Finite Group Databasebeta

← #28490980

Subgroups — #28490980

Order 15104.

466 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 466 conjugacy classes of subgroups — too many to draw. Only its 103 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#21435240C212yesmaximal
2#21434620C211yesmaximal, characteristic
3#21422659C212yesmaximal
4#21421941C211yesmaximal, characteristic
5C59×#1960C211yesmaximal, characteristic
6#16837959C2212yes—
7#16837811—22no—
8#16837811—22no—
9#16837798—22no—
10#16837754—22no—
11#16837732—24no—
12#16837684—24no—
13#16837455C2212yes—
14#16837440—22no—
15#16837138—24no—
16C2×C4⋊Q8×C59C2211yescharacteristic
17C2×#103×C59—22no—
18C2×#97×C59C2211yescharacteristic
19C59×#382C2211yescharacteristic
20#14273727D412yes—
21#14273727D412yes—
22#14273719—22no—
23#14273706—22no—
24#14273706—22no—
25C4×Dic118—22no—
26C4×Dic118—22no—
27#14273686—22no—
28#14273661—24no—
29#14273659—22no—
30#14273659—22no—
31#14273658—28no—
32C4⋊(C59⋊C8)—22no—
33#14273650—28no—
34C22⋊(C59⋊C8)D414yes—
35C4×C59⋊C8—22no—
36C22×Q8×C59—21no—
37C22×C8×C59D412yes—
38C4⋊Q8×C59—22no—
39C4⋊Q8×C59—21no—
40C4⋊Q8×C59D412yes—
41C2×C4⋊C4×C59—22no—
42C2×C4⋊C4×C59—21no—
43C2×C42×C59C2311yescharacteristic
44#103×C59—44no—
45#97×C59—22no—
46#95×C59—22no—
47C2×Q8×C59—22no—
48C2×Q8×C59—41no—
49C2×Q8×C59—42no—
50C2×Q8×C59—42no—
51C22×C4×C59—41no—
52C22×C4×C59—41no—
53C22×C4×C59C2×D412yes—
54C22×C4×C59C2×D411yescharacteristic
55C2×Dic118—22no—
56C2×Dic118—22no—
57C2×C8×C59—22no—
58C2×C8×C59—22no—
59C2×C8×C59SD1614yes—
60C4⋊C4×C59—24no—
61C4⋊C4×C59—42no—
62C4⋊C4×C59—42no—
63C42×C59C2×D411yescharacteristic
64C42×C59C2×D412yes—
65C42×C59#4111yescharacteristic
66C22⋊Dic59—42no—
67C4⋊Dic59—22no—
68C4⋊Dic59—22no—
69C4⋊Dic59—22no—
70C4⋊Dic59—22no—
71Dic59⋊C4—42no—
72Dic59⋊C4—42no—
73C4×Dic59—42no—
74C2×C59⋊C8—24no—
75C23×C59#12711yescharacteristic
76Q8×C59—44no—
77Q8×C59—82no—
78C2×C4×C59—42no—
79C2×C4×C59—42no—
80C2×C4×C59—81no—
81C2×C4×C59—81no—
82C2×C4×C59—82no—
83C2×C4×C59—81no—
84C2×C4×C59#12011yescharacteristic
85C2×C4×C59#12012yes—
86C2×C4×C59#12112yes—
87C2×C4×C59#12111yescharacteristic
88C2×C4×C59C2×SD1612yes—
89C2×C4×C59#13712yes—
90C2×Dic59—42no—
91C2×Dic59—42no—
92Dic118—44no—
93Dic118—82no—
94C8×C59—24no—
95C59⋊C8—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—82no—
104C4×C59—161no—
105C4×C59#44812yes—
106C4×C59#46112yes—
107Dic59—82no—
108Dic59—82no—
109#3229—592no—
110#3162—591no—
111#1960D5911yescharacteristic
112#1518—592no—
113#1281—591no—
114C2×C59—21no—
115C2×C59—21no—
116C2×C59#200912yes—
117C2×C59#201311yescharacteristic
118#533—592no—
119C2×C4⋊Q8C2×D5911yescharacteristic
120#501—1182no—
121#501—1182no—
122#498—1182no—
123#487—1182no—
124#483—1184no—
125#475—1184no—
126#431—592no—
127#427—1182no—
128C2×#103—22no—
129C2×#97C2×D5911yescharacteristic
130#382C2×D5911yescharacteristic
131#328—1184no—
132C59#1022711yescharacteristic, complemented, Sylow
133C22×Q8—21no—
134C22×C8C22⋊D5912yes—
135C4⋊Q8—21no—
136C4⋊Q8—22no—
137C4⋊Q8—592no—
138C4⋊Q8—592no—
139C4⋊Q8D23612yes—
140#125—1182no—
141C22⋊Q8—1182no—
142C22⋊Q8—1182no—
143C4×Q8—1182no—
144C4×Q8—1182no—
145#117—1182no—
146C2×C4⋊C4—22no—
147C2×C4⋊C4—21no—
148C2×C42C22×D5911yescharacteristic
149#107—1184no—
150#106—1188no—
151#106—1182no—
152#106—1182no—
153C4⋊C8—1182no—
154#103—44no—
155#103—1188no—
156C22⋊C8—594no—
157#97—22no—
158C4×C8—1182no—
159#95—22no—
160C2×Q8—22no—
161C2×Q8—41no—
162C2×Q8—42no—
163C2×Q8—42no—
164C2×Q8—1182no—
165C2×Q8—1182no—
166C22×C4—41no—
167C22×C4—41no—
168C22×C4D4×D5912yes—
169C22×C4C2×C22⋊D5911yescharacteristic
170C2×C8—22no—
171C2×C8—22no—
172C2×C8—1184no—
173C2×C8#1174567014yes—
174C4⋊C4—24no—
175C4⋊C4—42no—
176C4⋊C4—42no—
177C4⋊C4—1182no—
178C4⋊C4—1182no—
179C4⋊C4—1182no—
180C4⋊C4—1182no—
181C4⋊C4—2362no—
182C4⋊C4—2362no—
183C22⋊C4—2362no—
184C42—2362no—
185C42C2×D23611yescharacteristic
186C42#1174568511yescharacteristic
187C42D4×D5912yes—
188C23#1427372311yescharacteristic
189Q8—44no—
190Q8—82no—
191Q8—4722no—
192Q8—2364no—
193C2×C4—42no—
194C2×C4—42no—
195C2×C4—81no—
196C2×C4—81no—
197C2×C4—82no—
198C2×C4—81no—
199C2×C4—2362no—
200C2×C4—2362no—
201C2×C4#1427369511yescharacteristic
202C2×C4#1427369712yes—
203C2×C4#1427370012yes—
204C2×C4#1427370111yescharacteristic
205C2×C4C2×#1174567012yes—
206C2×C4#1427375712yes—
207C8—24no—
208C8—2364no—
209C22—22no—
210C22#1683731111yescharacteristic
211C22#1683777411yescharacteristic
212C22#1683779711yescharacteristic
213C4—22no—
214C4—22no—
215C4—82no—
216C4—161no—
217C4—4722no—
218C4—4722no—
219C4#1683754012yes—
220C4#1683760712yes—
221C2—21no—
222C2—21no—
223C2#2142515812yes—
224C2#2142517811yescharacteristic
subgroupG/H
centerC22#16837311
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#1960C2
socleC22×C59#392
prime radicalC23×C59#127
hypercenter#1960D59
hypocenterC59#10227
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #1960

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
#214352402
#214346202
#214226592
#214219412
C59×#19602
#1022759