Finite Group Databasebeta

← #44484580

Subgroups — #44484580

Order 30592.

316 conjugacy classes of subgroups; only the 101 normal subgroups are shown.

normal subgroups only

This group has 316 conjugacy classes of subgroups — too many to draw. Only its 101 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×#16838531C211yesmaximal, characteristic
2C2×#21439893C211yesmaximal, characteristic, complemented
3C2×#21439891C211yesmaximal, characteristic, complemented
4#29504629C211yesmaximal, characteristic
5#29504629C211yesmaximal, characteristic
6#29504535C211yesmaximal, characteristic, complemented
7#340×C239C211yesmaximal, characteristic, complemented
8C22×C4×D239C2211yescharacteristic
9C2×#16838531—22no—
10C2×#16838531—22no—
11C2×#16838531C414yescomplemented
12C22×C239⋊C8C2211yescharacteristic
13C2×C4⋊Dic239C2211yescharacteristic
14C2×C4⋊Dic239C2211yescharacteristic
15C2×(C2×D239)⋊C4—21no—
16C2×(C2×D239)⋊C4—21no—
17#21439893—22no—
18#21439891—22no—
19C239⋊#95—21no—
20C239⋊#95—21no—
21C22×C8×C239C2211yescharacteristic
22C2×C4⋊C4×C239C2211yescharacteristic
23C2×C4⋊C4×C239C2211yescharacteristic
24C23×D239D411yescharacteristic
25C22×Dic239—21no—
26C22×Dic239—21no—
27C22×Dic239D411yescharacteristic
28C2×C4×D239—21no—
29C2×C4×D239—21no—
30C2×C4×D239—21no—
31C2×C4×D239—21no—
32C2×C4×D239C2×C412yes—
33C2×C4×D239Q812yes—
34#16838531—28no—
35C2×C239⋊C8C2×C412yes—
36C2×C239⋊C8D412yes—
37C2×C239⋊C8D412yes—
38C4⋊Dic239—21no—
39C4⋊Dic239—21no—
40C4⋊Dic239—21no—
41C4⋊Dic239—21no—
42(C2×D239)⋊C4—42no—
43(C2×D239)⋊C4—42no—
44C22×C4×C239—21no—
45C22×C4×C239—21no—
46C22×C4×C239C2311yescharacteristic
47C2×C8×C239—21no—
48C2×C8×C239—21no—
49C2×C8×C239C2×C412yes—
50C4⋊C4×C239—21no—
51C4⋊C4×C239—21no—
52C4⋊C4×C239—21no—
53C4⋊C4×C239—21no—
54C22×D239—21no—
55C22×D239—21no—
56C22×D239—21no—
57C22×D239—21no—
58C22×D239—21no—
59C22×D239—21no—
60C22×D239C4⋊C412yes—
61C2×Dic239—21no—
62C2×Dic239—21no—
63C2×Dic239—41no—
64C2×Dic239—41no—
65C2×Dic239—41no—
66C2×Dic239—41no—
67C2×Dic239—41no—
68C2×Dic239—41no—
69C2×Dic239C4⋊C412yes—
70C4×D239—22no—
71C4×D239—22no—
72C4×D239—22no—
73C4×D239—22no—
74C239⋊C8C22⋊C414yescomplemented
75C23×C239C2×D411yescharacteristic
76C2×C4×C239—41no—
77C2×C4×C239—41no—
78C2×C4×C239—41no—
79C2×C4×C239—41no—
80C2×C4×C239—41no—
81C2×C4×C239—41no—
82C2×C4×C239C22×C411yescharacteristic
83C2×C4×C239C2×D411yescharacteristic
84C2×C4×C239C2×D411yescharacteristic
85C2×C4×C239C2×Q811yescharacteristic
86C2×C4×C239#4111yescharacteristic
87C2×C4×C239#4111yescharacteristic
88C8×C239—22no—
89C22×C239C2×C4⋊C411yescharacteristic
90C22×C239#12111yescharacteristic
91C22×C239#12111yescharacteristic
92C22×C239AGL(1,ℤ/8)11yescharacteristic
93C22×C239AGL(1,ℤ/8)11yescharacteristic
94C22×C239#13711yescharacteristic
95C22×C239#13711yescharacteristic
96C2×D239—22no—
97C2×D239—22no—
98C2×D239—22no—
99C2×D239—41no—
100C2×D239—41no—
101C2×D239—41no—
102C2×D239—41no—
103C4×C239—81no—
104C4×C239—81no—
105C4×C239C2×C22⋊C411yescharacteristic
106C4×C239#11711yescharacteristic
107C4×C239C22⋊Q811yescharacteristic
108C4×C239C22⋊Q811yescharacteristic
109Dic239—22no—
110Dic239—81no—
111Dic239—81no—
112C2×C239#38011yescharacteristic
113C2×C239#42811yescharacteristic
114C2×C239#42811yescharacteristic
115C2×C239#46811yescharacteristic
116C2×C239#46811yescharacteristic
117C2×C239#46911yescharacteristic
118C2×C239#47011yescharacteristic
119D239—42no—
120C239#180911yescharacteristic, complemented, Sylow
121#1809—2391nomaximal, Sylow
122C22×M16—2391no—
123C2×#107—2391no—
124C2×#106—2391no—
125#380—2391no—
126#380—2391no—
127#340—2391no—
128#340D23911yescharacteristic, complemented
129C23×C4—2391no—
130C2×M16—4782no—
131C2×M16—4782no—
132C2×M16—2394no—
133C22×C8—2391no—
134C22×C8C2×D23911yescharacteristic
135C2×C4⋊C4—2391no—
136C2×C4⋊C4—2391no—
137C2×C4⋊C4C2×D23911yescharacteristic
138C2×C4⋊C4C2×D23911yescharacteristic
139C2×C22⋊C4—4781no—
140C2×C22⋊C4—4781no—
141#107—4782no—
142#106—4782no—
143#95—4781no—
144#95—4781no—
145C24—2391no—
146C22×C4—21no—
147C22×C4—21no—
148C22×C4—4781no—
149C22×C4—4781no—
150C22×C4—4781no—
151C22×C4—4781no—
152C22×C4—4781no—
153C22×C4—4781no—
154C22×C4—2391no—
155C22×C4—2392no—
156C22×C4—2392no—
157C22×C4C22×D23911yescharacteristic
158M16—4788no—
159C2×C8—21no—
160C2×C8—21no—
161C2×C8—2392no—
162C2×C8—2392no—
163C2×C8—2392no—
164C2×C8C4×D23912yes—
165C4⋊C4—21no—
166C4⋊C4—21no—
167C4⋊C4—21no—
168C4⋊C4—21no—
169C4⋊C4—4781no—
170C4⋊C4—4781no—
171C4⋊C4—4781no—
172C4⋊C4—4781no—
173C22⋊C4—9562no—
174C22⋊C4—9562no—
175C23—4781no—
176C23—4781no—
177C23—4781no—
178C23—4781no—
179C23—4781no—
180C23—4781no—
181C23—2392no—
182C23D4×D23911yescharacteristic
183C2×C4—41no—
184C2×C4—41no—
185C2×C4—41no—
186C2×C4—41no—
187C2×C4—41no—
188C2×C4—41no—
189C2×C4—9561no—
190C2×C4—9561no—
191C2×C4—9561no—
192C2×C4—9561no—
193C2×C4—9561no—
194C2×C4—9561no—
195C2×C4—4781no—
196C2×C4—4781no—
197C2×C4—4782no—
198C2×C4—4782no—
199C2×C4—4782no—
200C2×C4—4782no—
201C2×C4—2392no—
202C2×C4C2×C4×D23911yescharacteristic
203C2×C4D4×D23911yescharacteristic
204C2×C4D4×D23911yescharacteristic
205C2×C4Q8×D23911yescharacteristic
206C2×C4#1683854811yescharacteristic
207C2×C4#1683854811yescharacteristic
208C8—22no—
209C8—2394no—
210C22—9561no—
211C22—9561no—
212C22—9561no—
213C22—9561no—
214C22—4782no—
215C22—4782no—
216C22—4782no—
217C22C4⋊C4×D23911yescharacteristic
218C22#2143993311yescharacteristic
219C22#2143993311yescharacteristic
220C22#2143998411yescharacteristic
221C22#2143998711yescharacteristic
222C22#2143998911yescharacteristic
223C22#2143999211yescharacteristic
224C4—81no—
225C4—81no—
226C4—19121no—
227C4—19121no—
228C4—4782no—
229C4C22⋊C4×D23911yescharacteristic
230C4#2143991711yescharacteristic
231C4#2143993811yescharacteristic
232C4#2143993811yescharacteristic
233C2—9562no—
234C2#2950463111yescharacteristic
235C2#2950481111yescharacteristic
236C2#2950481311yescharacteristic
237C2#2950501711yescharacteristic
238C2#2950502111yescharacteristic
239C2#2950502411yescharacteristic
240C2#2950502911yescharacteristic
subgroupG/H
centerC23D4×D239
commutatorC2×C4×C239C22×C4
FrattiniC22×C4C22×D239
Fitting#340×C239C2
socleC23×C239C2×D4
prime radicalC23×D239D4
cosocleC22×C4×C239C23
hypercenter#340D239
hypocenterC239#1809
LCSG ▷ C2×C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C23 ◁ C22×C4 ◁ #340

Complements

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

NH ≅ G/Ntype
2. C2×#21439893C2semidirect
3. C2×#21439891C2semidirect
6. #29504535C2semidirect
7. #340×C239C2semidirect
11. C2×#16838531C4semidirect
74. C239⋊C8C22⋊C4semidirect
120. C239#1809semidirect
128. #340D239semidirect

Maximal subgroups

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

subgroupindex
C22×#168385312
C2×#214398932
C2×#214398912
#295046292
#295045352
#340×C2392
#1809239