Finite Group Databasebeta

← #28400521

Subgroups — #28400521

Order 14464.

410 conjugacy classes of subgroups.

The subgroup lattice has 358 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22⋊Q8×D113C211yesmaximal, characteristic
2#117×D113C211yesmaximal, characteristic
3#20298940C211yesmaximal, characteristic, complemented
4#20298939C211yesmaximal, characteristic, complemented
5#20298936C211yesmaximal, characteristic, complemented
6#20298935C211yesmaximal, characteristic, complemented
7#20298932C211yesmaximal, characteristic, complemented
8#20298930C211yesmaximal, characteristic, complemented
9#20298927C211yesmaximal, characteristic, complemented
10#20298639C211yesmaximal, characteristic, complemented
11#20298637C211yesmaximal, characteristic, complemented
12#20298605C211yesmaximal, characteristic, complemented
13#20298605C211yesmaximal, characteristic, complemented
14#20298560C211yesmaximal, characteristic
15#485×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C22×C4×D113C2211yescharacteristic
18C2×#14268630C2211yescharacteristic
19C2×#14268630C2211yescharacteristic
20#16813602C2211yescharacteristic
21#16813601C2211yescharacteristic
22#16813600—21no—
23#16813599—21no—
24#16813598C2211yescharacteristic
25#16813581C2211yescharacteristic
26#16813580C2211yescharacteristic
27#16813580C2211yescharacteristic
28#16813579—21no—
29#16813578—21no—
30C4⋊C4×D113—21no—
31C4⋊C4×D113C2211yescharacteristic
32C4⋊C4×D113C2211yescharacteristic
33C4⋊C4×D113C2211yescharacteristic
34C22⋊C4×D113—21no—
35C22⋊C4×D113—21no—
36C42×D113—21no—
37#16813556C2211yescharacteristic, complemented
38#16813555C2211yescharacteristic, complemented
39#16813555C2211yescharacteristic, complemented
40#16813554C2211yescharacteristic, complemented
41#16813553C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813547C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813546C2211yescharacteristic, complemented
47#16813545C2211yescharacteristic, complemented
48#16813545C2211yescharacteristic, complemented
49C22⋊#11744751C2211yescharacteristic
50#16813534C2211yescharacteristic
51#16813534C2211yescharacteristic
52C22⋊Q8×C113C2211yescharacteristic
53#117×C113C2211yescharacteristic
54#107×C113C2211yescharacteristic, complemented
55#106×C113C2211yescharacteristic, complemented
56#103×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58C22⋊C8×C113C2211yescharacteristic
59C23×D113D411yescharacteristic
60C2×Dic226—21no—
61C2×Dic226C2311yescharacteristic
62Q8×D113—22no—
63Q8×D113—22no—
64C22×Dic113D411yescharacteristic
65C2×C4×D113—22no—
66C2×C4×D113—22no—
67C2×C4×D113—21no—
68C2×C4×D113—21no—
69C2×C4×D113—21no—
70C2×C4×D113—21no—
71C2×C4×D113D411yescharacteristic
72C2×C4×D113D411yescharacteristic
73C2×C4×D113C2311yescharacteristic
74C2×C4×D113C2311yescharacteristic
75#14268630—22no—
76#14268630—22no—
77C2×#11744751C2311yescharacteristic
78C2×#11744751C2311yescharacteristic
79C4⋊Dic113—21no—
80C4⋊Dic113C2311yescharacteristic
81C4⋊Dic113C2311yescharacteristic
82C4⋊Dic113C2311yescharacteristic
83#14268626—21no—
84#14268626—21no—
85#14268626—21no—
86#14268626—21no—
87#14268626—21no—
88C22⋊Dic113—21no—
89C22⋊Dic113—21no—
90#14268624—21no—
91#14268624—21no—
92#14268624—21no—
93#14268624—21no—
94C4×Dic113—21no—
95C4×Dic113—21no—
96C4×Dic113—21no—
97C2×Q8×C113C2311yescharacteristic
98C22×C4×C113C2311yescharacteristic
99C2×C8×C113C2311yescharacteristic
100C2×C8×C113C2311yescharacteristic
101C4⋊C4×C113—21no—
102C4⋊C4×C113C2311yescharacteristic
103C4⋊C4×C113C2311yescharacteristic
104C4⋊C4×C113C2311yescharacteristic
105C22⋊C4×C113—21no—
106C22⋊C4×C113—21no—
107C42×C113—21no—
108C23×C113C2×D411yescharacteristic
109C22×D113—22no—
110C22×D113—22no—
111C22×D113—41no—
112C22×D113C2×D411yescharacteristic
113C22×D113C2×D411yescharacteristic
114Q8×C113—21no—
115Q8×C113—21no—
116C2×C4×C113—21no—
117C2×C4×C113—21no—
118C2×C4×C113—21no—
119C2×C4×C113—21no—
120C2×C4×C113—21no—
121C2×C4×C113—21no—
122C2×C4×C113C2×D411yescharacteristic
123C2×C4×C113C2411yescharacteristic
124C2×Dic113—22no—
125C2×Dic113—21no—
126C2×Dic113—21no—
127C2×Dic113—21no—
128C2×Dic113—21no—
129C2×Dic113C2×D411yescharacteristic
130C2×Dic113C2×D411yescharacteristic
131C4×D113—22no—
132C4×D113—21no—
133C4×D113—21no—
134C4×D113—22no—
135C4×D113—42no—
136C4×D113—42no—
137C4×D113—42no—
138C4×D113—42no—
139C4×D113#4112yes—
140C4×D113#4112yes—
141Dic226—21no—
142Dic226—21no—
143Dic226—42no—
144C8×C113—21no—
145C8×C113—21no—
146#11744751—21no—
147#11744751—21no—
148C22×C113—21no—
149C22×C113—21no—
150C22×C113—21no—
151C22×C113C22×D411yescharacteristic
152C2×D113—21no—
153C2×D113—21no—
154C2×D113—21no—
155C2×D113—21no—
156C2×D113—44no—
157C2×D113#12312yes—
158C2×D113#13712yes—
159C4×C113—21no—
160C4×C113—41no—
161C4×C113—41no—
162C4×C113—41no—
163C4×C113—41no—
164C4×C113C2×#4111yescharacteristic
165C4×C113C2×#4111yescharacteristic
166Dic113—21no—
167Dic113—41no—
168Dic113—41no—
169Dic113—41no—
170Dic113—41no—
171Dic113#12312yes—
172C2×C113—41no—
173C2×C113C2×#12311yescharacteristic
174C2×C113C2×#13711yescharacteristic
175C2×C113#57511yescharacteristic
176D113—22no—
177D113—22no—
178#3095—1131nomaximal, Sylow
179C113#309511yescharacteristic, complemented, Sylow
180C2×C22⋊Q8—1131no—
181C2×#117—1131no—
182#485—1131no—
183#485—1131no—
184#485—1131no—
185#485D11311yescharacteristic, complemented
186#484—1131no—
187#484—1131no—
188#483—1131no—
189#483—1131no—
190#428—1131no—
191#428—1131no—
192#419—1131no—
193#419—1131no—
194#407—1131no—
195C22×Q8—1131no—
196C23×C4—1131no—
197C2×M16—1131no—
198C2×M16—1131no—
199C22⋊Q8—1131no—
200C22⋊Q8—1131no—
201C22⋊Q8—1131no—
202C22⋊Q8—2261no—
203C22⋊Q8—2261no—
204C22⋊Q8C2×D11311yescharacteristic
205#117—1131no—
206#117—1131no—
207#117—1131no—
208#117—2261no—
209#117—2261no—
210#117C2×D11311yescharacteristic
211C2×C4⋊C4—1131no—
212C2×C4⋊C4—1131no—
213C2×C4⋊C4—1131no—
214C2×C4⋊C4—2261no—
215C2×C22⋊C4—2261no—
216C2×C22⋊C4—2261no—
217C2×C42—2261no—
218#107—1131no—
219#107—1131no—
220#107—1131no—
221#107C2×D11311yescharacteristic, complemented
222#106—1131no—
223#106—1131no—
224#106—1131no—
225#106C2×D11311yescharacteristic, complemented
226#103—1131no—
227#103—1131no—
228#103—1131no—
229#103—1131no—
230#103—1131no—
231#103—1131no—
232#103C2×D11311yescharacteristic, complemented
233#103C2×D11311yescharacteristic, complemented
234C22⋊C8—1131no—
235C22⋊C8—1131no—
236C22⋊C8—1131no—
237C22⋊C8C2×D11311yescharacteristic
238C24—1131no—
239C2×Q8—1131no—
240C2×Q8—2261no—
241C2×Q8—2262no—
242C2×Q8—2262no—
243C2×Q8C22×D11311yescharacteristic
244C22×C4—1131no—
245C22×C4—1131no—
246C22×C4—1131no—
247C22×C4—1131no—
248C22×C4—1131no—
249C22×C4—2262no—
250C22×C4—2262no—
251C22×C4—2261no—
252C22×C4—2261no—
253C22×C4—2261no—
254C22×C4—2261no—
255C22×C4C22×D11311yescharacteristic
256M16—2262no—
257M16—2262no—
258C2×C8—1131no—
259C2×C8—1131no—
260C2×C8C22×D11311yescharacteristic
261C2×C8C22×D11311yescharacteristic
262C4⋊C4—21no—
263C4⋊C4—1131no—
264C4⋊C4—1131no—
265C4⋊C4—1131no—
266C4⋊C4—2261no—
267C4⋊C4—2261no—
268C4⋊C4—2261no—
269C4⋊C4—2261no—
270C4⋊C4—2261no—
271C4⋊C4—2261no—
272C4⋊C4C22×D11311yescharacteristic
273C4⋊C4C22×D11311yescharacteristic
274C4⋊C4C22×D11311yescharacteristic
275C22⋊C4—21no—
276C22⋊C4—21no—
277C22⋊C4—2261no—
278C22⋊C4—2261no—
279C22⋊C4—2261no—
280C22⋊C4—2261no—
281C22⋊C4—2261no—
282C22⋊C4—2261no—
283C42—21no—
284C42—2261no—
285C42—2261no—
286C42—2261no—
287C23—1131no—
288C23—1131no—
289C23—4521no—
290C23—2262no—
291C23—2262no—
292C23D4×D11311yescharacteristic
293Q8—21no—
294Q8—21no—
295Q8—4522no—
296Q8—2261no—
297Q8—2261no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—21no—
301C2×C4—21no—
302C2×C4—21no—
303C2×C4—21no—
304C2×C4—1131no—
305C2×C4—1132no—
306C2×C4—1132no—
307C2×C4—1131no—
308C2×C4—4522no—
309C2×C4—4522no—
310C2×C4—4522no—
311C2×C4—4522no—
312C2×C4—2262no—
313C2×C4—2262no—
314C2×C4—2262no—
315C2×C4—2261no—
316C2×C4—2261no—
317C2×C4—2261no—
318C2×C4—2261no—
319C2×C4—2261no—
320C2×C4—2261no—
321C2×C4D4×D11311yescharacteristic
322C2×C4C23×D11311yescharacteristic
323C8—21no—
324C8—21no—
325C8—2261no—
326C8—2261no—
327C22—21no—
328C22—21no—
329C22—21no—
330C22—1132no—
331C22—1132no—
332C22—4524no—
333C22—2261no—
334C22—2261no—
335C22—2261no—
336C22—2261no—
337C22C2×D4×D11311yescharacteristic
338C4—21no—
339C4—41no—
340C4—41no—
341C4—41no—
342C4—41no—
343C4—1132no—
344C4—4521no—
345C4—4521no—
346C4—4521no—
347C4—4521no—
348C4—2261no—
349C4#41×D11311yescharacteristic
350C4#41×D11311yescharacteristic
351C2—41no—
352C2—2262no—
353C2—2262no—
354C2#123×D11311yescharacteristic
355C2#137×D11311yescharacteristic
356C2#2029939511yescharacteristic
subgroupG/H
centerC22C2×D4×D113
commutator, cosocleC2×C4×C113C24
FrattiniC2×C4C23×D113
Fitting#485×C113C2
socleC22×C113C22×D4
prime radicalC23×D113D4
hypercenter#485D113
hypocenterC113#3095
LCSG ▷ C2×C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C22 ◁ C22×C4 ◁ #485

Complements

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

NH ≅ G/Ntype
3. #20298940C2semidirect
4. #20298939C2semidirect
5. #20298936C2semidirect
6. #20298935C2semidirect
7. #20298932C2semidirect
8. #20298930C2semidirect
9. #20298927C2semidirect
10. #20298639C2semidirect
11. #20298637C2semidirect
12. #20298605C2semidirect
13. #20298605C2semidirect
15. #485×C113C2semidirect
37. #16813556C22semidirect
38. #16813555C22semidirect
39. #16813555C22semidirect
40. #16813554C22semidirect
41. #16813553C22semidirect
42. #16813553C22semidirect
43. #16813547C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813546C22semidirect
47. #16813545C22semidirect
48. #16813545C22semidirect
54. #107×C113C22semidirect
55. #106×C113C22semidirect
56. #103×C113C22semidirect
57. #103×C113C22semidirect
179. C113#3095semidirect
185. #485D113semidirect
221. #107C2×D113semidirect
225. #106C2×D113semidirect
232. #103C2×D113semidirect
233. #103C2×D113semidirect

Maximal subgroups

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

subgroupindex
C22⋊Q8×D1132
#117×D1132
#202989402
#202989392
#202989362
#202989352
#202989322
#202989302
#202989272
#202986392
#202986372
#202986052
#202985602
#485×C1132
#3095113