Finite Group Databasebeta

← #28400819

Subgroups — #28400819

Order 14464.

418 conjugacy classes of subgroups.

The subgroup lattice has 376 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299204C211yesmaximal, characteristic, complemented
2#20299070C211yesmaximal, characteristic, complemented
3#20298925C211yesmaximal, characteristic, complemented
4#20298924C211yesmaximal, characteristic, complemented
5#20298895C211yesmaximal, characteristic, complemented
6#20298794C211yesmaximal, characteristic, complemented
7#20298793C211yesmaximal, characteristic, complemented
8#20298733C211yesmaximal, characteristic, complemented
9#20298733C211yesmaximal, characteristic, complemented
10#20298709C211yesmaximal, characteristic, complemented
11#20298707C211yesmaximal, characteristic, complemented
12#20298680C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#478×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×D904C2211yescharacteristic
18C2×D904C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20C2×#14268632C2211yescharacteristic
21#16813619C2211yescharacteristic, complemented
22#16813607—21no—
23#16813607—21no—
24#16813597—21no—
25#16813597—21no—
26#16813597C2211yescharacteristic
27#16813597C2211yescharacteristic
28C4×D452C2211yescharacteristic
29D4×Dic113C2211yescharacteristic
30#16813584C2211yescharacteristic
31#16813584C2211yescharacteristic, complemented
32#16813584C2211yescharacteristic, complemented
33C4×C22⋊D113—21no—
34#16813582—21no—
35#16813580C2211yescharacteristic
36#16813579C2211yescharacteristic
37C2×#14268624—21no—
38C22⋊C4×D113—21no—
39#16813555C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic, complemented
43#16813544C2211yescharacteristic, complemented
44#16813542C2211yescharacteristic
45#16813542C2211yescharacteristic
46#16813542C2211yescharacteristic, complemented
47#16813542C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52#125×C113C2211yescharacteristic, complemented
53C4×D4×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#102×C113C2211yescharacteristic
59C23×D113—21no—
60C2×D452—21no—
61C2×D452—21no—
62C2×D452—21no—
63C2×D452—21no—
64C2×D452C2311yescharacteristic
65C2×D452C2311yescharacteristic
66C2×D452C2311yescharacteristic
67C2×C22⋊D113—21no—
68D4×D113—22no—
69D4×D113—22no—
70C22×Dic113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113C2311yescharacteristic
76D904—22no—
77D904—22no—
78#14268632—22no—
79#14268632—22no—
80C2×#11744751C2311yescharacteristic
81C2×#11744751C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626D411yescharacteristic
84#14268626D411yescharacteristic
85C22⋊Dic113—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624D411yescharacteristic
94#14268624D411yescharacteristic
95C4×Dic113—21no—
96C4×Dic113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—24no—
111C22×D113—21no—
112C22×D113—21no—
113C22×D113—81no—
114C22×D113—81no—
115C22×D113C2×D411yescharacteristic
116D4×C113—21no—
117D4×C113#4112yes—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—81no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2411yescharacteristic
125C22⋊D113—24no—
126C2×Dic113—21no—
127C2×Dic113—81no—
128C2×Dic113C2×D411yescharacteristic
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131D452—21no—
132D452—21no—
133D452—21no—
134D452—21no—
135D452—21no—
136D452—81no—
137D452—81no—
138D452—81no—
139D452—81no—
140D452#4112yes—
141C4×D113—21no—
142C4×D113—21no—
143C4×D113—81no—
144C4×D113—81no—
145C4×D113—81no—
146C4×D113—81no—
147C8×C113—21no—
148C8×C113—21no—
149#11744751—21no—
150#11744751—21no—
151C22×C113—22no—
152C22×C113—41no—
153C22×C113—41no—
154C22×C113C22×D411yescharacteristic
155C2×D113—21no—
156C2×D113—22no—
157C2×D113—21no—
158C2×D113—21no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—41no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—41no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—84no—
168C4×C113—21no—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113—41no—
173C4×C113C2×#4111yescharacteristic
174C4×C113C2×#4111yescharacteristic
175Dic113—21no—
176Dic113—21no—
177Dic113—21no—
178Dic113—41no—
179C2×C113—42no—
180C2×C113#52511yescharacteristic
181C2×C113#57611yescharacteristic
182C2×C113#57611yescharacteristic
183D113—41no—
184D113—42no—
185D113—81no—
186D113—81no—
187#3122—1131nomaximal, Sylow
188C113#312211yescharacteristic, complemented, Sylow
189#540—1131no—
190#518—1131no—
191#482—1131no—
192#482—1131no—
193#478—1131no—
194#478D11311yescharacteristic, complemented
195#459—1131no—
196#459—1131no—
197#447—1131no—
198#447—1131no—
199#442—1131no—
200#442—1131no—
201C4×D8—1131no—
202C4×D8—1131no—
203#433—1131no—
204C22×D4—1131no—
205C2×D8—1131no—
206C2×D8—1131no—
207C2×D8—1131no—
208C2×D8—1131no—
209#127—1131no—
210#125C2×D11311yescharacteristic, complemented
211#123—2261no—
212#123—2261no—
213#121—1131no—
214#121—1131no—
215#121—2261no—
216#121—2261no—
217C4×D4—1131no—
218C4×D4—1131no—
219C4×D4—1131no—
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—2261no—
223C4×D4—2261no—
224C4×D4C2×D11311yescharacteristic
225#117—1131no—
226#117—1131no—
227C2×C22⋊C4—2261no—
228C2×C22⋊C4—2261no—
229#107—1131no—
230#107C2×D11311yescharacteristic, complemented
231#106—1131no—
232#106C2×D11311yescharacteristic, complemented
233C4⋊C8—1131no—
234C4⋊C8C2×D11311yescharacteristic, complemented
235#102—1131no—
236#102—1131no—
237#102—1131no—
238#102—1131no—
239#102—1131no—
240#102—1131no—
241#102C2×D11311yescharacteristic
242#102C2×D11311yescharacteristic
243C22⋊C8—1131no—
244C22⋊C8—1131no—
245#97—1131no—
246C4×C8—1131no—
247C24—2261no—
248C2×D4—1131no—
249C2×D4—1131no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4—2261no—
253C2×D4—2261no—
254C2×D4—2262no—
255C2×D4—2262no—
256C2×D4—2261no—
257C2×D4—2261no—
258C2×D4C22×D11311yescharacteristic
259C22×C4—21no—
260C22×C4—1131no—
261C22×C4—2261no—
262C22×C4—2261no—
263C22×C4—2261no—
264C22×C4—2261no—
265C22×C4—2261no—
266D8—2262no—
267D8—2262no—
268D8—2262no—
269D8—2262no—
270C2×C8—1131no—
271C2×C8—1131no—
272C2×C8C22×D11311yescharacteristic
273C2×C8C22×D11311yescharacteristic
274C4⋊C4—21no—
275C4⋊C4—21no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—1131no—
279C4⋊C4C22×D11311yescharacteristic
280C4⋊C4C22×D11311yescharacteristic
281C4⋊C4C22×D11311yescharacteristic
282C22⋊C4—21no—
283C22⋊C4—1131no—
284C22⋊C4—1131no—
285C22⋊C4—2261no—
286C22⋊C4—2261no—
287C22⋊C4—2261no—
288C22⋊C4—2261no—
289C22⋊C4—2261no—
290C22⋊C4—2261no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C42—1131no—
294C42—2261no—
295C42C22×D11311yescharacteristic
296C23—21no—
297C23—1131no—
298C23—9041no—
299C23—9041no—
300C23—2264no—
301C23—2261no—
302C23—2261no—
303C23—2261no—
304D4—21no—
305D4—1132no—
306D4—9041no—
307D4—9041no—
308D4—9041no—
309D4—9041no—
310D4—2264no—
311D4—2261no—
312D4—2261no—
313D4—2261no—
314D4—2261no—
315D4—2261no—
316D4#1426864812yes—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—81no—
321C2×C4—1131no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—9041no—
325C2×C4—9041no—
326C2×C4—9041no—
327C2×C4—9041no—
328C2×C4—9041no—
329C2×C4—2261no—
330C2×C4—2261no—
331C2×C4—2261no—
332C2×C4D4×D11311yescharacteristic
333C2×C4D4×D11311yescharacteristic
334C2×C4C23×D11311yescharacteristic
335C8—21no—
336C8—21no—
337C8—2261no—
338C8—2261no—
339C22—22no—
340C22—41no—
341C22—41no—
342C22—9044no—
343C22—4521no—
344C22—4521no—
345C22—4521no—
346C22—4521no—
347C22—4521no—
348C22—4521no—
349C22—4521no—
350C22—4521no—
351C22—2261no—
352C22—2262no—
353C22—2261no—
354C22—2261no—
355C22C2×D4×D11311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—41no—
361C4—4521no—
362C4—2261no—
363C4—2261no—
364C4—2261no—
365C4#41×D11311yescharacteristic
366C4C2×#1426864811yescharacteristic
367C2—42no—
368C2—9041no—
369C2—9041no—
370C2—4521no—
371C2—4522no—
372C2#2029911111yescharacteristic
373C2#2029940011yescharacteristic
374C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#478×C113C2
socleC22×C113C22×D4
hypercenter#478D113
hypocenterC113#3122
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #20299204C2semidirect
2. #20299070C2semidirect
3. #20298925C2semidirect
4. #20298924C2semidirect
5. #20298895C2semidirect
6. #20298794C2semidirect
7. #20298793C2semidirect
8. #20298733C2semidirect
9. #20298733C2semidirect
10. #20298709C2semidirect
11. #20298707C2semidirect
12. #20298680C2semidirect
13. #20298678C2semidirect
14. #20298658C2semidirect
15. #478×C113C2semidirect
21. #16813619C22semidirect
31. #16813584C22semidirect
32. #16813584C22semidirect
39. #16813555C22semidirect
40. #16813553C22semidirect
41. C4⋊#11744751C22semidirect
42. #16813544C22semidirect
43. #16813544C22semidirect
46. #16813542C22semidirect
47. #16813542C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
52. #125×C113C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. C4⋊C8×C113C22semidirect
188. C113#3122semidirect
194. #478D113semidirect
210. #125C2×D113semidirect
230. #107C2×D113semidirect
232. #106C2×D113semidirect
234. C4⋊C8C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992042
#202990702
#202989252
#202989242
#202988952
#202987942
#202987932
#202987332
#202987092
#202987072
#202986802
#202986782
#202986582
#478×C1132
#3122113