Finite Group Databasebeta

← C4×#15689020 #26137472

Subgroups — C4×#15689020 #26137472

Order 12032.

1918 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×#15689020C212yesmaximal
2C2×C4×Dic47⋊C4C211yesmaximal, characteristic
3C2×C4×Dic47⋊C4C211yesmaximal, characteristic
4C2×C4×Dic47⋊C4C211yesmaximal, characteristic
5C2×C4×C4⋊Dic47C211yesmaximal, characteristic
6C2×C42×Dic47C211yesmaximal, characteristic
7#20241622C212yesmaximal
8#20241619C212yesmaximal
9Dic47⋊#95C212yesmaximal
10C4×C47⋊#95C211yesmaximal, characteristic
11C4×#95×C47C211yesmaximal, characteristic
12C22×C4⋊Dic47C2212yes—
13C22×Dic47⋊C4C2212yes—
14C22×Dic47⋊C4C2212yes—
15C22×Dic47⋊C4C2211yescharacteristic
16C22×Dic47⋊C4C2211yescharacteristic
17C22×C4×Dic47C2211yescharacteristic
18C22×C4×Dic47C2212yes—
19C22×C4×Dic47C2212yes—
20C22×C4×Dic47C2211yescharacteristic
21C22×C4×Dic47C2211yescharacteristic
22C22×C4×Dic47C2211yescharacteristic
23#15689020C4116yesdirect product factor
24C4×Dic47⋊C4—24no—
25C4×Dic47⋊C4—24no—
26C4×Dic47⋊C4C418yescomplemented
27C4×C4⋊Dic47—24no—
28C2×C47⋊#95C2212yes—
29C2×C47⋊#95C2212yes—
30C2×C47⋊#95C2212yes—
31C2×C47⋊#95C2212yes—
32C2×C47⋊#95C2212yes—
33C2×C47⋊#95C2211yescharacteristic
34C2×C47⋊#95C2211yescharacteristic
35C42×Dic47—24no—
36C22×C42×C47C2211yescharacteristic
37C22×C42×C47C2211yescharacteristic
38C22×C42×C47C2211yescharacteristic
39C2×#95×C47C2212yes—
40C2×#95×C47C2212yes—
41C23×Dic47C2311yescharacteristic
42C23×Dic47C2312yes—
43C23×Dic47C2311yescharacteristic
44C23×Dic47C2311yescharacteristic
45C23×Dic47C2312yes—
46C23×Dic47C2311yescharacteristic
47C2×C4⋊Dic47—24no—
48C2×C4⋊Dic47—24no—
49C2×C4⋊Dic47C2×C418yes—
50C2×Dic47⋊C4—24no—
51C2×Dic47⋊C4—24no—
52C2×Dic47⋊C4—24no—
53C2×Dic47⋊C4—24no—
54C2×Dic47⋊C4—24no—
55C2×Dic47⋊C4C2×C414yes—
56C2×Dic47⋊C4C2×C418yes—
57C2×Dic47⋊C4C2×C418yes—
58C2×Dic47⋊C4C2×C414yes—
59C2×Dic47⋊C4C2×C418yes—
60C2×C4×Dic47—22no—
61C2×C4×Dic47—22no—
62C2×C4×Dic47—24no—
63C2×C4×Dic47—22no—
64C2×C4×Dic47—22no—
65C2×C4×Dic47—24no—
66C2×C4×Dic47—24no—
67C2×C4×Dic47—24no—
68C2×C4×Dic47—24no—
69C2×C4×Dic47—22no—
70C2×C4×Dic47—22no—
71C2×C4×Dic47—22no—
72C2×C4×Dic47C2×C414yes—
73C2×C4×Dic47C2×C418yes—
74C2×C4×Dic47C2×C414yes—
75C2×C4×Dic47D414yes—
76C2×C4×Dic47D414yes—
77C2×C4×Dic47Q814yes—
78C47⋊#95—24no—
79C47⋊#95—24no—
80C47⋊#95—24no—
81C47⋊#95—24no—
82C47⋊#95C2×C414yes—
83C47⋊#95C2×C414yes—
84C47⋊#95C2×C418yes—
85C23×C4×C47C2311yescharacteristic
86C23×C4×C47C2312yes—
87C23×C4×C47C2311yescharacteristic
88C23×C4×C47C2312yes—
89C23×C4×C47C2311yescharacteristic
90C2×C42×C47—22no—
91C2×C42×C47—22no—
92C2×C42×C47—22no—
93C2×C42×C47—22no—
94C2×C42×C47—22no—
95C2×C42×C47—22no—
96C2×C42×C47—22no—
97C2×C42×C47C2×C414yes—
98C2×C42×C47Q814yes—
99#95×C47—24no—
100#95×C47C2×C418yes—
101C24×C47C2411yescharacteristic
102C22×C4×C47—22no—
103C22×C4×C47—21no—
104C22×C4×C47—21no—
105C22×C4×C47—22no—
106C22×C4×C47—22no—
107C22×C4×C47—22no—
108C22×C4×C47—22no—
109C22×C4×C47—21no—
110C22×C4×C47—22no—
111C22×C4×C47—22no—
112C22×C4×C47—21no—
113C22×C4×C47—22no—
114C22×C4×C47—22no—
115C22×C4×C47—22no—
116C22×C4×C47—22no—
117C22×C4×C47—22no—
118C22×C4×C47—22no—
119C22×C4×C47C22×C412yes—
120C22×C4×C47C22×C414yes—
121C22×C4×C47C22×C412yes—
122C22×C4×C47C22×C414yes—
123C22×C4×C47C22×C414yes—
124C22×C4×C47C22×C412yes—
125C22×C4×C47C2×D412yes—
126C22×C4×C47C2×D412yes—
127C22×C4×C47C2×Q814yes—
128C22×C4×C47C2×Q812yes—
129C22×C4×C47C2×Q812yes—
130C22×C4×C47#4114yes—
131C22×C4×C47#4112yes—
132C22×C4×C47#4112yes—
133C22×Dic47—22no—
134C22×Dic47—21no—
135C22×Dic47—21no—
136C22×Dic47—22no—
137C22×Dic47—22no—
138C22×Dic47—22no—
139C22×Dic47—22no—
140C22×Dic47—22no—
141C22×Dic47—22no—
142C22×Dic47—21no—
143C22×Dic47—22no—
144C22×Dic47—22no—
145C22×Dic47—22no—
146C22×Dic47—22no—
147C22×Dic47—21no—
148C22×Dic47—22no—
149C22×Dic47—22no—
150C22×Dic47—22no—
151C22×Dic47—22no—
152C22×Dic47C22×C412yes—
153C22×Dic47C22×C414yes—
154C22×Dic47C22×C412yes—
155C22×Dic47C22×C414yes—
156C22×Dic47C22×C412yes—
157C22×Dic47C22×C414yes—
158C22×Dic47C22×C412yes—
159C22×Dic47C22×C414yes—
160C22×Dic47C2×D412yes—
161C22×Dic47C2×D414yes—
162C22×Dic47C2×D412yes—
163C22×Dic47C2×Q812yes—
164C22×Dic47C2×Q812yes—
165C22×Dic47#4114yes—
166C22×Dic47#4114yes—
167C42×C47—28no—
168C42×C47—28no—
169C42×C47—44no—
170C4⋊Dic47—216no—
171Dic47⋊C4—28no—
172Dic47⋊C4—216no—
173Dic47⋊C4—216no—
174Dic47⋊C4C42116yescomplemented
175C4×Dic47—216no—
176C4×Dic47—28no—
177C4×Dic47—28no—
178C4×Dic47—216no—
179C4×Dic47—44no—
180C4×Dic47C4⋊C4116yescomplemented
181C23×C47C23×C411yescharacteristic
182C23×C47C23×C412yes—
183C23×C47C22×D411yescharacteristic
184C23×C47C22×D411yescharacteristic
185C23×C47C22×Q811yescharacteristic
186C23×C47C22×Q811yescharacteristic
187C23×C47C2×#4112yes—
188C23×C47C2×#4112yes—
189C23×C47C2×#4111yescharacteristic
190C23×C47C2×#4111yescharacteristic
191C23×C47C2×#4112yes—
192C2×C4×C47—24no—
193C2×C4×C47—24no—
194C2×C4×C47—22no—
195C2×C4×C47—24no—
196C2×C4×C47—24no—
197C2×C4×C47—22no—
198C2×C4×C47—24no—
199C2×C4×C47—24no—
200C2×C4×C47—24no—
201C2×C4×C47—24no—
202C2×C4×C47—22no—
203C2×C4×C47—24no—
204C2×C4×C47—24no—
205C2×C4×C47—22no—
206C2×C4×C47—22no—
207C2×C4×C47—24no—
208C2×C4×C47—42no—
209C2×C4×C47—42no—
210C2×C4×C47—42no—
211C2×C4×C47—42no—
212C2×C4×C47—42no—
213C2×C4×C47—42no—
214C2×C4×C47C2×C4214yes—
215C2×C4×C47C2×C4⋊C414yes—
216C2×C4×C47C4×D414yes—
217C2×C4×C47C4×Q818yes—
218C2×C4×C47C4×Q814yes—
219C2×C4×C47#12114yes—
220C2×C4×C47C22⋊Q814yes—
221C2×C4×C47#12514yes—
222C2×C4×C47C4⋊Q814yes—
223C2×Dic47—24no—
224C2×Dic47—22no—
225C2×Dic47—24no—
226C2×Dic47—24no—
227C2×Dic47—22no—
228C2×Dic47—22no—
229C2×Dic47—22no—
230C2×Dic47—24no—
231C2×Dic47—24no—
232C2×Dic47—24no—
233C2×Dic47—24no—
234C2×Dic47—24no—
235C2×Dic47—24no—
236C2×Dic47—24no—
237C2×Dic47—22no—
238C2×Dic47—22no—
239C2×Dic47—24no—
240C2×Dic47—24no—
241C2×Dic47—22no—
242C2×Dic47—24no—
243C2×Dic47—42no—
244C2×Dic47—42no—
245C2×Dic47—42no—
246C2×Dic47—42no—
247C2×Dic47—42no—
248C2×Dic47—42no—
249C2×Dic47C2×C4214yes—
250C2×Dic47C2×C4214yes—
251C2×Dic47C2×C4⋊C414yes—
252C2×Dic47C2×C4⋊C414yes—
253C2×Dic47#11714yes—
254C2×Dic47C4×D418yes—
255C2×Dic47C4×D418yes—
256C2×Dic47C4×Q818yes—
257C4×#389—471nomaximal, Sylow
258C22×C47C22×C4211yescharacteristic
259C22×C47C22×C4⋊C411yescharacteristic
260C22×C47C2×#11711yescharacteristic
261C22×C47C2×C4×D412yes—
262C22×C47C2×C4×D412yes—
263C22×C47C2×C4×D411yescharacteristic
264C22×C47C2×C4×Q812yes—
265C22×C47C2×C4×Q812yes—
266C22×C47C2×C4×Q811yescharacteristic
267C22×C47C4×#4112yes—
268C22×C47C4×#4111yescharacteristic
269C22×C47C4×#4112yes—
270C22×C47C4×#4111yescharacteristic
271C22×C47C2×#12111yescharacteristic
272C22×C47C2×C22⋊Q811yescharacteristic
273C22×C47#52512yes—
274C22×C47C2×#12511yescharacteristic
275C22×C47#52912yes—
276C22×C47#52912yes—
277C22×C47C2×C4⋊Q811yescharacteristic
278C22×C47#53212yes—
279C22×C47#53312yes—
280C22×C47#53312yes—
281C4×C47—24no—
282C4×C47—28no—
283C4×C47—42no—
284C4×C47—44no—
285C4×C47#38918yescomplemented
286Dic47—24no—
287Dic47—24no—
288Dic47—28no—
289Dic47—42no—
290Dic47—44no—
291Dic47C4×C4⋊C418yescomplemented
292C2×#389—472no—
293C2×C4×C4⋊C4—471no—
294C2×C4×C4⋊C4—471no—
295C2×C4×C4⋊C4—471no—
296C2×C4×C4⋊C4—471no—
297C2×C43—471no—
298#1436—472no—
299#1436—472no—
300C4⋊#95—472no—
301C4×#95—471no—
302C4×#95D4711yescharacteristic
303C2×C47C2×C4×C4⋊C411yescharacteristic
304C2×C47C42×D411yescharacteristic
305C2×C47C42×Q811yescharacteristic
306C2×C47C2×#38911yescharacteristic
307C2×C47#229311yescharacteristic
308C2×C47#229511yescharacteristic
309C2×C47#229611yescharacteristic
310C2×C47C4×#12112yes—
311C2×C47C4×C22⋊Q812yes—
312C2×C47C4×#12512yes—
313C2×C47C4×C4⋊Q812yes—
314C22×C4⋊C4—471no—
315C22×C4⋊C4—471no—
316C22×C4⋊C4—472no—
317C22×C4⋊C4—472no—
318C22×C4⋊C4—472no—
319C22×C42—471no—
320C22×C42—472no—
321C22×C42—471no—
322C22×C42—471no—
323C22×C42—472no—
324C22×C42—471no—
325C22×C42C2×D4711yescharacteristic
326C22×C42C2×D4711yescharacteristic
327C22×C42C2×D4711yescharacteristic
328#389—4716no—
329C4×C4⋊C4—478no—
330C4×C4⋊C4—944no—
331C4×C4⋊C4—944no—
332C4×C4⋊C4—944no—
333C2×#95—472no—
334C2×#95—471no—
335C2×#95—471no—
336C2×#95—472no—
337C2×#95—472no—
338C2×#95—472no—
339C2×#95—472no—
340C2×#95C2×D4712yes—
341C2×#95C2×D4712yes—
342C43—944no—
343C47C4×#38911yescharacteristic, complemented, Sylow
344C23×C4—471no—
345C23×C4—471no—
346C23×C4—472no—
347C23×C4—471no—
348C23×C4—472no—
349C23×C4—471no—
350C23×C4C22×D4712yes—
351C23×C4C22×D4711yescharacteristic
352C23×C4C22×D4712yes—
353C23×C4C22×D4711yescharacteristic
354C23×C4C22×D4711yescharacteristic
355C2×C4⋊C4—474no—
356C2×C4⋊C4—478no—
357C2×C4⋊C4—474no—
358C2×C4⋊C4—478no—
359C2×C4⋊C4—478no—
360C2×C4⋊C4—478no—
361C2×C4⋊C4—944no—
362C2×C4⋊C4—944no—
363C2×C4⋊C4—944no—
364C2×C4⋊C4—944no—
365C2×C4⋊C4—944no—
366C2×C4⋊C4—944no—
367C2×C4⋊C4—944no—
368C2×C42—22no—
369C2×C42—22no—
370C2×C42—22no—
371C2×C42—22no—
372C2×C42—22no—
373C2×C42—22no—
374C2×C42—22no—
375C2×C42—474no—
376C2×C42—474no—
377C2×C42—474no—
378C2×C42—474no—
379C2×C42—478no—
380C2×C42—474no—
381C2×C42—944no—
382C2×C42—944no—
383C2×C42—944no—
384C2×C42—944no—
385C2×C42—944no—
386C2×C42—942no—
387C2×C42—942no—
388C2×C42—942no—
389C2×C42—942no—
390C2×C42—942no—
391C2×C42—942no—
392C2×C42—942no—
393C2×C42Dic9414yes—
394C2×C42C4×D4714yes—
395#95—24no—
396#95—474no—
397#95—474no—
398#95—478no—
399#95—944no—
400#95—944no—
401#95—944no—
402#95—944no—
403#95C4×D4718yes—
404C24C23×D4711yescharacteristic
405C22×C4—22no—
406C22×C4—21no—
407C22×C4—22no—
408C22×C4—22no—
409C22×C4—22no—
410C22×C4—21no—
411C22×C4—22no—
412C22×C4—21no—
413C22×C4—22no—
414C22×C4—22no—
415C22×C4—22no—
416C22×C4—22no—
417C22×C4—22no—
418C22×C4—21no—
419C22×C4—22no—
420C22×C4—22no—
421C22×C4—22no—
422C22×C4—472no—
423C22×C4—474no—
424C22×C4—472no—
425C22×C4—472no—
426C22×C4—474no—
427C22×C4—472no—
428C22×C4—472no—
429C22×C4—474no—
430C22×C4—474no—
431C22×C4—472no—
432C22×C4—474no—
433C22×C4—472no—
434C22×C4—474no—
435C22×C4—472no—
436C22×C4—474no—
437C22×C4—942no—
438C22×C4—941no—
439C22×C4—942no—
440C22×C4—942no—
441C22×C4—942no—
442C22×C4—941no—
443C22×C4—942no—
444C22×C4—942no—
445C22×C4—942no—
446C22×C4—941no—
447C22×C4—942no—
448C22×C4—942no—
449C22×C4—942no—
450C22×C4—942no—
451C22×C4—942no—
452C22×C4—941no—
453C22×C4—942no—
454C22×C4—942no—
455C22×C4—942no—
456C22×C4C2×Dic9414yes—
457C22×C4C2×Dic9412yes—
458C22×C4C2×C4×D4712yes—
459C22×C4C2×C4×D4714yes—
460C22×C4C2×C4×D4712yes—
461C22×C4C2×C4×D4714yes—
462C22×C4C2×C4×D4714yes—
463C22×C4C2×C4×D4712yes—
464C22×C4#1062535014yes—
465C22×C4#1062535012yes—
466C22×C4D4×D4712yes—
467C22×C4D4×D4712yes—
468C22×C4#1062535212yes—
469C22×C4Q8×D4712yes—
470C4⋊C4—4716no—
471C4⋊C4—948no—
472C4⋊C4—9416no—
473C4⋊C4—9416no—
474C4⋊C4—9416no—
475C42—28no—
476C42—28no—
477C42—44no—
478C42—4716no—
479C42—9416no—
480C42—9416no—
481C42—948no—
482C42—948no—
483C42—1884no—
484C23C22×C4×D4711yescharacteristic
485C23C22×C4×D4712yes—
486C23C2×D4×D4711yescharacteristic
487C23C2×D4×D4711yescharacteristic
488C23C2×Q8×D4711yescharacteristic
489C23C22×Dic9411yescharacteristic
490C23#41×D4712yes—
491C23#41×D4712yes—
492C23C2×#1062535211yescharacteristic
493C23C2×#1062535011yescharacteristic
494C23C2×#1062535012yes—
495C2×C4—24no—
496C2×C4—24no—
497C2×C4—22no—
498C2×C4—24no—
499C2×C4—24no—
500C2×C4—22no—
501C2×C4—24no—
502C2×C4—24no—
503C2×C4—24no—
504C2×C4—24no—
505C2×C4—22no—
506C2×C4—24no—
507C2×C4—24no—
508C2×C4—22no—
509C2×C4—22no—
510C2×C4—24no—
511C2×C4—42no—
512C2×C4—42no—
513C2×C4—42no—
514C2×C4—42no—
515C2×C4—42no—
516C2×C4—42no—
517C2×C4—474no—
518C2×C4—474no—
519C2×C4—474no—
520C2×C4—478no—
521C2×C4—478no—
522C2×C4—474no—
523C2×C4—474no—
524C2×C4—478no—
525C2×C4—944no—
526C2×C4—944no—
527C2×C4—942no—
528C2×C4—944no—
529C2×C4—942no—
530C2×C4—942no—
531C2×C4—942no—
532C2×C4—944no—
533C2×C4—944no—
534C2×C4—944no—
535C2×C4—944no—
536C2×C4—944no—
537C2×C4—944no—
538C2×C4—944no—
539C2×C4—942no—
540C2×C4—944no—
541C2×C4—944no—
542C2×C4—942no—
543C2×C4—942no—
544C2×C4—944no—
545C2×C4—1882no—
546C2×C4—1882no—
547C2×C4—1882no—
548C2×C4—1882no—
549C2×C4—1882no—
550C2×C4—1882no—
551C2×C4C42×D4714yes—
552C2×C4C4⋊C4×D4714yes—
553C2×C4(C22⋊D47)⋊C414yes—
554C2×C4C4×Dic9418yes—
555C2×C4C4×Dic9414yes—
556C2×C4#1309399714yes—
557C2×C4#1309400114yes—
558C2×C4#1309401414yes—
559C2×C4#1309402314yes—
560C22C2×C42×D4711yescharacteristic
561C22C2×C4⋊C4×D4711yescharacteristic
562C22#117×D4711yescharacteristic
563C22C4×D4×D4712yes—
564C22C4×D4×D4712yes—
565C22C2×(C22⋊D47)⋊C411yescharacteristic
566C22C4×Q8×D4712yes—
567C22C2×C4×Dic9411yescharacteristic
568C22C2×C4×Dic9412yes—
569C22C4×#1062535212yes—
570C22#1568959111yescharacteristic
571C22C4×#1062535011yescharacteristic
572C22C4×#1062535012yes—
573C22C2×#1309399711yescharacteristic
574C22C2×#1309400111yescharacteristic
575C22#1568963212yes—
576C22C2×#1309401411yescharacteristic
577C22#1568965112yes—
578C22#1568965312yes—
579C22C2×#1309402311yescharacteristic
580C22#1568967012yes—
581C22#1568967612yes—
582C22#1568967712yes—
583C4—28no—
584C4—24no—
585C4—42no—
586C4—44no—
587C4—478no—
588C4—944no—
589C4—948no—
590C4—944no—
591C4—1882no—
592C4—1884no—
593C4#1568902018yesdirect product factor
594C2C4×C4⋊C4×D4711yescharacteristic
595C2C4×(C22⋊D47)⋊C411yescharacteristic
596C2C42×Dic9411yescharacteristic
597C2C2×#1568902011yescharacteristic
598C2#2024585111yescharacteristic
599C2#2024586011yescharacteristic
600C2#2024586811yescharacteristic
601C2C4×#1309399712yes—
602C2C4×#1309400112yes—
603C2C4×#1309401412yes—
604C2C4×#1309402312yes—
subgroupG/H
centerC23×C4C22×D47
commutatorC22×C47C22×C42
FrattiniC24C23×D47
FittingC4×#95×C47C2
socle, prime radical, cosocleC24×C47C24
hypercenterC4×#95D47
hypocenterC47C4×#389
LCSG ▷ C22×C47 ▷ C47
UCSC1 ◁ C23×C4 ◁ C4×#95

Complements

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

NH ≅ G/Ntype
23. #15689020C4direct (N × H)
26. C4×Dic47⋊C4C4semidirect
174. Dic47⋊C4C42semidirect
180. C4×Dic47C4⋊C4semidirect
285. C4×C47#389semidirect
291. Dic47C4×C4⋊C4semidirect
343. C47C4×#389semidirect
593. C4#15689020direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#156890202
C2×C4×Dic47⋊C42
C2×C4×C4⋊Dic472
C2×C42×Dic472
#202416222
#202416192
Dic47⋊#952
C4×C47⋊#952
C4×#95×C472
C4×#38947