Finite Group Databasebeta

← #28399854

Subgroups — #28399854

Order 14464.

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

normal subgroups only

This group has 752 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×#16813668C211yesmaximal, characteristic
2C2×#16813652C211yesmaximal, characteristic, complemented
3C22×#14268636C211yesmaximal, characteristic, complemented
4#20299174C211yesmaximal, characteristic, complemented
5#20298763C214yesmaximal, complemented
6#20298750C214yesmaximal, complemented
7#20298602C211yesmaximal, characteristic, complemented
8#20298564C211yesmaximal, characteristic, complemented
9#416×C113C211yesmaximal, characteristic, complemented
10#16813668—24no—
11#16813668—24no—
12C2×#14268648C2212yes—
13C2×#14268647—21no—
14C2×#14268647C2211yescharacteristic
15C22×Dic226C2211yescharacteristic, complemented
16C22×D452—21no—
17C22×D452C2211yescharacteristic
18C2×D4×D113—22no—
19C2×D4×D113C2212yes—
20#16813652—24no—
21C2×#14268637C2212yescomplemented
22C2×#14268636—24no—
23C2×#14268636C2214yescomplemented
24C2×#14268635C2212yescomplemented
25C2×#14268631C2211yescharacteristic, complemented
26#16813622—21no—
27#16813610—21no—
28#16813606—22no—
29#16813602C2214yescomplemented
30#16813542C2214yescomplemented
31#16813534C2214yescomplemented
32C2×#41×C113C2211yescharacteristic
33C22×C8×C113C2211yescharacteristic, complemented
34#117×C113C2211yescharacteristic, complemented
35#103×C113C2212yescomplemented
36#102×C113C2212yescomplemented
37C23×D113—21no—
38C23×D113—22no—
39#14268648—24no—
40#14268648—24no—
41#14268647—28no—
42#14268647—22no—
43#14268647—22no—
44C2×Dic226—22no—
45C2×Dic226—22no—
46C2×Dic226—21no—
47C2×Dic226D411yescharacteristic
48C2×Dic226C2312yes—
49C2×D452—28no—
50C2×D452—22no—
51C2×D452—21no—
52C2×D452—22no—
53C2×D452D411yescharacteristic
54C2×D452D414yes—
55C2×D452C2312yes—
56C2×C22⋊D113—22no—
57C2×C22⋊D113D412yes—
58D4×D113—216no—
59D4×D113—24no—
60D4×D113—24no—
61C22×Dic113—21no—
62C2×C4×D113—22no—
63C2×C4×D113C2312yes—
64#14268637—24no—
65#14268636—28no—
66#14268635—24no—
67#14268631—22no—
68C2×#11744751C2312yes—
69C4⋊Dic113—24no—
70#14268624—24no—
71#41×C113—22no—
72#41×C113D414yes—
73C2×Q8×C113C2311yescharacteristic
74C2×D4×C113—21no—
75C2×D4×C113C2311yescharacteristic
76C22×C4×C113—21no—
77C22×C4×C113C2311yescharacteristic
78C2×C8×C113—22no—
79C2×C8×C113C2312yes—
80C4⋊C4×C113C2312yes—
81C22⋊C4×C113—21no—
82C42×C113—21no—
83C23×C113—21no—
84C23×C113C2×D411yescharacteristic
85C22×D113—22no—
86C22×D113—28no—
87C22×D113—24no—
88C22×D113—84no—
89C22×D113—82no—
90C22×D113C2×D412yes—
91Q8×C113—21no—
92Q8×C113C2×D412yes—
93D4×C113—24no—
94D4×C113—21no—
95D4×C113C2×D412yes—
96C2×C4×C113—21no—
97C2×C4×C113—24no—
98C2×C4×C113—22no—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2×D412yes—
101C2×C4×C113C2×D412yes—
102C2×C4×C113C2411yescharacteristic
103C22⋊D113—28no—
104C22⋊D113—24no—
105C2×Dic113—22no—
106C2×Dic113—42no—
107C2×Dic113C2×D412yes—
108D452—28no—
109D452—22no—
110D452—24no—
111D452—22no—
112D452C2×D414yes—
113C4×D113—28no—
114C4×D113—22no—
115C4×D113—22no—
116Dic226—22no—
117Dic226—22no—
118Dic226—22no—
119Dic226—42no—
120C8×C113—22no—
121#11744751—22no—
122C22×C113—22no—
123C22×C113—22no—
124C22×C113—42no—
125C22×C113#12012yes—
126C22×C113C22×D411yescharacteristic
127C2×D113—22no—
128C2×D113—24no—
129C2×D113—24no—
130C2×D113—44no—
131C2×D113—84no—
132C2×D113—88no—
133C4×C113—22no—
134C4×C113—42no—
135C4×C113#12012yes—
136C4×C113C22×D411yescharacteristic
137C4×C113C22×D411yescharacteristic
138Dic113—22no—
139Dic113—42no—
140C2×C113—22no—
141C2×C113—42no—
142C2×C113C2×#12011yescharacteristic
143C2×C113#57712yes—
144D113—42no—
145D113—44no—
146#3009—1131nomaximal, Sylow
147C113#300911yescharacteristic, complemented, Sylow
148C2×H(5,𝔽2)—1131no—
149C2×#137—1131no—
150C22×SD16—1131no—
151#536—1131no—
152#452—1134no—
153#450—1134no—
154#418—1131no—
155#416D11311yescharacteristic, complemented
156#408—1131no—
157H(5,𝔽2)—2264no—
158H(5,𝔽2)—2264no—
159C2×#41—1131no—
160C2×#41—1132no—
161C2×#41—2261no—
162C2×#41C2×D11311yescharacteristic
163C22×Q8—1131no—
164C22×D4—1132no—
165C22×D4—1131no—
166C22×D4—2261no—
167C22×D4—2262no—
168#137—2264no—
169C2×Q16—1132no—
170C2×SD16—1132no—
171C2×SD16—1134no—
172C2×SD16—2264no—
173C2×M16—1131no—
174C22×C8C2×D11311yescharacteristic, complemented
175C4⋊Q8—2261no—
176#124—2261no—
177#123—2262no—
178C22⋊Q8—1134no—
179#117C2×D11311yescharacteristic, complemented
180#103C2×D11312yescomplemented
181#102—1134no—
182#102C2×D11312yescomplemented
183C22⋊C8—1134no—
184C24—2262no—
185C24—2261no—
186#41—22no—
187#41—2268no—
188#41—2264no—
189#41—2264no—
190#41—2262no—
191#41—2262no—
192#41D45214yes—
193C2×Q8—1131no—
194C2×Q8—1132no—
195C2×Q8—2262no—
196C2×Q8—2262no—
197C2×Q8—2261no—
198C2×Q8C22×D11311yescharacteristic
199C2×D4—21no—
200C2×D4—1132no—
201C2×D4—1134no—
202C2×D4—1131no—
203C2×D4—1132no—
204C2×D4—2262no—
205C2×D4—2268no—
206C2×D4—2262no—
207C2×D4—2264no—
208C2×D4—22616no—
209C2×D4—2264no—
210C2×D4—2261no—
211C2×D4—2262no—
212C2×D4C22×D11311yescharacteristic
213C22×C4—21no—
214C22×C4—1132no—
215C22×C4—2262no—
216C22×C4—2261no—
217C22×C4C22×D11311yescharacteristic
218Q16—2264no—
219SD16—2268no—
220SD16—2264no—
221M16—2262no—
222C2×C8—22no—
223C2×C8—1132no—
224C2×C8C22×D11312yes—
225C4⋊C4—2264no—
226C4⋊C4C22×D11312yes—
227C22⋊C4—21no—
228C22⋊C4—2264no—
229C42—21no—
230C23—21no—
231C23—1132no—
232C23—9042no—
233C23—9044no—
234C23—2268no—
235C23—2264no—
236C23—2262no—
237C23D4×D11311yescharacteristic
238Q8—21no—
239Q8—4522no—
240Q8—2262no—
241Q8—2262no—
242Q8—2262no—
243Q8C2×D45212yes—
244D4—24no—
245D4—21no—
246D4—1134no—
247D4—2268no—
248D4—2268no—
249D4—2264no—
250D4—2264no—
251D4—2262no—
252D4—2262no—
253D4C2×D45212yes—
254C2×C4—21no—
255C2×C4—24no—
256C2×C4—22no—
257C2×C4—1132no—
258C2×C4—4522no—
259C2×C4—2268no—
260C2×C4—2262no—
261C2×C4—2262no—
262C2×C4—2262no—
263C2×C4D4×D11311yescharacteristic
264C2×C4D4×D11312yes—
265C2×C4C2×D45212yes—
266C2×C4C23×D11311yescharacteristic
267C8—22no—
268C8—2262no—
269C22—22no—
270C22—22no—
271C22—42no—
272C22—9044no—
273C22—9048no—
274C22—4524no—
275C22—2264no—
276C22—2262no—
277C22—2264no—
278C22#1681359212yes—
279C22C2×D4×D11311yescharacteristic
280C4—22no—
281C4—42no—
282C4—4522no—
283C4—2262no—
284C4#1681359212yes—
285C4C2×D4×D11311yescharacteristic
286C4C22×D45211yescharacteristic
287C2—22no—
288C2—42no—
289C2—4524no—
290C2—4522no—
291C2C2×#1681359211yescharacteristic
292C2#2029940512yes—
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#416×C113C2
socleC22×C113C22×D4
prime radicalC2×#16813668C2
hypercenter#416D113
hypocenterC113#3009
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #416

Complements

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

NH ≅ G/Ntype
2. C2×#16813652C2semidirect
3. C22×#14268636C2semidirect
4. #20299174C2semidirect
5. #20298763C2semidirect
6. #20298750C2semidirect
7. #20298602C2semidirect
8. #20298564C2semidirect
9. #416×C113C2semidirect
15. C22×Dic226C22semidirect
21. C2×#14268637C22semidirect
23. C2×#14268636C22semidirect
24. C2×#14268635C22semidirect
25. C2×#14268631C22semidirect
29. #16813602C22semidirect
30. #16813542C22semidirect
31. #16813534C22semidirect
33. C22×C8×C113C22semidirect
34. #117×C113C22semidirect
35. #103×C113C22semidirect
36. #102×C113C22semidirect
147. C113#3009semidirect
155. #416D113semidirect
174. C22×C8C2×D113semidirect
179. #117C2×D113semidirect
180. #103C2×D113semidirect
182. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
C2×#168136682
C2×#168136522
C22×#142686362
#202991742
#202987632
#202987502
#202986022
#202985642
#416×C1132
#3009113