Finite Group Databasebeta

← #44486501

Subgroups — #44486501

Order 30592.

216 conjugacy classes of subgroups; only the 49 normal subgroups are shown.

normal subgroups only

This group has 216 conjugacy classes of subgroups — too many to draw. Only its 49 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#29505572C211yesmaximal, characteristic
2#29505215C212yesmaximal, complemented
3#29505030C211yesmaximal, characteristic, complemented
4#29504583C212yesmaximal, complemented
5#349×C239C211yesmaximal, characteristic, complemented
6C2×#16838548—21no—
7#21439993—22no—
8#21439988—22no—
9#21439982—21no—
10#21439982C2212yes—
11C2×Dic956C2211yescharacteristic, complemented
12#21439939—21no—
13Dic1912—22no—
14#21439905—22no—
15#21439892C2211yescharacteristic, complemented
16#21439885—21no—
17C2×M16×C239C2211yescharacteristic
18M32×C239C2212yescomplemented
19#16838548—22no—
20#16838548—22no—
21#16838548—41no—
22#16838548—41no—
23C2×Dic478—21no—
24C2×Dic478—21no—
25C2×D956—21no—
26C2×C22⋊D239—41no—
27C2×C4×D239—41no—
28Dic956—21no—
29Dic956—22no—
30Dic956D412yes—
31#16838537—22no—
32#16838537—22no—
33D1912—21no—
34D1912D412yes—
35C4⋊Dic239—21no—
36Dic239⋊C4—41no—
37C22⋊Dic239—41no—
38C22×C4×C239D411yescharacteristic
39M16×C239—22no—
40C2×C8×C239D411yescharacteristic
41C2×C8×C239C2311yescharacteristic
42C16×C239—22no—
43C22×D239—41no—
44Dic478—22no—
45Dic478—41no—
46Dic478—41no—
47Dic478—41no—
48D956—22no—
49D956—41no—
50C22⋊D239—42no—
51C22⋊D239—42no—
52C2×Dic239—41no—
53C2×Dic239—41no—
54C2×Dic239—41no—
55C4×D239—42no—
56C4×D239—42no—
57C23×C239D811yescharacteristic
58C2×C4×C239—21no—
59C2×C4×C239—21no—
60C2×C4×C239D811yescharacteristic
61C2×C4×C239C2×D411yescharacteristic
62C8×C239—21no—
63C8×C239C2×D412yes—
64C22×C239—21no—
65C22×C239—41no—
66C22×C239C2×D811yescharacteristic
67C2×D239—42no—
68C2×D239—82no—
69C4×C239—21no—
70C4×C239#12011yescharacteristic
71C4×C239AGL(1,ℤ/8)11yescharacteristic
72Dic239—42no—
73Dic239—81no—
74Dic239—81no—
75C2×C239—21no—
76C2×C239—41no—
77C2×C239#44711yescharacteristic
78D239—82no—
79C239#219111yescharacteristic, complemented, Sylow
80#2191—2391nomaximal, Sylow
81#575—2391no—
82#510—2392no—
83#470—2391no—
84#360—2392no—
85#349D23911yescharacteristic, complemented
86C2×#41—4781no—
87#137—4782no—
88AGL(1,ℤ/8)—4782no—
89#135—4781no—
90#135—2392no—
91C2×Q16—2391no—
92C2×M16C2×D23911yescharacteristic
93C22⋊Q8—4781no—
94Q32—4782no—
95SD32—4782no—
96M32C2×D23912yescomplemented
97#106—2391no—
98#103—4781no—
99#41—9561no—
100#41—9561no—
101#41—4782no—
102#41—4782no—
103C2×Q8—4781no—
104C2×Q8—4781no—
105C2×D4—9561no—
106C2×D4—4781no—
107C22×C4—9561no—
108C22×C4D95611yescharacteristic
109Q16—4781no—
110Q16—4782no—
111Q16—2392no—
112SD16—4782no—
113SD16—4782no—
114D8—4781no—
115D8—2392no—
116M16—22no—
117C2×C8D95611yescharacteristic
118C2×C8C22×D23911yescharacteristic
119C4⋊C4—9561no—
120C4⋊C4—4781no—
121C22⋊C4—9561no—
122C16—22no—
123C23—9561no—
124C23D191211yescharacteristic
125Q8—9561no—
126Q8—9561no—
127Q8—9561no—
128Q8—4782no—
129D4—9561no—
130D4—9562no—
131D4—9562no—
132D4—4782no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—9562no—
136C2×C4—9561no—
137C2×C4—9561no—
138C2×C4—9561no—
139C2×C4—9562no—
140C2×C4D191211yescharacteristic
141C2×C4C2×D95611yescharacteristic
142C8—21no—
143C8D4×D23912yes—
144C22—21no—
145C22—41no—
146C22—19122no—
147C22—9562no—
148C22C2×D191211yescharacteristic
149C4—21no—
150C4—19121no—
151C4—19121no—
152C4—9562no—
153C4#2143993011yescharacteristic
154C4#2143998811yescharacteristic
155C2—21no—
156C2—41no—
157C2—19122no—
158C2#2950490811yescharacteristic
subgroupG/H
centerC2#29504908
commutator, cosocleC2×C8×C239C23
FrattiniC2×C8C22×D239
Fitting#349×C239C2
socleC2×C239#447
prime radical#29505572C2
hypercenter#349D239
hypocenterC239#2191
LCSG ▷ C2×C8×C239 ▷ C4×C239 ▷ C2×C239 ▷ C239
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #29505215C2semidirect
3. #29505030C2semidirect
4. #29504583C2semidirect
5. #349×C239C2semidirect
11. C2×Dic956C22semidirect
15. #21439892C22semidirect
18. M32×C239C22semidirect
79. C239#2191semidirect
85. #349D239semidirect
96. M32C2×D239semidirect

Maximal subgroups

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

subgroupindex
#295055722
#295052152
#295050302
#295045832
#349×C2392
#2191239