Finite Group Databasebeta

← #28492184

Subgroups — #28492184

Order 15104.

386 conjugacy classes of subgroups; only the 89 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 89 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#21432164C211yesmaximal, characteristic
2#21425065C212yesmaximal
3#21424229C211yesmaximal, characteristic
4C2×#16837143C212yesmaximal
5C59×#1295C211yesmaximal, characteristic
6C2×#14273719C2212yes—
7C2×#14273638C2211yescharacteristic
8#16837342—22no—
9#16837334—22no—
10#16837332—22no—
11#16837272C2211yescharacteristic
12#16837165—22no—
13#16837165—22no—
14#16837164—22no—
15#16837143—24no—
16C2×#97×C59C2212yes—
17C59×#382C2211yescharacteristic
18C22×C59⋊C8—21no—
19#14273719—22no—
20#14273719—22no—
21#14273719—22no—
22#14273719—22no—
23C2×C4⋊Dic59—21no—
24C2×C4⋊Dic59—22no—
25C2×C4⋊Dic59—22no—
26C2×C4⋊Dic59D412yes—
27C2×C4⋊Dic59D412yes—
28C2×Dic59⋊C4—22no—
29C2×Dic59⋊C4—22no—
30#14273638—21no—
31#14273638D412yes—
32C59⋊#95—24no—
33C59⋊#95—22no—
34C22×C8×C59—22no—
35C2×C4⋊C4×C59D412yes—
36C2×C42×C59C2311yescharacteristic
37#97×C59—22no—
38#97×C59—22no—
39#95×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59C2×D412yes—
42C22×C4×C59C2×D411yescharacteristic
43C22×Dic59—22no—
44C22×Dic59—22no—
45C22×Dic59—41no—
46C2×C8×C59—24no—
47C2×C8×C59—42no—
48C2×C8×C59—42no—
49C4⋊C4×C59—42no—
50C42×C59C2×D411yescharacteristic
51C42×C59#4111yescharacteristic
52C42×C59#4112yes—
53C4⋊Dic59—22no—
54C4⋊Dic59—22no—
55C4⋊Dic59—22no—
56C4⋊Dic59—22no—
57C4⋊Dic59—42no—
58C4⋊Dic59—44no—
59C4⋊Dic59—82no—
60Dic59⋊C4—42no—
61Dic59⋊C4—42no—
62Dic59⋊C4—42no—
63Dic59⋊C4—42no—
64C2×C59⋊C8—22no—
65C2×C59⋊C8—41no—
66C2×C59⋊C8—41no—
67C23×C59#12011yescharacteristic
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—42no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59#12112yes—
76C2×C4×C59#12111yescharacteristic
77C2×C4×C59#12312yes—
78C2×C4×C59#12411yescharacteristic
79C2×Dic59—42no—
80C2×Dic59—42no—
81C2×Dic59—42no—
82C2×Dic59—42no—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—82no—
86C2×Dic59—81no—
87C8×C59—44no—
88C59⋊C8—42no—
89#10428—591nomaximal, Sylow
90C22×C59#39411yescharacteristic
91C22×C59#45412yes—
92C22×C59#45411yescharacteristic
93C22×C59#45511yescharacteristic
94C22×C59#45612yes—
95C4×C59—22no—
96C4×C59—22no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—82no—
100Dic59—82no—
101Dic59—82no—
102Dic59—161no—
103#2822—591no—
104#1992—592no—
105#1836—591no—
106C2×#330—592no—
107#1295D5911yescharacteristic
108C2×C59#165811yescharacteristic
109C2×C59#166311yescharacteristic
110C2×C59#166412yes—
111C2×C59#203812yes—
112C2×C59#204011yescharacteristic
113C2×#125—592no—
114C2×#97—591no—
115C2×#97C2×D5912yes—
116#400—1182no—
117#398—1182no—
118#398—1182no—
119#384—591no—
120#382C2×D5911yescharacteristic
121#340—1182no—
122#340—1182no—
123#340—1182no—
124#330—1184no—
125C59#1042811yescharacteristic, complemented, Sylow
126C22×C8—22no—
127C22×C8—1181no—
128#125—1182no—
129#125—1182no—
130#125—1182no—
131#125—1182no—
132C2×C4⋊C4—592no—
133C2×C4⋊C4—592no—
134C2×C4⋊C4—1182no—
135C2×C4⋊C4—1182no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4—1181no—
138C2×C4⋊C4—1182no—
139C2×C4⋊C4D23612yes—
140C2×C42C22×D5911yescharacteristic
141#97—22no—
142#97—22no—
143#97—592no—
144#97—1181no—
145#95—22no—
146#95—1184no—
147#95—1182no—
148C22×C4—22no—
149C22×C4—1182no—
150C22×C4—1182no—
151C22×C4—2361no—
152C22×C4C2×D23611yescharacteristic
153C22×C4D4×D5912yes—
154C2×C8—24no—
155C2×C8—42no—
156C2×C8—42no—
157C2×C8—1182no—
158C2×C8—2361no—
159C2×C8—2361no—
160C4⋊C4—42no—
161C4⋊C4—1182no—
162C4⋊C4—1182no—
163C4⋊C4—1182no—
164C4⋊C4—1182no—
165C4⋊C4—4722no—
166C4⋊C4—2364no—
167C4⋊C4—2362no—
168C4⋊C4—2362no—
169C4⋊C4—2362no—
170C4⋊C4—2362no—
171C4⋊C4—2362no—
172C42#1174568512yes—
173C42D4×D5911yescharacteristic
174C42#1174568911yescharacteristic
175C23#1427369711yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—4722no—
184C2×C4—4721no—
185C2×C4—2362no—
186C2×C4—2362no—
187C2×C4—2362no—
188C2×C4—2362no—
189C2×C4—2362no—
190C2×C4—2362no—
191C2×C4#1427370012yes—
192C2×C4#1427370211yescharacteristic
193C2×C4#1427371212yes—
194C2×C4#1427371511yescharacteristic
195C8—44no—
196C8—2362no—
197C22#1683732011yescharacteristic
198C22#1683757612yes—
199C22#1683757711yescharacteristic
200C22#1683758211yescharacteristic
201C22#1683758612yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—9441no—
208C4—4722no—
209C4—4722no—
210C2#2142339911yescharacteristic
211C2#2142342511yescharacteristic
212C2#2142343312yes—
213C2#2142531612yes—
214C2#2142532611yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1295C2
socle, prime radicalC23×C59#120
hypercenter#1295D59
hypocenterC59#10428
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1295

Complements

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

NH ≅ G/Ntype
125. C59#10428semidirect

Maximal subgroups

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

subgroupindex
#214321642
#214250652
#214242292
C2×#168371432
C59×#12952
#1042859