Finite Group Databasebeta

← #28491789

Subgroups — #28491789

Order 15104.

400 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 400 conjugacy classes of subgroups — too many to draw. Only its 101 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#21425073C211yesmaximal, characteristic
2#21422659C212yesmaximal
3#21421954C212yesmaximal
4#21421929C211yesmaximal, characteristic
5C59×#2859C211yesmaximal, characteristic
6#16837959C2211yescharacteristic
7#16837455C2212yes—
8#16837426C2211yescharacteristic
9#16837162—21no—
10#16837162—21no—
11#16837138—24no—
12C2×#125×C59—21no—
13C59×#389—24no—
14C59×#384—21no—
15C59×#382C2212yes—
16C43×C59C2211yescharacteristic
17C2×#11745664—21no—
18#14273727Q812yes—
19#14273719—21no—
20#14273706—22no—
21C4×Dic118—22no—
22#14273686—21no—
23C4⋊(C59⋊C8)—22no—
24C4⋊(C59⋊C8)—22no—
25C22⋊(C59⋊C8)—22no—
26C4×C59⋊C8—22no—
27#125×C59—42no—
28#125×C59—42no—
29C2×C4⋊C4×C59—24no—
30C2×C4⋊C4×C59—24no—
31C2×C4⋊C4×C59—22no—
32C2×C42×C59—22no—
33C2×C42×C59D411yescharacteristic
34C2×C42×C59D411yescharacteristic
35C2×C42×C59C2311yescharacteristic
36#95×C59—22no—
37#95×C59D414yes—
38C22×C4×C59—21no—
39C22×C4×C59—21no—
40C22×C4×C59—24no—
41C22×C4×C59C2×D412yes—
42C22×C4×C59C2×D411yescharacteristic
43C2×Dic118—22no—
44C4⋊C4×C59—48no—
45C4⋊C4×C59—48no—
46C4⋊C4×C59—42no—
47C4⋊C4×C59—42no—
48C42×C59—21no—
49C42×C59—21no—
50C42×C59—44no—
51C42×C59SD1612yes—
52C42×C59Q1612yes—
53C42×C59C2×Q811yescharacteristic
54C42×C59#4111yescharacteristic
55C42×C59#4112yes—
56C22⋊Dic59—41no—
57C4⋊Dic59—22no—
58C4⋊Dic59—22no—
59Dic59⋊C4—42no—
60C4×Dic59—41no—
61#11745664—41no—
62#11745664—41no—
63C2×C59⋊C8—42no—
64C2×C59⋊C8—41no—
65C23×C59#12011yescharacteristic
66C2×C4×C59—24no—
67C2×C4×C59—22no—
68C2×C4×C59—22no—
69C2×C4×C59—42no—
70C2×C4×C59—42no—
71C2×C4×C59—48no—
72C2×C4×C59—44no—
73C2×C4×C59C22⋊Q812yes—
74C2×C4×C59C22⋊Q811yescharacteristic
75C2×C4×C59#12412yes—
76C2×C4×C59#12411yescharacteristic
77C2×C4×C59C2×SD1611yescharacteristic
78C2×C4×C59C2×Q1611yescharacteristic
79C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
80C2×C4×C59#13711yescharacteristic
81C2×Dic59—42no—
82Dic118—82no—
83C59⋊C8—82no—
84C59⋊C8—81no—
85#10365—591nomaximal, Sylow
86C22×C59—22no—
87C22×C59#39311yescharacteristic
88C22×C59#45011yescharacteristic
89C22×C59#45111yescharacteristic
90C4×C59—24no—
91C4×C59—22no—
92C4×C59—22no—
93C4×C59—42no—
94C4×C59—84no—
95C4×C59#47511yescharacteristic
96C4×C59#47711yescharacteristic
97C4×C59#48711yescharacteristic
98C4×C59#48911yescharacteristic
99Dic59—82no—
100#2859D5911yescharacteristic
101#1994—591no—
102#1518—592no—
103#1286—592no—
104#1276—591no—
105C2×C59—21no—
106C2×C59—21no—
107C2×C59#202411yescharacteristic
108C2×C59#203112yes—
109#533—591no—
110C2×#125—21no—
111#431—592no—
112#423—591no—
113#389—24no—
114#384—21no—
115#382C2×D5912yes—
116C43C2×D5911yescharacteristic
117#339—1181no—
118#339—1181no—
119#328—1184no—
120C59#1036511yescharacteristic, complemented, Sylow
121C2×M16—1181no—
122C4⋊Q8—592no—
123#125—42no—
124#125—42no—
125#125—1181no—
126C22⋊Q8—1182no—
127C4×Q8—1182no—
128#117—1181no—
129C2×C4⋊C4—24no—
130C2×C4⋊C4—24no—
131C2×C4⋊C4—22no—
132C2×C42—22no—
133C2×C42C22⋊D5911yescharacteristic
134C2×C42C22⋊D5911yescharacteristic
135C2×C42C22×D5911yescharacteristic
136C4⋊C8—1182no—
137C4⋊C8—1182no—
138C22⋊C8—1182no—
139C4×C8—1182no—
140#95—22no—
141#95C22⋊D5914yes—
142C2×Q8—1182no—
143C22×C4—21no—
144C22×C4—21no—
145C22×C4—24no—
146C22×C4C2×C22⋊D5912yes—
147C22×C4C2×C22⋊D5911yescharacteristic
148M16—2361no—
149M16—2361no—
150C2×C8—2362no—
151C2×C8—2361no—
152C4⋊C4—48no—
153C4⋊C4—48no—
154C4⋊C4—42no—
155C4⋊C4—42no—
156C4⋊C4—1182no—
157C4⋊C4—1182no—
158C4⋊C4—2362no—
159C22⋊C4—2361no—
160C42—21no—
161C42—21no—
162C42—44no—
163C42—2361no—
164C42#1174567012yes—
165C42#1174567212yes—
166C42Q8×D5911yescharacteristic
167C42#1174568911yescharacteristic
168C42#1174568912yes—
169C23#1427369611yescharacteristic
170Q8—4722no—
171C2×C4—24no—
172C2×C4—22no—
173C2×C4—22no—
174C2×C4—42no—
175C2×C4—42no—
176C2×C4—48no—
177C2×C4—44no—
178C2×C4—2362no—
179C2×C4#1427370312yes—
180C2×C4#1427370311yescharacteristic
181C2×C4#1427371612yes—
182C2×C4#1427371611yescharacteristic
183C2×C4C2×#1174567011yescharacteristic
184C2×C4C2×#1174567211yescharacteristic
185C2×C4#1427375311yescharacteristic
186C2×C4#1427375811yescharacteristic
187C8—4722no—
188C8—4721no—
189C22—22no—
190C22#1683731311yescharacteristic
191C22#1683755311yescharacteristic
192C22#1683755811yescharacteristic
193C4—24no—
194C4—22no—
195C4—22no—
196C4—42no—
197C4—84no—
198C4—4722no—
199C4#1683768411yescharacteristic
200C4#1683769411yescharacteristic
201C4#1683775411yescharacteristic
202C4#1683776411yescharacteristic
203C2—21no—
204C2—21no—
205C2#2142523411yescharacteristic
206C2#2142526512yes—
subgroupG/H
centerC22#16837313
commutator, cosocleC2×C42×C59C23
FrattiniC2×C42C22×D59
FittingC59×#2859C2
socleC22×C59#393
prime radicalC23×C59#120
hypercenter#2859D59
hypocenterC59#10365
LCSG ▷ C2×C42×C59 ▷ C22×C59 ▷ C59
UCSC1 ◁ C22 ◁ C2×C42 ◁ #2859

Complements

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

NH ≅ G/Ntype
120. C59#10365semidirect

Maximal subgroups

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

subgroupindex
#214250732
#214226592
#214219542
#214219292
C59×#28592
#1036559