Finite Group Databasebeta

← #26122750

Subgroups — #26122750

Order 12032.

926 conjugacy classes of subgroups.

The subgroup lattice has 618 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689105C211yesmaximal, characteristic
2C2×#15689096C211yesmaximal, characteristic
3C2×#15689089C211yesmaximal, characteristic
4C2×#15688895C211yesmaximal, characteristic, complemented
5C2×#15688893C211yesmaximal, characteristic, complemented
6#20243084C211yesmaximal, characteristic, complemented
7C2×C47×#405C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689105—22no—
13#15689105—22no—
14C2×#13093942C412yescomplemented
15C2×#13093940C412yescomplemented
16#15689096—22no—
17#15689096—22no—
18C2×#13093938C414yes—
19#15689089—22no—
20#15689089—21no—
21#15689089—21no—
22C2×(C2×D47)⋊C8C414yescomplemented
23#15688895—22no—
24#15688893—22no—
25#15688877—22no—
26C22×M16×C47C2211yescharacteristic
27C23×C8×C47C2211yescharacteristic
28C2×#117×C47C2211yescharacteristic
29C47×#405—22no—
30C47×#405—22no—
31C2×#97×C47—21no—
32C2×C4×C8×C47—21no—
33C2×#10625350—21no—
34C2×#10625350—21no—
35C2×#10625350—21no—
36C2×#10625350—21no—
37C2×#10625350—21no—
38C2×#10625350—21no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C22×Dic94C2×C411yescharacteristic
46C22×D188C2×C411yescharacteristic
47C22×C22⋊D47C2×C412yes—
48C22×C4×D47C2×C412yes—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C2×#10625329—21no—
52C2×#10625329—21no—
53C2×#10625329—21no—
54C2×#10625329—21no—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329C2×C412yes—
61C22×C47⋊C8—21no—
62C22×C47⋊C8C2×C412yes—
63#13093983—21no—
64#13093983—21no—
65#13093983—21no—
66#13093983—21no—
67C2×C4⋊Dic47—21no—
68C2×C22⋊Dic47C2×C412yes—
69C2×C4×Dic47—21no—
70#13093942—24no—
71#13093940—24no—
72#13093938—28no—
73(C2×D47)⋊C8—24no—
74(C2×D47)⋊C8—24no—
75C23×C4×C47C2311yescharacteristic
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C2×M16×C47—21no—
79C2×M16×C47C2×C412yes—
80C2×M16×C47D412yes—
81C2×M16×C47D412yes—
82C22×C8×C47—21no—
83C22×C8×C47—21no—
84C22×C8×C47—21no—
85C22×C8×C47—21no—
86C22×C8×C47—21no—
87C22×C8×C47C2×C412yes—
88C22×C8×C47D412yes—
89C22×C8×C47D411yescharacteristic
90C22×C8×C47D411yescharacteristic
91#117×C47—21no—
92#117×C47—21no—
93#117×C47D412yes—
94#117×C47D412yes—
95C2×C4⋊C4×C47—21no—
96C2×C22⋊C4×C47C2×C412yes—
97C2×C42×C47—21no—
98#97×C47—24no—
99C4×C8×C47—24no—
100C24×C47C22×C411yescharacteristic
101C23×D47C4212yes—
102C22×C4×C47—22no—
103C22×C4×C47C22×C411yescharacteristic
104C22×C4×C47C22×C411yescharacteristic
105C22×C4×C47C2×D411yescharacteristic
106C22×C4×C47C2×D411yescharacteristic
107C22×C4×C47C2×D411yescharacteristic
108C22×C4×C47C2×D411yescharacteristic
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C22×C4×C47#4111yescharacteristic
114C22×C4×C47#4111yescharacteristic
115C22×C4×C47#4111yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C2×C22⋊D47—22no—
118C2×C22⋊D47—22no—
119C2×C22⋊D47—22no—
120C2×C22⋊D47—22no—
121C2×C22⋊D47—22no—
122C2×C22⋊D47—22no—
123C22×Dic47—22no—
124C22×Dic47C4212yes—
125#10625350—41no—
126#10625350—41no—
127#10625350—41no—
128#10625350—41no—
129#10625350—41no—
130#10625350—41no—
131#10625350—41no—
132#10625350—41no—
133#10625350—41no—
134#10625350—41no—
135#10625350—41no—
136#10625350—41no—
137#10625350—41no—
138#10625350—41no—
139#10625350—41no—
140#10625350—41no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×D188—21no—
145C2×D188—21no—
146C2×D188—21no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×C4×D47—22no—
151C2×C4×D47—22no—
152C2×C4×D47—22no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156C2×Dic94—21no—
157C2×Dic94—21no—
158C2×Dic94—21no—
159M16×C47—22no—
160M16×C47—22no—
161M16×C47—22no—
162M16×C47C22⋊C414yes—
163C2×C8×C47—22no—
164C2×C8×C47—22no—
165C2×C8×C47—22no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—22no—
169C2×C8×C47—22no—
170C2×C8×C47—22no—
171C2×C8×C47—22no—
172C2×C8×C47—21no—
173C2×C8×C47—21no—
174C2×C8×C47C22⋊C412yes—
175C2×C8×C47C22⋊C412yes—
176C4⋊C4×C47—22no—
177C4⋊C4×C47—22no—
178C22⋊C4×C47—22no—
179C22⋊C4×C47C22⋊C414yes—
180C42×C47—22no—
181C42×C47—22no—
182C22⋊Dic47—22no—
183C22⋊Dic47—22no—
184C4⋊Dic47—41no—
185C4⋊Dic47—41no—
186C4×Dic47—41no—
187C4×Dic47—41no—
188#10625329—22no—
189#10625329—22no—
190#10625329—41no—
191#10625329—41no—
192#10625329—41no—
193#10625329—41no—
194#10625329—41no—
195#10625329—41no—
196C2×C47⋊C8—22no—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—41no—
201C2×C47⋊C8—41no—
202C23×C47—42no—
203C23×C47C2×C4211yescharacteristic
204C23×C47C2×C22⋊C411yescharacteristic
205C23×C47#11711yescharacteristic
206C23×C47C4×D411yescharacteristic
207C23×C47C4×D411yescharacteristic
208C23×C47C4×D411yescharacteristic
209C23×C47C4×D411yescharacteristic
210C22×D47—22no—
211C22×D47—22no—
212C22×D47—22no—
213C22×D47—44no—
214C2×C4×C47—24no—
215C2×C4×C47—44no—
216C2×C4×C47C2×C22⋊C411yescharacteristic
217C2×C4×C47C2×C22⋊C411yescharacteristic
218C2×C4×C47#11711yescharacteristic
219C2×C4×C47#11711yescharacteristic
220C2×C4×C47C4×D411yescharacteristic
221C2×C4×C47C4×D411yescharacteristic
222C2×C4×C47C4×D411yescharacteristic
223C2×C4×C47C4×D411yescharacteristic
224C2×C4×C47C4×D411yescharacteristic
225C2×C4×C47C4×D411yescharacteristic
226C2×C4×C47C4×D411yescharacteristic
227C2×C4×C47C4×D411yescharacteristic
228C2×C4×C47#12011yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47#12111yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12111yescharacteristic
235C2×C4×C47#12311yescharacteristic
236C2×C4×C47#12311yescharacteristic
237C2×C4×C47#12311yescharacteristic
238C2×C4×C47#12411yescharacteristic
239C2×C4×C47#12411yescharacteristic
240C2×C4×C47#12411yescharacteristic
241C2×C4×C47#12611yescharacteristic
242C2×C4×C47#12611yescharacteristic
243C2×C4×C47#12711yescharacteristic
244C22⋊D47—42no—
245C22⋊D47—42no—
246C22⋊D47—42no—
247C22⋊D47—42no—
248C2×Dic47—22no—
249C2×Dic47—22no—
250C2×Dic47—22no—
251C2×Dic47—44no—
252C2×Dic47—42no—
253D188—41no—
254D188—41no—
255D188—41no—
256D188—41no—
257C4×D47—42no—
258C4×D47—42no—
259C4×D47—42no—
260C4×D47—42no—
261Dic94—41no—
262Dic94—41no—
263Dic94—41no—
264Dic94—41no—
265C8×C47—22no—
266C8×C47—22no—
267C8×C47—24no—
268C47⋊C8—42no—
269C47⋊C8—42no—
270#10961—471nomaximal, Sylow
271C22×C47—22no—
272C22×C47—22no—
273C22×C47—22no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47C4×C22⋊C411yescharacteristic
279C22×C47C4×C22⋊C411yescharacteristic
280C22×C47C4×C22⋊C411yescharacteristic
281C22×C47#38611yescharacteristic
282C22×C47#38811yescharacteristic
283C22×C47#38811yescharacteristic
284C22×C47#39011yescharacteristic
285C2×D47—42no—
286C2×D47—44no—
287C2×D47—82no—
288C2×D47—82no—
289C4×C47—44no—
290C4×C47#38611yescharacteristic
291C4×C47#38611yescharacteristic
292C4×C47#38811yescharacteristic
293C4×C47#38811yescharacteristic
294C4×C47#38811yescharacteristic
295C4×C47#38811yescharacteristic
296C4×C47#39011yescharacteristic
297C4×C47#39011yescharacteristic
298Dic47—42no—
299Dic47—82no—
300C2×#413—471no—
301C2×#410—471no—
302C2×#408—471no—
303C2×#405D4711yescharacteristic, complemented
304C2×#344—471no—
305C2×#344—471no—
306#1729—471no—
307C2×C47—21no—
308C2×C47—21no—
309C2×C47—21no—
310C2×C47—21no—
311C2×C47—21no—
312C2×C47—21no—
313C2×C47#143711yescharacteristic
314C2×C47#175712yes—
315D47—82no—
316C22×#41—471no—
317C22×M16—471no—
318C22×M16—471no—
319C22×M16C2×D4711yescharacteristic
320C23×C8C2×D4711yescharacteristic
321C2×#117—471no—
322C2×#117C2×D4711yescharacteristic
323#413—942no—
324#413—942no—
325C2×#101—472no—
326C2×#100—472no—
327#410—942no—
328#410—942no—
329C2×#99—474no—
330#408—942no—
331#408—941no—
332#408—941no—
333C2×C22⋊C8—474no—
334#405—22no—
335#405—22no—
336C2×#97—21no—
337C2×C4×C8—21no—
338#344—942no—
339#344—942no—
340#336—942no—
341C47#1096111yescharacteristic, complemented, Sylow
342C2×#41—941no—
343C2×#41—941no—
344C2×#41—941no—
345C2×#41—941no—
346C2×#41—941no—
347C2×#41—941no—
348C2×#41—941no—
349C2×#41—941no—
350C2×#41—941no—
351C2×#41—941no—
352C2×#41—941no—
353C2×#41—941no—
354C22×Q8—471no—
355C22×D4—472no—
356C22×D4—471no—
357C23×C4—472no—
358C23×C4C22×D4711yescharacteristic
359C2×M16—21no—
360C2×M16—21no—
361C2×M16—21no—
362C2×M16—472no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16—941no—
371C2×M16—941no—
372C2×M16—941no—
373C2×M16—941no—
374C2×M16C4×D4712yes—
375C2×M16D18812yes—
376C2×M16C22⋊D4712yes—
377C22×C8—21no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—472no—
383C22×C8—941no—
384C22×C8C4×D4712yes—
385C22×C8D18812yes—
386C22×C8C22⋊D4711yescharacteristic
387C22×C8C22⋊D4711yescharacteristic
388#117—21no—
389#117—21no—
390#117—941no—
391#117—941no—
392#117—941no—
393#117—941no—
394#117D18812yes—
395#117C22⋊D4712yes—
396C2×C4⋊C4—21no—
397C2×C4⋊C4—941no—
398C2×C22⋊C4—472no—
399C2×C22⋊C4C4×D4712yes—
400C2×C42—21no—
401C2×C42—941no—
402#101—944no—
403#100—944no—
404#99—948no—
405C22⋊C8—944no—
406C22⋊C8—944no—
407#97—24no—
408C4×C8—24no—
409C24—472no—
410C24C2×C4×D4711yescharacteristic
411#41—1881no—
412#41—1881no—
413#41—1881no—
414#41—1881no—
415#41—1881no—
416#41—1881no—
417#41—1881no—
418#41—1881no—
419#41—1881no—
420#41—1881no—
421#41—1881no—
422#41—1881no—
423#41—1881no—
424#41—1881no—
425#41—1881no—
426#41—1881no—
427C2×Q8—941no—
428C2×Q8—941no—
429C2×Q8—941no—
430C2×Q8—941no—
431C2×Q8—941no—
432C2×Q8—941no—
433C2×D4—942no—
434C2×D4—942no—
435C2×D4—942no—
436C2×D4—942no—
437C2×D4—942no—
438C2×D4—942no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C2×D4—941no—
444C2×D4—941no—
445C22×C4—22no—
446C22×C4—472no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4C2×C4×D4711yescharacteristic
455C22×C4C2×C4×D4711yescharacteristic
456C22×C4C2×D18811yescharacteristic
457C22×C4C2×D18811yescharacteristic
458C22×C4C2×D18811yescharacteristic
459C22×C4#1062535011yescharacteristic
460C22×C4#1062535011yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4#1062535011yescharacteristic
463C22×C4#1062535011yescharacteristic
464C22×C4#1062535011yescharacteristic
465C22×C4C2×C22⋊D4711yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467C22×C4C2×C22⋊D4711yescharacteristic
468M16—22no—
469M16—22no—
470M16—22no—
471M16—942no—
472M16—942no—
473M16—1881no—
474M16—1881no—
475M16—1881no—
476M16—1881no—
477M16—1881no—
478M16—1881no—
479M16(C2×D47)⋊C414yes—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—22no—
483C2×C8—21no—
484C2×C8—22no—
485C2×C8—21no—
486C2×C8—22no—
487C2×C8—22no—
488C2×C8—22no—
489C2×C8—21no—
490C2×C8—21no—
491C2×C8—942no—
492C2×C8—942no—
493C2×C8—942no—
494C2×C8—942no—
495C2×C8—1881no—
496C2×C8—1881no—
497C2×C8(C2×D47)⋊C412yes—
498C2×C8(C2×D47)⋊C412yes—
499C4⋊C4—22no—
500C4⋊C4—22no—
501C4⋊C4—1881no—
502C4⋊C4—1881no—
503C22⋊C4—22no—
504C22⋊C4—942no—
505C22⋊C4—942no—
506C22⋊C4(C2×D47)⋊C414yes—
507C42—22no—
508C42—22no—
509C42—1881no—
510C42—1881no—
511C23—42no—
512C23—942no—
513C23—942no—
514C23—942no—
515C23—1884no—
516C23C42×D4711yescharacteristic
517C23C2×(C2×D47)⋊C411yescharacteristic
518C23#1309398111yescharacteristic
519C23C4×C22⋊D4711yescharacteristic
520C23C4×C22⋊D4711yescharacteristic
521C23C4×D18811yescharacteristic
522C23C4×D18811yescharacteristic
523Q8—1881no—
524Q8—1881no—
525Q8—1881no—
526Q8—1881no—
527D4—1882no—
528D4—1882no—
529D4—1882no—
530D4—1882no—
531D4—1881no—
532D4—1881no—
533D4—1881no—
534D4—1881no—
535C2×C4—24no—
536C2×C4—44no—
537C2×C4—942no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—1884no—
541C2×C4—1882no—
542C2×C4—1882no—
543C2×C4—1882no—
544C2×C4—1882no—
545C2×C4—1882no—
546C2×C4C2×(C2×D47)⋊C411yescharacteristic
547C2×C4C2×(C2×D47)⋊C411yescharacteristic
548C2×C4#1309398111yescharacteristic
549C2×C4#1309398111yescharacteristic
550C2×C4C4×C22⋊D4711yescharacteristic
551C2×C4C4×C22⋊D4711yescharacteristic
552C2×C4C4×C22⋊D4711yescharacteristic
553C2×C4C4×C22⋊D4711yescharacteristic
554C2×C4C4×D18811yescharacteristic
555C2×C4C4×D18811yescharacteristic
556C2×C4C4×D18811yescharacteristic
557C2×C4C4×D18811yescharacteristic
558C2×C4#1309399311yescharacteristic
559C2×C4#1309399811yescharacteristic
560C2×C4#1309399811yescharacteristic
561C2×C4#1309399811yescharacteristic
562C2×C4#1309399811yescharacteristic
563C2×C4#1309399811yescharacteristic
564C2×C4#1309399811yescharacteristic
565C2×C4#1309400711yescharacteristic
566C2×C4#1309400711yescharacteristic
567C2×C4#1309400711yescharacteristic
568C2×C4#1309401211yescharacteristic
569C2×C4#1309401211yescharacteristic
570C2×C4#1309401211yescharacteristic
571C2×C4#1309401811yescharacteristic
572C2×C4#1309401811yescharacteristic
573C2×C4#1309402111yescharacteristic
574C8—22no—
575C8—22no—
576C8—24no—
577C8—1882no—
578C8—1882no—
579C22—22no—
580C22—22no—
581C22—22no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—3762no—
587C22—3762no—
588C22—1882no—
589C22—1884no—
590C22C4×(C2×D47)⋊C411yescharacteristic
591C22C4×(C2×D47)⋊C411yescharacteristic
592C22C4×(C2×D47)⋊C411yescharacteristic
593C22#1568900211yescharacteristic
594C22#1568901411yescharacteristic
595C22#1568901411yescharacteristic
596C22#1568902511yescharacteristic
597C4—44no—
598C4—3762no—
599C4—1882no—
600C4#1568900211yescharacteristic
601C4#1568900211yescharacteristic
602C4#1568901411yescharacteristic
603C4#1568901411yescharacteristic
604C4#1568901411yescharacteristic
605C4#1568901411yescharacteristic
606C4#1568902511yescharacteristic
607C4#1568902511yescharacteristic
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—21no—
614C2—3762no—
615C2#2024162611yescharacteristic
616C2#2024318912yes—
subgroupG/H
centerC2×C4C2×(C2×D47)⋊C4
commutatorC23×C47C2×C42
FrattiniC23×C4C22×D47
FittingC2×C47×#405C2
socleC22×C47C4×C22⋊C4
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenterC2×#405D47
hypocenterC47#10961
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C8 ◁ C2×#405

Complements

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

NH ≅ G/Ntype
4. C2×#15688895C2semidirect
5. C2×#15688893C2semidirect
6. #20243084C2semidirect
7. C2×C47×#405C2semidirect
14. C2×#13093942C4semidirect
15. C2×#13093940C4semidirect
22. C2×(C2×D47)⋊C8C4semidirect
303. C2×#405D47semidirect
341. C47#10961semidirect

Maximal subgroups

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

subgroupindex
C2×#156891052
C2×#156890962
C2×#156890892
C2×#156888952
C2×#156888932
#202430842
C2×C47×#4052
#1096147