Finite Group Databasebeta

← #28491829

Subgroups — #28491829

Order 15104.

364 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 93 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#21425077C211yesmaximal, characteristic
2#21422594C212yesmaximal
3#21421999C212yesmaximal
4#21421925C211yesmaximal, characteristic
5C59×#2402C211yesmaximal, characteristic
6#16837959C2211yescharacteristic
7#16837455C2212yes—
8#16837426C2211yescharacteristic
9#16837162—22no—
10#16837138—22no—
11#16837138—22no—
12C59×#400—22no—
13C59×#398—22no—
14C4×C4⋊C4×C59—22no—
15C4×C4⋊C4×C59C2212yes—
16C59×#376C2211yescharacteristic
17C2×#11745664—21no—
18#14273727Q812yes—
19#14273719—21no—
20#14273706—22no—
21C4×Dic118—22no—
22#14273686—21no—
23C4⋊(C59⋊C8)—22no—
24C4⋊(C59⋊C8)—22no—
25C22⋊(C59⋊C8)—22no—
26C4×C59⋊C8—22no—
27C2×C4⋊C4×C59—22no—
28C2×C4⋊C4×C59—22no—
29C2×C4⋊C4×C59—22no—
30C2×C42×C59—22no—
31C2×C42×C59D412yes—
32C2×C42×C59C2311yescharacteristic
33#95×C59—22no—
34#95×C59—22no—
35#95×C59—22no—
36#95×C59D412yes—
37#95×C59D412yes—
38C22×C4×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2×D412yes—
42C22×C4×C59C2×D411yescharacteristic
43C2×Dic118—22no—
44C4⋊C4×C59—44no—
45C4⋊C4×C59—44no—
46C4⋊C4×C59—44no—
47C42×C59—22no—
48C42×C59—22no—
49C42×C59—42no—
50C42×C59—42no—
51C42×C59C2×Q811yescharacteristic
52C42×C59#4112yes—
53C42×C59#4111yescharacteristic
54C22⋊Dic59—41no—
55C4⋊Dic59—22no—
56C4⋊Dic59—22no—
57Dic59⋊C4—42no—
58C4×Dic59—41no—
59#11745664—42no—
60C2×C59⋊C8—42no—
61C2×C59⋊C8—41no—
62C23×C59#12011yescharacteristic
63C2×C4×C59—24no—
64C2×C4×C59—42no—
65C2×C4×C59—42no—
66C2×C4×C59—42no—
67C2×C4×C59—42no—
68C2×C4×C59—42no—
69C2×C4×C59—42no—
70C2×C4×C59—42no—
71C2×C4×C59—42no—
72C2×C4×C59—42no—
73C2×C4×C59C22⋊Q812yes—
74C2×C4×C59C22⋊Q811yescharacteristic
75C2×C4×C59#12412yes—
76C2×C4×C59#12411yescharacteristic
77C2×C4×C59#13512yes—
78C2×C4×C59#13712yes—
79C2×Dic59—42no—
80Dic118—82no—
81C59⋊C8—82no—
82C59⋊C8—81no—
83#10373—591nomaximal, Sylow
84C22×C59—22no—
85C22×C59#39311yescharacteristic
86C22×C59#45212yes—
87C4×C59—22no—
88C4×C59—22no—
89C4×C59—44no—
90C4×C59—82no—
91C4×C59—82no—
92C4×C59#47912yes—
93C4×C59#48811yescharacteristic
94C4×C59#49111yescharacteristic
95Dic59—82no—
96#2402D5911yescharacteristic
97#1995—591no—
98#1503—592no—
99#1303—592no—
100#1274—591no—
101C2×C59—22no—
102C2×C59#202611yescharacteristic
103C2×C59#203112yes—
104#533—591no—
105#431—592no—
106#423—591no—
107#400—22no—
108#398—22no—
109C4×C4⋊C4—22no—
110C4×C4⋊C4C2×D5912yes—
111#376C2×D5911yescharacteristic
112#339—1182no—
113#328—1182no—
114#328—1182no—
115C59#1037311yescharacteristic, complemented, Sylow
116C2×M16—1181no—
117C4⋊Q8—592no—
118#125—1181no—
119C22⋊Q8—1182no—
120C4×Q8—1182no—
121#117—1181no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C42—22no—
126C2×C42C22⋊D5912yes—
127C2×C42C22×D5911yescharacteristic
128C4⋊C8—1182no—
129C4⋊C8—1182no—
130C22⋊C8—1182no—
131C4×C8—1182no—
132#95—22no—
133#95—22no—
134#95—22no—
135#95C22⋊D5912yes—
136#95C22⋊D5912yes—
137C2×Q8—1182no—
138C22×C4—22no—
139C22×C4—22no—
140C22×C4—22no—
141C22×C4C2×C22⋊D5912yes—
142C22×C4C2×C22⋊D5911yescharacteristic
143M16—2362no—
144C2×C8—2362no—
145C2×C8—2361no—
146C4⋊C4—44no—
147C4⋊C4—44no—
148C4⋊C4—44no—
149C4⋊C4—1182no—
150C4⋊C4—1182no—
151C4⋊C4—2362no—
152C22⋊C4—2361no—
153C42—22no—
154C42—22no—
155C42—42no—
156C42—42no—
157C42—2361no—
158C42Q8×D5911yescharacteristic
159C42#1174568911yescharacteristic
160C42#1174568912yes—
161C23#1427369611yescharacteristic
162Q8—4722no—
163C2×C4—24no—
164C2×C4—42no—
165C2×C4—42no—
166C2×C4—42no—
167C2×C4—42no—
168C2×C4—42no—
169C2×C4—42no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—2362no—
174C2×C4#1427370312yes—
175C2×C4#1427370311yescharacteristic
176C2×C4#1427371612yes—
177C2×C4#1427371611yescharacteristic
178C2×C4#1427374712yes—
179C2×C4#1427375712yes—
180C8—4722no—
181C8—4721no—
182C22—22no—
183C22#1683731311yescharacteristic
184C22#1683756412yes—
185C4—22no—
186C4—22no—
187C4—44no—
188C4—82no—
189C4—82no—
190C4—4722no—
191C4#1683770612yes—
192C4#1683775911yescharacteristic
193C4#1683777211yescharacteristic
194C2—22no—
195C2#2142524411yescharacteristic
196C2#2142526512yes—
subgroupG/H
centerC2×C4#14273716
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2402C2
socleC22×C59#393
prime radicalC23×C59#120
hypercenter#2402D59
hypocenterC59#10373
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #2402

Complements

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

NH ≅ G/Ntype
115. C59#10373semidirect

Maximal subgroups

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

subgroupindex
#214250772
#214225942
#214219992
#214219252
C59×#24022
#1037359