Finite Group Databasebeta

← #28406555

Subgroups — #28406555

Order 14464.

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

normal subgroups only

This group has 376 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
1C22×#14268657C211yesmaximal, characteristic, complemented
2C2×#16813687C212yesmaximal, complemented
3C4×C22⋊#90673C211yesmaximal, characteristic, complemented
4#20299468C212yesmaximal, complemented
5#20299111C211yesmaximal, characteristic
6C2×#14268657—24no—
7C2×#14268657—21no—
8C2×#14268657C2212yes—
9C22×#11744753—21no—
10C2×C22⋊#90673—21no—
11C2×C4×#90673C2212yes—
12#16813687—24no—
13(C2×#90673)⋊C4—21no—
14C2×#14268648C2211yescharacteristic
15C22×C4×D113C2211yescharacteristic
16#16813607—21no—
17#16813598C411yescharacteristic, complemented
18#16813597C411yescharacteristic, complemented
19#16813596C411yescharacteristic, complemented
20#16813592—21no—
21#16813584—21no—
22#16813582—21no—
23#16813580C2211yescharacteristic
24C22⋊Q8×C113C411yescharacteristic, complemented
25C22×#90673—22no—
26#14268657—24no—
27#14268657—22no—
28#14268657D414yescomplemented
29C2×#11744753—24no—
30C2×#11744753—22no—
31C22⋊#90673—24no—
32C4×#90673—22no—
33C4×#90673—22no—
34C23×D113D411yescharacteristic
35#14268648—22no—
36#14268648—22no—
37C2×D452—21no—
38C2×D452—21no—
39C2×D452C2×C411yescharacteristic
40C2×C22⋊D113—21no—
41C22×Dic113D411yescharacteristic
42C2×C4×D113—22no—
43C2×C4×D113—22no—
44C2×C4×D113—21no—
45C2×C4×D113C2×C411yescharacteristic
46C2×C4×D113D411yescharacteristic
47C2×C4×D113D411yescharacteristic
48C2×C4×D113C2311yescharacteristic
49C4⋊Dic113C2×C411yescharacteristic
50#14268626—21no—
51#14268624—21no—
52#14268624—21no—
53#14268624—21no—
54#14268624—21no—
55C4×Dic113—21no—
56C2×Q8×C113C2×C411yescharacteristic
57C22×C4×C113C2×C411yescharacteristic
58C4⋊C4×C113—21no—
59C4⋊C4×C113C2×C411yescharacteristic
60C22⋊C4×C113—21no—
61C23×C113C22⋊C411yescharacteristic
62C22×D113—22no—
63C22×D113—22no—
64C22×D113—21no—
65C22×D113—41no—
66C22×D113C22⋊C411yescharacteristic
67C22×D113C2×D411yescharacteristic
68C2×#90673—24no—
69C2×#90673—42no—
70C2×#90673—42no—
71Q8×C113—22no—
72C2×C4×C113—22no—
73C2×C4×C113—21no—
74C2×C4×C113—21no—
75C2×C4×C113C22⋊C411yescharacteristic
76C2×C4×C113C22×C411yescharacteristic
77C22⋊D113—42no—
78C2×Dic113—21no—
79C2×Dic113—21no—
80C2×Dic113—21no—
81C2×Dic113C22⋊C411yescharacteristic
82C2×Dic113C2×D411yescharacteristic
83D452—22no—
84D452—42no—
85D452—42no—
86C4×D113—22no—
87C4×D113—22no—
88C4×D113—21no—
89C4×D113—21no—
90C4×D113—41no—
91C4×D113—41no—
92C4×D113C2×D412yes—
93C4×D113#4112yes—
94#11744753—24no—
95C22×C113—21no—
96C22×C113—21no—
97C22×C113#10412yescomplemented
98C22×C113C2×C22⋊C411yescharacteristic
99C2×D113—21no—
100C2×D113—21no—
101C2×D113—21no—
102C2×D113—21no—
103C2×D113—21no—
104C2×D113—44no—
105C2×D113—41no—
106C2×D113—41no—
107C2×D113—41no—
108C2×D113#12112yes—
109#90673—44no—
110C4×C113—21no—
111C4×C113—41no—
112C4×C113—41no—
113C4×C113C4×D412yes—
114Dic113—21no—
115Dic113—41no—
116Dic113#12011yescharacteristic
117Dic113#12311yescharacteristic
118C2×C113—22no—
119C2×C113#38611yescharacteristic
120C2×C113C2×#10411yescharacteristic
121C2×C113#42111yescharacteristic
122D113—22no—
123D113—41no—
124D113—81no—
125#1871—1131nomaximal, Sylow
126C113#187111yescharacteristic, complemented, Sylow
127C22×M16—1131no—
128#525—1131no—
129C2×#104—1132no—
130C4×C22⋊C4—1131no—
131#339—1132no—
132C2×#41—1131no—
133C23×C4—1131no—
134C2×M16—1132no—
135C2×M16—2264no—
136C2×M16—2261no—
137C22×C8—2261no—
138#123—2261no—
139C22⋊Q8—1131no—
140C22⋊Q8#9067311yescharacteristic, complemented
141#121—1131no—
142#121—1131no—
143#120—2261no—
144C4×D4—2261no—
145C4×D4—2261no—
146#117—1131no—
147C2×C22⋊C4—2261no—
148C2×C42—1132no—
149#104—2264no—
150#95—2261no—
151C24—1131no—
152#41—2262no—
153#41—2262no—
154C2×Q8C2×#9067311yescharacteristic
155C2×D4—1131no—
156C2×D4—2261no—
157C2×D4—2261no—
158C2×D4—2261no—
159C22×C4—1131no—
160C22×C4—1131no—
161C22×C4—1131no—
162C22×C4—1131no—
163C22×C4—1131no—
164C22×C4—2261no—
165C22×C4—2262no—
166C22×C4—2262no—
167C22×C4—2262no—
168C22×C4C2×#9067311yescharacteristic
169M16—1134no—
170M16—2262no—
171M16—2264no—
172C2×C8—2262no—
173C2×C8—2264no—
174C4⋊C4—21no—
175C4⋊C4—1131no—
176C4⋊C4—2261no—
177C4⋊C4C2×#9067311yescharacteristic
178C22⋊C4—21no—
179C22⋊C4—2261no—
180C22⋊C4—2261no—
181C22⋊C4—2261no—
182C22⋊C4—2264no—
183C22⋊C4—2261no—
184C42—2261no—
185C42—2262no—
186C42—2262no—
187C23—1131no—
188C23—1131no—
189C23—4521no—
190C23—2262no—
191C23—2261no—
192C23—2262no—
193C23C22⋊#9067311yescharacteristic
194Q8—22no—
195D4—4522no—
196D4—4522no—
197D4—4522no—
198D4—2262no—
199C2×C4—22no—
200C2×C4—21no—
201C2×C4—21no—
202C2×C4—1131no—
203C2×C4—1132no—
204C2×C4—1132no—
205C2×C4—1131no—
206C2×C4—4521no—
207C2×C4—4521no—
208C2×C4—4522no—
209C2×C4—4522no—
210C2×C4—2261no—
211C2×C4—2261no—
212C2×C4—2262no—
213C2×C4—2261no—
214C2×C4—2261no—
215C2×C4—2264no—
216C2×C4—2261no—
217C2×C4—2262no—
218C2×C4C22⋊#9067311yescharacteristic
219C2×C4C22×#9067311yescharacteristic
220C8—2264no—
221C22—21no—
222C22—21no—
223C22—1132no—
224C22—4524no—
225C22—4521no—
226C22—4521no—
227C22—4521no—
228C22—2261no—
229C22—2261no—
230C22—2261no—
231C22—2261no—
232C22—2261no—
233C22#1681368712yescomplemented
234C22C2×C22⋊#9067311yescharacteristic
235C4—21no—
236C4—41no—
237C4—41no—
238C4—1131no—
239C4—1131no—
240C4—4524no—
241C4—4521no—
242C4—2261no—
243C4D4×#9067312yes—
244C2—22no—
245C2—9041no—
246C2—4521no—
247C2—2262no—
248C2#2029954611yescharacteristic
249C2C2×#1681368711yescharacteristic
250C2#2029959511yescharacteristic
subgroupG/H
centerC22C2×C22⋊#90673
commutatorC2×C4×C113C22×C4
FrattiniC2×C4C22×#90673
FittingC22⋊Q8×C113C4
socleC22×C113C2×C22⋊C4
prime radical#20299111C2
cosocleC2×C4×D113C23
hypercenterC22⋊Q8#90673
hypocenterC113#1871
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#14268657C2semidirect
2. C2×#16813687C2semidirect
3. C4×C22⋊#90673C2semidirect
4. #20299468C2semidirect
17. #16813598C4semidirect
18. #16813597C4semidirect
19. #16813596C4semidirect
24. C22⋊Q8×C113C4semidirect
28. #14268657D4semidirect
97. C22×C113#104semidirect
126. C113#1871semidirect
140. C22⋊Q8#90673semidirect
233. C22#16813687semidirect

Maximal subgroups

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

subgroupindex
C22×#142686572
C2×#168136872
C4×C22⋊#906732
#202994682
#202991112
#1871113