Finite Group Databasebeta

← #28491769

Subgroups — #28491769

Order 15104.

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

normal subgroups only

This group has 392 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#21425068C212yesmaximal
2#21424915C211yesmaximal, characteristic
3#21421977C211yesmaximal, characteristic
4#21421977C212yesmaximal
5C59×#2845C211yesmaximal, characteristic
6C2×#14273727C2211yescharacteristic
7C2×#14273650—22no—
8C2×#14273638C2211yescharacteristic
9C2×#14273638C2212yes—
10#16837164—22no—
11#16837164—22no—
12C59×#398—22no—
13C59×#398—22no—
14C59×#398—22no—
15C59×#382C2211yescharacteristic
16C59×#382C2212yes—
17C22×Dic118—21no—
18C22×C59⋊C8—21no—
19C22×C59⋊C8—22no—
20#14273727—22no—
21#14273727—21no—
22#14273727Q812yes—
23C2×C4⋊Dic59—22no—
24#14273650—44no—
25#14273638—22no—
26#14273638—22no—
27#14273638—22no—
28C2×C4⋊C4×C59—22no—
29C2×C4⋊C4×C59—22no—
30C2×C4⋊C4×C59—22no—
31C2×C4⋊C4×C59D412yes—
32C2×C4⋊C4×C59D412yes—
33C2×C4⋊C4×C59D412yes—
34C2×C42×C59C2311yescharacteristic
35#95×C59—22no—
36#95×C59—22no—
37#95×C59—22no—
38#95×C59—22no—
39C22×C4×C59—22no—
40C22×C4×C59—22no—
41C22×C4×C59—22no—
42C22×C4×C59C2×D412yes—
43C22×C4×C59C2×D411yescharacteristic
44C22×Dic59—41no—
45C2×Dic118—22no—
46C2×Dic118—42no—
47C2×Dic118—42no—
48C2×Dic118—41no—
49C4⋊C4×C59—42no—
50C4⋊C4×C59—42no—
51C4⋊C4×C59—42no—
52C4⋊C4×C59—82no—
53C4⋊C4×C59—82no—
54C4⋊C4×C59—82no—
55C42×C59C2×Q811yescharacteristic
56C42×C59#4112yes—
57C42×C59#4111yescharacteristic
58C4⋊Dic59—24no—
59C4⋊Dic59—42no—
60C2×C59⋊C8—22no—
61C2×C59⋊C8—24no—
62C2×C59⋊C8—41no—
63C2×C59⋊C8—42no—
64C2×C59⋊C8—42no—
65C2×C59⋊C8—41no—
66C23×C59#12011yescharacteristic
67C2×C4×C59—21no—
68C2×C4×C59—21no—
69C2×C4×C59—22no—
70C2×C4×C59—22no—
71C2×C4×C59—42no—
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×C59C22⋊Q812yes—
81C2×C4×C59C22⋊Q811yescharacteristic
82C2×C4×C59#12412yes—
83C2×C4×C59#12411yescharacteristic
84C2×Dic59—42no—
85C2×Dic59—81no—
86C2×Dic59—81no—
87Dic118—44no—
88Dic118—82no—
89C59⋊C8—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—
103C4×C59—82no—
104Dic59—82no—
105#2845D5911yescharacteristic
106#1993—592no—
107#1960—591no—
108#1295—591no—
109#1295—592no—
110C2×C59#166112yes—
111C2×C59#166211yescharacteristic
112C2×C59#166311yescharacteristic
113C2×C59#202711yescharacteristic
114C2×C59#202812yes—
115C2×C4⋊Q8—591no—
116C2×#103—1182no—
117C2×#97—591no—
118C2×#97—592no—
119#398—22no—
120#398—22no—
121#398—22no—
122#382C2×D5911yescharacteristic
123#382C2×D5912yes—
124#340—1182no—
125#340—1182no—
126C59#1036111yescharacteristic, complemented, Sylow
127C22×Q8—1181no—
128C22×C8—1182no—
129C22×C8—1181no—
130C4⋊Q8—592no—
131C4⋊Q8—1182no—
132C4⋊Q8—1181no—
133C2×C4⋊C4—22no—
134C2×C4⋊C4—22no—
135C2×C4⋊C4—22no—
136C2×C4⋊C4—1182no—
137C2×C4⋊C4C22⋊D5912yes—
138C2×C4⋊C4C22⋊D5912yes—
139C2×C4⋊C4C22⋊D5912yes—
140C2×C42C22×D5911yescharacteristic
141#103—2364no—
142#97—1182no—
143#97—1182no—
144#97—1182no—
145#95—22no—
146#95—22no—
147#95—22no—
148#95—22no—
149C2×Q8—1182no—
150C2×Q8—2362no—
151C2×Q8—2362no—
152C2×Q8—2361no—
153C22×C4—22no—
154C22×C4—22no—
155C22×C4—22no—
156C22×C4—2361no—
157C22×C4C2×C22⋊D5912yes—
158C22×C4C2×C22⋊D5911yescharacteristic
159C2×C8—1182no—
160C2×C8—1184no—
161C2×C8—2361no—
162C2×C8—2362no—
163C2×C8—2362no—
164C2×C8—2361no—
165C4⋊C4—42no—
166C4⋊C4—42no—
167C4⋊C4—42no—
168C4⋊C4—82no—
169C4⋊C4—82no—
170C4⋊C4—82no—
171C4⋊C4—1184no—
172C4⋊C4—2362no—
173C42Q8×D5911yescharacteristic
174C42#1174568912yes—
175C42#1174568911yescharacteristic
176C23#1427369611yescharacteristic
177Q8—4722no—
178Q8—2364no—
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—42no—
188C2×C4—42no—
189C2×C4—42no—
190C2×C4—42no—
191C2×C4—42no—
192C2×C4—4721no—
193C2×C4—4721no—
194C2×C4—2362no—
195C2×C4#1427370312yes—
196C2×C4#1427370311yescharacteristic
197C2×C4#1427371612yes—
198C2×C4#1427371611yescharacteristic
199C8—2362no—
200C8—2364no—
201C22#1683731311yescharacteristic
202C22#1683757011yescharacteristic
203C22#1683757511yescharacteristic
204C22#1683758012yes—
205C22#1683758512yes—
206C4—21no—
207C4—21no—
208C4—22no—
209C4—22no—
210C4—82no—
211C4—82no—
212C4—82no—
213C4—4722no—
214C2#2142341312yes—
215C2#2142341911yescharacteristic
216C2#2142342411yescharacteristic
217C2#2142524911yescharacteristic
218C2#2142525412yes—
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2845C2
socle, prime radicalC23×C59#120
hypercenter#2845D59
hypocenterC59#10361
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C23 ◁ C2×C42 ◁ #2845

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
#214250682
#214249152
#214219772
C59×#28452
#1036159