Finite Group Databasebeta

← #28400815

Subgroups — #28400815

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#20299202C211yesmaximal, characteristic, complemented
2#20299070C211yesmaximal, characteristic, complemented
3#20298921C211yesmaximal, characteristic, complemented
4#20298920C211yesmaximal, characteristic, complemented
5#20298899C211yesmaximal, characteristic, complemented
6#20298898C211yesmaximal, characteristic, complemented
7#20298790C211yesmaximal, characteristic, complemented
8#20298730C211yesmaximal, characteristic, complemented
9#20298730C211yesmaximal, characteristic, complemented
10#20298710C211yesmaximal, characteristic, complemented
11#20298707C211yesmaximal, characteristic, complemented
12D8×Dic113C211yesmaximal, characteristic, complemented
13#20298678C211yesmaximal, characteristic, complemented
14#20298658C211yesmaximal, characteristic, complemented
15#459×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268632C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19#16813614C2211yescharacteristic, complemented
20#16813603—21no—
21#16813603—21no—
22#16813594—21no—
23#16813594—21no—
24#16813593C2211yescharacteristic
25#16813593C2211yescharacteristic
26C4×D452C2211yescharacteristic
27D4×Dic113C2211yescharacteristic
28D4×Dic113C2211yescharacteristic, complemented
29D4×Dic113C2211yescharacteristic, complemented
30#16813584C2211yescharacteristic
31C4×C22⋊D113—21no—
32#16813582—21no—
33#16813580C2211yescharacteristic
34#16813579C2211yescharacteristic
35C2×#14268624—21no—
36C22⋊C4×D113—21no—
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41C4⋊#11744751C2211yescharacteristic, complemented
42#16813544C2211yescharacteristic
43#16813544C2211yescharacteristic
44#16813543C2211yescharacteristic
45#16813543C2211yescharacteristic
46#16813543C2211yescharacteristic, complemented
47#16813543C2211yescharacteristic, complemented
48#16813534C2211yescharacteristic
49#16813534C2211yescharacteristic
50#16813532C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C2×D8×C113C2211yescharacteristic
53C2×D8×C113C2211yescharacteristic
54#127×C113C2211yescharacteristic, complemented
55C4×D4×C113C2211yescharacteristic
56C4⋊C8×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×D452C2311yescharacteristic
61C2×C22⋊D113—21no—
62C2×C22⋊D113—21no—
63C2×C22⋊D113—21no—
64D4×D113—22no—
65D4×D113—22no—
66C22×Dic113—21no—
67C22×Dic113—21no—
68C22×Dic113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72#14268632—22no—
73#14268632—22no—
74C2×#11744751C2311yescharacteristic
75C2×#11744751C2311yescharacteristic
76C4⋊Dic113C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84C22⋊Dic113—21no—
85C22⋊Dic113—21no—
86C22⋊Dic113—21no—
87C22⋊Dic113—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624D411yescharacteristic
92#14268624D411yescharacteristic
93C4×Dic113—21no—
94C4×Dic113C2311yescharacteristic
95C2×D4×C113—21no—
96C2×D4×C113—21no—
97C2×D4×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C2×D4×C113C2311yescharacteristic
100C22×C4×C113—21no—
101D8×C113—22no—
102D8×C113—22no—
103C2×C8×C113C2311yescharacteristic
104C2×C8×C113C2311yescharacteristic
105C4⋊C4×C113C2311yescharacteristic
106C22⋊C4×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C23×C113—21no—
110C23×C113—21no—
111C22×D113—21no—
112C22×D113—24no—
113C22×D113—81no—
114C22×D113—81no—
115C22×D113C2×D411yescharacteristic
116D4×C113—21no—
117D4×C113—21no—
118D4×C113—21no—
119D4×C113—21no—
120D4×C113—21no—
121D4×C113—81no—
122D4×C113—81no—
123D4×C113#4112yes—
124C2×C4×C113—21no—
125C2×C4×C113—81no—
126C2×C4×C113C2×D411yescharacteristic
127C2×C4×C113C2×D411yescharacteristic
128C2×C4×C113C2411yescharacteristic
129C22⋊D113—24no—
130C22⋊D113—81no—
131C22⋊D113—81no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—81no—
136C2×Dic113—81no—
137C2×Dic113—81no—
138C2×Dic113C2×D411yescharacteristic
139C2×Dic113C2×D411yescharacteristic
140C2×Dic113C2×D411yescharacteristic
141D452—21no—
142D452#4112yes—
143C4×D113—21no—
144C4×D113—21no—
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×C113—41no—
155C22×C113—41no—
156C22×C113—41no—
157C22×C113—41no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C2×D113—21no—
162C2×D113—22no—
163C2×D113—21no—
164C2×D113—21no—
165C2×D113—41no—
166C2×D113—41no—
167C2×D113—84no—
168C4×C113—21no—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113C2×#4111yescharacteristic
172C4×C113C2×#4111yescharacteristic
173Dic113—21no—
174Dic113—21no—
175Dic113—21no—
176Dic113—41no—
177Dic113—41no—
178Dic113—41no—
179C2×C113—42no—
180C2×C113—81no—
181C2×C113—81no—
182C2×C113#52511yescharacteristic
183C2×C113#57611yescharacteristic
184C2×C113#57611yescharacteristic
185D113—41no—
186D113—42no—
187#3122—1131nomaximal, Sylow
188C113#312211yescharacteristic, complemented, Sylow
189#540—1131no—
190#518—1131no—
191#482—1131no—
192#482—1131no—
193#478—1131no—
194#478—1131no—
195#459—1131no—
196#459D11311yescharacteristic, complemented
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×D8C2×D11311yescharacteristic
208C2×D8C2×D11311yescharacteristic
209#127C2×D11311yescharacteristic, complemented
210#125—1131no—
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#107—1131no—
231#106—1131no—
232#106—1131no—
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, complemented
242#102C2×D11311yescharacteristic, complemented
243C22⋊C8—1131no—
244C22⋊C8—1131no—
245#97—1131no—
246C4×C8—1131no—
247C24—2261no—
248C2×D4—21no—
249C2×D4—21no—
250C2×D4—1131no—
251C2×D4—2261no—
252C2×D4—2262no—
253C2×D4—2261no—
254C2×D4—2261no—
255C2×D4—2262no—
256C2×D4C22×D11311yescharacteristic
257C2×D4C22×D11311yescharacteristic
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—22no—
267D8—22no—
268D8—2262no—
269D8—2262no—
270C2×C8—1131no—
271C2×C8—1131no—
272C2×C8C22×D11311yescharacteristic
273C2×C8C22×D11311yescharacteristic
274C4⋊C4—1131no—
275C4⋊C4—1131no—
276C4⋊C4—1131no—
277C4⋊C4—1131no—
278C4⋊C4—1131no—
279C4⋊C4—2261no—
280C4⋊C4—2261no—
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—21no—
298C23—21no—
299C23—1131no—
300C23—9041no—
301C23—9041no—
302C23—2264no—
303C23—2261no—
304D4—21no—
305D4—21no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—81no—
310D4—81no—
311D4—1132no—
312D4—9041no—
313D4—9041no—
314D4—2264no—
315D4—2261no—
316D4#1426864612yes—
317C2×C4—21no—
318C2×C4—81no—
319C2×C4—1131no—
320C2×C4—1131no—
321C2×C4—1131no—
322C2×C4—9041no—
323C2×C4—9041no—
324C2×C4—9041no—
325C2×C4—9041no—
326C2×C4—9041no—
327C2×C4—2261no—
328C2×C4—2261no—
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—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—41no—
347C22—41no—
348C22—9044no—
349C22—4521no—
350C22—4521no—
351C22—2261no—
352C22—2262no—
353C22—2261no—
354C22—2261no—
355C22C2×D4×D11311yescharacteristic
356C4—21no—
357C4—21no—
358C4—41no—
359C4—4521no—
360C4—4521no—
361C4—4521no—
362C4—2261no—
363C4—2261no—
364C4—2261no—
365C4#41×D11311yescharacteristic
366C4C2×#1426864611yescharacteristic
367C2—42no—
368C2—81no—
369C2—81no—
370C2—4521no—
371C2—4522no—
372C2#2029910811yescharacteristic
373C2#2029939911yescharacteristic
374C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#459×C113C2
socleC22×C113C22×D4
hypercenter#459D113
hypocenterC113#3122
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #459

Complements

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

NH ≅ G/Ntype
1. #20299202C2semidirect
2. #20299070C2semidirect
3. #20298921C2semidirect
4. #20298920C2semidirect
5. #20298899C2semidirect
6. #20298898C2semidirect
7. #20298790C2semidirect
8. #20298730C2semidirect
9. #20298730C2semidirect
10. #20298710C2semidirect
11. #20298707C2semidirect
12. D8×Dic113C2semidirect
13. #20298678C2semidirect
14. #20298658C2semidirect
15. #459×C113C2semidirect
19. #16813614C22semidirect
28. D4×Dic113C22semidirect
29. D4×Dic113C22semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. C4⋊#11744751C22semidirect
46. #16813543C22semidirect
47. #16813543C22semidirect
50. #16813532C22semidirect
51. C8×Dic113C22semidirect
54. #127×C113C22semidirect
56. C4⋊C8×C113C22semidirect
57. #102×C113C22semidirect
58. #102×C113C22semidirect
188. C113#3122semidirect
196. #459D113semidirect
209. #127C2×D113semidirect
234. C4⋊C8C2×D113semidirect
241. #102C2×D113semidirect
242. #102C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992022
#202990702
#202989212
#202989202
#202988992
#202988982
#202987902
#202987302
#202987102
#202987072
D8×Dic1132
#202986782
#202986582
#459×C1132
#3122113