Finite Group Databasebeta

← #44483666

Subgroups — #44483666

Order 30592.

314 conjugacy classes of subgroups; only the 59 normal subgroups are shown.

normal subgroups only

This group has 314 conjugacy classes of subgroups — too many to draw. Only its 59 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
1D4×D956C211yesmaximal, characteristic
2#29505145C211yesmaximal, characteristic, complemented
3#29505063C211yesmaximal, characteristic, complemented
4#29505062C211yesmaximal, characteristic, complemented
5#29504515C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic, complemented
7D4⋊C8×C239C211yesmaximal, characteristic, complemented
8C22×D956—21no—
9C2×D4×D239—21no—
10C2×#16838537—22no—
11#21439960C2211yescharacteristic, complemented
12#21439957C2211yescharacteristic
13#21439935—21no—
14#21439934—21no—
15#21439930—22no—
16C4×D956C2211yescharacteristic
17#21439892—21no—
18#21439891—21no—
19C4⋊(C239⋊C8)C2211yescharacteristic, complemented
20#21439882—21no—
21#21439881—21no—
22C4×D4×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic, complemented
24C4×C8×C239C2211yescharacteristic, complemented
25C23×D239—22no—
26C2×Dic478—21no—
27C2×D956—22no—
28C2×D956—21no—
29C2×D956—21no—
30C2×D956—42no—
31C2×D956—42no—
32C2×D956D411yescharacteristic
33C2×D956D412yes—
34C2×C22⋊D239—22no—
35D4×D239—42no—
36D4×D239—42no—
37C2×C4×D239—21no—
38#16838537—44no—
39C2×C239⋊C8—21no—
40C4⋊Dic239—21no—
41C4⋊Dic239—21no—
42C4⋊Dic239D411yescharacteristic
43(C2×D239)⋊C4—22no—
44(C2×D239)⋊C4—21no—
45C2×D4×C239D411yescharacteristic
46C22×C4×C239—21no—
47C2×C8×C239—21no—
48C2×C8×C239—21no—
49C4⋊C4×C239D411yescharacteristic
50C22⋊C4×C239—21no—
51C42×C239C2311yescharacteristic
52C22×D239—21no—
53C22×D239—22no—
54C22×D239—44no—
55C22×D239—44no—
56C22×D239—82no—
57Dic478—42no—
58D956—21no—
59D956—42no—
60D956—44no—
61D956—41no—
62D956—41no—
63D956—41no—
64D956—41no—
65D956SD1612yescomplemented
66C22⋊D239—44no—
67C2×Dic239—21no—
68C2×Dic239—41no—
69C4×D239—41no—
70C4×D239—41no—
71C239⋊C8—41no—
72C23×C239—21no—
73D4×C239—21no—
74D4×C239SD1612yescomplemented
75C2×C4×C239—21no—
76C2×C4×C239—41no—
77C2×C4×C239—41no—
78C2×C4×C239C2×D411yescharacteristic
79C2×C4×C239C2×D411yescharacteristic
80C2×C4×C239C2×D411yescharacteristic
81C8×C239—22no—
82C8×C239—41no—
83C22×C239—22no—
84C22×C239—41no—
85C22×C239—41no—
86C22×C239#12011yescharacteristic
87C2×D239—22no—
88C2×D239—41no—
89C2×D239—41no—
90C2×D239—42no—
91C2×D239—42no—
92C2×D239—42no—
93C2×D239—88no—
94C4×C239—21no—
95C4×C239—41no—
96C4×C239C2×SD1611yescharacteristic
97C4×C239C2×SD1611yescharacteristic
98C4×C239AGL(1,ℤ/8)11yescharacteristic
99C4×C239AGL(1,ℤ/8)11yescharacteristic
100Dic239—41no—
101Dic239—81no—
102C2×C239—42no—
103C2×C239#45011yescharacteristic
104C2×C239#45011yescharacteristic
105C2×C239#45311yescharacteristic
106D239—42no—
107D239—82no—
108C239#162911yescharacteristic, complemented, Sylow
109#1629—2391nomaximal, Sylow
110D42—2391no—
111#492—2391no—
112#476—2391no—
113#476—2391no—
114#331—2391no—
115D4⋊C8—2391no—
116D4⋊C8D23911yescharacteristic, complemented
117C22×D4—4781no—
118C22×D4—4781no—
119C2×SD16—4782no—
120C4⋊Q8—2391no—
121#127—2391no—
122#121—4781no—
123#121—4781no—
124#120—4782no—
125C4×D4—2391no—
126C4×D4C2×D23911yescharacteristic
127#106—4781no—
128#106—4781no—
129C4⋊C8—2391no—
130C4⋊C8C2×D23911yescharacteristic, complemented
131#102—4781no—
132#102—4781no—
133C4×C8C2×D23911yescharacteristic, complemented
134C24—4782no—
135C2×Q8—4781no—
136C2×D4—9562no—
137C2×D4—9562no—
138C2×D4—9562no—
139C2×D4—9562no—
140C2×D4—4782no—
141C2×D4—4782no—
142C2×D4—4781no—
143C2×D4—4781no—
144C2×D4—2392no—
145C2×D4—2391no—
146C2×D4D95611yescharacteristic
147C22×C4—21no—
148C22×C4—4781no—
149SD16—9564no—
150C2×C8—21no—
151C2×C8—21no—
152C2×C8—4781no—
153C4⋊C4—4781no—
154C4⋊C4—4781no—
155C4⋊C4—2391no—
156C4⋊C4D95611yescharacteristic
157C22⋊C4—21no—
158C22⋊C4—4782no—
159C22⋊C4—4781no—
160C42C22×D23911yescharacteristic
161C23—21no—
162C23—19122no—
163C23—9564no—
164C23—9564no—
165C23—4782no—
166C23—4781no—
167Q8—9562no—
168D4—21no—
169D4—9562no—
170D4—9564no—
171D4—9564no—
172D4—9561no—
173D4—9561no—
174D4—9561no—
175D4—9561no—
176D4—4781no—
177D4—2392no—
178D4#1683853712yescomplemented
179C2×C4—21no—
180C2×C4—41no—
181C2×C4—41no—
182C2×C4—9561no—
183C2×C4—9561no—
184C2×C4—9561no—
185C2×C4—4781no—
186C2×C4D4×D23911yescharacteristic
187C2×C4D4×D23911yescharacteristic
188C2×C4C2×D95611yescharacteristic
189C8—22no—
190C8—41no—
191C8—9561no—
192C22—22no—
193C22—41no—
194C22—41no—
195C22—19128no—
196C22—9562no—
197C22—9562no—
198C22—9562no—
199C22—9561no—
200C22—9561no—
201C22—4782no—
202C22#2143993011yescharacteristic
203C4—21no—
204C4—41no—
205C4—19121no—
206C4—9561no—
207C4SD16×D23911yescharacteristic
208C4C2×#1683853711yescharacteristic
209C4#2143998411yescharacteristic
210C4#2143998811yescharacteristic
211C2—42no—
212C2—19122no—
213C2—9562no—
214C2#2950492411yescharacteristic
215C2#2950492511yescharacteristic
216C2#2950494111yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
FittingD4⋊C8×C239C2
socleC22×C239#120
prime radicalD4×D956C2
hypercenterD4⋊C8D239
hypocenterC239#1629
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ D4⋊C8

Complements

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

NH ≅ G/Ntype
2. #29505145C2semidirect
3. #29505063C2semidirect
4. #29505062C2semidirect
5. #29504515C2semidirect
6. #29504501C2semidirect
7. D4⋊C8×C239C2semidirect
11. #21439960C22semidirect
19. C4⋊(C239⋊C8)C22semidirect
23. C4⋊C8×C239C22semidirect
24. C4×C8×C239C22semidirect
65. D956SD16semidirect
74. D4×C239SD16semidirect
108. C239#1629semidirect
116. D4⋊C8D239semidirect
130. C4⋊C8C2×D239semidirect
133. C4×C8C2×D239semidirect
178. D4#16838537semidirect

Maximal subgroups

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

subgroupindex
D4×D9562
#295051452
#295050632
#295050622
#295045152
#295045012
D4⋊C8×C2392
#1629239