Finite Group Databasebeta

← #28492180

Subgroups — #28492180

Order 15104.

386 conjugacy classes of subgroups; only the 93 normal subgroups are shown.

normal subgroups only

This group has 386 conjugacy classes of subgroups — too many to draw. Only its 93 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#21425066C212yesmaximal
2#21424229C211yesmaximal, characteristic
3C2×#16837144C212yesmaximal
4#21421977C211yesmaximal, characteristic
5C59×#2822C211yesmaximal, characteristic
6C2×#14273638C2212yes—
7C2×#14273638C2211yescharacteristic
8#16837272C2211yescharacteristic
9#16837164—22no—
10#16837164—22no—
11#16837164—22no—
12#16837144—24no—
13C2×#125×C59C2212yes—
14C59×#400—22no—
15C59×#398—22no—
16C59×#398—22no—
17C59×#382C2211yescharacteristic
18C22×C59⋊C8—22no—
19C22×C59⋊C8—21no—
20C2×C4⋊Dic59—22no—
21C2×C4⋊Dic59—21no—
22#14273638—21no—
23#14273638—22no—
24#14273638—22no—
25#14273638D412yes—
26#125×C59—22no—
27#125×C59—22no—
28#125×C59—22no—
29#125×C59—22no—
30C2×C4⋊C4×C59—22no—
31C2×C4⋊C4×C59—22no—
32C2×C4⋊C4×C59—22no—
33C2×C4⋊C4×C59D412yes—
34C2×C4⋊C4×C59D412yes—
35C2×C4⋊C4×C59D412yes—
36C2×C42×C59C2311yescharacteristic
37#95×C59—24no—
38#95×C59—22no—
39#95×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59—22no—
42C22×C4×C59—22no—
43C22×C4×C59C2×D412yes—
44C22×C4×C59C2×D411yescharacteristic
45C22×Dic59—41no—
46C4⋊C4×C59—22no—
47C4⋊C4×C59—22no—
48C4⋊C4×C59—22no—
49C4⋊C4×C59—22no—
50C4⋊C4×C59—42no—
51C4⋊C4×C59—42no—
52C4⋊C4×C59—42no—
53C4⋊C4×C59—42no—
54C4⋊C4×C59—42no—
55C4⋊C4×C59—82no—
56C42×C59C2×D411yescharacteristic
57C42×C59#4111yescharacteristic
58C42×C59#4112yes—
59C4⋊Dic59—42no—
60C4⋊Dic59—44no—
61C2×C59⋊C8—24no—
62C2×C59⋊C8—22no—
63C2×C59⋊C8—42no—
64C2×C59⋊C8—41no—
65C2×C59⋊C8—41no—
66C2×C59⋊C8—42no—
67C23×C59#12011yescharacteristic
68C2×C4×C59—22no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—42no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—42no—
76C2×C4×C59—42no—
77C2×C4×C59—42no—
78C2×C4×C59—42no—
79C2×C4×C59—42no—
80C2×C4×C59—42no—
81C2×C4×C59#12111yescharacteristic
82C2×C4×C59#12112yes—
83C2×C4×C59#12312yes—
84C2×C4×C59#12411yescharacteristic
85C2×Dic59—81no—
86C2×Dic59—82no—
87C59⋊C8—44no—
88C59⋊C8—42no—
89#10428—591nomaximal, Sylow
90C22×C59#39411yescharacteristic
91C22×C59#45411yescharacteristic
92C22×C59#45412yes—
93C22×C59#45511yescharacteristic
94C22×C59#45612yes—
95C4×C59—22no—
96C4×C59—22no—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—82no—
100C4×C59—82no—
101C4×C59—82no—
102Dic59—161no—
103#2822D5911yescharacteristic
104#1992—592no—
105#1836—591no—
106C2×#330—592no—
107#1295—591no—
108C2×C59#165811yescharacteristic
109C2×C59#166311yescharacteristic
110C2×C59#166412yes—
111C2×C59#203812yes—
112C2×C59#204011yescharacteristic
113C2×#125C2×D5912yes—
114C2×#97—591no—
115C2×#97—592no—
116#400—22no—
117#398—22no—
118#398—22no—
119#384—591no—
120#382C2×D5911yescharacteristic
121#340—1182no—
122#340—1182no—
123#340—1182no—
124#330—1184no—
125C59#1042811yescharacteristic, complemented, Sylow
126C22×C8—1182no—
127C22×C8—1181no—
128#125—22no—
129#125—22no—
130#125—22no—
131#125—22no—
132C2×C4⋊C4—22no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—1181no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4C22⋊D5912yes—
138C2×C4⋊C4C22⋊D5912yes—
139C2×C4⋊C4C22⋊D5912yes—
140C2×C42C22×D5911yescharacteristic
141#97—592no—
142#97—1182no—
143#97—1181no—
144#97—1182no—
145#95—24no—
146#95—22no—
147#95—22no—
148C22×C4—22no—
149C22×C4—22no—
150C22×C4—22no—
151C22×C4—2361no—
152C22×C4C2×C22⋊D5911yescharacteristic
153C22×C4C2×C22⋊D5912yes—
154C2×C8—1184no—
155C2×C8—1182no—
156C2×C8—2362no—
157C2×C8—2361no—
158C2×C8—2361no—
159C2×C8—2362no—
160C4⋊C4—22no—
161C4⋊C4—22no—
162C4⋊C4—22no—
163C4⋊C4—22no—
164C4⋊C4—42no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—42no—
169C4⋊C4—82no—
170C4⋊C4—2364no—
171C4⋊C4—2362no—
172C42D4×D5911yescharacteristic
173C42#1174568711yescharacteristic
174C42#1174568712yes—
175C23#1427369611yescharacteristic
176C2×C4—22no—
177C2×C4—21no—
178C2×C4—21no—
179C2×C4—22no—
180C2×C4—42no—
181C2×C4—42no—
182C2×C4—42no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—42no—
188C2×C4—42no—
189C2×C4—4721no—
190C2×C4—4722no—
191C2×C4#1427369811yescharacteristic
192C2×C4#1427369912yes—
193C2×C4#1427370812yes—
194C2×C4#1427371411yescharacteristic
195C8—2364no—
196C8—2362no—
197C22#1683731611yescharacteristic
198C22#1683757511yescharacteristic
199C22#1683757512yes—
200C22#1683758011yescharacteristic
201C22#1683758512yes—
202C4—22no—
203C4—22no—
204C4—21no—
205C4—21no—
206C4—82no—
207C4—82no—
208C4—82no—
209C4—9441no—
210C2#2142339811yescharacteristic
211C2#2142342411yescharacteristic
212C2#2142343012yes—
213C2#2142531012yes—
214C2#2142532211yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2822C2
socle, prime radicalC23×C59#120
hypercenter#2822D59
hypocenterC59#10428
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2822

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
#214250662
#214242292
C2×#168371442
#214219772
C59×#28222
#1042859