Finite Group Databasebeta

← #26185525

Subgroups — #26185525

Order 12032.

634 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#20252350C211yesmaximal, characteristic
2#20252049C211yesmaximal, characteristic
3#20251953C211yesmaximal, characteristic
4#20242176C211yesmaximal, characteristic, complemented
5#20242175C211yesmaximal, characteristic, complemented
6#20242172C211yesmaximal, characteristic, complemented
7#20242171C211yesmaximal, characteristic, complemented
8#20242161C211yesmaximal, characteristic, complemented
9#20242157C211yesmaximal, characteristic, complemented
10#20242155C211yesmaximal, characteristic, complemented
11#20242154C211yesmaximal, characteristic, complemented
12#20242145C211yesmaximal, characteristic, complemented
13#20242137C211yesmaximal, characteristic, complemented
14#334×D47C211yesmaximal, characteristic, complemented
15C47×#1565C211yesmaximal, characteristic, complemented
16C2×#13094030—21no—
17C4×#10625350C2211yescharacteristic
18#15689251C411yescharacteristic
19#15689251C411yescharacteristic
20#15689199C411yescharacteristic
21#15689199C411yescharacteristic
22#15689196C411yescharacteristic
23#15689196C411yescharacteristic
24#15689192C411yescharacteristic
25#15689192C411yescharacteristic
26#15689182—21no—
27#15689181—21no—
28#15689180C2211yescharacteristic
29#15689179C2211yescharacteristic
30#15689176C2211yescharacteristic
31#15689175C2211yescharacteristic
32#15689174C2211yescharacteristic
33#15689174C2211yescharacteristic
34#15689149—21no—
35#15689148—21no—
36#15689148—21no—
37#15689147C2211yescharacteristic
38#15689145C2211yescharacteristic
39#15689145C2211yescharacteristic
40#15689145C2211yescharacteristic
41C4⋊C8×D47C2211yescharacteristic
42C4⋊C8×D47C2211yescharacteristic
43C4⋊C8×D47C2211yescharacteristic
44#15689088—21no—
45#15689077—21no—
46C4×#10625324C2211yescharacteristic
47C4×C8×D47C2211yescharacteristic
48#15688876C2211yescharacteristic
49#15688876C2211yescharacteristic
50#15688875C2211yescharacteristic
51#15688875C2211yescharacteristic
52#15688875C2211yescharacteristic
53#15688875C2211yescharacteristic
54#15688874C2211yescharacteristic
55#15688874C2211yescharacteristic
56#15688873C2211yescharacteristic
57#15688873C2211yescharacteristic
58#15688873C2211yescharacteristic
59#15688873C2211yescharacteristic
60C47×#431C2211yescharacteristic
61C2×C4⋊C8×C47C2211yescharacteristic
62C4×M16×C47C2211yescharacteristic
63C47×#335C2211yescharacteristic
64C47×#335C2211yescharacteristic
65C47×#334C2211yescharacteristic
66C47×#334C2211yescharacteristic
67C2×#10625350D411yescharacteristic
68#13094030—44no—
69C2×#10625329—21no—
70C2×#10625324—21no—
71C2×#10625324—21no—
72C2×#10625324—21no—
73C2×#10625324C2×C411yescharacteristic
74C2×#10625324C2×C411yescharacteristic
75C2×C8×D47—21no—
76C2×C8×D47—21no—
77C2×C8×D47—21no—
78C2×C8×D47C2×C411yescharacteristic
79C2×C8×D47C2×C411yescharacteristic
80C4×Dic94C2×C411yescharacteristic
81C4×Dic94Q811yescharacteristic
82C4×D188C2×C411yescharacteristic
83C4×D188Q811yescharacteristic
84C4×C22⋊D47C2×C411yescharacteristic
85C4×C22⋊D47C2×C411yescharacteristic
86C4×C22⋊D47Q811yescharacteristic
87C4×C22⋊D47Q811yescharacteristic
88#13093983D411yescharacteristic
89#13093981D411yescharacteristic
90#13093981D411yescharacteristic
91C42×D47C2311yescharacteristic
92C42×D47C2311yescharacteristic
93C4⋊(C47⋊C8)—21no—
94C4⋊(C47⋊C8)C2×C411yescharacteristic
95C4⋊(C47⋊C8)C2×C411yescharacteristic
96C4⋊(C47⋊C8)C2311yescharacteristic
97C4⋊(C47⋊C8)C2311yescharacteristic
98C4⋊(C47⋊C8)C2311yescharacteristic
99C4⋊(C47⋊C8)C2311yescharacteristic
100Dic47⋊C8—21no—
101Dic47⋊C8—21no—
102Dic47⋊C8—21no—
103Dic47⋊C8—21no—
104Dic47⋊C8—21no—
105Dic47⋊C8—21no—
106Dic47⋊C8C2×C411yescharacteristic
107Dic47⋊C8C2×C411yescharacteristic
108Dic47⋊C8C2×C411yescharacteristic
109Dic47⋊C8C2×C411yescharacteristic
110C22⋊(C47⋊C8)—21no—
111C22⋊(C47⋊C8)C2×C411yescharacteristic
112C22⋊(C47⋊C8)C2×C411yescharacteristic
113(C2×D47)⋊C8—21no—
114(C2×D47)⋊C8—21no—
115(C2×D47)⋊C8C2×C411yescharacteristic
116(C2×D47)⋊C8C2×C411yescharacteristic
117(C2×D47)⋊C8C2×C411yescharacteristic
118(C2×D47)⋊C8C2×C411yescharacteristic
119#13093935—21no—
120#13093934—21no—
121#13093934C2×C411yescharacteristic
122#13093934C2×C411yescharacteristic
123C4×C47⋊C8C2311yescharacteristic
124C4×C47⋊C8C2311yescharacteristic
125C8×Dic47—21no—
126C8×Dic47C2×C411yescharacteristic
127C8×Dic47C2×C411yescharacteristic
128C2×M16×C47C2×C411yescharacteristic
129C2×M16×C47C2×C411yescharacteristic
130C22×C8×C47—21no—
131C2×C42×C47C2311yescharacteristic
132C4⋊C8×C47—21no—
133C4⋊C8×C47C2311yescharacteristic
134C4⋊C8×C47C2311yescharacteristic
135C4⋊C8×C47C2311yescharacteristic
136C4⋊C8×C47C2311yescharacteristic
137C22⋊C8×C47—21no—
138#97×C47C2×C411yescharacteristic
139#97×C47C2×C411yescharacteristic
140C4×C8×C47—21no—
141C4×C8×C47C2311yescharacteristic
142C4×C8×C47C2311yescharacteristic
143C22×C4×C47C22×C411yescharacteristic
144C22×C4×C47C2×D411yescharacteristic
145C22×C4×C47C2×Q811yescharacteristic
146C2×C22⋊D47C4⋊C411yescharacteristic
147C2×C22⋊D47C4⋊C411yescharacteristic
148#10625350—22no—
149#10625350—22no—
150C2×D188C4⋊C411yescharacteristic
151C2×C4×D47C22×C411yescharacteristic
152C2×C4×D47C22×C411yescharacteristic
153C2×C4×D47C2×D411yescharacteristic
154C2×C4×D47C2×D411yescharacteristic
155C2×C4×D47C2×Q811yescharacteristic
156C2×C4×D47C2×Q811yescharacteristic
157C2×Dic94C4⋊C411yescharacteristic
158M16×C47—22no—
159M16×C47—41no—
160C2×C8×C47—21no—
161C2×C8×C47—21no—
162C2×C8×C47—21no—
163C2×C8×C47—21no—
164C2×C8×C47—42no—
165C2×C8×C47C22×C411yescharacteristic
166C2×C8×C47C22×C411yescharacteristic
167C2×C8×C47C22×C411yescharacteristic
168C2×C8×C47C22×C411yescharacteristic
169C42×C47C22×C411yescharacteristic
170C42×C47C2×D411yescharacteristic
171C42×C47C2×Q811yescharacteristic
172C42×C47C2411yescharacteristic
173C22⋊Dic47C4⋊C411yescharacteristic
174C22⋊Dic47C4⋊C411yescharacteristic
175(C2×D47)⋊C4C4⋊C411yescharacteristic
176(C2×D47)⋊C4C4⋊C411yescharacteristic
177(C2×D47)⋊C4C4⋊C411yescharacteristic
178(C2×D47)⋊C4C4⋊C411yescharacteristic
179C4⋊Dic47C4⋊C411yescharacteristic
180C4⋊Dic47C4⋊C411yescharacteristic
181Dic47⋊C4C4⋊C411yescharacteristic
182Dic47⋊C4C4⋊C411yescharacteristic
183Dic47⋊C4C4⋊C411yescharacteristic
184Dic47⋊C4C4⋊C411yescharacteristic
185C4×Dic47C22×C411yescharacteristic
186C4×Dic47C22×C411yescharacteristic
187C4×Dic47C2×D411yescharacteristic
188C4×Dic47C2×D411yescharacteristic
189C4×Dic47C2×Q811yescharacteristic
190C4×Dic47C2×Q811yescharacteristic
191#10625329—42no—
192C2×C47⋊C8—21no—
193C2×C47⋊C8—21no—
194C2×C47⋊C8—21no—
195C2×C47⋊C8—21no—
196C2×C47⋊C8C22×C411yescharacteristic
197C2×C47⋊C8C22×C411yescharacteristic
198C2×C47⋊C8C22×C411yescharacteristic
199C2×C47⋊C8C22×C411yescharacteristic
200#10625324—22no—
201#10625324—41no—
202#10625324—42no—
203#10625324—42no—
204#10625324—42no—
205C8×D47—22no—
206C8×D47—41no—
207C8×D47—42no—
208C8×D47—42no—
209C8×D47—42no—
210C23×C47C2×C4⋊C411yescharacteristic
211C22×D47C2×C4⋊C411yescharacteristic
212C22×D47C2×C4⋊C411yescharacteristic
213C2×C4×C47—21no—
214C2×C4×C47—21no—
215C2×C4×C47—21no—
216C2×C4×C47—21no—
217C2×C4×C47—41no—
218C2×C4×C47C2×C4⋊C411yescharacteristic
219C2×C4×C47C2×C4⋊C411yescharacteristic
220C2×C4×C47C2×C4⋊C411yescharacteristic
221C2×C4×C47C23×C411yescharacteristic
222C2×C4×C47C22×D411yescharacteristic
223C2×C4×C47C22×Q811yescharacteristic
224C22⋊D47—22no—
225C22⋊D47—22no—
226C2×Dic47C2×C4⋊C411yescharacteristic
227C2×Dic47C2×C4⋊C411yescharacteristic
228C2×Dic47C2×C4⋊C411yescharacteristic
229C2×Dic47C2×C4⋊C411yescharacteristic
230C2×Dic47C2×C4⋊C411yescharacteristic
231C2×Dic47C2×C4⋊C411yescharacteristic
232D188—22no—
233C4×D47—21no—
234C4×D47—21no—
235C4×D47—21no—
236C4×D47—21no—
237C4×D47—21no—
238C4×D47—21no—
239C4×D47—41no—
240C4×D47—41no—
241C4×D47AGL(1,ℤ/8)12yes—
242C4×D47#13712yes—
243Dic94—22no—
244C8×C47—21no—
245C8×C47—21no—
246C8×C47—21no—
247C8×C47—41no—
248C8×C47—41no—
249C8×C47—41no—
250C8×C47—41no—
251C8×C47#13112yescomplemented
252C47⋊C8—21no—
253C47⋊C8—21no—
254C47⋊C8—21no—
255C47⋊C8—21no—
256C47⋊C8—41no—
257C47⋊C8—41no—
258C47⋊C8—41no—
259C47⋊C8—41no—
260#17830—471nomaximal, Sylow
261C22×C47—21no—
262C22×C47—21no—
263C22×C47—21no—
264C22×C47C22×C4⋊C411yescharacteristic
265C2×D47—21no—
266C2×D47—21no—
267C2×D47—21no—
268C2×D47—21no—
269C2×D47—21no—
270C2×D47#42812yes—
271C4×C47—21no—
272C4×C47—21no—
273C4×C47—21no—
274C4×C47—21no—
275C4×C47C2×#13111yescharacteristic
276C4×C47#56811yescharacteristic
277C4×C47C2×AGL(1,ℤ/8)11yescharacteristic
278C4×C47C2×#13711yescharacteristic
279Dic47—21no—
280Dic47—21no—
281Dic47—21no—
282Dic47—21no—
283Dic47—21no—
284Dic47#42812yes—
285#2965—471no—
286#2925—471no—
287#2906—471no—
288#1574—471no—
289#1574—471no—
290#1573—471no—
291#1573—471no—
292#1571—471no—
293#1570—471no—
294#1569—471no—
295#1569—471no—
296#1567—471no—
297#1565—471no—
298#1565D4711yescharacteristic, complemented
299C2×#334—471no—
300C2×C47—41no—
301C2×C47#290611yescharacteristic
302C2×C47C2×#42811yescharacteristic
303C2×C47#291611yescharacteristic
304D47—22no—
305D47—41no—
306C2×#131—941no—
307C4×#41—471no—
308#446—471no—
309#446—471no—
310#436—471no—
311#436—471no—
312#435—471no—
313#435—471no—
314#435—471no—
315#435—471no—
316#433—941no—
317#433—941no—
318#432—471no—
319#432—471no—
320#431—471no—
321#431—471no—
322#431—471no—
323#431—471no—
324#431C2×D4711yescharacteristic
325#424—941no—
326#424—941no—
327#424—941no—
328#423—471no—
329#423—471no—
330#423—471no—
331#423—471no—
332C2×C4⋊C8—471no—
333C2×C4⋊C8—471no—
334C2×C4⋊C8—471no—
335C2×C4⋊C8C2×D4711yescharacteristic
336#408—941no—
337#405—941no—
338C4×M16—471no—
339C4×M16C2×D4711yescharacteristic
340C2×C4×C8—471no—
341#335—471no—
342#335—471no—
343#335—471no—
344#335—471no—
345#335—471no—
346#335—471no—
347#335C2×D4711yescharacteristic
348#335C2×D4711yescharacteristic
349#334—471no—
350#334—471no—
351#334—471no—
352#334—471no—
353#334—471no—
354#334—471no—
355#334C2×D4711yescharacteristic
356#334C2×D4711yescharacteristic
357C47#1783011yescharacteristic, complemented, Sylow
358C2×#41—471no—
359#131—1884no—
360C2×M16—471no—
361C2×M16—471no—
362C2×M16—941no—
363C2×M16—941no—
364C2×M16—941no—
365C2×M16—941no—
366C2×M16C4×D4711yescharacteristic
367C2×M16C4×D4711yescharacteristic
368C22×C8—21no—
369C22×C8—471no—
370C22×C8—471no—
371C22×C8—941no—
372C22×C8—941no—
373C22×C8—941no—
374C4×Q8—471no—
375C4×Q8—471no—
376C4×D4—471no—
377C4×D4—471no—
378C4×D4—471no—
379C4×D4—471no—
380C4×D4—471no—
381C4×D4—471no—
382#117—471no—
383#117—471no—
384#117—471no—
385C2×C42—471no—
386C2×C42—471no—
387C2×C42C22×D4711yescharacteristic
388C4⋊C8—21no—
389C4⋊C8—471no—
390C4⋊C8—471no—
391C4⋊C8—471no—
392C4⋊C8—471no—
393C4⋊C8—471no—
394C4⋊C8—471no—
395C4⋊C8—471no—
396C4⋊C8—471no—
397C4⋊C8—471no—
398C4⋊C8—471no—
399C4⋊C8—941no—
400C4⋊C8—941no—
401C4⋊C8—941no—
402C4⋊C8—941no—
403C4⋊C8—941no—
404C4⋊C8—941no—
405C4⋊C8—941no—
406C4⋊C8C22×D4711yescharacteristic
407C4⋊C8C22×D4711yescharacteristic
408C4⋊C8C22×D4711yescharacteristic
409C4⋊C8C22×D4711yescharacteristic
410C22⋊C8—21no—
411C22⋊C8—471no—
412C22⋊C8—471no—
413C22⋊C8—471no—
414C22⋊C8—471no—
415C22⋊C8—471no—
416C22⋊C8—471no—
417C22⋊C8—941no—
418C22⋊C8—941no—
419C22⋊C8—941no—
420#97—471no—
421#97—471no—
422#97—941no—
423#97—941no—
424#97C4×D4711yescharacteristic
425#97C4×D4711yescharacteristic
426C4×C8—21no—
427C4×C8—471no—
428C4×C8—471no—
429C4×C8—471no—
430C4×C8—471no—
431C4×C8—941no—
432C4×C8C22×D4711yescharacteristic
433C4×C8C22×D4711yescharacteristic
434#41—942no—
435#41—942no—
436C2×Q8—471no—
437C2×D4—471no—
438C2×D4—471no—
439C2×D4—471no—
440C22×C4—471no—
441C22×C4—471no—
442C22×C4—471no—
443C22×C4—471no—
444C22×C4—471no—
445C22×C4—471no—
446C22×C4C2×C4×D4711yescharacteristic
447C22×C4D4×D4711yescharacteristic
448C22×C4Q8×D4711yescharacteristic
449M16—22no—
450M16—41no—
451M16—942no—
452M16—1881no—
453M16—1882no—
454M16—1882no—
455M16—1882no—
456M16—1882no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—42no—
462C2×C8—471no—
463C2×C8—471no—
464C2×C8—471no—
465C2×C8—471no—
466C2×C8—942no—
467C2×C8—941no—
468C2×C8—941no—
469C2×C8—941no—
470C2×C8—941no—
471C2×C8—1881no—
472C2×C8—1882no—
473C2×C8—1882no—
474C2×C8—1882no—
475C2×C8C2×C4×D4711yescharacteristic
476C2×C8C2×C4×D4711yescharacteristic
477C2×C8C2×C4×D4711yescharacteristic
478C2×C8C2×C4×D4711yescharacteristic
479C4⋊C4—471no—
480C4⋊C4—471no—
481C4⋊C4—471no—
482C4⋊C4—471no—
483C4⋊C4—471no—
484C4⋊C4—471no—
485C22⋊C4—471no—
486C22⋊C4—471no—
487C22⋊C4—471no—
488C22⋊C4—471no—
489C22⋊C4—471no—
490C22⋊C4—471no—
491C42—471no—
492C42—471no—
493C42—471no—
494C42—471no—
495C42—471no—
496C42—471no—
497C42C2×C4×D4711yescharacteristic
498C42D4×D4711yescharacteristic
499C42Q8×D4711yescharacteristic
500C42C23×D4711yescharacteristic
501C23—471no—
502C23—471no—
503C23C4⋊C4×D4711yescharacteristic
504Q8—942no—
505D4—942no—
506D4—942no—
507D4—942no—
508C2×C4—21no—
509C2×C4—21no—
510C2×C4—21no—
511C2×C4—21no—
512C2×C4—41no—
513C2×C4—471no—
514C2×C4—472no—
515C2×C4—472no—
516C2×C4—471no—
517C2×C4—471no—
518C2×C4—471no—
519C2×C4—471no—
520C2×C4—471no—
521C2×C4—941no—
522C2×C4—941no—
523C2×C4—941no—
524C2×C4—941no—
525C2×C4—941no—
526C2×C4—941no—
527C2×C4—1881no—
528C2×C4—1881no—
529C2×C4C4⋊C4×D4711yescharacteristic
530C2×C4C4⋊C4×D4711yescharacteristic
531C2×C4C4⋊C4×D4711yescharacteristic
532C2×C4C22×C4×D4711yescharacteristic
533C2×C4C2×D4×D4711yescharacteristic
534C2×C4C2×Q8×D4711yescharacteristic
535C8—21no—
536C8—21no—
537C8—21no—
538C8—41no—
539C8—41no—
540C8—41no—
541C8—41no—
542C8—941no—
543C8—941no—
544C8—941no—
545C8—941no—
546C8—1881no—
547C8—1881no—
548C8—1881no—
549C8—1881no—
550C8#1309403012yescomplemented
551C22—21no—
552C22—21no—
553C22—21no—
554C22—472no—
555C22—941no—
556C22—941no—
557C22—941no—
558C22—941no—
559C22—941no—
560C22C2×C4⋊C4×D4711yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—472no—
566C4—941no—
567C4—941no—
568C4—941no—
569C4—941no—
570C4—941no—
571C4C2×#1309403011yescharacteristic
572C4#1568988911yescharacteristic
573C4AGL(1,ℤ/8)×D4711yescharacteristic
574C4#137×D4711yescharacteristic
575C2—41no—
576C2—942no—
577C2—1881no—
578C2#2025195311yescharacteristic
579C2#428×D4711yescharacteristic
580C2#2025199811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D47
commutatorC2×C4×C47C23×C4
FrattiniC42C23×D47
FittingC47×#1565C2
socleC22×C47C22×C4⋊C4
prime radicalC2×#10625350D4
cosocleC42×C47C24
hypercenter#1565D47
hypocenterC47#17830
LCSG ▷ C2×C4×C47 ▷ C2×C47 ▷ C47
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1565

Complements

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

NH ≅ G/Ntype
4. #20242176C2semidirect
5. #20242175C2semidirect
6. #20242172C2semidirect
7. #20242171C2semidirect
8. #20242161C2semidirect
9. #20242157C2semidirect
10. #20242155C2semidirect
11. #20242154C2semidirect
12. #20242145C2semidirect
13. #20242137C2semidirect
14. #334×D47C2semidirect
15. C47×#1565C2semidirect
251. C8×C47#131semidirect
298. #1565D47semidirect
357. C47#17830semidirect
550. C8#13094030semidirect

Maximal subgroups

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

subgroupindex
#202523502
#202520492
#202519532
#202421762
#202421752
#202421722
#202421712
#202421612
#202421572
#202421552
#202421542
#202421452
#202421372
#334×D472
C47×#15652
#1783047