Finite Group Databasebeta

← #28502939

Subgroups — #28502939

Order 15104.

224 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 63 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#21426352C211yesmaximal, characteristic, complemented
2#21426177C211yesmaximal, characteristic, complemented
3#21426172C211yesmaximal, characteristic
4#21422172C211yesmaximal, characteristic, complemented
5#21422134C211yesmaximal, characteristic, complemented
6#21422132C211yesmaximal, characteristic, complemented
7C59×#2170C211yesmaximal, characteristic, complemented
8#16837842—21no—
9#16837837—21no—
10C2×#14273672—21no—
11C2×#14273672—21no—
12#16837782C2211yescharacteristic
13#16837779C2211yescharacteristic
14#16837223C2211yescharacteristic
15#16837223C2211yescharacteristic
16#16837217—21no—
17#16837214—21no—
18C59×#504—21no—
19C59×#443C2211yescharacteristic
20C59×#364C2211yescharacteristic
21C59×#350—21no—
22C4×C16×C59C2211yescharacteristic
23C2×Dic236—21no—
24C2×Dic236—21no—
25C2×D472—21no—
26C2×D472—21no—
27#14273727—21no—
28#14273724—21no—
29#14273673—41no—
30#14273672—42no—
31#14273672—41no—
32#14273672—41no—
33#14273671—41no—
34#14273670—41no—
35#14273668—41no—
36#14273667—21no—
37#14273667—21no—
38#135×C59D411yescharacteristic
39#131×C59—21no—
40M32×C59—21no—
41M32×C59—41no—
42C2×C16×C59—41no—
43C2×C16×C59D411yescharacteristic
44C2×C16×C59D411yescharacteristic
45#108×C59D411yescharacteristic
46#104×C59—21no—
47C4×C8×C59C2311yescharacteristic
48#41×C59—21no—
49C2×D236—41no—
50C2×D236—81no—
51C2×Dic118—41no—
52Q16×C59D811yescharacteristic
53SD16×C59—21no—
54D8×C59D811yescharacteristic
55M16×C59—21no—
56M16×C59—41no—
57C2×C8×C59—41no—
58C2×C8×C59C2×D411yescharacteristic
59C2×C8×C59C2×D411yescharacteristic
60C42×C59#4111yescharacteristic
61C4⋊Dic59—81no—
62Dic236—41no—
63Dic236—41no—
64Dic236—41no—
65Dic236—41no—
66D472—41no—
67D472—41no—
68D472—41no—
69D472—41no—
70C16×C59—21no—
71C16×C59—41no—
72C16×C59D811yescharacteristic
73C16×C59D811yescharacteristic
74C59⋊C16—41no—
75C59⋊C16—41no—
76C22×D59—81no—
77Q8×C59—21no—
78D4×C59—21no—
79D4×C59—41no—
80C2×C4×C59—21no—
81C2×C4×C59—41no—
82C2×C4×C59#12111yescharacteristic
83C2×Dic59—81no—
84D236—81no—
85D236—81no—
86D236—162no—
87Dic118—81no—
88Dic118—81no—
89C8×C59—41no—
90C8×C59C2×D811yescharacteristic
91C8×C59C2×D811yescharacteristic
92C8×C59#13511yescharacteristic
93C8×C59AGL(1,ℤ/8)11yescharacteristic
94#12438—591nomaximal, Sylow
95C22×C59—41no—
96C22×C59#47211yescharacteristic
97C2×D59—162no—
98C2×D59—161no—
99C4×C59—22no—
100C4×C59—41no—
101C4×C59#45911yescharacteristic
102C4×C59#46611yescharacteristic
103Dic59—161no—
104#2248—591no—
105#2214—591no—
106#2213—591no—
107#2170D5911yescharacteristic, complemented
108#1373—591no—
109#1358—591no—
110#1357—591no—
111C2×C59—21no—
112C2×C59—81no—
113C2×C59#166711yescharacteristic
114D59—321no—
115#510—1181no—
116#509—1181no—
117C2×SD32—1181no—
118C2×SD32—1181no—
119#504—21no—
120#494—591no—
121#493—591no—
122#443C2×D5911yescharacteristic
123#364—591no—
124#364—591no—
125#364C2×D5911yescharacteristic
126#362—1181no—
127#361—1181no—
128#350—21no—
129C4×C16C2×D5911yescharacteristic
130C59#1243811yescharacteristic, complemented, Sylow
131#135D23611yescharacteristic
132C2×Q16—1181no—
133C2×Q16—1181no—
134C2×D8—1181no—
135C2×D8—1181no—
136#131—21no—
137C4⋊Q8—1181no—
138#127—1181no—
139Q32—2361no—
140SD32—2362no—
141SD32—2361no—
142SD32—2361no—
143SD32—2361no—
144SD32—2361no—
145D16—2361no—
146M32—21no—
147M32—41no—
148M32—1181no—
149M32—1181no—
150C2×C16—41no—
151C2×C16C22⋊D5911yescharacteristic
152C2×C16C22⋊D5911yescharacteristic
153#108D23611yescharacteristic
154#104—21no—
155C4×C8C22×D5911yescharacteristic
156#41—21no—
157C2×Q8—2361no—
158C2×D4—4721no—
159C2×D4—2361no—
160Q16—2361no—
161Q16—2361no—
162Q16—2361no—
163Q16—2361no—
164Q16D47211yescharacteristic
165SD16—21no—
166D8—2361no—
167D8—2361no—
168D8—2361no—
169D8—2361no—
170D8D47211yescharacteristic
171M16—21no—
172M16—41no—
173C2×C8—41no—
174C2×C8C2×D23611yescharacteristic
175C2×C8C2×C22⋊D5911yescharacteristic
176C4⋊C4—4721no—
177C42#1174568511yescharacteristic
178C16—21no—
179C16—41no—
180C16—2361no—
181C16—2361no—
182C16#1174566911yescharacteristic
183C16#1174566911yescharacteristic
184C23—4721no—
185Q8—21no—
186Q8—4721no—
187Q8—4721no—
188D4—21no—
189D4—41no—
190D4—9442no—
191D4—4721no—
192D4—4721no—
193C2×C4—21no—
194C2×C4—41no—
195C2×C4—4721no—
196C2×C4#1427370111yescharacteristic
197C8—41no—
198C8C2×#1174566911yescharacteristic
199C8C2×D47211yescharacteristic
200C8#1427374911yescharacteristic
201C8#1427375211yescharacteristic
202C22—41no—
203C22—9442no—
204C22—9441no—
205C22#1683767211yescharacteristic
206C4—22no—
207C4—41no—
208C4—9441no—
209C4#1683759711yescharacteristic
210C4#1683763811yescharacteristic
211C2—21no—
212C2—81no—
213C2—18881no—
214C2#2142345111yescharacteristic
subgroupG/H
centerC2#21423451
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#2170C2
socleC2×C59#1667
prime radical#21426172C2
hypercenter#2170D59
hypocenterC59#12438
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2170

Complements

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

NH ≅ G/Ntype
1. #21426352C2semidirect
2. #21426177C2semidirect
4. #21422172C2semidirect
5. #21422134C2semidirect
6. #21422132C2semidirect
7. C59×#2170C2semidirect
107. #2170D59semidirect
130. C59#12438semidirect

Maximal subgroups

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

subgroupindex
#214263522
#214261772
#214261722
#214221722
#214221342
#214221322
C59×#21702
#1243859