Finite Group Databasebeta

← #28405983

Subgroups — #28405983

Order 14464.

274 conjugacy classes of subgroups; only the 58 normal subgroups are shown.

normal subgroups only

This group has 274 conjugacy classes of subgroups — too many to draw. Only its 58 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#20299569C211yesmaximal, characteristic
2#20299541C211yesmaximal, characteristic
3#20299452C212yesmaximal, complemented
4#20299451C212yesmaximal, complemented
5C22⋊Q8×D113C211yesmaximal, characteristic
6C2×#14268657—21no—
7C2×C22⋊#90673—21no—
8#16813679C2212yes—
9C22⋊#11744753—21no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4C2212yes—
12C2×Q8×D113C411yescharacteristic, complemented
13C22×C4×D113C2211yescharacteristic
14#16813602C2211yescharacteristic
15#16813601C411yescharacteristic, complemented
16#16813600—21no—
17#16813599—21no—
18#16813598C2211yescharacteristic
19C4⋊C4×D113—21no—
20C4⋊C4×D113C411yescharacteristic, complemented
21C22⋊C4×D113—21no—
22C22⋊Q8×C113C411yescharacteristic, complemented
23C22×#90673—22no—
24#14268657—42no—
25C2×#11744753—22no—
26C22⋊#90673—42no—
27C23×D113D411yescharacteristic
28C2×Dic226—21no—
29C2×Dic226C2×C411yescharacteristic
30Q8×D113—42no—
31C22×Dic113D411yescharacteristic
32C2×C4×D113—21no—
33C2×C4×D113—21no—
34C2×C4×D113—42no—
35C2×C4×D113C2×C411yescharacteristic
36C2×C4×D113D411yescharacteristic
37C2×C4×D113D411yescharacteristic
38C2×C4×D113C2311yescharacteristic
39C4⋊Dic113—21no—
40C4⋊Dic113C2×C411yescharacteristic
41#14268626—21no—
42#14268626—21no—
43#14268626—21no—
44C22⋊Dic113—21no—
45#14268624—21no—
46#14268624—21no—
47C2×Q8×C113C2×C411yescharacteristic
48C22×C4×C113C2×C411yescharacteristic
49C4⋊C4×C113—21no—
50C4⋊C4×C113C2×C411yescharacteristic
51C22⋊C4×C113—21no—
52C23×C113C22⋊C411yescharacteristic
53C22×D113—22no—
54C22×D113—22no—
55C22×D113—41no—
56C22×D113C22⋊C411yescharacteristic
57C22×D113C2×D411yescharacteristic
58C2×#90673—42no—
59C2×#90673—42no—
60C2×#90673—42no—
61Q8×C113—41no—
62C2×C4×C113—21no—
63C2×C4×C113—21no—
64C2×C4×C113—41no—
65C2×C4×C113C22⋊C411yescharacteristic
66C2×C4×C113C22×C411yescharacteristic
67C2×Dic113—21no—
68C2×Dic113—21no—
69C2×Dic113—41no—
70C2×Dic113C22⋊C411yescharacteristic
71C2×Dic113C2×D411yescharacteristic
72C4×D113—22no—
73C4×D113—22no—
74C4×D113—41no—
75C4×D113—41no—
76C4×D113—42no—
77C4×D113—42no—
78Dic226—42no—
79Dic226—41no—
80#11744753—42no—
81C22×C113—21no—
82C22×C113—21no—
83C22×C113—21no—
84C22×C113C2×C22⋊C411yescharacteristic
85C2×D113—21no—
86C2×D113—21no—
87C2×D113—21no—
88C2×D113—21no—
89C2×D113—44no—
90C2×D113#9912yes—
91C2×D113#13712yes—
92#90673—82no—
93C4×C113—21no—
94C4×C113—21no—
95C4×C113—41no—
96C4×C113—41no—
97Dic113—21no—
98Dic113—21no—
99Dic113—41no—
100Dic113—41no—
101C2×C113—41no—
102C2×C113C2×#9911yescharacteristic
103C2×C113#41911yescharacteristic
104C2×C113#42111yescharacteristic
105D113—22no—
106D113—22no—
107#1511—1131nomaximal, Sylow
108C113#151111yescharacteristic, complemented, Sylow
109C2×C22⋊Q8—1131no—
110#407—1131no—
111#381—1131no—
112#328—1132no—
113#328—1132no—
114C22×Q8—1131no—
115C23×C4—1131no—
116C2×M16—2261no—
117C22⋊Q8—1131no—
118C22⋊Q8—1131no—
119C22⋊Q8—1131no—
120C22⋊Q8—2261no—
121C22⋊Q8—2261no—
122C22⋊Q8#9067311yescharacteristic, complemented
123C2×C4⋊C4—1131no—
124C2×C4⋊C4—2261no—
125C2×C22⋊C4—2261no—
126C2×C22⋊C4—2261no—
127C22⋊C8—1132no—
128C22⋊C8—2261no—
129#95—1132no—
130#95—2261no—
131C24—1131no—
132C2×Q8—1131no—
133C2×Q8—4522no—
134C2×Q8—2261no—
135C2×Q8C2×#9067311yescharacteristic
136C22×C4—1131no—
137C22×C4—1131no—
138C22×C4—1131no—
139C22×C4—1131no—
140C22×C4—1131no—
141C22×C4—4522no—
142C22×C4—2261no—
143C22×C4—2261no—
144C22×C4—2262no—
145C22×C4C2×#9067311yescharacteristic
146M16—4522no—
147C2×C8—2262no—
148C4⋊C4—21no—
149C4⋊C4—1131no—
150C4⋊C4—2261no—
151C4⋊C4—2261no—
152C4⋊C4—2261no—
153C4⋊C4—2261no—
154C4⋊C4C2×#9067311yescharacteristic
155C22⋊C4—21no—
156C22⋊C4—4522no—
157C22⋊C4—2261no—
158C22⋊C4—2261no—
159C22⋊C4—2261no—
160C23—1131no—
161C23—1131no—
162C23—4521no—
163C23—2262no—
164C23—2262no—
165C23C22⋊#9067311yescharacteristic
166Q8—41no—
167Q8—4521no—
168Q8—4522no—
169C2×C4—21no—
170C2×C4—21no—
171C2×C4—41no—
172C2×C4—1131no—
173C2×C4—1131no—
174C2×C4—4521no—
175C2×C4—4521no—
176C2×C4—4522no—
177C2×C4—4522no—
178C2×C4—4522no—
179C2×C4—4522no—
180C2×C4—4522no—
181C2×C4—4521no—
182C2×C4—2262no—
183C2×C4—2262no—
184C2×C4—2261no—
185C2×C4—2261no—
186C2×C4C22⋊#9067311yescharacteristic
187C2×C4C22×#9067311yescharacteristic
188C8—4522no—
189C22—21no—
190C22—21no—
191C22—21no—
192C22—1132no—
193C22—1132no—
194C22—4524no—
195C22—2261no—
196C22—2261no—
197C22—2261no—
198C22—2261no—
199C22C2×C22⋊#9067311yescharacteristic
200C4—21no—
201C4—21no—
202C4—41no—
203C4—41no—
204C4—9042no—
205C4—4521no—
206C4—4521no—
207C4—2261no—
208C4—2261no—
209C2—41no—
210C2—2262no—
211C2—2262no—
212C2D113⋊#9911yescharacteristic
213C2#2029959111yescharacteristic
214C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC23×D113D4
cosocleC2×C4×D113C23
hypercenterC22⋊Q8#90673
hypocenterC113#1511
LCSG ▷ C2×C4×C113 ▷ C22×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
3. #20299452C2semidirect
4. #20299451C2semidirect
12. C2×Q8×D113C4semidirect
15. #16813601C4semidirect
20. C4⋊C4×D113C4semidirect
22. C22⋊Q8×C113C4semidirect
108. C113#1511semidirect
122. C22⋊Q8#90673semidirect

Maximal subgroups

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

subgroupindex
#202995692
#202995412
#202994522
#202994512
C22⋊Q8×D1132
#1511113