Finite Group Databasebeta

← #28502942

Subgroups — #28502942

Order 15104.

224 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 55 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#21426353C211yesmaximal, characteristic, complemented
2#21426174C211yesmaximal, characteristic, complemented
3#21426173C211yesmaximal, characteristic
4#21425932C211yesmaximal, characteristic, complemented
5#21422171C211yesmaximal, characteristic, complemented
6#21422132C211yesmaximal, characteristic, complemented
7C59×#1358C211yesmaximal, characteristic, complemented
8#16837843—21no—
9#16837840—21no—
10C2×#14273670—21no—
11C2×#14273670—21no—
12#16837820—21no—
13#16837779C2211yescharacteristic
14#16837520C2211yescharacteristic
15#16837223C2211yescharacteristic
16#16837218—21no—
17#16837216—21no—
18#16837187—21no—
19C4×C59⋊C16C2211yescharacteristic
20C59×#494C2211yescharacteristic
21C59×#364C2211yescharacteristic
22C59×#364C2211yescharacteristic
23#14273749D411yescharacteristic
24C2×D472—21no—
25C2×D472—21no—
26#14273733—21no—
27#14273724—21no—
28#14273673—41no—
29#14273672—41no—
30#14273670—42no—
31#14273670—41no—
32#14273670—41no—
33#14273670—41no—
34D944—41no—
35#14273667—21no—
36#14273666—41no—
37C2×C59⋊C16D411yescharacteristic
38C2×C59⋊C16D411yescharacteristic
39C16×D59—41no—
40#14273663D411yescharacteristic
41#14273655—21no—
42C2×Q16×C59—21no—
43C2×Q16×C59—21no—
44C4⋊Q8×C59—21no—
45M32×C59—21no—
46M32×C59—21no—
47C4×C8×C59C2311yescharacteristic
48C2×Q8×C59—41no—
49#11745685—21no—
50C2×D236—41no—
51C2×D236—81no—
52Q16×C59—41no—
53Q16×C59—41no—
54Q16×C59—41no—
55Q16×C59—41no—
56C2×C8×C59C2×D411yescharacteristic
57C2×C8×C59C2×D411yescharacteristic
58C4⋊C4×C59—81no—
59C42×C59#4111yescharacteristic
60#11745664—21no—
61Dic236D811yescharacteristic
62D472—41no—
63D472—41no—
64D472—41no—
65D472—41no—
66D472D811yescharacteristic
67#11745660—21no—
68#11745659—41no—
69C8×D59—41no—
70C16×C59—41no—
71C16×C59—41no—
72C59⋊C16—21no—
73C59⋊C16—41no—
74C59⋊C16D811yescharacteristic
75C59⋊C16D811yescharacteristic
76C22×D59—81no—
77Q8×C59—81no—
78Q8×C59—81no—
79C2×C4×C59—21no—
80C2×C4×C59—81no—
81C2×C4×C59#12111yescharacteristic
82C22⋊D59—41no—
83D236—21no—
84D236—81no—
85D236—81no—
86D236—162no—
87C4×D59—41no—
88Dic118—21no—
89C8×C59C2×D811yescharacteristic
90C8×C59C2×D811yescharacteristic
91C8×C59#13511yescharacteristic
92C8×C59AGL(1,ℤ/8)11yescharacteristic
93C59⋊C8—41no—
94#12438—591nomaximal, Sylow
95C22×C59#47211yescharacteristic
96C2×D59—41no—
97C2×D59—162no—
98C2×D59—161no—
99C4×C59—22no—
100C4×C59—161no—
101C4×C59#45911yescharacteristic
102C4×C59#46611yescharacteristic
103Dic59—41no—
104#2248—591no—
105#2214—591no—
106#2213—591no—
107#2170—591no—
108#1373—591no—
109#1358D5911yescharacteristic, complemented
110#1357—591no—
111C2×C59—21no—
112C2×C59#166711yescharacteristic
113D59—81no—
114D59—321no—
115#510—1181no—
116#509—1181no—
117C2×SD32—1181no—
118C2×SD32—1181no—
119#504—1181no—
120#494C2×D5911yescharacteristic
121#493—591no—
122#443—591no—
123#364—591no—
124#364C2×D5911yescharacteristic
125#364C2×D5911yescharacteristic
126#362—1181no—
127#361—1181no—
128#350—1181no—
129C4×C16—591no—
130C59#1243811yescharacteristic, complemented, Sylow
131#135—591no—
132C2×Q16—21no—
133C2×Q16—21no—
134C2×D8—1181no—
135C2×D8—1181no—
136#131—1181no—
137C4⋊Q8—21no—
138#127—1181no—
139Q32—2361no—
140SD32—2361no—
141SD32—2361no—
142SD32—2361no—
143SD32—2362no—
144SD32—2361no—
145D16—2361no—
146M32—21no—
147M32—21no—
148M32—1181no—
149M32—2361no—
150C2×C16—591no—
151C2×C16—591no—
152C2×C16—2361no—
153#108—591no—
154#104—1181no—
155C4×C8C22×D5911yescharacteristic
156#41—1181no—
157C2×Q8—41no—
158C2×D4—4721no—
159C2×D4—2361no—
160Q16—41no—
161Q16—41no—
162Q16—41no—
163Q16—41no—
164Q16—591no—
165SD16—1181no—
166D8—591no—
167D8—2361no—
168D8—2361no—
169D8—2361no—
170D8—2361no—
171M16—1181no—
172M16—2361no—
173C2×C8—2361no—
174C2×C8D4×D5911yescharacteristic
175C2×C8D4×D5911yescharacteristic
176C4⋊C4—81no—
177C42#1174568511yescharacteristic
178C16—41no—
179C16—41no—
180C16—591no—
181C16—591no—
182C16—1181no—
183C16—2361no—
184C23—4721no—
185Q8—81no—
186Q8—81no—
187Q8—1181no—
188D4—1181no—
189D4—9442no—
190D4—4721no—
191D4—4721no—
192D4—2361no—
193C2×C4—21no—
194C2×C4—81no—
195C2×C4—2361no—
196C2×C4#1427370011yescharacteristic
197C8—2361no—
198C8D8×D5911yescharacteristic
199C8D8×D5911yescharacteristic
200C8#1427374811yescharacteristic
201C8#1427375411yescharacteristic
202C22—9442no—
203C22—9441no—
204C22—2361no—
205C22#1683767111yescharacteristic
206C4—22no—
207C4—161no—
208C4—2361no—
209C4#1683759611yescharacteristic
210C4#1683763711yescharacteristic
211C2—21no—
212C2—18881no—
213C2—4721no—
214C2#2142345011yescharacteristic
subgroupG/H
centerC2#21423450
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1358C2
socleC2×C59#1667
prime radical#21426173C2
hypercenter#1358D59
hypocenterC59#12438
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #1358

Complements

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

NH ≅ G/Ntype
1. #21426353C2semidirect
2. #21426174C2semidirect
4. #21425932C2semidirect
5. #21422171C2semidirect
6. #21422132C2semidirect
7. C59×#1358C2semidirect
109. #1358D59semidirect
130. C59#12438semidirect

Maximal subgroups

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

subgroupindex
#214263532
#214261742
#214261732
#214259322
#214221712
#214221322
C59×#13582
#1243859