Finite Group Databasebeta

← #26139771

Subgroups — #26139771

Order 12032.

2574 conjugacy classes of subgroups.

The subgroup lattice has 646 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094013C211yesmaximal, characteristic
2C22×C4×D188C211yesmaximal, characteristic
3C2×#15689030C211yesmaximal, characteristic, complemented
4C2×#15689024C211yesmaximal, characteristic
5#20241636C214yesmaximal, complemented
6#20241617C211yesmaximal, characteristic, complemented
7(C2×D47)⋊#95C214yesmaximal, complemented
8C4×C47⋊#95C211yesmaximal, characteristic, complemented
9C2×C47×#391C211yesmaximal, characteristic, complemented
10C23×D188C2211yescharacteristic
11C23×C4×D47C2212yes—
12C2×#13094013—24no—
13C2×#13094013—24no—
14C2×#13094013C418yescomplemented
15C2×C4×D188—24no—
16C2×C4×D188—24no—
17C2×C4×D188—24no—
18C22×C4⋊Dic47C2211yescharacteristic
19C22×(C2×D47)⋊C4C2212yes—
20C22×(C2×D47)⋊C4C2214yes—
21C22×(C2×D47)⋊C4C2214yes—
22C22×C4×Dic47C2211yescharacteristic
23C22×C4×Dic47C2211yescharacteristic
24#15689030—24no—
25#15689024—24no—
26C2×C47⋊#95C2214yes—
27C2×C47⋊#95C2212yes—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2214yes—
30C23×Q8×C47C2211yescharacteristic
31C22×C4⋊C4×C47C2211yescharacteristic
32C22×C42×C47C2211yescharacteristic
33C47×#391—24no—
34C2×#95×C47C2212yes—
35C2×#95×C47C2212yes—
36C24×D47C2312yes—
37C22×D188—22no—
38C22×D188—22no—
39C22×D188—22no—
40C22×D188—22no—
41C22×D188C2×C414yes—
42C22×D188D414yes—
43C22×D188D414yes—
44C23×Dic47C2312yes—
45C23×Dic47C2312yes—
46C23×Dic47C2312yes—
47C22×C4×D47—24no—
48C22×C4×D47—24no—
49C22×C4×D47—24no—
50C22×C4×D47—28no—
51C22×C4×D47—44no—
52#13094013—232no—
53C4×D188—232no—
54C2×C4⋊Dic47—22no—
55C2×C4⋊Dic47—22no—
56C2×C4⋊Dic47D414yes—
57C2×(C2×D47)⋊C4—24no—
58C2×(C2×D47)⋊C4—28no—
59C2×(C2×D47)⋊C4—28no—
60C2×(C2×D47)⋊C4—24no—
61C2×(C2×D47)⋊C4—24no—
62C2×(C2×D47)⋊C4—28no—
63C2×(C2×D47)⋊C4—28no—
64C2×(C2×D47)⋊C4—44no—
65C2×(C2×D47)⋊C4C2×C4116yescomplemented
66C2×C4×Dic47—22no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—22no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47C2×C414yescomplemented
72C47⋊#95—24no—
73C47⋊#95—28no—
74C47⋊#95—24no—
75C47⋊#95—44no—
76C22×Q8×C47—22no—
77C22×Q8×C47—22no—
78C22×Q8×C47—22no—
79C22×Q8×C47—22no—
80C22×Q8×C47—22no—
81C22×Q8×C47—22no—
82C22×Q8×C47C2×C414yescomplemented
83C23×C4×C47C2312yes—
84C23×C4×C47C2312yes—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2311yescharacteristic
87C23×C4×C47C2311yescharacteristic
88C2×C4⋊C4×C47—22no—
89C2×C4⋊C4×C47—22no—
90C2×C4⋊C4×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47—22no—
93C2×C42×C47D414yes—
94#95×C47—24no—
95#95×C47—24no—
96C24×C47C2411yescharacteristic
97C23×D47—22no—
98C23×D47—22no—
99C23×D47—24no—
100C23×D47—24no—
101C23×D47—22no—
102C23×D47—22no—
103C23×D47—24no—
104C23×D47—24no—
105C23×D47C22×C414yes—
106C23×D47C2×D414yes—
107C23×D47C2×D414yes—
108C2×Q8×C47—28no—
109C2×Q8×C47—28no—
110C2×Q8×C47—28no—
111C2×Q8×C47—44no—
112C2×Q8×C47—44no—
113C2×Q8×C47—44no—
114C2×Q8×C47—44no—
115C22×C4×C47—21no—
116C22×C4×C47—21no—
117C22×C4×C47—22no—
118C22×C4×C47—21no—
119C22×C4×C47—21no—
120C22×C4×C47—22no—
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×C47—22no—
128C22×C4×C47—22no—
129C22×C4×C47—22no—
130C22×C4×C47—22no—
131C22×C4×C47—24no—
132C22×C4×C47—24no—
133C22×C4×C47C22×C414yes—
134C22×C4×C47C22×C412yes—
135C22×C4×C47C2×D412yes—
136C22×C4×C47C2×D412yes—
137C22×C4×C47C2×D412yes—
138C22×C4×C47C2×D412yes—
139C22×C4×C47C2×D412yes—
140C22×C4×C47C2×D412yes—
141C22×C4×C47#4114yes—
142C22×C4×C47#4112yes—
143C22×C4×C47#4112yes—
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—24no—
155C22×Dic47—22no—
156C22×Dic47—24no—
157C22×Dic47—22no—
158C22×Dic47—22no—
159C22×Dic47—22no—
160C22×Dic47C22×C414yes—
161C22×Dic47C2×D414yes—
162C22×Dic47#4114yes—
163C2×D188—28no—
164C2×D188—28no—
165C2×D188—28no—
166C2×D188—28no—
167C2×D188—28no—
168C2×D188—28no—
169C2×D188C22⋊C4116yes—
170C2×C4×D47—216no—
171C2×C4×D47—416no—
172C2×C4×D47—416no—
173C2×C4×D47—48no—
174C2×C4×D47—48no—
175C4⋊C4×C47—44no—
176C42×C47—28no—
177(C2×D47)⋊C4—216no—
178(C2×D47)⋊C4—232no—
179(C2×D47)⋊C4—416no—
180C4⋊Dic47—28no—
181C4×Dic47—28no—
182C4×Dic47—44no—
183C23×C47C23×C411yescharacteristic
184C23×C47C22×D411yescharacteristic
185C23×C47C22×D411yescharacteristic
186C23×C47C22×D411yescharacteristic
187C23×C47C22×D411yescharacteristic
188C23×C47C2×#4112yes—
189C23×C47C2×#4111yescharacteristic
190C23×C47C2×#4111yescharacteristic
191C23×C47C2×#4112yes—
192C23×C47H(5,𝔽2)12yes—
193C23×C472−1+412yes—
194C22×D47—24no—
195C22×D47—24no—
196C22×D47—28no—
197C22×D47—28no—
198C22×D47—24no—
199C22×D47—24no—
200C22×D47—24no—
201C22×D47—24no—
202C22×D47—28no—
203C22×D47—28no—
204C22×D47—28no—
205C22×D47—28no—
206C22×D47—42no—
207C22×D47—44no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—42no—
211C22×D47—44no—
212C22×D47—44no—
213C22×D47—44no—
214C22×D47—44no—
215C22×D47—44no—
216C22×D47C2×C22⋊C418yes—
217Q8×C47—416no—
218C2×C4×C47—22no—
219C2×C4×C47—22no—
220C2×C4×C47—24no—
221C2×C4×C47—24no—
222C2×C4×C47—24no—
223C2×C4×C47—24no—
224C2×C4×C47—24no—
225C2×C4×C47—22no—
226C2×C4×C47—22no—
227C2×C4×C47—22no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47—42no—
231C2×C4×C47—42no—
232C2×C4×C47—42no—
233C2×C4×C47—42no—
234C2×C4×C47—42no—
235C2×C4×C47—42no—
236C2×C4×C47—42no—
237C2×C4×C47—44no—
238C2×C4×C47—44no—
239C2×C4×C47C2×C22⋊C414yes—
240C2×C4×C47C4×D414yes—
241C2×C4×C47C4×D414yes—
242C2×C4×C47#12014yes—
243C2×C4×C47#12114yes—
244C2×C4×C47#12114yes—
245C2×C4×C47#12314yes—
246C2×C4×C47#12414yescomplemented
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—24no—
251C2×Dic47—24no—
252C2×Dic47—24no—
253C2×Dic47—28no—
254C2×Dic47—24no—
255C2×Dic47—42no—
256C2×Dic47—42no—
257C2×Dic47—42no—
258C2×Dic47—42no—
259C2×Dic47—44no—
260C2×Dic47—42no—
261C2×Dic47—42no—
262C2×Dic47—42no—
263C2×Dic47—42no—
264C2×Dic47—42no—
265C2×Dic47—42no—
266D188—232no—
267C4×D47—432no—
268#14027—471nomaximal, Sylow
269C22×C47C22×C22⋊C411yescharacteristic
270C22×C47C2×C4×D411yescharacteristic
271C22×C47C2×C4×D411yescharacteristic
272C22×C47C4×#4112yes—
273C22×C47#52012yes—
274C22×C47C2×#12011yescharacteristic
275C22×C47C2×#12111yescharacteristic
276C22×C47C2×#12111yescharacteristic
277C22×C47C2×#12311yescharacteristic
278C22×C47C2×#12411yescharacteristic
279C22×C47#52912yes—
280C22×C47#53211yescharacteristic
281C22×C47#53511yescharacteristic
282C22×C47#53611yescharacteristic
283C22×C47#54212yes—
284C22×C47#54612yes—
285C22×C47#54612yes—
286C22×C47#54612yes—
287C22×C47#54712yes—
288C22×C47#54712yes—
289C22×C47#54812yes—
290C22×C47#55612yes—
291C22×C47#55912yes—
292C2×D47—216no—
293C2×D47—28no—
294C2×D47—44no—
295C2×D47—48no—
296C2×D47—48no—
297C2×D47—44no—
298C2×D47—44no—
299C2×D47—48no—
300C2×D47—44no—
301C2×D47—44no—
302C2×D47—44no—
303C4×C47—24no—
304C4×C47—42no—
305C4×C47—44no—
306C4×C47—82no—
307C4×C47#38618yes—
308Dic47—44no—
309Dic47—44no—
310Dic47—44no—
311C22×#124—471no—
312C22×C4×D4—471no—
313C2×#391—471no—
314C2×#391D4711yescharacteristic, complemented
315C2×#390—471no—
316#1440—474no—
317C4⋊#95—471no—
318C22⋊#95—474no—
319C4×#95—471no—
320C2×C47C2×#38611yescharacteristic
321C2×C47C4×#12411yescharacteristic
322C2×C47#232611yescharacteristic
323C2×C47#233912yes—
324C2×C47#236712yes—
325C2×C47#242712yes—
326C2×C47#243211yescharacteristic
327C2×C47#243511yescharacteristic
328C2×C47#244712yes—
329C2×C47#254411yescharacteristic
330C2×C47#254711yescharacteristic
331D47—48no—
332C23×Q8C2×D4711yescharacteristic
333C23×D4—471no—
334C24×C4—472no—
335C2×#124—478no—
336C2×#124—944no—
337C2×#124—944no—
338C2×C4×D4—944no—
339C2×C4×D4—944no—
340C2×C4×D4—944no—
341C22×C4⋊C4—471no—
342C22×C4⋊C4C2×D4711yescharacteristic
343C22×C22⋊C4—474no—
344C22×C22⋊C4—472no—
345C22×C22⋊C4—474no—
346C22×C42—471no—
347C22×C42—471no—
348C22×C42C2×D4711yescharacteristic
349#391—24no—
350#391—944no—
351#390—944no—
352C2×#95—472no—
353C2×#95—472no—
354C2×#95—474no—
355C2×#95—474no—
356C2×#95C2×D4712yes—
357C2×#95C2×D4712yes—
358C47#1402711yescharacteristic, complemented, Sylow
359C25—472no—
360C22×Q8—22no—
361C22×Q8—22no—
362C22×Q8—22no—
363C22×Q8—22no—
364C22×Q8—22no—
365C22×Q8—22no—
366C22×Q8C4×D4714yescomplemented
367C22×D4—474no—
368C22×D4—474no—
369C22×D4—474no—
370C22×D4—942no—
371C22×D4—942no—
372C22×D4—942no—
373C22×D4—942no—
374C23×C4—472no—
375C23×C4—472no—
376C23×C4—472no—
377C23×C4—944no—
378C23×C4—944no—
379C23×C4—944no—
380C23×C4—948no—
381C23×C4—1884no—
382C23×C4C22×D4712yes—
383C23×C4C22×D4712yes—
384C23×C4C22×D4711yescharacteristic
385C23×C4C22×D4711yescharacteristic
386C23×C4C22×D4711yescharacteristic
387#124—9432no—
388C4×D4—9432no—
389C2×C4⋊C4—22no—
390C2×C4⋊C4—22no—
391C2×C4⋊C4—22no—
392C2×C4⋊C4—474no—
393C2×C4⋊C4—942no—
394C2×C4⋊C4—942no—
395C2×C22⋊C4—4716no—
396C2×C22⋊C4—944no—
397C2×C22⋊C4—944no—
398C2×C22⋊C4—948no—
399C2×C22⋊C4—948no—
400C2×C22⋊C4—944no—
401C2×C22⋊C4—948no—
402C2×C22⋊C4—948no—
403C2×C22⋊C4—1884no—
404C2×C42—22no—
405C2×C42—22no—
406C2×C42—474no—
407C2×C42—942no—
408C2×C42—942no—
409C2×C42—942no—
410C2×C42—942no—
411C2×C42—942no—
412C2×C42C22⋊D4714yes—
413#95—24no—
414#95—24no—
415#95—944no—
416#95—948no—
417#95—944no—
418#95—1884no—
419C24—474no—
420C24—474no—
421C24—474no—
422C24—942no—
423C24—942no—
424C24—944no—
425C24—942no—
426C24—942no—
427C24—944no—
428C24—944no—
429C24—944no—
430C24C23×D4711yescharacteristic
431C2×Q8—28no—
432C2×Q8—28no—
433C2×Q8—28no—
434C2×Q8—44no—
435C2×Q8—44no—
436C2×Q8—44no—
437C2×Q8—44no—
438C2×D4—4716no—
439C2×D4—948no—
440C2×D4—948no—
441C2×D4—948no—
442C2×D4—948no—
443C2×D4—948no—
444C2×D4—948no—
445C22×C4—21no—
446C22×C4—21no—
447C22×C4—22no—
448C22×C4—22no—
449C22×C4—21no—
450C22×C4—21no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—22no—
460C22×C4—24no—
461C22×C4—22no—
462C22×C4—24no—
463C22×C4—474no—
464C22×C4—474no—
465C22×C4—474no—
466C22×C4—9416no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—942no—
471C22×C4—942no—
472C22×C4—942no—
473C22×C4—942no—
474C22×C4—942no—
475C22×C4—942no—
476C22×C4—942no—
477C22×C4—944no—
478C22×C4—942no—
479C22×C4—944no—
480C22×C4—942no—
481C22×C4—942no—
482C22×C4—942no—
483C22×C4—18816no—
484C22×C4—18816no—
485C22×C4—1888no—
486C22×C4—1888no—
487C22×C4C2×C4×D4714yes—
488C22×C4C2×C4×D4712yes—
489C22×C4#1062535012yes—
490C22×C4D4×D4712yes—
491C22×C4D4×D4712yes—
492C22×C4D4×D4712yes—
493C22×C4#1062535212yes—
494C22×C4#1062535414yes—
495C22×C4C2×C22⋊D4712yes—
496C22×C4C2×C22⋊D4712yes—
497C22×C4C2×C22⋊D4712yes—
498C4⋊C4—44no—
499C4⋊C4—948no—
500C22⋊C4—9432no—
501C22⋊C4—9416no—
502C22⋊C4—18816no—
503C42—28no—
504C42—948no—
505C42—1884no—
506C23—478no—
507C23—948no—
508C23—948no—
509C23—948no—
510C23—948no—
511C23—944no—
512C23—944no—
513C23—948no—
514C23—948no—
515C23—944no—
516C23—944no—
517C23—944no—
518C23—944no—
519C23—1884no—
520C23—1884no—
521C23—1884no—
522C23—1884no—
523C23—1884no—
524C23—1882no—
525C23—1884no—
526C23—1882no—
527C23—1882no—
528C23—1882no—
529C23C22×C4×D4711yescharacteristic
530C23C2×D4×D4711yescharacteristic
531C23C2×D4×D4711yescharacteristic
532C23C2×D4×D4711yescharacteristic
533C23C22×C22⋊D4711yescharacteristic
534C23#41×D4712yes—
535C23C2×#1062535211yescharacteristic
536C23C2×#1062535011yescharacteristic
537C23C2×#1062535412yes—
538C23#1309407012yes—
539C23#1309407212yes—
540Q8—416no—
541D4—9432no—
542C2×C4—24no—
543C2×C4—24no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—42no—
553C2×C4—42no—
554C2×C4—42no—
555C2×C4—42no—
556C2×C4—42no—
557C2×C4—42no—
558C2×C4—44no—
559C2×C4—44no—
560C2×C4—42no—
561C2×C4—42no—
562C2×C4—42no—
563C2×C4—948no—
564C2×C4—944no—
565C2×C4—944no—
566C2×C4—944no—
567C2×C4—944no—
568C2×C4—944no—
569C2×C4—944no—
570C2×C4—944no—
571C2×C4—18832no—
572C2×C4—1882no—
573C2×C4—1882no—
574C2×C4—1882no—
575C2×C4—1884no—
576C2×C4—1882no—
577C2×C4—1882no—
578C2×C4—1882no—
579C2×C4—1882no—
580C2×C4—1882no—
581C2×C4—1882no—
582C2×C4—1882no—
583C2×C4C22⋊C4×D4714yes—
584C2×C4(C22⋊D47)⋊C414yes—
585C2×C4C4×C22⋊D4714yes—
586C2×C4#1309399214yes—
587C2×C4#1309399514yes—
588C2×C4#1309399714yes—
589C2×C4#1309400614yes—
590C2×C4#1309401314yescomplemented
591C22—948no—
592C22—9416no—
593C22—1884no—
594C22—1884no—
595C22—1884no—
596C22—1884no—
597C22—1888no—
598C22—1884no—
599C22—1888no—
600C22—1888no—
601C22—1884no—
602C22C2×C22⋊C4×D4711yescharacteristic
603C22C2×(C22⋊D47)⋊C411yescharacteristic
604C22C2×C4×C22⋊D4711yescharacteristic
605C22C4×#1062535412yes—
606C22#1568960512yes—
607C22C2×#1309399211yescharacteristic
608C22C2×#1309399511yescharacteristic
609C22C2×#1309399711yescharacteristic
610C22C2×#1309400611yescharacteristic
611C22C2×#1309401311yescharacteristic
612C22#1568966012yes—
613C22#1568966911yescharacteristic
614C22#1568968711yescharacteristic
615C22#1568969711yescharacteristic
616C22#1568974512yes—
617C22#1568976412yes—
618C22#1568976412yes—
619C22#1568976612yes—
620C22#1568977512yes—
621C22#1568977612yes—
622C22#1568978312yes—
623C22#1568984712yes—
624C22#1568985512yes—
625C4—24no—
626C4—44no—
627C4—42no—
628C4—82no—
629C4—1884no—
630C4—1884no—
631C4—1884no—
632C4#1568899918yes—
633C2—1888no—
634C2C2×#1568899911yescharacteristic
635C2C4×#1309401311yescharacteristic
636C2#2024609511yescharacteristic
637C2#2024621712yes—
638C2#2024646412yes—
639C2#2024696612yes—
640C2#2024701711yescharacteristic
641C2#2024704011yescharacteristic
642C2#2024717612yes—
643C2#2024836011yescharacteristic
644C2#2024838411yescharacteristic
subgroupG/H
center, FrattiniC24C23×D47
commutatorC23×C47C23×C4
FittingC2×C47×#391C2
socle, cosocleC24×C47C24
prime radicalC23×D188C22
hypercenterC2×#391D47
hypocenterC47#14027
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#391

Complements

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

NH ≅ G/Ntype
3. C2×#15689030C2semidirect
5. #20241636C2semidirect
6. #20241617C2semidirect
7. (C2×D47)⋊#95C2semidirect
8. C4×C47⋊#95C2semidirect
9. C2×C47×#391C2semidirect
14. C2×#13094013C4semidirect
65. C2×(C2×D47)⋊C4C2×C4semidirect
71. C2×C4×Dic47C2×C4semidirect
82. C22×Q8×C47C2×C4semidirect
246. C2×C4×C47#124semidirect
314. C2×#391D47semidirect
358. C47#14027semidirect
366. C22×Q8C4×D47semidirect
590. C2×C4#13094013semidirect

Maximal subgroups

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

subgroupindex
C22×#130940132
C22×C4×D1882
C2×#156890302
C2×#156890242
#202416362
#202416172
(C2×D47)⋊#952
C4×C47⋊#952
C2×C47×#3912
#1402747