Finite Group Databasebeta

← #28482364

Subgroups — #28482364

Order 15104.

342 conjugacy classes of subgroups.

The subgroup lattice has 326 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21424247C211yesmaximal, characteristic
2#21424212C211yesmaximal, characteristic
3#21423841C211yesmaximal, characteristic
4#21421931C211yesmaximal, characteristic
5#21421930C211yesmaximal, characteristic
6#21421930C211yesmaximal, characteristic
7C59×#1277C211yesmaximal, characteristic
8C2×C4⋊(C59⋊C8)C2211yescharacteristic
9C2×C4⋊(C59⋊C8)C2211yescharacteristic
10C2×Dic59⋊C8—21no—
11C2×Dic59⋊C8—21no—
12C2×C4×C59⋊C8C2211yescharacteristic
13C42×Dic59C2211yescharacteristic
14#16837156—21no—
15#16837156—21no—
16#16837156C411yescharacteristic
17#16837156C411yescharacteristic
18#16837156C411yescharacteristic
19#16837156C411yescharacteristic
20C2×C4⋊C8×C59C2211yescharacteristic
21C2×C4⋊C8×C59C2211yescharacteristic
22C2×C4×C8×C59C2211yescharacteristic
23C22×C59⋊C8—21no—
24C22×C59⋊C8—21no—
25C22×C59⋊C8C2×C411yescharacteristic
26C22×C59⋊C8C2×C411yescharacteristic
27C2×C4×Dic59C2×C411yescharacteristic
28C2×C4×Dic59C2×C411yescharacteristic
29C2×C4×Dic59D411yescharacteristic
30C2×C4×Dic59D411yescharacteristic
31C2×C4×Dic59Q811yescharacteristic
32C2×C4×Dic59Q811yescharacteristic
33C4⋊(C59⋊C8)—21no—
34C4⋊(C59⋊C8)—21no—
35C4⋊(C59⋊C8)—21no—
36C4⋊(C59⋊C8)—21no—
37Dic59⋊C8—42no—
38Dic59⋊C8—42no—
39C4×C59⋊C8—21no—
40C4×C59⋊C8—21no—
41C22×C8×C59—21no—
42C22×C8×C59—21no—
43C22×C8×C59C2×C411yescharacteristic
44C22×C8×C59C2×C411yescharacteristic
45C2×C42×C59C2311yescharacteristic
46C4⋊C8×C59—21no—
47C4⋊C8×C59—21no—
48C4⋊C8×C59—21no—
49C4⋊C8×C59—21no—
50C4×C8×C59—21no—
51C4×C8×C59—21no—
52C22×C4×C59C22×C411yescharacteristic
53C22×C4×C59C2×D411yescharacteristic
54C22×C4×C59C2×Q811yescharacteristic
55C22×Dic59C4⋊C411yescharacteristic
56C22×Dic59C4⋊C411yescharacteristic
57C22×Dic59C4⋊C411yescharacteristic
58C22×Dic59C4⋊C411yescharacteristic
59C2×C8×C59—21no—
60C2×C8×C59—21no—
61C2×C8×C59—21no—
62C2×C8×C59—21no—
63C2×C8×C59—21no—
64C2×C8×C59—21no—
65C2×C8×C59—41no—
66C2×C8×C59—41no—
67C2×C8×C59—41no—
68C2×C8×C59—41no—
69C2×C8×C59—41no—
70C2×C8×C59—41no—
71C42×C59#4111yescharacteristic
72C42×C59#4111yescharacteristic
73C42×C59#4111yescharacteristic
74C42×C59#4111yescharacteristic
75C4×Dic59—21no—
76C4×Dic59—21no—
77C4×Dic59—21no—
78C4×Dic59—21no—
79C4×Dic59—21no—
80C4×Dic59—21no—
81C4×Dic59—21no—
82C4×Dic59—21no—
83C4×Dic59—22no—
84C4×Dic59—22no—
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—41no—
92C2×C59⋊C8—41no—
93C2×C59⋊C8—41no—
94C2×C59⋊C8—41no—
95C2×C59⋊C8—41no—
96C2×C59⋊C8—41no—
97C23×C59C2×C4⋊C411yescharacteristic
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59#11711yescharacteristic
101C2×C4×C59#11711yescharacteristic
102C2×C4×C59#12411yescharacteristic
103C2×C4×C59#12411yescharacteristic
104C2×C4×C59#12511yescharacteristic
105C2×C4×C59#12511yescharacteristic
106C2×C4×C59#13111yescharacteristic
107C2×C4×C59#13111yescharacteristic
108C2×C4×C59#13111yescharacteristic
109C2×C4×C59#13111yescharacteristic
110C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
111C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
112C2×C4×C59#13711yescharacteristic
113C2×C4×C59#13711yescharacteristic
114C2×Dic59—21no—
115C2×Dic59—21no—
116C2×Dic59—21no—
117C2×Dic59—21no—
118C2×Dic59—21no—
119C2×Dic59—21no—
120C2×Dic59—21no—
121C2×Dic59—21no—
122C2×Dic59—21no—
123C2×Dic59—21no—
124C2×Dic59#10812yes—
125C2×Dic59#10812yes—
126C8×C59—41no—
127C8×C59—41no—
128C8×C59—81no—
129C8×C59—81no—
130C59⋊C8—41no—
131C59⋊C8—41no—
132C59⋊C8—81no—
133C59⋊C8—81no—
134#8789—591nomaximal, Sylow
135C22×C59#38211yescharacteristic
136C22×C59#42411yescharacteristic
137C22×C59#42411yescharacteristic
138C22×C59#42811yescharacteristic
139C22×C59#42811yescharacteristic
140C22×C59C2×#10811yescharacteristic
141C22×C59C2×#10811yescharacteristic
142C4×C59—21no—
143C4×C59—21no—
144C4×C59#43311yescharacteristic
145C4×C59#43311yescharacteristic
146C4×C59#43311yescharacteristic
147C4×C59#43311yescharacteristic
148C4×C59#48911yescharacteristic
149C4×C59#48911yescharacteristic
150C4×C59#49011yescharacteristic
151C4×C59#49111yescharacteristic
152Dic59—22no—
153Dic59—22no—
154Dic59—41no—
155Dic59—41no—
156#1842—591no—
157#1831—591no—
158#1744—591no—
159#1277—591no—
160#1277—591no—
161#1277—591no—
162#1277D5911yescharacteristic
163C2×C59#157311yescharacteristic
164C2×C59#157311yescharacteristic
165C2×C59#157411yescharacteristic
166C2×C59#157411yescharacteristic
167C2×C59#183211yescharacteristic
168C2×C59#183611yescharacteristic
169C2×C59#183711yescharacteristic
170C2×C4⋊C8—591no—
171C2×C4⋊C8—591no—
172C2×C4⋊C8—1181no—
173C2×C4⋊C8—1181no—
174C2×C4⋊C8C2×D5911yescharacteristic
175C2×C4⋊C8C2×D5911yescharacteristic
176C2×C4×C8—591no—
177C2×C4×C8C2×D5911yescharacteristic
178C43—591no—
179#336—591no—
180#336—591no—
181#336—591no—
182#336—591no—
183#336—1181no—
184#336—1181no—
185C59#878911yescharacteristic, complemented, Sylow
186C22×C8—21no—
187C22×C8—21no—
188C22×C8—591no—
189C22×C8—591no—
190C22×C8—1181no—
191C22×C8—1181no—
192C22×C8C4×D5911yescharacteristic
193C22×C8C4×D5911yescharacteristic
194C2×C42—591no—
195C2×C42—591no—
196C2×C42—591no—
197C2×C42—591no—
198C2×C42—591no—
199C2×C42—591no—
200C2×C42C22×D5911yescharacteristic
201C4⋊C8—21no—
202C4⋊C8—21no—
203C4⋊C8—21no—
204C4⋊C8—21no—
205C4⋊C8—1181no—
206C4⋊C8—1181no—
207C4⋊C8—1181no—
208C4⋊C8—1181no—
209C4⋊C8—2362no—
210C4⋊C8—2362no—
211C4×C8—21no—
212C4×C8—21no—
213C4×C8—1181no—
214C4×C8—1181no—
215C22×C4—591no—
216C22×C4—591no—
217C22×C4—591no—
218C22×C4—591no—
219C22×C4C2×C4×D5911yescharacteristic
220C22×C4D4×D5911yescharacteristic
221C22×C4Q8×D5911yescharacteristic
222C2×C8—21no—
223C2×C8—21no—
224C2×C8—21no—
225C2×C8—21no—
226C2×C8—21no—
227C2×C8—21no—
228C2×C8—41no—
229C2×C8—41no—
230C2×C8—41no—
231C2×C8—41no—
232C2×C8—41no—
233C2×C8—41no—
234C2×C8—1181no—
235C2×C8—1181no—
236C2×C8—1181no—
237C2×C8—1181no—
238C2×C8—1181no—
239C2×C8—1181no—
240C2×C8—2361no—
241C2×C8—2361no—
242C2×C8—2361no—
243C2×C8—2361no—
244C2×C8—2361no—
245C2×C8—2361no—
246C42—1182no—
247C42—1182no—
248C42—1181no—
249C42—1181no—
250C42—1181no—
251C42—1181no—
252C42—1181no—
253C42—1181no—
254C42—1181no—
255C42—1181no—
256C42#1174568511yescharacteristic
257C42#1174568511yescharacteristic
258C42#1174568711yescharacteristic
259C42#1174568711yescharacteristic
260C23C4⋊C4×D5911yescharacteristic
261C2×C4—21no—
262C2×C4—21no—
263C2×C4—592no—
264C2×C4—592no—
265C2×C4—1181no—
266C2×C4—1181no—
267C2×C4—1181no—
268C2×C4—1181no—
269C2×C4—1181no—
270C2×C4—1181no—
271C2×C4—1181no—
272C2×C4—1181no—
273C2×C4—1181no—
274C2×C4—1181no—
275C2×C4#1427368311yescharacteristic
276C2×C4#1427368411yescharacteristic
277C2×C4#1427371311yescharacteristic
278C2×C4#1427371311yescharacteristic
279C2×C4#1427371711yescharacteristic
280C2×C4#1427371711yescharacteristic
281C2×C4#1427373311yescharacteristic
282C2×C4#1427373311yescharacteristic
283C2×C4#1427373511yescharacteristic
284C2×C4#1427373511yescharacteristic
285C2×C4#1427375111yescharacteristic
286C2×C4#1427375411yescharacteristic
287C2×C4#1427375611yescharacteristic
288C2×C4#1427375911yescharacteristic
289C8—41no—
290C8—41no—
291C8—81no—
292C8—81no—
293C8—4721no—
294C8—4721no—
295C8—2361no—
296C8—2361no—
297C22#1683726611yescharacteristic
298C22#1683742711yescharacteristic
299C22#1683742711yescharacteristic
300C22#1683744111yescharacteristic
301C22#1683744311yescharacteristic
302C22#108×D5911yescharacteristic
303C22#108×D5911yescharacteristic
304C4—21no—
305C4—21no—
306C4—1182no—
307C4—1182no—
308C4—2361no—
309C4—2361no—
310C4#1683746011yescharacteristic
311C4#1683746011yescharacteristic
312C4#1683746111yescharacteristic
313C4#1683746411yescharacteristic
314C4#1683776011yescharacteristic
315C4#1683776311yescharacteristic
316C4#1683776511yescharacteristic
317C4#1683776911yescharacteristic
318C2#2142287811yescharacteristic
319C2#2142288011yescharacteristic
320C2#2142288311yescharacteristic
321C2#2142288611yescharacteristic
322C2#2142421411yescharacteristic
323C2#2142422811yescharacteristic
324C2#2142423211yescharacteristic
subgroupG/H
centerC22×C4D4×D59
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1277C2
socle, prime radicalC23×C59C2×C4⋊C4
cosocleC2×C42×C59C23
hypercenter#1277D59
hypocenterC59#8789
LCSG ▷ C22×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22×C4 ◁ C2×C42 ◁ #1277

Complements

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

NH ≅ G/Ntype
185. C59#8789semidirect

Maximal subgroups

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

subgroupindex
#214242472
#214242122
#214238412
#214219312
#214219302
C59×#12772
#878959