Finite Group Databasebeta

← #26225865

Subgroups — #26225865

Order 12032.

1170 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689651C211yesmaximal, characteristic
2C2×#15689175C211yesmaximal, characteristic, complemented
3C2×C4⋊C8×D47C211yesmaximal, characteristic, complemented
4#20244322C212yesmaximal, complemented
5#20244180C212yesmaximal, complemented
6#20243679C212yesmaximal, complemented
7#20243677C212yesmaximal, complemented
8#20243372C211yesmaximal, characteristic, complemented
9#20243369C211yesmaximal, characteristic, complemented
10#20243369C211yesmaximal, characteristic, complemented
11C47×#1798C211yesmaximal, characteristic, complemented
12C22×C8×D47C2212yes—
13#15689651—24no—
14#15689651—24no—
15C2×#13094019C411yescharacteristic
16C2×#13094017C411yescharacteristic
17C2×#13094014C411yescharacteristic
18C2×#13094010C411yescharacteristic
19C2×#13094009C411yescharacteristic
20C2×#13094006C411yescharacteristic
21C2×#13094002C411yescharacteristic
22C2×#13093997C411yescharacteristic
23C2×C4×Dic94C2211yescharacteristic
24C2×C4×D188C2211yescharacteristic
25C2×C4×C22⋊D47C2211yescharacteristic
26C2×C4×C22⋊D47C2211yescharacteristic
27C2×#13093981C2211yescharacteristic
28C2×C42×D47C2211yescharacteristic
29#15689175—24no—
30C2×C4⋊(C47⋊C8)C2211yescharacteristic
31C2×C4⋊(C47⋊C8)C2211yescharacteristic
32C2×Dic47⋊C8C2212yes—
33C4⋊C8×D47—24no—
34C2×C22⋊(C47⋊C8)C2212yes—
35C2×(C2×D47)⋊C8C2212yes—
36C2×(C2×D47)⋊C8C2212yes—
37C2×(C2×D47)⋊C8C2212yes—
38C2×C8×Dic47C2212yes—
39#15688878C2212yes—
40#15688877C2212yes—
41#15688877C2212yes—
42C2×#117×C47C2211yescharacteristic
43C2×C4⋊C8×C47C2211yescharacteristic
44C2×C4⋊C8×C47C2211yescharacteristic
45C2×C22⋊C8×C47C2212yes—
46C47×#336C2212yes—
47C22×Dic94C2×C411yescharacteristic
48C22×D188C2×C411yescharacteristic
49C22×C22⋊D47C2×C411yescharacteristic
50C22×C22⋊D47C2×C411yescharacteristic
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47C2×C411yescharacteristic
53C22×C4×D47C2311yescharacteristic
54C22×C4×D47C2311yescharacteristic
55C22×C47⋊C8C2312yes—
56C22×C47⋊C8C2312yes—
57C2×C8×D47—24no—
58C2×C8×D47—42no—
59C2×C8×D47—42no—
60#13094019—24no—
61#13094017—24no—
62#13094014—24no—
63#13094010—24no—
64#13094009—24no—
65#13094006—24no—
66#13094002—24no—
67#13093997—24no—
68C4×Dic94—22no—
69C4×Dic94—22no—
70C4×D188—22no—
71C4×D188—22no—
72C4×C22⋊D47—22no—
73C4×C22⋊D47—22no—
74C4×C22⋊D47—22no—
75C4×C22⋊D47—22no—
76#13093981—22no—
77#13093981—22no—
78C2×C4⋊Dic47C2×C411yescharacteristic
79C2×C4⋊Dic47C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4C2×C411yescharacteristic
82C2×Dic47⋊C4C2×C411yescharacteristic
83C2×Dic47⋊C4C2×C411yescharacteristic
84C2×Dic47⋊C4C2×C411yescharacteristic
85C2×Dic47⋊C4C2×C411yescharacteristic
86C2×C22⋊Dic47C2×C411yescharacteristic
87C2×C22⋊Dic47C2×C411yescharacteristic
88C2×(C2×D47)⋊C4C2×C411yescharacteristic
89C2×(C2×D47)⋊C4C2×C411yescharacteristic
90C2×(C2×D47)⋊C4C2×C411yescharacteristic
91C2×(C2×D47)⋊C4C2×C411yescharacteristic
92C2×(C2×D47)⋊C4C2×C411yescharacteristic
93C2×(C2×D47)⋊C4C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2311yescharacteristic
97C2×C4×Dic47C2311yescharacteristic
98C42×D47D414yes—
99C42×D47D414yes—
100C4⋊(C47⋊C8)—22no—
101C4⋊(C47⋊C8)—22no—
102Dic47⋊C8—24no—
103C22⋊(C47⋊C8)—42no—
104(C2×D47)⋊C8—24no—
105(C2×D47)⋊C8—42no—
106(C2×D47)⋊C8—42no—
107C8×Dic47—24no—
108C23×C4×C47C2311yescharacteristic
109C22×C8×C47C2312yes—
110C22×C8×C47C2312yes—
111#117×C47—22no—
112#117×C47—22no—
113C2×C4⋊C4×C47C2×C411yescharacteristic
114C2×C4⋊C4×C47C2×C411yescharacteristic
115C2×C22⋊C4×C47C2×C411yescharacteristic
116C2×C22⋊C4×C47C2×C411yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C4⋊C8×C47—22no—
120C4⋊C8×C47—22no—
121C22⋊C8×C47—42no—
122C24×C47C22×C411yescharacteristic
123C23×D47C22×C411yescharacteristic
124C23×D47C22×C411yescharacteristic
125C22×C4×C47—21no—
126C22×C4×C47—21no—
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47C22×C411yescharacteristic
132C22×C4×C47C22×C411yescharacteristic
133C22×C4×C47C22×C411yescharacteristic
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C22×C411yescharacteristic
136C22×C4×C47C2411yescharacteristic
137C2×C22⋊D47—22no—
138C2×C22⋊D47—24no—
139C2×C22⋊D47—22no—
140C2×C22⋊D47—24no—
141C22×Dic47C22×C411yescharacteristic
142C22×Dic47C22×C411yescharacteristic
143C22×Dic47C22×C411yescharacteristic
144C22×Dic47C22×C411yescharacteristic
145C22×Dic47C22×C411yescharacteristic
146C22×Dic47C22×C411yescharacteristic
147C2×D188—22no—
148C2×D188—24no—
149C2×C4×D47—24no—
150C2×C4×D47—21no—
151C2×C4×D47—21no—
152C2×C4×D47—21no—
153C2×C4×D47—21no—
154C2×C4×D47—24no—
155C2×C4×D47—21no—
156C2×C4×D47—21no—
157C2×C4×D47—21no—
158C2×C4×D47—21no—
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47C22⋊C414yes—
162C2×C4×D47C22⋊C414yes—
163C2×C4×D47C2×D412yes—
164C2×C4×D47C2×D412yes—
165C2×Dic94—22no—
166C2×Dic94—24no—
167C2×C8×C47—22no—
168C2×C8×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—22no—
173C4⋊C4×C47—22no—
174C4⋊C4×C47—22no—
175C22⋊C4×C47—22no—
176C22⋊C4×C47—22no—
177C42×C47—21no—
178C42×C47—21no—
179C42×C47C2×D412yes—
180C42×C47C2×D412yes—
181C22⋊Dic47—22no—
182C22⋊Dic47—22no—
183(C2×D47)⋊C4—22no—
184(C2×D47)⋊C4—22no—
185(C2×D47)⋊C4—22no—
186(C2×D47)⋊C4—22no—
187(C2×D47)⋊C4—22no—
188(C2×D47)⋊C4—22no—
189C4⋊Dic47—22no—
190C4⋊Dic47—22no—
191Dic47⋊C4—22no—
192Dic47⋊C4—22no—
193Dic47⋊C4—22no—
194Dic47⋊C4—22no—
195Dic47⋊C4—22no—
196Dic47⋊C4—22no—
197C4×Dic47—21no—
198C4×Dic47—21no—
199C4×Dic47C22⋊C414yes—
200C4×Dic47C22⋊C414yes—
201C4×Dic47C2×D412yes—
202C4×Dic47C2×D412yes—
203C2×C47⋊C8—22no—
204C2×C47⋊C8—22no—
205C2×C47⋊C8—22no—
206C2×C47⋊C8—22no—
207C2×C47⋊C8—22no—
208C2×C47⋊C8—22no—
209C8×D47—48no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—22no—
214C23×C47—22no—
215C23×C47C23×C411yescharacteristic
216C22×D47—21no—
217C22×D47—21no—
218C22×D47—22no—
219C22×D47—21no—
220C22×D47—21no—
221C22×D47—21no—
222C22×D47—22no—
223C22×D47—22no—
224C22×D47C2×C22⋊C412yes—
225C22×D47#13114yes—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—41no—
236C2×C4×C47—41no—
237C2×C4×C47—41no—
238C2×C4×C47—41no—
239C2×C4×C47C2×C22⋊C412yes—
240C2×C4×C47C2×C22⋊C412yes—
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47H(5,𝔽2)11yescharacteristic
244C2×C4×C47H(5,𝔽2)11yescharacteristic
245C2×C4×C472−1+411yescharacteristic
246C2×C4×C472−1+411yescharacteristic
247C22⋊D47—44no—
248C22⋊D47—44no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—22no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—22no—
258C2×Dic47—22no—
259C2×Dic47C2×C22⋊C412yes—
260C2×Dic47C2×C22⋊C412yes—
261C2×Dic47C2×C22⋊C412yes—
262C2×Dic47#13114yes—
263D188—44no—
264C4×D47—28no—
265C4×D47—22no—
266C4×D47—22no—
267C4×D47—22no—
268C4×D47—22no—
269C4×D47—28no—
270C4×D47—41no—
271C4×D47—41no—
272C4×D47—41no—
273C4×D47—41no—
274Dic94—44no—
275C8×C47—42no—
276C8×C47—42no—
277C47⋊C8—42no—
278C47⋊C8—42no—
279#21848—471nomaximal, Sylow
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—42no—
284C22×C47—42no—
285C22×C47C22×C22⋊C411yescharacteristic
286C22×C47#52011yescharacteristic
287C22×C47#52011yescharacteristic
288C22×C47C2×#13112yes—
289C22×C47C2×#13112yes—
290C2×D47—22no—
291C2×D47—22no—
292C2×D47—24no—
293C2×D47—24no—
294C2×D47—41no—
295C2×D47—41no—
296C2×D47—41no—
297C2×D47—42no—
298C2×D47—42no—
299C2×D47#40814yes—
300C4×C47—22no—
301C4×C47—22no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47#53511yescharacteristic
306C4×C47#53611yescharacteristic
307C4×C47#53711yescharacteristic
308C4×C47#53711yescharacteristic
309Dic47—22no—
310Dic47—22no—
311Dic47—41no—
312Dic47—41no—
313Dic47—41no—
314Dic47#40814yes—
315C2×#529—471no—
316C2×#431—471no—
317C22×C4⋊C8—471no—
318#1984—472no—
319#1954—472no—
320#1869—472no—
321#1869—472no—
322#1798—471no—
323#1798—471no—
324#1798—471no—
325#1798D4711yescharacteristic, complemented
326C2×C47—81no—
327C2×C47#231111yescharacteristic
328C2×C47C2×#40811yescharacteristic
329C2×C47C2×#40811yescharacteristic
330C2×C47#299412yes—
331C2×C47#299412yes—
332D47—24no—
333D47—81no—
334C23×C8—472no—
335#529—944no—
336#529—944no—
337C2×#126—471no—
338C2×#126—471no—
339C2×#125—471no—
340C2×#124—471no—
341C2×#123—471no—
342C2×#123—471no—
343C2×C22⋊Q8—471no—
344C2×#121—471no—
345C2×C4×Q8—471no—
346C2×C4×D4—471no—
347C2×C4×D4—471no—
348C2×C4×D4—471no—
349C2×#117—471no—
350C2×#117C2×D4711yescharacteristic
351C22×C42—471no—
352#431—944no—
353C2×C4⋊C8—472no—
354C2×C4⋊C8—471no—
355C2×C4⋊C8—471no—
356C2×C4⋊C8—944no—
357C2×C4⋊C8C2×D4711yescharacteristic
358C2×C4⋊C8C2×D4711yescharacteristic
359C2×C22⋊C8—472no—
360C2×C22⋊C8—472no—
361C2×C22⋊C8—472no—
362C2×C22⋊C8—472no—
363C2×C22⋊C8C2×D4712yes—
364C2×C4×C8—472no—
365#336—472no—
366#336—472no—
367#336—472no—
368#336C2×D4712yes—
369C47#2184811yescharacteristic, complemented, Sylow
370C22×Q8—471no—
371C22×D4—471no—
372C22×D4—471no—
373C22×D4—471no—
374C23×C4—471no—
375C23×C4—471no—
376C23×C4—471no—
377C23×C4—471no—
378C23×C4C22×D4711yescharacteristic
379C22×C8—472no—
380C22×C8—472no—
381C22×C8—944no—
382C22×C8—1882no—
383C22×C8—1882no—
384C22×C8C22×D4712yes—
385C22×C8C22×D4712yes—
386#126—944no—
387#126—944no—
388#125—944no—
389#124—944no—
390#123—944no—
391#123—944no—
392C22⋊Q8—944no—
393#121—944no—
394C4×Q8—942no—
395C4×Q8—942no—
396C4×D4—942no—
397C4×D4—942no—
398C4×D4—942no—
399C4×D4—942no—
400C4×D4—942no—
401C4×D4—942no—
402#117—22no—
403#117—22no—
404#117—942no—
405#117—942no—
406C2×C4⋊C4—471no—
407C2×C4⋊C4—471no—
408C2×C4⋊C4—471no—
409C2×C4⋊C4—471no—
410C2×C4⋊C4—471no—
411C2×C4⋊C4—471no—
412C2×C4⋊C4—471no—
413C2×C4⋊C4—471no—
414C2×C4⋊C4C4×D4711yescharacteristic
415C2×C4⋊C4C4×D4711yescharacteristic
416C2×C22⋊C4—471no—
417C2×C22⋊C4—471no—
418C2×C22⋊C4—471no—
419C2×C22⋊C4—471no—
420C2×C22⋊C4—471no—
421C2×C22⋊C4—471no—
422C2×C22⋊C4—471no—
423C2×C22⋊C4—471no—
424C2×C22⋊C4C4×D4711yescharacteristic
425C2×C22⋊C4C4×D4711yescharacteristic
426C2×C42—471no—
427C2×C42—471no—
428C2×C42—471no—
429C2×C42—474no—
430C2×C42—474no—
431C2×C42—471no—
432C2×C42C22×D4711yescharacteristic
433C2×C42C22×D4711yescharacteristic
434C4⋊C8—22no—
435C4⋊C8—22no—
436C4⋊C8—944no—
437C4⋊C8—942no—
438C4⋊C8—942no—
439C22⋊C8—42no—
440C22⋊C8—944no—
441C22⋊C8—1882no—
442C22⋊C8—1882no—
443C22⋊C8—1882no—
444C4×C8—944no—
445C24—471no—
446C24—471no—
447C24C2×C4×D4711yescharacteristic
448C2×Q8—942no—
449C2×Q8—944no—
450C2×D4—942no—
451C2×D4—944no—
452C2×D4—942no—
453C2×D4—944no—
454C2×D4—942no—
455C2×D4—944no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—471no—
463C22×C4—471no—
464C22×C4—471no—
465C22×C4—474no—
466C22×C4—474no—
467C22×C4—472no—
468C22×C4—472no—
469C22×C4—471no—
470C22×C4—471no—
471C22×C4—471no—
472C22×C4—944no—
473C22×C4—944no—
474C22×C4—941no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—941no—
480C22×C4—941no—
481C22×C4—941no—
482C22×C4—941no—
483C22×C4—941no—
484C22×C4C2×C4×D4711yescharacteristic
485C22×C4C2×C4×D4711yescharacteristic
486C22×C4C2×C4×D4711yescharacteristic
487C22×C4C2×C4×D4711yescharacteristic
488C22×C4C2×C4×D4711yescharacteristic
489C22×C4C23×D4711yescharacteristic
490C2×C8—22no—
491C2×C8—22no—
492C2×C8—22no—
493C2×C8—22no—
494C2×C8—22no—
495C2×C8—22no—
496C2×C8—942no—
497C2×C8—942no—
498C2×C8—942no—
499C2×C8—942no—
500C2×C8—942no—
501C2×C8—942no—
502C2×C8—1888no—
503C4⋊C4—22no—
504C4⋊C4—22no—
505C4⋊C4—942no—
506C4⋊C4—942no—
507C4⋊C4—942no—
508C4⋊C4—942no—
509C4⋊C4—942no—
510C4⋊C4—942no—
511C4⋊C4—942no—
512C4⋊C4—942no—
513C22⋊C4—22no—
514C22⋊C4—22no—
515C22⋊C4—942no—
516C22⋊C4—942no—
517C22⋊C4—942no—
518C22⋊C4—942no—
519C22⋊C4—942no—
520C22⋊C4—942no—
521C22⋊C4—942no—
522C22⋊C4—942no—
523C42—21no—
524C42—21no—
525C42—474no—
526C42—474no—
527C42—472no—
528C42—472no—
529C42—941no—
530C42—941no—
531C42D4×D4712yes—
532C42D4×D4712yes—
533C23—21no—
534C23—21no—
535C23—21no—
536C23—22no—
537C23—22no—
538C23—472no—
539C23—474no—
540C23—941no—
541C23—941no—
542C23—942no—
543C23—941no—
544C23—941no—
545C23—941no—
546C23—942no—
547C23—942no—
548C23C22×C4×D4711yescharacteristic
549Q8—1884no—
550D4—1884no—
551D4—1884no—
552D4—1884no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—21no—
556C2×C4—21no—
557C2×C4—21no—
558C2×C4—21no—
559C2×C4—21no—
560C2×C4—22no—
561C2×C4—22no—
562C2×C4—41no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—41no—
566C2×C4—472no—
567C2×C4—474no—
568C2×C4—472no—
569C2×C4—472no—
570C2×C4—948no—
571C2×C4—948no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—942no—
575C2×C4—942no—
576C2×C4—942no—
577C2×C4—942no—
578C2×C4—942no—
579C2×C4—941no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—941no—
583C2×C4—941no—
584C2×C4—942no—
585C2×C4—942no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4C22⋊C4×D4712yes—
591C2×C4C22⋊C4×D4712yes—
592C2×C4C2×D4×D4711yescharacteristic
593C2×C4C2×D4×D4711yescharacteristic
594C2×C4#1309406911yescharacteristic
595C2×C4#1309407011yescharacteristic
596C2×C4#1309407111yescharacteristic
597C2×C4#1309407211yescharacteristic
598C8—42no—
599C8—42no—
600C8—1882no—
601C8—1882no—
602C22—42no—
603C22—42no—
604C22—41no—
605C22—41no—
606C22—41no—
607C22—474no—
608C22—944no—
609C22—944no—
610C22—942no—
611C22—942no—
612C22—1882no—
613C22—1882no—
614C22—1881no—
615C22—1881no—
616C22—1881no—
617C22C2×C22⋊C4×D4711yescharacteristic
618C22#1568960311yescharacteristic
619C22#1568960411yescharacteristic
620C22#131×D4712yes—
621C22#131×D4712yes—
622C4—22no—
623C4—22no—
624C4—41no—
625C4—41no—
626C4—41no—
627C4—474no—
628C4—942no—
629C4—942no—
630C4—1881no—
631C4—1881no—
632C4—1881no—
633C4#1568968911yescharacteristic
634C4#1568969611yescharacteristic
635C4#1568970211yescharacteristic
636C4#1568970311yescharacteristic
637C2—81no—
638C2—944no—
639C2—3761no—
640C2#2024597711yescharacteristic
641C2#408×D4711yescharacteristic
642C2#408×D4711yescharacteristic
643C2#2025254212yes—
644C2#2025254612yes—
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1798C2
prime radicalC2×#13093997C4
cosocleC22×C4×C47C24
hypercenter#1798D47
hypocenterC47#21848
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1798

Complements

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

NH ≅ G/Ntype
2. C2×#15689175C2semidirect
3. C2×C4⋊C8×D47C2semidirect
4. #20244322C2semidirect
5. #20244180C2semidirect
6. #20243679C2semidirect
7. #20243677C2semidirect
8. #20243372C2semidirect
9. #20243369C2semidirect
10. #20243369C2semidirect
11. C47×#1798C2semidirect
325. #1798D47semidirect
369. C47#21848semidirect

Maximal subgroups

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

subgroupindex
C2×#156896512
C2×#156891752
C2×C4⋊C8×D472
#202443222
#202441802
#202436792
#202436772
#202433722
#202433692
C47×#17982
#2184847