—41no—
256Q8×C47—41no—
257Q8×C47—41no—
258Q8×C47C4×D414yes—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—21no—
262C2×C4×C47—22no—
263C2×C4×C47—21no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—22no—
268C2×C4×C47—22no—
269C2×C4×C47—22no—
270C2×C4×C47—22no—
271C2×C4×C47—48no—
272C2×C4×C47—41no—
273C2×C4×C47—41no—
274C2×C4×C47—41no—
275C2×C4×C47—41no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47C4×D412yes—
279C2×C4×C47C23×C411yescharacteristic
280C2×C4×C47C22×D411yescharacteristic
281C2×C4×C47C2×#4111yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47H(5,𝔽2)11yescharacteristic
284C2×C4×C47H(5,𝔽2)11yescharacteristic
285C2×Dic47—21no—
286C2×Dic47—21no—
287C2×Dic47—22no—
288C2×Dic47—21no—
289C2×Dic47—21no—
290C2×Dic47—21no—
291C2×Dic47—21no—
292C2×Dic47—21no—
293C2×Dic47—21no—
294C2×Dic47—21no—
295C2×Dic47—21no—
296C2×Dic47—21no—
297C2×Dic47—21no—
298C2×Dic47—41no—
299C2×Dic47—41no—
300C2×Dic47—41no—
301C2×Dic47—41no—
302C2×Dic47—41no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—84no—
310C8×C47—22no—
311C8×C47—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—42no—
333C4×C47—42no—
334C4×C47C2×C4×D411yescharacteristic
335C4×C47#51811yescharacteristic
336C4×C47#54611yescharacteristic
337C4×C47#55111yescharacteristic
338Dic47—41no—
339Dic47—42no—
340Dic47—41no—
341Dic47—41no—
342Dic47—41no—
343Dic47—81no—
344Dic47—81no—
345Dic47—81no—
346C2×#451D4711yescharacteristic
347C2×#441—471no—
348C22×#103—471no—
349#2360—471no—
350Q8×C22⋊C4—471no—
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×Q16C2×D4711yescharacteristic
371C22×Q16C2×D4711yescharacteristic
372C23×C8—471no—
373C2×C22⋊Q8C2×D4711yescharacteristic
374C2×C4×Q8—471no—
375C2×C4×Q8—471no—
376C2×C4×Q8—471no—
377C22×C4⋊C4—471no—
378#451Dic4718yescomplemented
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—944no—
389C2×#103C2×D4711yescharacteristic
390C2×#103C2×D4711yescharacteristic
391C2×C22⋊C8C2×D4711yescharacteristic
392C2×#97—471no—
393C2×#97—471no—
394#391—471no—
395#391—471no—
396#391—471no—
397#391—941no—
398#391—941no—
399#389—471no—
400#389—941no—
401#387—941no—
402#385—941no—
403#380—471no—
404#380—941no—
405C4×C4⋊C4—471no—
406C4×C22⋊C4—471no—
407C4×C22⋊C4—941no—
408C4×C22⋊C4—941no—
409#340—471no—
410#340—471no—
411#340—471no—
412#340—471no—
413#336—471no—
414#336—471no—
415C47#2285911yescharacteristic, complemented, Sylow
416C22×Q8—21no—
417C22×Q8—22no—
418C22×Q8—22no—
419C22×Q8—22no—
420C22×Q8—41no—
421C22×Q8—41no—
422C22×Q8C2×Dic4714yes—
423C22×Q8C22×D4711yescharacteristic
424C22×Q8C22×D4711yescharacteristic
425C22×Q8C22×D4711yescharacteristic
426C23×C4—21no—
427C23×C4—941no—
428C23×C4C22×D4711yescharacteristic
429C2×Q16—22no—
430C2×Q16—22no—
431C2×Q16—41no—
432C2×Q16—41no—
433C2×Q16C2×Dic4714yescomplemented
434C2×Q16C2×Dic4714yescomplemented
435C22×C8—471no—
436C22×C8—471no—
437C22×C8—942no—
438C22×C8—942no—
439C22×C8—1881no—
440C22×C8C22×D4711yescharacteristic
441C22×C8C22×D4711yescharacteristic
442C22⋊Q8—22no—
443C22⋊Q8C2×Dic4714yes—
444C4×Q8—942no—
445C4×Q8—942no—
446C4×Q8—942no—
447C4×Q8—1881no—
448C4×Q8—1881no—
449C4×Q8—1881no—
450C2×C4⋊C4—21no—
451C2×C4⋊C4—471no—
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—941no—
461C2×C4⋊C4—1881no—
462C2×C4⋊C4C22×D4711yescharacteristic
463C2×C22⋊C4—21no—
464C2×C22⋊C4—471no—
465C2×C22⋊C4—471no—
466C2×C22⋊C4—941no—
467C2×C42—471no—
468C2×C42—471no—
469C2×C42—941no—
470C2×C42—941no—
471C2×C42—941no—
472C2×C42—941no—
473#106—942no—
474#106—1881no—
475#103—474no—
476#103—942no—
477#103—942no—
478#103—942no—
479#103—942no—
480#103—1881no—
481#103C2×Dic4714yescomplemented
482#103C2×Dic4714yescomplemented
483C22⋊C8C2×Dic4714yes—
484#97—942no—
485#97—1881no—
486#95—471no—
487#95—471no—
488#95—941no—
489#95—941no—
490#95—941no—
491#95—941no—
492#95—941no—
493#95—941no—
494#95—941no—
495#95—941no—
496#95—941no—
497C24D4×D4711yescharacteristic
498C2×Q8—24no—
499C2×Q8—21no—
500C2×Q8—21no—
501C2×Q8—21no—
502C2×Q8—21no—
503C2×Q8—21no—
504C2×Q8—28no—
505C2×Q8—21no—
506C2×Q8—21no—
507C2×Q8—21no—
508C2×Q8—21no—
509C2×Q8—21no—
510C2×Q8—21no—
511C2×Q8—21no—
512C2×Q8—21no—
513C2×Q8—42no—
514C2×Q8—42no—
515C2×Q8—44no—
516C2×Q8—44no—
517C2×Q8—44no—
518C2×Q8D4×D4712yes—
519C2×Q8#1062535212yes—
520C2×Q8C22×Dic4712yes—
521C2×Q8C22×Dic4712yes—
522C2×Q8C22×Dic4712yes—
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—471no—
535C22×C4—471no—
536C22×C4—471no—
537C22×C4—471no—
538C22×C4—941no—
539C22×C4—941no—
540C22×C4—941no—
541C22×C4—941no—
542C22×C4—3761no—
543C22×C4—1882no—
544C22×C4—1882no—
545C22×C4D4×D4711yescharacteristic
546C22×C4#1062535212yes—
547C22×C4C22×Dic4712yes—
548C22×C4C23×D4711yescharacteristic
549Q16—28no—
550Q16—44no—
551C2×C8—21no—
552C2×C8—21no—
553C2×C8—21no—
554C2×C8—21no—
555C2×C8—472no—
556C2×C8—941no—
557C2×C8—941no—
558C2×C8—941no—
559C2×C8—941no—
560C2×C8—941no—
561C2×C8—1884no—
562C2×C8C22×Dic4712yes—
563C2×C8C22×Dic4712yes—
564C4⋊C4—24no—
565C4⋊C4—21no—
566C4⋊C4—472no—
567C4⋊C4—941no—
568C4⋊C4—941no—
569C4⋊C4—941no—
570C4⋊C4—941no—
571C4⋊C4—941no—
572C4⋊C4—941no—
573C4⋊C4—941no—
574C4⋊C4—3761no—
575C4⋊C4—1882no—
576C4⋊C4—1882no—
577C4⋊C4—1882no—
578C4⋊C4—1882no—
579C4⋊C4C22×Dic4712yes—
580C22⋊C4—24no—
581C22⋊C4—942no—
582C22⋊C4—942no—
583C22⋊C4—1882no—
584C42—941no—
585C42—941no—
586C42—941no—
587C42—941no—
588C42—3761no—
589C42—1882no—
590C42—1882no—
591C42—1882no—
592C23—21no—
593C23—21no—
594C23—21no—
595C23—21no—
596C23D4×Dic4712yes—
597C23#1309405612yes—
598C23#1309405612yes—
599C23C2×D4×D4711yescharacteristic
600Q8—22no—
601Q8—22no—
602Q8—22no—
603Q8—22no—
604Q8—22no—
605Q8—22no—
606Q8—22no—
607Q8—48no—
608Q8—41no—
609Q8—41no—
610Q8—41no—
611Q8—41no—
612Q8D4×Dic4714yes—
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—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—48no—
626C2×C4—41no—
627C2×C4—41no—
628C2×C4—41no—
629C2×C4—41no—
630C2×C4—41no—
631C2×C4—41no—
632C2×C4—941no—
633C2×C4—941no—
634C2×C4—942no—
635C2×C4—941no—
636C2×C4—941no—
637C2×C4—941no—
638C2×C4—941no—
639C2×C4—941no—
640C2×C4—941no—
641C2×C4—941no—
642C2×C4—941no—
643C2×C4—941no—
644C2×C4—941no—
645C2×C4—3764no—
646C2×C4—1881no—
647C2×C4—1881no—
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×C4D4×Dic4712yes—
658C2×C4C23×Dic4711yescharacteristic
659C2×C4C2×D4×D4711yescharacteristic
660C2×C4C2×#1062535211yescharacteristic
661C2×C4C2×#1062535211yescharacteristic
662C2×C4#1309406911yescharacteristic
663C2×C4#1309406911yescharacteristic
664C8—22no—
665C8—22no—
666C8—942no—
667C8—1881no—
668C22—22no—
669C22—22no—
670C22—22no—
671C22—22no—
672C22—22no—
673C22—22no—
674C22#1568923014yescomplemented
675C22C2×D4×Dic4711yescharacteristic
676C22#1568975511yescharacteristic
677C22#1568976011yescharacteristic
678C22C2×#1309405611yescharacteristic
679C22C2×#1309405611yescharacteristic
680C22#1568993211yescharacteristic
681C22#1568993911yescharacteristic
682C4—22no—
683C4—24no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—3761no—
688C4—3761no—
689C4—3761no—
690C4—1881no—
691C4—1881no—
692C4—1882no—
693C4—1881no—
694C4—1881no—
695C4C2×D4×Dic4711yescharacteristic
696C4#1568959811yescharacteristic
697C4#1568976011yescharacteristic
698C4#1568980411yescharacteristic
699C2—24no—
700C2#2024637211yescharacteristic
701C2C2×#1568923011yescharacteristic
702C2#2025223211yescharacteristic
703C2#2025489111yescharacteristic
704C2#2025496211yescharacteristic
705C2#2025544311yescharacteristic
706C2#2025550311yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#451C2
socleC23×C47C22×D4
prime radicalC24×C47C2×D4
cosocleC22×C4×C47C24
hypercenterC2×#451D47
hypocenterC47#22859
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#451

Complements

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

NH ≅ G/Ntype
1. C2×#15689230C2semidirect
5. #20244260C2semidirect
6. #20244080C2semidirect
7. #20244024C2semidirect
9. #20243731C2semidirect
10. #20243731C2semidirect
11. #20243658C2semidirect
13. #20243220C2semidirect
58. C47×#451C4semidirect
131. C2×Q16×C47C2×C4semidirect
132. C2×Q16×C47C2×C4semidirect
140. #103×C47C2×C4semidirect
141. #103×C47C2×C4semidirect
321. C22×C47#441semidirect
378. #451Dic47semidirect
415. C47#22859semidirect
433. C2×Q16C2×Dic47semidirect
434. C2×Q16C2×Dic47semidirect
481. #103C2×Dic47semidirect
482. #103C2×Dic47semidirect
674. C22#15689230semidirect

Maximal subgroups

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

subgroupindex
C2×#156892302
C22×#130939482
#202463972
Q8×C22⋊Dic472
#202442602
#202440802
#202440242
#202438122
#202437312
#202436582
#202435832
#202432202
#202431672
C2×C47×#4512
#2285947