Finite Group Databasebeta

← #28509509

Subgroups — #28509509

Order 15104.

216 conjugacy classes of subgroups; only the 51 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 51 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#21426411C211yesmaximal, characteristic, complemented
2#21426409C211yesmaximal, characteristic, complemented
3#21426344C211yesmaximal, characteristic, complemented
4#21425976C211yesmaximal, characteristic, complemented
5#21422293C211yesmaximal, characteristic, complemented
6#21422285C211yesmaximal, characteristic, complemented
7C59×#1419C211yesmaximal, characteristic, complemented
8#16837834C2211yescharacteristic
9C2×D944C2211yescharacteristic
10C2×#14273668—21no—
11#16837777—21no—
12#16837518—21no—
13#16837241—21no—
14#16837240—21no—
15D1888—21no—
16#16837237—21no—
17#16837236C2211yescharacteristic
18#16837208—21no—
19C16×Dic59C2211yescharacteristic
20C2×D16×C59C2211yescharacteristic
21C59×M64C2211yescharacteristic
22C59×#368C2211yescharacteristic
23#14273749—21no—
24C2×D472—21no—
25C2×#11745669—41no—
26#14273735—41no—
27#14273723—41no—
28Dic472D411yescharacteristic, complemented
29#14273672—21no—
30D944—21no—
31D944—21no—
32D944D411yescharacteristic, complemented
33#14273668—42no—
34C2×C59⋊C16D411yescharacteristic
35#14273653—41no—
36C8×Dic59D411yescharacteristic
37C59⋊C32—21no—
38C2×D8×C59—21no—
39D16×C59—21no—
40D16×C59—21no—
41C2×C16×C59C2311yescharacteristic
42#108×C59—21no—
43C32×C59—21no—
44C2×D4×C59—41no—
45C2×C22⋊D59—82no—
46#11745685—41no—
47C2×D236—41no—
48D8×C59—41no—
49D8×C59—41no—
50M16×C59—41no—
51C2×C8×C59C2×D411yescharacteristic
52#11745669—81no—
53#11745669—81no—
54C4×Dic59D811yescharacteristic
55C2×C59⋊C8D811yescharacteristic
56Dic236—21no—
57D472—21no—
58D472—41no—
59D472—41no—
60#11745660—41no—
61#11745659—81no—
62C8×D59—81no—
63C16×C59C2×D411yescharacteristic
64C16×C59#4111yescharacteristic
65C59⋊C16—21no—
66C23×C59—81no—
67C22×D59—81no—
68D4×C59—81no—
69D4×C59—81no—
70C2×C4×C59C2×D811yescharacteristic
71C22⋊D59—81no—
72C22⋊D59—164no—
73C2×Dic59—21no—
74D236—41no—
75D236—81no—
76D236—81no—
77C4×D59—81no—
78Dic118—41no—
79C8×C59—81no—
80C8×C59#12111yescharacteristic
81C8×C59AGL(1,ℤ/8)11yescharacteristic
82C59⋊C8D1611yescharacteristic
83C59⋊C8D1611yescharacteristic
84#13692—591nomaximal, Sylow
85C22×C59—162no—
86C22×C59—161no—
87C22×C59#50911yescharacteristic
88C2×D59—81no—
89C2×D59—162no—
90C2×D59—161no—
91C4×C59#45911yescharacteristic
92C4×C59C2×D1611yescharacteristic
93Dic59—22no—
94Dic59—81no—
95#2263—591no—
96#2263—591no—
97#2246—591no—
98#2178—591no—
99#1422—591no—
100#1419—591no—
101#1419D5911yescharacteristic, complemented
102C2×C59—21no—
103C2×C59—321no—
104C2×C59#220611yescharacteristic
105D59—161no—
106D59—321no—
107#508—591no—
108C2×D16—591no—
109C2×D16—1181no—
110C2×D16C2×D5911yescharacteristic
111#493—1181no—
112#443—1181no—
113SD64—1181no—
114SD64—1181no—
115D32—1181no—
116D32—1181no—
117M64—591no—
118M64C2×D5911yescharacteristic
119#368C2×D5911yescharacteristic
120#359—1181no—
121C4×C16—591no—
122C59#1369211yescharacteristic, complemented, Sylow
123#135—1181no—
124C2×D8—21no—
125C2×D8—1181no—
126C2×D8—2361no—
127#131—2361no—
128#127—2361no—
129Q32—591no—
130SD32—1181no—
131D16—21no—
132D16—21no—
133D16—591no—
134D16—1181no—
135D16—1181no—
136D16—2362no—
137C2×C16—591no—
138C2×C16C22×D5911yescharacteristic
139#108—21no—
140#104—2361no—
141C4×C8—591no—
142C32—21no—
143C32—1181no—
144#41—2361no—
145C2×D4—41no—
146C2×D4—4722no—
147C2×D4—2361no—
148Q16—1181no—
149SD16—2361no—
150D8—41no—
151D8—41no—
152D8—1181no—
153D8—4721no—
154D8—4721no—
155D8—2361no—
156D8—2361no—
157M16—41no—
158M16—4721no—
159C2×C8—591no—
160C2×C8—4721no—
161C2×C8D4×D5911yescharacteristic
162C42—591no—
163C16—1181no—
164C16#1174568511yescharacteristic
165C16D4×D5911yescharacteristic
166C23—81no—
167C23—4721no—
168Q8—2361no—
169D4—81no—
170D4—81no—
171D4—9444no—
172D4—4721no—
173D4—4721no—
174D4—4721no—
175D4—2361no—
176C2×C4—1181no—
177C2×C4—4721no—
178C2×C4D8×D5911yescharacteristic
179C8—81no—
180C8—591no—
181C8—591no—
182C8#1427370011yescharacteristic
183C8#1427375411yescharacteristic
184C22—162no—
185C22—161no—
186C22—9442no—
187C22—9441no—
188C22—4721no—
189C22#1683783911yescharacteristic
190C4—1182no—
191C4—4721no—
192C4#1683759611yescharacteristic
193C4D16×D5911yescharacteristic
194C2—21no—
195C2—321no—
196C2—18881no—
197C2—9441no—
198C2#2142613011yescharacteristic
subgroupG/H
centerC2#21426130
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1419C2
socleC2×C59#2206
hypercenter#1419D59
hypocenterC59#13692
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1419

Complements

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

NH ≅ G/Ntype
1. #21426411C2semidirect
2. #21426409C2semidirect
3. #21426344C2semidirect
4. #21425976C2semidirect
5. #21422293C2semidirect
6. #21422285C2semidirect
7. C59×#1419C2semidirect
28. Dic472D4semidirect
32. D944D4semidirect
101. #1419D59semidirect
122. C59#13692semidirect

Maximal subgroups

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

subgroupindex
#214264112
#214264092
#214263442
#214259762
#214222932
#214222852
C59×#14192
#1369259