Finite Group Databasebeta

← #28493589

Subgroups — #28493589

Order 15104.

236 conjugacy classes of subgroups; only the 69 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 69 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#21422824C211yesmaximal, characteristic
2#21422794C211yesmaximal, characteristic
3#21422570C211yesmaximal, characteristic
4#21422007C211yesmaximal, characteristic
5#21421966C211yesmaximal, characteristic
6#21421958C211yesmaximal, characteristic
7C59×#1570C211yesmaximal, characteristic
8#16837959C2211yescharacteristic
9#16837459C2211yescharacteristic
10#16837459C2211yescharacteristic
11#16837459C2211yescharacteristic
12#16837150—21no—
13#16837149—21no—
14#16837149—21no—
15#16837147—21no—
16#16837134—22no—
17C59×#431C2211yescharacteristic
18C59×#423C2211yescharacteristic
19C2×C4⋊C8×C59C2211yescharacteristic
20C59×#334—22no—
21#14273727D411yescharacteristic
22#14273727D411yescharacteristic
23#14273719—21no—
24#14273706—21no—
25#14273706—21no—
26C4×Dic118—21no—
27C4×Dic118—21no—
28#14273686—21no—
29C4⋊(C59⋊C8)—21no—
30C4⋊(C59⋊C8)—21no—
31C4⋊(C59⋊C8)—21no—
32C22⋊(C59⋊C8)—21no—
33C22⋊(C59⋊C8)—21no—
34C22⋊(C59⋊C8)—21no—
35#14273638—21no—
36#14273638—21no—
37#14273638—21no—
38C2×M16×C59—21no—
39C22×C8×C59—21no—
40C2×C42×C59C2311yescharacteristic
41C4⋊C8×C59—21no—
42C4⋊C8×C59—21no—
43C4⋊C8×C59—21no—
44C4⋊C8×C59—21no—
45C4⋊C8×C59—21no—
46C22⋊C8×C59—21no—
47C4×C8×C59D412yes—
48C22×C4×C59#4111yescharacteristic
49C22×C4×C59#4111yescharacteristic
50C22×C4×C59#4111yescharacteristic
51C2×Dic118—21no—
52C2×Dic118—21no—
53M16×C59—81no—
54C2×C8×C59—22no—
55C2×C8×C59—41no—
56C2×C8×C59—41no—
57C2×C8×C59—81no—
58C42×C59C2×D411yescharacteristic
59C42×C59C2×D411yescharacteristic
60C42×C59#4111yescharacteristic
61C42×C59#4111yescharacteristic
62C22⋊Dic59—41no—
63C4⋊Dic59—21no—
64C4⋊Dic59—21no—
65C4⋊Dic59—21no—
66C4⋊Dic59—21no—
67Dic59⋊C4—41no—
68Dic59⋊C4—41no—
69C4×Dic59—41no—
70C2×C59⋊C8—41no—
71C2×C59⋊C8—41no—
72C2×C59⋊C8—41no—
73C23×C59#12611yescharacteristic
74C2×C4×C59—21no—
75C2×C4×C59—21no—
76C2×C4×C59—41no—
77C2×C4×C59—41no—
78C2×C4×C59#12111yescharacteristic
79C2×C4×C59#12311yescharacteristic
80C2×C4×C59#12311yescharacteristic
81C2×C4×C59#12311yescharacteristic
82C2×C4×C59#12411yescharacteristic
83C2×C4×C59#12611yescharacteristic
84C2×Dic59—41no—
85C2×Dic59—41no—
86Dic118—41no—
87Dic118—41no—
88Dic118—81no—
89C8×C59—42no—
90C8×C59—81no—
91C8×C59—81no—
92C59⋊C8—81no—
93C59⋊C8—81no—
94C59⋊C8—81no—
95#10648—591nomaximal, Sylow
96C22×C59—21no—
97C22×C59—21no—
98C22×C59—21no—
99C22×C59#39711yescharacteristic
100C4×C59—21no—
101C4×C59—21no—
102C4×C59—21no—
103C4×C59—21no—
104C4×C59—21no—
105C4×C59#47111yescharacteristic
106C4×C59#47111yescharacteristic
107Dic59—81no—
108Dic59—81no—
109#1570D5911yescharacteristic
110#1559—591no—
111#1552—591no—
112#1497—591no—
113#1307—591no—
114#1290—591no—
115#1287—591no—
116C2×C59—41no—
117C2×C59#207911yescharacteristic
118C2×C59#208011yescharacteristic
119C2×C59#208211yescharacteristic
120#533—591no—
121#432—591no—
122#432—591no—
123#432—591no—
124#431C2×D5911yescharacteristic
125#423C2×D5911yescharacteristic
126C2×C4⋊C8C2×D5911yescharacteristic
127#334—22no—
128#333—1181no—
129#332—1181no—
130#332—1181no—
131#332—1181no—
132Q8⋊C8—1182no—
133C59#1064811yescharacteristic, complemented, Sylow
134C2×M16—21no—
135C22×C8—21no—
136C4⋊Q8—591no—
137C4⋊Q8—591no—
138#125—1181no—
139C22⋊Q8—1181no—
140C22⋊Q8—1181no—
141C4×Q8—1181no—
142C4×Q8—1181no—
143#117—1181no—
144C2×C42C22×D5911yescharacteristic
145C4⋊C8—21no—
146C4⋊C8—21no—
147C4⋊C8—21no—
148C4⋊C8—21no—
149C4⋊C8—21no—
150C4⋊C8—1181no—
151C4⋊C8—1181no—
152C4⋊C8—1181no—
153C22⋊C8—21no—
154C22⋊C8—1181no—
155C22⋊C8—1181no—
156C22⋊C8—1181no—
157#97—1181no—
158#97—1181no—
159#97—1181no—
160C4×C8C22⋊D5912yes—
161C2×Q8—1181no—
162C2×Q8—1181no—
163C22×C4#1174568511yescharacteristic
164C22×C4#1174568711yescharacteristic
165C22×C4#1174568911yescharacteristic
166M16—81no—
167C2×C8—22no—
168C2×C8—41no—
169C2×C8—41no—
170C2×C8—81no—
171C2×C8—2361no—
172C2×C8—2361no—
173C2×C8—2361no—
174C4⋊C4—1181no—
175C4⋊C4—1181no—
176C4⋊C4—1181no—
177C4⋊C4—1181no—
178C4⋊C4—2361no—
179C4⋊C4—2361no—
180C22⋊C4—2361no—
181C42—2361no—
182C42#1174568511yescharacteristic
183C42D4×D5911yescharacteristic
184C42#1174568911yescharacteristic
185C42C2×C22⋊D5911yescharacteristic
186C23#1427372211yescharacteristic
187Q8—4721no—
188Q8—2361no—
189Q8—2361no—
190C2×C4—21no—
191C2×C4—21no—
192C2×C4—41no—
193C2×C4—41no—
194C2×C4—2361no—
195C2×C4—2361no—
196C2×C4#1427369811yescharacteristic
197C2×C4#1427371011yescharacteristic
198C2×C4#1427371211yescharacteristic
199C2×C4#1427371211yescharacteristic
200C2×C4#1427371611yescharacteristic
201C2×C4#1427372211yescharacteristic
202C8—42no—
203C8—81no—
204C8—81no—
205C8—4721no—
206C8—4721no—
207C8—4721no—
208C22—21no—
209C22—21no—
210C22—21no—
211C22#1683732811yescharacteristic
212C4—21no—
213C4—21no—
214C4—21no—
215C4—21no—
216C4—21no—
217C4—4721no—
218C4—4721no—
219C4#1683766211yescharacteristic
220C4#1683766211yescharacteristic
221C2—41no—
222C2#2142554211yescharacteristic
223C2#2142554711yescharacteristic
224C2#2142556111yescharacteristic
subgroupG/H
centerC22#16837328
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1570C2
socleC22×C59#397
prime radicalC23×C59#126
hypercenter#1570D59
hypocenterC59#10648
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1570

Complements

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

NH ≅ G/Ntype
133. C59#10648semidirect

Maximal subgroups

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

subgroupindex
#214228242
#214227942
#214225702
#214220072
#214219662
#214219582
C59×#15702
#1064859