Finite Group Databasebeta

← #28486393

Subgroups — #28486393

Order 15104.

432 conjugacy classes of subgroups; only the 107 normal subgroups are shown.

normal subgroups only

This group has 432 conjugacy classes of subgroups — too many to draw. Only its 107 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
2#21422814C212yesmaximal
3#21422440C211yesmaximal, characteristic
4#21421953C212yesmaximal
5C59×#2983C211yesmaximal, characteristic
6C2×#14273727C2211yescharacteristic
7#16837459C2212yes—
8#16837341—21no—
9#16837341—21no—
10#16837309C412yes—
11#16837308—21no—
12#16837308—21no—
13#16837267C412yes—
14C4×C4⋊Dic59C2211yescharacteristic
15#16837149—24no—
16#16837128—21no—
17#16837128—21no—
18C2×C4×Q8×C59C2211yescharacteristic
19C59×#446—24no—
20C59×#432—21no—
21C59×#432C2212yes—
22C59×#431—21no—
23C22×Dic118—21no—
24#14273727—22no—
25#14273727—22no—
26C2×C4⋊Dic59—21no—
27C2×C4⋊Dic59—21no—
28C2×C4⋊Dic59C2×C412yes—
29C2×C4×Dic59C2×C412yes—
30C4⋊(C59⋊C8)—22no—
31C22⋊(C59⋊C8)—22no—
32#14273638—22no—
33C59⋊#95—22no—
34C59⋊#95—22no—
35C59⋊#95—22no—
36C59⋊#95—22no—
37C59⋊#95—21no—
38C22×Q8×C59C2×C411yescharacteristic
39C4×Q8×C59—22no—
40C4×Q8×C59—22no—
41C2×C4⋊C4×C59C2×C411yescharacteristic
42C2×C4⋊C4×C59D411yescharacteristic
43C2×C4⋊C4×C59D411yescharacteristic
44C2×C42×C59D411yescharacteristic
45C2×C42×C59D411yescharacteristic
46C2×C42×C59C2311yescharacteristic
47C4⋊C8×C59—22no—
48C4⋊C8×C59—22no—
49C4⋊C8×C59D414yes—
50C22⋊C8×C59—22no—
51#97×C59—22no—
52#97×C59—22no—
53C4×C8×C59—22no—
54C2×Q8×C59—22no—
55C2×Q8×C59—22no—
56C2×Q8×C59—41no—
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
64C22×Dic59—22no—
65C22×Dic59—22no—
66C2×Dic118—44no—
67C2×Dic118—41no—
68C2×Dic118—41no—
69C2×C8×C59—24no—
70C4⋊C4×C59—22no—
71C4⋊C4×C59—22no—
72C4⋊C4×C59—22no—
73C42×C59—21no—
74C42×C59—21no—
75C42×C59—21no—
76C42×C59—21no—
77C42×C59C2×D412yes—
78C42×C59#4112yes—
79C4⋊Dic59—24no—
80C4⋊Dic59—42no—
81C4⋊Dic59—42no—
82C4×Dic59—42no—
83C2×C59⋊C8—42no—
84C23×C59C2×C22⋊C411yescharacteristic
85Q8×C59—44no—
86C2×C4×C59—21no—
87C2×C4×C59—21no—
88C2×C4×C59—21no—
89C2×C4×C59—21no—
90C2×C4×C59—22no—
91C2×C4×C59—21no—
92C2×C4×C59—21no—
93C2×C4×C59—21no—
94C2×C4×C59—21no—
95C2×C4×C59—21no—
96C2×C4×C59—41no—
97C2×C4×C59—41no—
98C2×C4×C59—41no—
99C2×C4×C59#10112yes—
100C2×C4×C59C4×D412yes—
101C2×C4×C59#12011yescharacteristic
102C2×C4×C59#12112yes—
103C2×C4×C59#12311yescharacteristic
104C2×Dic59—42no—
105C2×Dic59—44no—
106C2×Dic59—42no—
107C2×Dic59—42no—
108C2×Dic59—42no—
109Dic118—82no—
110Dic118—82no—
111C8×C59—44no—
112C59⋊C8—82no—
113#9456—591nomaximal, Sylow
114C22×C59—21no—
115C22×C59—21no—
116C22×C59#38611yescharacteristic
117C22×C59C2×#10111yescharacteristic
118C22×C59#41311yescharacteristic
119C4×C59—21no—
120C4×C59—22no—
121C4×C59—22no—
122C4×C59—22no—
123C4×C59—41no—
124C4×C59—41no—
125C4×C59—41no—
126C4×C59#45412yes—
127Dic59—82no—
128Dic59—82no—
129#2983D5911yescharacteristic
130#2568—591no—
131#1556—592no—
132#1467—591no—
133#1285—592no—
134C2×C59—21no—
135C2×C59—21no—
136C2×C59#188811yescharacteristic
137C2×C59#190111yescharacteristic
138C2×C59#190911yescharacteristic
139C2×C4⋊Q8—591no—
140C2×C4×Q8C2×D5911yescharacteristic
141#446—24no—
142#432—21no—
143#432—592no—
144#432C2×D5912yes—
145#431—21no—
146#400—1181no—
147#400—1181no—
148#391—592no—
149#391—1181no—
150#391—1181no—
151#382—592no—
152C4×C4⋊C4—591no—
153#332—1184no—
154#324—1181no—
155#324—1181no—
156C59#945611yescharacteristic, complemented, Sylow
157C22×Q8—1181no—
158C22×Q8C4×D5911yescharacteristic
159C4⋊Q8—1182no—
160C4⋊Q8—1182no—
161C4×Q8—22no—
162C4×Q8—22no—
163C2×C4⋊C4—592no—
164C2×C4⋊C4—1181no—
165C2×C4⋊C4—1181no—
166C2×C4⋊C4C4×D5911yescharacteristic
167C2×C4⋊C4D23611yescharacteristic
168C2×C4⋊C4D23611yescharacteristic
169C2×C42—592no—
170C2×C42C22⋊D5911yescharacteristic
171C2×C42C22⋊D5911yescharacteristic
172C2×C42C22×D5911yescharacteristic
173C4⋊C8—22no—
174C4⋊C8—22no—
175C4⋊C8—1182no—
176C4⋊C8C22⋊D5914yes—
177C22⋊C8—22no—
178C22⋊C8—1182no—
179#97—22no—
180#97—22no—
181#97—1182no—
182C4×C8—22no—
183#95—1182no—
184#95—1182no—
185#95—1182no—
186#95—1182no—
187#95—1181no—
188C2×Q8—22no—
189C2×Q8—22no—
190C2×Q8—41no—
191C2×Q8—2364no—
192C2×Q8—2361no—
193C2×Q8—2361no—
194C22×C4—1182no—
195C22×C4—1182no—
196C22×C4(C2×D59)⋊C411yescharacteristic
197C22×C4(C2×D59)⋊C411yescharacteristic
198C22×C4(C2×D59)⋊C411yescharacteristic
199C22×C4(C2×D59)⋊C411yescharacteristic
200C22×C4C2×C4×D5911yescharacteristic
201C22×C4C2×D23611yescharacteristic
202C22×C4C2×C22⋊D5911yescharacteristic
203C2×C8—24no—
204C2×C8—2362no—
205C4⋊C4—22no—
206C4⋊C4—22no—
207C4⋊C4—22no—
208C4⋊C4—1184no—
209C4⋊C4—2362no—
210C4⋊C4—2362no—
211C42—21no—
212C42—21no—
213C42—21no—
214C42—21no—
215C42—2362no—
216C42#1174568512yes—
217C42C2×C22⋊D5912yes—
218C23C2×(C2×D59)⋊C411yescharacteristic
219Q8—44no—
220Q8—4722no—
221Q8—4722no—
222C2×C4—21no—
223C2×C4—21no—
224C2×C4—21no—
225C2×C4—21no—
226C2×C4—22no—
227C2×C4—21no—
228C2×C4—21no—
229C2×C4—21no—
230C2×C4—21no—
231C2×C4—21no—
232C2×C4—41no—
233C2×C4—41no—
234C2×C4—41no—
235C2×C4—2362no—
236C2×C4—2362no—
237C2×C4—2364no—
238C2×C4—2362no—
239C2×C4—2362no—
240C2×C4#1427364512yes—
241C2×C4C4×C22⋊D5912yes—
242C2×C4#1427369611yescharacteristic
243C2×C4#1427370112yes—
244C2×C4#1427371011yescharacteristic
245C8—44no—
246C8—4722no—
247C22—21no—
248C22—21no—
249C22#1683728111yescharacteristic
250C22C2×#1427364511yescharacteristic
251C22#1683738411yescharacteristic
252C4—21no—
253C4—22no—
254C4—22no—
255C4—22no—
256C4—41no—
257C4—41no—
258C4—41no—
259C4—4722no—
260C4—4722no—
261C4#1683757512yes—
262C2—21no—
263C2—21no—
264C2#2142449911yescharacteristic
265C2#2142456411yescharacteristic
266C2#2142461811yescharacteristic
subgroupG/H
centerC22#16837281
commutatorC22×C4×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#2983C2
socleC22×C59#386
prime radicalC23×C59C2×C22⋊C4
cosocleC2×C42×C59C23
hypercenter#2983D59
hypocenterC59#9456
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2983

Complements

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

NH ≅ G/Ntype
156. C59#9456semidirect

Maximal subgroups

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

subgroupindex
#214293082
#214228142
#214224402
#214219532
C59×#29832
#945659