Finite Group Databasebeta

← #28399821

Subgroups — #28399821

Order 14464.

806 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 806 conjugacy classes of subgroups — too many to draw. Only its 141 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×#14268646C211yesmaximal, characteristic, complemented
2C2×#16813646C212yesmaximal, complemented
3#121×D113C211yesmaximal, characteristic, complemented
4#20298744C212yesmaximal, complemented
5#20298740C212yesmaximal, complemented
6#20298739C211yesmaximal, characteristic, complemented
7#20298736C211yesmaximal, characteristic, complemented
8#20298732C211yesmaximal, characteristic, complemented
9#20298596C212yesmaximal, complemented
10#20298560C211yesmaximal, characteristic, complemented
11#447×C113C211yesmaximal, characteristic, complemented
12C2×#14268646—28no—
13C2×#14268646—21no—
14C2×#14268646—21no—
15C2×#14268646C2212yes—
16C2×#14268646C2212yescomplemented
17C22×Dic226C2211yescharacteristic, complemented
18C22×C22⋊D113—21no—
19C2×D4×D113—21no—
20C2×D4×D113C2211yescharacteristic, complemented
21C23×Dic113—21no—
22C22×C4×D113C2211yescharacteristic
23#16813646—28no—
24C2×#14268636C2212yescomplemented
25C2×#14268635C2212yescomplemented
26C2×#14268632C2212yescomplemented
27C2×#14268630C2212yescomplemented
28#16813597C2211yescharacteristic, complemented
29#16813596C2211yescharacteristic
30#16813595—21no—
31#16813594—21no—
32#16813593C2211yescharacteristic, complemented
33C4⋊C4×D113C2211yescharacteristic, complemented
34C22⋊C4×D113—21no—
35#16813547C2212yescomplemented
36#16813545C2212yescomplemented
37#16813543C2212yescomplemented
38C22⋊#11744751C2211yescharacteristic, complemented
39#16813534C2212yescomplemented
40C22×D4×C113C2211yescharacteristic, complemented
41C2×D8×C113C2212yescomplemented
42#121×C113C2211yescharacteristic
43#102×C113C2212yescomplemented
44C22⋊C8×C113C2211yescharacteristic, complemented
45C23×D113—21no—
46C23×D113D411yescharacteristic
47#14268646—28no—
48#14268646—28no—
49#14268646—24no—
50#14268646—24no—
51#14268646—24no—
52#14268646D418yescomplemented
53C2×Dic226—21no—
54C2×Dic226—24no—
55C2×Dic226C2312yes—
56C2×D452—21no—
57C2×D452C2311yescharacteristic
58C2×C22⋊D113—28no—
59C2×C22⋊D113—22no—
60C2×C22⋊D113—22no—
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64D4×D113—24no—
65D4×D113—44no—
66C22×Dic113—28no—
67C22×Dic113—21no—
68C22×Dic113—22no—
69C22×Dic113—22no—
70C22×Dic113D411yescharacteristic
71C2×C4×D113—24no—
72C2×C4×D113—21no—
73C2×C4×D113D411yescharacteristic
74C2×C4×D113D411yescharacteristic
75C2×C4×D113C2311yescharacteristic
76C2×C4×D113C2311yescharacteristic
77#14268636—24no—
78#14268635—24no—
79#14268632—24no—
80#14268630—24no—
81C2×#11744751C2312yes—
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84C22⋊Dic113—21no—
85#14268624—21no—
86#14268624—21no—
87C24×C113—21no—
88C2×D4×C113—24no—
89C2×D4×C113—21no—
90C2×D4×C113—21no—
91C2×D4×C113C2311yescharacteristic
92C2×D4×C113C2312yes—
93C22×C4×C113C2311yescharacteristic
94D8×C113—24no—
95C2×C8×C113C2312yes—
96C4⋊C4×C113C2311yescharacteristic
97C22⋊C4×C113—21no—
98C23×C113—24no—
99C23×C113—22no—
100C23×C113—21no—
101C23×C113—42no—
102C23×C113—42no—
103C23×C113C2×D411yescharacteristic
104C22×D113—22no—
105C22×D113—22no—
106C22×D113—21no—
107C22×D113—41no—
108C22×D113—42no—
109C22×D113—42no—
110C22×D113—42no—
111C22×D113C2×D411yescharacteristic
112C22×D113C2×D411yescharacteristic
113D4×C113—24no—
114D4×C113—22no—
115D4×C113—22no—
116D4×C113—42no—
117D4×C113C2×D414yescomplemented
118C2×C4×C113—22no—
119C2×C4×C113—21no—
120C2×C4×C113C2×D411yescharacteristic
121C2×C4×C113C2411yescharacteristic
122C22⋊D113—28no—
123C22⋊D113—28no—
124C22⋊D113—42no—
125C22⋊D113—42no—
126C22⋊D113—42no—
127C2×Dic113—24no—
128C2×Dic113—28no—
129C2×Dic113—22no—
130C2×Dic113—22no—
131C2×Dic113—28no—
132C2×Dic113—21no—
133C2×Dic113C2×D411yescharacteristic
134C2×Dic113C2×D411yescharacteristic
135D452—22no—
136D452—42no—
137C4×D113—22no—
138C4×D113—22no—
139C4×D113—22no—
140C4×D113—42no—
141C4×D113C2×D414yes—
142Dic226—24no—
143Dic226—22no—
144Dic226C2×D414yescomplemented
145C8×C113—22no—
146#11744751—22no—
147C22×C113—21no—
148C22×C113—21no—
149C22×C113—24no—
150C22×C113—48no—
151C22×C113—42no—
152C22×C113—42no—
153C22×C113—41no—
154C22×C113—41no—
155C22×C113—41no—
156C22×C113AGL(1,ℤ/8)12yescomplemented
157C22×C113C22×D411yescharacteristic
158C2×D113—21no—
159C2×D113—21no—
160C2×D113—21no—
161C2×D113—21no—
162C2×D113—21no—
163C2×D113—44no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—84no—
168C2×D113#12012yes—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113C22×D412yes—
172Dic113—24no—
173Dic113—21no—
174Dic113—41no—
175Dic113#12012yes—
176C2×C113—22no—
177C2×C113—44no—
178C2×C113—81no—
179C2×C113C2×#12011yescharacteristic
180C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
181C2×C113#57511yescharacteristic
182D113—22no—
183D113—41no—
184D113—81no—
185#3006—1131nomaximal, Sylow
186C113#300611yescharacteristic, complemented, Sylow
187C22×#41—1131no—
188C2×AGL(1,ℤ/8)—1132no—
189C2×#121—1131no—
190#449—1132no—
191#449—1132no—
192#448—1131no—
193#448—1131no—
194#447—1131no—
195#447D11311yescharacteristic, complemented
196#417—1132no—
197#407—1131no—
198C2×#41—1132no—
199C2×#41—1132no—
200C2×#41—2261no—
201C2×#41—2261no—
202C2×#41—2268no—
203C22×Q8—1131no—
204C22×D4—1131no—
205C22×D4—2261no—
206C22×D4—2261no—
207C22×D4C2×D11311yescharacteristic, complemented
208C23×C4—1131no—
209C23×C4—2261no—
210AGL(1,ℤ/8)—2268no—
211C2×SD16—1132no—
212C2×SD16—1132no—
213C2×D8—1132no—
214C2×D8C2×D11312yescomplemented
215C2×M16—1132no—
216#121—1131no—
217#121—1131no—
218#121—1131no—
219#121—2261no—
220#121—2261no—
221#121C2×D11311yescharacteristic
222C2×C4⋊C4—1131no—
223C2×C22⋊C4—2261no—
224#103—1132no—
225#103—1132no—
226#102—1132no—
227#102C2×D11312yescomplemented
228C22⋊C8—1131no—
229C22⋊C8—1132no—
230C22⋊C8C2×D11311yescharacteristic, complemented
231C24—21no—
232C24—1131no—
233C24—2261no—
234#41—1138no—
235#41—2264no—
236#41—2264no—
237#41—2268no—
238#41—2268no—
239#41—2264no—
240C2×Q8—1132no—
241C2×Q8—2264no—
242C2×Q8—2261no—
243C2×D4—24no—
244C2×D4—21no—
245C2×D4—21no—
246C2×D4—1131no—
247C2×D4—4524no—
248C2×D4—2261no—
249C2×D4—2264no—
250C2×D4—2261no—
251C2×D4—2261no—
252C2×D4—2261no—
253C2×D4—2262no—
254C2×D4—2262no—
255C2×D4—2268no—
256C2×D4C22×D11311yescharacteristic
257C2×D4C22×D11312yes—
258C22×C4—1131no—
259C22×C4—1131no—
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—2264no—
264C22×C4—2261no—
265C22×C4—2262no—
266C22×C4—2262no—
267C22×C4—2268no—
268C22×C4—2261no—
269C22×C4C22×D11311yescharacteristic
270SD16—2264no—
271SD16—2264no—
272D8—24no—
273D8—2264no—
274M16—2264no—
275C2×C8—1132no—
276C2×C8C22×D11312yes—
277C4⋊C4—1131no—
278C4⋊C4—2261no—
279C4⋊C4C22×D11311yescharacteristic
280C22⋊C4—21no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C23—24no—
285C23—22no—
286C23—21no—
287C23—42no—
288C23—42no—
289C23—1131no—
290C23—1131no—
291C23—4521no—
292C23—4522no—
293C23—4522no—
294C23—4522no—
295C23—2262no—
296C23—2261no—
297C23—2262no—
298C23D4×D11311yescharacteristic
299Q8—1134no—
300Q8—2264no—
301Q8—2262no—
302D4—24no—
303D4—22no—
304D4—22no—
305D4—42no—
306D4—4522no—
307D4—4522no—
308D4—4522no—
309D4—4522no—
310D4—2268no—
311D4—2268no—
312D4—2262no—
313D4D4×D11314yescomplemented
314C2×C4—22no—
315C2×C4—21no—
316C2×C4—1131no—
317C2×C4—1134no—
318C2×C4—1131no—
319C2×C4—4522no—
320C2×C4—2262no—
321C2×C4—2262no—
322C2×C4—2262no—
323C2×C4—2268no—
324C2×C4—2261no—
325C2×C4—2264no—
326C2×C4—2268no—
327C2×C4—2262no—
328C2×C4—2262no—
329C2×C4D4×D11311yescharacteristic
330C2×C4C23×D11311yescharacteristic
331C8—22no—
332C8—2262no—
333C22—21no—
334C22—21no—
335C22—24no—
336C22—48no—
337C22—42no—
338C22—42no—
339C22—41no—
340C22—41no—
341C22—41no—
342C22—1132no—
343C22—9044no—
344C22—4524no—
345C22—4521no—
346C22—4521no—
347C22—4521no—
348C22—2261no—
349C22—2261no—
350C22—2261no—
351C22—2261no—
352C22—2261no—
353C22#1681364612yescomplemented
354C22C2×D4×D11311yescharacteristic
355C4—21no—
356C4—41no—
357C4—1132no—
358C4—4521no—
359C4—2261no—
360C4—2264no—
361C4C2×D4×D11312yes—
362C2—22no—
363C2—44no—
364C2—81no—
365C2—9041no—
366C2—4521no—
367C2—2262no—
368C2#120×D11311yescharacteristic
369C2C2×#1681364611yescharacteristic
370C2#2029939411yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#447×C113C2
socleC22×C113C22×D4
hypercenter#447D113
hypocenterC113#3006
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×#14268646C2semidirect
2. C2×#16813646C2semidirect
3. #121×D113C2semidirect
4. #20298744C2semidirect
5. #20298740C2semidirect
6. #20298739C2semidirect
7. #20298736C2semidirect
8. #20298732C2semidirect
9. #20298596C2semidirect
10. #20298560C2semidirect
11. #447×C113C2semidirect
16. C2×#14268646C22semidirect
17. C22×Dic226C22semidirect
20. C2×D4×D113C22semidirect
24. C2×#14268636C22semidirect
25. C2×#14268635C22semidirect
26. C2×#14268632C22semidirect
27. C2×#14268630C22semidirect
28. #16813597C22semidirect
32. #16813593C22semidirect
33. C4⋊C4×D113C22semidirect
35. #16813547C22semidirect
36. #16813545C22semidirect
37. #16813543C22semidirect
38. C22⋊#11744751C22semidirect
39. #16813534C22semidirect
40. C22×D4×C113C22semidirect
41. C2×D8×C113C22semidirect
43. #102×C113C22semidirect
44. C22⋊C8×C113C22semidirect
52. #14268646D4semidirect
117. D4×C113C2×D4semidirect
144. Dic226C2×D4semidirect
156. C22×C113AGL(1,ℤ/8)semidirect
186. C113#3006semidirect
195. #447D113semidirect
207. C22×D4C2×D113semidirect
214. C2×D8C2×D113semidirect
227. #102C2×D113semidirect
230. C22⋊C8C2×D113semidirect
313. D4D4×D113semidirect
353. C22#16813646semidirect

Maximal subgroups

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

subgroupindex
C22×#142686462
C2×#168136462
#121×D1132
#202987442
#202987402
#202987392
#202987362
#202987322
#202985962
#202985602
#447×C1132
#3006113