Finite Group Databasebeta

← #26187502

Subgroups — #26187502

Order 12032.

642 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253435C211yesmaximal, characteristic
2#20252544C211yesmaximal, characteristic, complemented
3#20252423C211yesmaximal, characteristic, complemented
4#20242299C211yesmaximal, characteristic, complemented
5#20242287C211yesmaximal, characteristic, complemented
6#20242234C211yesmaximal, characteristic, complemented
7#20242221C211yesmaximal, characteristic, complemented
8#20242220C211yesmaximal, characteristic, complemented
9#20242214C211yesmaximal, characteristic, complemented
10#20242209C211yesmaximal, characteristic, complemented
11#20242197C211yesmaximal, characteristic, complemented
12#20242171C211yesmaximal, characteristic, complemented
13#20241849C211yesmaximal, characteristic, complemented
14#20241680C211yesmaximal, characteristic, complemented
15C2×C47×D4⋊C8C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689458C411yescharacteristic
18#15689441C411yescharacteristic
19#15689423C411yescharacteristic
20#15689423C411yescharacteristic
21#15689338C411yescharacteristic
22#15689338C411yescharacteristic
23#15689274C411yescharacteristic
24#15689257C411yescharacteristic
25#15689250C2211yescharacteristic, complemented
26#15689247C2211yescharacteristic, complemented
27C4×#10625335C2211yescharacteristic
28C4×#10625335C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689201C2211yescharacteristic
32#15689201C2211yescharacteristic
33#15689200C2211yescharacteristic, complemented
34#15689195—21no—
35#15689195—21no—
36#15689194—21no—
37D4×C47⋊C8C2211yescharacteristic
38D4×C47⋊C8C2211yescharacteristic
39#15689188C2211yescharacteristic, complemented
40C8×C22⋊D47—21no—
41#15689183—21no—
42#15689180C2211yescharacteristic
43#15689176C2211yescharacteristic
44#15689176C2211yescharacteristic
45#15689148—21no—
46#15689087—21no—
47C2×C22⋊(C47⋊C8)—21no—
48#15688875C2211yescharacteristic, complemented
49#15688875C2211yescharacteristic, complemented
50#15688873C2211yescharacteristic, complemented
51#15688873C2211yescharacteristic, complemented
52#15688855C2211yescharacteristic, complemented
53#15688855C2211yescharacteristic, complemented
54#15688852C2211yescharacteristic, complemented
55#15688852C2211yescharacteristic, complemented
56#15688845C2211yescharacteristic, complemented
57#15688845C2211yescharacteristic, complemented
58#15688845C2211yescharacteristic, complemented
59#15688845C2211yescharacteristic, complemented
60C2×C4×D4×C47C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C2×C4×C8×C47C2211yescharacteristic
63C47×D4⋊C8C2211yescharacteristic
64C47×D4⋊C8C2211yescharacteristic
65C47×D4⋊C8C2211yescharacteristic
66C47×D4⋊C8C2211yescharacteristic
67C2×#10625335C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625334C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625324—21no—
74C22×C47⋊C8—21no—
75C22×C47⋊C8—21no—
76C2×C8×D47—21no—
77#13094018—21no—
78#13094016C2×C411yescharacteristic
79#13094012C2×C411yescharacteristic
80#13094007—21no—
81#13094003C2×C411yescharacteristic
82#13093998C2×C411yescharacteristic
83C4×Dic94C2311yescharacteristic
84C4×D188C2311yescharacteristic
85C4×C22⋊D47—21no—
86#13093981—21no—
87#13093957C2×C411yescharacteristic
88#13093957C2×C411yescharacteristic
89#13093955C2×C411yescharacteristic
90#13093955C2×C411yescharacteristic
91C4⋊(C47⋊C8)C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2×C411yescharacteristic
93C4⋊(C47⋊C8)D411yescharacteristic
94C4⋊(C47⋊C8)D411yescharacteristic
95C4⋊(C47⋊C8)C2311yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97Dic47⋊C8—21no—
98Dic47⋊C8—21no—
99#13093947C2×C411yescharacteristic
100#13093947C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102#13093945C2×C411yescharacteristic
103#13093945C2×C411yescharacteristic
104#13093945C2×C411yescharacteristic
105#13093944C2×C411yescharacteristic
106#13093944C2×C411yescharacteristic
107C22⋊(C47⋊C8)—21no—
108C22⋊(C47⋊C8)—21no—
109C22⋊(C47⋊C8)—21no—
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)—21no—
112C22⋊(C47⋊C8)C2×C411yescharacteristic
113C22⋊(C47⋊C8)C2×C411yescharacteristic
114C22⋊(C47⋊C8)D411yescharacteristic
115C22⋊(C47⋊C8)D411yescharacteristic
116(C2×D47)⋊C8—21no—
117(C2×D47)⋊C8—21no—
118#13093935—21no—
119#13093934—21no—
120C4×C47⋊C8C2311yescharacteristic
121C4×C47⋊C8C2311yescharacteristic
122C4×C47⋊C8C2311yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C8×Dic47—21no—
125C22×D4×C47C2×C411yescharacteristic
126C23×C4×C47—21no—
127C22×C8×C47—21no—
128C22×C8×C47—21no—
129C4×D4×C47—21no—
130C4×D4×C47—21no—
131C4×D4×C47C2×C411yescharacteristic
132C4×D4×C47C2×C411yescharacteristic
133C4×D4×C47C2311yescharacteristic
134C4×D4×C47C2311yescharacteristic
135C2×C4⋊C4×C47C2×C411yescharacteristic
136C2×C22⋊C4×C47—21no—
137C2×C42×C47C2311yescharacteristic
138C4⋊C8×C47—21no—
139C4⋊C8×C47C2311yescharacteristic
140C4⋊C8×C47C2311yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C24×C47—21no—
145C2×D4×C47—22no—
146C2×D4×C47—21no—
147C2×D4×C47—41no—
148C2×D4×C47C22×C411yescharacteristic
149C2×D4×C47C22×C411yescharacteristic
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47—21no—
153C22×C4×C47—21no—
154C22×C4×C47—21no—
155C22×C4×C47—81no—
156C22×C4×C47—81no—
157C22×C4×C47C22×C411yescharacteristic
158C22×C4×C47C2×D411yescharacteristic
159C22×C4×C47#4111yescharacteristic
160C2×C22⋊D47—21no—
161C2×D188C22×C411yescharacteristic
162C2×C4×D47—21no—
163C2×Dic94C22×C411yescharacteristic
164C2×C8×C47—21no—
165C2×C8×C47—21no—
166C2×C8×C47—21no—
167C2×C8×C47—21no—
168C2×C8×C47—42no—
169C2×C8×C47—81no—
170C4⋊C4×C47—21no—
171C4⋊C4×C47C22×C411yescharacteristic
172C4⋊C4×C47C22×C411yescharacteristic
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C22⋊C4×C47—21no—
176C22⋊C4×C47—21no—
177C42×C47C22×C411yescharacteristic
178C42×C47C2×D411yescharacteristic
179C42×C47#4111yescharacteristic
180C42×C47C2411yescharacteristic
181C22⋊Dic47—21no—
182#10625335—22no—
183#10625335—41no—
184#10625334—22no—
185#10625334—41no—
186(C2×D47)⋊C4—21no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189(C2×D47)⋊C4—21no—
190C4⋊Dic47C22×C411yescharacteristic
191C4⋊Dic47C22×C411yescharacteristic
192Dic47⋊C4—21no—
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196C4×Dic47—21no—
197#10625329—81no—
198#10625329—81no—
199C2×C47⋊C8—21no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—81no—
202C2×C47⋊C8—81no—
203C2×C47⋊C8C22×C411yescharacteristic
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C2×D411yescharacteristic
208C2×C47⋊C8C2×D411yescharacteristic
209C2×C47⋊C8C2×D411yescharacteristic
210C2×C47⋊C8C2×D411yescharacteristic
211#10625324—81no—
212C8×D47—81no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—42no—
216C23×C47—42no—
217C23×C47—81no—
218C23×C47C4×D411yescharacteristic
219C22×D47—21no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47—21no—
223D4×C47—42no—
224D4×C47#13112yes—
225C2×C4×C47—22no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—21no—
231C2×C4×C47—21no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—41no—
236C2×C4×C47—81no—
237C2×C4×C47—81no—
238C2×C4×C47—81no—
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C4×D411yescharacteristic
242C2×C4×C47C23×C411yescharacteristic
243C2×C4×C47C22×D411yescharacteristic
244C2×C4×C47C2×#4111yescharacteristic
245C22⋊D47—42no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248C2×Dic47—21no—
249D188—21no—
250D188—21no—
251C4×D47—41no—
252C4×D47—41no—
253Dic94—21no—
254Dic94—21no—
255C8×C47—41no—
256C8×C47—41no—
257C8×C47—41no—
258C8×C47—41no—
259C47⋊C8—21no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—21no—
265C47⋊C8—21no—
266C47⋊C8—21no—
267C47⋊C8—41no—
268C47⋊C8—41no—
269#18020—471nomaximal, Sylow
270C22×C47—21no—
271C22×C47—21no—
272C22×C47—22no—
273C22×C47—41no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—84no—
279C22×C47#44412yes—
280C22×C47C2×C4×D411yescharacteristic
281C2×D47—41no—
282C2×D47—41no—
283C2×D47—41no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—21no—
288C4×C47—41no—
289C4×C47—41no—
290C4×C47C2×#13111yescharacteristic
291C4×C47#56811yescharacteristic
292C4×C47#57611yescharacteristic
293C4×C47#57711yescharacteristic
294Dic47—41no—
295Dic47—41no—
296Dic47—41no—
297#3105—471no—
298#2994—471no—
299#2974—471no—
300#1594—471no—
301#1592—471no—
302#1583—471no—
303#1582—471no—
304#1581—471no—
305#1581—471no—
306#1580—471no—
307SD16⋊C8—471no—
308#1573—471no—
309#1494—471no—
310C2×D4⋊C8D4711yescharacteristic, complemented
311#1452—471no—
312C2×C47—22no—
313C2×C47—42no—
314C2×C47—81no—
315C2×C47#293311yescharacteristic
316C2×C47#294611yescharacteristic
317C2×C47C2×#44411yescharacteristic
318D47—81no—
319#529—471no—
320C2×C4×D4C2×D4711yescharacteristic
321#484—471no—
322#481—471no—
323#478—471no—
324#478—471no—
325#463—471no—
326#463—471no—
327#450—471no—
328#447—471no—
329#446—471no—
330C8×Q8—471no—
331C4×SD16—471no—
332C4×SD16—471no—
333C4×D8—471no—
334C4×D8—471no—
335#436—471no—
336#436—471no—
337#436—471no—
338#435—941no—
339#435—941no—
340#435—941no—
341C8×D4—471no—
342C8×D4—471no—
343C8×D4—471no—
344C8×D4—941no—
345#433—941no—
346#432—471no—
347#431—471no—
348#431—471no—
349#424—941no—
350C2×C4⋊C8C2×D4711yescharacteristic
351#407—941no—
352C2×C22⋊C8—941no—
353C2×C4×C8C2×D4711yescharacteristic
354#335—471no—
355#335—471no—
356#334—471no—
357#334—471no—
358Q8⋊C8—471no—
359Q8⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8C2×D4711yescharacteristic
363D4⋊C8C2×D4711yescharacteristic
364D4⋊C8C2×D4711yescharacteristic
365D4⋊C8C2×D4711yescharacteristic
366#322—471no—
367#322—471no—
368#322—471no—
369#322—471no—
370C47#1802011yescharacteristic, complemented, Sylow
371C22×D4C4×D4711yescharacteristic
372C23×C4—21no—
373C2×SD16—471no—
374C2×SD16—471no—
375C2×D8—471no—
376C2×D8—471no—
377C2×M16—941no—
378C2×M16—941no—
379C2×M16—941no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—941no—
383C22×C8—941no—
384C22×C8—941no—
385#126—941no—
386#125—471no—
387#124—471no—
388#123—941no—
389C22⋊Q8—471no—
390#121—471no—
391C4×Q8—471no—
392C4×D4—21no—
393C4×D4—21no—
394C4×D4—471no—
395C4×D4—941no—
396C4×D4C4×D4711yescharacteristic
397C4×D4C4×D4711yescharacteristic
398C4×D4C22×D4711yescharacteristic
399C4×D4C22×D4711yescharacteristic
400#117—941no—
401C2×C4⋊C4C4×D4711yescharacteristic
402C2×C22⋊C4—21no—
403C2×C42C22×D4711yescharacteristic
404#107—471no—
405#107—471no—
406#106—471no—
407#106—471no—
408C4⋊C8—21no—
409C4⋊C8—471no—
410C4⋊C8—471no—
411C4⋊C8—471no—
412C4⋊C8—471no—
413C4⋊C8—471no—
414C4⋊C8—471no—
415C4⋊C8—941no—
416C4⋊C8—941no—
417C4⋊C8C22×D4711yescharacteristic
418C4⋊C8C22×D4711yescharacteristic
419#103—471no—
420#103—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425#102—471no—
426#102—471no—
427C22⋊C8—471no—
428C22⋊C8—471no—
429C22⋊C8—471no—
430C22⋊C8—471no—
431C22⋊C8—941no—
432C22⋊C8—941no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8—941no—
437C22⋊C8—941no—
438#97—941no—
439#97—941no—
440C4×C8—21no—
441C4×C8—471no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—471no—
445C4×C8—941no—
446C4×C8C22×D4711yescharacteristic
447C4×C8C22×D4711yescharacteristic
448C24—21no—
449C2×Q8—471no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—41no—
453C2×D4—471no—
454C2×D4—941no—
455C2×D4C2×C4×D4711yescharacteristic
456C2×D4C2×C4×D4711yescharacteristic
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—21no—
462C22×C4—81no—
463C22×C4—81no—
464C22×C4—941no—
465C22×C4C2×C4×D4711yescharacteristic
466C22×C4D4×D4711yescharacteristic
467C22×C4#1062535211yescharacteristic
468SD16—942no—
469SD16—1881no—
470D8—942no—
471D8—1881no—
472M16—3761no—
473M16—3761no—
474M16—3761no—
475C2×C8—21no—
476C2×C8—21no—
477C2×C8—21no—
478C2×C8—21no—
479C2×C8—42no—
480C2×C8—81no—
481C2×C8—471no—
482C2×C8—471no—
483C2×C8—471no—
484C2×C8—471no—
485C2×C8—471no—
486C2×C8—471no—
487C2×C8—471no—
488C2×C8—471no—
489C2×C8—941no—
490C2×C8—941no—
491C2×C8—3761no—
492C2×C8—3761no—
493C2×C8—3761no—
494C4⋊C4—21no—
495C4⋊C4—471no—
496C4⋊C4—471no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4—941no—
500C4⋊C4—941no—
501C4⋊C4C2×C4×D4711yescharacteristic
502C4⋊C4C2×C4×D4711yescharacteristic
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—21no—
506C22⋊C4—21no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C22⋊C4—941no—
510C22⋊C4—941no—
511C22⋊C4—941no—
512C42—941no—
513C42C2×C4×D4711yescharacteristic
514C42D4×D4711yescharacteristic
515C42#1062535211yescharacteristic
516C42C23×D4711yescharacteristic
517C23—21no—
518C23—21no—
519C23—42no—
520C23—42no—
521C23—81no—
522C23—941no—
523C23(C22⋊D47)⋊C411yescharacteristic
524Q8—941no—
525Q8—941no—
526D4—21no—
527D4—21no—
528D4—21no—
529D4—42no—
530D4—941no—
531D4—941no—
532D4—1882no—
533D4#1309403012yes—
534C2×C4—22no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—21no—
539C2×C4—21no—
540C2×C4—21no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—41no—
545C2×C4—81no—
546C2×C4—81no—
547C2×C4—81no—
548C2×C4—941no—
549C2×C4—941no—
550C2×C4—941no—
551C2×C4—1881no—
552C2×C4—1881no—
553C2×C4(C22⋊D47)⋊C411yescharacteristic
554C2×C4(C22⋊D47)⋊C411yescharacteristic
555C2×C4(C22⋊D47)⋊C411yescharacteristic
556C2×C4C22×C4×D4711yescharacteristic
557C2×C4C2×D4×D4711yescharacteristic
558C2×C4C2×#1062535211yescharacteristic
559C8—41no—
560C8—41no—
561C8—41no—
562C8—41no—
563C8—941no—
564C8—941no—
565C8—941no—
566C8—941no—
567C8—941no—
568C8—941no—
569C8—941no—
570C8—941no—
571C8—1881no—
572C8—1881no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—41no—
581C22—84no—
582C22—1881no—
583C22—1881no—
584C22—1881no—
585C22#1568924212yes—
586C22C2×(C22⋊D47)⋊C411yescharacteristic
587C4—21no—
588C4—21no—
589C4—21no—
590C4—21no—
591C4—41no—
592C4—41no—
593C4—1881no—
594C4—1881no—
595C4—1881no—
596C4C2×#1309403011yescharacteristic
597C4#1568988911yescharacteristic
598C4#1568992411yescharacteristic
599C4#1568992911yescharacteristic
600C2—22no—
601C2—42no—
602C2—81no—
603C2—3761no—
604C2#2025210911yescharacteristic
605C2#2025221411yescharacteristic
606C2C2×#1568924211yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC2×C47×D4⋊C8C2
socleC22×C47C2×C4×D4
prime radical#15689257C4
cosocleC42×C47C24
hypercenterC2×D4⋊C8D47
hypocenterC47#18020
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ C2×D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #20252544C2semidirect
3. #20252423C2semidirect
4. #20242299C2semidirect
5. #20242287C2semidirect
6. #20242234C2semidirect
7. #20242221C2semidirect
8. #20242220C2semidirect
9. #20242214C2semidirect
10. #20242209C2semidirect
11. #20242197C2semidirect
12. #20242171C2semidirect
13. #20241849C2semidirect
14. #20241680C2semidirect
15. C2×C47×D4⋊C8C2semidirect
25. #15689250C22semidirect
26. #15689247C22semidirect
33. #15689200C22semidirect
39. #15689188C22semidirect
48. #15688875C22semidirect
49. #15688875C22semidirect
50. #15688873C22semidirect
51. #15688873C22semidirect
52. #15688855C22semidirect
53. #15688855C22semidirect
54. #15688852C22semidirect
55. #15688852C22semidirect
56. #15688845C22semidirect
57. #15688845C22semidirect
58. #15688845C22semidirect
59. #15688845C22semidirect
310. C2×D4⋊C8D47semidirect
370. C47#18020semidirect

Maximal subgroups

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

subgroupindex
#202534352
#202525442
#202524232
#202422992
#202422872
#202422342
#202422212
#202422202
#202422142
#202422092
#202421972
#202421712
#202418492
#202416802
C2×C47×D4⋊C82
#1802047