Finite Group Databasebeta

← #28492789

Subgroups — #28492789

Order 15104.

344 conjugacy classes of subgroups; only the 77 normal subgroups are shown.

normal subgroups only

This group has 344 conjugacy classes of subgroups — too many to draw. Only its 77 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#21435441C211yesmaximal, characteristic
2#21424215C211yesmaximal, characteristic
3#21422797C212yesmaximal
4#21422609C212yesmaximal
5C59×#1290C211yesmaximal, characteristic
6#16837959C2212yes—
7#16837698—22no—
8#16837643—22no—
9#16837613—22no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11#16837248C2211yescharacteristic
12#16837156—22no—
13#16837149—22no—
14#16837147—22no—
15#16837140—24no—
16C59×#432C2212yes—
17C2×C4⋊C8×C59C2211yescharacteristic
18C2×Dic236—22no—
19C22×C59⋊C8—21no—
20#14273727D412yes—
21#14273727D412yes—
22#14273719—22no—
23#14273706—22no—
24#14273706—22no—
25C4×Dic118—22no—
26C4×Dic118—22no—
27#14273686—22no—
28C2×C4×Dic59—21no—
29#14273661—22no—
30C4⋊(C59⋊C8)—22no—
31#14273652—24no—
32C59⋊#95—21no—
33C59⋊#95D412yes—
34C22×C8×C59D412yes—
35C2×C42×C59C2311yescharacteristic
36C4⋊C8×C59—22no—
37C4⋊C8×C59—22no—
38C22⋊C8×C59—22no—
39#97×C59—22no—
40C22×C4×C59C2×D411yescharacteristic
41C22×C4×C59C2×D411yescharacteristic
42C22×C4×C59#4111yescharacteristic
43C22×Dic59—22no—
44C2×Dic118—22no—
45C2×Dic118—22no—
46C2×C8×C59—22no—
47C2×C8×C59—42no—
48C2×C8×C59—42no—
49C42×C59C2×D412yes—
50C42×C59#4112yes—
51C22⋊Dic59—42no—
52C4⋊Dic59—22no—
53C4⋊Dic59—22no—
54C4⋊Dic59—22no—
55C4⋊Dic59—22no—
56Dic59⋊C4—42no—
57Dic59⋊C4—42no—
58C4×Dic59—41no—
59C4×Dic59—41no—
60C4×Dic59—42no—
61C2×C59⋊C8—42no—
62C2×C59⋊C8—41no—
63Dic236—82no—
64C23×C59#12111yescharacteristic
65C2×C4×C59—22no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—41no—
69C2×C4×C59#12011yescharacteristic
70C2×C4×C59#12112yes—
71C2×C4×C59#12312yes—
72C2×C4×C59#12411yescharacteristic
73C2×Dic59—42no—
74C2×Dic59—42no—
75C2×Dic59—42no—
76C2×Dic59—42no—
77C2×Dic59—42no—
78Dic118—42no—
79Dic118—42no—
80Dic118—82no—
81C8×C59—42no—
82C8×C59—82no—
83C59⋊C8—81no—
84#10517—591nomaximal, Sylow
85C22×C59—21no—
86C22×C59—21no—
87C22×C59#39411yescharacteristic
88C22×C59#47312yes—
89C4×C59—22no—
90C4×C59—21no—
91C4×C59—22no—
92C4×C59#45411yescharacteristic
93C4×C59#45511yescharacteristic
94Dic59—82no—
95Dic59—82no—
96Dic59—82no—
97#3249—591no—
98#1832—591no—
99#1552—592no—
100#1506—592no—
101#1290D5911yescharacteristic
102C2×C59—22no—
103C2×C59#204011yescharacteristic
104C2×C59#204711yescharacteristic
105C2×C59#205311yescharacteristic
106#533—592no—
107#477—1182no—
108#467—1182no—
109#462—1182no—
110#432C2×D5912yes—
111C2×C4⋊C8—591no—
112C2×C4⋊C8C2×D5911yescharacteristic
113#376—591no—
114#336—1182no—
115#332—1182no—
116#332—1182no—
117#328—1184no—
118C59#1051711yescharacteristic, complemented, Sylow
119C2×Q16—1182no—
120C22×C8—1181no—
121C22×C8D23612yes—
122C4⋊Q8—592no—
123C4⋊Q8—592no—
124#125—1182no—
125C22⋊Q8—1182no—
126C22⋊Q8—1182no—
127C4×Q8—1182no—
128C4×Q8—1182no—
129#117—1182no—
130C2×C42—1181no—
131C2×C42C22×D5911yescharacteristic
132#107—1182no—
133C4⋊C8—22no—
134C4⋊C8—22no—
135C4⋊C8—1182no—
136#103—1184no—
137C22⋊C8—22no—
138#97—22no—
139#95—592no—
140#95—1181no—
141C2×Q8—1182no—
142C2×Q8—1182no—
143C22×C4—1182no—
144C22×C4C2×D23611yescharacteristic
145C22×C4D4×D5911yescharacteristic
146C22×C4#1174568911yescharacteristic
147Q16—4722no—
148C2×C8—22no—
149C2×C8—42no—
150C2×C8—42no—
151C2×C8—2362no—
152C2×C8—2361no—
153C4⋊C4—1182no—
154C4⋊C4—1182no—
155C4⋊C4—1182no—
156C4⋊C4—1182no—
157C4⋊C4—2362no—
158C4⋊C4—2362no—
159C22⋊C4—2362no—
160C42—2361no—
161C42—2361no—
162C42—2362no—
163C42#1174568512yes—
164C42D4×D5912yes—
165C23#1427370211yescharacteristic
166Q8—4722no—
167Q8—2362no—
168Q8—2362no—
169C2×C4—22no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—2362no—
174C2×C4—2362no—
175C2×C4—2362no—
176C2×C4—2362no—
177C2×C4—2362no—
178C2×C4#1427369711yescharacteristic
179C2×C4#1427370012yes—
180C2×C4#1427371212yes—
181C2×C4#1427371511yescharacteristic
182C8—42no—
183C8—82no—
184C8—4721no—
185C22—21no—
186C22—21no—
187C22#1683732011yescharacteristic
188C22#1683767812yes—
189C4—21no—
190C4—22no—
191C4—22no—
192C4—4722no—
193C4—4722no—
194C4—4722no—
195C4#1683757711yescharacteristic
196C4#1683758211yescharacteristic
197C2—22no—
198C2#2142532611yescharacteristic
199C2#2142536511yescharacteristic
200C2#2142540311yescharacteristic
subgroupG/H
centerC22#16837320
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1290C2
socleC22×C59#394
prime radicalC23×C59#121
hypercenter#1290D59
hypocenterC59#10517
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1290

Complements

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

NH ≅ G/Ntype
118. C59#10517semidirect

Maximal subgroups

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

subgroupindex
#214354412
#214242152
#214227972
#214226092
C59×#12902
#1051759