Finite Group Databasebeta

← C2×#20249129 #26382636

Subgroups — C2×#20249129 #26382636

Order 12032.

3718 conjugacy classes of subgroups.

The subgroup lattice has 600 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13094006C212yesmaximal, complemented
2C22×#13093995C211yesmaximal, characteristic
3C22×C4⋊C4×D47C211yesmaximal, characteristic, complemented
4#20249129C2116yesmaximal, direct product factor
5C2×#15689055C211yesmaximal, characteristic, complemented
6C2×#15689053C211yesmaximal, characteristic, complemented
7C2×#15689046C212yesmaximal, complemented
8C2×#15689046C212yesmaximal, complemented
9C2×#15689037C211yesmaximal, characteristic, complemented
10C2×#15688999C212yesmaximal, complemented
11C2×#15688982C211yesmaximal, characteristic, complemented
12C2×C47×#394C211yesmaximal, characteristic, complemented
13C23×C22⋊D47C2212yes—
14C23×C4×D47C2211yescharacteristic
15C23×C4×D47C2211yescharacteristic
16C23×C4×D47C2211yescharacteristic
17C2×#13094006—216no—
18C2×#13094006C22116yescomplemented
19C2×#13093995—28no—
20C2×#13093995C2218yes—
21C22×C4⋊Dic47C2211yescharacteristic
22C22×C4⋊Dic47C2212yes—
23C22×C4⋊Dic47C2211yescharacteristic
24C22×Dic47⋊C4C2211yescharacteristic
25C22×Dic47⋊C4C2211yescharacteristic
26C22×Dic47⋊C4C2212yes—
27C22×Dic47⋊C4C2212yes—
28C2×C4⋊C4×D47—28no—
29C2×C4⋊C4×D47C2218yescomplemented
30C22×C22⋊Dic47C2212yes—
31C22×C22⋊Dic47C2212yes—
32C22×C22⋊Dic47C2212yes—
33C22×(C2×D47)⋊C4C2212yes—
34#15689055C2218yescomplemented
35#15689053C2218yescomplemented
36#15689046C22116yescomplemented
37#15689046C22116yescomplemented
38#15689037C2218yescomplemented
39#15688999C22116yescomplemented
40#15688982C2218yescomplemented
41C2×C47⋊#95C2211yescharacteristic
42C2×C47⋊#95C2212yes—
43C2×C47⋊#95C2212yes—
44C23×D4×C47C2211yescharacteristic
45C22×C4⋊C4×C47C2211yescharacteristic
46C22×C22⋊C4×C47C2212yes—
47C22×C22⋊C4×C47C2212yes—
48C47×#394C2218yescomplemented
49C2×#95×C47C2211yescharacteristic
50C24×D47C2311yescharacteristic
51C22×C22⋊D47—28no—
52C22×C22⋊D47—28no—
53C22×C22⋊D47—28no—
54C22×C22⋊D47C2318yes—
55C23×Dic47C2312yes—
56C23×Dic47C2311yescharacteristic
57C23×Dic47C2312yes—
58C23×Dic47C2311yescharacteristic
59C23×Dic47C2311yescharacteristic
60C22×C4×D47—24no—
61C22×C4×D47—24no—
62C22×C4×D47—24no—
63C22×C4×D47—44no—
64C22×C4×D47—44no—
65C22×C4×D47D418yes—
66C22×C4×D47D418yescomplemented
67C22×C4×D47C2314yes—
68C22×C4×D47C2314yes—
69C22×C4×D47C2314yes—
70#13094006—264no—
71#13093995—232no—
72C2×C4⋊Dic47—24no—
73C2×C4⋊Dic47—24no—
74C2×C4⋊Dic47—28no—
75C2×C4⋊Dic47C2314yes—
76C2×C4⋊Dic47C2318yes—
77C2×C4⋊Dic47C2314yes—
78C2×Dic47⋊C4—24no—
79C2×Dic47⋊C4—28no—
80C2×Dic47⋊C4—24no—
81C2×Dic47⋊C4—44no—
82C2×Dic47⋊C4C2314yes—
83C2×Dic47⋊C4C2314yes—
84C2×Dic47⋊C4C2318yes—
85C2×Dic47⋊C4C2318yes—
86C4⋊C4×D47—232no—
87C2×C22⋊Dic47—28no—
88C2×C22⋊Dic47—28no—
89C2×C22⋊Dic47—44no—
90C2×C22⋊Dic47C2318yes—
91C2×C22⋊Dic47C2318yes—
92C2×C22⋊Dic47C2318yes—
93C2×(C2×D47)⋊C4—28no—
94C2×(C2×D47)⋊C4C2318yes—
95C47⋊#95C2314yes—
96C47⋊#95C2318yes—
97C47⋊#95C2318yes—
98C25×C47C2312yes—
99C22×D4×C47—24no—
100C22×D4×C47—44no—
101C22×D4×C47C2314yes—
102C23×C4×C47C2311yescharacteristic
103C23×C4×C47C2312yes—
104C23×C4×C47C2311yescharacteristic
105C23×C4×C47C2311yescharacteristic
106C2×C4⋊C4×C47—24no—
107C2×C4⋊C4×C47C2314yes—
108C2×C22⋊C4×C47—28no—
109C2×C22⋊C4×C47—44no—
110C2×C22⋊C4×C47C2318yes—
111C2×C22⋊C4×C47C2318yes—
112#95×C47C2314yes—
113C24×C47—24no—
114C24×C47—24no—
115C24×C47—24no—
116C24×C47—24no—
117C24×C47—24no—
118C24×C47—24no—
119C24×C47—24no—
120C24×C47C2414yes—
121C24×C47C2411yescharacteristic
122C23×D47—24no—
123C23×D47—24no—
124C23×D47C2×D414yes—
125C23×D47C2×D414yes—
126C23×D47#4114yes—
127C23×D47C2412yes—
128C2×D4×C47—28no—
129C2×D4×C47—48no—
130C2×D4×C47—416no—
131C22×C4×C47—22no—
132C22×C4×C47—22no—
133C22×C4×C47—24no—
134C22×C4×C47—24no—
135C22×C4×C47—22no—
136C22×C4×C47—24no—
137C22×C4×C47—24no—
138C22×C4×C47—24no—
139C22×C4×C47C2×D414yes—
140C22×C4×C47C2×D414yes—
141C22×C4×C47C2412yes—
142C22×C4×C47C2414yes—
143C22×C4×C47C2412yes—
144C22×C4×C47C2412yes—
145C2×C22⋊D47—216no—
146C2×C22⋊D47—216no—
147C2×C22⋊D47—216no—
148C2×C22⋊D47—432no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—24no—
152C22×Dic47—24no—
153C22×Dic47—24no—
154C22×Dic47—22no—
155C22×Dic47—24no—
156C22×Dic47—24no—
157C22×Dic47—24no—
158C22×Dic47—24no—
159C22×Dic47—24no—
160C22×Dic47C2×D414yes—
161C22×Dic47C2×D414yes—
162C22×Dic47C2414yes—
163C22×Dic47C2412yes—
164C22×Dic47C2414yes—
165C22×Dic47C2412yes—
166C22×Dic47C2412yes—
167C2×C4×D47—232no—
168C2×C4×D47—28no—
169C2×C4×D47—28no—
170C2×C4×D47—28no—
171C2×C4×D47—416no—
172C2×C4×D47—48no—
173C2×C4×D47—48no—
174C2×C4×D47—416no—
175C2×C4×D47C2×D4116yes—
176C2×C4×D47C2×D4116yescomplemented
177C4⋊C4×C47—28no—
178C22⋊C4×C47—216no—
179C22⋊C4×C47—48no—
180C22⋊Dic47—216no—
181C22⋊Dic47—216no—
182C22⋊Dic47—48no—
183(C2×D47)⋊C4—216no—
184C4⋊Dic47—28no—
185C4⋊Dic47—28no—
186C4⋊Dic47—216no—
187Dic47⋊C4—28no—
188Dic47⋊C4—216no—
189Dic47⋊C4—28no—
190Dic47⋊C4—48no—
191C23×C47—24no—
192C23×C47—24no—
193C23×C47—24no—
194C23×C47—24no—
195C23×C47—24no—
196C23×C47—24no—
197C23×C47—24no—
198C23×C47—48no—
199C23×C47—48no—
200C23×C47—48no—
201C23×C47—48no—
202C23×C47—48no—
203C23×C47—48no—
204C23×C47—48no—
205C23×C47C22×D412yes—
206C23×C47C22×D412yes—
207C23×C47C2×#4112yes—
208C23×C47H(5,𝔽2)14yes—
209C23×C472−1+414yes—
210C23×C47C2511yescharacteristic
211C22×D47—28no—
212C22×D47—28no—
213C22×D47—216no—
214C22×D47—216no—
215C22×D47—24no—
216C22×D47—24no—
217C22×D47#121116yes—
218C22×D47C22×D414yes—
219C22×D47C22×D414yes—
220C22×D47C2×#4114yes—
221D4×C47—416no—
222C2×C4×C47—28no—
223C2×C4×C47—28no—
224C2×C4×C47—22no—
225C2×C4×C47—22no—
226C2×C4×C47—24no—
227C2×C4×C47—22no—
228C2×C4×C47—24no—
229C2×C4×C47—24no—
230C2×C4×C47—24no—
231C2×C4×C47—24no—
232C2×C4×C47—44no—
233C2×C4×C47—48no—
234C2×C4×C47C22×D414yes—
235C2×C4×C47C22×D414yes—
236C22⋊D47—432no—
237C2×Dic47—28no—
238C2×Dic47—28no—
239C2×Dic47—22no—
240C2×Dic47—22no—
241C2×Dic47—24no—
242C2×Dic47—22no—
243C2×Dic47—24no—
244C2×Dic47—24no—
245C2×Dic47—24no—
246C2×Dic47—24no—
247C2×Dic47—24no—
248C2×Dic47—24no—
249C2×Dic47—24no—
250C2×Dic47—48no—
251C2×Dic47—44no—
252C2×Dic47—48no—
253C2×Dic47C22×D414yes—
254C2×Dic47C22×D414yes—
255C4×D47—232no—
256C4×D47—416no—
257C4×D47—416no—
258C2×#2618—471nomaximal, Sylow
259C22×C47—44no—
260C22×C47—44no—
261C22×C47—44no—
262C22×C47—44no—
263C22×C47—44no—
264C22×C47—44no—
265C22×C47—44no—
266C22×C47—816no—
267C22×C47C2×#12114yes—
268C22×C47#53414yes—
269C22×C47#53614yes—
270C22×C47#53718yes—
271C22×C47#53918yes—
272C22×C47C23×D411yescharacteristic
273C22×C47C23×D411yescharacteristic
274C22×C47C22×#4111yescharacteristic
275C22×C47C2×H(5,𝔽2)12yes—
276C22×C47C2×2−1+412yes—
277C2×D47—232no—
278C2×D47—24no—
279C2×D47—24no—
280C2×D47—28no—
281C2×D47—28no—
282C2×D47C2×#12118yes—
283C4×C47—24no—
284C4×C47—24no—
285C4×C47—42no—
286C4×C47—44no—
287Dic47—24no—
288Dic47—24no—
289Dic47—44no—
290Dic47—42no—
291Dic47—44no—
292C22×#123—472no—
293C22×#121—471no—
294C23×C4⋊C4—471no—
295#2618—4716no—
296C2×#398—471no—
297C2×#398—471no—
298C2×#396—472no—
299C2×#396—472no—
300C2×#394—471no—
301C2×#394D4711yescharacteristic, complemented
302C2×#386—472no—
303C2×#380—471no—
304C2×C47—84no—
305C2×C47#261818yescomplemented
306C2×C47C22×#12111yescharacteristic
307C2×C47C2×#53411yescharacteristic
308C2×C47C2×#53611yescharacteristic
309C2×C47C2×#53712yes—
310C2×C47C2×#53912yes—
311D47—28no—
312C23×D4—472no—
313C23×D4C2×D4711yescharacteristic
314C24×C4—471no—
315C24×C4—471no—
316C24×C4—471no—
317C2×#123—4716no—
318C2×#123—9416no—
319C2×#121—478no—
320C2×#121—948no—
321C22×C4⋊C4—471no—
322C22×C4⋊C4—471no—
323C22×C4⋊C4—471no—
324C22×C4⋊C4—472no—
325C22×C4⋊C4—472no—
326C22×C4⋊C4—471no—
327C22×C4⋊C4—472no—
328C22×C4⋊C4—478no—
329C22×C4⋊C4—948no—
330C22×C4⋊C4C2×D4711yescharacteristic
331C22×C22⋊C4—472no—
332C22×C22⋊C4—472no—
333C22×C22⋊C4—472no—
334C22×C22⋊C4—472no—
335C22×C22⋊C4C2×D4712yes—
336C22×C22⋊C4C2×D4712yes—
337#398—478no—
338#398—478no—
339#396—4716no—
340#396—4716no—
341#394—478no—
342#394C2×D4718yescomplemented
343#386—4716no—
344#380—478no—
345C2×#95—471no—
346C2×#95—472no—
347C2×#95—472no—
348C2×#95C2×D4711yescharacteristic
349C47C2×#261811yescharacteristic, complemented, Sylow
350C25—471no—
351C25C22×D4712yes—
352C22×D4—24no—
353C22×D4—44no—
354C22×D4—478no—
355C22×D4—948no—
356C22×D4—948no—
357C22×D4—948no—
358C22×D4C22×D4714yes—
359C23×C4—471no—
360C23×C4—471no—
361C23×C4—478no—
362C23×C4—474no—
363C23×C4—478no—
364C23×C4—474no—
365C23×C4—472no—
366C23×C4—471no—
367C23×C4—472no—
368C23×C4—474no—
369C23×C4—944no—
370C23×C4—944no—
371C23×C4—944no—
372C23×C4—1884no—
373C23×C4—1884no—
374C23×C4C22×D4712yes—
375C23×C4C22×D4711yescharacteristic
376C23×C4C22×D4711yescharacteristic
377C23×C4C22×D4711yescharacteristic
378#123—9464no—
379#121—9432no—
380C2×C4⋊C4—24no—
381C2×C4⋊C4—474no—
382C2×C4⋊C4—474no—
383C2×C4⋊C4—474no—
384C2×C4⋊C4—474no—
385C2×C4⋊C4—478no—
386C2×C4⋊C4—478no—
387C2×C4⋊C4—478no—
388C2×C4⋊C4—9432no—
389C2×C4⋊C4—944no—
390C2×C4⋊C4—944no—
391C2×C4⋊C4—948no—
392C2×C4⋊C4—944no—
393C2×C4⋊C4—944no—
394C2×C4⋊C4—948no—
395C2×C4⋊C4—1884no—
396C2×C4⋊C4C22×D4714yes—
397C2×C22⋊C4—28no—
398C2×C22⋊C4—44no—
399C2×C22⋊C4—478no—
400C2×C22⋊C4—478no—
401C2×C22⋊C4—478no—
402C2×C22⋊C4—478no—
403C2×C22⋊C4—948no—
404C2×C22⋊C4—948no—
405C2×C22⋊C4—948no—
406C2×C22⋊C4—1884no—
407C2×C22⋊C4C22×D4718yes—
408C2×C22⋊C4C22×D4718yes—
409#95—474no—
410#95—478no—
411#95—478no—
412#95C22×D4714yes—
413C24—24no—
414C24—24no—
415C24—24no—
416C24—24no—
417C24—24no—
418C24—24no—
419C24—24no—
420C24—474no—
421C24—474no—
422C24—474no—
423C24—472no—
424C24—944no—
425C24—944no—
426C24C23×D4714yes—
427C24C23×D4711yescharacteristic
428C2×D4—28no—
429C2×D4—48no—
430C2×D4—416no—
431C2×D4—9416no—
432C2×D4—9416no—
433C2×D4—9416no—
434C2×D4—18832no—
435C22×C4—22no—
436C22×C4—22no—
437C22×C4—24no—
438C22×C4—24no—
439C22×C4—22no—
440C22×C4—24no—
441C22×C4—24no—
442C22×C4—24no—
443C22×C4—474no—
444C22×C4—474no—
445C22×C4—472no—
446C22×C4—472no—
447C22×C4—4716no—
448C22×C4—4716no—
449C22×C4—474no—
450C22×C4—472no—
451C22×C4—474no—
452C22×C4—948no—
453C22×C4—9432no—
454C22×C4—948no—
455C22×C4—948no—
456C22×C4—942no—
457C22×C4—942no—
458C22×C4—944no—
459C22×C4—944no—
460C22×C4—944no—
461C22×C4—942no—
462C22×C4—944no—
463C22×C4—944no—
464C22×C4—944no—
465C22×C4—944no—
466C22×C4—944no—
467C22×C4—18816no—
468C22×C4—1888no—
469C22×C4—1888no—
470C22×C4—18816no—
471C22×C4D4×D4714yes—
472C22×C4D4×D4714yes—
473C22×C4C23×D4712yes—
474C22×C4C23×D4714yes—
475C22×C4C23×D4712yes—
476C22×C4C23×D4712yes—
477C4⋊C4—28no—
478C4⋊C4—948no—
479C4⋊C4—948no—
480C4⋊C4—9416no—
481C4⋊C4—948no—
482C4⋊C4—9416no—
483C4⋊C4—948no—
484C4⋊C4—1888no—
485C22⋊C4—216no—
486C22⋊C4—48no—
487C22⋊C4—9416no—
488C22⋊C4—9416no—
489C22⋊C4—9416no—
490C22⋊C4—1888no—
491C23—24no—
492C23—24no—
493C23—24no—
494C23—24no—
495C23—24no—
496C23—24no—
497C23—24no—
498C23—48no—
499C23—48no—
500C23—48no—
501C23—48no—
502C23—48no—
503C23—48no—
504C23—48no—
505C23—4716no—
506C23—474no—
507C23—474no—
508C23—474no—
509C23—948no—
510C23—948no—
511C23—944no—
512C23—944no—
513C23—9416no—
514C23—9416no—
515C23C2×D4×D4712yes—
516C23C2×D4×D4712yes—
517C23#41×D4712yes—
518C23#1309406914yes—
519C23#1309407114yes—
520C23C24×D4711yescharacteristic
521D4—416no—
522D4—18832no—
523C2×C4—28no—
524C2×C4—28no—
525C2×C4—22no—
526C2×C4—22no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—22no—
530C2×C4—24no—
531C2×C4—24no—
532C2×C4—24no—
533C2×C4—44no—
534C2×C4—48no—
535C2×C4—474no—
536C2×C4—474no—
537C2×C4—9432no—
538C2×C4—948no—
539C2×C4—948no—
540C2×C4—942no—
541C2×C4—942no—
542C2×C4—944no—
543C2×C4—944no—
544C2×C4—944no—
545C2×C4—942no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—944no—
551C2×C4—18816no—
552C2×C4—18816no—
553C2×C4—1888no—
554C2×C4—1884no—
555C2×C4—1888no—
556C2×C4C2×D4×D4714yes—
557C2×C4C2×D4×D4714yes—
558C22—44no—
559C22—44no—
560C22—44no—
561C22—44no—
562C22—44no—
563C22—44no—
564C22—44no—
565C22—816no—
566C22—478no—
567C22—9432no—
568C22—944no—
569C22—944no—
570C22—948no—
571C22—948no—
572C22#121×D4714yes—
573C22#1568968314yes—
574C22#1568969314yes—
575C22#1568970218yes—
576C22#1568971618yes—
577C22C22×D4×D4711yescharacteristic
578C22C22×D4×D4711yescharacteristic
579C22C2×#41×D4711yescharacteristic
580C22C2×#1309406912yes—
581C22C2×#1309407112yes—
582C4—24no—
583C4—24no—
584C4—42no—
585C4—44no—
586C4—944no—
587C4—944no—
588C4—1884no—
589C4—1882no—
590C4—1884no—
591C2—84no—
592C2—948no—
593C2#2024912918yesdirect product factor
594C2C2×#121×D4711yescharacteristic
595C2C2×#1568968311yescharacteristic
596C2C2×#1568969311yescharacteristic
597C2C2×#1568970212yes—
598C2C2×#1568971612yes—
subgroupG/H
centerC24C23×D47
commutator, cosocleC23×C47C25
FrattiniC23C24×D47
FittingC2×C47×#394C2
socleC24×C47C24
prime radicalC22×#13093995C2
hypercenterC2×#394D47
hypocenterC47C2×#2618
LCSG ▷ C23×C47 ▷ C47
UCSC1 ◁ C24 ◁ C2×#394

Complements

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

NH ≅ G/Ntype
1. C22×#13094006C2semidirect
3. C22×C4⋊C4×D47C2semidirect
4. #20249129C2direct (N × H)
5. C2×#15689055C2semidirect
6. C2×#15689053C2semidirect
7. C2×#15689046C2semidirect
8. C2×#15689046C2semidirect
9. C2×#15689037C2semidirect
10. C2×#15688999C2semidirect
11. C2×#15688982C2semidirect
12. C2×C47×#394C2semidirect
18. C2×#13094006C22semidirect
29. C2×C4⋊C4×D47C22semidirect
34. #15689055C22semidirect
35. #15689053C22semidirect
36. #15689046C22semidirect
37. #15689046C22semidirect
38. #15689037C22semidirect
39. #15688999C22semidirect
40. #15688982C22semidirect
48. C47×#394C22semidirect
66. C22×C4×D47D4semidirect
176. C2×C4×D47C2×D4semidirect
301. C2×#394D47semidirect
305. C2×C47#2618semidirect
342. #394C2×D47semidirect
349. C47C2×#2618semidirect
593. C2#20249129direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130940062
C22×#130939952
C22×C4⋊C4×D472
#202491292
C2×#156890552
C2×#156890532
C2×#156890462
C2×#156890372
C2×#156889992
C2×#156889822
C2×C47×#3942
C2×#261847