Finite Group Databasebeta

← #28502052

Subgroups — #28502052

Order 15104.

262 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 262 conjugacy classes of subgroups — too many to draw. Only its 55 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#21435550C211yesmaximal, characteristic
2#21426315C212yesmaximal
3#21422089C212yesmaximal
4#21422049C211yesmaximal, characteristic
5C59×#2103C211yesmaximal, characteristic
6#16838014—21no—
7#16837710—22no—
8#16837660C2212yes—
9#16837643—21no—
10#16837613—22no—
11#16837226—22no—
12#16837217—22no—
13#16837184C2212yes—
14C59×#430C2211yescharacteristic
15C59×#424C2211yescharacteristic
16C59×#344—21no—
17C59×#341—21no—
18C59×#338C2211yescharacteristic
19C2×Dic236—21no—
20C2×Dic236D412yes—
21#14273727—21no—
22#14273720—42no—
23#14273719—21no—
24#14273717—42no—
25#14273706—22no—
26C4×Dic118—22no—
27#14273667—22no—
28#14273661—21no—
29#14273659D412yes—
30#14273652—22no—
31#14273652—22no—
32C2×M16×C59—21no—
33C2×M16×C59—21no—
34C2×M16×C59C2311yescharacteristic
35C22×C8×C59D411yescharacteristic
36#117×C59D411yescharacteristic
37#108×C59—22no—
38C4⋊C8×C59—22no—
39C22×C4×C59C2×D411yescharacteristic
40C2×Dic118—22no—
41M16×C59—41no—
42M16×C59—41no—
43M16×C59—41no—
44M16×C59—41no—
45M16×C59—41no—
46C2×C8×C59—21no—
47C2×C8×C59—41no—
48C2×C8×C59—41no—
49C2×C8×C59—41no—
50C2×C8×C59C2×D412yes—
51C4⋊C4×C59—21no—
52C22⋊C4×C59SD1612yes—
53C42×C59—21no—
54C22⋊Dic59—42no—
55C4⋊Dic59—22no—
56C4⋊Dic59—42no—
57Dic59⋊C4—42no—
58Dic59⋊C4—42no—
59Dic59⋊C4—42no—
60C4×Dic59—42no—
61Dic236—42no—
62Dic236—81no—
63C59⋊C16—42no—
64C23×C59C2×SD1611yescharacteristic
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59#12011yescharacteristic
69C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
70C2×Dic59—42no—
71C2×Dic59—42no—
72Dic118—42no—
73Dic118—42no—
74C8×C59—22no—
75C8×C59—41no—
76C8×C59—81no—
77C8×C59—81no—
78#12305—591nomaximal, Sylow
79C22×C59—21no—
80C22×C59—41no—
81C22×C59#45011yescharacteristic
82C4×C59—21no—
83C4×C59—42no—
84C4×C59#45411yescharacteristic
85C4×C59#45811yescharacteristic
86Dic59—82no—
87Dic59—82no—
88#3261—591no—
89#2239—592no—
90#2103D5911yescharacteristic
91#1342—592no—
92#1328—591no—
93C2×C59—21no—
94C2×C59—41no—
95C2×C59#161611yescharacteristic
96#541—1181no—
97#479—1182no—
98#470—592no—
99#467—1181no—
100#462—1182no—
101#430C2×D5911yescharacteristic
102#424C2×D5911yescharacteristic
103#365—1182no—
104#362—1182no—
105#349—592no—
106#344—21no—
107#341—21no—
108#338C2×D5911yescharacteristic
109C59#1230511yescharacteristic, complemented, Sylow
110C2×Q16—592no—
111C2×Q16—1181no—
112C2×M16—21no—
113C2×M16—21no—
114C2×M16C22×D5911yescharacteristic
115C22×C8C22⋊D5911yescharacteristic
116C4⋊Q8—1181no—
117#126—2362no—
118#125—1181no—
119#125—2362no—
120C22⋊Q8—1182no—
121C4×Q8—1182no—
122#117C22⋊D5911yescharacteristic
123M32—1182no—
124#108—22no—
125#107—1181no—
126#106—592no—
127C4⋊C8—22no—
128#103—1182no—
129#103—1182no—
130C2×Q8—1182no—
131C22×C4C2×C22⋊D5911yescharacteristic
132Q16—4721no—
133Q16—2362no—
134M16—41no—
135M16—41no—
136M16—41no—
137M16—41no—
138M16—41no—
139C2×C8—21no—
140C2×C8—41no—
141C2×C8—41no—
142C2×C8—41no—
143C2×C8D4×D5912yes—
144C4⋊C4—21no—
145C4⋊C4—1182no—
146C4⋊C4—2362no—
147C4⋊C4—2362no—
148C4⋊C4—2362no—
149C4⋊C4—2362no—
150C22⋊C4—2362no—
151C22⋊C4#1174567112yes—
152C42—21no—
153C42—2362no—
154C16—2362no—
155C23C2×#1174567111yescharacteristic
156Q8—2362no—
157Q8—2362no—
158C2×C4—21no—
159C2×C4—21no—
160C2×C4—22no—
161C2×C4—2362no—
162C2×C4—2362no—
163C2×C4#1427369511yescharacteristic
164C2×C4#1427375211yescharacteristic
165C8—22no—
166C8—41no—
167C8—81no—
168C8—81no—
169C22—21no—
170C22—41no—
171C22#1683755211yescharacteristic
172C4—21no—
173C4—42no—
174C4—4722no—
175C4—4722no—
176C4#1683757411yescharacteristic
177C4#1683759111yescharacteristic
178C2—21no—
179C2—41no—
180C2#2142313211yescharacteristic
subgroupG/H
centerC2#21423132
commutator, cosocleC2×M16×C59C23
FrattiniC2×M16C22×D59
FittingC59×#2103C2
socleC2×C59#1616
prime radicalC23×C59C2×SD16
hypercenter#2103D59
hypocenterC59#12305
LCSG ▷ C2×M16×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #2103

Complements

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

NH ≅ G/Ntype
109. C59#12305semidirect

Maximal subgroups

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

subgroupindex
#214355502
#214263152
#214220892
#214220492
C59×#21032
#1230559