Finite Group Databasebeta

← #28392527

Subgroups — #28392527

Order 14464.

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#20299398C211yesmaximal, characteristic
2#20299041C212yesmaximal, complemented
3#20298856C211yesmaximal, characteristic, complemented
4#20298409C212yesmaximal, complemented
5#349×C113C211yesmaximal, characteristic, complemented
6C2×#14268647—21no—
7#16813655—22no—
8#16813650—22no—
9#16813644—21no—
10#16813644C2212yes—
11C2×Dic452C2211yescharacteristic, complemented
12#16813601—21no—
13Dic904—22no—
14#16813567—22no—
15#16813554C2211yescharacteristic, complemented
16#16813547—21no—
17C2×M16×C113C2211yescharacteristic
18M32×C113C2212yescomplemented
19#14268647—22no—
20#14268647—22no—
21#14268647—41no—
22#14268647—41no—
23C2×Dic226—21no—
24C2×Dic226—21no—
25C2×D452—21no—
26C2×C22⋊D113—41no—
27C2×C4×D113—41no—
28Dic452—21no—
29Dic452—22no—
30Dic452D412yes—
31#14268636—22no—
32#14268636—22no—
33D904—21no—
34D904D412yes—
35C4⋊Dic113—21no—
36#14268626—41no—
37C22⋊Dic113—41no—
38C22×C4×C113D411yescharacteristic
39M16×C113—22no—
40C2×C8×C113D411yescharacteristic
41C2×C8×C113C2311yescharacteristic
42C16×C113—22no—
43C23×C113D811yescharacteristic
44C22×D113—41no—
45C2×C4×C113—21no—
46C2×C4×C113—21no—
47C2×C4×C113D811yescharacteristic
48C2×C4×C113C2×D411yescharacteristic
49C22⋊D113—42no—
50C22⋊D113—42no—
51C2×Dic113—41no—
52C2×Dic113—41no—
53C2×Dic113—41no—
54D452—22no—
55D452—41no—
56C4×D113—42no—
57C4×D113—42no—
58Dic226—22no—
59Dic226—41no—
60Dic226—41no—
61Dic226—41no—
62C8×C113—21no—
63C8×C113C2×D412yes—
64C22×C113—21no—
65C22×C113—41no—
66C22×C113C2×D811yescharacteristic
67C2×D113—42no—
68C2×D113—82no—
69C4×C113—21no—
70C4×C113#12011yescharacteristic
71C4×C113AGL(1,ℤ/8)11yescharacteristic
72Dic113—42no—
73Dic113—81no—
74Dic113—81no—
75C2×C113—21no—
76C2×C113—41no—
77C2×C113#44711yescharacteristic
78D113—82no—
79#2191—1131nomaximal, Sylow
80C113#219111yescharacteristic, complemented, Sylow
81#575—1131no—
82#510—1132no—
83#470—1131no—
84#360—1132no—
85#349D11311yescharacteristic, complemented
86C2×#41—2261no—
87#137—2262no—
88AGL(1,ℤ/8)—2262no—
89#135—1132no—
90#135—2261no—
91C2×Q16—1131no—
92C2×M16C2×D11311yescharacteristic
93C22⋊Q8—2261no—
94Q32—2262no—
95SD32—2262no—
96M32C2×D11312yescomplemented
97#106—1131no—
98#103—2261no—
99#41—4521no—
100#41—4521no—
101#41—2262no—
102#41—2262no—
103C2×Q8—2261no—
104C2×Q8—2261no—
105C2×D4—4521no—
106C2×D4—2261no—
107C22×C4—4521no—
108C22×C4D45211yescharacteristic
109Q16—1132no—
110Q16—2261no—
111Q16—2262no—
112SD16—2262no—
113SD16—2262no—
114D8—1132no—
115D8—2261no—
116M16—22no—
117C2×C8D45211yescharacteristic
118C2×C8C22×D11311yescharacteristic
119C4⋊C4—4521no—
120C4⋊C4—2261no—
121C22⋊C4—4521no—
122C16—22no—
123C23—4521no—
124C23D90411yescharacteristic
125Q8—4521no—
126Q8—4521no—
127Q8—4521no—
128Q8—2262no—
129D4—4521no—
130D4—4522no—
131D4—4522no—
132D4—2262no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—4522no—
136C2×C4—4521no—
137C2×C4—4521no—
138C2×C4—4521no—
139C2×C4—4522no—
140C2×C4D90411yescharacteristic
141C2×C4C2×D45211yescharacteristic
142C8—21no—
143C8D4×D11312yes—
144C22—21no—
145C22—41no—
146C22—9042no—
147C22—4522no—
148C22C2×D90411yescharacteristic
149C4—21no—
150C4—9041no—
151C4—9041no—
152C4—4522no—
153C4#1681359211yescharacteristic
154C4#1681365011yescharacteristic
155C2—21no—
156C2—41no—
157C2—9042no—
158C2#2029873411yescharacteristic
subgroupG/H
centerC2#20298734
commutator, cosocleC2×C8×C113C23
FrattiniC2×C8C22×D113
Fitting#349×C113C2
socleC2×C113#447
prime radical#20299398C2
hypercenter#349D113
hypocenterC113#2191
LCSG ▷ C2×C8×C113 ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #20299041C2semidirect
3. #20298856C2semidirect
4. #20298409C2semidirect
5. #349×C113C2semidirect
11. C2×Dic452C22semidirect
15. #16813554C22semidirect
18. M32×C113C22semidirect
80. C113#2191semidirect
85. #349D113semidirect
96. M32C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202993982
#202990412
#202988562
#202984092
#349×C1132
#2191113