Finite Group Databasebeta

← #26233537

Subgroups — #26233537

Order 12032.

1150 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20246281C211yesmaximal, characteristic, complemented
2D4×C22⋊Dic47C211yesmaximal, characteristic
3#20244087C211yesmaximal, characteristic, complemented
4#20244073C211yesmaximal, characteristic, complemented
5#20244017C211yesmaximal, characteristic, complemented
6#20244010C211yesmaximal, characteristic, complemented
7#20243651C211yesmaximal, characteristic, complemented
8#20243637C211yesmaximal, characteristic, complemented
9#20243483C211yesmaximal, characteristic, complemented
10#20243421C211yesmaximal, characteristic, complemented
11#20243319C211yesmaximal, characteristic
12#20243215C211yesmaximal, characteristic, complemented
13#102×Dic47C211yesmaximal, characteristic, complemented
14#20243169C211yesmaximal, characteristic, complemented
15C2×C47×#418C211yesmaximal, characteristic
16C2×D4×Dic47C2211yescharacteristic
17C2×D4×Dic47C2211yescharacteristic
18C22×C22⋊Dic47—21no—
19C2×#13093958C2211yescharacteristic, complemented
20C2×#13093956C2211yescharacteristic, complemented
21C2×#13093945C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26C2×#13093934C2211yescharacteristic, complemented
27C2×C8×Dic47C2211yescharacteristic, complemented
28#15689026C2211yescharacteristic
29#15689026C2211yescharacteristic
30#15689022C2211yescharacteristic, complemented
31#15689022C2211yescharacteristic, complemented
32#15689016—21no—
33#15689016—21no—
34#15689003—21no—
35#15689003—21no—
36#15688991—21no—
37#15688983C2211yescharacteristic
38#15688983C2211yescharacteristic
39#15688979—21no—
40C4⋊C4×Dic47C2211yescharacteristic, complemented
41C4⋊C4×Dic47C2211yescharacteristic, complemented
42C4×C4⋊Dic47—21no—
43C4×C22⋊Dic47C2211yescharacteristic
44#15688886C2211yescharacteristic, complemented
45#15688886C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688885C2211yescharacteristic, complemented
48#15688885C2211yescharacteristic, complemented
49#15688885C2211yescharacteristic, complemented
50#15688877C2211yescharacteristic, complemented
51#15688877C2211yescharacteristic, complemented
52C23×D4×C47C2211yescharacteristic
53C22×M16×C47C2211yescharacteristic
54C2×#117×C47C2211yescharacteristic
55C47×#418C418yescomplemented
56C2×#102×C47C2211yescharacteristic
57C2×#102×C47C2211yescharacteristic
58C2×#102×C47C2211yescharacteristic
59C2×#102×C47C2211yescharacteristic
60C23×Dic47—21no—
61C23×Dic47—21no—
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64D4×Dic47—22no—
65D4×Dic47—22no—
66D4×Dic47—41no—
67D4×Dic47—41no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47—21no—
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C22⋊Dic47—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80C2×C22⋊Dic47—21no—
81C2×C22⋊Dic47—21no—
82C2×C22⋊Dic47—44no—
83C2×C22⋊Dic47D411yescharacteristic
84C2×C22⋊Dic47D411yescharacteristic
85C2×C4×Dic47—21no—
86C2×C4×Dic47—21no—
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89#13093958—41no—
90#13093956—41no—
91#13093945—22no—
92#13093945—22no—
93#13093945—41no—
94#13093945—41no—
95C22⋊(C47⋊C8)—22no—
96#13093934—41no—
97C8×Dic47—41no—
98C47⋊#95—21no—
99C47⋊#95—21no—
100C47⋊#95—21no—
101C47⋊#95—21no—
102C47⋊#95—21no—
103C47⋊#95—21no—
104C47⋊#95D411yescharacteristic
105C47⋊#95D411yescharacteristic
106C25×C47—21no—
107C22×D4×C47—22no—
108C22×D4×C47—22no—
109C22×D4×C47—21no—
110C22×D4×C47—22no—
111C22×D4×C47—41no—
112C22×D4×C47—41no—
113C22×D4×C47C2×C414yes—
114C22×D4×C47C2311yescharacteristic
115C22×D4×C47C2311yescharacteristic
116C23×C4×C47C2311yescharacteristic
117C2×M16×C47—41no—
118C2×M16×C47—41no—
119C2×M16×C47C2×C414yescomplemented
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122#117×C47—22no—
123#117×C47C2×C414yescomplemented
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C22⋊C4×C47—21no—
127C2×C42×C47—21no—
128#102×C47C2×C414yes—
129#102×C47C2×C414yes—
130#102×C47C2×C414yescomplemented
131#102×C47C2×C414yescomplemented
132C24×C47—21no—
133C24×C47—21no—
134C24×C47—24no—
135C24×C47—42no—
136C24×C47—42no—
137C24×C47—42no—
138C24×C47—42no—
139C24×C47—81no—
140C24×C47—81no—
141C24×C47C2×D411yescharacteristic
142C2×D4×C47—28no—
143C2×D4×C47—24no—
144C2×D4×C47—21no—
145C2×D4×C47—21no—
146C2×D4×C47—21no—
147C2×D4×C47—21no—
148C2×D4×C47—21no—
149C2×D4×C47—21no—
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—44no—
153C2×D4×C47—44no—
154C2×D4×C47—44no—
155C2×D4×C47—42no—
156C2×D4×C47—42no—
157C2×D4×C47C22×C412yes—
158C2×D4×C47C22×C412yes—
159C2×D4×C47#4112yes—
160C2×D4×C47#4112yes—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47—21no—
164C22×C4×C47—21no—
165C22×C4×C47—21no—
166C22×C4×C47—21no—
167C22×C4×C47C22×C412yes—
168C22×C4×C47C2×D411yescharacteristic
169C22×C4×C47#4112yes—
170C22×C4×C47C2411yescharacteristic
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—42no—
176C22×Dic47—42no—
177C22×Dic47—42no—
178C22×Dic47—42no—
179C22×Dic47—81no—
180C22×Dic47—81no—
181C22×Dic47C2×D411yescharacteristic
182C22×Dic47C2×D411yescharacteristic
183C22×Dic47C2×D411yescharacteristic
184C22×Dic47C2×D411yescharacteristic
185M16×C47—44no—
186C2×C8×C47—21no—
187C2×C8×C47—21no—
188C2×C8×C47—21no—
189C2×C8×C47—21no—
190C2×C8×C47C22×C412yes—
191C2×C8×C47C22×C412yes—
192C4⋊C4×C47—21no—
193C4⋊C4×C47—21no—
194C4⋊C4×C47C22×C412yes—
195C4⋊C4×C47C22×C412yes—
196C22⋊C4×C47—24no—
197C42×C47—24no—
198C22⋊Dic47—22no—
199C22⋊Dic47—41no—
200C22⋊Dic47—42no—
201C22⋊Dic47—42no—
202C22⋊Dic47—42no—
203C22⋊Dic47—42no—
204C22⋊Dic47—42no—
205C22⋊Dic47—81no—
206C22⋊Dic47—81no—
207C22⋊Dic47—81no—
208C4⋊Dic47—21no—
209C4⋊Dic47—21no—
210C4⋊Dic47—21no—
211C4⋊Dic47—21no—
212C4⋊Dic47—21no—
213C4⋊Dic47—21no—
214C4⋊Dic47—21no—
215C4⋊Dic47—21no—
216C4⋊Dic47—42no—
217C4⋊Dic47—42no—
218C4×Dic47—21no—
219C4×Dic47—21no—
220C4×Dic47—21no—
221C4×Dic47—21no—
222C4×Dic47—81no—
223C4×Dic47—81no—
224C2×C47⋊C8—21no—
225C2×C47⋊C8—21no—
226C2×C47⋊C8—21no—
227C2×C47⋊C8—21no—
228C2×C47⋊C8—21no—
229C2×C47⋊C8—21no—
230C23×C47—22no—
231C23×C47—22no—
232C23×C47—22no—
233C23×C47—21no—
234C23×C47—21no—
235C23×C47—21no—
236C23×C47—21no—
237C23×C47—21no—
238C23×C47—21no—
239C23×C47—22no—
240C23×C47—48no—
241C23×C47—48no—
242C23×C47—41no—
243C23×C47—41no—
244C23×C47—41no—
245C23×C47—41no—
246C23×C47—41no—
247C23×C47—41no—
248C23×C47—41no—
249C23×C47—41no—
250C23×C47—41no—
251C23×C47—41no—
252C23×C47—84no—
253C23×C47—84no—
254C23×C47—84no—
255C23×C47—84no—
256C23×C47—84no—
257C23×C47C4×D412yes—
258C23×C47C22×D411yescharacteristic
259D4×C47—22no—
260D4×C47—22no—
261D4×C47—22no—
262D4×C47—22no—
263D4×C47—22no—
264D4×C47—48no—
265D4×C47—41no—
266D4×C47—41no—
267D4×C47#11714yes—
268C2×C4×C47—21no—
269C2×C4×C47—21no—
270C2×C4×C47—22no—
271C2×C4×C47—22no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—41no—
277C2×C4×C47—41no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47C4×D412yes—
281C2×C4×C47C23×C411yescharacteristic
282C2×C4×C47C2×#4111yescharacteristic
283C2×C4×C47C2×#4111yescharacteristic
284C2×C4×C47C2×#4111yescharacteristic
285C2×C4×C47H(5,𝔽2)11yescharacteristic
286C2×C4×C47H(5,𝔽2)11yescharacteristic
287C2×Dic47—21no—
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—41no—
310C2×Dic47—84no—
311C2×Dic47—84no—
312C2×Dic47AGL(1,ℤ/8)12yes—
313C8×C47—22no—
314C8×C47—22no—
315C47⋊C8—41no—
316C47⋊C8—41no—
317#22580—471nomaximal, Sylow
318C22×C47—22no—
319C22×C47—24no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—41no—
325C22×C47—42no—
326C22×C47—42no—
327C22×C47—41no—
328C22×C47—41no—
329C22×C47—42no—
330C22×C47—42no—
331C22×C47—41no—
332C22×C47—42no—
333C22×C47—42no—
334C22×C47—42no—
335C22×C47—816no—
336C22×C47—81no—
337C22×C47—81no—
338C22×C47—81no—
339C22×C47—81no—
340C22×C47C2×C4×D411yescharacteristic
341C22×C47#54611yescharacteristic
342C22×C47#54611yescharacteristic
343C22×C47C2×AGL(1,ℤ/8)11yescharacteristic
344C22×C47#57511yescharacteristic
345C22×C47#57611yescharacteristic
346C22×C47#57711yescharacteristic
347C4×C47—22no—
348C4×C47—42no—
349C4×C47—42no—
350C4×C47C2×#11711yescharacteristic
351C4×C47#51811yescharacteristic
352C4×C47#55111yescharacteristic
353C4×C47#55111yescharacteristic
354Dic47—22no—
355Dic47—41no—
356Dic47—41no—
357Dic47—41no—
358Dic47—81no—
359Dic47—81no—
360Dic47—81no—
361Dic47—81no—
362C2×#418D4711yescharacteristic
363#2347—471no—
364D4×C22⋊C4—471no—
365#1936—471no—
366#1934—471no—
367#1926—471no—
368#1925—471no—
369#1864—471no—
370#1862—471no—
371#1825—471no—
372#1809—471no—
373#1786—471no—
374#1762—471no—
375C4×#102—471no—
376#1753—471no—
377C2×C47—42no—
378C2×C47—44no—
379C2×C47—82no—
380C2×C47#234211yescharacteristic
381C2×C47C4×AGL(1,ℤ/8)11yescharacteristic
382C2×C47#294611yescharacteristic
383C2×C47#331111yescharacteristic
384C2×C47#331811yescharacteristic
385C2×C47#332211yescharacteristic
386C2×C47#332411yescharacteristic
387C23×D4C2×D4711yescharacteristic
388C22×M16C2×D4711yescharacteristic
389C2×C4×D4—471no—
390C2×C4×D4—471no—
391C2×#117C2×D4711yescharacteristic
392C22×C22⋊C4—941no—
393C2×#107—471no—
394C2×#106—471no—
395#418Dic4718yescomplemented
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102C2×D4711yescharacteristic
401C2×#102C2×D4711yescharacteristic
402C2×#102C2×D4711yescharacteristic
403C2×#102C2×D4711yescharacteristic
404C2×C22⋊C8—471no—
405C2×#97—471no—
406C2×C4×C8—471no—
407#390—471no—
408#390—471no—
409#389—471no—
410#389—471no—
411#388—941no—
412#388—941no—
413#386—941no—
414#386—941no—
415#383—941no—
416#380—471no—
417#380—471no—
418#379—941no—
419C4×C4⋊C4—471no—
420C4×C4⋊C4—471no—
421C4×C4⋊C4—941no—
422C4×C22⋊C4—471no—
423#340—471no—
424#340—471no—
425#340—471no—
426#340—471no—
427#340—471no—
428#340—471no—
429#336—471no—
430#336—471no—
431C47#2258011yescharacteristic, complemented, Sylow
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—21no—
436C22×D4—22no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C2×Dic4714yes—
440C22×D4C22×D4711yescharacteristic
441C22×D4C22×D4711yescharacteristic
442C23×C4—941no—
443C23×C4—941no—
444C23×C4C22×D4711yescharacteristic
445C2×M16—41no—
446C2×M16—41no—
447C2×M16C2×Dic4714yescomplemented
448C22×C8—471no—
449C22×C8—471no—
450C22×C8C22×D4711yescharacteristic
451C22×C8C22×D4711yescharacteristic
452C4×D4—942no—
453C4×D4—942no—
454C4×D4—1881no—
455C4×D4—1881no—
456#117—22no—
457#117C2×Dic4714yescomplemented
458C2×C4⋊C4—471no—
459C2×C4⋊C4—471no—
460C2×C4⋊C4—471no—
461C2×C4⋊C4—471no—
462C2×C4⋊C4—941no—
463C2×C4⋊C4—941no—
464C2×C4⋊C4C22×D4711yescharacteristic
465C2×C4⋊C4C22×D4711yescharacteristic
466C2×C22⋊C4—21no—
467C2×C22⋊C4—471no—
468C2×C22⋊C4—471no—
469C2×C22⋊C4—941no—
470C2×C22⋊C4—941no—
471C2×C22⋊C4—941no—
472C2×C22⋊C4—941no—
473C2×C22⋊C4—941no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4—941no—
477C2×C22⋊C4—1884no—
478C2×C42—21no—
479C2×C42—471no—
480C2×C42—471no—
481C2×C42—941no—
482C2×C42—941no—
483#107—1881no—
484#106—1881no—
485#102—942no—
486#102—942no—
487#102—1881no—
488#102—1881no—
489#102C2×Dic4714yes—
490#102C2×Dic4714yes—
491#102C2×Dic4714yescomplemented
492#102C2×Dic4714yescomplemented
493C22⋊C8—942no—
494#97—1881no—
495C4×C8—1881no—
496#95—471no—
497#95—471no—
498#95—941no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95—941no—
503#95—941no—
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24D4×D4711yescharacteristic
514C2×D4—28no—
515C2×D4—24no—
516C2×D4—21no—
517C2×D4—21no—
518C2×D4—21no—
519C2×D4—21no—
520C2×D4—21no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—44no—
525C2×D4—44no—
526C2×D4—44no—
527C2×D4—42no—
528C2×D4—42no—
529C2×D4#1062535012yes—
530C2×D4#1062535012yes—
531C2×D4C22×Dic4712yes—
532C2×D4C22×Dic4712yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—471no—
540C22×C4—471no—
541C22×C4—471no—
542C22×C4—471no—
543C22×C4—941no—
544C22×C4—941no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—3761no—
548C22×C4—3761no—
549C22×C4—1882no—
550C22×C4—1882no—
551C22×C4—1882no—
552C22×C4—1882no—
553C22×C4D4×D4711yescharacteristic
554C22×C4#1062535212yes—
555C22×C4C22×Dic4712yes—
556C22×C4C23×D4711yescharacteristic
557M16—44no—
558C2×C8—21no—
559C2×C8—21no—
560C2×C8—21no—
561C2×C8—21no—
562C2×C8—941no—
563C2×C8—941no—
564C2×C8—941no—
565C2×C8—941no—
566C2×C8—941no—
567C2×C8—941no—
568C2×C8C22×Dic4712yes—
569C2×C8C22×Dic4712yes—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—941no—
573C4⋊C4—941no—
574C4⋊C4—941no—
575C4⋊C4—941no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—1882no—
581C4⋊C4—1882no—
582C4⋊C4C22×Dic4712yes—
583C4⋊C4C22×Dic4712yes—
584C22⋊C4—24no—
585C22⋊C4—942no—
586C22⋊C4—3761no—
587C22⋊C4—3761no—
588C22⋊C4—3761no—
589C22⋊C4—1882no—
590C22⋊C4—1881no—
591C22⋊C4—1882no—
592C22⋊C4—1882no—
593C22⋊C4—1882no—
594C22⋊C4—1882no—
595C42—24no—
596C42—941no—
597C42—941no—
598C42—941no—
599C42—941no—
600C42—3761no—
601C42—3761no—
602C23—22no—
603C23—22no—
604C23—21no—
605C23—21no—
606C23—22no—
607C23—21no—
608C23—21no—
609C23—21no—
610C23—21no—
611C23—22no—
612C23—48no—
613C23—48no—
614C23—41no—
615C23—41no—
616C23—41no—
617C23—41no—
618C23—41no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—84no—
625C23—84no—
626C23—84no—
627C23—84no—
628C23—84no—
629C23D4×Dic4712yes—
630C23C2×D4×D4711yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1309398314yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—41no—
649C2×C4—41no—
650C2×C4—41no—
651C2×C4—41no—
652C2×C4—472no—
653C2×C4—941no—
654C2×C4—941no—
655C2×C4—941no—
656C2×C4—941no—
657C2×C4—941no—
658C2×C4—941no—
659C2×C4—941no—
660C2×C4—941no—
661C2×C4—941no—
662C2×C4—941no—
663C2×C4—941no—
664C2×C4—3764no—
665C2×C4—3764no—
666C2×C4—1881no—
667C2×C4—1881no—
668C2×C4—1881no—
669C2×C4—1881no—
670C2×C4—1881no—
671C2×C4—1881no—
672C2×C4—1881no—
673C2×C4—1881no—
674C2×C4—1881no—
675C2×C4—1881no—
676C2×C4—1881no—
677C2×C4—1881no—
678C2×C4D4×Dic4712yes—
679C2×C4C23×Dic4711yescharacteristic
680C2×C4C2×#1062535211yescharacteristic
681C2×C4C2×#1062535011yescharacteristic
682C2×C4C2×#1062535011yescharacteristic
683C2×C4#1309406911yescharacteristic
684C2×C4#1309406911yescharacteristic
685C8—22no—
686C8—22no—
687C8—1881no—
688C8—1881no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—41no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×D4×Dic4711yescharacteristic
712C22#1568976311yescharacteristic
713C22#1568976311yescharacteristic
714C22AGL(1,ℤ/8)×D4711yescharacteristic
715C22#1568991911yescharacteristic
716C22#1568992711yescharacteristic
717C22#1568993311yescharacteristic
718C4—22no—
719C4—42no—
720C4—42no—
721C4—942no—
722C4—3761no—
723C4—3761no—
724C4—3761no—
725C4—3761no—
726C4—1881no—
727C4—1881no—
728C4—1881no—
729C4C2×#1309398311yescharacteristic
730C4#1568959811yescharacteristic
731C4#1568979911yescharacteristic
732C4#1568979911yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#2024623711yescharacteristic
737C2AGL(1,ℤ/8)×Dic4711yescharacteristic
738C2#2025222111yescharacteristic
739C2#2025542511yescharacteristic
740C2#2025553011yescharacteristic
741C2#2025558511yescharacteristic
742C2#2025561511yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC2×C47×#418C2
socleC23×C47C22×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterC2×#418D47
hypocenterC47#22580
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#418

Complements

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

NH ≅ G/Ntype
1. #20246281C2semidirect
3. #20244087C2semidirect
4. #20244073C2semidirect
5. #20244017C2semidirect
6. #20244010C2semidirect
7. #20243651C2semidirect
8. #20243637C2semidirect
9. #20243483C2semidirect
10. #20243421C2semidirect
12. #20243215C2semidirect
13. #102×Dic47C2semidirect
14. #20243169C2semidirect
19. C2×#13093958C22semidirect
20. C2×#13093956C22semidirect
26. C2×#13093934C22semidirect
27. C2×C8×Dic47C22semidirect
30. #15689022C22semidirect
31. #15689022C22semidirect
40. C4⋊C4×Dic47C22semidirect
41. C4⋊C4×Dic47C22semidirect
44. #15688886C22semidirect
45. #15688886C22semidirect
46. #15688885C22semidirect
47. #15688885C22semidirect
48. #15688885C22semidirect
49. #15688885C22semidirect
50. #15688877C22semidirect
51. #15688877C22semidirect
55. C47×#418C4semidirect
119. C2×M16×C47C2×C4semidirect
123. #117×C47C2×C4semidirect
130. #102×C47C2×C4semidirect
131. #102×C47C2×C4semidirect
395. #418Dic47semidirect
431. C47#22580semidirect
447. C2×M16C2×Dic47semidirect
457. #117C2×Dic47semidirect
491. #102C2×Dic47semidirect
492. #102C2×Dic47semidirect

Maximal subgroups

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

subgroupindex
#202462812
D4×C22⋊Dic472
#202440872
#202440732
#202440172
#202440102
#202436512
#202436372
#202434832
#202434212
#202433192
#202432152
#102×Dic472
#202431692
C2×C47×#4182
#2258047