Finite Group Databasebeta

← #28406007

Subgroups — #28406007

Order 14464.

220 conjugacy classes of subgroups; only the 66 normal subgroups are shown.

normal subgroups only

This group has 220 conjugacy classes of subgroups — too many to draw. Only its 66 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#20299617C211yesmaximal, characteristic
2#20299542C211yesmaximal, characteristic
3#20299452C212yesmaximal
4#20299451C212yesmaximal
5#20299152C211yesmaximal, characteristic
6C2×C4⋊#90673—21no—
7C4⋊#11744753—21no—
8#16813679C2212yes—
9C4×#11744753—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—
25C4⋊#90673—42no—
26C2×Dic226—21no—
27C2×Dic226C2×C411yescharacteristic
28C2×C4×D113D411yescharacteristic
29C2×C4×D113D411yescharacteristic
30C2×C4×D113C2311yescharacteristic
31C4⋊Dic113—21no—
32C4⋊Dic113C2×C411yescharacteristic
33#14268626—21no—
34#14268626—21no—
35#14268626—21no—
36#14268626—21no—
37#14268626—21no—
38#14268624—21no—
39#14268624—21no—
40C4×Dic113—21no—
41C4×Dic113C2×C411yescharacteristic
42C4×Dic113D411yescharacteristic
43C4×Dic113D411yescharacteristic
44C2×Q8×C113C2×C411yescharacteristic
45C4⋊C4×C113—21no—
46C4⋊C4×C113C2×C411yescharacteristic
47C42×C113—21no—
48C42×C113C2×C411yescharacteristic
49C22×D113C2×D411yescharacteristic
50C2×#90673—42no—
51C2×#90673—42no—
52C2×#90673—42no—
53Q8×C113—41no—
54C2×C4×C113—21no—
55C2×C4×C113—21no—
56C2×C4×C113C22⋊C411yescharacteristic
57C2×C4×C113C22⋊C411yescharacteristic
58C2×C4×C113C22×C411yescharacteristic
59C2×Dic113—21no—
60C2×Dic113—21no—
61C2×Dic113C22⋊C411yescharacteristic
62C2×Dic113C22⋊C411yescharacteristic
63C2×Dic113C2×D411yescharacteristic
64C4×D113—41no—
65C4×D113—41no—
66C4×D113SD1612yes—
67C4×D113Q1612yes—
68Dic226—42no—
69Dic226—41no—
70#11744753—42no—
71C22×C113C2×C22⋊C411yescharacteristic
72C2×D113—21no—
73C2×D113—21no—
74C2×D113C2×SD1611yescharacteristic
75C2×D113C2×Q1611yescharacteristic
76#90673—82no—
77C4×C113—21no—
78C4×C113—21no—
79C4×C113—41no—
80C4×C113—41no—
81C4×C113#10312yes—
82Dic113—21no—
83Dic113—21no—
84Dic113—41no—
85Dic113—41no—
86Dic113#10312yes—
87C2×C113#41011yescharacteristic
88C2×C113C2×#10311yescharacteristic
89C2×C113#42111yescharacteristic
90D113—21no—
91D113—21no—
92#1518—1131nomaximal, Sylow
93C113#151811yescharacteristic, complemented, Sylow
94#533—1131no—
95#431—1131no—
96#382—1131no—
97#328—1132no—
98#328—1132no—
99C4⋊Q8—1131no—
100C4⋊Q8—1131no—
101#125—2261no—
102C22⋊Q8—1131no—
103C22⋊Q8—1131no—
104C22⋊Q8—2261no—
105C4×Q8—1131no—
106C4×Q8—2261no—
107C4×Q8#9067311yescharacteristic, complemented
108#117—2261no—
109C2×C4⋊C4—2261no—
110C2×C42—1131no—
111C4⋊C8—2261no—
112C22⋊C8—1132no—
113C4×C8—2261no—
114#95—1132no—
115#95—2261no—
116C2×Q8—1131no—
117C2×Q8—2261no—
118C2×Q8C2×#9067311yescharacteristic
119C22×C4—1131no—
120C22×C4—1131no—
121C22×C4—1131no—
122C22×C4—2262no—
123C2×C8—2262no—
124C4⋊C4—21no—
125C4⋊C4—1131no—
126C4⋊C4—4522no—
127C4⋊C4—2261no—
128C4⋊C4—2261no—
129C4⋊C4—2261no—
130C4⋊C4—2261no—
131C4⋊C4—2261no—
132C4⋊C4—2261no—
133C4⋊C4C2×#9067311yescharacteristic
134C22⋊C4—2261no—
135C22⋊C4—2261no—
136C42—21no—
137C42—1131no—
138C42—1131no—
139C42—1131no—
140C42—2261no—
141C42C2×#9067311yescharacteristic
142C23—1131no—
143Q8—41no—
144Q8—4521no—
145Q8—4522no—
146C2×C4—21no—
147C2×C4—21no—
148C2×C4—1131no—
149C2×C4—1132no—
150C2×C4—1132no—
151C2×C4—1131no—
152C2×C4—1131no—
153C2×C4—4521no—
154C2×C4—4521no—
155C2×C4—4522no—
156C2×C4—4522no—
157C2×C4—4522no—
158C2×C4—2261no—
159C2×C4—2261no—
160C2×C4C22⋊#9067311yescharacteristic
161C2×C4C22⋊#9067311yescharacteristic
162C2×C4C22×#9067311yescharacteristic
163C8—4522no—
164C22—1131no—
165C22—1131no—
166C22—2261no—
167C22—2261no—
168C22C2×C22⋊#9067311yescharacteristic
169C4—21no—
170C4—21no—
171C4—41no—
172C4—41no—
173C4—1132no—
174C4—9042no—
175C4—4521no—
176C4—4521no—
177C4—2261no—
178C4—2261no—
179C4#1681368512yes—
180C2—2261no—
181C2—2261no—
182C2#2029957711yescharacteristic
183C2C2×#1681368511yescharacteristic
184C2#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#1518
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
93. C113#1518semidirect
107. C4×Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202996172
#202995422
#202994522
#202994512
#202991522
#1518113