Finite Group Databasebeta

← #28405996

Subgroups — #28405996

Order 14464.

208 conjugacy classes of subgroups; only the 56 normal subgroups are shown.

normal subgroups only

This group has 208 conjugacy classes of subgroups — too many to draw. Only its 56 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#20299620C211yesmaximal, characteristic
2#20299543C211yesmaximal, characteristic
3#20299452C212yesmaximal
4#20299451C212yesmaximal
5#20299152C211yesmaximal, characteristic
6C4⋊#11744753—21no—
7#16813679C2212yes—
8#16813677—21no—
9(C2×#90673)⋊C4—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12#16813621C411yescharacteristic, complemented
13#16813620C411yescharacteristic, complemented
14#16813612—21no—
15#16813602C2211yescharacteristic
16#16813600—21no—
17#16813598C2211yescharacteristic
18C4×Dic226—21no—
19C4×Dic226C411yescharacteristic, complemented
20#16813579—21no—
21C42×D113C2211yescharacteristic
22C4×Q8×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24C2×#11744753—22no—
25C2×Dic226—21no—
26C2×Dic226C2×C411yescharacteristic
27C2×C4×D113D411yescharacteristic
28C2×C4×D113D411yescharacteristic
29C2×C4×D113C2311yescharacteristic
30C4⋊Dic113—21no—
31C4⋊Dic113C2×C411yescharacteristic
32#14268626—21no—
33#14268626—21no—
34#14268626—21no—
35#14268626—21no—
36#14268626—21no—
37#14268624—21no—
38#14268624—21no—
39C4×Dic113—21no—
40C4×Dic113C2×C411yescharacteristic
41C4×Dic113D411yescharacteristic
42C4×Dic113D411yescharacteristic
43C2×Q8×C113C2×C411yescharacteristic
44C4⋊C4×C113—21no—
45C4⋊C4×C113C2×C411yescharacteristic
46C42×C113—21no—
47C42×C113C2×C411yescharacteristic
48C22×D113C2×D411yescharacteristic
49C2×#90673—42no—
50C2×#90673—42no—
51C2×#90673—42no—
52Q8×C113—41no—
53C2×C4×C113—21no—
54C2×C4×C113—21no—
55C2×C4×C113C22⋊C411yescharacteristic
56C2×C4×C113C22⋊C411yescharacteristic
57C2×C4×C113C22×C411yescharacteristic
58C2×Dic113—21no—
59C2×Dic113—21no—
60C2×Dic113C22⋊C411yescharacteristic
61C2×Dic113C22⋊C411yescharacteristic
62C2×Dic113C2×D411yescharacteristic
63C4×D113—22no—
64C4×D113—41no—
65C4×D113—41no—
66Dic226—42no—
67Dic226—41no—
68#11744753—42no—
69C22×C113C2×C22⋊C411yescharacteristic
70C2×D113—21no—
71C2×D113—21no—
72C2×D113#13712yes—
73#90673—82no—
74C4×C113—21no—
75C4×C113—21no—
76C4×C113—21no—
77C4×C113—41no—
78C4×C113—41no—
79Dic113—21no—
80Dic113—21no—
81Dic113—21no—
82Dic113—41no—
83Dic113—41no—
84C2×C113#41011yescharacteristic
85C2×C113#41911yescharacteristic
86C2×C113#42111yescharacteristic
87D113—22no—
88#1515—1131nomaximal, Sylow
89C113#151511yescharacteristic, complemented, Sylow
90#533—1131no—
91#432—1131no—
92#383—1131no—
93#328—1132no—
94#328—1132no—
95C4⋊Q8—1131no—
96C4⋊Q8—1131no—
97#125—2261no—
98C22⋊Q8—1131no—
99C22⋊Q8—1131no—
100C22⋊Q8—2261no—
101C4×Q8—1131no—
102C4×Q8—2261no—
103C4×Q8#9067311yescharacteristic, complemented
104#117—2261no—
105C2×C42—1131no—
106C4⋊C8—2261no—
107C22⋊C8—1132no—
108#97—2261no—
109#95—1132no—
110#95—2261no—
111#95—2261no—
112C2×Q8—1131no—
113C2×Q8—2261no—
114C2×Q8C2×#9067311yescharacteristic
115C22×C4—1131no—
116C22×C4—1131no—
117C22×C4—1131no—
118C22×C4—2262no—
119C2×C8—2262no—
120C4⋊C4—21no—
121C4⋊C4—1131no—
122C4⋊C4—2261no—
123C4⋊C4—2261no—
124C4⋊C4—2261no—
125C4⋊C4—2261no—
126C4⋊C4—2261no—
127C4⋊C4—2261no—
128C4⋊C4C2×#9067311yescharacteristic
129C22⋊C4—2261no—
130C22⋊C4—2261no—
131C42—21no—
132C42—1131no—
133C42—1131no—
134C42—1131no—
135C42—2261no—
136C42C2×#9067311yescharacteristic
137C23—1131no—
138Q8—41no—
139Q8—4521no—
140Q8—4522no—
141C2×C4—21no—
142C2×C4—21no—
143C2×C4—1131no—
144C2×C4—1131no—
145C2×C4—1131no—
146C2×C4—4521no—
147C2×C4—4521no—
148C2×C4—4522no—
149C2×C4—4522no—
150C2×C4—4522no—
151C2×C4—2262no—
152C2×C4—2261no—
153C2×C4—2261no—
154C2×C4C22⋊#9067311yescharacteristic
155C2×C4C22⋊#9067311yescharacteristic
156C2×C4C22×#9067311yescharacteristic
157C8—4522no—
158C22—1132no—
159C22—2261no—
160C22—2261no—
161C22C2×C22⋊#9067311yescharacteristic
162C4—21no—
163C4—21no—
164C4—21no—
165C4—41no—
166C4—41no—
167C4—9042no—
168C4—4521no—
169C4—4521no—
170C4—2261no—
171C4—2261no—
172C4—2261no—
173C2—2262no—
174C2#2029957711yescharacteristic
175C2#2029959111yescharacteristic
176C2#2029959511yescharacteristic
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#1515
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ C4×Q8

Complements

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

NH ≅ G/Ntype
12. #16813621C4semidirect
13. #16813620C4semidirect
19. C4×Dic226C4semidirect
22. C4×Q8×C113C4semidirect
89. C113#1515semidirect
103. C4×Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996202
#202995432
#202994522
#202994512
#202991522
#1515113