Finite Group Databasebeta

← C4×SD16×D113 #28399327

Subgroups — C4×SD16×D113 #28399327

Order 14464.

552 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
1C2×SD16×D113C211yesmaximal, characteristic
2C4×Q8×D113C211yesmaximal, characteristic, complemented
3C4×D4×D113C211yesmaximal, characteristic
4#20298689C211yesmaximal, characteristic, complemented
5C4×#14268636C211yesmaximal, characteristic, complemented
6SD16×Dic113C211yesmaximal, characteristic, complemented
7C4×#14268634C211yesmaximal, characteristic, complemented
8#20298685C211yesmaximal, characteristic, complemented
9C4×#14268635C211yesmaximal, characteristic, complemented
10#20298683C211yesmaximal, characteristic, complemented
11#106×D113C211yesmaximal, characteristic, complemented
12#103×D113C211yesmaximal, characteristic, complemented
13#102×D113C211yesmaximal, characteristic
14C4×C8×D113C211yesmaximal, characteristic, complemented
15C4×SD16×C113C211yesmaximal, characteristic, complemented
16C2×Q8×D113C2211yescharacteristic
17C2×D4×D113C2211yescharacteristic
18C22×C4×D113—21no—
19C2×#14268636C2211yescharacteristic
20C2×#14268635C2211yescharacteristic
21C2×#14268634C2211yescharacteristic
22SD16×D113C418yesdirect product factor
23C2×C8×D113C2211yescharacteristic
24C2×C8×D113C2211yescharacteristic
25Q8×Dic113C2211yescharacteristic, complemented
26C4×Dic226—21no—
27C4×Dic226C2211yescharacteristic, complemented
28#16813587—21no—
29#16813587C2211yescharacteristic, complemented
30C4×D452C2211yescharacteristic
31D4×Dic113C2211yescharacteristic
32#16813584C2211yescharacteristic
33C4×C22⋊D113—21no—
34#16813582—21no—
35C4⋊C4×D113—21no—
36C4⋊C4×D113C2211yescharacteristic
37C4⋊C4×D113C2211yescharacteristic
38C22⋊C4×D113—21no—
39C42×D113—21no—
40C42×D113C2211yescharacteristic
41#16813554C2211yescharacteristic, complemented
42#16813553C2211yescharacteristic, complemented
43#16813553C2211yescharacteristic, complemented
44#16813547C2211yescharacteristic, complemented
45#16813546C2211yescharacteristic, complemented
46#16813545C2211yescharacteristic, complemented
47#16813544C2211yescharacteristic
48#16813543C2211yescharacteristic
49#16813542C2211yescharacteristic
50C4×#11744751C2211yescharacteristic, complemented
51C8×Dic113C2211yescharacteristic, complemented
52C8×Dic113C2211yescharacteristic, complemented
53C2×SD16×C113C2211yescharacteristic
54C4×Q8×C113C2211yescharacteristic, complemented
55C4×D4×C113C2211yescharacteristic
56#106×C113C2211yescharacteristic, complemented
57#103×C113C2211yescharacteristic, complemented
58#102×C113C2211yescharacteristic
59C4×C8×C113C2211yescharacteristic, complemented
60C23×D113—21no—
61C2×Dic226—21no—
62C2×Dic226C2311yescharacteristic
63Q8×D113—22no—
64Q8×D113C2×C414yescomplemented
65C2×D452C2311yescharacteristic
66C2×C22⋊D113—21no—
67D4×D113—22no—
68D4×D113C2×C414yes—
69C22×Dic113—21no—
70C2×C4×D113—21no—
71C2×C4×D113—21no—
72C2×C4×D113—21no—
73C2×C4×D113—21no—
74C2×C4×D113—21no—
75C2×C4×D113—44no—
76C2×C4×D113D411yescharacteristic
77C2×C4×D113D411yescharacteristic
78C2×C4×D113C2311yescharacteristic
79#14268636C2×C414yescomplemented
80#14268635C2×C414yescomplemented
81#14268634C2×C414yescomplemented
82C2×#11744751C2311yescharacteristic
83C2×#11744751C2311yescharacteristic
84C8×D113—22no—
85C8×D113C2×C414yescomplemented
86C4⋊Dic113—21no—
87C4⋊Dic113C2311yescharacteristic
88C4⋊Dic113C2311yescharacteristic
89#14268626—21no—
90#14268626—21no—
91#14268626—21no—
92#14268626—21no—
93C22⋊Dic113—21no—
94#14268624—21no—
95#14268624—21no—
96C4×Dic113—21no—
97C4×Dic113—21no—
98C4×Dic113—21no—
99C4×Dic113D411yescharacteristic
100C4×Dic113D411yescharacteristic
101C4×Dic113C2311yescharacteristic
102C2×Q8×C113C2311yescharacteristic
103C2×D4×C113C2311yescharacteristic
104C22×C4×C113—21no—
105SD16×C113C2×C414yescomplemented
106C2×C8×C113C2311yescharacteristic
107C2×C8×C113C2311yescharacteristic
108C4⋊C4×C113—21no—
109C4⋊C4×C113C2311yescharacteristic
110C4⋊C4×C113C2311yescharacteristic
111C22⋊C4×C113—21no—
112C42×C113—21no—
113C42×C113C2311yescharacteristic
114C23×C113—21no—
115C22×D113—21no—
116C22×D113—24no—
117C22×D113—42no—
118C22×D113—42no—
119C22×D113C2×D411yescharacteristic
120Q8×C113—21no—
121Q8×C113C22×C412yescomplemented
122D4×C113—21no—
123D4×C113C22×C412yes—
124C2×C4×C113—21no—
125C2×C4×C113—21no—
126C2×C4×C113—21no—
127C2×C4×C113—42no—
128C2×C4×C113C2×D411yescharacteristic
129C2×C4×C113C2×D411yescharacteristic
130C2×C4×C113C2411yescharacteristic
131C22⋊D113—24no—
132C2×Dic113—21no—
133C2×Dic113—21no—
134C2×Dic113—21no—
135C2×Dic113—42no—
136C2×Dic113C2×D411yescharacteristic
137C2×Dic113C2×D411yescharacteristic
138C2×Dic113C2×D411yescharacteristic
139D452—21no—
140D452C22×C412yes—
141C4×D113—24no—
142C4×D113—22no—
143C4×D113—42no—
144C4×D113—42no—
145C4×D113—42no—
146C4×D113—42no—
147C4×D113SD1614yesdirect product factor
148C4×D113C22×C412yes—
149C4×D113#4112yes—
150Dic226—21no—
151Dic226—24no—
152Dic226C22×C412yescomplemented
153C8×C113—21no—
154C8×C113C22×C412yescomplemented
155#11744751—21no—
156#11744751C22×C412yescomplemented
157C22×C113—22no—
158C22×C113—41no—
159C22×C113—41no—
160C22×C113C22×D411yescharacteristic
161C2×D113—22no—
162C2×D113—41no—
163C2×D113—41no—
164C2×D113—48no—
165C2×D113C4×D412yes—
166C2×D113C2×SD1612yes—
167C2×D113#13512yes—
168C4×C113—22no—
169C4×C113—21no—
170C4×C113—41no—
171C4×C113—41no—
172C4×C113C2×SD1612yescomplemented
173C4×C113C23×C411yescharacteristic
174C4×C113C2×#4111yescharacteristic
175Dic113—22no—
176Dic113—21no—
177Dic113—41no—
178Dic113—41no—
179Dic113C4×D412yes—
180Dic113C2×SD1612yescomplemented
181C2×C113—42no—
182C2×C113C2×C4×D411yescharacteristic
183C2×C113C22×SD1611yescharacteristic
184C2×C113C2×#13511yescharacteristic
185D113—42no—
186D113C4×SD1614yesdirect product factor
187C2×C4×SD16—1131nomaximal, Sylow
188C113C2×C4×SD1611yescharacteristic, complemented, Sylow
189C22×SD16—1131no—
190C2×C4×Q8—1131no—
191C2×C4×D4—1131no—
192C4×SD16—1131no—
193C4×SD16—1131no—
194C4×SD16—1131no—
195C4×SD16—1131no—
196C4×SD16—1131no—
197C4×SD16—1131no—
198C4×SD16—1131no—
199C4×SD16D11311yescharacteristic, direct product factor
200C2×#106—1131no—
201C2×#103—1131no—
202C2×#102—1131no—
203C2×C4×C8—1131no—
204C22×Q8—1131no—
205C22×D4—1131no—
206C23×C4—2261no—
207C2×SD16—1131no—
208C2×SD16—1131no—
209C2×SD16—1138no—
210C2×SD16—1131no—
211C2×SD16C2×D11311yescharacteristic
212C22×C8—1131no—
213C22×C8—1131no—
214C4×Q8—1131no—
215C4×Q8—1131no—
216C4×Q8—1131no—
217C4×Q8—2261no—
218C4×Q8—2261no—
219C4×Q8C2×D11311yescharacteristic, complemented
220C4×D4—1131no—
221C4×D4—1131no—
222C4×D4—1131no—
223C4×D4—2261no—
224C4×D4—2261no—
225C4×D4C2×D11311yescharacteristic
226C2×C4⋊C4—1131no—
227C2×C4⋊C4—1131no—
228C2×C4⋊C4—2261no—
229C2×C22⋊C4—2261no—
230C2×C42—1131no—
231C2×C42—2261no—
232#106—1131no—
233#106—1131no—
234#106—1131no—
235#106C2×D11311yescharacteristic, complemented
236#103—1131no—
237#103—1131no—
238#103—1131no—
239#103C2×D11311yescharacteristic, complemented
240#102—1131no—
241#102—1131no—
242#102—1131no—
243#102C2×D11311yescharacteristic
244C4×C8—1131no—
245C4×C8—1131no—
246C4×C8—1131no—
247C4×C8C2×D11311yescharacteristic, complemented
248C24—2261no—
249C2×Q8—1134no—
250C2×Q8—1131no—
251C2×Q8—2261no—
252C2×Q8—2262no—
253C2×Q8C22×D11311yescharacteristic
254C2×D4—1134no—
255C2×D4—1131no—
256C2×D4—2262no—
257C2×D4—2261no—
258C2×D4C22×D11311yescharacteristic
259C22×C4—21no—
260C22×C4—1131no—
261C22×C4—1131no—
262C22×C4—1131no—
263C22×C4—4524no—
264C22×C4—2261no—
265C22×C4—2261no—
266C22×C4—2261no—
267C22×C4—2261no—
268C22×C4—2261no—
269C22×C4—2261no—
270SD16—1134no—
271SD16—1134no—
272SD16—1134no—
273SD16C4×D11314yesdirect product factor
274C2×C8—1131no—
275C2×C8—1134no—
276C2×C8—1131no—
277C2×C8—2262no—
278C2×C8C22×D11311yescharacteristic
279C2×C8C22×D11311yescharacteristic
280C4⋊C4—21no—
281C4⋊C4—1131no—
282C4⋊C4—1131no—
283C4⋊C4—2261no—
284C4⋊C4—2261no—
285C4⋊C4—2261no—
286C4⋊C4—2261no—
287C4⋊C4—2261no—
288C4⋊C4C22×D11311yescharacteristic
289C4⋊C4C22×D11311yescharacteristic
290C22⋊C4—21no—
291C22⋊C4—2261no—
292C22⋊C4—2261no—
293C22⋊C4—2261no—
294C42—21no—
295C42—1131no—
296C42—1131no—
297C42—1131no—
298C42—2261no—
299C42—2261no—
300C42—2261no—
301C42C22×D11311yescharacteristic
302C23—21no—
303C23—1131no—
304C23—4522no—
305C23—4522no—
306C23—2264no—
307C23—2261no—
308Q8—21no—
309Q8—1132no—
310Q8—2264no—
311Q8—2261no—
312Q8C2×C4×D11312yescomplemented
313D4—21no—
314D4—1132no—
315D4—2264no—
316D4—2261no—
317D4C2×C4×D11312yes—
318C2×C4—21no—
319C2×C4—21no—
320C2×C4—21no—
321C2×C4—42no—
322C2×C4—1131no—
323C2×C4—1131no—
324C2×C4—1134no—
325C2×C4—1132no—
326C2×C4—1132no—
327C2×C4—1131no—
328C2×C4—4522no—
329C2×C4—4522no—
330C2×C4—4522no—
331C2×C4—4522no—
332C2×C4—4522no—
333C2×C4—2262no—
334C2×C4—2264no—
335C2×C4—2261no—
336C2×C4—2261no—
337C2×C4—2261no—
338C2×C4D4×D11311yescharacteristic
339C2×C4D4×D11311yescharacteristic
340C2×C4C23×D11311yescharacteristic
341C8—21no—
342C8—1132no—
343C8—2261no—
344C8C2×C4×D11312yescomplemented
345C22—22no—
346C22—41no—
347C22—41no—
348C22—1132no—
349C22—1132no—
350C22—1132no—
351C22—4528no—
352C22—4521no—
353C22—4521no—
354C22—2262no—
355C22C2×D4×D11311yescharacteristic
356C4—22no—
357C4—21no—
358C4—41no—
359C4—41no—
360C4—1132no—
361C4—1132no—
362C4—4521no—
363C4—4521no—
364C4—2262no—
365C4—2261no—
366C4SD16×D11312yesdirect product factor
367C4C22×C4×D11311yescharacteristic
368C4#41×D11311yescharacteristic
369C2—42no—
370C2—1134no—
371C2—4522no—
372C2C4×D4×D11311yescharacteristic
373C2C2×SD16×D11311yescharacteristic
374C2#135×D11311yescharacteristic
subgroupG/H
centerC2×C4D4×D113
commutatorC4×C113C23×C4
FrattiniC2×C4C23×D113
FittingC4×SD16×C113C2
socleC22×C113C22×D4
prime radicalC2×D4×D113C22
cosocleC2×C4×C113C24
hypercenterC4×SD16D113
hypocenterC113C2×C4×SD16
LCSG ▷ C4×C113 ▷ C2×C113 ▷ C113
UCSC1 ◁ C2×C4 ◁ C42 ◁ C4×SD16

Complements

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

NH ≅ G/Ntype
2. C4×Q8×D113C2semidirect
4. #20298689C2semidirect
5. C4×#14268636C2semidirect
6. SD16×Dic113C2semidirect
7. C4×#14268634C2semidirect
8. #20298685C2semidirect
9. C4×#14268635C2semidirect
10. #20298683C2semidirect
11. #106×D113C2semidirect
12. #103×D113C2semidirect
14. C4×C8×D113C2semidirect
15. C4×SD16×C113C2semidirect
22. SD16×D113C4direct (N × H)
25. Q8×Dic113C22semidirect
27. C4×Dic226C22semidirect
29. #16813587C22semidirect
41. #16813554C22semidirect
42. #16813553C22semidirect
43. #16813553C22semidirect
44. #16813547C22semidirect
45. #16813546C22semidirect
46. #16813545C22semidirect
50. C4×#11744751C22semidirect
51. C8×Dic113C22semidirect
52. C8×Dic113C22semidirect
54. C4×Q8×C113C22semidirect
56. #106×C113C22semidirect
57. #103×C113C22semidirect
59. C4×C8×C113C22semidirect
64. Q8×D113C2×C4semidirect
79. #14268636C2×C4semidirect
80. #14268635C2×C4semidirect
81. #14268634C2×C4semidirect
85. C8×D113C2×C4semidirect
105. SD16×C113C2×C4semidirect
121. Q8×C113C22×C4semidirect
147. C4×D113SD16direct (N × H)
152. Dic226C22×C4semidirect
154. C8×C113C22×C4semidirect
156. #11744751C22×C4semidirect
172. C4×C113C2×SD16semidirect
180. Dic113C2×SD16semidirect
186. D113C4×SD16direct (N × H)
188. C113C2×C4×SD16semidirect
199. C4×SD16D113direct (N × H)
219. C4×Q8C2×D113semidirect
235. #106C2×D113semidirect
239. #103C2×D113semidirect
247. C4×C8C2×D113semidirect
273. SD16C4×D113direct (N × H)
312. Q8C2×C4×D113semidirect
344. C8C2×C4×D113semidirect
366. C4SD16×D113direct (N × H)

Maximal subgroups

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

subgroupindex
C2×SD16×D1132
C4×Q8×D1132
C4×D4×D1132
#202986892
C4×#142686362
SD16×Dic1132
C4×#142686342
#202986852
C4×#142686352
#202986832
#106×D1132
#103×D1132
#102×D1132
C4×C8×D1132
C4×SD16×C1132
C2×C4×SD16113