Finite Group Databasebeta

← #28498040

Subgroups — #28498040

Order 15104.

292 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 292 conjugacy classes of subgroups — too many to draw. Only its 89 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#21433029C211yesmaximal, characteristic
2#21425896C211yesmaximal, characteristic
3#21425892C211yesmaximal, characteristic
4#21422038C211yesmaximal, characteristic
5#21422037C211yesmaximal, characteristic
6#21422037C211yesmaximal, characteristic
7C59×#1323C211yesmaximal, characteristic
8#16837955C411yescharacteristic
9#16837531—21no—
10#16837531—21no—
11#16837526—21no—
12#16837526—21no—
13#16837428C2211yescharacteristic
14#16837425C411yescharacteristic
15#16837360C411yescharacteristic
16#16837358C411yescharacteristic
17C2×C8×Dic59C2211yescharacteristic
18Dic59⋊C16—21no—
19Dic59⋊C16—21no—
20C22⋊(C59⋊C16)C2211yescharacteristic
21C22⋊(C59⋊C16)C2211yescharacteristic
22#16837177—21no—
23C16×Dic59—21no—
24C59×#424C2211yescharacteristic
25C59×C22⋊C16C2211yescharacteristic
26C59×C22⋊C16C2211yescharacteristic
27C2×#11745664C2×C411yescharacteristic
28C22×C59⋊C8C2×C411yescharacteristic
29#14273726C811yescharacteristic
30#14273726C811yescharacteristic
31#14273718C811yescharacteristic
32#14273718C811yescharacteristic
33#14273704—21no—
34#14273704—21no—
35C4×Dic118—21no—
36C4×Dic118—21no—
37#14273686C2×C411yescharacteristic
38C2×C4×Dic59C2×C411yescharacteristic
39C2×C59⋊C16—21no—
40C2×C59⋊C16—21no—
41Dic59⋊C8—21no—
42Dic59⋊C8—21no—
43Dic59⋊C8—21no—
44Dic59⋊C8—21no—
45#14273638—21no—
46#14273637—21no—
47C4×C59⋊C8—21no—
48C8×Dic59—21no—
49C8×Dic59D411yescharacteristic
50C8×Dic59D411yescharacteristic
51C8×Dic59D411yescharacteristic
52C8×Dic59D411yescharacteristic
53C2×M16×C59C2×C411yescharacteristic
54C22×C8×C59C2311yescharacteristic
55#117×C59C2×C411yescharacteristic
56C2×C16×C59—21no—
57C2×C16×C59—21no—
58C4⋊C8×C59—21no—
59C4⋊C8×C59—21no—
60C22×C4×C59C22×C411yescharacteristic
61C22×Dic59M1611yescharacteristic
62C22×Dic59M1611yescharacteristic
63C2×Dic118—21no—
64C2×Dic118—21no—
65M16×C59—41no—
66C2×C8×C59—21no—
67C2×C8×C59—41no—
68C2×C8×C59C2×D411yescharacteristic
69C2×C8×C59C2×D411yescharacteristic
70C4⋊C4×C59C2×C811yescharacteristic
71C4⋊C4×C59C2×C811yescharacteristic
72C22⋊C4×C59—21no—
73C42×C59—21no—
74C22⋊Dic59—21no—
75C4⋊Dic59—21no—
76C4⋊Dic59—21no—
77C4⋊Dic59C2×C811yescharacteristic
78C4⋊Dic59C2×C811yescharacteristic
79Dic59⋊C4—21no—
80Dic59⋊C4—21no—
81Dic59⋊C4—21no—
82Dic59⋊C4—21no—
83C4×Dic59—21no—
84C4×Dic59C22⋊C411yescharacteristic
85C4×Dic59C22⋊C411yescharacteristic
86C4×Dic59C2×C811yescharacteristic
87C4×Dic59C2×C811yescharacteristic
88#11745664—41no—
89C2×C59⋊C8—22no—
90C2×C59⋊C8—21no—
91C2×C59⋊C8C22⋊C411yescharacteristic
92C2×C59⋊C8C22⋊C411yescharacteristic
93C16×C59—41no—
94C16×C59—41no—
95C59⋊C16—41no—
96C59⋊C16—41no—
97C23×C59C2×M1611yescharacteristic
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59C2×C22⋊C411yescharacteristic
103C2×C4×C59C22×C811yescharacteristic
104C2×Dic59—22no—
105C2×Dic59—21no—
106C2×Dic59—21no—
107C2×Dic59—41no—
108C2×Dic59C22⋊C811yescharacteristic
109C2×Dic59C22⋊C811yescharacteristic
110C2×Dic59C22⋊C811yescharacteristic
111C2×Dic59C22⋊C811yescharacteristic
112Dic118—42no—
113Dic118—42no—
114C8×C59—21no—
115C8×C59—21no—
116C8×C59—41no—
117C59⋊C8—21no—
118C59⋊C8—41no—
119C59⋊C8#10112yes—
120#11498—591nomaximal, Sylow
121C22×C59—21no—
122C22×C59—21no—
123C22×C59—21no—
124C22×C59C2×C22⋊C811yescharacteristic
125C4×C59—21no—
126C4×C59—41no—
127C4×C59—41no—
128C4×C59#41011yescharacteristic
129C4×C59C2×#10111yescharacteristic
130Dic59—21no—
131Dic59—21no—
132Dic59—21no—
133Dic59—41no—
134Dic59—41no—
135Dic59#35012yes—
136#2960—591no—
137#2163—591no—
138#2162—591no—
139#1323—591no—
140#1323—591no—
141#1323—591no—
142#1323D5911yescharacteristic
143C2×C59—41no—
144C2×C59#146111yescharacteristic
145C2×C59C2×#35011yescharacteristic
146C2×C59#211711yescharacteristic
147#533—591no—
148#446—1181no—
149#446—1181no—
150C8×Q8—1181no—
151C8×Q8—1181no—
152#424—591no—
153#424C2×D5911yescharacteristic
154#423—591no—
155#405—591no—
156#405—591no—
157C2×C4×C8—591no—
158C4⋊C16—1181no—
159C4⋊C16—1181no—
160C22⋊C16—591no—
161C22⋊C16—591no—
162C22⋊C16C2×D5911yescharacteristic
163C22⋊C16C2×D5911yescharacteristic
164#346—1181no—
165C4×C16—1181no—
166C59#1149811yescharacteristic, complemented, Sylow
167C2×M16—591no—
168C2×M16C4×D5911yescharacteristic
169C22×C8—591no—
170C22×C8C22×D5911yescharacteristic
171C4⋊Q8—591no—
172C4⋊Q8—591no—
173#125—591no—
174#125—591no—
175C22⋊Q8—1181no—
176C22⋊Q8—1181no—
177C4×Q8—1181no—
178C4×Q8—1181no—
179#117—591no—
180#117C4×D5911yescharacteristic
181C2×C42—591no—
182C2×C16—21no—
183C2×C16—21no—
184C2×C16—1181no—
185C2×C16—1181no—
186C4⋊C8—21no—
187C4⋊C8—21no—
188C4⋊C8—1181no—
189C4⋊C8—1181no—
190C4⋊C8—1181no—
191C4⋊C8—1181no—
192#97—1181no—
193#97—1181no—
194C4×C8—591no—
195C4×C8—591no—
196C4×C8—591no—
197C4×C8—591no—
198C4×C8—1181no—
199C4×C8—1181no—
200C2×Q8—1181no—
201C2×Q8—1181no—
202C22×C4—591no—
203C22×C4—591no—
204C22×C4C2×C4×D5911yescharacteristic
205M16—41no—
206M16—2361no—
207C2×C8—21no—
208C2×C8—41no—
209C2×C8—591no—
210C2×C8—591no—
211C2×C8—1182no—
212C2×C8—1181no—
213C2×C8D4×D5911yescharacteristic
214C2×C8D4×D5911yescharacteristic
215C4⋊C4—591no—
216C4⋊C4—591no—
217C4⋊C4—1181no—
218C4⋊C4—1181no—
219C4⋊C4—1181no—
220C4⋊C4—1181no—
221C4⋊C4—1181no—
222C4⋊C4—1181no—
223C4⋊C4C8×D5911yescharacteristic
224C4⋊C4C8×D5911yescharacteristic
225C22⋊C4—21no—
226C22⋊C4—1181no—
227C42—21no—
228C42—591no—
229C42—591no—
230C42—591no—
231C42—591no—
232C42—1181no—
233C16—41no—
234C16—41no—
235C16—2361no—
236C16—2361no—
237C23M16×D5911yescharacteristic
238Q8—2362no—
239Q8—2362no—
240C2×C4—21no—
241C2×C4—21no—
242C2×C4—21no—
243C2×C4—21no—
244C2×C4—591no—
245C2×C4—591no—
246C2×C4—591no—
247C2×C4—591no—
248C2×C4—1182no—
249C2×C4—1181no—
250C2×C4—1181no—
251C2×C4—2361no—
252C2×C4C22⋊C4×D5911yescharacteristic
253C2×C4C2×C8×D5911yescharacteristic
254C8—21no—
255C8—21no—
256C8—41no—
257C8—592no—
258C8—1181no—
259C8—2361no—
260C22—21no—
261C22—21no—
262C22—21no—
263C22C22⋊C8×D5911yescharacteristic
264C4—21no—
265C4—41no—
266C4—41no—
267C4—592no—
268C4—1181no—
269C4—1181no—
270C4—1181no—
271C4—2361no—
272C4—2361no—
273C4#1683737411yescharacteristic
274C4#101×D5911yescharacteristic
275C2—41no—
276C2#2142241811yescharacteristic
277C2#350×D5911yescharacteristic
278C2#2142572211yescharacteristic
subgroupG/H
centerC2×C4C22⋊C4×D59
commutatorC2×C4×C59C22×C8
FrattiniC22×C8C22×D59
FittingC59×#1323C2
socleC22×C59C2×C22⋊C8
prime radicalC23×C59C2×M16
cosocleC22×C8×C59C23
hypercenter#1323D59
hypocenterC59#11498
LCSG ▷ C2×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C22×C8 ◁ #1323

Complements

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

NH ≅ G/Ntype
166. C59#11498semidirect

Maximal subgroups

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

subgroupindex
#214330292
#214258962
#214258922
#214220382
#214220372
C59×#13232
#1149859