Finite Group Databasebeta

← #28406762

Subgroups — #28406762

Order 14464.

244 conjugacy classes of subgroups; only the 70 normal subgroups are shown.

normal subgroups only

This group has 244 conjugacy classes of subgroups — too many to draw. Only its 70 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#20299603C211yesmaximal, characteristic
2#20299534C211yesmaximal, characteristic
3#20299468C214yesmaximal
4#20299153C211yesmaximal, characteristic
5C2×#14268657C2212yes—
6C2×C4×#90673C2212yes—
7#16813689—21no—
8#16813689—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4—21no—
11#16813622C411yescharacteristic, complemented
12#16813613C412yescomplemented
13#16813602—21no—
14#16813598—21no—
15Q8×Dic113—21no—
16#16813587—21no—
17#16813580C2212yes—
18C42×D113C2211yescharacteristic
19C4⋊Q8×C113C411yescharacteristic, complemented
20C22×#90673—22no—
21#14268657—24no—
22C2×#11744753—22no—
23C4×#90673—22no—
24C4×#90673Q814yescomplemented
25C2×Dic226—21no—
26C2×C4×D113D411yescharacteristic
27C2×C4×D113D411yescharacteristic
28C2×C4×D113C2311yescharacteristic
29C4⋊Dic113—21no—
30C4⋊Dic113—22no—
31C4⋊Dic113C2×C412yes—
32#14268626—22no—
33#14268624—22no—
34C4×Dic113—22no—
35C4×Dic113C2×C411yescharacteristic
36C4×Dic113D411yescharacteristic
37C4×Dic113D411yescharacteristic
38C2×Q8×C113—21no—
39C4⋊C4×C113—21no—
40C4⋊C4×C113C2×C412yes—
41C42×C113C2×C411yescharacteristic
42C22×D113C2×D411yescharacteristic
43C2×#90673—24no—
44C2×#90673—42no—
45C2×#90673—42no—
46Q8×C113—42no—
47C2×C4×C113—22no—
48C2×C4×C113C22⋊C411yescharacteristic
49C2×C4×C113C22⋊C411yescharacteristic
50C2×C4×C113C22×C411yescharacteristic
51C2×Dic113—22no—
52C2×Dic113C22⋊C411yescharacteristic
53C2×Dic113C22⋊C411yescharacteristic
54C2×Dic113C2×D411yescharacteristic
55C4×D113—41no—
56C4×D113—41no—
57C4×D113C2×Q812yes—
58C4×D113#4112yes—
59Dic226—42no—
60#11744753—42no—
61C22×C113C2×C22⋊C411yescharacteristic
62C2×D113—21no—
63C2×D113—21no—
64C2×D113C22⋊Q812yes—
65#90673—44no—
66C4×C113—21no—
67C4×C113—21no—
68C4×C113—42no—
69C4×C113C4×Q812yes—
70Dic113—21no—
71Dic113—21no—
72Dic113—42no—
73Dic113#12411yescharacteristic
74Dic113C4⋊Q811yescharacteristic
75C2×C113#39111yescharacteristic
76C2×C113#42111yescharacteristic
77C2×C113#42111yescharacteristic
78D113—22no—
79#1995—1131nomaximal, Sylow
80C113#199511yescharacteristic, complemented, Sylow
81#533—1131no—
82#423—1131no—
83#376—1131no—
84#339—1134no—
85C2×M16—1132no—
86C4⋊Q8—1131no—
87C4⋊Q8#9067311yescharacteristic, complemented
88#125—1132no—
89C22⋊Q8—2261no—
90C22⋊Q8—2261no—
91C4×Q8—2261no—
92C4×Q8—2261no—
93#117—1132no—
94C2×C42—1131no—
95C2×C42—1132no—
96C4⋊C8—2261no—
97C4⋊C8—2261no—
98#95—2261no—
99#95—2261no—
100C2×Q8—21no—
101C2×Q8—2261no—
102C22×C4—1131no—
103C22×C4—1131no—
104C22×C4—1131no—
105C22×C4—2262no—
106M16—2264no—
107C2×C8—2262no—
108C4⋊C4—21no—
109C4⋊C4—1132no—
110C4⋊C4—2262no—
111C4⋊C4—2262no—
112C4⋊C4—2261no—
113C4⋊C4C2×#9067312yes—
114C22⋊C4—2262no—
115C42—1131no—
116C42—1131no—
117C42—1131no—
118C42—1134no—
119C42—2262no—
120C42—2262no—
121C42C2×#9067311yescharacteristic
122C23—1131no—
123Q8—42no—
124Q8—4522no—
125C2×C4—22no—
126C2×C4—1131no—
127C2×C4—1132no—
128C2×C4—1132no—
129C2×C4—1131no—
130C2×C4—1131no—
131C2×C4—4521no—
132C2×C4—4521no—
133C2×C4—4522no—
134C2×C4—4522no—
135C2×C4—2264no—
136C2×C4—2262no—
137C2×C4C22⋊#9067311yescharacteristic
138C2×C4C22⋊#9067311yescharacteristic
139C2×C4C22×#9067311yescharacteristic
140C8—4522no—
141C22—1132no—
142C22—2261no—
143C22—2261no—
144C22C2×C22⋊#9067311yescharacteristic
145C4—21no—
146C4—21no—
147C4—42no—
148C4—1131no—
149C4—1131no—
150C4—4524no—
151C4—4522no—
152C4—2261no—
153C4—2261no—
154C4Q8×#9067312yes—
155C2—2262no—
156C2(C2×#90673)⋊Q811yescharacteristic
157C2#2029959611yescharacteristic
158C2#2029959711yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC4⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC22×D113C2×D4
cosocleC2×C4×D113C23
hypercenterC4⋊Q8#90673
hypocenterC113#1995
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4⋊Q8

Complements

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

NH ≅ G/Ntype
11. #16813622C4semidirect
12. #16813613C4semidirect
19. C4⋊Q8×C113C4semidirect
24. C4×#90673Q8semidirect
80. C113#1995semidirect
87. C4⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996032
#202995342
#202994682
#202991532
#1995113