Finite Group Databasebeta

← #28406714

Subgroups — #28406714

Order 14464.

408 conjugacy classes of subgroups; only the 74 normal subgroups are shown.

normal subgroups only

This group has 408 conjugacy classes of subgroups — too many to draw. Only its 74 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×#16813681C214yesmaximal, complemented
2#20299540C211yesmaximal, characteristic, complemented
3C4×C22⋊#90673C211yesmaximal, characteristic, complemented
4C2×#16813597C211yesmaximal, characteristic
5C2×C4⋊#90673—21no—
6C2×C22⋊#90673C2212yes—
7C2×C22⋊#90673C2212yes—
8C2×C4×#90673—21no—
9#16813681—28no—
10(C2×#90673)⋊C4—21no—
11(C2×#90673)⋊C4—21no—
12C22×D452C411yescharacteristic, complemented
13C22×D452C2212yes—
14C22×C4×D113C2211yescharacteristic
15#16813597—21no—
16#16813597—21no—
17#16813597—21no—
18#16813597—21no—
19C2×#14268624C412yescomplemented
20C2×C4⋊C4×C113C411yescharacteristic, complemented
21C22×#90673—22no—
22C22×#90673—22no—
23C4⋊#90673—42no—
24C22⋊#90673—22no—
25C22⋊#90673—24no—
26C22⋊#90673D414yescomplemented
27C4×#90673—42no—
28C23×D113C2×C412yes—
29C23×D113C2311yescharacteristic
30C2×D452—22no—
31C2×D452—22no—
32C2×D452—24no—
33C2×D452—24no—
34C2×D452—21no—
35C2×D452—21no—
36C2×D452—42no—
37C22×Dic113C2×C411yescharacteristic
38C2×C4×D113—42no—
39C2×C4×D113D411yescharacteristic
40C2×C4×D113D411yescharacteristic
41C2×C4×D113D411yescharacteristic
42C2×C4×D113D411yescharacteristic
43#14268624—22no—
44#14268624—22no—
45C22×C4×C113C2×C412yes—
46C22×C4×C113C2×C411yescharacteristic
47C4⋊C4×C113—21no—
48C4⋊C4×C113—21no—
49C23×C113C22×C411yescharacteristic
50C22×D113—22no—
51C22×D113—24no—
52C22×D113—41no—
53C22×D113—41no—
54C22×D113—42no—
55C22×D113—42no—
56C22×D113C2×D411yescharacteristic
57C22×D113C2×D411yescharacteristic
58C22×D113C2×D412yes—
59C22×D113#4112yes—
60C2×#90673—24no—
61C2×#90673—42no—
62C2×#90673—42no—
63C2×#90673—42no—
64C2×#90673—42no—
65C2×#90673—42no—
66C2×C4×C113—22no—
67C2×C4×C113—22no—
68C2×C4×C113—24no—
69C2×C4×C113C22⋊C411yescharacteristic
70C2×C4×C113C22⋊C411yescharacteristic
71C2×Dic113—41no—
72C2×Dic113C22⋊C411yescharacteristic
73C2×Dic113C22⋊C411yescharacteristic
74D452—42no—
75D452—44no—
76D452—42no—
77D452—42no—
78D452—42no—
79C4×D113—22no—
80C4×D113—22no—
81C4×D113—41no—
82C4×D113—41no—
83C22×C113—21no—
84C22×C113—21no—
85C22×C113C2×C22⋊C411yescharacteristic
86C22×C113C4×D412yes—
87C2×D113—21no—
88C2×D113—21no—
89C2×D113—21no—
90C2×D113—21no—
91C2×D113—42no—
92C2×D113—42no—
93C2×D113—42no—
94C2×D113—42no—
95C2×D113—42no—
96C2×D113—84no—
97C2×D113#12112yes—
98C2×D113#12411yescharacteristic
99C2×D113#12711yescharacteristic
100#90673—44no—
101#90673—82no—
102C4×C113—21no—
103C4×C113—42no—
104C4×C113#9912yescomplemented
105Dic113—21no—
106Dic113—21no—
107C2×C113—22no—
108C2×C113#39011yescharacteristic
109C2×C113C2×#9911yescharacteristic
110C2×C113#41011yescharacteristic
111D113—22no—
112D113—21no—
113D113—21no—
114D113—82no—
115#1964—1131nomaximal, Sylow
116C113#196411yescharacteristic, complemented, Sylow
117C2×#121—1131no—
118C2×#99—1134no—
119#380—1131no—
120C4×C22⋊C4—1131no—
121C22×D4—1132no—
122C22×D4—1131no—
123C23×C4—1131no—
124#121—2261no—
125#121—2261no—
126#121—2261no—
127#121—2261no—
128C2×C4⋊C4—2261no—
129C2×C4⋊C4#9067311yescharacteristic, complemented
130C2×C22⋊C4—1132no—
131C2×C22⋊C4—1132no—
132C2×C22⋊C4—1132no—
133C2×C42—2261no—
134#99—2268no—
135#95—2261no—
136#95—2261no—
137C24—1131no—
138C24—1132no—
139C2×D4—4522no—
140C2×D4—2264no—
141C2×D4—2262no—
142C2×D4—2262no—
143C2×D4—2264no—
144C2×D4—2261no—
145C2×D4—2261no—
146C22×C4—1131no—
147C22×C4—1131no—
148C22×C4—1131no—
149C22×C4—1131no—
150C22×C4—1131no—
151C22×C4—4522no—
152C22×C4—2262no—
153C22×C4—2262no—
154C22×C4C2×#9067312yes—
155C22×C4C2×#9067311yescharacteristic
156C4⋊C4—21no—
157C4⋊C4—21no—
158C4⋊C4—4522no—
159C22⋊C4—1134no—
160C22⋊C4—2262no—
161C22⋊C4—2262no—
162C22⋊C4—2264no—
163C22⋊C4—2262no—
164C42—4522no—
165C23—1132no—
166C23—1132no—
167C23—1131no—
168C23—1131no—
169C23—4522no—
170C23—4522no—
171C23—4521no—
172C23—4521no—
173C23—2264no—
174C23—2262no—
175C23C22×#9067311yescharacteristic
176D4—4522no—
177D4—4522no—
178D4—4524no—
179D4—4522no—
180D4—4522no—
181C2×C4—22no—
182C2×C4—22no—
183C2×C4—24no—
184C2×C4—1131no—
185C2×C4—1131no—
186C2×C4—4521no—
187C2×C4—4521no—
188C2×C4—4522no—
189C2×C4—4522no—
190C2×C4—4522no—
191C2×C4—4522no—
192C2×C4—4522no—
193C2×C4—4521no—
194C2×C4—2264no—
195C2×C4—2262no—
196C2×C4—2262no—
197C2×C4C22⋊#9067311yescharacteristic
198C2×C4C22⋊#9067311yescharacteristic
199C22—21no—
200C22—21no—
201C22—1131no—
202C22—1132no—
203C22—1131no—
204C22—9044no—
205C22—4522no—
206C22—4522no—
207C22—4522no—
208C22—4522no—
209C22—4522no—
210C22—2261no—
211C22—2261no—
212C22—2261no—
213C22—2261no—
214C22C2×C22⋊#9067311yescharacteristic
215C22D4×#9067312yes—
216C4—21no—
217C4—42no—
218C4—9042no—
219C4—4524no—
220C4—2261no—
221C4—2261no—
222C4#1681368112yescomplemented
223C2—22no—
224C2—9042no—
225C2—2261no—
226C2—2262no—
227C2—2261no—
228C2#2029955011yescharacteristic
229C2C2×#1681368111yescharacteristic
230C2#2029957911yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC23×C113C22×C4
FrattiniC23C22×#90673
FittingC2×C4⋊C4×C113C4
socleC22×C113C2×C22⋊C4
prime radicalC2×#16813597C2
cosocleC23×D113C23
hypercenterC2×C4⋊C4#90673
hypocenterC113#1964
LCSG ▷ C23×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#16813681C2semidirect
2. #20299540C2semidirect
3. C4×C22⋊#90673C2semidirect
12. C22×D452C4semidirect
19. C2×#14268624C4semidirect
20. C2×C4⋊C4×C113C4semidirect
26. C22⋊#90673D4semidirect
104. C4×C113#99semidirect
116. C113#1964semidirect
129. C2×C4⋊C4#90673semidirect
222. C4#16813681semidirect

Maximal subgroups

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

subgroupindex
C2×#168136812
#202995402
C4×C22⋊#906732
C2×#168135972
#1964113