Finite Group Databasebeta

← #28483062

Subgroups — #28483062

Order 15104.

428 conjugacy classes of subgroups; only the 111 normal subgroups are shown.

normal subgroups only

This group has 428 conjugacy classes of subgroups — too many to draw. Only its 111 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#21427282C211yesmaximal, characteristic
2#21424262C212yesmaximal
3C2×#16837144C211yesmaximal, characteristic
4#21421978C212yesmaximal
5C59×#1992C211yesmaximal, characteristic
6C2×#14273660—22no—
7C2×#14273658—22no—
8C2×#14273638C2212yes—
9#16837301—22no—
10#16837288—22no—
11#16837288—22no—
12#16837268C2212yes—
13#16837144C414yescomplemented
14C2×#125×C59C2211yescharacteristic
15C2×#97×C59C2211yescharacteristic
16C59×#384C2211yescharacteristic
17C59×#340—22no—
18C22×C59⋊C8—22no—
19C2×C4⋊Dic59—22no—
20C2×C4⋊Dic59D412yes—
21C2×C4⋊Dic59D412yes—
22C2×C4×Dic59—22no—
23#14273660—44no—
24#14273658—44no—
25#14273638—22no—
26#14273638C2×C414yes—
27C59⋊#95—22no—
28C59⋊#95—22no—
29C59⋊#95—22no—
30C59⋊#95—22no—
31C22×C8×C59—21no—
32#125×C59—22no—
33#125×C59C2×C412yes—
34#125×C59Q812yes—
35C2×C4⋊C4×C59—22no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59—22no—
38C2×C4⋊C4×C59D412yes—
39C2×C42×C59C2311yescharacteristic
40#97×C59—22no—
41C22×C4×C59—22no—
42C22×C4×C59—41no—
43C22×C4×C59C2×D411yescharacteristic
44C22×C4×C59C2×D412yes—
45C22×Dic59—22no—
46C22×Dic59—22no—
47C2×C8×C59—22no—
48C2×C8×C59—41no—
49C2×C8×C59—41no—
50C4⋊C4×C59—24no—
51C4⋊C4×C59—24no—
52C4⋊C4×C59—22no—
53C4⋊C4×C59—42no—
54C4⋊C4×C59—42no—
55C4⋊C4×C59—42no—
56C4⋊C4×C59C4⋊C414yes—
57C42×C59C22×C411yescharacteristic
58C42×C59C2×Q811yescharacteristic
59C42×C59#4112yes—
60C4⋊Dic59—42no—
61C4⋊Dic59—42no—
62C4⋊Dic59—82no—
63C4×Dic59—82no—
64C2×C59⋊C8—24no—
65C2×C59⋊C8—24no—
66C2×C59⋊C8—24no—
67C23×C59#12011yescharacteristic
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—22no—
71C2×C4×C59—21no—
72C2×C4×C59—24no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—82no—
76C2×C4×C59—81no—
77C2×C4×C59C2×C4⋊C411yescharacteristic
78C2×C4×C59C4×D412yes—
79C2×C4×C59C22⋊Q812yes—
80C2×C4×C59#12311yescharacteristic
81C2×Dic59—42no—
82C2×Dic59—42no—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—42no—
86C2×Dic59—42no—
87C8×C59—42no—
88C59⋊C8—28no—
89#8913—591nomaximal, Sylow
90C22×C59#38511yescharacteristic
91C22×C59#45312yes—
92C22×C59#45411yescharacteristic
93C22×C59#45612yes—
94C22×C59#45611yescharacteristic
95C4×C59—21no—
96C4×C59—21no—
97C4×C59—22no—
98C4×C59—22no—
99C4×C59—44no—
100C4×C59—161no—
101Dic59—82no—
102Dic59—82no—
103#2382—591no—
104#1992D5911yescharacteristic
105#1847—592no—
106C2×#330—591no—
107#1295—592no—
108C2×C59#165611yescharacteristic
109C2×C59#166012yes—
110C2×C59#166311yescharacteristic
111C2×C59#185711yescharacteristic
112C2×C59#185912yes—
113C2×#125C2×D5911yescharacteristic
114C2×#107—1182no—
115C2×#106—1182no—
116C2×#97—592no—
117C2×#97C2×D5911yescharacteristic
118#389—1182no—
119#387—1182no—
120#387—1182no—
121#384C2×D5911yescharacteristic
122#382—592no—
123#340—22no—
124#330—594no—
125C59#891311yescharacteristic, complemented, Sylow
126C22×C8—21no—
127C22×C8—1182no—
128#125—22no—
129#125Dic11812yes—
130#125C4×D5912yes—
131C2×C4⋊C4—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—21no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4C22⋊D5912yes—
138C2×C42—1182no—
139C2×C42C22×D5911yescharacteristic
140#107—2364no—
141#106—2364no—
142#97—22no—
143#97—594no—
144#97—1182no—
145#95—1182no—
146#95—1182no—
147#95—1182no—
148#95—1182no—
149C22×C4—22no—
150C22×C4—41no—
151C22×C4—1182no—
152C22×C4—1182no—
153C22×C4D4×D5912yes—
154C22×C4C2×C22⋊D5911yescharacteristic
155C2×C8—22no—
156C2×C8—41no—
157C2×C8—41no—
158C2×C8—1184no—
159C2×C8—1184no—
160C2×C8—1184no—
161C4⋊C4—24no—
162C4⋊C4—24no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—4722no—
168C4⋊C4—2362no—
169C4⋊C4—2362no—
170C4⋊C4Dic59⋊C414yes—
171C42—4722no—
172C42C2×Dic11811yescharacteristic
173C42C2×C4×D5911yescharacteristic
174C42#1174568712yes—
175C23#1427369511yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—22no—
179C2×C4—21no—
180C2×C4—24no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—82no—
184C2×C4—81no—
185C2×C4—2362no—
186C2×C4—2362no—
187C2×C4—2362no—
188C2×C4—2362no—
189C2×C4—2362no—
190C2×C4—2362no—
191C2×C4C2×Dic59⋊C411yescharacteristic
192C2×C4(C22⋊D59)⋊C412yes—
193C2×C4#1427370412yes—
194C2×C4#1427370811yescharacteristic
195C8—42no—
196C8—1188no—
197C22#1683727411yescharacteristic
198C22#1683756812yes—
199C22#1683757411yescharacteristic
200C22#1683758312yes—
201C22#1683758411yescharacteristic
202C4—21no—
203C4—21no—
204C4—22no—
205C4—22no—
206C4—44no—
207C4—161no—
208C4—4722no—
209C4—4722no—
210C2#2142338811yescharacteristic
211C2#2142340612yes—
212C2#2142342211yescharacteristic
213C2#2142431011yescharacteristic
214C2#2142432012yes—
subgroupG/H
centerC23#14273695
commutatorC42×C59C22×C4
FrattiniC2×C42C22×D59
FittingC59×#1992C2
socle, prime radicalC23×C59#120
cosocleC2×C42×C59C23
hypercenter#1992D59
hypocenterC59#8913
LCSG ▷ C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1992

Complements

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

NH ≅ G/Ntype
13. #16837144C4semidirect
125. C59#8913semidirect

Maximal subgroups

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

subgroupindex
#214272822
#214242622
C2×#168371442
#214219782
C59×#19922
#891359