Finite Group Databasebeta

← #26144693

Subgroups — #26144693

Order 12032.

2118 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689025C211yesmaximal, characteristic
2C2×#15689001C212yesmaximal
3C2×#15688997C212yesmaximal, complemented
4C2×#15688994C212yesmaximal, complemented
5#20241640C212yesmaximal, complemented
6#20241634C212yesmaximal, complemented
7#20241630C212yesmaximal, complemented
8#20241618C211yesmaximal, characteristic, complemented
9C47×C4⋊#95C211yesmaximal, characteristic, complemented
10C23×D188C2211yescharacteristic
11C23×C4×D47C2212yes—
12C22×C4⋊Dic47C2211yescharacteristic
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×(C2×D47)⋊C4C2212yes—
18C22×(C2×D47)⋊C4C2212yes—
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2212yes—
21#15689025C418yescomplemented
22#15689001—28no—
23#15688997—28no—
24#15688994—28no—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C22×C4⋊C4×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C2×#95×C47C2212yes—
34C2×#95×C47C2212yes—
35C24×D47C2312yes—
36C22×D188—41no—
37C22×D188—41no—
38C22×D188—41no—
39C22×D188—41no—
40C22×D188C2×C414yes—
41C22×D188D414yes—
42C22×D188Q814yes—
43C23×Dic47C2312yes—
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C22×C4×D47—24no—
47C22×C4×D47—24no—
48C22×C4×D47—24no—
49C22×C4×D47—42no—
50C22×C4×D47—42no—
51C22×C4×D47—42no—
52C22×C4×D47—42no—
53C2×C4⋊Dic47—22no—
54C2×C4⋊Dic47—41no—
55C2×C4⋊Dic47—41no—
56C2×C4⋊Dic47—41no—
57C2×C4⋊Dic47—41no—
58C2×C4⋊Dic47—41no—
59C2×C4⋊Dic47—41no—
60C2×C4⋊Dic47C2×C414yescomplemented
61C2×C4⋊Dic47D414yescomplemented
62C2×Dic47⋊C4—24no—
63C2×Dic47⋊C4—24no—
64C2×Dic47⋊C4—42no—
65C2×(C2×D47)⋊C4—24no—
66C2×(C2×D47)⋊C4—24no—
67C2×(C2×D47)⋊C4—24no—
68C2×(C2×D47)⋊C4—24no—
69C2×(C2×D47)⋊C4—24no—
70C2×(C2×D47)⋊C4—24no—
71C2×(C2×D47)⋊C4—24no—
72C2×(C2×D47)⋊C4—24no—
73C2×(C2×D47)⋊C4—24no—
74C2×(C2×D47)⋊C4—42no—
75C2×(C2×D47)⋊C4—42no—
76C2×(C2×D47)⋊C4—42no—
77C2×(C2×D47)⋊C4—42no—
78C2×(C2×D47)⋊C4C2×C418yescomplemented
79C2×(C2×D47)⋊C4C2×C418yescomplemented
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95—24no—
83C47⋊#95—24no—
84C47⋊#95—42no—
85C23×C4×C47C2312yes—
86C23×C4×C47C2312yes—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2311yescharacteristic
89C23×C4×C47C2311yescharacteristic
90C2×C4⋊C4×C47—22no—
91C2×C4⋊C4×C47—41no—
92C2×C4⋊C4×C47—41no—
93C2×C4⋊C4×C47—41no—
94C2×C4⋊C4×C47—41no—
95C2×C4⋊C4×C47D414yescomplemented
96C2×C42×C47—41no—
97C2×C42×C47—41no—
98C2×C42×C47C2×C414yescomplemented
99#95×C47—24no—
100#95×C47—24no—
101C24×C47C2411yescharacteristic
102C23×D47—22no—
103C23×D47—22no—
104C23×D47—22no—
105C23×D47—22no—
106C23×D47—22no—
107C23×D47—22no—
108C23×D47—22no—
109C23×D47—22no—
110C23×D47—22no—
111C23×D47—22no—
112C23×D47—22no—
113C23×D47—22no—
114C23×D47C22×C414yes—
115C23×D47C2×D414yes—
116C23×D47C2×Q814yes—
117C22×C4×C47—21no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—21no—
124C22×C4×C47—21no—
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—22no—
135C22×C4×C47—22no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—22no—
142C22×C4×C47C22×C412yes—
143C22×C4×C47C22×C412yes—
144C22×C4×C47C22×C412yes—
145C22×C4×C47C2×D414yes—
146C22×C4×C47C2×D412yes—
147C22×C4×C47C2×D412yes—
148C22×C4×C47C2×D412yes—
149C22×C4×C47C2×Q812yes—
150C22×C4×C47#4112yes—
151C22×C4×C47#4112yes—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47—22no—
156C22×Dic47—22no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47—22no—
161C22×Dic47—22no—
162C22×Dic47—22no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—22no—
168C22×Dic47—22no—
169C22×Dic47—22no—
170C22×Dic47—22no—
171C22×Dic47C22×C414yes—
172C22×Dic47C2×D414yes—
173C2×D188—44no—
174C2×D188—44no—
175C2×D188—44no—
176C2×D188—44no—
177C2×D188—44no—
178C2×D188—44no—
179C2×D188C4⋊C4116yescomplemented
180C2×C4×D47—48no—
181C2×C4×D47—48no—
182C2×C4×D47—48no—
183C2×C4×D47—48no—
184C2×C4×D47—48no—
185C2×C4×D47—48no—
186C2×C4×D47—48no—
187C4⋊C4×C47—44no—
188C4⋊C4×C47—44no—
189C42×C47—44no—
190(C2×D47)⋊C4—216no—
191(C2×D47)⋊C4—216no—
192(C2×D47)⋊C4—48no—
193(C2×D47)⋊C4—48no—
194(C2×D47)⋊C4—48no—
195C4⋊Dic47—44no—
196C4⋊Dic47—44no—
197C4⋊Dic47—44no—
198Dic47⋊C4—48no—
199C23×C47C23×C411yescharacteristic
200C23×C47C22×D411yescharacteristic
201C23×C47C22×D411yescharacteristic
202C23×C47C22×D411yescharacteristic
203C23×C47C22×Q811yescharacteristic
204C23×C47C2×#4111yescharacteristic
205C23×C47C2×#4111yescharacteristic
206C23×C47H(5,𝔽2)11yescharacteristic
207C23×C47H(5,𝔽2)11yescharacteristic
208C23×C47H(5,𝔽2)11yescharacteristic
209C23×C47H(5,𝔽2)11yescharacteristic
210C23×C47H(5,𝔽2)11yescharacteristic
211C23×C47H(5,𝔽2)11yescharacteristic
212C23×C472−1+411yescharacteristic
213C23×C472−1+411yescharacteristic
214C22×D47—24no—
215C22×D47—24no—
216C22×D47—24no—
217C22×D47—24no—
218C22×D47—24no—
219C22×D47—24no—
220C22×D47—24no—
221C22×D47—24no—
222C22×D47—24no—
223C22×D47—24no—
224C22×D47—24no—
225C22×D47—24no—
226C22×D47—24no—
227C22×D47—24no—
228C22×D47—24no—
229C22×D47—24no—
230C22×D47—24no—
231C22×D47—24no—
232C22×D47—42no—
233C22×D47—42no—
234C22×D47—42no—
235C22×D47—42no—
236C22×D47—42no—
237C22×D47—42no—
238C22×D47—42no—
239C22×D47—42no—
240C22×D47—42no—
241C22×D47—42no—
242C22×D47—42no—
243C22×D47—42no—
244C22×D47—42no—
245C22×D47—42no—
246C22×D47—42no—
247C22×D47—42no—
248C22×D47C2×C4⋊C418yes—
249C2×C4×C47—22no—
250C2×C4×C47—22no—
251C2×C4×C47—22no—
252C2×C4×C47—22no—
253C2×C4×C47—22no—
254C2×C4×C47—22no—
255C2×C4×C47—22no—
256C2×C4×C47—22no—
257C2×C4×C47—22no—
258C2×C4×C47—22no—
259C2×C4×C47—22no—
260C2×C4×C47—22no—
261C2×C4×C47—22no—
262C2×C4×C47—22no—
263C2×C4×C47—22no—
264C2×C4×C47—22no—
265C2×C4×C47—22no—
266C2×C4×C47—22no—
267C2×C4×C47—24no—
268C2×C4×C47—24no—
269C2×C4×C47—24no—
270C2×C4×C47—42no—
271C2×C4×C47—42no—
272C2×C4×C47—42no—
273C2×C4×C47—42no—
274C2×C4×C47—42no—
275C2×C4×C47—42no—
276C2×C4×C47—42no—
277C2×C4×C47—42no—
278C2×C4×C47—42no—
279C2×C4×C47—42no—
280C2×C4×C47—42no—
281C2×C4×C47C2×C4⋊C414yes—
282C2×C4×C47C4×D414yes—
283C2×C4×C47C4×D414yes—
284C2×Dic47—24no—
285C2×Dic47—24no—
286C2×Dic47—24no—
287C2×Dic47—24no—
288C2×Dic47—24no—
289C2×Dic47—24no—
290C2×Dic47—42no—
291C2×Dic47—42no—
292C2×Dic47—42no—
293C2×Dic47—42no—
294C2×Dic47—42no—
295C2×Dic47—42no—
296C2×Dic47—42no—
297C2×Dic47—42no—
298C2×Dic47—42no—
299C2×Dic47—42no—
300C2×Dic47—42no—
301C2×Dic47—42no—
302C2×Dic47—42no—
303C2×Dic47—42no—
304C2×Dic47—42no—
305D188—416no—
306C4×D47—432no—
307#14440—471nomaximal, Sylow
308C22×C47C22×C4⋊C411yescharacteristic
309C22×C47C2×C4×D411yescharacteristic
310C22×C47C2×C4×D411yescharacteristic
311C22×C47#51811yescharacteristic
312C22×C47#51811yescharacteristic
313C22×C47#52011yescharacteristic
314C22×C47#52011yescharacteristic
315C22×C47#53411yescharacteristic
316C22×C47#53411yescharacteristic
317C22×C47#53411yescharacteristic
318C22×C47#53411yescharacteristic
319C22×C47#53711yescharacteristic
320C22×C47#53711yescharacteristic
321C22×C47#53811yescharacteristic
322C22×C47#53811yescharacteristic
323C22×C47#53911yescharacteristic
324C22×C47#53911yescharacteristic
325C22×C47#54311yescharacteristic
326C22×C47#54311yescharacteristic
327C22×C47D4211yescharacteristic
328C22×C47D4211yescharacteristic
329C22×C47D4211yescharacteristic
330C22×C47#54711yescharacteristic
331C22×C47#54711yescharacteristic
332C22×C47D4×Q811yescharacteristic
333C22×C47D4×Q811yescharacteristic
334C22×C47#55011yescharacteristic
335C22×C47#55011yescharacteristic
336C22×C47#55411yescharacteristic
337C22×C47#55411yescharacteristic
338C22×C47#55911yescharacteristic
339C22×C47H(3,𝔽4)11yescharacteristic
340C22×C47#56211yescharacteristic
341C22×C47#56211yescharacteristic
342C22×C47#56311yescharacteristic
343C2×D47—28no—
344C2×D47—28no—
345C2×D47—28no—
346C2×D47—44no—
347C2×D47—44no—
348C2×D47—44no—
349C2×D47—44no—
350C2×D47—44no—
351C2×D47—44no—
352C2×D47—44no—
353C2×D47—44no—
354C2×D47—44no—
355C2×D47—44no—
356C2×D47—44no—
357C2×D47—44no—
358C4×C47—24no—
359C4×C47—24no—
360C4×C47—24no—
361C4×C47—44no—
362C4×C47—82no—
363Dic47—44no—
364Dic47—44no—
365Dic47—82no—
366C2×#390—471no—
367C2×#386—472no—
368C2×#385—472no—
369C2×#385—472no—
370#1441—472no—
371#1439—472no—
372#1439—472no—
373C4⋊#95—471no—
374C4⋊#95D4711yescharacteristic, complemented
375C2×C47#231511yescharacteristic
376C2×C47#232511yescharacteristic
377C2×C47#232511yescharacteristic
378C2×C47D4×C4⋊C411yescharacteristic
379C2×C47D4×C4⋊C411yescharacteristic
380C2×C47#236611yescharacteristic
381C2×C47#237911yescharacteristic
382C2×C47#267911yescharacteristic
383C2×C47#268211yescharacteristic
384C2×C47#268211yescharacteristic
385C2×C47#268311yescharacteristic
386C2×C47#272411yescharacteristic
387C2×C47#273211yescharacteristic
388C2×C47#273211yescharacteristic
389C2×C47#280411yescharacteristic
390D47—48no—
391C23×D4—471no—
392C24×C4—472no—
393C22×C4⋊C4—471no—
394C22×C4⋊C4—471no—
395C22×C4⋊C4—472no—
396C22×C4⋊C4—471no—
397C22×C4⋊C4C2×D4711yescharacteristic
398C22×C4⋊C4C2×D4711yescharacteristic
399C22×C22⋊C4—472no—
400C22×C22⋊C4—472no—
401C22×C22⋊C4—472no—
402C22×C22⋊C4—472no—
403C22×C22⋊C4—472no—
404C22×C42C2×D4711yescharacteristic
405#390—478no—
406#386—948no—
407#385—948no—
408#385—948no—
409C2×#95—472no—
410C2×#95—472no—
411C2×#95—472no—
412C2×#95—472no—
413C2×#95—472no—
414C2×#95C2×D4712yes—
415C2×#95C2×D4712yes—
416C47#1444011yescharacteristic, complemented, Sylow
417C25—472no—
418C22×D4—474no—
419C22×D4—474no—
420C22×D4—474no—
421C22×D4—1881no—
422C22×D4—1881no—
423C22×D4—1881no—
424C22×D4—1881no—
425C23×C4—472no—
426C23×C4—472no—
427C23×C4—472no—
428C23×C4—944no—
429C23×C4—944no—
430C23×C4—944no—
431C23×C4—1882no—
432C23×C4—1882no—
433C23×C4—1882no—
434C23×C4—1882no—
435C23×C4C22×D4712yes—
436C23×C4C22×D4712yes—
437C23×C4C22×D4711yescharacteristic
438C23×C4C22×D4711yescharacteristic
439C23×C4C22×D4711yescharacteristic
440C2×C4⋊C4—22no—
441C2×C4⋊C4—41no—
442C2×C4⋊C4—41no—
443C2×C4⋊C4—41no—
444C2×C4⋊C4—41no—
445C2×C4⋊C4—474no—
446C2×C4⋊C4—474no—
447C2×C4⋊C4—944no—
448C2×C4⋊C4—944no—
449C2×C4⋊C4—942no—
450C2×C4⋊C4—1882no—
451C2×C4⋊C4—1881no—
452C2×C4⋊C4—1881no—
453C2×C4⋊C4—1881no—
454C2×C4⋊C4—1881no—
455C2×C4⋊C4—1881no—
456C2×C4⋊C4—1881no—
457C2×C4⋊C4D18814yescomplemented
458C2×C22⋊C4—478no—
459C2×C22⋊C4—478no—
460C2×C22⋊C4—944no—
461C2×C22⋊C4—944no—
462C2×C22⋊C4—944no—
463C2×C22⋊C4—944no—
464C2×C22⋊C4—944no—
465C2×C22⋊C4—944no—
466C2×C22⋊C4—944no—
467C2×C22⋊C4—944no—
468C2×C22⋊C4—944no—
469C2×C22⋊C4—1882no—
470C2×C22⋊C4—1882no—
471C2×C22⋊C4—1882no—
472C2×C22⋊C4—1882no—
473C2×C42—41no—
474C2×C42—41no—
475C2×C42C4×D4714yescomplemented
476#95—24no—
477#95—24no—
478#95—944no—
479#95—944no—
480#95—944no—
481#95—944no—
482#95—1882no—
483C24—474no—
484C24—474no—
485C24—474no—
486C24—942no—
487C24—942no—
488C24—942no—
489C24—942no—
490C24—942no—
491C24—942no—
492C24—942no—
493C24—942no—
494C24—942no—
495C24—942no—
496C24—942no—
497C24—942no—
498C24C23×D4711yescharacteristic
499C2×D4—4716no—
500C2×D4—1884no—
501C2×D4—1884no—
502C2×D4—1884no—
503C2×D4—1884no—
504C2×D4—1884no—
505C2×D4—1884no—
506C22×C4—21no—
507C22×C4—21no—
508C22×C4—21no—
509C22×C4—21no—
510C22×C4—21no—
511C22×C4—21no—
512C22×C4—21no—
513C22×C4—21no—
514C22×C4—21no—
515C22×C4—21no—
516C22×C4—21no—
517C22×C4—21no—
518C22×C4—22no—
519C22×C4—22no—
520C22×C4—22no—
521C22×C4—22no—
522C22×C4—22no—
523C22×C4—22no—
524C22×C4—22no—
525C22×C4—22no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—22no—
531C22×C4—474no—
532C22×C4—474no—
533C22×C4—942no—
534C22×C4—942no—
535C22×C4—942no—
536C22×C4—942no—
537C22×C4—942no—
538C22×C4—942no—
539C22×C4—942no—
540C22×C4—942no—
541C22×C4—942no—
542C22×C4—942no—
543C22×C4—942no—
544C22×C4—942no—
545C22×C4—942no—
546C22×C4—942no—
547C22×C4—942no—
548C22×C4—942no—
549C22×C4—942no—
550C22×C4—942no—
551C22×C4—942no—
552C22×C4—1888no—
553C22×C4—1888no—
554C22×C4—1888no—
555C22×C4—1888no—
556C22×C4—1888no—
557C22×C4—1888no—
558C22×C4—1888no—
559C22×C4C2×C4×D4712yes—
560C22×C4C2×C4×D4712yes—
561C22×C4C2×C4×D4712yes—
562C22×C4C2×D18814yes—
563C22×C4C2×D18812yes—
564C22×C4#1062535012yes—
565C22×C4D4×D4712yes—
566C22×C4D4×D4712yes—
567C22×C4Q8×D4712yes—
568C22×C4#1062535412yes—
569C4⋊C4—44no—
570C4⋊C4—44no—
571C4⋊C4—1884no—
572C4⋊C4—1884no—
573C4⋊C4—1888no—
574C4⋊C4—1884no—
575C22⋊C4—9416no—
576C22⋊C4—9416no—
577C22⋊C4—1888no—
578C22⋊C4—1888no—
579C22⋊C4—1888no—
580C42—44no—
581C23—478no—
582C23—944no—
583C23—944no—
584C23—944no—
585C23—944no—
586C23—944no—
587C23—944no—
588C23—944no—
589C23—944no—
590C23—944no—
591C23—944no—
592C23—944no—
593C23—944no—
594C23—944no—
595C23—944no—
596C23—944no—
597C23—944no—
598C23—944no—
599C23—944no—
600C23—1882no—
601C23—1882no—
602C23—1882no—
603C23—1882no—
604C23—1882no—
605C23—1882no—
606C23—1882no—
607C23—1882no—
608C23—1882no—
609C23—1882no—
610C23—1882no—
611C23—1882no—
612C23—1882no—
613C23—1882no—
614C23—1882no—
615C23—1882no—
616C23C22×C4×D4711yescharacteristic
617C23C2×D4×D4711yescharacteristic
618C23C2×D4×D4711yescharacteristic
619C23C22×D18811yescharacteristic
620C23C2×Q8×D4711yescharacteristic
621C23C2×#1062535011yescharacteristic
622C23C2×#1062535411yescharacteristic
623C23#1309406911yescharacteristic
624C23#1309406911yescharacteristic
625C23#1309406911yescharacteristic
626C23#1309407011yescharacteristic
627C23#1309407011yescharacteristic
628C23#1309407011yescharacteristic
629C23#1309407111yescharacteristic
630C23#1309407211yescharacteristic
631D4—18816no—
632C2×C4—22no—
633C2×C4—22no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—22no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—22no—
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—24no—
651C2×C4—24no—
652C2×C4—24no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—42no—
657C2×C4—42no—
658C2×C4—42no—
659C2×C4—42no—
660C2×C4—42no—
661C2×C4—42no—
662C2×C4—42no—
663C2×C4—42no—
664C2×C4—944no—
665C2×C4—944no—
666C2×C4—944no—
667C2×C4—944no—
668C2×C4—944no—
669C2×C4—944no—
670C2×C4—18832no—
671C2×C4—1882no—
672C2×C4—1882no—
673C2×C4—1882no—
674C2×C4—1882no—
675C2×C4—1882no—
676C2×C4—1882no—
677C2×C4—1882no—
678C2×C4—1882no—
679C2×C4—1882no—
680C2×C4—1882no—
681C2×C4—1882no—
682C2×C4—1882no—
683C2×C4—1882no—
684C2×C4—1882no—
685C2×C4—1882no—
686C2×C4C4⋊C4×D4714yes—
687C2×C4#1309398614yes—
688C2×C4C4×D18814yes—
689C22—948no—
690C22—948no—
691C22—948no—
692C22—1884no—
693C22—1884no—
694C22—1884no—
695C22—1884no—
696C22—1884no—
697C22—1884no—
698C22—1884no—
699C22—1884no—
700C22—1884no—
701C22—1884no—
702C22—1884no—
703C22—1884no—
704C22C2×C4⋊C4×D4711yescharacteristic
705C22C2×#1309398611yescharacteristic
706C22C2×C4×D18811yescharacteristic
707C22#1568959611yescharacteristic
708C22#1568959711yescharacteristic
709C22#1568960311yescharacteristic
710C22#1568960411yescharacteristic
711C22#1568968111yescharacteristic
712C22#1568968111yescharacteristic
713C22#1568968111yescharacteristic
714C22#1568968511yescharacteristic
715C22#1568970011yescharacteristic
716C22#1568970411yescharacteristic
717C22#1568971111yescharacteristic
718C22#1568971311yescharacteristic
719C22#1568972011yescharacteristic
720C22#1568972211yescharacteristic
721C22#1568974811yescharacteristic
722C22#1568974811yescharacteristic
723C22#1568975811yescharacteristic
724C22D4×D18811yescharacteristic
725C22D4×D18811yescharacteristic
726C22#1568977611yescharacteristic
727C22#1568977811yescharacteristic
728C22#1568978811yescharacteristic
729C22Q8×D18811yescharacteristic
730C22#1568979411yescharacteristic
731C22#1568979511yescharacteristic
732C22#1568983311yescharacteristic
733C22#1568983411yescharacteristic
734C22#1568985811yescharacteristic
735C22#1568986511yescharacteristic
736C22#1568986711yescharacteristic
737C22#1568987111yescharacteristic
738C22#1568987711yescharacteristic
739C4—24no—
740C4—24no—
741C4—24no—
742C4—44no—
743C4—82no—
744C4—3762no—
745C4—1884no—
746C4—1884no—
747C2—1888no—
748C2#2024600111yescharacteristic
749C2#2024608811yescharacteristic
750C2#2024609111yescharacteristic
751C2#2024628811yescharacteristic
752C2C4⋊C4×D18811yescharacteristic
753C2#2024645211yescharacteristic
754C2#2024655911yescharacteristic
755C2#2024972311yescharacteristic
756C2#2024975011yescharacteristic
757C2#2024975111yescharacteristic
758C2#2024975911yescharacteristic
759C2#2025031711yescharacteristic
760C2#2025040411yescharacteristic
761C2#2025040611yescharacteristic
762C2#2025133211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC47×C4⋊#95C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC4⋊#95D47
hypocenterC47#14440
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
3. C2×#15688997C2semidirect
4. C2×#15688994C2semidirect
5. #20241640C2semidirect
6. #20241634C2semidirect
7. #20241630C2semidirect
8. #20241618C2semidirect
9. C47×C4⋊#95C2semidirect
21. #15689025C4semidirect
60. C2×C4⋊Dic47C2×C4semidirect
61. C2×C4⋊Dic47D4semidirect
78. C2×(C2×D47)⋊C4C2×C4semidirect
79. C2×(C2×D47)⋊C4C2×C4semidirect
95. C2×C4⋊C4×C47D4semidirect
98. C2×C42×C47C2×C4semidirect
179. C2×D188C4⋊C4semidirect
374. C4⋊#95D47semidirect
416. C47#14440semidirect
457. C2×C4⋊C4D188semidirect
475. C2×C42C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156890252
C2×#156890012
C2×#156889972
C2×#156889942
#202416402
#202416342
#202416302
#202416182
C47×C4⋊#952
#1444047