Finite Group Databasebeta

← #26233865

Subgroups — #26233865

Order 12032.

780 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689181C211yesmaximal, characteristic
2#20245871C211yesmaximal, characteristic
3#20244108C211yesmaximal, characteristic, complemented
4#20244103C211yesmaximal, characteristic, complemented
5#20243952C211yesmaximal, characteristic, complemented
6#20243952C211yesmaximal, characteristic, complemented
7#20243949C211yesmaximal, characteristic, complemented
8#20243942C211yesmaximal, characteristic, complemented
9#20243457C211yesmaximal, characteristic
10#20243456C211yesmaximal, characteristic
11#20243370C211yesmaximal, characteristic
12#20243264C211yesmaximal, characteristic, complemented
13#20243256C211yesmaximal, characteristic, complemented
14#20243156C211yesmaximal, characteristic
15C2×C47×#432C211yesmaximal, characteristic
16C2×#13093983C2211yescharacteristic
17C2×#13093983C2211yescharacteristic
18#15689181—24no—
19C2×Dic47⋊C8C2211yescharacteristic
20C2×Dic47⋊C8C2211yescharacteristic
21C2×Dic47⋊C8C2211yescharacteristic
22C2×Dic47⋊C8C2211yescharacteristic
23C2×C22⋊(C47⋊C8)C2211yescharacteristic
24C2×C22⋊(C47⋊C8)C2211yescharacteristic
25C2×#13093934C2211yescharacteristic
26C2×#13093934C2211yescharacteristic
27C2×C8×Dic47C2211yescharacteristic
28C2×C8×Dic47C2211yescharacteristic
29#15689021C411yescharacteristic
30#15689021C411yescharacteristic
31#15689021C411yescharacteristic
32#15689021C411yescharacteristic
33#15688996C411yescharacteristic
34#15688996C411yescharacteristic
35#15688996C411yescharacteristic
36#15688996C411yescharacteristic
37C4×Dic47⋊C4C2211yescharacteristic
38C4×Dic47⋊C4C2211yescharacteristic
39C4×Dic47⋊C4C2211yescharacteristic
40C4×Dic47⋊C4C2211yescharacteristic
41#15688878C2211yescharacteristic
42#15688878C2211yescharacteristic
43#15688878C2211yescharacteristic
44#15688878C2211yescharacteristic
45#15688877C2211yescharacteristic
46#15688877C2211yescharacteristic
47#15688877C2211yescharacteristic
48#15688877C2211yescharacteristic
49#15688877C2211yescharacteristic
50#15688877C2211yescharacteristic
51#15688877C2211yescharacteristic
52#15688877C2211yescharacteristic
53C22×C42×C47C2211yescharacteristic
54C47×#432—24no—
55C2×C4⋊C8×C47C2211yescharacteristic
56C2×C4⋊C8×C47C2211yescharacteristic
57C2×C22⋊C8×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C2×#97×C47C2211yescharacteristic
60C2×#97×C47C2211yescharacteristic
61C22×C47⋊C8C2311yescharacteristic
62C22×C47⋊C8C2311yescharacteristic
63C22×C47⋊C8C2311yescharacteristic
64C22×C47⋊C8C2311yescharacteristic
65#13093983—22no—
66#13093983—22no—
67#13093983—22no—
68#13093983—22no—
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×C4⋊Dic47C2×C411yescharacteristic
71C2×C4⋊Dic47C2×C411yescharacteristic
72C2×C4⋊Dic47C2×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×Dic47⋊C4C2×C411yescharacteristic
81C2×C22⋊Dic47C2×C411yescharacteristic
82C2×C22⋊Dic47C2×C411yescharacteristic
83C2×C22⋊Dic47C2×C411yescharacteristic
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×C4×Dic47C2311yescharacteristic
86C2×C4×Dic47C2311yescharacteristic
87C2×C4×Dic47C2311yescharacteristic
88C2×C4×Dic47C2311yescharacteristic
89Dic47⋊C8—22no—
90Dic47⋊C8—22no—
91Dic47⋊C8—22no—
92Dic47⋊C8—22no—
93C22⋊(C47⋊C8)—22no—
94C22⋊(C47⋊C8)—22no—
95#13093934—22no—
96#13093934—22no—
97C8×Dic47—22no—
98C8×Dic47—22no—
99C47⋊#95C2×C411yescharacteristic
100C47⋊#95C2×C411yescharacteristic
101C47⋊#95C2×C411yescharacteristic
102C47⋊#95C2×C411yescharacteristic
103C47⋊#95C2×C411yescharacteristic
104C47⋊#95C2×C411yescharacteristic
105C47⋊#95C2×C411yescharacteristic
106C47⋊#95C2×C411yescharacteristic
107C23×C4×C47C2×C411yescharacteristic
108C23×C4×C47C2×C411yescharacteristic
109C23×C4×C47C2311yescharacteristic
110C22×C8×C47C2311yescharacteristic
111C22×C8×C47C2311yescharacteristic
112C22×C8×C47C2311yescharacteristic
113C22×C8×C47C2311yescharacteristic
114C2×C42×C47—22no—
115C2×C42×C47—22no—
116C2×C42×C47C2×C411yescharacteristic
117C2×C42×C47C2×C411yescharacteristic
118C2×C42×C47C2311yescharacteristic
119C2×C42×C47C2311yescharacteristic
120C4⋊C8×C47—22no—
121C4⋊C8×C47—22no—
122C22⋊C8×C47—22no—
123C22⋊C8×C47D414yes—
124#97×C47—22no—
125#97×C47—22no—
126C24×C47C22×C411yescharacteristic
127C22×C4×C47—21no—
128C22×C4×C47—21no—
129C22×C4×C47—21no—
130C22×C4×C47—21no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—22no—
134C22×C4×C47—41no—
135C22×C4×C47—41no—
136C22×C4×C47—41no—
137C22×C4×C47C22×C411yescharacteristic
138C22×C4×C47C22×C411yescharacteristic
139C22×C4×C47C22×C411yescharacteristic
140C22×C4×C47C22×C411yescharacteristic
141C22×C4×C47C22×C411yescharacteristic
142C22×C4×C47C2×D412yes—
143C22×C4×C47#4112yes—
144C22×C4×C47C2411yescharacteristic
145C22×Dic47C22×C411yescharacteristic
146C22×Dic47C22×C411yescharacteristic
147C22×Dic47C22×C411yescharacteristic
148C22×Dic47C22×C411yescharacteristic
149C22×Dic47C22×C411yescharacteristic
150C22×Dic47C22×C411yescharacteristic
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C411yescharacteristic
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×C47—21no—
163C2×C8×C47C2×D412yes—
164C2×C8×C47C2×D412yes—
165C42×C47—22no—
166C42×C47—22no—
167C42×C47—21no—
168C42×C47—21no—
169C42×C47—21no—
170C42×C47—21no—
171C22⋊Dic47—22no—
172C22⋊Dic47—22no—
173C22⋊Dic47—22no—
174C22⋊Dic47—22no—
175C4⋊Dic47—22no—
176C4⋊Dic47—22no—
177C4⋊Dic47—22no—
178C4⋊Dic47—22no—
179Dic47⋊C4—22no—
180Dic47⋊C4—22no—
181Dic47⋊C4—41no—
182Dic47⋊C4—41no—
183Dic47⋊C4—41no—
184Dic47⋊C4—41no—
185Dic47⋊C4—41no—
186Dic47⋊C4—41no—
187C4×Dic47—21no—
188C4×Dic47—21no—
189C4×Dic47—21no—
190C4×Dic47—21no—
191C4×Dic47—21no—
192C4×Dic47—21no—
193C4×Dic47#4112yes—
194C4×Dic47#4112yes—
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—21no—
207C23×C47—21no—
208C23×C47—21no—
209C23×C47—21no—
210C23×C47—21no—
211C23×C47—21no—
212C23×C47—21no—
213C23×C47C4×D412yes—
214C23×C47C23×C411yescharacteristic
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—21no—
218C2×C4×C47—21no—
219C2×C4×C47—22no—
220C2×C4×C47—22no—
221C2×C4×C47—22no—
222C2×C4×C47—22no—
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—21no—
232C2×C4×C47—44no—
233C2×C4×C47—44no—
234C2×C4×C47C4×D412yes—
235C2×C4×C47#13112yes—
236C2×C4×C47C22×D411yescharacteristic
237C2×C4×C47C2×#4111yescharacteristic
238C2×C4×C47C2×#4111yescharacteristic
239C2×C4×C47C2×#4111yescharacteristic
240C2×C4×C472−1+411yescharacteristic
241C2×C4×C472−1+411yescharacteristic
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—21no—
261C2×Dic47—21no—
262C2×Dic47—21no—
263C2×Dic47—21no—
264C2×Dic47#11712yes—
265C2×Dic47#11712yes—
266C8×C47—22no—
267C8×C47—22no—
268C8×C47—41no—
269C8×C47—41no—
270C47⋊C8—41no—
271C47⋊C8—41no—
272C47⋊C8—41no—
273C47⋊C8—41no—
274#22605—471nomaximal, Sylow
275C22×C47—22no—
276C22×C47—22no—
277C22×C47—22no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47—41no—
282C22×C47C2×#11711yescharacteristic
283C22×C47C2×C4×D411yescharacteristic
284C22×C47#51911yescharacteristic
285C22×C47C2×#13111yescharacteristic
286C22×C47#56811yescharacteristic
287C22×C47#56811yescharacteristic
288C22×C47#56811yescharacteristic
289C4×C47—22no—
290C4×C47—22no—
291C4×C47—41no—
292C4×C47—41no—
293C4×C47—41no—
294C4×C47#54711yescharacteristic
295C4×C47#54711yescharacteristic
296C4×C47#55211yescharacteristic
297C4×C47#55211yescharacteristic
298Dic47—22no—
299Dic47—22no—
300Dic47—41no—
301Dic47—41no—
302Dic47—41no—
303Dic47—41no—
304Dic47—41no—
305Dic47—41no—
306C2×#433—471no—
307C2×#432D4711yescharacteristic
308#2296—471no—
309#1940—471no—
310#1939—471no—
311#1917—471no—
312#1917—471no—
313#1917—471no—
314#1916—471no—
315#1818—471no—
316#1817—471no—
317#1798—471no—
318#1771—471no—
319#1770—471no—
320#1750—471no—
321C2×C47—42no—
322C2×C47#234411yescharacteristic
323C2×C47#292311yescharacteristic
324C2×C47#292511yescharacteristic
325C2×C47#293011yescharacteristic
326C2×C47#293311yescharacteristic
327C2×C47#298511yescharacteristic
328C2×C47#298711yescharacteristic
329C2×#117—471no—
330C2×#117—471no—
331C22×C42C2×D4711yescharacteristic
332#433—944no—
333#432—24no—
334C2×C4⋊C8—471no—
335C2×C4⋊C8—471no—
336C2×C4⋊C8—471no—
337C2×C4⋊C8—471no—
338C2×C4⋊C8C2×D4711yescharacteristic
339C2×C4⋊C8C2×D4711yescharacteristic
340C2×C22⋊C8—471no—
341C2×C22⋊C8—471no—
342C2×C22⋊C8C2×D4711yescharacteristic
343C2×C22⋊C8C2×D4711yescharacteristic
344C2×#97—471no—
345C2×#97—471no—
346C2×#97C2×D4711yescharacteristic
347C2×#97C2×D4711yescharacteristic
348C2×C4×C8—471no—
349C2×C4×C8—471no—
350#389—471no—
351#389—471no—
352#389—471no—
353#389—471no—
354#385—471no—
355#385—471no—
356#385—471no—
357#385—471no—
358C4×C4⋊C4—471no—
359C4×C4⋊C4—471no—
360C4×C4⋊C4—471no—
361C4×C4⋊C4—471no—
362#336—471no—
363#336—471no—
364#336—471no—
365#336—471no—
366#336—471no—
367#336—471no—
368#336—471no—
369#336—471no—
370#336—471no—
371#336—471no—
372#336—471no—
373#336—471no—
374C47#2260511yescharacteristic, complemented, Sylow
375C23×C4C4×D4711yescharacteristic
376C23×C4C4×D4711yescharacteristic
377C23×C4C22×D4711yescharacteristic
378C22×C8—471no—
379C22×C8—471no—
380C22×C8—471no—
381C22×C8—471no—
382C22×C8C22×D4711yescharacteristic
383C22×C8C22×D4711yescharacteristic
384C22×C8C22×D4711yescharacteristic
385C22×C8C22×D4711yescharacteristic
386#117—942no—
387#117—942no—
388#117—942no—
389#117—942no—
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⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—471no—
401C2×C4⋊C4—471no—
402C2×C22⋊C4—471no—
403C2×C22⋊C4—471no—
404C2×C22⋊C4—471no—
405C2×C22⋊C4—471no—
406C2×C42—22no—
407C2×C42—22no—
408C2×C42—471no—
409C2×C42—471no—
410C2×C42—471no—
411C2×C42—471no—
412C2×C42C4×D4711yescharacteristic
413C2×C42C4×D4711yescharacteristic
414C2×C42C22×D4711yescharacteristic
415C2×C42C22×D4711yescharacteristic
416C4⋊C8—22no—
417C4⋊C8—22no—
418C4⋊C8—942no—
419C4⋊C8—942no—
420C4⋊C8—942no—
421C4⋊C8—942no—
422C22⋊C8—22no—
423C22⋊C8—942no—
424C22⋊C8—942no—
425C22⋊C8C22⋊D4714yes—
426#97—22no—
427#97—22no—
428#97—942no—
429#97—942no—
430C4×C8—942no—
431C4×C8—942no—
432#95—471no—
433#95—471no—
434#95—471no—
435#95—471no—
436#95—471no—
437#95—471no—
438#95—471no—
439#95—471no—
440C24C2×C4×D4711yescharacteristic
441C22×C4—21no—
442C22×C4—21no—
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—22no—
448C22×C4—41no—
449C22×C4—41no—
450C22×C4—41no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—471no—
454C22×C4—471no—
455C22×C4—471no—
456C22×C4—471no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4C2×C4×D4711yescharacteristic
460C22×C4C2×C4×D4711yescharacteristic
461C22×C4C2×C4×D4711yescharacteristic
462C22×C4C2×C4×D4711yescharacteristic
463C22×C4C2×C4×D4711yescharacteristic
464C22×C4#1062535012yes—
465C22×C4C2×C22⋊D4712yes—
466C22×C4C23×D4711yescharacteristic
467C2×C8—21no—
468C2×C8—21no—
469C2×C8—21no—
470C2×C8—21no—
471C2×C8—21no—
472C2×C8—21no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—21no—
476C2×C8—21no—
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×C8—941no—
487C2×C8—941no—
488C2×C8—941no—
489C2×C8C2×C22⋊D4712yes—
490C2×C8C2×C22⋊D4712yes—
491C4⋊C4—942no—
492C4⋊C4—942no—
493C4⋊C4—942no—
494C4⋊C4—942no—
495C4⋊C4—942no—
496C4⋊C4—942no—
497C4⋊C4—1881no—
498C4⋊C4—1881no—
499C4⋊C4—1881no—
500C4⋊C4—1881no—
501C4⋊C4—1881no—
502C4⋊C4—1881no—
503C22⋊C4—942no—
504C22⋊C4—942no—
505C22⋊C4—942no—
506C22⋊C4—942no—
507C42—22no—
508C42—22no—
509C42—21no—
510C42—21no—
511C42—21no—
512C42—21no—
513C42—472no—
514C42—472no—
515C42—941no—
516C42—941no—
517C42—941no—
518C42—941no—
519C42—941no—
520C42—941no—
521C23—21no—
522C23—21no—
523C23—21no—
524C23—21no—
525C23—21no—
526C23—21no—
527C23C4×C22⋊D4712yes—
528C23C22×C4×D4711yescharacteristic
529C2×C4—21no—
530C2×C4—21no—
531C2×C4—21no—
532C2×C4—21no—
533C2×C4—22no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
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—44no—
547C2×C4—44no—
548C2×C4—472no—
549C2×C4—472no—
550C2×C4—941no—
551C2×C4—941no—
552C2×C4—941no—
553C2×C4—941no—
554C2×C4—941no—
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—941no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—941no—
572C2×C4C4×C22⋊D4712yes—
573C2×C4#1309403212yes—
574C2×C4C22×C22⋊D4711yescharacteristic
575C2×C4#41×D4711yescharacteristic
576C2×C4#41×D4711yescharacteristic
577C2×C4C2×#1062535011yescharacteristic
578C2×C4#1309407111yescharacteristic
579C2×C4#1309407111yescharacteristic
580C8—22no—
581C8—22no—
582C8—41no—
583C8—41no—
584C8—1881no—
585C8—1881no—
586C8—1881no—
587C8—1881no—
588C22—22no—
589C22—22no—
590C22—22no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—41no—
595C22#117×D4711yescharacteristic
596C22C2×C4×C22⋊D4711yescharacteristic
597C22#1568960011yescharacteristic
598C22C2×#1309403211yescharacteristic
599C22#1568988911yescharacteristic
600C22#1568988911yescharacteristic
601C22#1568988911yescharacteristic
602C4—22no—
603C4—22no—
604C4—41no—
605C4—41no—
606C4—41no—
607C4—942no—
608C4—942no—
609C4—1881no—
610C4—1881no—
611C4—1881no—
612C4—1881no—
613C4—1881no—
614C4—1881no—
615C4#1568977211yescharacteristic
616C4#1568977211yescharacteristic
617C4#1568980611yescharacteristic
618C4#1568980611yescharacteristic
619C2—42no—
620C2#2024625811yescharacteristic
621C2#2025203411yescharacteristic
622C2#2025205511yescharacteristic
623C2#2025209111yescharacteristic
624C2#2025211311yescharacteristic
625C2#2025248511yescharacteristic
626C2#2025249311yescharacteristic
subgroupG/H
center, FrattiniC22×C4C23×D47
commutator, socleC23×C47C23×C4
FittingC2×C47×#432C2
prime radicalC24×C47C22×C4
cosocleC22×C4×C47C24
hypercenterC2×#432D47
hypocenterC47#22605
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×#432

Complements

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

NH ≅ G/Ntype
3. #20244108C2semidirect
4. #20244103C2semidirect
5. #20243952C2semidirect
6. #20243952C2semidirect
7. #20243949C2semidirect
8. #20243942C2semidirect
12. #20243264C2semidirect
13. #20243256C2semidirect
374. C47#22605semidirect

Maximal subgroups

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

subgroupindex
C2×#156891812
#202458712
#202441082
#202441032
#202439522
#202439492
#202439422
#202434572
#202434562
#202433702
#202432642
#202432562
#202431562
C2×C47×#4322
#2260547