Finite Group Databasebeta

← #26233593

Subgroups — #26233593

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
1C2×#15689128C211yesmaximal, characteristic
2#20246271C211yesmaximal, characteristic, complemented
3#20244088C211yesmaximal, characteristic, complemented
4#20244074C211yesmaximal, characteristic, complemented
5#20244012C211yesmaximal, characteristic, complemented
6#20244005C211yesmaximal, characteristic, complemented
7#20243649C211yesmaximal, characteristic, complemented
8#20243635C211yesmaximal, characteristic, complemented
9#20243480C211yesmaximal, characteristic, complemented
10#20243419C211yesmaximal, characteristic, complemented
11#20243319C211yesmaximal, characteristic
12#20243213C211yesmaximal, characteristic, complemented
13C4×#13093945C211yesmaximal, characteristic, complemented
14#20243172C211yesmaximal, characteristic, complemented
15D4×C22⋊C4×C47C211yesmaximal, characteristic
16C22×#10625329C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18C2×#13093957C2211yescharacteristic, complemented
19C2×#13093955C2211yescharacteristic, complemented
20#15689128C418yescomplemented
21C2×#13093945C2211yescharacteristic
22C2×#13093945C2211yescharacteristic
23C2×#13093945C2211yescharacteristic
24C2×#13093945C2211yescharacteristic
25C2×#13093945C2211yescharacteristic
26C2×#13093945C2211yescharacteristic
27C2×#13093945C2211yescharacteristic
28C2×#13093945C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×#13093935C2211yescharacteristic, complemented
31C2×C4×C47⋊C8C2211yescharacteristic, complemented
32#15689021C2211yescharacteristic, complemented
33#15689021C2211yescharacteristic, complemented
34#15689011—21no—
35#15689011—21no—
36#15688987—21no—
37#15688983C2211yescharacteristic
38C4×C4⋊Dic47C2211yescharacteristic, complemented
39C4×C4⋊Dic47C2211yescharacteristic, complemented
40#15688968—21no—
41#15688885C2211yescharacteristic, complemented
42#15688885C2211yescharacteristic, complemented
43#15688885C2211yescharacteristic, complemented
44#15688885C2211yescharacteristic, complemented
45#15688885C2211yescharacteristic, complemented
46#15688885C2211yescharacteristic, complemented
47#15688878C2211yescharacteristic, complemented
48#15688878C2211yescharacteristic, complemented
49C23×D4×C47C2211yescharacteristic
50C2×C4×D4×C47C2211yescharacteristic
51C2×C4×D4×C47C2211yescharacteristic
52C22×C22⋊C4×C47—21no—
53C47×#390C2211yescharacteristic
54C47×#390C2211yescharacteristic
55C47×#386—21no—
56C47×#386—21no—
57C47×#380C2211yescharacteristic
58C47×#379—21no—
59C4×C22⋊C4×C47C2211yescharacteristic
60C2×#10625329—41no—
61C2×#10625329—41no—
62C2×#10625329C2×C414yescomplemented
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13093983—22no—
68#13093983C2×C414yescomplemented
69C2×C4⋊Dic47C2311yescharacteristic
70C2×C4⋊Dic47C2311yescharacteristic
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×Dic47⋊C4—21no—
74C2×Dic47⋊C4—21no—
75C2×C22⋊Dic47—21no—
76C2×C22⋊Dic47—21no—
77C2×C4×Dic47—21no—
78C2×C4×Dic47—21no—
79C2×C4×Dic47—21no—
80#13093957—41no—
81#13093955—41no—
82#13093945—22no—
83#13093945—22no—
84#13093945—41no—
85#13093945—41no—
86#13093945C2×C414yes—
87#13093945C2×C414yes—
88#13093945C2×C414yescomplemented
89#13093945C2×C414yescomplemented
90C22⋊(C47⋊C8)—22no—
91#13093935—41no—
92C4×C47⋊C8—41no—
93C47⋊#95—21no—
94C47⋊#95—21no—
95C47⋊#95—21no—
96C47⋊#95—21no—
97C47⋊#95—21no—
98C25×C47—21no—
99C22×D4×C47—22no—
100C22×D4×C47—22no—
101C22×D4×C47—21no—
102C22×D4×C47—22no—
103C22×D4×C47—41no—
104C22×D4×C47—41no—
105C22×D4×C47C2×C414yes—
106C22×D4×C47C2311yescharacteristic
107C22×D4×C47C2311yescharacteristic
108C23×C4×C47—21no—
109C23×C4×C47—21no—
110C23×C4×C47C2311yescharacteristic
111C4×D4×C47—22no—
112C4×D4×C47—22no—
113C4×D4×C47—41no—
114C4×D4×C47—41no—
115C2×C4⋊C4×C47C2311yescharacteristic
116C2×C4⋊C4×C47C2311yescharacteristic
117C2×C22⋊C4×C47—21no—
118C2×C22⋊C4×C47—21no—
119C2×C22⋊C4×C47—21no—
120C2×C22⋊C4×C47—21no—
121C2×C22⋊C4×C47—21no—
122C2×C22⋊C4×C47—21no—
123C2×C22⋊C4×C47—21no—
124C2×C22⋊C4×C47—44no—
125C2×C22⋊C4×C47D411yescharacteristic
126C2×C22⋊C4×C47D411yescharacteristic
127C2×C42×C47C2311yescharacteristic
128C2×C42×C47C2311yescharacteristic
129#95×C47—21no—
130#95×C47D411yescharacteristic
131#95×C47D411yescharacteristic
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×C47—42no—
168C22×C4×C47—42no—
169C22×C4×C47—42no—
170C22×C4×C47—42no—
171C22×C4×C47—81no—
172C22×C4×C47—81no—
173C22×C4×C47C22×C412yes—
174C22×C4×C47C2×D411yescharacteristic
175C22×C4×C47C2×D411yescharacteristic
176C22×C4×C47C2×D411yescharacteristic
177C22×C4×C47C2×D411yescharacteristic
178C22×C4×C47C2×D411yescharacteristic
179C22×C4×C47#4112yes—
180C22×C4×C47C2411yescharacteristic
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—21no—
185C4⋊C4×C47—21no—
186C4⋊C4×C47—21no—
187C4⋊C4×C47—21no—
188C4⋊C4×C47—21no—
189C22⋊C4×C47—22no—
190C22⋊C4×C47—41no—
191C22⋊C4×C47—42no—
192C22⋊C4×C47—42no—
193C22⋊C4×C47—42no—
194C22⋊C4×C47—42no—
195C22⋊C4×C47—42no—
196C22⋊C4×C47—81no—
197C22⋊C4×C47—81no—
198C42×C47—21no—
199C42×C47—21no—
200C42×C47—21no—
201C42×C47—21no—
202C22⋊Dic47—24no—
203C22⋊Dic47—81no—
204C4⋊Dic47—21no—
205C4⋊Dic47—21no—
206C4⋊Dic47—21no—
207C4⋊Dic47—21no—
208C4⋊Dic47—21no—
209C4⋊Dic47—21no—
210C4⋊Dic47C22×C412yes—
211C4⋊Dic47C22×C412yes—
212Dic47⋊C4—81no—
213Dic47⋊C4—81no—
214C4×Dic47—24no—
215C4×Dic47—42no—
216C4×Dic47—42no—
217#10625329—44no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
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⋊C8C22×C412yes—
229C2×C47⋊C8C22×C412yes—
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—21no—
271C2×C4×C47—21no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—21no—
277C2×C4×C47—21no—
278C2×C4×C47—21no—
279C2×C4×C47—21no—
280C2×C4×C47—21no—
281C2×C4×C47—21no—
282C2×C4×C47—21no—
283C2×C4×C47—21no—
284C2×C4×C47—21no—
285C2×C4×C47—41no—
286C2×C4×C47—41no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—84no—
292C2×C4×C47—84no—
293C2×C4×C47C4×D412yes—
294C2×C4×C47AGL(1,ℤ/8)12yes—
295C2×C4×C47C23×C411yescharacteristic
296C2×C4×C47C2×#4111yescharacteristic
297C2×C4×C47C2×#4111yescharacteristic
298C2×C4×C47C2×#4111yescharacteristic
299C2×C4×C47H(5,𝔽2)11yescharacteristic
300C2×C4×C47H(5,𝔽2)11yescharacteristic
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—41no—
304C2×Dic47—41no—
305C2×Dic47—41no—
306C2×Dic47—41no—
307C2×Dic47—41no—
308C2×Dic47—41no—
309C2×Dic47—41no—
310C2×Dic47—41no—
311C2×Dic47—41no—
312C2×Dic47—41no—
313C47⋊C8—22no—
314C47⋊C8—22no—
315C47⋊C8—41no—
316C47⋊C8—41no—
317#22584—471nomaximal, Sylow
318C22×C47—22no—
319C22×C47—24no—
320C22×C47—22no—
321C22×C47—22no—
322C22×C47—42no—
323C22×C47—42no—
324C22×C47—42no—
325C22×C47—41no—
326C22×C47—41no—
327C22×C47—42no—
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—22no—
349C4×C47—41no—
350C4×C47—41no—
351C4×C47—41no—
352C4×C47—81no—
353C4×C47—81no—
354C4×C47C2×#11711yescharacteristic
355C4×C47#51811yescharacteristic
356C4×C47#55111yescharacteristic
357C4×C47#55111yescharacteristic
358Dic47—42no—
359Dic47—42no—
360Dic47—81no—
361Dic47—81no—
362C2×#418—471no—
363#2346—471no—
364D4×C22⋊C4D4711yescharacteristic
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#331011yescharacteristic
384C2×C47#331911yescharacteristic
385C2×C47#332311yescharacteristic
386C2×C47#332511yescharacteristic
387C23×D4C2×D4711yescharacteristic
388C22×M16—471no—
389C2×C4×D4C2×D4711yescharacteristic
390C2×C4×D4C2×D4711yescharacteristic
391C2×#117—471no—
392C22×C22⋊C4—21no—
393C2×#107—471no—
394C2×#106—471no—
395#418—478no—
396C2×#102—471no—
397C2×#102—471no—
398C2×#102—471no—
399C2×#102—471no—
400C2×#102—471no—
401C2×#102—471no—
402C2×#102—471no—
403C2×#102—471no—
404C2×C22⋊C8—471no—
405C2×#97—471no—
406C2×C4×C8—471no—
407#390C2×D4711yescharacteristic
408#390C2×D4711yescharacteristic
409#389—471no—
410#389—471no—
411#388—941no—
412#388—941no—
413#386—21no—
414#386—21no—
415#382—941no—
416#380—471no—
417#380C2×D4711yescharacteristic
418#379—21no—
419C4×C4⋊C4—471no—
420C4×C4⋊C4—471no—
421C4×C22⋊C4C2×D4711yescharacteristic
422#376—941no—
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#2258411yescharacteristic, complemented, Sylow
432C25—21no—
433C22×D4—22no—
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—41no—
438C22×D4—41no—
439C22×D4C4×D4714yes—
440C22×D4C22×D4711yescharacteristic
441C22×D4C22×D4711yescharacteristic
442C23×C4—21no—
443C23×C4—21no—
444C23×C4C22×D4711yescharacteristic
445C2×M16—474no—
446C2×M16—1881no—
447C2×M16—1881no—
448C22×C8—471no—
449C22×C8—471no—
450C22×C8—471no—
451C22×C8—471no—
452C4×D4—22no—
453C4×D4—22no—
454C4×D4—41no—
455C4×D4—41no—
456#117—474no—
457#117—942no—
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—21no—
468C2×C22⋊C4—21no—
469C2×C22⋊C4—21no—
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—21no—
473C2×C22⋊C4—44no—
474C2×C22⋊C4—941no—
475C2×C22⋊C4—941no—
476C2×C22⋊C4C22⋊D4711yescharacteristic
477C2×C22⋊C4C22⋊D4711yescharacteristic
478C2×C42—941no—
479C2×C42—941no—
480C2×C42—941no—
481C2×C42C22×D4711yescharacteristic
482C2×C42C22×D4711yescharacteristic
483#107—1881no—
484#106—1881no—
485#102—474no—
486#102—474no—
487#102—474no—
488#102—474no—
489#102—942no—
490#102—942no—
491#102—1881no—
492#102—1881no—
493C22⋊C8—942no—
494#97—1881no—
495C4×C8—1881no—
496#95—21no—
497#95—941no—
498#95—941no—
499#95—941no—
500#95—941no—
501#95—941no—
502#95C22⋊D4711yescharacteristic
503#95C22⋊D4711yescharacteristic
504C24—21no—
505C24—21no—
506C24—24no—
507C24—42no—
508C24—42no—
509C24—42no—
510C24—42no—
511C24—81no—
512C24—81no—
513C24C2×C22⋊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×D4C2×C4×D4712yes—
530C2×D4C2×C4×D4712yes—
531C2×D4#1062535212yes—
532C2×D4#1062535212yes—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—21no—
538C22×C4—21no—
539C22×C4—42no—
540C22×C4—42no—
541C22×C4—42no—
542C22×C4—42no—
543C22×C4—81no—
544C22×C4—81no—
545C22×C4—941no—
546C22×C4—941no—
547C22×C4—941no—
548C22×C4—941no—
549C22×C4C2×C4×D4712yes—
550C22×C4#1062535012yes—
551C22×C4C2×C22⋊D4711yescharacteristic
552C22×C4C2×C22⋊D4711yescharacteristic
553C22×C4C2×C22⋊D4711yescharacteristic
554C22×C4C2×C22⋊D4711yescharacteristic
555C22×C4C2×C22⋊D4711yescharacteristic
556C22×C4C23×D4711yescharacteristic
557M16—1884no—
558C2×C8—472no—
559C2×C8—472no—
560C2×C8—941no—
561C2×C8—941no—
562C2×C8—941no—
563C2×C8—941no—
564C2×C8—941no—
565C2×C8—941no—
566C2×C8—941no—
567C2×C8—941no—
568C2×C8—941no—
569C2×C8—941no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—21no—
574C4⋊C4—472no—
575C4⋊C4—472no—
576C4⋊C4—941no—
577C4⋊C4—941no—
578C4⋊C4—941no—
579C4⋊C4—941no—
580C4⋊C4—941no—
581C4⋊C4—941no—
582C4⋊C4—3761no—
583C4⋊C4—3761no—
584C22⋊C4—22no—
585C22⋊C4—41no—
586C22⋊C4—42no—
587C22⋊C4—42no—
588C22⋊C4—42no—
589C22⋊C4—42no—
590C22⋊C4—42no—
591C22⋊C4—81no—
592C22⋊C4—81no—
593C22⋊C4—944no—
594C22⋊C4—3761no—
595C42—21no—
596C42—21no—
597C42—21no—
598C42—21no—
599C42—944no—
600C42—1882no—
601C42—1882no—
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—
629C23C4×C22⋊D4712yes—
630C23C22×C22⋊D4711yescharacteristic
631D4—22no—
632D4—22no—
633D4—22no—
634D4—22no—
635D4—22no—
636D4—48no—
637D4—41no—
638D4—41no—
639D4#1309398014yes—
640C2×C4—21no—
641C2×C4—21no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—84no—
664C2×C4—84no—
665C2×C4—942no—
666C2×C4—942no—
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×C4C4×C22⋊D4712yes—
678C2×C4#1309405012yes—
679C2×C4C22×C4×D4711yescharacteristic
680C2×C4C2×#1062535211yescharacteristic
681C2×C4C2×#1062535211yescharacteristic
682C2×C4C2×#1062535011yescharacteristic
683C2×C4#1309406911yescharacteristic
684C2×C4#1309406911yescharacteristic
685C8—942no—
686C8—942no—
687C8—1881no—
688C8—1881no—
689C22—22no—
690C22—22no—
691C22—22no—
692C22—24no—
693C22—42no—
694C22—41no—
695C22—42no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—42no—
700C22—41no—
701C22—42no—
702C22—41no—
703C22—42no—
704C22—42no—
705C22—42no—
706C22—816no—
707C22—81no—
708C22—81no—
709C22—81no—
710C22—81no—
711C22C2×C4×C22⋊D4711yescharacteristic
712C22#1568976711yescharacteristic
713C22#1568976711yescharacteristic
714C22C2×#1309405011yescharacteristic
715C22#1568992111yescharacteristic
716C22#1568992611yescharacteristic
717C22#1568993411yescharacteristic
718C4—22no—
719C4—22no—
720C4—41no—
721C4—41no—
722C4—41no—
723C4—81no—
724C4—81no—
725C4—3761no—
726C4—3761no—
727C4—1882no—
728C4—1882no—
729C4C2×#1309398011yescharacteristic
730C4#1568959611yescharacteristic
731C4#1568979911yescharacteristic
732C4#1568979911yescharacteristic
733C2—42no—
734C2—44no—
735C2—82no—
736C2#2024623311yescharacteristic
737C2C4×#1309405011yescharacteristic
738C2#2025222011yescharacteristic
739C2#2025540911yescharacteristic
740C2#2025554411yescharacteristic
741C2#2025560411yescharacteristic
742C2#2025563011yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingD4×C22⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC23×D4×C47C22
cosocleC22×C4×C47C24
hypercenterD4×C22⋊C4D47
hypocenterC47#22584
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ D4×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. #20246271C2semidirect
3. #20244088C2semidirect
4. #20244074C2semidirect
5. #20244012C2semidirect
6. #20244005C2semidirect
7. #20243649C2semidirect
8. #20243635C2semidirect
9. #20243480C2semidirect
10. #20243419C2semidirect
12. #20243213C2semidirect
13. C4×#13093945C2semidirect
14. #20243172C2semidirect
18. C2×#13093957C22semidirect
19. C2×#13093955C22semidirect
20. #15689128C4semidirect
30. C2×#13093935C22semidirect
31. C2×C4×C47⋊C8C22semidirect
32. #15689021C22semidirect
33. #15689021C22semidirect
38. C4×C4⋊Dic47C22semidirect
39. C4×C4⋊Dic47C22semidirect
41. #15688885C22semidirect
42. #15688885C22semidirect
43. #15688885C22semidirect
44. #15688885C22semidirect
45. #15688885C22semidirect
46. #15688885C22semidirect
47. #15688878C22semidirect
48. #15688878C22semidirect
62. C2×#10625329C2×C4semidirect
68. #13093983C2×C4semidirect
88. #13093945C2×C4semidirect
89. #13093945C2×C4semidirect
431. C47#22584semidirect

Maximal subgroups

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

subgroupindex
C2×#156891282
#202462712
#202440882
#202440742
#202440122
#202440052
#202436492
#202436352
#202434802
#202434192
#202433192
#202432132
C4×#130939452
#202431722
D4×C22⋊C4×C472
#2258447