Finite Group Databasebeta

← #44486028

Subgroups — #44486028

Order 30592.

230 conjugacy classes of subgroups; only the 87 normal subgroups are shown.

normal subgroups only

This group has 230 conjugacy classes of subgroups — too many to draw. Only its 87 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
1C2×#21439892C211yesmaximal, characteristic
2C2×#21439891C211yesmaximal, characteristic
3#29504668C211yesmaximal, characteristic
4#29504641C211yesmaximal, characteristic
5#29504534C211yesmaximal, characteristic
6#29504526C211yesmaximal, characteristic
7#340×C239C211yesmaximal, characteristic
8C22×C239⋊C8C2211yescharacteristic
9C2×C4⋊Dic239C2211yescharacteristic
10C2×C4⋊Dic239C2211yescharacteristic
11C2×Dic239⋊C4—21no—
12C2×Dic239⋊C4—21no—
13C2×Dic239⋊C4—21no—
14C2×C4×Dic239C2211yescharacteristic
15#21439892—22no—
16#21439891—22no—
17C239⋊#95—21no—
18C22×C8×C239C2211yescharacteristic
19C2×C4⋊C4×C239C2211yescharacteristic
20C2×C4⋊C4×C239C2211yescharacteristic
21C22×Dic239—21no—
22C22×Dic239—21no—
23C22×Dic239D411yescharacteristic
24C22×Dic239D411yescharacteristic
25C2×C239⋊C8—21no—
26C2×C239⋊C8—21no—
27C2×C239⋊C8Q812yes—
28C4⋊Dic239—21no—
29C4⋊Dic239—21no—
30C4⋊Dic239—21no—
31C4⋊Dic239D412yes—
32Dic239⋊C4—42no—
33Dic239⋊C4—42no—
34Dic239⋊C4—42no—
35C4×Dic239—21no—
36C4×Dic239—21no—
37C22×C4×C239—21no—
38C22×C4×C239—21no—
39C22×C4×C239C2311yescharacteristic
40C2×C8×C239—21no—
41C2×C8×C239—21no—
42C2×C8×C239Q812yes—
43C4⋊C4×C239—21no—
44C4⋊C4×C239—21no—
45C4⋊C4×C239—21no—
46C4⋊C4×C239—21no—
47C2×Dic239—21no—
48C2×Dic239—21no—
49C2×Dic239—21no—
50C2×Dic239—21no—
51C2×Dic239—22no—
52C2×Dic239—41no—
53C2×Dic239—41no—
54C2×Dic239—41no—
55C2×Dic239—41no—
56C2×Dic239—41no—
57C2×Dic239SD1612yes—
58C2×Dic239SD1612yes—
59C239⋊C8—22no—
60C23×C239C2×D411yescharacteristic
61C2×C4×C239—41no—
62C2×C4×C239—41no—
63C2×C4×C239—41no—
64C2×C4×C239—41no—
65C2×C4×C239—41no—
66C2×C4×C239—41no—
67C2×C4×C239C2×D411yescharacteristic
68C2×C4×C239C2×Q811yescharacteristic
69C2×C4×C239C2×Q811yescharacteristic
70C2×C4×C239#4111yescharacteristic
71C2×C4×C239#4111yescharacteristic
72C2×C4×C239#4111yescharacteristic
73C8×C239—22no—
74C22×C239#12111yescharacteristic
75C22×C239#12311yescharacteristic
76C22×C239C4⋊Q811yescharacteristic
77C22×C239C2×SD1611yescharacteristic
78C22×C239C2×SD1611yescharacteristic
79C22×C239AGL(1,ℤ/8)11yescharacteristic
80C22×C239#13711yescharacteristic
81C4×C239—81no—
82C4×C239—81no—
83C4×C239C22⋊Q811yescharacteristic
84C4×C239C22⋊Q811yescharacteristic
85C4×C239#12511yescharacteristic
86C4×C239#12511yescharacteristic
87Dic239—22no—
88Dic239—22no—
89Dic239—42no—
90Dic239—81no—
91C2×C239#39811yescharacteristic
92C2×C239#46011yescharacteristic
93C2×C239#46111yescharacteristic
94C2×C239#48111yescharacteristic
95C2×C239#48311yescharacteristic
96C2×C239#49811yescharacteristic
97C2×C239#50111yescharacteristic
98C239#208411yescharacteristic, complemented, Sylow
99#2084—2391nomaximal, Sylow
100C2×#106—2391no—
101C2×#106—2391no—
102#389—2391no—
103#384—2391no—
104#340—2391no—
105#340D23911yescharacteristic
106#336—2391no—
107C22×C8—2391no—
108C22×C8C2×D23911yescharacteristic
109C2×C4⋊C4—4781no—
110C2×C4⋊C4—4781no—
111C2×C4⋊C4—4781no—
112C2×C4⋊C4—2391no—
113C2×C4⋊C4—2391no—
114C2×C4⋊C4C2×D23911yescharacteristic
115C2×C4⋊C4C2×D23911yescharacteristic
116C2×C42—2391no—
117#106—4782no—
118#106—4782no—
119#95—4781no—
120C22×C4—21no—
121C22×C4—21no—
122C22×C4—4781no—
123C22×C4—4781no—
124C22×C4—2391no—
125C22×C4—2391no—
126C22×C4C22×D23911yescharacteristic
127C2×C8—21no—
128C2×C8—21no—
129C2×C8—4781no—
130C2×C8—4781no—
131C2×C8—2392no—
132C2×C8Dic47812yes—
133C4⋊C4—21no—
134C4⋊C4—21no—
135C4⋊C4—21no—
136C4⋊C4—21no—
137C4⋊C4—9562no—
138C4⋊C4—9562no—
139C4⋊C4—9562no—
140C4⋊C4—4781no—
141C4⋊C4—4781no—
142C4⋊C4—4781no—
143C4⋊C4—2392no—
144C42—4781no—
145C42—4781no—
146C23D4×D23911yescharacteristic
147C2×C4—41no—
148C2×C4—41no—
149C2×C4—41no—
150C2×C4—41no—
151C2×C4—41no—
152C2×C4—41no—
153C2×C4—9561no—
154C2×C4—9561no—
155C2×C4—9561no—
156C2×C4—9561no—
157C2×C4—9561no—
158C2×C4—4782no—
159C2×C4—4781no—
160C2×C4—4781no—
161C2×C4—4781no—
162C2×C4—4781no—
163C2×C4—2392no—
164C2×C4—2392no—
165C2×C4D4×D23911yescharacteristic
166C2×C4Q8×D23911yescharacteristic
167C2×C4C2×Dic47811yescharacteristic
168C2×C4#1683854711yescharacteristic
169C2×C4#1683854811yescharacteristic
170C2×C4#1683854811yescharacteristic
171C8—22no—
172C8—4782no—
173C22#2143993311yescharacteristic
174C22#2143994211yescharacteristic
175C22#2143995911yescharacteristic
176C22SD16×D23911yescharacteristic
177C22SD16×D23911yescharacteristic
178C22#2143998411yescharacteristic
179C22#2143999211yescharacteristic
180C4—81no—
181C4—81no—
182C4—19121no—
183C4—9562no—
184C4—4782no—
185C4—4782no—
186C4#2143993711yescharacteristic
187C4#2143993811yescharacteristic
188C4#2143995011yescharacteristic
189C4#2143995211yescharacteristic
190C2#2950470611yescharacteristic
191C2#2950497111yescharacteristic
192C2#2950497611yescharacteristic
193C2#2950508911yescharacteristic
194C2#2950510111yescharacteristic
195C2#2950516911yescharacteristic
196C2#2950518011yescharacteristic
subgroupG/H
centerC23D4×D239
commutator, cosocleC22×C4×C239C23
FrattiniC22×C4C22×D239
Fitting#340×C239C2
socle, prime radicalC23×C239C2×D4
hypercenter#340D239
hypocenterC239#2084
LCSG ▷ C22×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
98. C239#2084semidirect

Maximal subgroups

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

subgroupindex
C2×#214398922
C2×#214398912
#295046682
#295046412
#295045342
#295045262
#340×C2392
#2084239