Finite Group Databasebeta

← C2×#20243175 #26213923

Subgroups — C2×#20243175 #26213923

Order 12032.

2242 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D47)⋊C4C211yesmaximal, characteristic
2C22×#13093938C212yesmaximal
3C2×C22⋊C4×Dic47C212yesmaximal, complemented
4#20243175C218yesmaximal, direct product factor
5C2×#15688890C211yesmaximal, characteristic, complemented
6C2×C47×#342C211yesmaximal, characteristic, complemented
7C23×C22⋊D47C2211yescharacteristic
8C24×Dic47C2211yescharacteristic
9C23×C4×D47C411yescharacteristic, complemented
10C2×(C22⋊D47)⋊C4—22no—
11C2×(C22⋊D47)⋊C4—22no—
12C2×(C22⋊D47)⋊C4—24no—
13C2×(C22⋊D47)⋊C4C414yescomplemented
14C2×(C22⋊D47)⋊C4C2214yes—
15C22×Dic47⋊C4C411yescharacteristic, complemented
16C22×C22⋊Dic47C2212yes—
17C22×(C2×D47)⋊C4C411yescharacteristic, complemented
18C22×C4×Dic47—22no—
19C22×C4×Dic47C411yescharacteristic, complemented
20C2×#13093938C4116yescomplemented
21C2×#13093938C2218yes—
22C22⋊C4×Dic47—24no—
23C22⋊C4×Dic47C2218yescomplemented
24C2×C47⋊#95—22no—
25#15688890C2214yescomplemented
26C22×C22⋊C4×C47C2211yescharacteristic
27C22×C22⋊C4×C47C2212yes—
28C47×#342C2214yescomplemented
29C24×D47C2×C411yescharacteristic
30C22×C22⋊D47—22no—
31C22×C22⋊D47—22no—
32C22×C22⋊D47—22no—
33C22×C22⋊D47—22no—
34C22×C22⋊D47C2×C418yes—
35C22×C22⋊D47C2×C412yes—
36C22×C22⋊D47C2312yes—
37C23×Dic47—22no—
38C23×Dic47—44no—
39C23×Dic47C2×C411yescharacteristic
40C23×Dic47C2×C411yescharacteristic
41C23×Dic47C2×C411yescharacteristic
42C23×Dic47C2×C412yes—
43C23×Dic47D412yes—
44C23×Dic47D412yes—
45C23×Dic47D414yes—
46C23×Dic47C2312yes—
47C22×C4×D47—21no—
48C22×C4×D47—22no—
49C22×C4×D47—21no—
50C22×C4×D47—44no—
51C22×C4×D47C2×C414yescomplemented
52(C22⋊D47)⋊C4—28no—
53(C22⋊D47)⋊C4—28no—
54(C22⋊D47)⋊C4—28no—
55(C22⋊D47)⋊C4—28no—
56C2×Dic47⋊C4—22no—
57C2×Dic47⋊C4—22no—
58C2×Dic47⋊C4C2×C414yescomplemented
59C2×C22⋊Dic47—22no—
60C2×C22⋊Dic47—24no—
61C2×C22⋊Dic47C2×C418yescomplemented
62C2×C22⋊Dic47C2314yes—
63C2×(C2×D47)⋊C4—22no—
64C2×(C2×D47)⋊C4—22no—
65C2×(C2×D47)⋊C4C2×C414yescomplemented
66C2×C4×Dic47—21no—
67C2×C4×Dic47—22no—
68C2×C4×Dic47—21no—
69C2×C4×Dic47—28no—
70C2×C4×Dic47—48no—
71C2×C4×Dic47C2×C414yescomplemented
72#13093938C2×C4132yescomplemented
73C47⋊#95—28no—
74C25×C47C2311yescharacteristic
75C23×C4×C47—22no—
76C23×C4×C47C2×C411yescharacteristic
77C23×C4×C47C2×C411yescharacteristic
78C2×C22⋊C4×C47—22no—
79C2×C22⋊C4×C47—22no—
80C2×C22⋊C4×C47—22no—
81C2×C22⋊C4×C47—24no—
82C2×C22⋊C4×C47C2×C412yes—
83C2×C22⋊C4×C47C2×C418yescomplemented
84C2×C22⋊C4×C47C2312yes—
85C2×C22⋊C4×C47C2314yes—
86C24×C47—42no—
87C24×C47—42no—
88C24×C47C22×C411yescharacteristic
89C24×C47C22×C411yescharacteristic
90C24×C47C22×C414yes—
91C24×C47C2×D412yes—
92C24×C47C2×D412yes—
93C24×C47#4112yes—
94C24×C47#4112yes—
95C24×C47C2411yescharacteristic
96C23×D47—21no—
97C23×D47—21no—
98C23×D47—22no—
99C23×D47—42no—
100C23×D47—42no—
101C23×D47C4214yescomplemented
102C23×D47C22×C412yes—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—21no—
106C22×C4×C47—21no—
107C22×C4×C47—28no—
108C22×C4×C47—24no—
109C22×C4×C47—44no—
110C22×C4×C47—44no—
111C22×C4×C47—42no—
112C22×C4×C47—42no—
113C22×C4×C47C22×C412yes—
114C22×C4×C47C22×C412yes—
115C2×C22⋊D47—24no—
116C2×C22⋊D47—24no—
117C2×C22⋊D47—28no—
118C2×C22⋊D47—28no—
119C2×C22⋊D47—28no—
120C2×C22⋊D47—28no—
121C2×C22⋊D47—24no—
122C2×C22⋊D47—22no—
123C2×C22⋊D47—22no—
124C2×C22⋊D47C4218yescomplemented
125C2×C22⋊D47C22×C418yes—
126C22×Dic47—21no—
127C22×Dic47—21no—
128C22×Dic47—22no—
129C22×Dic47—28no—
130C22×Dic47—24no—
131C22×Dic47—28no—
132C22×Dic47—24no—
133C22×Dic47—44no—
134C22×Dic47—48no—
135C22×Dic47—44no—
136C22×Dic47—42no—
137C22×Dic47—44no—
138C22×Dic47—44no—
139C22×Dic47—44no—
140C22×Dic47C4214yescomplemented
141C22×Dic47C22⋊C411yescharacteristic
142C22×Dic47C22⋊C412yes—
143C22×Dic47C22⋊C412yes—
144C22×Dic47C22⋊C414yes—
145C22×Dic47C22⋊C412yes—
146C22×Dic47C22⋊C414yes—
147C22×Dic47C22⋊C411yescharacteristic
148C22×Dic47C22×C412yes—
149C22×Dic47C22×C412yes—
150C22×Dic47C22×C412yes—
151C22×Dic47C2×D414yes—
152C22×Dic47C2×D414yes—
153C2×C4×D47—24no—
154C2×C4×D47—24no—
155C2×C4×D47—44no—
156C2×C4×D47—48no—
157C2×C4×D47—44no—
158C2×C4×D47—48no—
159C22⋊C4×C47—24no—
160C22⋊C4×C47—28no—
161C22⋊C4×C47—24no—
162C22⋊C4×C47—24no—
163C22⋊C4×C47C22×C418yescomplemented
164C22⋊Dic47—28no—
165C22⋊Dic47—24no—
166C22⋊Dic47C22×C418yescomplemented
167(C2×D47)⋊C4—28no—
168Dic47⋊C4—28no—
169C4×Dic47—24no—
170C4×Dic47—24no—
171C4×Dic47—416no—
172C23×C47—24no—
173C23×C47—22no—
174C23×C47—24no—
175C23×C47—22no—
176C23×C47—41no—
177C23×C47—42no—
178C23×C47—41no—
179C23×C47—41no—
180C23×C47—48no—
181C23×C47—42no—
182C23×C47—44no—
183C23×C47—44no—
184C23×C47—41no—
185C23×C47C2×C4212yes—
186C23×C47C2×C4212yes—
187C23×C47C2×C22⋊C412yes—
188C23×C47C2×C22⋊C411yescharacteristic
189C23×C47C2×C22⋊C411yescharacteristic
190C23×C47#11712yes—
191C23×C47#11712yes—
192C23×C47C4×D414yes—
193C23×C47C4×D414yes—
194C23×C47C4×D414yes—
195C23×C47C4×D414yes—
196C23×C47C23×C411yescharacteristic
197C23×C47C23×C412yes—
198C23×C47C22×D412yes—
199C23×C47C2×#4111yescharacteristic
200C23×C47C2×#4111yescharacteristic
201C22×D47—22no—
202C22×D47—22no—
203C22×D47—24no—
204C22×D47—24no—
205C22×D47—42no—
206C22×D47—42no—
207C22×D47—48no—
208C22×D47—42no—
209C22×D47—42no—
210C22×D47—42no—
211C22×D47—48no—
212C22×D47—42no—
213C22×D47C2×C4214yescomplemented
214C2×C4×C47—22no—
215C2×C4×C47—22no—
216C2×C4×C47—28no—
217C2×C4×C47—44no—
218C2×C4×C47—42no—
219C2×C4×C47—44no—
220C2×C4×C47—416no—
221C2×C4×C47—42no—
222C2×C4×C47—42no—
223C2×C4×C47—42no—
224C2×C4×C47—42no—
225C2×C4×C47—42no—
226C22⋊D47—28no—
227C22⋊D47—28no—
228C22⋊D47—216no—
229C2×Dic47—22no—
230C2×Dic47—22no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—22no—
234C2×Dic47—24no—
235C2×Dic47—28no—
236C2×Dic47—24no—
237C2×Dic47—24no—
238C2×Dic47—28no—
239C2×Dic47—28no—
240C2×Dic47—44no—
241C2×Dic47—42no—
242C2×Dic47—42no—
243C2×Dic47—44no—
244C2×Dic47—44no—
245C2×Dic47—44no—
246C2×Dic47—416no—
247C2×Dic47#9914yescomplemented
248C2×Dic47C2×C4214yescomplemented
249C2×Dic47C2×C22⋊C412yes—
250C2×Dic47C2×C22⋊C414yes—
251C2×Dic47C2×C22⋊C412yes—
252C4×D47—48no—
253C4×D47—48no—
254C2×C4×#99—471nomaximal, Sylow
255C22×C47—22no—
256C22×C47—21no—
257C22×C47—21no—
258C22×C47—22no—
259C22×C47—22no—
260C22×C47—21no—
261C22×C47—21no—
262C22×C47—22no—
263C22×C47—28no—
264C22×C47—28no—
265C22×C47—24no—
266C22×C47—24no—
267C22×C47—42no—
268C22×C47—42no—
269C22×C47—44no—
270C22×C47—44no—
271C22×C47—42no—
272C22×C47—41no—
273C22×C47—41no—
274C22×C47C4×C22⋊C412yes—
275C22×C47C4×C22⋊C414yes—
276C22×C47C4×C22⋊C412yes—
277C22×C47C2×#9912yes—
278C22×C47#41012yes—
279C22×C47C22×C4211yescharacteristic
280C22×C47C22×C22⋊C411yescharacteristic
281C22×C47C2×#11711yescharacteristic
282C22×C47C2×C4×D412yes—
283C22×C47C2×C4×D412yes—
284C2×D47—24no—
285C2×D47—44no—
286C2×D47—48no—
287C2×D47—42no—
288C2×D47—42no—
289C2×D47—48no—
290C2×D47—44no—
291C4×C47—48no—
292C4×C47—42no—
293C4×C47—42no—
294Dic47—22no—
295Dic47—24no—
296Dic47—24no—
297Dic47—48no—
298Dic47C2×#9914yescomplemented
299C22×C4×D4—471no—
300C22×#99—472no—
301C2×C4×C22⋊C4—472no—
302C4×#99—478no—
303C2×#342—471no—
304C2×#342D4711yescharacteristic, complemented
305C2×C47—22no—
306C2×C47—22no—
307C2×C47—21no—
308C2×C47—22no—
309C2×C47—21no—
310C2×C47—24no—
311C2×C47C4×#9914yescomplemented
312C2×C47C2×C4×C22⋊C411yescharacteristic
313C2×C47C22×#9911yescharacteristic
314C2×C47C2×#41011yescharacteristic
315D47—44no—
316C23×D4—471no—
317C24×C4—471no—
318C24×C4—471no—
319C2×C4×D4—474no—
320C2×C4×D4—474no—
321C2×C4×D4—942no—
322C2×C4×D4—942no—
323C2×C4×D4—944no—
324C22×C4⋊C4—471no—
325C22×C22⋊C4—472no—
326C22×C22⋊C4—471no—
327C22×C22⋊C4C2×D4711yescharacteristic
328C22×C22⋊C4C2×D4712yes—
329C22×C42—471no—
330C22×C42—942no—
331C2×#99—4716no—
332C2×#99—478no—
333C4×C22⋊C4—478no—
334C4×C22⋊C4—944no—
335C2×#95—942no—
336#342—474no—
337#342C2×D4714yescomplemented
338C47C2×C4×#9911yescharacteristic, complemented, Sylow
339C25—471no—
340C25C22×D4711yescharacteristic
341C22×D4—472no—
342C22×D4—478no—
343C22×D4—472no—
344C22×D4—942no—
345C22×D4—942no—
346C22×D4—942no—
347C22×D4—942no—
348C23×C4—22no—
349C23×C4—471no—
350C23×C4—471no—
351C23×C4—472no—
352C23×C4—471no—
353C23×C4—472no—
354C23×C4—472no—
355C23×C4—474no—
356C23×C4—472no—
357C23×C4—474no—
358C23×C4—942no—
359C23×C4—941no—
360C23×C4—941no—
361C23×C4—942no—
362C23×C4—1884no—
363C23×C4—1884no—
364C23×C4C4×D4711yescharacteristic
365C23×C4C4×D4711yescharacteristic
366C4×D4—948no—
367C4×D4—948no—
368C4×D4—948no—
369C4×D4—948no—
370C2×C4⋊C4—474no—
371C2×C4⋊C4—942no—
372C2×C4⋊C4—942no—
373C2×C22⋊C4—22no—
374C2×C22⋊C4—22no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—24no—
377C2×C22⋊C4—478no—
378C2×C22⋊C4—474no—
379C2×C22⋊C4—474no—
380C2×C22⋊C4—942no—
381C2×C22⋊C4—942no—
382C2×C22⋊C4—942no—
383C2×C22⋊C4—944no—
384C2×C22⋊C4C4×D4712yes—
385C2×C22⋊C4C4×D4718yescomplemented
386C2×C22⋊C4C22×D4712yes—
387C2×C22⋊C4C22×D4714yes—
388C2×C42—474no—
389C2×C42—942no—
390C2×C42—941no—
391C2×C42—941no—
392C2×C42—948no—
393C2×C42—1888no—
394#99—4732no—
395#95—948no—
396C24—42no—
397C24—42no—
398C24—474no—
399C24—472no—
400C24—941no—
401C24—941no—
402C24—942no—
403C24—1882no—
404C24—1882no—
405C24C2×C4×D4711yescharacteristic
406C24C2×C4×D4711yescharacteristic
407C24C2×C4×D4714yes—
408C24D4×D4712yes—
409C24D4×D4712yes—
410C24#1062535212yes—
411C24#1062535412yes—
412C24C23×D4711yescharacteristic
413C2×D4—478no—
414C2×D4—478no—
415C2×D4—944no—
416C2×D4—944no—
417C2×D4—948no—
418C2×D4—948no—
419C2×D4—948no—
420C2×D4—948no—
421C2×D4—944no—
422C2×D4—942no—
423C2×D4—942no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—28no—
429C22×C4—24no—
430C22×C4—44no—
431C22×C4—44no—
432C22×C4—42no—
433C22×C4—42no—
434C22×C4—471no—
435C22×C4—474no—
436C22×C4—472no—
437C22×C4—474no—
438C22×C4—471no—
439C22×C4—472no—
440C22×C4—472no—
441C22×C4—472no—
442C22×C4—474no—
443C22×C4—472no—
444C22×C4—474no—
445C22×C4—472no—
446C22×C4—474no—
447C22×C4—944no—
448C22×C4—944no—
449C22×C4—948no—
450C22×C4—944no—
451C22×C4—941no—
452C22×C4—941no—
453C22×C4—942no—
454C22×C4—948no—
455C22×C4—944no—
456C22×C4—1884no—
457C22×C4—1888no—
458C22×C4—1884no—
459C22×C4—1888no—
460C22×C4—1884no—
461C22×C4—1888no—
462C22×C4—1884no—
463C22×C4—1882no—
464C22×C4—1884no—
465C22×C4—1884no—
466C22×C4—1884no—
467C22×C4C2×C4×D4712yes—
468C22×C4C2×C4×D4712yes—
469C4⋊C4—948no—
470C22⋊C4—24no—
471C22⋊C4—28no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—478no—
475C22⋊C4—948no—
476C22⋊C4—948no—
477C22⋊C4—944no—
478C22⋊C4C2×C4×D4718yescomplemented
479C42—944no—
480C42—944no—
481C42—18816no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—42no—
492C23—44no—
493C23—44no—
494C23—41no—
495C23—474no—
496C23—944no—
497C23—944no—
498C23—942no—
499C23—942no—
500C23—1882no—
501C23—1882no—
502C23—1888no—
503C23—1882no—
504C23—1882no—
505C23—1888no—
506C23—1882no—
507C23—1882no—
508C23C42×D4712yes—
509C23C42×D4712yes—
510C23C22⋊C4×D4712yes—
511C23C22⋊C4×D4711yescharacteristic
512C23C22⋊C4×D4711yescharacteristic
513C23#1309398212yes—
514C23#1309398212yes—
515C23(C22⋊D47)⋊C414yes—
516C23(C22⋊D47)⋊C414yes—
517C23#1309398614yes—
518C23#1309398614yes—
519C23C22×C4×D4711yescharacteristic
520C23C22×C4×D4712yes—
521C23C2×D4×D4712yes—
522C23C2×#1062535211yescharacteristic
523C23C2×#1062535411yescharacteristic
524D4—9416no—
525D4—948no—
526D4—948no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—28no—
530C2×C4—44no—
531C2×C4—44no—
532C2×C4—416no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—42no—
536C2×C4—42no—
537C2×C4—42no—
538C2×C4—42no—
539C2×C4—472no—
540C2×C4—474no—
541C2×C4—474no—
542C2×C4—472no—
543C2×C4—474no—
544C2×C4—948no—
545C2×C4—948no—
546C2×C4—944no—
547C2×C4—944no—
548C2×C4—944no—
549C2×C4—944no—
550C2×C4—942no—
551C2×C4—942no—
552C2×C4—944no—
553C2×C4—942no—
554C2×C4—948no—
555C2×C4—1888no—
556C2×C4—1888no—
557C2×C4—1884no—
558C2×C4—1884no—
559C2×C4—1882no—
560C2×C4—1882no—
561C2×C4—1884no—
562C2×C4—1884no—
563C2×C4—18816no—
564C22—22no—
565C22—21no—
566C22—21no—
567C22—22no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—28no—
573C22—28no—
574C22—24no—
575C22—24no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—42no—
581C22—41no—
582C22—41no—
583C22—944no—
584C22—1884no—
585C22—1888no—
586C22—1884no—
587C22—1882no—
588C22—1882no—
589C22—1888no—
590C22#1568897012yes—
591C22#1568897014yes—
592C22#1568897012yes—
593C22#99×D4712yes—
594C22#1568909512yes—
595C22C2×C42×D4711yescharacteristic
596C22C2×C22⋊C4×D4711yescharacteristic
597C22C2×#1309398211yescharacteristic
598C22C2×(C22⋊D47)⋊C412yes—
599C22C2×#1309398612yes—
600C4—48no—
601C4—42no—
602C4—42no—
603C4—474no—
604C4—942no—
605C4—944no—
606C4—944no—
607C4—1888no—
608C2—22no—
609C2—22no—
610C2—22no—
611C2—21no—
612C2—21no—
613C2—24no—
614C2—1884no—
615C2#2024317514yesdirect product factor
616C2C2×#1568897011yescharacteristic
617C2C2×#99×D4711yescharacteristic
618C2C2×#1568909511yescharacteristic
subgroupG/H
centerC23C22⋊C4×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC2×C47×#342C2
socleC23×C47C2×C22⋊C4
prime radicalC23×C22⋊D47C22
cosocleC24×C47C24
hypercenterC2×#342D47
hypocenterC47C2×C4×#99
LCSG ▷ C22×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×C22⋊C4×Dic47C2semidirect
4. #20243175C2direct (N × H)
5. C2×#15688890C2semidirect
6. C2×C47×#342C2semidirect
9. C23×C4×D47C4semidirect
13. C2×(C22⋊D47)⋊C4C4semidirect
15. C22×Dic47⋊C4C4semidirect
17. C22×(C2×D47)⋊C4C4semidirect
19. C22×C4×Dic47C4semidirect
20. C2×#13093938C4semidirect
23. C22⋊C4×Dic47C22semidirect
25. #15688890C22semidirect
28. C47×#342C22semidirect
51. C22×C4×D47C2×C4semidirect
58. C2×Dic47⋊C4C2×C4semidirect
61. C2×C22⋊Dic47C2×C4semidirect
65. C2×(C2×D47)⋊C4C2×C4semidirect
71. C2×C4×Dic47C2×C4semidirect
72. #13093938C2×C4semidirect
83. C2×C22⋊C4×C47C2×C4semidirect
101. C23×D47C42semidirect
124. C2×C22⋊D47C42semidirect
140. C22×Dic47C42semidirect
163. C22⋊C4×C47C22×C4semidirect
166. C22⋊Dic47C22×C4semidirect
213. C22×D47C2×C42semidirect
247. C2×Dic47#99semidirect
248. C2×Dic47C2×C42semidirect
298. Dic47C2×#99semidirect
304. C2×#342D47semidirect
311. C2×C47C4×#99semidirect
337. #342C2×D47semidirect
338. C47C2×C4×#99semidirect
385. C2×C22⋊C4C4×D47semidirect
478. C22⋊C4C2×C4×D47semidirect
615. C2#20243175direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D47)⋊C42
C22×#130939382
C2×C22⋊C4×Dic472
#202431752
C2×#156888902
C2×C47×#3422
C2×C4×#9947