Finite Group Databasebeta

← #28509531

Subgroups — #28509531

Order 15104.

204 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 59 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
1C2×#16837241C211yesmaximal, characteristic, complemented
2C2×C32×D59C211yesmaximal, characteristic, complemented
3#21426188C211yesmaximal, characteristic, complemented
4#21426183C211yesmaximal, characteristic
5#21422276C211yesmaximal, characteristic, complemented
6#21422273C211yesmaximal, characteristic, complemented
7C59×#1424C211yesmaximal, characteristic, complemented
8C2×Dic472C2211yescharacteristic
9C2×D944C2211yescharacteristic
10C2×C16×D59C2211yescharacteristic
11#16837644—21no—
12#16837639—21no—
13#16837241—22no—
14C2×C59⋊C32C2211yescharacteristic
15C32×D59—22no—
16#16837205—21no—
17#16837202—21no—
18C2×C32×C59C2211yescharacteristic
19C59×#366C2211yescharacteristic
20C59×#366C2211yescharacteristic
21C2×Dic236—21no—
22C2×D472—21no—
23C2×C8×D59D411yescharacteristic
24#14273707—41no—
25#14273702—41no—
26Dic472—21no—
27Dic472—21no—
28D944—21no—
29D944—21no—
30C2×C59⋊C16D411yescharacteristic
31C16×D59—21no—
32C16×D59—21no—
33#14273650—41no—
34#14273647—41no—
35C59⋊C32—21no—
36C2×C16×C59C2311yescharacteristic
37#107×C59—21no—
38#107×C59—21no—
39C32×C59D412yescomplemented
40C2×D236—41no—
41C2×D236—81no—
42C2×C4×D59D811yescharacteristic
43C2×Dic118—41no—
44C2×C8×C59C2×D411yescharacteristic
45C4⋊C4×C59—41no—
46C4⋊C4×C59—41no—
47(C2×D59)⋊C4—81no—
48(C2×D59)⋊C4—81no—
49C4⋊Dic59—81no—
50C2×C59⋊C8D811yescharacteristic
51Dic236—41no—
52Dic236—41no—
53D472—41no—
54D472—41no—
55C8×D59—21no—
56C8×D59—21no—
57C16×C59C2×D411yescharacteristic
58C16×C59#4111yescharacteristic
59C59⋊C16—21no—
60C22×D59—81no—
61C22×D59D1611yescharacteristic
62C2×C4×C59—81no—
63C2×C4×C59—81no—
64C2×C4×C59C2×D811yescharacteristic
65C2×Dic59—81no—
66C2×Dic59D1611yescharacteristic
67D236—81no—
68D236—81no—
69D236—162no—
70C4×D59—21no—
71C4×D59—21no—
72Dic118—81no—
73Dic118—81no—
74C8×C59#12111yescharacteristic
75C8×C59#13511yescharacteristic
76C59⋊C8—21no—
77#13696—591nomaximal, Sylow
78C22×C59C2×D1611yescharacteristic
79C2×D59—21no—
80C2×D59—21no—
81C2×D59—161no—
82C2×D59—161no—
83C2×D59—161no—
84C2×D59SD6412yescomplemented
85C4×C59—161no—
86C4×C59—161no—
87C4×C59#46611yescharacteristic
88C4×C59#50811yescharacteristic
89Dic59—21no—
90Dic59—161no—
91C2×SD64—591no—
92C22×C32—591no—
93#2216—591no—
94#2215—591no—
95#1424D5911yescharacteristic, complemented
96#1416—591no—
97#1415—591no—
98C2×C59#221511yescharacteristic
99C2×C59C2×SD6411yescharacteristic
100C2×C59#226211yescharacteristic
101D59—22no—
102D59—321no—
103C2×Q32—591no—
104C2×D16—591no—
105C22×C16—591no—
106#467—1181no—
107#466—1181no—
108SD64—1182no—
109C2×C32—591no—
110C2×C32—1182no—
111C2×C32C2×D5911yescharacteristic
112#366C2×D5911yescharacteristic
113#366C2×D5911yescharacteristic
114#358—1181no—
115#357—1181no—
116C59#1369611yescharacteristic, complemented, Sylow
117C2×Q16—1181no—
118C2×D8—1181no—
119C22×C8—591no—
120C22⋊Q8—2361no—
121#121—2361no—
122Q32—1181no—
123Q32—1181no—
124D16—1181no—
125D16—1181no—
126C2×C16—591no—
127C2×C16—1181no—
128C2×C16—1181no—
129C2×C16C22×D5911yescharacteristic
130#107—21no—
131#107—21no—
132#103—2361no—
133#102—2361no—
134C32—1181no—
135C32D23612yescomplemented
136C2×Q8—2361no—
137C2×D4—4721no—
138C2×D4—2361no—
139C22×C4—591no—
140Q16—2361no—
141Q16—2361no—
142D8—2361no—
143D8—2361no—
144C2×C8—591no—
145C2×C8—1181no—
146C2×C8—1181no—
147C2×C8D4×D5911yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—41no—
150C4⋊C4—4721no—
151C22⋊C4—4721no—
152C22⋊C4—4721no—
153C16—1181no—
154C16C2×D23611yescharacteristic
155C16#1174568911yescharacteristic
156C23—591no—
157C23—4721no—
158Q8—4721no—
159Q8—4721no—
160D4—9442no—
161D4—4721no—
162D4—4721no—
163C2×C4—81no—
164C2×C4—81no—
165C2×C4—591no—
166C2×C4—1181no—
167C2×C4—1181no—
168C2×C4—4721no—
169C2×C4D8×D5911yescharacteristic
170C8—1181no—
171C8#1427370211yescharacteristic
172C8#1427375011yescharacteristic
173C22—592no—
174C22—1181no—
175C22—1181no—
176C22—9441no—
177C22—9441no—
178C22—9441no—
179C22D16×D5911yescharacteristic
180C4—161no—
181C4—161no—
182C4—1181no—
183C4—9441no—
184C4#1683763911yescharacteristic
185C4#1683783511yescharacteristic
186C2—18881no—
187C2—1182no—
188C2#2142618311yescharacteristic
189C2SD64×D5911yescharacteristic
190C2#2142640411yescharacteristic
subgroupG/H
centerC22D16×D59
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1424C2
socleC22×C59C2×D16
prime radical#21426183C2
hypercenter#1424D59
hypocenterC59#13696
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1424

Complements

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

NH ≅ G/Ntype
1. C2×#16837241C2semidirect
2. C2×C32×D59C2semidirect
3. #21426188C2semidirect
5. #21422276C2semidirect
6. #21422273C2semidirect
7. C59×#1424C2semidirect
39. C32×C59D4semidirect
84. C2×D59SD64semidirect
95. #1424D59semidirect
116. C59#13696semidirect
135. C32D236semidirect

Maximal subgroups

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

subgroupindex
C2×#168372412
C2×C32×D592
#214261882
#214261832
#214222762
#214222732
C59×#14242
#1369659