Finite Group Databasebeta

← #26137880

Subgroups — #26137880

Order 12032.

2390 conjugacy classes of subgroups.

The subgroup lattice has 678 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689025C211yesmaximal, characteristic
2C2×#15689001C212yesmaximal
3C2×C4×(C2×D47)⋊C4C212yesmaximal, complemented
4C2×#15688970C212yesmaximal, complemented
5#20241626C212yesmaximal, complemented
6#20241624C212yesmaximal, complemented
7#20241622C212yesmaximal, complemented
8C4×C47⋊#95C211yesmaximal, characteristic, complemented
9C4×#95×C47C211yesmaximal, characteristic, complemented
10C23×D188C2211yescharacteristic
11C23×C4×D47C2212yes—
12C22×C4⋊Dic47C2211yescharacteristic
13C22×(C2×D47)⋊C4C2212yes—
14C22×(C2×D47)⋊C4C2212yes—
15C22×(C2×D47)⋊C4C2212yes—
16C22×(C2×D47)⋊C4C2212yes—
17C22×(C2×D47)⋊C4C2212yes—
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2212yes—
20#15689025C418yescomplemented
21#15689001C4116yescomplemented
22C4×(C2×D47)⋊C4—28no—
23#15688970—28no—
24C2×C47⋊#95C2211yescharacteristic
25C2×C47⋊#95C2212yes—
26C2×C47⋊#95C2212yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2211yescharacteristic
30C22×C42×C47C2212yes—
31C22×C42×C47C2211yescharacteristic
32C2×#95×C47C2211yescharacteristic
33C2×#95×C47C2212yes—
34C2×#95×C47C2211yescharacteristic
35C24×D47C2312yes—
36C22×D188—42no—
37C22×D188—41no—
38C22×D188—41no—
39C22×D188C2×C418yes—
40C22×D188C2×C414yes—
41C23×Dic47C2312yes—
42C23×Dic47C2312yes—
43C23×Dic47C2312yes—
44C22×C4×D47—24no—
45C22×C4×D47—24no—
46C22×C4×D47—24no—
47C22×C4×D47—24no—
48C22×C4×D47—42no—
49C22×C4×D47—42no—
50C22×C4×D47C2×C418yescomplemented
51C2×C4⋊Dic47—41no—
52C2×C4⋊Dic47—41no—
53C2×C4⋊Dic47C2×C414yescomplemented
54C2×(C2×D47)⋊C4—24no—
55C2×(C2×D47)⋊C4—24no—
56C2×(C2×D47)⋊C4—24no—
57C2×(C2×D47)⋊C4—24no—
58C2×(C2×D47)⋊C4—24no—
59C2×(C2×D47)⋊C4—24no—
60C2×(C2×D47)⋊C4—24no—
61C2×(C2×D47)⋊C4—24no—
62C2×(C2×D47)⋊C4—42no—
63C2×(C2×D47)⋊C4—42no—
64C2×(C2×D47)⋊C4C2×C418yes—
65C2×(C2×D47)⋊C4C2×C418yes—
66C2×(C2×D47)⋊C4C2×C418yescomplemented
67C2×(C2×D47)⋊C4C2×C418yescomplemented
68C2×(C2×D47)⋊C4C2×C418yescomplemented
69C2×C4×Dic47—24no—
70C2×C4×Dic47—24no—
71C2×C4×Dic47—24no—
72C2×C4×Dic47—24no—
73C2×C4×Dic47—42no—
74C2×C4×Dic47—42no—
75C47⋊#95—24no—
76C47⋊#95—22no—
77C47⋊#95—24no—
78C47⋊#95—42no—
79C47⋊#95C2×C418yescomplemented
80C47⋊#95D414yescomplemented
81C23×C4×C47C2312yes—
82C23×C4×C47C2311yescharacteristic
83C23×C4×C47C2311yescharacteristic
84C23×C4×C47C2312yes—
85C23×C4×C47C2311yescharacteristic
86C2×C42×C47—24no—
87C2×C42×C47—24no—
88C2×C42×C47—42no—
89C2×C42×C47—42no—
90C2×C42×C47C2×C414yescomplemented
91#95×C47—22no—
92#95×C47C2×C418yescomplemented
93#95×C47D414yescomplemented
94C24×C47C2411yescharacteristic
95C23×D47—22no—
96C23×D47—22no—
97C23×D47—22no—
98C23×D47—22no—
99C23×D47—22no—
100C23×D47—22no—
101C23×D47—22no—
102C23×D47—22no—
103C23×D47—22no—
104C23×D47—22no—
105C23×D47—22no—
106C23×D47—22no—
107C23×D47C22×C414yes—
108C23×D47C22×C414yes—
109C23×D47C22×C414yes—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—22no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47—21no—
120C22×C4×C47—21no—
121C22×C4×C47—22no—
122C22×C4×C47—22no—
123C22×C4×C47—22no—
124C22×C4×C47—22no—
125C22×C4×C47—22no—
126C22×C4×C47—22no—
127C22×C4×C47C22×C414yes—
128C22×C4×C47C22×C412yes—
129C22×C4×C47C22×C414yes—
130C22×C4×C47C22×C412yes—
131C22×C4×C47C22×C412yes—
132C22×C4×C47C22×C414yes—
133C22×C4×C47C2×D414yes—
134C22×C4×C47C2×D412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47#4114yes—
137C22×C4×C47#4112yes—
138C22×C4×C47#4112yes—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—22no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—22no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47—22no—
153C22×Dic47—22no—
154C22×Dic47—22no—
155C22×Dic47C22×C414yes—
156C22×Dic47C22×C414yes—
157C22×Dic47C22×C414yes—
158C22×Dic47C2×D414yes—
159C22×Dic47#4114yes—
160C2×D188—44no—
161C2×D188—44no—
162C2×D188—48no—
163C2×D188—48no—
164C2×D188C42116yescomplemented
165C2×C4×D47—216no—
166C2×C4×D47—216no—
167C2×C4×D47—48no—
168C2×C4×D47—48no—
169C2×C4×D47—48no—
170C2×C4×D47—48no—
171C2×C4×D47—48no—
172C42×C47—44no—
173C42×C47—48no—
174(C2×D47)⋊C4—216no—
175(C2×D47)⋊C4—216no—
176(C2×D47)⋊C4—216no—
177(C2×D47)⋊C4—216no—
178(C2×D47)⋊C4—48no—
179C4⋊Dic47—44no—
180C4×Dic47—48no—
181C4×Dic47—48no—
182C23×C47C23×C412yes—
183C23×C47C23×C411yescharacteristic
184C23×C47C22×D411yescharacteristic
185C23×C47C22×D411yescharacteristic
186C23×C47C2×#4112yes—
187C23×C47C2×#4112yes—
188C23×C47C2×#4111yescharacteristic
189C23×C47C2×#4111yescharacteristic
190C23×C47H(5,𝔽2)12yes—
191C23×C47H(5,𝔽2)11yescharacteristic
192C23×C47H(5,𝔽2)11yescharacteristic
193C22×D47—24no—
194C22×D47—24no—
195C22×D47—24no—
196C22×D47—24no—
197C22×D47—24no—
198C22×D47—24no—
199C22×D47—24no—
200C22×D47—24no—
201C22×D47—24no—
202C22×D47—24no—
203C22×D47—24no—
204C22×D47—24no—
205C22×D47—24no—
206C22×D47—24no—
207C22×D47—24no—
208C22×D47—24no—
209C22×D47—24no—
210C22×D47—24no—
211C22×D47—42no—
212C22×D47—42no—
213C22×D47—42no—
214C22×D47—42no—
215C22×D47—42no—
216C22×D47—42no—
217C22×D47—42no—
218C22×D47—42no—
219C22×D47—42no—
220C22×D47—42no—
221C22×D47—42no—
222C22×D47—42no—
223C22×D47—42no—
224C22×D47—42no—
225C22×D47—42no—
226C22×D47—42no—
227C22×D47C2×C4218yes—
228C2×C4×C47—24no—
229C2×C4×C47—22no—
230C2×C4×C47—22no—
231C2×C4×C47—22no—
232C2×C4×C47—22no—
233C2×C4×C47—22no—
234C2×C4×C47—22no—
235C2×C4×C47—24no—
236C2×C4×C47—24no—
237C2×C4×C47—24no—
238C2×C4×C47—24no—
239C2×C4×C47—24no—
240C2×C4×C47—24no—
241C2×C4×C47—24no—
242C2×C4×C47—24no—
243C2×C4×C47—24no—
244C2×C4×C47—24no—
245C2×C4×C47—24no—
246C2×C4×C47—24no—
247C2×C4×C47—24no—
248C2×C4×C47—24no—
249C2×C4×C47—42no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—42no—
253C2×C4×C47C2×C4214yes—
254C2×C4×C47C4×D414yes—
255C2×C4×C47C4×D414yes—
256C2×C4×C47C4×D418yes—
257C2×Dic47—24no—
258C2×Dic47—24no—
259C2×Dic47—24no—
260C2×Dic47—24no—
261C2×Dic47—24no—
262C2×Dic47—24no—
263C2×Dic47—24no—
264C2×Dic47—24no—
265C2×Dic47—24no—
266C2×Dic47—24no—
267C2×Dic47—24no—
268C2×Dic47—24no—
269C2×Dic47—42no—
270C2×Dic47—42no—
271C2×Dic47—42no—
272C2×Dic47—42no—
273C2×Dic47—42no—
274C2×Dic47—42no—
275C2×Dic47—42no—
276C2×Dic47—42no—
277C2×Dic47C4×D418yes—
278D188—416no—
279C4×D47—432no—
280#13824—471nomaximal, Sylow
281C22×C47C22×C4211yescharacteristic
282C22×C47C2×C4×D412yes—
283C22×C47C2×C4×D411yescharacteristic
284C22×C47C2×C4×D412yes—
285C22×C47C2×C4×D411yescharacteristic
286C22×C47C4×#4111yescharacteristic
287C22×C47C4×#4112yes—
288C22×C47C4×#4111yescharacteristic
289C22×C47C4×#4112yes—
290C22×C47#51812yes—
291C22×C47#51812yes—
292C22×C47#51811yescharacteristic
293C22×C47#51811yescharacteristic
294C22×C47D4211yescharacteristic
295C22×C47#54612yes—
296C22×C47#54612yes—
297C22×C47#55011yescharacteristic
298C22×C47#55011yescharacteristic
299C22×C47#55112yes—
300C22×C47#55312yes—
301C22×C47#55312yes—
302C22×C47#55512yes—
303C22×C47#55911yescharacteristic
304C2×D47—28no—
305C2×D47—28no—
306C2×D47—28no—
307C2×D47—44no—
308C2×D47—44no—
309C2×D47—44no—
310C2×D47—44no—
311C2×D47—44no—
312C2×D47—44no—
313C2×D47—44no—
314C2×D47—44no—
315C2×D47—44no—
316C2×D47—44no—
317C2×D47—44no—
318C2×D47—44no—
319C4×C47—28no—
320C4×C47—24no—
321C4×C47—24no—
322C4×C47—24no—
323C4×C47—44no—
324Dic47—28no—
325Dic47—44no—
326Dic47—44no—
327C2×#390—471no—
328C2×#386—472no—
329C2×C4×C22⋊C4—472no—
330C2×C4×C22⋊C4—472no—
331#1437—472no—
332#1437—472no—
333#1436—472no—
334C4×#95—471no—
335C4×#95D4711yescharacteristic, complemented
336C2×C47C42×D411yescharacteristic
337C2×C47C42×D411yescharacteristic
338C2×C47#227311yescharacteristic
339C2×C47#235812yes—
340C2×C47#236312yes—
341C2×C47#236312yes—
342C2×C47#236411yescharacteristic
343C2×C47#236411yescharacteristic
344C2×C47#236611yescharacteristic
345C2×C47#237211yescharacteristic
346C2×C47#237412yes—
347D47—48no—
348C23×D4—471no—
349C24×C4—472no—
350C22×C4⋊C4—471no—
351C22×C22⋊C4—472no—
352C22×C22⋊C4—472no—
353C22×C22⋊C4—472no—
354C22×C22⋊C4—472no—
355C22×C22⋊C4—472no—
356C22×C42—472no—
357C22×C42—472no—
358C22×C42C2×D4712yes—
359C22×C42C2×D4711yescharacteristic
360#390—478no—
361#386—4716no—
362C4×C22⋊C4—948no—
363C4×C22⋊C4—948no—
364C2×#95—472no—
365C2×#95—471no—
366C2×#95—471no—
367C2×#95—472no—
368C2×#95—472no—
369C2×#95—472no—
370C2×#95C2×D4711yescharacteristic
371C2×#95C2×D4712yes—
372C2×#95C2×D4711yescharacteristic
373C47#1382411yescharacteristic, complemented, Sylow
374C25—472no—
375C22×D4—478no—
376C22×D4—474no—
377C22×D4—1882no—
378C22×D4—1881no—
379C22×D4—1881no—
380C23×C4—472no—
381C23×C4—472no—
382C23×C4—472no—
383C23×C4—478no—
384C23×C4—944no—
385C23×C4—944no—
386C23×C4—944no—
387C23×C4—944no—
388C23×C4—1882no—
389C23×C4—1882no—
390C23×C4C22×D4712yes—
391C23×C4C22×D4711yescharacteristic
392C23×C4C22×D4711yescharacteristic
393C23×C4C22×D4712yes—
394C23×C4C22×D4711yescharacteristic
395C2×C4⋊C4—474no—
396C2×C4⋊C4—1881no—
397C2×C4⋊C4—1881no—
398C2×C22⋊C4—478no—
399C2×C22⋊C4—478no—
400C2×C22⋊C4—478no—
401C2×C22⋊C4—478no—
402C2×C22⋊C4—478no—
403C2×C22⋊C4—944no—
404C2×C22⋊C4—944no—
405C2×C22⋊C4—944no—
406C2×C22⋊C4—944no—
407C2×C22⋊C4—944no—
408C2×C22⋊C4—944no—
409C2×C22⋊C4—944no—
410C2×C22⋊C4—944no—
411C2×C22⋊C4—1882no—
412C2×C22⋊C4—1882no—
413C2×C42—24no—
414C2×C42—24no—
415C2×C42—42no—
416C2×C42—42no—
417C2×C42—944no—
418C2×C42—944no—
419C2×C42—944no—
420C2×C42—944no—
421C2×C42—1882no—
422C2×C42—1882no—
423C2×C42C4×D4714yescomplemented
424#95—22no—
425#95—478no—
426#95—474no—
427#95—944no—
428#95—944no—
429#95—942no—
430#95—1882no—
431#95C4×D4718yescomplemented
432#95D18814yescomplemented
433C24—474no—
434C24—474no—
435C24—474no—
436C24—942no—
437C24—942no—
438C24—942no—
439C24—942no—
440C24—942no—
441C24—942no—
442C24—942no—
443C24—942no—
444C24—942no—
445C24—942no—
446C24—942no—
447C24—942no—
448C24C23×D4711yescharacteristic
449C2×D4—4716no—
450C2×D4—1888no—
451C2×D4—1888no—
452C2×D4—1884no—
453C2×D4—1884no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—22no—
461C22×C4—22no—
462C22×C4—22no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4—22no—
466C22×C4—22no—
467C22×C4—22no—
468C22×C4—22no—
469C22×C4—22no—
470C22×C4—22no—
471C22×C4—474no—
472C22×C4—474no—
473C22×C4—474no—
474C22×C4—474no—
475C22×C4—474no—
476C22×C4—9416no—
477C22×C4—942no—
478C22×C4—942no—
479C22×C4—942no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—942no—
484C22×C4—942no—
485C22×C4—942no—
486C22×C4—942no—
487C22×C4—942no—
488C22×C4—942no—
489C22×C4—942no—
490C22×C4—942no—
491C22×C4—942no—
492C22×C4—942no—
493C22×C4—9416no—
494C22×C4—1888no—
495C22×C4—1888no—
496C22×C4—1888no—
497C22×C4—1888no—
498C22×C4—1888no—
499C22×C4C2×C4×D4714yes—
500C22×C4C2×C4×D4714yes—
501C22×C4C2×C4×D4712yes—
502C22×C4C2×C4×D4712yes—
503C22×C4C2×C4×D4714yes—
504C22×C4C2×C4×D4712yes—
505C22×C4C2×D18814yes—
506C22×C4C2×D18812yes—
507C22×C4#1062535012yes—
508C22×C4#1062535014yes—
509C22×C4D4×D4712yes—
510C22×C4#1062535412yes—
511C4⋊C4—1884no—
512C22⋊C4—9416no—
513C22⋊C4—9416no—
514C22⋊C4—9416no—
515C22⋊C4—9416no—
516C22⋊C4—1888no—
517C42—44no—
518C42—48no—
519C42—1888no—
520C42—1888no—
521C23—478no—
522C23—944no—
523C23—944no—
524C23—944no—
525C23—944no—
526C23—944no—
527C23—944no—
528C23—944no—
529C23—944no—
530C23—944no—
531C23—944no—
532C23—944no—
533C23—944no—
534C23—944no—
535C23—944no—
536C23—944no—
537C23—944no—
538C23—944no—
539C23—944no—
540C23—1882no—
541C23—1882no—
542C23—1882no—
543C23—1882no—
544C23—1882no—
545C23—1882no—
546C23—1882no—
547C23—1882no—
548C23—1882no—
549C23—1882no—
550C23—1882no—
551C23—1882no—
552C23—1882no—
553C23—1882no—
554C23—1882no—
555C23—1882no—
556C23C22×C4×D4712yes—
557C23C22×C4×D4711yescharacteristic
558C23C2×D4×D4711yescharacteristic
559C23C22×D18811yescharacteristic
560C23#41×D4712yes—
561C23C2×#1062535012yes—
562C23C2×#1062535011yescharacteristic
563C23C2×#1062535411yescharacteristic
564C23#1309406912yes—
565C23#1309407011yescharacteristic
566C23#1309407011yescharacteristic
567D4—18816no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—24no—
571C2×C4—24no—
572C2×C4—24no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—22no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—22no—
585C2×C4—22no—
586C2×C4—24no—
587C2×C4—24no—
588C2×C4—24no—
589C2×C4—42no—
590C2×C4—42no—
591C2×C4—42no—
592C2×C4—42no—
593C2×C4—478no—
594C2×C4—944no—
595C2×C4—944no—
596C2×C4—944no—
597C2×C4—944no—
598C2×C4—944no—
599C2×C4—944no—
600C2×C4—944no—
601C2×C4—944no—
602C2×C4—944no—
603C2×C4—944no—
604C2×C4—944no—
605C2×C4—944no—
606C2×C4—18832no—
607C2×C4—1882no—
608C2×C4—1882no—
609C2×C4—1882no—
610C2×C4—1882no—
611C2×C4—1882no—
612C2×C4—1882no—
613C2×C4—1882no—
614C2×C4—1882no—
615C2×C4C42×D4714yes—
616C2×C4#1309398614yes—
617C2×C4C4×D18814yes—
618C2×C4C4×D18818yes—
619C22—948no—
620C22—948no—
621C22—948no—
622C22—1884no—
623C22—1884no—
624C22—1884no—
625C22—1884no—
626C22—1884no—
627C22—1884no—
628C22—1884no—
629C22—1884no—
630C22—1884no—
631C22—1884no—
632C22—1884no—
633C22—1884no—
634C22C2×C42×D4711yescharacteristic
635C22C4×D4×D4712yes—
636C22C2×#1309398611yescharacteristic
637C22C2×C4×D18812yes—
638C22C2×C4×D18811yescharacteristic
639C22#1568959111yescharacteristic
640C22C4×#1062535012yes—
641C22C4×#1062535011yescharacteristic
642C22C4×#1062535412yes—
643C22#1568959512yes—
644C22#1568959512yes—
645C22#1568959611yescharacteristic
646C22#1568959711yescharacteristic
647C22D4×D18811yescharacteristic
648C22#1568976312yes—
649C22#1568976812yes—
650C22#1568979411yescharacteristic
651C22#1568979511yescharacteristic
652C22#1568979712yes—
653C22#1568982112yes—
654C22#1568982212yes—
655C22#1568983612yes—
656C22#1568985811yescharacteristic
657C4—28no—
658C4—24no—
659C4—24no—
660C4—24no—
661C4—44no—
662C4—948no—
663C4—1884no—
664C4—1884no—
665C2—1888no—
666C2C4×#1309398611yescharacteristic
667C2C42×D18811yescharacteristic
668C2#2024574011yescharacteristic
669C2#2024637012yes—
670C2#2024642712yes—
671C2#2024642812yes—
672C2#2024643511yescharacteristic
673C2#2024643811yescharacteristic
674C2#2024645211yescharacteristic
675C2#2024649811yescharacteristic
676C2#2024651712yes—
subgroupG/H
center, FrattiniC24C23×D47
commutatorC22×C47C22×C42
FittingC4×#95×C47C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC4×#95D47
hypocenterC47#13824
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C24 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
3. C2×C4×(C2×D47)⋊C4C2semidirect
4. C2×#15688970C2semidirect
5. #20241626C2semidirect
6. #20241624C2semidirect
7. #20241622C2semidirect
8. C4×C47⋊#95C2semidirect
9. C4×#95×C47C2semidirect
20. #15689025C4semidirect
21. #15689001C4semidirect
50. C22×C4×D47C2×C4semidirect
53. C2×C4⋊Dic47C2×C4semidirect
66. C2×(C2×D47)⋊C4C2×C4semidirect
67. C2×(C2×D47)⋊C4C2×C4semidirect
68. C2×(C2×D47)⋊C4C2×C4semidirect
79. C47⋊#95C2×C4semidirect
80. C47⋊#95D4semidirect
90. C2×C42×C47C2×C4semidirect
92. #95×C47C2×C4semidirect
93. #95×C47D4semidirect
164. C2×D188C42semidirect
335. C4×#95D47semidirect
373. C47#13824semidirect
423. C2×C42C4×D47semidirect
431. #95C4×D47semidirect
432. #95D188semidirect

Maximal subgroups

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

subgroupindex
C2×#156890252
C2×#156890012
C2×C4×(C2×D47)⋊C42
C2×#156889702
#202416262
#202416242
#202416222
C4×C47⋊#952
C4×#95×C472
#1382447