Finite Group Databasebeta

← #28492783

Subgroups — #28492783

Order 15104.

364 conjugacy classes of subgroups; only the 79 normal subgroups are shown.

normal subgroups only

This group has 364 conjugacy classes of subgroups — too many to draw. Only its 79 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#21422794C212yesmaximal
3#21422607C212yesmaximal
4#21421966C211yesmaximal, characteristic
5C59×#1843C211yesmaximal, characteristic
6#16837959C2212yes—
7#16837698—22no—
8#16837643—22no—
9#16837613—22no—
10#16837459C2212yes—
11#16837149—22no—
12#16837147—22no—
13#16837138—24no—
14C2×C4⋊C8×C59—22no—
15C2×C4⋊C8×C59C2211yescharacteristic
16C2×C4⋊C8×C59C2211yescharacteristic
17C59×#376C2211yescharacteristic
18C2×Dic236—22no—
19#14273727D412yes—
20#14273727D412yes—
21#14273719—22no—
22#14273706—22no—
23#14273706—22no—
24C4×Dic118—22no—
25C4×Dic118—22no—
26#14273686—22no—
27#14273661—22no—
28C4⋊(C59⋊C8)—22no—
29#14273652—24no—
30C22⋊(C59⋊C8)—22no—
31#14273638—22no—
32C22×C8×C59—21no—
33C22×C8×C59D412yes—
34C2×C42×C59—21no—
35C2×C42×C59C2311yescharacteristic
36C4⋊C8×C59—22no—
37C4⋊C8×C59—22no—
38C4⋊C8×C59—44no—
39#95×C59—21no—
40#95×C59D412yes—
41C22×C4×C59—22no—
42C22×C4×C59C2×D411yescharacteristic
43C22×C4×C59C2×D411yescharacteristic
44C22×C4×C59#4111yescharacteristic
45C2×Dic118—22no—
46C2×Dic118—22no—
47C2×C8×C59—22no—
48C2×C8×C59—42no—
49C2×C8×C59—42no—
50C2×C8×C59—41no—
51C42×C59—22no—
52C42×C59—22no—
53C42×C59C2×D412yes—
54C42×C59#4112yes—
55C22⋊Dic59—42no—
56C4⋊Dic59—22no—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59C4⋊Dic59—22no—
60Dic59⋊C4—42no—
61Dic59⋊C4—42no—
62C4×Dic59—42no—
63C2×C59⋊C8—42no—
64Dic236—82no—
65C23×C59#12111yescharacteristic
66C2×C4×C59—22no—
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—24no—
70C2×C4×C59—41no—
71C2×C4×C59—42no—
72C2×C4×C59—42no—
73C2×C4×C59#12011yescharacteristic
74C2×C4×C59#12112yes—
75C2×C4×C59#12312yes—
76C2×C4×C59#12411yescharacteristic
77C2×Dic59—42no—
78C2×Dic59—42no—
79Dic118—42no—
80Dic118—42no—
81Dic118—82no—
82C8×C59—42no—
83C8×C59—81no—
84C59⋊C8—82no—
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—44no—
94C4×C59#45311yescharacteristic
95C4×C59#45611yescharacteristic
96Dic59—82no—
97Dic59—82no—
98#3249—591no—
99#1843D5911yescharacteristic
100#1552—592no—
101#1506—592no—
102#1290—591no—
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#432—592no—
112C2×C4⋊C8—22no—
113C2×C4⋊C8C2×D5911yescharacteristic
114C2×C4⋊C8C2×D5911yescharacteristic
115#376C2×D5911yescharacteristic
116#332—1182no—
117#332—1182no—
118#328—1184no—
119C59#1051611yescharacteristic, complemented, Sylow
120C2×Q16—1182no—
121C22×C8—21no—
122C22×C8C22⋊D5912yes—
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—21no—
132C2×C42C22×D5911yescharacteristic
133#107—1182no—
134C4⋊C8—22no—
135C4⋊C8—22no—
136C4⋊C8—44no—
137C4⋊C8—1182no—
138#103—1184no—
139C22⋊C8—1182no—
140#97—1182no—
141#95—21no—
142#95D23612yes—
143C2×Q8—1182no—
144C2×Q8—1182no—
145C22×C4—22no—
146C22×C4C2×D23611yescharacteristic
147C22×C4#1174568511yescharacteristic
148C22×C4C2×C22⋊D5911yescharacteristic
149Q16—4722no—
150C2×C8—22no—
151C2×C8—42no—
152C2×C8—42no—
153C2×C8—41no—
154C2×C8—2362no—
155C4⋊C4—1182no—
156C4⋊C4—1182no—
157C4⋊C4—1182no—
158C4⋊C4—1182no—
159C4⋊C4—2362no—
160C4⋊C4—2362no—
161C22⋊C4—2362no—
162C42—22no—
163C42—22no—
164C42—2362no—
165C42D4×D5912yes—
166C42#1174568912yes—
167C23#1427370111yescharacteristic
168Q8—4722no—
169Q8—2362no—
170Q8—2362no—
171C2×C4—22no—
172C2×C4—21no—
173C2×C4—21no—
174C2×C4—24no—
175C2×C4—41no—
176C2×C4—42no—
177C2×C4—42no—
178C2×C4—2362no—
179C2×C4—2362no—
180C2×C4#1427369511yescharacteristic
181C2×C4#1427370212yes—
182C2×C4#1427371212yes—
183C2×C4#1427371611yescharacteristic
184C8—42no—
185C8—81no—
186C8—4722no—
187C22—21no—
188C22—21no—
189C22#1683731911yescharacteristic
190C22#1683767712yes—
191C4—21no—
192C4—22no—
193C4—22no—
194C4—44no—
195C4—4722no—
196C4—4722no—
197C4#1683756911yescharacteristic
198C4#1683758411yescharacteristic
199C2—22no—
200C2#2142532011yescharacteristic
201C2#2142536411yescharacteristic
202C2#2142540211yescharacteristic
subgroupG/H
centerC22#16837319
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1843C2
socleC22×C59#394
prime radicalC23×C59#121
hypercenter#1843D59
hypocenterC59#10516
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1843

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
#214227942
#214226072
#214219662
C59×#18432
#1051659