Finite Group Databasebeta

← #26228292

Subgroups — #26228292

Order 12032.

786 conjugacy classes of subgroups.

The subgroup lattice has 632 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689251C211yesmaximal, characteristic, complemented
2C2×#15689177C211yesmaximal, characteristic
3C4×#13094001C211yesmaximal, characteristic
4#20244326C211yesmaximal, characteristic, complemented
5#20244109C211yesmaximal, characteristic, complemented
6#20244108C211yesmaximal, characteristic, complemented
7#20244105C211yesmaximal, characteristic, complemented
8#20244003C211yesmaximal, characteristic
9#20243991C211yesmaximal, characteristic
10#20243991C211yesmaximal, characteristic
11#20243952C211yesmaximal, characteristic, complemented
12#20243946C211yesmaximal, characteristic, complemented
13#20243366C211yesmaximal, characteristic
14#20243261C211yesmaximal, characteristic, complemented
15C47×#1924C211yesmaximal, characteristic
16C2×#13094001C411yescharacteristic
17C2×C4×Dic94C2211yescharacteristic
18C22×C4×Dic47C2211yescharacteristic
19#15689251—24no—
20#15689177—24no—
21C2×C4⋊(C47⋊C8)C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×Dic47⋊C8C2211yescharacteristic
25C2×Dic47⋊C8C2211yescharacteristic
26C2×Dic47⋊C8C2211yescharacteristic
27C2×Dic47⋊C8C2211yescharacteristic
28C2×C22⋊(C47⋊C8)C2211yescharacteristic
29C2×C22⋊(C47⋊C8)C2211yescharacteristic
30C2×#13093935C2211yescharacteristic
31C2×#13093934C2211yescharacteristic
32C2×#13093934C2211yescharacteristic
33C2×C8×Dic47C2211yescharacteristic
34C2×C8×Dic47C2211yescharacteristic
35#15689027C411yescharacteristic
36#15689020C411yescharacteristic
37#15689010C411yescharacteristic
38#15689006C411yescharacteristic
39#15688998C411yescharacteristic
40#15688995C411yescharacteristic
41#15688981C411yescharacteristic
42C4×Dic47⋊C4C2211yescharacteristic
43C4×Dic47⋊C4C2211yescharacteristic
44C4×C4⋊Dic47C2211yescharacteristic
45C4×C22⋊Dic47C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53#15688877C2211yescharacteristic
54C2×C4⋊C8×C47C2211yescharacteristic
55C2×C22⋊C8×C47C2211yescharacteristic
56C2×C22⋊C8×C47C2211yescharacteristic
57C2×#97×C47C2211yescharacteristic
58C4×C22⋊C4×C47C2211yescharacteristic
59C47×#336C2211yescharacteristic
60C47×#336C2211yescharacteristic
61C22×Dic94C2×C411yescharacteristic
62C23×Dic47C2×C411yescharacteristic
63C23×Dic47C2×C411yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67C22×C47⋊C8C2311yescharacteristic
68#13094001—24no—
69C4×Dic94—22no—
70C4×Dic94—22no—
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×C4⋊Dic47C2×C411yescharacteristic
73C2×C4⋊Dic47C2×C411yescharacteristic
74C2×Dic47⋊C4C2×C411yescharacteristic
75C2×Dic47⋊C4C2×C411yescharacteristic
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×C22⋊Dic47C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×C4×Dic47—22no—
83C2×C4×Dic47—22no—
84C2×C4×Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2×C411yescharacteristic
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89C2×C4×Dic47C2311yescharacteristic
90C4⋊(C47⋊C8)—22no—
91Dic47⋊C8—22no—
92Dic47⋊C8—22no—
93Dic47⋊C8—22no—
94Dic47⋊C8—22no—
95Dic47⋊C8—22no—
96Dic47⋊C8—41no—
97C22⋊(C47⋊C8)—22no—
98C22⋊(C47⋊C8)—41no—
99#13093935—41no—
100#13093934—22no—
101#13093934D414yes—
102C8×Dic47—22no—
103C8×Dic47—41no—
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C47⋊#95C2×C411yescharacteristic
112C23×C4×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C22×C8×C47C2311yescharacteristic
116C22×C8×C47C2311yescharacteristic
117C2×C22⋊C4×C47C2×C411yescharacteristic
118C2×C22⋊C4×C47C2×C411yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C2×C42×C47C2311yescharacteristic
121C4⋊C8×C47—41no—
122C22⋊C8×C47—22no—
123C22⋊C8×C47—41no—
124#97×C47—22no—
125#95×C47C2×C411yescharacteristic
126#95×C47C2×C411yescharacteristic
127C24×C47C22×C411yescharacteristic
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—21no—
132C22×C4×C47—21no—
133C22×C4×C47—21no—
134C22×C4×C47C22×C411yescharacteristic
135C22×C4×C47C22×C411yescharacteristic
136C22×C4×C47C22×C411yescharacteristic
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C2411yescharacteristic
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—41no—
145C22×Dic47—41no—
146C22×Dic47C22×C411yescharacteristic
147C22×Dic47C22×C411yescharacteristic
148C22×Dic47C22×C411yescharacteristic
149C22×Dic47C22×C411yescharacteristic
150C22×Dic47C22×C411yescharacteristic
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C411yescharacteristic
153C22×Dic47C22×C411yescharacteristic
154C2×Dic94—22no—
155C2×Dic94—22no—
156C2×Dic94—41no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47C2×D412yes—
169C22⋊C4×C47—22no—
170C22⋊C4×C47—41no—
171C42×C47—21no—
172C42×C47—21no—
173C42×C47—21no—
174C42×C47—21no—
175C22⋊Dic47—41no—
176C22⋊Dic47M1614yes—
177C4⋊Dic47—22no—
178C4⋊Dic47—22no—
179C4⋊Dic47—22no—
180Dic47⋊C4—22no—
181Dic47⋊C4—22no—
182Dic47⋊C4—22no—
183Dic47⋊C4—22no—
184Dic47⋊C4—22no—
185Dic47⋊C4—41no—
186C4×Dic47—21no—
187C4×Dic47—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—22no—
193C4×Dic47—22no—
194C4×Dic47C2×D412yes—
195C4×Dic47#4112yes—
196C2×C47⋊C8—21no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—21no—
207C2×C47⋊C8C2×D412yes—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47C2×M1612yes—
215C23×C47C23×C411yescharacteristic
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47C22×D411yescharacteristic
236C2×C4×C47C2×#4111yescharacteristic
237C2×C4×C47H(5,𝔽2)11yescharacteristic
238C2×C4×C472−1+411yescharacteristic
239C2×C4×C472−1+411yescharacteristic
240C2×C4×C472−1+411yescharacteristic
241C2×Dic47—21no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—21no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249C2×Dic47—21no—
250C2×Dic47—21no—
251C2×Dic47—21no—
252C2×Dic47—21no—
253C2×Dic47—21no—
254C2×Dic47—21no—
255C2×Dic47—21no—
256C2×Dic47—21no—
257C2×Dic47—21no—
258C2×Dic47—21no—
259C2×Dic47—21no—
260C2×Dic47—44no—
261C2×Dic47—44no—
262C2×Dic47C4×D412yes—
263C2×Dic47C4×D412yes—
264C2×Dic47C2×M1612yes—
265C2×Dic47C2×M1612yes—
266C2×Dic47#13112yes—
267Dic94—44no—
268C8×C47—22no—
269C8×C47—41no—
270C8×C47—41no—
271C8×C47—41no—
272C47⋊C8—22no—
273C47⋊C8—41no—
274C47⋊C8—41no—
275C47⋊C8—41no—
276#22108—471nomaximal, Sylow
277C22×C47—22no—
278C22×C47—22no—
279C22×C47—22no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47—41no—
284C22×C47C2×C4×D411yescharacteristic
285C22×C47#51911yescharacteristic
286C22×C47#52011yescharacteristic
287C22×C47C22×M1611yescharacteristic
288C22×C47C2×#13111yescharacteristic
289C22×C47#56811yescharacteristic
290C22×C47#56811yescharacteristic
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47—41no—
295C4×C47—41no—
296C4×C47#53611yescharacteristic
297C4×C47#53711yescharacteristic
298C4×C47#54111yescharacteristic
299C4×C47#54211yescharacteristic
300Dic47—22no—
301Dic47—22no—
302Dic47—22no—
303Dic47—22no—
304Dic47—22no—
305Dic47—41no—
306Dic47—41no—
307Dic47—41no—
308C2×#446—471no—
309C2×#432—471no—
310C4×C22⋊Q8—471no—
311#1985—471no—
312#1940—471no—
313#1940—471no—
314#1939—471no—
315#1924—471no—
316#1924D4711yescharacteristic
317#1923—471no—
318#1923—471no—
319#1917—471no—
320#1916—471no—
321#1797—471no—
322#1771—471no—
323C2×C47—42no—
324C2×C47#232311yescharacteristic
325C2×C47#293311yescharacteristic
326C2×C47D4×M1611yescharacteristic
327C2×C47#298311yescharacteristic
328C2×C47#298511yescharacteristic
329C2×C47#299011yescharacteristic
330C2×C47#299511yescharacteristic
331C2×C22⋊Q8—471no—
332C2×C4×Q8—471no—
333C22×C42—471no—
334#446—944no—
335#432—944no—
336C2×C4⋊C8—471no—
337C2×C4⋊C8—471no—
338C2×C4⋊C8—471no—
339C2×C4⋊C8—471no—
340C2×C4⋊C8—471no—
341C2×C4⋊C8—471no—
342C2×C4⋊C8—471no—
343C2×C4⋊C8C2×D4711yescharacteristic
344C2×C22⋊C8—471no—
345C2×C22⋊C8—471no—
346C2×C22⋊C8C2×D4711yescharacteristic
347C2×C22⋊C8C2×D4711yescharacteristic
348C2×#97—471no—
349C2×#97—471no—
350C2×#97—471no—
351C2×#97C2×D4711yescharacteristic
352C2×C4×C8—471no—
353C2×C4×C8—471no—
354#391—471no—
355#389—471no—
356#387—471no—
357#387—471no—
358#385—471no—
359#385—471no—
360#380—471no—
361C4×C4⋊C4—471no—
362C4×C4⋊C4—471no—
363C4×C4⋊C4—471no—
364C4×C22⋊C4—471no—
365C4×C22⋊C4C2×D4711yescharacteristic
366#336—471no—
367#336—471no—
368#336—471no—
369#336—471no—
370#336—471no—
371#336—471no—
372#336—471no—
373#336—471no—
374#336C2×D4711yescharacteristic
375#336C2×D4711yescharacteristic
376C47#2210811yescharacteristic, complemented, Sylow
377C22×Q8—471no—
378C23×C4—471no—
379C23×C4—471no—
380C23×C4C22×D4711yescharacteristic
381C22×C8—471no—
382C22×C8—471no—
383C22×C8—471no—
384C22×C8—471no—
385C22×C8C22×D4711yescharacteristic
386C22×C8C22×D4711yescharacteristic
387C22×C8C22×D4711yescharacteristic
388C22×C8C22×D4711yescharacteristic
389C22⋊Q8—944no—
390C4×Q8—942no—
391C4×Q8—942no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—471no—
401C2×C22⋊C4—471no—
402C2×C22⋊C4—471no—
403C2×C22⋊C4C4×D4711yescharacteristic
404C2×C22⋊C4C4×D4711yescharacteristic
405C2×C42—471no—
406C2×C42—471no—
407C2×C42—471no—
408C2×C42—471no—
409C2×C42—471no—
410C2×C42—471no—
411C2×C42—942no—
412C2×C42—942no—
413C2×C42C22×D4711yescharacteristic
414C2×C42C22×D4711yescharacteristic
415C4⋊C8—41no—
416C4⋊C8—942no—
417C4⋊C8—942no—
418C4⋊C8—942no—
419C4⋊C8—942no—
420C4⋊C8—942no—
421C4⋊C8—942no—
422C4⋊C8—1881no—
423C22⋊C8—22no—
424C22⋊C8—41no—
425C22⋊C8—942no—
426C22⋊C8—1881no—
427#97—22no—
428#97—474no—
429#97—942no—
430#97—1881no—
431C4×C8—942no—
432C4×C8—1881no—
433#95—471no—
434#95—471no—
435#95—471no—
436#95—471no—
437#95—471no—
438#95—471no—
439#95—471no—
440#95—471no—
441#95C4×D4711yescharacteristic
442#95C4×D4711yescharacteristic
443C24C2×C4×D4711yescharacteristic
444C2×Q8—942no—
445C2×Q8—942no—
446C2×Q8—1881no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—21no—
452C22×C4—21no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—471no—
460C22×C4—471no—
461C22×C4—942no—
462C22×C4—942no—
463C22×C4—942no—
464C22×C4—942no—
465C22×C4—1881no—
466C22×C4—1881no—
467C22×C4C2×C4×D4711yescharacteristic
468C22×C4C2×C4×D4711yescharacteristic
469C22×C4C2×C4×D4711yescharacteristic
470C22×C4C2×C4×D4711yescharacteristic
471C22×C4C2×C4×D4711yescharacteristic
472C22×C4C23×D4711yescharacteristic
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—21no—
480C2×C8—21no—
481C2×C8—21no—
482C2×C8—21no—
483C2×C8—21no—
484C2×C8—472no—
485C2×C8—941no—
486C2×C8—941no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8D4×D4712yes—
497C4⋊C4—942no—
498C4⋊C4—942no—
499C4⋊C4—942no—
500C4⋊C4—942no—
501C4⋊C4—942no—
502C4⋊C4—942no—
503C4⋊C4—942no—
504C4⋊C4—942no—
505C4⋊C4—1881no—
506C22⋊C4—22no—
507C22⋊C4—41no—
508C22⋊C4—474no—
509C22⋊C4—1881no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—21no—
514C42—472no—
515C42—472no—
516C42—942no—
517C42—942no—
518C42—941no—
519C42—941no—
520C42—941no—
521C42—941no—
522C42—941no—
523C42—941no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23—21no—
528C23—21no—
529C23—21no—
530C23M16×D4712yes—
531C23C22×C4×D4711yescharacteristic
532Q8—1884no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—21no—
544C2×C4—21no—
545C2×C4—21no—
546C2×C4—21no—
547C2×C4—21no—
548C2×C4—41no—
549C2×C4—41no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—472no—
553C2×C4—472no—
554C2×C4—472no—
555C2×C4—472no—
556C2×C4—472no—
557C2×C4—941no—
558C2×C4—941no—
559C2×C4—941no—
560C2×C4—941no—
561C2×C4—941no—
562C2×C4—941no—
563C2×C4—941no—
564C2×C4—941no—
565C2×C4—941no—
566C2×C4—941no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4—941no—
573C2×C4—941no—
574C2×C4—941no—
575C2×C4—941no—
576C2×C4—1884no—
577C2×C4—1884no—
578C2×C4C2×D4×D4711yescharacteristic
579C2×C4#41×D4711yescharacteristic
580C2×C4#1309406911yescharacteristic
581C2×C4#1309407111yescharacteristic
582C2×C4#1309407111yescharacteristic
583C2×C4#1309407111yescharacteristic
584C8—22no—
585C8—41no—
586C8—41no—
587C8—41no—
588C8—942no—
589C8—1881no—
590C8—1881no—
591C8—1881no—
592C22—22no—
593C22—22no—
594C22—22no—
595C22—41no—
596C22—41no—
597C22—41no—
598C22—41no—
599C22C4×D4×D4711yescharacteristic
600C22#1568960011yescharacteristic
601C22#1568960211yescharacteristic
602C22C2×M16×D4711yescharacteristic
603C22#131×D4711yescharacteristic
604C22#1568988811yescharacteristic
605C22#1568988911yescharacteristic
606C4—41no—
607C4—41no—
608C4—41no—
609C4—41no—
610C4—41no—
611C4—942no—
612C4—942no—
613C4—942no—
614C4—942no—
615C4—942no—
616C4—1881no—
617C4—1881no—
618C4—1881no—
619C4#1568969511yescharacteristic
620C4#1568970211yescharacteristic
621C4#1568973011yescharacteristic
622C4#1568973711yescharacteristic
623C2—42no—
624C2#2024606711yescharacteristic
625C2#2025211711yescharacteristic
626C2#2025212111yescharacteristic
627C2#2025247211yescharacteristic
628C2#2025248011yescharacteristic
629C2#2025250811yescharacteristic
630C2#2025255911yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1924C2
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenter#1924D47
hypocenterC47#22108
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1924

Complements

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

NH ≅ G/Ntype
1. C2×#15689251C2semidirect
4. #20244326C2semidirect
5. #20244109C2semidirect
6. #20244108C2semidirect
7. #20244105C2semidirect
11. #20243952C2semidirect
12. #20243946C2semidirect
14. #20243261C2semidirect
376. C47#22108semidirect

Maximal subgroups

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

subgroupindex
C2×#156892512
C2×#156891772
C4×#130940012
#202443262
#202441092
#202441082
#202441052
#202440032
#202439912
#202439522
#202439462
#202433662
#202432612
C47×#19242
#2210847