Finite Group Databasebeta

← #44485406

Subgroups — #44485406

Order 30592.

312 conjugacy classes of subgroups; only the 103 normal subgroups are shown.

normal subgroups only

This group has 312 conjugacy classes of subgroups — too many to draw. Only its 103 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
1C22×#16838538C211yesmaximal, characteristic
2C2×#21439893C211yesmaximal, characteristic
3C2×#21439885C211yesmaximal, characteristic
4C2×C8×Dic239C211yesmaximal, characteristic
5#29504679C211yesmaximal, characteristic
6#29504677C211yesmaximal, characteristic
7C2×#103×C239C211yesmaximal, characteristic
8C22×Dic478C2211yescharacteristic
9C2×#16838538—22no—
10C2×#16838538—22no—
11C2×#16838538C414yescomplemented
12C22×C239⋊C8C2211yescharacteristic
13C2×C4⋊Dic239C2211yescharacteristic
14C2×C4×Dic239C2211yescharacteristic
15#21439893—22no—
16#21439885—22no—
17C8×Dic239—22no—
18C239⋊#95—22no—
19C239⋊#95—22no—
20C22×Q8×C239C2211yescharacteristic
21C22×C8×C239C2211yescharacteristic
22C2×C4⋊C4×C239C2211yescharacteristic
23#103×C239—22no—
24C2×Dic478—21no—
25C2×Dic478—21no—
26C2×Dic478—21no—
27C2×Dic478—21no—
28C2×Dic478—21no—
29C2×Dic478C2×C412yes—
30C22×Dic239—21no—
31C22×Dic239—21no—
32C22×Dic239D412yes—
33#16838538—28no—
34C2×C239⋊C8C2×C412yes—
35C2×C239⋊C8D412yes—
36C2×C239⋊C8D412yes—
37C4⋊Dic239—21no—
38C4⋊Dic239—21no—
39C4×Dic239—21no—
40C4×Dic239—21no—
41C2×Q8×C239—21no—
42C2×Q8×C239—21no—
43C2×Q8×C239—21no—
44C2×Q8×C239—21no—
45C2×Q8×C239—21no—
46C2×Q8×C239C2×C412yes—
47C22×C4×C239—21no—
48C22×C4×C239—21no—
49C22×C4×C239C2311yescharacteristic
50C2×C8×C239—21no—
51C2×C8×C239—21no—
52C2×C8×C239D412yes—
53C4⋊C4×C239—21no—
54C4⋊C4×C239—21no—
55Dic478—22no—
56Dic478—22no—
57Dic478—41no—
58Dic478—41no—
59C2×Dic239—22no—
60C2×Dic239—22no—
61C2×Dic239—22no—
62C2×Dic239—41no—
63C2×Dic239—41no—
64C2×Dic239—41no—
65C2×Dic239—42no—
66C2×Dic239Q1614yescomplemented
67C239⋊C8C22⋊C414yes—
68C23×C239C2×D411yescharacteristic
69Q8×C239—22no—
70Q8×C239—22no—
71Q8×C239—41no—
72Q8×C239—41no—
73C2×C4×C239—22no—
74C2×C4×C239—41no—
75C2×C4×C239—41no—
76C2×C4×C239—41no—
77C2×C4×C239—42no—
78C2×C4×C239C22×C411yescharacteristic
79C2×C4×C239C2×D411yescharacteristic
80C2×C4×C239C2×D411yescharacteristic
81C2×C4×C239C2×D411yescharacteristic
82C2×C4×C239#4111yescharacteristic
83C2×C4×C239#4111yescharacteristic
84C8×C239—22no—
85C22×C239C4×D411yescharacteristic
86C22×C239#12111yescharacteristic
87C22×C239#12711yescharacteristic
88C22×C239C2×Q1612yes—
89C22×C239#13512yes—
90C4×C239—42no—
91C4×C239—81no—
92C4×C239C2×C22⋊C411yescharacteristic
93C4×C239C4×D411yescharacteristic
94C4×C239#12111yescharacteristic
95C4×C239#12411yescharacteristic
96Dic239—24no—
97Dic239—42no—
98Dic239—81no—
99C2×C239#39011yescharacteristic
100C2×C239C4×Q1612yes—
101C2×C239#46712yes—
102C2×C239#49411yescharacteristic
103C2×C239#49511yescharacteristic
104C239#196911yescharacteristic, complemented, Sylow
105#1969—2391nomaximal, Sylow
106C22×Q16—2391no—
107C2×#107—2391no—
108C2×#103—2391no—
109C2×#103D23911yescharacteristic
110C2×C4×C8—2391no—
111#391—2391no—
112#391—2391no—
113C22×Q8—2391no—
114C22×Q8C2×D23911yescharacteristic
115C2×Q16—4782no—
116C2×Q16—4782no—
117C2×Q16—2394no—
118C22×C8—2391no—
119C22×C8C2×D23911yescharacteristic
120C2×C4⋊C4—2391no—
121C2×C4⋊C4C2×D23911yescharacteristic
122C2×C42—2391no—
123#107—4782no—
124#103—22no—
125#103—4782no—
126C4×C8—4782no—
127#95—4782no—
128#95—4782no—
129C2×Q8—21no—
130C2×Q8—21no—
131C2×Q8—21no—
132C2×Q8—21no—
133C2×Q8—21no—
134C2×Q8—4781no—
135C2×Q8—4781no—
136C2×Q8—4781no—
137C2×Q8—4781no—
138C2×Q8—4781no—
139C2×Q8—2392no—
140C2×Q8C4×D23912yes—
141C22×C4—21no—
142C22×C4—21no—
143C22×C4—4781no—
144C22×C4—4781no—
145C22×C4—2392no—
146C22×C4C22×D23911yescharacteristic
147Q16—4788no—
148C2×C8—21no—
149C2×C8—21no—
150C2×C8—2392no—
151C2×C8—2392no—
152C2×C8—2392no—
153C2×C8C22⋊D23912yes—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—4781no—
157C4⋊C4—4781no—
158C42—4781no—
159C42—4781no—
160C23D4×D23911yescharacteristic
161Q8—22no—
162Q8—22no—
163Q8—41no—
164Q8—41no—
165Q8—9561no—
166Q8—9561no—
167Q8—4782no—
168Q8—4782no—
169C2×C4—22no—
170C2×C4—41no—
171C2×C4—41no—
172C2×C4—41no—
173C2×C4—42no—
174C2×C4—9561no—
175C2×C4—9562no—
176C2×C4—9561no—
177C2×C4—9561no—
178C2×C4—4782no—
179C2×C4—4782no—
180C2×C4—4782no—
181C2×C4—2394no—
182C2×C4C2×C4×D23911yescharacteristic
183C2×C4D4×D23911yescharacteristic
184C2×C4D4×D23911yescharacteristic
185C2×C4C2×C22⋊D23911yescharacteristic
186C2×C4#1683854711yescharacteristic
187C2×C4#1683854811yescharacteristic
188C8—22no—
189C8—2394no—
190C22(C22⋊D239)⋊C411yescharacteristic
191C22#2143993311yescharacteristic
192C22#2143995611yescharacteristic
193C22Q16×D23912yes—
194C22#2143998112yes—
195C4—42no—
196C4—81no—
197C4—19121no—
198C4—9562no—
199C4—4784no—
200C4C22⋊C4×D23911yescharacteristic
201C4C4×C22⋊D23911yescharacteristic
202C4#2143993211yescharacteristic
203C4#2143994611yescharacteristic
204C2#2950467211yescharacteristic
205C2#2950486412yes—
206C2#2950501212yes—
207C2#2950515011yescharacteristic
208C2#2950515311yescharacteristic
subgroupG/H
centerC23D4×D239
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
FittingC2×#103×C239C2
socle, prime radicalC23×C239C2×D4
cosocleC22×C4×C239C23
hypercenterC2×#103D239
hypocenterC239#1969
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C23 ◁ C22×C4 ◁ C2×#103

Complements

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

NH ≅ G/Ntype
11. C2×#16838538C4semidirect
66. C2×Dic239Q16semidirect
104. C239#1969semidirect

Maximal subgroups

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

subgroupindex
C22×#168385382
C2×#214398932
C2×#214398852
C2×C8×Dic2392
#295046792
#295046772
C2×#103×C2392
#1969239