Finite Group Databasebeta

← #26139651

Subgroups — #26139651

Order 12032.

2590 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D47C211yesmaximal, characteristic
2C2×#15689002C211yesmaximal, characteristic
3C2×#15689002C211yesmaximal, characteristic
4C2×#15688996C211yesmaximal, characteristic, complemented
5#20241646C212yesmaximal, complemented
6#20241632C212yesmaximal, complemented
7#20241619C212yesmaximal, complemented
8#20241611C211yesmaximal, characteristic, complemented
9#20241611C211yesmaximal, characteristic, complemented
10(C2×D47)⋊#95C212yesmaximal, complemented
11C22×#95×C47C211yesmaximal, characteristic, complemented
12C23×C22⋊D47C2211yescharacteristic
13C23×C4×D47C2211yescharacteristic
14C2×C4×C22⋊D47—24no—
15C2×C4×C22⋊D47—24no—
16C2×C4×C22⋊D47—24no—
17C22×Dic47⋊C4C2211yescharacteristic
18C22×Dic47⋊C4C2212yes—
19C22×C22⋊Dic47C2211yescharacteristic
20C22×C22⋊Dic47C2211yescharacteristic
21C22×C22⋊Dic47C2211yescharacteristic
22C22×(C2×D47)⋊C4C2211yescharacteristic
23C22×(C2×D47)⋊C4C2212yes—
24C22×(C2×D47)⋊C4C2212yes—
25C22×C4×Dic47C2211yescharacteristic
26#15689002—24no—
27#15689002C418yescomplemented
28#15688996—24no—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2212yes—
34C2×C47⋊#95C2212yes—
35C2×C47⋊#95C2212yes—
36C24×C4×C47C2211yescharacteristic
37C24×C4×C47C2211yescharacteristic
38C24×C4×C47C2211yescharacteristic
39C2×#95×C47—24no—
40C2×#95×C47C2212yes—
41C2×#95×C47C2212yes—
42C24×D47C2311yescharacteristic
43C22×C22⋊D47—22no—
44C22×C22⋊D47—22no—
45C22×C22⋊D47—22no—
46C22×C22⋊D47—22no—
47C22×C22⋊D47C2×C414yes—
48C22×C22⋊D47D414yes—
49C22×C22⋊D47Q814yes—
50C23×Dic47C2312yes—
51C23×Dic47C2312yes—
52C23×Dic47C2311yescharacteristic
53C23×Dic47C2311yescharacteristic
54C23×Dic47C2311yescharacteristic
55C22×C4×D47—22no—
56C22×C4×D47—22no—
57C22×C4×D47—22no—
58C22×C4×D47—24no—
59C22×C4×D47—42no—
60C4×C22⋊D47—232no—
61C2×Dic47⋊C4—22no—
62C2×Dic47⋊C4—22no—
63C2×Dic47⋊C4—22no—
64C2×Dic47⋊C4—24no—
65C2×Dic47⋊C4—24no—
66C2×Dic47⋊C4—42no—
67C2×C22⋊Dic47—22no—
68C2×C22⋊Dic47—22no—
69C2×C22⋊Dic47—22no—
70C2×C22⋊Dic47—22no—
71C2×C22⋊Dic47—22no—
72C2×C22⋊Dic47—22no—
73C2×C22⋊Dic47—22no—
74C2×C22⋊Dic47C2×C414yescomplemented
75C2×C22⋊Dic47D414yes—
76C2×(C2×D47)⋊C4—22no—
77C2×(C2×D47)⋊C4—22no—
78C2×(C2×D47)⋊C4—22no—
79C2×(C2×D47)⋊C4—24no—
80C2×(C2×D47)⋊C4—24no—
81C2×(C2×D47)⋊C4—42no—
82C2×(C2×D47)⋊C4—42no—
83C2×(C2×D47)⋊C4—42no—
84C2×(C2×D47)⋊C4C2×C418yescomplemented
85C2×C4×Dic47—22no—
86C2×C4×Dic47—22no—
87C2×C4×Dic47—22no—
88C47⋊#95—24no—
89C47⋊#95—24no—
90C47⋊#95—24no—
91C47⋊#95—42no—
92C47⋊#95—42no—
93C47⋊#95—42no—
94C47⋊#95C2×C418yescomplemented
95C25×C47C2311yescharacteristic
96C23×C4×C47—22no—
97C23×C4×C47—22no—
98C23×C4×C47—22no—
99C23×C4×C47—22no—
100C23×C4×C47—22no—
101C23×C4×C47—24no—
102C23×C4×C47—24no—
103C23×C4×C47—22no—
104C23×C4×C47—22no—
105C23×C4×C47—42no—
106C23×C4×C47—42no—
107C23×C4×C47—42no—
108C23×C4×C47—42no—
109C23×C4×C47C2×C414yescomplemented
110C23×C4×C47D414yes—
111C23×C4×C47C2312yes—
112C23×C4×C47C2311yescharacteristic
113C23×C4×C47C2312yes—
114C23×C4×C47C2311yescharacteristic
115#95×C47—24no—
116#95×C47—24no—
117C24×C47—22no—
118C24×C47—22no—
119C24×C47—22no—
120C24×C47—22no—
121C24×C47C22×C412yes—
122C24×C47C2×D412yes—
123C24×C47C2×D412yes—
124C24×C47C2×D412yes—
125C24×C47C2×Q812yes—
126C24×C47#4112yes—
127C24×C47#4112yes—
128C24×C47C2411yescharacteristic
129C23×D47—21no—
130C23×D47—21no—
131C23×D47—22no—
132C23×D47—22no—
133C23×D47—21no—
134C23×D47—21no—
135C23×D47—22no—
136C23×D47—22no—
137C23×D47C22×C412yes—
138C23×D47C2×D412yes—
139C23×D47C2×Q812yes—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—22no—
143C22×C4×C47—28no—
144C22×C4×C47—28no—
145C22×C4×C47—28no—
146C22×C4×C47—22no—
147C22×C4×C47—22no—
148C22×C4×C47—21no—
149C22×C4×C47—21no—
150C22×C4×C47—22no—
151C22×C4×C47—22no—
152C22×C4×C47—22no—
153C22×C4×C47—22no—
154C22×C4×C47—22no—
155C22×C4×C47—22no—
156C22×C4×C47—22no—
157C22×C4×C47—22no—
158C22×C4×C47—22no—
159C22×C4×C47—22no—
160C22×C4×C47—22no—
161C22×C4×C47—22no—
162C22×C4×C47—28no—
163C22×C4×C47—48no—
164C22×C4×C47—44no—
165C22×C4×C47—48no—
166C22×C4×C47—48no—
167C22×C4×C47—48no—
168C22×C4×C47—48no—
169C22×C4×C47—44no—
170C22×C4×C47—44no—
171C22×C4×C47—44no—
172C22×C4×C47—48no—
173C22×C4×C47—44no—
174C22×C4×C47C22×C414yes—
175C22×C4×C47C2×D412yes—
176C22×C4×C47C2×D412yes—
177C22×C4×C47#4114yes—
178C22×C4×C47#4114yes—
179C2×C22⋊D47—28no—
180C2×C22⋊D47—28no—
181C2×C22⋊D47—28no—
182C2×C22⋊D47—28no—
183C2×C22⋊D47—28no—
184C2×C22⋊D47—28no—
185C2×C22⋊D47C4⋊C4116yescomplemented
186C22×Dic47—21no—
187C22×Dic47—21no—
188C22×Dic47—21no—
189C22×Dic47—21no—
190C22×Dic47—22no—
191C22×Dic47—21no—
192C22×Dic47—21no—
193C22×Dic47—21no—
194C22×Dic47—21no—
195C22×Dic47—22no—
196C22×Dic47—22no—
197C22×Dic47—22no—
198C22×Dic47—22no—
199C22×Dic47—22no—
200C22×Dic47—22no—
201C22×Dic47—22no—
202C22×Dic47—22no—
203C22×Dic47—22no—
204C22×Dic47—22no—
205C22×Dic47—22no—
206C22×Dic47—22no—
207C22×Dic47—22no—
208C22×Dic47—22no—
209C22×Dic47—22no—
210C22×Dic47—22no—
211C22×Dic47C22×C414yes—
212C22×Dic47C22×C412yes—
213C22×Dic47C2×D412yes—
214C22×Dic47C2×D412yes—
215C22×Dic47C2×D412yes—
216C22×Dic47C2×Q812yes—
217C2×C4×D47—28no—
218C2×C4×D47—48no—
219C2×C4×D47—48no—
220C2×C4×D47—44no—
221C2×C4×D47—44no—
222C22⋊Dic47—28no—
223C22⋊Dic47—28no—
224C22⋊Dic47—44no—
225(C2×D47)⋊C4—28no—
226(C2×D47)⋊C4—48no—
227(C2×D47)⋊C4—48no—
228Dic47⋊C4—28no—
229Dic47⋊C4—48no—
230C4×Dic47—28no—
231C23×C47—24no—
232C23×C47—24no—
233C23×C47—22no—
234C23×C47—22no—
235C23×C47—24no—
236C23×C47—22no—
237C23×C47—22no—
238C23×C47—24no—
239C23×C47—24no—
240C23×C47—24no—
241C23×C47—24no—
242C23×C47—24no—
243C23×C47—24no—
244C23×C47—24no—
245C23×C47—24no—
246C23×C47—24no—
247C23×C47C2×C4⋊C414yes—
248C23×C47C4×D414yes—
249C23×C47C4×D414yes—
250C23×C47#12014yes—
251C23×C47C22⋊Q814yes—
252C23×C47C22⋊Q814yes—
253C23×C47#12314yes—
254C23×C47C23×C411yescharacteristic
255C23×C47C22×D411yescharacteristic
256C23×C47C22×D411yescharacteristic
257C23×C47C22×D411yescharacteristic
258C23×C47C22×Q811yescharacteristic
259C23×C47C2×#4111yescharacteristic
260C23×C47C2×#4112yes—
261C23×C47C2×#4112yes—
262C23×C47C2×#4111yescharacteristic
263C23×C47H(5,𝔽2)12yes—
264C23×C47H(5,𝔽2)12yes—
265C22×D47—22no—
266C22×D47—22no—
267C22×D47—24no—
268C22×D47—24no—
269C22×D47—22no—
270C22×D47—22no—
271C22×D47—22no—
272C22×D47—22no—
273C22×D47—24no—
274C22×D47—24no—
275C22×D47—24no—
276C22×D47—24no—
277C22×D47—41no—
278C22×D47—41no—
279C22×D47—42no—
280C22×D47—41no—
281C22×D47—41no—
282C22×D47—42no—
283C22×D47—42no—
284C22×D47—42no—
285C22×D47—42no—
286C22×D47—42no—
287C22×D47C2×C4⋊C414yes—
288C2×C4×C47—22no—
289C2×C4×C47—22no—
290C2×C4×C47—24no—
291C2×C4×C47—24no—
292C2×C4×C47—24no—
293C2×C4×C47—24no—
294C2×C4×C47—24no—
295C2×C4×C47—22no—
296C2×C4×C47—22no—
297C2×C4×C47—24no—
298C2×C4×C47—22no—
299C2×C4×C47—24no—
300C2×C4×C47—24no—
301C2×C4×C47—416no—
302C2×C4×C47—416no—
303C2×C4×C47—416no—
304C2×C4×C47—42no—
305C2×C4×C47—42no—
306C2×C4×C47—42no—
307C2×C4×C47—42no—
308C2×C4×C47—42no—
309C2×C4×C47—42no—
310C2×C4×C47—42no—
311C2×C4×C47—42no—
312C2×C4×C47—42no—
313C2×C4×C47—42no—
314C2×C4×C47#12314yes—
315C22⋊D47—232no—
316C2×Dic47—22no—
317C2×Dic47—22no—
318C2×Dic47—22no—
319C2×Dic47—22no—
320C2×Dic47—22no—
321C2×Dic47—22no—
322C2×Dic47—24no—
323C2×Dic47—24no—
324C2×Dic47—24no—
325C2×Dic47—22no—
326C2×Dic47—22no—
327C2×Dic47—24no—
328C2×Dic47—24no—
329C2×Dic47—41no—
330C2×Dic47—41no—
331C2×Dic47—41no—
332C2×Dic47—41no—
333C2×Dic47—42no—
334C2×Dic47—42no—
335C2×Dic47—42no—
336C2×Dic47—42no—
337C2×Dic47—42no—
338C2×Dic47—42no—
339C2×Dic47—42no—
340C2×Dic47—42no—
341C2×Dic47—42no—
342C2×Dic47—42no—
343C2×Dic47—42no—
344C2×Dic47—42no—
345C2×Dic47—42no—
346C2×Dic47C2×C4⋊C414yes—
347C4×D47—416no—
348#14016—471nomaximal, Sylow
349C22×C47—24no—
350C22×C47—24no—
351C22×C47—28no—
352C22×C47—28no—
353C22×C47—24no—
354C22×C47—24no—
355C22×C47—28no—
356C22×C47—28no—
357C22×C47—24no—
358C22×C47—24no—
359C22×C47#38518yes—
360C22×C47C22×C4⋊C411yescharacteristic
361C22×C47C2×C4×D411yescharacteristic
362C22×C47C2×C4×D411yescharacteristic
363C22×C47C4×#4112yes—
364C22×C47#51812yes—
365C22×C47C2×#12011yescharacteristic
366C22×C47C2×C22⋊Q811yescharacteristic
367C22×C47C2×C22⋊Q811yescharacteristic
368C22×C47C2×#12311yescharacteristic
369C22×C47C2×#12311yescharacteristic
370C22×C47#52511yescharacteristic
371C22×C47#52912yes—
372C22×C47#53411yescharacteristic
373C22×C47#53511yescharacteristic
374C22×C47#53812yes—
375C22×C47#54612yes—
376C22×C47#54612yes—
377C22×C47#54612yes—
378C22×C47#54612yes—
379C22×C47#55312yes—
380C22×C47#55312yes—
381C22×C47#55412yes—
382C22×C47#55412yes—
383C2×D47—28no—
384C2×D47—24no—
385C2×D47—42no—
386C2×D47—42no—
387C2×D47—44no—
388C2×D47—42no—
389C2×D47—42no—
390C2×D47—44no—
391C2×D47—44no—
392C2×D47—42no—
393C2×D47—42no—
394C4×C47—24no—
395C4×C47—44no—
396C4×C47—44no—
397C4×C47—42no—
398Dic47—24no—
399Dic47—44no—
400Dic47—42no—
401Dic47—42no—
402Dic47—82no—
403C22×C4×D4—471no—
404C2×#386—471no—
405C2×#386—471no—
406C2×#385—471no—
407C22×#95D4711yescharacteristic, complemented
408#1442—472no—
409#1439—472no—
410#1436—472no—
411C22⋊#95—472no—
412C22⋊#95—471no—
413C22⋊#95—471no—
414C2×C47—28no—
415C2×C47C2×#38511yescharacteristic
416C2×C47C4×#12311yescharacteristic
417C2×C47#232111yescharacteristic
418C2×C47#234912yes—
419C2×C47#236412yes—
420C2×C47#240411yescharacteristic
421C2×C47#240511yescharacteristic
422C2×C47#244412yes—
423C2×C47#245012yes—
424C2×C47#248711yescharacteristic
425C2×C47#257911yescharacteristic
426D47—44no—
427C23×D4—471no—
428C24×C4—471no—
429C24×C4C2×D4711yescharacteristic
430C24×C4C2×D4711yescharacteristic
431C24×C4C2×D4711yescharacteristic
432C2×C4×D4—944no—
433C2×C4×D4—944no—
434C2×C4×D4—944no—
435C22×C4⋊C4—471no—
436C22×C4⋊C4—472no—
437C22×C22⋊C4—471no—
438C22×C22⋊C4—471no—
439C22×C22⋊C4—472no—
440C22×C22⋊C4—471no—
441C22×C22⋊C4—471no—
442C22×C22⋊C4—472no—
443C22×C42—471no—
444#386—478no—
445#386—944no—
446#385—944no—
447C2×#95—24no—
448C2×#95—472no—
449C2×#95—472no—
450C2×#95—472no—
451C2×#95—472no—
452C2×#95—472no—
453C2×#95—472no—
454C2×#95—472no—
455C2×#95C2×D4712yes—
456C2×#95C2×D4712yes—
457C47#1401611yescharacteristic, complemented, Sylow
458C25—471no—
459C25C22×D4711yescharacteristic
460C22×D4—474no—
461C22×D4—474no—
462C22×D4—474no—
463C22×D4—942no—
464C22×D4—942no—
465C22×D4—942no—
466C22×D4—942no—
467C23×C4—22no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—22no—
471C23×C4—22no—
472C23×C4—24no—
473C23×C4—24no—
474C23×C4—22no—
475C23×C4—22no—
476C23×C4—42no—
477C23×C4—42no—
478C23×C4—42no—
479C23×C4—42no—
480C23×C4—471no—
481C23×C4—471no—
482C23×C4—472no—
483C23×C4—471no—
484C23×C4—472no—
485C23×C4—942no—
486C23×C4—942no—
487C23×C4—942no—
488C23×C4—944no—
489C23×C4—1882no—
490C23×C4C4×D4714yescomplemented
491C23×C4C22⋊D4714yes—
492C23×C4C22×D4712yes—
493C23×C4C22×D4712yes—
494C23×C4C22×D4711yescharacteristic
495C23×C4C22×D4711yescharacteristic
496C4×D4—9432no—
497C2×C4⋊C4—942no—
498C2×C4⋊C4—942no—
499C2×C4⋊C4—942no—
500C2×C4⋊C4—944no—
501C2×C4⋊C4—944no—
502C2×C4⋊C4—1882no—
503C2×C22⋊C4—474no—
504C2×C22⋊C4—474no—
505C2×C22⋊C4—478no—
506C2×C22⋊C4—942no—
507C2×C22⋊C4—942no—
508C2×C22⋊C4—942no—
509C2×C22⋊C4—942no—
510C2×C22⋊C4—942no—
511C2×C22⋊C4—942no—
512C2×C22⋊C4—942no—
513C2×C22⋊C4—944no—
514C2×C22⋊C4—942no—
515C2×C22⋊C4—942no—
516C2×C22⋊C4—942no—
517C2×C22⋊C4—944no—
518C2×C22⋊C4—1882no—
519C2×C22⋊C4—1882no—
520C2×C22⋊C4—1882no—
521C2×C42—942no—
522C2×C42—942no—
523C2×C42—942no—
524#95—24no—
525#95—24no—
526#95—478no—
527#95—944no—
528#95—944no—
529#95—944no—
530#95—1882no—
531#95—1882no—
532#95—1882no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—472no—
538C24—472no—
539C24—472no—
540C24—941no—
541C24—941no—
542C24—942no—
543C24—942no—
544C24—941no—
545C24—941no—
546C24—942no—
547C24—942no—
548C24C2×C4×D4712yes—
549C24#1062535012yes—
550C24D4×D4712yes—
551C24D4×D4712yes—
552C24Q8×D4712yes—
553C24#1062535412yes—
554C24C2×C22⋊D4712yes—
555C24C23×D4711yescharacteristic
556C2×D4—4716no—
557C2×D4—948no—
558C2×D4—948no—
559C2×D4—948no—
560C2×D4—948no—
561C2×D4—948no—
562C2×D4—948no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—22no—
566C22×C4—28no—
567C22×C4—28no—
568C22×C4—28no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—21no—
572C22×C4—21no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—22no—
585C22×C4—28no—
586C22×C4—48no—
587C22×C4—44no—
588C22×C4—48no—
589C22×C4—48no—
590C22×C4—48no—
591C22×C4—48no—
592C22×C4—44no—
593C22×C4—44no—
594C22×C4—44no—
595C22×C4—48no—
596C22×C4—44no—
597C22×C4—472no—
598C22×C4—472no—
599C22×C4—472no—
600C22×C4—474no—
601C22×C4—472no—
602C22×C4—472no—
603C22×C4—948no—
604C22×C4—941no—
605C22×C4—941no—
606C22×C4—941no—
607C22×C4—941no—
608C22×C4—942no—
609C22×C4—941no—
610C22×C4—941no—
611C22×C4—941no—
612C22×C4—941no—
613C22×C4—942no—
614C22×C4—942no—
615C22×C4—942no—
616C22×C4—942no—
617C22×C4—942no—
618C22×C4—942no—
619C22×C4—942no—
620C22×C4—942no—
621C22×C4—942no—
622C22×C4—942no—
623C22×C4—942no—
624C22×C4—942no—
625C22×C4—942no—
626C22×C4—942no—
627C22×C4—942no—
628C22×C4—942no—
629C22×C4—1888no—
630C22×C4—1888no—
631C22×C4—1884no—
632C22×C4—1884no—
633C22×C4C2×C4×D4714yes—
634C22×C4#1062535014yes—
635C22×C4#1062535014yes—
636C22×C4C2×C22⋊D4712yes—
637C22×C4C2×C22⋊D4712yes—
638C4⋊C4—948no—
639C4⋊C4—1888no—
640C22⋊C4—948no—
641C22⋊C4—948no—
642C22⋊C4—948no—
643C22⋊C4—1888no—
644C22⋊C4—1888no—
645C22⋊C4—1884no—
646C42—948no—
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—22no—
658C23—22no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—474no—
664C23—944no—
665C23—944no—
666C23—944no—
667C23—944no—
668C23—942no—
669C23—942no—
670C23—944no—
671C23—944no—
672C23—942no—
673C23—942no—
674C23—942no—
675C23—942no—
676C23—1882no—
677C23—1882no—
678C23—1882no—
679C23—1882no—
680C23—1881no—
681C23—1881no—
682C23—1882no—
683C23—1881no—
684C23—1881no—
685C23—1882no—
686C23C4⋊C4×D4714yes—
687C23C4×C22⋊D4714yes—
688C23#1309398614yes—
689C23#1309399214yes—
690C23#1309400014yes—
691C23#1309400214yes—
692C23#1309400914yes—
693C23C22×C4×D4711yescharacteristic
694C23C2×D4×D4711yescharacteristic
695C23C2×D4×D4711yescharacteristic
696C23C22×C22⋊D4711yescharacteristic
697C23C2×Q8×D4711yescharacteristic
698C23C2×#1062535012yes—
699C23C2×#1062535012yes—
700C23C2×#1062535011yescharacteristic
701C23C2×#1062535411yescharacteristic
702C23#1309406912yes—
703C23#1309406912yes—
704D4—9432no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—22no—
715C2×C4—22no—
716C2×C4—24no—
717C2×C4—22no—
718C2×C4—416no—
719C2×C4—416no—
720C2×C4—416no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—42no—
730C2×C4—42no—
731C2×C4—474no—
732C2×C4—942no—
733C2×C4—942no—
734C2×C4—942no—
735C2×C4—942no—
736C2×C4—942no—
737C2×C4—942no—
738C2×C4—944no—
739C2×C4—944no—
740C2×C4—944no—
741C2×C4—944no—
742C2×C4—944no—
743C2×C4—942no—
744C2×C4—942no—
745C2×C4—18816no—
746C2×C4—1882no—
747C2×C4—1882no—
748C2×C4—1882no—
749C2×C4—1882no—
750C2×C4—1882no—
751C2×C4—1882no—
752C2×C4—1882no—
753C2×C4—1882no—
754C2×C4—1882no—
755C2×C4—1882no—
756C2×C4—1882no—
757C2×C4—1882no—
758C2×C4—1882no—
759C2×C4—1881no—
760C2×C4—1881no—
761C2×C4—1881no—
762C2×C4—1881no—
763C2×C4#1309400714yes—
764C22—28no—
765C22—24no—
766C22—28no—
767C22—24no—
768C22—24no—
769C22—24no—
770C22—28no—
771C22—28no—
772C22—24no—
773C22—24no—
774C22—948no—
775C22—944no—
776C22—1882no—
777C22—1884no—
778C22—1882no—
779C22—1882no—
780C22—1882no—
781C22—1884no—
782C22—1884no—
783C22—1882no—
784C22—1882no—
785C22#1568899418yes—
786C22C2×C4⋊C4×D4711yescharacteristic
787C22C2×C4×C22⋊D4711yescharacteristic
788C22C2×#1309398611yescharacteristic
789C22C4×#1062535012yes—
790C22#1568959612yes—
791C22C2×#1309399211yescharacteristic
792C22C2×#1309400011yescharacteristic
793C22C2×#1309400211yescharacteristic
794C22C2×#1309400711yescharacteristic
795C22C2×#1309400911yescharacteristic
796C22#1568963411yescharacteristic
797C22#1568965712yes—
798C22#1568968211yescharacteristic
799C22#1568969011yescharacteristic
800C22#1568971112yes—
801C22#1568976312yes—
802C22#1568976312yes—
803C22#1568976312yes—
804C22#1568976312yes—
805C22#1568982112yes—
806C22#1568982112yes—
807C22#1568982812yes—
808C22#1568982812yes—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—42no—
813C4—944no—
814C4—3762no—
815C4—1884no—
816C4—1882no—
817C4—1882no—
818C2—28no—
819C2—1884no—
820C2C2×#1568899411yescharacteristic
821C2C4×#1309400711yescharacteristic
822C2#2024604611yescharacteristic
823C2#2024629512yes—
824C2#2024643512yes—
825C2#2024670711yescharacteristic
826C2#2024671511yescharacteristic
827C2#2024713812yes—
828C2#2024721212yes—
829C2#2024769911yescharacteristic
830C2#2024873511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC22×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC23×C22⋊D47C22
hypercenterC22×#95D47
hypocenterC47#14016
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C22×#95

Complements

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

NH ≅ G/Ntype
4. C2×#15688996C2semidirect
5. #20241646C2semidirect
6. #20241632C2semidirect
7. #20241619C2semidirect
8. #20241611C2semidirect
9. #20241611C2semidirect
10. (C2×D47)⋊#95C2semidirect
11. C22×#95×C47C2semidirect
27. #15689002C4semidirect
74. C2×C22⋊Dic47C2×C4semidirect
84. C2×(C2×D47)⋊C4C2×C4semidirect
94. C47⋊#95C2×C4semidirect
109. C23×C4×C47C2×C4semidirect
185. C2×C22⋊D47C4⋊C4semidirect
407. C22×#95D47semidirect
457. C47#14016semidirect
490. C23×C4C4×D47semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D472
C2×#156890022
C2×#156889962
#202416462
#202416322
#202416192
#202416112
(C2×D47)⋊#952
C22×#95×C472
#1401647