Finite Group Databasebeta

← #26220035

Subgroups — #26220035

Order 12032.

1598 conjugacy classes of subgroups.

The subgroup lattice has 686 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#15689701C211yesmaximal, characteristic
2C2×#15689097C211yesmaximal, characteristic, complemented
3C2×#15689096C211yesmaximal, characteristic, complemented
4C2×#15689096C211yesmaximal, characteristic, complemented
5#20246004C211yesmaximal, characteristic, complemented
6#20245744C211yesmaximal, characteristic, complemented
7#20244222C218yesmaximal, complemented
8C2×C47×#410C211yesmaximal, characteristic, complemented
9C22×#10625350C2211yescharacteristic
10#15689701—22no—
11#15689701—22no—
12#15689701—22no—
13#15689701—22no—
14C2×#13094003C412yescomplemented
15C2×#13094000C412yescomplemented
16C2×#13093998C412yescomplemented
17C2×#13093996C2214yes—
18C2×#13093995C412yescomplemented
19C2×#13093983C2211yescharacteristic
20C2×#13093983C2211yescharacteristic
21C22×C4⋊Dic47C2211yescharacteristic
22#15689097—24no—
23#15689096—24no—
24#15689096—24no—
25C2×#13093939C2214yes—
26C2×#13093938C2214yes—
27C2×#13093938C2214yes—
28#15689021—22no—
29#15689019—22no—
30#15688981C2214yes—
31C4⋊C4×Dic47—22no—
32C4×C4⋊Dic47—22no—
33C22⋊C4×Dic47C2214yes—
34C22×#41×C47C2211yescharacteristic
35C2×#117×C47C2211yescharacteristic
36C2×#117×C47C2211yescharacteristic
37C47×#410—24no—
38C2×#99×C47C2214yes—
39C2×#10625350—22no—
40C2×#10625350—22no—
41C2×#10625350—21no—
42C2×#10625350—21no—
43C2×#10625350—21no—
44C2×#10625350—21no—
45C2×#10625350—22no—
46C2×#10625350—22no—
47C22×Dic94C2×C411yescharacteristic
48C22×D188C2×C411yescharacteristic
49C22×C22⋊D47C2×C414yes—
50C22×C22⋊D47C2312yes—
51C23×Dic47C2312yes—
52C22×C4×D47C2×C412yes—
53#13094003—24no—
54#13094003—24no—
55#13094000—24no—
56#13094000—24no—
57#13093998—24no—
58#13093998—24no—
59#13093996—28no—
60#13093996—28no—
61#13093995—24no—
62#13093995—24no—
63#13093983—22no—
64#13093983—22no—
65#13093983—22no—
66#13093983D414yescomplemented
67C2×C4⋊Dic47—21no—
68C2×C4⋊Dic47—21no—
69C2×C4⋊Dic47C2×C412yes—
70C2×C4⋊Dic47C2×C412yes—
71C2×C4⋊Dic47D412yes—
72C2×C4⋊Dic47D412yes—
73C2×C4⋊Dic47D412yes—
74C2×C4⋊Dic47D412yes—
75C2×Dic47⋊C4—24no—
76C2×Dic47⋊C4C2×C414yes—
77C2×C22⋊Dic47C2×C414yes—
78C2×C22⋊Dic47C2312yes—
79C2×C22⋊Dic47C2312yes—
80C2×(C2×D47)⋊C4C2×C414yes—
81C2×C4×Dic47—21no—
82C2×C4×Dic47—21no—
83C2×C4×Dic47—24no—
84#13093939—28no—
85#13093938—28no—
86#13093938—28no—
87C47⋊#95—24no—
88C47⋊#95—24no—
89C2×#41×C47—22no—
90C2×#41×C47—22no—
91C2×#41×C47—21no—
92C2×#41×C47—21no—
93C2×#41×C47—21no—
94C2×#41×C47—21no—
95C2×#41×C47—22no—
96C2×#41×C47—22no—
97C22×Q8×C47C2×C411yescharacteristic
98C22×D4×C47C2×C411yescharacteristic
99C22×D4×C47C2312yes—
100C23×C4×C47C2×C412yes—
101C23×C4×C47C2311yescharacteristic
102#117×C47—22no—
103#117×C47—22no—
104#117×C47—22no—
105#117×C47D414yescomplemented
106C2×C4⋊C4×C47—21no—
107C2×C4⋊C4×C47—21no—
108C2×C22⋊C4×C47C2312yes—
109C2×C22⋊C4×C47C2312yes—
110C2×C42×C47—21no—
111C2×C42×C47—21no—
112#99×C47—28no—
113C24×C47C22×C412yes—
114C24×C47C2411yescharacteristic
115C23×D47C22×C412yes—
116#41×C47—42no—
117#41×C47—42no—
118#41×C47—42no—
119#41×C47—42no—
120#41×C47—42no—
121#41×C47—42no—
122#41×C47—42no—
123#41×C47—42no—
124C2×Q8×C47—21no—
125C2×Q8×C47—21no—
126C2×Q8×C47—22no—
127C2×Q8×C47—22no—
128C2×D4×C47—22no—
129C2×D4×C47—22no—
130C2×D4×C47—22no—
131C2×D4×C47—22no—
132C2×D4×C47—22no—
133C2×D4×C47—22no—
134C2×D4×C47—21no—
135C2×D4×C47—21no—
136C2×D4×C47—22no—
137C2×D4×C47—22no—
138C22×C4×C47—22no—
139C22×C4×C47—22no—
140C22×C4×C47—22no—
141C22×C4×C47—24no—
142C22×C4×C47—24no—
143C22×C4×C47—22no—
144C22×C4×C47C22×C412yes—
145C22×C4×C47C22×C411yescharacteristic
146C22×C4×C47C22×C411yescharacteristic
147C22×C4×C47C2×D411yescharacteristic
148C22×C4×C47C2×D411yescharacteristic
149C22×C4×C47C2×D411yescharacteristic
150C22×C4×C47C2×D411yescharacteristic
151C22×C4×C47C2×D412yes—
152C22×C4×C47C2×D412yes—
153C22×C4×C47#4112yes—
154C22×C4×C47#4112yes—
155C2×C22⋊D47—22no—
156C2×C22⋊D47—22no—
157C2×C22⋊D47—22no—
158C2×C22⋊D47—22no—
159C2×C22⋊D47—22no—
160C2×C22⋊D47—22no—
161C2×C22⋊D47—28no—
162C2×C22⋊D47—84no—
163C22×Dic47—22no—
164C22×Dic47—22no—
165C22×Dic47—82no—
166C22×Dic47C22×C412yes—
167C22×Dic47C22×C414yes—
168C22×Dic47C2×D414yes—
169C22×Dic47C2×D414yes—
170#10625350—42no—
171#10625350—42no—
172#10625350—42no—
173#10625350—42no—
174#10625350—42no—
175#10625350—42no—
176#10625350—42no—
177#10625350—42no—
178C2×D188—21no—
179C2×D188—21no—
180C2×D188—22no—
181C2×D188—22no—
182C2×C4×D47—22no—
183C2×C4×D47—22no—
184C2×C4×D47—24no—
185C2×C4×D47—24no—
186C2×Dic94—21no—
187C2×Dic94—21no—
188C2×Dic94—22no—
189C2×Dic94—22no—
190C4⋊C4×C47—24no—
191C4⋊C4×C47—42no—
192C22⋊C4×C47—22no—
193C22⋊C4×C47—22no—
194C22⋊C4×C47—22no—
195C22⋊C4×C47C2×D414yes—
196C42×C47—24no—
197C42×C47—42no—
198C22⋊Dic47—22no—
199C22⋊Dic47—28no—
200C22⋊Dic47—22no—
201C22⋊Dic47—22no—
202C22⋊Dic47C2×D414yes—
203(C2×D47)⋊C4—28no—
204C4⋊Dic47—24no—
205C4⋊Dic47—42no—
206C4⋊Dic47C22⋊C414yes—
207C4⋊Dic47C22⋊C414yes—
208C4⋊Dic47C22⋊C414yes—
209C4⋊Dic47C22⋊C414yes—
210Dic47⋊C4—28no—
211Dic47⋊C4—84no—
212C4×Dic47—24no—
213C4×Dic47—42no—
214C4×Dic47—84no—
215C23×C47—22no—
216C23×C47—22no—
217C23×C47—22no—
218C23×C47—41no—
219C23×C47—41no—
220C23×C47—42no—
221C23×C47—42no—
222C23×C47C23×C411yescharacteristic
223C23×C47C22×D411yescharacteristic
224C23×C47C22×D411yescharacteristic
225C23×C47C22×D411yescharacteristic
226C23×C47C22×D411yescharacteristic
227C23×C47C2×#4111yescharacteristic
228C23×C47C2×#4111yescharacteristic
229C22×D47—22no—
230C22×D47—22no—
231C22×D47—22no—
232C22×D47—42no—
233C22×D47—42no—
234Q8×C47—42no—
235Q8×C47—42no—
236D4×C47—42no—
237D4×C47—42no—
238D4×C47—42no—
239D4×C47—42no—
240D4×C47—42no—
241D4×C47—42no—
242C2×C4×C47—22no—
243C2×C4×C47—22no—
244C2×C4×C47—22no—
245C2×C4×C47—24no—
246C2×C4×C47—42no—
247C2×C4×C47—42no—
248C2×C4×C47—44no—
249C2×C4×C47—44no—
250C2×C4×C47—42no—
251C2×C4×C47—42no—
252C2×C4×C47—42no—
253C2×C4×C47C2×C22⋊C411yescharacteristic
254C2×C4×C47C2×C22⋊C411yescharacteristic
255C2×C4×C47C2×C22⋊C411yescharacteristic
256C2×C4×C47C2×C22⋊C411yescharacteristic
257C2×C4×C47C4×D412yes—
258C2×C4×C47C4×D412yes—
259C2×C4×C47C4×D412yes—
260C2×C4×C47C4×D412yes—
261C2×C4×C47#12112yes—
262C2×C4×C47#12112yes—
263C2×C4×C47#12112yes—
264C2×C4×C47#12112yes—
265C2×C4×C47#12412yes—
266C2×C4×C47#12412yes—
267C2×C4×C47#12712yes—
268C2×C4×C47#12712yes—
269C22⋊D47—42no—
270C22⋊D47—42no—
271C22⋊D47—42no—
272C22⋊D47—42no—
273C22⋊D47—88no—
274C2×Dic47—22no—
275C2×Dic47—22no—
276C2×Dic47—22no—
277C2×Dic47—24no—
278C2×Dic47—44no—
279C2×Dic47—44no—
280C2×Dic47—44no—
281C2×Dic47—42no—
282C2×Dic47—42no—
283C2×Dic47—42no—
284C2×Dic47—42no—
285C2×Dic47—42no—
286C2×Dic47C2×C22⋊C418yes—
287D188—42no—
288D188—42no—
289C4×D47—44no—
290C4×D47—44no—
291Dic94—42no—
292Dic94—42no—
293#21214—471nomaximal, Sylow
294C22×C47—21no—
295C22×C47—21no—
296C22×C47—21no—
297C22×C47—21no—
298C22×C47—21no—
299C22×C47—21no—
300C22×C47—41no—
301C22×C47—41no—
302C22×C47—41no—
303C22×C47—41no—
304C22×C47—42no—
305C22×C47—42no—
306C22×C47—42no—
307C22×C47—82no—
308C22×C47—82no—
309C22×C47C22×C22⋊C411yescharacteristic
310C22×C47C2×C4×D411yescharacteristic
311C22×C47C2×C4×D411yescharacteristic
312C22×C47C2×#12111yescharacteristic
313C22×C47C2×#12111yescharacteristic
314C22×C47C2×#12411yescharacteristic
315C22×C47C2×#12711yescharacteristic
316C2×D47—42no—
317C2×D47—42no—
318C2×D47—42no—
319C2×D47—82no—
320C2×D47—82no—
321C4×C47—44no—
322C4×C47—42no—
323C4×C47—82no—
324C4×C47#39012yes—
325C4×C47#39012yes—
326C4×C47#39012yes—
327C4×C47#39012yes—
328Dic47—28no—
329Dic47—44no—
330Dic47—42no—
331Dic47—82no—
332C2×#537—471no—
333C2×#410—471no—
334C2×#410—471no—
335C2×#410—471no—
336C2×#410D4711yescharacteristic, complemented
337#2316—471no—
338#2274—471no—
339#1964—478no—
340C2×C47—21no—
341C2×C47—21no—
342C2×C47—21no—
343C2×C47—21no—
344C2×C47—21no—
345C2×C47—21no—
346C2×C47—82no—
347C2×C47C2×#39011yescharacteristic
348C2×C47#288311yescharacteristic
349C2×C47#288411yescharacteristic
350D47—82no—
351C22×#41—471no—
352C22×#41C2×D4711yescharacteristic
353#537—942no—
354#537—942no—
355#537—942no—
356#537—942no—
357C2×C22⋊Q8—472no—
358C2×C22⋊Q8—472no—
359C2×#121—472no—
360C2×#121—474no—
361C2×#121—472no—
362C2×#117—471no—
363C2×#117—471no—
364C2×#117C2×D4711yescharacteristic
365C2×#117C2×D4711yescharacteristic
366C22×C4⋊C4—471no—
367#410—24no—
368#410—944no—
369#410—944no—
370#410—944no—
371C2×#99—474no—
372C2×#99—474no—
373C2×#99—474no—
374C2×#99C2×D4714yes—
375#389—942no—
376#389—942no—
377#380—474no—
378C4×C4⋊C4—942no—
379C4×C4⋊C4—942no—
380C4×C22⋊C4—474no—
381C47#2121411yescharacteristic, complemented, Sylow
382C2×#41—22no—
383C2×#41—21no—
384C2×#41—21no—
385C2×#41—21no—
386C2×#41—21no—
387C2×#41—22no—
388C2×#41—22no—
389C2×#41—22no—
390C2×#41—942no—
391C2×#41—941no—
392C2×#41—941no—
393C2×#41—941no—
394C2×#41—941no—
395C2×#41—942no—
396C2×#41—942no—
397C2×#41—942no—
398C22×Q8—471no—
399C22×Q8C4×D4711yescharacteristic
400C22×D4—472no—
401C22×D4—474no—
402C22×D4—471no—
403C22×D4C4×D4711yescharacteristic
404C22×D4C22×D4712yes—
405C23×C4—472no—
406C23×C4—472no—
407C23×C4C4×D4712yes—
408C23×C4C22×D4711yescharacteristic
409C22⋊Q8—944no—
410C22⋊Q8—944no—
411C22⋊Q8—944no—
412C22⋊Q8—944no—
413#121—944no—
414#121—944no—
415#121—944no—
416#121—944no—
417#121—948no—
418#121—948no—
419#117—22no—
420#117—22no—
421#117—22no—
422#117—474no—
423#117—942no—
424#117—942no—
425#117—942no—
426#117C22⋊D4714yescomplemented
427C2×C4⋊C4—21no—
428C2×C4⋊C4—21no—
429C2×C4⋊C4—472no—
430C2×C4⋊C4—472no—
431C2×C4⋊C4—472no—
432C2×C4⋊C4—472no—
433C2×C4⋊C4—472no—
434C2×C4⋊C4—472no—
435C2×C4⋊C4—474no—
436C2×C4⋊C4—941no—
437C2×C4⋊C4—944no—
438C2×C4⋊C4—941no—
439C2×C22⋊C4—472no—
440C2×C22⋊C4—474no—
441C2×C22⋊C4—474no—
442C2×C22⋊C4—472no—
443C2×C22⋊C4C22×D4712yes—
444C2×C22⋊C4C22×D4712yes—
445C2×C42—21no—
446C2×C42—21no—
447C2×C42—941no—
448C2×C42—944no—
449C2×C42—941no—
450#99—28no—
451#99—948no—
452#99—948no—
453#99—948no—
454#95—944no—
455#95—944no—
456C24—472no—
457C24C2×C4×D4712yes—
458C24C23×D4711yescharacteristic
459#41—42no—
460#41—42no—
461#41—42no—
462#41—42no—
463#41—42no—
464#41—42no—
465#41—42no—
466#41—42no—
467#41—1882no—
468#41—1882no—
469#41—1882no—
470#41—1882no—
471#41—1882no—
472#41—1882no—
473#41—1882no—
474#41—1882no—
475C2×Q8—21no—
476C2×Q8—21no—
477C2×Q8—22no—
478C2×Q8—22no—
479C2×Q8—941no—
480C2×Q8—941no—
481C2×Q8—942no—
482C2×Q8—942no—
483C2×D4—22no—
484C2×D4—22no—
485C2×D4—22no—
486C2×D4—22no—
487C2×D4—22no—
488C2×D4—22no—
489C2×D4—21no—
490C2×D4—21no—
491C2×D4—22no—
492C2×D4—22no—
493C2×D4—948no—
494C2×D4—942no—
495C2×D4—942no—
496C2×D4—942no—
497C2×D4—942no—
498C2×D4—942no—
499C2×D4—942no—
500C2×D4—941no—
501C2×D4—941no—
502C2×D4—942no—
503C2×D4—942no—
504C2×D4—3764no—
505C22×C4—22no—
506C22×C4—22no—
507C22×C4—22no—
508C22×C4—24no—
509C22×C4—24no—
510C22×C4—22no—
511C22×C4—474no—
512C22×C4—474no—
513C22×C4—474no—
514C22×C4—472no—
515C22×C4—942no—
516C22×C4—942no—
517C22×C4—942no—
518C22×C4—944no—
519C22×C4—944no—
520C22×C4—942no—
521C22×C4—3762no—
522C22×C4C2×C4×D4712yes—
523C22×C4C2×C4×D4711yescharacteristic
524C22×C4C2×C4×D4711yescharacteristic
525C22×C4#1062535012yes—
526C22×C4D4×D4711yescharacteristic
527C22×C4D4×D4711yescharacteristic
528C22×C4D4×D4711yescharacteristic
529C22×C4D4×D4711yescharacteristic
530C22×C4D4×D4712yes—
531C22×C4#1062535212yes—
532C22×C4C2×C22⋊D4712yes—
533C4⋊C4—24no—
534C4⋊C4—42no—
535C4⋊C4—474no—
536C4⋊C4—474no—
537C4⋊C4—474no—
538C4⋊C4—474no—
539C4⋊C4—948no—
540C4⋊C4—944no—
541C4⋊C4—3764no—
542C4⋊C4—1882no—
543C22⋊C4—22no—
544C22⋊C4—22no—
545C22⋊C4—22no—
546C22⋊C4—474no—
547C22⋊C4—948no—
548C22⋊C4—948no—
549C22⋊C4—942no—
550C22⋊C4—942no—
551C22⋊C4—942no—
552C22⋊C4C2×C22⋊D4714yes—
553C42—24no—
554C42—42no—
555C42—944no—
556C42—3764no—
557C42—1882no—
558C23—22no—
559C23—22no—
560C23—22no—
561C23—41no—
562C23—41no—
563C23—42no—
564C23—42no—
565C23—942no—
566C23—942no—
567C23—942no—
568C23—1882no—
569C23—1882no—
570C23C22×C4×D4711yescharacteristic
571C23C2×D4×D4711yescharacteristic
572C23C2×D4×D4711yescharacteristic
573C23C2×D4×D4711yescharacteristic
574C23C22×C22⋊D4711yescharacteristic
575C23C2×#1062535211yescharacteristic
576C23C2×#1062535011yescharacteristic
577Q8—42no—
578Q8—42no—
579Q8—1882no—
580Q8—1882no—
581D4—42no—
582D4—42no—
583D4—42no—
584D4—42no—
585D4—42no—
586D4—42no—
587D4—3768no—
588D4—1882no—
589D4—1882no—
590D4—1882no—
591D4—1882no—
592D4—1882no—
593D4—1882no—
594C2×C4—22no—
595C2×C4—22no—
596C2×C4—22no—
597C2×C4—24no—
598C2×C4—42no—
599C2×C4—42no—
600C2×C4—44no—
601C2×C4—44no—
602C2×C4—42no—
603C2×C4—42no—
604C2×C4—42no—
605C2×C4—478no—
606C2×C4—942no—
607C2×C4—942no—
608C2×C4—942no—
609C2×C4—944no—
610C2×C4—1884no—
611C2×C4—1884no—
612C2×C4—1884no—
613C2×C4—1882no—
614C2×C4—1882no—
615C2×C4—1882no—
616C2×C4—1882no—
617C2×C4—1882no—
618C2×C4—1884no—
619C2×C4—1884no—
620C2×C4C22⋊C4×D4711yescharacteristic
621C2×C4C22⋊C4×D4711yescharacteristic
622C2×C4C22⋊C4×D4711yescharacteristic
623C2×C4C22⋊C4×D4711yescharacteristic
624C2×C4(C22⋊D47)⋊C412yes—
625C2×C4(C22⋊D47)⋊C412yes—
626C2×C4C4×C22⋊D4712yes—
627C2×C4C4×C22⋊D4712yes—
628C2×C4#1309399612yes—
629C2×C4#1309399612yes—
630C2×C4#1309399712yes—
631C2×C4#1309399712yes—
632C2×C4#1309401012yes—
633C2×C4#1309401012yes—
634C2×C4#1309402012yes—
635C2×C4#1309402012yes—
636C22—21no—
637C22—21no—
638C22—21no—
639C22—21no—
640C22—21no—
641C22—21no—
642C22—41no—
643C22—41no—
644C22—41no—
645C22—41no—
646C22—42no—
647C22—42no—
648C22—42no—
649C22—82no—
650C22—82no—
651C22—3762no—
652C22—3762no—
653C22—1882no—
654C22—1882no—
655C22—1882no—
656C22C2×C22⋊C4×D4711yescharacteristic
657C22C2×(C22⋊D47)⋊C411yescharacteristic
658C22C2×C4×C22⋊D4711yescharacteristic
659C22C2×#1309399611yescharacteristic
660C22C2×#1309399711yescharacteristic
661C22C2×#1309401011yescharacteristic
662C22C2×#1309402011yescharacteristic
663C4—44no—
664C4—42no—
665C4—82no—
666C4—948no—
667C4—3762no—
668C4—1884no—
669C4—1882no—
670C4#1568902312yes—
671C4#1568902312yes—
672C4#1568902312yes—
673C4#1568902312yes—
674C2—21no—
675C2—21no—
676C2—21no—
677C2—21no—
678C2—21no—
679C2—21no—
680C2—82no—
681C2—3762no—
682C2C2×#1568902311yescharacteristic
683C2#2025184711yescharacteristic
684C2#2025185011yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D47
commutatorC23×C47C23×C4
FrattiniC24C23×D47
FittingC2×C47×#410C2
socleC22×C47C22×C22⋊C4
prime radicalC2×#15689701C2
cosocleC24×C47C24
hypercenterC2×#410D47
hypocenterC47#21214
LCSG ▷ C23×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#410

Complements

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

NH ≅ G/Ntype
2. C2×#15689097C2semidirect
3. C2×#15689096C2semidirect
4. C2×#15689096C2semidirect
5. #20246004C2semidirect
6. #20245744C2semidirect
7. #20244222C2semidirect
8. C2×C47×#410C2semidirect
14. C2×#13094003C4semidirect
15. C2×#13094000C4semidirect
16. C2×#13093998C4semidirect
18. C2×#13093995C4semidirect
66. #13093983D4semidirect
105. #117×C47D4semidirect
336. C2×#410D47semidirect
381. C47#21214semidirect
426. #117C22⋊D47semidirect

Maximal subgroups

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

subgroupindex
C2×#156897012
C2×#156890972
C2×#156890962
#202460042
#202457442
#202442222
C2×C47×#4102
#2121447