Finite Group Databasebeta

← #27300314

Subgroups — #27300314

Order 13568.

440 conjugacy classes of subgroups.

The subgroup lattice has 402 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#405×D53C211yesmaximal, characteristic
2#20276325C211yesmaximal, characteristic
3C2×#16810402C211yesmaximal, characteristic
4#20272805C211yesmaximal, characteristic, complemented
5#20272804C211yesmaximal, characteristic, complemented
6#20272803C211yesmaximal, characteristic, complemented
7C53×#1379C211yesmaximal, characteristic, complemented
8C2×M16×D53C411yescharacteristic
9C22×C8×D53C2211yescharacteristic
10#117×D53C411yescharacteristic
11C2×#13133157C2211yescharacteristic
12C22×#11719908C2211yescharacteristic
13#16810581C411yescharacteristic
14#16810580—21no—
15#16810579C411yescharacteristic
16#16810578C2211yescharacteristic
17#16810577—21no—
18#97×D53—21no—
19C4×C8×D53—21no—
20#16810402—21no—
21#16810402—21no—
22#16810402—21no—
23#16810402—21no—
24C2×M32×C53C2211yescharacteristic
25C22×C16×C53C2211yescharacteristic
26C53×#405C2211yescharacteristic
27C22×C4×D53C2×C411yescharacteristic
28C2×#11719917C2×C411yescharacteristic
29C2×#11719912—21no—
30M16×D53—22no—
31M16×D53—22no—
32C22×#88322C2×C411yescharacteristic
33C2×C8×D53—21no—
34C2×C8×D53—21no—
35C2×C8×D53—21no—
36C2×C8×D53—21no—
37C2×C8×D53—21no—
38C2×C8×D53D411yescharacteristic
39C2×C8×D53D411yescharacteristic
40C2×C8×D53D411yescharacteristic
41C2×C8×D53D411yescharacteristic
42#13133176C2×C411yescharacteristic
43#13133175C811yescharacteristic
44#13133175C811yescharacteristic
45#13133174—21no—
46#13133173—21no—
47C4⋊C4×D53C811yescharacteristic
48C4⋊C4×D53C811yescharacteristic
49C22⋊C4×D53—21no—
50C42×D53—21no—
51#13133157—21no—
52#13133157—21no—
53C2×#11719908—21no—
54C2×#11719908—21no—
55C2×#11719908—21no—
56C2×#11719908—21no—
57#13133128—21no—
58#13133127—21no—
59#13133127—21no—
60C4×#88322—21no—
61C8×Dic53—21no—
62C8×Dic53—21no—
63C2×M16×C53C2×C411yescharacteristic
64C22×C8×C53C2311yescharacteristic
65#117×C53C2×C411yescharacteristic
66M32×C53—21no—
67M32×C53—21no—
68C2×C16×C53—21no—
69C2×C16×C53—21no—
70C2×C16×C53—21no—
71C2×C16×C53—21no—
72#97×C53—21no—
73C4×C8×C53—21no—
74C23×D53M1611yescharacteristic
75C22×C4×C53C22×C411yescharacteristic
76C22×Dic53M1611yescharacteristic
77C2×C4×D53—21no—
78C2×C4×D53—21no—
79C2×C4×D53—21no—
80C2×C4×D53—21no—
81C2×C4×D53—21no—
82C2×C4×D53—21no—
83C2×C4×D53C22⋊C411yescharacteristic
84C2×C4×D53C22⋊C411yescharacteristic
85C2×C4×D53C2×C811yescharacteristic
86C2×C4×D53C2×C811yescharacteristic
87M16×C53—21no—
88M16×C53M1612yes—
89C2×C8×C53—21no—
90C2×C8×C53C2×D411yescharacteristic
91C2×C8×C53C2×D411yescharacteristic
92C2×C8×C53#4111yescharacteristic
93C2×C8×C53#4111yescharacteristic
94C2×C8×C53#4111yescharacteristic
95C2×C8×C53#4111yescharacteristic
96C4⋊C4×C53C2×C811yescharacteristic
97C4⋊C4×C53C2×C811yescharacteristic
98C22⋊C4×C53—21no—
99C42×C53—21no—
100C22⋊Dic53—21no—
101#11719921—21no—
102#11719921—21no—
103C4⋊Dic53C2×C811yescharacteristic
104C4⋊Dic53C2×C811yescharacteristic
105#11719919—21no—
106#11719919—21no—
107C4×Dic53—21no—
108C4×Dic53—21no—
109C4×Dic53—21no—
110#11719917—21no—
111#11719917M1612yes—
112C2×#88322—21no—
113C2×#88322—21no—
114C2×#88322—21no—
115C2×#88322C22⋊C411yescharacteristic
116C2×#88322C22⋊C411yescharacteristic
117#11719912—24no—
118C8×D53—24no—
119C8×D53—21no—
120C8×D53—21no—
121C8×D53—21no—
122C8×D53—21no—
123C8×D53—21no—
124C8×D53—21no—
125C8×D53—21no—
126C8×D53—21no—
127C16×C53—41no—
128C16×C53—41no—
129#11719908—41no—
130#11719908—41no—
131C23×C53C2×M1611yescharacteristic
132C22×D53—21no—
133C22×D53—21no—
134C22×D53—22no—
135C22×D53—41no—
136C22×D53C22⋊C811yescharacteristic
137C22×D53C22⋊C811yescharacteristic
138C2×C4×C53—21no—
139C2×C4×C53—21no—
140C2×C4×C53C2×C22⋊C411yescharacteristic
141C2×C4×C53#11711yescharacteristic
142C2×C4×C53#11711yescharacteristic
143C2×C4×C53C22×C811yescharacteristic
144C2×C4×C53C2×M1611yescharacteristic
145C2×C4×C53C2×M1611yescharacteristic
146C2×Dic53—21no—
147C2×Dic53—21no—
148C2×Dic53—21no—
149C2×Dic53—21no—
150C2×Dic53C22⋊C811yescharacteristic
151C2×Dic53C22⋊C811yescharacteristic
152C4×D53—21no—
153C4×D53—21no—
154C4×D53—21no—
155C4×D53—21no—
156C4×D53—21no—
157C4×D53—21no—
158C4×D53—21no—
159C4×D53—21no—
160C4×D53—42no—
161C4×D53—42no—
162C8×C53—22no—
163C8×C53#12311yescharacteristic
164C8×C53#12311yescharacteristic
165C8×C53#12311yescharacteristic
166C8×C53#12311yescharacteristic
167#88322—21no—
168#88322—21no—
169#88322—22no—
170#12848—531nomaximal, Sylow
171C22×C53—21no—
172C22×C53—21no—
173C22×C53C2×C22⋊C811yescharacteristic
174C22×C53#43211yescharacteristic
175C22×C53#43211yescharacteristic
176C2×D53—21no—
177C2×D53—21no—
178C2×D53—21no—
179C2×D53—21no—
180C2×D53—21no—
181C2×D53—42no—
182C2×D53—42no—
183C2×D53#35012yes—
184C4×C53—41no—
185C4×C53—41no—
186C4×C53#38111yescharacteristic
187C4×C53#40711yescharacteristic
188C4×C53#43111yescharacteristic
189C4×C53#43111yescharacteristic
190Dic53—21no—
191Dic53—21no—
192Dic53—41no—
193Dic53—41no—
194C2×#405—531no—
195#2112—531no—
196C2×C22⋊C16—531no—
197#1379—531no—
198#1379—531no—
199#1379—531no—
200#1379D5311yescharacteristic, complemented
201C2×C53—21no—
202C2×C53—21no—
203C2×C53#181711yescharacteristic
204C2×C53C2×#35011yescharacteristic
205C2×C53#211711yescharacteristic
206D53—22no—
207D53—41no—
208C22×M16—531no—
209C23×C8—531no—
210C2×#117—531no—
211C2×M32—531no—
212C2×M32C2×D5311yescharacteristic
213C22×C16—531no—
214C22×C16C2×D5311yescharacteristic
215#405—531no—
216#405—531no—
217#405—531no—
218#405—1061no—
219#405—1061no—
220#405C2×D5311yescharacteristic
221C2×#97—1061no—
222C2×C4×C8—1061no—
223C22⋊C16—1061no—
224C22⋊C16—1061no—
225C22⋊C16—1061no—
226C22⋊C16—1061no—
227C53#1284811yescharacteristic, complemented, Sylow
228C23×C4—531no—
229C2×M16—531no—
230C2×M16—1061no—
231C2×M16—1062no—
232C2×M16—1062no—
233C2×M16C4×D5311yescharacteristic
234C22×C8—531no—
235C22×C8—531no—
236C22×C8—531no—
237C22×C8—531no—
238C22×C8—531no—
239C22×C8—1061no—
240C22×C8—1061no—
241C22×C8—1061no—
242C22×C8—1061no—
243C22×C8—1061no—
244C22×C8C22×D5311yescharacteristic
245#117—531no—
246#117—531no—
247#117—531no—
248#117—1061no—
249#117—1061no—
250#117C4×D5311yescharacteristic
251C2×C4⋊C4—531no—
252C2×C4⋊C4—531no—
253C2×C22⋊C4—1061no—
254C2×C42—1061no—
255M32—21no—
256M32—21no—
257M32—1061no—
258M32—1061no—
259C2×C16—21no—
260C2×C16—21no—
261C2×C16—21no—
262C2×C16—21no—
263C2×C16—1061no—
264C2×C16—1061no—
265C2×C16—1061no—
266C2×C16—1061no—
267#97—21no—
268#97—1061no—
269#97—1061no—
270#97—1061no—
271C4×C8—21no—
272C4×C8—1061no—
273C4×C8—1061no—
274C4×C8—1061no—
275C24—531no—
276C22×C4—531no—
277C22×C4—531no—
278C22×C4—531no—
279C22×C4—531no—
280C22×C4—531no—
281C22×C4—1061no—
282C22×C4—1061no—
283C22×C4—1061no—
284C22×C4—1061no—
285C22×C4—1061no—
286C22×C4—1061no—
287C22×C4C2×C4×D5311yescharacteristic
288M16—21no—
289M16—532no—
290M16—1064no—
291M16—1061no—
292M16#1171991212yes—
293C2×C8—21no—
294C2×C8—531no—
295C2×C8—531no—
296C2×C8—1064no—
297C2×C8—1061no—
298C2×C8—1061no—
299C2×C8—1061no—
300C2×C8—1061no—
301C2×C8—1061no—
302C2×C8—1061no—
303C2×C8—1061no—
304C2×C8—1061no—
305C2×C8—1061no—
306C2×C8—1061no—
307C2×C8—1061no—
308C2×C8#1171994511yescharacteristic
309C2×C8#1171994511yescharacteristic
310C2×C8D4×D5311yescharacteristic
311C2×C8D4×D5311yescharacteristic
312C2×C8#1171994711yescharacteristic
313C2×C8#1171994911yescharacteristic
314C4⋊C4—531no—
315C4⋊C4—531no—
316C4⋊C4—1061no—
317C4⋊C4—1061no—
318C4⋊C4C8×D5311yescharacteristic
319C4⋊C4C8×D5311yescharacteristic
320C22⋊C4—21no—
321C22⋊C4—1061no—
322C22⋊C4—1061no—
323C22⋊C4—1061no—
324C42—21no—
325C42—1061no—
326C42—1061no—
327C42—1061no—
328C16—41no—
329C16—41no—
330C16—2121no—
331C16—2121no—
332C23—531no—
333C23—531no—
334C23—1062no—
335C23—1061no—
336C23—1061no—
337C23—2121no—
338C23M16×D5311yescharacteristic
339C2×C4—21no—
340C2×C4—21no—
341C2×C4—531no—
342C2×C4—531no—
343C2×C4—1061no—
344C2×C4—1061no—
345C2×C4—1061no—
346C2×C4—1061no—
347C2×C4—1061no—
348C2×C4—1061no—
349C2×C4—1061no—
350C2×C4—1061no—
351C2×C4—1061no—
352C2×C4—1061no—
353C2×C4—1061no—
354C2×C4—1061no—
355C2×C4—2122no—
356C2×C4—2122no—
357C2×C4C22⋊C4×D5311yescharacteristic
358C2×C4#1313317411yescharacteristic
359C2×C4#1313317511yescharacteristic
360C2×C4C2×C8×D5311yescharacteristic
361C2×C4M16×D5311yescharacteristic
362C2×C4C2×#1171991211yescharacteristic
363C8—22no—
364C8—1062no—
365C8—1061no—
366C8—1061no—
367C8#1313319911yescharacteristic
368C8#1313319911yescharacteristic
369C8#1313320211yescharacteristic
370C8#1313320211yescharacteristic
371C22—21no—
372C22—21no—
373C22—532no—
374C22—1061no—
375C22—1061no—
376C22—1061no—
377C22—1061no—
378C22—1061no—
379C22—2122no—
380C22—2122no—
381C22C22⋊C8×D5311yescharacteristic
382C22#1681067811yescharacteristic
383C22#1681067911yescharacteristic
384C4—41no—
385C4—41no—
386C4—1061no—
387C4—1061no—
388C4—2121no—
389C4—2121no—
390C4#1681048511yescharacteristic
391C4#1681058511yescharacteristic
392C4#1681067411yescharacteristic
393C4#1681067511yescharacteristic
394C2—21no—
395C2—21no—
396C2—1062no—
397C2—2121no—
398C2#2027478211yescharacteristic
399C2#350×D5311yescharacteristic
400C2#2027634111yescharacteristic
subgroupG/H
centerC2×C8D4×D53
commutatorC2×C4×C53C22×C8
FrattiniC22×C8C22×D53
FittingC53×#1379C2
socleC22×C53C2×C22⋊C8
prime radicalC23×D53M16
cosocleC22×C8×C53C23
hypercenter#1379D53
hypocenterC53#12848
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C2×C8 ◁ C22×C8 ◁ #1379

Complements

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

NH ≅ G/Ntype
4. #20272805C2semidirect
5. #20272804C2semidirect
6. #20272803C2semidirect
7. C53×#1379C2semidirect
200. #1379D53semidirect
227. C53#12848semidirect

Maximal subgroups

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

subgroupindex
#405×D532
#202763252
C2×#168104022
#202728052
#202728042
#202728032
C53×#13792
#1284853