Finite Group Databasebeta

← #44483621

Subgroups — #44483621

Order 30592.

236 conjugacy classes of subgroups; only the 55 normal subgroups are shown.

normal subgroups only

This group has 236 conjugacy classes of subgroups — too many to draw. Only its 55 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#29505483C211yesmaximal, characteristic, complemented
2#29505146C211yesmaximal, characteristic, complemented
3#29504973C211yesmaximal, characteristic, complemented
4#29504968C211yesmaximal, characteristic
5#29504502C211yesmaximal, characteristic, complemented
6#29504499C211yesmaximal, characteristic, complemented
7#333×C239C211yesmaximal, characteristic, complemented
8C2×#16838537—21no—
9C2×#16838535—22no—
10C2×D1912—21no—
11#21439957C2211yescharacteristic
12#21439951—21no—
13#21439940—21no—
14#21439936—22no—
15C4×Dic478C2211yescharacteristic
16C4×D956C2211yescharacteristic
17#21439922—21no—
18C4⋊C4×D239—21no—
19#21439882—21no—
20#21439882—21no—
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—22no—
31C2×C4×D239—21no—
32#16838537—42no—
33#16838535—44no—
34D1912—42no—
35C2×C239⋊C8—21no—
36C4⋊Dic239—22no—
37C4⋊Dic239D411yescharacteristic
38C4⋊Dic239D411yescharacteristic
39Dic239⋊C4—22no—
40Dic239⋊C4—21no—
41(C2×D239)⋊C4—22no—
42(C2×D239)⋊C4—21no—
43C4×Dic239—21no—
44C2×Q8×C239D412yes—
45C2×C8×C239—21no—
46C2×C8×C239—21no—
47C4⋊C4×C239—21no—
48C4⋊C4×C239—21no—
49C42×C239C2311yescharacteristic
50C22×D239—21no—
51C22×D239—41no—
52Dic478—21no—
53Dic478—21no—
54D956—21no—
55D956—42no—
56D956—41no—
57D956—41no—
58D956—41no—
59D956—41no—
60D956SD1612yescomplemented
61C2×Dic239—21no—
62C2×Dic239—21no—
63C2×Dic239—21no—
64C4×D239—41no—
65C4×D239—41no—
66C4×D239—82no—
67C239⋊C8—22no—
68Q8×C239—42no—
69C2×C4×C239—22no—
70C2×C4×C239C2×D411yescharacteristic
71C2×C4×C239C2×D411yescharacteristic
72C2×C4×C239C2×D411yescharacteristic
73C8×C239—41no—
74C8×C239—41no—
75C22×C239#12011yescharacteristic
76C2×D239—22no—
77C2×D239—41no—
78C2×D239—41no—
79C2×D239—81no—
80C2×D239—81no—
81C2×D239—81no—
82C4×C239—21no—
83C4×C239—42no—
84C4×C239C2×SD1611yescharacteristic
85C4×C239#13511yescharacteristic
86C4×C239AGL(1,ℤ/8)11yescharacteristic
87C4×C239#13711yescharacteristic
88Dic239—41no—
89Dic239—41no—
90Dic239—41no—
91C2×C239#44811yescharacteristic
92C2×C239#44911yescharacteristic
93C2×C239#45311yescharacteristic
94D239—42no—
95D239—161no—
96C239#162211yescharacteristic, complemented, Sylow
97#1622—2391nomaximal, Sylow
98#554—2391no—
99#492—2391no—
100#460—2391no—
101#459—2391no—
102#333D23911yescharacteristic, complemented
103Q8⋊C8—2391no—
104D4⋊C8—2391no—
105C2×SD16—4781no—
106C2×SD16—4782no—
107C2×D8—4781no—
108C4⋊Q8C2×D23911yescharacteristic
109#127—2391no—
110#125—4781no—
111C22⋊Q8—4781no—
112C22⋊Q8—4782no—
113C4×Q8—2391no—
114C4×D4—4781no—
115C4×D4—2391no—
116C2×C4⋊C4—4781no—
117C4⋊C8C2×D23911yescharacteristic
118C4⋊C8C2×D23911yescharacteristic
119#102—4781no—
120#102—4781no—
121C4×C8—2391no—
122C2×Q8—2391no—
123C2×Q8D95612yes—
124C2×D4—4781no—
125C2×D4—4781no—
126C2×D4—4781no—
127C2×D4—2391no—
128C22×C4—4782no—
129C22×C4—4781no—
130SD16—9562no—
131SD16—9564no—
132D8—9562no—
133C2×C8—21no—
134C2×C8—21no—
135C2×C8—4781no—
136C4⋊C4—21no—
137C4⋊C4—21no—
138C4⋊C4—4782no—
139C4⋊C4—4782no—
140C4⋊C4—4781no—
141C4⋊C4—2391no—
142C4⋊C4—2391no—
143C22⋊C4—4782no—
144C22⋊C4—4781no—
145C42—4781no—
146C42C22×D23911yescharacteristic
147C23—9561no—
148C23—4781no—
149Q8—42no—
150Q8—4781no—
151Q8—4781no—
152D4—9562no—
153D4—9561no—
154D4—9561no—
155D4—9561no—
156D4—9561no—
157D4—4781no—
158D4—2392no—
159C2×C4—22no—
160C2×C4—19122no—
161C2×C4—9561no—
162C2×C4—9561no—
163C2×C4—4781no—
164C2×C4—4781no—
165C2×C4—4781no—
166C2×C4D4×D23911yescharacteristic
167C2×C4D4×D23911yescharacteristic
168C2×C4C2×D95611yescharacteristic
169C8—41no—
170C8—41no—
171C8—4782no—
172C22—19121no—
173C22—19121no—
174C22—19121no—
175C22—9561no—
176C22—9561no—
177C22—4782no—
178C22#2143993011yescharacteristic
179C4—21no—
180C4—42no—
181C4—9561no—
182C4—9561no—
183C4—9561no—
184C4SD16×D23911yescharacteristic
185C4#2143998311yescharacteristic
186C4#2143998711yescharacteristic
187C4#2143999211yescharacteristic
188C2—9562no—
189C2—38241no—
190C2#2950491211yescharacteristic
191C2#2950492011yescharacteristic
192C2#2950494211yescharacteristic
subgroupG/H
centerC22#21439930
commutator, cosocleC42×C239C23
FrattiniC42C22×D239
Fitting#333×C239C2
socleC22×C239#120
prime radical#29504968C2
hypercenter#333D239
hypocenterC239#1622
LCSG ▷ C42×C239 ▷ C22×C239 ▷ C239
UCSC1 ◁ C22 ◁ C42 ◁ #333

Complements

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

NH ≅ G/Ntype
1. #29505483C2semidirect
2. #29505146C2semidirect
3. #29504973C2semidirect
5. #29504502C2semidirect
6. #29504499C2semidirect
7. #333×C239C2semidirect
60. D956SD16semidirect
96. C239#1622semidirect
102. #333D239semidirect

Maximal subgroups

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

subgroupindex
#295054832
#295051462
#295049732
#295049682
#295045022
#295044992
#333×C2392
#1622239