Finite Group Databasebeta

← #26245002

Subgroups — #26245002

Order 12032.

960 conjugacy classes of subgroups.

The subgroup lattice has 616 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689172C211yesmaximal, characteristic, complemented
2C2×#15689171C211yesmaximal, characteristic, complemented
3C2×#15689105C211yesmaximal, characteristic
4C2×#15689105C211yesmaximal, characteristic
5C2×#15689105C211yesmaximal, characteristic
6#20244788C214yesmaximal, complemented
7#20244785C214yesmaximal, complemented
8C2×C47⋊#338C211yesmaximal, characteristic, complemented
9C2×C47×#430C211yesmaximal, characteristic, complemented
10C22×#10625350C2211yescharacteristic
11C22×#10625329C2211yescharacteristic
12C22×#10625329C2211yescharacteristic
13C22×#10625329C2211yescharacteristic
14#15689172—22no—
15#15689172C2214yes—
16#15689171—22no—
17#15689171C2214yes—
18C2×#13093960—22no—
19C2×#13093959—22no—
20#15689105—22no—
21#15689105—22no—
22#15689105—22no—
23#15689105—22no—
24#15689105—22no—
25#15689105—22no—
26C2×#13093942C2212yes—
27C2×#13093942C2212yes—
28C2×#13093942C2212yes—
29C2×#13093940C2212yes—
30C2×#13093940C2212yes—
31C2×#13093940C2212yes—
32C47⋊#338C2214yes—
33C22×M16×C47C2211yescharacteristic
34C22×M16×C47C2211yescharacteristic
35C22×M16×C47C2211yescharacteristic
36C47×#430—22no—
37C47×#430C2214yes—
38C2×#108×C47—22no—
39C2×#10625350—21no—
40C2×#10625350—21no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—21no—
46C2×#10625350—21no—
47C2×#10625350—21no—
48C2×#10625350—21no—
49C2×#10625350—21no—
50C2×#10625350—21no—
51C22×Dic94C2311yescharacteristic
52C22×D188C2311yescharacteristic
53C22×C22⋊D47Q812yes—
54C22×C4×D47Q812yes—
55C2×#10625329—21no—
56C2×#10625329—21no—
57C2×#10625329—21no—
58C2×#10625329—21no—
59C2×#10625329—21no—
60C2×#10625329—21no—
61C2×#10625329—21no—
62C2×#10625329—21no—
63C2×#10625329—21no—
64C2×#10625329—21no—
65C2×#10625329—21no—
66C2×#10625329—21no—
67C2×#10625329—21no—
68C2×#10625329D412yes—
69C2×#10625329D412yes—
70C2×#10625329C2312yes—
71C2×#10625329C2312yes—
72C2×#10625329C2312yes—
73C22×C47⋊C8—21no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76#13093960—28no—
77#13093959—28no—
78#13093942—24no—
79#13093942—24no—
80#13093942—24no—
81#13093940—24no—
82#13093940—24no—
83#13093940—24no—
84C23×C4×C47C2311yescharacteristic
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47—21no—
89C2×M16×C47—21no—
90C2×M16×C47—21no—
91C2×M16×C47—21no—
92C2×M16×C47—21no—
93C2×M16×C47—21no—
94C2×M16×C47—21no—
95C2×M16×C47—21no—
96C2×M16×C47D412yes—
97C2×M16×C47D412yes—
98C2×M16×C47D412yes—
99C2×M16×C47D412yes—
100C2×M16×C47C2312yes—
101C2×M16×C47C2312yes—
102C2×M16×C47C2312yes—
103C22×C8×C47—21no—
104C22×C8×C47—21no—
105C22×C8×C47—21no—
106#108×C47—28no—
107C24×C47C2×Q811yescharacteristic
108C23×D47C2×Q812yes—
109C22×C4×C47C2×D411yescharacteristic
110C22×C4×C47C2×D411yescharacteristic
111C22×C4×C47C2×D411yescharacteristic
112C22×C4×C47C2×D411yescharacteristic
113C22×C4×C47C2×D411yescharacteristic
114C22×C4×C47C2×D411yescharacteristic
115C22×C4×C47C2×Q811yescharacteristic
116C22×C4×C47#4111yescharacteristic
117C22×C4×C47#4111yescharacteristic
118C22×C4×C47#4111yescharacteristic
119C22×C4×C47#4111yescharacteristic
120C22×C4×C47#4111yescharacteristic
121C22×C4×C47#4111yescharacteristic
122C22×C4×C47C2411yescharacteristic
123C2×C22⋊D47—22no—
124C2×C22⋊D47—22no—
125C2×C22⋊D47—22no—
126C2×C22⋊D47—22no—
127C2×C22⋊D47—22no—
128C2×C22⋊D47—22no—
129C22×Dic47C2×Q812yes—
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—
141#10625350—41no—
142#10625350—41no—
143#10625350—41no—
144#10625350—41no—
145#10625350—41no—
146C2×D188—21no—
147C2×D188—21no—
148C2×D188—21no—
149C2×D188—21no—
150C2×D188—21no—
151C2×D188—21no—
152C2×C4×D47—22no—
153C2×C4×D47—22no—
154C2×C4×D47—22no—
155C2×C4×D47—22no—
156C2×C4×D47—22no—
157C2×C4×D47—22no—
158C2×Dic94—21no—
159C2×Dic94—21no—
160C2×Dic94—21no—
161C2×Dic94—21no—
162C2×Dic94—21no—
163C2×Dic94—21no—
164M16×C47—22no—
165M16×C47—22no—
166M16×C47—22no—
167M16×C47—22no—
168M16×C47—22no—
169M16×C47—22no—
170M16×C47—22no—
171M16×C47—22no—
172M16×C47—41no—
173M16×C47—41no—
174M16×C47C2×D414yes—
175M16×C47C2×D414yes—
176C2×C8×C47—22no—
177C2×C8×C47—22no—
178C2×C8×C47—22no—
179C2×C8×C47—22no—
180C2×C8×C47—22no—
181C2×C8×C47—22no—
182C2×C8×C47—22no—
183C2×C8×C47—41no—
184C2×C8×C47—41no—
185#10625329—22no—
186#10625329—22no—
187#10625329—22no—
188#10625329—22no—
189#10625329—22no—
190#10625329—22no—
191#10625329—22no—
192#10625329—41no—
193#10625329—41no—
194#10625329—41no—
195#10625329—41no—
196#10625329C2×D414yes—
197C2×C47⋊C8—22no—
198C2×C47⋊C8—22no—
199C2×C47⋊C8—22no—
200C2×C47⋊C8—22no—
201C2×C47⋊C8—22no—
202C2×C47⋊C8—41no—
203C2×C47⋊C8—41no—
204C2×C47⋊C8—41no—
205C2×C47⋊C8—41no—
206C23×C47—81no—
207C23×C47C22⋊Q811yescharacteristic
208C23×C47C22⋊Q811yescharacteristic
209C23×C47C22⋊Q811yescharacteristic
210C23×C47C22⋊Q811yescharacteristic
211C23×C47C22⋊Q811yescharacteristic
212C23×C47C22⋊Q811yescharacteristic
213C23×C47C22×Q811yescharacteristic
214C22×D47—22no—
215C22×D47—22no—
216C22×D47—22no—
217C22×D47—82no—
218C2×C4×C47#12111yescharacteristic
219C2×C4×C47#12111yescharacteristic
220C2×C4×C47#12111yescharacteristic
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#12111yescharacteristic
228C2×C4×C47#12111yescharacteristic
229C2×C4×C47#12111yescharacteristic
230C2×C4×C47C22⋊Q811yescharacteristic
231C2×C4×C47C22⋊Q811yescharacteristic
232C2×C4×C47C22⋊Q811yescharacteristic
233C2×C4×C47C22⋊Q811yescharacteristic
234C2×C4×C47C22⋊Q811yescharacteristic
235C2×C4×C47C22⋊Q811yescharacteristic
236C2×C4×C47#12611yescharacteristic
237C2×C4×C47#12611yescharacteristic
238C2×C4×C47#12611yescharacteristic
239C2×C4×C47#12611yescharacteristic
240C2×C4×C47C22×D411yescharacteristic
241C2×C4×C47C22×D411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C2×C4×C47C2×#4111yescharacteristic
246C22⋊D47—42no—
247C22⋊D47—42no—
248C22⋊D47—42no—
249C22⋊D47—42no—
250C2×Dic47—22no—
251C2×Dic47—22no—
252C2×Dic47—22no—
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—24no—
266C8×C47—24no—
267C8×C47—42no—
268C47⋊C8—24no—
269C47⋊C8—42no—
270C47⋊C8—42no—
271#23622—471nomaximal, Sylow
272C22×C47—41no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—41no—
279C22×C47#39611yescharacteristic
280C22×C47#39611yescharacteristic
281C22×C47#39611yescharacteristic
282C22×C47#39611yescharacteristic
283C22×C47C2×C22⋊Q811yescharacteristic
284C22×C47C2×C22⋊Q811yescharacteristic
285C22×C47C2×C22⋊Q811yescharacteristic
286C2×D47—42no—
287C2×D47—82no—
288C2×D47—82no—
289C2×D47—82no—
290C4×C47#39611yescharacteristic
291C4×C47#39611yescharacteristic
292C4×C47#39611yescharacteristic
293C4×C47#39611yescharacteristic
294C4×C47C2×#12111yescharacteristic
295C4×C47C2×#12111yescharacteristic
296C4×C47C2×#12111yescharacteristic
297C4×C47C2×#12611yescharacteristic
298Dic47—42no—
299C2×#430—471no—
300C2×#430—471no—
301C2×#430D4711yescharacteristic, complemented
302C2×#413—471no—
303C2×#413—471no—
304C2×#413—471no—
305#2070—474no—
306#2069—474no—
307C2×#338—471no—
308C2×C47—21no—
309C2×C47—21no—
310C2×C47—21no—
311C2×C47—21no—
312C2×C47—21no—
313C2×C47—21no—
314C2×C47—21no—
315C2×C47C2×#39611yescharacteristic
316D47—82no—
317C22×#41—471no—
318C22×M16—471no—
319C22×M16—471no—
320C22×M16—471no—
321C22×M16C2×D4711yescharacteristic
322C22×M16C2×D4711yescharacteristic
323C22×M16C2×D4711yescharacteristic
324#430—22no—
325#430—474no—
326#430—474no—
327#430—942no—
328#430—942no—
329#430C2×D4714yes—
330C2×#108—22no—
331C2×#108—942no—
332C2×#108—942no—
333#413—942no—
334#413—942no—
335#413—942no—
336#413—942no—
337#413—942no—
338#413—942no—
339C2×#101—472no—
340C2×#101—472no—
341C2×#101—472no—
342C2×#100—472no—
343C2×#100—472no—
344C2×#100—472no—
345#338—474no—
346C47#2362211yescharacteristic, complemented, Sylow
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—
356C2×#41—941no—
357C2×#41—941no—
358C2×#41—941no—
359C22×Q8—471no—
360C22×D4—472no—
361C22×D4—471no—
362C23×C4—472no—
363C23×C4C22×D4711yescharacteristic
364C2×M16—21no—
365C2×M16—21no—
366C2×M16—21no—
367C2×M16—21no—
368C2×M16—21no—
369C2×M16—21no—
370C2×M16—21no—
371C2×M16—21no—
372C2×M16—21no—
373C2×M16—21no—
374C2×M16—21no—
375C2×M16—472no—
376C2×M16—472no—
377C2×M16—472no—
378C2×M16—472no—
379C2×M16—472no—
380C2×M16—941no—
381C2×M16—941no—
382C2×M16—941no—
383C2×M16—941no—
384C2×M16—941no—
385C2×M16—941no—
386C2×M16—941no—
387C2×M16—941no—
388C2×M16—941no—
389C2×M16—941no—
390C2×M16—941no—
391C2×M16—941no—
392C2×M16—941no—
393C2×M16D18812yes—
394C2×M16D18812yes—
395C2×M16C22⋊D4712yes—
396C2×M16C22⋊D4712yes—
397C2×M16C22×D4712yes—
398C2×M16C22×D4712yes—
399C2×M16C22×D4712yes—
400C22×C8—21no—
401C22×C8—21no—
402C22×C8—21no—
403C22×C8—941no—
404C22×C8—941no—
405C22×C8—941no—
406#108—28no—
407#108—948no—
408#108—948no—
409#101—944no—
410#101—944no—
411#101—944no—
412#100—944no—
413#100—944no—
414#100—944no—
415C24—472no—
416C24Q8×D4711yescharacteristic
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—
427#41—1881no—
428#41—1881no—
429#41—1881no—
430#41—1881no—
431#41—1881no—
432#41—1881no—
433C2×Q8—941no—
434C2×Q8—941no—
435C2×Q8—941no—
436C2×Q8—941no—
437C2×Q8—941no—
438C2×Q8—941no—
439C2×D4—942no—
440C2×D4—942no—
441C2×D4—942no—
442C2×D4—942no—
443C2×D4—942no—
444C2×D4—942no—
445C2×D4—941no—
446C2×D4—941no—
447C2×D4—941no—
448C2×D4—941no—
449C2×D4—941no—
450C2×D4—941no—
451C22×C4—472no—
452C22×C4—942no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4C2×D18811yescharacteristic
459C22×C4C2×D18811yescharacteristic
460C22×C4#1062535011yescharacteristic
461C22×C4#1062535011yescharacteristic
462C22×C4D4×D4711yescharacteristic
463C22×C4D4×D4711yescharacteristic
464C22×C4#1062535211yescharacteristic
465C22×C4#1062535211yescharacteristic
466C22×C4Q8×D4711yescharacteristic
467C22×C4#1062535411yescharacteristic
468C22×C4#1062535411yescharacteristic
469C22×C4C2×C22⋊D4711yescharacteristic
470C22×C4C2×C22⋊D4711yescharacteristic
471C22×C4C23×D4711yescharacteristic
472M16—22no—
473M16—22no—
474M16—22no—
475M16—22no—
476M16—22no—
477M16—22no—
478M16—22no—
479M16—22no—
480M16—41no—
481M16—41no—
482M16—474no—
483M16—942no—
484M16—942no—
485M16—942no—
486M16—942no—
487M16—942no—
488M16—942no—
489M16—942no—
490M16—1881no—
491M16—1881no—
492M16—1881no—
493M16—1881no—
494M16C2×D18814yes—
495M16C2×C22⋊D4714yes—
496C2×C8—22no—
497C2×C8—22no—
498C2×C8—22no—
499C2×C8—22no—
500C2×C8—22no—
501C2×C8—22no—
502C2×C8—22no—
503C2×C8—41no—
504C2×C8—41no—
505C2×C8—942no—
506C2×C8—942no—
507C2×C8—942no—
508C2×C8—942no—
509C2×C8—942no—
510C2×C8—1881no—
511C2×C8—1881no—
512C2×C8—1881no—
513C2×C8—1881no—
514C23—81no—
515C23—942no—
516C23—942no—
517C23—942no—
518C23—3762no—
519C23#1309400011yescharacteristic
520C23#1309400011yescharacteristic
521C23#1309400211yescharacteristic
522C23#1309400211yescharacteristic
523C23#1309400411yescharacteristic
524C23#1309400411yescharacteristic
525C23C2×Q8×D4711yescharacteristic
526Q8—1881no—
527Q8—1881no—
528Q8—1881no—
529Q8—1881no—
530D4—1882no—
531D4—1882no—
532D4—1882no—
533D4—1882no—
534D4—1881no—
535D4—1881no—
536D4—1881no—
537D4—1881no—
538C2×C4—942no—
539C2×C4—942no—
540C2×C4—942no—
541C2×C4—1882no—
542C2×C4—1882no—
543C2×C4—1882no—
544C2×C4—1882no—
545C2×C4#1309399611yescharacteristic
546C2×C4#1309399611yescharacteristic
547C2×C4#1309399611yescharacteristic
548C2×C4#1309399611yescharacteristic
549C2×C4#1309399811yescharacteristic
550C2×C4#1309399811yescharacteristic
551C2×C4#1309399811yescharacteristic
552C2×C4#1309399811yescharacteristic
553C2×C4#1309399911yescharacteristic
554C2×C4#1309399911yescharacteristic
555C2×C4#1309399911yescharacteristic
556C2×C4#1309399911yescharacteristic
557C2×C4#1309400011yescharacteristic
558C2×C4#1309400011yescharacteristic
559C2×C4#1309400211yescharacteristic
560C2×C4#1309400211yescharacteristic
561C2×C4#1309400411yescharacteristic
562C2×C4#1309400411yescharacteristic
563C2×C4#1309401911yescharacteristic
564C2×C4#1309401911yescharacteristic
565C2×C4#1309401911yescharacteristic
566C2×C4#1309401911yescharacteristic
567C2×C4C2×D4×D4711yescharacteristic
568C2×C4C22×C22⋊D4711yescharacteristic
569C2×C4C22×D18811yescharacteristic
570C2×C4C2×#1062535211yescharacteristic
571C2×C4C2×#1062535011yescharacteristic
572C2×C4C2×#1062535411yescharacteristic
573C8—24no—
574C8—24no—
575C8—42no—
576C8—944no—
577C8—1882no—
578C8—1882no—
579C22—41no—
580C22—41no—
581C22—41no—
582C22—41no—
583C22—41no—
584C22—41no—
585C22—41no—
586C22—3762no—
587C22—3762no—
588C22—3762no—
589C22—1882no—
590C22#1568904511yescharacteristic
591C22#1568904511yescharacteristic
592C22#1568904511yescharacteristic
593C22#1568904511yescharacteristic
594C22C2×#1309400011yescharacteristic
595C22C2×#1309400211yescharacteristic
596C22C2×#1309400411yescharacteristic
597C4—1882no—
598C4#1568904511yescharacteristic
599C4#1568904511yescharacteristic
600C4#1568904511yescharacteristic
601C4#1568904511yescharacteristic
602C4C2×#1309399611yescharacteristic
603C4C2×#1309399811yescharacteristic
604C4C2×#1309399911yescharacteristic
605C4C2×#1309401911yescharacteristic
606C2—21no—
607C2—21no—
608C2—21no—
609C2—21no—
610C2—21no—
611C2—21no—
612C2—21no—
613C2—3762no—
614C2C2×#1568904511yescharacteristic
subgroupG/H
centerC4#15689045
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#430C2
socleC2×C47C2×#396
prime radicalC22×#10625350C22
hypercenterC2×#430D47
hypocenterC47#23622
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C4 ◁ C23×C4 ◁ C2×#430

Complements

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

NH ≅ G/Ntype
1. C2×#15689172C2semidirect
2. C2×#15689171C2semidirect
6. #20244788C2semidirect
7. #20244785C2semidirect
8. C2×C47⋊#338C2semidirect
9. C2×C47×#430C2semidirect
301. C2×#430D47semidirect
346. C47#23622semidirect

Maximal subgroups

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

subgroupindex
C2×#156891722
C2×#156891712
C2×#156891052
#202447882
#202447852
C2×C47⋊#3382
C2×C47×#4302
#2362247