Finite Group Databasebeta

← #26152980

Subgroups — #26152980

Order 12032.

1906 conjugacy classes of subgroups.

The subgroup lattice has 836 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689046C212yesmaximal, complemented
2C2×#15689026C211yesmaximal, characteristic
3C2×#15689026C211yesmaximal, characteristic
4C2×#15689022C211yesmaximal, characteristic, complemented
5C2×#15689021C211yesmaximal, characteristic, complemented
6C2×#15689019C211yesmaximal, characteristic, complemented
7#20241633C212yesmaximal, complemented
8#20241631C212yesmaximal, complemented
9#20241631C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C47×#390C211yesmaximal, characteristic
12C22×C4⋊Dic47C2212yes—
13C22×C4⋊Dic47C2211yescharacteristic
14C22×C4⋊Dic47C2211yescharacteristic
15C22×Dic47⋊C4C2212yes—
16C22×Dic47⋊C4C2212yes—
17C22×C22⋊Dic47C2212yes—
18C22×C22⋊Dic47C2212yes—
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23#15689046—28no—
24#15689026—24no—
25#15689026—24no—
26#15689022—24no—
27#15689021—24no—
28#15689019—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2211yescharacteristic
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C2×C47⋊#95C2211yescharacteristic
36C23×D4×C47C2211yescharacteristic
37C22×C4⋊C4×C47C2211yescharacteristic
38C22×C22⋊C4×C47C2212yes—
39C22×C22⋊C4×C47C2212yes—
40C22×C42×C47C2211yescharacteristic
41C47×#390—24no—
42C23×Dic47C2311yescharacteristic
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C23×Dic47C2311yescharacteristic
48C2×C4⋊Dic47—22no—
49C2×C4⋊Dic47—22no—
50C2×C4⋊Dic47—22no—
51C2×C4⋊Dic47—22no—
52C2×C4⋊Dic47—24no—
53C2×C4⋊Dic47—24no—
54C2×C4⋊Dic47—42no—
55C2×C4⋊Dic47D414yes—
56C2×C4⋊Dic47D414yes—
57C2×Dic47⋊C4—24no—
58C2×Dic47⋊C4—24no—
59C2×Dic47⋊C4—24no—
60C2×Dic47⋊C4—24no—
61C2×Dic47⋊C4—42no—
62C2×Dic47⋊C4—42no—
63C2×C22⋊Dic47—24no—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47—24no—
68C2×C22⋊Dic47—24no—
69C2×C22⋊Dic47—24no—
70C2×C22⋊Dic47—24no—
71C2×C22⋊Dic47—42no—
72C2×C22⋊Dic47—42no—
73C2×C22⋊Dic47—42no—
74C2×C22⋊Dic47—42no—
75C2×C4×Dic47—22no—
76C2×C4×Dic47—22no—
77C2×C4×Dic47—22no—
78C2×C4×Dic47—22no—
79C2×C4×Dic47—22no—
80C2×C4×Dic47—22no—
81C47⋊#95—24no—
82C47⋊#95—22no—
83C47⋊#95—24no—
84C47⋊#95—24no—
85C47⋊#95—22no—
86C47⋊#95—22no—
87C47⋊#95D414yescomplemented
88C25×C47C2312yes—
89C22×D4×C47—22no—
90C22×D4×C47—22no—
91C22×D4×C47—22no—
92C22×D4×C47—22no—
93C22×D4×C47—22no—
94C22×D4×C47—22no—
95C22×D4×C47Q814yes—
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2312yes—
98C23×C4×C47C2311yescharacteristic
99C23×C4×C47C2311yescharacteristic
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47D414yes—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—24no—
106C2×C22⋊C4×C47—24no—
107C2×C22⋊C4×C47—42no—
108C2×C22⋊C4×C47—42no—
109C2×C42×C47—22no—
110C2×C42×C47—22no—
111C2×C42×C47—22no—
112C24×C47—22no—
113C24×C47—22no—
114C24×C47—22no—
115C24×C47—22no—
116C24×C47—22no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47—22no—
122C24×C47—22no—
123C24×C47—22no—
124C24×C47—22no—
125C24×C47—22no—
126C24×C47C2×Q814yes—
127C24×C47C2411yescharacteristic
128C2×D4×C47—28no—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C2×D4×C47—44no—
132C2×D4×C47—44no—
133C2×D4×C47—44no—
134C2×D4×C47—44no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—22no—
144C22×C4×C47—22no—
145C22×C4×C47—21no—
146C22×C4×C47—21no—
147C22×C4×C47—21no—
148C22×C4×C47—21no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D414yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47C2×D412yes—
157C22×C4×C47C2×D412yes—
158C22×C4×C47C2×Q812yes—
159C22×C4×C47#4112yes—
160C22×C4×C47#4112yes—
161C22×C4×C47#4112yes—
162C22×C4×C47#4112yes—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—22no—
166C22×Dic47—22no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—21no—
172C22×Dic47—21no—
173C22×Dic47—22no—
174C22×Dic47—22no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—21no—
182C22×Dic47—21no—
183C22×Dic47—22no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—22no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—21no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—21no—
196C22×Dic47—21no—
197C22×Dic47—21no—
198C22×Dic47—21no—
199C22×Dic47C2×D414yes—
200C22×Dic47C2×D414yes—
201C22×Dic47C2×D412yes—
202C22×Dic47C2×D412yes—
203C22×Dic47#4112yes—
204C22×Dic47#4112yes—
205C4⋊C4×C47—28no—
206C22⋊C4×C47—48no—
207C22⋊C4×C47—48no—
208C42×C47—44no—
209C22⋊Dic47—48no—
210C22⋊Dic47—48no—
211C22⋊Dic47—48no—
212C22⋊Dic47—48no—
213C4⋊Dic47—28no—
214C4⋊Dic47—28no—
215C4⋊Dic47—48no—
216Dic47⋊C4—48no—
217Dic47⋊C4—48no—
218C4×Dic47—44no—
219C4×Dic47—44no—
220C23×C47—24no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—42no—
228C23×C47—42no—
229C23×C47—42no—
230C23×C47—42no—
231C23×C47—42no—
232C23×C47—42no—
233C23×C47—42no—
234C23×C47—42no—
235C23×C47—42no—
236C23×C47—42no—
237C23×C47—42no—
238C23×C47—42no—
239C23×C47—42no—
240C23×C47—42no—
241C23×C47—42no—
242C23×C47—42no—
243C23×C47—42no—
244C23×C47—42no—
245C23×C47—42no—
246C23×C47—42no—
247C23×C47—42no—
248C23×C47—42no—
249C23×C47—42no—
250C23×C47—42no—
251C23×C47—42no—
252C23×C47—42no—
253C23×C47—42no—
254C23×C47—42no—
255C23×C47C22×D411yescharacteristic
256C23×C47C22×D411yescharacteristic
257C23×C47C22×D411yescharacteristic
258C23×C47C22×D411yescharacteristic
259C23×C47C22×Q811yescharacteristic
260C23×C47C2×#4111yescharacteristic
261C23×C47C2×#4111yescharacteristic
262C23×C47C2×#4111yescharacteristic
263C23×C47C2×#4111yescharacteristic
264C23×C47C2×#4111yescharacteristic
265C23×C47C2×#4111yescharacteristic
266C23×C47H(5,𝔽2)11yescharacteristic
267C23×C47H(5,𝔽2)11yescharacteristic
268C23×C47H(5,𝔽2)11yescharacteristic
269C23×C472−1+411yescharacteristic
270D4×C47—416no—
271C2×C4×C47—24no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—24no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—24no—
279C2×C4×C47—22no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—42no—
283C2×C4×C47—41no—
284C2×C4×C47—42no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—41no—
288C2×C4×C47—41no—
289C2×C4×C47—41no—
290C2×C4×C47—41no—
291C2×C4×C47—42no—
292C2×C4×C47#12114yes—
293C2×C4×C47#12114yes—
294C2×C4×C47#12114yes—
295C2×C4×C47C22⋊Q814yes—
296C2×C4×C47C22⋊Q814yes—
297C2×C4×C47C22⋊Q814yes—
298C2×C4×C47#12614yes—
299C2×Dic47—24no—
300C2×Dic47—24no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—24no—
307C2×Dic47—22no—
308C2×Dic47—24no—
309C2×Dic47—22no—
310C2×Dic47—22no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—24no—
314C2×Dic47—24no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—41no—
318C2×Dic47—41no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—42no—
322C2×Dic47—42no—
323C2×Dic47—41no—
324C2×Dic47—42no—
325C2×Dic47—42no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—41no—
329C2×Dic47—42no—
330C2×Dic47—42no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—42no—
336C2×Dic47—41no—
337C2×Dic47—41no—
338C2×Dic47—42no—
339C2×Dic47—41no—
340C2×Dic47—41no—
341#15141—471nomaximal, Sylow
342C22×C47—44no—
343C22×C47—44no—
344C22×C47—44no—
345C22×C47—44no—
346C22×C47—44no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—82no—
350C22×C47—82no—
351C22×C47—82no—
352C22×C47—82no—
353C22×C47—82no—
354C22×C47—82no—
355C22×C47—82no—
356C22×C47—82no—
357C22×C47C2×#12111yescharacteristic
358C22×C47C2×#12111yescharacteristic
359C22×C47C2×#12111yescharacteristic
360C22×C47C2×C22⋊Q811yescharacteristic
361C22×C47C2×C22⋊Q811yescharacteristic
362C22×C47C2×C22⋊Q811yescharacteristic
363C22×C47C2×#12611yescharacteristic
364C22×C47#52911yescharacteristic
365C22×C47#52911yescharacteristic
366C22×C47#52911yescharacteristic
367C22×C47#53211yescharacteristic
368C22×C47#53211yescharacteristic
369C22×C47#53211yescharacteristic
370C22×C47#54011yescharacteristic
371C22×C47#54011yescharacteristic
372C22×C47#54011yescharacteristic
373C22×C47#54211yescharacteristic
374C22×C47#54211yescharacteristic
375C22×C47#54211yescharacteristic
376C22×C47D4211yescharacteristic
377C22×C47D4211yescharacteristic
378C22×C47D4211yescharacteristic
379C22×C47#54611yescharacteristic
380C22×C47#54611yescharacteristic
381C22×C47#54611yescharacteristic
382C22×C47#54811yescharacteristic
383C22×C47#54811yescharacteristic
384C22×C47#54811yescharacteristic
385C22×C47D4×Q811yescharacteristic
386C22×C47#55011yescharacteristic
387C22×C47#55011yescharacteristic
388C22×C47#55011yescharacteristic
389C22×C47#55411yescharacteristic
390C22×C47#55411yescharacteristic
391C22×C47#55411yescharacteristic
392C4×C47—42no—
393C4×C47—42no—
394C4×C47—44no—
395C4×C47#39618yescomplemented
396Dic47—42no—
397Dic47—42no—
398Dic47—44no—
399Dic47—44no—
400Dic47—42no—
401Dic47—42no—
402C2×#396—472no—
403C2×#390—471no—
404C2×#390—471no—
405C2×#390D4711yescharacteristic
406C2×#389—471no—
407C2×#389—471no—
408C2×#389—471no—
409#1439—472no—
410#1439—472no—
411#1439—472no—
412C4×#95—471no—
413C2×C47—84no—
414C2×C47C2×#39611yescharacteristic
415C2×C47#242611yescharacteristic
416C2×C47#242611yescharacteristic
417C2×C47#242611yescharacteristic
418C2×C47#242811yescharacteristic
419C2×C47#242811yescharacteristic
420C2×C47#242811yescharacteristic
421C2×C47#245211yescharacteristic
422C2×C47#245211yescharacteristic
423C2×C47#245211yescharacteristic
424C2×C47#245411yescharacteristic
425C2×C47#245411yescharacteristic
426C2×C47#245411yescharacteristic
427C2×C47#264411yescharacteristic
428C2×C47#286011yescharacteristic
429C23×D4C2×D4711yescharacteristic
430C22×C4⋊C4—471no—
431C22×C4⋊C4—471no—
432C22×C4⋊C4—472no—
433C22×C4⋊C4—472no—
434C22×C4⋊C4—472no—
435C22×C4⋊C4C2×D4711yescharacteristic
436C22×C22⋊C4—472no—
437C22×C22⋊C4—472no—
438C22×C22⋊C4—472no—
439C22×C22⋊C4—472no—
440C22×C22⋊C4C2×D4712yes—
441C22×C22⋊C4C2×D4712yes—
442C22×C42—471no—
443C22×C42—471no—
444C22×C42C2×D4711yescharacteristic
445#396—948no—
446#390—24no—
447#390—944no—
448#390—944no—
449#389—944no—
450#389—944no—
451#389—944no—
452C2×#95—471no—
453C2×#95—471no—
454C2×#95—471no—
455C2×#95—471no—
456C2×#95—472no—
457C2×#95—472no—
458C2×#95—472no—
459C47#1514111yescharacteristic, complemented, Sylow
460C25C22×D4712yes—
461C22×D4—22no—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4—22no—
467C22×D4Dic9414yes—
468C23×C4—472no—
469C23×C4—472no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—471no—
474C23×C4C22×D4711yescharacteristic
475C23×C4C22×D4711yescharacteristic
476C23×C4C22×D4712yes—
477C23×C4C22×D4711yescharacteristic
478C2×C4⋊C4—22no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—474no—
481C2×C4⋊C4—474no—
482C2×C4⋊C4—942no—
483C2×C4⋊C4—942no—
484C2×C4⋊C4—942no—
485C2×C4⋊C4—942no—
486C2×C4⋊C4—944no—
487C2×C4⋊C4—944no—
488C2×C4⋊C4—944no—
489C2×C4⋊C4—944no—
490C2×C4⋊C4—944no—
491C2×C4⋊C4—944no—
492C2×C4⋊C4—1882no—
493C2×C4⋊C4—1882no—
494C2×C4⋊C4—1882no—
495C2×C4⋊C4C22⋊D4714yes—
496C2×C22⋊C4—24no—
497C2×C22⋊C4—24no—
498C2×C22⋊C4—24no—
499C2×C22⋊C4—24no—
500C2×C22⋊C4—42no—
501C2×C22⋊C4—42no—
502C2×C22⋊C4—944no—
503C2×C22⋊C4—944no—
504C2×C22⋊C4—944no—
505C2×C22⋊C4—944no—
506C2×C22⋊C4—944no—
507C2×C22⋊C4—944no—
508C2×C22⋊C4—944no—
509C2×C22⋊C4—944no—
510C2×C22⋊C4—1882no—
511C2×C22⋊C4—1882no—
512C2×C22⋊C4—1882no—
513C2×C22⋊C4—1882no—
514C2×C42—22no—
515C2×C42—22no—
516C2×C42—22no—
517C2×C42—942no—
518C2×C42—942no—
519C2×C42—942no—
520C2×C42—942no—
521C2×C42—942no—
522C2×C42—942no—
523#95—474no—
524#95—942no—
525#95—942no—
526#95—944no—
527#95—944no—
528#95—942no—
529#95—944no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic9414yes—
545C24C23×D4711yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—44no—
550C2×D4—44no—
551C2×D4—44no—
552C2×D4—44no—
553C22×C4—21no—
554C22×C4—22no—
555C22×C4—21no—
556C22×C4—22no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—21no—
570C22×C4—21no—
571C22×C4—472no—
572C22×C4—472no—
573C22×C4—474no—
574C22×C4—474no—
575C22×C4—472no—
576C22×C4—472no—
577C22×C4—941no—
578C22×C4—942no—
579C22×C4—941no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—942no—
585C22×C4—942no—
586C22×C4—941no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—942no—
592C22×C4—942no—
593C22×C4—941no—
594C22×C4—941no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—942no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—942no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—942no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4C2×Dic9412yes—
614C22×C4#1062535012yes—
615C22×C4D4×D4712yes—
616C22×C4D4×D4712yes—
617C22×C4D4×D4712yes—
618C22×C4#1062535212yes—
619C22×C4#1062535212yes—
620C22×C4#1062535212yes—
621C22×C4C2×C22⋊D4714yes—
622C22×C4C2×C22⋊D4712yes—
623C4⋊C4—28no—
624C4⋊C4—948no—
625C4⋊C4—948no—
626C4⋊C4—1888no—
627C4⋊C4—1888no—
628C4⋊C4—1888no—
629C22⋊C4—48no—
630C22⋊C4—48no—
631C22⋊C4—1888no—
632C22⋊C4—1888no—
633C22⋊C4—1888no—
634C22⋊C4—1888no—
635C42—44no—
636C42—1884no—
637C42—1884no—
638C23—24no—
639C23—24no—
640C23—24no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—42no—
646C23—42no—
647C23—42no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—42no—
652C23—42no—
653C23—42no—
654C23—42no—
655C23—42no—
656C23—42no—
657C23—42no—
658C23—42no—
659C23—42no—
660C23—42no—
661C23—42no—
662C23—42no—
663C23—42no—
664C23—42no—
665C23—42no—
666C23—42no—
667C23—42no—
668C23—42no—
669C23—42no—
670C23—42no—
671C23—42no—
672C23—42no—
673C23C2×D4×D4711yescharacteristic
674C23C2×D4×D4711yescharacteristic
675C23C2×D4×D4711yescharacteristic
676C23C22×C22⋊D4711yescharacteristic
677C23C22×Dic9411yescharacteristic
678C23#41×D4711yescharacteristic
679C23#41×D4711yescharacteristic
680C23C2×#1062535211yescharacteristic
681C23C2×#1062535211yescharacteristic
682C23C2×#1062535211yescharacteristic
683C23C2×#1062535011yescharacteristic
684C23#1309406911yescharacteristic
685C23#1309406911yescharacteristic
686C23#1309407011yescharacteristic
687C23#1309407111yescharacteristic
688D4—416no—
689C2×C4—22no—
690C2×C4—24no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—24no—
694C2×C4—22no—
695C2×C4—24no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—42no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—42no—
705C2×C4—41no—
706C2×C4—41no—
707C2×C4—42no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—942no—
711C2×C4—942no—
712C2×C4—944no—
713C2×C4—942no—
714C2×C4—944no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—944no—
718C2×C4—942no—
719C2×C4—944no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—944no—
723C2×C4—944no—
724C2×C4—942no—
725C2×C4—942no—
726C2×C4—942no—
727C2×C4—942no—
728C2×C4—1881no—
729C2×C4—1881no—
730C2×C4—1882no—
731C2×C4—1882no—
732C2×C4—1881no—
733C2×C4—1881no—
734C2×C4—1881no—
735C2×C4—1881no—
736C2×C4—1882no—
737C2×C4—1881no—
738C2×C4—1881no—
739C2×C4—1882no—
740C2×C4—1881no—
741C2×C4—1881no—
742C2×C4—1881no—
743C2×C4—1881no—
744C2×C4—1881no—
745C2×C4—1881no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1881no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4—1881no—
752C2×C4#1309399514yes—
753C2×C4#1309399614yes—
754C2×C4#1309399714yes—
755C2×C4#1309400114yes—
756C2×C4#1309400114yes—
757C2×C4#1309400314yes—
758C2×C4#1309401714yes—
759C22—44no—
760C22—44no—
761C22—44no—
762C22—44no—
763C22—44no—
764C22—44no—
765C22—44no—
766C22—82no—
767C22—82no—
768C22—82no—
769C22—82no—
770C22—82no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22C2×#1309399511yescharacteristic
775C22C2×#1309399611yescharacteristic
776C22C2×#1309399711yescharacteristic
777C22C2×#1309400111yescharacteristic
778C22C2×#1309400111yescharacteristic
779C22C2×#1309400311yescharacteristic
780C22C2×#1309401711yescharacteristic
781C22#1568965211yescharacteristic
782C22#1568965411yescharacteristic
783C22#1568965511yescharacteristic
784C22#1568966811yescharacteristic
785C22#1568967011yescharacteristic
786C22#1568967111yescharacteristic
787C22#1568972411yescharacteristic
788C22#1568972611yescharacteristic
789C22#1568972711yescharacteristic
790C22#1568973811yescharacteristic
791C22#1568974011yescharacteristic
792C22#1568974211yescharacteristic
793C22D4×C22⋊D4711yescharacteristic
794C22#1568975711yescharacteristic
795C22#1568975811yescharacteristic
796C22#1568976611yescharacteristic
797C22#1568976711yescharacteristic
798C22#1568977011yescharacteristic
799C22#1568977911yescharacteristic
800C22#1568978011yescharacteristic
801C22#1568978111yescharacteristic
802C22D4×Dic9411yescharacteristic
803C22#1568979111yescharacteristic
804C22#1568979211yescharacteristic
805C22#1568979311yescharacteristic
806C22#1568983011yescharacteristic
807C22#1568983211yescharacteristic
808C22#1568983211yescharacteristic
809C4—42no—
810C4—42no—
811C4—44no—
812C4—1882no—
813C4—1882no—
814C4—1884no—
815C4—1882no—
816C4—1884no—
817C4—1882no—
818C4#1568904618yescomplemented
819C2—84no—
820C2C2×#1568904611yescharacteristic
821C2#2024695011yescharacteristic
822C2#2024695511yescharacteristic
823C2#2024695711yescharacteristic
824C2#2024697211yescharacteristic
825C2#2024697711yescharacteristic
826C2#2024697911yescharacteristic
827C2#2024723211yescharacteristic
828C2#2024724011yescharacteristic
829C2#2024724111yescharacteristic
830C2#2024725411yescharacteristic
831C2#2024726211yescharacteristic
832C2#2024726311yescharacteristic
833C2#2024934911yescharacteristic
834C2#2025175211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutator, socle, cosocleC24×C47C24
FittingC2×C47×#390C2
prime radicalC23×D4×C47C22
hypercenterC2×#390D47
hypocenterC47#15141
LCSG ▷ C24×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
1. C2×#15689046C2semidirect
4. C2×#15689022C2semidirect
5. C2×#15689021C2semidirect
6. C2×#15689019C2semidirect
7. #20241633C2semidirect
8. #20241631C2semidirect
9. #20241631C2semidirect
10. C4×C47⋊#95C2semidirect
87. C47⋊#95D4semidirect
395. C4×C47#396semidirect
459. C47#15141semidirect
818. C4#15689046semidirect

Maximal subgroups

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

subgroupindex
C2×#156890462
C2×#156890262
C2×#156890222
C2×#156890212
C2×#156890192
#202416332
#202416312
C4×C47⋊#952
C2×C47×#3902
#1514147