Finite Group Databasebeta

← #27282636

Subgroups — #27282636

Order 13568.

382 conjugacy classes of subgroups.

The subgroup lattice has 328 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20275433C211yesmaximal, characteristic
2C4×#13133150C211yesmaximal, characteristic
3C2×#16810373C211yesmaximal, characteristic
4C2×#16810345C211yesmaximal, characteristic
5#20272556C211yesmaximal, characteristic
6#20272554C211yesmaximal, characteristic
7C53×#1939C211yesmaximal, characteristic
8C2×#13133150C411yescharacteristic
9C2×#13133150C411yescharacteristic
10C2×C4⋊#88322C2211yescharacteristic
11C2×#13133146—21no—
12C2×C4×#88322C2211yescharacteristic
13C2×C4×#88322C2211yescharacteristic
14C4×C4⋊Dic53C2211yescharacteristic
15#16810385C411yescharacteristic
16#16810385C411yescharacteristic
17#16810377—21no—
18#16810373—22no—
19#16810345—22no—
20C2×C4⋊C8×C53—21no—
21C2×C4⋊C8×C53C2211yescharacteristic
22C2×C4×C8×C53C2211yescharacteristic
23C4×C4⋊C4×C53C2211yescharacteristic
24C53×#336—21no—
25C22×#88322—21no—
26C22×#88322—21no—
27C22×#88322C2×C411yescharacteristic
28C22×#88322C2×C411yescharacteristic
29C2×C4⋊Dic53C2×C411yescharacteristic
30C2×C4⋊Dic53C2×C411yescharacteristic
31C2×C4×Dic53—21no—
32#13133150—22no—
33#13133150C814yescomplemented
34C4⋊#88322—21no—
35C4⋊#88322—21no—
36#13133146—42no—
37C4×#88322—21no—
38C4×#88322D412yes—
39C4×#88322Q812yes—
40C4×#88322Q812yes—
41#13133124—21no—
42C22×C8×C53—21no—
43C22×C8×C53D411yescharacteristic
44C22×C8×C53D411yescharacteristic
45C2×C4⋊C4×C53C2×C411yescharacteristic
46C2×C4⋊C4×C53C2×C411yescharacteristic
47C2×C42×C53—21no—
48C2×C42×C53C2311yescharacteristic
49C4⋊C8×C53—21no—
50C4⋊C8×C53—21no—
51C4⋊C8×C53—42no—
52C4×C8×C53—21no—
53C4×C8×C53—21no—
54#95×C53—21no—
55C22×C4×C53—21no—
56C22×C4×C53—21no—
57C22×C4×C53C22×C411yescharacteristic
58C22×C4×C53C2×D411yescharacteristic
59C22×C4×C53#4111yescharacteristic
60C22×Dic53—21no—
61C22×Dic53—21no—
62C2×C8×C53—21no—
63C2×C8×C53—21no—
64C2×C8×C53—21no—
65C2×C8×C53—21no—
66C2×C8×C53—21no—
67C2×C8×C53—21no—
68C2×C8×C53—41no—
69C2×C8×C53—41no—
70C2×C8×C53—41no—
71C4⋊C4×C53—21no—
72C4⋊C4×C53—21no—
73C4⋊C4×C53—21no—
74C4⋊C4×C53C2×C812yes—
75C42×C53—41no—
76C42×C53—41no—
77C42×C53C2×D411yescharacteristic
78C42×C53C2×Q811yescharacteristic
79C42×C53C2×Q811yescharacteristic
80C42×C53#4111yescharacteristic
81C4⋊Dic53—21no—
82C4⋊Dic53—21no—
83C4⋊Dic53—21no—
84C4⋊Dic53C2×C812yes—
85C4×Dic53—41no—
86C4×Dic53—41no—
87C2×#88322—21no—
88C2×#88322—21no—
89C2×#88322—22no—
90C2×#88322—41no—
91C2×#88322—41no—
92C2×#88322—41no—
93C2×#88322—41no—
94C2×#88322—41no—
95C2×#88322C4⋊C412yes—
96C2×#88322C4⋊C412yes—
97C2×#88322C2×C812yes—
98C2×#88322M1612yes—
99C23×C53C4×D411yescharacteristic
100C2×C4×C53—21no—
101C2×C4×C53—21no—
102C2×C4×C53—22no—
103C2×C4×C53—41no—
104C2×C4×C53—41no—
105C2×C4×C53—41no—
106C2×C4×C53—41no—
107C2×C4×C53—41no—
108C2×C4×C53C2×C4⋊C411yescharacteristic
109C2×C4×C53C4×Q811yescharacteristic
110C2×C4×C53#12111yescharacteristic
111C2×C4×C53C22⋊Q811yescharacteristic
112C2×C4×C53#12511yescharacteristic
113C2×C4×C53C4⋊Q811yescharacteristic
114C2×C4×C53C22×C811yescharacteristic
115C2×C4×C53C2×M1611yescharacteristic
116C2×C4×C53#13111yescharacteristic
117C2×C4×C53#13111yescharacteristic
118C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C53AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C53#13711yescharacteristic
121C2×C4×C53#13711yescharacteristic
122C2×Dic53—22no—
123C2×Dic53—41no—
124C2×Dic53—41no—
125C2×Dic53—41no—
126C2×Dic53—41no—
127C2×Dic53—41no—
128C8×C53—41no—
129C8×C53—41no—
130C8×C53—81no—
131#88322—22no—
132#88322—42no—
133#88322—81no—
134#88322C4⋊C814yescomplemented
135#9595—531nomaximal, Sylow
136C22×C53#38911yescharacteristic
137C22×C53C8×D411yescharacteristic
138C22×C53#43611yescharacteristic
139C22×C53#44111yescharacteristic
140C22×C53#44211yescharacteristic
141C22×C53#44411yescharacteristic
142C22×C53#44411yescharacteristic
143C4×C53—21no—
144C4×C53—21no—
145C4×C53—42no—
146C4×C53—81no—
147C4×C53C2×C4⋊C811yescharacteristic
148C4×C53#42411yescharacteristic
149C4×C53C8×Q811yescharacteristic
150C4×C53#44611yescharacteristic
151C4×C53#46811yescharacteristic
152C4×C53#46811yescharacteristic
153C4×C53#50111yescharacteristic
154C4×C53#50111yescharacteristic
155Dic53—42no—
156Dic53—81no—
157#1939—531no—
158#1939D5311yescharacteristic
159C4×#107—531no—
160C2×#334—531no—
161C2×#322—531no—
162#1279—531no—
163#1279—531no—
164C2×C53#157911yescharacteristic
165C2×C53#158011yescharacteristic
166C2×C53#159311yescharacteristic
167C2×C53#159411yescharacteristic
168C2×C53#193911yescharacteristic
169C2×C53#194311yescharacteristic
170C2×C53#194611yescharacteristic
171C2×#107—531no—
172C2×#107—531no—
173C2×C4⋊C8—21no—
174C2×C4⋊C8—531no—
175C2×C4⋊C8—1061no—
176C2×C4⋊C8C2×D5311yescharacteristic
177C2×C4×C8—531no—
178C2×C4×C8—531no—
179C2×C4×C8C2×D5311yescharacteristic
180C4×C4⋊C4—531no—
181C4×C4⋊C4C2×D5311yescharacteristic
182#340—531no—
183#340—531no—
184#336—21no—
185#336—1061no—
186#334—1062no—
187#322—1062no—
188C53#959511yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—531no—
191C22×C8—531no—
192C22×C8—1061no—
193C22×C8—1061no—
194C22×C8C22⋊D5311yescharacteristic
195C22×C8C22⋊D5311yescharacteristic
196C2×C4⋊C4—531no—
197C2×C4⋊C4—531no—
198C2×C4⋊C4C4×D5311yescharacteristic
199C2×C4⋊C4C4×D5311yescharacteristic
200C2×C42—21no—
201C2×C42—1061no—
202C2×C42C22×D5311yescharacteristic
203#107—534no—
204#107—1062no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—42no—
208C4⋊C8—1061no—
209C4⋊C8—1061no—
210C4⋊C8—2122no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—532no—
214C4×C8—532no—
215C4×C8—532no—
216C4×C8—1061no—
217#95—21no—
218#95—1061no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1061no—
222C22×C4—1061no—
223C22×C4C2×C4×D5311yescharacteristic
224C22×C4#1171994511yescharacteristic
225C22×C4C2×C22⋊D5311yescharacteristic
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—21no—
229C2×C8—21no—
230C2×C8—21no—
231C2×C8—21no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—41no—
235C2×C8—532no—
236C2×C8—532no—
237C2×C8—532no—
238C2×C8—532no—
239C2×C8—1061no—
240C2×C8—1061no—
241C2×C8—1062no—
242C2×C8—2121no—
243C2×C8—2121no—
244C2×C8—2121no—
245C2×C8—2121no—
246C2×C8—2121no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—532no—
251C4⋊C4—1061no—
252C4⋊C4—1061no—
253C4⋊C4—1061no—
254C4⋊C4C8×D5312yes—
255C42—41no—
256C42—41no—
257C42—2121no—
258C42—2121no—
259C42D4×D5311yescharacteristic
260C42#1171994711yescharacteristic
261C42Q8×D5311yescharacteristic
262C42Q8×D5311yescharacteristic
263C23C4×C22⋊D5311yescharacteristic
264C2×C4—21no—
265C2×C4—21no—
266C2×C4—22no—
267C2×C4—41no—
268C2×C4—41no—
269C2×C4—41no—
270C2×C4—41no—
271C2×C4—41no—
272C2×C4—1062no—
273C2×C4—2121no—
274C2×C4—2121no—
275C2×C4—2121no—
276C2×C4—2121no—
277C2×C4—2121no—
278C2×C4C4⋊C4×D5311yescharacteristic
279C2×C4#1313318211yescharacteristic
280C2×C4#1313318911yescharacteristic
281C2×C4#1313319511yescharacteristic
282C2×C4#1313320711yescharacteristic
283C2×C4#1313321511yescharacteristic
284C2×C4C2×C8×D5311yescharacteristic
285C2×C4M16×D5311yescharacteristic
286C2×C4#1313322311yescharacteristic
287C2×C4#1313322511yescharacteristic
288C2×C4#1313324211yescharacteristic
289C2×C4#1313324311yescharacteristic
290C2×C4#1313324711yescharacteristic
291C2×C4#1313324811yescharacteristic
292C8—41no—
293C8—41no—
294C8—81no—
295C8—534no—
296C8—1062no—
297C8—4241no—
298C8—2122no—
299C22#1681051811yescharacteristic
300C22C8×C22⋊D5311yescharacteristic
301C22#1681069911yescharacteristic
302C22#1681072811yescharacteristic
303C22#1681073311yescharacteristic
304C22#1681074311yescharacteristic
305C22#1681074311yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—4241no—
311C4—2122no—
312C4C4⋊C8×D5311yescharacteristic
313C4#1681064811yescharacteristic
314C4#1681074711yescharacteristic
315C4#1681075211yescharacteristic
316C4#1681086711yescharacteristic
317C4#1681087111yescharacteristic
318C4#1681102911yescharacteristic
319C4#1681103311yescharacteristic
320C2#2027353211yescharacteristic
321C2#2027353711yescharacteristic
322C2#2027362211yescharacteristic
323C2#2027362711yescharacteristic
324C2#2027543011yescharacteristic
325C2#2027545011yescharacteristic
326C2#2027546511yescharacteristic
subgroupG/H
centerC22×C4C2×C22⋊D53
commutatorC2×C4×C53C22×C8
FrattiniC2×C42C22×D53
FittingC53×#1939C2
socle, prime radicalC23×C53C4×D4
cosocleC2×C42×C53C23
hypercenter#1939D53
hypocenterC53#9595
LCSG ▷ C2×C4×C53 ▷ C2×C53 ▷ C53
UCSC1 ◁ C22×C4 ◁ C2×C4×C8 ◁ #1939

Complements

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

NH ≅ G/Ntype
33. #13133150C8semidirect
134. #88322C4⋊C8semidirect
188. C53#9595semidirect

Maximal subgroups

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

subgroupindex
#202754332
C4×#131331502
C2×#168103732
C2×#168103452
#202725562
#202725542
C53×#19392
#959553