Finite Group Databasebeta

← #28399865

Subgroups — #28399865

Order 14464.

700 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 700 conjugacy classes of subgroups — too many to draw. Only its 149 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×#16813670C211yesmaximal, characteristic
2C2×#16813653C211yesmaximal, characteristic, complemented
3#20299172C211yesmaximal, characteristic, complemented
4#20298759C214yesmaximal, complemented
5#20298752C214yesmaximal, complemented
6#20298607C211yesmaximal, characteristic, complemented
7#20298595C211yesmaximal, characteristic, complemented
8#20298564C211yesmaximal, characteristic, complemented
9C22×Q16×C113C211yesmaximal, characteristic, complemented
10#16813670—24no—
11#16813670—24no—
12C2×#14268648—21no—
13C2×#14268648C2212yes—
14C2×#14268647—22no—
15C2×#14268647C2211yescharacteristic
16C2×#14268647C2211yescharacteristic
17C2×Q8×D113—21no—
18C2×Q8×D113C2212yes—
19#16813653—24no—
20C2×#14268637C2212yes—
21C2×#14268634C2212yes—
22C2×#14268631C2211yescharacteristic
23#16813620—21no—
24#16813611—21no—
25#16813605—22no—
26#16813598C2214yes—
27#16813581C2211yescharacteristic
28#16813547C2212yes—
29#16813546C2214yes—
30#16813544C2212yes—
31#16813534C2214yes—
32C22×Q8×C113C2211yescharacteristic
33C22×Q8×C113C2211yescharacteristic
34C2×Q16×C113—24no—
35C2×Q16×C113C2214yes—
36C22×C8×C113C2211yescharacteristic
37#14268648—28no—
38#14268648—24no—
39#14268648—24no—
40#14268647—216no—
41#14268647—22no—
42#14268647—22no—
43#14268647—22no—
44#14268647D414yes—
45C2×Dic226—22no—
46C2×Dic226D411yescharacteristic
47C2×Dic226C2311yescharacteristic
48Q8×D113—28no—
49Q8×D113—24no—
50Q8×D113—24no—
51C2×D452—22no—
52C2×D452D411yescharacteristic
53C2×D452C2311yescharacteristic
54C2×C22⋊D113—21no—
55C2×C22⋊D113D412yes—
56C2×C4×D113—22no—
57C2×C4×D113—21no—
58C2×C4×D113—22no—
59C2×C4×D113C2312yes—
60#14268637—24no—
61#14268634—24no—
62#14268631—22no—
63C2×#11744751C2312yes—
64C4⋊Dic113C2312yes—
65#14268626—24no—
66C22⋊Dic113—21no—
67#14268624—24no—
68C4×Dic113—21no—
69C2×Q8×C113—21no—
70C2×Q8×C113—22no—
71C2×Q8×C113—21no—
72C2×Q8×C113—22no—
73C2×Q8×C113—22no—
74C2×Q8×C113D414yes—
75C2×Q8×C113C2312yes—
76C2×Q8×C113C2312yes—
77C22×C4×C113—21no—
78C22×C4×C113—21no—
79C22×C4×C113C2311yescharacteristic
80Q16×C113—28no—
81C2×C8×C113—22no—
82C2×C8×C113C2312yes—
83C23×C113C2×D411yescharacteristic
84C22×D113—21no—
85C22×D113C2×D412yes—
86Q8×C113—24no—
87Q8×C113—22no—
88Q8×C113—22no—
89Q8×C113—22no—
90Q8×C113—42no—
91Q8×C113C2×D414yes—
92C2×C4×C113—24no—
93C2×C4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—42no—
96C2×C4×C113C2×D411yescharacteristic
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2411yescharacteristic
100C22⋊D113—24no—
101C22⋊D113—24no—
102C2×Dic113—21no—
103C2×Dic113—22no—
104C2×Dic113C2×D412yes—
105D452—28no—
106D452—22no—
107D452—21no—
108D452C2×D412yes—
109C4×D113—28no—
110C4×D113—28no—
111C4×D113—24no—
112C4×D113—22no—
113C4×D113—22no—
114Dic226—28no—
115Dic226—22no—
116Dic226—21no—
117Dic226C2×D412yes—
118C8×C113—22no—
119#11744751—22no—
120C22×C113—22no—
121C22×C113#12012yes—
122C22×C113C22×D411yescharacteristic
123C2×D113—22no—
124C2×D113—22no—
125C2×D113—24no—
126C2×D113—42no—
127C4×C113—24no—
128C4×C113—42no—
129C4×C113#12012yes—
130C4×C113C22×D411yescharacteristic
131C4×C113C22×D411yescharacteristic
132Dic113—22no—
133Dic113—22no—
134Dic113—42no—
135C2×C113—22no—
136C2×C113C2×#12011yescharacteristic
137C2×C113#57812yes—
138D113—42no—
139D113—42no—
140#3011—1131nomaximal, Sylow
141C113#301111yescharacteristic, complemented, Sylow
142C2×2−1+4—1131no—
143C2×#137—1131no—
144C22×Q16D11311yescharacteristic, complemented
145#536—1131no—
146#452—1134no—
147#451—1134no—
148#419—1131no—
149#416—1131no—
150#408—1131no—
1512−1+4—2264no—
1522−1+4—2264no—
153C2×#41—1131no—
154C2×#41—1132no—
155C2×#41—1131no—
156C2×#41—2262no—
157C2×#41—2261no—
158C22×Q8—1132no—
159C22×Q8—2261no—
160C22×Q8C2×D11311yescharacteristic
161C22×Q8C2×D11311yescharacteristic
162#137—2264no—
163C2×Q16—24no—
164C2×Q16—1132no—
165C2×Q16C2×D11314yes—
166C2×SD16—1132no—
167C2×M16—1131no—
168C22×C8C2×D11311yescharacteristic
169C4⋊Q8—2261no—
170#124—2261no—
171#123—2262no—
172C22⋊Q8—1134no—
173#117—1131no—
174#103—1134no—
175#103—1132no—
176#102—1132no—
177C22⋊C8—1134no—
178#41—1134no—
179#41—22616no—
180#41—2264no—
181#41—2268no—
182#41—2264no—
183#41—2262no—
184#41—2262no—
185#41—2262no—
186C2×Q8—21no—
187C2×Q8—22no—
188C2×Q8—21no—
189C2×Q8—22no—
190C2×Q8—22no—
191C2×Q8—1131no—
192C2×Q8—1131no—
193C2×Q8—2262no—
194C2×Q8—2264no—
195C2×Q8—2268no—
196C2×Q8—2264no—
197C2×Q8C22⋊D11314yes—
198C2×Q8C22×D11312yes—
199C2×Q8C22×D11312yes—
200C2×D4—1132no—
201C2×D4—1131no—
202C2×D4—1131no—
203C2×D4—2262no—
204C2×D4—2261no—
205C22×C4—21no—
206C22×C4—21no—
207C22×C4—1132no—
208C22×C4—2262no—
209C22×C4—2262no—
210C22×C4—2261no—
211C22×C4C22×D11311yescharacteristic
212Q16—28no—
213Q16—2264no—
214SD16—2264no—
215M16—2262no—
216C2×C8—22no—
217C2×C8—1132no—
218C2×C8C22×D11312yes—
219C4⋊C4—1132no—
220C4⋊C4—2264no—
221C22⋊C4—2264no—
222C22⋊C4—2261no—
223C42—2261no—
224C23—1132no—
225C23—2261no—
226C23D4×D11311yescharacteristic
227Q8—24no—
228Q8—22no—
229Q8—22no—
230Q8—22no—
231Q8—42no—
232Q8—1132no—
233Q8—2268no—
234Q8—2262no—
235Q8—2261no—
236Q8C2×C22⋊D11314yes—
237D4—1132no—
238D4—2268no—
239D4—2264no—
240D4—2264no—
241D4—2262no—
242D4—2261no—
243C2×C4—24no—
244C2×C4—22no—
245C2×C4—22no—
246C2×C4—42no—
247C2×C4—1132no—
248C2×C4—2268no—
249C2×C4—2268no—
250C2×C4—2262no—
251C2×C4—2261no—
252C2×C4—2264no—
253C2×C4—2262no—
254C2×C4—2262no—
255C2×C4D4×D11311yescharacteristic
256C2×C4D4×D11312yes—
257C2×C4C2×C22⋊D11312yes—
258C2×C4C23×D11311yescharacteristic
259C8—22no—
260C8—2262no—
261C22—22no—
262C22—4522no—
263C22—2262no—
264C22—2262no—
265C22—2264no—
266C22#1681359012yes—
267C22C2×D4×D11311yescharacteristic
268C4—24no—
269C4—42no—
270C4—4522no—
271C4—2262no—
272C4—2262no—
273C4#1681359012yes—
274C4C2×D4×D11311yescharacteristic
275C4C22×C22⋊D11311yescharacteristic
276C2—22no—
277C2—4522no—
278C2—4522no—
279C2C2×#1681359011yescharacteristic
280C2#2029941112yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
FittingC22×Q16×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813670C2
hypercenterC22×Q16D113
hypocenterC113#3011
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ C22×Q16

Complements

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

NH ≅ G/Ntype
2. C2×#16813653C2semidirect
3. #20299172C2semidirect
4. #20298759C2semidirect
5. #20298752C2semidirect
6. #20298607C2semidirect
7. #20298595C2semidirect
8. #20298564C2semidirect
9. C22×Q16×C113C2semidirect
141. C113#3011semidirect
144. C22×Q16D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136702
C2×#168136532
#202991722
#202987592
#202987522
#202986072
#202985952
#202985642
C22×Q16×C1132
#3011113