Finite Group Databasebeta

← #28487235

Subgroups — #28487235

Order 15104.

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#21424815C211yesmaximal, characteristic
2#21424812C211yesmaximal, characteristic
3C4×#14273660C211yesmaximal, characteristic
4C2×#16837152C211yesmaximal, characteristic
5C2×#16837124C211yesmaximal, characteristic
6#21421936C211yesmaximal, characteristic
7C59×#1279C211yesmaximal, characteristic
8C2×#14273660C411yescharacteristic
9C2×#14273660C411yescharacteristic
10C2×C4⋊(C59⋊C8)—21no—
11C2×C4⋊(C59⋊C8)C2211yescharacteristic
12C2×Dic59⋊C8—21no—
13C2×C4×C59⋊C8C2211yescharacteristic
14C2×C4×C59⋊C8C2211yescharacteristic
15C4×C4⋊Dic59C2211yescharacteristic
16#16837164C411yescharacteristic
17#16837164C411yescharacteristic
18#16837157—21no—
19#16837156—21no—
20#16837152—22no—
21#16837124—22no—
22C2×C4⋊C8×C59C2211yescharacteristic
23C2×C4×C8×C59C2211yescharacteristic
24C4×C4⋊C4×C59C2211yescharacteristic
25C22×C59⋊C8—21no—
26C22×C59⋊C8C2×C411yescharacteristic
27C22×C59⋊C8C2×C411yescharacteristic
28C22×C59⋊C8D411yescharacteristic
29C22×C59⋊C8D411yescharacteristic
30C2×C4⋊Dic59C2×C411yescharacteristic
31C2×C4⋊Dic59C2×C411yescharacteristic
32C2×C4×Dic59—21no—
33#14273660—22no—
34#14273660C814yescomplemented
35C4⋊(C59⋊C8)—21no—
36C4⋊(C59⋊C8)—21no—
37C4⋊(C59⋊C8)—42no—
38Dic59⋊C8—42no—
39C4×C59⋊C8—21no—
40C4×C59⋊C8—21no—
41C4×C59⋊C8D412yes—
42C4×C59⋊C8Q812yes—
43C59⋊#95—21no—
44C22×C8×C59—21no—
45C22×C8×C59—21no—
46C2×C4⋊C4×C59C2×C411yescharacteristic
47C2×C4⋊C4×C59C2×C411yescharacteristic
48C2×C42×C59—21no—
49C2×C42×C59C2311yescharacteristic
50C4⋊C8×C59—21no—
51C4⋊C8×C59—21no—
52C4×C8×C59—21no—
53C4×C8×C59Q812yes—
54#95×C59—21no—
55C22×C4×C59—21no—
56C22×C4×C59—21no—
57C22×C4×C59C22×C411yescharacteristic
58C22×C4×C59C2×D411yescharacteristic
59C22×C4×C59#4111yescharacteristic
60C22×Dic59—21no—
61C22×Dic59—21no—
62C2×C8×C59—22no—
63C2×C8×C59—41no—
64C2×C8×C59—41no—
65C2×C8×C59—41no—
66C2×C8×C59—41no—
67C2×C8×C59—41no—
68C4⋊C4×C59—21no—
69C4⋊C4×C59—21no—
70C4⋊C4×C59—21no—
71C4⋊C4×C59C2×C812yes—
72C42×C59—41no—
73C42×C59—41no—
74C42×C59C2×D411yescharacteristic
75C42×C59C2×Q811yescharacteristic
76C42×C59C2×Q811yescharacteristic
77C42×C59#4111yescharacteristic
78C4⋊Dic59—21no—
79C4⋊Dic59—21no—
80C4⋊Dic59—21no—
81C4⋊Dic59C2×C812yes—
82C4×Dic59—41no—
83C4×Dic59—41no—
84C2×C59⋊C8—21no—
85C2×C59⋊C8—21no—
86C2×C59⋊C8—21no—
87C2×C59⋊C8—21no—
88C2×C59⋊C8—21no—
89C2×C59⋊C8—21no—
90C2×C59⋊C8—21no—
91C2×C59⋊C8—21no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8C4⋊C412yes—
96C2×C59⋊C8C4⋊C412yes—
97C2×C59⋊C8C2×C812yes—
98C2×C59⋊C8M1612yes—
99C23×C59C4×D411yescharacteristic
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—22no—
103C2×C4×C59—41no—
104C2×C4×C59—41no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—41no—
108C2×C4×C59C2×C4⋊C411yescharacteristic
109C2×C4×C59C4×Q811yescharacteristic
110C2×C4×C59#12111yescharacteristic
111C2×C4×C59C22⋊Q811yescharacteristic
112C2×C4×C59#12511yescharacteristic
113C2×C4×C59C4⋊Q811yescharacteristic
114C2×C4×C59C22×C811yescharacteristic
115C2×C4×C59C2×M1611yescharacteristic
116C2×C4×C59#13111yescharacteristic
117C2×C4×C59#13111yescharacteristic
118C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
119C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
120C2×C4×C59#13711yescharacteristic
121C2×C4×C59#13711yescharacteristic
122C2×Dic59—22no—
123C2×Dic59—41no—
124C2×Dic59—41no—
125C2×Dic59—41no—
126C2×Dic59—41no—
127C2×Dic59—41no—
128C8×C59—42no—
129C8×C59—81no—
130C59⋊C8—22no—
131C59⋊C8—41no—
132C59⋊C8—41no—
133C59⋊C8—81no—
134C59⋊C8C4⋊C814yescomplemented
135#9595—591nomaximal, Sylow
136C22×C59#38911yescharacteristic
137C22×C59C8×D411yescharacteristic
138C22×C59#43611yescharacteristic
139C22×C59#44111yescharacteristic
140C22×C59#44211yescharacteristic
141C22×C59#44411yescharacteristic
142C22×C59#44411yescharacteristic
143C4×C59—21no—
144C4×C59—21no—
145C4×C59—42no—
146C4×C59—81no—
147C4×C59C2×C4⋊C811yescharacteristic
148C4×C59#42411yescharacteristic
149C4×C59C8×Q811yescharacteristic
150C4×C59#44611yescharacteristic
151C4×C59#46811yescharacteristic
152C4×C59#46811yescharacteristic
153C4×C59#50111yescharacteristic
154C4×C59#50111yescharacteristic
155Dic59—42no—
156Dic59—81no—
157#1939—591no—
158#1939—591no—
159C4×#107—591no—
160C2×#334—591no—
161C2×#322—591no—
162#1279—591no—
163#1279D5911yescharacteristic
164C2×C59#157911yescharacteristic
165C2×C59#158011yescharacteristic
166C2×C59#159311yescharacteristic
167C2×C59#159411yescharacteristic
168C2×C59#193911yescharacteristic
169C2×C59#194311yescharacteristic
170C2×C59#194611yescharacteristic
171C2×#107—591no—
172C2×#107—591no—
173C2×C4⋊C8—591no—
174C2×C4⋊C8—1181no—
175C2×C4⋊C8—1181no—
176C2×C4⋊C8C2×D5911yescharacteristic
177C2×C4×C8—591no—
178C2×C4×C8—591no—
179C2×C4×C8C2×D5911yescharacteristic
180C4×C4⋊C4—591no—
181C4×C4⋊C4C2×D5911yescharacteristic
182#340—591no—
183#340—591no—
184#336—1181no—
185#336—1181no—
186#334—1182no—
187#322—1182no—
188C59#959511yescharacteristic, complemented, Sylow
189C22×C8—21no—
190C22×C8—21no—
191C22×C8—591no—
192C22×C8—591no—
193C22×C8—591no—
194C22×C8—591no—
195C22×C8—1181no—
196C2×C4⋊C4—591no—
197C2×C4⋊C4—591no—
198C2×C4⋊C4C4×D5911yescharacteristic
199C2×C4⋊C4C4×D5911yescharacteristic
200C2×C42—21no—
201C2×C42—1181no—
202C2×C42C22×D5911yescharacteristic
203#107—594no—
204#107—1182no—
205C4⋊C8—21no—
206C4⋊C8—21no—
207C4⋊C8—1181no—
208C4⋊C8—1181no—
209C4⋊C8—2362no—
210C4⋊C8—2362no—
211C4×C8—21no—
212C4×C8—592no—
213C4×C8—592no—
214C4×C8—1181no—
215C4×C8—1181no—
216C4×C8Dic11812yes—
217#95—21no—
218#95—1181no—
219C22×C4—21no—
220C22×C4—21no—
221C22×C4—1181no—
222C22×C4—1181no—
223C22×C4C2×C4×D5911yescharacteristic
224C22×C4D4×D5911yescharacteristic
225C22×C4#1174568711yescharacteristic
226C2×C8—22no—
227C2×C8—41no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—592no—
233C2×C8—592no—
234C2×C8—592no—
235C2×C8—592no—
236C2×C8—1181no—
237C2×C8—1181no—
238C2×C8—1181no—
239C2×C8—1181no—
240C2×C8—1181no—
241C2×C8—1181no—
242C2×C8—1181no—
243C2×C8—1181no—
244C2×C8—2361no—
245C2×C8—2361no—
246C2×C8—2361no—
247C4⋊C4—21no—
248C4⋊C4—21no—
249C4⋊C4—21no—
250C4⋊C4—592no—
251C4⋊C4—1181no—
252C4⋊C4—1181no—
253C4⋊C4—1181no—
254C4⋊C4C8×D5912yes—
255C42—41no—
256C42—41no—
257C42—2361no—
258C42—2361no—
259C42C2×Dic11811yescharacteristic
260C42#1174568511yescharacteristic
261C42D4×D5911yescharacteristic
262C42Q8×D5911yescharacteristic
263C23(C22⋊D59)⋊C411yescharacteristic
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—1182no—
273C2×C4—2361no—
274C2×C4—2361no—
275C2×C4—2361no—
276C2×C4—2361no—
277C2×C4—2361no—
278C2×C4C4⋊C4×D5911yescharacteristic
279C2×C4C4×Dic11811yescharacteristic
280C2×C4#1427370011yescharacteristic
281C2×C4#1427370411yescharacteristic
282C2×C4#1427371711yescharacteristic
283C2×C4#1427372611yescharacteristic
284C2×C4C2×C8×D5911yescharacteristic
285C2×C4M16×D5911yescharacteristic
286C2×C4#1427373311yescharacteristic
287C2×C4#1427373511yescharacteristic
288C2×C4#1427375111yescharacteristic
289C2×C4#1427375411yescharacteristic
290C2×C4#1427375611yescharacteristic
291C2×C4#1427375911yescharacteristic
292C8—42no—
293C8—81no—
294C8—594no—
295C8—1182no—
296C8—4721no—
297C8—2361no—
298C8—2361no—
299C22#1683729911yescharacteristic
300C22(C22⋊D59)⋊C811yescharacteristic
301C22#1683747711yescharacteristic
302C22#1683750611yescharacteristic
303C22#1683751111yescharacteristic
304C22#1683752111yescharacteristic
305C22#1683752111yescharacteristic
306C4—21no—
307C4—21no—
308C4—42no—
309C4—81no—
310C4—4721no—
311C4—2362no—
312C4C4⋊C8×D5911yescharacteristic
313C4#1683742711yescharacteristic
314C4C8×Dic11811yescharacteristic
315C4#1683753011yescharacteristic
316C4#1683764711yescharacteristic
317C4#1683765111yescharacteristic
318C4#1683780911yescharacteristic
319C4#1683781011yescharacteristic
320C2#2142291211yescharacteristic
321C2#2142291711yescharacteristic
322C2#2142300211yescharacteristic
323C2#2142300711yescharacteristic
324C2#2142481311yescharacteristic
325C2#2142483311yescharacteristic
326C2#2142484811yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC2×C4×C59C22×C8
FrattiniC2×C42C22×D59
FittingC59×#1279C2
socle, prime radicalC23×C59C4×D4
cosocleC2×C42×C59C23
hypercenter#1279D59
hypocenterC59#9595
LCSG ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1279

Complements

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

NH ≅ G/Ntype
34. #14273660C8semidirect
134. C59⋊C8C4⋊C8semidirect
188. C59#9595semidirect

Maximal subgroups

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

subgroupindex
#214248152
#214248122
C4×#142736602
C2×#168371522
C2×#168371242
#214219362
C59×#12792
#959559