Finite Group Databasebeta

← #28493193

Subgroups — #28493193

Order 15104.

382 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 382 conjugacy classes of subgroups — too many to draw. Only its 97 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#21424265C212yesmaximal
2#21424229C211yesmaximal, characteristic
3#21421977C211yesmaximal, characteristic
4#21421977C212yesmaximal
5C59×#2845C211yesmaximal, characteristic
6C2×#14273660—22no—
7C2×#14273658—22no—
8C2×#14273638C2211yescharacteristic
9C2×#14273638C2212yes—
10#16837272C2211yescharacteristic
11#16837164—22no—
12C59×#398—22no—
13C59×#398—22no—
14C59×#398—22no—
15C59×#382C2211yescharacteristic
16C59×#382C2212yes—
17C22×C59⋊C8—22no—
18C22×C59⋊C8—21no—
19C2×C4⋊Dic59—21no—
20C2×C4⋊Dic59—22no—
21#14273660—44no—
22#14273658—44no—
23#14273638—22no—
24#14273638—21no—
25#14273638Q814yes—
26#14273638Q812yes—
27C2×C4⋊C4×C59—22no—
28C2×C4⋊C4×C59—22no—
29C2×C4⋊C4×C59—22no—
30C2×C4⋊C4×C59D412yes—
31C2×C4⋊C4×C59D412yes—
32C2×C4⋊C4×C59D412yes—
33C2×C42×C59C2311yescharacteristic
34#95×C59—22no—
35#95×C59—22no—
36#95×C59—22no—
37#95×C59—22no—
38C22×C4×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2×D412yes—
42C22×C4×C59C2×D411yescharacteristic
43C22×Dic59—41no—
44C4⋊C4×C59—42no—
45C4⋊C4×C59—42no—
46C4⋊C4×C59—42no—
47C4⋊C4×C59—82no—
48C4⋊C4×C59—82no—
49C4⋊C4×C59—82no—
50C42×C59C2×Q812yes—
51C42×C59C2×Q811yescharacteristic
52C42×C59#4111yescharacteristic
53C4⋊Dic59—42no—
54C4⋊Dic59—42no—
55C4⋊Dic59—42no—
56C2×C59⋊C8—24no—
57C2×C59⋊C8—24no—
58C2×C59⋊C8—24no—
59C2×C59⋊C8—22no—
60C2×C59⋊C8—41no—
61C2×C59⋊C8—41no—
62C23×C59#12011yescharacteristic
63C2×C4×C59—22no—
64C2×C4×C59—21no—
65C2×C4×C59—21no—
66C2×C4×C59—22no—
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×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—42no—
76C2×C4×C59C22⋊Q812yes—
77C2×C4×C59C22⋊Q811yescharacteristic
78C2×C4×C59C4⋊Q812yes—
79C2×C4×C59C4⋊Q811yescharacteristic
80C2×Dic59—82no—
81C2×Dic59—81no—
82C59⋊C8—28no—
83C59⋊C8—42no—
84#10585—591nomaximal, Sylow
85C22×C59#39511yescharacteristic
86C22×C59#45312yes—
87C22×C59#45411yescharacteristic
88C22×C59#45511yescharacteristic
89C22×C59#45612yes—
90C4×C59—22no—
91C4×C59—22no—
92C4×C59—21no—
93C4×C59—21no—
94C4×C59—82no—
95C4×C59—82no—
96C4×C59—82no—
97Dic59—161no—
98#2845D5911yescharacteristic
99#1847—592no—
100#1836—591no—
101#1295—591no—
102#1295—592no—
103C2×C59#165611yescharacteristic
104C2×C59#166112yes—
105C2×C59#166311yescharacteristic
106C2×C59#206012yes—
107C2×C59#206111yescharacteristic
108C2×#107—1182no—
109C2×#106—1182no—
110C2×#97—591no—
111C2×#97—592no—
112#398—22no—
113#398—22no—
114#398—22no—
115#384—591no—
116#382C2×D5911yescharacteristic
117#382C2×D5912yes—
118#340—1182no—
119C59#1058511yescharacteristic, complemented, Sylow
120C22×C8—1182no—
121C22×C8—1181no—
122C2×C4⋊C4—22no—
123C2×C4⋊C4—22no—
124C2×C4⋊C4—22no—
125C2×C4⋊C4—1181no—
126C2×C4⋊C4—1182no—
127C2×C4⋊C4C22⋊D5912yes—
128C2×C4⋊C4C22⋊D5912yes—
129C2×C4⋊C4C22⋊D5912yes—
130C2×C42C22×D5911yescharacteristic
131#107—2364no—
132#106—2364no—
133#97—594no—
134#97—592no—
135#97—1182no—
136#97—1181no—
137#95—22no—
138#95—22no—
139#95—22no—
140#95—22no—
141C22×C4—22no—
142C22×C4—22no—
143C22×C4—22no—
144C22×C4—2361no—
145C22×C4C2×C22⋊D5912yes—
146C22×C4C2×C22⋊D5911yescharacteristic
147C2×C8—1184no—
148C2×C8—1184no—
149C2×C8—1184no—
150C2×C8—1182no—
151C2×C8—2361no—
152C2×C8—2361no—
153C4⋊C4—42no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—82no—
157C4⋊C4—82no—
158C4⋊C4—82no—
159C4⋊C4—2362no—
160C4⋊C4—2362no—
161C4⋊C4—2362no—
162C42Q8×D5912yes—
163C42Q8×D5911yescharacteristic
164C42#1174568911yescharacteristic
165C23#1427369611yescharacteristic
166C2×C4—22no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—42no—
171C2×C4—42no—
172C2×C4—42no—
173C2×C4—42no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—42no—
179C2×C4—4722no—
180C2×C4—4721no—
181C2×C4#1427370312yes—
182C2×C4#1427370311yescharacteristic
183C2×C4#1427372512yes—
184C2×C4#1427372511yescharacteristic
185C8—1188no—
186C8—2362no—
187C22#1683732111yescharacteristic
188C22#1683757012yes—
189C22#1683757511yescharacteristic
190C22#1683758011yescharacteristic
191C22#1683758512yes—
192C4—22no—
193C4—22no—
194C4—21no—
195C4—21no—
196C4—82no—
197C4—82no—
198C4—82no—
199C4—9441no—
200C2#2142338911yescharacteristic
201C2#2142341312yes—
202C2#2142342411yescharacteristic
203C2#2142543812yes—
204C2#2142544311yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2845C2
socle, prime radicalC23×C59#120
hypercenter#2845D59
hypocenterC59#10585
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

Complements

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

NH ≅ G/Ntype
119. C59#10585semidirect

Maximal subgroups

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

subgroupindex
#214242652
#214242292
#214219772
C59×#28452
#1058559