Finite Group Databasebeta

← C2×#20244838 #26245196

Subgroups — C2×#20244838 #26245196

Order 12032.

906 conjugacy classes of subgroups.

The subgroup lattice has 606 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689150C211yesmaximal, characteristic, complemented
2C2×#15689119C211yesmaximal, characteristic
3C2×#15689107C211yesmaximal, characteristic
4#20244838C218yesmaximal, direct product factor
5C2×#15688894C211yesmaximal, characteristic, complemented
6C2×#15688887C211yesmaximal, characteristic, complemented
7C2×#15688879C211yesmaximal, characteristic, complemented
8C2×C47×#421C211yesmaximal, characteristic
9C22×#10625329C2211yescharacteristic
10C22×#10625329C2211yescharacteristic
11C23×C47⋊C8C2211yescharacteristic
12C2×#13093983C2211yescharacteristic
13#15689150—22no—
14#15689150C2214yescomplemented
15C2×C4⋊(C47⋊C8)—22no—
16#15689119—22no—
17#15689119C2214yes—
18C2×#13093948—21no—
19C2×#13093945—21no—
20#15689107—22no—
21#15689107C2214yes—
22C2×#13093943—21no—
23C2×#13093941—21no—
24#15688894C2214yescomplemented
25#15688887C2214yescomplemented
26#15688879C2214yescomplemented
27C22×#41×C47C2211yescharacteristic
28C22×M16×C47C2211yescharacteristic
29C2×#117×C47C2211yescharacteristic
30C47×#421—22no—
31C47×#421C2214yes—
32C2×#104×C47—22no—
33C2×#10625329—21no—
34C2×#10625329—21no—
35C2×#10625329—21no—
36C2×#10625329—21no—
37C2×#10625329—21no—
38C2×#10625329—21no—
39C2×#10625329—21no—
40C2×#10625329—21no—
41C2×#10625329—21no—
42C2×#10625329—21no—
43C2×#10625329C2312yes—
44C2×#10625329C2312yes—
45C22×C47⋊C8—21no—
46C22×C47⋊C8—21no—
47C22×C47⋊C8—21no—
48C22×C47⋊C8—21no—
49C22×C47⋊C8—21no—
50C22×C47⋊C8—21no—
51C22×C47⋊C8—21no—
52C22×C47⋊C8—21no—
53C22×C47⋊C8C2312yes—
54#13093983—21no—
55#13093983—21no—
56#13093983—21no—
57#13093983C2312yes—
58C2×C4⋊Dic47—21no—
59C2×C22⋊Dic47—21no—
60C2×C4×Dic47—21no—
61C4⋊(C47⋊C8)—28no—
62#13093948—24no—
63#13093945—24no—
64#13093943—24no—
65#13093941—24no—
66C2×#41×C47—21no—
67C2×#41×C47—21no—
68C2×#41×C47—21no—
69C2×#41×C47—21no—
70C2×#41×C47—21no—
71C2×#41×C47—21no—
72C2×#41×C47—21no—
73C2×#41×C47—21no—
74C2×#41×C47—21no—
75C2×#41×C47—21no—
76C2×#41×C47D412yes—
77C2×#41×C47C2312yes—
78C22×Q8×C47D411yescharacteristic
79C22×D4×C47—21no—
80C22×D4×C47D411yescharacteristic
81C23×C4×C47—21no—
82C23×C4×C47C2311yescharacteristic
83C2×M16×C47—21no—
84C2×M16×C47—21no—
85C2×M16×C47—21no—
86C2×M16×C47—21no—
87C2×M16×C47—21no—
88C2×M16×C47C2312yes—
89C22×C8×C47—21no—
90#117×C47—21no—
91#117×C47—21no—
92#117×C47D412yes—
93#117×C47C2312yes—
94C2×C4⋊C4×C47—21no—
95C2×C22⋊C4×C47—21no—
96C2×C42×C47D412yes—
97#104×C47—28no—
98C24×C47—21no—
99C24×C47#4111yescharacteristic
100#41×C47—22no—
101#41×C47—22no—
102#41×C47—22no—
103#41×C47—22no—
104#41×C47—22no—
105#41×C47—22no—
106#41×C47—22no—
107#41×C47—22no—
108#41×C47—41no—
109#41×C47—41no—
110#41×C47—41no—
111#41×C47—41no—
112#41×C47—41no—
113#41×C47—41no—
114#41×C47—41no—
115#41×C47—41no—
116C2×Q8×C47—21no—
117C2×Q8×C47—21no—
118C2×Q8×C47—21no—
119C2×Q8×C47—21no—
120C2×Q8×C47—21no—
121C2×Q8×C47C2×D412yes—
122C2×D4×C47—22no—
123C2×D4×C47—22no—
124C2×D4×C47—21no—
125C2×D4×C47—21no—
126C2×D4×C47—21no—
127C2×D4×C47—21no—
128C2×D4×C47—21no—
129C2×D4×C47—41no—
130C2×D4×C47—41no—
131C2×D4×C47—41no—
132C2×D4×C47—41no—
133C2×D4×C47C2×D412yes—
134C22×C4×C47—22no—
135C22×C4×C47—21no—
136C22×C4×C47—22no—
137C22×C4×C47—22no—
138C22×C4×C47—41no—
139C22×C4×C47—41no—
140C22×C4×C47—41no—
141C22×C4×C47—41no—
142C22×C4×C47C2×D411yescharacteristic
143C22×C4×C47C2×D411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×D411yescharacteristic
146C22×C4×C47#4111yescharacteristic
147C22×C4×C47#4111yescharacteristic
148C22×C4×C47#4111yescharacteristic
149C22×C4×C47#4111yescharacteristic
150C22×C4×C47#4111yescharacteristic
151C22×C4×C47#4111yescharacteristic
152C22×C4×C47#4111yescharacteristic
153C22×C4×C47#4111yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C22×C4×C47C2411yescharacteristic
156C22×Dic47—41no—
157M16×C47—22no—
158M16×C47—22no—
159M16×C47—41no—
160M16×C47—41no—
161C2×C8×C47—22no—
162C2×C8×C47—41no—
163C2×C8×C47—41no—
164C4⋊C4×C47—22no—
165C4⋊C4×C47—22no—
166C22⋊C4×C47—22no—
167C22⋊C4×C47—22no—
168C42×C47—22no—
169C42×C47C2×D414yes—
170C22⋊Dic47—22no—
171C22⋊Dic47—41no—
172C4⋊Dic47—22no—
173C4⋊Dic47—41no—
174C4×Dic47—22no—
175C4×Dic47—41no—
176#10625329—22no—
177#10625329—22no—
178#10625329—22no—
179#10625329—22no—
180#10625329—41no—
181#10625329—41no—
182#10625329—41no—
183#10625329—41no—
184C2×C47⋊C8—22no—
185C2×C47⋊C8—22no—
186C2×C47⋊C8—22no—
187C2×C47⋊C8—22no—
188C2×C47⋊C8—22no—
189C2×C47⋊C8—41no—
190C2×C47⋊C8—41no—
191C2×C47⋊C8—41no—
192C2×C47⋊C8—41no—
193C2×C47⋊C8—41no—
194C2×C47⋊C8—41no—
195C2×C47⋊C8—41no—
196C2×C47⋊C8—41no—
197C23×C47—22no—
198C23×C47—42no—
199C23×C47—41no—
200C23×C47—41no—
201C23×C47—82no—
202C23×C47#12311yescharacteristic
203C23×C47#12311yescharacteristic
204C23×C47#12311yescharacteristic
205C23×C47#12311yescharacteristic
206C23×C47#12611yescharacteristic
207C23×C47#12611yescharacteristic
208C23×C47C2×#4111yescharacteristic
209Q8×C47—22no—
210Q8×C47—22no—
211Q8×C47—41no—
212Q8×C47—41no—
213D4×C47—22no—
214D4×C47—22no—
215D4×C47—42no—
216D4×C47—42no—
217D4×C47—42no—
218D4×C47—42no—
219D4×C47—41no—
220D4×C47—41no—
221C2×C4×C47—24no—
222C2×C4×C47—22no—
223C2×C4×C47—44no—
224C2×C4×C47—41no—
225C2×C4×C47—41no—
226C2×C4×C47—42no—
227C2×C4×C47—42no—
228C2×C4×C47—42no—
229C2×C4×C47—42no—
230C2×C4×C47#12111yescharacteristic
231C2×C4×C47#12111yescharacteristic
232C2×C4×C47#12111yescharacteristic
233C2×C4×C47#12111yescharacteristic
234C2×C4×C47#12311yescharacteristic
235C2×C4×C47#12311yescharacteristic
236C2×C4×C47#12311yescharacteristic
237C2×C4×C47#12311yescharacteristic
238C2×C4×C47#12311yescharacteristic
239C2×C4×C47#12311yescharacteristic
240C2×C4×C47#12311yescharacteristic
241C2×C4×C47#12311yescharacteristic
242C2×C4×C47#12411yescharacteristic
243C2×C4×C47#12411yescharacteristic
244C2×C4×C47#12411yescharacteristic
245C2×C4×C47#12411yescharacteristic
246C2×C4×C47#12611yescharacteristic
247C2×C4×C47#12611yescharacteristic
248C2×C4×C47#12611yescharacteristic
249C2×C4×C47#12611yescharacteristic
250C2×C4×C47#12611yescharacteristic
251C2×C4×C47#12611yescharacteristic
252C2×C4×C47C22×D411yescharacteristic
253C2×C4×C47C22×D411yescharacteristic
254C2×C4×C47C2×#4111yescharacteristic
255C2×C4×C47C2×#4111yescharacteristic
256C2×C4×C47C2×#4111yescharacteristic
257C2×C4×C47C2×#4111yescharacteristic
258C2×Dic47—42no—
259C2×Dic47—82no—
260C8×C47—42no—
261C47⋊C8—42no—
262C47⋊C8—42no—
263C47⋊C8—42no—
264C2×#2080—471nomaximal, Sylow
265C22×C47—22no—
266C22×C47—22no—
267C22×C47—22no—
268C22×C47—41no—
269C22×C47—41no—
270C22×C47—41no—
271C22×C47—41no—
272C22×C47—42no—
273C22×C47—82no—
274C22×C47—82no—
275C22×C47—82no—
276C22×C47#39711yescharacteristic
277C22×C47#39711yescharacteristic
278C22×C47#39711yescharacteristic
279C22×C47#39711yescharacteristic
280C22×C47C2×#12311yescharacteristic
281C22×C47C2×#12311yescharacteristic
282C22×C47C2×#12611yescharacteristic
283C4×C47—44no—
284C4×C47—42no—
285C4×C47#39711yescharacteristic
286C4×C47#39711yescharacteristic
287C4×C47#39711yescharacteristic
288C4×C47#39711yescharacteristic
289C4×C47C2×#12111yescharacteristic
290C4×C47C2×#12311yescharacteristic
291C4×C47C2×#12411yescharacteristic
292C4×C47C2×#12611yescharacteristic
293Dic47—82no—
294C2×#424—471no—
295C2×#421D4711yescharacteristic
296C2×#416—471no—
297C2×#413—471no—
298#2080—478no—
299C2×#344—471no—
300C2×#341—471no—
301C2×H(3,ℤ/4)—471no—
302C2×C47—21no—
303C2×C47—21no—
304C2×C47—21no—
305C2×C47—21no—
306C2×C47—21no—
307C2×C47—21no—
308C2×C47—82no—
309C2×C47#208012yescomplemented
310C2×C47C2×#39711yescharacteristic
311C22×#41C2×D4711yescharacteristic
312C22×M16—471no—
313C22×M16—471no—
314C22×M16C2×D4711yescharacteristic
315C23×C8—471no—
316C2×#117—471no—
317C2×#117C2×D4711yescharacteristic
318#424—474no—
319#424—942no—
320C2×C4⋊C8—942no—
321#421—22no—
322#421C2×D4714yes—
323C2×#104—22no—
324#416—474no—
325#416—942no—
326C2×#103—941no—
327C2×#102—941no—
328#413—474no—
329#413—942no—
330C2×#101—941no—
331C2×#100—941no—
332#344—474no—
333#341—474no—
334H(3,ℤ/4)—474no—
335C47C2×#208011yescharacteristic, complemented, Sylow
336C2×#41—21no—
337C2×#41—21no—
338C2×#41—21no—
339C2×#41—21no—
340C2×#41—21no—
341C2×#41—21no—
342C2×#41—21no—
343C2×#41—21no—
344C2×#41—21no—
345C2×#41—21no—
346C2×#41D18812yes—
347C2×#41C22×D4712yes—
348C22×Q8D18811yescharacteristic
349C22×D4—21no—
350C22×D4D18811yescharacteristic
351C23×C4—21no—
352C23×C4C22×D4711yescharacteristic
353C2×M16—21no—
354C2×M16—21no—
355C2×M16—21no—
356C2×M16—21no—
357C2×M16—21no—
358C2×M16—472no—
359C2×M16—472no—
360C2×M16—941no—
361C2×M16—941no—
362C2×M16—941no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16—941no—
367C2×M16—941no—
368C2×M16—941no—
369C2×M16—941no—
370C2×M16C22×D4712yes—
371C22×C8—21no—
372C22×C8—472no—
373C22×C8—941no—
374C22×C8—941no—
375C22×C8—941no—
376C22×C8—941no—
377C22×C8—941no—
378C22×C8—941no—
379C22×C8—941no—
380C22×C8—941no—
381#117—21no—
382#117—21no—
383#117—472no—
384#117—941no—
385#117—941no—
386#117—941no—
387#117C22⋊D4712yes—
388#117C22×D4712yes—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—941no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—941no—
393C2×C42—941no—
394C2×C42C22⋊D4712yes—
395C4⋊C8—948no—
396#104—28no—
397#103—944no—
398#102—944no—
399#101—944no—
400#100—944no—
401C24—21no—
402C24#1062535211yescharacteristic
403#41—22no—
404#41—22no—
405#41—22no—
406#41—22no—
407#41—22no—
408#41—22no—
409#41—22no—
410#41—22no—
411#41—41no—
412#41—41no—
413#41—41no—
414#41—41no—
415#41—41no—
416#41—41no—
417#41—41no—
418#41—41no—
419C2×Q8—21no—
420C2×Q8—21no—
421C2×Q8—21no—
422C2×Q8—21no—
423C2×Q8—21no—
424C2×Q8C2×D18812yes—
425C2×D4—22no—
426C2×D4—22no—
427C2×D4—21no—
428C2×D4—21no—
429C2×D4—21no—
430C2×D4—21no—
431C2×D4—21no—
432C2×D4—41no—
433C2×D4—41no—
434C2×D4—41no—
435C2×D4—41no—
436C2×D4C2×D18812yes—
437C22×C4—22no—
438C22×C4—21no—
439C22×C4—22no—
440C22×C4—22no—
441C22×C4—41no—
442C22×C4—41no—
443C22×C4—41no—
444C22×C4—41no—
445C22×C4—1881no—
446C22×C4C2×D18811yescharacteristic
447C22×C4C2×D18811yescharacteristic
448C22×C4#1062535011yescharacteristic
449C22×C4#1062535011yescharacteristic
450C22×C4#1062535211yescharacteristic
451C22×C4#1062535211yescharacteristic
452C22×C4#1062535211yescharacteristic
453C22×C4#1062535211yescharacteristic
454C22×C4#1062535211yescharacteristic
455C22×C4#1062535211yescharacteristic
456C22×C4#1062535211yescharacteristic
457C22×C4C2×C22⋊D4711yescharacteristic
458C22×C4C2×C22⋊D4711yescharacteristic
459C22×C4C23×D4711yescharacteristic
460M16—22no—
461M16—22no—
462M16—41no—
463M16—41no—
464M16—942no—
465M16—942no—
466M16—942no—
467M16—942no—
468M16—1881no—
469M16—1881no—
470M16—1881no—
471M16—1881no—
472C2×C8—22no—
473C2×C8—41no—
474C2×C8—41no—
475C2×C8—942no—
476C2×C8—942no—
477C2×C8—942no—
478C2×C8—942no—
479C2×C8—942no—
480C2×C8—1881no—
481C2×C8—1881no—
482C2×C8—1881no—
483C2×C8—1881no—
484C2×C8—1881no—
485C2×C8—1881no—
486C2×C8—1881no—
487C2×C8—1881no—
488C4⋊C4—22no—
489C4⋊C4—22no—
490C4⋊C4—942no—
491C4⋊C4—1881no—
492C22⋊C4—22no—
493C22⋊C4—22no—
494C22⋊C4—942no—
495C22⋊C4—1881no—
496C42—22no—
497C42—942no—
498C42—1881no—
499C42C2×C22⋊D4714yes—
500C23—22no—
501C23—42no—
502C23—41no—
503C23—41no—
504C23—82no—
505C23#1309400511yescharacteristic
506C23#1309400511yescharacteristic
507C23#1309400811yescharacteristic
508C23#1309400811yescharacteristic
509C23#1309401711yescharacteristic
510C23#1309401711yescharacteristic
511C23C2×#1062535211yescharacteristic
512Q8—22no—
513Q8—22no—
514Q8—41no—
515Q8—41no—
516D4—22no—
517D4—22no—
518D4—42no—
519D4—42no—
520D4—42no—
521D4—42no—
522D4—41no—
523D4—41no—
524C2×C4—24no—
525C2×C4—22no—
526C2×C4—44no—
527C2×C4—41no—
528C2×C4—41no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—3762no—
534C2×C4—1882no—
535C2×C4#1309399811yescharacteristic
536C2×C4#1309399811yescharacteristic
537C2×C4#1309399811yescharacteristic
538C2×C4#1309399811yescharacteristic
539C2×C4#1309400511yescharacteristic
540C2×C4#1309400511yescharacteristic
541C2×C4#1309400811yescharacteristic
542C2×C4#1309400811yescharacteristic
543C2×C4#1309400811yescharacteristic
544C2×C4#1309400811yescharacteristic
545C2×C4#1309400811yescharacteristic
546C2×C4#1309400811yescharacteristic
547C2×C4#1309401111yescharacteristic
548C2×C4#1309401111yescharacteristic
549C2×C4#1309401111yescharacteristic
550C2×C4#1309401111yescharacteristic
551C2×C4#1309401711yescharacteristic
552C2×C4#1309401711yescharacteristic
553C2×C4#1309401711yescharacteristic
554C2×C4#1309401711yescharacteristic
555C2×C4#1309401711yescharacteristic
556C2×C4#1309401711yescharacteristic
557C2×C4C22×C22⋊D4711yescharacteristic
558C2×C4C22×D18811yescharacteristic
559C2×C4C2×#1062535211yescharacteristic
560C2×C4C2×#1062535211yescharacteristic
561C2×C4C2×#1062535211yescharacteristic
562C2×C4C2×#1062535011yescharacteristic
563C8—42no—
564C8—1882no—
565C8—1882no—
566C8—1882no—
567C22—22no—
568C22—22no—
569C22—22no—
570C22—41no—
571C22—41no—
572C22—41no—
573C22—41no—
574C22—42no—
575C22—82no—
576C22—82no—
577C22—82no—
578C22#1568904811yescharacteristic
579C22#1568904811yescharacteristic
580C22#1568904811yescharacteristic
581C22#1568904811yescharacteristic
582C22C2×#1309400511yescharacteristic
583C22C2×#1309400811yescharacteristic
584C22C2×#1309401711yescharacteristic
585C4—44no—
586C4—42no—
587C4—3762no—
588C4#1568904811yescharacteristic
589C4#1568904811yescharacteristic
590C4#1568904811yescharacteristic
591C4#1568904811yescharacteristic
592C4C2×#1309399811yescharacteristic
593C4C2×#1309400811yescharacteristic
594C4C2×#1309401111yescharacteristic
595C4C2×#1309401711yescharacteristic
596C2—21no—
597C2—21no—
598C2—21no—
599C2—21no—
600C2—21no—
601C2—21no—
602C2—82no—
603C2#2024483812yesdirect product factor
604C2C2×#1568904811yescharacteristic
subgroupG/H
centerC2×C4#13094011
commutator, cosocleC22×C4×C47C24
FrattiniC22×C4C23×D47
FittingC2×C47×#421C2
socleC22×C47#397
prime radicalC22×#41×C47C22
hypercenterC2×#421D47
hypocenterC47C2×#2080
LCSG ▷ C22×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C23×C4 ◁ C2×#421

Complements

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

NH ≅ G/Ntype
1. C2×#15689150C2semidirect
4. #20244838C2direct (N × H)
5. C2×#15688894C2semidirect
6. C2×#15688887C2semidirect
7. C2×#15688879C2semidirect
14. #15689150C22semidirect
24. #15688894C22semidirect
25. #15688887C22semidirect
26. #15688879C22semidirect
309. C2×C47#2080semidirect
335. C47C2×#2080semidirect
603. C2#20244838direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156891502
C2×#156891192
C2×#156891072
#202448382
C2×#156888942
C2×#156888872
C2×#156888792
C2×C47×#4212
C2×#208047