Finite Group Databasebeta

← #28502047

Subgroups — #28502047

Order 15104.

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

normal subgroups only

This group has 286 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#21435535C211yesmaximal, characteristic
2#21426310C212yesmaximal, complemented
3#21422086C212yesmaximal, complemented
4#21422049C211yesmaximal, characteristic, complemented
5C59×#2103C211yesmaximal, characteristic, complemented
6#16838007—21no—
7#16837703—22no—
8#16837655C2212yes—
9#16837638—21no—
10#16837598—22no—
11#16837226—22no—
12#16837214—22no—
13#16837184C2212yes—
14C59×#430C2211yescharacteristic
15C59×#424C2211yescharacteristic
16C59×#344—21no—
17C59×#341—21no—
18C59×#338C2211yescharacteristic
19C2×D472—21no—
20C2×D472D412yes—
21#14273724—21no—
22#14273719—21no—
23#14273712—42no—
24#14273701—22no—
25#14273700—42no—
26C4×D236—22no—
27#14273667—22no—
28#14273661—21no—
29#14273659D412yes—
30#14273649—22no—
31#14273649—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×C22⋊D59—42no—
41C2×D236—22no—
42C2×D236—42no—
43C2×C4×D59—42no—
44M16×C59—41no—
45M16×C59—41no—
46M16×C59—41no—
47M16×C59—41no—
48M16×C59—41no—
49C2×C8×C59—21no—
50C2×C8×C59—41no—
51C2×C8×C59—41no—
52C2×C8×C59—41no—
53C2×C8×C59C2×D412yes—
54C4⋊C4×C59—21no—
55C22⋊C4×C59SD1612yes—
56C42×C59—21no—
57(C2×D59)⋊C4—42no—
58(C2×D59)⋊C4—42no—
59C4⋊Dic59—22no—
60Dic59⋊C4—42no—
61D472—42no—
62D472—81no—
63C59⋊C16—42no—
64C23×C59C2×SD1611yescharacteristic
65C22×D59—42no—
66C2×C4×C59—21no—
67C2×C4×C59—21no—
68C2×C4×C59—22no—
69C2×C4×C59#12011yescharacteristic
70C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
71C22⋊D59—162no—
72C2×Dic59—42no—
73D236—42no—
74D236—42no—
75D236—162no—
76C4×D59—162no—
77C8×C59—22no—
78C8×C59—41no—
79C8×C59—81no—
80C8×C59—81no—
81#12304—591nomaximal, Sylow
82C22×C59—21no—
83C22×C59—41no—
84C22×C59#45011yescharacteristic
85C2×D59—82no—
86C2×D59—82no—
87C2×D59—82no—
88C4×C59—21no—
89C4×C59—42no—
90C4×C59#45411yescharacteristic
91C4×C59#45811yescharacteristic
92Dic59—82no—
93#3259—591no—
94#2238—592no—
95#2103D5911yescharacteristic, complemented
96#1341—592no—
97#1328—591no—
98C2×C59—21no—
99C2×C59—41no—
100C2×C59#161611yescharacteristic
101D59—162no—
102#540—1181no—
103#478—1182no—
104#469—592no—
105#466—1181no—
106#459—1182no—
107#430C2×D5911yescharacteristic
108#424C2×D5911yescharacteristic
109#365—1182no—
110#361—1182no—
111#349—592no—
112#344—21no—
113#341—21no—
114#338C2×D5911yescharacteristic
115C59#1230411yescharacteristic, complemented, Sylow
116C2×D8—592no—
117C2×D8—1181no—
118C2×M16—21no—
119C2×M16—21no—
120C2×M16C22×D5911yescharacteristic
121C22×C8C22⋊D5911yescharacteristic
122#127—1181no—
123#125—1181no—
124#123—2362no—
125#121—1182no—
126#121—2362no—
127C4×D4—1182no—
128#117C22⋊D5911yescharacteristic
129M32—1182no—
130#108—22no—
131#107—1181no—
132#106—592no—
133C4⋊C8—22no—
134#102—1182no—
135#102—1182no—
136C2×D4—1182no—
137C2×D4—2362no—
138C2×D4—2362no—
139C22×C4—2362no—
140C22×C4C2×C22⋊D5911yescharacteristic
141D8—4721no—
142D8—2362no—
143M16—41no—
144M16—41no—
145M16—41no—
146M16—41no—
147M16—41no—
148C2×C8—21no—
149C2×C8—41no—
150C2×C8—41no—
151C2×C8—41no—
152C2×C8D4×D5912yes—
153C4⋊C4—21no—
154C4⋊C4—1182no—
155C4⋊C4—2362no—
156C22⋊C4—2362no—
157C22⋊C4—2362no—
158C22⋊C4#1174567112yes—
159C42—21no—
160C16—2362no—
161C23—2362no—
162C23C2×#1174567111yescharacteristic
163D4—9442no—
164D4—9442no—
165D4—2362no—
166D4—2362no—
167C2×C4—21no—
168C2×C4—21no—
169C2×C4—22no—
170C2×C4—9442no—
171C2×C4—2362no—
172C2×C4#1427369511yescharacteristic
173C2×C4#1427375211yescharacteristic
174C8—22no—
175C8—41no—
176C8—81no—
177C8—81no—
178C22—21no—
179C22—41no—
180C22—4722no—
181C22—4722no—
182C22—4722no—
183C22#1683755211yescharacteristic
184C4—21no—
185C4—42no—
186C4—4722no—
187C4#1683757411yescharacteristic
188C4#1683759111yescharacteristic
189C2—21no—
190C2—41no—
191C2—9442no—
192C2#2142313211yescharacteristic
subgroupG/H
centerC2#21423132
commutator, cosocleC2×M16×C59C23
FrattiniC2×M16C22×D59
FittingC59×#2103C2
socleC2×C59#1616
prime radical#21435535C2
hypercenter#2103D59
hypocenterC59#12304
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
2. #21426310C2semidirect
3. #21422086C2semidirect
4. #21422049C2semidirect
5. C59×#2103C2semidirect
95. #2103D59semidirect
115. C59#12304semidirect

Maximal subgroups

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

subgroupindex
#214355352
#214263102
#214220862
#214220492
C59×#21032
#1230459