Finite Group Databasebeta

← #27277455

Subgroups — #27277455

Order 13568.

540 conjugacy classes of subgroups.

The subgroup lattice has 472 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20277119C211yesmaximal, characteristic
2#20274692C211yesmaximal, characteristic
3C4×#13133129C211yesmaximal, characteristic
4#20272556C211yesmaximal, characteristic, complemented
5#20272555C211yesmaximal, characteristic, complemented
6#20272554C211yesmaximal, characteristic, complemented
7C53×#1279C211yesmaximal, characteristic, complemented
8C2×#13133174—21no—
9C2×C42×D53C2211yescharacteristic
10C2×C4⋊#88322C2211yescharacteristic
11C2×#13133129—21no—
12C2×#13133129—21no—
13C2×C4×#88322C2211yescharacteristic
14#16810492C411yescharacteristic
15#16810492C411yescharacteristic
16#16810487—21no—
17#16810482—21no—
18#16810480C411yescharacteristic
19#16810480C411yescharacteristic
20C4×#11719919—21no—
21C4×C4⋊Dic53C2211yescharacteristic
22#16810377—21no—
23#16810377—21no—
24C2×C4⋊C8×C53C2211yescharacteristic
25C2×C4×C8×C53C2211yescharacteristic
26C4×C4⋊C4×C53C2211yescharacteristic
27C22×C4×D53C2×C411yescharacteristic
28C22×C4×D53D411yescharacteristic
29C22×C4×D53D411yescharacteristic
30C22×#88322—21no—
31C22×#88322—21no—
32#13133174—42no—
33#13133174—42no—
34C2×C4⋊Dic53C2×C411yescharacteristic
35C2×C4⋊Dic53C2×C411yescharacteristic
36C2×#11719919—21no—
37C2×#11719919—21no—
38C2×#11719919—21no—
39C2×#11719919—21no—
40C2×#11719921—21no—
41C2×#11719921—21no—
42C2×C4×Dic53—21no—
43C2×C4×Dic53C2×C411yescharacteristic
44C2×C4×Dic53D411yescharacteristic
45C2×C4×Dic53D411yescharacteristic
46C42×D53—21no—
47C42×D53—21no—
48C42×D53—21no—
49C42×D53—21no—
50C4⋊#88322—21no—
51C4⋊#88322—21no—
52#13133129—24no—
53#13133129—42no—
54C4×#88322—21no—
55C4×#88322—21no—
56#13133124—21no—
57#13133124—21no—
58#13133124—21no—
59C22×C8×C53—21no—
60C22×C8×C53—21no—
61C2×C4⋊C4×C53C2×C411yescharacteristic
62C2×C4⋊C4×C53C2×C411yescharacteristic
63C2×C42×C53—21no—
64C2×C42×C53C2311yescharacteristic
65C4⋊C8×C53—21no—
66C4⋊C8×C53—21no—
67C4×C8×C53—21no—
68C4×C8×C53—21no—
69#95×C53—21no—
70C23×D53C22⋊C411yescharacteristic
71C22×C4×C53—21no—
72C22×C4×C53—21no—
73C22×C4×C53C22×C411yescharacteristic
74C22×C4×C53C2×D411yescharacteristic
75C22×C4×C53C2×D411yescharacteristic
76C22×Dic53—21no—
77C22×Dic53—21no—
78C22×Dic53C22⋊C411yescharacteristic
79C22×Dic53C22⋊C411yescharacteristic
80C22×Dic53C22⋊C411yescharacteristic
81C2×C4×D53—21no—
82C2×C4×D53—21no—
83C2×C4×D53—21no—
84C2×C4×D53—21no—
85C2×C4×D53—21no—
86C2×C4×D53—21no—
87C2×C4×D53—21no—
88C2×C4×D53—21no—
89C2×C4×D53—21no—
90C2×C4×D53—21no—
91C2×C4×D53—21no—
92C2×C4×D53—21no—
93C2×C4×D53—22no—
94C2×C4×D53—41no—
95C2×C4×D53SD1612yes—
96C2×C4×D53Q1612yes—
97C2×C8×C53—22no—
98C2×C8×C53—41no—
99C2×C8×C53—41no—
100C2×C8×C53—41no—
101C2×C8×C53—41no—
102C2×C8×C53—41no—
103C4⋊C4×C53—21no—
104C4⋊C4×C53—21no—
105C4⋊C4×C53—21no—
106C4⋊C4×C53—21no—
107C42×C53—41no—
108C42×C53—41no—
109C42×C53#4111yescharacteristic
110C42×C53#4111yescharacteristic
111C42×C53#4111yescharacteristic
112C42×C53#4111yescharacteristic
113#11719921—42no—
114#11719921—42no—
115C4⋊Dic53—21no—
116C4⋊Dic53—21no—
117C4⋊Dic53—21no—
118C4⋊Dic53—21no—
119#11719919—42no—
120#11719919—42no—
121#11719919—42no—
122#11719919—42no—
123C4×Dic53—21no—
124C4×Dic53—21no—
125C4×Dic53—21no—
126C4×Dic53—21no—
127C4×Dic53—21no—
128C4×Dic53—21no—
129C4×Dic53—41no—
130C4×Dic53—41no—
131C2×#88322—22no—
132C2×#88322—41no—
133C2×#88322—41no—
134C2×#88322—41no—
135C2×#88322—41no—
136C2×#88322—41no—
137C23×C53C2×C22⋊C411yescharacteristic
138C22×D53—21no—
139C22×D53—21no—
140C22×D53—21no—
141C22×D53—21no—
142C22×D53—21no—
143C22×D53—21no—
144C22×D53#10312yes—
145C2×C4×C53—21no—
146C2×C4×C53—21no—
147C2×C4×C53—41no—
148C2×C4×C53—41no—
149C2×C4×C53—41no—
150C2×C4×C53—41no—
151C2×C4×C53—41no—
152C2×C4×C53—41no—
153C2×C4×C53#11711yescharacteristic
154C2×C4×C53#11711yescharacteristic
155C2×C4×C53#12311yescharacteristic
156C2×C4×C53#12311yescharacteristic
157C2×C4×C53#12311yescharacteristic
158C2×C4×C53#12311yescharacteristic
159C2×C4×C53#13111yescharacteristic
160C2×C4×C53#13111yescharacteristic
161C2×C4×C53#13111yescharacteristic
162C2×C4×C53#13111yescharacteristic
163C2×C4×C53C2×SD1611yescharacteristic
164C2×C4×C53C2×Q1611yescharacteristic
165C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
166C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
167C2×Dic53—21no—
168C2×Dic53—21no—
169C2×Dic53—21no—
170C2×Dic53—21no—
171C2×Dic53—21no—
172C2×Dic53—21no—
173C2×Dic53—21no—
174C2×Dic53—41no—
175C2×Dic53—41no—
176C2×Dic53—41no—
177C2×Dic53—41no—
178C2×Dic53—41no—
179C2×Dic53—41no—
180C2×Dic53#10312yes—
181C2×Dic53#10412yes—
182C4×D53—22no—
183C4×D53—22no—
184C4×D53—22no—
185C4×D53—22no—
186C4×D53—42no—
187C4×D53—42no—
188C4×D53—41no—
189C4×D53—41no—
190C4×D53—41no—
191C4×D53—41no—
192C8×C53—42no—
193C8×C53—81no—
194#88322—42no—
195#88322—81no—
196#8710—531nomaximal, Sylow
197C22×C53#38111yescharacteristic
198C22×C53#40811yescharacteristic
199C22×C53#40811yescharacteristic
200C22×C53C2×#10311yescharacteristic
201C22×C53#41811yescharacteristic
202C22×C53C2×#10411yescharacteristic
203C22×C53#42111yescharacteristic
204C2×D53—22no—
205C2×D53—22no—
206C2×D53—22no—
207C2×D53—41no—
208C2×D53—41no—
209C2×D53—41no—
210C2×D53—41no—
211C4×C53—21no—
212C4×C53—21no—
213C4×C53—81no—
214C4×C53—81no—
215C4×C53#43311yescharacteristic
216C4×C53#43311yescharacteristic
217C4×C53#43311yescharacteristic
218C4×C53#43311yescharacteristic
219C4×C53#48111yescharacteristic
220C4×C53#48111yescharacteristic
221C4×C53#48411yescharacteristic
222C4×C53#48411yescharacteristic
223Dic53—22no—
224Dic53—22no—
225Dic53—41no—
226Dic53—81no—
227Dic53—81no—
228#2285—531no—
229#1797—531no—
230C4×C22⋊C8—531no—
231#1279—531no—
232#1279—531no—
233#1279—531no—
234#1279D5311yescharacteristic, complemented
235C2×C53#148111yescharacteristic
236C2×C53#148411yescharacteristic
237C2×C53#149311yescharacteristic
238C2×C53#149611yescharacteristic
239C2×C53#181811yescharacteristic
240C2×C53#182411yescharacteristic
241C2×C53#182611yescharacteristic
242D53—42no—
243C2×#117—1061no—
244C22×C42—531no—
245C2×C4⋊C8—531no—
246C2×C4⋊C8C2×D5311yescharacteristic
247C2×C22⋊C8—1061no—
248C2×C22⋊C8—1061no—
249C2×C4×C8—531no—
250C2×C4×C8C2×D5311yescharacteristic
251#384—531no—
252#384—531no—
253#382—1061no—
254#380—531no—
255#380—531no—
256#380—1061no—
257C4×C4⋊C4—531no—
258C4×C4⋊C4—1061no—
259C4×C4⋊C4C2×D5311yescharacteristic
260#336—1061no—
261#336—1061no—
262C53#871011yescharacteristic, complemented, Sylow
263C23×C4—531no—
264C23×C4—531no—
265C23×C4—531no—
266C22×C8—21no—
267C22×C8—21no—
268C22×C8—1061no—
269C22×C8—1061no—
270#117—2122no—
271#117—2122no—
272C2×C4⋊C4—531no—
273C2×C4⋊C4—531no—
274C2×C4⋊C4—1061no—
275C2×C4⋊C4—1061no—
276C2×C4⋊C4—1061no—
277C2×C4⋊C4—1061no—
278C2×C4⋊C4C4×D5311yescharacteristic
279C2×C4⋊C4C4×D5311yescharacteristic
280C2×C22⋊C4—1061no—
281C2×C22⋊C4—1061no—
282C2×C42—21no—
283C2×C42—531no—
284C2×C42—531no—
285C2×C42—531no—
286C2×C42—1061no—
287C2×C42—1061no—
288C2×C42—1061no—
289C2×C42—1061no—
290C2×C42—1061no—
291C2×C42C22×D5311yescharacteristic
292C4⋊C8—21no—
293C4⋊C8—21no—
294C4⋊C8—1061no—
295C4⋊C8—1061no—
296C22⋊C8—1064no—
297C22⋊C8—2122no—
298C4×C8—21no—
299C4×C8—21no—
300C4×C8—1061no—
301C4×C8—1061no—
302#95—21no—
303#95—1061no—
304#95—1061no—
305#95—1061no—
306C24—531no—
307C22×C4—21no—
308C22×C4—21no—
309C22×C4—531no—
310C22×C4—531no—
311C22×C4—532no—
312C22×C4—532no—
313C22×C4—531no—
314C22×C4—1062no—
315C22×C4—1061no—
316C22×C4—1061no—
317C22×C4—1061no—
318C22×C4—1061no—
319C22×C4—1061no—
320C22×C4—1061no—
321C22×C4—1061no—
322C22×C4—1061no—
323C22×C4—1061no—
324C22×C4—1061no—
325C22×C4—1061no—
326C22×C4—1061no—
327C22×C4—1061no—
328C22×C4—1061no—
329C22×C4—2121no—
330C22×C4C2×C4×D5311yescharacteristic
331C22×C4D4×D5311yescharacteristic
332C22×C4D4×D5311yescharacteristic
333C2×C8—22no—
334C2×C8—41no—
335C2×C8—41no—
336C2×C8—41no—
337C2×C8—41no—
338C2×C8—41no—
339C2×C8—1062no—
340C2×C8—2121no—
341C2×C8—2121no—
342C2×C8—2121no—
343C2×C8—2121no—
344C2×C8—2121no—
345C4⋊C4—21no—
346C4⋊C4—21no—
347C4⋊C4—21no—
348C4⋊C4—21no—
349C4⋊C4—1061no—
350C4⋊C4—1061no—
351C4⋊C4—1061no—
352C4⋊C4—1061no—
353C4⋊C4—2122no—
354C4⋊C4—2122no—
355C4⋊C4—2122no—
356C4⋊C4—2122no—
357C22⋊C4—2122no—
358C22⋊C4—2122no—
359C42—41no—
360C42—41no—
361C42—1061no—
362C42—1061no—
363C42—1061no—
364C42—1061no—
365C42—1061no—
366C42—1061no—
367C42—2121no—
368C42—2121no—
369C42#1171994511yescharacteristic
370C42#1171994511yescharacteristic
371C42#1171994711yescharacteristic
372C42#1171994911yescharacteristic
373C23—532no—
374C23—1061no—
375C23—1061no—
376C23—1061no—
377C23—1061no—
378C23—1061no—
379C23—1061no—
380C23C22⋊C4×D5311yescharacteristic
381C2×C4—21no—
382C2×C4—21no—
383C2×C4—41no—
384C2×C4—41no—
385C2×C4—41no—
386C2×C4—41no—
387C2×C4—41no—
388C2×C4—41no—
389C2×C4—532no—
390C2×C4—532no—
391C2×C4—1061no—
392C2×C4—1061no—
393C2×C4—1061no—
394C2×C4—1061no—
395C2×C4—1062no—
396C2×C4—1062no—
397C2×C4—1062no—
398C2×C4—1062no—
399C2×C4—1061no—
400C2×C4—1061no—
401C2×C4—1061no—
402C2×C4—2122no—
403C2×C4—2122no—
404C2×C4—2121no—
405C2×C4—2121no—
406C2×C4—2121no—
407C2×C4—2121no—
408C2×C4—2121no—
409C2×C4—2121no—
410C2×C4—2121no—
411C2×C4—2121no—
412C2×C4—2121no—
413C2×C4—2121no—
414C2×C4#1313317411yescharacteristic
415C2×C4#1313317511yescharacteristic
416C2×C4#1313319911yescharacteristic
417C2×C4#1313319911yescharacteristic
418C2×C4#1313320211yescharacteristic
419C2×C4#1313320211yescharacteristic
420C2×C4#1313322311yescharacteristic
421C2×C4#1313322311yescharacteristic
422C2×C4#1313322511yescharacteristic
423C2×C4#1313322511yescharacteristic
424C2×C4SD16×D5311yescharacteristic
425C2×C4Q16×D5311yescharacteristic
426C2×C4#1313324111yescharacteristic
427C2×C4#1313324411yescharacteristic
428C8—42no—
429C8—81no—
430C8—4241no—
431C8—2122no—
432C22—1062no—
433C22—1062no—
434C22—1062no—
435C22—2121no—
436C22—2121no—
437C22—2121no—
438C22—2121no—
439C22#1681048511yescharacteristic
440C22#1681058811yescharacteristic
441C22#1681058811yescharacteristic
442C22#103×D5311yescharacteristic
443C22#1681062611yescharacteristic
444C22#104×D5311yescharacteristic
445C22#1681063811yescharacteristic
446C4—21no—
447C4—21no—
448C4—81no—
449C4—81no—
450C4—1062no—
451C4—1062no—
452C4—4241no—
453C4—4241no—
454C4—2121no—
455C4#1681068211yescharacteristic
456C4#1681068311yescharacteristic
457C4#1681068311yescharacteristic
458C4#1681068511yescharacteristic
459C4#1681094011yescharacteristic
460C4#1681094311yescharacteristic
461C4#1681095711yescharacteristic
462C4#1681096011yescharacteristic
463C2—2122no—
464C2#2027311611yescharacteristic
465C2#2027313011yescharacteristic
466C2#2027316811yescharacteristic
467C2#2027318211yescharacteristic
468C2#2027478511yescharacteristic
469C2#2027480411yescharacteristic
470C2#2027481311yescharacteristic
subgroupG/H
centerC22×C4D4×D53
commutatorC22×C4×C53C22×C4
FrattiniC2×C42C22×D53
FittingC53×#1279C2
socleC23×C53C2×C22⋊C4
prime radicalC23×D53C22⋊C4
cosocleC2×C42×C53C23
hypercenter#1279D53
hypocenterC53#8710
LCSG ▷ C22×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
4. #20272556C2semidirect
5. #20272555C2semidirect
6. #20272554C2semidirect
7. C53×#1279C2semidirect
234. #1279D53semidirect
262. C53#8710semidirect

Maximal subgroups

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

subgroupindex
#202771192
#202746922
C4×#131331292
#202725562
#202725552
#202725542
C53×#12792
#871053