Finite Group Databasebeta

← #28492784

Subgroups — #28492784

Order 15104.

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

normal subgroups only

This group has 364 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#21424249C211yesmaximal, characteristic
3#21422797C212yesmaximal
4#21422609C212yesmaximal
5C59×#1290C211yesmaximal, characteristic
6#16837959C2212yes—
7#16837698—22no—
8#16837643—22no—
9#16837613—22no—
10C2×C4⋊(C59⋊C8)C2211yescharacteristic
11C2×Dic59⋊C8—22no—
12#16837248C2211yescharacteristic
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—
31Dic59⋊C8—44no—
32#14273652—24no—
33C59⋊#95—21no—
34C59⋊#95D412yes—
35C22×C8×C59D412yes—
36C2×C42×C59C2311yescharacteristic
37C4⋊C8×C59—22no—
38C4⋊C8×C59—22no—
39C22⋊C8×C59—22no—
40#97×C59—22no—
41C22×C4×C59C2×D411yescharacteristic
42C22×C4×C59C2×D411yescharacteristic
43C22×C4×C59#4111yescharacteristic
44C22×Dic59—22no—
45C2×Dic118—22no—
46C2×Dic118—22no—
47C2×C8×C59—22no—
48C2×C8×C59—42no—
49C2×C8×C59—42no—
50C42×C59C2×D412yes—
51C42×C59#4112yes—
52C22⋊Dic59—42no—
53C4⋊Dic59—22no—
54C4⋊Dic59—22no—
55C4⋊Dic59—22no—
56C4⋊Dic59—22no—
57Dic59⋊C4—42no—
58Dic59⋊C4—42no—
59C4×Dic59—22no—
60C4×Dic59—22no—
61C4×Dic59—42no—
62C2×C59⋊C8—42no—
63C2×C59⋊C8—41no—
64Dic236—82no—
65C23×C59#12111yescharacteristic
66C2×C4×C59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—41no—
70C2×C4×C59#12011yescharacteristic
71C2×C4×C59#12112yes—
72C2×C4×C59#12312yes—
73C2×C4×C59#12411yescharacteristic
74C2×Dic59—24no—
75C2×Dic59—42no—
76C2×Dic59—42no—
77C2×Dic59—42no—
78C2×Dic59—42no—
79Dic118—42no—
80Dic118—42no—
81Dic118—82no—
82C8×C59—42no—
83C8×C59—82no—
84C59⋊C8—81no—
85#10516—591nomaximal, Sylow
86C22×C59—21no—
87C22×C59—21no—
88C22×C59#39411yescharacteristic
89C22×C59#47312yes—
90C4×C59—22no—
91C4×C59—21no—
92C4×C59—22no—
93C4×C59#45311yescharacteristic
94C4×C59#45611yescharacteristic
95Dic59—44no—
96Dic59—82no—
97Dic59—82no—
98#3249—591no—
99#1843—591no—
100#1552—592no—
101#1506—592no—
102#1290D5911yescharacteristic
103C2×C59—22no—
104C2×C59#203911yescharacteristic
105C2×C59#204711yescharacteristic
106C2×C59#205311yescharacteristic
107#533—592no—
108#477—1182no—
109#467—1182no—
110#462—1182no—
111#432C2×D5912yes—
112C2×C4⋊C8—591no—
113C2×C4⋊C8—1182no—
114C2×C4⋊C8C2×D5911yescharacteristic
115#376—591no—
116#332—1182no—
117#332—1182no—
118#328—1184no—
119C59#1051611yescharacteristic, complemented, Sylow
120C2×Q16—1182no—
121C22×C8—1181no—
122C22×C8D23612yes—
123C4⋊Q8—592no—
124C4⋊Q8—592no—
125#125—1182no—
126C22⋊Q8—1182no—
127C22⋊Q8—1182no—
128C4×Q8—1182no—
129C4×Q8—1182no—
130#117—1182no—
131C2×C42—1181no—
132C2×C42C22×D5911yescharacteristic
133#107—1182no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—1182no—
137C4⋊C8—2364no—
138#103—1184no—
139C22⋊C8—22no—
140#97—22no—
141#95—592no—
142#95—1181no—
143C2×Q8—1182no—
144C2×Q8—1182no—
145C22×C4—1182no—
146C22×C4C2×D23611yescharacteristic
147C22×C4D4×D5911yescharacteristic
148C22×C4#1174568911yescharacteristic
149Q16—4722no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—2362no—
154C2×C8—2361no—
155C4⋊C4—1182no—
156C4⋊C4—1182no—
157C4⋊C4—1182no—
158C4⋊C4—1182no—
159C4⋊C4—2362no—
160C4⋊C4—2362no—
161C22⋊C4—2362no—
162C42—1182no—
163C42—1182no—
164C42—2362no—
165C42#1174568512yes—
166C42D4×D5912yes—
167C23#1427370211yescharacteristic
168Q8—4722no—
169Q8—2362no—
170Q8—2362no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—41no—
175C2×C4—1184no—
176C2×C4—2362no—
177C2×C4—2362no—
178C2×C4—2362no—
179C2×C4—2362no—
180C2×C4#1427369711yescharacteristic
181C2×C4#1427370012yes—
182C2×C4#1427371212yes—
183C2×C4#1427371511yescharacteristic
184C8—42no—
185C8—82no—
186C8—4721no—
187C22—21no—
188C22—21no—
189C22#1683732011yescharacteristic
190C22#1683767812yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—4722no—
195C4—4722no—
196C4—2364no—
197C4#1683757211yescharacteristic
198C4#1683758711yescharacteristic
199C2—22no—
200C2#2142532111yescharacteristic
201C2#2142536511yescharacteristic
202C2#2142540311yescharacteristic
subgroupG/H
centerC22#16837320
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1290C2
socleC22×C59#394
prime radicalC23×C59#121
hypercenter#1290D59
hypocenterC59#10516
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
119. C59#10516semidirect

Maximal subgroups

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

subgroupindex
#214354412
#214242492
#214227972
#214226092
C59×#12902
#1051659