Finite Group Databasebeta

← #28502857

Subgroups — #28502857

Order 15104.

218 conjugacy classes of subgroups; only the 63 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 63 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#21426235C211yesmaximal, characteristic
2#21426147C211yesmaximal, characteristic
3#21423694C211yesmaximal, characteristic
4#21422902C211yesmaximal, characteristic
5#21422159C211yesmaximal, characteristic
6#21422144C211yesmaximal, characteristic
7C59×#1364C211yesmaximal, characteristic
8C2×Dic472—21no—
9#16837798—21no—
10#16837782C2211yescharacteristic
11#16837752—21no—
12#16837526—21no—
13C4×Dic236C2211yescharacteristic
14#16837229—21no—
15C4⋊(C59⋊C16)C2211yescharacteristic
16#16837207—21no—
17#16837205—21no—
18#16837132—21no—
19C8×C59⋊C8C2211yescharacteristic
20C59×#500C2211yescharacteristic
21C59×C4⋊C16C2211yescharacteristic
22C59×#335C2211yescharacteristic
23C2×Dic236—21no—
24C2×Dic236—21no—
25C2×Dic236D411yescharacteristic
26#14273727—21no—
27C4×Dic118—21no—
28Dic472—42no—
29C2×C59⋊C16—21no—
30#14273661D411yescharacteristic
31#14273658—42no—
32Dic59⋊C8—41no—
33#14273652—21no—
34#14273651—41no—
35#14273651—41no—
36C4×C59⋊C8D411yescharacteristic
37C4×C59⋊C8D411yescharacteristic
38C8×Dic59—41no—
39C4⋊Q8×C59—21no—
40C2×C16×C59—21no—
41#107×C59—21no—
42#107×C59—21no—
43C4⋊C8×C59—21no—
44C4×C8×C59C2311yescharacteristic
45C2×Q8×C59—41no—
46C2×Dic118—21no—
47C2×Dic118—41no—
48C2×C8×C59—41no—
49C2×C8×C59C2×D411yescharacteristic
50C2×C8×C59#4111yescharacteristic
51C4⋊C4×C59—41no—
52C4⋊C4×C59—41no—
53C42×C59C2×D411yescharacteristic
54C4⋊Dic59—21no—
55C4⋊Dic59—41no—
56C4⋊Dic59—41no—
57Dic59⋊C4—41no—
58C4×Dic59—41no—
59C2×C59⋊C8—21no—
60C2×C59⋊C8D811yescharacteristic
61C2×C59⋊C8D811yescharacteristic
62Dic236—21no—
63Dic236—41no—
64Dic236—41no—
65Dic236—81no—
66Dic236SD1612yes—
67C16×C59—41no—
68C59⋊C16—41no—
69Q8×C59—81no—
70Q8×C59—81no—
71C2×C4×C59—81no—
72C2×C4×C59#12111yescharacteristic
73C2×C4×C59C2×D811yescharacteristic
74C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
75C2×Dic59—41no—
76C2×Dic59—41no—
77C2×Dic59—81no—
78Dic118—22no—
79Dic118—41no—
80Dic118—81no—
81Dic118—81no—
82C8×C59—21no—
83C8×C59—81no—
84C8×C59C2×SD1611yescharacteristic
85C8×C59#13511yescharacteristic
86C59⋊C8—22no—
87C59⋊C8—21no—
88C59⋊C8—21no—
89#12423—591nomaximal, Sylow
90C22×C59#45911yescharacteristic
91C4×C59—21no—
92C4×C59—161no—
93C4×C59#46511yescharacteristic
94C4×C59#47111yescharacteristic
95C4×C59#50811yescharacteristic
96C4×C59#51011yescharacteristic
97Dic59—42no—
98Dic59—81no—
99Dic59—161no—
100#2225—591no—
101#2209—591no—
102#1707—591no—
103C8×Q16—591no—
104#1367—591no—
105#1364D5911yescharacteristic
106#1362—591no—
107C2×C59#166511yescharacteristic
108C2×C59#221111yescharacteristic
109C2×C59#221411yescharacteristic
110C2×Q32—1181no—
111#500C2×D5911yescharacteristic
112#498—1181no—
113#494—591no—
114#487—1181no—
115C8×Q8—1181no—
116C4×Q16—591no—
117#367—1181no—
118C4⋊C16—591no—
119C4⋊C16C2×D5911yescharacteristic
120#358—1181no—
121#358—1181no—
122#335C2×D5911yescharacteristic
123Q8⋊C8—1181no—
124C82—591no—
125C59#1242311yescharacteristic, complemented, Sylow
126C2×Q16—591no—
127C2×Q16—1181no—
128C2×Q16—1181no—
129C4⋊Q8—21no—
130C4⋊Q8—1181no—
131C4×Q8—1181no—
132Q32—2362no—
133C2×C16—21no—
134C2×C16—1181no—
135#107—21no—
136#107—21no—
137#107—591no—
138#106—2362no—
139C4⋊C8—21no—
140C4⋊C8—2361no—
141#103—1181no—
142#103—2361no—
143#103—2361no—
144C4×C8—591no—
145C4×C8—591no—
146C4×C8—2361no—
147C4×C8C22×D5911yescharacteristic
148C2×Q8—41no—
149C2×Q8—1181no—
150C2×Q8—2361no—
151Q16—592no—
152Q16—1181no—
153Q16—4721no—
154Q16—2361no—
155Q16—2361no—
156C2×C8—41no—
157C2×C8—591no—
158C2×C8—591no—
159C2×C8—1181no—
160C2×C8#1174568511yescharacteristic
161C2×C8D4×D5911yescharacteristic
162C4⋊C4—41no—
163C4⋊C4—41no—
164C4⋊C4—1181no—
165C4⋊C4—2361no—
166C4⋊C4—2361no—
167C4⋊C4—2361no—
168C42—2361no—
169C42D4×D5911yescharacteristic
170C16—41no—
171C16—2361no—
172Q8—81no—
173Q8—81no—
174Q8—1182no—
175Q8—4721no—
176Q8—4721no—
177Q8—2361no—
178C2×C4—81no—
179C2×C4—4721no—
180C2×C4—2361no—
181C2×C4—2361no—
182C2×C4#1427370011yescharacteristic
183C2×C4D8×D5911yescharacteristic
184C2×C4#1427375411yescharacteristic
185C8—21no—
186C8—81no—
187C8—1182no—
188C8—1181no—
189C8—1181no—
190C8SD16×D5911yescharacteristic
191C8#1427375011yescharacteristic
192C22#1683759611yescharacteristic
193C4—21no—
194C4—161no—
195C4—9441no—
196C4—4721no—
197C4—2362no—
198C4#1683763411yescharacteristic
199C4#1683766811yescharacteristic
200C4#1683783111yescharacteristic
201C4#1683784111yescharacteristic
202C2#2142344011yescharacteristic
203C2#2142615711yescharacteristic
204C2#2142617611yescharacteristic
subgroupG/H
centerC22#16837596
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1364C2
socle, prime radicalC22×C59#459
hypercenter#1364D59
hypocenterC59#12423
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C4×C8 ◁ #1364

Complements

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

NH ≅ G/Ntype
125. C59#12423semidirect

Maximal subgroups

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

subgroupindex
#214262352
#214261472
#214236942
#214229022
#214221592
#214221442
C59×#13642
#1242359