Finite Group Databasebeta

← #26224133

Subgroups — #26224133

Order 12032.

730 conjugacy classes of subgroups.

The subgroup lattice has 638 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253170C211yesmaximal, characteristic
2#20252329C211yesmaximal, characteristic, complemented
3#20251817C211yesmaximal, characteristic
4#20244163C211yesmaximal, characteristic, complemented
5#20243990C211yesmaximal, characteristic, complemented
6#20243990C211yesmaximal, characteristic, complemented
7#20243664C211yesmaximal, characteristic
8#20243664C211yesmaximal, characteristic
9#20243409C211yesmaximal, characteristic
10#20243271C211yesmaximal, characteristic, complemented
11#20243266C211yesmaximal, characteristic, complemented
12#20243263C211yesmaximal, characteristic, complemented
13#20243229C211yesmaximal, characteristic
14#20243222C211yesmaximal, characteristic
15C47×#1986C211yesmaximal, characteristic, complemented
16C2×#13094032C2211yescharacteristic
17C2×#13094032C2211yescharacteristic
18C4×#10625350C2211yescharacteristic
19#15689427C411yescharacteristic, complemented
20#15689427C411yescharacteristic, complemented
21#15689420C411yescharacteristic, complemented
22#15689420C411yescharacteristic, complemented
23#15689415C411yescharacteristic, complemented
24#15689410C411yescharacteristic, complemented
25#15689405C411yescharacteristic, complemented
26#15689400C411yescharacteristic, complemented
27#15689254—21no—
28#15689254—21no—
29#15689254—21no—
30#15689254—21no—
31C2×#13093959C2211yescharacteristic
32C2×#13093959C2211yescharacteristic
33#15689159C2211yescharacteristic
34#15689159C2211yescharacteristic
35#15689150C2211yescharacteristic
36#15689150C2211yescharacteristic
37#15689147C2211yescharacteristic
38C2×C4⋊(C47⋊C8)C2211yescharacteristic
39C2×#13093952C2211yescharacteristic
40C2×#13093952C2211yescharacteristic
41#15689117C2211yescharacteristic
42#15689117C2211yescharacteristic
43#15689081C2211yescharacteristic
44#15689081C2211yescharacteristic
45#15689079C2211yescharacteristic
46#15689079C2211yescharacteristic
47#15689077—21no—
48#15689077—21no—
49#15689075—21no—
50C2×#13093935C2211yescharacteristic
51C2×#13093935C2211yescharacteristic
52#97×D47—21no—
53C2×C4×C47⋊C8C2211yescharacteristic
54#15688887C2211yescharacteristic
55#15688887C2211yescharacteristic
56#15688883C2211yescharacteristic
57#15688883C2211yescharacteristic
58#15688878C2211yescharacteristic
59#15688878C2211yescharacteristic
60C47×#533C2211yescharacteristic
61C4×M16×C47C2211yescharacteristic
62C4×C4⋊C4×C47C2211yescharacteristic
63C47×#339C2211yescharacteristic
64C47×#339C2211yescharacteristic
65C47×#339C2211yescharacteristic
66C47×#339C2211yescharacteristic
67C2×#10625350C2311yescharacteristic
68#13094032—22no—
69#13094032—22no—
70#13094032—22no—
71#13094032Q814yescomplemented
72C2×#10625329C2311yescharacteristic
73C2×#10625329C2311yescharacteristic
74C2×#10625324—21no—
75C2×#10625324—21no—
76C22×C47⋊C8C2311yescharacteristic
77C22×C47⋊C8C2311yescharacteristic
78C22×C47⋊C8C2311yescharacteristic
79C22×C47⋊C8C2311yescharacteristic
80C2×C8×D47—21no—
81C2×C8×D47—21no—
82C4×Dic94C2×C411yescharacteristic
83C4×Dic94C2×C411yescharacteristic
84C4×D188C2×C411yescharacteristic
85C4×D188C2×C411yescharacteristic
86C4×C22⋊D47—21no—
87C4×C22⋊D47—21no—
88#13093983C2311yescharacteristic
89#13093981—21no—
90C42×D47—21no—
91#13093959—22no—
92#13093959—22no—
93#13093957C2×C411yescharacteristic
94#13093957C2×C411yescharacteristic
95#13093957C2×C411yescharacteristic
96#13093957C2×C411yescharacteristic
97#13093955C2×C411yescharacteristic
98#13093955C2×C411yescharacteristic
99#13093955C2×C411yescharacteristic
100#13093955C2×C411yescharacteristic
101C4⋊(C47⋊C8)—21no—
102C4⋊(C47⋊C8)—21no—
103C4⋊(C47⋊C8)—21no—
104C4⋊(C47⋊C8)—21no—
105C4⋊(C47⋊C8)—21no—
106C4⋊(C47⋊C8)—21no—
107C4⋊(C47⋊C8)C2×C411yescharacteristic
108C4⋊(C47⋊C8)C2×C411yescharacteristic
109C4⋊(C47⋊C8)C2×C411yescharacteristic
110C4⋊(C47⋊C8)C2×C411yescharacteristic
111#13093952—22no—
112#13093952—22no—
113#13093947C2×C411yescharacteristic
114#13093947C2×C411yescharacteristic
115#13093947C2×C411yescharacteristic
116#13093947C2×C411yescharacteristic
117#13093944C2×C411yescharacteristic
118#13093944C2×C411yescharacteristic
119#13093944C2×C411yescharacteristic
120#13093944C2×C411yescharacteristic
121#13093935—21no—
122#13093935—21no—
123#13093935—22no—
124#13093935D411yescharacteristic
125#13093935D411yescharacteristic
126#13093935D411yescharacteristic
127#13093935D411yescharacteristic
128#13093934—21no—
129#13093934—21no—
130C4×C47⋊C8—21no—
131C4×C47⋊C8—21no—
132C4×C47⋊C8—22no—
133C8×Dic47—21no—
134C8×Dic47—21no—
135C2×M16×C47C2311yescharacteristic
136C2×M16×C47C2311yescharacteristic
137C4⋊Q8×C47C2×C411yescharacteristic
138C4⋊Q8×C47C2×C411yescharacteristic
139#125×C47C2×C411yescharacteristic
140#125×C47C2×C411yescharacteristic
141C22⋊Q8×C47—21no—
142C22⋊Q8×C47—21no—
143C4×Q8×C47—21no—
144C4×Q8×C47—21no—
145#117×C47C2311yescharacteristic
146#117×C47C2311yescharacteristic
147C2×C4⋊C4×C47—21no—
148C2×C42×C47C2311yescharacteristic
149C2×C42×C47C2311yescharacteristic
150C2×C42×C47C2311yescharacteristic
151#97×C47—21no—
152C4×C8×C47—21no—
153#95×C47—21no—
154C2×Q8×C47—21no—
155C2×Q8×C47—21no—
156C22×C4×C47—21no—
157C22×C4×C47—21no—
158C22×C4×C47#4111yescharacteristic
159C22×C4×C47#4111yescharacteristic
160C22×C4×C47C2411yescharacteristic
161C2×C22⋊D47—21no—
162#10625350—21no—
163#10625350—21no—
164#10625350C2×Q812yes—
165#10625350#4112yes—
166C2×D188C22×C411yescharacteristic
167C2×C4×D47—21no—
168C2×C4×D47—21no—
169C2×C4×D47—21no—
170C2×Dic94C22×C411yescharacteristic
171M16×C47—21no—
172M16×C47—21no—
173M16×C47C2×Q812yes—
174M16×C47#4112yes—
175C2×C8×C47—21no—
176C2×C8×C47—21no—
177C4⋊C4×C47—21no—
178C4⋊C4×C47—21no—
179C4⋊C4×C47—21no—
180C4⋊C4×C47—21no—
181C4⋊C4×C47—21no—
182C4⋊C4×C47—21no—
183C4⋊C4×C47—42no—
184C4⋊C4×C47C22×C411yescharacteristic
185C4⋊C4×C47C22×C411yescharacteristic
186C4⋊C4×C47C22×C411yescharacteristic
187C4⋊C4×C47C22×C411yescharacteristic
188C22⋊C4×C47—21no—
189C22⋊C4×C47—21no—
190C42×C47—21no—
191C42×C47—21no—
192C42×C47—21no—
193C42×C47—21no—
194C42×C47—21no—
195C42×C47—21no—
196C42×C47C22×C411yescharacteristic
197C42×C47C22×C411yescharacteristic
198C42×C47C2×D411yescharacteristic
199C42×C47C2×D411yescharacteristic
200C22⋊Dic47—21no—
201(C2×D47)⋊C4—21no—
202(C2×D47)⋊C4—21no—
203C4⋊Dic47C22×C411yescharacteristic
204C4⋊Dic47C22×C411yescharacteristic
205Dic47⋊C4—21no—
206Dic47⋊C4—21no—
207C4×Dic47—21no—
208C4×Dic47—21no—
209C4×Dic47—21no—
210#10625329—21no—
211#10625329—21no—
212#10625329—21no—
213#10625329—21no—
214C2×C47⋊C8—21no—
215C2×C47⋊C8—21no—
216C2×C47⋊C8—21no—
217C2×C47⋊C8—21no—
218C2×C47⋊C8—21no—
219C2×C47⋊C8—21no—
220C2×C47⋊C8—21no—
221C2×C47⋊C8—21no—
222C2×C47⋊C8C22×C411yescharacteristic
223C2×C47⋊C8C22×C411yescharacteristic
224C2×C47⋊C8C22×C411yescharacteristic
225C2×C47⋊C8C22×C411yescharacteristic
226C2×C47⋊C8C2×D411yescharacteristic
227C2×C47⋊C8C2×D411yescharacteristic
228C2×C47⋊C8C2×D411yescharacteristic
229C2×C47⋊C8C2×D411yescharacteristic
230C2×C47⋊C8C2×Q812yes—
231C2×C47⋊C8#4112yes—
232#10625324—24no—
233#10625324—24no—
234C8×D47—24no—
235C8×D47—24no—
236C23×C47C2×#4111yescharacteristic
237C22×D47—21no—
238Q8×C47—81no—
239Q8×C47—81no—
240C2×C4×C47—22no—
241C2×C4×C47—21no—
242C2×C4×C47—21no—
243C2×C4×C47—21no—
244C2×C4×C47—21no—
245C2×C4×C47—41no—
246C2×C4×C47—41no—
247C2×C4×C47—41no—
248C2×C4×C47—41no—
249C2×C4×C47—41no—
250C2×C4×C47—41no—
251C2×C4×C47—41no—
252C2×C4×C47C4×D411yescharacteristic
253C2×C4×C47C4×D411yescharacteristic
254C2×C4×C47C4×D411yescharacteristic
255C2×C4×C47C4×D411yescharacteristic
256C2×C4×C47C23×C411yescharacteristic
257C2×C4×C47C22×D411yescharacteristic
258C2×C4×C47C22×Q811yescharacteristic
259C2×C4×C47C2×#4111yescharacteristic
260C2×C4×C47C2×#4111yescharacteristic
261C2×C4×C47C2×#4111yescharacteristic
262C22⋊D47—22no—
263C22⋊D47—22no—
264C2×Dic47—21no—
265C2×Dic47—21no—
266C2×Dic47—21no—
267D188—21no—
268D188C4×Q812yes—
269C4×D47—22no—
270C4×D47—22no—
271C4×D47—81no—
272C4×D47—81no—
273Dic94—21no—
274Dic94C4×Q812yes—
275C8×C47—22no—
276C8×C47—22no—
277C47⋊C8—21no—
278C47⋊C8—21no—
279C47⋊C8—21no—
280C47⋊C8—21no—
281C47⋊C8—21no—
282C47⋊C8—21no—
283C47⋊C8—41no—
284C47⋊C8—41no—
285C47⋊C8C22⋊Q812yes—
286C47⋊C8C22⋊Q812yes—
287#21629—471nomaximal, Sylow
288C22×C47—21no—
289C22×C47—21no—
290C22×C47C2×C4×D411yescharacteristic
291C22×C47#52911yescharacteristic
292C22×C47#53311yescharacteristic
293C2×D47—22no—
294C2×D47—41no—
295C2×D47—41no—
296C4×C47—21no—
297C4×C47—21no—
298C4×C47—21no—
299C4×C47—21no—
300C4×C47—42no—
301C4×C47—41no—
302C4×C47—41no—
303C4×C47—41no—
304C4×C47—41no—
305C4×C47—81no—
306C4×C47C2×C4×Q811yescharacteristic
307C4×C47C4×#4111yescharacteristic
308C4×C47C2×C22⋊Q811yescharacteristic
309C4×C47#52511yescharacteristic
310Dic47—22no—
311Dic47—41no—
312Dic47—41no—
313#3076—471no—
314#2961—471no—
315#2875—471no—
316#1986D4711yescharacteristic, complemented
317#1950—471no—
318#1922—471no—
319#1922—471no—
320#1866—471no—
321#1866—471no—
322#1806—471no—
323#1773—471no—
324#1772—471no—
325#1771—471no—
326#1765—471no—
327#1764—471no—
328C2×C47—21no—
329C2×C47—21no—
330C2×C47C4×C22⋊Q811yescharacteristic
331C2×C47#295611yescharacteristic
332C2×C47#295711yescharacteristic
333D47—42no—
334C2×#131—471no—
335C2×#131—471no—
336#533C2×D4711yescharacteristic
337C4×#41—471no—
338#479—471no—
339#479—471no—
340#478—471no—
341#478—471no—
342#477—471no—
343#476—471no—
344#475—471no—
345#474—471no—
346#446—941no—
347#446—941no—
348#446—941no—
349#446—941no—
350C2×#108—471no—
351C2×#108—471no—
352#427—471no—
353#427—471no—
354#424—471no—
355#424—471no—
356#423—471no—
357C2×C4⋊C8—471no—
358C2×#104—471no—
359C2×#104—471no—
360#416—471no—
361#416—471no—
362#405—471no—
363#405—471no—
364#405—471no—
365#405—471no—
366#405—941no—
367#405—941no—
368C4×M16—941no—
369C4×M16C2×D4711yescharacteristic
370C2×#97—471no—
371C2×#97—471no—
372C2×#97—941no—
373C2×C4×C8—471no—
374C4×C4⋊C4C2×D4711yescharacteristic
375#341—471no—
376#341—471no—
377#339—471no—
378#339—471no—
379#339C2×D4711yescharacteristic
380#339C2×D4711yescharacteristic
381#339C2×D4711yescharacteristic
382#339C2×D4711yescharacteristic
383#336—471no—
384#336—471no—
385C47#2162911yescharacteristic, complemented, Sylow
386C2×#41—471no—
387#131—474no—
388#131—942no—
389#131—942no—
390#131—942no—
391C2×M16—471no—
392C2×M16—471no—
393C2×M16—941no—
394C2×M16—941no—
395C2×M16C22×D4711yescharacteristic
396C2×M16C22×D4711yescharacteristic
397C22×C8—471no—
398C22×C8—471no—
399C22×C8—471no—
400C22×C8—471no—
401C22×C8—941no—
402C22×C8—941no—
403C4⋊Q8C4×D4711yescharacteristic
404C4⋊Q8C4×D4711yescharacteristic
405#125C4×D4711yescharacteristic
406#125C4×D4711yescharacteristic
407C22⋊Q8—21no—
408C22⋊Q8—21no—
409C4×Q8—21no—
410C4×Q8—21no—
411C4×Q8—471no—
412C4×Q8—471no—
413C4×D4—471no—
414C4×D4—471no—
415C4×D4—941no—
416C4×D4—941no—
417#117—471no—
418#117—941no—
419#117C22×D4711yescharacteristic
420#117C22×D4711yescharacteristic
421C2×C4⋊C4—21no—
422C2×C42—941no—
423C2×C42C22×D4711yescharacteristic
424C2×C42C22×D4711yescharacteristic
425C2×C42C22×D4711yescharacteristic
426#108—942no—
427#108—942no—
428#107—471no—
429#107—471no—
430#107—471no—
431#107—471no—
432#106—471no—
433#106—471no—
434#106—471no—
435#106—471no—
436C4⋊C8—471no—
437C4⋊C8—471no—
438C4⋊C8—471no—
439C4⋊C8—471no—
440C4⋊C8—941no—
441C4⋊C8—941no—
442C4⋊C8—941no—
443C4⋊C8—941no—
444C4⋊C8—941no—
445C4⋊C8—941no—
446#104—942no—
447#104—942no—
448#103—471no—
449#103—471no—
450#103—471no—
451#103—471no—
452#102—471no—
453#102—471no—
454#102—471no—
455#102—471no—
456#97—21no—
457#97—471no—
458#97—471no—
459#97—471no—
460#97—471no—
461#97—942no—
462#97—941no—
463#97—941no—
464#97—941no—
465#97—941no—
466C4×C8—21no—
467C4×C8—942no—
468C4×C8—941no—
469C4×C8—941no—
470C4×C8—941no—
471C4×C8—941no—
472#95—21no—
473#41—472no—
474#41—472no—
475#41—941no—
476#41—941no—
477C2×Q8—21no—
478C2×Q8—21no—
479C2×Q8—471no—
480C2×D4—471no—
481C2×D4—941no—
482C22×C4—21no—
483C22×C4—21no—
484C22×C4—941no—
485C22×C4—941no—
486C22×C4—941no—
487C22×C4#1062535211yescharacteristic
488C22×C4#1062535211yescharacteristic
489C22×C4C23×D4711yescharacteristic
490M16—21no—
491M16—21no—
492M16—944no—
493M16—944no—
494M16—941no—
495M16—941no—
496M16—941no—
497M16—941no—
498M16Q8×D4712yes—
499M16#1062535412yes—
500C2×C8—21no—
501C2×C8—21no—
502C2×C8—471no—
503C2×C8—471no—
504C2×C8—472no—
505C2×C8—472no—
506C2×C8—471no—
507C2×C8—471no—
508C2×C8—471no—
509C2×C8—471no—
510C2×C8—471no—
511C2×C8—471no—
512C2×C8—944no—
513C2×C8—944no—
514C2×C8—941no—
515C2×C8—941no—
516C2×C8—941no—
517C2×C8—941no—
518C2×C8—941no—
519C2×C8—941no—
520C2×C8—941no—
521C2×C8—941no—
522C4⋊C4—21no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—21no—
526C4⋊C4—21no—
527C4⋊C4—21no—
528C4⋊C4—42no—
529C4⋊C4—471no—
530C4⋊C4—471no—
531C4⋊C4—941no—
532C4⋊C4—941no—
533C4⋊C4C2×C4×D4711yescharacteristic
534C4⋊C4C2×C4×D4711yescharacteristic
535C4⋊C4C2×C4×D4711yescharacteristic
536C4⋊C4C2×C4×D4711yescharacteristic
537C22⋊C4—21no—
538C22⋊C4—21no—
539C22⋊C4—941no—
540C22⋊C4—941no—
541C22⋊C4—941no—
542C42—21no—
543C42—21no—
544C42—21no—
545C42—21no—
546C42—21no—
547C42—21no—
548C42—941no—
549C42—941no—
550C42—941no—
551C42C2×C4×D4711yescharacteristic
552C42C2×C4×D4711yescharacteristic
553C42D4×D4711yescharacteristic
554C42D4×D4711yescharacteristic
555C23—941no—
556C23C2×#1062535211yescharacteristic
557Q8—81no—
558Q8—81no—
559Q8—472no—
560Q8—941no—
561D4—472no—
562D4—942no—
563D4—942no—
564D4—941no—
565C2×C4—22no—
566C2×C4—21no—
567C2×C4—21no—
568C2×C4—21no—
569C2×C4—21no—
570C2×C4—41no—
571C2×C4—41no—
572C2×C4—41no—
573C2×C4—41no—
574C2×C4—41no—
575C2×C4—41no—
576C2×C4—41no—
577C2×C4—941no—
578C2×C4—942no—
579C2×C4—942no—
580C2×C4—941no—
581C2×C4—941no—
582C2×C4—3761no—
583C2×C4—3761no—
584C2×C4(C22⋊D47)⋊C411yescharacteristic
585C2×C4(C22⋊D47)⋊C411yescharacteristic
586C2×C4(C22⋊D47)⋊C411yescharacteristic
587C2×C4(C22⋊D47)⋊C411yescharacteristic
588C2×C4C22×C4×D4711yescharacteristic
589C2×C4C2×D4×D4711yescharacteristic
590C2×C4C2×Q8×D4711yescharacteristic
591C2×C4#41×D4711yescharacteristic
592C2×C4#41×D4711yescharacteristic
593C2×C4C2×#1062535411yescharacteristic
594C8—22no—
595C8—22no—
596C8—472no—
597C8—472no—
598C8—941no—
599C8—941no—
600C8—941no—
601C8—941no—
602C8—941no—
603C8—941no—
604C8—1881no—
605C8—1881no—
606C22—21no—
607C22—21no—
608C22—942no—
609C22—1881no—
610C22—1881no—
611C22C2×(C22⋊D47)⋊C411yescharacteristic
612C22#1568965211yescharacteristic
613C22#1568967811yescharacteristic
614C4—21no—
615C4—21no—
616C4—21no—
617C4—21no—
618C4—42no—
619C4—41no—
620C4—41no—
621C4—41no—
622C4—41no—
623C4—81no—
624C4—942no—
625C4—1881no—
626C4—1881no—
627C4C4×Q8×D4711yescharacteristic
628C4C4×#1062535411yescharacteristic
629C4C22⋊Q8×D4711yescharacteristic
630C4#1568963611yescharacteristic
631C2—21no—
632C2—21no—
633C2—1882no—
634C2#2024592611yescharacteristic
635C2#2025229411yescharacteristic
636C2#2025230111yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC22×C4C23×D47
FittingC47×#1986C2
socleC22×C47C2×C4×D4
prime radicalC2×#10625350C23
cosocleC22×C4×C47C24
hypercenter#1986D47
hypocenterC47#21629
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1986

Complements

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

NH ≅ G/Ntype
2. #20252329C2semidirect
4. #20244163C2semidirect
5. #20243990C2semidirect
6. #20243990C2semidirect
10. #20243271C2semidirect
11. #20243266C2semidirect
12. #20243263C2semidirect
15. C47×#1986C2semidirect
19. #15689427C4semidirect
20. #15689427C4semidirect
21. #15689420C4semidirect
22. #15689420C4semidirect
23. #15689415C4semidirect
24. #15689410C4semidirect
25. #15689405C4semidirect
26. #15689400C4semidirect
71. #13094032Q8semidirect
316. #1986D47semidirect
385. C47#21629semidirect

Maximal subgroups

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

subgroupindex
#202531702
#202523292
#202518172
#202441632
#202439902
#202436642
#202434092
#202432712
#202432662
#202432632
#202432292
#202432222
C47×#19862
#2162947