Finite Group Databasebeta

← #26022205

Subgroups — #26022205

Order 11392.

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#19152398C211yesmaximal, characteristic
2#19152041C212yesmaximal, complemented
3#19151856C211yesmaximal, characteristic, complemented
4#19151409C212yesmaximal, complemented
5#349×C89C211yesmaximal, characteristic, complemented
6C2×#13083574—21no—
7#15668045—22no—
8#15668040—22no—
9#15668034—21no—
10#15668034C2212yes—
11C2×Dic356C2211yescharacteristic, complemented
12#15667991—21no—
13Dic712—22no—
14#15667957—22no—
15#15667944C2211yescharacteristic, complemented
16#15667937—21no—
17C2×M16×C89C2211yescharacteristic
18M32×C89C2212yescomplemented
19#13083574—22no—
20#13083574—22no—
21#13083574—41no—
22#13083574—41no—
23C2×Dic178—21no—
24C2×Dic178—21no—
25C2×D356—21no—
26C2×C22⋊D89—41no—
27C2×C4×D89—41no—
28Dic356—21no—
29Dic356—22no—
30Dic356D412yes—
31#13083563—22no—
32#13083563—22no—
33D712—21no—
34D712D412yes—
35C4⋊Dic89—21no—
36#13083553—41no—
37C22⋊Dic89—41no—
38C22×C4×C89D411yescharacteristic
39M16×C89—22no—
40C2×C8×C89D411yescharacteristic
41C2×C8×C89C2311yescharacteristic
42C16×C89—22no—
43C23×C89D811yescharacteristic
44C22×D89—41no—
45C2×C4×C89—21no—
46C2×C4×C89—21no—
47C2×C4×C89D811yescharacteristic
48C2×C4×C89C2×D411yescharacteristic
49C22⋊D89—42no—
50C22⋊D89—42no—
51C2×Dic89—41no—
52C2×Dic89—41no—
53C2×Dic89—41no—
54D356—22no—
55D356—41no—
56C4×D89—42no—
57C4×D89—42no—
58Dic178—22no—
59Dic178—41no—
60Dic178—41no—
61Dic178—41no—
62C8×C89—21no—
63C8×C89C2×D412yes—
64C22×C89—21no—
65C22×C89—41no—
66C22×C89C2×D811yescharacteristic
67C2×D89—42no—
68C2×D89—82no—
69C4×C89—21no—
70C4×C89#12011yescharacteristic
71C4×C89AGL(1,ℤ/8)11yescharacteristic
72Dic89—42no—
73Dic89—81no—
74Dic89—81no—
75C2×C89—21no—
76C2×C89—41no—
77C2×C89#44711yescharacteristic
78D89—82no—
79#2191—891nomaximal, Sylow
80C89#219111yescharacteristic, complemented, Sylow
81#575—891no—
82#510—892no—
83#470—891no—
84#360—892no—
85#349D8911yescharacteristic, complemented
86C2×#41—1781no—
87#137—1782no—
88AGL(1,ℤ/8)—1782no—
89#135—892no—
90#135—1781no—
91C2×Q16—891no—
92C2×M16C2×D8911yescharacteristic
93C22⋊Q8—1781no—
94Q32—1782no—
95SD32—1782no—
96M32C2×D8912yescomplemented
97#106—891no—
98#103—1781no—
99#41—3561no—
100#41—3561no—
101#41—1782no—
102#41—1782no—
103C2×Q8—1781no—
104C2×Q8—1781no—
105C2×D4—3561no—
106C2×D4—1781no—
107C22×C4—3561no—
108C22×C4D35611yescharacteristic
109Q16—892no—
110Q16—1781no—
111Q16—1782no—
112SD16—1782no—
113SD16—1782no—
114D8—892no—
115D8—1781no—
116M16—22no—
117C2×C8D35611yescharacteristic
118C2×C8C22×D8911yescharacteristic
119C4⋊C4—3561no—
120C4⋊C4—1781no—
121C22⋊C4—3561no—
122C16—22no—
123C23—3561no—
124C23D71211yescharacteristic
125Q8—3561no—
126Q8—3561no—
127Q8—3561no—
128Q8—1782no—
129D4—3561no—
130D4—3562no—
131D4—3562no—
132D4—1782no—
133C2×C4—21no—
134C2×C4—21no—
135C2×C4—3562no—
136C2×C4—3561no—
137C2×C4—3562no—
138C2×C4—3561no—
139C2×C4—3561no—
140C2×C4D71211yescharacteristic
141C2×C4C2×D35611yescharacteristic
142C8—21no—
143C8D4×D8912yes—
144C22—21no—
145C22—41no—
146C22—3562no—
147C22—7122no—
148C22C2×D71211yescharacteristic
149C4—21no—
150C4—3562no—
151C4—7121no—
152C4—7121no—
153C4#1566798211yescharacteristic
154C4#1566804011yescharacteristic
155C2—21no—
156C2—41no—
157C2—7122no—
158C2#1915173411yescharacteristic
subgroupG/H
centerC2#19151734
commutator, cosocleC2×C8×C89C23
FrattiniC2×C8C22×D89
Fitting#349×C89C2
socleC2×C89#447
prime radical#19152398C2
hypercenter#349D89
hypocenterC89#2191
LCSG ▷ C2×C8×C89 ▷ C4×C89 ▷ C2×C89 ▷ C89
UCSC1 ◁ C2 ◁ C2×C4 ◁ C2×M16 ◁ #349

Complements

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

NH ≅ G/Ntype
2. #19152041C2semidirect
3. #19151856C2semidirect
4. #19151409C2semidirect
5. #349×C89C2semidirect
11. C2×Dic356C22semidirect
15. #15667944C22semidirect
18. M32×C89C22semidirect
80. C89#2191semidirect
85. #349D89semidirect
96. M32C2×D89semidirect

Maximal subgroups

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

subgroupindex
#191523982
#191520412
#191518562
#191514092
#349×C892
#219189