Finite Group Databasebeta

← #28499338

Subgroups — #28499338

Order 15104.

378 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 87 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#21429308C211yesmaximal, characteristic
2C4×#14273646C211yesmaximal, characteristic
3#21422124C214yesmaximal
4C59×#1467C211yesmaximal, characteristic
5C2×#14273727C411yescharacteristic
6C2×#14273646—21no—
7C4×#11745664—21no—
8#16837341C412yes—
9#16837341C2212yes—
10#16837309—21no—
11#16837308—21no—
12#16837308—21no—
13#16837267—21no—
14C4×C4⋊Dic59C411yescharacteristic
15#16837171C2212yes—
16C2×C4×Q8×C59C2211yescharacteristic
17C59×#432—21no—
18C59×#324—21no—
19C59×#324C2212yes—
20C22×Dic118—21no—
21C2×#11745664—22no—
22#14273727—41no—
23#14273727—41no—
24C2×C4⋊Dic59—21no—
25C2×C4⋊Dic59—21no—
26C2×C4⋊Dic59C2×C412yes—
27C2×C4×Dic59—21no—
28#14273646—24no—
29#14273638—41no—
30C4×C59⋊C8—41no—
31C59⋊#95—22no—
32C59⋊#95—22no—
33C59⋊#95—22no—
34C59⋊#95—22no—
35C59⋊#95C2×C412yes—
36C22×Q8×C59D411yescharacteristic
37C4×Q8×C59—41no—
38C4×Q8×C59—41no—
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59D411yescharacteristic
41C2×C4⋊C4×C59C2311yescharacteristic
42C2×C42×C59C2×C411yescharacteristic
43C2×C42×C59D411yescharacteristic
44C2×C42×C59D411yescharacteristic
45C4⋊C8×C59—41no—
46C22⋊C8×C59—22no—
47#97×C59—41no—
48C2×Q8×C59—22no—
49C2×Q8×C59—22no—
50C2×Q8×C59—41no—
51C22×C4×C59C22⋊C411yescharacteristic
52C22×C4×C59C22⋊C411yescharacteristic
53C22×C4×C59C22⋊C411yescharacteristic
54C22×C4×C59C22⋊C411yescharacteristic
55C22×C4×C59C22×C411yescharacteristic
56C22×C4×C59C2×D411yescharacteristic
57C22×C4×C59C2×D411yescharacteristic
58C22×Dic59—22no—
59C22×Dic59—22no—
60C2×Dic118—44no—
61C2×Dic118—41no—
62C2×Dic118—41no—
63C2×C8×C59—42no—
64C4⋊C4×C59—41no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—41no—
67C42×C59—21no—
68C42×C59—21no—
69C42×C59—21no—
70C42×C59—21no—
71C42×C59—21no—
72C42×C59—21no—
73C4⋊Dic59—42no—
74C4⋊Dic59—42no—
75C4⋊Dic59—42no—
76C4×Dic59—42no—
77#11745664—24no—
78#11745664—42no—
79C2×C59⋊C8—42no—
80C23×C59C2×C22⋊C411yescharacteristic
81Q8×C59—44no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—22no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—41no—
94C2×C4×C59—41no—
95C2×C4×C59—41no—
96C2×C4×C59#9911yescharacteristic
97C2×C4×C59#9911yescharacteristic
98C2×C4×C59#10412yes—
99C2×C4×C59#13712yes—
100C2×Dic59—42no—
101C2×Dic59—44no—
102C2×Dic59—42no—
103C2×Dic59—42no—
104C2×Dic59—42no—
105Dic118—82no—
106Dic118—82no—
107C8×C59—82no—
108C59⋊C8—44no—
109#11794—591nomaximal, Sylow
110C22×C59—21no—
111C22×C59—21no—
112C22×C59C2×#9911yescharacteristic
113C22×C59#41911yescharacteristic
114C22×C59C2×#10411yescharacteristic
115C4×C59—21no—
116C4×C59—22no—
117C4×C59—22no—
118C4×C59—41no—
119C4×C59—41no—
120C4×C59—41no—
121C4×C59—41no—
122C4×C59#35512yes—
123Dic59—82no—
124Dic59—82no—
125#2568—591no—
126C4×#101—591no—
127#1467D5911yescharacteristic
128#1353—594no—
129C2×C59—21no—
130C2×C59—21no—
131C2×C59#150811yescharacteristic
132C2×C59#212311yescharacteristic
133C2×C59C2×#35511yescharacteristic
134C2×C4⋊Q8—591no—
135C2×C4×Q8C2×D5911yescharacteristic
136#432—21no—
137C2×#101—1181no—
138C4×M16—1181no—
139#400—592no—
140#400—592no—
141#391—1181no—
142#391—1181no—
143#391—1181no—
144#382—1181no—
145C4×C4⋊C4—591no—
146#343—592no—
147#324—21no—
148#324C2×D5912yes—
149C59#1179411yescharacteristic, complemented, Sylow
150C22×Q8—1181no—
151C22×Q8D23611yescharacteristic
152C2×M16—1182no—
153C4⋊Q8—2361no—
154C4⋊Q8—2361no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—592no—
158C2×C4⋊C4—1181no—
159C2×C4⋊C4—1181no—
160C2×C4⋊C4C4×D5911yescharacteristic
161C2×C4⋊C4C22⋊D5911yescharacteristic
162C2×C4⋊C4C22×D5911yescharacteristic
163C2×C42—1181no—
164C2×C42C4×D5911yescharacteristic
165C2×C42D23611yescharacteristic
166C2×C42C22⋊D5911yescharacteristic
167C4⋊C8—41no—
168#101—1184no—
169C22⋊C8—22no—
170#97—41no—
171#97—2361no—
172C4×C8—2361no—
173#95—592no—
174#95—1182no—
175#95—1182no—
176#95—1182no—
177#95—1182no—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—2364no—
182C2×Q8—2361no—
183C2×Q8—2361no—
184C22×C4—1182no—
185C22×C4—1182no—
186C22×C4(C2×D59)⋊C411yescharacteristic
187C22×C4(C2×D59)⋊C411yescharacteristic
188C22×C4(C2×D59)⋊C411yescharacteristic
189C22×C4(C2×D59)⋊C411yescharacteristic
190C22×C4C2×C4×D5911yescharacteristic
191C22×C4C2×D23611yescharacteristic
192C22×C4C2×C22⋊D5911yescharacteristic
193M16—1184no—
194M16—2362no—
195C2×C8—42no—
196C2×C8—2362no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—2362no—
201C4⋊C4—2362no—
202C4⋊C4—2362no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—2362no—
210C23C2×(C2×D59)⋊C411yescharacteristic
211Q8—44no—
212Q8—4722no—
213Q8—4722no—
214C2×C4—21no—
215C2×C4—21no—
216C2×C4—21no—
217C2×C4—21no—
218C2×C4—22no—
219C2×C4—21no—
220C2×C4—21no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—41no—
228C2×C4—2362no—
229C2×C4—2362no—
230C2×C4—2364no—
231C2×C4—2362no—
232C2×C4—2362no—
233C2×C4#1427364111yescharacteristic
234C2×C4#1427364111yescharacteristic
235C2×C4#1427365312yes—
236C2×C4#1427376012yes—
237C8—82no—
238C8—2364no—
239C22—21no—
240C22—21no—
241C22C2×#1427364111yescharacteristic
242C22#1683741211yescharacteristic
243C22C2×#1427365311yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—4722no—
252C4—4722no—
253C4#1683719812yes—
254C2—21no—
255C2—21no—
256C2#2142261711yescharacteristic
257C2#2142574911yescharacteristic
258C2C2×#1683719811yescharacteristic
subgroupG/H
centerC22C2×#14273641
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#1467C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#1467D59
hypocenterC59#11794
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #1467

Complements

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

NH ≅ G/Ntype
149. C59#11794semidirect

Maximal subgroups

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

subgroupindex
#214293082
C4×#142736462
#214221242
C59×#14672
#1179459