Finite Group Databasebeta

← #44483659

Subgroups — #44483659

Order 30592.

216 conjugacy classes of subgroups; only the 53 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 53 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#29505496C211yesmaximal, characteristic, complemented
2#29505120C211yesmaximal, characteristic, complemented
3#29504973C211yesmaximal, characteristic, complemented
4#29504968C211yesmaximal, characteristic
5#29504502C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#332×C239C211yesmaximal, characteristic, complemented
8C2×#16838537—21no—
9C2×D1912—21no—
10#21439957C2211yescharacteristic
11#21439955—22no—
12#21439949—21no—
13#21439940—21no—
14Q8×Dic239—21no—
15C4×Dic478C2211yescharacteristic
16C4×D956C2211yescharacteristic
17#21439918—21no—
18#21439882—21no—
19#21439882—21no—
20#21439880—22no—
21C4×C239⋊C8C2211yescharacteristic
22C4⋊Q8×C239C2211yescharacteristic
23C4⋊C8×C239C2211yescharacteristic
24C4⋊C8×C239C2211yescharacteristic
25C2×Dic478D411yescharacteristic
26C2×D956—21no—
27C2×D956—21no—
28C2×D956—21no—
29C2×D956D411yescharacteristic
30C2×C4×D239—21no—
31#16838537—42no—
32D1912—42no—
33C2×C239⋊C8—21no—
34C4⋊Dic239—22no—
35C4⋊Dic239D411yescharacteristic
36C4⋊Dic239D411yescharacteristic
37Dic239⋊C4—21no—
38(C2×D239)⋊C4—22no—
39(C2×D239)⋊C4—22no—
40(C2×D239)⋊C4—21no—
41C4×Dic239—22no—
42C4×Dic239—21no—
43C2×Q8×C239—21no—
44C2×C8×C239—21no—
45C2×C8×C239—21no—
46C4⋊C4×C239—21no—
47C4⋊C4×C239D412yes—
48C42×C239C2311yescharacteristic
49C22×D239—21no—
50C22×D239—41no—
51Dic478—21no—
52Dic478—21no—
53D956—21no—
54D956—21no—
55D956—42no—
56D956—41no—
57D956—41no—
58D956—41no—
59D956—41no—
60C2×Dic239—21no—
61C2×Dic239—21no—
62C2×Dic239—21no—
63C4×D239—41no—
64C4×D239—41no—
65C239⋊C8—41no—
66Q8×C239—41no—
67Q8×C239—41no—
68C2×C4×C239—22no—
69C2×C4×C239C2×D411yescharacteristic
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C8×C239—41no—
73C8×C239—41no—
74C22×C239#12011yescharacteristic
75C2×D239—41no—
76C2×D239—41no—
77C2×D239—41no—
78C2×D239—81no—
79C2×D239—81no—
80C2×D239—81no—
81C4×C239—21no—
82C4×C239—42no—
83C4×C239#13511yescharacteristic
84C4×C239#13511yescharacteristic
85C4×C239AGL(1,ℤ/8)11yescharacteristic
86C4×C239AGL(1,ℤ/8)11yescharacteristic
87Dic239—41no—
88Dic239—41no—
89Dic239—41no—
90C2×C239#44911yescharacteristic
91C2×C239#44911yescharacteristic
92C2×C239#45411yescharacteristic
93D239—81no—
94D239—161no—
95C239#162811yescharacteristic, complemented, Sylow
96#1628—2391nomaximal, Sylow
97#556—2391no—
98#486—2391no—
99#460—2391no—
100#459—2391no—
101#332D23911yescharacteristic, complemented
102Q8⋊C8—2391no—
103D4⋊C8—2391no—
104C2×SD16—4781no—
105C2×D8—4781no—
106C4⋊Q8C2×D23911yescharacteristic
107#127—2391no—
108#126—4782no—
109#124—4781no—
110C22⋊Q8—4781no—
111C4×Q8—4781no—
112C4×Q8—2391no—
113C4×D4—2391no—
114#117—4781no—
115C4⋊C8C2×D23911yescharacteristic
116C4⋊C8C2×D23911yescharacteristic
117#102—4781no—
118#102—4781no—
119#102—4782no—
120C4×C8—2391no—
121C2×Q8—21no—
122C2×Q8—2391no—
123C2×D4—4781no—
124C2×D4—4781no—
125C2×D4—4781no—
126C2×D4—2391no—
127C22×C4—4781no—
128SD16—9562no—
129D8—9562no—
130C2×C8—21no—
131C2×C8—21no—
132C2×C8—4781no—
133C4⋊C4—21no—
134C4⋊C4—4782no—
135C4⋊C4—4781no—
136C4⋊C4—2391no—
137C4⋊C4—2391no—
138C4⋊C4D95612yes—
139C22⋊C4—4782no—
140C22⋊C4—4782no—
141C22⋊C4—4781no—
142C42—4782no—
143C42—4781no—
144C42C22×D23911yescharacteristic
145C23—9561no—
146C23—4781no—
147Q8—41no—
148Q8—41no—
149Q8—4781no—
150Q8—4781no—
151D4—9562no—
152D4—9561no—
153D4—9561no—
154D4—9561no—
155D4—9561no—
156D4—4781no—
157D4—4781no—
158C2×C4—22no—
159C2×C4—9561no—
160C2×C4—9561no—
161C2×C4—4781no—
162C2×C4—4781no—
163C2×C4—4781no—
164C2×C4D4×D23911yescharacteristic
165C2×C4D4×D23911yescharacteristic
166C2×C4C2×D95611yescharacteristic
167C8—41no—
168C8—41no—
169C8—9561no—
170C22—19121no—
171C22—19121no—
172C22—19121no—
173C22—9561no—
174C22—9561no—
175C22—9561no—
176C22#2143993011yescharacteristic
177C4—21no—
178C4—42no—
179C4—9561no—
180C4—9561no—
181C4—9561no—
182C4#2143998111yescharacteristic
183C4#2143998311yescharacteristic
184C4#2143998411yescharacteristic
185C4#2143998711yescharacteristic
186C2—19121no—
187C2—38241no—
188C2#2950491811yescharacteristic
189C2#2950492011yescharacteristic
190C2#2950494711yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#332×C239C2
socleC22×C239#120
prime radical#29504968C2
hypercenter#332D239
hypocenterC239#1628
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #332

Complements

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

NH ≅ G/Ntype
1. #29505496C2semidirect
2. #29505120C2semidirect
3. #29504973C2semidirect
5. #29504502C2semidirect
6. #29504499C2semidirect
7. #332×C239C2semidirect
95. C239#1628semidirect
101. #332D239semidirect

Maximal subgroups

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

subgroupindex
#295054962
#295051202
#295049732
#295049682
#295045022
#295044992
#332×C2392
#1628239