Finite Group Databasebeta

← #26234411

Subgroups — #26234411

Order 12032.

982 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×(C22⋊D47)⋊C8C211yesmaximal, characteristic
2C2×#15689160C211yesmaximal, characteristic, complemented
3C2×#15689159C211yesmaximal, characteristic, complemented
4#20246338C211yesmaximal, characteristic
5#20246332C211yesmaximal, characteristic
6#20244145C211yesmaximal, characteristic, complemented
7#20244143C211yesmaximal, characteristic, complemented
8#20243589C211yesmaximal, characteristic, complemented
9#20243588C211yesmaximal, characteristic, complemented
10#20243586C211yesmaximal, characteristic, complemented
11#20243543C211yesmaximal, characteristic, complemented
12#20243412C211yesmaximal, characteristic, complemented
13#20243411C211yesmaximal, characteristic, complemented
14#20243276C211yesmaximal, characteristic, complemented
15C47×#1854C211yesmaximal, characteristic, complemented
16C23×C47⋊C8C2211yescharacteristic
17C22×C8×D47C2211yescharacteristic
18C2×C4×C22⋊D47C2211yescharacteristic
19C2×#13093983C2211yescharacteristic
20C2×#13093982C2211yescharacteristic
21C2×#13093982C2211yescharacteristic
22(C22⋊D47)⋊C8C418yescomplemented
23#15689160—24no—
24#15689159—24no—
25C2×#13093958C2211yescharacteristic
26C2×#13093957C2211yescharacteristic
27C2×#13093957C2211yescharacteristic
28C2×#13093956C2211yescharacteristic
29C2×#13093955C2211yescharacteristic
30C2×#13093955C2211yescharacteristic
31C2×#13093955C2211yescharacteristic
32C2×#13093955C2211yescharacteristic
33C2×Dic47⋊C8C2211yescharacteristic
34C2×(C2×D47)⋊C8C2211yescharacteristic
35C2×C8×Dic47C2211yescharacteristic
36#15689023—21no—
37#15689023—21no—
38#15689017—21no—
39#15689014—21no—
40#15689012—21no—
41#15689011—21no—
42#15688992C2211yescharacteristic
43#15688992C2211yescharacteristic
44#15688983C2211yescharacteristic
45#15688980C2211yescharacteristic
46#15688980C2211yescharacteristic
47C4⋊C4×Dic47C2211yescharacteristic
48C4⋊C4×Dic47C2211yescharacteristic
49C4×Dic47⋊C4—21no—
50#15688974—21no—
51#15688886C2211yescharacteristic
52#15688886C2211yescharacteristic
53#15688885C2211yescharacteristic
54#15688885C2211yescharacteristic
55C2×#117×C47C2211yescharacteristic
56C2×#107×C47C2211yescharacteristic
57C2×#106×C47C2211yescharacteristic
58C2×C22⋊C8×C47C2211yescharacteristic
59C47×#380C2211yescharacteristic
60C47×#340C2211yescharacteristic
61C47×#340C2211yescharacteristic
62C22×C22⋊D47D411yescharacteristic
63C22×C4×D47C2311yescharacteristic
64C22×C47⋊C8—22no—
65C22×C47⋊C8—22no—
66C22×C47⋊C8C2×C414yes—
67C22×C47⋊C8C2311yescharacteristic
68C22×C47⋊C8C2311yescharacteristic
69C2×C8×D47—22no—
70C2×C8×D47—22no—
71C2×C8×D47C2×C414yes—
72C4×C22⋊D47C2×C414yes—
73C4×C22⋊D47Q814yes—
74#13093983—22no—
75#13093983—41no—
76#13093982—22no—
77#13093982—22no—
78#13093982—41no—
79#13093982—41no—
80C2×C4⋊Dic47C2311yescharacteristic
81C2×C4⋊Dic47C2311yescharacteristic
82C2×C4⋊Dic47C2311yescharacteristic
83C2×C4⋊Dic47C2311yescharacteristic
84C2×Dic47⋊C4—21no—
85C2×Dic47⋊C4—21no—
86C2×Dic47⋊C4—21no—
87C2×Dic47⋊C4—21no—
88C2×Dic47⋊C4D411yescharacteristic
89C2×C22⋊Dic47—21no—
90C2×C22⋊Dic47—21no—
91C2×C22⋊Dic47D411yescharacteristic
92C2×(C2×D47)⋊C4—21no—
93C2×(C2×D47)⋊C4—21no—
94C2×(C2×D47)⋊C4—21no—
95C2×(C2×D47)⋊C4—21no—
96C2×(C2×D47)⋊C4D411yescharacteristic
97C2×C4×Dic47—21no—
98C2×C4×Dic47—21no—
99C2×C4×Dic47—21no—
100C2×C4×Dic47—21no—
101C2×C4×Dic47—21no—
102C2×C4×Dic47C2311yescharacteristic
103#13093958—22no—
104#13093957—22no—
105#13093957—22no—
106#13093956—41no—
107#13093955—22no—
108#13093955—22no—
109#13093955—22no—
110#13093955D414yescomplemented
111Dic47⋊C8C2×C414yes—
112(C2×D47)⋊C8C2×C414yes—
113C8×Dic47C2×C414yes—
114C47⋊#95—21no—
115C47⋊#95—21no—
116C47⋊#95—21no—
117C47⋊#95—21no—
118C47⋊#95—21no—
119C23×C4×C47C2311yescharacteristic
120C22×C8×C47C2311yescharacteristic
121C22×C8×C47C2311yescharacteristic
122#117×C47—22no—
123#117×C47—41no—
124C2×C4⋊C4×C47C2311yescharacteristic
125C2×C4⋊C4×C47C2311yescharacteristic
126C2×C4⋊C4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2311yescharacteristic
128C2×C22⋊C4×C47—21no—
129C2×C22⋊C4×C47—21no—
130C2×C42×C47—21no—
131#107×C47—22no—
132#106×C47—41no—
133C22⋊C8×C47C2×C414yes—
134#95×C47—21no—
135C24×C47C2×D411yescharacteristic
136C23×D47C2×D411yescharacteristic
137C22×C4×C47—21no—
138C22×C4×C47—21no—
139C22×C4×C47—21no—
140C22×C4×C47—21no—
141C22×C4×C47—21no—
142C22×C4×C47—21no—
143C22×C4×C47—21no—
144C22×C4×C47—21no—
145C22×C4×C47C22×C412yes—
146C22×C4×C47C2×D411yescharacteristic
147C22×C4×C47C2×Q812yes—
148C22×C4×C47C2411yescharacteristic
149C2×C22⋊D47—22no—
150C2×C22⋊D47—22no—
151C2×C22⋊D47C4⋊C414yes—
152C22×Dic47—21no—
153C22×Dic47—21no—
154C22×Dic47—21no—
155C22×Dic47—21no—
156C22×Dic47C2×D411yescharacteristic
157C22×Dic47C2×D411yescharacteristic
158C22×Dic47C2×D411yescharacteristic
159C2×C4×D47—21no—
160C2×C4×D47—21no—
161C2×C4×D47—21no—
162C2×C4×D47—21no—
163C2×C4×D47C22×C412yes—
164C2×C4×D47C2×Q812yes—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—21no—
169C2×C8×C47C22×C412yes—
170C2×C8×C47C22×C412yes—
171C4⋊C4×C47—21no—
172C4⋊C4×C47—21no—
173C4⋊C4×C47—21no—
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47C2×D412yes—
179C22⋊C4×C47—42no—
180C22⋊C4×C47—81no—
181C42×C47—42no—
182C22⋊Dic47—42no—
183C22⋊Dic47—81no—
184C22⋊Dic47C4⋊C414yes—
185(C2×D47)⋊C4—42no—
186(C2×D47)⋊C4—42no—
187(C2×D47)⋊C4—81no—
188(C2×D47)⋊C4—81no—
189(C2×D47)⋊C4C4⋊C414yes—
190C4⋊Dic47—21no—
191C4⋊Dic47—21no—
192C4⋊Dic47—21no—
193C4⋊Dic47—21no—
194C4⋊Dic47—21no—
195C4⋊Dic47—21no—
196C4⋊Dic47—21no—
197C4⋊Dic47C2×D412yes—
198Dic47⋊C4—42no—
199Dic47⋊C4—42no—
200Dic47⋊C4—81no—
201Dic47⋊C4—81no—
202Dic47⋊C4C4⋊C414yes—
203C4×Dic47—42no—
204C4×Dic47—42no—
205C4×Dic47—42no—
206C4×Dic47—42no—
207C4×Dic47—42no—
208C4×Dic47C22×C412yes—
209C4×Dic47C2×Q812yes—
210C2×C47⋊C8—21no—
211C2×C47⋊C8—21no—
212C2×C47⋊C8—28no—
213C2×C47⋊C8C22×C412yes—
214C2×C47⋊C8C22×C412yes—
215C2×C47⋊C8C2×D412yes—
216C2×C47⋊C8#4112yes—
217C8×D47—28no—
218C23×C47—21no—
219C23×C47—21no—
220C23×C47—21no—
221C23×C47—21no—
222C23×C47—21no—
223C23×C47—21no—
224C23×C47C2×C4⋊C412yes—
225C23×C47C22×D411yescharacteristic
226C22×D47—21no—
227C22×D47—21no—
228C22×D47—21no—
229C22×D47—21no—
230C22×D47—21no—
231C22×D47—21no—
232C22×D47C2×C4⋊C412yes—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—22no—
236C2×C4×C47—22no—
237C2×C4×C47—22no—
238C2×C4×C47—22no—
239C2×C4×C47—22no—
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×C47C2×C4⋊C412yes—
252C2×C4×C47C23×C411yescharacteristic
253C2×C4×C47C22×D411yescharacteristic
254C2×C4×C47C22×Q811yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47H(5,𝔽2)11yescharacteristic
257C2×C4×C472−1+411yescharacteristic
258C22⋊D47—28no—
259C2×Dic47—21no—
260C2×Dic47—21no—
261C2×Dic47—21no—
262C2×Dic47—21no—
263C2×Dic47—22no—
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×Dic47C2×C4⋊C412yes—
276C2×Dic47C2×C4⋊C412yes—
277C2×Dic47C2×C4⋊C412yes—
278C2×Dic47#13512yes—
279C2×Dic47#13512yes—
280C4×D47—22no—
281C4×D47—22no—
282C4×D47—22no—
283C4×D47—22no—
284C8×C47—22no—
285C8×C47—22no—
286C47⋊C8—22no—
287C47⋊C8C4×D414yes—
288#22657—471nomaximal, Sylow
289C22×C47—22no—
290C22×C47—22no—
291C22×C47—22no—
292C22×C47—41no—
293C22×C47—41no—
294C22×C47—41no—
295C22×C47—41no—
296C22×C47C22×C4⋊C411yescharacteristic
297C22×C47D4211yescharacteristic
298C22×C47#54711yescharacteristic
299C22×C47C2×#13511yescharacteristic
300C22×C47C2×#13511yescharacteristic
301C22×C47#57711yescharacteristic
302C22×C47#57711yescharacteristic
303C2×D47—22no—
304C2×D47—22no—
305C2×D47—22no—
306C2×D47—41no—
307C2×D47—41no—
308C2×D47—41no—
309C2×D47—41no—
310C4×C47—22no—
311C4×C47—42no—
312C4×C47—81no—
313C4×C47—81no—
314C4×C47—81no—
315C4×C47C2×C4×D411yescharacteristic
316C4×C47#52011yescharacteristic
317C4×C47D4×Q811yescharacteristic
318C4×C47#55411yescharacteristic
319Dic47—22no—
320Dic47—22no—
321Dic47—42no—
322Dic47—81no—
323Dic47—81no—
324Dic47—81no—
325Dic47#42714yescomplemented
326C2×C8×D4—471no—
327C2×#427—471no—
328C2×#427—471no—
329#2354—471no—
330#2354—471no—
331#1947—471no—
332#1947—471no—
333#1854—471no—
334#1854—471no—
335#1854—471no—
336#1854D4711yescharacteristic, complemented
337#1844—471no—
338#1807—471no—
339#1807—471no—
340C4×#106—471no—
341C2×C47—42no—
342C2×C47D4×C4⋊C411yescharacteristic
343C2×C47C2×#42711yescharacteristic
344C2×C47#291211yescharacteristic
345C2×C47#328411yescharacteristic
346C2×C47#328411yescharacteristic
347C2×C47#334011yescharacteristic
348C2×C47#334011yescharacteristic
349D47—42no—
350C23×C8—471no—
351C23×C8—471no—
352C2×C4×D4—471no—
353C2×#117—471no—
354C2×#117—471no—
355C2×#117—471no—
356C2×#117C2×D4711yescharacteristic
357C8×D4—478no—
358#427—944no—
359#427—944no—
360C2×#107—471no—
361C2×#107—471no—
362C2×#107—471no—
363C2×#107C2×D4711yescharacteristic
364C2×#106—471no—
365C2×#106—471no—
366C2×#106—471no—
367C2×#106—471no—
368C2×#106—471no—
369C2×#106C2×D4711yescharacteristic
370C2×C4⋊C8—471no—
371C2×C22⋊C8—471no—
372C2×C22⋊C8C2×D4711yescharacteristic
373C2×C4×C8—471no—
374#390—941no—
375#390—941no—
376#388—941no—
377#388—941no—
378#388—941no—
379#388—941no—
380#384—471no—
381#384—471no—
382#380—471no—
383#380—471no—
384#380—471no—
385#380C2×D4711yescharacteristic
386C4×C4⋊C4—471no—
387C4×C4⋊C4—471no—
388C4×C4⋊C4—941no—
389C4×C4⋊C4—941no—
390#340—471no—
391#340—471no—
392#340—471no—
393#340—471no—
394#340C2×D4711yescharacteristic
395#340C2×D4711yescharacteristic
396C47#2265711yescharacteristic, complemented, Sylow
397C22×D4—471no—
398C23×C4—471no—
399C23×C4C22×D4711yescharacteristic
400C22×C8—471no—
401C22×C8—474no—
402C22×C8—471no—
403C22×C8—474no—
404C22×C8—942no—
405C22×C8—942no—
406C22×C8—942no—
407C22×C8—942no—
408C22×C8C22×D4711yescharacteristic
409C22×C8C22×D4711yescharacteristic
410C4×D4—474no—
411C4×D4—474no—
412#117—22no—
413#117—41no—
414#117—942no—
415#117—942no—
416#117—942no—
417#117—1881no—
418#117—1881no—
419#117—1881no—
420C2×C4⋊C4—471no—
421C2×C4⋊C4—471no—
422C2×C4⋊C4—471no—
423C2×C4⋊C4—471no—
424C2×C4⋊C4—471no—
425C2×C4⋊C4—941no—
426C2×C4⋊C4—941no—
427C2×C4⋊C4—941no—
428C2×C4⋊C4—941no—
429C2×C4⋊C4C22×D4711yescharacteristic
430C2×C4⋊C4C22×D4711yescharacteristic
431C2×C4⋊C4C22×D4711yescharacteristic
432C2×C4⋊C4C22×D4711yescharacteristic
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—471no—
436C2×C22⋊C4—471no—
437C2×C22⋊C4—941no—
438C2×C22⋊C4—941no—
439C2×C22⋊C4—941no—
440C2×C22⋊C4—941no—
441C2×C22⋊C4—941no—
442C2×C22⋊C4—941no—
443C2×C42—21no—
444C2×C42—471no—
445C2×C42—941no—
446C2×C42—941no—
447C2×C42—941no—
448C2×C42—941no—
449C2×C42—941no—
450#107—22no—
451#107—942no—
452#107—942no—
453#107—942no—
454#106—41no—
455#106—474no—
456#106—942no—
457#106—942no—
458#106—942no—
459#106—1881no—
460C4⋊C8—474no—
461C22⋊C8—474no—
462C22⋊C8C4×D4714yes—
463C4×C8—474no—
464#95—21no—
465#95—941no—
466#95—941no—
467#95—941no—
468#95—941no—
469#95—941no—
470C24—471no—
471C24D4×D4711yescharacteristic
472C2×D4—474no—
473C2×D4—942no—
474C2×D4—942no—
475C22×C4—21no—
476C22×C4—21no—
477C22×C4—21no—
478C22×C4—21no—
479C22×C4—21no—
480C22×C4—21no—
481C22×C4—21no—
482C22×C4—21no—
483C22×C4—471no—
484C22×C4—471no—
485C22×C4—471no—
486C22×C4—472no—
487C22×C4—472no—
488C22×C4—941no—
489C22×C4—941no—
490C22×C4—941no—
491C22×C4—941no—
492C22×C4—941no—
493C22×C4—941no—
494C22×C4—941no—
495C22×C4—941no—
496C22×C4C2×C4×D4712yes—
497C22×C4D4×D4711yescharacteristic
498C22×C4Q8×D4712yes—
499C22×C4C23×D4711yescharacteristic
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—21no—
503C2×C8—21no—
504C2×C8—472no—
505C2×C8—472no—
506C2×C8—472no—
507C2×C8—472no—
508C2×C8—948no—
509C2×C8—948no—
510C2×C8—941no—
511C2×C8—941no—
512C2×C8C2×C4×D4712yes—
513C2×C8C2×C4×D4712yes—
514C4⋊C4—21no—
515C4⋊C4—21no—
516C4⋊C4—21no—
517C4⋊C4—21no—
518C4⋊C4—21no—
519C4⋊C4—21no—
520C4⋊C4—21no—
521C4⋊C4—474no—
522C4⋊C4—472no—
523C4⋊C4—941no—
524C4⋊C4—941no—
525C4⋊C4—941no—
526C4⋊C4—941no—
527C4⋊C4—941no—
528C4⋊C4—941no—
529C4⋊C4—941no—
530C4⋊C4—3761no—
531C4⋊C4—3761no—
532C4⋊C4—1882no—
533C4⋊C4—1882no—
534C4⋊C4D4×D4712yes—
535C22⋊C4—42no—
536C22⋊C4—81no—
537C22⋊C4—474no—
538C22⋊C4—474no—
539C22⋊C4—3761no—
540C22⋊C4—3761no—
541C22⋊C4—3761no—
542C22⋊C4—1882no—
543C22⋊C4—1882no—
544C22⋊C4—1882no—
545C42—42no—
546C42—472no—
547C42—472no—
548C42—1882no—
549C42—1882no—
550C42—1882no—
551C42—1882no—
552C42—1882no—
553C23—21no—
554C23—21no—
555C23—21no—
556C23—21no—
557C23—21no—
558C23—21no—
559C23—472no—
560C23—941no—
561C23—941no—
562C23—941no—
563C23—941no—
564C23—941no—
565C23—941no—
566C23C4⋊C4×D4712yes—
567C23C2×D4×D4711yescharacteristic
568D4—948no—
569C2×C4—21no—
570C2×C4—21no—
571C2×C4—22no—
572C2×C4—22no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—41no—
577C2×C4—41no—
578C2×C4—41no—
579C2×C4—41no—
580C2×C4—41no—
581C2×C4—41no—
582C2×C4—41no—
583C2×C4—41no—
584C2×C4—41no—
585C2×C4—41no—
586C2×C4—41no—
587C2×C4—472no—
588C2×C4—472no—
589C2×C4—472no—
590C2×C4—472no—
591C2×C4—472no—
592C2×C4—941no—
593C2×C4—941no—
594C2×C4—941no—
595C2×C4—941no—
596C2×C4—942no—
597C2×C4—942no—
598C2×C4—942no—
599C2×C4—942no—
600C2×C4—942no—
601C2×C4—1881no—
602C2×C4—1881no—
603C2×C4—1881no—
604C2×C4—1881no—
605C2×C4—1881no—
606C2×C4—1881no—
607C2×C4—1881no—
608C2×C4—1881no—
609C2×C4—1881no—
610C2×C4—1881no—
611C2×C4—1881no—
612C2×C4C4⋊C4×D4712yes—
613C2×C4C22×C4×D4711yescharacteristic
614C2×C4C2×D4×D4711yescharacteristic
615C2×C4C2×Q8×D4711yescharacteristic
616C2×C4#41×D4711yescharacteristic
617C2×C4#1309406911yescharacteristic
618C2×C4#1309407111yescharacteristic
619C8—22no—
620C8—22no—
621C8—474no—
622C8—942no—
623C22—22no—
624C22—22no—
625C22—22no—
626C22—41no—
627C22—41no—
628C22—41no—
629C22—41no—
630C22—942no—
631C22—942no—
632C22—942no—
633C22—1881no—
634C22—1881no—
635C22—1881no—
636C22—1881no—
637C22C2×C4⋊C4×D4711yescharacteristic
638C22#1568975511yescharacteristic
639C22#1568977111yescharacteristic
640C22#135×D4711yescharacteristic
641C22#135×D4711yescharacteristic
642C22#1568993211yescharacteristic
643C22#1568993311yescharacteristic
644C4—22no—
645C4—42no—
646C4—81no—
647C4—81no—
648C4—81no—
649C4—474no—
650C4—942no—
651C4—942no—
652C4—3761no—
653C4—3761no—
654C4—3761no—
655C4—1882no—
656C4C4×D4×D4711yescharacteristic
657C4#1568960211yescharacteristic
658C4#1568978611yescharacteristic
659C4#1568982711yescharacteristic
660C2—42no—
661C2—1882no—
662C2#2024628611yescharacteristic
663C2#427×D4711yescharacteristic
664C2#2025198211yescharacteristic
665C2#2025511111yescharacteristic
666C2#2025511611yescharacteristic
667C2#2025579411yescharacteristic
668C2#2025579911yescharacteristic
subgroupG/H
centerC23C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1854C2
socleC23×C47C22×D4
prime radicalC22×C22⋊D47D4
cosocleC22×C4×C47C24
hypercenter#1854D47
hypocenterC47#22657
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1854

Complements

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

NH ≅ G/Ntype
2. C2×#15689160C2semidirect
3. C2×#15689159C2semidirect
6. #20244145C2semidirect
7. #20244143C2semidirect
8. #20243589C2semidirect
9. #20243588C2semidirect
10. #20243586C2semidirect
11. #20243543C2semidirect
12. #20243412C2semidirect
13. #20243411C2semidirect
14. #20243276C2semidirect
15. C47×#1854C2semidirect
22. (C22⋊D47)⋊C8C4semidirect
110. #13093955D4semidirect
325. Dic47#427semidirect
336. #1854D47semidirect
396. C47#22657semidirect

Maximal subgroups

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

subgroupindex
C2×(C22⋊D47)⋊C82
C2×#156891602
C2×#156891592
#202463382
#202463322
#202441452
#202441432
#202435892
#202435882
#202435862
#202435432
#202434122
#202434112
#202432762
C47×#18542
#2265747