Finite Group Databasebeta

← #28499337

Subgroups — #28499337

Order 15104.

378 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 378 conjugacy classes of subgroups — too many to draw. Only its 95 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
1C4×#14273646C211yesmaximal, characteristic
2#21422440C211yesmaximal, characteristic
3#21422123C214yesmaximal
4C59×#2568C211yesmaximal, characteristic
5#16837459—21no—
6C2×#14273646—21no—
7C4×#11745664—21no—
8#16837171C2212yes—
9#16837128—21no—
10#16837128C2212yes—
11C2×C4⋊Q8×C59C411yescharacteristic
12C2×C4×Q8×C59C2211yescharacteristic
13C59×#400C412yes—
14C59×#400C2212yes—
15C59×#391—21no—
16C59×#391—21no—
17C59×#391—21no—
18C59×#382—21no—
19C4×C4⋊C4×C59C411yescharacteristic
20C2×#11745664—22no—
21C4⋊(C59⋊C8)—41no—
22#14273646—24no—
23C22⋊(C59⋊C8)—22no—
24#14273638—41no—
25#14273638—41no—
26C4×C59⋊C8—41no—
27C22×Q8×C59—21no—
28C22×Q8×C59D411yescharacteristic
29C4⋊Q8×C59—41no—
30C4⋊Q8×C59—41no—
31C4×Q8×C59—41no—
32C4×Q8×C59—41no—
33C2×C4⋊C4×C59—21no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59C2×C412yes—
36C2×C4⋊C4×C59C2×C411yescharacteristic
37C2×C4⋊C4×C59D411yescharacteristic
38C2×C4⋊C4×C59C2311yescharacteristic
39C2×C42×C59—21no—
40C2×C42×C59C2×C411yescharacteristic
41C2×C42×C59D411yescharacteristic
42C2×C42×C59D411yescharacteristic
43#95×C59—22no—
44#95×C59—22no—
45#95×C59—22no—
46#95×C59—22no—
47#95×C59C2×C412yes—
48C2×Q8×C59—22no—
49C2×Q8×C59—22no—
50C2×Q8×C59—41no—
51C2×Q8×C59—44no—
52C2×Q8×C59—41no—
53C2×Q8×C59—41no—
54C22×C4×C59—22no—
55C22×C4×C59—22no—
56C22×C4×C59C22⋊C411yescharacteristic
57C22×C4×C59C22⋊C411yescharacteristic
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22×C411yescharacteristic
61C22×C4×C59C2×D411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C4⋊C4×C59—41no—
64C4⋊C4×C59—41no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—42no—
67C4⋊C4×C59—42no—
68C4⋊C4×C59—42no—
69C42×C59—21no—
70C42×C59—21no—
71C42×C59—21no—
72C42×C59—21no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—42no—
76#11745664—24no—
77#11745664—42no—
78C2×C59⋊C8—42no—
79C2×C59⋊C8—42no—
80C23×C59C2×C22⋊C411yescharacteristic
81Q8×C59—44no—
82Q8×C59—82no—
83Q8×C59—82no—
84C2×C4×C59—21no—
85C2×C4×C59—21no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—22no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—41no—
96C2×C4×C59—41no—
97C2×C4×C59—41no—
98C2×C4×C59—42no—
99C2×C4×C59—42no—
100C2×C4×C59—44no—
101C2×C4×C59—42no—
102C2×C4×C59—42no—
103C2×C4×C59#9911yescharacteristic
104C2×C4×C59#9911yescharacteristic
105C2×C4×C59#10412yes—
106C2×C4×C59#13712yes—
107C59⋊C8—44no—
108C59⋊C8—82no—
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—82no—
123C4×C59—82no—
124C4×C59#35512yes—
125#2568D5911yescharacteristic
126C4×#101—591no—
127#1467—591no—
128#1353—594no—
129C2×C59—21no—
130C2×C59—21no—
131C2×C59#150811yescharacteristic
132C2×C59#212311yescharacteristic
133C2×C59C2×#35511yescharacteristic
134C2×C4⋊Q8Dic5911yescharacteristic
135C2×C4×Q8C2×D5911yescharacteristic
136#432—1181no—
137C2×#101—1181no—
138C4×M16—1181no—
139#400Dic5912yes—
140#400C2×D5912yes—
141#391—21no—
142#391—21no—
143#391—21no—
144#382—21no—
145C4×C4⋊C4Dic5911yescharacteristic
146#343—592no—
147#324—592no—
148#324—1181no—
149C59#1179411yescharacteristic, complemented, Sylow
150C22×Q8—21no—
151C22×Q8C22⋊D5911yescharacteristic
152C2×M16—1182no—
153C4⋊Q8—41no—
154C4⋊Q8—41no—
155C4×Q8—41no—
156C4×Q8—41no—
157C2×C4⋊C4—21no—
158C2×C4⋊C4—21no—
159C2×C4⋊C4C2×Dic5912yes—
160C2×C4⋊C4C2×Dic5911yescharacteristic
161C2×C4⋊C4C22⋊D5911yescharacteristic
162C2×C4⋊C4C22×D5911yescharacteristic
163C2×C42—21no—
164C2×C42C2×Dic5911yescharacteristic
165C2×C42C22⋊D5911yescharacteristic
166C2×C42C22⋊D5911yescharacteristic
167C4⋊C8—2361no—
168#101—1184no—
169C22⋊C8—1182no—
170#97—2361no—
171#97—2361no—
172C4×C8—2361no—
173#95—22no—
174#95—22no—
175#95—22no—
176#95—22no—
177#95C2×Dic5912yes—
178C2×Q8—22no—
179C2×Q8—22no—
180C2×Q8—41no—
181C2×Q8—44no—
182C2×Q8—41no—
183C2×Q8—41no—
184C22×C4—22no—
185C22×C4—22no—
186C22×C4C22⋊Dic5911yescharacteristic
187C22×C4C22⋊Dic5911yescharacteristic
188C22×C4C22⋊Dic5911yescharacteristic
189C22×C4C22⋊Dic5911yescharacteristic
190C22×C4C22×Dic5911yescharacteristic
191C22×C4C2×C22⋊D5911yescharacteristic
192C22×C4C2×C22⋊D5911yescharacteristic
193M16—1184no—
194M16—2362no—
195C2×C8—2362no—
196C2×C8—2362no—
197C4⋊C4—41no—
198C4⋊C4—41no—
199C4⋊C4—41no—
200C4⋊C4—42no—
201C4⋊C4—42no—
202C4⋊C4—42no—
203C42—21no—
204C42—21no—
205C42—21no—
206C42—21no—
207C42—21no—
208C42—21no—
209C42—42no—
210C23C2×C22⋊Dic5911yescharacteristic
211Q8—44no—
212Q8—82no—
213Q8—82no—
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—42no—
229C2×C4—42no—
230C2×C4—44no—
231C2×C4—42no—
232C2×C4—42no—
233C2×C4#1427364211yescharacteristic
234C2×C4#1427364211yescharacteristic
235C2×C4#1427365412yes—
236C2×C4#1427375812yes—
237C8—4722no—
238C8—2364no—
239C22—21no—
240C22—21no—
241C22C2×#1427364211yescharacteristic
242C22#1683741111yescharacteristic
243C22C2×#1427365411yescharacteristic
244C4—22no—
245C4—22no—
246C4—21no—
247C4—41no—
248C4—41no—
249C4—41no—
250C4—41no—
251C4—82no—
252C4—82no—
253C4#1683719912yes—
254C2—21no—
255C2—21no—
256C2#2142261611yescharacteristic
257C2#2142575011yescharacteristic
258C2C2×#1683719911yescharacteristic
subgroupG/H
centerC22C2×#14273642
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2568C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#2568D59
hypocenterC59#11794
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2568

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
C4×#142736462
#214224402
#214221232
C59×#25682
#1179459