Finite Group Databasebeta

← #28493189

Subgroups — #28493189

Order 15104.

374 conjugacy classes of subgroups; only the 95 normal subgroups are shown.

normal subgroups only

This group has 374 conjugacy classes of subgroups — too many to draw. Only its 95 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#21432368C211yesmaximal, characteristic
2#21424231C212yesmaximal
3#21421978C212yesmaximal
4#21421977C211yesmaximal, characteristic
5C59×#1847C211yesmaximal, characteristic
6C2×#14273638C2212yes—
7#16837344—22no—
8#16837341—21no—
9#16837323—22no—
10#16837322—21no—
11#16837268C2212yes—
12#16837164—22no—
13#16837164—22no—
14C2×#107×C59—21no—
15C2×#106×C59—21no—
16C2×#97×C59C2211yescharacteristic
17C59×#384C2211yescharacteristic
18C59×#382C2211yescharacteristic
19C22×Dic118—21no—
20C22×C59⋊C8—22no—
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59D412yes—
23C2×C4⋊Dic59D412yes—
24C2×Dic59⋊C4—22no—
25#14273638—22no—
26#14273638Q814yescomplemented
27C59⋊#95—21no—
28C59⋊#95—22no—
29C59⋊#95—21no—
30C59⋊#95—22no—
31C59⋊#95—22no—
32C22×C8×C59—21no—
33C2×C4⋊C4×C59—22no—
34C2×C4⋊C4×C59—21no—
35C2×C4⋊C4×C59D411yescharacteristic
36C2×C4⋊C4×C59D411yescharacteristic
37C2×C42×C59C2311yescharacteristic
38#107×C59—42no—
39#106×C59—42no—
40#97×C59—21no—
41#97×C59Q812yescomplemented
42#95×C59—22no—
43C22×C4×C59—21no—
44C22×C4×C59—21no—
45C22×C4×C59—41no—
46C22×C4×C59C2×D412yes—
47C22×C4×C59C2×D411yescharacteristic
48C22×Dic59—22no—
49C22×Dic59—22no—
50C2×Dic118—81no—
51C2×Dic118—82no—
52C2×C8×C59—22no—
53C2×C8×C59—22no—
54C2×C8×C59—22no—
55C4⋊C4×C59—41no—
56C4⋊C4×C59—41no—
57C4⋊C4×C59—41no—
58C4⋊C4×C59—41no—
59C4⋊C4×C59—44no—
60C42×C59C2×Q811yescharacteristic
61C42×C59C2×Q812yes—
62C42×C59#4111yescharacteristic
63C4⋊Dic59—42no—
64C4⋊Dic59—42no—
65C4⋊Dic59—81no—
66Dic59⋊C4—82no—
67C2×C59⋊C8—24no—
68C2×C59⋊C8—42no—
69C2×C59⋊C8—42no—
70C23×C59#12011yescharacteristic
71C2×C4×C59—21no—
72C2×C4×C59—22no—
73C2×C4×C59—22no—
74C2×C4×C59—21no—
75C2×C4×C59—41no—
76C2×C4×C59—41no—
77C2×C4×C59—42no—
78C2×C4×C59—42no—
79C2×C4×C59—81no—
80C2×C4×C59—82no—
81C2×C4×C59C22⋊Q812yes—
82C2×C4×C59C22⋊Q811yescharacteristic
83C2×C4×C59C4⋊Q811yescharacteristic
84C2×C4×C59C4⋊Q812yes—
85C2×Dic59—42no—
86C2×Dic59—42no—
87C2×Dic59—42no—
88C2×Dic59—42no—
89C2×Dic59—42no—
90C2×Dic59—42no—
91Dic118—84no—
92C8×C59—24no—
93C59⋊C8—44no—
94#10584—591nomaximal, Sylow
95C22×C59#39511yescharacteristic
96C22×C59#45311yescharacteristic
97C22×C59#45412yes—
98C22×C59#45512yes—
99C22×C59#45611yescharacteristic
100C4×C59—21no—
101C4×C59—21no—
102C4×C59—22no—
103C4×C59—22no—
104C4×C59—81no—
105C4×C59—81no—
106C4×C59—161no—
107Dic59—82no—
108Dic59—82no—
109#2844—591no—
110#1847D5911yescharacteristic
111#1836—592no—
112#1295—592no—
113#1295—591no—
114C2×C59#165711yescharacteristic
115C2×C59#165911yescharacteristic
116C2×C59#166412yes—
117C2×C59#206011yescharacteristic
118C2×C59#206112yes—
119C2×#107—21no—
120C2×#106—21no—
121C2×#97—592no—
122C2×#97C2×D5911yescharacteristic
123#400—1182no—
124#400—1181no—
125#395—1182no—
126#395—1181no—
127#384C2×D5911yescharacteristic
128#382—592no—
129#382C2×D5911yescharacteristic
130#340—1182no—
131#340—1182no—
132C59#1058411yescharacteristic, complemented, Sylow
133C22×Q8—1181no—
134C22×C8—21no—
135C22×C8—1182no—
136C2×C4⋊C4—22no—
137C2×C4⋊C4—21no—
138C2×C4⋊C4—592no—
139C2×C4⋊C4—592no—
140C2×C4⋊C4—1182no—
141C2×C4⋊C4—1181no—
142C2×C4⋊C4C22⋊D5911yescharacteristic
143C2×C4⋊C4C22⋊D5911yescharacteristic
144C2×C42C22×D5911yescharacteristic
145#107—42no—
146#106—42no—
147#97—21no—
148#97—594no—
149#97—1182no—
150#97Dic11812yescomplemented
151#95—22no—
152#95—1182no—
153#95—1181no—
154#95—1181no—
155#95—1182no—
156#95—1182no—
157C2×Q8—4721no—
158C2×Q8—4722no—
159C22×C4—21no—
160C22×C4—21no—
161C22×C4—41no—
162C22×C4—1182no—
163C22×C4—1182no—
164C22×C4D4×D5912yes—
165C22×C4C2×C22⋊D5911yescharacteristic
166C2×C8—22no—
167C2×C8—22no—
168C2×C8—22no—
169C2×C8—1184no—
170C2×C8—2362no—
171C2×C8—2362no—
172C4⋊C4—41no—
173C4⋊C4—41no—
174C4⋊C4—41no—
175C4⋊C4—41no—
176C4⋊C4—44no—
177C4⋊C4—4722no—
178C4⋊C4—4721no—
179C4⋊C4—2362no—
180C4⋊C4—2362no—
181C42C2×Dic11811yescharacteristic
182C42#1174568511yescharacteristic
183C42Q8×D5912yes—
184C23#1427369511yescharacteristic
185Q8—4724no—
186C2×C4—21no—
187C2×C4—22no—
188C2×C4—22no—
189C2×C4—21no—
190C2×C4—41no—
191C2×C4—41no—
192C2×C4—42no—
193C2×C4—42no—
194C2×C4—81no—
195C2×C4—82no—
196C2×C4—2362no—
197C2×C4—2362no—
198C2×C4—2362no—
199C2×C4—2362no—
200C2×C4—2362no—
201C2×C4—2362no—
202C2×C4#1427370512yes—
203C2×C4#1427370611yescharacteristic
204C2×C4#1427372511yescharacteristic
205C2×C4#1427372612yes—
206C8—24no—
207C8—2364no—
208C22#1683732211yescharacteristic
209C22#1683756911yescharacteristic
210C22#1683757312yes—
211C22#1683757812yes—
212C22#1683758411yescharacteristic
213C4—21no—
214C4—21no—
215C4—22no—
216C4—22no—
217C4—81no—
218C4—81no—
219C4—161no—
220C4—4722no—
221C4—4722no—
222C2#2142339211yescharacteristic
223C2#2142340011yescharacteristic
224C2#2142342812yes—
225C2#2142544111yescharacteristic
226C2#2142544412yes—
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1847C2
socle, prime radicalC23×C59#120
hypercenter#1847D59
hypocenterC59#10584
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1847

Complements

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

NH ≅ G/Ntype
26. #14273638Q8semidirect
41. #97×C59Q8semidirect
132. C59#10584semidirect
150. #97Dic118semidirect

Maximal subgroups

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

subgroupindex
#214323682
#214242312
#214219782
#214219772
C59×#18472
#1058459