Finite Group Databasebeta

← #28489541

Subgroups — #28489541

Order 15104.

566 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 566 conjugacy classes of subgroups — too many to draw. Only its 103 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#21434123C212yesmaximal
2#21427389C211yesmaximal, characteristic, complemented
3#21422524C212yesmaximal, complemented
4#21421925C211yesmaximal, characteristic, complemented
5C59×#1963C211yesmaximal, characteristic
6C2×C4×Dic118C2212yes—
7#16837718—22no—
8#16837684—22no—
9#16837599—22no—
10#16837540—22no—
11C4×#11745670—24no—
12#16837455C2212yes—
13#16837334—22no—
14#16837323—22no—
15C4×C4⋊Dic59—22no—
16#16837132—24no—
17C59×#532C2211yescharacteristic
18C59×#423C2211yescharacteristic
19C2×#104×C59—22no—
20C59×#376C2211yescharacteristic
21C22×Dic118D412yes—
22C2×#11745670—24no—
23C4×Dic118—22no—
24C4×Dic118—22no—
25C4×Dic118—22no—
26C4×Dic118—22no—
27C2×C4⋊Dic59—24no—
28C2×C4⋊Dic59D412yes—
29C2×Dic59⋊C4—22no—
30C2×C4×Dic59—22no—
31#14273658—24no—
32C4⋊(C59⋊C8)—22no—
33#14273650—24no—
34#14273648—24no—
35C22⋊(C59⋊C8)—22no—
36C4×C59⋊C8D414yes—
37C59⋊#95—22no—
38C59⋊#95—22no—
39C2×#41×C59—21no—
40C2×M16×C59—21no—
41C4⋊Q8×C59D411yescharacteristic
42#127×C59D411yescharacteristic
43#124×C59—21no—
44#121×C59—22no—
45C4×D4×C59—22no—
46C2×C42×C59D412yes—
47C2×C42×C59C2311yescharacteristic
48C4⋊C8×C59—22no—
49#104×C59—44no—
50#95×C59—22no—
51#41×C59—42no—
52#41×C59—42no—
53C2×Q8×C59—21no—
54C2×D4×C59—22no—
55C2×D4×C59—21no—
56C2×D4×C59—41no—
57C22×C4×C59—22no—
58C22×C4×C59—41no—
59C22×C4×C59C2×D412yes—
60C22×C4×C59C2×D411yescharacteristic
61C22×Dic59—22no—
62C22×Dic59—22no—
63C2×Dic118—22no—
64C2×Dic118—22no—
65C2×Dic118—44no—
66M16×C59—42no—
67C2×C8×C59—41no—
68C4⋊C4×C59—22no—
69C22⋊C4×C59—42no—
70C42×C59—22no—
71C42×C59SD1614yescomplemented
72C42×C59C2×D411yescharacteristic
73C42×C59C2×D412yes—
74C42×C59#4111yescharacteristic
75#11745670—48no—
76C4⋊Dic59—22no—
77C4⋊Dic59—22no—
78C4⋊Dic59—48no—
79Dic59⋊C4—42no—
80Dic59⋊C4—42no—
81C4×Dic59—42no—
82C4×Dic59—42no—
83C2×C59⋊C8—24no—
84C23×C59—41no—
85C23×C59#12011yescharacteristic
86Q8×C59—42no—
87D4×C59—44no—
88D4×C59—42no—
89D4×C59—82no—
90C2×C4×C59—24no—
91C2×C4×C59—42no—
92C2×C4×C59—44no—
93C2×C4×C59—41no—
94C2×C4×C59—81no—
95C2×C4×C59—81no—
96C2×C4×C59#12012yes—
97C2×C4×C59#12112yes—
98C2×C4×C59#12111yescharacteristic
99C2×C4×C59#12711yescharacteristic
100C2×C4×C59C2×SD1612yes—
101C2×C4×C59#13712yes—
102C2×Dic59—24no—
103C2×Dic59—42no—
104C2×Dic59—42no—
105C2×Dic59—44no—
106C2×Dic59—42no—
107Dic118—24no—
108Dic118—24no—
109Dic118—42no—
110Dic118—42no—
111C8×C59—81no—
112C59⋊C8—44no—
113#10014—591nomaximal, Sylow
114C22×C59—22no—
115C22×C59—82no—
116C22×C59—81no—
117C22×C59#39211yescharacteristic
118C22×C59#44812yes—
119C4×C59—22no—
120C4×C59—22no—
121C4×C59—44no—
122C4×C59—81no—
123C4×C59#46112yes—
124C4×C59#49211yescharacteristic
125C4×C59#49711yescharacteristic
126Dic59—44no—
127Dic59—82no—
128#3103—592no—
129#2399—591no—
130#1963D5911yescharacteristic
131#1487—592no—
132#1274—591no—
133C2×C59—22no—
134C2×C59—161no—
135C2×C59#201012yes—
136C2×C59#201311yescharacteristic
137#532C2×D5911yescharacteristic
138C2×C4×Q8—592no—
139#481—1182no—
140#475—1182no—
141#460—1182no—
142#448—1182no—
143C4×SD16—1184no—
144#431—592no—
145#423C2×D5911yescharacteristic
146C2×#104—22no—
147#398—1182no—
148#395—1182no—
149C4×C4⋊C4—1182no—
150#376C2×D5911yescharacteristic
151Q8⋊C8—1184no—
152C59#1001411yescharacteristic, complemented, Sylow
153C2×#41—21no—
154C22×Q8—592no—
155C2×SD16—1184no—
156C2×M16—21no—
157C4⋊Q8D23611yescharacteristic
158#127D23611yescharacteristic
159#124—21no—
160#121—22no—
161C4×Q8—1182no—
162C4×Q8—1182no—
163C4×Q8—1182no—
164C4×Q8—1182no—
165C4×D4—22no—
166C2×C4⋊C4—592no—
167C2×C4⋊C4—1184no—
168C2×C4⋊C4—1182no—
169C2×C42—1182no—
170C2×C42C22⋊D5912yes—
171C2×C42C22×D5911yescharacteristic
172#106—1184no—
173C4⋊C8—22no—
174C4⋊C8—1182no—
175#104—44no—
176#103—1184no—
177#102—1184no—
178C22⋊C8—1182no—
179C4×C8—594no—
180#95—22no—
181#95—1182no—
182#95—1182no—
183#41—42no—
184#41—42no—
185C2×Q8—21no—
186C2×Q8—1182no—
187C2×Q8—1182no—
188C2×Q8—2364no—
189C2×D4—22no—
190C2×D4—21no—
191C2×D4—41no—
192C22×C4—22no—
193C22×C4—41no—
194C22×C4—1182no—
195C22×C4—1182no—
196C22×C4D4×D5912yes—
197C22×C4C2×C22⋊D5911yescharacteristic
198SD16—2368no—
199M16—42no—
200C2×C8—41no—
201C2×C8—1184no—
202C4⋊C4—22no—
203C4⋊C4—1182no—
204C4⋊C4—1182no—
205C4⋊C4—2368no—
206C4⋊C4—2362no—
207C4⋊C4—2362no—
208C22⋊C4—42no—
209C42—22no—
210C42—2362no—
211C42—2362no—
212C42#1174567014yescomplemented
213C42C2×D23611yescharacteristic
214C42#1174568511yescharacteristic
215C42D4×D5912yes—
216C23—41no—
217C23#1427369511yescharacteristic
218Q8—42no—
219Q8—1184no—
220Q8—1184no—
221Q8—2362no—
222Q8—2362no—
223D4—44no—
224D4—42no—
225D4—82no—
226C2×C4—24no—
227C2×C4—42no—
228C2×C4—44no—
229C2×C4—41no—
230C2×C4—81no—
231C2×C4—81no—
232C2×C4—1184no—
233C2×C4—2364no—
234C2×C4—2362no—
235C2×C4—2362no—
236C2×C4—2362no—
237C2×C4#1427369712yes—
238C2×C4#1427370012yes—
239C2×C4#1427370111yescharacteristic
240C2×C4#1427372311yescharacteristic
241C2×C4C2×#1174567012yes—
242C2×C4#1427375712yes—
243C8—81no—
244C8—2364no—
245C22—22no—
246C22—82no—
247C22—81no—
248C22#1683731111yescharacteristic
249C22#1683754012yes—
250C4—22no—
251C4—22no—
252C4—44no—
253C4—81no—
254C4—4722no—
255C4—2364no—
256C4#1683760712yes—
257C4#1683777411yescharacteristic
258C4#1683779711yescharacteristic
259C2—22no—
260C2—161no—
261C2#2142516212yes—
262C2#2142517811yescharacteristic
subgroupG/H
centerC2×C4#14273723
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1963C2
socleC22×C59#392
prime radicalC59×#532C22
hypercenter#1963D59
hypocenterC59#10014
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #1963

Complements

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

NH ≅ G/Ntype
2. #21427389C2semidirect
3. #21422524C2semidirect
4. #21421925C2semidirect
71. C42×C59SD16semidirect
152. C59#10014semidirect
212. C42#11745670semidirect

Maximal subgroups

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

subgroupindex
#214341232
#214273892
#214225242
#214219252
C59×#19632
#1001459