Finite Group Databasebeta

← #28498196

Subgroups — #28498196

Order 15104.

270 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 270 conjugacy classes of subgroups — too many to draw. Only its 71 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#21433029C211yesmaximal, characteristic
2#21425909C212yesmaximal
3#21422049C211yesmaximal, characteristic
4#21422046C212yesmaximal
5C59×#1328C211yesmaximal, characteristic
6#16837955C411yescharacteristic
7#16837531—22no—
8#16837526—22no—
9#16837428C411yescharacteristic
10#16837425C2211yescharacteristic
11#16837360C2211yescharacteristic
12#16837358C411yescharacteristic
13C2×C8×Dic59C411yescharacteristic
14#16837222—22no—
15#16837184C2212yes—
16#16837179—22no—
17C59×#424C2211yescharacteristic
18C59×#349C2212yes—
19C2×#11745664C2×C411yescharacteristic
20C22×C59⋊C8C2×C411yescharacteristic
21#14273726—21no—
22#14273718—21no—
23#14273704—22no—
24C4×Dic118—22no—
25#14273686C2×C411yescharacteristic
26C2×C4×Dic59C2×C411yescharacteristic
27#14273667—22no—
28Dic59⋊C8—22no—
29Dic59⋊C8—22no—
30#14273638—21no—
31#14273637D412yes—
32C4×C59⋊C8—21no—
33C8×Dic59—21no—
34C8×Dic59—21no—
35C8×Dic59D412yes—
36C2×M16×C59C2311yescharacteristic
37C22×C8×C59C2×C411yescharacteristic
38#117×C59C2×C411yescharacteristic
39M32×C59—22no—
40C4⋊C8×C59—22no—
41C22×C4×C59C22×C411yescharacteristic
42C22×Dic59—21no—
43C2×Dic118—22no—
44M16×C59—41no—
45C2×C8×C59—21no—
46C2×C8×C59—41no—
47C2×C8×C59C2×D412yes—
48C4⋊C4×C59—21no—
49C22⋊C4×C59M1612yes—
50C42×C59—21no—
51C22⋊Dic59—21no—
52C4⋊Dic59—22no—
53C4⋊Dic59—21no—
54Dic59⋊C4—22no—
55Dic59⋊C4—22no—
56C4×Dic59—21no—
57C4×Dic59C22⋊C412yes—
58C4×Dic59M1611yescharacteristic
59C4×Dic59M1611yescharacteristic
60#11745664—41no—
61C2×C59⋊C8—22no—
62C2×C59⋊C8—21no—
63C2×C59⋊C8C22⋊C411yescharacteristic
64C2×C59⋊C8C22⋊C411yescharacteristic
65C16×C59—42no—
66C59⋊C16—42no—
67C23×C59C2×M1611yescharacteristic
68C2×C4×C59—21no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59C2×C22⋊C411yescharacteristic
72C2×C4×C59C2×M1611yescharacteristic
73C2×Dic59—21no—
74C2×Dic59—21no—
75C2×Dic59—22no—
76C2×Dic59—42no—
77Dic118—44no—
78C8×C59—22no—
79C8×C59—41no—
80C59⋊C8—21no—
81C59⋊C8—41no—
82C59⋊C8#10112yes—
83#11539—591nomaximal, Sylow
84C22×C59—21no—
85C22×C59—41no—
86C22×C59#40711yescharacteristic
87C4×C59—21no—
88C4×C59—42no—
89C4×C59#41011yescharacteristic
90C4×C59C2×#10111yescharacteristic
91Dic59—22no—
92Dic59—42no—
93Dic59—41no—
94#2960—591no—
95#2166—592no—
96#1328—591no—
97#1328D5911yescharacteristic
98#1327—592no—
99C2×C59—21no—
100C2×C59—41no—
101C2×C59#146711yescharacteristic
102#533—591no—
103#446—1182no—
104C8×Q8—1182no—
105#424—591no—
106#424C2×D5911yescharacteristic
107#423—591no—
108#405—591no—
109#405—591no—
110C2×C4×C8—591no—
111#364—1182no—
112#349—592no—
113#349C2×D5912yes—
114#347—1182no—
115C59#1153911yescharacteristic, complemented, Sylow
116C2×M16—591no—
117C2×M16C22×D5911yescharacteristic
118C22×C8—591no—
119C22×C8C4×D5911yescharacteristic
120C4⋊Q8—1181no—
121#125—1181no—
122C22⋊Q8—1182no—
123C4×Q8—1182no—
124#117—591no—
125#117C4×D5911yescharacteristic
126C2×C42—591no—
127M32—22no—
128M32—1182no—
129C4⋊C8—22no—
130C4⋊C8—1182no—
131C4⋊C8—1182no—
132#97—592no—
133#97—1181no—
134C4×C8—592no—
135C4×C8—1181no—
136C4×C8—1181no—
137C4×C8—1181no—
138C2×Q8—1182no—
139C22×C4—1181no—
140C22×C4C2×C4×D5911yescharacteristic
141M16—41no—
142M16—2361no—
143C2×C8—21no—
144C2×C8—41no—
145C2×C8—591no—
146C2×C8—591no—
147C2×C8—1182no—
148C2×C8—1181no—
149C2×C8D4×D5912yes—
150C4⋊C4—21no—
151C4⋊C4—1182no—
152C4⋊C4—1182no—
153C4⋊C4—1182no—
154C4⋊C4—1181no—
155C22⋊C4—1181no—
156C22⋊C4#1174565912yes—
157C42—21no—
158C42—592no—
159C42—591no—
160C42—591no—
161C42—1181no—
162C16—42no—
163C16—2362no—
164C23C2×#1174565911yescharacteristic
165Q8—2364no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—22no—
169C2×C4—1181no—
170C2×C4—1181no—
171C2×C4—1182no—
172C2×C4—2362no—
173C2×C4C22⋊C4×D5911yescharacteristic
174C2×C4M16×D5911yescharacteristic
175C8—22no—
176C8—41no—
177C8—592no—
178C8—1181no—
179C8—2361no—
180C22—21no—
181C22—41no—
182C22#1683736411yescharacteristic
183C4—21no—
184C4—42no—
185C4—1182no—
186C4—2361no—
187C4—2362no—
188C4#1683737411yescharacteristic
189C4#101×D5911yescharacteristic
190C2—21no—
191C2—41no—
192C2#2142243811yescharacteristic
subgroupG/H
centerC4#16837374
commutatorC22×C4×C59C22×C4
FrattiniC2×M16C22×D59
FittingC59×#1328C2
socleC2×C59#1467
prime radicalC23×C59C2×M16
cosocleC2×M16×C59C23
hypercenter#1328D59
hypocenterC59#11539
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1328

Complements

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

NH ≅ G/Ntype
115. C59#11539semidirect

Maximal subgroups

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

subgroupindex
#214330292
#214259092
#214220492
#214220462
C59×#13282
#1153959