Finite Group Databasebeta

← #447×D113 #28399747

Subgroups — #447×D113 #28399747

Order 14464.

1048 conjugacy classes of subgroups; only the 155 normal subgroups are shown.

normal subgroups only

This group has 1048 conjugacy classes of subgroups — too many to draw. Only its 155 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×D4×D113C211yesmaximal, characteristic, complemented
2C2×D8×D113C212yesmaximal, complemented
3#121×D113C211yesmaximal, characteristic, complemented
4#20298734C211yesmaximal, characteristic, complemented
5#20298733C212yesmaximal, complemented
6#20298732C211yesmaximal, characteristic, complemented
7#20298731C211yesmaximal, characteristic, complemented
8#20298730C212yesmaximal, complemented
9#102×D113C212yesmaximal, complemented
10C22⋊C8×D113C211yesmaximal, characteristic, complemented
11#447×C113C211yesmaximal, characteristic, complemented
12C24×D113—21no—
13C22×D452C2211yescharacteristic, complemented
14C22×C22⋊D113—21no—
15C2×D4×D113—28no—
16C2×D4×D113—21no—
17C2×D4×D113—21no—
18C2×D4×D113—21no—
19C2×D4×D113C2212yes—
20C2×D4×D113C2212yescomplemented
21C2×D4×D113C2211yescharacteristic, complemented
22C22×C4×D113C2211yescharacteristic
23C2×D904C2212yescomplemented
24C2×#14268632C2212yescomplemented
25C2×#14268632C2212yescomplemented
26D8×D113—28no—
27C2×C8×D113C2212yescomplemented
28#16813597C2211yescharacteristic, complemented
29#16813596C2211yescharacteristic, complemented
30#16813595—21no—
31#16813594—21no—
32#16813593C2211yescharacteristic, complemented
33C4⋊C4×D113C2211yescharacteristic, complemented
34C22⋊C4×D113—21no—
35#16813544C2212yescomplemented
36#16813543C2212yescomplemented
37#16813542C2212yescomplemented
38C22⋊#11744751C2211yescharacteristic, complemented
39#16813534C2212yescomplemented
40C22×D4×C113C2211yescharacteristic, complemented
41C2×D8×C113C2212yescomplemented
42#121×C113C2211yescharacteristic, complemented
43#102×C113C2212yescomplemented
44C22⋊C8×C113C2211yescharacteristic, complemented
45C23×D113—28no—
46C23×D113—21no—
47C23×D113—22no—
48C23×D113—22no—
49C23×D113—21no—
50C23×D113—44no—
51C23×D113—44no—
52C23×D113D411yescharacteristic
53C2×D452—21no—
54C2×D452—24no—
55C2×D452—21no—
56C2×D452C2312yes—
57C2×D452C2311yescharacteristic, complemented
58C2×C22⋊D113—28no—
59C2×C22⋊D113—21no—
60C2×C22⋊D113—21no—
61C2×C22⋊D113—22no—
62C2×C22⋊D113—22no—
63C2×C22⋊D113—21no—
64D4×D113—28no—
65D4×D113—28no—
66D4×D113—24no—
67D4×D113—24no—
68D4×D113—24no—
69D4×D113—24no—
70D4×D113—44no—
71D4×D113D418yescomplemented
72C22×Dic113D411yescharacteristic
73C2×C4×D113—24no—
74C2×C4×D113—21no—
75C2×C4×D113D411yescharacteristic
76C2×C4×D113D411yescharacteristic
77C2×C4×D113C2311yescharacteristic
78C2×C4×D113C2311yescharacteristic
79D904—24no—
80#14268632—24no—
81#14268632—24no—
82C2×#11744751C2312yescomplemented
83C8×D113—24no—
84C4⋊Dic113C2311yescharacteristic, complemented
85#14268626—21no—
86C22⋊Dic113—21no—
87#14268624—21no—
88#14268624—21no—
89C24×C113—21no—
90C2×D4×C113—24no—
91C2×D4×C113—21no—
92C2×D4×C113—21no—
93C2×D4×C113C2312yes—
94C2×D4×C113C2311yescharacteristic, complemented
95C22×C4×C113C2311yescharacteristic
96D8×C113—24no—
97C2×C8×C113C2312yescomplemented
98C4⋊C4×C113C2311yescharacteristic, complemented
99C22⋊C4×C113—21no—
100C23×C113—24no—
101C23×C113—22no—
102C23×C113—21no—
103C23×C113—42no—
104C23×C113—42no—
105C23×C113C2×D411yescharacteristic
106C22×D113—22no—
107C22×D113—22no—
108C22×D113—28no—
109C22×D113—24no—
110C22×D113—22no—
111C22×D113—28no—
112C22×D113—21no—
113C22×D113—44no—
114C22×D113—432no—
115C22×D113—42no—
116C22×D113—42no—
117C22×D113—44no—
118C22×D113—44no—
119C22×D113—44no—
120C22×D113—42no—
121C22×D113—42no—
122C22×D113—42no—
123C22×D113D814yescomplemented
124C22×D113C2×D411yescharacteristic
125C22×D113C2×D411yescharacteristic
126D4×C113—24no—
127D4×C113—22no—
128D4×C113—22no—
129D4×C113—42no—
130D4×C113C2×D414yescomplemented
131C2×C4×C113—22no—
132C2×C4×C113—21no—
133C2×C4×C113C2×D411yescharacteristic
134C2×C4×C113C2411yescharacteristic
135C22⋊D113—28no—
136C22⋊D113—28no—
137C22⋊D113—42no—
138C22⋊D113—42no—
139C22⋊D113—42no—
140C2×Dic113—22no—
141C2×Dic113—21no—
142C2×Dic113C2×D411yescharacteristic
143C2×Dic113C2×D411yescharacteristic
144D452—24no—
145D452—22no—
146D452—22no—
147D452—42no—
148D452C2×D414yescomplemented
149C4×D113—22no—
150C4×D113—22no—
151C4×D113—22no—
152C4×D113—42no—
153C4×D113C2×D414yes—
154C8×C113—22no—
155#11744751—22no—
156C22×C113—21no—
157C22×C113—21no—
158C22×C113—24no—
159C22×C113—48no—
160C22×C113—42no—
161C22×C113—42no—
162C22×C113—41no—
163C22×C113—41no—
164C22×C113—41no—
165C22×C113C2×D812yescomplemented
166C22×C113C22×D411yescharacteristic
167C2×D113—21no—
168C2×D113—21no—
169C2×D113—28no—
170C2×D113—24no—
171C2×D113—416no—
172C2×D113—48no—
173C2×D113—42no—
174C2×D113—42no—
175C2×D113—416no—
176C2×D113—41no—
177C2×D113—41no—
178C2×D113—41no—
179C2×D113—84no—
180C2×D113#12012yes—
181C2×D113C2×D812yes—
182C2×D113C2×D812yescomplemented
183C2×D113AGL(1,ℤ/8)12yes—
184C4×C113—21no—
185C4×C113—41no—
186C4×C113C22×D412yes—
187Dic113—21no—
188Dic113—41no—
189Dic113#12012yes—
190C2×C113—22no—
191C2×C113—44no—
192C2×C113—81no—
193C2×C113C2×#12011yescharacteristic
194C2×C113C22×D811yescharacteristic
195C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
196D113—22no—
197D113—44no—
198D113—81no—
199D113#44714yesdirect product factor
200C2×#447—1131nomaximal, Sylow
201C113C2×#44711yescharacteristic, complemented, Sylow
202C23×D4—1131no—
203C22×D8—1132no—
204C2×#121—1131no—
205#447—1131no—
206#447—1132no—
207#447—1131no—
208#447—1132no—
209#447—1131no—
210#447D11311yescharacteristic, direct product factor
211C2×#102—1132no—
212C2×C22⋊C8—1131no—
213C25—2261no—
214C22×D4—1132no—
215C22×D4—1132no—
216C22×D4—1131no—
217C22×D4—1131no—
218C22×D4—2261no—
219C22×D4—2261no—
220C22×D4—2261no—
221C22×D4—2268no—
222C22×D4—2261no—
223C22×D4C2×D11311yescharacteristic, complemented
224C23×C4—1131no—
225C2×D8—1132no—
226C2×D8—1132no—
227C2×D8—1132no—
228C2×D8—2268no—
229C2×D8C2×D11312yescomplemented
230C22×C8—1132no—
231#121—1131no—
232#121—1131no—
233#121—1131no—
234#121—2261no—
235#121—2261no—
236#121C2×D11311yescharacteristic, complemented
237C2×C4⋊C4—1131no—
238C2×C22⋊C4—2261no—
239#102—1132no—
240#102—1132no—
241#102—1132no—
242#102C2×D11312yescomplemented
243C22⋊C8—1131no—
244C22⋊C8—1132no—
245C22⋊C8C2×D11311yescharacteristic, complemented
246C24—21no—
247C24—1131no—
248C24—4524no—
249C24—4524no—
250C24—2261no—
251C24—2262no—
252C24—2262no—
253C24—2268no—
254C24—2261no—
255C2×D4—24no—
256C2×D4—21no—
257C2×D4—21no—
258C2×D4—1138no—
259C2×D4—1132no—
260C2×D4—1131no—
261C2×D4—4524no—
262C2×D4—2264no—
263C2×D4—2261no—
264C2×D4—2264no—
265C2×D4—2264no—
266C2×D4—2261no—
267C2×D4—2262no—
268C2×D4—2262no—
269C2×D4—2264no—
270C2×D4—2268no—
271C2×D4—2268no—
272C2×D4—2261no—
273C2×D4—2261no—
274C2×D4—2268no—
275C2×D4—2264no—
276C2×D4—2261no—
277C2×D4C22×D11312yes—
278C2×D4C22×D11311yescharacteristic, complemented
279C22×C4—1131no—
280C22×C4—1131no—
281C22×C4—1131no—
282C22×C4—1131no—
283C22×C4—1131no—
284C22×C4—2264no—
285C22×C4—2261no—
286C22×C4C22×D11311yescharacteristic
287D8—24no—
288D8—2264no—
289D8—2264no—
290D8—2264no—
291C2×C8—1132no—
292C2×C8—2264no—
293C2×C8C22×D11312yescomplemented
294C4⋊C4—1131no—
295C4⋊C4—2261no—
296C4⋊C4C22×D11311yescharacteristic, complemented
297C22⋊C4—21no—
298C22⋊C4—2261no—
299C22⋊C4—2261no—
300C22⋊C4—2261no—
301C23—24no—
302C23—22no—
303C23—21no—
304C23—42no—
305C23—42no—
306C23—1131no—
307C23—1134no—
308C23—1131no—
309C23—4522no—
310C23—4522no—
311C23—4522no—
312C23—4522no—
313C23—4524no—
314C23—4524no—
315C23—4524no—
316C23—45232no—
317C23—4524no—
318C23—4522no—
319C23—2268no—
320C23—2262no—
321C23—2262no—
322C23—2264no—
323C23—2268no—
324C23—2261no—
325C23—2262no—
326C23D4×D11311yescharacteristic
327D4—24no—
328D4—22no—
329D4—22no—
330D4—42no—
331D4—1134no—
332D4—4522no—
333D4—4522no—
334D4—4522no—
335D4—4522no—
336D4—2264no—
337D4—2268no—
338D4—2268no—
339D4—2262no—
340D4—2262no—
341D4D4×D11314yescomplemented
342C2×C4—22no—
343C2×C4—21no—
344C2×C4—1131no—
345C2×C4—1134no—
346C2×C4—1131no—
347C2×C4—4522no—
348C2×C4—2262no—
349C2×C4—2262no—
350C2×C4—2262no—
351C2×C4—2261no—
352C2×C4—2262no—
353C2×C4D4×D11311yescharacteristic
354C2×C4C23×D11311yescharacteristic
355C8—22no—
356C8—2262no—
357C22—21no—
358C22—21no—
359C22—24no—
360C22—48no—
361C22—42no—
362C22—42no—
363C22—41no—
364C22—41no—
365C22—41no—
366C22—1132no—
367C22—1132no—
368C22—1132no—
369C22—1132no—
370C22—9044no—
371C22—4528no—
372C22—45216no—
373C22—45216no—
374C22—4521no—
375C22—4521no—
376C22—4521no—
377C22—4522no—
378C22—4522no—
379C22—2268no—
380C22—2264no—
381C22—2261no—
382C22—2261no—
383C22D8×D11312yescomplemented
384C22C2×D4×D11311yescharacteristic
385C4—21no—
386C4—41no—
387C4—1132no—
388C4—4521no—
389C4—2261no—
390C4C2×D4×D11312yes—
391C2—22no—
392C2—44no—
393C2—81no—
394C2—1134no—
395C2—9041no—
396C2—4524no—
397C2—2262no—
398C2#120×D11311yescharacteristic
399C2C2×D8×D11311yescharacteristic
400C2AGL(1,ℤ/8)×D11311yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113C2×#447
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #447

Complements

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

NH ≅ G/Ntype
1. C22×D4×D113C2semidirect
2. C2×D8×D113C2semidirect
3. #121×D113C2semidirect
4. #20298734C2semidirect
5. #20298733C2semidirect
6. #20298732C2semidirect
7. #20298731C2semidirect
8. #20298730C2semidirect
9. #102×D113C2semidirect
10. C22⋊C8×D113C2semidirect
11. #447×C113C2semidirect
13. C22×D452C22semidirect
20. C2×D4×D113C22semidirect
21. C2×D4×D113C22semidirect
23. C2×D904C22semidirect
24. C2×#14268632C22semidirect
25. C2×#14268632C22semidirect
27. C2×C8×D113C22semidirect
28. #16813597C22semidirect
29. #16813596C22semidirect
32. #16813593C22semidirect
33. C4⋊C4×D113C22semidirect
35. #16813544C22semidirect
36. #16813543C22semidirect
37. #16813542C22semidirect
38. C22⋊#11744751C22semidirect
39. #16813534C22semidirect
40. C22×D4×C113C22semidirect
41. C2×D8×C113C22semidirect
42. #121×C113C22semidirect
43. #102×C113C22semidirect
44. C22⋊C8×C113C22semidirect
57. C2×D452C23semidirect
71. D4×D113D4semidirect
82. C2×#11744751C23semidirect
84. C4⋊Dic113C23semidirect
94. C2×D4×C113C23semidirect
97. C2×C8×C113C23semidirect
98. C4⋊C4×C113C23semidirect
123. C22×D113D8semidirect
130. D4×C113C2×D4semidirect
148. D452C2×D4semidirect
165. C22×C113C2×D8semidirect
182. C2×D113C2×D8semidirect
199. D113#447direct (N × H)
201. C113C2×#447semidirect
210. #447D113direct (N × H)
223. C22×D4C2×D113semidirect
229. C2×D8C2×D113semidirect
236. #121C2×D113semidirect
242. #102C2×D113semidirect
245. C22⋊C8C2×D113semidirect
278. C2×D4C22×D113semidirect
293. C2×C8C22×D113semidirect
296. C4⋊C4C22×D113semidirect
341. D4D4×D113semidirect
383. C22D8×D113semidirect

Maximal subgroups

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

subgroupindex
C22×D4×D1132
C2×D8×D1132
#121×D1132
#202987342
#202987332
#202987322
#202987312
#202987302
#102×D1132
C22⋊C8×D1132
#447×C1132
C2×#447113