Finite Group Databasebeta

← #28490027

Subgroups — #28490027

Order 15104.

500 conjugacy classes of subgroups; only the 97 normal subgroups are shown.

normal subgroups only

This group has 500 conjugacy classes of subgroups — too many to draw. Only its 97 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
1C2×#16837811C212yesmaximal
2#21432164C211yesmaximal, characteristic
3#21424915C211yesmaximal, characteristic
4C2×#16837143C212yesmaximal
5C59×#1295C211yesmaximal, characteristic
6C2×#14273727C2211yescharacteristic
7C2×#14273719C2212yes—
8#16837811—24no—
9#16837811—24no—
10C2×#14273661—22no—
11C2×#14273659—22no—
12C2×#14273650—22no—
13C2×#14273638C2211yescharacteristic
14#16837342—22no—
15#16837334—22no—
16#16837332—22no—
17#16837143—24no—
18C2×#97×C59C2212yes—
19C59×#382C2211yescharacteristic
20C22×Dic118—21no—
21C22×C59⋊C8—21no—
22#14273727—22no—
23#14273727—21no—
24#14273727D412yes—
25#14273719—22no—
26#14273719—22no—
27#14273719—22no—
28#14273719—22no—
29C2×C4⋊Dic59—22no—
30C2×C4⋊Dic59—22no—
31C2×C4⋊Dic59D412yes—
32C2×C4⋊Dic59D412yes—
33C2×Dic59⋊C4—22no—
34C2×Dic59⋊C4—22no—
35#14273661—28no—
36#14273659—28no—
37#14273650—44no—
38#14273638—22no—
39C59⋊#95—24no—
40C59⋊#95—22no—
41C22×C8×C59—22no—
42C2×C4⋊C4×C59D412yes—
43C2×C42×C59C2311yescharacteristic
44#97×C59—22no—
45#97×C59D414yes—
46#95×C59—22no—
47C22×C4×C59—22no—
48C22×C4×C59C2×D412yes—
49C22×C4×C59C2×D411yescharacteristic
50C22×Dic59—22no—
51C22×Dic59—22no—
52C22×Dic59—41no—
53C2×Dic118—22no—
54C2×Dic118—42no—
55C2×Dic118—42no—
56C2×Dic118—41no—
57C2×C8×C59—28no—
58C2×C8×C59—24no—
59C4⋊C4×C59—42no—
60C42×C59C2×D411yescharacteristic
61C42×C59C2×D412yes—
62C42×C59#4111yescharacteristic
63C4⋊Dic59—22no—
64C4⋊Dic59—24no—
65C4⋊Dic59—22no—
66C4⋊Dic59—22no—
67C4⋊Dic59—22no—
68C4⋊Dic59—42no—
69C4⋊Dic59—82no—
70Dic59⋊C4—42no—
71Dic59⋊C4—42no—
72Dic59⋊C4—42no—
73Dic59⋊C4—42no—
74C2×C59⋊C8—22no—
75C2×C59⋊C8—41no—
76C2×C59⋊C8—41no—
77C23×C59#12011yescharacteristic
78C2×C4×C59—21no—
79C2×C4×C59—21no—
80C2×C4×C59—24no—
81C2×C4×C59—42no—
82C2×C4×C59—44no—
83C2×C4×C59#12012yes—
84C2×C4×C59#12111yescharacteristic
85C2×C4×C59#12112yes—
86C2×C4×C59#12711yescharacteristic
87C2×Dic59—42no—
88C2×Dic59—42no—
89C2×Dic59—42no—
90C2×Dic59—42no—
91C2×Dic59—42no—
92C2×Dic59—44no—
93C2×Dic59—81no—
94C2×Dic59—81no—
95Dic118—44no—
96Dic118—82no—
97C8×C59—28no—
98C59⋊C8—42no—
99#10087—591nomaximal, Sylow
100C22×C59#39211yescharacteristic
101C22×C59#45311yescharacteristic
102C22×C59#45411yescharacteristic
103C22×C59#45614yes—
104C4×C59—22no—
105C4×C59—22no—
106C4×C59—21no—
107C4×C59—21no—
108C4×C59—82no—
109Dic59—82no—
110Dic59—82no—
111Dic59—82no—
112C2×#501—592no—
113#2822—591no—
114#1960—591no—
115C2×#330—592no—
116#1295D5911yescharacteristic
117C2×C59#166012yes—
118C2×C59#166312yes—
119C2×C59#200512yes—
120C2×C59#200611yescharacteristic
121C2×C4⋊Q8—591no—
122C2×#125—592no—
123#501—1184no—
124#501—1184no—
125C2×#107—1182no—
126C2×#106—1182no—
127C2×#103—1182no—
128C2×#97—591no—
129C2×#97C2×D5912yes—
130#400—1182no—
131#398—1182no—
132#398—1182no—
133#382C2×D5911yescharacteristic
134#330—1184no—
135C59#1008711yescharacteristic, complemented, Sylow
136C22×Q8—1181no—
137C22×C8—22no—
138C22×C8—1181no—
139C4⋊Q8—592no—
140C4⋊Q8—1182no—
141C4⋊Q8—1181no—
142#125—1182no—
143#125—1182no—
144#125—1182no—
145#125—1182no—
146C2×C4⋊C4—592no—
147C2×C4⋊C4—592no—
148C2×C4⋊C4—1182no—
149C2×C4⋊C4—1182no—
150C2×C4⋊C4—1182no—
151C2×C4⋊C4—1182no—
152C2×C4⋊C4D23612yes—
153C2×C42C22×D5911yescharacteristic
154#107—1188no—
155#106—1188no—
156#103—2364no—
157#97—22no—
158#97—1182no—
159#97D23614yes—
160#95—22no—
161#95—1184no—
162#95—1182no—
163C2×Q8—1182no—
164C2×Q8—2362no—
165C2×Q8—2362no—
166C2×Q8—2361no—
167C22×C4—22no—
168C22×C4—1182no—
169C22×C4—1182no—
170C22×C4—2361no—
171C22×C4C2×D23611yescharacteristic
172C22×C4D4×D5912yes—
173C2×C8—28no—
174C2×C8—24no—
175C2×C8—1182no—
176C2×C8—2361no—
177C2×C8—2361no—
178C4⋊C4—42no—
179C4⋊C4—1182no—
180C4⋊C4—1184no—
181C4⋊C4—1182no—
182C4⋊C4—1182no—
183C4⋊C4—1182no—
184C4⋊C4—4722no—
185C4⋊C4—2362no—
186C4⋊C4—2362no—
187C4⋊C4—2362no—
188C4⋊C4—2362no—
189C4⋊C4—2362no—
190C42C2×D23612yes—
191C42D4×D5911yescharacteristic
192C42#1174568911yescharacteristic
193C23#1427369711yescharacteristic
194Q8—4722no—
195Q8—2364no—
196C2×C4—21no—
197C2×C4—21no—
198C2×C4—24no—
199C2×C4—42no—
200C2×C4—44no—
201C2×C4—4721no—
202C2×C4—4721no—
203C2×C4—2362no—
204C2×C4—2362no—
205C2×C4—2362no—
206C2×C4—2362no—
207C2×C4—2362no—
208C2×C4—2364no—
209C2×C4#1427369712yes—
210C2×C4#1427370212yes—
211C2×C4#1427370211yescharacteristic
212C2×C4#1427372411yescharacteristic
213C8—28no—
214C8—2362no—
215C22#1683731211yescharacteristic
216C22#1683757211yescharacteristic
217C22#1683757711yescharacteristic
218C22#1683758614yes—
219C4—22no—
220C4—22no—
221C4—21no—
222C4—21no—
223C4—82no—
224C4—4722no—
225C4—4722no—
226C4—4722no—
227C2#2142340812yes—
228C2#2142342512yes—
229C2#2142513512yes—
230C2#2142514011yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1295C2
socle, prime radicalC23×C59#120
hypercenter#1295D59
hypocenterC59#10087
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
135. C59#10087semidirect

Maximal subgroups

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

subgroupindex
C2×#168378112
#214321642
#214249152
C2×#168371432
C59×#12952
#1008759