Finite Group Databasebeta

← #44483724

Subgroups — #44483724

Order 30592.

308 conjugacy classes of subgroups; only the 57 normal subgroups are shown.

normal subgroups only

This group has 308 conjugacy classes of subgroups — too many to draw. Only its 57 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#29505407C211yesmaximal, characteristic
2#29505049C211yesmaximal, characteristic, complemented
3#29504974C211yesmaximal, characteristic, complemented
4#29504516C211yesmaximal, characteristic, complemented
5#29504501C211yesmaximal, characteristic, complemented
6#29504501C211yesmaximal, characteristic, complemented
7#486×C239C211yesmaximal, characteristic, complemented
8C2×D4×D239—21no—
9C2×D4×D239—21no—
10C2×#16838535—21no—
11#21439931—21no—
12#21439931—21no—
13#21439928—22no—
14C4×D956C2211yescharacteristic
15C4×D956C2211yescharacteristic
16#21439893—21no—
17C4⋊(C239⋊C8)C2211yescharacteristic, complemented
18C4⋊(C239⋊C8)C2211yescharacteristic, complemented
19#21439884—21no—
20#21439880—21no—
21C4⋊Q8×C239C2211yescharacteristic, complemented
22#127×C239C2211yescharacteristic
23#102×C239—22no—
24C4×C8×C239C2211yescharacteristic, complemented
25C23×D239—22no—
26C2×D956D411yescharacteristic
27C2×D956D411yescharacteristic
28C2×C22⋊D239—22no—
29C2×C22⋊D239—22no—
30D4×D239—42no—
31D4×D239—42no—
32D4×D239—42no—
33D4×D239—42no—
34C2×C4×D239—21no—
35C2×C4×D239—21no—
36#16838535—42no—
37C2×C239⋊C8—21no—
38C2×C239⋊C8—21no—
39C4⋊Dic239D411yescharacteristic
40C4⋊Dic239D411yescharacteristic
41C22⋊Dic239—22no—
42(C2×D239)⋊C4—21no—
43(C2×D239)⋊C4—21no—
44C2×Q8×C239—21no—
45C2×D4×C239—21no—
46C2×D4×C239—21no—
47C2×D4×C239D412yes—
48C2×C8×C239—21no—
49C4⋊C4×C239—21no—
50C4⋊C4×C239—21no—
51C42×C239C2311yescharacteristic
52C22×D239—21no—
53C22×D239—21no—
54C22×D239—44no—
55C22×D239—44no—
56C22×D239—82no—
57D956—21no—
58D956—21no—
59D956D812yes—
60D956SD1612yescomplemented
61C22⋊D239—44no—
62C22⋊D239—44no—
63C2×Dic239—21no—
64C2×Dic239—21no—
65C4×D239—41no—
66C4×D239—41no—
67C4×D239—41no—
68C4×D239—41no—
69C239⋊C8—41no—
70C239⋊C8—41no—
71C23×C239—22no—
72Q8×C239—41no—
73Q8×C239—41no—
74D4×C239—42no—
75D4×C239—41no—
76D4×C239—41no—
77D4×C239—41no—
78D4×C239—41no—
79C2×C4×C239—41no—
80C2×C4×C239C2×D411yescharacteristic
81C2×C4×C239C2×D411yescharacteristic
82C2×C4×C239C2×D411yescharacteristic
83C8×C239—41no—
84C22×C239—42no—
85C22×C239—42no—
86C22×C239—42no—
87C22×C239#12011yescharacteristic
88C2×D239—22no—
89C2×D239—22no—
90C2×D239—41no—
91C2×D239—41no—
92C2×D239—41no—
93C2×D239—41no—
94C2×D239—88no—
95C4×C239—21no—
96C4×C239—81no—
97C4×C239C2×D811yescharacteristic
98C4×C239C2×SD1611yescharacteristic
99C4×C239AGL(1,ℤ/8)11yescharacteristic
100C4×C239AGL(1,ℤ/8)11yescharacteristic
101Dic239—41no—
102Dic239—41no—
103C2×C239—82no—
104C2×C239#44711yescharacteristic
105C2×C239#45011yescharacteristic
106C2×C239#45511yescharacteristic
107D239—42no—
108D239—42no—
109C239#163911yescharacteristic, complemented, Sylow
110#1639—2391nomaximal, Sylow
111D42—2391no—
112#486D23911yescharacteristic, complemented
113#474—2391no—
114#461—2391no—
115#331—2391no—
116D4⋊C8—2391no—
117D4⋊C8—2391no—
118C22×D4—4781no—
119C22×D4—4781no—
120C2×SD16—4781no—
121C4⋊Q8C2×D23911yescharacteristic, complemented
122#127C2×D23911yescharacteristic
123#121—4781no—
124#121—4781no—
125#120—4782no—
126C4×D4—2391no—
127C4×D4—2391no—
128#107—4781no—
129C4⋊C8—2391no—
130C4⋊C8—2391no—
131#103—4781no—
132#102—22no—
133#102—4781no—
134C4×C8C2×D23911yescharacteristic, complemented
135C24—4782no—
136C2×Q8—21no—
137C2×D4—21no—
138C2×D4—21no—
139C2×D4—9562no—
140C2×D4—9562no—
141C2×D4—9562no—
142C2×D4—9562no—
143C2×D4—4782no—
144C2×D4—4782no—
145C2×D4—2391no—
146C2×D4—2391no—
147C2×D4C22⋊D23912yes—
148C22×C4—4781no—
149C22×C4—4781no—
150SD16—9562no—
151C2×C8—21no—
152C2×C8—4781no—
153C2×C8—4781no—
154C4⋊C4—21no—
155C4⋊C4—21no—
156C4⋊C4—2391no—
157C4⋊C4—2391no—
158C22⋊C4—4782no—
159C22⋊C4—4781no—
160C22⋊C4—4781no—
161C42C22×D23911yescharacteristic
162C23—22no—
163C23—19122no—
164C23—9564no—
165C23—9564no—
166C23—4781no—
167C23—4781no—
168Q8—41no—
169Q8—41no—
170D4—42no—
171D4—41no—
172D4—41no—
173D4—41no—
174D4—41no—
175D4—9564no—
176D4—9564no—
177D4—4781no—
178D4—4781no—
179D4—2392no—
180D4—2392no—
181C2×C4—41no—
182C2×C4—9561no—
183C2×C4—9561no—
184C2×C4—9561no—
185C2×C4—9561no—
186C2×C4—4781no—
187C2×C4—4781no—
188C2×C4D4×D23911yescharacteristic
189C2×C4D4×D23911yescharacteristic
190C2×C4C2×C22⋊D23911yescharacteristic
191C8—41no—
192C8—9561no—
193C8—9561no—
194C22—42no—
195C22—42no—
196C22—42no—
197C22—19128no—
198C22—9561no—
199C22—9561no—
200C22—9561no—
201C22—9561no—
202C22—4782no—
203C22—4782no—
204C22#2143992811yescharacteristic
205C4—21no—
206C4—81no—
207C4—9561no—
208C4—9561no—
209C4D8×D23911yescharacteristic
210C4SD16×D23911yescharacteristic
211C4#2143998411yescharacteristic
212C4#2143998711yescharacteristic
213C2—82no—
214C2—9562no—
215C2—9562no—
216C2#2950490411yescharacteristic
217C2#2950492111yescharacteristic
218C2#2950494911yescharacteristic
subgroupG/H
centerC22#21439928
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#486×C239C2
socleC22×C239#120
prime radical#29505407C2
hypercenter#486D239
hypocenterC239#1639
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #486

Complements

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

NH ≅ G/Ntype
2. #29505049C2semidirect
3. #29504974C2semidirect
4. #29504516C2semidirect
5. #29504501C2semidirect
6. #29504501C2semidirect
7. #486×C239C2semidirect
17. C4⋊(C239⋊C8)C22semidirect
18. C4⋊(C239⋊C8)C22semidirect
21. C4⋊Q8×C239C22semidirect
24. C4×C8×C239C22semidirect
60. D956SD16semidirect
109. C239#1639semidirect
112. #486D239semidirect
121. C4⋊Q8C2×D239semidirect
134. C4×C8C2×D239semidirect

Maximal subgroups

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

subgroupindex
#295054072
#295050492
#295049742
#295045162
#295045012
#486×C2392
#1639239