Finite Group Databasebeta

← #26234079

Subgroups — #26234079

Order 12032.

744 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20245792C211yesmaximal, characteristic
2#20244105C211yesmaximal, characteristic, complemented
3#20244103C211yesmaximal, characteristic, complemented
4#20243954C211yesmaximal, characteristic, complemented
5#20243953C211yesmaximal, characteristic, complemented
6#20243944C211yesmaximal, characteristic, complemented
7#20243371C211yesmaximal, characteristic
8#20243369C211yesmaximal, characteristic
9#20243367C211yesmaximal, characteristic
10#20243254C211yesmaximal, characteristic, complemented
11C8×Dic47⋊C4C211yesmaximal, characteristic, complemented
12#20243155C211yesmaximal, characteristic
13#20243153C211yesmaximal, characteristic
14#20243145C211yesmaximal, characteristic
15C47×#1916C211yesmaximal, characteristic, complemented
16C2×#13093981C2211yescharacteristic
17C2×#13093981C2211yescharacteristic
18C2×C42×D47C2211yescharacteristic
19C2×C4⋊(C47⋊C8)C2211yescharacteristic
20C2×Dic47⋊C8C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×Dic47⋊C8C2211yescharacteristic
24C2×(C2×D47)⋊C8C2211yescharacteristic
25C2×(C2×D47)⋊C8C2211yescharacteristic
26C2×(C2×D47)⋊C8C2211yescharacteristic
27C2×(C2×D47)⋊C8C2211yescharacteristic
28C2×#13093935C2211yescharacteristic
29C2×#13093934C2211yescharacteristic
30C2×C8×Dic47C2211yescharacteristic
31C2×C8×Dic47C2211yescharacteristic
32C2×C8×Dic47C2211yescharacteristic
33#15688992C411yescharacteristic
34#15688992C411yescharacteristic
35#15688987C411yescharacteristic
36#15688987C411yescharacteristic
37#15688982C411yescharacteristic
38#15688982C411yescharacteristic
39#15688980C411yescharacteristic
40#15688980C411yescharacteristic
41C4×Dic47⋊C4C2211yescharacteristic
42C4×Dic47⋊C4C2211yescharacteristic
43C4×C4⋊Dic47C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688878C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52C2×C4⋊C8×C47C2211yescharacteristic
53C2×C4×C8×C47C2211yescharacteristic
54C4×C4⋊C4×C47C2211yescharacteristic
55C47×#336C2211yescharacteristic
56C47×#336C2211yescharacteristic
57C47×#336C2211yescharacteristic
58C47×#336C2211yescharacteristic
59C22×C4×D47C2×C411yescharacteristic
60C22×C4×D47C2×C411yescharacteristic
61C22×C4×D47C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66#13093981—41no—
67#13093981—41no—
68#13093981—41no—
69#13093981—41no—
70C2×C4⋊Dic47C2×C411yescharacteristic
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×Dic47⋊C4C2×C411yescharacteristic
73C2×Dic47⋊C4C2×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×(C2×D47)⋊C4C2×C411yescharacteristic
81C2×(C2×D47)⋊C4C2×C411yescharacteristic
82C2×(C2×D47)⋊C4C2×C411yescharacteristic
83C2×(C2×D47)⋊C4C2×C411yescharacteristic
84C2×C4×Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2×C411yescharacteristic
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89C42×D47—22no—
90C42×D47—22no—
91C4⋊(C47⋊C8)—41no—
92Dic47⋊C8—22no—
93Dic47⋊C8—22no—
94Dic47⋊C8—41no—
95Dic47⋊C8—41no—
96(C2×D47)⋊C8—22no—
97(C2×D47)⋊C8—22no—
98(C2×D47)⋊C8—22no—
99(C2×D47)⋊C8Q814yes—
100#13093935—41no—
101#13093934—41no—
102C8×Dic47—22no—
103C8×Dic47—22no—
104C8×Dic47—41no—
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C47⋊#95C2×C411yescharacteristic
108C47⋊#95C2×C411yescharacteristic
109C47⋊#95C2×C411yescharacteristic
110C47⋊#95C2×C411yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C22×C8×C47C2311yescharacteristic
115C2×C4⋊C4×C47C2×C411yescharacteristic
116C2×C4⋊C4×C47C2×C411yescharacteristic
117C2×C42×C47C2311yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—41no—
121C4×C8×C47—41no—
122#95×C47C2×C411yescharacteristic
123#95×C47C2×C411yescharacteristic
124C23×D47C22×C411yescharacteristic
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C22×C411yescharacteristic
131C22×C4×C47C2411yescharacteristic
132C22×Dic47C22×C411yescharacteristic
133C22×Dic47C22×C411yescharacteristic
134C22×Dic47C22×C411yescharacteristic
135C22×Dic47C22×C411yescharacteristic
136C22×Dic47C22×C411yescharacteristic
137C22×Dic47C22×C411yescharacteristic
138C22×Dic47C22×C411yescharacteristic
139C2×C4×D47—21no—
140C2×C4×D47—21no—
141C2×C4×D47—21no—
142C2×C4×D47—21no—
143C2×C4×D47—22no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—41no—
149C2×C4×D47C2×Q812yes—
150C2×C4×D47#4112yes—
151C2×C8×C47—21no—
152C2×C8×C47—21no—
153C2×C8×C47—21no—
154C2×C8×C47—21no—
155C2×C8×C47—21no—
156C2×C8×C47—21no—
157C2×C8×C47—21no—
158C2×C8×C47—21no—
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47C2×Q812yes—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—41no—
165C42×C47—21no—
166C42×C47—21no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171(C2×D47)⋊C4—41no—
172(C2×D47)⋊C4—41no—
173(C2×D47)⋊C4—41no—
174(C2×D47)⋊C4—41no—
175C4⋊Dic47—22no—
176C4⋊Dic47—41no—
177Dic47⋊C4—22no—
178Dic47⋊C4—22no—
179Dic47⋊C4—22no—
180Dic47⋊C4—22no—
181Dic47⋊C4—41no—
182Dic47⋊C4—41no—
183Dic47⋊C4—41no—
184Dic47⋊C4—41no—
185C4×Dic47—21no—
186C4×Dic47—21no—
187C4×Dic47—21no—
188C4×Dic47—21no—
189C4×Dic47—22no—
190C4×Dic47—22no—
191C4×Dic47#4112yes—
192C4×Dic47#4112yes—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
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⋊C8C2×Q812yes—
205C23×C47C23×C411yescharacteristic
206C22×D47—21no—
207C22×D47—21no—
208C22×D47—21no—
209C22×D47—21no—
210C22×D47—21no—
211C22×D47—21no—
212C22×D47C4×Q812yes—
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
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#13112yes—
231C2×C4×C47C22×Q811yescharacteristic
232C2×C4×C47C2×#4111yescharacteristic
233C2×C4×C47C2×#4111yescharacteristic
234C2×C4×C47C2×#4111yescharacteristic
235C2×C4×C47H(5,𝔽2)11yescharacteristic
236C2×C4×C47H(5,𝔽2)11yescharacteristic
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—21no—
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#11712yes—
254C2×Dic47#11712yes—
255C2×Dic47C4×Q812yes—
256C2×Dic47#13112yes—
257C2×Dic47#13112yes—
258C4×D47—22no—
259C4×D47—22no—
260C4×D47—22no—
261C4×D47—22no—
262C4×D47—44no—
263C4×D47—44no—
264C8×C47—22no—
265C8×C47—41no—
266C8×C47—41no—
267C8×C47—41no—
268C47⋊C8—22no—
269C47⋊C8—41no—
270C47⋊C8—41no—
271C47⋊C8—41no—
272#22626—471nomaximal, Sylow
273C22×C47C2×#11711yescharacteristic
274C22×C47C2×C4×Q811yescharacteristic
275C22×C47#51811yescharacteristic
276C22×C47C2×#13111yescharacteristic
277C22×C47C2×#13111yescharacteristic
278C22×C47C2×#13111yescharacteristic
279C22×C47#56811yescharacteristic
280C2×D47—22no—
281C2×D47—22no—
282C2×D47—22no—
283C2×D47—41no—
284C2×D47—41no—
285C2×D47—41no—
286C2×D47—41no—
287C4×C47—22no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47#55311yescharacteristic
294C4×C47#55311yescharacteristic
295C4×C47#55411yescharacteristic
296C4×C47#55411yescharacteristic
297Dic47—22no—
298Dic47—22no—
299Dic47—41no—
300Dic47—41no—
301Dic47—41no—
302Dic47—41no—
303Dic47#43314yes—
304#2285—471no—
305#1939—471no—
306#1939—471no—
307#1917—471no—
308#1917—471no—
309#1916—471no—
310#1916D4711yescharacteristic, complemented
311#1798—471no—
312#1798—471no—
313#1797—471no—
314#1770—471no—
315C8×C4⋊C4—471no—
316#1750—471no—
317#1750—471no—
318C4×C22⋊C8—471no—
319C2×C47#234511yescharacteristic
320C2×C47C2×#43311yescharacteristic
321C2×C47#292411yescharacteristic
322C2×C47#296011yescharacteristic
323C2×C47#296211yescharacteristic
324C2×C47#297911yescharacteristic
325C2×C47#298111yescharacteristic
326D47—42no—
327C2×#117—471no—
328C2×#117—471no—
329C22×C42—471no—
330C2×C4⋊C8—471no—
331C2×C4⋊C8—471no—
332C2×C4⋊C8—471no—
333C2×C4⋊C8—471no—
334C2×C4⋊C8—471no—
335C2×C4⋊C8C2×D4711yescharacteristic
336C2×C22⋊C8—471no—
337C2×C22⋊C8—471no—
338C2×C22⋊C8—471no—
339C2×C22⋊C8—471no—
340C2×#97—471no—
341C2×#97—471no—
342C2×C4×C8—471no—
343C2×C4×C8—471no—
344C2×C4×C8—471no—
345C2×C4×C8C2×D4711yescharacteristic
346#384—471no—
347#384—471no—
348#382—471no—
349#382—471no—
350#380—471no—
351#380—471no—
352#380—471no—
353#380—471no—
354C4×C4⋊C4—471no—
355C4×C4⋊C4—471no—
356C4×C4⋊C4—471no—
357C4×C4⋊C4C2×D4711yescharacteristic
358#336—471no—
359#336—471no—
360#336—471no—
361#336—471no—
362#336—471no—
363#336—471no—
364#336—471no—
365#336—471no—
366#336C2×D4711yescharacteristic
367#336C2×D4711yescharacteristic
368#336C2×D4711yescharacteristic
369#336C2×D4711yescharacteristic
370C47#2262611yescharacteristic, complemented, Sylow
371C23×C4—471no—
372C23×C4—471no—
373C23×C4—471no—
374C22×C8—471no—
375C22×C8—471no—
376C22×C8—471no—
377C22×C8—471no—
378C22×C8C22×D4711yescharacteristic
379C22×C8C22×D4711yescharacteristic
380C22×C8C22×D4711yescharacteristic
381C22×C8C22×D4711yescharacteristic
382#117—1881no—
383#117—1881no—
384#117—1881no—
385#117—1881no—
386C2×C4⋊C4—471no—
387C2×C4⋊C4—471no—
388C2×C4⋊C4—471no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—471no—
394C2×C4⋊C4—471no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4C4×D4711yescharacteristic
397C2×C4⋊C4C4×D4711yescharacteristic
398C2×C22⋊C4—471no—
399C2×C22⋊C4—471no—
400C2×C22⋊C4—471no—
401C2×C22⋊C4—471no—
402C2×C42—471no—
403C2×C42—471no—
404C2×C42—471no—
405C2×C42—471no—
406C2×C42—471no—
407C2×C42—942no—
408C2×C42—942no—
409C2×C42C22×D4711yescharacteristic
410C2×C42C22×D4711yescharacteristic
411C2×C42C22×D4711yescharacteristic
412C4⋊C8—41no—
413C4⋊C8—942no—
414C4⋊C8—942no—
415C4⋊C8—1881no—
416C4⋊C8—1881no—
417C4⋊C8—1881no—
418C22⋊C8—474no—
419C22⋊C8—942no—
420C22⋊C8—942no—
421C22⋊C8—942no—
422#97—1881no—
423#97—1881no—
424C4×C8—41no—
425C4×C8—942no—
426C4×C8—942no—
427C4×C8—1881no—
428#95—471no—
429#95—471no—
430#95—471no—
431#95—471no—
432#95—471no—
433#95—471no—
434#95C4×D4711yescharacteristic
435#95C4×D4711yescharacteristic
436C24—471no—
437C22×C4—471no—
438C22×C4—471no—
439C22×C4—471no—
440C22×C4—472no—
441C22×C4—472no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4—942no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—942no—
455C22×C4—1881no—
456C22×C4C2×C4×D4711yescharacteristic
457C22×C4C2×C4×D4711yescharacteristic
458C22×C4C2×C4×D4711yescharacteristic
459C22×C4C2×C4×D4711yescharacteristic
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C23×D4711yescharacteristic
463C2×C8—21no—
464C2×C8—21no—
465C2×C8—21no—
466C2×C8—21no—
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—472no—
475C2×C8—941no—
476C2×C8—941no—
477C2×C8—941no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—941no—
486C2×C8Q8×D4712yes—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—942no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—942no—
493C4⋊C4—942no—
494C4⋊C4—1881no—
495C4⋊C4—1881no—
496C4⋊C4—1881no—
497C4⋊C4—1881no—
498C4⋊C4—1881no—
499C22⋊C4—1881no—
500C22⋊C4—1881no—
501C22⋊C4—1881no—
502C22⋊C4—1881no—
503C42—21no—
504C42—21no—
505C42—21no—
506C42—21no—
507C42—21no—
508C42—21no—
509C42—472no—
510C42—472no—
511C42—942no—
512C42—942no—
513C42—941no—
514C42—941no—
515C42—941no—
516C42—941no—
517C23—472no—
518C23—941no—
519C23—941no—
520C23—941no—
521C23—941no—
522C23—941no—
523C23—941no—
524C23C22×C4×D4711yescharacteristic
525C2×C4—21no—
526C2×C4—21no—
527C2×C4—21no—
528C2×C4—21no—
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
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—472no—
543C2×C4—472no—
544C2×C4—472no—
545C2×C4—472no—
546C2×C4—472no—
547C2×C4—941no—
548C2×C4—941no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—942no—
554C2×C4—942no—
555C2×C4—941no—
556C2×C4—941no—
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—1884no—
568C2×C4—1884no—
569C2×C4#1309403012yes—
570C2×C4C2×Q8×D4711yescharacteristic
571C2×C4#41×D4711yescharacteristic
572C2×C4#41×D4711yescharacteristic
573C2×C4#41×D4711yescharacteristic
574C2×C4#1309406911yescharacteristic
575C2×C4#1309407011yescharacteristic
576C8—22no—
577C8—41no—
578C8—41no—
579C8—41no—
580C8—942no—
581C8—1881no—
582C8—1881no—
583C8—1881no—
584C22—942no—
585C22—942no—
586C22—942no—
587C22—1881no—
588C22—1881no—
589C22—1881no—
590C22—1881no—
591C22#117×D4711yescharacteristic
592C22C4×Q8×D4711yescharacteristic
593C22#1568959511yescharacteristic
594C22#131×D4711yescharacteristic
595C22#131×D4711yescharacteristic
596C22C2×#1309403011yescharacteristic
597C22#1568988911yescharacteristic
598C4—22no—
599C4—41no—
600C4—41no—
601C4—41no—
602C4—41no—
603C4—41no—
604C4—474no—
605C4—942no—
606C4—942no—
607C4—1881no—
608C4—1881no—
609C4—1881no—
610C4—1881no—
611C4#1568981811yescharacteristic
612C4#1568982411yescharacteristic
613C4#1568982711yescharacteristic
614C4#1568982911yescharacteristic
615C2—1882no—
616C2#2024626211yescharacteristic
617C2#433×D4711yescharacteristic
618C2#2025204111yescharacteristic
619C2#2025231711yescharacteristic
620C2#2025233311yescharacteristic
621C2#2025245111yescharacteristic
622C2#2025246011yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC47×#1916C2
prime radicalC23×D47C22×C4
cosocleC22×C4×C47C24
hypercenter#1916D47
hypocenterC47#22626
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ #1916

Complements

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

NH ≅ G/Ntype
2. #20244105C2semidirect
3. #20244103C2semidirect
4. #20243954C2semidirect
5. #20243953C2semidirect
6. #20243944C2semidirect
10. #20243254C2semidirect
11. C8×Dic47⋊C4C2semidirect
15. C47×#1916C2semidirect
310. #1916D47semidirect
370. C47#22626semidirect

Maximal subgroups

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

subgroupindex
#202457922
#202441052
#202441032
#202439542
#202439532
#202439442
#202433712
#202433692
#202433672
#202432542
C8×Dic47⋊C42
#202431552
#202431532
#202431452
C47×#19162
#2262647