Finite Group Databasebeta

← #28502841

Subgroups — #28502841

Order 15104.

218 conjugacy classes of subgroups; only the 71 normal subgroups are shown.

normal subgroups only

This group has 218 conjugacy classes of subgroups — too many to draw. Only its 71 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#21426249C211yesmaximal, characteristic
2#21426147C211yesmaximal, characteristic
3#21423693C211yesmaximal, characteristic
4C8×Dic236C211yesmaximal, characteristic
5#21422153C211yesmaximal, characteristic
6#21422146C211yesmaximal, characteristic
7C59×#1367C211yesmaximal, characteristic
8C2×Dic472—21no—
9#16837807C2211yescharacteristic
10#16837800—21no—
11#16837782C2211yescharacteristic
12#16837753—21no—
13C8×Dic118—21no—
14C4×Dic236C2211yescharacteristic
15#16837228—21no—
16#16837207—21no—
17#16837207—21no—
18#16837155C2211yescharacteristic
19#16837134—21no—
20C59×C4⋊C16C2211yescharacteristic
21C59×C4⋊C16C2211yescharacteristic
22C82×C59C2211yescharacteristic
23C2×Dic236—21no—
24C2×Dic236—21no—
25C2×Dic236D411yescharacteristic
26#14273727—21no—
27#14273727—21no—
28C4×Dic118—21no—
29Dic472—42no—
30#14273661—21no—
31#14273661—21no—
32#14273661D411yescharacteristic
33#14273659—41no—
34#14273659—41no—
35C4⋊(C59⋊C8)—21no—
36Dic59⋊C8—41no—
37#14273652—21no—
38#14273652—42no—
39C8×Dic59—41no—
40C2×C16×C59—21no—
41C2×C16×C59—21no—
42C4×C8×C59D411yescharacteristic
43C4×C8×C59D411yescharacteristic
44C4×C8×C59C2311yescharacteristic
45C2×Dic118—21no—
46C2×Dic118—41no—
47C2×Dic118—41no—
48C2×C8×C59—21no—
49C2×C8×C59D811yescharacteristic
50C2×C8×C59D811yescharacteristic
51C2×C8×C59C2×D411yescharacteristic
52C2×C8×C59#4111yescharacteristic
53C42×C59C2×D411yescharacteristic
54C4⋊Dic59—21no—
55C4⋊Dic59—41no—
56C4⋊Dic59—41no—
57C4⋊Dic59—41no—
58C4⋊Dic59—41no—
59Dic59⋊C4—41no—
60C4×Dic59—41no—
61C2×C59⋊C8—41no—
62Dic236—21no—
63Dic236—41no—
64Dic236—41no—
65Dic236—81no—
66Dic236SD1612yes—
67C16×C59—41no—
68C16×C59—41no—
69C2×C4×C59#12111yescharacteristic
70C2×C4×C59C2×D811yescharacteristic
71C2×C4×C59AGL(1,ℤ/8)11yescharacteristic
72C2×Dic59—41no—
73C2×Dic59—41no—
74C2×Dic59—81no—
75C2×Dic59—81no—
76Dic118—22no—
77Dic118—41no—
78Dic118—82no—
79Dic118—81no—
80Dic118—81no—
81C8×C59—21no—
82C8×C59—21no—
83C8×C59—41no—
84C8×C59Q3212yescomplemented
85C8×C59C2×SD1611yescharacteristic
86C8×C59#13511yescharacteristic
87C59⋊C8—81no—
88#12421—591nomaximal, Sylow
89C22×C59#45911yescharacteristic
90C4×C59—21no—
91C4×C59#46511yescharacteristic
92C4×C59#47111yescharacteristic
93C4×C59C2×Q3211yescharacteristic
94C4×C59#51011yescharacteristic
95Dic59—42no—
96Dic59—81no—
97Dic59—161no—
98Dic59—161no—
99#2227—591no—
100#2209—591no—
101#1707—591no—
102C8×Q16—591no—
103#1367D5911yescharacteristic
104#1365—591no—
105#1362—591no—
106C2×C59#166511yescharacteristic
107C2×C59#220911yescharacteristic
108C2×C59#221211yescharacteristic
109C2×Q32—1181no—
110#500—591no—
111#498—1181no—
112#494—591no—
113#487—1181no—
114C8×Q8—1181no—
115C4×Q16—591no—
116#366—1181no—
117C4⋊C16C2×D5911yescharacteristic
118C4⋊C16C2×D5911yescharacteristic
119#358—1181no—
120#358—1181no—
121#335—591no—
122Q8⋊C8—1181no—
123C82C2×D5911yescharacteristic
124C59#1242111yescharacteristic, complemented, Sylow
125C2×Q16—591no—
126C2×Q16—1181no—
127C2×Q16—1181no—
128C4⋊Q8—1181no—
129C4⋊Q8—1181no—
130C4×Q8—1181no—
131Q32—2362no—
132C2×C16—21no—
133C2×C16—21no—
134#107—591no—
135#107—1181no—
136#107—1181no—
137#106—2361no—
138#106—2361no—
139C4⋊C8—1181no—
140C4⋊C8—2361no—
141#103—1181no—
142#103—2362no—
143C4×C8—2361no—
144C4×C8D23611yescharacteristic
145C4×C8D23611yescharacteristic
146C4×C8C22×D5911yescharacteristic
147C2×Q8—1181no—
148C2×Q8—2361no—
149C2×Q8—2361no—
150Q16—592no—
151Q16—1181no—
152Q16—4721no—
153Q16—2361no—
154Q16—2361no—
155C2×C8—21no—
156C2×C8—2361no—
157C2×C8D47211yescharacteristic
158C2×C8D47211yescharacteristic
159C2×C8D4×D5911yescharacteristic
160C2×C8#1174568911yescharacteristic
161C4⋊C4—1181no—
162C4⋊C4—2361no—
163C4⋊C4—2361no—
164C4⋊C4—2361no—
165C4⋊C4—2361no—
166C4⋊C4—2361no—
167C42—2361no—
168C42C2×D23611yescharacteristic
169C16—41no—
170C16—41no—
171Q8—1182no—
172Q8—4722no—
173Q8—4721no—
174Q8—4721no—
175Q8—2361no—
176C2×C4—4721no—
177C2×C4—4721no—
178C2×C4—2361no—
179C2×C4—2361no—
180C2×C4#1427370211yescharacteristic
181C2×C4C2×D47211yescharacteristic
182C2×C4#1427375511yescharacteristic
183C8—21no—
184C8—21no—
185C8—41no—
186C8—4721no—
187C8Dic47212yescomplemented
188C8SD16×D5911yescharacteristic
189C8#1427374811yescharacteristic
190C22#1683759811yescharacteristic
191C4—21no—
192C4—9441no—
193C4—9441no—
194C4—4721no—
195C4—2362no—
196C4#1683763211yescharacteristic
197C4#1683766611yescharacteristic
198C4C2×Dic47211yescharacteristic
199C4#1683784511yescharacteristic
200C2#2142343811yescharacteristic
201C2#2142614711yescharacteristic
202C2#2142616611yescharacteristic
subgroupG/H
centerC22#16837598
commutator, cosocleC4×C8×C59C23
FrattiniC4×C8C22×D59
FittingC59×#1367C2
socle, prime radicalC22×C59#459
hypercenter#1367D59
hypocenterC59#12421
LCSG ▷ C4×C8×C59 ▷ C2×C4×C59 ▷ C2×C59 ▷ C59
UCSC1 ◁ C22 ◁ C42 ◁ C82 ◁ #1367

Complements

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

NH ≅ G/Ntype
84. C8×C59Q32semidirect
124. C59#12421semidirect
187. C8Dic472semidirect

Maximal subgroups

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

subgroupindex
#214262492
#214261472
#214236932
C8×Dic2362
#214221532
#214221462
C59×#13672
#1242159