Finite Group Databasebeta

← #28403278

Subgroups — #28403278

Order 14464.

396 conjugacy classes of subgroups.

The subgroup lattice has 360 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#20299304C211yesmaximal, characteristic, complemented
2#20299268C211yesmaximal, characteristic, complemented
3#20298961C211yesmaximal, characteristic, complemented
4#20298943C211yesmaximal, characteristic, complemented
5#20298900C211yesmaximal, characteristic, complemented
6#20298895C211yesmaximal, characteristic, complemented
7#20298886C211yesmaximal, characteristic, complemented
8#20298792C211yesmaximal, characteristic, complemented
9#20298792C211yesmaximal, characteristic, complemented
10#20298790C211yesmaximal, characteristic, complemented
11#20298726C211yesmaximal, characteristic, complemented
12#20298711C211yesmaximal, characteristic, complemented
13#20298707C211yesmaximal, characteristic, complemented
14#20298678C211yesmaximal, characteristic, complemented
15#490×C113C211yesmaximal, characteristic, complemented
16C2×#14268646—21no—
17C2×D904C2211yescharacteristic
18C2×#14268632C2211yescharacteristic
19C2×#14268632C2211yescharacteristic
20#16813621C2211yescharacteristic
21#16813618C2211yescharacteristic
22#16813618C2211yescharacteristic
23#16813613C2211yescharacteristic
24#16813602—21no—
25#16813600—21no—
26#16813600—21no—
27#16813594—21no—
28#16813594—21no—
29#16813593—21no—
30C4×Dic226C2211yescharacteristic
31C4×D452C2211yescharacteristic
32C4×D452C2211yescharacteristic
33D4×Dic113C2211yescharacteristic
34D4×Dic113C2211yescharacteristic
35#16813584C2211yescharacteristic
36#16813584C2211yescharacteristic
37C4⋊C4×D113—21no—
38#16813555C2211yescharacteristic
39#16813554C2211yescharacteristic
40#16813553C2211yescharacteristic
41C4⋊#11744751C2211yescharacteristic
42#16813551C2211yescharacteristic
43#16813551C2211yescharacteristic
44#16813544C2211yescharacteristic
45#16813544C2211yescharacteristic
46#16813543C2211yescharacteristic
47#16813543C2211yescharacteristic
48#16813542C2211yescharacteristic
49#16813542C2211yescharacteristic
50#16813532C2211yescharacteristic
51C8×Dic113C2211yescharacteristic
52#127×C113C2211yescharacteristic
53#125×C113C2211yescharacteristic
54#102×C113C2211yescharacteristic
55#102×C113C2211yescharacteristic
56#102×C113C2211yescharacteristic
57#102×C113C2211yescharacteristic
58#97×C113C2211yescharacteristic
59#14268646—44no—
60C2×Dic226—21no—
61C2×Dic226D411yescharacteristic
62C2×D452C2311yescharacteristic
63C2×D452C2311yescharacteristic
64C2×C22⋊D113—21no—
65C2×C22⋊D113—21no—
66C2×C22⋊D113—21no—
67C2×C22⋊D113—21no—
68C22×Dic113—21no—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74D904—22no—
75#14268632—22no—
76#14268632—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113D411yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626D411yescharacteristic
86#14268626D411yescharacteristic
87C22⋊Dic113—21no—
88C22⋊Dic113—21no—
89#14268624—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93C4×Dic113C2311yescharacteristic
94C4×Dic113C2311yescharacteristic
95C2×D4×C113—21no—
96C2×D4×C113—21no—
97C2×D4×C113C2311yescharacteristic
98C2×D4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113—21no—
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C42×C113C2311yescharacteristic
106C23×C113—21no—
107C23×C113—21no—
108C22×D113—21no—
109C22×D113—21no—
110D4×C113—21no—
111D4×C113—21no—
112D4×C113—21no—
113D4×C113—21no—
114D4×C113—42no—
115D4×C113—81no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113C2×D411yescharacteristic
119C2×C4×C113C2×D411yescharacteristic
120C2×C4×C113C2411yescharacteristic
121C22⋊D113—42no—
122C22⋊D113—42no—
123C22⋊D113—81no—
124C22⋊D113—81no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—42no—
128C2×Dic113—42no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C2×Dic113C2×D411yescharacteristic
132C2×Dic113C2×D411yescharacteristic
133D452—21no—
134D452—21no—
135D452—21no—
136D452#4112yescomplemented
137C4×D113—42no—
138C4×D113—42no—
139C4×D113—81no—
140C4×D113—81no—
141Dic226—22no—
142Dic226—81no—
143C8×C113—21no—
144C8×C113—21no—
145#11744751—21no—
146#11744751—21no—
147C22×C113—41no—
148C22×C113—41no—
149C22×C113—41no—
150C22×C113—41no—
151C22×C113—41no—
152C22×C113—41no—
153C22×C113C22×D411yescharacteristic
154C2×D113—22no—
155C2×D113—41no—
156C2×D113—41no—
157C2×D113—41no—
158C2×D113—41no—
159C2×D113—41no—
160C4×C113—21no—
161C4×C113—21no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C1132−1+411yescharacteristic
166Dic113—21no—
167Dic113—21no—
168Dic113—21no—
169Dic113—41no—
170Dic113—41no—
171Dic113AGL(1,ℤ/8)12yes—
172C2×C113—81no—
173C2×C113—81no—
174C2×C113#54811yescharacteristic
175C2×C113C2×AGL(1,ℤ/8)11yescharacteristic
176C2×C113#57611yescharacteristic
177D113—42no—
178D113—81no—
179#3366—1131nomaximal, Sylow
180C113#336611yescharacteristic, complemented, Sylow
181#554—1131no—
182#550—1131no—
183#490—1131no—
184#490D11311yescharacteristic, complemented
185#486—1131no—
186#478—1131no—
187#478—1131no—
188#476—1131no—
189#459—1131no—
190#459—1131no—
191#459—1131no—
192#446—1131no—
193#442—1131no—
194#442—1131no—
195C4×D8—1131no—
196C2×#41—2261no—
197C2×D8—1131no—
198C2×D8—1131no—
199C2×D8—1131no—
200C4⋊Q8—1131no—
201#127—1131no—
202#127—1131no—
203#127C2×D11311yescharacteristic
204#125—1131no—
205#125C2×D11311yescharacteristic
206C22⋊Q8—2261no—
207C22⋊Q8—2261no—
208C22⋊Q8—2261no—
209#121—2261no—
210#121—2261no—
211#121—2261no—
212C4×Q8—1131no—
213C4×D4—1131no—
214C4×D4—1131no—
215C4×D4—1131no—
216C4×D4—1131no—
217C4×D4—1131no—
218C4×D4—1131no—
219C2×C4⋊C4—2261no—
220#107—1131no—
221#106—1131no—
222#106—1131no—
223C4⋊C8—1131no—
224C4⋊C8—1131no—
225C4⋊C8—1131no—
226#102—1131no—
227#102—1131no—
228#102—1131no—
229#102—1131no—
230#102—1131no—
231#102—1131no—
232#102C2×D11311yescharacteristic
233#102C2×D11311yescharacteristic
234#102C2×D11311yescharacteristic
235#102C2×D11311yescharacteristic
236#97—1131no—
237#97C2×D11311yescharacteristic
238C4×C8—1131no—
239#41—4524no—
240C2×Q8—1131no—
241C2×Q8—2261no—
242C2×D4—21no—
243C2×D4—21no—
244C2×D4—1131no—
245C2×D4—1131no—
246C2×D4—2261no—
247C2×D4—2261no—
248C2×D4—2261no—
249C2×D4—2261no—
250C2×D4C22×D11311yescharacteristic
251C2×D4C22×D11311yescharacteristic
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4—2261no—
256C22×C4—2261no—
257C22×C4—2261no—
258D8—2262no—
259D8—2262no—
260D8—2262no—
261C2×C8—1131no—
262C2×C8—1131no—
263C2×C8C22×D11311yescharacteristic
264C2×C8C22×D11311yescharacteristic
265C4⋊C4—21no—
266C4⋊C4—21no—
267C4⋊C4—1131no—
268C4⋊C4—1131no—
269C4⋊C4—1131no—
270C4⋊C4—1131no—
271C4⋊C4—1131no—
272C4⋊C4—2261no—
273C4⋊C4—2261no—
274C4⋊C4—2261no—
275C4⋊C4C22×D11311yescharacteristic
276C4⋊C4C22×D11311yescharacteristic
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C42—1131no—
284C42—1131no—
285C42C22×D11311yescharacteristic
286C23—21no—
287C23—21no—
288C23—2261no—
289C23—2261no—
290Q8—9041no—
291Q8—2262no—
292D4—21no—
293D4—21no—
294D4—21no—
295D4—21no—
296D4—42no—
297D4—81no—
298D4—1132no—
299D4—9041no—
300D4—9041no—
301D4—4522no—
302D4—4522no—
303D4—2261no—
304D4—2261no—
305D4—2261no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—1131no—
309C2×C4—1131no—
310C2×C4—1131no—
311C2×C4—1131no—
312C2×C4—9041no—
313C2×C4—9041no—
314C2×C4—4522no—
315C2×C4—4522no—
316C2×C4—4522no—
317C2×C4—4522no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4D4×D11311yescharacteristic
321C2×C4D4×D11311yescharacteristic
322C2×C4C23×D11311yescharacteristic
323C8—21no—
324C8—21no—
325C8—2261no—
326C8—2261no—
327C22—41no—
328C22—41no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—4521no—
334C22—4521no—
335C22—4521no—
336C22—4521no—
337C22—4521no—
338C22—2262no—
339C22C2×D4×D11311yescharacteristic
340C4—21no—
341C4—21no—
342C4—41no—
343C4—41no—
344C4—1132no—
345C4—4521no—
346C4—4521no—
347C4—2261no—
348C4—2261no—
349C4—2261no—
350C4#41×D11311yescharacteristic
351C4#1681366911yescharacteristic
352C2—81no—
353C2—81no—
354C2—9041no—
355C2—4522no—
356C2#2029925611yescharacteristic
357C2AGL(1,ℤ/8)×D11311yescharacteristic
358C2#2029940211yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#490×C113C2
socleC22×C113C22×D4
hypercenter#490D113
hypocenterC113#3366
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C42 ◁ #490

Complements

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

NH ≅ G/Ntype
1. #20299304C2semidirect
2. #20299268C2semidirect
3. #20298961C2semidirect
4. #20298943C2semidirect
5. #20298900C2semidirect
6. #20298895C2semidirect
7. #20298886C2semidirect
8. #20298792C2semidirect
9. #20298792C2semidirect
10. #20298790C2semidirect
11. #20298726C2semidirect
12. #20298711C2semidirect
13. #20298707C2semidirect
14. #20298678C2semidirect
15. #490×C113C2semidirect
136. D452#41semidirect
180. C113#3366semidirect
184. #490D113semidirect

Maximal subgroups

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

subgroupindex
#202993042
#202992682
#202989612
#202989432
#202989002
#202988952
#202988862
#202987922
#202987902
#202987262
#202987112
#202987072
#202986782
#490×C1132
#3366113