Finite Group Databasebeta

← #28400762

Subgroups — #28400762

Order 14464.

406 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299220C211yesmaximal, characteristic, complemented
2#20299070C211yesmaximal, characteristic, complemented
3#20298937C211yesmaximal, characteristic, complemented
4#20298925C211yesmaximal, characteristic, complemented
5#20298886C211yesmaximal, characteristic, complemented
6#20298877C211yesmaximal, characteristic, complemented
7#20298816C211yesmaximal, characteristic, complemented
8#20298815C211yesmaximal, characteristic, complemented
9#20298747C211yesmaximal, characteristic, complemented
10#20298733C211yesmaximal, characteristic
11#20298711C211yesmaximal, characteristic, complemented
12C4×#14268634C211yesmaximal, characteristic, complemented
13C4×#14268632C211yesmaximal, characteristic, complemented
14#20298660C211yesmaximal, characteristic, complemented
15#440×C113C211yesmaximal, characteristic, complemented
16C2×D4×D113C2211yescharacteristic
17C2×#14268634C2211yescharacteristic
18C2×D904C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20#16813621C2211yescharacteristic, complemented
21#16813616—21no—
22#16813611C2211yescharacteristic, complemented
23#16813610—21no—
24#16813607—21no—
25#16813600—21no—
26#16813598C2211yescharacteristic
27#16813597C2211yescharacteristic
28C4×D452C2211yescharacteristic
29C4×D452C2211yescharacteristic, complemented
30D4×Dic113C2211yescharacteristic
31#16813584C2211yescharacteristic
32C4×C22⋊D113—21no—
33#16813582—21no—
34#16813580C2211yescharacteristic
35#16813579C2211yescharacteristic
36C2×#14268624—21no—
37C22⋊C4×D113—21no—
38#16813555C2211yescharacteristic, complemented
39#16813554C2211yescharacteristic, complemented
40#16813553C2211yescharacteristic, complemented
41#16813551C2211yescharacteristic, complemented
42#16813551C2211yescharacteristic, complemented
43#16813546C2211yescharacteristic, complemented
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic, complemented
46#16813543C2211yescharacteristic
47#16813542C2211yescharacteristic
48#16813542C2211yescharacteristic, complemented
49#16813534C2211yescharacteristic
50#16813534C2211yescharacteristic
51C4×#11744751C2211yescharacteristic, complemented
52C2×SD16×C113C2211yescharacteristic
53C4×Q8×C113C2211yescharacteristic, complemented
54C4×D4×C113C2211yescharacteristic
55#107×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic, complemented
59C23×D113—21no—
60C2×Dic226—21no—
61C2×D452—21no—
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65D4×D113—22no—
66D4×D113—22no—
67C22×Dic113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113C2311yescharacteristic
72#14268634—22no—
73D904—22no—
74#14268632—22no—
75C2×#11744751C2311yescharacteristic
76C2×#11744751C2311yescharacteristic
77C4⋊Dic113C2311yescharacteristic
78C4⋊Dic113C2311yescharacteristic
79#14268626—21no—
80#14268626—21no—
81#14268626D411yescharacteristic
82#14268626D411yescharacteristic
83C22⋊Dic113—21no—
84#14268624—21no—
85#14268624—21no—
86#14268624—21no—
87#14268624—21no—
88#14268624—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624D411yescharacteristic
93#14268624D411yescharacteristic
94C4×Dic113—21no—
95C4×Dic113C2311yescharacteristic
96C2×Q8×C113C2311yescharacteristic
97C2×D4×C113C2311yescharacteristic
98C22×C4×C113—21no—
99SD16×C113—22no—
100C2×C8×C113C2311yescharacteristic
101C2×C8×C113C2311yescharacteristic
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C42×C113—21no—
107C42×C113C2311yescharacteristic
108C23×C113—21no—
109C22×D113—21no—
110C22×D113—24no—
111C22×D113—21no—
112C22×D113—81no—
113C22×D113—81no—
114C22×D113C2×D411yescharacteristic
115Q8×C113—21no—
116Q8×C113—21no—
117D4×C113—21no—
118D4×C113#4112yes—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113—81no—
123C2×C4×C113C2×D411yescharacteristic
124C2×C4×C113C2×D411yescharacteristic
125C2×C4×C113C2411yescharacteristic
126C22⋊D113—24no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113—81no—
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133D452—21no—
134D452—21no—
135D452—21no—
136D452—81no—
137D452#4112yes—
138C4×D113—21no—
139C4×D113—21no—
140C4×D113—81no—
141C4×D113—81no—
142C4×D113—81no—
143Dic226—81no—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—22no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—22no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C2×D113—41no—
161C2×D113—84no—
162C4×C113—21no—
163C4×C113—21no—
164C4×C113—41no—
165C4×C113—41no—
166C4×C113—41no—
167C4×C113C2×#4111yescharacteristic
168C4×C113C2×#4111yescharacteristic
169Dic113—21no—
170Dic113—21no—
171Dic113—21no—
172Dic113—41no—
173Dic113—41no—
174C2×C113—42no—
175C2×C113#52511yescharacteristic
176C2×C113#57611yescharacteristic
177C2×C113#57711yescharacteristic
178D113—41no—
179D113—42no—
180D113—81no—
181#3118—1131nomaximal, Sylow
182C113#311811yescharacteristic, complemented, Sylow
183#542—1131no—
184#518—1131no—
185#485—1131no—
186#482—1131no—
187#476—1131no—
188#474—1131no—
189#463—1131no—
190#463—1131no—
191#450—1131no—
192#447—1131no—
193#442—1131no—
194#440D11311yescharacteristic, complemented
195C4×SD16—1131no—
196C4×D8—1131no—
197#433—1131no—
198C22×D4—1131no—
199C2×SD16—1131no—
200C2×SD16C2×D11311yescharacteristic
201C2×D8—1131no—
202C2×D8—1131no—
203C4⋊Q8—1131no—
204#126—2261no—
205#124—1131no—
206#124—2261no—
207#123—2261no—
208C22⋊Q8—1131no—
209C22⋊Q8—2261no—
210#121—1131no—
211C4×Q8C2×D11311yescharacteristic, complemented
212C4×D4—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—2261no—
217C4×D4—2261no—
218C4×D4C2×D11311yescharacteristic
219#117—1131no—
220#117—1131no—
221C2×C22⋊C4—2261no—
222C2×C22⋊C4—2261no—
223#107—1131no—
224#107C2×D11311yescharacteristic, complemented
225#106—1131no—
226#106—1131no—
227C4⋊C8—1131no—
228C4⋊C8—1131no—
229#103—1131no—
230#103C2×D11311yescharacteristic, complemented
231#102—1131no—
232#102—1131no—
233#102—1131no—
234#102—1131no—
235#102—1131no—
236#102C2×D11311yescharacteristic
237C22⋊C8—1131no—
238C22⋊C8—1131no—
239#97C2×D11311yescharacteristic, complemented
240C4×C8—1131no—
241C24—2261no—
242C2×Q8—2261no—
243C2×Q8C22×D11311yescharacteristic
244C2×D4—1131no—
245C2×D4—1131no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2262no—
249C2×D4—2262no—
250C2×D4C22×D11311yescharacteristic
251C22×C4—21no—
252C22×C4—1131no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257SD16—22no—
258SD16—2262no—
259D8—2262no—
260D8—2262no—
261C2×C8—1131no—
262C2×C8—1131no—
263C2×C8C22×D11311yescharacteristic
264C2×C8C22×D11311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—1131no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4C22×D11311yescharacteristic
273C4⋊C4C22×D11311yescharacteristic
274C22⋊C4—21no—
275C22⋊C4—1131no—
276C22⋊C4—1131no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C22⋊C4—2261no—
284C22⋊C4—2261no—
285C22⋊C4—2261no—
286C42—21no—
287C42—1131no—
288C42—2261no—
289C42C22×D11311yescharacteristic
290C23—21no—
291C23—1131no—
292C23—9041no—
293C23—9041no—
294C23—2264no—
295C23—2261no—
296C23—2261no—
297Q8—21no—
298Q8—21no—
299Q8—9041no—
300D4—21no—
301D4—1132no—
302D4—9041no—
303D4—2264no—
304D4—2261no—
305D4—2261no—
306D4—2261no—
307D4#1426864712yes—
308C2×C4—21no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—81no—
312C2×C4—1131no—
313C2×C4—1131no—
314C2×C4—1131no—
315C2×C4—9041no—
316C2×C4—9041no—
317C2×C4—9041no—
318C2×C4—9041no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4—2261no—
322C2×C4—2261no—
323C2×C4D4×D11311yescharacteristic
324C2×C4D4×D11311yescharacteristic
325C2×C4C23×D11311yescharacteristic
326C8—21no—
327C8—21no—
328C8—2261no—
329C8—2261no—
330C22—22no—
331C22—41no—
332C22—41no—
333C22—9044no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—4521no—
339C22—2261no—
340C22—2262no—
341C22—2261no—
342C22—2261no—
343C22C2×D4×D11311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—4521no—
350C4—4521no—
351C4—2261no—
352C4—2261no—
353C4—2261no—
354C4#41×D11311yescharacteristic
355C4C2×#1426864711yescharacteristic
356C2—42no—
357C2—9041no—
358C2—4521no—
359C2—4522no—
360C2#2029910711yescharacteristic
361C2#2029940211yescharacteristic
362C2#2029940711yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#440×C113C2
socleC22×C113C22×D4
prime radical#20298733C2
hypercenter#440D113
hypocenterC113#3118
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #440

Complements

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

NH ≅ G/Ntype
1. #20299220C2semidirect
2. #20299070C2semidirect
3. #20298937C2semidirect
4. #20298925C2semidirect
5. #20298886C2semidirect
6. #20298877C2semidirect
7. #20298816C2semidirect
8. #20298815C2semidirect
9. #20298747C2semidirect
11. #20298711C2semidirect
12. C4×#14268634C2semidirect
13. C4×#14268632C2semidirect
14. #20298660C2semidirect
15. #440×C113C2semidirect
20. #16813621C22semidirect
22. #16813611C22semidirect
29. C4×D452C22semidirect
38. #16813555C22semidirect
39. #16813554C22semidirect
40. #16813553C22semidirect
41. #16813551C22semidirect
42. #16813551C22semidirect
43. #16813546C22semidirect
45. #16813544C22semidirect
48. #16813542C22semidirect
51. C4×#11744751C22semidirect
53. C4×Q8×C113C22semidirect
55. #107×C113C22semidirect
56. #103×C113C22semidirect
58. #97×C113C22semidirect
182. C113#3118semidirect
194. #440D113semidirect
211. C4×Q8C2×D113semidirect
224. #107C2×D113semidirect
230. #103C2×D113semidirect
239. #97C2×D113semidirect

Maximal subgroups

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

subgroupindex
#202992202
#202990702
#202989372
#202989252
#202988862
#202988772
#202988162
#202988152
#202987472
#202987332
#202987112
C4×#142686342
C4×#142686322
#202986602
#440×C1132
#3118113