Finite Group Databasebeta

← #28476239

Subgroups — #28476239

Order 15104.

224 conjugacy classes of subgroups; only the 41 normal subgroups are shown.

normal subgroups only

This group has 224 conjugacy classes of subgroups — too many to draw. Only its 41 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#21425325C211yesmaximal, characteristic
2#21421977C211yesmaximal, characteristic, complemented
3C59×#1324C211yesmaximal, characteristic, complemented
4#16837983C411yescharacteristic
5C2×#14273655—21no—
6#16837401—21no—
7C2×#14273638—21no—
8#16837171C411yescharacteristic
9C59×#382C2211yescharacteristic
10C59×#324—21no—
11C2×#11745685—21no—
12C2×#11745664—21no—
13C22×C59⋊C8—41no—
14#14273707—41no—
15#14273702—41no—
16#14273701—41no—
17#14273655—41no—
18#14273655—41no—
19#14273650—41no—
20#14273647—41no—
21#14273638—22no—
22#14273638—41no—
23C2×C4⋊C4×C59C2×C411yescharacteristic
24C2×C4⋊C4×C59D411yescharacteristic
25C2×C42×C59D411yescharacteristic
26C22⋊C8×C59—41no—
27#95×C59—41no—
28C22×C4×C59—21no—
29C22×C4×C59—21no—
30C22×C4×C59—21no—
31C22×C4×C59C22⋊C411yescharacteristic
32C2×C22⋊D59—41no—
33#11745685—41no—
34#11745685—41no—
35#11745685—41no—
36#11745685—41no—
37C2×D236—21no—
38C2×D236—41no—
39C2×C4×D59—41no—
40C2×Dic118—21no—
41C2×C8×C59—81no—
42C4⋊C4×C59—41no—
43C4⋊C4×C59—41no—
44C42×C59—21no—
45C42×C59D811yescharacteristic
46C42×C59SD1611yescharacteristic
47(C2×D59)⋊C4—42no—
48C4⋊Dic59—41no—
49#11745664—41no—
50#11745664—41no—
51C2×C59⋊C8—42no—
52C2×C59⋊C8—42no—
53C2×C59⋊C8—42no—
54C2×C59⋊C8—41no—
55C23×C59#9911yescharacteristic
56C22×D59—41no—
57C2×C4×C59—21no—
58C2×C4×C59—21no—
59C2×C4×C59—21no—
60C2×C4×C59—21no—
61C2×C4×C59—41no—
62C2×C4×C59—41no—
63C2×C4×C59—41no—
64C2×C4×C59—41no—
65C2×C4×C59—81no—
66C2×C4×C59—81no—
67C2×C4×C59#10211yescharacteristic
68C2×C4×C59#10411yescharacteristic
69C22⋊D59—81no—
70C22⋊D59—81no—
71C2×Dic59—41no—
72D236—41no—
73D236—41no—
74D236—161no—
75C4×D59—81no—
76C4×D59—81no—
77Dic118—41no—
78Dic118—41no—
79C8×C59—161no—
80C59⋊C8—44no—
81C59⋊C8—81no—
82#7416—591nomaximal, Sylow
83C22×C59—21no—
84C22×C59—21no—
85C22×C59#32711yescharacteristic
86C22×C59AΣL(1,𝔽16)11yescharacteristic
87C22×C59#35511yescharacteristic
88C2×D59—81no—
89C2×D59—81no—
90C2×D59—81no—
91C4×C59—21no—
92C4×C59—21no—
93C4×C59—41no—
94C4×C59—41no—
95C4×C59—81no—
96C4×C59—81no—
97Dic59—81no—
98#2040—591no—
99#1324D5911yescharacteristic, complemented
100#1295—591no—
101C2×C59—21no—
102C2×C59—21no—
103C2×C59#134511yescharacteristic
104C2×C59#140311yescharacteristic
105C2×C59#140411yescharacteristic
106D59—161no—
107#537—591no—
108C2×#104—1181no—
109#417—1181no—
110C2×#97—1181no—
111#382C2×D5911yescharacteristic
112#343—591no—
113#324—21no—
114C59#741611yescharacteristic, complemented, Sylow
115C2×#41—1181no—
116C2×M16—1181no—
117C22×C8—2361no—
118C22⋊Q8—2361no—
119#121—2361no—
120#121—2361no—
121C2×C4⋊C4C4×D5911yescharacteristic
122C2×C4⋊C4C22⋊D5911yescharacteristic
123C2×C42D23611yescharacteristic
124#104—2361no—
125#104—2361no—
126#103—2361no—
127#102—2361no—
128C22⋊C8—41no—
129#97—1182no—
130#97—2361no—
131#95—41no—
132#41—2361no—
133#41—2361no—
134#41—2361no—
135#41—2361no—
136C2×Q8—1181no—
137C2×D4—1181no—
138C2×D4—2361no—
139C2×D4—2361no—
140C22×C4—21no—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—2361no—
144C22×C4(C2×D59)⋊C411yescharacteristic
145M16—2361no—
146M16—2361no—
147C2×C8—81no—
148C2×C8—2361no—
149C2×C8—2362no—
150C2×C8—2362no—
151C2×C8—2362no—
152C4⋊C4—41no—
153C4⋊C4—41no—
154C4⋊C4—2361no—
155C22⋊C4—2362no—
156C42—21no—
157C42#1174566011yescharacteristic
158C42D47211yescharacteristic
159C23—2361no—
160C23#1427364111yescharacteristic
161Q8—2361no—
162Q8—2361no—
163D4—9441no—
164D4—4721no—
165D4—4721no—
166D4—2361no—
167D4—2361no—
168C2×C4—21no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—21no—
172C2×C4—41no—
173C2×C4—41no—
174C2×C4—41no—
175C2×C4—41no—
176C2×C4—81no—
177C2×C4—81no—
178C2×C4—4721no—
179C2×C4—4721no—
180C2×C4—2361no—
181C2×C4#1427364911yescharacteristic
182C2×C4#1427365311yescharacteristic
183C8—161no—
184C8—4721no—
185C8—2364no—
186C22—21no—
187C22—21no—
188C22—4721no—
189C22—4721no—
190C22—4721no—
191C22#1683713711yescharacteristic
192C22#1683718811yescharacteristic
193C22#1683719811yescharacteristic
194C4—21no—
195C4—21no—
196C4—41no—
197C4—41no—
198C4—81no—
199C4—81no—
200C4—4721no—
201C2—21no—
202C2—21no—
203C2—9441no—
204C2#2142210011yescharacteristic
205C2#2142224311yescharacteristic
206C2#2142224611yescharacteristic
subgroupG/H
centerC22#16837188
commutatorC2×C4⋊C4×C59C2×C4
Frattini#382C2×D59
FittingC59×#1324C2
socleC22×C59AΣL(1,𝔽16)
prime radical#16837983C4
cosocleC59×#382C22
hypercenter#1324D59
hypocenterC59#7416
LCSG ▷ C2×C4⋊C4×C59 ▷ C22×C4×C59 ▷ C22×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C23 ◁ C22×C4 ◁ #382 ◁ #1324

Complements

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

NH ≅ G/Ntype
2. #21421977C2semidirect
3. C59×#1324C2semidirect
99. #1324D59semidirect
114. C59#7416semidirect

Maximal subgroups

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

subgroupindex
#214253252
#214219772
C59×#13242
#741659