Finite Group Databasebeta

← #26186457

Subgroups — #26186457

Order 12032.

620 conjugacy classes of subgroups.

The subgroup lattice has 582 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20253406C211yesmaximal, characteristic
2#20252539C211yesmaximal, characteristic, complemented
3#20242259C211yesmaximal, characteristic, complemented
4#20242252C211yesmaximal, characteristic, complemented
5#20242231C211yesmaximal, characteristic, complemented
6#20242224C211yesmaximal, characteristic, complemented
7#20242210C211yesmaximal, characteristic, complemented
8#20242205C211yesmaximal, characteristic, complemented
9C8×#10625336C211yesmaximal, characteristic, complemented
10C8×#10625335C211yesmaximal, characteristic, complemented
11#20242158C211yesmaximal, characteristic, complemented
12#20241827C211yesmaximal, characteristic, complemented
13#20241799C211yesmaximal, characteristic, complemented
14#20241683C211yesmaximal, characteristic, complemented
15C47×#2988C211yesmaximal, characteristic, complemented
16#15689657C2211yescharacteristic
17#15689464C411yescharacteristic
18#15689447C411yescharacteristic
19#15689430C411yescharacteristic
20#15689423C411yescharacteristic
21#15689345C411yescharacteristic
22#15689338C411yescharacteristic
23#15689285C411yescharacteristic
24#15689268C411yescharacteristic
25#15689253C2211yescharacteristic
26C8×Dic94C2211yescharacteristic
27C4×#10625337C2211yescharacteristic
28C4×#10625336C2211yescharacteristic
29C4×#10625335C2211yescharacteristic
30C4×#10625334C2211yescharacteristic
31#15689202C2211yescharacteristic
32#15689198—21no—
33#15689197—21no—
34C8×D188C2211yescharacteristic
35#15689183—21no—
36#15689176C2211yescharacteristic
37#15689148—21no—
38#15689147C2211yescharacteristic
39C4×#10625329C2211yescharacteristic
40#15688873C2211yescharacteristic
41#15688873C2211yescharacteristic
42#15688873C2211yescharacteristic
43#15688873C2211yescharacteristic
44Q8⋊(C47⋊C8)C2211yescharacteristic
45Q8⋊(C47⋊C8)C2211yescharacteristic
46#15688853C2211yescharacteristic
47#15688853C2211yescharacteristic
48D4⋊(C47⋊C8)C2211yescharacteristic
49D4⋊(C47⋊C8)C2211yescharacteristic
50#15688850C2211yescharacteristic
51#15688850C2211yescharacteristic
52#15688845C2211yescharacteristic
53#15688845C2211yescharacteristic
54#15688844C2211yescharacteristic
55C8×C47⋊C8C2211yescharacteristic
56C4×#41×C47C2211yescharacteristic
57C8×Q8×C47C2211yescharacteristic
58C8×Q8×C47C2211yescharacteristic
59C8×D4×C47—21no—
60C8×D4×C47—21no—
61C8×D4×C47C2211yescharacteristic
62C8×D4×C47C2211yescharacteristic
63C47×#431—21no—
64C47×#431C2211yescharacteristic
65C2×C4⋊C8×C47—21no—
66C2×C4⋊C8×C47C2211yescharacteristic
67C2×#10625337C2×C411yescharacteristic
68C2×#10625335C2×C411yescharacteristic
69C2×#10625336C2×C411yescharacteristic
70C2×#10625334C2×C411yescharacteristic
71C2×#10625329—21no—
72C2×#10625329—21no—
73C2×#10625324—21no—
74C2×C8×D47—21no—
75#13094018—21no—
76#13094016C2×C411yescharacteristic
77#13094012C2×C411yescharacteristic
78#13094007—21no—
79#13094003C2×C411yescharacteristic
80#13093998C2×C411yescharacteristic
81C4×Dic94C2311yescharacteristic
82C4×D188C2311yescharacteristic
83C4×C22⋊D47—21no—
84#13093981—21no—
85#13093957C2×C411yescharacteristic
86#13093957C2×C411yescharacteristic
87#13093955C2×C411yescharacteristic
88#13093955C2×C411yescharacteristic
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#13093948C2×C411yescharacteristic
97#13093948C2×C411yescharacteristic
98#13093947C2×C411yescharacteristic
99#13093947C2×C411yescharacteristic
100#13093945C2×C411yescharacteristic
101#13093945C2×C411yescharacteristic
102#13093944C2×C411yescharacteristic
103#13093944C2×C411yescharacteristic
104C22⋊(C47⋊C8)C2×C411yescharacteristic
105C22⋊(C47⋊C8)C2×C411yescharacteristic
106(C2×D47)⋊C8—21no—
107(C2×D47)⋊C8—21no—
108#13093935—21no—
109#13093934—21no—
110C4×C47⋊C8C2311yescharacteristic
111C4×C47⋊C8C2311yescharacteristic
112C4×C47⋊C8C2311yescharacteristic
113C4×C47⋊C8C2311yescharacteristic
114C8×Dic47—21no—
115C2×#41×C47C2×C411yescharacteristic
116C22×C8×C47—21no—
117C22×C8×C47—21no—
118C22×C8×C47—21no—
119C4×Q8×C47C2×C411yescharacteristic
120C4×Q8×C47C2311yescharacteristic
121C4×D4×C47—21no—
122C4×D4×C47—21no—
123C4×D4×C47C2×C411yescharacteristic
124C4×D4×C47C2311yescharacteristic
125#117×C47—21no—
126#117×C47C2×C411yescharacteristic
127C2×C42×C47—21no—
128C2×C42×C47C2311yescharacteristic
129C4⋊C8×C47—21no—
130C4⋊C8×C47—21no—
131C4⋊C8×C47—21no—
132C4⋊C8×C47D411yescharacteristic
133C4⋊C8×C47D411yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C22⋊C8×C47—21no—
137C22⋊C8×C47—21no—
138C22⋊C8×C47D411yescharacteristic
139C22⋊C8×C47D411yescharacteristic
140C4×C8×C47—21no—
141C4×C8×C47—21no—
142C4×C8×C47C2311yescharacteristic
143C4×C8×C47C2311yescharacteristic
144#41×C47—22no—
145#41×C47—22no—
146C2×Q8×C47C22×C411yescharacteristic
147C2×D4×C47—21no—
148C2×D4×C47C22×C411yescharacteristic
149C22×C4×C47—21no—
150C22×C4×C47—21no—
151C22×C4×C47—21no—
152C22×C4×C47C22×C411yescharacteristic
153C22×C4×C47C2×D411yescharacteristic
154C22×C4×C47#4111yescharacteristic
155C2×C22⋊D47—21no—
156C2×D188C22×C411yescharacteristic
157C2×C4×D47—21no—
158C2×Dic94C22×C411yescharacteristic
159C2×C8×C47—21no—
160C2×C8×C47—21no—
161C2×C8×C47—81no—
162C2×C8×C47—81no—
163C2×C8×C47—81no—
164C2×C8×C47C2×D411yescharacteristic
165C2×C8×C47C2×D411yescharacteristic
166C2×C8×C47C2×D411yescharacteristic
167C2×C8×C47C2×D411yescharacteristic
168C4⋊C4×C47—21no—
169C4⋊C4×C47—21no—
170C4⋊C4×C47C22×C411yescharacteristic
171C4⋊C4×C47C22×C411yescharacteristic
172C22⋊C4×C47—21no—
173C22⋊C4×C47—21no—
174C22⋊C4×C47—21no—
175C42×C47—21no—
176C42×C47—21no—
177C42×C47—21no—
178C42×C47C22×C411yescharacteristic
179C42×C47C2×D411yescharacteristic
180C42×C47#4111yescharacteristic
181C42×C47C2411yescharacteristic
182C22⋊Dic47—21no—
183#10625337—22no—
184#10625336—22no—
185#10625335—22no—
186#10625334—22no—
187(C2×D47)⋊C4—21no—
188(C2×D47)⋊C4—21no—
189(C2×D47)⋊C4—21no—
190(C2×D47)⋊C4—21no—
191C4⋊Dic47C22×C411yescharacteristic
192C4⋊Dic47C22×C411yescharacteristic
193Dic47⋊C4—21no—
194Dic47⋊C4—21no—
195Dic47⋊C4—21no—
196Dic47⋊C4—21no—
197C4×Dic47—21no—
198#10625329—42no—
199#10625329—81no—
200C2×C47⋊C8—21no—
201C2×C47⋊C8—21no—
202C2×C47⋊C8—21no—
203C2×C47⋊C8—21no—
204C2×C47⋊C8C22×C411yescharacteristic
205C2×C47⋊C8C22×C411yescharacteristic
206C2×C47⋊C8C22×C411yescharacteristic
207C2×C47⋊C8C22×C411yescharacteristic
208#10625324—81no—
209C8×D47—81no—
210C23×C47—21no—
211C23×C47C4×D411yescharacteristic
212C22×D47—21no—
213Q8×C47—21no—
214Q8×C47#13112yes—
215D4×C47—24no—
216D4×C47—21no—
217D4×C47#13112yes—
218C2×C4×C47—24no—
219C2×C4×C47—21no—
220C2×C4×C47—21no—
221C2×C4×C47—21no—
222C2×C4×C47—21no—
223C2×C4×C47—21no—
224C2×C4×C47—21no—
225C2×C4×C47—21no—
226C2×C4×C47—41no—
227C2×C4×C47—41no—
228C2×C4×C47—41no—
229C2×C4×C47—81no—
230C2×C4×C47C4×D411yescharacteristic
231C2×C4×C47C4×D411yescharacteristic
232C2×C4×C47C4×D411yescharacteristic
233C2×C4×C47C23×C411yescharacteristic
234C2×C4×C47C22×D411yescharacteristic
235C2×C4×C47C2×#4111yescharacteristic
236C22⋊D47—81no—
237C2×Dic47—21no—
238C2×Dic47—21no—
239C2×Dic47—21no—
240D188—21no—
241D188—21no—
242C4×D47—41no—
243C4×D47—41no—
244Dic94—21no—
245Dic94—21no—
246C8×C47—21no—
247C8×C47—21no—
248C8×C47—21no—
249C8×C47—21no—
250C8×C47—41no—
251C8×C47—41no—
252C47⋊C8—22no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—21no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259C47⋊C8—41no—
260#17927—471nomaximal, Sylow
261C22×C47—21no—
262C22×C47—22no—
263C22×C47—21no—
264C22×C47—21no—
265C22×C47—41no—
266C22×C47—41no—
267C22×C47C2×C4×D411yescharacteristic
268C2×D47—41no—
269C2×D47—41no—
270C2×D47—41no—
271C4×C47—21no—
272C4×C47—22no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47—21no—
276C4×C47—41no—
277C4×C47—41no—
278C4×C47C2×#13111yescharacteristic
279C4×C47C2×#13111yescharacteristic
280C4×C47#57711yescharacteristic
281C4×C47#57711yescharacteristic
282Dic47—41no—
283Dic47—41no—
284Dic47—41no—
285#3102—471no—
286#2993—471no—
287#2988D4711yescharacteristic, complemented
288#1587—471no—
289#1586—471no—
290#1583—471no—
291#1582—471no—
292#1580—471no—
293#1579—471no—
294C8×SD16—471no—
295C8×SD16—471no—
296#1570—471no—
297#1489—471no—
298#1483—471no—
299#1453—471no—
300C2×C47—41no—
301C2×C47—42no—
302C2×C47#292911yescharacteristic
303C2×C47#295211yescharacteristic
304C2×C47#295611yescharacteristic
305D47—81no—
306#529—471no—
307C4×#41C2×D4711yescharacteristic
308#485—471no—
309#482—471no—
310#479—471no—
311#478—471no—
312#464—471no—
313#463—471no—
314#452—471no—
315#449—471no—
316#446—471no—
317C8×Q8—471no—
318C8×Q8C2×D4711yescharacteristic
319C8×Q8C2×D4711yescharacteristic
320C4×Q16—471no—
321C4×SD16—471no—
322C4×SD16—471no—
323C4×D8—471no—
324#436—471no—
325#436—941no—
326#435—941no—
327C8×D4—21no—
328C8×D4—21no—
329C8×D4—471no—
330C8×D4C2×D4711yescharacteristic
331C8×D4C2×D4711yescharacteristic
332#433—941no—
333#431—21no—
334#431—471no—
335#431C2×D4711yescharacteristic
336#424—941no—
337#423—471no—
338C2×C4⋊C8—21no—
339C2×C4⋊C8C2×D4711yescharacteristic
340C4×M16—471no—
341#334—471no—
342#334—471no—
343#334—471no—
344#334—471no—
345Q8⋊C8—471no—
346Q8⋊C8—471no—
347Q8⋊C8—471no—
348Q8⋊C8—471no—
349D4⋊C8—471no—
350D4⋊C8—471no—
351D4⋊C8—471no—
352D4⋊C8—471no—
353#322—471no—
354#322—471no—
355#322—471no—
356C82—471no—
357C47#1792711yescharacteristic, complemented, Sylow
358C2×#41C4×D4711yescharacteristic
359C2×Q16—471no—
360C2×SD16—471no—
361C2×SD16—471no—
362C2×D8—471no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C22×C8—21no—
367C22×C8—21no—
368C22×C8—21no—
369C22×C8—941no—
370#126—941no—
371#125—471no—
372#124—471no—
373#123—941no—
374C22⋊Q8—471no—
375#121—471no—
376C4×Q8—471no—
377C4×Q8C4×D4711yescharacteristic
378C4×Q8C22×D4711yescharacteristic
379C4×D4—21no—
380C4×D4—21no—
381C4×D4—471no—
382C4×D4—941no—
383C4×D4C4×D4711yescharacteristic
384C4×D4C22×D4711yescharacteristic
385#117—21no—
386#117—941no—
387#117C4×D4711yescharacteristic
388C2×C42—21no—
389C2×C42C22×D4711yescharacteristic
390#107—471no—
391#107—471no—
392#106—471no—
393#106—471no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—21no—
397C4⋊C8—471no—
398C4⋊C8—471no—
399C4⋊C8—471no—
400C4⋊C8—471no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8—941no—
404C4⋊C8C22⋊D4711yescharacteristic
405C4⋊C8C22⋊D4711yescharacteristic
406C4⋊C8C22×D4711yescharacteristic
407C4⋊C8C22×D4711yescharacteristic
408#103—471no—
409#103—471no—
410#103—471no—
411#103—471no—
412#102—471no—
413#102—471no—
414#102—471no—
415#102—471no—
416C22⋊C8—21no—
417C22⋊C8—21no—
418C22⋊C8—471no—
419C22⋊C8—471no—
420C22⋊C8—941no—
421C22⋊C8—941no—
422C22⋊C8C22⋊D4711yescharacteristic
423C22⋊C8C22⋊D4711yescharacteristic
424#97—941no—
425#97—941no—
426C4×C8—21no—
427C4×C8—21no—
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—471no—
431C4×C8—471no—
432C4×C8—941no—
433C4×C8C22×D4711yescharacteristic
434C4×C8C22×D4711yescharacteristic
435#41—22no—
436#41—22no—
437C2×Q8—471no—
438C2×Q8C2×C4×D4711yescharacteristic
439C2×D4—21no—
440C2×D4—471no—
441C2×D4—941no—
442C2×D4C2×C4×D4711yescharacteristic
443C22×C4—21no—
444C22×C4—21no—
445C22×C4—21no—
446C22×C4—941no—
447C22×C4C2×C4×D4711yescharacteristic
448C22×C4#1062535011yescharacteristic
449C22×C4C2×C22⋊D4711yescharacteristic
450Q16—942no—
451SD16—942no—
452SD16—942no—
453D8—942no—
454M16—3761no—
455M16—3761no—
456M16—1882no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—81no—
460C2×C8—81no—
461C2×C8—81no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—941no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—3761no—
471C2×C8C2×C22⋊D4711yescharacteristic
472C2×C8C2×C22⋊D4711yescharacteristic
473C2×C8C2×C22⋊D4711yescharacteristic
474C2×C8C2×C22⋊D4711yescharacteristic
475C4⋊C4—21no—
476C4⋊C4—21no—
477C4⋊C4—471no—
478C4⋊C4—471no—
479C4⋊C4—941no—
480C4⋊C4—941no—
481C4⋊C4—941no—
482C4⋊C4—941no—
483C4⋊C4C2×C4×D4711yescharacteristic
484C4⋊C4C2×C4×D4711yescharacteristic
485C22⋊C4—21no—
486C22⋊C4—21no—
487C22⋊C4—21no—
488C22⋊C4—941no—
489C22⋊C4—941no—
490C22⋊C4—941no—
491C22⋊C4—941no—
492C22⋊C4—941no—
493C42—21no—
494C42—21no—
495C42—21no—
496C42—941no—
497C42C2×C4×D4711yescharacteristic
498C42#1062535011yescharacteristic
499C42C2×C22⋊D4711yescharacteristic
500C42C23×D4711yescharacteristic
501C23—21no—
502C23—941no—
503C23C4×C22⋊D4711yescharacteristic
504Q8—21no—
505Q8—941no—
506Q8—941no—
507Q8#1309403012yes—
508D4—24no—
509D4—21no—
510D4—941no—
511D4—941no—
512D4—3761no—
513D4#1309403012yes—
514C2×C4—24no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—21no—
519C2×C4—21no—
520C2×C4—21no—
521C2×C4—21no—
522C2×C4—41no—
523C2×C4—41no—
524C2×C4—41no—
525C2×C4—81no—
526C2×C4—941no—
527C2×C4—941no—
528C2×C4—941no—
529C2×C4—1881no—
530C2×C4—1881no—
531C2×C4C4×C22⋊D4711yescharacteristic
532C2×C4C4×C22⋊D4711yescharacteristic
533C2×C4C4×C22⋊D4711yescharacteristic
534C2×C4C22×C4×D4711yescharacteristic
535C2×C4C22×C22⋊D4711yescharacteristic
536C2×C4C2×#1062535011yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—942no—
544C8—941no—
545C8—941no—
546C8—941no—
547C8—941no—
548C8—1881no—
549C8—1881no—
550C8—1881no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—22no—
555C22—41no—
556C22—41no—
557C22—1881no—
558C22—1881no—
559C22—1881no—
560C22C2×C4×C22⋊D4711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—22no—
566C4—41no—
567C4—41no—
568C4—1881no—
569C4—1881no—
570C4—1881no—
571C4C2×#1309403011yescharacteristic
572C4C2×#1309403011yescharacteristic
573C4#1568993111yescharacteristic
574C4#1568993411yescharacteristic
575C2—41no—
576C2—42no—
577C2—3761no—
578C2#2025208211yescharacteristic
579C2#2025226911yescharacteristic
580C2#2025229511yescharacteristic
subgroupG/H
centerC2×C4C22×C22⋊D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#2988C2
socleC22×C47C2×C4×D4
prime radical#15689268C4
cosocleC42×C47C24
hypercenter#2988D47
hypocenterC47#17927
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ #431 ◁ #2988

Complements

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

NH ≅ G/Ntype
2. #20252539C2semidirect
3. #20242259C2semidirect
4. #20242252C2semidirect
5. #20242231C2semidirect
6. #20242224C2semidirect
7. #20242210C2semidirect
8. #20242205C2semidirect
9. C8×#10625336C2semidirect
10. C8×#10625335C2semidirect
11. #20242158C2semidirect
12. #20241827C2semidirect
13. #20241799C2semidirect
14. #20241683C2semidirect
15. C47×#2988C2semidirect
287. #2988D47semidirect
357. C47#17927semidirect

Maximal subgroups

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

subgroupindex
#202534062
#202525392
#202422592
#202422522
#202422312
#202422242
#202422102
#202422052
C8×#106253362
C8×#106253352
#202421582
#202418272
#202417992
#202416832
C47×#29882
#1792747