Finite Group Databasebeta

← #26213937

Subgroups — #26213937

Order 12032.

1606 conjugacy classes of subgroups.

The subgroup lattice has 630 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689602C211yesmaximal, characteristic
2C2×#15689095C212yesmaximal
3#20245743C212yesmaximal, complemented
4#99×Dic47C212yesmaximal, complemented
5C4×#13093938C212yesmaximal, complemented
6C4×#13093939C211yesmaximal, characteristic, complemented
7#20243175C212yesmaximal, complemented
8#20243119C212yesmaximal, complemented
9C4×#99×C47C211yesmaximal, characteristic, complemented
10C22×#10625352C2211yescharacteristic
11#15689602—24no—
12#15689602—24no—
13C2×C4×Dic94C411yescharacteristic, complemented
14C2×#13093989C411yescharacteristic, complemented
15C2×D4×Dic47C2211yescharacteristic
16C2×C4×C22⋊D47C411yescharacteristic, complemented
17C2×C4×C22⋊D47C2211yescharacteristic
18C2×(C22⋊D47)⋊C4C411yescharacteristic, complemented
19C2×(C22⋊D47)⋊C4C2211yescharacteristic
20C2×#13093981C411yescharacteristic, complemented
21C2×#13093980C411yescharacteristic, complemented
22C2×#13093980C2214yes—
23C2×#13093980C2211yescharacteristic
24C22×Dic47⋊C4C411yescharacteristic, complemented
25C22×Dic47⋊C4C2211yescharacteristic
26C2×C4⋊C4×D47C411yescharacteristic, complemented
27#15689095C4116yescomplemented
28C2×#13093939C2212yes—
29C2×#13093938C2214yes—
30C4×Dic47⋊C4—24no—
31#15688974—24no—
32C22⋊C4×Dic47C2214yes—
33C4×C22⋊Dic47C2212yes—
34#15688890C2212yes—
35#15688889C2214yes—
36C2×C4×D4×C47C2211yescharacteristic
37C2×#99×C47C2212yes—
38C4×C22⋊C4×C47C2212yes—
39C47×#342C2212yes—
40C2×#10625352—24no—
41C2×#10625352—24no—
42C2×#10625352C2×C418yes—
43C22×Dic94C2×C411yescharacteristic
44C22×C22⋊D47C2×C411yescharacteristic
45C22×C22⋊D47C2311yescharacteristic
46C23×Dic47C2×C411yescharacteristic
47C23×Dic47C2×C411yescharacteristic
48C23×Dic47C2311yescharacteristic
49C23×Dic47C2311yescharacteristic
50C22×C4×D47C2×C411yescharacteristic
51C22×C4×D47C2×C411yescharacteristic
52C22×C4×D47C2×C411yescharacteristic
53C4×Dic94—22no—
54C4×Dic94—22no—
55#13093989—24no—
56D4×Dic47—24no—
57C4×C22⋊D47—22no—
58C4×C22⋊D47—22no—
59C4×C22⋊D47—22no—
60C4×C22⋊D47—22no—
61(C22⋊D47)⋊C4—24no—
62(C22⋊D47)⋊C4—24no—
63#13093981—22no—
64#13093981—22no—
65#13093980—24no—
66#13093980—28no—
67#13093980—24no—
68#13093980C2×C4116yescomplemented
69C2×C4⋊Dic47C2×C411yescharacteristic
70C2×Dic47⋊C4—24no—
71C2×Dic47⋊C4—22no—
72C2×Dic47⋊C4—22no—
73C2×Dic47⋊C4C2×C411yescharacteristic
74C2×Dic47⋊C4C2×C411yescharacteristic
75C2×Dic47⋊C4C2×C411yescharacteristic
76C2×Dic47⋊C4C2×C411yescharacteristic
77C2×Dic47⋊C4C2×C411yescharacteristic
78C2×Dic47⋊C4C2×C411yescharacteristic
79C2×Dic47⋊C4C2×C411yescharacteristic
80C2×Dic47⋊C4C2×C411yescharacteristic
81C2×Dic47⋊C4D414yes—
82C2×Dic47⋊C4D414yes—
83C4⋊C4×D47—24no—
84C2×C22⋊Dic47C2×C411yescharacteristic
85C2×C22⋊Dic47C2311yescharacteristic
86C2×C22⋊Dic47C2314yes—
87C2×(C2×D47)⋊C4C2×C411yescharacteristic
88C2×(C2×D47)⋊C4C2×C411yescharacteristic
89C2×C4×Dic47—24no—
90C2×C4×Dic47—22no—
91C2×C4×Dic47—24no—
92C2×C4×Dic47C2×C411yescharacteristic
93C2×C4×Dic47C2×C411yescharacteristic
94C2×C4×Dic47C2×C411yescharacteristic
95C2×C4×Dic47C2×C411yescharacteristic
96C2×C4×Dic47C2×C411yescharacteristic
97#13093939C2×C418yescomplemented
98#13093938C2×C4116yescomplemented
99C47⋊#95—22no—
100C47⋊#95—24no—
101C22×D4×C47C2311yescharacteristic
102C23×C4×C47C2×C411yescharacteristic
103C23×C4×C47C2311yescharacteristic
104C4×D4×C47—22no—
105C4×D4×C47—22no—
106C2×C4⋊C4×C47C2×C411yescharacteristic
107C2×C22⋊C4×C47C2×C411yescharacteristic
108C2×C22⋊C4×C47C2311yescharacteristic
109C2×C22⋊C4×C47C2314yes—
110C2×C42×C47—22no—
111C2×C42×C47C2×C411yescharacteristic
112#99×C47C2×C418yescomplemented
113#95×C47—22no—
114C24×C47C22×C411yescharacteristic
115C24×C47C2411yescharacteristic
116C23×D47C22×C411yescharacteristic
117C2×D4×C47—22no—
118C2×D4×C47—22no—
119C2×D4×C47C22×C414yes—
120C22×C4×C47—24no—
121C22×C4×C47—21no—
122C22×C4×C47—21no—
123C22×C4×C47—81no—
124C22×C4×C47—81no—
125C22×C4×C47C22×C411yescharacteristic
126C22×C4×C47C22×C411yescharacteristic
127C22×C4×C47C22×C411yescharacteristic
128C22×C4×C47C22×C411yescharacteristic
129C22×C4×C47C22×C411yescharacteristic
130C22×C4×C47C2×D412yes—
131C22×C4×C47C2×D412yes—
132C2×C22⋊D47—22no—
133C2×C22⋊D47—22no—
134C2×C22⋊D47—22no—
135C2×C22⋊D47—22no—
136C2×C22⋊D47C4214yescomplemented
137C2×C22⋊D47C22×C414yes—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—24no—
141C22×Dic47—22no—
142C22×Dic47—81no—
143C22×Dic47—81no—
144C22×Dic47C4214yescomplemented
145C22×Dic47C22×C411yescharacteristic
146C22×Dic47C22×C411yescharacteristic
147C22×Dic47C22×C411yescharacteristic
148C22×Dic47C22×C411yescharacteristic
149C22×Dic47C22×C411yescharacteristic
150C22×Dic47C22×C411yescharacteristic
151C22×Dic47C22×C411yescharacteristic
152C22×Dic47C22×C414yes—
153C22×Dic47C2×D414yes—
154C22×Dic47C2×D414yes—
155C22×Dic47#4114yes—
156#10625352—216no—
157#10625352—216no—
158C2×C4×D47—22no—
159C2×C4×D47—22no—
160C2×C4×D47—22no—
161C2×C4×D47—22no—
162C2×C4×D47—81no—
163C2×C4×D47—81no—
164C2×C4×D47C4214yescomplemented
165C2×Dic94—22no—
166C2×Dic94—22no—
167C2×Dic94C4214yescomplemented
168C4⋊C4×C47—22no—
169C22⋊C4×C47—22no—
170C22⋊C4×C47—24no—
171C22⋊C4×C47—22no—
172C22⋊C4×C47C22×C418yes—
173C42×C47—21no—
174C42×C47—21no—
175C42×C47—82no—
176C22⋊Dic47—22no—
177C22⋊Dic47—24no—
178C22⋊Dic47—22no—
179C22⋊Dic47C22×C418yes—
180(C2×D47)⋊C4—21no—
181(C2×D47)⋊C4—21no—
182(C2×D47)⋊C4—22no—
183C4⋊Dic47—22no—
184Dic47⋊C4—21no—
185Dic47⋊C4—21no—
186Dic47⋊C4—22no—
187Dic47⋊C4—22no—
188Dic47⋊C4—22no—
189Dic47⋊C4—216no—
190Dic47⋊C4C22⋊C414yes—
191Dic47⋊C4C22⋊C412yes—
192Dic47⋊C4C22⋊C412yes—
193Dic47⋊C4C22⋊C414yes—
194Dic47⋊C4C22⋊C412yes—
195Dic47⋊C4C22⋊C412yes—
196C4×Dic47—22no—
197C4×Dic47—22no—
198C4×Dic47—22no—
199C4×Dic47—22no—
200C4×Dic47—22no—
201C4×Dic47—216no—
202C4×Dic47—84no—
203C4×Dic47—82no—
204C23×C47—21no—
205C23×C47—21no—
206C23×C47—41no—
207C23×C47—41no—
208C23×C47—41no—
209C23×C47—41no—
210C23×C47C2×C4212yes—
211C23×C47C23×C411yescharacteristic
212C23×C47C23×C412yes—
213C23×C47C22×D412yes—
214C23×C47C2×#4112yes—
215C22×D47—21no—
216C22×D47—21no—
217C22×D47—41no—
218C22×D47—41no—
219C22×D47C2×C4212yes—
220D4×C47—28no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—28no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—41no—
229C2×C4×C47—41no—
230C2×C4×C47—44no—
231C2×C4×C47—44no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—81no—
235C2×C4×C47—81no—
236C2×C4×C47C2×C4212yes—
237C2×C4×C47C2×C22⋊C412yes—
238C2×C4×C47C2×C22⋊C411yescharacteristic
239C2×C4×C47C2×C22⋊C411yescharacteristic
240C22⋊D47—28no—
241C22⋊D47—28no—
242C2×Dic47—21no—
243C2×Dic47—21no—
244C2×Dic47—28no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—28no—
248C2×Dic47—44no—
249C2×Dic47—41no—
250C2×Dic47—41no—
251C2×Dic47—44no—
252C2×Dic47—44no—
253C2×Dic47—41no—
254C2×Dic47—41no—
255C2×Dic47—82no—
256C2×Dic47C2×C4212yes—
257C2×Dic47C2×C4212yes—
258C2×Dic47C2×C4212yes—
259C2×Dic47C2×C22⋊C412yes—
260C2×Dic47C2×C22⋊C412yes—
261C2×Dic47C2×C22⋊C412yes—
262C2×Dic47C2×C22⋊C412yes—
263C2×Dic47#11712yes—
264C2×Dic47#11712yes—
265C2×Dic47C4×D418yes—
266C2×Dic47C4×D418yes—
267C4×D47—28no—
268C4×D47—82no—
269C4×D47—82no—
270Dic94—28no—
271#20393—471nomaximal, Sylow
272C22×C47—22no—
273C22×C47—21no—
274C22×C47—22no—
275C22×C47—21no—
276C22×C47—22no—
277C22×C47—42no—
278C22×C47—42no—
279C22×C47—42no—
280C22×C47—42no—
281C22×C47—41no—
282C22×C47—41no—
283C22×C47C22×C4211yescharacteristic
284C22×C47C22×C22⋊C411yescharacteristic
285C22×C47C2×#11711yescharacteristic
286C22×C47C2×C4×D414yes—
287C2×D47—22no—
288C2×D47—42no—
289C2×D47—41no—
290C2×D47—41no—
291C2×D47—42no—
292C4×C47—22no—
293C4×C47—21no—
294C4×C47—21no—
295C4×C47—22no—
296C4×C47—48no—
297C4×C47—41no—
298C4×C47—41no—
299Dic47—22no—
300Dic47—22no—
301Dic47—22no—
302Dic47—48no—
303Dic47—41no—
304Dic47—41no—
305Dic47C4×C22⋊C414yes—
306Dic47C4×C22⋊C414yes—
307C2×#520—471no—
308C2×#410—472no—
309#2274—472no—
310C4×#99—472no—
311C4×#99—472no—
312C4×#99—472no—
313C4×#99—471no—
314C4×#99D4711yescharacteristic, complemented
315#1740—472no—
316C2×C47—24no—
317C2×C47—21no—
318C2×C47—21no—
319C2×C47—42no—
320C2×C47C2×C4×C22⋊C411yescharacteristic
321C2×C47#288311yescharacteristic
322C2×C47#288411yescharacteristic
323D47—42no—
324C22×#41—471no—
325#520—944no—
326#520—944no—
327C2×C4×Q8—471no—
328C2×C4×Q8—471no—
329C2×C4×D4—471no—
330C2×C4×D4—471no—
331C2×C4×D4—471no—
332C2×C4×D4—471no—
333C2×C4×D4—471no—
334C2×C4×D4C2×D4711yescharacteristic
335C2×#117—471no—
336C2×#117—471no—
337C2×#117—471no—
338C2×#117—474no—
339C22×C4⋊C4—471no—
340C22×C4⋊C4—471no—
341C22×C4⋊C4—471no—
342#410—4716no—
343C2×#99—472no—
344C2×#99—474no—
345C2×#99C2×D4712yes—
346C4×C4⋊C4—944no—
347C4×C4⋊C4—944no—
348C4×C22⋊C4—472no—
349C4×C22⋊C4—474no—
350C4×C22⋊C4C2×D4712yes—
351#342—474no—
352#342—472no—
353#342C2×D4712yes—
354C47#2039311yescharacteristic, complemented, Sylow
355C2×#41—478no—
356C2×#41—944no—
357C2×#41—944no—
358C22×Q8—471no—
359C22×D4—471no—
360C22×D4—471no—
361C22×D4C22×D4711yescharacteristic
362C23×C4—471no—
363C23×C4—471no—
364C23×C4—471no—
365C23×C4—471no—
366C23×C4—471no—
367C23×C4—471no—
368C23×C4—471no—
369C23×C4C4×D4711yescharacteristic
370C23×C4C22×D4711yescharacteristic
371C4×Q8—942no—
372C4×Q8—942no—
373C4×Q8—944no—
374C4×D4—22no—
375C4×D4—22no—
376C4×D4—944no—
377C4×D4—944no—
378C4×D4—942no—
379C4×D4—942no—
380C4×D4—944no—
381C4×D4—942no—
382C4×D4—942no—
383#117—4716no—
384#117—942no—
385#117—942no—
386#117—944no—
387#117—944no—
388#117—948no—
389C2×C4⋊C4—471no—
390C2×C4⋊C4—471no—
391C2×C4⋊C4—471no—
392C2×C4⋊C4—471no—
393C2×C4⋊C4—474no—
394C2×C4⋊C4—474no—
395C2×C4⋊C4—471no—
396C2×C4⋊C4—471no—
397C2×C4⋊C4—471no—
398C2×C4⋊C4—471no—
399C2×C4⋊C4—471no—
400C2×C4⋊C4—944no—
401C2×C4⋊C4—942no—
402C2×C4⋊C4—942no—
403C2×C4⋊C4—944no—
404C2×C4⋊C4C4×D4711yescharacteristic
405C2×C22⋊C4—474no—
406C2×C22⋊C4—471no—
407C2×C22⋊C4—471no—
408C2×C22⋊C4—471no—
409C2×C22⋊C4—471no—
410C2×C22⋊C4C4×D4711yescharacteristic
411C2×C22⋊C4C22×D4711yescharacteristic
412C2×C22⋊C4C22×D4714yes—
413C2×C42—22no—
414C2×C42—471no—
415C2×C42—471no—
416C2×C42—471no—
417C2×C42—471no—
418C2×C42—471no—
419C2×C42—944no—
420C2×C42—944no—
421C2×C42—942no—
422C2×C42C4×D4711yescharacteristic
423#99—478no—
424#99—4716no—
425#99C4×D4718yescomplemented
426#95—22no—
427#95—944no—
428#95—942no—
429C24—471no—
430C24C2×C4×D4711yescharacteristic
431C24C23×D4711yescharacteristic
432#41—9416no—
433#41—9416no—
434C2×Q8—474no—
435C2×Q8—942no—
436C2×Q8—942no—
437C2×D4—22no—
438C2×D4—22no—
439C2×D4—474no—
440C2×D4—474no—
441C2×D4—942no—
442C2×D4—942no—
443C2×D4—942no—
444C2×D4—942no—
445C2×D4C2×C4×D4714yes—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—21no—
449C22×C4—81no—
450C22×C4—81no—
451C22×C4—471no—
452C22×C4—471no—
453C22×C4—474no—
454C22×C4—474no—
455C22×C4—474no—
456C22×C4—474no—
457C22×C4—471no—
458C22×C4—471no—
459C22×C4—471no—
460C22×C4—474no—
461C22×C4—474no—
462C22×C4—471no—
463C22×C4—471no—
464C22×C4—942no—
465C22×C4—942no—
466C22×C4—942no—
467C22×C4—942no—
468C22×C4—942no—
469C22×C4—942no—
470C22×C4—944no—
471C22×C4—942no—
472C22×C4—3761no—
473C22×C4—3761no—
474C22×C4—3761no—
475C22×C4—3761no—
476C22×C4C2×C4×D4711yescharacteristic
477C22×C4C2×C4×D4711yescharacteristic
478C22×C4C2×C4×D4711yescharacteristic
479C22×C4C2×C4×D4711yescharacteristic
480C22×C4C2×C4×D4711yescharacteristic
481C22×C4D4×D4712yes—
482C22×C4D4×D4712yes—
483C4⋊C4—22no—
484C4⋊C4—472no—
485C4⋊C4—472no—
486C4⋊C4—474no—
487C4⋊C4—472no—
488C4⋊C4—472no—
489C4⋊C4—474no—
490C4⋊C4—942no—
491C4⋊C4—942no—
492C4⋊C4—942no—
493C4⋊C4—9416no—
494C4⋊C4—942no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C22⋊C4—22no—
498C22⋊C4—24no—
499C22⋊C4—22no—
500C22⋊C4—478no—
501C22⋊C4—942no—
502C22⋊C4—942no—
503C22⋊C4—942no—
504C22⋊C4—944no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4C2×C4×D4718yes—
508C42—21no—
509C42—21no—
510C42—82no—
511C42—942no—
512C42—942no—
513C42—942no—
514C42—942no—
515C42—9416no—
516C42—942no—
517C42—3762no—
518C42—3764no—
519C23—21no—
520C23—21no—
521C23—41no—
522C23—41no—
523C23—41no—
524C23—41no—
525C23—472no—
526C23—941no—
527C23—941no—
528C23—1881no—
529C23—1881no—
530C23C42×D4712yes—
531C23C22×C4×D4711yescharacteristic
532C23C22×C4×D4712yes—
533C23C2×D4×D4712yes—
534C23#41×D4712yes—
535Q8—948no—
536D4—28no—
537D4—948no—
538D4—948no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—21no—
543C2×C4—28no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—44no—
549C2×C4—44no—
550C2×C4—41no—
551C2×C4—41no—
552C2×C4—81no—
553C2×C4—81no—
554C2×C4—472no—
555C2×C4—472no—
556C2×C4—472no—
557C2×C4—472no—
558C2×C4—472no—
559C2×C4—472no—
560C2×C4—478no—
561C2×C4—478no—
562C2×C4—472no—
563C2×C4—472no—
564C2×C4—472no—
565C2×C4—948no—
566C2×C4—948no—
567C2×C4—941no—
568C2×C4—941no—
569C2×C4—941no—
570C2×C4—941no—
571C2×C4—948no—
572C2×C4—3762no—
573C2×C4—3762no—
574C2×C4—3762no—
575C2×C4—1884no—
576C2×C4—1881no—
577C2×C4—1881no—
578C2×C4—1884no—
579C2×C4—1884no—
580C2×C4—1881no—
581C2×C4—1881no—
582C2×C4C42×D4712yes—
583C2×C4C22⋊C4×D4711yescharacteristic
584C2×C4C22⋊C4×D4711yescharacteristic
585C2×C4C22⋊C4×D4712yes—
586C22—22no—
587C22—21no—
588C22—22no—
589C22—21no—
590C22—22no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22—42no—
595C22—41no—
596C22—41no—
597C22—942no—
598C22—1882no—
599C22—1882no—
600C22—1881no—
601C22—1881no—
602C22C2×C42×D4711yescharacteristic
603C22C2×C22⋊C4×D4711yescharacteristic
604C22#117×D4711yescharacteristic
605C22C4×D4×D4714yes—
606C4—21no—
607C4—21no—
608C4—22no—
609C4—22no—
610C4—48no—
611C4—41no—
612C4—41no—
613C4—474no—
614C4—474no—
615C4—942no—
616C4—942no—
617C4—942no—
618C4—1888no—
619C4—1881no—
620C4—1881no—
621C2—24no—
622C2—21no—
623C2—21no—
624C2—42no—
625C2—1882no—
626C2C4×C22⋊C4×D4711yescharacteristic
627C2#2025184611yescharacteristic
628C2#2025185011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#99×C47C2
socleC22×C47C22×C22⋊C4
prime radicalC22×#10625352C22
cosocleC24×C47C24
hypercenterC4×#99D47
hypocenterC47#20393
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C4×#99

Complements

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

NH ≅ G/Ntype
3. #20245743C2semidirect
4. #99×Dic47C2semidirect
5. C4×#13093938C2semidirect
6. C4×#13093939C2semidirect
7. #20243175C2semidirect
8. #20243119C2semidirect
9. C4×#99×C47C2semidirect
13. C2×C4×Dic94C4semidirect
14. C2×#13093989C4semidirect
16. C2×C4×C22⋊D47C4semidirect
18. C2×(C22⋊D47)⋊C4C4semidirect
20. C2×#13093981C4semidirect
21. C2×#13093980C4semidirect
24. C22×Dic47⋊C4C4semidirect
26. C2×C4⋊C4×D47C4semidirect
27. #15689095C4semidirect
68. #13093980C2×C4semidirect
97. #13093939C2×C4semidirect
98. #13093938C2×C4semidirect
112. #99×C47C2×C4semidirect
136. C2×C22⋊D47C42semidirect
144. C22×Dic47C42semidirect
164. C2×C4×D47C42semidirect
167. C2×Dic94C42semidirect
314. C4×#99D47semidirect
354. C47#20393semidirect
425. #99C4×D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156896022
C2×#156890952
#202457432
#99×Dic472
C4×#130939382
C4×#130939392
#202431752
#202431192
C4×#99×C472
#2039347