Finite Group Databasebeta

← #28509043

Subgroups — #28509043

Order 15104.

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

normal subgroups only

This group has 326 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#21425761C212yesmaximal
2#21422267C214yesmaximal, complemented
3C59×#3142C211yesmaximal, characteristic
4#16837376—22no—
5#16837197—22no—
6#16837195C2214yes—
7C59×#532C2211yescharacteristic
8C2×#125×C59C411yescharacteristic, complemented
9C59×#491C412yescomplemented
10C59×#490C2212yes—
11C59×#488—22no—
12C59×#417—22no—
13C4×M16×C59C411yescharacteristic, complemented
14#14273686—42no—
15#14273642—24no—
16#14273642—42no—
17C2×#41×C59D412yes—
18C2×M16×C59—21no—
19C4⋊Q8×C59C2×C411yescharacteristic
20#127×C59C2311yescharacteristic
21#125×C59—21no—
22#125×C59—41no—
23#125×C59C2×C412yes—
24#124×C59D412yes—
25#121×C59—41no—
26C4×D4×C59—41no—
27C2×C4⋊C4×C59—21no—
28C2×C4⋊C4×C59—41no—
29C2×C42×C59C2×C411yescharacteristic
30#103×C59—24no—
31#102×C59—24no—
32#97×C59C2×C412yes—
33C4×C8×C59—21no—
34#41×C59—42no—
35#41×C59—42no—
36C2×Q8×C59C22⋊C412yes—
37C2×D4×C59—22no—
38C2×D4×C59—41no—
39C2×D4×C59C2×D412yes—
40C22×C4×C59—21no—
41C22×C4×C59—22no—
42C22×C4×C59—41no—
43C22×C4×C59C22⋊C411yescharacteristic
44M16×C59—42no—
45C2×C8×C59—22no—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—41no—
48C4⋊C4×C59—42no—
49C4⋊C4×C59—42no—
50C4⋊C4×C59—41no—
51C22⋊C4×C59—42no—
52C42×C59—21no—
53C42×C59C22⋊C411yescharacteristic
54C42×C59C22×C411yescharacteristic
55C22⋊Dic59—44no—
56C4⋊Dic59—82no—
57C4×Dic59—82no—
58C23×C59—22no—
59C23×C59#9911yescharacteristic
60Q8×C59—42no—
61D4×C59—42no—
62D4×C59—82no—
63D4×C59—82no—
64C2×C4×C59—22no—
65C2×C4×C59—21no—
66C2×C4×C59—21no—
67C2×C4×C59—22no—
68C2×C4×C59—42no—
69C2×C4×C59—42no—
70C2×C4×C59—42no—
71C2×C4×C59—81no—
72C2×C4×C59—82no—
73C2×C4×C59#9911yescharacteristic
74C2×C4×C59C2×C22⋊C411yescharacteristic
75C2×Dic59—84no—
76C8×C59—42no—
77#13596—591nomaximal, Sylow
78C22×C59—21no—
79C22×C59—41no—
80C22×C59—42no—
81C22×C59—82no—
82C22×C59C2×#9911yescharacteristic
83C4×C59—21no—
84C4×C59—41no—
85C4×C59—41no—
86C4×C59—42no—
87C4×C59—82no—
88C4×C59#35412yes—
89Dic59—164no—
90#3142D5911yescharacteristic
91#2126—592no—
92#1412—594no—
93C2×C59—21no—
94C2×C59—41no—
95C2×C59—82no—
96C2×C59C2×#35411yescharacteristic
97#532C2×D5911yescharacteristic
98C2×#125Dic5911yescharacteristic, complemented
99#491Dic5912yescomplemented
100#490C2×D5912yes—
101#488—22no—
102#417—22no—
103#410—1182no—
104C4×M16Dic5911yescharacteristic, complemented
105#354—1182no—
106#353—594no—
107C59#1359611yescharacteristic, complemented, Sylow
108C2×#41C22⋊D5912yes—
109C2×M16—21no—
110C4⋊Q8C2×Dic5911yescharacteristic
111#127C22×D5911yescharacteristic
112#125—21no—
113#125—41no—
114#125C2×Dic5912yes—
115#124C22⋊D5912yes—
116#121—41no—
117C4×D4—41no—
118#117—2362no—
119C2×C4⋊C4—21no—
120C2×C4⋊C4—41no—
121C2×C42C2×Dic5911yescharacteristic
122#103—24no—
123#102—24no—
124#99—1184no—
125#99—2362no—
126#97C2×Dic5912yes—
127C4×C8—21no—
128#41—42no—
129#41—42no—
130C2×Q8C22⋊Dic5912yes—
131C2×D4—22no—
132C2×D4—41no—
133C2×D4C2×C22⋊D5912yes—
134C22×C4—21no—
135C22×C4—22no—
136C22×C4—41no—
137C22×C4C22⋊Dic5911yescharacteristic
138M16—42no—
139C2×C8—22no—
140C4⋊C4—22no—
141C4⋊C4—41no—
142C4⋊C4—42no—
143C4⋊C4—42no—
144C4⋊C4—41no—
145C4⋊C4—4722no—
146C22⋊C4—42no—
147C22⋊C4—2364no—
148C42—21no—
149C42—4722no—
150C42C22⋊Dic5911yescharacteristic
151C42C22×Dic5911yescharacteristic
152C23—22no—
153C23#1427364211yescharacteristic
154Q8—42no—
155D4—42no—
156D4—82no—
157D4—82no—
158C2×C4—22no—
159C2×C4—21no—
160C2×C4—21no—
161C2×C4—22no—
162C2×C4—42no—
163C2×C4—42no—
164C2×C4—42no—
165C2×C4—81no—
166C2×C4—82no—
167C2×C4—4724no—
168C2×C4#1427364211yescharacteristic
169C2×C4C2×C22⋊Dic5911yescharacteristic
170C8—42no—
171C22—21no—
172C22—41no—
173C22—42no—
174C22—82no—
175C22C2×#1427364211yescharacteristic
176C4—21no—
177C4—41no—
178C4—41no—
179C4—42no—
180C4—82no—
181C4—9444no—
182C4#1683719712yes—
183C2—21no—
184C2—41no—
185C2—82no—
186C2C2×#1683719711yescharacteristic
subgroupG/H
centerC2C2×#16837197
commutatorC42×C59C22×C4
Frattini#127C22×D59
FittingC59×#3142C2
socleC2×C59C2×#354
prime radicalC59×#532C22
cosocle#127×C59C23
hypercenter#3142D59
hypocenterC59#13596
LCSG ▷ C42×C59 ▷ C2×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C22×C4 ◁ #532 ◁ #3142

Complements

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

NH ≅ G/Ntype
2. #21422267C2semidirect
8. C2×#125×C59C4semidirect
9. C59×#491C4semidirect
13. C4×M16×C59C4semidirect
98. C2×#125Dic59semidirect
99. #491Dic59semidirect
104. C4×M16Dic59semidirect
107. C59#13596semidirect

Maximal subgroups

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

subgroupindex
#214257612
#214222672
C59×#31422
#1359659