Finite Group Databasebeta

← #27280276

Subgroups — #27280276

Order 13568.

678 conjugacy classes of subgroups.

The subgroup lattice has 478 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#16810815C211yesmaximal, characteristic
2C2×C8×D212C211yesmaximal, characteristic, complemented
3#20274712C211yesmaximal, characteristic, complemented
4C2×#16810367C211yesmaximal, characteristic, complemented
5#20272598C211yesmaximal, characteristic, complemented
6#20272550C211yesmaximal, characteristic, complemented
7C53×#1957C211yesmaximal, characteristic, complemented
8C22×#11719922—21no—
9C22×C8×D53—21no—
10C2×C4×D212C2211yescharacteristic
11#16810815—22no—
12#16810815C414yescomplemented
13C8×D212—22no—
14C8×D212—22no—
15C2×C4⋊#88322C2211yescharacteristic
16C2×C4⋊#88322C2211yescharacteristic
17C2×C4⋊#88322C2211yescharacteristic
18C2×#13133138—21no—
19C2×#13133137—21no—
20C2×#13133129—21no—
21#16810385—21no—
22#16810367—22no—
23C2×#127×C53C2211yescharacteristic
24C2×#102×C53—21no—
25C2×#102×C53—21no—
26C2×C4×C8×C53C2211yescharacteristic
27C53×#384C2211yescharacteristic
28C22×D212D411yescharacteristic
29C22×C4×D53—21no—
30C2×#11719922—24no—
31C2×#11719922—42no—
32C2×#11719922—42no—
33C22×#88322—21no—
34C22×#88322—21no—
35C22×#88322—21no—
36C2×C8×D53—24no—
37C2×C8×D53—42no—
38C2×C8×D53—42no—
39C4×D212—21no—
40C4×D212—21no—
41C4×D212C2×C412yes—
42C4×D212D412yes—
43C2×C4⋊Dic53D411yescharacteristic
44C2×#11719921—21no—
45C4⋊#88322—21no—
46C4⋊#88322—21no—
47C4⋊#88322—21no—
48C4⋊#88322—21no—
49C4⋊#88322C2×C412yes—
50C4⋊#88322D412yes—
51#13133138—24no—
52#13133137—42no—
53#13133129—24no—
54C22×D4×C53—21no—
55C22×D4×C53—21no—
56C22×D4×C53—21no—
57C22×C8×C53D411yescharacteristic
58C22×C8×C53D411yescharacteristic
59#127×C53—21no—
60#127×C53—21no—
61#127×C53—21no—
62#127×C53C2×C412yes—
63C2×C4⋊C4×C53—21no—
64C2×C4⋊C4×C53—21no—
65C2×C4⋊C4×C53—21no—
66C2×C42×C53C2311yescharacteristic
67#102×C53—42no—
68#102×C53—42no—
69C4×C8×C53—21no—
70C4×C8×C53—21no—
71C24×C53—41no—
72C23×D53—21no—
73C2×D4×C53—22no—
74C2×D4×C53—22no—
75C2×D4×C53—22no—
76C2×D4×C53—41no—
77C2×D4×C53—41no—
78C2×D4×C53—41no—
79C2×D4×C53—41no—
80C2×D4×C53—41no—
81C2×D4×C53—41no—
82C2×D4×C53—41no—
83C2×D4×C53—41no—
84C2×D4×C53—41no—
85C2×D4×C53—41no—
86C2×D4×C53—41no—
87C2×D4×C53—81no—
88C2×D4×C53—81no—
89C22×C4×C53—41no—
90C22×C4×C53C2×D411yescharacteristic
91C22×C4×C53C2×D411yescharacteristic
92C22×C4×C53#4111yescharacteristic
93C22×Dic53—21no—
94C2×D212—21no—
95C2×D212—21no—
96C2×D212—21no—
97C2×D212C22⋊C412yes—
98C2×D212D812yes—
99C2×D212SD1612yes—
100C2×C4×D53—22no—
101C2×C4×D53—22no—
102C2×C4×D53—41no—
103C2×C4×D53—41no—
104C2×C4×D53—41no—
105C2×C4×D53—41no—
106C2×C8×C53—21no—
107C2×C8×C53—21no—
108C2×C8×C53—21no—
109C2×C8×C53—21no—
110C2×C8×C53—21no—
111C2×C8×C53D812yescomplemented
112C4⋊C4×C53—41no—
113C4⋊C4×C53—41no—
114C4⋊C4×C53—41no—
115C4⋊C4×C53—41no—
116C4⋊C4×C53—81no—
117C42×C53C22×C411yescharacteristic
118C42×C53C2×D411yescharacteristic
119C42×C53C2×D411yescharacteristic
120C42×C53#4111yescharacteristic
121#11719922—48no—
122#11719921—22no—
123#11719921—22no—
124C4⋊Dic53—21no—
125C4⋊Dic53C22⋊C412yes—
126C2×#88322—22no—
127C2×#88322—22no—
128C2×#88322—41no—
129C2×#88322—41no—
130C2×#88322—41no—
131C2×#88322—41no—
132C2×#88322—41no—
133C2×#88322—41no—
134C2×#88322—41no—
135C8×D53—48no—
136C23×C53—42no—
137C23×C53—81no—
138C23×C53—81no—
139C23×C53—81no—
140C23×C53—81no—
141C23×C53—81no—
142C23×C53—81no—
143C23×C53#12111yescharacteristic
144C22×D53—22no—
145C22×D53—22no—
146C22×D53—22no—
147C22×D53—41no—
148C22×D53—41no—
149C22×D53—41no—
150C22×D53—41no—
151D4×C53—42no—
152D4×C53—42no—
153D4×C53—42no—
154D4×C53—42no—
155D4×C53—82no—
156D4×C53—82no—
157D4×C53—81no—
158D4×C53—81no—
159D4×C53—81no—
160D4×C53—81no—
161C2×C4×C53—21no—
162C2×C4×C53—21no—
163C2×C4×C53—81no—
164C2×C4×C53—81no—
165C2×C4×C53—81no—
166C2×C4×C53C2×C22⋊C411yescharacteristic
167C2×C4×C53C4×D411yescharacteristic
168C2×C4×C53C4×D411yescharacteristic
169C2×C4×C53#12011yescharacteristic
170C2×C4×C53#12111yescharacteristic
171C2×C4×C53#12311yescharacteristic
172C2×C4×C53C2×D811yescharacteristic
173C2×C4×C53C2×D811yescharacteristic
174C2×C4×C53C2×SD1611yescharacteristic
175C2×C4×C53#13511yescharacteristic
176C2×C4×C53#13511yescharacteristic
177C2×C4×C53#13511yescharacteristic
178C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
179C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
180C2×Dic53—22no—
181C2×Dic53—41no—
182C2×Dic53—41no—
183D212—22no—
184D212—22no—
185D212—22no—
186D212#10214yescomplemented
187C4×D53—42no—
188C4×D53—42no—
189C4×D53—42no—
190C4×D53—42no—
191C8×C53—22no—
192C8×C53—41no—
193#88322—42no—
194#88322—42no—
195#88322—81no—
196#9221—531nomaximal, Sylow
197C22×C53—82no—
198C22×C53—82no—
199C22×C53—82no—
200C22×C53—161no—
201C22×C53—161no—
202C22×C53—161no—
203C22×C53—161no—
204C22×C53#38611yescharacteristic
205C22×C53#45911yescharacteristic
206C22×C53#46311yescharacteristic
207C22×C53#46511yescharacteristic
208C22×C53#46611yescharacteristic
209C22×C53#47111yescharacteristic
210C22×C53#47211yescharacteristic
211C2×D53—24no—
212C2×D53—42no—
213C2×D53—42no—
214C2×D53—42no—
215C2×D53—42no—
216C2×D53—42no—
217C2×D53—42no—
218C4×C53—21no—
219C4×C53—21no—
220C4×C53—161no—
221C4×C53C2×#10211yescharacteristic
222C4×C53#41611yescharacteristic
223C4×C53C4×D811yescharacteristic
224C4×C53#44211yescharacteristic
225C4×C53#44711yescharacteristic
226C4×C53#44911yescharacteristic
227C4×C53#46511yescharacteristic
228C4×C53#46611yescharacteristic
229Dic53—42no—
230C2×#459—531no—
231C2×C8×D4—531no—
232#1957D5311yescharacteristic, complemented
233#1802—531no—
234C2×#331—531no—
235#1296—531no—
236#1277—531no—
237C2×C53—162no—
238C2×C53#166511yescharacteristic
239C2×C53#166711yescharacteristic
240C2×C53#167711yescharacteristic
241C2×C53#168111yescharacteristic
242C2×C53#187911yescharacteristic
243C2×C53#189311yescharacteristic
244C2×C53#190711yescharacteristic
245D53—44no—
246C22×D8—1061no—
247C23×C8—1061no—
248C2×#127C2×D5311yescharacteristic
249C2×C4×D4—531no—
250#459—534no—
251#459—1062no—
252C8×D4—1062no—
253C8×D4—1062no—
254C2×C4⋊C8—531no—
255C2×C4⋊C8—531no—
256C2×C4⋊C8—531no—
257C2×#102—21no—
258C2×#102—21no—
259C2×#102—1061no—
260C2×#102—1061no—
261C2×C22⋊C8—1061no—
262C2×C4×C8C2×D5311yescharacteristic
263#384C2×D5311yescharacteristic
264#340—1061no—
265#331—1062no—
266C53#922111yescharacteristic, complemented, Sylow
267C22×D4—21no—
268C22×D4—21no—
269C22×D4—21no—
270C22×D4—531no—
271C23×C4—1061no—
272C2×D8—1064no—
273C2×D8—2122no—
274C2×D8—2122no—
275C22×C8—1064no—
276C22×C8—1061no—
277C22×C8—1061no—
278C22×C8—1061no—
279C22×C8—2122no—
280C22×C8—2122no—
281C22×C8C22⋊D5311yescharacteristic
282C22×C8C22⋊D5311yescharacteristic
283#127—21no—
284#127—21no—
285#127—21no—
286#127C4×D5312yes—
287C4×D4—532no—
288C4×D4—532no—
289C4×D4—1061no—
290C4×D4—1061no—
291C2×C4⋊C4—21no—
292C2×C4⋊C4—21no—
293C2×C4⋊C4—21no—
294C2×C4⋊C4—531no—
295C2×C22⋊C4—1061no—
296C2×C42C22×D5311yescharacteristic
297C4⋊C8—532no—
298C4⋊C8—532no—
299C4⋊C8—1061no—
300C4⋊C8—1061no—
301C4⋊C8—1061no—
302C4⋊C8—1061no—
303#102—42no—
304#102—42no—
305#102—1064no—
306#102—2122no—
307C22⋊C8—1064no—
308C4×C8—21no—
309C4×C8—21no—
310C24—41no—
311C24—1061no—
312C2×D4—22no—
313C2×D4—22no—
314C2×D4—22no—
315C2×D4—41no—
316C2×D4—41no—
317C2×D4—41no—
318C2×D4—41no—
319C2×D4—41no—
320C2×D4—41no—
321C2×D4—41no—
322C2×D4—41no—
323C2×D4—41no—
324C2×D4—41no—
325C2×D4—41no—
326C2×D4—81no—
327C2×D4—81no—
328C2×D4—532no—
329C2×D4—532no—
330C2×D4—532no—
331C2×D4—1061no—
332C2×D4—1061no—
333C2×D4—1061no—
334C22×C4—41no—
335C22×C4—1061no—
336C22×C4—1062no—
337C22×C4—1062no—
338C22×C4—2121no—
339C22×C4—2121no—
340C22×C4—2121no—
341C22×C4—2121no—
342C22×C4D4×D5311yescharacteristic
343C22×C4#1171994711yescharacteristic
344C22×C4C2×C22⋊D5311yescharacteristic
345D8—2128no—
346C2×C8—21no—
347C2×C8—21no—
348C2×C8—21no—
349C2×C8—21no—
350C2×C8—21no—
351C2×C8—1062no—
352C2×C8—1062no—
353C2×C8—2128no—
354C2×C8—2121no—
355C2×C8—2121no—
356C2×C8—2121no—
357C2×C8—2121no—
358C2×C8—2121no—
359C2×C8—2121no—
360C2×C8—2121no—
361C2×C8#1171992212yescomplemented
362C4⋊C4—41no—
363C4⋊C4—41no—
364C4⋊C4—41no—
365C4⋊C4—41no—
366C4⋊C4—81no—
367C4⋊C4—532no—
368C4⋊C4—1061no—
369C22⋊C4—1062no—
370C22⋊C4—1062no—
371C42C2×C4×D5311yescharacteristic
372C42#1171994511yescharacteristic
373C42D4×D5311yescharacteristic
374C42D4×D5311yescharacteristic
375C23—42no—
376C23—81no—
377C23—81no—
378C23—81no—
379C23—81no—
380C23—81no—
381C23—81no—
382C23—1062no—
383C23—1062no—
384C23—1062no—
385C23—2121no—
386C23—2121no—
387C23—2121no—
388C23—2121no—
389C23#1313318811yescharacteristic
390D4—42no—
391D4—42no—
392D4—42no—
393D4—42no—
394D4—82no—
395D4—82no—
396D4—81no—
397D4—81no—
398D4—81no—
399D4—81no—
400D4—534no—
401D4—1062no—
402D4—1062no—
403D4—1062no—
404C2×C4—21no—
405C2×C4—21no—
406C2×C4—81no—
407C2×C4—81no—
408C2×C4—81no—
409C2×C4—1062no—
410C2×C4—2121no—
411C2×C4—2121no—
412C2×C4—2122no—
413C2×C4—2122no—
414C2×C4—2122no—
415C2×C4—2122no—
416C2×C4C22⋊C4×D5311yescharacteristic
417C2×C4#1313317711yescharacteristic
418C2×C4C4×C22⋊D5311yescharacteristic
419C2×C4#1313318511yescharacteristic
420C2×C4#1313319011yescharacteristic
421C2×C4#1313319911yescharacteristic
422C2×C4D8×D5311yescharacteristic
423C2×C4C2×#1171992211yescharacteristic
424C2×C4SD16×D5311yescharacteristic
425C2×C4#1313323611yescharacteristic
426C2×C4#1313323711yescharacteristic
427C2×C4#1313323811yescharacteristic
428C2×C4#1313324211yescharacteristic
429C2×C4#1313324311yescharacteristic
430C8—22no—
431C8—41no—
432C8—4241no—
433C8—2122no—
434C8—2122no—
435C22—82no—
436C22—82no—
437C22—82no—
438C22—161no—
439C22—161no—
440C22—161no—
441C22—161no—
442C22—1064no—
443C22—2122no—
444C22—2122no—
445C22—2122no—
446C22—2122no—
447C22—2122no—
448C22—2122no—
449C22#1681049911yescharacteristic
450C22#1681081511yescharacteristic
451C22#1681083511yescharacteristic
452C22#1681084911yescharacteristic
453C22#1681085611yescharacteristic
454C22#1681088311yescharacteristic
455C22#1681089011yescharacteristic
456C4—21no—
457C4—21no—
458C4—161no—
459C4—2122no—
460C4#102×D5311yescharacteristic
461C4#1681061611yescharacteristic
462C4C4×#1171992211yescharacteristic
463C4#1681073311yescharacteristic
464C4#1681075611yescharacteristic
465C4#1681076611yescharacteristic
466C4#1681085111yescharacteristic
467C4#1681085811yescharacteristic
468C2—162no—
469C2—2124no—
470C2#2027405311yescharacteristic
471C2#2027406711yescharacteristic
472C2#2027412111yescharacteristic
473C2#2027414911yescharacteristic
474C2#2027506611yescharacteristic
475C2#2027514011yescharacteristic
476C2#2027522611yescharacteristic
subgroupG/H
centerC23#13133188
commutatorC42×C53C22×C4
FrattiniC2×C42C22×D53
FittingC53×#1957C2
socleC23×C53#121
prime radicalC2×#16810815C2
cosocleC2×C42×C53C23
hypercenter#1957D53
hypocenterC53#9221
LCSG ▷ C42×C53 ▷ C22×C53 ▷ C53
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1957

Complements

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

NH ≅ G/Ntype
2. C2×C8×D212C2semidirect
3. #20274712C2semidirect
4. C2×#16810367C2semidirect
5. #20272598C2semidirect
6. #20272550C2semidirect
7. C53×#1957C2semidirect
12. #16810815C4semidirect
111. C2×C8×C53D8semidirect
186. D212#102semidirect
232. #1957D53semidirect
266. C53#9221semidirect
361. C2×C8#11719922semidirect

Maximal subgroups

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

subgroupindex
C2×#168108152
C2×C8×D2122
#202747122
C2×#168103672
#202725982
#202725502
C53×#19572
#922153