Finite Group Databasebeta

← #28499284

Subgroups — #28499284

Order 15104.

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

normal subgroups only

This group has 414 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#21422102C214yesmaximal
4C59×#2546C211yesmaximal, characteristic
5#16837459—21no—
6C2×#14273646—21no—
7C4×#11745664—21no—
8#16837171C2212yes—
9#16837128—21no—
10#16837128C2212yes—
11C2×C4⋊Q8×C59—21no—
12C2×C4⋊Q8×C59C411yescharacteristic
13C2×C4×Q8×C59C2211yescharacteristic
14C59×#398C412yes—
15C59×#398C2212yes—
16C59×#391—21no—
17C59×#389—21no—
18C59×#389—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—44no—
32C4×Q8×C59—41no—
33C4×Q8×C59—41no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59—21no—
36C2×C4⋊C4×C59—22no—
37C2×C4⋊C4×C59—22no—
38C2×C4⋊C4×C59C2×C412yes—
39C2×C4⋊C4×C59C2×C411yescharacteristic
40C2×C4⋊C4×C59D411yescharacteristic
41C2×C4⋊C4×C59C2311yescharacteristic
42C2×C42×C59—21no—
43C2×C42×C59C2×C411yescharacteristic
44C2×C42×C59D411yescharacteristic
45C2×C42×C59D411yescharacteristic
46#95×C59—22no—
47#95×C59—22no—
48#95×C59C2×C412yes—
49C2×Q8×C59—22no—
50C2×Q8×C59—22no—
51C2×Q8×C59—41no—
52C2×Q8×C59—42no—
53C2×Q8×C59—42no—
54C2×Q8×C59—42no—
55C22×C4×C59—22no—
56C22×C4×C59—22no—
57C22×C4×C59C22⋊C411yescharacteristic
58C22×C4×C59C22⋊C411yescharacteristic
59C22×C4×C59C22⋊C411yescharacteristic
60C22×C4×C59C22⋊C411yescharacteristic
61C22×C4×C59C22×C411yescharacteristic
62C22×C4×C59C2×D411yescharacteristic
63C22×C4×C59C2×D411yescharacteristic
64C4⋊C4×C59—24no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—41no—
67C4⋊C4×C59—41no—
68C4⋊C4×C59—44no—
69C4⋊C4×C59—42no—
70C4⋊C4×C59—41no—
71C4⋊C4×C59—41no—
72C4⋊C4×C59—44no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59—21no—
78C42×C59—21no—
79C42×C59—42no—
80#11745664—24no—
81#11745664—42no—
82C2×C59⋊C8—42no—
83C2×C59⋊C8—42no—
84C23×C59C2×C22⋊C411yescharacteristic
85Q8×C59—44no—
86Q8×C59—84no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—21no—
91C2×C4×C59—22no—
92C2×C4×C59—24no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—21no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—42no—
100C2×C4×C59—42no—
101C2×C4×C59—41no—
102C2×C4×C59—41no—
103C2×C4×C59—41no—
104C2×C4×C59—42no—
105C2×C4×C59—42no—
106C2×C4×C59—42no—
107C2×C4×C59#9911yescharacteristic
108C2×C4×C59#9911yescharacteristic
109C2×C4×C59#10412yes—
110C2×C4×C59AGL(1,ℤ/8)12yes—
111C59⋊C8—44no—
112C59⋊C8—82no—
113#11782—591nomaximal, Sylow
114C22×C59—21no—
115C22×C59—21no—
116C22×C59C2×#9911yescharacteristic
117C22×C59#41811yescharacteristic
118C22×C59C2×#10411yescharacteristic
119C4×C59—21no—
120C4×C59—22no—
121C4×C59—22no—
122C4×C59—44no—
123C4×C59—41no—
124C4×C59—41no—
125C4×C59—41no—
126C4×C59—41no—
127C4×C59—82no—
128C4×C59#35612yes—
129#2546D5911yescharacteristic
130C4×#101—591no—
131#1467—591no—
132#1346—594no—
133C2×C59—21no—
134C2×C59—21no—
135C2×C59#150711yescharacteristic
136C2×C59#212311yescharacteristic
137C2×C59C2×#35611yescharacteristic
138C2×C4⋊Q8—21no—
139C2×C4⋊Q8Dic5911yescharacteristic
140C2×C4×Q8C2×D5911yescharacteristic
141#432—1181no—
142C2×#101—1181no—
143C4×M16—1181no—
144#398Dic5912yes—
145#398C2×D5912yes—
146#391—21no—
147#389—21no—
148#389—21no—
149C4×C4⋊C4Dic5911yescharacteristic
150#343—592no—
151#324—592no—
152#324—1181no—
153C59#1178211yescharacteristic, complemented, Sylow
154C22×Q8—21no—
155C22×Q8C22⋊D5911yescharacteristic
156C2×M16—1182no—
157C4⋊Q8—41no—
158C4⋊Q8—41no—
159C4⋊Q8—44no—
160C4×Q8—41no—
161C4×Q8—41no—
162C2×C4⋊C4—21no—
163C2×C4⋊C4—22no—
164C2×C4⋊C4—21no—
165C2×C4⋊C4—22no—
166C2×C4⋊C4C2×Dic5912yes—
167C2×C4⋊C4C2×Dic5911yescharacteristic
168C2×C4⋊C4C22⋊D5911yescharacteristic
169C2×C4⋊C4C22×D5911yescharacteristic
170C2×C42—21no—
171C2×C42C2×Dic5911yescharacteristic
172C2×C42C22⋊D5911yescharacteristic
173C2×C42C22⋊D5911yescharacteristic
174C4⋊C8—2361no—
175#101—1184no—
176C22⋊C8—1182no—
177#97—2361no—
178#97—2361no—
179C4×C8—2361no—
180#95—22no—
181#95—22no—
182#95C2×Dic5912yes—
183C2×Q8—22no—
184C2×Q8—22no—
185C2×Q8—41no—
186C2×Q8—42no—
187C2×Q8—42no—
188C2×Q8—42no—
189C22×C4—22no—
190C22×C4—22no—
191C22×C4C22⋊Dic5911yescharacteristic
192C22×C4C22⋊Dic5911yescharacteristic
193C22×C4C22⋊Dic5911yescharacteristic
194C22×C4C22⋊Dic5911yescharacteristic
195C22×C4C22×Dic5911yescharacteristic
196C22×C4C2×C22⋊D5911yescharacteristic
197C22×C4C2×C22⋊D5911yescharacteristic
198M16—1184no—
199M16—2362no—
200C2×C8—2362no—
201C2×C8—2362no—
202C4⋊C4—24no—
203C4⋊C4—41no—
204C4⋊C4—41no—
205C4⋊C4—41no—
206C4⋊C4—42no—
207C4⋊C4—44no—
208C4⋊C4—41no—
209C4⋊C4—41no—
210C4⋊C4—44no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—21no—
216C42—21no—
217C42—42no—
218C23C2×C22⋊Dic5911yescharacteristic
219Q8—44no—
220Q8—84no—
221C2×C4—21no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—22no—
226C2×C4—24no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—42no—
234C2×C4—42no—
235C2×C4—41no—
236C2×C4—41no—
237C2×C4—41no—
238C2×C4—42no—
239C2×C4—42no—
240C2×C4—42no—
241C2×C4#1427364211yescharacteristic
242C2×C4#1427364211yescharacteristic
243C2×C4#1427365412yes—
244C2×C4#1427375312yes—
245C8—4722no—
246C8—2364no—
247C22—21no—
248C22—21no—
249C22C2×#1427364211yescharacteristic
250C22#1683740711yescharacteristic
251C22C2×#1427365411yescharacteristic
252C4—22no—
253C4—22no—
254C4—21no—
255C4—44no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—41no—
260C4—82no—
261C4#1683720112yes—
262C2—21no—
263C2—21no—
264C2#2142261211yescharacteristic
265C2#2142575011yescharacteristic
266C2C2×#1683720111yescharacteristic
subgroupG/H
centerC22C2×#14273642
commutatorC22×C4×C59C22×C4
FrattiniC2×C4⋊C4C22×D59
FittingC59×#2546C2
socleC22×C59C2×#99
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C4⋊C4×C59C23
hypercenter#2546D59
hypocenterC59#11782
LCSG ▷ C22×C4×C59 ▷ C23×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4×Q8 ◁ #2546

Complements

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

NH ≅ G/Ntype
153. C59#11782semidirect

Maximal subgroups

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

subgroupindex
C4×#142736462
#214224402
#214221022
C59×#25462
#1178259