Finite Group Databasebeta

← #28399927

Subgroups — #28399927

Order 14464.

724 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 724 conjugacy classes of subgroups — too many to draw. Only its 145 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
1#20299434C211yesmaximal, characteristic, complemented
2#20299398C212yesmaximal, complemented
3#20299144C211yesmaximal, characteristic, complemented
4#20298783C212yesmaximal, complemented
5#20298778C212yesmaximal, complemented
6#20298773C212yesmaximal, complemented
7#20298768C212yesmaximal, complemented
8C2×#16813548C212yesmaximal, complemented
9#413×C113C211yesmaximal, characteristic, complemented
10#16813670C2212yes—
11#16813669—22no—
12#16813668—22no—
13#16813667—22no—
14#16813667C2212yes—
15C2×#14268647—22no—
16C2×#14268647C2212yes—
17C2×#14268647C2211yescharacteristic, complemented
18#41×D113—24no—
19#16813655—22no—
20#16813655C2214yescomplemented
21#16813650—22no—
22#16813650C2214yescomplemented
23#16813644—24no—
24#16813620C2211yescharacteristic, complemented
25#16813618C2211yescharacteristic, complemented
26#16813611C2211yescharacteristic, complemented
27#16813609C2211yescharacteristic, complemented
28#16813594—22no—
29C4×C22⋊D113—22no—
30C2×C4×Dic113C2211yescharacteristic, complemented
31#16813548C2214yescomplemented
32#16813548C2214yescomplemented
33C2×#41×C113C2211yescharacteristic
34C2×M16×C113C2212yescomplemented
35#101×C113C2212yescomplemented
36#100×C113C2212yescomplemented
37#14268648—24no—
38#14268647—24no—
39#14268647—24no—
40#14268647—22no—
41#14268647—24no—
42#14268647—22no—
43#14268647—22no—
44#14268647—22no—
45#14268647D414yescomplemented
46#14268647C2314yes—
47#14268646—28no—
48#14268646—24no—
49C2×Dic226—22no—
50C2×Dic226D412yescomplemented
51C2×Dic226C2311yescharacteristic
52Q8×D113—24no—
53C2×D452—22no—
54C2×D452D412yescomplemented
55C2×D452C2311yescharacteristic
56C2×C22⋊D113—24no—
57C2×C22⋊D113—22no—
58C2×C22⋊D113—22no—
59C2×C22⋊D113—21no—
60D4×D113—28no—
61D4×D113—24no—
62C22×Dic113—21no—
63C2×C4×D113—24no—
64C2×C4×D113—22no—
65C2×C4×D113—21no—
66Dic452—24no—
67#14268636—24no—
68#14268636—24no—
69D904—24no—
70#14268626—22no—
71C22⋊Dic113—22no—
72#14268624—22no—
73C4×Dic113—21no—
74C4×Dic113C2311yescharacteristic
75C4×Dic113C2311yescharacteristic
76#41×C113—22no—
77#41×C113—22no—
78C2×Q8×C113C2311yescharacteristic
79C2×D4×C113D412yes—
80C2×D4×C113C2311yescharacteristic
81C22×C4×C113D412yes—
82C22×C4×C113C2311yescharacteristic
83M16×C113—22no—
84M16×C113C2314yes—
85C2×C8×C113—22no—
86C23×C113C2×D412yes—
87C23×C113C2×D411yescharacteristic
88C22×D113—24no—
89C22×D113—22no—
90C22×D113—21no—
91Q8×C113—22no—
92D4×C113—24no—
93D4×C113—22no—
94C2×C4×C113—22no—
95C2×C4×C113—22no—
96C2×C4×C113C2×D412yes—
97C2×C4×C113C2×D412yes—
98C2×C4×C113C2×D412yes—
99C2×C4×C113C2×D411yescharacteristic
100C2×C4×C113C2411yescharacteristic
101C22⋊D113—28no—
102C22⋊D113—24no—
103C22⋊D113—24no—
104C22⋊D113—44no—
105C22⋊D113—42no—
106C2×Dic113—24no—
107C2×Dic113—22no—
108C2×Dic113—21no—
109C2×Dic113—21no—
110C2×Dic113—21no—
111C2×Dic113—42no—
112D452—24no—
113D452—22no—
114D452—22no—
115D452C2×D414yes—
116C4×D113—28no—
117C4×D113—24no—
118C4×D113—24no—
119C4×D113—41no—
120C4×D113—41no—
121Dic226—24no—
122Dic226—22no—
123Dic226—22no—
124Dic226C2×D414yes—
125C8×C113—24no—
126C22×C113—22no—
127C22×C113—41no—
128C22×C113—42no—
129C22×C113#12012yes—
130C22×C113C22×D411yescharacteristic
131C2×D113—24no—
132C2×D113—42no—
133C2×D113—41no—
134C2×D113—82no—
135C2×D113—84no—
136C4×C113—22no—
137C4×C113#12011yescharacteristic
138C4×C113#12011yescharacteristic
139C4×C113C22×D412yes—
140Dic113—22no—
141Dic113—24no—
142Dic113—41no—
143Dic113—41no—
144C2×C113—21no—
145C2×C113—22no—
146C2×C113—42no—
147C2×C113C2×#12011yescharacteristic
148D113—44no—
149D113—81no—
150#3018—1131nomaximal, Sylow
151C113#301811yescharacteristic, complemented, Sylow
152#585—1131no—
153#575—1132no—
154#532—1131no—
155#456—1132no—
156#455—1132no—
157#454—1132no—
158#453—1132no—
159C2×#104—1132no—
160#413D11311yescharacteristic, complemented
1612−1+4—1132no—
1622−1+4—2262no—
163H(5,𝔽2)—1132no—
164H(5,𝔽2)—2262no—
165H(5,𝔽2)—2262no—
166C2×#41—1132no—
167C2×#41—1131no—
168C2×#41—2264no—
169C2×#41—2262no—
170C2×#41C2×D11311yescharacteristic
171#137—1134no—
172#137—2262no—
173AGL(1,ℤ/8)—1134no—
174AGL(1,ℤ/8)—2262no—
175#135—2264no—
176C2×M16C2×D11312yescomplemented
177C4⋊Q8—1131no—
178#127—1131no—
179#124—1131no—
180#124—1131no—
181#121—2262no—
182C4×D4—2262no—
183C2×C42—1131no—
184#104—1134no—
185#104—1134no—
186#101C2×D11312yescomplemented
187#100C2×D11312yescomplemented
188#41—22no—
189#41—22no—
190#41—1134no—
191#41—1134no—
192#41—2264no—
193#41—2264no—
194#41—2262no—
195#41—2262no—
196#41—2264no—
197#41—2268no—
198#41—2264no—
199#41—2262no—
200#41—2262no—
201#41—2264no—
202C2×Q8—1132no—
203C2×Q8—1131no—
204C2×Q8—2262no—
205C2×Q8—2264no—
206C2×Q8C22×D11311yescharacteristic
207C2×D4—1132no—
208C2×D4—1131no—
209C2×D4—2262no—
210C2×D4—2264no—
211C2×D4—2268no—
212C2×D4—2262no—
213C2×D4—2261no—
214C2×D4—2262no—
215C2×D4—2264no—
216C2×D4D45212yes—
217C2×D4C22×D11311yescharacteristic
218C22×C4—2264no—
219C22×C4—2261no—
220C22×C4—2261no—
221C22×C4—2262no—
222C22×C4D45212yes—
223C22×C4C22×D11311yescharacteristic
224Q16—2264no—
225SD16—2264no—
226SD16—2264no—
227D8—2264no—
228M16—22no—
229M16C22×D11314yes—
230C2×C8—22no—
231C4⋊C4—2262no—
232C22⋊C4—2262no—
233C22⋊C4—2262no—
234C42—1131no—
235C42—1131no—
236C42—2261no—
237C23—2264no—
238C23—2262no—
239C23—2261no—
240C23C2×D45212yes—
241C23C2×D45211yescharacteristic
242Q8—22no—
243Q8—1134no—
244Q8—2264no—
245Q8—2262no—
246Q8—2262no—
247D4—24no—
248D4—22no—
249D4—1134no—
250D4—4522no—
251D4—4524no—
252D4—2264no—
253D4—2268no—
254D4—2264no—
255D4—2264no—
256D4—2262no—
257D4—2262no—
258C2×C4—22no—
259C2×C4—22no—
260C2×C4—4522no—
261C2×C4—4521no—
262C2×C4—4521no—
263C2×C4—2268no—
264C2×C4—2261no—
265C2×C4—2261no—
266C2×C4—2264no—
267C2×C4—2262no—
268C2×C4—2261no—
269C2×C4—2264no—
270C2×C4—2264no—
271C2×C4D4×D11312yes—
272C2×C4D4×D11312yes—
273C2×C4C2×D45212yes—
274C2×C4C2×D45211yescharacteristic
275C2×C4C23×D11311yescharacteristic
276C8—24no—
277C22—22no—
278C22—41no—
279C22—42no—
280C22—9042no—
281C22—9044no—
282C22—4522no—
283C22—4521no—
284C22—2264no—
285C22#1681359212yes—
286C22C22×D45211yescharacteristic
287C4—22no—
288C4—4521no—
289C4—4521no—
290C4—2262no—
291C4—2264no—
292C4#1681359211yescharacteristic
293C4#1681359211yescharacteristic
294C4C2×D4×D11312yes—
295C2—21no—
296C2—22no—
297C2—42no—
298C2—9041no—
299C2—4524no—
300C2C2×#1681359211yescharacteristic
subgroupG/H
centerC4#16813592
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#413×C113C2
socleC2×C113C2×#120
hypercenter#413D113
hypocenterC113#3018
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C4 ◁ C22×C4 ◁ #413

Complements

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

NH ≅ G/Ntype
1. #20299434C2semidirect
2. #20299398C2semidirect
3. #20299144C2semidirect
4. #20298783C2semidirect
5. #20298778C2semidirect
6. #20298773C2semidirect
7. #20298768C2semidirect
8. C2×#16813548C2semidirect
9. #413×C113C2semidirect
17. C2×#14268647C22semidirect
20. #16813655C22semidirect
22. #16813650C22semidirect
24. #16813620C22semidirect
25. #16813618C22semidirect
26. #16813611C22semidirect
27. #16813609C22semidirect
30. C2×C4×Dic113C22semidirect
31. #16813548C22semidirect
32. #16813548C22semidirect
34. C2×M16×C113C22semidirect
35. #101×C113C22semidirect
36. #100×C113C22semidirect
45. #14268647D4semidirect
50. C2×Dic226D4semidirect
54. C2×D452D4semidirect
151. C113#3018semidirect
160. #413D113semidirect
176. C2×M16C2×D113semidirect
186. #101C2×D113semidirect
187. #100C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202994342
#202993982
#202991442
#202987832
#202987782
#202987732
#202987682
C2×#168135482
#413×C1132
#3018113