Finite Group Databasebeta

← #28509553

Subgroups — #28509553

Order 15104.

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

normal subgroups only

This group has 188 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
1C2×#16837237C211yesmaximal, characteristic, complemented
2#21426391C211yesmaximal, characteristic, complemented
3#21426217C211yesmaximal, characteristic, complemented
4#21426213C211yesmaximal, characteristic, complemented
5#21422299C211yesmaximal, characteristic, complemented
6#21422287C211yesmaximal, characteristic, complemented
7C59×#1419C211yesmaximal, characteristic, complemented
8C2×D944C2211yescharacteristic
9#16837818C2211yescharacteristic
10#16837673—21no—
11#16837669—21no—
12#16837237—21no—
13#16837237—21no—
14#16837235—21no—
15C2×C59⋊C32C2211yescharacteristic
16C32×D59—21no—
17#16837232C2211yescharacteristic
18#16837215—21no—
19#16837214—21no—
20C2×D16×C59C2211yescharacteristic
21C59×M64C2211yescharacteristic
22C59×#368C2211yescharacteristic
23#14273755—41no—
24#14273753—41no—
25C2×D472—21no—
26#14273733D411yescharacteristic
27D944—21no—
28D944—21no—
29#14273667D411yescharacteristic
30#14273666—21no—
31C16×D59—21no—
32#14273663—21no—
33#14273644—41no—
34#14273643—41no—
35C59⋊C32D411yescharacteristic
36C59⋊C32D411yescharacteristic
37C2×D8×C59—21no—
38D16×C59—21no—
39D16×C59—21no—
40C2×C16×C59C2311yescharacteristic
41#108×C59—21no—
42C32×C59—21no—
43C2×D4×C59—41no—
44#11745685D811yescharacteristic
45C2×D236—41no—
46D8×C59—41no—
47D8×C59—41no—
48M16×C59—41no—
49C2×C8×C59C2×D411yescharacteristic
50#11745670—81no—
51#11745669—81no—
52#11745664—41no—
53#11745664D811yescharacteristic
54D472—41no—
55D472—41no—
56D472—81no—
57#11745660—81no—
58#11745659—21no—
59C8×D59—21no—
60C16×C59C2×D411yescharacteristic
61C16×C59#4111yescharacteristic
62C59⋊C16—21no—
63C23×C59—81no—
64C22×D59—81no—
65D4×C59—81no—
66D4×C59—81no—
67C2×C4×C59C2×D811yescharacteristic
68C22⋊D59—21no—
69D236—81no—
70D236—81no—
71D236D1611yescharacteristic
72C4×D59—21no—
73Dic118D1611yescharacteristic
74C8×C59—81no—
75C8×C59#12111yescharacteristic
76C8×C59#13511yescharacteristic
77C59⋊C8—21no—
78C59⋊C8—81no—
79#13700—591nomaximal, Sylow
80C22×C59—161no—
81C22×C59—321no—
82C22×C59#50811yescharacteristic
83C2×D59—21no—
84C2×D59—161no—
85C2×D59—321no—
86C4×C59#46611yescharacteristic
87C4×C59C2×D1611yescharacteristic
88Dic59—21no—
89C2×D32—591no—
90#2258—591no—
91#2221—591no—
92#2221—591no—
93#1425—591no—
94#1419—591no—
95#1419D5911yescharacteristic, complemented
96C2×C59—21no—
97C2×C59—321no—
98C2×C59#221511yescharacteristic
99D59—41no—
100D59—321no—
101C2×D16—591no—
102C2×D16C2×D5911yescharacteristic
103#504—591no—
104#472—1181no—
105#472—1181no—
106D32—1181no—
107D32—1181no—
108M64—1181no—
109M64C2×D5911yescharacteristic
110C2×C32—591no—
111C2×C32—1181no—
112#368—591no—
113#368C2×D5911yescharacteristic
114#361—1181no—
115#361—1181no—
116C59#1370011yescharacteristic, complemented, Sylow
117AGL(1,ℤ/8)—2361no—
118AGL(1,ℤ/8)—2361no—
119C2×D8—21no—
120C2×D8—1181no—
121#131—591no—
122D16—21no—
123D16—21no—
124D16—1181no—
125D16—1181no—
126M32—591no—
127M32—1181no—
128C2×C16—1181no—
129C2×C16C22×D5911yescharacteristic
130#108—21no—
131#108—1181no—
132#100—2361no—
133#100—2361no—
134C32—21no—
135C32—591no—
136C32—591no—
137#41—591no—
138C2×D4—41no—
139C2×D4—2361no—
140SD16—4721no—
141SD16—4721no—
142D8—41no—
143D8—41no—
144D8—4721no—
145D8—4721no—
146D8—2361no—
147D8—2361no—
148M16—41no—
149M16—591no—
150M16—1181no—
151M16—2361no—
152C2×C8—1181no—
153C2×C8D4×D5911yescharacteristic
154C16—1181no—
155C16#1174568511yescharacteristic
156C16D4×D5911yescharacteristic
157C23—81no—
158C23—4721no—
159Q8—591no—
160D4—81no—
161D4—81no—
162D4—591no—
163D4—1181no—
164D4—4721no—
165D4—4721no—
166C2×C4—1181no—
167C2×C4D8×D5911yescharacteristic
168C8—81no—
169C8—1181no—
170C8—4721no—
171C8#1427370011yescharacteristic
172C8#1427374811yescharacteristic
173C22—161no—
174C22—321no—
175C22—18881no—
176C22—1181no—
177C22—9441no—
178C22#1683783311yescharacteristic
179C4—1181no—
180C4#1683763711yescharacteristic
181C4D16×D5911yescharacteristic
182C2—21no—
183C2—321no—
184C2—18881no—
185C2—2361no—
186C2#2142618111yescharacteristic
subgroupG/H
centerC2#21426181
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1419C2
socleC2×C59#2215
hypercenter#1419D59
hypocenterC59#13700
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. C2×#16837237C2semidirect
2. #21426391C2semidirect
3. #21426217C2semidirect
4. #21426213C2semidirect
5. #21422299C2semidirect
6. #21422287C2semidirect
7. C59×#1419C2semidirect
95. #1419D59semidirect
116. C59#13700semidirect

Maximal subgroups

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

subgroupindex
C2×#168372372
#214263912
#214262172
#214262132
#214222992
#214222872
C59×#14192
#1370059