Finite Group Databasebeta

← #28491762

Subgroups — #28491762

Order 15104.

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

normal subgroups only

This group has 400 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#21432368C211yesmaximal, characteristic
2#21425070C212yesmaximal
3#21421978C212yesmaximal
4#21421977C211yesmaximal, characteristic
5C59×#1960C211yesmaximal, characteristic
6C2×#14273638C2212yes—
7#16837344—22no—
8#16837341—21no—
9#16837323—22no—
10#16837322—21no—
11#16837268C2212yes—
12#16837164—22no—
13#16837164—22no—
14C2×C4⋊Q8×C59C2211yescharacteristic
15C2×#103×C59—21no—
16C2×#103×C59—21no—
17C2×#97×C59C2211yescharacteristic
18C59×#382C2211yescharacteristic
19C22×Dic118—21no—
20C22×C59⋊C8—22no—
21C2×C4⋊Dic59—21no—
22C2×C4⋊Dic59D412yes—
23C2×C4⋊Dic59D412yes—
24C2×Dic59⋊C4—22no—
25#14273638—22no—
26#14273638—22no—
27C59⋊#95—21no—
28C59⋊#95—22no—
29C59⋊#95—21no—
30C59⋊#95—22no—
31C59⋊#95—22no—
32C22×Q8×C59—21no—
33C22×C8×C59—21no—
34C4⋊Q8×C59—22no—
35C4⋊Q8×C59—21no—
36C4⋊Q8×C59Q812yescomplemented
37C2×C4⋊C4×C59—22no—
38C2×C4⋊C4×C59D411yescharacteristic
39C2×C4⋊C4×C59D411yescharacteristic
40C2×C42×C59C2311yescharacteristic
41#103×C59—42no—
42#103×C59—42no—
43#97×C59—22no—
44#95×C59—22no—
45C2×Q8×C59—22no—
46C2×Q8×C59—41no—
47C2×Q8×C59—41no—
48C2×Q8×C59—41no—
49C2×Q8×C59—41no—
50C2×Q8×C59—41no—
51C22×C4×C59—21no—
52C22×C4×C59—21no—
53C22×C4×C59—41no—
54C22×C4×C59C2×D412yes—
55C22×C4×C59C2×D411yescharacteristic
56C22×Dic59—22no—
57C22×Dic59—22no—
58C2×Dic118—81no—
59C2×Dic118—82no—
60C2×C8×C59—22no—
61C2×C8×C59—41no—
62C2×C8×C59—41no—
63C4⋊C4×C59—24no—
64C4⋊C4×C59—41no—
65C4⋊C4×C59—41no—
66C4⋊C4×C59—42no—
67C42×C59C2×Q811yescharacteristic
68C42×C59#4111yescharacteristic
69C42×C59#4112yes—
70C4⋊Dic59—42no—
71C4⋊Dic59—42no—
72C4⋊Dic59—81no—
73Dic59⋊C4—82no—
74C2×C59⋊C8—24no—
75C2×C59⋊C8—42no—
76C2×C59⋊C8—42no—
77C23×C59#12011yescharacteristic
78Q8×C59—42no—
79Q8×C59—42no—
80Q8×C59—81no—
81Q8×C59—81no—
82C2×C4×C59—21no—
83C2×C4×C59—21no—
84C2×C4×C59—22no—
85C2×C4×C59—22no—
86C2×C4×C59—42no—
87C2×C4×C59—41no—
88C2×C4×C59—41no—
89C2×C4×C59—42no—
90C2×C4×C59—42no—
91C2×C4×C59—81no—
92C2×C4×C59—81no—
93C2×C4×C59C22⋊Q812yes—
94C2×C4×C59C22⋊Q811yescharacteristic
95C2×C4×C59#12412yes—
96C2×C4×C59#12411yescharacteristic
97C2×Dic59—42no—
98C2×Dic59—42no—
99C2×Dic59—42no—
100C2×Dic59—42no—
101C2×Dic59—42no—
102C2×Dic59—42no—
103Dic118—84no—
104C8×C59—42no—
105C59⋊C8—44no—
106#10359—591nomaximal, Sylow
107C22×C59#39311yescharacteristic
108C22×C59#45311yescharacteristic
109C22×C59#45411yescharacteristic
110C22×C59#45512yes—
111C22×C59#45612yes—
112C4×C59—21no—
113C4×C59—21no—
114C4×C59—22no—
115C4×C59—22no—
116C4×C59—81no—
117C4×C59—81no—
118C4×C59—82no—
119Dic59—82no—
120Dic59—82no—
121#2844—591no—
122#1993—592no—
123#1960D5911yescharacteristic
124#1295—592no—
125#1295—591no—
126C2×C59#165911yescharacteristic
127C2×C59#166011yescharacteristic
128C2×C59#166412yes—
129C2×C59#202711yescharacteristic
130C2×C59#202812yes—
131C2×C4⋊Q8C2×D5911yescharacteristic
132C2×#103—21no—
133C2×#103—21no—
134C2×#97—592no—
135C2×#97C2×D5911yescharacteristic
136#400—1182no—
137#400—1181no—
138#395—1182no—
139#395—1181no—
140#382—592no—
141#382C2×D5911yescharacteristic
142#340—1182no—
143#340—1182no—
144C59#1035911yescharacteristic, complemented, Sylow
145C22×Q8—21no—
146C22×Q8—1181no—
147C22×C8—21no—
148C22×C8—1182no—
149C4⋊Q8—21no—
150C4⋊Q8—22no—
151C4⋊Q8Dic11812yescomplemented
152C2×C4⋊C4—22no—
153C2×C4⋊C4—592no—
154C2×C4⋊C4—592no—
155C2×C4⋊C4—1182no—
156C2×C4⋊C4—1181no—
157C2×C4⋊C4C22⋊D5911yescharacteristic
158C2×C4⋊C4C22⋊D5911yescharacteristic
159C2×C42C22×D5911yescharacteristic
160#103—42no—
161#103—42no—
162#97—22no—
163#97—1182no—
164#97—1182no—
165#95—22no—
166#95—1182no—
167#95—1181no—
168#95—1181no—
169#95—1182no—
170#95—1182no—
171C2×Q8—22no—
172C2×Q8—41no—
173C2×Q8—41no—
174C2×Q8—41no—
175C2×Q8—41no—
176C2×Q8—41no—
177C2×Q8—4721no—
178C2×Q8—4722no—
179C22×C4—21no—
180C22×C4—21no—
181C22×C4—41no—
182C22×C4—1182no—
183C22×C4—1182no—
184C22×C4D4×D5912yes—
185C22×C4C2×C22⋊D5911yescharacteristic
186C2×C8—22no—
187C2×C8—41no—
188C2×C8—41no—
189C2×C8—1184no—
190C2×C8—2362no—
191C2×C8—2362no—
192C4⋊C4—24no—
193C4⋊C4—41no—
194C4⋊C4—41no—
195C4⋊C4—42no—
196C4⋊C4—4722no—
197C4⋊C4—4721no—
198C4⋊C4—2362no—
199C4⋊C4—2362no—
200C42C2×Dic11811yescharacteristic
201C42#1174568511yescharacteristic
202C42#1174568712yes—
203C23#1427369511yescharacteristic
204Q8—42no—
205Q8—42no—
206Q8—81no—
207Q8—81no—
208Q8—4724no—
209C2×C4—21no—
210C2×C4—21no—
211C2×C4—22no—
212C2×C4—22no—
213C2×C4—41no—
214C2×C4—41no—
215C2×C4—42no—
216C2×C4—42no—
217C2×C4—42no—
218C2×C4—81no—
219C2×C4—81no—
220C2×C4—2362no—
221C2×C4—2362no—
222C2×C4—2362no—
223C2×C4—2362no—
224C2×C4—2362no—
225C2×C4—2362no—
226C2×C4#1427370412yes—
227C2×C4#1427370611yescharacteristic
228C2×C4#1427371312yes—
229C2×C4#1427371411yescharacteristic
230C8—42no—
231C8—2364no—
232C22#1683731411yescharacteristic
233C22#1683756911yescharacteristic
234C22#1683757411yescharacteristic
235C22#1683757812yes—
236C22#1683758312yes—
237C4—21no—
238C4—21no—
239C4—22no—
240C4—22no—
241C4—81no—
242C4—81no—
243C4—82no—
244C4—4722no—
245C4—4722no—
246C2#2142340011yescharacteristic
247C2#2142340511yescharacteristic
248C2#2142342712yes—
249C2#2142525211yescharacteristic
250C2#2142525512yes—
subgroupG/H
centerC23#14273695
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1960C2
socle, prime radicalC23×C59#120
hypercenter#1960D59
hypocenterC59#10359
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
36. C4⋊Q8×C59Q8semidirect
144. C59#10359semidirect
151. C4⋊Q8Dic118semidirect

Maximal subgroups

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

subgroupindex
#214323682
#214250702
#214219782
#214219772
C59×#19602
#1035959