Finite Group Databasebeta

← #26107647

Subgroups — #26107647

Order 12032.

1088 conjugacy classes of subgroups.

The subgroup lattice has 610 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D47C211yesmaximal, characteristic
2#20243365C211yesmaximal, characteristic
3C4×(C2×D47)⋊C8C211yesmaximal, characteristic
4C2×#15688855C211yesmaximal, characteristic, complemented
5C2×Q8⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
6C2×#15688853C211yesmaximal, characteristic, complemented
7C2×C47×Q8⋊C8C211yesmaximal, characteristic, complemented
8C22×Q8×D47C411yescharacteristic
9C2×Q8×Dic47C411yescharacteristic
10C2×C4×Dic94—21no—
11C2×C4×Dic94C2211yescharacteristic
12C2×#13093989—21no—
13C2×#13093989C411yescharacteristic
14C4×Q8×D47—22no—
15C4×Q8×D47—22no—
16C4×Q8×D47—22no—
17C4×Q8×D47—22no—
18C2×C4⋊C4×D47—21no—
19C2×C4⋊C4×D47C411yescharacteristic
20C2×C42×D47—21no—
21C2×C42×D47C2211yescharacteristic
22C2×C4⋊(C47⋊C8)C2211yescharacteristic
23C2×(C2×D47)⋊C8—21no—
24C2×(C2×D47)⋊C8—21no—
25C2×C4×C47⋊C8C2211yescharacteristic
26#15688877—21no—
27#15688877—21no—
28#15688855—22no—
29Q8⋊(C47⋊C8)—22no—
30#15688853—22no—
31C2×C4×Q8×C47C2211yescharacteristic
32C2×C4⋊C8×C47C2211yescharacteristic
33C2×C4×C8×C47C2211yescharacteristic
34C47×Q8⋊C8—22no—
35C22×Dic94—21no—
36C22×Dic94C2×C411yescharacteristic
37C2×Q8×D47—22no—
38C2×Q8×D47—22no—
39C2×Q8×D47—22no—
40C2×Q8×D47—22no—
41C2×Q8×D47—22no—
42C2×Q8×D47C814yescomplemented
43C22×C4×D47—21no—
44C22×C4×D47—21no—
45C22×C4×D47C2×C411yescharacteristic
46C22×C4×D47D411yescharacteristic
47C22×C4×D47D411yescharacteristic
48C22×C47⋊C8—21no—
49C22×C47⋊C8—21no—
50Q8×Dic47—22no—
51Q8×Dic47—22no—
52C4×Dic94—24no—
53C4×Dic94—24no—
54C4×Dic94—21no—
55C4×Dic94—21no—
56C4×Dic94D412yes—
57C4×Dic94D412yes—
58#13093989—24no—
59#13093989—24no—
60#13093989—22no—
61#13093989—22no—
62C2×C4⋊Dic47—21no—
63C2×C4⋊Dic47C2×C411yescharacteristic
64C2×Dic47⋊C4—21no—
65C2×Dic47⋊C4—21no—
66C2×Dic47⋊C4—21no—
67C4⋊C4×D47—24no—
68C4⋊C4×D47—24no—
69C4⋊C4×D47—22no—
70C4⋊C4×D47—22no—
71C2×C4×Dic47—21no—
72C2×C4×Dic47—21no—
73C2×C4×Dic47—21no—
74C2×C4×Dic47C2×C411yescharacteristic
75C2×C4×Dic47D411yescharacteristic
76C2×C4×Dic47D411yescharacteristic
77C42×D47—24no—
78C42×D47—24no—
79C42×D47—21no—
80C42×D47—21no—
81C42×D47—21no—
82C42×D47—21no—
83C4⋊(C47⋊C8)—21no—
84C4⋊(C47⋊C8)—21no—
85(C2×D47)⋊C8—24no—
86(C2×D47)⋊C8—42no—
87C4×C47⋊C8—21no—
88C4×C47⋊C8—21no—
89C22×Q8×C47C2×C411yescharacteristic
90C22×C8×C47—21no—
91C22×C8×C47—21no—
92C4×Q8×C47—21no—
93C4×Q8×C47—21no—
94C4×Q8×C47D412yes—
95C4×Q8×C47D412yes—
96C2×C4⋊C4×C47—21no—
97C2×C4⋊C4×C47C2×C411yescharacteristic
98C2×C42×C47—21no—
99C2×C42×C47C2311yescharacteristic
100C4⋊C8×C47—21no—
101C4⋊C8×C47—21no—
102C4×C8×C47—21no—
103C4×C8×C47—21no—
104C23×D47C22⋊C411yescharacteristic
105C2×Q8×C47—21no—
106C2×Q8×C47—21no—
107C2×Q8×C47—21no—
108C2×Q8×C47C22⋊C412yes—
109C2×Q8×C47C2×C812yes—
110C2×Q8×C47M1612yes—
111C22×C4×C47—21no—
112C22×C4×C47—21no—
113C22×C4×C47C22×C411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×D411yescharacteristic
116C22×Dic47—21no—
117C22×Dic47—21no—
118C22×Dic47C22⋊C411yescharacteristic
119C22×Dic47C22⋊C411yescharacteristic
120C22×Dic47C22⋊C411yescharacteristic
121Q8×D47—28no—
122Q8×D47—28no—
123Q8×D47—28no—
124Q8×D47—28no—
125C2×C4×D47—24no—
126C2×C4×D47—24no—
127C2×C4×D47—24no—
128C2×C4×D47—21no—
129C2×C4×D47—21no—
130C2×C4×D47—21no—
131C2×C4×D47—21no—
132C2×C4×D47—21no—
133C2×C4×D47—21no—
134C2×C4×D47—21no—
135C2×C4×D47—21no—
136C2×C4×D47—24no—
137C2×C4×D47—22no—
138C2×C4×D47—21no—
139C2×C4×D47—21no—
140C2×C4×D47—41no—
141C2×C4×D47—42no—
142C2×C4×D47—42no—
143C2×C4×D47C2×C812yes—
144C2×C4×D47M1612yes—
145C2×C4×D47SD1612yes—
146C2×C4×D47Q1612yes—
147C2×Dic94—24no—
148C2×Dic94—24no—
149C2×Dic94—21no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—24no—
153C2×Dic94C22⋊C412yes—
154C2×Dic94C2×C812yes—
155C2×Dic94M1612yes—
156C2×C8×C47—22no—
157C2×C8×C47—41no—
158C2×C8×C47—41no—
159C2×C8×C47—41no—
160C2×C8×C47—41no—
161C2×C8×C47—41no—
162C4⋊C4×C47—21no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47C22⋊C412yes—
166C42×C47—22no—
167C42×C47—22no—
168C42×C47C2×D411yescharacteristic
169C42×C47C2×D411yescharacteristic
170C42×C47C2×D411yescharacteristic
171C42×C47C2×D411yescharacteristic
172C4⋊Dic47—24no—
173C4⋊Dic47—21no—
174C4⋊Dic47C22⋊C412yes—
175Dic47⋊C4—24no—
176Dic47⋊C4—24no—
177Dic47⋊C4—22no—
178Dic47⋊C4—22no—
179C4×Dic47—24no—
180C4×Dic47—24no—
181C4×Dic47—21no—
182C4×Dic47—21no—
183C4×Dic47—22no—
184C4×Dic47—22no—
185C4×Dic47—21no—
186C4×Dic47—21no—
187C4×Dic47—21no—
188C4×Dic47—21no—
189C2×C47⋊C8—22no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8—41no—
192C2×C47⋊C8—41no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C23×C47C2×C22⋊C411yescharacteristic
196C22×D47—21no—
197C22×D47—21no—
198C22×D47—21no—
199C22×D47—21no—
200C22×D47C22⋊C812yes—
201C22×D47#10312yes—
202C22×D47#10412yes—
203Q8×C47—22no—
204Q8×C47—22no—
205Q8×C47—22no—
206Q8×C47C22⋊C814yescomplemented
207C2×C4×C47—22no—
208C2×C4×C47—22no—
209C2×C4×C47—22no—
210C2×C4×C47—21no—
211C2×C4×C47—21no—
212C2×C4×C47—22no—
213C2×C4×C47—41no—
214C2×C4×C47—41no—
215C2×C4×C47C2×C22⋊C411yescharacteristic
216C2×C4×C47C2×C22⋊C411yescharacteristic
217C2×C4×C47#12011yescharacteristic
218C2×C4×C47#12011yescharacteristic
219C2×C4×C47#12011yescharacteristic
220C2×C4×C47#12011yescharacteristic
221C2×C4×C47C22×C811yescharacteristic
222C2×C4×C47C2×M1611yescharacteristic
223C2×C4×C47C2×M1611yescharacteristic
224C2×C4×C47C2×M1611yescharacteristic
225C2×C4×C47C2×SD1611yescharacteristic
226C2×C4×C47C2×Q1611yescharacteristic
227C2×C4×C47#13711yescharacteristic
228C2×C4×C47#13711yescharacteristic
229C2×Dic47—21no—
230C2×Dic47—21no—
231C2×Dic47—22no—
232C2×Dic47—22no—
233C2×Dic47—21no—
234C2×Dic47—22no—
235C2×Dic47—21no—
236C2×Dic47—21no—
237C2×Dic47—22no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240C2×Dic47—41no—
241C2×Dic47—41no—
242C2×Dic47C22⋊C812yes—
243C2×Dic47#10312yes—
244C4×D47—216no—
245C4×D47—22no—
246C4×D47—22no—
247C4×D47—22no—
248C4×D47—22no—
249C4×D47—22no—
250C4×D47—22no—
251C4×D47—22no—
252C4×D47—22no—
253C4×D47—42no—
254C4×D47—42no—
255C4×D47—48no—
256Dic94—216no—
257Dic94—22no—
258Dic94—22no—
259Dic94—22no—
260Dic94C22⋊C814yescomplemented
261C8×C47—42no—
262C8×C47—81no—
263C47⋊C8—42no—
264C47⋊C8—81no—
265#8311—471nomaximal, Sylow
266C22×C47#37911yescharacteristic
267C22×C47C2×C22⋊C811yescharacteristic
268C22×C47#40711yescharacteristic
269C22×C47C2×#10311yescharacteristic
270C22×C47#41911yescharacteristic
271C22×C47C2×#10411yescharacteristic
272C22×C47#42111yescharacteristic
273C2×D47—22no—
274C2×D47—22no—
275C2×D47—22no—
276C2×D47—22no—
277C2×D47—22no—
278C2×D47—22no—
279C2×D47Q8⋊C814yescomplemented
280C4×C47—24no—
281C4×C47—21no—
282C4×C47—21no—
283C4×C47—42no—
284C4×C47C2×C22⋊C811yescharacteristic
285C4×C47C2×C22⋊C811yescharacteristic
286C4×C47#40711yescharacteristic
287C4×C47#40711yescharacteristic
288C4×C47#44811yescharacteristic
289C4×C47#44811yescharacteristic
290C4×C47#45111yescharacteristic
291C4×C47#45111yescharacteristic
292Dic47—22no—
293Dic47—24no—
294Dic47—22no—
295Dic47—41no—
296Dic47—42no—
297C22×C4×Q8—471no—
298#1797—471no—
299C4×C22⋊C8—471no—
300C2×Q8⋊C8—471no—
301C2×Q8⋊C8—471no—
302C2×Q8⋊C8—471no—
303C2×Q8⋊C8D4711yescharacteristic, complemented
304C2×C47C2×Q8⋊C811yescharacteristic
305C2×C47#147911yescharacteristic
306C2×C47#148711yescharacteristic
307C2×C47#149111yescharacteristic
308C2×C47#177911yescharacteristic
309C2×C47#178711yescharacteristic
310C2×C47#178911yescharacteristic
311D47—24no—
312C23×Q8—471no—
313C2×C4×Q8—471no—
314C2×C4×Q8—471no—
315C2×C4×Q8—471no—
316C2×C4×Q8—941no—
317C2×C4×Q8—941no—
318C2×C4×Q8—942no—
319C2×C4×Q8—942no—
320C2×C4×Q8—942no—
321C2×C4×Q8—942no—
322C2×C4×Q8C2×D4711yescharacteristic
323C22×C4⋊C4—471no—
324C22×C4⋊C4—941no—
325C22×C42—471no—
326C22×C42—941no—
327C2×C4⋊C8—471no—
328C2×C4⋊C8C2×D4711yescharacteristic
329C2×C22⋊C8—941no—
330C2×C22⋊C8—941no—
331C2×C4×C8—471no—
332C2×C4×C8C2×D4711yescharacteristic
333#336—941no—
334#336—941no—
335Q8⋊C8—22no—
336Q8⋊C8—942no—
337Q8⋊C8—942no—
338Q8⋊C8—942no—
339C47#831111yescharacteristic, complemented, Sylow
340C22×Q8—474no—
341C22×Q8—471no—
342C22×Q8—941no—
343C22×Q8—942no—
344C22×Q8—942no—
345C22×Q8—942no—
346C22×Q8—942no—
347C22×Q8—942no—
348C22×Q8C4×D4711yescharacteristic
349C23×C4—471no—
350C23×C4—471no—
351C23×C4—471no—
352C23×C4—941no—
353C23×C4—941no—
354C22×C8—21no—
355C22×C8—21no—
356C22×C8—941no—
357C22×C8—941no—
358C4×Q8—21no—
359C4×Q8—21no—
360C4×Q8—472no—
361C4×Q8—472no—
362C4×Q8—944no—
363C4×Q8—944no—
364C4×Q8—942no—
365C4×Q8—944no—
366C4×Q8—944no—
367C4×Q8—942no—
368C4×Q8—942no—
369C4×Q8—942no—
370C4×Q8—941no—
371C4×Q8—941no—
372C4×Q8D18812yes—
373C4×Q8C22⋊D4712yes—
374C2×C4⋊C4—21no—
375C2×C4⋊C4—471no—
376C2×C4⋊C4—942no—
377C2×C4⋊C4—944no—
378C2×C4⋊C4—944no—
379C2×C4⋊C4—941no—
380C2×C4⋊C4—941no—
381C2×C4⋊C4—941no—
382C2×C4⋊C4—941no—
383C2×C4⋊C4—942no—
384C2×C4⋊C4C4×D4711yescharacteristic
385C2×C42—21no—
386C2×C42—471no—
387C2×C42—471no—
388C2×C42—471no—
389C2×C42—944no—
390C2×C42—944no—
391C2×C42—941no—
392C2×C42—941no—
393C2×C42—941no—
394C2×C42—941no—
395C2×C42—941no—
396C2×C42—941no—
397C2×C42—941no—
398C2×C42C22×D4711yescharacteristic
399C4⋊C8—21no—
400C4⋊C8—21no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C22⋊C8—944no—
404C22⋊C8—1882no—
405C4×C8—21no—
406C4×C8—21no—
407C4×C8—941no—
408C4×C8—941no—
409C24—471no—
410C2×Q8—21no—
411C2×Q8—21no—
412C2×Q8—21no—
413C2×Q8—472no—
414C2×Q8—472no—
415C2×Q8—472no—
416C2×Q8—944no—
417C2×Q8—944no—
418C2×Q8—944no—
419C2×Q8—948no—
420C2×Q8—948no—
421C2×Q8—948no—
422C2×Q8—948no—
423C2×Q8—941no—
424C2×Q8—941no—
425C2×Q8—941no—
426C2×Q8C8×D4712yes—
427C2×Q8#1062532412yes—
428C2×Q8(C2×D47)⋊C412yes—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—471no—
432C22×C4—471no—
433C22×C4—472no—
434C22×C4—472no—
435C22×C4—472no—
436C22×C4—472no—
437C22×C4—471no—
438C22×C4—944no—
439C22×C4—944no—
440C22×C4—944no—
441C22×C4—942no—
442C22×C4—944no—
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—1881no—
456C22×C4—1882no—
457C22×C4—1882no—
458C22×C4C2×C4×D4711yescharacteristic
459C22×C4D4×D4711yescharacteristic
460C22×C4D4×D4711yescharacteristic
461C2×C8—22no—
462C2×C8—41no—
463C2×C8—41no—
464C2×C8—41no—
465C2×C8—41no—
466C2×C8—41no—
467C2×C8—942no—
468C2×C8—1881no—
469C2×C8—1881no—
470C2×C8—1881no—
471C2×C8—1881no—
472C2×C8—1881no—
473C4⋊C4—21no—
474C4⋊C4—22no—
475C4⋊C4—22no—
476C4⋊C4—472no—
477C4⋊C4—944no—
478C4⋊C4—944no—
479C4⋊C4—944no—
480C4⋊C4—941no—
481C4⋊C4—942no—
482C4⋊C4—942no—
483C4⋊C4(C2×D47)⋊C412yes—
484C42—22no—
485C42—22no—
486C42—944no—
487C42—944no—
488C42—941no—
489C42—941no—
490C42—941no—
491C42—941no—
492C42—942no—
493C42—941no—
494C42—941no—
495C42—942no—
496C42C2×D18811yescharacteristic
497C42D4×D4711yescharacteristic
498C42D4×D4711yescharacteristic
499C42C2×C22⋊D4711yescharacteristic
500C23—472no—
501C23—472no—
502C23—472no—
503C23—941no—
504C23—941no—
505C23—941no—
506C23—941no—
507C23C22⋊C4×D4711yescharacteristic
508Q8—22no—
509Q8—22no—
510Q8—22no—
511Q8—474no—
512Q8—9416no—
513Q8—942no—
514Q8—942no—
515Q8—942no—
516Q8(C2×D47)⋊C814yescomplemented
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—22no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—22no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—472no—
526C2×C4—472no—
527C2×C4—9416no—
528C2×C4—941no—
529C2×C4—941no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—941no—
533C2×C4—942no—
534C2×C4—941no—
535C2×C4—942no—
536C2×C4—942no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—941no—
545C2×C4—941no—
546C2×C4—941no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1888no—
550C2×C4—1881no—
551C2×C4—1881no—
552C2×C4C22⋊C4×D4711yescharacteristic
553C2×C4C2×(C2×D47)⋊C411yescharacteristic
554C2×C4#1309399211yescharacteristic
555C2×C4#1309399211yescharacteristic
556C2×C4#1309399411yescharacteristic
557C2×C4#1309399411yescharacteristic
558C2×C4C2×C8×D4711yescharacteristic
559C2×C4M16×D4711yescharacteristic
560C2×C4M16×D4711yescharacteristic
561C2×C4C2×#1062532411yescharacteristic
562C2×C4SD16×D4711yescharacteristic
563C2×C4Q16×D4711yescharacteristic
564C2×C4#1309405311yescharacteristic
565C2×C4#1309405611yescharacteristic
566C8—42no—
567C8—81no—
568C8—3761no—
569C8—1882no—
570C22—474no—
571C22—942no—
572C22—942no—
573C22—942no—
574C22—942no—
575C22—942no—
576C22—942no—
577C22#1568897811yescharacteristic
578C22C22⋊C8×D4711yescharacteristic
579C22#1568908511yescharacteristic
580C22#103×D4711yescharacteristic
581C22#1568913011yescharacteristic
582C22#104×D4711yescharacteristic
583C22#1568913811yescharacteristic
584C4—24no—
585C4—21no—
586C4—21no—
587C4—42no—
588C4—942no—
589C4—944no—
590C4—942no—
591C4—1881no—
592C4—1882no—
593C4C22⋊C8×D4711yescharacteristic
594C4C2×(C2×D47)⋊C811yescharacteristic
595C4#1568908511yescharacteristic
596C4#1568908611yescharacteristic
597C4#1568926011yescharacteristic
598C4#1568926311yescharacteristic
599C4#1568927711yescharacteristic
600C4#1568928011yescharacteristic
601C2—944no—
602C2Q8⋊C8×D4711yescharacteristic
603C2#2024178111yescharacteristic
604C2#2024181511yescharacteristic
605C2#2024183311yescharacteristic
606C2#2024329711yescharacteristic
607C2#2024332111yescharacteristic
608C2#2024333011yescharacteristic
subgroupG/H
centerC22×C4D4×D47
commutatorC2×C4×C47C22×C8
FrattiniC2×C42C22×D47
FittingC2×C47×Q8⋊C8C2
socleC23×C47C2×C22⋊C4
prime radicalC23×D47C22⋊C4
cosocleC2×C42×C47C23
hypercenterC2×Q8⋊C8D47
hypocenterC47#8311
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ C2×Q8⋊C8

Complements

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

NH ≅ G/Ntype
4. C2×#15688855C2semidirect
5. C2×Q8⋊(C47⋊C8)C2semidirect
6. C2×#15688853C2semidirect
7. C2×C47×Q8⋊C8C2semidirect
42. C2×Q8×D47C8semidirect
206. Q8×C47C22⋊C8semidirect
260. Dic94C22⋊C8semidirect
279. C2×D47Q8⋊C8semidirect
303. C2×Q8⋊C8D47semidirect
339. C47#8311semidirect
516. Q8(C2×D47)⋊C8semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D472
#202433652
C4×(C2×D47)⋊C82
C2×#156888552
C2×Q8⋊(C47⋊C8)2
C2×#156888532
C2×C47×Q8⋊C82
#831147