Finite Group Databasebeta

← #28492185

Subgroups — #28492185

Order 15104.

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

normal subgroups only

This group has 402 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#21424265C211yesmaximal, characteristic
3C2×#16837144C212yesmaximal
4#21421977C211yesmaximal, characteristic
5C59×#2822C211yesmaximal, characteristic
6C2×#14273660—21no—
7C2×#14273658—21no—
8C2×#14273638C2212yes—
9C2×#14273638C2211yescharacteristic
10#16837272C2211yescharacteristic
11#16837164—22no—
12#16837164—22no—
13#16837144—24no—
14C2×#125×C59C2212yes—
15C59×#400—22no—
16C59×#398—21no—
17C59×#398—21no—
18C59×#398—22no—
19C59×#382C2211yescharacteristic
20C22×C59⋊C8—21no—
21C22×C59⋊C8—22no—
22C2×C4⋊Dic59—22no—
23C2×C4⋊Dic59—21no—
24#14273660—42no—
25#14273658—42no—
26#14273638—21no—
27#14273638—22no—
28#14273638—22no—
29#14273638D412yes—
30#125×C59—22no—
31#125×C59—22no—
32#125×C59—22no—
33#125×C59—22no—
34C2×C4⋊C4×C59—22no—
35C2×C4⋊C4×C59—22no—
36C2×C4⋊C4×C59—21no—
37C2×C4⋊C4×C59—21no—
38C2×C4⋊C4×C59D412yes—
39C2×C4⋊C4×C59D412yes—
40C2×C4⋊C4×C59D411yescharacteristic
41C2×C4⋊C4×C59D411yescharacteristic
42C2×C42×C59C2311yescharacteristic
43#95×C59—22no—
44#95×C59—22no—
45#95×C59—21no—
46#95×C59—21no—
47#95×C59—22no—
48C22×C4×C59—21no—
49C22×C4×C59—21no—
50C22×C4×C59—22no—
51C22×C4×C59—22no—
52C22×C4×C59C2×D412yes—
53C22×C4×C59C2×D411yescharacteristic
54C22×Dic59—41no—
55C4⋊C4×C59—22no—
56C4⋊C4×C59—22no—
57C4⋊C4×C59—22no—
58C4⋊C4×C59—22no—
59C4⋊C4×C59—41no—
60C4⋊C4×C59—41no—
61C4⋊C4×C59—42no—
62C4⋊C4×C59—42no—
63C4⋊C4×C59—42no—
64C4⋊C4×C59—42no—
65C4⋊C4×C59—81no—
66C4⋊C4×C59—81no—
67C42×C59C2×D411yescharacteristic
68C42×C59#4111yescharacteristic
69C42×C59#4112yes—
70C4⋊Dic59—41no—
71C4⋊Dic59—41no—
72C4⋊Dic59—44no—
73C2×C59⋊C8—22no—
74C2×C59⋊C8—22no—
75C2×C59⋊C8—22no—
76C2×C59⋊C8—24no—
77C2×C59⋊C8—42no—
78C2×C59⋊C8—42no—
79C23×C59#12011yescharacteristic
80C2×C4×C59—21no—
81C2×C4×C59—22no—
82C2×C4×C59—22no—
83C2×C4×C59—21no—
84C2×C4×C59—42no—
85C2×C4×C59—42no—
86C2×C4×C59—41no—
87C2×C4×C59—41no—
88C2×C4×C59—42no—
89C2×C4×C59—42no—
90C2×C4×C59—42no—
91C2×C4×C59—42no—
92C2×C4×C59—42no—
93C2×C4×C59—42no—
94C2×C4×C59#12111yescharacteristic
95C2×C4×C59#12112yes—
96C2×C4×C59#12312yes—
97C2×C4×C59#12411yescharacteristic
98C2×Dic59—81no—
99C2×Dic59—82no—
100C59⋊C8—24no—
101C59⋊C8—44no—
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—
114C4×C59—82no—
115C4×C59—82no—
116Dic59—161no—
117#2822D5911yescharacteristic
118#1992—592no—
119#1847—591no—
120C2×#330—592no—
121#1295—591no—
122C2×C59#165711yescharacteristic
123C2×C59#166011yescharacteristic
124C2×C59#166312yes—
125C2×C59#203812yes—
126C2×C59#203911yescharacteristic
127C2×#125C2×D5912yes—
128C2×#107—1181no—
129C2×#106—1181no—
130C2×#97—591no—
131C2×#97—592no—
132#400—22no—
133#398—21no—
134#398—21no—
135#398—22no—
136#384—591no—
137#382C2×D5911yescharacteristic
138#340—1182no—
139#340—1182no—
140#330—1184no—
141C59#1042911yescharacteristic, complemented, Sylow
142C22×C8—1181no—
143C22×C8—1182no—
144#125—22no—
145#125—22no—
146#125—22no—
147#125—22no—
148C2×C4⋊C4—22no—
149C2×C4⋊C4—22no—
150C2×C4⋊C4—21no—
151C2×C4⋊C4—21no—
152C2×C4⋊C4—1182no—
153C2×C4⋊C4—1181no—
154C2×C4⋊C4C22⋊D5912yes—
155C2×C4⋊C4C22⋊D5912yes—
156C2×C4⋊C4C22⋊D5911yescharacteristic
157C2×C4⋊C4C22⋊D5911yescharacteristic
158C2×C42C22×D5911yescharacteristic
159#107—2362no—
160#106—2362no—
161#97—592no—
162#97—1182no—
163#97—1181no—
164#97—1182no—
165#95—22no—
166#95—22no—
167#95—21no—
168#95—21no—
169#95—22no—
170C22×C4—21no—
171C22×C4—21no—
172C22×C4—22no—
173C22×C4—22no—
174C22×C4—2361no—
175C22×C4C2×C22⋊D5911yescharacteristic
176C22×C4C2×C22⋊D5912yes—
177C2×C8—1182no—
178C2×C8—1182no—
179C2×C8—1182no—
180C2×C8—1184no—
181C2×C8—2362no—
182C2×C8—2362no—
183C4⋊C4—22no—
184C4⋊C4—22no—
185C4⋊C4—22no—
186C4⋊C4—22no—
187C4⋊C4—41no—
188C4⋊C4—41no—
189C4⋊C4—42no—
190C4⋊C4—42no—
191C4⋊C4—42no—
192C4⋊C4—42no—
193C4⋊C4—81no—
194C4⋊C4—81no—
195C4⋊C4—2361no—
196C4⋊C4—2361no—
197C4⋊C4—2364no—
198C42D4×D5911yescharacteristic
199C42#1174568711yescharacteristic
200C42#1174568712yes—
201C23#1427369611yescharacteristic
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—42no—
211C2×C4—42no—
212C2×C4—42no—
213C2×C4—42no—
214C2×C4—42no—
215C2×C4—42no—
216C2×C4—4721no—
217C2×C4—4722no—
218C2×C4#1427369811yescharacteristic
219C2×C4#1427369912yes—
220C2×C4#1427370812yes—
221C2×C4#1427371411yescharacteristic
222C8—1184no—
223C8—2364no—
224C22#1683731611yescharacteristic
225C22#1683757011yescharacteristic
226C22#1683757512yes—
227C22#1683758512yes—
228C22#1683758511yescharacteristic
229C4—22no—
230C4—22no—
231C4—21no—
232C4—21no—
233C4—81no—
234C4—81no—
235C4—82no—
236C4—82no—
237C4—9441no—
238C2#2142339411yescharacteristic
239C2#2142340711yescharacteristic
240C2#2142342412yes—
241C2#2142531012yes—
242C2#2142531711yescharacteristic
subgroupG/H
centerC23#14273696
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2822C2
socle, prime radicalC23×C59#120
hypercenter#2822D59
hypocenterC59#10429
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
141. C59#10429semidirect

Maximal subgroups

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

subgroupindex
#214250662
#214242652
C2×#168371442
#214219772
C59×#28222
#1042959