Finite Group Databasebeta

← #28492189

Subgroups — #28492189

Order 15104.

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

normal subgroups only

This group has 402 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#21424265C211yesmaximal, characteristic
4C2×#16837143C212yesmaximal
5C59×#1295C211yesmaximal, characteristic
6C2×#14273719C2212yes—
7C2×#14273660—21no—
8C2×#14273658—21no—
9C2×#14273638C2211yescharacteristic
10#16837342—22no—
11#16837334—22no—
12#16837332—21no—
13#16837332—21no—
14#16837272C2211yescharacteristic
15#16837165—22no—
16#16837165—22no—
17#16837143—24no—
18C2×#97×C59C2212yes—
19C59×#382C2211yescharacteristic
20C22×C59⋊C8—21no—
21#14273719—22no—
22#14273719—22no—
23#14273719—22no—
24#14273719—22no—
25C2×C4⋊Dic59—22no—
26C2×C4⋊Dic59—21no—
27C2×C4⋊Dic59—21no—
28C2×C4⋊Dic59—21no—
29C2×C4⋊Dic59D412yes—
30C2×C4⋊Dic59D412yes—
31C2×Dic59⋊C4—22no—
32C2×Dic59⋊C4—22no—
33#14273660—42no—
34#14273658—42no—
35#14273638—21no—
36#14273638D412yes—
37C59⋊#95—22no—
38C59⋊#95—22no—
39C59⋊#95—21no—
40C59⋊#95—21no—
41C22×C8×C59—22no—
42C2×C4⋊C4×C59D411yescharacteristic
43C2×C4⋊C4×C59D411yescharacteristic
44C2×C42×C59C2311yescharacteristic
45#97×C59—22no—
46#97×C59—22no—
47#95×C59—22no—
48C22×C4×C59—21no—
49C22×C4×C59—21no—
50C22×C4×C59C2×D412yes—
51C22×C4×C59C2×D411yescharacteristic
52C22×Dic59—22no—
53C22×Dic59—22no—
54C22×Dic59—41no—
55C2×C8×C59—24no—
56C2×C8×C59—42no—
57C2×C8×C59—42no—
58C4⋊C4×C59—41no—
59C4⋊C4×C59—41no—
60C42×C59C2×D411yescharacteristic
61C42×C59#4111yescharacteristic
62C42×C59#4112yes—
63C4⋊Dic59—22no—
64C4⋊Dic59—22no—
65C4⋊Dic59—22no—
66C4⋊Dic59—22no—
67C4⋊Dic59—41no—
68C4⋊Dic59—41no—
69C4⋊Dic59—44no—
70C4⋊Dic59—81no—
71C4⋊Dic59—81no—
72Dic59⋊C4—42no—
73Dic59⋊C4—42no—
74Dic59⋊C4—42no—
75Dic59⋊C4—42no—
76C2×C59⋊C8—22no—
77C2×C59⋊C8—22no—
78C2×C59⋊C8—22no—
79C23×C59#12011yescharacteristic
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—21no—
83C2×C4×C59—22no—
84C2×C4×C59—41no—
85C2×C4×C59—41no—
86C2×C4×C59—42no—
87C2×C4×C59—42no—
88C2×C4×C59#12112yes—
89C2×C4×C59#12111yescharacteristic
90C2×C4×C59#12312yes—
91C2×C4×C59#12411yescharacteristic
92C2×Dic59—42no—
93C2×Dic59—42no—
94C2×Dic59—42no—
95C2×Dic59—42no—
96C2×Dic59—42no—
97C2×Dic59—42no—
98C2×Dic59—81no—
99C2×Dic59—82no—
100C8×C59—44no—
101C59⋊C8—24no—
102#10429—591nomaximal, Sylow
103C22×C59#39411yescharacteristic
104C22×C59#45311yescharacteristic
105C22×C59#45412yes—
106C22×C59#45612yes—
107C22×C59#45611yescharacteristic
108C4×C59—22no—
109C4×C59—22no—
110C4×C59—21no—
111C4×C59—21no—
112C4×C59—81no—
113C4×C59—81no—
114Dic59—82no—
115Dic59—82no—
116Dic59—161no—
117#2822—591no—
118#1992—592no—
119#1847—591no—
120C2×#330—592no—
121#1295D5911yescharacteristic
122C2×C59#165711yescharacteristic
123C2×C59#166011yescharacteristic
124C2×C59#166312yes—
125C2×C59#203812yes—
126C2×C59#203911yescharacteristic
127C2×#125—592no—
128C2×#107—1181no—
129C2×#106—1181no—
130C2×#97—591no—
131C2×#97C2×D5912yes—
132#400—1182no—
133#398—1182no—
134#398—1181no—
135#398—1181no—
136#384—591no—
137#382C2×D5911yescharacteristic
138#340—1182no—
139#340—1182no—
140#330—1184no—
141C59#1042911yescharacteristic, complemented, Sylow
142C22×C8—22no—
143C22×C8—1181no—
144#125—1182no—
145#125—1182no—
146#125—1182no—
147#125—1182no—
148C2×C4⋊C4—592no—
149C2×C4⋊C4—592no—
150C2×C4⋊C4—1181no—
151C2×C4⋊C4—1181no—
152C2×C4⋊C4—1182no—
153C2×C4⋊C4—1182no—
154C2×C4⋊C4—1181no—
155C2×C4⋊C4—1182no—
156C2×C4⋊C4D23611yescharacteristic
157C2×C4⋊C4D23611yescharacteristic
158C2×C42C22×D5911yescharacteristic
159#107—2362no—
160#106—2362no—
161#97—22no—
162#97—22no—
163#97—592no—
164#97—1181no—
165#95—22no—
166#95—1182no—
167#95—1182no—
168#95—1181no—
169#95—1181no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—1182no—
173C22×C4—1182no—
174C22×C4—2361no—
175C22×C4C2×D23611yescharacteristic
176C22×C4D4×D5912yes—
177C2×C8—24no—
178C2×C8—42no—
179C2×C8—42no—
180C2×C8—1182no—
181C2×C8—1182no—
182C2×C8—1182no—
183C4⋊C4—41no—
184C4⋊C4—41no—
185C4⋊C4—1182no—
186C4⋊C4—1182no—
187C4⋊C4—1182no—
188C4⋊C4—1182no—
189C4⋊C4—4721no—
190C4⋊C4—4721no—
191C4⋊C4—2361no—
192C4⋊C4—2361no—
193C4⋊C4—2364no—
194C4⋊C4—2362no—
195C4⋊C4—2362no—
196C4⋊C4—2362no—
197C4⋊C4—2362no—
198C42#1174568512yes—
199C42D4×D5911yescharacteristic
200C42#1174568911yescharacteristic
201C23#1427369711yescharacteristic
202C2×C4—21no—
203C2×C4—22no—
204C2×C4—22no—
205C2×C4—21no—
206C2×C4—41no—
207C2×C4—41no—
208C2×C4—42no—
209C2×C4—42no—
210C2×C4—4721no—
211C2×C4—4722no—
212C2×C4—2362no—
213C2×C4—2362no—
214C2×C4—2362no—
215C2×C4—2362no—
216C2×C4—2362no—
217C2×C4—2362no—
218C2×C4#1427370012yes—
219C2×C4#1427370211yescharacteristic
220C2×C4#1427371212yes—
221C2×C4#1427371511yescharacteristic
222C8—44no—
223C8—1184no—
224C22#1683732011yescharacteristic
225C22#1683757211yescharacteristic
226C22#1683757612yes—
227C22#1683758612yes—
228C22#1683758711yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—9441no—
236C4—4722no—
237C4—4722no—
238C2#2142339511yescharacteristic
239C2#2142340811yescharacteristic
240C2#2142342612yes—
241C2#2142531612yes—
242C2#2142532111yescharacteristic
subgroupG/H
centerC23#14273697
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1295C2
socle, prime radicalC23×C59#120
hypercenter#1295D59
hypocenterC59#10429
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
141. C59#10429semidirect

Maximal subgroups

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

subgroupindex
#214321642
#214250652
#214242652
C2×#168371432
C59×#12952
#1042959