Finite Group Databasebeta

← #28486374

Subgroups — #28486374

Order 15104.

468 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 468 conjugacy classes of subgroups — too many to draw. Only its 111 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#21433181C211yesmaximal, characteristic
2#21422822C212yesmaximal
3#21422440C211yesmaximal, characteristic
4#21421952C212yesmaximal
5C59×#2546C211yesmaximal, characteristic
6#16837533—24no—
7#16837459—21no—
8#16837459C2212yes—
9#16837459C2212yes—
10#16837455—21no—
11#16837151—24no—
12#16837128—21no—
13#16837128—21no—
14C2×C4⋊Q8×C59C412yes—
15C2×C4⋊Q8×C59C2211yescharacteristic
16C2×C4×Q8×C59C2211yescharacteristic
17C59×#398—21no—
18C59×#398—21no—
19C59×#391C412yes—
20C59×#389—21no—
21C59×#389—21no—
22C4×C4⋊C4×C59C2211yescharacteristic
23C4⋊(C59⋊C8)—22no—
24C4⋊(C59⋊C8)—22no—
25C4⋊(C59⋊C8)—22no—
26C4⋊(C59⋊C8)D414yes—
27C22⋊(C59⋊C8)—22no—
28C22⋊(C59⋊C8)—22no—
29#14273638—22no—
30#14273638—22no—
31#14273638—22no—
32C4×C59⋊C8—22no—
33C22×Q8×C59C2×C412yes—
34C22×Q8×C59C2×C411yescharacteristic
35C4⋊Q8×C59—22no—
36C4⋊Q8×C59—22no—
37C4⋊Q8×C59—44no—
38C4×Q8×C59—22no—
39C4×Q8×C59—22no—
40C2×C4⋊C4×C59—21no—
41C2×C4⋊C4×C59—22no—
42C2×C4⋊C4×C59—22no—
43C2×C4⋊C4×C59—21no—
44C2×C4⋊C4×C59—21no—
45C2×C4⋊C4×C59C2×C411yescharacteristic
46C2×C4⋊C4×C59D411yescharacteristic
47C2×C4⋊C4×C59D411yescharacteristic
48C2×C42×C59C2×C412yes—
49C2×C42×C59D411yescharacteristic
50C2×C42×C59D411yescharacteristic
51C2×C42×C59C2311yescharacteristic
52#95×C59—22no—
53#95×C59—22no—
54#95×C59—21no—
55C2×Q8×C59—22no—
56C2×Q8×C59—22no—
57C2×Q8×C59—24no—
58C2×Q8×C59—41no—
59C2×Q8×C59—42no—
60C2×Q8×C59—42no—
61C22×C4×C59—22no—
62C22×C4×C59—22no—
63C22×C4×C59C22⋊C411yescharacteristic
64C22×C4×C59C22⋊C411yescharacteristic
65C22×C4×C59C22⋊C411yescharacteristic
66C22×C4×C59C22⋊C411yescharacteristic
67C22×C4×C59C22×C411yescharacteristic
68C22×C4×C59C2×D411yescharacteristic
69C22×C4×C59C2×D411yescharacteristic
70C4⋊C4×C59—24no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—22no—
73C4⋊C4×C59—22no—
74C4⋊C4×C59—44no—
75C4⋊C4×C59—44no—
76C4⋊C4×C59—41no—
77C4⋊C4×C59—42no—
78C4⋊C4×C59—41no—
79C42×C59—21no—
80C42×C59—21no—
81C42×C59—21no—
82C42×C59—21no—
83C42×C59—42no—
84C42×C59C2×D412yes—
85C42×C59#4112yes—
86C2×C59⋊C8—24no—
87C2×C59⋊C8—42no—
88C23×C59C2×C22⋊C411yescharacteristic
89Q8×C59—44no—
90Q8×C59—84no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—22no—
96C2×C4×C59—24no—
97C2×C4×C59—21no—
98C2×C4×C59—21no—
99C2×C4×C59—21no—
100C2×C4×C59—21no—
101C2×C4×C59—21no—
102C2×C4×C59—41no—
103C2×C4×C59—42no—
104C2×C4×C59—42no—
105C2×C4×C59—41no—
106C2×C4×C59—41no—
107C2×C4×C59—42no—
108C2×C4×C59—42no—
109C2×C4×C59—42no—
110C2×C4×C59#10012yes—
111C2×C4×C59C4×D412yes—
112C2×C4×C59#12011yescharacteristic
113C2×C4×C59#12112yes—
114C2×C4×C59#12311yescharacteristic
115C59⋊C8—44no—
116C59⋊C8—82no—
117#9452—591nomaximal, Sylow
118C22×C59—21no—
119C22×C59—21no—
120C22×C59#38611yescharacteristic
121C22×C59C2×#10011yescharacteristic
122C22×C59#41311yescharacteristic
123C4×C59—21no—
124C4×C59—22no—
125C4×C59—22no—
126C4×C59—22no—
127C4×C59—44no—
128C4×C59—41no—
129C4×C59—41no—
130C4×C59—41no—
131C4×C59—82no—
132C4×C59#45612yes—
133#2983—591no—
134#2546D5911yescharacteristic
135#1558—592no—
136#1467—591no—
137#1285—592no—
138C2×C59—21no—
139C2×C59—21no—
140C2×C59#188611yescharacteristic
141C2×C59#190011yescharacteristic
142C2×C59#190911yescharacteristic
143C2×C4⋊Q8Dic5912yes—
144C2×C4⋊Q8C2×D5911yescharacteristic
145C2×C4×Q8C2×D5911yescharacteristic
146#446—1184no—
147#432—592no—
148#432—592no—
149#432—1181no—
150#431—1181no—
151#398—21no—
152#398—21no—
153#391Dic5912yes—
154#389—21no—
155#389—21no—
156C4×C4⋊C4C2×D5911yescharacteristic
157#333—1184no—
158#324—1181no—
159#324—1181no—
160C59#945211yescharacteristic, complemented, Sylow
161C22×Q8C2×Dic5912yes—
162C22×Q8C2×Dic5911yescharacteristic
163C4⋊Q8—22no—
164C4⋊Q8—22no—
165C4⋊Q8—44no—
166C4×Q8—22no—
167C4×Q8—22no—
168C2×C4⋊C4—21no—
169C2×C4⋊C4—22no—
170C2×C4⋊C4—22no—
171C2×C4⋊C4—21no—
172C2×C4⋊C4—21no—
173C2×C4⋊C4C2×Dic5911yescharacteristic
174C2×C4⋊C4C22⋊D5911yescharacteristic
175C2×C4⋊C4C22⋊D5911yescharacteristic
176C2×C42C2×Dic5912yes—
177C2×C42C22⋊D5911yescharacteristic
178C2×C42C22⋊D5911yescharacteristic
179C2×C42C22×D5911yescharacteristic
180C4⋊C8—594no—
181C4⋊C8—1182no—
182C4⋊C8—1182no—
183C4⋊C8—1182no—
184C22⋊C8—1182no—
185C22⋊C8—1182no—
186#97—1182no—
187#97—1182no—
188#97—1182no—
189C4×C8—1182no—
190#95—22no—
191#95—22no—
192#95—21no—
193C2×Q8—22no—
194C2×Q8—22no—
195C2×Q8—24no—
196C2×Q8—41no—
197C2×Q8—42no—
198C2×Q8—42no—
199C22×C4—22no—
200C22×C4—22no—
201C22×C4C22⋊Dic5911yescharacteristic
202C22×C4C22⋊Dic5911yescharacteristic
203C22×C4C22⋊Dic5911yescharacteristic
204C22×C4C22⋊Dic5911yescharacteristic
205C22×C4C22×Dic5911yescharacteristic
206C22×C4C2×C22⋊D5911yescharacteristic
207C22×C4C2×C22⋊D5911yescharacteristic
208C2×C8—1184no—
209C2×C8—2362no—
210C4⋊C4—24no—
211C4⋊C4—22no—
212C4⋊C4—22no—
213C4⋊C4—22no—
214C4⋊C4—44no—
215C4⋊C4—44no—
216C4⋊C4—41no—
217C4⋊C4—42no—
218C4⋊C4—41no—
219C42—21no—
220C42—21no—
221C42—21no—
222C42—21no—
223C42—42no—
224C42D4×D5912yes—
225C42#1174568712yes—
226C23C2×C22⋊Dic5911yescharacteristic
227Q8—44no—
228Q8—84no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—21no—
233C2×C4—22no—
234C2×C4—24no—
235C2×C4—21no—
236C2×C4—21no—
237C2×C4—21no—
238C2×C4—21no—
239C2×C4—21no—
240C2×C4—41no—
241C2×C4—42no—
242C2×C4—42no—
243C2×C4—41no—
244C2×C4—41no—
245C2×C4—42no—
246C2×C4—42no—
247C2×C4—42no—
248C2×C4#1427364412yes—
249C2×C4D4×Dic5912yes—
250C2×C4#1427369511yescharacteristic
251C2×C4#1427369912yes—
252C2×C4#1427370811yescharacteristic
253C8—4722no—
254C8—2364no—
255C22—21no—
256C22—21no—
257C22#1683728211yescharacteristic
258C22C2×#1427364411yescharacteristic
259C22#1683738611yescharacteristic
260C4—21no—
261C4—22no—
262C4—22no—
263C4—22no—
264C4—44no—
265C4—41no—
266C4—41no—
267C4—41no—
268C4—82no—
269C4#1683758412yes—
270C2—21no—
271C2—21no—
272C2#2142449011yescharacteristic
273C2#2142456011yescharacteristic
274C2#2142461911yescharacteristic
subgroupG/H
centerC22#16837282
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2546C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2546D59
hypocenterC59#9452
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2546

Complements

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

NH ≅ G/Ntype
160. C59#9452semidirect

Maximal subgroups

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

subgroupindex
#214331812
#214228222
#214224402
#214219522
C59×#25462
#945259