Finite Group Databasebeta

← #26186370

Subgroups — #26186370

Order 12032.

638 conjugacy classes of subgroups.

The subgroup lattice has 604 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20252499C211yesmaximal, characteristic, complemented
2#20252464C211yesmaximal, characteristic, complemented
3#20242267C211yesmaximal, characteristic, complemented
4#20242253C211yesmaximal, characteristic, complemented
5#20242232C211yesmaximal, characteristic, complemented
6#20242218C211yesmaximal, characteristic, complemented
7#20242212C211yesmaximal, characteristic, complemented
8SD16⋊(C47⋊C8)C211yesmaximal, characteristic, complemented
9SD16×C47⋊C8C211yesmaximal, characteristic, complemented
10D8×C47⋊C8C211yesmaximal, characteristic, complemented
11#20242173C211yesmaximal, characteristic, complemented
12#20241822C211yesmaximal, characteristic, complemented
13#20241787C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#3106C211yesmaximal, characteristic
16Q8×C47⋊C8C2211yescharacteristic
17Q8×C47⋊C8C2211yescharacteristic
18#15689201C2211yescharacteristic
19#15689201C2211yescharacteristic
20#15689195—21no—
21#15689195—21no—
22D4×C47⋊C8—21no—
23D4×C47⋊C8—21no—
24D4×C47⋊C8C2211yescharacteristic
25D4×C47⋊C8C2211yescharacteristic
26D4×C47⋊C8C2211yescharacteristic
27D4×C47⋊C8C2211yescharacteristic
28#15689180C2211yescharacteristic
29#15689176—21no—
30#15689176C2211yescharacteristic
31#15689176C2211yescharacteristic
32C2×C4⋊(C47⋊C8)—21no—
33C2×C4⋊(C47⋊C8)C2211yescharacteristic
34#15689090—21no—
35#15689090—21no—
36#15688876C2211yescharacteristic
37#15688876C2211yescharacteristic
38#15688874C2211yescharacteristic
39#15688874C2211yescharacteristic
40Q8⋊(C47⋊C8)C2211yescharacteristic
41Q8⋊(C47⋊C8)C2211yescharacteristic
42D4⋊(C47⋊C8)C2211yescharacteristic
43D4⋊(C47⋊C8)C2211yescharacteristic
44D4⋊(C47⋊C8)C2211yescharacteristic
45D4⋊(C47⋊C8)C2211yescharacteristic
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48#15688845C2211yescharacteristic
49#15688845C2211yescharacteristic
50#15688844C2211yescharacteristic
51C8×C47⋊C8C2211yescharacteristic
52C47×#532C2211yescharacteristic
53C4×#41×C47C2211yescharacteristic
54C47×#482C411yescharacteristic
55C47×#482C411yescharacteristic
56C47×#477C411yescharacteristic
57C47×#476C411yescharacteristic
58C47×#460C411yescharacteristic
59C47×#459C411yescharacteristic
60C47×#449C411yescharacteristic
61C47×#449C411yescharacteristic
62C4×SD16×C47C2211yescharacteristic
63C4×SD16×C47C2211yescharacteristic
64C4×D8×C47C2211yescharacteristic
65C4×D8×C47C2211yescharacteristic
66C47×#431C2211yescharacteristic
67C2×#10625329—21no—
68C2×#10625329—21no—
69C22×C47⋊C8—21no—
70C22×C47⋊C8—21no—
71C22×C47⋊C8—21no—
72C22×C47⋊C8—21no—
73C22×C47⋊C8—21no—
74C4⋊(C47⋊C8)—21no—
75C4⋊(C47⋊C8)—21no—
76C4⋊(C47⋊C8)—21no—
77C4⋊(C47⋊C8)—21no—
78C4⋊(C47⋊C8)D411yescharacteristic
79C4⋊(C47⋊C8)D411yescharacteristic
80C4⋊(C47⋊C8)C2311yescharacteristic
81C4⋊(C47⋊C8)C2311yescharacteristic
82C4⋊(C47⋊C8)C2311yescharacteristic
83C4⋊(C47⋊C8)C2311yescharacteristic
84C22⋊(C47⋊C8)—21no—
85C22⋊(C47⋊C8)—21no—
86C22⋊(C47⋊C8)—21no—
87C22⋊(C47⋊C8)—21no—
88C22⋊(C47⋊C8)—21no—
89C22⋊(C47⋊C8)—21no—
90C22⋊(C47⋊C8)—21no—
91C22⋊(C47⋊C8)—21no—
92C22⋊(C47⋊C8)D411yescharacteristic
93C22⋊(C47⋊C8)D411yescharacteristic
94#13093935—21no—
95C4×C47⋊C8—21no—
96C4×C47⋊C8—21no—
97C4×C47⋊C8C2311yescharacteristic
98C4×C47⋊C8C2311yescharacteristic
99C4×C47⋊C8C2311yescharacteristic
100C4×C47⋊C8C2311yescharacteristic
101C2×#41×C47—21no—
102C2×#41×C47C2×C411yescharacteristic
103C2×SD16×C47C2×C411yescharacteristic
104C2×SD16×C47C2×C411yescharacteristic
105C2×D8×C47C2×C411yescharacteristic
106C2×D8×C47C2×C411yescharacteristic
107C4⋊Q8×C47C2×C411yescharacteristic
108#127×C47C2×C411yescharacteristic
109#124×C47—21no—
110#121×C47—21no—
111#121×C47C2×C411yescharacteristic
112#121×C47C2×C411yescharacteristic
113C4×Q8×C47C2×C411yescharacteristic
114C4×Q8×C47C2311yescharacteristic
115C4×D4×C47—21no—
116C4×D4×C47—21no—
117C4×D4×C47—21no—
118C4×D4×C47C2×C411yescharacteristic
119C4×D4×C47C2311yescharacteristic
120C4×D4×C47C2311yescharacteristic
121C4×D4×C47C2311yescharacteristic
122#117×C47—21no—
123#117×C47C2×C411yescharacteristic
124C2×C42×C47—21no—
125C2×C42×C47C2311yescharacteristic
126#107×C47C2×C411yescharacteristic
127#107×C47C2×C411yescharacteristic
128#106×C47C2×C411yescharacteristic
129#106×C47C2×C411yescharacteristic
130C4⋊C8×C47C2×C411yescharacteristic
131C4⋊C8×C47C2×C411yescharacteristic
132#103×C47C2×C411yescharacteristic
133#103×C47C2×C411yescharacteristic
134#102×C47C2×C411yescharacteristic
135#102×C47C2×C411yescharacteristic
136#102×C47C2×C411yescharacteristic
137#102×C47C2×C411yescharacteristic
138#102×C47C2×C411yescharacteristic
139#102×C47C2×C411yescharacteristic
140C22⋊C8×C47C2×C411yescharacteristic
141C22⋊C8×C47C2×C411yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—22no—
146#41×C47—81no—
147#41×C47—81no—
148C2×Q8×C47—21no—
149C2×Q8×C47C22×C411yescharacteristic
150C2×D4×C47—21no—
151C2×D4×C47—21no—
152C2×D4×C47—21no—
153C2×D4×C47—21no—
154C2×D4×C47—21no—
155C2×D4×C47C22×C411yescharacteristic
156C2×D4×C47C22×C411yescharacteristic
157C2×D4×C47C22×C411yescharacteristic
158C22×C4×C47—21no—
159C22×C4×C47—21no—
160C22×C4×C47—21no—
161C22×C4×C47—21no—
162C22×C4×C47—21no—
163C22×C4×C47C22×C411yescharacteristic
164C22×C4×C47C2×D411yescharacteristic
165C22×C4×C47#4111yescharacteristic
166SD16×C47—22no—
167SD16×C47—22no—
168D8×C47—22no—
169D8×C47—22no—
170C2×C8×C47C22×C411yescharacteristic
171C2×C8×C47C22×C411yescharacteristic
172C2×C8×C47C22×C411yescharacteristic
173C2×C8×C47C22×C411yescharacteristic
174C4⋊C4×C47—21no—
175C4⋊C4×C47—21no—
176C4⋊C4×C47—21no—
177C4⋊C4×C47C22×C411yescharacteristic
178C4⋊C4×C47C22×C411yescharacteristic
179C4⋊C4×C47C22×C411yescharacteristic
180C4⋊C4×C47C22×C411yescharacteristic
181C22⋊C4×C47—21no—
182C22⋊C4×C47—21no—
183C22⋊C4×C47—21no—
184C22⋊C4×C47—21no—
185C22⋊C4×C47—21no—
186C22⋊C4×C47—21no—
187C22⋊C4×C47—21no—
188C42×C47—21no—
189C42×C47—21no—
190C42×C47—21no—
191C42×C47C22×C411yescharacteristic
192C42×C47C2×D411yescharacteristic
193C42×C47#4111yescharacteristic
194C42×C47C2411yescharacteristic
195#10625329—81no—
196#10625329—81no—
197C2×C47⋊C8—21no—
198C2×C47⋊C8—21no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—81no—
204C2×C47⋊C8—81no—
205C2×C47⋊C8—81no—
206C2×C47⋊C8—81no—
207C2×C47⋊C8—81no—
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210C2×C47⋊C8C2×D411yescharacteristic
211C2×C47⋊C8C2×D411yescharacteristic
212C23×C47—21no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47C4×D411yescharacteristic
216Q8×C47—21no—
217Q8×C47—81no—
218Q8×C47#13112yes—
219D4×C47—24no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—21no—
224D4×C47—21no—
225D4×C47—81no—
226D4×C47—81no—
227D4×C47—81no—
228D4×C47—81no—
229D4×C47#13112yes—
230C2×C4×C47—24no—
231C2×C4×C47—21no—
232C2×C4×C47—21no—
233C2×C4×C47—21no—
234C2×C4×C47—21no—
235C2×C4×C47—21no—
236C2×C4×C47—21no—
237C2×C4×C47—21no—
238C2×C4×C47—21no—
239C2×C4×C47—21no—
240C2×C4×C47—41no—
241C2×C4×C47—41no—
242C2×C4×C47—41no—
243C2×C4×C47—41no—
244C2×C4×C47—41no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—81no—
248C2×C4×C47C4×D411yescharacteristic
249C2×C4×C47C4×D411yescharacteristic
250C2×C4×C47C4×D411yescharacteristic
251C2×C4×C47C23×C411yescharacteristic
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C2×#4111yescharacteristic
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C47⋊C8—21no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—41no—
263C47⋊C8—41no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#17920—471nomaximal, Sylow
269C22×C47—21no—
270C22×C47—22no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47—41no—
281C22×C47C2×C4×D411yescharacteristic
282C4×C47—21no—
283C4×C47—22no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47—41no—
291C4×C47C2×#13111yescharacteristic
292C4×C47C2×#13111yescharacteristic
293C4×C47#57611yescharacteristic
294C4×C47#57711yescharacteristic
295#3106D4711yescharacteristic
296#2988—471no—
297#2981—471no—
298#1588—471no—
299#1586—471no—
300#1583—471no—
301#1581—471no—
302#1580—471no—
303SD16⋊C8—471no—
304C8×SD16—471no—
305C8×D8—471no—
306#1573—471no—
307#1488—471no—
308#1480—471no—
309#1454—471no—
310C2×C47—41no—
311C2×C47—42no—
312C2×C47—81no—
313C2×C47—81no—
314C2×C47#292911yescharacteristic
315C2×C47#294611yescharacteristic
316C2×C47#295711yescharacteristic
317#532C2×D4711yescharacteristic
318C4×#41C2×D4711yescharacteristic
319#482Dic4711yescharacteristic
320#482Dic4711yescharacteristic
321#477Dic4711yescharacteristic
322#476Dic4711yescharacteristic
323#460Dic4711yescharacteristic
324#459Dic4711yescharacteristic
325#449Dic4711yescharacteristic
326#449Dic4711yescharacteristic
327C8×Q8—471no—
328C8×Q8—471no—
329C4×SD16C2×D4711yescharacteristic
330C4×SD16C2×D4711yescharacteristic
331C4×D8C2×D4711yescharacteristic
332C4×D8C2×D4711yescharacteristic
333#436—471no—
334#436—471no—
335#435—941no—
336#435—941no—
337C8×D4—471no—
338C8×D4—471no—
339C8×D4—471no—
340C8×D4—471no—
341C8×D4—941no—
342C8×D4—941no—
343#432—471no—
344#431—471no—
345#431—471no—
346#431—941no—
347#431C2×D4711yescharacteristic
348C2×C4⋊C8—471no—
349C2×C4⋊C8—941no—
350#408—941no—
351#408—941no—
352#335—471no—
353#335—471no—
354#334—471no—
355#334—471no—
356Q8⋊C8—471no—
357Q8⋊C8—471no—
358D4⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364#322—471no—
365#322—471no—
366#322—471no—
367C82—471no—
368C47#1792011yescharacteristic, complemented, Sylow
369C2×#41—21no—
370C2×#41C2×Dic4711yescharacteristic
371C2×SD16C2×Dic4711yescharacteristic
372C2×SD16C2×Dic4711yescharacteristic
373C2×D8C2×Dic4711yescharacteristic
374C2×D8C2×Dic4711yescharacteristic
375C2×M16—941no—
376C2×M16—941no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381C22×C8—941no—
382C4⋊Q8C2×Dic4711yescharacteristic
383#127C2×Dic4711yescharacteristic
384#124—21no—
385#121—21no—
386#121C2×Dic4711yescharacteristic
387#121C2×Dic4711yescharacteristic
388C4×Q8C2×Dic4711yescharacteristic
389C4×Q8C22×D4711yescharacteristic
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—21no—
393C4×D4C2×Dic4711yescharacteristic
394C4×D4C22×D4711yescharacteristic
395C4×D4C22×D4711yescharacteristic
396C4×D4C22×D4711yescharacteristic
397#117—21no—
398#117C2×Dic4711yescharacteristic
399C2×C42—21no—
400C2×C42C22×D4711yescharacteristic
401#107C2×Dic4711yescharacteristic
402#107C2×Dic4711yescharacteristic
403#106C2×Dic4711yescharacteristic
404#106C2×Dic4711yescharacteristic
405C4⋊C8—471no—
406C4⋊C8—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8—941no—
415C4⋊C8C2×Dic4711yescharacteristic
416C4⋊C8C2×Dic4711yescharacteristic
417#103C2×Dic4711yescharacteristic
418#103C2×Dic4711yescharacteristic
419#102C2×Dic4711yescharacteristic
420#102C2×Dic4711yescharacteristic
421#102C2×Dic4711yescharacteristic
422#102C2×Dic4711yescharacteristic
423#102C2×Dic4711yescharacteristic
424#102C2×Dic4711yescharacteristic
425C22⋊C8—471no—
426C22⋊C8—471no—
427C22⋊C8—941no—
428C22⋊C8—941no—
429C22⋊C8—941no—
430C22⋊C8—941no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8C2×Dic4711yescharacteristic
436C22⋊C8C2×Dic4711yescharacteristic
437#97—941no—
438C4×C8—471no—
439C4×C8—471no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—941no—
443C4×C8—941no—
444C4×C8C22×D4711yescharacteristic
445C4×C8C22×D4711yescharacteristic
446#41—22no—
447#41—22no—
448#41—81no—
449#41—81no—
450C2×Q8—21no—
451C2×Q8C22×Dic4711yescharacteristic
452C2×D4—21no—
453C2×D4—21no—
454C2×D4—21no—
455C2×D4—21no—
456C2×D4—21no—
457C2×D4C22×Dic4711yescharacteristic
458C2×D4C22×Dic4711yescharacteristic
459C2×D4C22×Dic4711yescharacteristic
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—21no—
463C22×C4—21no—
464C22×C4—21no—
465C22×C4D4×D4711yescharacteristic
466C22×C4#1062535211yescharacteristic
467C22×C4C22×Dic4711yescharacteristic
468SD16—22no—
469SD16—22no—
470D8—22no—
471D8—22no—
472M16—3761no—
473M16—3761no—
474C2×C8—471no—
475C2×C8—471no—
476C2×C8—471no—
477C2×C8—471no—
478C2×C8—941no—
479C2×C8—941no—
480C2×C8—941no—
481C2×C8—941no—
482C2×C8—941no—
483C2×C8—941no—
484C2×C8—3761no—
485C2×C8—3761no—
486C2×C8—3761no—
487C2×C8—3761no—
488C2×C8—3761no—
489C2×C8C22×Dic4711yescharacteristic
490C2×C8C22×Dic4711yescharacteristic
491C2×C8C22×Dic4711yescharacteristic
492C2×C8C22×Dic4711yescharacteristic
493C4⋊C4—21no—
494C4⋊C4—21no—
495C4⋊C4—21no—
496C4⋊C4C22×Dic4711yescharacteristic
497C4⋊C4C22×Dic4711yescharacteristic
498C4⋊C4C22×Dic4711yescharacteristic
499C4⋊C4C22×Dic4711yescharacteristic
500C22⋊C4—21no—
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C42—21no—
508C42—21no—
509C42—21no—
510C42D4×D4711yescharacteristic
511C42#1062535211yescharacteristic
512C42C22×Dic4711yescharacteristic
513C42C23×D4711yescharacteristic
514C23—21no—
515C23—21no—
516C23—21no—
517C23D4×Dic4711yescharacteristic
518Q8—21no—
519Q8—81no—
520Q8#1309403112yes—
521D4—24no—
522D4—21no—
523D4—21no—
524D4—21no—
525D4—21no—
526D4—21no—
527D4—81no—
528D4—81no—
529D4—81no—
530D4—81no—
531D4#1309403112yes—
532C2×C4—24no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—21no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—41no—
546C2×C4—41no—
547C2×C4—41no—
548C2×C4—41no—
549C2×C4—81no—
550C2×C4D4×Dic4711yescharacteristic
551C2×C4D4×Dic4711yescharacteristic
552C2×C4D4×Dic4711yescharacteristic
553C2×C4C23×Dic4711yescharacteristic
554C2×C4C2×D4×D4711yescharacteristic
555C2×C4C2×#1062535211yescharacteristic
556C8—21no—
557C8—21no—
558C8—21no—
559C8—21no—
560C8—941no—
561C8—941no—
562C8—941no—
563C8—941no—
564C8—1881no—
565C8—1881no—
566C8—1881no—
567C8—1881no—
568C8—1881no—
569C8—1881no—
570C22—21no—
571C22—21no—
572C22—21no—
573C22—22no—
574C22—41no—
575C22—41no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22C2×D4×Dic4711yescharacteristic
583C4—21no—
584C4—21no—
585C4—21no—
586C4—21no—
587C4—22no—
588C4—41no—
589C4—41no—
590C4—41no—
591C4—41no—
592C4C2×#1309403111yescharacteristic
593C4C2×#1309403111yescharacteristic
594C4#1568992711yescharacteristic
595C4#1568993311yescharacteristic
596C2—41no—
597C2—42no—
598C2—81no—
599C2—81no—
600C2#2025208311yescharacteristic
601C2#2025222111yescharacteristic
602C2#2025230511yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
Fitting, prime radicalC47×#3106C2
socleC22×C47C2×C4×D4
cosocleC42×C47C24
hypercenter#3106D47
hypocenterC47#17920
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3106

Complements

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

NH ≅ G/Ntype
1. #20252499C2semidirect
2. #20252464C2semidirect
3. #20242267C2semidirect
4. #20242253C2semidirect
5. #20242232C2semidirect
6. #20242218C2semidirect
7. #20242212C2semidirect
8. SD16⋊(C47⋊C8)C2semidirect
9. SD16×C47⋊C8C2semidirect
10. D8×C47⋊C8C2semidirect
11. #20242173C2semidirect
12. #20241822C2semidirect
13. #20241787C2semidirect
14. #20241688C2semidirect
368. C47#17920semidirect

Maximal subgroups

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

subgroupindex
#202524992
#202524642
#202422672
#202422532
#202422322
#202422182
#202422122
SD16⋊(C47⋊C8)2
SD16×C47⋊C82
D8×C47⋊C82
#202421732
#202418222
#202417872
#202416882
C47×#31062
#1792047