Finite Group Databasebeta

← #26124725

Subgroups — #26124725

Order 12032.

790 conjugacy classes of subgroups.

The subgroup lattice has 666 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15688878C211yesmaximal, characteristic
2C2×#15688877C211yesmaximal, characteristic
3C2×#15688877C211yesmaximal, characteristic
4C2×#15688877C211yesmaximal, characteristic
5C2×#15688877C211yesmaximal, characteristic
6C4×C47⋊#95C211yesmaximal, characteristic
7C2×C47×#336C211yesmaximal, characteristic
8C23×C47⋊C8C2211yescharacteristic
9C23×C47⋊C8C2211yescharacteristic
10C22×C4×Dic47C2211yescharacteristic
11C22×C4×Dic47C2211yescharacteristic
12C2×C47⋊#95C411yescharacteristic
13C2×C47⋊#95C411yescharacteristic
14C2×C47⋊#95C411yescharacteristic
15C2×C47⋊#95C411yescharacteristic
16#15688878—22no—
17#15688877—22no—
18#15688877—22no—
19#15688877—22no—
20#15688877—22no—
21C23×C8×C47C2211yescharacteristic
22C23×C8×C47C2211yescharacteristic
23C22×C42×C47C2211yescharacteristic
24C47×#336—22no—
25C23×Dic47C2×C411yescharacteristic
26C23×Dic47C2×C411yescharacteristic
27C23×Dic47C2×C411yescharacteristic
28C23×Dic47C2×C411yescharacteristic
29C22×C47⋊C8—21no—
30C22×C47⋊C8—21no—
31C22×C47⋊C8—21no—
32C22×C47⋊C8—21no—
33C22×C47⋊C8—21no—
34C22×C47⋊C8—21no—
35C22×C47⋊C8—21no—
36C22×C47⋊C8—21no—
37C22×C47⋊C8—21no—
38C22×C47⋊C8—21no—
39C22×C47⋊C8—21no—
40C22×C47⋊C8—21no—
41C22×C47⋊C8D412yes—
42C22×C47⋊C8D412yes—
43C2×C4×Dic47—21no—
44C2×C4×Dic47—21no—
45C2×C4×Dic47—21no—
46C2×C4×Dic47—21no—
47C2×C4×Dic47—21no—
48C2×C4×Dic47—21no—
49C2×C4×Dic47—21no—
50C2×C4×Dic47—21no—
51C2×C4×Dic47—21no—
52C2×C4×Dic47—21no—
53C2×C4×Dic47—21no—
54C2×C4×Dic47—21no—
55C47⋊#95—22no—
56C47⋊#95—22no—
57C47⋊#95—22no—
58C47⋊#95C814yescomplemented
59C23×C4×C47C2×C411yescharacteristic
60C23×C4×C47C2×C411yescharacteristic
61C23×C4×C47C2311yescharacteristic
62C22×C8×C47—21no—
63C22×C8×C47—21no—
64C22×C8×C47—21no—
65C22×C8×C47—21no—
66C22×C8×C47—21no—
67C22×C8×C47—21no—
68C22×C8×C47—21no—
69C22×C8×C47—21no—
70C22×C8×C47—21no—
71C22×C8×C47—21no—
72C22×C8×C47—21no—
73C22×C8×C47—21no—
74C22×C8×C47D412yes—
75C22×C8×C47Q812yes—
76C2×C42×C47—21no—
77C2×C42×C47—21no—
78C2×C42×C47—21no—
79C2×C42×C47—21no—
80C2×C42×C47—21no—
81C2×C42×C47—21no—
82C24×C47C22×C411yescharacteristic
83C22×C4×C47—21no—
84C22×C4×C47—21no—
85C22×C4×C47—21no—
86C22×C4×C47—21no—
87C22×C4×C47—21no—
88C22×C4×C47—21no—
89C22×C4×C47—21no—
90C22×C4×C47—21no—
91C22×C4×C47—21no—
92C22×C4×C47—21no—
93C22×C4×C47—21no—
94C22×C4×C47—21no—
95C22×C4×C47C2×C812yes—
96C22×C4×C47M1612yes—
97C22×C4×C47C2×D411yescharacteristic
98C22×C4×C47C2×D411yescharacteristic
99C22×C4×C47C2×D411yescharacteristic
100C22×C4×C47C2×Q811yescharacteristic
101C22×C4×C47#4111yescharacteristic
102C22×C4×C47#4111yescharacteristic
103C22×C4×C47#4111yescharacteristic
104C22×C4×C47#4111yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×Dic47—21no—
112C22×Dic47—21no—
113C22×Dic47—21no—
114C22×Dic47—21no—
115C22×Dic47—21no—
116C22×Dic47—21no—
117C22×Dic47—21no—
118C22×Dic47—21no—
119C22×Dic47—21no—
120C22×Dic47—21no—
121C22×Dic47—21no—
122C22×Dic47—21no—
123C22×Dic47—21no—
124C22×Dic47—21no—
125C22×Dic47—21no—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—21no—
129C22×Dic47—21no—
130C22×Dic47—21no—
131C22×Dic47—21no—
132C22×Dic47—21no—
133C22×Dic47—21no—
134C22×Dic47—21no—
135C22×Dic47C2×C812yes—
136C22×Dic47C2×C812yes—
137C22×Dic47M1612yes—
138C22×Dic47M1612yes—
139C2×C8×C47—22no—
140C2×C8×C47—22no—
141C2×C8×C47—22no—
142C2×C8×C47—22no—
143C2×C8×C47—22no—
144C2×C8×C47—22no—
145C2×C8×C47—41no—
146C2×C8×C47—41no—
147C2×C8×C47—41no—
148C2×C8×C47—41no—
149C2×C8×C47—41no—
150C2×C8×C47—41no—
151C2×C8×C47—41no—
152C2×C8×C47—41no—
153C42×C47—41no—
154C42×C47—41no—
155C42×C47—41no—
156C42×C47—41no—
157C4×Dic47—41no—
158C4×Dic47—41no—
159C4×Dic47—41no—
160C4×Dic47—41no—
161C4×Dic47—41no—
162C4×Dic47—41no—
163C4×Dic47—41no—
164C4×Dic47—41no—
165C2×C47⋊C8—22no—
166C2×C47⋊C8—22no—
167C2×C47⋊C8—22no—
168C2×C47⋊C8—22no—
169C2×C47⋊C8—22no—
170C2×C47⋊C8—22no—
171C2×C47⋊C8—41no—
172C2×C47⋊C8—41no—
173C2×C47⋊C8—41no—
174C2×C47⋊C8—41no—
175C2×C47⋊C8—41no—
176C2×C47⋊C8—41no—
177C2×C47⋊C8—41no—
178C2×C47⋊C8—41no—
179C23×C47#11711yescharacteristic
180C23×C47#11711yescharacteristic
181C23×C47#11711yescharacteristic
182C23×C47C4×D411yescharacteristic
183C23×C47C4×D411yescharacteristic
184C23×C47C4×D411yescharacteristic
185C23×C47C4×Q811yescharacteristic
186C23×C47C22×C811yescharacteristic
187C23×C47C2×M1611yescharacteristic
188C23×C47C2×M1611yescharacteristic
189C23×C47C2×M1611yescharacteristic
190C23×C47#13111yescharacteristic
191C23×C47#13111yescharacteristic
192C23×C47#13111yescharacteristic
193C23×C47#13111yescharacteristic
194C2×C4×C47—22no—
195C2×C4×C47—22no—
196C2×C4×C47—22no—
197C2×C4×C47—22no—
198C2×C4×C47—22no—
199C2×C4×C47—22no—
200C2×C4×C47—41no—
201C2×C4×C47—41no—
202C2×C4×C47—41no—
203C2×C4×C47—41no—
204C2×C4×C47—41no—
205C2×C4×C47—41no—
206C2×C4×C47—41no—
207C2×C4×C47—41no—
208C2×C4×C47#12111yescharacteristic
209C2×C4×C47#12111yescharacteristic
210C2×C4×C47#12111yescharacteristic
211C2×C4×C47C22⋊Q811yescharacteristic
212C2×C4×C47C22⋊Q811yescharacteristic
213C2×C4×C47C22⋊Q811yescharacteristic
214C2×C4×C47#12311yescharacteristic
215C2×C4×C47#12311yescharacteristic
216C2×C4×C47#12311yescharacteristic
217C2×C4×C47#12311yescharacteristic
218C2×C4×C47#12311yescharacteristic
219C2×C4×C47#12311yescharacteristic
220C2×C4×C47#12411yescharacteristic
221C2×C4×C47#12411yescharacteristic
222C2×C4×C47#12411yescharacteristic
223C2×C4×C47#12511yescharacteristic
224C2×C4×C47#12511yescharacteristic
225C2×C4×C47#12511yescharacteristic
226C2×C4×C47#12611yescharacteristic
227C2×C4×C47#12611yescharacteristic
228C2×C4×C47#12611yescharacteristic
229C2×C4×C47#12611yescharacteristic
230C2×C4×C47#12611yescharacteristic
231C2×C4×C47#12611yescharacteristic
232C2×C4×C47#12611yescharacteristic
233C2×C4×C47#12611yescharacteristic
234C2×C4×C47#12611yescharacteristic
235C2×C4×C47#12611yescharacteristic
236C2×Dic47—22no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—22no—
242C2×Dic47—22no—
243C2×Dic47—22no—
244C2×Dic47—22no—
245C2×Dic47—22no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—41no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—41no—
252C2×Dic47—41no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—41no—
256C2×Dic47—41no—
257C2×Dic47—41no—
258C2×Dic47—41no—
259C2×Dic47—41no—
260C2×Dic47—41no—
261C2×Dic47—41no—
262C2×Dic47—41no—
263C2×Dic47—41no—
264C8×C47—42no—
265C8×C47—42no—
266C47⋊C8—42no—
267C47⋊C8—42no—
268#11298—471nomaximal, Sylow
269C22×C47#38311yescharacteristic
270C22×C47#38711yescharacteristic
271C22×C47#38711yescharacteristic
272C22×C47#38711yescharacteristic
273C22×C47#38811yescharacteristic
274C22×C47#38811yescharacteristic
275C22×C47#38811yescharacteristic
276C22×C47#43111yescharacteristic
277C22×C47#43111yescharacteristic
278C22×C47#43111yescharacteristic
279C22×C47#43211yescharacteristic
280C22×C47#43211yescharacteristic
281C22×C47#43211yescharacteristic
282C22×C47#43311yescharacteristic
283C22×C47#43311yescharacteristic
284C22×C47#43311yescharacteristic
285C22×C47#43311yescharacteristic
286C22×C47#43311yescharacteristic
287C22×C47#43311yescharacteristic
288C22×C47C8×D411yescharacteristic
289C22×C47C8×D411yescharacteristic
290C22×C47C8×D411yescharacteristic
291C22×C47#43511yescharacteristic
292C22×C47#43511yescharacteristic
293C22×C47#43511yescharacteristic
294C22×C47#43511yescharacteristic
295C22×C47#43511yescharacteristic
296C22×C47#43511yescharacteristic
297C22×C47#43611yescharacteristic
298C22×C47#43611yescharacteristic
299C22×C47#43611yescharacteristic
300C22×C47C8×Q811yescharacteristic
301C22×C47#44611yescharacteristic
302C22×C47#44611yescharacteristic
303C22×C47#44611yescharacteristic
304C4×C47—42no—
305C4×C47—42no—
306C4×C47#39611yescharacteristic
307C4×C47#39711yescharacteristic
308C4×C47#39711yescharacteristic
309C4×C47#39711yescharacteristic
310C4×C47#40011yescharacteristic
311C4×C47#40011yescharacteristic
312C4×C47#40011yescharacteristic
313C4×C47#40111yescharacteristic
314Dic47—42no—
315Dic47—42no—
316Dic47—42no—
317Dic47—42no—
318C2×#336—471no—
319C2×#336—471no—
320C2×#336—471no—
321C2×#336—471no—
322C2×#336—471no—
323C2×#336D4711yescharacteristic
324C4×#95—471no—
325C2×C47#144311yescharacteristic
326C2×C47#183911yescharacteristic
327C2×C47#184011yescharacteristic
328C2×C47#191611yescharacteristic
329C2×C47#191611yescharacteristic
330C2×C47#191611yescharacteristic
331C2×C47#191711yescharacteristic
332C2×C47#191711yescharacteristic
333C2×C47#191711yescharacteristic
334C2×C47#192311yescharacteristic
335C2×C47#192311yescharacteristic
336C2×C47#192311yescharacteristic
337C2×C47#192411yescharacteristic
338C2×C47#192411yescharacteristic
339C2×C47#192411yescharacteristic
340C23×C8—471no—
341C23×C8—471no—
342C23×C8C2×D4711yescharacteristic
343C23×C8C2×D4711yescharacteristic
344C22×C42—471no—
345C22×C42—471no—
346C22×C42C2×D4711yescharacteristic
347C2×#95—471no—
348C2×#95—471no—
349C2×#95—471no—
350C2×#95—471no—
351#336—22no—
352#336—942no—
353#336—942no—
354#336—942no—
355#336—942no—
356#336—942no—
357C47#1129811yescharacteristic, complemented, Sylow
358C23×C4—471no—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—471no—
362C23×C4C4×D4711yescharacteristic
363C23×C4C4×D4711yescharacteristic
364C23×C4C22×D4711yescharacteristic
365C22×C8—21no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—21no—
370C22×C8—21no—
371C22×C8—21no—
372C22×C8—21no—
373C22×C8—21no—
374C22×C8—21no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—472no—
378C22×C8—472no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C22×C8—941no—
383C22×C8—941no—
384C22×C8—941no—
385C22×C8—941no—
386C22×C8—941no—
387C22×C8—941no—
388C22×C8—941no—
389C22×C8—941no—
390C22×C8—941no—
391C22×C8Dic9412yes—
392C22×C8C22⋊D4712yes—
393C2×C42—21no—
394C2×C42—21no—
395C2×C42—21no—
396C2×C42—21no—
397C2×C42—21no—
398C2×C42—21no—
399C2×C42—941no—
400C2×C42—941no—
401C2×C42—941no—
402C2×C42—941no—
403C2×C42—941no—
404C2×C42—941no—
405C2×C42—941no—
406C2×C42—941no—
407C2×C42—941no—
408C2×C42—941no—
409C2×C42—941no—
410C2×C42—941no—
411#95—474no—
412#95—942no—
413#95—942no—
414#95—942no—
415C24C2×C4×D4711yescharacteristic
416C22×C4—21no—
417C22×C4—21no—
418C22×C4—21no—
419C22×C4—21no—
420C22×C4—21no—
421C22×C4—21no—
422C22×C4—21no—
423C22×C4—21no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—472no—
429C22×C4—472no—
430C22×C4—472no—
431C22×C4—472no—
432C22×C4—941no—
433C22×C4—941no—
434C22×C4—941no—
435C22×C4—941no—
436C22×C4—941no—
437C22×C4—941no—
438C22×C4—941no—
439C22×C4—941no—
440C22×C4—941no—
441C22×C4—941no—
442C22×C4—941no—
443C22×C4—941no—
444C22×C4—941no—
445C22×C4—941no—
446C22×C4—941no—
447C22×C4—941no—
448C22×C4—941no—
449C22×C4—941no—
450C22×C4—941no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—941no—
454C22×C4—941no—
455C22×C4—941no—
456C22×C4C8×D4712yes—
457C22×C4#1062532412yes—
458C22×C4C2×Dic9411yescharacteristic
459C22×C4#1062535011yescharacteristic
460C22×C4#1062535011yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4#1062535011yescharacteristic
463C22×C4D4×D4711yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4#1062535211yescharacteristic
466C22×C4#1062535211yescharacteristic
467C22×C4#1062535211yescharacteristic
468C22×C4#1062535211yescharacteristic
469C22×C4#1062535411yescharacteristic
470C22×C4#1062535411yescharacteristic
471C22×C4C2×C22⋊D4711yescharacteristic
472C2×C8—22no—
473C2×C8—22no—
474C2×C8—22no—
475C2×C8—22no—
476C2×C8—22no—
477C2×C8—22no—
478C2×C8—41no—
479C2×C8—41no—
480C2×C8—41no—
481C2×C8—41no—
482C2×C8—41no—
483C2×C8—41no—
484C2×C8—41no—
485C2×C8—41no—
486C2×C8—942no—
487C2×C8—942no—
488C2×C8—942no—
489C2×C8—942no—
490C2×C8—942no—
491C2×C8—942no—
492C2×C8—1881no—
493C2×C8—1881no—
494C2×C8—1881no—
495C2×C8—1881no—
496C2×C8—1881no—
497C2×C8—1881no—
498C2×C8—1881no—
499C2×C8—1881no—
500C42—41no—
501C42—41no—
502C42—41no—
503C42—41no—
504C42—1881no—
505C42—1881no—
506C42—1881no—
507C42—1881no—
508C42—1881no—
509C42—1881no—
510C42—1881no—
511C42—1881no—
512C23#1309398011yescharacteristic
513C23#1309398111yescharacteristic
514C23#1309398211yescharacteristic
515C23(C22⋊D47)⋊C411yescharacteristic
516C23C4×C22⋊D4711yescharacteristic
517C23#1309398611yescharacteristic
518C23C4×Dic9411yescharacteristic
519C23C2×C8×D4711yescharacteristic
520C23M16×D4711yescharacteristic
521C23M16×D4711yescharacteristic
522C23C2×#1062532411yescharacteristic
523C23#1309403011yescharacteristic
524C23#1309403011yescharacteristic
525C23#1309403211yescharacteristic
526C23#1309403211yescharacteristic
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—22no—
530C2×C4—22no—
531C2×C4—22no—
532C2×C4—22no—
533C2×C4—41no—
534C2×C4—41no—
535C2×C4—41no—
536C2×C4—41no—
537C2×C4—41no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—942no—
545C2×C4—942no—
546C2×C4—942no—
547C2×C4—942no—
548C2×C4—942no—
549C2×C4—942no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—942no—
553C2×C4—1881no—
554C2×C4—1881no—
555C2×C4—1881no—
556C2×C4—1881no—
557C2×C4—1881no—
558C2×C4—1881no—
559C2×C4—1881no—
560C2×C4—1881no—
561C2×C4—1881no—
562C2×C4—1881no—
563C2×C4—1881no—
564C2×C4—1881no—
565C2×C4—1881no—
566C2×C4—1881no—
567C2×C4—1881no—
568C2×C4—1881no—
569C2×C4#1309399511yescharacteristic
570C2×C4#1309399611yescharacteristic
571C2×C4#1309399711yescharacteristic
572C2×C4#1309400111yescharacteristic
573C2×C4#1309400111yescharacteristic
574C2×C4#1309400311yescharacteristic
575C2×C4#1309400511yescharacteristic
576C2×C4#1309400611yescharacteristic
577C2×C4#1309400711yescharacteristic
578C2×C4#1309400911yescharacteristic
579C2×C4#1309400911yescharacteristic
580C2×C4#1309400911yescharacteristic
581C2×C4#1309401011yescharacteristic
582C2×C4#1309401011yescharacteristic
583C2×C4#1309401311yescharacteristic
584C2×C4#1309401511yescharacteristic
585C2×C4#1309401511yescharacteristic
586C2×C4#1309401611yescharacteristic
587C2×C4#1309401711yescharacteristic
588C2×C4#1309401711yescharacteristic
589C2×C4#1309401711yescharacteristic
590C2×C4#1309401711yescharacteristic
591C2×C4#1309401811yescharacteristic
592C2×C4#1309401911yescharacteristic
593C2×C4#1309401911yescharacteristic
594C2×C4#1309401911yescharacteristic
595C2×C4#1309401911yescharacteristic
596C2×C4#1309401911yescharacteristic
597C8—42no—
598C8—42no—
599C8—1882no—
600C8—1882no—
601C22#1568899011yescharacteristic
602C22#1568900611yescharacteristic
603C22#1568900711yescharacteristic
604C22#1568901011yescharacteristic
605C22#1568901111yescharacteristic
606C22#1568901211yescharacteristic
607C22#1568901311yescharacteristic
608C22#1568917311yescharacteristic
609C22#1568917411yescharacteristic
610C22#1568917511yescharacteristic
611C22#1568917711yescharacteristic
612C22#1568917811yescharacteristic
613C22#1568917911yescharacteristic
614C22#1568918111yescharacteristic
615C22#1568918111yescharacteristic
616C22#1568918211yescharacteristic
617C22#1568918311yescharacteristic
618C22#1568918311yescharacteristic
619C22#1568918511yescharacteristic
620C22(C22⋊D47)⋊C811yescharacteristic
621C22C8×C22⋊D4711yescharacteristic
622C22#1568918811yescharacteristic
623C22#1568919111yescharacteristic
624C22#1568919211yescharacteristic
625C22#1568919311yescharacteristic
626C22#1568919311yescharacteristic
627C22#1568919411yescharacteristic
628C22#1568919711yescharacteristic
629C22#1568919811yescharacteristic
630C22#1568919911yescharacteristic
631C22#1568920011yescharacteristic
632C22C8×Dic9411yescharacteristic
633C22#1568925111yescharacteristic
634C22#1568925111yescharacteristic
635C22#1568925311yescharacteristic
636C4—42no—
637C4—42no—
638C4—1882no—
639C4—1882no—
640C4—1882no—
641C4—1882no—
642C4#1568904611yescharacteristic
643C4#1568904911yescharacteristic
644C4#1568905111yescharacteristic
645C4#1568905211yescharacteristic
646C4#1568906211yescharacteristic
647C4#1568906511yescharacteristic
648C4#1568906511yescharacteristic
649C4C47⋊#40111yescharacteristic
650C2#2024164911yescharacteristic
651C2#2024353011yescharacteristic
652C2#2024353211yescharacteristic
653C2#2024394411yescharacteristic
654C2#2024394511yescharacteristic
655C2#2024394811yescharacteristic
656C2#2024395111yescharacteristic
657C2#2024395211yescharacteristic
658C2#2024395511yescharacteristic
659C2#2024399111yescharacteristic
660C2#2024399211yescharacteristic
661C2#2024399311yescharacteristic
662C2#2024399811yescharacteristic
663C2#2024399911yescharacteristic
664C2#2024400011yescharacteristic
subgroupG/H
center, FrattiniC23×C4C22×D47
commutatorC23×C47C22×C8
FittingC2×C47×#336C2
socle, prime radicalC24×C47C22×C4
cosocleC23×C4×C47C23
hypercenterC2×#336D47
hypocenterC47#11298
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C2×#336

Complements

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

NH ≅ G/Ntype
58. C47⋊#95C8semidirect
357. C47#11298semidirect

Maximal subgroups

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

subgroupindex
C2×#156888782
C2×#156888772
C4×C47⋊#952
C2×C47×#3362
#1129847