Finite Group Databasebeta

← #28491770

Subgroups — #28491770

Order 15104.

392 conjugacy classes of subgroups; only the 91 normal subgroups are shown.

normal subgroups only

This group has 392 conjugacy classes of subgroups — too many to draw. Only its 91 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#21432371C211yesmaximal, characteristic
2#21425070C212yesmaximal
3#21421978C212yesmaximal
4#21421977C211yesmaximal, characteristic
5C59×#1960C211yesmaximal, characteristic
6C2×#14273638C2212yes—
7#16837336—22no—
8#16837335—22no—
9#16837334—22no—
10#16837268C2212yes—
11#16837164—22no—
12#16837164—22no—
13C2×C4⋊Q8×C59C2211yescharacteristic
14C2×#103×C59—22no—
15C2×#97×C59C2211yescharacteristic
16C59×#382C2211yescharacteristic
17C22×C59⋊C8—22no—
18C2×C4⋊Dic59—22no—
19C2×C4⋊Dic59D412yes—
20C2×C4⋊Dic59D412yes—
21C2×Dic59⋊C4—22no—
22C2×Dic59⋊C4—22no—
23#14273638—22no—
24#14273638—22no—
25C59⋊#95—22no—
26C59⋊#95—22no—
27C59⋊#95—22no—
28C22×Q8×C59—21no—
29C22×C8×C59—21no—
30C4⋊Q8×C59—22no—
31C4⋊Q8×C59—21no—
32C4⋊Q8×C59Q812yes—
33C2×C4⋊C4×C59—22no—
34C2×C4⋊C4×C59D412yes—
35C2×C42×C59C2311yescharacteristic
36#103×C59—44no—
37#97×C59—22no—
38#95×C59—22no—
39C2×Q8×C59—22no—
40C2×Q8×C59—42no—
41C2×Q8×C59—42no—
42C2×Q8×C59—41no—
43C22×C4×C59—22no—
44C22×C4×C59—41no—
45C22×C4×C59C2×D412yes—
46C22×C4×C59C2×D411yescharacteristic
47C22×Dic59—22no—
48C22×Dic59—22no—
49C2×C8×C59—22no—
50C2×C8×C59—41no—
51C2×C8×C59—41no—
52C4⋊C4×C59—24no—
53C4⋊C4×C59—42no—
54C4⋊C4×C59—42no—
55C42×C59C2×Q811yescharacteristic
56C42×C59#4111yescharacteristic
57C42×C59#4112yes—
58C4⋊Dic59—42no—
59C4⋊Dic59—42no—
60C4⋊Dic59—82no—
61Dic59⋊C4—82no—
62Dic59⋊C4—82no—
63C2×C59⋊C8—24no—
64C2×C59⋊C8—42no—
65C2×C59⋊C8—42no—
66C23×C59#12011yescharacteristic
67Q8×C59—44no—
68Q8×C59—82no—
69C2×C4×C59—21no—
70C2×C4×C59—21no—
71C2×C4×C59—22no—
72C2×C4×C59—22no—
73C2×C4×C59—42no—
74C2×C4×C59—42no—
75C2×C4×C59—42no—
76C2×C4×C59—42no—
77C2×C4×C59—81no—
78C2×C4×C59—81no—
79C2×C4×C59C22⋊Q812yes—
80C2×C4×C59C22⋊Q811yescharacteristic
81C2×C4×C59#12412yes—
82C2×C4×C59#12411yescharacteristic
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—42no—
86C2×Dic59—42no—
87C2×Dic59—42no—
88C2×Dic59—42no—
89C8×C59—42no—
90C59⋊C8—44no—
91#10361—591nomaximal, Sylow
92C22×C59#39311yescharacteristic
93C22×C59#45311yescharacteristic
94C22×C59#45411yescharacteristic
95C22×C59#45512yes—
96C22×C59#45612yes—
97C4×C59—21no—
98C4×C59—21no—
99C4×C59—22no—
100C4×C59—22no—
101C4×C59—82no—
102C4×C59—82no—
103Dic59—82no—
104Dic59—82no—
105#2845—591no—
106#1993—592no—
107#1960D5911yescharacteristic
108#1295—592no—
109#1295—591no—
110C2×C59#166112yes—
111C2×C59#166211yescharacteristic
112C2×C59#166311yescharacteristic
113C2×C59#202711yescharacteristic
114C2×C59#202812yes—
115C2×C4⋊Q8C2×D5911yescharacteristic
116C2×#103—22no—
117C2×#97—592no—
118C2×#97C2×D5911yescharacteristic
119#398—1182no—
120#398—1182no—
121#398—1182no—
122#382—592no—
123#382C2×D5911yescharacteristic
124#340—1182no—
125#340—1182no—
126C59#1036111yescharacteristic, complemented, Sylow
127C22×Q8—21no—
128C22×C8—21no—
129C22×C8—1182no—
130C4⋊Q8—21no—
131C4⋊Q8—22no—
132C4⋊Q8Dic11812yes—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—592no—
135C2×C4⋊C4—592no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4—1182no—
138C2×C4⋊C4—1182no—
139C2×C4⋊C4C22⋊D5912yes—
140C2×C42C22×D5911yescharacteristic
141#103—44no—
142#97—22no—
143#97—1182no—
144#97—1182no—
145#95—22no—
146#95—1182no—
147#95—1182no—
148#95—1182no—
149C2×Q8—22no—
150C2×Q8—42no—
151C2×Q8—42no—
152C2×Q8—41no—
153C22×C4—22no—
154C22×C4—41no—
155C22×C4—1182no—
156C22×C4—1182no—
157C22×C4D4×D5912yes—
158C22×C4C2×C22⋊D5911yescharacteristic
159C2×C8—22no—
160C2×C8—41no—
161C2×C8—41no—
162C2×C8—1184no—
163C2×C8—2362no—
164C2×C8—2362no—
165C4⋊C4—24no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—4722no—
169C4⋊C4—4722no—
170C4⋊C4—4722no—
171C4⋊C4—2362no—
172C4⋊C4—2362no—
173C42C2×Dic11811yescharacteristic
174C42#1174568511yescharacteristic
175C42#1174568712yes—
176C23#1427369511yescharacteristic
177Q8—44no—
178Q8—82no—
179C2×C4—21no—
180C2×C4—21no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—42no—
184C2×C4—42no—
185C2×C4—42no—
186C2×C4—42no—
187C2×C4—81no—
188C2×C4—81no—
189C2×C4—2362no—
190C2×C4—2362no—
191C2×C4—2362no—
192C2×C4—2362no—
193C2×C4—2362no—
194C2×C4—2362no—
195C2×C4#1427370412yes—
196C2×C4#1427370611yescharacteristic
197C2×C4#1427371312yes—
198C2×C4#1427371411yescharacteristic
199C8—42no—
200C8—2364no—
201C22#1683731411yescharacteristic
202C22#1683756911yescharacteristic
203C22#1683757411yescharacteristic
204C22#1683757812yes—
205C22#1683758312yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—4722no—
213C4—4722no—
214C2#2142341012yes—
215C2#2142341711yescharacteristic
216C2#2142342211yescharacteristic
217C2#2142525211yescharacteristic
218C2#2142525512yes—
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1960C2
socle, prime radicalC23×C59#120
hypercenter#1960D59
hypocenterC59#10361
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1960

Complements

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

NH ≅ G/Ntype
126. C59#10361semidirect

Maximal subgroups

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

subgroupindex
#214323712
#214250702
#214219782
#214219772
C59×#19602
#1036159