Finite Group Databasebeta

← #28391602

Subgroups — #28391602

Order 14464.

394 conjugacy classes of subgroups; only the 73 normal subgroups are shown.

normal subgroups only

This group has 394 conjugacy classes of subgroups — too many to draw. Only its 73 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
1C2×#16813652C211yesmaximal, characteristic, complemented
2#20299162C211yesmaximal, characteristic
3C2×#16813610C211yesmaximal, characteristic, complemented
4#20298608C211yesmaximal, characteristic, complemented
5C2×#16813538C211yesmaximal, characteristic, complemented
6#20298358C211yesmaximal, characteristic, complemented
7C2×#104×C113C211yesmaximal, characteristic, complemented
8C22×Dic226C2211yescharacteristic
9C22×D452C2211yescharacteristic
10#16813652—22no—
11#16813652—22no—
12C2×#14268637—21no—
13C2×#14268635—21no—
14C2×#14268631C2211yescharacteristic
15#16813618—21no—
16#16813611—21no—
17#16813610—22no—
18#16813610—22no—
19#16813596—22no—
20#16813590—22no—
21#16813581C2211yescharacteristic
22C2×#14268624—22no—
23#16813547—22no—
24#16813538—22no—
25C2×#41×C113C2211yescharacteristic
26C2×M16×C113C2211yescharacteristic
27C2×C42×C113C2211yescharacteristic
28#104×C113—22no—
29C23×D113D412yes—
30C2×Dic226—21no—
31C2×Dic226—21no—
32C2×Dic226—21no—
33C2×Dic226—21no—
34C2×Dic226—21no—
35C2×Dic226D412yescomplemented
36C2×D452—21no—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452—21no—
40C2×D452—21no—
41C2×D452—21no—
42C2×C22⋊D113—24no—
43C22×Dic113—21no—
44#14268637—24no—
45#14268635—24no—
46#14268631—21no—
47#14268631D412yescomplemented
48C2×#11744751—21no—
49C4⋊Dic113D412yes—
50C22⋊Dic113—21no—
51#14268624—28no—
52#14268624—24no—
53C4×Dic113—21no—
54#41×C113—21no—
55#41×C113—21no—
56#41×C113—21no—
57#41×C113—21no—
58C2×Q8×C113D411yescharacteristic
59C2×D4×C113—21no—
60C2×D4×C113D411yescharacteristic
61C22×C4×C113—21no—
62C22×C4×C113—21no—
63C22×C4×C113C2311yescharacteristic
64M16×C113—21no—
65M16×C113—21no—
66C2×C8×C113—21no—
67C42×C113—21no—
68C42×C113D412yescomplemented
69C23×C113—21no—
70C23×C113C2×D411yescharacteristic
71C22×D113—22no—
72C22×D113—22no—
73C22×D113—22no—
74C22×D113—44no—
75Q8×C113—21no—
76Q8×C113—21no—
77D4×C113—21no—
78D4×C113—21no—
79D4×C113—41no—
80D4×C113—41no—
81C2×C4×C113—22no—
82C2×C4×C113—21no—
83C2×C4×C113—42no—
84C2×C4×C113—41no—
85C2×C4×C113—41no—
86C2×C4×C113C2×D411yescharacteristic
87C2×C4×C113C2×D411yescharacteristic
88C2×C4×C113C2×D411yescharacteristic
89C2×C4×C113C2×D411yescharacteristic
90C2×C4×C113C2×D411yescharacteristic
91C2×C4×C113#4111yescharacteristic
92C22⋊D113—84no—
93C2×Dic113—22no—
94C2×Dic113—22no—
95C2×Dic113—41no—
96C2×Dic113—41no—
97D452—41no—
98D452—41no—
99D452—41no—
100D452—41no—
101Dic226—22no—
102Dic226—22no—
103Dic226—41no—
104Dic226—41no—
105C8×C113—41no—
106#11744751—22no—
107C22×C113—22no—
108C22×C113—41no—
109C22×C113—42no—
110C22×C113#12011yescharacteristic
111C22×C113#12011yescharacteristic
112C22×C113#12111yescharacteristic
113C2×D113—44no—
114C2×D113—42no—
115C2×D113—44no—
116C2×D113—82no—
117C4×C113—42no—
118C4×C113—41no—
119C4×C113#12011yescharacteristic
120C4×C113#12111yescharacteristic
121C4×C113#12111yescharacteristic
122C4×C113#12711yescharacteristic
123Dic113—42no—
124Dic113—42no—
125C2×C113—21no—
126C2×C113—21no—
127C2×C113—81no—
128C2×C113#39211yescharacteristic
129C2×C113#45512yes—
130D113—82no—
131#2004—1131nomaximal, Sylow
132C113#200411yescharacteristic, complemented, Sylow
133C2×#137—1131no—
134#535—1131no—
135C2×#124—1131no—
136C2×#104D11311yescharacteristic, complemented
137#419—1131no—
138C2×#100—1131no—
139#339—1131no—
140C2×#41C2×D11311yescharacteristic
141C22×Q8—1131no—
142C22×D4—1131no—
143#137—2262no—
144#137—2262no—
145C2×Q16—2261no—
146C2×SD16—2261no—
147C2×M16—1131no—
148C2×M16C2×D11311yescharacteristic
149#127—2261no—
150#124—2262no—
151#124—2261no—
152#124—2262no—
153#121—2262no—
154#120—2262no—
155#117—1131no—
156C2×C22⋊C4—2262no—
157C2×C42C2×D11311yescharacteristic
158#104—22no—
159#103—2262no—
160#100—2262no—
161C24—1132no—
162#41—21no—
163#41—21no—
164#41—21no—
165#41—21no—
166C2×Q8—1132no—
167C2×Q8—2261no—
168C2×Q8—2261no—
169C2×Q8—2261no—
170C2×Q8—2261no—
171C2×Q8—2261no—
172C2×Q8D45211yescharacteristic
173C2×D4—21no—
174C2×D4—2264no—
175C2×D4—2261no—
176C2×D4—2261no—
177C2×D4—2261no—
178C2×D4—2261no—
179C2×D4—2261no—
180C2×D4—2261no—
181C2×D4D45211yescharacteristic
182C22×C4—21no—
183C22×C4—21no—
184C22×C4—2261no—
185C22×C4C22×D11311yescharacteristic
186Q16—2264no—
187SD16—2264no—
188M16—21no—
189M16—21no—
190M16—1132no—
191M16—2261no—
192C2×C8—21no—
193C2×C8—2261no—
194C4⋊C4—1132no—
195C22⋊C4—2268no—
196C22⋊C4—2264no—
197C22⋊C4—2261no—
198C42—21no—
199C42—2261no—
200C42C22⋊D11312yescomplemented
201C23—21no—
202C23—4524no—
203C23—2262no—
204C23—2262no—
205C23—2262no—
206C23D4×D11311yescharacteristic
207Q8—21no—
208Q8—21no—
209Q8—4521no—
210Q8—4521no—
211Q8—2262no—
212Q8—2262no—
213D4—21no—
214D4—21no—
215D4—41no—
216D4—41no—
217D4—9044no—
218D4—4521no—
219D4—4521no—
220D4—4521no—
221D4—4521no—
222C2×C4—22no—
223C2×C4—21no—
224C2×C4—42no—
225C2×C4—41no—
226C2×C4—41no—
227C2×C4—4521no—
228C2×C4—4521no—
229C2×C4—2262no—
230C2×C4—2262no—
231C2×C4D4×D11311yescharacteristic
232C2×C4D4×D11311yescharacteristic
233C2×C4D4×D11311yescharacteristic
234C2×C4C2×C22⋊D11311yescharacteristic
235C2×C4C2×D45211yescharacteristic
236C2×C4#1426864711yescharacteristic
237C8—41no—
238C8—2262no—
239C22—22no—
240C22—41no—
241C22—42no—
242C22—9042no—
243C22—4524no—
244C22—4522no—
245C22—4524no—
246C22#1681359011yescharacteristic
247C22#1681359211yescharacteristic
248C22#1681359511yescharacteristic
249C4—42no—
250C4—41no—
251C4—4522no—
252C4—4522no—
253C4#1681359211yescharacteristic
254C4#1681359511yescharacteristic
255C4#1681359611yescharacteristic
256C4#1681361811yescharacteristic
257C2—21no—
258C2—21no—
259C2—81no—
260C2—9042no—
261C2#2029850711yescharacteristic
262C2#2029877712yes—
subgroupG/H
centerC22#16813592
commutator, cosocleC22×C4×C113C23
FrattiniC22×C4C22×D113
FittingC2×#104×C113C2
socleC22×C113#120
prime radical#20299162C2
hypercenterC2×#104D113
hypocenterC113#2004
LCSG ▷ C22×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#16813652C2semidirect
3. C2×#16813610C2semidirect
4. #20298608C2semidirect
5. C2×#16813538C2semidirect
6. #20298358C2semidirect
7. C2×#104×C113C2semidirect
35. C2×Dic226D4semidirect
47. #14268631D4semidirect
68. C42×C113D4semidirect
132. C113#2004semidirect
136. C2×#104D113semidirect
200. C42C22⋊D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136522
#202991622
C2×#168136102
#202986082
C2×#168135382
#202983582
C2×#104×C1132
#2004113