Finite Group Databasebeta

← #26186338

Subgroups — #26186338

Order 12032.

648 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
1#20253435C211yesmaximal, characteristic
2#20252539C211yesmaximal, characteristic, complemented
3#20242252C211yesmaximal, characteristic, complemented
4#20242245C211yesmaximal, characteristic, complemented
5#20242224C211yesmaximal, characteristic, complemented
6#20242217C211yesmaximal, characteristic, complemented
7#20242210C211yesmaximal, characteristic, complemented
8#20242200C211yesmaximal, characteristic, complemented
9C8×#10625335C211yesmaximal, characteristic, complemented
10C8×#10625334C211yesmaximal, characteristic, complemented
11#20242176C211yesmaximal, characteristic, complemented
12#20241813C211yesmaximal, characteristic, complemented
13#20241794C211yesmaximal, characteristic, complemented
14#20241688C211yesmaximal, characteristic, complemented
15C47×#2972C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689458C411yescharacteristic
18#15689441C411yescharacteristic
19#15689423C411yescharacteristic
20#15689423C411yescharacteristic
21#15689338C411yescharacteristic
22#15689338C411yescharacteristic
23#15689274C411yescharacteristic
24#15689257C411yescharacteristic
25#15689253C2211yescharacteristic, complemented
26C8×Dic94C2211yescharacteristic, complemented
27C4×#10625335C2211yescharacteristic
28C4×#10625335C2211yescharacteristic
29C4×#10625334C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689202C2211yescharacteristic, complemented
32#15689198—21no—
33#15689197—21no—
34C8×D188C2211yescharacteristic, complemented
35#15689183—21no—
36#15689176C2211yescharacteristic
37#15689176C2211yescharacteristic
38#15689148—21no—
39#15689147C2211yescharacteristic
40#15688875C2211yescharacteristic, complemented
41#15688875C2211yescharacteristic, complemented
42#15688873C2211yescharacteristic, complemented
43#15688873C2211yescharacteristic, complemented
44#15688853C2211yescharacteristic, complemented
45#15688853C2211yescharacteristic, complemented
46D4⋊(C47⋊C8)C2211yescharacteristic
47D4⋊(C47⋊C8)C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50#15688850C2211yescharacteristic, complemented
51#15688850C2211yescharacteristic, complemented
52#15688845C2211yescharacteristic, complemented
53#15688845C2211yescharacteristic, complemented
54#15688844C2211yescharacteristic, complemented
55C8×C47⋊C8C2211yescharacteristic, complemented
56C2×C4×D4×C47C2211yescharacteristic
57C8×D4×C47—21no—
58C8×D4×C47—21no—
59C8×D4×C47C2211yescharacteristic
60C8×D4×C47C2211yescharacteristic
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#431C2211yescharacteristic
64C47×#431C2211yescharacteristic
65C2×C22⋊C8×C47—21no—
66C2×C22⋊C8×C47—21no—
67C2×#10625335C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625334C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625324—21no—
73C2×C8×D47—21no—
74#13094018—21no—
75#13094016C2×C411yescharacteristic
76#13094012C2×C411yescharacteristic
77#13094007—21no—
78#13094003C2×C411yescharacteristic
79#13093998C2×C411yescharacteristic
80C4×Dic94C2311yescharacteristic
81C4×D188C2311yescharacteristic
82C4×C22⋊D47—21no—
83#13093981—21no—
84#13093957C2×C411yescharacteristic
85#13093957C2×C411yescharacteristic
86#13093955C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88C4⋊(C47⋊C8)—21no—
89C4⋊(C47⋊C8)—21no—
90C4⋊(C47⋊C8)C2×C411yescharacteristic
91C4⋊(C47⋊C8)C2×C411yescharacteristic
92C4⋊(C47⋊C8)C2311yescharacteristic
93C4⋊(C47⋊C8)C2311yescharacteristic
94Dic47⋊C8—21no—
95Dic47⋊C8—21no—
96#13093947C2×C411yescharacteristic
97#13093947C2×C411yescharacteristic
98#13093945C2×C411yescharacteristic
99#13093945C2×C411yescharacteristic
100#13093945C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102#13093944C2×C411yescharacteristic
103#13093944C2×C411yescharacteristic
104C22⋊(C47⋊C8)—21no—
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106C22⋊(C47⋊C8)C2×C411yescharacteristic
107(C2×D47)⋊C8—21no—
108(C2×D47)⋊C8—21no—
109#13093934—21no—
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
114C8×Dic47—21no—
115C22×D4×C47C2×C411yescharacteristic
116C23×C4×C47—21no—
117C22×C8×C47—21no—
118C22×C8×C47—21no—
119C22×C8×C47—21no—
120C22×C8×C47—21no—
121C4×D4×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47C2×C411yescharacteristic
124C4×D4×C47C2×C411yescharacteristic
125C4×D4×C47C2311yescharacteristic
126C4×D4×C47C2311yescharacteristic
127C2×C4⋊C4×C47C2×C411yescharacteristic
128C2×C22⋊C4×C47—21no—
129C2×C42×C47C2311yescharacteristic
130C4⋊C8×C47D411yescharacteristic
131C4⋊C8×C47D411yescharacteristic
132C4⋊C8×C47C2311yescharacteristic
133C4⋊C8×C47C2311yescharacteristic
134C22⋊C8×C47—21no—
135C22⋊C8×C47—21no—
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47—21no—
139C22⋊C8×C47D411yescharacteristic
140C22⋊C8×C47D411yescharacteristic
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144C24×C47—21no—
145C2×D4×C47—22no—
146C2×D4×C47—22no—
147C2×D4×C47—21no—
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—81no—
167C2×C8×C47—81no—
168C2×C8×C47—81no—
169C2×C8×C47—81no—
170C2×C8×C47C2×D411yescharacteristic
171C2×C8×C47C2×D411yescharacteristic
172C2×C8×C47C2×D411yescharacteristic
173C2×C8×C47C2×D411yescharacteristic
174C4⋊C4×C47—21no—
175C4⋊C4×C47C22×C411yescharacteristic
176C4⋊C4×C47C22×C411yescharacteristic
177C22⋊C4×C47—21no—
178C22⋊C4×C47—21no—
179C22⋊C4×C47—21no—
180C22⋊C4×C47—21no—
181C42×C47C22×C411yescharacteristic
182C42×C47C2×D411yescharacteristic
183C42×C47#4111yescharacteristic
184C42×C47C2411yescharacteristic
185C22⋊Dic47—21no—
186#10625335—22no—
187#10625335—22no—
188#10625334—22no—
189#10625334—22no—
190(C2×D47)⋊C4—21no—
191(C2×D47)⋊C4—21no—
192(C2×D47)⋊C4—21no—
193(C2×D47)⋊C4—21no—
194C4⋊Dic47C22×C411yescharacteristic
195C4⋊Dic47C22×C411yescharacteristic
196Dic47⋊C4—21no—
197Dic47⋊C4—21no—
198Dic47⋊C4—21no—
199Dic47⋊C4—21no—
200C4×Dic47—21no—
201#10625329—81no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8—21no—
205C2×C47⋊C8—21no—
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208C2×C47⋊C8C22×C411yescharacteristic
209C2×C47⋊C8C22×C411yescharacteristic
210#10625324—81no—
211C8×D47—81no—
212C23×C47—24no—
213C23×C47—21no—
214C23×C47—21no—
215C23×C47—81no—
216C23×C47—81no—
217C23×C47C4×D411yescharacteristic
218C22×D47—21no—
219D4×C47—24no—
220D4×C47—21no—
221D4×C47—21no—
222D4×C47#13112yes—
223D4×C47#13112yes—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—21no—
227C2×C4×C47—21no—
228C2×C4×C47—21no—
229C2×C4×C47—21no—
230C2×C4×C47—41no—
231C2×C4×C47—41no—
232C2×C4×C47—41no—
233C2×C4×C47—41no—
234C2×C4×C47—41no—
235C2×C4×C47—81no—
236C2×C4×C47—81no—
237C2×C4×C47—81no—
238C2×C4×C47C4×D411yescharacteristic
239C2×C4×C47C4×D411yescharacteristic
240C2×C4×C47C4×D411yescharacteristic
241C2×C4×C47C23×C411yescharacteristic
242C2×C4×C47C22×D411yescharacteristic
243C2×C4×C47C2×#4111yescharacteristic
244C22⋊D47—81no—
245C2×Dic47—21no—
246C2×Dic47—21no—
247C2×Dic47—21no—
248D188—21no—
249D188—21no—
250C4×D47—41no—
251C4×D47—41no—
252Dic94—21no—
253Dic94—21no—
254C8×C47—21no—
255C8×C47—21no—
256C8×C47—21no—
257C8×C47—21no—
258C8×C47—41no—
259C8×C47—41no—
260C47⋊C8—21no—
261C47⋊C8—21no—
262C47⋊C8—21no—
263C47⋊C8—21no—
264C47⋊C8—41no—
265C47⋊C8—41no—
266C47⋊C8—41no—
267C47⋊C8—41no—
268#17918—471nomaximal, Sylow
269C22×C47—21no—
270C22×C47—22no—
271C22×C47—22no—
272C22×C47—21no—
273C22×C47—21no—
274C22×C47—41no—
275C22×C47—41no—
276C22×C47—41no—
277C22×C47—41no—
278C22×C47—84no—
279C22×C47C2×C4×D411yescharacteristic
280C2×D47—41no—
281C2×D47—41no—
282C2×D47—41no—
283C4×C47—21no—
284C4×C47—21no—
285C4×C47—21no—
286C4×C47—21no—
287C4×C47—41no—
288C4×C47—41no—
289C4×C47C2×#13111yescharacteristic
290C4×C47C2×#13111yescharacteristic
291C4×C47#57611yescharacteristic
292C4×C47#57711yescharacteristic
293Dic47—41no—
294Dic47—41no—
295Dic47—41no—
296#3105—471no—
297#2993—471no—
298#2972D4711yescharacteristic, complemented
299#1586—471no—
300#1585—471no—
301#1582—471no—
302#1581—471no—
303#1580—471no—
304SD16⋊C8—471no—
305C8×SD16—471no—
306C8×D8—471no—
307#1574—471no—
308#1486—471no—
309#1482—471no—
310#1454—471no—
311C2×C47—41no—
312C2×C47—42no—
313C2×C47—42no—
314C2×C47#292911yescharacteristic
315C2×C47#294611yescharacteristic
316C2×C47#295711yescharacteristic
317D47—81no—
318#529—471no—
319C2×C4×D4C2×D4711yescharacteristic
320#484—471no—
321#481—471no—
322#478—471no—
323#478—471no—
324#463—471no—
325#463—471no—
326#450—471no—
327#447—471no—
328#446—471no—
329C8×Q8—471no—
330C4×SD16—471no—
331C4×SD16—471no—
332C4×D8—471no—
333C4×D8—471no—
334#436—471no—
335#436—941no—
336#435—941no—
337C8×D4—21no—
338C8×D4—21no—
339C8×D4—471no—
340C8×D4C2×D4711yescharacteristic
341C8×D4C2×D4711yescharacteristic
342C8×D4C2×D4711yescharacteristic
343C8×D4C2×D4711yescharacteristic
344#433—941no—
345#431—471no—
346#431—471no—
347#431C2×D4711yescharacteristic
348#431C2×D4711yescharacteristic
349#424—941no—
350#423—471no—
351C2×C22⋊C8—21no—
352C2×C22⋊C8—21no—
353#335—471no—
354#335—471no—
355#334—471no—
356#334—471no—
357Q8⋊C8—471no—
358Q8⋊C8—471no—
359D4⋊C8—471no—
360D4⋊C8—471no—
361D4⋊C8—471no—
362D4⋊C8—471no—
363D4⋊C8—471no—
364D4⋊C8—471no—
365#322—471no—
366#322—471no—
367#322—471no—
368C82—471no—
369C47#1791811yescharacteristic, complemented, Sylow
370C22×D4C4×D4711yescharacteristic
371C23×C4—21no—
372C2×SD16—471no—
373C2×SD16—471no—
374C2×D8—471no—
375C2×D8—471no—
376C2×M16—941no—
377C2×M16—941no—
378C22×C8—21no—
379C22×C8—21no—
380C22×C8—21no—
381C22×C8—21no—
382C22×C8—941no—
383#126—941no—
384#125—471no—
385#124—471no—
386#123—941no—
387C22⋊Q8—471no—
388#121—471no—
389C4×Q8—471no—
390C4×D4—21no—
391C4×D4—21no—
392C4×D4—471no—
393C4×D4—941no—
394C4×D4C4×D4711yescharacteristic
395C4×D4C4×D4711yescharacteristic
396C4×D4C22×D4711yescharacteristic
397C4×D4C22×D4711yescharacteristic
398#117—941no—
399C2×C4⋊C4C4×D4711yescharacteristic
400C2×C22⋊C4—21no—
401C2×C42C22×D4711yescharacteristic
402#107—471no—
403#107—471no—
404#106—471no—
405#106—471no—
406C4⋊C8—471no—
407C4⋊C8—471no—
408C4⋊C8—471no—
409C4⋊C8—471no—
410C4⋊C8—941no—
411C4⋊C8—941no—
412C4⋊C8—941no—
413C4⋊C8—941no—
414C4⋊C8C22⋊D4711yescharacteristic
415C4⋊C8C22⋊D4711yescharacteristic
416C4⋊C8C22×D4711yescharacteristic
417C4⋊C8C22×D4711yescharacteristic
418#103—471no—
419#103—471no—
420#102—471no—
421#102—471no—
422#102—471no—
423#102—471no—
424#102—471no—
425#102—471no—
426C22⋊C8—21no—
427C22⋊C8—21no—
428C22⋊C8—21no—
429C22⋊C8—21no—
430C22⋊C8—21no—
431C22⋊C8—471no—
432C22⋊C8—471no—
433C22⋊C8—941no—
434C22⋊C8—941no—
435C22⋊C8—941no—
436C22⋊C8C22⋊D4711yescharacteristic
437C22⋊C8C22⋊D4711yescharacteristic
438#97—941no—
439C4×C8—21no—
440C4×C8—471no—
441C4×C8—471no—
442C4×C8—471no—
443C4×C8—471no—
444C4×C8—941no—
445C4×C8C22×D4711yescharacteristic
446C4×C8C22×D4711yescharacteristic
447C24—21no—
448C2×Q8—471no—
449C2×D4—22no—
450C2×D4—22no—
451C2×D4—21no—
452C2×D4—471no—
453C2×D4—941no—
454C2×D4C2×C4×D4711yescharacteristic
455C2×D4C2×C4×D4711yescharacteristic
456C22×C4—21no—
457C22×C4—21no—
458C22×C4—21no—
459C22×C4—21no—
460C22×C4—21no—
461C22×C4—81no—
462C22×C4—81no—
463C22×C4—941no—
464C22×C4C2×C4×D4711yescharacteristic
465C22×C4#1062535011yescharacteristic
466C22×C4C2×C22⋊D4711yescharacteristic
467SD16—942no—
468SD16—942no—
469D8—942no—
470D8—942no—
471M16—3761no—
472M16—3761no—
473C2×C8—21no—
474C2×C8—21no—
475C2×C8—81no—
476C2×C8—81no—
477C2×C8—81no—
478C2×C8—81no—
479C2×C8—471no—
480C2×C8—471no—
481C2×C8—471no—
482C2×C8—471no—
483C2×C8—941no—
484C2×C8—941no—
485C2×C8—941no—
486C2×C8—941no—
487C2×C8—3761no—
488C2×C8C2×C22⋊D4711yescharacteristic
489C2×C8C2×C22⋊D4711yescharacteristic
490C2×C8C2×C22⋊D4711yescharacteristic
491C2×C8C2×C22⋊D4711yescharacteristic
492C4⋊C4—21no—
493C4⋊C4—471no—
494C4⋊C4—471no—
495C4⋊C4—941no—
496C4⋊C4—941no—
497C4⋊C4—941no—
498C4⋊C4—941no—
499C4⋊C4C2×C4×D4711yescharacteristic
500C4⋊C4C2×C4×D4711yescharacteristic
501C22⋊C4—21no—
502C22⋊C4—21no—
503C22⋊C4—21no—
504C22⋊C4—21no—
505C22⋊C4—941no—
506C22⋊C4—941no—
507C22⋊C4—941no—
508C22⋊C4—941no—
509C22⋊C4—941no—
510C42—941no—
511C42C2×C4×D4711yescharacteristic
512C42#1062535011yescharacteristic
513C42C2×C22⋊D4711yescharacteristic
514C42C23×D4711yescharacteristic
515C23—24no—
516C23—21no—
517C23—21no—
518C23—81no—
519C23—81no—
520C23—941no—
521C23C4×C22⋊D4711yescharacteristic
522Q8—941no—
523Q8—941no—
524D4—24no—
525D4—21no—
526D4—21no—
527D4—941no—
528D4—941no—
529D4—3761no—
530D4#1309403012yes—
531D4#1309403012yes—
532C2×C4—21no—
533C2×C4—21no—
534C2×C4—21no—
535C2×C4—21no—
536C2×C4—21no—
537C2×C4—21no—
538C2×C4—41no—
539C2×C4—41no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—81no—
544C2×C4—81no—
545C2×C4—81no—
546C2×C4—941no—
547C2×C4—941no—
548C2×C4—941no—
549C2×C4—1881no—
550C2×C4—1881no—
551C2×C4C4×C22⋊D4711yescharacteristic
552C2×C4C4×C22⋊D4711yescharacteristic
553C2×C4C4×C22⋊D4711yescharacteristic
554C2×C4C22×C4×D4711yescharacteristic
555C2×C4C22×C22⋊D4711yescharacteristic
556C2×C4C2×#1062535011yescharacteristic
557C8—21no—
558C8—21no—
559C8—21no—
560C8—21no—
561C8—41no—
562C8—41no—
563C8—941no—
564C8—941no—
565C8—941no—
566C8—941no—
567C8—1881no—
568C8—1881no—
569C8—1881no—
570C8—1881no—
571C22—21no—
572C22—21no—
573C22—21no—
574C22—22no—
575C22—22no—
576C22—41no—
577C22—41no—
578C22—41no—
579C22—41no—
580C22—84no—
581C22—1881no—
582C22—1881no—
583C22—1881no—
584C22C2×C4×C22⋊D4711yescharacteristic
585C4—21no—
586C4—21no—
587C4—21no—
588C4—21no—
589C4—41no—
590C4—41no—
591C4—1881no—
592C4—1881no—
593C4—1881no—
594C4C2×#1309403011yescharacteristic
595C4C2×#1309403011yescharacteristic
596C4#1568992611yescharacteristic
597C4#1568993411yescharacteristic
598C2—41no—
599C2—42no—
600C2—42no—
601C2—3761no—
602C2#2025208211yescharacteristic
603C2#2025222011yescharacteristic
604C2#2025230311yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2972C2
socleC22×C47C2×C4×D4
prime radical#15689257C4
cosocleC42×C47C24
hypercenter#2972D47
hypocenterC47#17918
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2972

Complements

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

NH ≅ G/Ntype
2. #20252539C2semidirect
3. #20242252C2semidirect
4. #20242245C2semidirect
5. #20242224C2semidirect
6. #20242217C2semidirect
7. #20242210C2semidirect
8. #20242200C2semidirect
9. C8×#10625335C2semidirect
10. C8×#10625334C2semidirect
11. #20242176C2semidirect
12. #20241813C2semidirect
13. #20241794C2semidirect
14. #20241688C2semidirect
15. C47×#2972C2semidirect
25. #15689253C22semidirect
26. C8×Dic94C22semidirect
31. #15689202C22semidirect
34. C8×D188C22semidirect
40. #15688875C22semidirect
41. #15688875C22semidirect
42. #15688873C22semidirect
43. #15688873C22semidirect
44. #15688853C22semidirect
45. #15688853C22semidirect
50. #15688850C22semidirect
51. #15688850C22semidirect
52. #15688845C22semidirect
53. #15688845C22semidirect
54. #15688844C22semidirect
55. C8×C47⋊C8C22semidirect
298. #2972D47semidirect
369. C47#17918semidirect

Maximal subgroups

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

subgroupindex
#202534352
#202525392
#202422522
#202422452
#202422242
#202422172
#202422102
#202422002
C8×#106253352
C8×#106253342
#202421762
#202418132
#202417942
#202416882
C47×#29722
#1791847