Finite Group Databasebeta

← #26260612

Subgroups — #26260612

Order 12032.

854 conjugacy classes of subgroups.

The subgroup lattice has 656 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20247696C211yesmaximal, characteristic
2#20244945C211yesmaximal, characteristic, complemented
3#20244860C211yesmaximal, characteristic, complemented
4#20244814C211yesmaximal, characteristic, complemented
5#20244814C211yesmaximal, characteristic, complemented
6#20243959C211yesmaximal, characteristic, complemented
7#20243959C211yesmaximal, characteristic, complemented
8#20243681C211yesmaximal, characteristic
9#20243576C211yesmaximal, characteristic, complemented
10#20243576C211yesmaximal, characteristic, complemented
11#20243474C211yesmaximal, characteristic, complemented
12#20243472C211yesmaximal, characteristic, complemented
13#20243415C211yesmaximal, characteristic, complemented
14C2×#15688885C211yesmaximal, characteristic, complemented
15D4×C4⋊C4×C47C211yesmaximal, characteristic
16C23×C47⋊C8C2211yescharacteristic
17C2×#13094005—21no—
18C22×C4⋊Dic47C2211yescharacteristic
19C2×#13093957C2211yescharacteristic
20C2×#13093957C2211yescharacteristic
21C2×#13093957C2211yescharacteristic
22C2×#13093957C2211yescharacteristic
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×C22⋊(C47⋊C8)C2211yescharacteristic
26#15689053—21no—
27#15689048—21no—
28#15689021C2211yescharacteristic
29#15689021C2211yescharacteristic
30#15688984—21no—
31#15688983C2211yescharacteristic
32#15688983C2211yescharacteristic
33#15688983C2211yescharacteristic
34#15688885C2211yescharacteristic
35#15688885C2211yescharacteristic
36#15688885C2211yescharacteristic
37#15688885C2211yescharacteristic
38#15688885C2211yescharacteristic
39#15688885C2211yescharacteristic
40#15688885C2211yescharacteristic
41#15688885C2211yescharacteristic
42#15688885C2211yescharacteristic
43#15688885C2211yescharacteristic
44#15688885C2211yescharacteristic
45#15688885C2211yescharacteristic
46#15688878C2211yescharacteristic
47#15688878C2211yescharacteristic
48C2×C4×D4×C47—21no—
49C2×C4×D4×C47C2211yescharacteristic
50C22×C4⋊C4×C47C2211yescharacteristic
51C22×C4⋊C4×C47C2211yescharacteristic
52C47×#389—21no—
53C47×#385—21no—
54C47×#385—21no—
55C47×#384C2211yescharacteristic
56C47×#380C2211yescharacteristic
57C47×#380C2211yescharacteristic
58C4×C4⋊C4×C47C2211yescharacteristic
59C23×Dic47—21no—
60C22×C47⋊C8—22no—
61C22×C47⋊C8—22no—
62C22×C47⋊C8—41no—
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65C22×C47⋊C8C2311yescharacteristic
66C22×C47⋊C8C2311yescharacteristic
67#13094005—44no—
68C2×C4⋊Dic47—22no—
69C2×C4⋊Dic47—22no—
70C2×C4⋊Dic47—21no—
71C2×C4⋊Dic47C2311yescharacteristic
72C2×C4⋊Dic47C2311yescharacteristic
73C2×C4⋊Dic47C2311yescharacteristic
74C2×C4⋊Dic47C2311yescharacteristic
75C2×Dic47⋊C4—21no—
76C2×Dic47⋊C4—21no—
77C2×C22⋊Dic47—21no—
78C2×C22⋊Dic47—21no—
79C2×C22⋊Dic47—21no—
80#13093957—22no—
81#13093957—22no—
82#13093957—41no—
83#13093957—41no—
84C22⋊(C47⋊C8)—22no—
85C22⋊(C47⋊C8)—22no—
86C22⋊(C47⋊C8)—41no—
87C47⋊#95—21no—
88C47⋊#95—21no—
89C47⋊#95—21no—
90C47⋊#95—21no—
91C47⋊#95—21no—
92C22×D4×C47D411yescharacteristic
93C23×C4×C47—21no—
94C23×C4×C47—21no—
95C23×C4×C47C2311yescharacteristic
96C23×C4×C47C2311yescharacteristic
97C4×D4×C47—22no—
98C4×D4×C47—22no—
99C4×D4×C47—44no—
100C2×C4⋊C4×C47—22no—
101C2×C4⋊C4×C47—22no—
102C2×C4⋊C4×C47—21no—
103C2×C4⋊C4×C47—21no—
104C2×C4⋊C4×C47—21no—
105C2×C4⋊C4×C47—21no—
106C2×C4⋊C4×C47—41no—
107C2×C4⋊C4×C47—41no—
108C2×C4⋊C4×C47D411yescharacteristic
109C2×C4⋊C4×C47C2311yescharacteristic
110C2×C4⋊C4×C47C2311yescharacteristic
111C2×C4⋊C4×C47C2311yescharacteristic
112C2×C4⋊C4×C47C2311yescharacteristic
113C2×C22⋊C4×C47—21no—
114C2×C22⋊C4×C47—21no—
115C2×C22⋊C4×C47D411yescharacteristic
116C2×C22⋊C4×C47D411yescharacteristic
117C2×C42×C47—21no—
118C2×C42×C47C2311yescharacteristic
119#95×C47—21no—
120#95×C47—21no—
121#95×C47—21no—
122C24×C47C2×D411yescharacteristic
123C24×C47C2×D411yescharacteristic
124C2×D4×C47—22no—
125C2×D4×C47—22no—
126C2×D4×C47D814yes—
127C22×C4×C47—21no—
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×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—42no—
142C22×C4×C47—42no—
143C22×C4×C47—42no—
144C22×C4×C47—42no—
145C22×C4×C47—81no—
146C22×C4×C47—81no—
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47#4112yes—
152C22×C4×C47#4112yes—
153C22×C4×C47C2411yescharacteristic
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47—21no—
157C22×Dic47—21no—
158C22×Dic47—42no—
159C22×Dic47—42no—
160C22×Dic47—42no—
161C4⋊C4×C47—22no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—21no—
164C4⋊C4×C47—21no—
165C4⋊C4×C47—21no—
166C4⋊C4×C47—21no—
167C4⋊C4×C47—21no—
168C4⋊C4×C47—21no—
169C4⋊C4×C47—42no—
170C4⋊C4×C47—42no—
171C4⋊C4×C47—42no—
172C4⋊C4×C47—81no—
173C4⋊C4×C47#4112yes—
174C22⋊C4×C47—22no—
175C22⋊C4×C47—22no—
176C22⋊C4×C47—42no—
177C22⋊C4×C47—42no—
178C42×C47—21no—
179C42×C47—21no—
180C42×C47—42no—
181C22⋊Dic47—42no—
182C22⋊Dic47—42no—
183C22⋊Dic47—42no—
184C4⋊Dic47—21no—
185C4⋊Dic47—21no—
186C4⋊Dic47—21no—
187C4⋊Dic47—21no—
188C4⋊Dic47—21no—
189C4⋊Dic47—21no—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—42no—
193Dic47⋊C4—42no—
194Dic47⋊C4—42no—
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⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8—44no—
207C2×C47⋊C8#4112yes—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—21no—
216C23×C47—21no—
217C23×C47—21no—
218C23×C47#12312yes—
219C23×C47C2×D812yes—
220C23×C47C2×D812yes—
221C23×C47#13712yes—
222C23×C47C22×D411yescharacteristic
223D4×C47—28no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—22no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—22no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—41no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47—41no—
253C2×C4×C47—41no—
254C2×C4×C47—84no—
255C2×C4×C47—84no—
256C2×C4×C47#12312yes—
257C2×C4×C47C2×D812yes—
258C2×C4×C47C2×#4111yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C2×C4×C47H(5,𝔽2)11yescharacteristic
263C2×C4×C472−1+411yescharacteristic
264C2×Dic47—41no—
265C2×Dic47—41no—
266C2×Dic47—41no—
267C2×Dic47—41no—
268C2×Dic47—41no—
269C2×Dic47—41no—
270C2×Dic47—41no—
271C2×Dic47—41no—
272C2×Dic47—41no—
273C2×Dic47—41no—
274C2×Dic47—41no—
275C2×Dic47—41no—
276C2×Dic47—84no—
277C47⋊C8—22no—
278C47⋊C8—41no—
279C47⋊C8—41no—
280C47⋊C8—41no—
281#24933—471nomaximal, Sylow
282C22×C47—22no—
283C22×C47—22no—
284C22×C47—22no—
285C22×C47—22no—
286C22×C47—22no—
287C22×C47—22no—
288C22×C47—22no—
289C22×C47—22no—
290C22×C47—22no—
291C22×C47—41no—
292C22×C47—41no—
293C22×C47—41no—
294C22×C47—41no—
295C22×C47#48014yes—
296C22×C47C2×#12311yescharacteristic
297C22×C47#54611yescharacteristic
298C22×C47#54711yescharacteristic
299C22×C47C22×D811yescharacteristic
300C22×C47C2×#13711yescharacteristic
301C22×C47#57711yescharacteristic
302C22×C47#57811yescharacteristic
303C4×C47—22no—
304C4×C47—22no—
305C4×C47—41no—
306C4×C47—41no—
307C4×C47—42no—
308C4×C47—81no—
309C4×C47—81no—
310C4×C47—81no—
311C4×C47#52911yescharacteristic
312C4×C47#53911yescharacteristic
313C4×C47#55111yescharacteristic
314C4×C47#55211yescharacteristic
315Dic47—81no—
316Dic47—81no—
317Dic47—81no—
318Dic47—81no—
319#2486—471no—
320D4×C4⋊C4D4711yescharacteristic
321#2099—471no—
322#2083—471no—
323#2075—471no—
324#2075—471no—
325#1918—471no—
326#1918—471no—
327#1869—471no—
328#1852—471no—
329#1852—471no—
330#1823—471no—
331#1823—471no—
332#1808—471no—
333C2×#340—471no—
334C2×C47—24no—
335C2×C47—42no—
336C2×C47#241911yescharacteristic
337C2×C47C2×#48011yescharacteristic
338C2×C47#309711yescharacteristic
339C2×C47#329411yescharacteristic
340C2×C47#331211yescharacteristic
341C2×C47#333411yescharacteristic
342C2×C47#334411yescharacteristic
343C23×C8—471no—
344C2×#123—941no—
345C2×C4×D4—21no—
346C2×C4×D4C2×D4711yescharacteristic
347C22×C4⋊C4—471no—
348C22×C4⋊C4C2×D4711yescharacteristic
349C22×C4⋊C4C2×D4711yescharacteristic
350C2×#107—471no—
351C2×#107—471no—
352C2×#107—471no—
353C2×#107—471no—
354C2×C22⋊C8—471no—
355C2×C22⋊C8—471no—
356C2×C22⋊C8—471no—
357#398—941no—
358#397—941no—
359#389—21no—
360#389—471no—
361#389—471no—
362#385—21no—
363#385—21no—
364#384C2×D4711yescharacteristic
365#381—941no—
366#380—471no—
367#380—471no—
368#380—471no—
369#380C2×D4711yescharacteristic
370#380C2×D4711yescharacteristic
371C4×C4⋊C4C2×D4711yescharacteristic
372#340—471no—
373#340—471no—
374#340—471no—
375#340—471no—
376#340—471no—
377#340—471no—
378#340—471no—
379#340—471no—
380#340—471no—
381#340—471no—
382#340—471no—
383#340—471no—
384#336—471no—
385#336—471no—
386C47#2493311yescharacteristic, complemented, Sylow
387C22×D4C22⋊D4711yescharacteristic
388C23×C4—21no—
389C23×C4—21no—
390C23×C4—941no—
391C23×C4C22×D4711yescharacteristic
392C23×C4C22×D4711yescharacteristic
393C22×C8—471no—
394C22×C8—471no—
395C22×C8—471no—
396C22×C8—471no—
397C22×C8—942no—
398C22×C8—942no—
399C22×C8—1881no—
400#123—1884no—
401C4×D4—22no—
402C4×D4—22no—
403C4×D4—44no—
404C2×C4⋊C4—22no—
405C2×C4⋊C4—22no—
406C2×C4⋊C4—21no—
407C2×C4⋊C4—21no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—21no—
410C2×C4⋊C4—41no—
411C2×C4⋊C4—41no—
412C2×C4⋊C4—471no—
413C2×C4⋊C4—471no—
414C2×C4⋊C4—471no—
415C2×C4⋊C4—471no—
416C2×C4⋊C4—942no—
417C2×C4⋊C4—942no—
418C2×C4⋊C4—941no—
419C2×C4⋊C4—941no—
420C2×C4⋊C4—941no—
421C2×C4⋊C4C22⋊D4711yescharacteristic
422C2×C4⋊C4C22×D4711yescharacteristic
423C2×C4⋊C4C22×D4711yescharacteristic
424C2×C4⋊C4C22×D4711yescharacteristic
425C2×C4⋊C4C22×D4711yescharacteristic
426C2×C22⋊C4—21no—
427C2×C22⋊C4—21no—
428C2×C22⋊C4—941no—
429C2×C22⋊C4—941no—
430C2×C22⋊C4—941no—
431C2×C22⋊C4C22⋊D4711yescharacteristic
432C2×C22⋊C4C22⋊D4711yescharacteristic
433C2×C42—21no—
434C2×C42C22×D4711yescharacteristic
435#107—942no—
436#107—942no—
437#107—1881no—
438#107—1881no—
439C22⋊C8—942no—
440C22⋊C8—942no—
441C22⋊C8—1881no—
442#95—21no—
443#95—21no—
444#95—21no—
445#95—941no—
446#95—941no—
447#95—941no—
448#95—941no—
449#95—941no—
450C24C2×C22⋊D4711yescharacteristic
451C24C2×C22⋊D4711yescharacteristic
452C2×D4—22no—
453C2×D4—22no—
454C2×D4#1062533414yes—
455C22×C4—21no—
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—21no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—21no—
469C22×C4—42no—
470C22×C4—42no—
471C22×C4—42no—
472C22×C4—42no—
473C22×C4—81no—
474C22×C4—81no—
475C22×C4—941no—
476C22×C4—941no—
477C22×C4—941no—
478C22×C4—941no—
479C22×C4—1882no—
480C22×C4—1882no—
481C22×C4—1882no—
482C22×C4#1062535012yes—
483C22×C4#1062535012yes—
484C22×C4C2×C22⋊D4711yescharacteristic
485C22×C4C2×C22⋊D4711yescharacteristic
486C22×C4C2×C22⋊D4711yescharacteristic
487C22×C4C2×C22⋊D4711yescharacteristic
488C22×C4C23×D4711yescharacteristic
489C2×C8—472no—
490C2×C8—941no—
491C2×C8—941no—
492C2×C8—941no—
493C2×C8—941no—
494C2×C8—941no—
495C2×C8—941no—
496C2×C8—941no—
497C2×C8—941no—
498C2×C8—941no—
499C2×C8—941no—
500C2×C8—941no—
501C2×C8—1884no—
502C4⋊C4—22no—
503C4⋊C4—21no—
504C4⋊C4—21no—
505C4⋊C4—21no—
506C4⋊C4—21no—
507C4⋊C4—21no—
508C4⋊C4—21no—
509C4⋊C4—21no—
510C4⋊C4—42no—
511C4⋊C4—42no—
512C4⋊C4—42no—
513C4⋊C4—81no—
514C4⋊C4—941no—
515C4⋊C4—941no—
516C4⋊C4—941no—
517C4⋊C4—941no—
518C4⋊C4—941no—
519C4⋊C4—941no—
520C4⋊C4—941no—
521C4⋊C4—941no—
522C4⋊C4—1882no—
523C4⋊C4—1882no—
524C4⋊C4—1882no—
525C4⋊C4#1062535212yes—
526C22⋊C4—22no—
527C22⋊C4—22no—
528C22⋊C4—42no—
529C22⋊C4—42no—
530C22⋊C4—1882no—
531C22⋊C4—1882no—
532C22⋊C4—1882no—
533C42—21no—
534C42—21no—
535C42—42no—
536C23—21no—
537C23—21no—
538C23—21no—
539C23—21no—
540C23—21no—
541C23—21no—
542C23—21no—
543C23—21no—
544C23—21no—
545C23—21no—
546C23#1309400712yes—
547C23C2×#1062533412yes—
548C23C2×#1062533412yes—
549C23#1309405512yes—
550C23C22×C22⋊D4711yescharacteristic
551D4—28no—
552C2×C4—21no—
553C2×C4—21no—
554C2×C4—21no—
555C2×C4—21no—
556C2×C4—22no—
557C2×C4—22no—
558C2×C4—22no—
559C2×C4—22no—
560C2×C4—22no—
561C2×C4—21no—
562C2×C4—21no—
563C2×C4—21no—
564C2×C4—21no—
565C2×C4—21no—
566C2×C4—21no—
567C2×C4—41no—
568C2×C4—41no—
569C2×C4—41no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—84no—
583C2×C4—84no—
584C2×C4—3764no—
585C2×C4—1881no—
586C2×C4—1881no—
587C2×C4—1881no—
588C2×C4—1881no—
589C2×C4—1881no—
590C2×C4—1881no—
591C2×C4—1881no—
592C2×C4—1881no—
593C2×C4—1881no—
594C2×C4—1881no—
595C2×C4—1881no—
596C2×C4—1881no—
597C2×C4#1309400712yes—
598C2×C4C2×#1062533412yes—
599C2×C4#41×D4711yescharacteristic
600C2×C4C2×#1062535211yescharacteristic
601C2×C4C2×#1062535011yescharacteristic
602C2×C4C2×#1062535011yescharacteristic
603C2×C4#1309406911yescharacteristic
604C2×C4#1309407111yescharacteristic
605C8—942no—
606C8—1881no—
607C8—1881no—
608C8—1881no—
609C22—22no—
610C22—22no—
611C22—22no—
612C22—22no—
613C22—22no—
614C22—22no—
615C22—22no—
616C22—22no—
617C22—22no—
618C22—41no—
619C22—41no—
620C22—41no—
621C22—41no—
622C22#1568943614yes—
623C22C2×#1309400711yescharacteristic
624C22#1568976711yescharacteristic
625C22#1568977211yescharacteristic
626C22C22×#1062533411yescharacteristic
627C22C2×#1309405511yescharacteristic
628C22#1568993411yescharacteristic
629C22#1568993811yescharacteristic
630C4—22no—
631C4—22no—
632C4—41no—
633C4—41no—
634C4—42no—
635C4—81no—
636C4—81no—
637C4—81no—
638C4—3761no—
639C4—3761no—
640C4—3761no—
641C4—3761no—
642C4#1568965311yescharacteristic
643C4#1568971511yescharacteristic
644C4#1568980211yescharacteristic
645C4#1568981311yescharacteristic
646C2—24no—
647C2—42no—
648C2#2024685911yescharacteristic
649C2C2×#1568943611yescharacteristic
650C2#2025335711yescharacteristic
651C2#2025520111yescharacteristic
652C2#2025543911yescharacteristic
653C2#2025573111yescharacteristic
654C2#2025583711yescharacteristic
subgroupG/H
centerC23C22×C22⋊D47
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingD4×C4⋊C4×C47C2
socleC23×C47C22×D4
prime radicalC22×D4×C47D4
hypercenterD4×C4⋊C4D47
hypocenterC47#24933
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ D4×C4⋊C4

Complements

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

NH ≅ G/Ntype
2. #20244945C2semidirect
3. #20244860C2semidirect
4. #20244814C2semidirect
5. #20244814C2semidirect
6. #20243959C2semidirect
7. #20243959C2semidirect
9. #20243576C2semidirect
10. #20243576C2semidirect
11. #20243474C2semidirect
12. #20243472C2semidirect
13. #20243415C2semidirect
14. C2×#15688885C2semidirect
386. C47#24933semidirect

Maximal subgroups

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

subgroupindex
#202476962
#202449452
#202448602
#202448142
#202439592
#202436812
#202435762
#202434742
#202434722
#202434152
C2×#156888852
D4×C4⋊C4×C472
#2493347