Finite Group Databasebeta

← #28502927

Subgroups — #28502927

Order 15104.

234 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 234 conjugacy classes of subgroups — too many to draw. Only its 59 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#21426345C211yesmaximal, characteristic, complemented
2#21426172C211yesmaximal, characteristic, complemented
3#21425933C211yesmaximal, characteristic, complemented
4#21422171C211yesmaximal, characteristic, complemented
5#21422133C211yesmaximal, characteristic, complemented
6#21422132C211yesmaximal, characteristic, complemented
7C59×#2213C211yesmaximal, characteristic, complemented
8#16837837—21no—
9C2×#14273668—21no—
10C2×#14273668—21no—
11#16837819—21no—
12#16837779C2211yescharacteristic
13#16837223C2211yescharacteristic
14#16837223C2211yescharacteristic
15#16837214—21no—
16#16837186—21no—
17C4×C59⋊C16C2211yescharacteristic
18C59×#509—21no—
19C59×#493C2211yescharacteristic
20C59×#443C2211yescharacteristic
21C59×#364C2211yescharacteristic
22C59×#361—21no—
23C2×D472—21no—
24C2×D472—21no—
25#14273724—21no—
26#14273670—41no—
27#14273668—42no—
28#14273668—41no—
29#14273668—41no—
30#14273668—41no—
31#14273667—21no—
32#14273667—21no—
33#14273667—41no—
34C2×C59⋊C16—41no—
35C2×C59⋊C16D411yescharacteristic
36C2×C59⋊C16D411yescharacteristic
37#135×C59D411yescharacteristic
38C2×D8×C59—21no—
39C2×D8×C59—21no—
40#131×C59—21no—
41#127×C59—21no—
42SD32×C59—41no—
43D16×C59—41no—
44M32×C59—21no—
45#108×C59D411yescharacteristic
46#104×C59—21no—
47C4×C8×C59C2311yescharacteristic
48#41×C59—21no—
49C2×D4×C59—41no—
50C2×D4×C59—81no—
51C2×D236—41no—
52C2×D236—81no—
53Q16×C59D811yescharacteristic
54SD16×C59—21no—
55D8×C59—41no—
56D8×C59—41no—
57D8×C59—41no—
58D8×C59—41no—
59D8×C59D811yescharacteristic
60M16×C59—21no—
61M16×C59—41no—
62C2×C8×C59—41no—
63C2×C8×C59C2×D411yescharacteristic
64C2×C8×C59C2×D411yescharacteristic
65C42×C59#4111yescharacteristic
66D472—41no—
67D472—41no—
68D472—41no—
69D472—41no—
70C16×C59—41no—
71C59⋊C16—21no—
72C59⋊C16—41no—
73C59⋊C16—41no—
74C59⋊C16D811yescharacteristic
75C59⋊C16D811yescharacteristic
76C23×C59—81no—
77C22×D59—81no—
78Q8×C59—21no—
79D4×C59—21no—
80D4×C59—41no—
81D4×C59—81no—
82D4×C59—81no—
83D4×C59—162no—
84C2×C4×C59—21no—
85C2×C4×C59—41no—
86C2×C4×C59#12111yescharacteristic
87D236—81no—
88D236—81no—
89D236—162no—
90C8×C59—41no—
91C8×C59C2×D811yescharacteristic
92C8×C59C2×D811yescharacteristic
93C8×C59#13511yescharacteristic
94C8×C59AGL(1,ℤ/8)11yescharacteristic
95#12436—591nomaximal, Sylow
96C22×C59—41no—
97C22×C59—162no—
98C22×C59—161no—
99C22×C59#47211yescharacteristic
100C2×D59—162no—
101C2×D59—161no—
102C4×C59—22no—
103C4×C59—41no—
104C4×C59#45911yescharacteristic
105C4×C59#46611yescharacteristic
106#2246—591no—
107#2213—591no—
108#2213D5911yescharacteristic, complemented
109#2170—591no—
110#1373—591no—
111#1357—591no—
112#1357—591no—
113C2×C59—21no—
114C2×C59—81no—
115C2×C59—321no—
116C2×C59#166711yescharacteristic
117D59—321no—
118#509—21no—
119#509—1181no—
120C2×D16—1181no—
121C2×D16—1181no—
122#504—1181no—
123#493—591no—
124#493C2×D5911yescharacteristic
125#443C2×D5911yescharacteristic
126#364—591no—
127#364—591no—
128#364C2×D5911yescharacteristic
129#361—21no—
130#361—1181no—
131#350—1181no—
132C4×C16—591no—
133C59#1243611yescharacteristic, complemented, Sylow
134#135C22⋊D5911yescharacteristic
135C2×D8—21no—
136C2×D8—21no—
137C2×D8—1181no—
138C2×D8—1181no—
139#131—21no—
140#127—21no—
141#127—1181no—
142SD32—41no—
143SD32—2361no—
144D16—41no—
145D16—2361no—
146D16—2361no—
147D16—2362no—
148D16—2361no—
149M32—21no—
150M32—1181no—
151M32—1181no—
152M32—2361no—
153C2×C16—591no—
154C2×C16—591no—
155C2×C16—2361no—
156#108C22⋊D5911yescharacteristic
157#104—21no—
158C4×C8C22×D5911yescharacteristic
159#41—21no—
160C2×D4—41no—
161C2×D4—81no—
162C2×D4—4721no—
163C2×D4—2361no—
164Q16#1174566911yescharacteristic
165SD16—21no—
166D8—41no—
167D8—41no—
168D8—41no—
169D8—41no—
170D8—2361no—
171D8—2361no—
172D8—2361no—
173D8—2361no—
174D8#1174566911yescharacteristic
175M16—21no—
176M16—41no—
177C2×C8—41no—
178C2×C8D4×D5911yescharacteristic
179C2×C8C2×C22⋊D5911yescharacteristic
180C42#1174568711yescharacteristic
181C16—41no—
182C16—591no—
183C16—591no—
184C16—1181no—
185C16—2361no—
186C16—2361no—
187C23—81no—
188C23—4721no—
189Q8—21no—
190D4—21no—
191D4—41no—
192D4—81no—
193D4—81no—
194D4—162no—
195D4—9442no—
196D4—4721no—
197D4—4721no—
198C2×C4—21no—
199C2×C4—41no—
200C2×C4#1427369911yescharacteristic
201C8—41no—
202C8D8×D5911yescharacteristic
203C8C2×#1174566911yescharacteristic
204C8#1427374711yescharacteristic
205C8#1427375111yescharacteristic
206C22—41no—
207C22—162no—
208C22—161no—
209C22—9442no—
210C22—9441no—
211C22#1683767011yescharacteristic
212C4—22no—
213C4—41no—
214C4#1683759511yescharacteristic
215C4#1683763611yescharacteristic
216C2—21no—
217C2—81no—
218C2—321no—
219C2—18881no—
220C2#2142344911yescharacteristic
subgroupG/H
centerC2#21423449
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#2213C2
socleC2×C59#1667
hypercenter#2213D59
hypocenterC59#12436
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C2 ◁ C2×C4 ◁ C4×C8 ◁ #2213

Complements

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

NH ≅ G/Ntype
1. #21426345C2semidirect
2. #21426172C2semidirect
3. #21425933C2semidirect
4. #21422171C2semidirect
5. #21422133C2semidirect
6. #21422132C2semidirect
7. C59×#2213C2semidirect
108. #2213D59semidirect
133. C59#12436semidirect

Maximal subgroups

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

subgroupindex
#214263452
#214261722
#214259332
#214221712
#214221332
#214221322
C59×#22132
#1243659