Finite Group Databasebeta

← #27354269

Subgroups — #27354269

Order 13568.

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#20284735C211yesmaximal, characteristic
2#20283860C211yesmaximal, characteristic, complemented
3#20283824C211yesmaximal, characteristic, complemented
4#20273585C211yesmaximal, characteristic, complemented
5#20273578C211yesmaximal, characteristic, complemented
6#20273557C211yesmaximal, characteristic, complemented
7#20273550C211yesmaximal, characteristic, complemented
8#20273538C211yesmaximal, characteristic, complemented
9#20273533C211yesmaximal, characteristic, complemented
10#20273514C211yesmaximal, characteristic, complemented
11#20273514C211yesmaximal, characteristic, complemented
12#20273152C211yesmaximal, characteristic, complemented
13#20273126C211yesmaximal, characteristic, complemented
14#20273010C211yesmaximal, characteristic, complemented
15C53×#1570C211yesmaximal, characteristic, complemented
16#16811157C2211yescharacteristic
17C4×#11719945C2211yescharacteristic
18#16810965C411yescharacteristic
19#16810948C411yescharacteristic
20#16810931C411yescharacteristic
21#16810924C411yescharacteristic
22#16810846C411yescharacteristic
23#16810839C411yescharacteristic
24#16810787C411yescharacteristic
25#16810770C411yescharacteristic
26#16810750C2211yescharacteristic
27#16810747C2211yescharacteristic
28#16810747C2211yescharacteristic
29#16810747C2211yescharacteristic
30C4×Dic212C2211yescharacteristic
31C4×#11719913C2211yescharacteristic
32C4×#11719913C2211yescharacteristic
33C4×D424C2211yescharacteristic
34#16810700C2211yescharacteristic
35#16810699—21no—
36#16810692—21no—
37#16810688C2211yescharacteristic
38#16810688C2211yescharacteristic
39#16810688C2211yescharacteristic
40C8×C22⋊D53—21no—
41C8×C22⋊D53—21no—
42#16810683—21no—
43#16810676C2211yescharacteristic
44#16810675—21no—
45#16810648—21no—
46C4⋊C8×D53—21no—
47C4×#11719917C2211yescharacteristic
48#16810353C2211yescharacteristic
49#16810353C2211yescharacteristic
50#16810353C2211yescharacteristic
51#16810353C2211yescharacteristic
52#16810350C2211yescharacteristic
53#16810350C2211yescharacteristic
54#16810350C2211yescharacteristic
55#16810350C2211yescharacteristic
56#16810345C2211yescharacteristic
57#16810345C2211yescharacteristic
58#16810344C2211yescharacteristic
59C8×#88322C2211yescharacteristic
60C53×#431C2211yescharacteristic
61C53×#423C2211yescharacteristic
62C2×C4⋊C8×C53C2211yescharacteristic
63C53×#334C2211yescharacteristic
64C53×#334C2211yescharacteristic
65C53×#334C2211yescharacteristic
66C53×#334C2211yescharacteristic
67C2×#11719945C2×C411yescharacteristic
68C2×Dic212C2×C411yescharacteristic
69C2×#11719913C2×C411yescharacteristic
70C2×#11719913C2×C411yescharacteristic
71C2×D424C2×C411yescharacteristic
72C2×#11719917—21no—
73C2×#11719912—21no—
74C2×C8×D53—21no—
75C2×C8×D53—21no—
76C2×C8×D53—21no—
77#13133211—21no—
78#13133209C2×C411yescharacteristic
79#13133205C2×C411yescharacteristic
80#13133200—21no—
81#13133196C2×C411yescharacteristic
82#13133191C2×C411yescharacteristic
83C4×Dic106C2×C411yescharacteristic
84C4×Dic106C2311yescharacteristic
85C4×Dic106C2311yescharacteristic
86C4×D212C2×C411yescharacteristic
87C4×D212C2311yescharacteristic
88C4×D212C2311yescharacteristic
89C4×C22⋊D53—21no—
90C4×C22⋊D53—21no—
91C4×C22⋊D53—21no—
92#13133176C2×C411yescharacteristic
93#13133174—21no—
94#13133174—21no—
95C42×D53—21no—
96#13133151C2×C411yescharacteristic
97#13133151C2×C411yescharacteristic
98#13133149C2×C411yescharacteristic
99#13133149C2×C411yescharacteristic
100C4⋊#88322D411yescharacteristic
101C4⋊#88322D411yescharacteristic
102#13133146—21no—
103#13133146—21no—
104#13133146—21no—
105#13133146—21no—
106#13133142C2×C411yescharacteristic
107#13133142C2×C411yescharacteristic
108#13133142C2×C411yescharacteristic
109#13133142C2×C411yescharacteristic
110#13133139C2×C411yescharacteristic
111#13133139C2×C411yescharacteristic
112#13133139C2×C411yescharacteristic
113#13133139C2×C411yescharacteristic
114C22⋊#88322D411yescharacteristic
115C22⋊#88322D411yescharacteristic
116#13133129—21no—
117#13133129—21no—
118#13133129—21no—
119#13133129—21no—
120#13133128—21no—
121#13133127—21no—
122C4×#88322C2311yescharacteristic
123C4×#88322C2311yescharacteristic
124C4×#88322C2311yescharacteristic
125C4×#88322C2311yescharacteristic
126C8×Dic53—21no—
127C8×Dic53—21no—
128C8×Dic53—21no—
129C2×M16×C53—21no—
130C22×C8×C53—21no—
131C2×C42×C53C2311yescharacteristic
132C4⋊C8×C53—21no—
133C4⋊C8×C53—21no—
134C4⋊C8×C53C2×C411yescharacteristic
135C4⋊C8×C53C2×C411yescharacteristic
136C4⋊C8×C53C2311yescharacteristic
137C4⋊C8×C53C2311yescharacteristic
138C4⋊C8×C53C2311yescharacteristic
139C4⋊C8×C53C2311yescharacteristic
140C22⋊C8×C53C2×C411yescharacteristic
141C22⋊C8×C53C2×C411yescharacteristic
142C4×C8×C53C2311yescharacteristic
143C4×C8×C53C2311yescharacteristic
144C22×C4×C53C22×C411yescharacteristic
145C22×C4×C53C2×D411yescharacteristic
146C22×C4×C53#4111yescharacteristic
147C2×C22⋊D53—21no—
148C2×C22⋊D53—21no—
149#11719945—22no—
150#11719945—22no—
151C2×D212C22×C411yescharacteristic
152C2×D212C22×C411yescharacteristic
153C2×C4×D53—21no—
154C2×C4×D53—21no—
155C2×C4×D53—21no—
156C2×C4×D53—21no—
157C2×Dic106C22×C411yescharacteristic
158C2×Dic106C22×C411yescharacteristic
159M16×C53—81no—
160C2×C8×C53—21no—
161C2×C8×C53—21no—
162C2×C8×C53—21no—
163C2×C8×C53—21no—
164C2×C8×C53—81no—
165C2×C8×C53C22×C411yescharacteristic
166C2×C8×C53C22×C411yescharacteristic
167C2×C8×C53C22×C411yescharacteristic
168C2×C8×C53C22×C411yescharacteristic
169C42×C53C22×C411yescharacteristic
170C42×C53C2×D411yescharacteristic
171C42×C53#4111yescharacteristic
172C42×C53C2411yescharacteristic
173C22⋊Dic53—21no—
174C22⋊Dic53—21no—
175#11719921—21no—
176#11719921—21no—
177#11719921—21no—
178#11719921—21no—
179#11719921—21no—
180#11719921—21no—
181C4⋊Dic53C22×C411yescharacteristic
182C4⋊Dic53C22×C411yescharacteristic
183C4⋊Dic53C22×C411yescharacteristic
184C4⋊Dic53C22×C411yescharacteristic
185#11719919—21no—
186#11719919—21no—
187#11719919—21no—
188#11719919—21no—
189#11719919—21no—
190#11719919—21no—
191C4×Dic53—21no—
192C4×Dic53—21no—
193C4×Dic53—21no—
194C4×Dic53—21no—
195#11719917—42no—
196C2×#88322—21no—
197C2×#88322—21no—
198C2×#88322C2×D411yescharacteristic
199C2×#88322C2×D411yescharacteristic
200C2×#88322C2×D411yescharacteristic
201C2×#88322C2×D411yescharacteristic
202Dic212—22no—
203D424—22no—
204#11719913—22no—
205#11719913—22no—
206#11719912—81no—
207C8×D53—81no—
208C8×D53—81no—
209C8×D53—81no—
210C23×C53C4×D411yescharacteristic
211C22×D53—21no—
212C22×D53—21no—
213C2×C4×C53—21no—
214C2×C4×C53—21no—
215C2×C4×C53—21no—
216C2×C4×C53—21no—
217C2×C4×C53—41no—
218C2×C4×C53C4×D411yescharacteristic
219C2×C4×C53C4×D411yescharacteristic
220C2×C4×C53C4×D411yescharacteristic
221C2×C4×C53C23×C411yescharacteristic
222C2×C4×C53C22×D411yescharacteristic
223C2×C4×C53C2×#4111yescharacteristic
224C22⋊D53—24no—
225C22⋊D53—81no—
226C2×Dic53—21no—
227C2×Dic53—21no—
228C2×Dic53—21no—
229C2×Dic53—21no—
230C2×Dic53—21no—
231C2×Dic53—21no—
232D212—21no—
233D212—21no—
234D212—21no—
235D212#13112yes—
236C4×D53—24no—
237C4×D53—41no—
238C4×D53—41no—
239C4×D53—41no—
240C4×D53—41no—
241C4×D53—81no—
242Dic106—21no—
243Dic106—21no—
244Dic106—21no—
245Dic106#13112yes—
246C8×C53—21no—
247C8×C53—21no—
248C8×C53—21no—
249C8×C53—21no—
250C8×C53—41no—
251C8×C53—41no—
252C8×C53—41no—
253C8×C53—41no—
254#88322—22no—
255#88322—21no—
256#88322—21no—
257#88322—21no—
258#88322—21no—
259#88322—41no—
260#17927—531nomaximal, Sylow
261C22×C53—21no—
262C22×C53—21no—
263C22×C53—21no—
264C22×C53C2×C4×D411yescharacteristic
265C2×D53—22no—
266C2×D53—41no—
267C2×D53—41no—
268C2×D53—41no—
269C2×D53—41no—
270C2×D53—41no—
271C4×C53—21no—
272C4×C53—21no—
273C4×C53—21no—
274C4×C53—21no—
275C4×C53C2×#13111yescharacteristic
276C4×C53C2×#13111yescharacteristic
277C4×C53#57711yescharacteristic
278C4×C53#57711yescharacteristic
279Dic53—22no—
280Dic53—41no—
281Dic53—41no—
282Dic53—41no—
283Dic53—41no—
284Dic53—41no—
285#3102—531no—
286#2993—531no—
287#2988—531no—
288#1587—531no—
289#1586—531no—
290#1583—531no—
291#1582—531no—
292#1580—531no—
293#1579—531no—
294C8×SD16—531no—
295C8×SD16—531no—
296#1570D5311yescharacteristic, complemented
297#1489—531no—
298#1483—531no—
299#1453—531no—
300C2×C53—41no—
301C2×C53#292911yescharacteristic
302C2×C53#295211yescharacteristic
303C2×C53#295611yescharacteristic
304D53—42no—
305D53—81no—
306#529—531no—
307C4×#41—531no—
308#485—531no—
309#482—531no—
310#479—531no—
311#478—531no—
312#464—531no—
313#463—531no—
314#452—531no—
315#449—531no—
316#446—531no—
317C8×Q8—531no—
318C8×Q8—531no—
319C8×Q8—531no—
320C4×Q16—531no—
321C4×SD16—531no—
322C4×SD16—531no—
323C4×D8—531no—
324#436—531no—
325#436—1061no—
326#435—1061no—
327C8×D4—531no—
328C8×D4—531no—
329C8×D4—531no—
330C8×D4—1061no—
331C8×D4—1061no—
332#433—1061no—
333#431—531no—
334#431—1061no—
335#431C2×D5311yescharacteristic
336#424—1061no—
337#423C2×D5311yescharacteristic
338C2×C4⋊C8—1061no—
339C2×C4⋊C8C2×D5311yescharacteristic
340C4×M16—531no—
341#334C2×D5311yescharacteristic
342#334C2×D5311yescharacteristic
343#334C2×D5311yescharacteristic
344#334C2×D5311yescharacteristic
345Q8⋊C8—531no—
346Q8⋊C8—531no—
347Q8⋊C8—531no—
348Q8⋊C8—531no—
349D4⋊C8—531no—
350D4⋊C8—531no—
351D4⋊C8—531no—
352D4⋊C8—531no—
353#322—531no—
354#322—531no—
355#322—531no—
356C82—531no—
357C53#1792711yescharacteristic, complemented, Sylow
358C2×#41—531no—
359C2×Q16—531no—
360C2×SD16—531no—
361C2×SD16—531no—
362C2×D8—531no—
363C2×M16—21no—
364C2×M16—1061no—
365C2×M16—1061no—
366C22×C8—21no—
367C22×C8—1061no—
368C22×C8—1061no—
369C22×C8—1061no—
370#126—1061no—
371#125—531no—
372#124—531no—
373#123—1061no—
374C22⋊Q8—531no—
375#121—531no—
376C4×Q8—531no—
377C4×Q8—531no—
378C4×Q8—531no—
379C4×D4—531no—
380C4×D4—531no—
381C4×D4—531no—
382C4×D4—1061no—
383C4×D4—1061no—
384C4×D4—1061no—
385#117—531no—
386#117—1061no—
387#117—1061no—
388C2×C42—1061no—
389C2×C42C22×D5311yescharacteristic
390#107—531no—
391#107—531no—
392#106—531no—
393#106—531no—
394C4⋊C8—21no—
395C4⋊C8—21no—
396C4⋊C8—531no—
397C4⋊C8—531no—
398C4⋊C8—1061no—
399C4⋊C8—1061no—
400C4⋊C8—1061no—
401C4⋊C8—1061no—
402C4⋊C8C4×D5311yescharacteristic
403C4⋊C8C4×D5311yescharacteristic
404C4⋊C8C22×D5311yescharacteristic
405C4⋊C8C22×D5311yescharacteristic
406C4⋊C8C22×D5311yescharacteristic
407C4⋊C8C22×D5311yescharacteristic
408#103—531no—
409#103—531no—
410#103—531no—
411#103—531no—
412#102—531no—
413#102—531no—
414#102—531no—
415#102—531no—
416C22⋊C8—531no—
417C22⋊C8—531no—
418C22⋊C8—1061no—
419C22⋊C8—1061no—
420C22⋊C8—1061no—
421C22⋊C8—1061no—
422C22⋊C8C4×D5311yescharacteristic
423C22⋊C8C4×D5311yescharacteristic
424#97—1061no—
425#97—1061no—
426C4×C8—531no—
427C4×C8—531no—
428C4×C8—531no—
429C4×C8—531no—
430C4×C8—1061no—
431C4×C8—1061no—
432C4×C8—1061no—
433C4×C8C22×D5311yescharacteristic
434C4×C8C22×D5311yescharacteristic
435#41—1062no—
436#41—1062no—
437C2×Q8—531no—
438C2×Q8—531no—
439C2×D4—531no—
440C2×D4—531no—
441C2×D4—1061no—
442C2×D4—1061no—
443C22×C4—1061no—
444C22×C4—1061no—
445C22×C4—1061no—
446C22×C4—1061no—
447C22×C4C2×C4×D5311yescharacteristic
448C22×C4D4×D5311yescharacteristic
449C22×C4#1171994911yescharacteristic
450Q16—1062no—
451SD16—1062no—
452SD16—1062no—
453D8—1062no—
454M16—81no—
455M16—4241no—
456M16—2122no—
457C2×C8—21no—
458C2×C8—21no—
459C2×C8—21no—
460C2×C8—21no—
461C2×C8—81no—
462C2×C8—531no—
463C2×C8—531no—
464C2×C8—531no—
465C2×C8—531no—
466C2×C8—1061no—
467C2×C8—1061no—
468C2×C8—4241no—
469C2×C8—4241no—
470C2×C8—4241no—
471C2×C8C2×C4×D5311yescharacteristic
472C2×C8C2×C4×D5311yescharacteristic
473C2×C8C2×C4×D5311yescharacteristic
474C2×C8C2×C4×D5311yescharacteristic
475C4⋊C4—531no—
476C4⋊C4—531no—
477C4⋊C4—531no—
478C4⋊C4—531no—
479C4⋊C4—1061no—
480C4⋊C4—1061no—
481C4⋊C4—1061no—
482C4⋊C4—1061no—
483C4⋊C4—1061no—
484C4⋊C4—1061no—
485C22⋊C4—1061no—
486C22⋊C4—1061no—
487C22⋊C4—1061no—
488C22⋊C4—1061no—
489C22⋊C4—1061no—
490C22⋊C4—1061no—
491C22⋊C4—1061no—
492C22⋊C4—1061no—
493C42—1061no—
494C42—1061no—
495C42—1061no—
496C42—1061no—
497C42C2×C4×D5311yescharacteristic
498C42D4×D5311yescharacteristic
499C42#1171994911yescharacteristic
500C42C23×D5311yescharacteristic
501C23—1061no—
502C23—1061no—
503C23#1313317911yescharacteristic
504Q8—532no—
505Q8—1061no—
506Q8—1061no—
507Q8—1061no—
508D4—532no—
509D4—1064no—
510D4—1061no—
511D4—1061no—
512D4—1061no—
513D4—4241no—
514C2×C4—21no—
515C2×C4—21no—
516C2×C4—21no—
517C2×C4—21no—
518C2×C4—41no—
519C2×C4—1064no—
520C2×C4—1061no—
521C2×C4—1061no—
522C2×C4—1061no—
523C2×C4—1061no—
524C2×C4—1061no—
525C2×C4—1061no—
526C2×C4—4241no—
527C2×C4—2121no—
528C2×C4—2121no—
529C2×C4—2121no—
530C2×C4—2121no—
531C2×C4#1313317911yescharacteristic
532C2×C4#1313317911yescharacteristic
533C2×C4#1313317911yescharacteristic
534C2×C4C22×C4×D5311yescharacteristic
535C2×C4C2×D4×D5311yescharacteristic
536C2×C4C2×#1171994911yescharacteristic
537C8—21no—
538C8—21no—
539C8—21no—
540C8—21no—
541C8—41no—
542C8—41no—
543C8—41no—
544C8—41no—
545C8—1062no—
546C8—1061no—
547C8—1061no—
548C8—1061no—
549C8—1061no—
550C8—2121no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—1062no—
555C22—2121no—
556C22—2121no—
557C22—2121no—
558C22—2121no—
559C22—2121no—
560C22C2×#1313317911yescharacteristic
561C4—21no—
562C4—21no—
563C4—21no—
564C4—21no—
565C4—1062no—
566C4—2121no—
567C4—2121no—
568C4—2121no—
569C4—2121no—
570C4—2121no—
571C4#131×D5311yescharacteristic
572C4#131×D5311yescharacteristic
573C4#1681142911yescharacteristic
574C4#1681142911yescharacteristic
575C2—41no—
576C2—4241no—
577C2—2122no—
578C2#2028340811yescharacteristic
579C2#2028359811yescharacteristic
580C2#2028362411yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D53
commutatorC2×C4×C53C23×C4
FrattiniC42C23×D53
FittingC53×#1570C2
socleC22×C53C2×C4×D4
prime radical#16810770C4
cosocleC42×C53C24
hypercenter#1570D53
hypocenterC53#17927
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
2. #20283860C2semidirect
3. #20283824C2semidirect
4. #20273585C2semidirect
5. #20273578C2semidirect
6. #20273557C2semidirect
7. #20273550C2semidirect
8. #20273538C2semidirect
9. #20273533C2semidirect
10. #20273514C2semidirect
11. #20273514C2semidirect
12. #20273152C2semidirect
13. #20273126C2semidirect
14. #20273010C2semidirect
15. C53×#1570C2semidirect
296. #1570D53semidirect
357. C53#17927semidirect

Maximal subgroups

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

subgroupindex
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