Finite Group Databasebeta

← #26123888

Subgroups — #26123888

Order 12032.

870 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×#15689096C211yesmaximal, characteristic
2#20251832C211yesmaximal, characteristic
3#20245981C211yesmaximal, characteristic
4#20243107C211yesmaximal, characteristic, complemented
5C2×#15688880C211yesmaximal, characteristic, complemented
6C2×#15688879C211yesmaximal, characteristic, complemented
7C47×#1736C211yesmaximal, characteristic, complemented
8C22×#10625350C2211yescharacteristic
9C22×#10625329C2211yescharacteristic
10C2×#13093983C2211yescharacteristic
11C2×#13093983C2211yescharacteristic
12#15689096—22no—
13#15689096—22no—
14C2×#13093938—22no—
15#15689091—22no—
16#15689089—22no—
17#15689086—22no—
18#15689028C412yescomplemented
19#15689024C412yescomplemented
20#15689002—22no—
21#15688980—22no—
22#15688885—22no—
23#15688880—22no—
24#15688879—22no—
25C22×M16×C47C2211yescharacteristic
26C2×#117×C47C2211yescharacteristic
27C22×C4⋊C4×C47C2211yescharacteristic
28C47×#340—22no—
29C2×#10625350—21no—
30C2×#10625350—21no—
31C2×#10625350—21no—
32C2×#10625350—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—
41C22×Dic94C2×C411yescharacteristic
42C22×D188C2×C411yescharacteristic
43C22×C22⋊D47D412yes—
44C22×C4×D47D412yes—
45C2×#10625329—21no—
46C2×#10625329—21no—
47C2×#10625329—21no—
48C2×#10625329—21no—
49C2×#10625329—21no—
50C2×#10625329—21no—
51C22×C47⋊C8D412yes—
52#13093983—21no—
53#13093983—21no—
54#13093983—21no—
55#13093983—21no—
56#13093983—21no—
57#13093983—21no—
58#13093983—21no—
59#13093983D412yes—
60C2×C4⋊Dic47—21no—
61C2×C4⋊Dic47—21no—
62C2×C22⋊Dic47—21no—
63C2×C22⋊Dic47—21no—
64C2×(C2×D47)⋊C4—24no—
65C2×C4×Dic47—21no—
66C2×C4×Dic47C2×C412yes—
67#13093938—28no—
68(C2×D47)⋊C8—28no—
69C47⋊#95—24no—
70C23×C4×C47—21no—
71C23×C4×C47C2311yescharacteristic
72C2×M16×C47—21no—
73C2×M16×C47—21no—
74C2×M16×C47—21no—
75C2×M16×C47—21no—
76C2×M16×C47—21no—
77C2×M16×C47—21no—
78C22×C8×C47D412yes—
79#117×C47—21no—
80#117×C47—21no—
81#117×C47—21no—
82#117×C47D412yes—
83C2×C4⋊C4×C47—21no—
84C2×C4⋊C4×C47—21no—
85C2×C4⋊C4×C47—21no—
86C2×C4⋊C4×C47—21no—
87C2×C4⋊C4×C47—21no—
88C2×C4⋊C4×C47—21no—
89C2×C4⋊C4×C47C2×C412yes—
90C2×C22⋊C4×C47—21no—
91C2×C42×C47—21no—
92C24×C47C2×D411yescharacteristic
93C23×D47C22⋊C412yes—
94C22×C4×C47—22no—
95C22×C4×C47—41no—
96C22×C4×C47—41no—
97C22×C4×C47—41no—
98C22×C4×C47—82no—
99C22×C4×C47C22×C411yescharacteristic
100C22×C4×C47C2×D411yescharacteristic
101C22×C4×C47C2×D411yescharacteristic
102C22×C4×C47C2×D411yescharacteristic
103C22×C4×C47C2×D411yescharacteristic
104C22×C4×C47C2×D411yescharacteristic
105C22×C4×C47#4111yescharacteristic
106C22×C4×C47#4111yescharacteristic
107C22×C4×C47#4111yescharacteristic
108C22×C4×C47#4111yescharacteristic
109C22×C4×C47#4111yescharacteristic
110C22×C4×C47#4111yescharacteristic
111C22×C4×C47#4111yescharacteristic
112C22×C4×C47#4111yescharacteristic
113C2×C22⋊D47—22no—
114C2×C22⋊D47—22no—
115C2×C22⋊D47—22no—
116C2×C22⋊D47—22no—
117C2×C22⋊D47—22no—
118C2×C22⋊D47—22no—
119C22×Dic47—22no—
120C22×Dic47—41no—
121C22×Dic47C22⋊C412yes—
122#10625350—41no—
123#10625350—41no—
124#10625350—41no—
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—
138C2×D188—21no—
139C2×D188—21no—
140C2×D188—21no—
141C2×D188—21no—
142C2×D188—21no—
143C2×D188—21no—
144C2×C4×D47—22no—
145C2×C4×D47—22no—
146C2×C4×D47—22no—
147C2×C4×D47—22no—
148C2×C4×D47—22no—
149C2×C4×D47—22no—
150C2×Dic94—21no—
151C2×Dic94—21no—
152C2×Dic94—21no—
153C2×Dic94—21no—
154C2×Dic94—21no—
155C2×Dic94—21no—
156M16×C47—41no—
157M16×C47—41no—
158M16×C47—41no—
159M16×C47—41no—
160C2×C8×C47—22no—
161C2×C8×C47—22no—
162C2×C8×C47—22no—
163C4⋊C4×C47—22no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C4⋊C4×C47—41no—
167C4⋊C4×C47—41no—
168C4⋊C4×C47—41no—
169C22⋊C4×C47—22no—
170C22⋊C4×C47—41no—
171C42×C47—22no—
172C42×C47—41no—
173C22⋊Dic47—22no—
174C22⋊Dic47—41no—
175C22⋊Dic47—41no—
176C22⋊Dic47—41no—
177(C2×D47)⋊C4—84no—
178C4⋊Dic47—22no—
179C4⋊Dic47—41no—
180C4⋊Dic47—41no—
181C4⋊Dic47—41no—
182C4×Dic47—22no—
183C4×Dic47—22no—
184C4×Dic47—22no—
185C4×Dic47—41no—
186#10625329—41no—
187#10625329—41no—
188#10625329—41no—
189#10625329—41no—
190C2×C47⋊C8—22no—
191C2×C47⋊C8—22no—
192C2×C47⋊C8—22no—
193C23×C47—41no—
194C23×C47—41no—
195C23×C47C2×C22⋊C411yescharacteristic
196C23×C47#12011yescharacteristic
197C23×C47#12111yescharacteristic
198C23×C47#12111yescharacteristic
199C23×C47#12311yescharacteristic
200C23×C47#12311yescharacteristic
201C23×C47#12311yescharacteristic
202C22×D47—22no—
203C22×D47—22no—
204C22×D47—22no—
205C22×D47—42no—
206C22×D47—42no—
207C2×C4×C47—44no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—81no—
211C2×C4×C47—81no—
212C2×C4×C47—82no—
213C2×C4×C47—82no—
214C2×C4×C47#11711yescharacteristic
215C2×C4×C47#11711yescharacteristic
216C2×C4×C47C4×D411yescharacteristic
217C2×C4×C47C4×D411yescharacteristic
218C2×C4×C47C4×D411yescharacteristic
219C2×C4×C47C4×D411yescharacteristic
220C2×C4×C47#12011yescharacteristic
221C2×C4×C47#12111yescharacteristic
222C2×C4×C47#12111yescharacteristic
223C2×C4×C47#12111yescharacteristic
224C2×C4×C47#12111yescharacteristic
225C2×C4×C47#12111yescharacteristic
226C2×C4×C47#12111yescharacteristic
227C2×C4×C47#12311yescharacteristic
228C2×C4×C47#12311yescharacteristic
229C2×C4×C47#12311yescharacteristic
230C2×C4×C47#12311yescharacteristic
231C2×C4×C47#12311yescharacteristic
232C2×C4×C47#12311yescharacteristic
233C2×C4×C47#12311yescharacteristic
234C2×C4×C47#12411yescharacteristic
235C2×C4×C47#12411yescharacteristic
236C2×C4×C47#12411yescharacteristic
237C2×C4×C47#12411yescharacteristic
238C2×C4×C47#12611yescharacteristic
239C2×C4×C47#12611yescharacteristic
240C2×C4×C47#12611yescharacteristic
241C2×C4×C47#12611yescharacteristic
242C22⋊D47—42no—
243C22⋊D47—42no—
244C22⋊D47—42no—
245C22⋊D47—42no—
246C2×Dic47—22no—
247C2×Dic47—22no—
248C2×Dic47—22no—
249C2×Dic47—42no—
250C2×Dic47—42no—
251C2×Dic47—42no—
252C2×Dic47—42no—
253C2×Dic47—81no—
254C2×Dic47—81no—
255D188—41no—
256D188—41no—
257D188—41no—
258D188—41no—
259C4×D47—42no—
260C4×D47—42no—
261C4×D47—42no—
262C4×D47—42no—
263Dic94—41no—
264Dic94—41no—
265Dic94—41no—
266Dic94—41no—
267C8×C47—42no—
268C47⋊C8—42no—
269#11154—471nomaximal, Sylow
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—21no—
275C22×C47—21no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47—41no—
280C22×C47#38111yescharacteristic
281C22×C47#38611yescharacteristic
282C22×C47#38611yescharacteristic
283C22×C47#39411yescharacteristic
284C22×C47#39411yescharacteristic
285C22×C47#39711yescharacteristic
286C22×C47#39711yescharacteristic
287C2×D47—44no—
288C2×D47—42no—
289C2×D47—42no—
290C2×D47—42no—
291C2×D47—82no—
292C4×C47—82no—
293C4×C47—82no—
294C4×C47#38811yescharacteristic
295C4×C47#38811yescharacteristic
296C4×C47#38811yescharacteristic
297C4×C47#38811yescharacteristic
298C4×C47#39411yescharacteristic
299C4×C47#39411yescharacteristic
300C4×C47#39711yescharacteristic
301C4×C47#39711yescharacteristic
302Dic47—42no—
303Dic47—82no—
304Dic47—82no—
305C2×#410—471no—
306#2879—471no—
307#2311—471no—
308#1736—471no—
309#1736D4711yescharacteristic, complemented
310C2×H(3,ℤ/4)—471no—
311C2×H(3,ℤ/4)—471no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47—21no—
315C2×C47—21no—
316C2×C47—21no—
317C2×C47—21no—
318C2×C47#144011yescharacteristic
319C2×C47#190911yescharacteristic
320C2×C47#191011yescharacteristic
321D47—82no—
322C22×#41—471no—
323C22×M16—471no—
324C22×M16C2×D4711yescharacteristic
325C2×#117—471no—
326C2×#117—471no—
327C2×#117C2×D4711yescharacteristic
328C22×C4⋊C4C2×D4711yescharacteristic
329#410—942no—
330#410—942no—
331C2×#99—942no—
332#408—942no—
333#408—942no—
334#407—942no—
335#391—472no—
336#390—472no—
337#386—942no—
338#380—942no—
339#340—22no—
340#340—942no—
341H(3,ℤ/4)—942no—
342H(3,ℤ/4)—942no—
343C47#1115411yescharacteristic, complemented, Sylow
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—
354C2×#41—941no—
355C2×#41—941no—
356C22×Q8—471no—
357C22×D4—472no—
358C22×D4—471no—
359C23×C4—21no—
360C23×C4—472no—
361C23×C4C22×D4711yescharacteristic
362C2×M16—21no—
363C2×M16—21no—
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16—941no—
371C2×M16—941no—
372C2×M16—941no—
373C2×M16—941no—
374C22×C8—472no—
375C22×C8C22⋊D4712yes—
376#117—21no—
377#117—21no—
378#117—21no—
379#117—472no—
380#117—941no—
381#117—941no—
382#117—941no—
383#117—941no—
384#117—941no—
385#117—941no—
386#117—941no—
387#117D18812yes—
388C2×C4⋊C4—21no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—21no—
394C2×C4⋊C4—941no—
395C2×C4⋊C4—941no—
396C2×C4⋊C4C4×D4712yes—
397C2×C22⋊C4—21no—
398C2×C22⋊C4—941no—
399C2×C22⋊C4—944no—
400C2×C22⋊C4—941no—
401C2×C42—21no—
402C2×C42—472no—
403C2×C42—941no—
404#99—948no—
405C22⋊C8—948no—
406#95—944no—
407C24—472no—
408C24D4×D4711yescharacteristic
409#41—1881no—
410#41—1881no—
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—
425C2×Q8—941no—
426C2×Q8—941no—
427C2×Q8—941no—
428C2×Q8—941no—
429C2×Q8—941no—
430C2×Q8—941no—
431C2×D4—942no—
432C2×D4—942no—
433C2×D4—942no—
434C2×D4—942no—
435C2×D4—942no—
436C2×D4—942no—
437C2×D4—941no—
438C2×D4—941no—
439C2×D4—941no—
440C2×D4—941no—
441C2×D4—941no—
442C2×D4—941no—
443C22×C4—22no—
444C22×C4—41no—
445C22×C4—41no—
446C22×C4—41no—
447C22×C4—82no—
448C22×C4—472no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—1881no—
457C22×C4C2×C4×D4711yescharacteristic
458C22×C4C2×D18811yescharacteristic
459C22×C4#1062535011yescharacteristic
460C22×C4#1062535011yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4#1062535011yescharacteristic
463C22×C4D4×D4711yescharacteristic
464C22×C4D4×D4711yescharacteristic
465C22×C4D4×D4711yescharacteristic
466C22×C4#1062535211yescharacteristic
467C22×C4#1062535211yescharacteristic
468C22×C4#1062535411yescharacteristic
469C22×C4#1062535411yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471M16—41no—
472M16—41no—
473M16—41no—
474M16—41no—
475M16—1881no—
476M16—1881no—
477M16—1881no—
478M16—1881no—
479C2×C8—22no—
480C2×C8—22no—
481C2×C8—22no—
482C2×C8—942no—
483C2×C8—942no—
484C2×C8—942no—
485C4⋊C4—22no—
486C4⋊C4—22no—
487C4⋊C4—22no—
488C4⋊C4—41no—
489C4⋊C4—41no—
490C4⋊C4—41no—
491C4⋊C4—942no—
492C4⋊C4—1881no—
493C4⋊C4—1881no—
494C4⋊C4—1881no—
495C22⋊C4—22no—
496C22⋊C4—41no—
497C22⋊C4—942no—
498C22⋊C4—3764no—
499C22⋊C4—1881no—
500C22⋊C4—1881no—
501C22⋊C4—1881no—
502C42—22no—
503C42—41no—
504C42—942no—
505C42—942no—
506C42—942no—
507C42—1881no—
508C23—41no—
509C23—41no—
510C23—942no—
511C23—942no—
512C23—942no—
513C23—1882no—
514C23—1882no—
515C23C22⋊C4×D4711yescharacteristic
516C23#1309399411yescharacteristic
517C23#1309399511yescharacteristic
518C23#1309399711yescharacteristic
519C23#1309400611yescharacteristic
520C23#1309400911yescharacteristic
521C23#1309400911yescharacteristic
522Q8—1881no—
523Q8—1881no—
524Q8—1881no—
525Q8—1881no—
526D4—1882no—
527D4—1882no—
528D4—1882no—
529D4—1882no—
530D4—1881no—
531D4—1881no—
532D4—1881no—
533D4—1881no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—81no—
538C2×C4—81no—
539C2×C4—82no—
540C2×C4—82no—
541C2×C4—942no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—3761no—
545C2×C4—3761no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4—1882no—
552C2×C4—1882no—
553C2×C4—1882no—
554C2×C4#1309398111yescharacteristic
555C2×C4#1309398211yescharacteristic
556C2×C4(C22⋊D47)⋊C411yescharacteristic
557C2×C4C4×C22⋊D4711yescharacteristic
558C2×C4#1309398611yescharacteristic
559C2×C4C4×D18811yescharacteristic
560C2×C4#1309399211yescharacteristic
561C2×C4#1309399611yescharacteristic
562C2×C4#1309399711yescharacteristic
563C2×C4#1309399711yescharacteristic
564C2×C4#1309399811yescharacteristic
565C2×C4#1309399911yescharacteristic
566C2×C4#1309399911yescharacteristic
567C2×C4#1309400611yescharacteristic
568C2×C4#1309400611yescharacteristic
569C2×C4#1309400711yescharacteristic
570C2×C4#1309400811yescharacteristic
571C2×C4#1309400911yescharacteristic
572C2×C4#1309400911yescharacteristic
573C2×C4#1309400911yescharacteristic
574C2×C4#1309401011yescharacteristic
575C2×C4#1309401011yescharacteristic
576C2×C4#1309401211yescharacteristic
577C2×C4#1309401311yescharacteristic
578C2×C4#1309401811yescharacteristic
579C2×C4#1309401911yescharacteristic
580C2×C4#1309401911yescharacteristic
581C2×C4#1309401911yescharacteristic
582C8—42no—
583C8—1882no—
584C22—21no—
585C22—21no—
586C22—21no—
587C22—21no—
588C22—21no—
589C22—21no—
590C22—41no—
591C22—41no—
592C22—41no—
593C22—41no—
594C22—3762no—
595C22—1884no—
596C22—1882no—
597C22—1882no—
598C22—1882no—
599C22#1568898511yescharacteristic
600C22#1568899911yescharacteristic
601C22#1568900111yescharacteristic
602C22#1568903911yescharacteristic
603C22#1568904111yescharacteristic
604C22#1568904911yescharacteristic
605C22#1568905211yescharacteristic
606C4—82no—
607C4—82no—
608C4—3762no—
609C4—3762no—
610C4—1882no—
611C4#1568901211yescharacteristic
612C4#1568901311yescharacteristic
613C4#1568901411yescharacteristic
614C4#1568901511yescharacteristic
615C4#1568903811yescharacteristic
616C4#1568904011yescharacteristic
617C4#1568905011yescharacteristic
618C4#1568905211yescharacteristic
619C2—21no—
620C2—21no—
621C2—21no—
622C2—21no—
623C2—21no—
624C2—21no—
625C2—3762no—
626C2#2024163611yescharacteristic
627C2#2024390711yescharacteristic
628C2#2024391211yescharacteristic
subgroupG/H
centerC22#15688999
commutatorC22×C4×C47C22×C4
FrattiniC23×C4C22×D47
FittingC47×#1736C2
socleC22×C47#386
prime radicalC22×#10625350C22
cosocleC23×C4×C47C23
hypercenter#1736D47
hypocenterC47#11154
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1736

Complements

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

NH ≅ G/Ntype
4. #20243107C2semidirect
5. C2×#15688880C2semidirect
6. C2×#15688879C2semidirect
7. C47×#1736C2semidirect
18. #15689028C4semidirect
19. #15689024C4semidirect
309. #1736D47semidirect
343. C47#11154semidirect

Maximal subgroups

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

subgroupindex
C2×#156890962
#202518322
#202459812
#202431072
C2×#156888802
C2×#156888792
C47×#17362
#1115447