Finite Group Databasebeta

← #26138611

Subgroups — #26138611

Order 12032.

2314 conjugacy classes of subgroups.

The subgroup lattice has 840 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×D4×Dic47C211yesmaximal, characteristic
2C2×#15689026C211yesmaximal, characteristic
3C2×#15688984C212yesmaximal, complemented
4#20241635C212yesmaximal, complemented
5#20241635C212yesmaximal, complemented
6#20241618C211yesmaximal, characteristic, complemented
7#20241617C211yesmaximal, characteristic, complemented
8#20241617C211yesmaximal, characteristic, complemented
9#20241610C212yesmaximal, complemented
10C4×C47⋊#95C211yesmaximal, characteristic, complemented
11C2×C47×#390C211yesmaximal, characteristic
12C24×Dic47C2212yes—
13C2×D4×Dic47—24no—
14C2×D4×Dic47—24no—
15C2×D4×Dic47C418yescomplemented
16C22×C4⋊Dic47C2211yescharacteristic
17C22×C4⋊Dic47C2211yescharacteristic
18C22×C22⋊Dic47C2212yes—
19C22×C22⋊Dic47C2212yes—
20C22×C22⋊Dic47C2212yes—
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23#15689026—24no—
24#15688984—28no—
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2211yescharacteristic
29C2×C47⋊#95C2211yescharacteristic
30C2×C47⋊#95C2211yescharacteristic
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2211yescharacteristic
35C23×D4×C47C2211yescharacteristic
36C22×C4⋊C4×C47C2211yescharacteristic
37C22×C22⋊C4×C47C2212yes—
38C22×C22⋊C4×C47C2212yes—
39C22×C42×C47C2211yescharacteristic
40C47×#390—24no—
41C23×Dic47—24no—
42C23×Dic47—24no—
43C23×Dic47—24no—
44C23×Dic47—24no—
45C23×Dic47—42no—
46C23×Dic47—42no—
47C23×Dic47C2×C418yes—
48C23×Dic47C2312yes—
49C23×Dic47C2311yescharacteristic
50C23×Dic47C2312yes—
51C23×Dic47C2311yescharacteristic
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54D4×Dic47—232no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47—22no—
57C2×C4⋊Dic47—22no—
58C2×C4⋊Dic47—22no—
59C2×C4⋊Dic47—22no—
60C2×C4⋊Dic47C2×C414yes—
61C2×C22⋊Dic47—24no—
62C2×C22⋊Dic47—24no—
63C2×C22⋊Dic47—24no—
64C2×C22⋊Dic47—24no—
65C2×C22⋊Dic47—24no—
66C2×C22⋊Dic47—24no—
67C2×C22⋊Dic47—42no—
68C2×C22⋊Dic47—42no—
69C2×C22⋊Dic47C2×C418yes—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47—22no—
73C2×C4×Dic47—22no—
74C2×C4×Dic47—22no—
75C2×C4×Dic47C2×C414yes—
76C47⋊#95—24no—
77C47⋊#95—22no—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—22no—
81C47⋊#95—22no—
82C47⋊#95—42no—
83C47⋊#95—42no—
84C47⋊#95—42no—
85C47⋊#95D414yescomplemented
86C25×C47C2312yes—
87C22×D4×C47—22no—
88C22×D4×C47—22no—
89C22×D4×C47—22no—
90C22×D4×C47—22no—
91C22×D4×C47C2×C414yes—
92C22×D4×C47D414yes—
93C22×D4×C47D414yes—
94C23×C4×C47C2312yes—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C23×C4×C47C2311yescharacteristic
98C2×C4⋊C4×C47—22no—
99C2×C4⋊C4×C47—22no—
100C2×C4⋊C4×C47—22no—
101C2×C22⋊C4×C47—24no—
102C2×C22⋊C4×C47—24no—
103C2×C22⋊C4×C47—24no—
104C2×C22⋊C4×C47—24no—
105C2×C22⋊C4×C47—42no—
106C2×C22⋊C4×C47—42no—
107C2×C42×C47—22no—
108C2×C42×C47—22no—
109C2×C42×C47—22no—
110C24×C47—22no—
111C24×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×C47C22×C414yes—
123C24×C47C2×D414yes—
124C24×C47C2×D414yes—
125C24×C47C2411yescharacteristic
126C2×D4×C47—28no—
127C2×D4×C47—28no—
128C2×D4×C47—28no—
129C2×D4×C47—28no—
130C2×D4×C47—28no—
131C2×D4×C47—28no—
132C2×D4×C47C22⋊C4116yes—
133C22×C4×C47—21no—
134C22×C4×C47—21no—
135C22×C4×C47—21no—
136C22×C4×C47—21no—
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47—22no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—22no—
149C22×C4×C47—22no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47C22×C412yes—
153C22×C4×C47C2×D412yes—
154C22×C4×C47C2×D412yes—
155C22×C4×C47C2×D412yes—
156C22×C4×C47#4112yes—
157C22×C4×C47#4112yes—
158C22×C4×C47#4112yes—
159C22×C4×C47#4112yes—
160C22×C4×C47#4112yes—
161C22×Dic47—21no—
162C22×Dic47—21no—
163C22×Dic47—21no—
164C22×Dic47—21no—
165C22×Dic47—216no—
166C22×Dic47—22no—
167C22×Dic47—21no—
168C22×Dic47—21no—
169C22×Dic47—21no—
170C22×Dic47—21no—
171C22×Dic47—22no—
172C22×Dic47—22no—
173C22×Dic47—21no—
174C22×Dic47—21no—
175C22×Dic47—21no—
176C22×Dic47—21no—
177C22×Dic47—21no—
178C22×Dic47—21no—
179C22×Dic47—21no—
180C22×Dic47—21no—
181C22×Dic47—22no—
182C22×Dic47—21no—
183C22×Dic47—21no—
184C22×Dic47—22no—
185C22×Dic47—22no—
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—216no—
191C22×Dic47—22no—
192C22×Dic47—22no—
193C22×Dic47—22no—
194C22×Dic47—22no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—48no—
199C22×Dic47—48no—
200C22×Dic47—48no—
201C22×Dic47—48no—
202C22×Dic47—48no—
203C22×Dic47C22×C412yes—
204C22×Dic47C22×C414yes—
205C22×Dic47C22×C412yes—
206C22×Dic47C2×D412yes—
207C22×Dic47C2×D412yes—
208C22×Dic47#4112yes—
209C22×Dic47#4112yes—
210C4⋊C4×C47—44no—
211C22⋊C4×C47—48no—
212C22⋊C4×C47—48no—
213C42×C47—44no—
214C22⋊Dic47—216no—
215C22⋊Dic47—48no—
216C22⋊Dic47—48no—
217C4⋊Dic47—28no—
218C4⋊Dic47—44no—
219C4×Dic47—28no—
220C4×Dic47—44no—
221C23×C47—24no—
222C23×C47—24no—
223C23×C47—24no—
224C23×C47—24no—
225C23×C47—24no—
226C23×C47—24no—
227C23×C47—24no—
228C23×C47—24no—
229C23×C47—24no—
230C23×C47—24no—
231C23×C47—24no—
232C23×C47—24no—
233C23×C47—24no—
234C23×C47—24no—
235C23×C47—24no—
236C23×C47—24no—
237C23×C47—24no—
238C23×C47—24no—
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×C47C2×C22⋊C418yes—
256C23×C47C23×C411yescharacteristic
257C23×C47C22×D411yescharacteristic
258C23×C47C22×D411yescharacteristic
259C23×C47C22×D411yescharacteristic
260C23×C47C2×#4111yescharacteristic
261C23×C47C2×#4111yescharacteristic
262C23×C47C2×#4111yescharacteristic
263C23×C47C2×#4111yescharacteristic
264C23×C47C2×#4111yescharacteristic
265C23×C47C2×#4111yescharacteristic
266C23×C47C2×#4111yescharacteristic
267C23×C47H(5,𝔽2)11yescharacteristic
268C23×C47H(5,𝔽2)11yescharacteristic
269C23×C47H(5,𝔽2)11yescharacteristic
270C23×C472−1+411yescharacteristic
271D4×C47—232no—
272C2×C4×C47—22no—
273C2×C4×C47—22no—
274C2×C4×C47—22no—
275C2×C4×C47—22no—
276C2×C4×C47—22no—
277C2×C4×C47—22no—
278C2×C4×C47—41no—
279C2×C4×C47—41no—
280C2×C4×C47—41no—
281C2×C4×C47—41no—
282C2×C4×C47—41no—
283C2×C4×C47—41no—
284C2×C4×C47—41no—
285C2×C4×C47—41no—
286C2×C4×C47—42no—
287C2×C4×C47—42no—
288C2×C4×C47—42no—
289C2×C4×C47—42no—
290C2×C4×C47—42no—
291C2×C4×C47—42no—
292C2×C4×C47—42no—
293C2×C4×C47C2×C22⋊C414yes—
294C2×C4×C47#11714yes—
295C2×C4×C47#11714yes—
296C2×C4×C47#12314yes—
297C2×C4×C47#12314yes—
298C2×C4×C47#12314yes—
299C2×C4×C47#12314yes—
300C2×Dic47—22no—
301C2×Dic47—22no—
302C2×Dic47—22no—
303C2×Dic47—22no—
304C2×Dic47—22no—
305C2×Dic47—22no—
306C2×Dic47—22no—
307C2×Dic47—24no—
308C2×Dic47—24no—
309C2×Dic47—22no—
310C2×Dic47—24no—
311C2×Dic47—22no—
312C2×Dic47—22no—
313C2×Dic47—22no—
314C2×Dic47—22no—
315C2×Dic47—22no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—432no—
319C2×Dic47—41no—
320C2×Dic47—41no—
321C2×Dic47—41no—
322C2×Dic47—41no—
323C2×Dic47—42no—
324C2×Dic47—42no—
325C2×Dic47—41no—
326C2×Dic47—41no—
327C2×Dic47—41no—
328C2×Dic47—42no—
329C2×Dic47—42no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—41no—
334C2×Dic47—41no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47C4×D414yes—
343#13916—471nomaximal, Sylow
344C22×C47—28no—
345C22×C47—28no—
346C22×C47—28no—
347C22×C47—44no—
348C22×C47—44no—
349C22×C47—44no—
350C22×C47—44no—
351C22×C47—44no—
352C22×C47—44no—
353C22×C47—44no—
354C22×C47—44no—
355C22×C47—44no—
356C22×C47—44no—
357C22×C47—44no—
358C22×C47—44no—
359C22×C47C22×C22⋊C411yescharacteristic
360C22×C47C2×#11711yescharacteristic
361C22×C47C2×#11711yescharacteristic
362C22×C47C2×C4×D411yescharacteristic
363C22×C47C4×#4111yescharacteristic
364C22×C47#51811yescharacteristic
365C22×C47#52011yescharacteristic
366C22×C47C2×#12311yescharacteristic
367C22×C47C2×#12311yescharacteristic
368C22×C47C2×#12311yescharacteristic
369C22×C47C2×#12311yescharacteristic
370C22×C47#52911yescharacteristic
371C22×C47#52911yescharacteristic
372C22×C47#53211yescharacteristic
373C22×C47#53211yescharacteristic
374C22×C47#54011yescharacteristic
375C22×C47#54011yescharacteristic
376C22×C47#54211yescharacteristic
377C22×C47#54211yescharacteristic
378C22×C47D4211yescharacteristic
379C22×C47D4211yescharacteristic
380C22×C47#54611yescharacteristic
381C22×C47#54611yescharacteristic
382C22×C47#54611yescharacteristic
383C22×C47#54611yescharacteristic
384C22×C47#54711yescharacteristic
385C22×C47#54711yescharacteristic
386C22×C47#54711yescharacteristic
387C22×C47#55011yescharacteristic
388C22×C47#55311yescharacteristic
389C22×C47#55311yescharacteristic
390C22×C47#55511yescharacteristic
391C22×C47#55611yescharacteristic
392C22×C47#55911yescharacteristic
393C22×C47#55911yescharacteristic
394C4×C47—42no—
395C4×C47—42no—
396C4×C47—82no—
397C4×C47#38118yescomplemented
398Dic47—24no—
399Dic47—44no—
400Dic47—42no—
401Dic47—42no—
402Dic47—42no—
403Dic47—82no—
404C22×C4×D4—471no—
405C2×#390—471no—
406C2×#390D4711yescharacteristic
407C2×#381—472no—
408#1440—472no—
409#1440—472no—
410C4⋊#95—471no—
411C4⋊#95—471no—
412C4⋊#95—471no—
413C22⋊#95—472no—
414C4×#95—471no—
415C2×C47—48no—
416C2×C47C2×#38111yescharacteristic
417C2×C47#229311yescharacteristic
418C2×C47#231911yescharacteristic
419C2×C47D4×C22⋊C411yescharacteristic
420C2×C47#233911yescharacteristic
421C2×C47#235411yescharacteristic
422C2×C47#235711yescharacteristic
423C2×C47#242011yescharacteristic
424C2×C47#242011yescharacteristic
425C2×C47#242211yescharacteristic
426C2×C47#242211yescharacteristic
427C2×C47#244511yescharacteristic
428C2×C47#244511yescharacteristic
429C2×C47#244711yescharacteristic
430C2×C47#244711yescharacteristic
431C23×D4C2×D4711yescharacteristic
432C24×C4—472no—
433C2×C4×D4—478no—
434C2×C4×D4—944no—
435C2×C4×D4—944no—
436C22×C4⋊C4—471no—
437C22×C4⋊C4—471no—
438C22×C4⋊C4C2×D4711yescharacteristic
439C22×C22⋊C4—472no—
440C22×C22⋊C4—472no—
441C22×C22⋊C4—472no—
442C22×C22⋊C4C2×D4712yes—
443C22×C22⋊C4C2×D4712yes—
444C22×C42—471no—
445C22×C42—471no—
446C22×C42C2×D4711yescharacteristic
447#390—24no—
448#390—944no—
449#381—948no—
450C2×#95—471no—
451C2×#95—471no—
452C2×#95—471no—
453C2×#95—471no—
454C2×#95—472no—
455C2×#95—472no—
456C2×#95—472no—
457C2×#95—472no—
458C2×#95—472no—
459C2×#95—472no—
460C47#1391611yescharacteristic, complemented, Sylow
461C25C22×D4712yes—
462C22×D4—22no—
463C22×D4—22no—
464C22×D4—22no—
465C22×D4—22no—
466C22×D4C4×D4714yes—
467C22×D4D18814yes—
468C22×D4C22⋊D4714yes—
469C23×C4—471no—
470C23×C4—471no—
471C23×C4—471no—
472C23×C4—471no—
473C23×C4—472no—
474C23×C4—478no—
475C23×C4—472no—
476C23×C4—944no—
477C23×C4—944no—
478C23×C4—944no—
479C23×C4—944no—
480C23×C4—1882no—
481C23×C4—1882no—
482C23×C4C22×D4712yes—
483C23×C4C22×D4711yescharacteristic
484C23×C4C22×D4711yescharacteristic
485C23×C4C22×D4711yescharacteristic
486C4×D4—9432no—
487C2×C4⋊C4—22no—
488C2×C4⋊C4—22no—
489C2×C4⋊C4—22no—
490C2×C4⋊C4—474no—
491C2×C4⋊C4—942no—
492C2×C4⋊C4—942no—
493C2×C4⋊C4—942no—
494C2×C4⋊C4—942no—
495C2×C4⋊C4—942no—
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—478no—
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—1882no—
510C2×C22⋊C4—1882no—
511C2×C42—22no—
512C2×C42—22no—
513C2×C42—22no—
514C2×C42—474no—
515C2×C42—942no—
516C2×C42—942no—
517C2×C42—942no—
518C2×C42—942no—
519C2×C42—942no—
520#95—474no—
521#95—942no—
522#95—942no—
523#95—944no—
524#95—944no—
525#95—944no—
526#95—942no—
527#95—1882no—
528#95—1882no—
529#95—1882no—
530C24—22no—
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—22no—
539C24—22no—
540C24—22no—
541C24—22no—
542C24C2×C4×D4714yes—
543C24C2×D18814yes—
544C24C2×C22⋊D4714yes—
545C24C23×D4711yescharacteristic
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—28no—
549C2×D4—28no—
550C2×D4—28no—
551C2×D4—28no—
552C2×D4(C2×D47)⋊C4116yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—22no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—472no—
573C22×C4—472no—
574C22×C4—472no—
575C22×C4—472no—
576C22×C4—474no—
577C22×C4—472no—
578C22×C4—472no—
579C22×C4—9416no—
580C22×C4—941no—
581C22×C4—941no—
582C22×C4—941no—
583C22×C4—941no—
584C22×C4—9416no—
585C22×C4—942no—
586C22×C4—941no—
587C22×C4—942no—
588C22×C4—941no—
589C22×C4—941no—
590C22×C4—941no—
591C22×C4—942no—
592C22×C4—941no—
593C22×C4—941no—
594C22×C4—942no—
595C22×C4—941no—
596C22×C4—941no—
597C22×C4—941no—
598C22×C4—941no—
599C22×C4—941no—
600C22×C4—941no—
601C22×C4—941no—
602C22×C4—941no—
603C22×C4—942no—
604C22×C4—941no—
605C22×C4—942no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—941no—
609C22×C4—942no—
610C22×C4—942no—
611C22×C4—942no—
612C22×C4—942no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—1888no—
617C22×C4—1888no—
618C22×C4—1888no—
619C22×C4—1888no—
620C22×C4—1888no—
621C22×C4C2×C4×D4712yes—
622C22×C4C2×D18812yes—
623C22×C4D4×D4712yes—
624C22×C4#1062535212yes—
625C22×C4#1062535212yes—
626C22×C4#1062535212yes—
627C22×C4#1062535212yes—
628C22×C4#1062535212yes—
629C22×C4C2×C22⋊D4712yes—
630C4⋊C4—44no—
631C4⋊C4—948no—
632C4⋊C4—1884no—
633C22⋊C4—48no—
634C22⋊C4—48no—
635C22⋊C4—9416no—
636C22⋊C4—1888no—
637C22⋊C4—1888no—
638C42—44no—
639C42—948no—
640C42—1884no—
641C23—24no—
642C23—24no—
643C23—24no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
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—
673C23—42no—
674C23—42no—
675C23C2×(C2×D47)⋊C418yes—
676C23C22×C4×D4711yescharacteristic
677C23C2×D4×D4711yescharacteristic
678C23C22×C22⋊D4711yescharacteristic
679C23C22×D18811yescharacteristic
680C23#41×D4711yescharacteristic
681C23#41×D4711yescharacteristic
682C23C2×#1062535211yescharacteristic
683C23C2×#1062535211yescharacteristic
684C23C2×#1062535211yescharacteristic
685C23C2×#1062535211yescharacteristic
686C23C2×#1062535211yescharacteristic
687C23#1309406911yescharacteristic
688C23#1309406911yescharacteristic
689C23#1309407011yescharacteristic
690C23#1309407111yescharacteristic
691D4—232no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—22no—
695C2×C4—22no—
696C2×C4—22no—
697C2×C4—22no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—42no—
707C2×C4—42no—
708C2×C4—42no—
709C2×C4—42no—
710C2×C4—42no—
711C2×C4—42no—
712C2×C4—42no—
713C2×C4—474no—
714C2×C4—942no—
715C2×C4—942no—
716C2×C4—942no—
717C2×C4—942no—
718C2×C4—942no—
719C2×C4—942no—
720C2×C4—942no—
721C2×C4—942no—
722C2×C4—942no—
723C2×C4—942no—
724C2×C4—942no—
725C2×C4—944no—
726C2×C4—944no—
727C2×C4—942no—
728C2×C4—944no—
729C2×C4—942no—
730C2×C4—942no—
731C2×C4—942no—
732C2×C4—18832no—
733C2×C4—1882no—
734C2×C4—1882no—
735C2×C4—1882no—
736C2×C4—1882no—
737C2×C4—1882no—
738C2×C4—1882no—
739C2×C4—1882no—
740C2×C4—1881no—
741C2×C4—1882no—
742C2×C4—1882no—
743C2×C4—1882no—
744C2×C4—1881no—
745C2×C4—1881no—
746C2×C4—1881no—
747C2×C4—1882no—
748C2×C4—1881no—
749C2×C4—1881no—
750C2×C4—1881no—
751C2×C4—1881no—
752C2×C4—1881no—
753C2×C4—1881no—
754C2×C4—1881no—
755C2×C4—1881no—
756C2×C4C2×(C2×D47)⋊C414yes—
757C2×C4#1309398014yes—
758C2×C4#1309398014yes—
759C2×C4#1309400514yes—
760C2×C4#1309400514yes—
761C2×C4#1309400814yes—
762C2×C4#1309400814yes—
763C22—28no—
764C22—28no—
765C22—28no—
766C22—44no—
767C22—44no—
768C22—44no—
769C22—44no—
770C22—44no—
771C22—44no—
772C22—44no—
773C22—44no—
774C22—44no—
775C22—44no—
776C22—44no—
777C22—44no—
778C22C22×(C2×D47)⋊C411yescharacteristic
779C22C2×#1309398011yescharacteristic
780C22C2×#1309398011yescharacteristic
781C22C4×D4×D4711yescharacteristic
782C22C4×#1062535211yescharacteristic
783C22#1568959511yescharacteristic
784C22#1568960211yescharacteristic
785C22C2×#1309400511yescharacteristic
786C22C2×#1309400511yescharacteristic
787C22C2×#1309400811yescharacteristic
788C22C2×#1309400811yescharacteristic
789C22#1568965211yescharacteristic
790C22#1568965411yescharacteristic
791C22#1568966811yescharacteristic
792C22#1568967111yescharacteristic
793C22#1568972611yescharacteristic
794C22#1568972711yescharacteristic
795C22#1568974011yescharacteristic
796C22#1568974211yescharacteristic
797C22D4×C22⋊D4711yescharacteristic
798C22D4×D18811yescharacteristic
799C22#1568976111yescharacteristic
800C22#1568976711yescharacteristic
801C22#1568976811yescharacteristic
802C22#1568976811yescharacteristic
803C22#1568977211yescharacteristic
804C22#1568977311yescharacteristic
805C22#1568977711yescharacteristic
806C22#1568979311yescharacteristic
807C22#1568982011yescharacteristic
808C22#1568982511yescharacteristic
809C22#1568983711yescharacteristic
810C22#1568984211yescharacteristic
811C22#1568985511yescharacteristic
812C22#1568985911yescharacteristic
813C4—42no—
814C4—42no—
815C4—82no—
816C4—944no—
817C4—3762no—
818C4—1882no—
819C4—1882no—
820C4—1884no—
821C4—1882no—
822C4#1568898418yescomplemented
823C2—48no—
824C2C2×#1568898411yescharacteristic
825C2#2024585011yescharacteristic
826C2#2024602511yescharacteristic
827C2D4×(C2×D47)⋊C411yescharacteristic
828C2#2024621311yescharacteristic
829C2#2024633611yescharacteristic
830C2#2024636011yescharacteristic
831C2#2024687611yescharacteristic
832C2#2024687811yescharacteristic
833C2#2024689811yescharacteristic
834C2#2024690011yescharacteristic
835C2#2024714911yescharacteristic
836C2#2024715111yescharacteristic
837C2#2024717111yescharacteristic
838C2#2024717311yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#390C2
socle, cosocleC24×C47C24
prime radicalC23×D4×C47C22
hypercenterC2×#390D47
hypocenterC47#13916
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
3. C2×#15688984C2semidirect
4. #20241635C2semidirect
5. #20241635C2semidirect
6. #20241618C2semidirect
7. #20241617C2semidirect
8. #20241617C2semidirect
9. #20241610C2semidirect
10. C4×C47⋊#95C2semidirect
15. C2×D4×Dic47C4semidirect
85. C47⋊#95D4semidirect
397. C4×C47#381semidirect
460. C47#13916semidirect
822. C4#15688984semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic472
C2×#156890262
C2×#156889842
#202416352
#202416182
#202416172
#202416102
C4×C47⋊#952
C2×C47×#3902
#1391647