Finite Group Databasebeta

← #28490983

Subgroups — #28490983

Order 15104.

466 conjugacy classes of subgroups; only the 105 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 105 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#21435242C212yesmaximal
2#21434620C211yesmaximal, characteristic
3#21424916C211yesmaximal, characteristic
4#21422661C212yesmaximal
5C59×#1281C211yesmaximal, characteristic
6#16837959C2212yes—
7C2×#14273727C2211yescharacteristic
8#16837811—22no—
9#16837811—22no—
10#16837800—22no—
11#16837753—22no—
12#16837733—24no—
13#16837688—24no—
14#16837440—22no—
15C2×#14273652—22no—
16#16837268C2211yescharacteristic
17#16837140—24no—
18C59×#431C2212yes—
19C2×#97×C59C2211yescharacteristic
20C22×Dic118—21no—
21#14273727—22no—
22#14273727—21no—
23#14273727D412yes—
24#14273727D412yes—
25#14273727D412yes—
26#14273719—22no—
27#14273706—22no—
28#14273706—22no—
29C4×Dic118—22no—
30C4×Dic118—22no—
31#14273686—22no—
32C2×C4⋊Dic59—22no—
33C2×C4⋊Dic59—21no—
34#14273661—24no—
35#14273659—28no—
36#14273659—22no—
37#14273659—22no—
38#14273652—28no—
39#14273652—44no—
40C59⋊#95—22no—
41C22×C8×C59D412yes—
42C2×C42×C59C2311yescharacteristic
43C4⋊C8×C59—22no—
44C22⋊C8×C59D414yes—
45#97×C59—22no—
46C4×C8×C59—22no—
47C22×C4×C59C2×D412yes—
48C22×C4×C59C2×D411yescharacteristic
49C22×Dic59—41no—
50C22×Dic59—41no—
51C2×Dic118—22no—
52C2×Dic118—22no—
53C2×Dic118—22no—
54C2×Dic118—42no—
55C2×Dic118—42no—
56C2×Dic118—41no—
57C2×C8×C59—22no—
58C2×C8×C59—22no—
59C2×C8×C59—24no—
60C2×C8×C59SD1614yes—
61C42×C59C2×D412yes—
62C42×C59C2×D411yescharacteristic
63C42×C59#4111yescharacteristic
64C22⋊Dic59—42no—
65C4⋊Dic59—24no—
66C4⋊Dic59—22no—
67C4⋊Dic59—22no—
68C4⋊Dic59—22no—
69C4⋊Dic59—22no—
70C4⋊Dic59—42no—
71C4⋊Dic59—42no—
72Dic59⋊C4—42no—
73Dic59⋊C4—42no—
74C4×Dic59—42no—
75C23×C59#12711yescharacteristic
76C2×C4×C59—42no—
77C2×C4×C59#12012yes—
78C2×C4×C59#12011yescharacteristic
79C2×C4×C59#12112yes—
80C2×C4×C59#12111yescharacteristic
81C2×C4×C59C2×SD1612yes—
82C2×C4×C59#13712yes—
83C2×Dic59—42no—
84C2×Dic59—42no—
85C2×Dic59—42no—
86C2×Dic59—81no—
87C2×Dic59—81no—
88C2×Dic59—82no—
89C2×Dic59—81no—
90Dic118—44no—
91Dic118—44no—
92Dic118—82no—
93Dic118—82no—
94C8×C59—24no—
95C8×C59—44no—
96#10227—591nomaximal, Sylow
97C22×C59—22no—
98C22×C59#39211yescharacteristic
99C22×C59#49211yescharacteristic
100C22×C59#49711yescharacteristic
101C4×C59—22no—
102C4×C59—22no—
103C4×C59#44812yes—
104C4×C59#46112yes—
105Dic59—82no—
106Dic59—82no—
107Dic59—82no—
108Dic59—161no—
109#3229—592no—
110#3162—591no—
111#1960—591no—
112#1518—592no—
113#1281D5911yescharacteristic
114C2×C59—21no—
115C2×C59—21no—
116C2×C59#200912yes—
117C2×C59#201311yescharacteristic
118#533—592no—
119C2×C4⋊Q8—591no—
120#501—1182no—
121#501—1182no—
122#498—1182no—
123#487—1182no—
124#483—1184no—
125#475—1184no—
126#431C2×D5912yes—
127#427—1182no—
128C2×#103—1182no—
129C2×#97C2×D5911yescharacteristic
130#382—591no—
131#328—1184no—
132C59#1022711yescharacteristic, complemented, Sylow
133C22×Q8—1181no—
134C22×C8D23612yes—
135C4⋊Q8—592no—
136C4⋊Q8—592no—
137C4⋊Q8—592no—
138C4⋊Q8—1182no—
139C4⋊Q8—1181no—
140#125—1182no—
141C22⋊Q8—1182no—
142C22⋊Q8—1182no—
143C4×Q8—1182no—
144C4×Q8—1182no—
145#117—1182no—
146C2×C4⋊C4—1182no—
147C2×C4⋊C4—1181no—
148C2×C42C22×D5911yescharacteristic
149#107—1184no—
150#106—1182no—
151#106—1182no—
152#106—1188no—
153C4⋊C8—22no—
154#103—1188no—
155#103—2364no—
156C22⋊C8D23614yes—
157#97—22no—
158C4×C8—22no—
159#95—1182no—
160C2×Q8—1182no—
161C2×Q8—1182no—
162C2×Q8—1182no—
163C2×Q8—2362no—
164C2×Q8—2362no—
165C2×Q8—2361no—
166C22×C4—2361no—
167C22×C4—2361no—
168C22×C4C2×D23612yes—
169C22×C4C2×D23611yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—24no—
173C2×C8#1174566014yes—
174C4⋊C4—1184no—
175C4⋊C4—1182no—
176C4⋊C4—1182no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—2362no—
180C4⋊C4—2362no—
181C4⋊C4—2362no—
182C4⋊C4—2362no—
183C22⋊C4—2362no—
184C42—2362no—
185C42D4×D5912yes—
186C42D4×D5911yescharacteristic
187C42#1174568911yescharacteristic
188C23#1427372411yescharacteristic
189Q8—4722no—
190Q8—4722no—
191Q8—2364no—
192Q8—2364no—
193C2×C4—42no—
194C2×C4—4722no—
195C2×C4—4721no—
196C2×C4—4721no—
197C2×C4—4721no—
198C2×C4—2362no—
199C2×C4—2362no—
200C2×C4—2362no—
201C2×C4#1427369712yes—
202C2×C4#1427369711yescharacteristic
203C2×C4#1427370212yes—
204C2×C4#1427370211yescharacteristic
205C2×C4C2×#1174566012yes—
206C2×C4#1427376012yes—
207C8—24no—
208C8—44no—
209C22—22no—
210C22#1683731211yescharacteristic
211C22#1683777511yescharacteristic
212C22#1683779611yescharacteristic
213C4—22no—
214C4—22no—
215C4—9441no—
216C4—4722no—
217C4—4722no—
218C4—4722no—
219C4#1683754312yes—
220C4#1683760812yes—
221C2—21no—
222C2—21no—
223C2#2142515912yes—
224C2#2142518111yescharacteristic
subgroupG/H
centerC22#16837312
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1281C2
socleC22×C59#392
prime radicalC23×C59#127
hypercenter#1281D59
hypocenterC59#10227
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1281

Complements

Splittings G = N ⋊ H with N normal; H ≅ G/N.

NH ≅ G/Ntype
132. C59#10227semidirect

Maximal subgroups

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

subgroupindex
#214352422
#214346202
#214249162
#214226612
C59×#12812
#1022759