Finite Group Databasebeta

← #28498198

Subgroups — #28498198

Order 15104.

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

normal subgroups only

This group has 262 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#21433033C211yesmaximal, characteristic
2#21425909C212yesmaximal
3#21422048C212yesmaximal
4#21422047C211yesmaximal, characteristic
5C59×#1327C211yesmaximal, characteristic
6#16837959C411yescharacteristic
7#16837531—22no—
8#16837531—22no—
9#16837430C411yescharacteristic
10#16837430C2211yescharacteristic
11#16837360C411yescharacteristic
12#16837360C2211yescharacteristic
13C2×#14273638C411yescharacteristic
14#16837222—22no—
15#16837184C2212yes—
16#16837179—22no—
17C59×#423C2211yescharacteristic
18C59×#349C2212yes—
19C22×C59⋊C8C2×C411yescharacteristic
20C22×C59⋊C8C2×C411yescharacteristic
21#14273727—21no—
22#14273719—21no—
23#14273706—22no—
24C4×Dic118—22no—
25#14273686C2×C411yescharacteristic
26#14273686C2×C411yescharacteristic
27#14273667—22no—
28Dic59⋊C8—22no—
29Dic59⋊C8—22no—
30#14273638—21no—
31#14273638—21no—
32#14273637—21no—
33#14273637D412yes—
34C8×Dic59—21no—
35C8×Dic59D412yes—
36C2×M16×C59C2×C411yescharacteristic
37C2×M16×C59C2311yescharacteristic
38C2×C42×C59C2×C411yescharacteristic
39M32×C59—22no—
40C4⋊C8×C59—22no—
41C22×C4×C59—21no—
42C22×C4×C59C22×C411yescharacteristic
43C2×Dic118—22no—
44M16×C59—41no—
45M16×C59—41no—
46C2×C8×C59—21no—
47C2×C8×C59C2×D412yes—
48C42×C59—21no—
49C42×C59M1611yescharacteristic
50C42×C59M1611yescharacteristic
51C22⋊Dic59—21no—
52C22⋊Dic59M1612yes—
53C4⋊Dic59—22no—
54C4⋊Dic59—21no—
55C4⋊Dic59—21no—
56Dic59⋊C4—24no—
57C4×Dic59—21no—
58C4×Dic59C22⋊C412yes—
59C2×C59⋊C8—22no—
60C2×C59⋊C8—21no—
61C2×C59⋊C8—41no—
62C2×C59⋊C8C22⋊C411yescharacteristic
63C2×C59⋊C8C22⋊C411yescharacteristic
64C16×C59—42no—
65C59⋊C16—42no—
66C23×C59C2×M1611yescharacteristic
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—81no—
72C2×C4×C59C2×C22⋊C411yescharacteristic
73C2×C4×C59C2×M1611yescharacteristic
74C2×Dic59—22no—
75C2×Dic59—22no—
76Dic118—82no—
77C8×C59—22no—
78C8×C59—41no—
79C59⋊C8—21no—
80C59⋊C8—41no—
81C59⋊C8#10112yes—
82#11540—591nomaximal, Sylow
83C22×C59—21no—
84C22×C59—41no—
85C22×C59#40711yescharacteristic
86C4×C59—21no—
87C4×C59—41no—
88C4×C59—41no—
89C4×C59#41011yescharacteristic
90C4×C59C2×#10111yescharacteristic
91Dic59—42no—
92Dic59—42no—
93#2961—591no—
94#2166—592no—
95#1328—592no—
96#1327—591no—
97#1327D5911yescharacteristic
98C2×C59—21no—
99C2×C59—41no—
100C2×C59#146711yescharacteristic
101#533—591no—
102#446—1182no—
103#446—1182no—
104#424—591no—
105#424—591no—
106#423C2×D5911yescharacteristic
107#405—591no—
108#405—591no—
109C2×#97—591no—
110#364—1182no—
111#349—592no—
112#349C2×D5912yes—
113#347—1182no—
114C59#1154011yescharacteristic, complemented, Sylow
115C2×M16C4×D5911yescharacteristic
116C2×M16C22×D5911yescharacteristic
117C22×C8—591no—
118C22×C8—591no—
119C4⋊Q8—1181no—
120#125—1181no—
121C22⋊Q8—1182no—
122C4×Q8—1182no—
123#117—591no—
124#117—591no—
125C2×C42C4×D5911yescharacteristic
126M32—22no—
127M32—1182no—
128C4⋊C8—22no—
129C4⋊C8—1182no—
130C4⋊C8—1182no—
131#97—592no—
132#97—1181no—
133#97—1181no—
134#97—1181no—
135C4×C8—592no—
136C4×C8—1181no—
137C2×Q8—1182no—
138C22×C4—21no—
139C22×C4C2×C4×D5911yescharacteristic
140M16—41no—
141M16—41no—
142C2×C8—21no—
143C2×C8—591no—
144C2×C8—591no—
145C2×C8—1182no—
146C2×C8—1181no—
147C2×C8—2361no—
148C2×C8D4×D5912yes—
149C4⋊C4—1184no—
150C4⋊C4—1182no—
151C4⋊C4—1181no—
152C4⋊C4—1181no—
153C22⋊C4—592no—
154C22⋊C4—1181no—
155C42—21no—
156C42—592no—
157C42—1181no—
158C42#1174565911yescharacteristic
159C42#1174565911yescharacteristic
160C16—42no—
161C16—2362no—
162C23M16×D5911yescharacteristic
163Q8—4722no—
164C2×C4—21no—
165C2×C4—21no—
166C2×C4—21no—
167C2×C4—21no—
168C2×C4—81no—
169C2×C4—1182no—
170C2×C4—1182no—
171C2×C4C22⋊C4×D5911yescharacteristic
172C2×C4C2×#1174565911yescharacteristic
173C8—22no—
174C8—41no—
175C8—592no—
176C8—1181no—
177C8—2361no—
178C22—21no—
179C22—41no—
180C22#1683736411yescharacteristic
181C4—21no—
182C4—41no—
183C4—41no—
184C4—2362no—
185C4—2362no—
186C4#1683737411yescharacteristic
187C4#101×D5911yescharacteristic
188C2—21no—
189C2—41no—
190C2#2142243811yescharacteristic
subgroupG/H
centerC4#16837374
commutatorC22×C4×C59C22×C4
FrattiniC2×M16C22×D59
FittingC59×#1327C2
socleC2×C59#1467
prime radicalC23×C59C2×M16
cosocleC2×M16×C59C23
hypercenter#1327D59
hypocenterC59#11540
LCSG ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C4 ◁ C2×C4 ◁ C2×M16 ◁ #1327

Complements

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

NH ≅ G/Ntype
114. C59#11540semidirect

Maximal subgroups

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

subgroupindex
#214330332
#214259092
#214220482
#214220472
C59×#13272
#1154059