Finite Group Databasebeta

← #28509533

Subgroups — #28509533

Order 15104.

204 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 204 conjugacy classes of subgroups — too many to draw. Only its 57 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×#16837239C211yesmaximal, characteristic, complemented
2C2×C32×D59C211yesmaximal, characteristic, complemented
3#21426184C211yesmaximal, characteristic, complemented
4#21426183C211yesmaximal, characteristic
5#21422297C211yesmaximal, characteristic, complemented
6#21422275C211yesmaximal, characteristic, complemented
7C59×#1416C211yesmaximal, characteristic, complemented
8C2×D944C2211yescharacteristic
9C2×C16×D59C2211yescharacteristic
10#16837640—21no—
11#16837639—21no—
12#16837239—22no—
13C2×C59⋊C32C2211yescharacteristic
14C32×D59—22no—
15#16837228C2211yescharacteristic
16#16837206—21no—
17#16837202—21no—
18C2×Q32×C59C2211yescharacteristic
19C2×C32×C59C2211yescharacteristic
20C59×#366C2211yescharacteristic
21C2×D472—21no—
22C2×C8×D59D411yescharacteristic
23#14273703—41no—
24#14273702—41no—
25D944—21no—
26D944—21no—
27C2×C59⋊C16D411yescharacteristic
28C16×D59—21no—
29C16×D59—21no—
30#14273661—21no—
31#14273651—41no—
32#14273647—41no—
33C59⋊C32D412yescomplemented
34C2×Q16×C59—21no—
35Q32×C59—21no—
36Q32×C59—21no—
37C2×C16×C59C2311yescharacteristic
38#107×C59—21no—
39C32×C59—21no—
40C2×Q8×C59—41no—
41C2×D236—41no—
42C2×D236—81no—
43C2×C4×D59D811yescharacteristic
44Q16×C59—41no—
45Q16×C59—41no—
46C2×C8×C59C2×D411yescharacteristic
47C4⋊C4×C59—41no—
48(C2×D59)⋊C4—81no—
49(C2×D59)⋊C4—81no—
50C4⋊Dic59—41no—
51Dic59⋊C4—81no—
52C2×C59⋊C8D811yescharacteristic
53D472—41no—
54D472—41no—
55C8×D59—21no—
56C8×D59—21no—
57C16×C59C2×D411yescharacteristic
58C16×C59#4111yescharacteristic
59C59⋊C16—21no—
60C22×D59—81no—
61C22×D59D1611yescharacteristic
62Q8×C59—81no—
63Q8×C59—81no—
64C2×C4×C59—81no—
65C2×C4×C59—81no—
66C2×C4×C59C2×D811yescharacteristic
67C2×Dic59—81no—
68C2×Dic59D1611yescharacteristic
69D236—81no—
70D236—81no—
71D236—162no—
72C4×D59—21no—
73C4×D59—21no—
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#1424—591no—
96#1416D5911yescharacteristic, complemented
97#1415—591no—
98C2×C59#221511yescharacteristic
99C2×C59C2×SD6411yescharacteristic
100C2×C59#226211yescharacteristic
101D59—22no—
102D59—321no—
103C2×Q32C2×D5911yescharacteristic
104C2×D16—591no—
105C22×C16—591no—
106#467—1181no—
107#466—1181no—
108SD64—1182no—
109C2×C32—591no—
110C2×C32—1182no—
111C2×C32C2×D5911yescharacteristic
112#366—591no—
113#366C2×D5911yescharacteristic
114#358—1181no—
115#357—1181no—
116C59#1369611yescharacteristic, complemented, Sylow
117C2×Q16—21no—
118C2×D8—1181no—
119C22×C8—591no—
120C22⋊Q8—2361no—
121#121—2361no—
122Q32—21no—
123Q32—21no—
124D16—1181no—
125D16—1181no—
126C2×C16—591no—
127C2×C16—1181no—
128C2×C16—1181no—
129C2×C16C22×D5911yescharacteristic
130#107—21no—
131#107—1181no—
132#103—2361no—
133#102—2361no—
134C32—21no—
135C32—592no—
136C2×Q8—41no—
137C2×D4—4721no—
138C2×D4—2361no—
139C22×C4—591no—
140Q16—41no—
141Q16—41no—
142D8—2361no—
143D8—2361no—
144C2×C8—591no—
145C2×C8—1181no—
146C2×C8—1181no—
147C2×C8D4×D5911yescharacteristic
148C4⋊C4—41no—
149C4⋊C4—4721no—
150C4⋊C4—2361no—
151C22⋊C4—4721no—
152C22⋊C4—4721no—
153C16—1181no—
154C16#1174568511yescharacteristic
155C16D4×D5911yescharacteristic
156C23—591no—
157C23—4721no—
158Q8—81no—
159Q8—81no—
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#1427370011yescharacteristic
172C8#1427374811yescharacteristic
173C22—592no—
174C22—1181no—
175C22—1181no—
176C22—9441no—
177C22—9441no—
178C22—9441no—
179C22D16×D5911yescharacteristic
180C4—161no—
181C4—161no—
182C4—1181no—
183C4—9441no—
184C4#1683763711yescharacteristic
185C4#1683783311yescharacteristic
186C2—18881no—
187C2—1182no—
188C2#2142618111yescharacteristic
189C2SD64×D5911yescharacteristic
190C2#2142640611yescharacteristic
subgroupG/H
centerC22D16×D59
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1416C2
socleC22×C59C2×D16
prime radical#21426183C2
hypercenter#1416D59
hypocenterC59#13696
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1416

Complements

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

NH ≅ G/Ntype
1. C2×#16837239C2semidirect
2. C2×C32×D59C2semidirect
3. #21426184C2semidirect
5. #21422297C2semidirect
6. #21422275C2semidirect
7. C59×#1416C2semidirect
33. C59⋊C32D4semidirect
84. C2×D59SD64semidirect
96. #1416D59semidirect
116. C59#13696semidirect

Maximal subgroups

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

subgroupindex
C2×#168372392
C2×C32×D592
#214261842
#214261832
#214222972
#214222752
C59×#14162
#1369659