Finite Group Databasebeta

← #28509567

Subgroups — #28509567

Order 15104.

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

normal subgroups only

This group has 184 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×#16837239C211yesmaximal, characteristic, complemented
2#21426391C211yesmaximal, characteristic, complemented
3#21426218C211yesmaximal, characteristic, complemented
4#21426217C211yesmaximal, characteristic
5#21422299C211yesmaximal, characteristic, complemented
6#21422287C211yesmaximal, characteristic, complemented
7C59×#1420C211yesmaximal, characteristic, complemented
8C2×D944C2211yescharacteristic
9#16837818C2211yescharacteristic
10#16837674—21no—
11#16837673—21no—
12#16837239—21no—
13#16837239—21no—
14#16837235—21no—
15C2×C59⋊C32C2211yescharacteristic
16C32×D59—21no—
17#16837232C2211yescharacteristic
18#16837218—21no—
19#16837214—21no—
20C2×Q32×C59C2211yescharacteristic
21C59×M64C2211yescharacteristic
22C59×#368C2211yescharacteristic
23#14273758—41no—
24#14273755—41no—
25C2×D472—21no—
26#14273733D411yescharacteristic
27D944—21no—
28D944—21no—
29#14273667D411yescharacteristic
30#14273666—21no—
31C16×D59—21no—
32#14273663—21no—
33#14273646—41no—
34#14273643—41no—
35C59⋊C32D411yescharacteristic
36C59⋊C32D411yescharacteristic
37C2×Q16×C59—21no—
38Q32×C59—21no—
39Q32×C59—21no—
40C2×C16×C59C2311yescharacteristic
41#108×C59—21no—
42C32×C59—21no—
43C2×Q8×C59—41no—
44#11745685D811yescharacteristic
45C2×D236—41no—
46Q16×C59—41no—
47Q16×C59—41no—
48M16×C59—41no—
49C2×C8×C59C2×D411yescharacteristic
50#11745672—81no—
51#11745671—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—
63C22×D59—81no—
64Q8×C59—81no—
65Q8×C59—81no—
66C2×C4×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#13702—591nomaximal, Sylow
80C22×C59#50811yescharacteristic
81C2×D59—21no—
82C2×D59—161no—
83C2×D59—321no—
84C4×C59—161no—
85C4×C59#46611yescharacteristic
86C4×C59C2×D1611yescharacteristic
87Dic59—21no—
88C2×SD64—591no—
89#2258—591no—
90#2222—591no—
91#2221—591no—
92#1425—591no—
93#1420D5911yescharacteristic, complemented
94#1419—591no—
95C2×C59—21no—
96C2×C59#221511yescharacteristic
97D59—41no—
98D59—321no—
99C2×Q32C2×D5911yescharacteristic
100C2×D16—591no—
101#504—591no—
102#473—1181no—
103#472—1181no—
104SD64—1181no—
105SD64—1181no—
106M64—1181no—
107M64C2×D5911yescharacteristic
108C2×C32—591no—
109C2×C32—1181no—
110#368—591no—
111#368C2×D5911yescharacteristic
112#362—1181no—
113#361—1181no—
114C59#1370211yescharacteristic, complemented, Sylow
115#137—2361no—
116AGL(1,ℤ/8)—2361no—
117C2×Q16—21no—
118C2×D8—1181no—
119#131—591no—
120Q32—21no—
121Q32—21no—
122D16—1181no—
123D16—1181no—
124M32—591no—
125M32—1181no—
126C2×C16—1181no—
127C2×C16C22×D5911yescharacteristic
128#108—21no—
129#108—1181no—
130#101—2361no—
131#100—2361no—
132C32—21no—
133C32—591no—
134C32—591no—
135#41—591no—
136C2×Q8—41no—
137C2×D4—2361no—
138Q16—41no—
139Q16—41no—
140Q16—4721no—
141SD16—4721no—
142SD16—4721no—
143D8—4721no—
144D8—2361no—
145D8—2361no—
146M16—41no—
147M16—591no—
148M16—1181no—
149M16—2361no—
150C2×C8—1181no—
151C2×C8D4×D5911yescharacteristic
152C16—1181no—
153C16#1174568511yescharacteristic
154C16D4×D5911yescharacteristic
155C23—4721no—
156Q8—81no—
157Q8—81no—
158Q8—591no—
159D4—591no—
160D4—1181no—
161D4—4721no—
162D4—4721no—
163C2×C4—81no—
164C2×C4—1181no—
165C2×C4D8×D5911yescharacteristic
166C8—81no—
167C8—1181no—
168C8—4721no—
169C8#1427370011yescharacteristic
170C8#1427374811yescharacteristic
171C22—18881no—
172C22—1181no—
173C22—9441no—
174C22#1683783311yescharacteristic
175C4—161no—
176C4—1181no—
177C4#1683763711yescharacteristic
178C4D16×D5911yescharacteristic
179C2—21no—
180C2—18881no—
181C2—2361no—
182C2#2142618111yescharacteristic
subgroupG/H
centerC2#21426181
commutator, cosocleC2×C16×C59C23
FrattiniC2×C16C22×D59
FittingC59×#1420C2
socleC2×C59#2215
prime radical#21426217C2
hypercenter#1420D59
hypocenterC59#13702
LCSG ▷ C2×C16×C59 ▷ C8×C59 ▷ C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×C8 ◁ C2×C16 ◁ #1420

Complements

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

NH ≅ G/Ntype
1. C2×#16837239C2semidirect
2. #21426391C2semidirect
3. #21426218C2semidirect
5. #21422299C2semidirect
6. #21422287C2semidirect
7. C59×#1420C2semidirect
93. #1420D59semidirect
114. C59#13702semidirect

Maximal subgroups

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

subgroupindex
C2×#168372392
#214263912
#214262182
#214262172
#214222992
#214222872
C59×#14202
#1370259