Finite Group Databasebeta

← C2×#10623196 #13081964

Subgroups — C2×#10623196 #13081964

Order 1408.

1144 conjugacy classes of subgroups.

The subgroup lattice has 416 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C11×#123C211yesmaximal, characteristic, complemented
2C2×#66992C211yesmaximal, characteristic
3C2×D4×Dic11C211yesmaximal, characteristic, complemented
4C2×#66982C211yesmaximal, characteristic, complemented
5C22×C4⋊Dic11C211yesmaximal, characteristic, complemented
6#10623196C2116yesmaximal, direct product factor
7C2×#66951C211yesmaximal, characteristic, complemented
8C2×#66950C211yesmaximal, characteristic, complemented
9C2×#66943C211yesmaximal, characteristic, complemented
10C2×#66942C211yesmaximal, characteristic, complemented
11C2×#66939C211yesmaximal, characteristic, complemented
12C2×#66936C211yesmaximal, characteristic, complemented
13C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
14C2×#66932C211yesmaximal, characteristic, complemented
15C2×#66931C211yesmaximal, characteristic, complemented
16C2×#66931C211yesmaximal, characteristic, complemented
17C22×D4×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C22×C22⋊D11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C23×Dic11C2211yescharacteristic
22C23×Dic11C2211yescharacteristic
23C23×Dic11C2211yescharacteristic
24C22×C4×D11C2211yescharacteristic
25C22×Dic22C2211yescharacteristic
26C11×#123C2218yescomplemented
27C2×C11×C4⋊C4C2211yescharacteristic
28C2×C11×C4⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2211yescharacteristic
32C2×C22⋊Dic11C2211yescharacteristic
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35#66992C2218yes—
36D4×Dic11C2218yescomplemented
37#66982C2218yescomplemented
38C2×(C2×D11)⋊C4C2211yescharacteristic
39C2×(C2×D11)⋊C4C2211yescharacteristic
40C2×(C2×D11)⋊C4C2211yescharacteristic
41C2×(C2×D11)⋊C4C2211yescharacteristic
42C2×C4⋊Dic11C2211yescharacteristic
43C2×C4⋊Dic11C2211yescharacteristic
44C2×C4⋊Dic11C2211yescharacteristic
45C2×C4⋊Dic11C2211yescharacteristic
46C2×C4⋊Dic11C2211yescharacteristic
47C2×C4⋊Dic11C2211yescharacteristic
48C2×C4⋊Dic11C2218yescomplemented
49C2×Dic11⋊C4C2211yescharacteristic
50C2×Dic11⋊C4C2211yescharacteristic
51C2×Dic11⋊C4C2211yescharacteristic
52C2×Dic11⋊C4C2211yescharacteristic
53C2×Dic11⋊C4C2211yescharacteristic
54C2×Dic11⋊C4C2211yescharacteristic
55C2×C4×Dic11C2211yescharacteristic
56C2×C4×Dic11C2211yescharacteristic
57#66951C2218yescomplemented
58#66950C2218yescomplemented
59#66943C2218yescomplemented
60#66942C2218yescomplemented
61#66939C2218yescomplemented
62#66936C2218yescomplemented
63(C22⋊D11)⋊C4C2218yescomplemented
64#66932C2218yescomplemented
65#66931C2218yescomplemented
66#66931C2218yescomplemented
67C24×C11C2311yescharacteristic
68C24×C11C2311yescharacteristic
69C23×D11C2311yescharacteristic
70C2×D4×C11—24no—
71C2×D4×C11C2314yes—
72C22×C4×C11—24no—
73C22×C4×C11C2311yescharacteristic
74C22×C4×C11C2311yescharacteristic
75C22×C4×C11C2311yescharacteristic
76C22×C4×C11C2311yescharacteristic
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2314yes—
79C2×C22⋊D11—24no—
80C2×C22⋊D11—42no—
81C2×C22⋊D11C2314yes—
82C2×C22⋊D11C2314yes—
83C22×Dic11—42no—
84C22×Dic11—42no—
85C22×Dic11—42no—
86C22×Dic11C2311yescharacteristic
87C22×Dic11C2311yescharacteristic
88C22×Dic11C2311yescharacteristic
89C22×Dic11C2311yescharacteristic
90C22×Dic11C2311yescharacteristic
91C22×Dic11C2311yescharacteristic
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2314yes—
94C22×Dic11C2314yes—
95C22×Dic11C2314yes—
96C2×C4×D11—42no—
97C2×C4×D11C2314yes—
98C2×Dic22—42no—
99C2×Dic22C2314yes—
100C11×C4⋊C4C2314yes—
101C11×C4⋊C4C2314yes—
102C11×C22⋊C4C2314yes—
103C11×C22⋊C4C2314yes—
104C11×C22⋊C4C2314yes—
105C22⋊Dic11C2314yes—
106C22⋊Dic11C2314yes—
107C22⋊Dic11C2314yes—
108(C2×D11)⋊C4C2314yes—
109(C2×D11)⋊C4C2314yes—
110(C2×D11)⋊C4C2314yes—
111(C2×D11)⋊C4C2314yes—
112C4⋊Dic11C2314yes—
113C4⋊Dic11C2314yes—
114C4⋊Dic11C2314yes—
115C4⋊Dic11C2314yes—
116C4⋊Dic11C2314yes—
117C4⋊Dic11C2314yes—
118Dic11⋊C4C2314yes—
119Dic11⋊C4C2314yes—
120Dic11⋊C4C2314yes—
121Dic11⋊C4C2314yes—
122Dic11⋊C4C2314yes—
123Dic11⋊C4C2314yes—
124C4×Dic11C2314yes—
125C4×Dic11C2314yes—
126C2×#539—111nomaximal, Sylow
127C23×C11—22no—
128C23×C11—22no—
129C23×C11—22no—
130C23×C11—22no—
131C23×C11—22no—
132C23×C11#4114yes—
133C23×C11C2412yes—
134C23×C11C2412yes—
135C23×C11C2411yescharacteristic
136C22×D11—22no—
137C22×D11—22no—
138C22×D11—22no—
139C22×D11C2412yes—
140D4×C11—28no—
141C2×C4×C11—28no—
142C2×C4×C11—22no—
143C2×C4×C11—22no—
144C2×C4×C11—22no—
145C2×C4×C11—22no—
146C2×C4×C11—22no—
147C2×C4×C11C2412yes—
148C2×C4×C11C2412yes—
149C2×C4×C11C2412yes—
150C2×C4×C11C2412yes—
151C2×C4×C11C2412yes—
152C22⋊D11—28no—
153C22⋊D11—44no—
154C2×Dic11—22no—
155C2×Dic11—22no—
156C2×Dic11—22no—
157C2×Dic11—22no—
158C2×Dic11—22no—
159C2×Dic11—22no—
160C2×Dic11—22no—
161C2×Dic11—44no—
162C2×Dic11—44no—
163C2×Dic11—44no—
164C2×Dic11C2412yes—
165C2×Dic11C2412yes—
166C2×Dic11C2412yes—
167C2×Dic11C2412yes—
168C2×Dic11C2412yes—
169C2×Dic11C2412yes—
170C2×Dic11C2412yes—
171C4×D11—44no—
172Dic22—44no—
173#539—1116no—
174C2×#126—111no—
175C2×#126—111no—
176C2×#125—111no—
177C2×#125—111no—
178C2×#123—111no—
179C2×#123—111no—
180C2×#123—111no—
181C2×#123D1111yescharacteristic, complemented
182C2×C22⋊Q8—111no—
183C2×C22⋊Q8—111no—
184C2×C22⋊Q8—111no—
185C2×#121—111no—
186C2×C4×D4—111no—
187C2×C4×D4—111no—
188C22×C4⋊C4—111no—
189C22×C11—28no—
190C22×C11—22no—
191C22×C11—22no—
192C22×C11—22no—
193C22×C11—22no—
194C22×C11—22no—
195C22×C11—44no—
196C22×C11C2×#4114yes—
197C22×C11C2×#4112yes—
198C22×C11H(5,𝔽2)12yes—
199C22×C112−1+412yes—
200C22×C11C2511yescharacteristic
201C2×D11—22no—
202C2×D11—22no—
203C2×D11—22no—
204C2×D11—44no—
205C4×C11—22no—
206C4×C11—22no—
207C4×C11—22no—
208C4×C11—22no—
209C4×C11—22no—
210Dic11—22no—
211Dic11—22no—
212Dic11—22no—
213Dic11—22no—
214Dic11—22no—
215Dic11—22no—
216Dic11—22no—
217C22×Q8—111no—
218C22×D4—111no—
219C22×D4—111no—
220C22×D4C2×D1111yescharacteristic
221C23×C4—111no—
222C23×C4—111no—
223C23×C4—111no—
224C23×C4—111no—
225C23×C4C2×D1111yescharacteristic
226#126—118no—
227#126—118no—
228#125—118no—
229#125—118no—
230#123—118no—
231#123—118no—
232#123—118no—
233#123C2×D1118yescomplemented
234C22⋊Q8—118no—
235C22⋊Q8—118no—
236C22⋊Q8—118no—
237#121—118no—
238C4×D4—118no—
239C4×D4—118no—
240C2×C4⋊C4—111no—
241C2×C4⋊C4—111no—
242C2×C4⋊C4—111no—
243C2×C4⋊C4—111no—
244C2×C4⋊C4—118no—
245C2×C4⋊C4—111no—
246C2×C4⋊C4—111no—
247C2×C4⋊C4—111no—
248C2×C4⋊C4—111no—
249C2×C4⋊C4—111no—
250C2×C4⋊C4—111no—
251C2×C4⋊C4—111no—
252C2×C4⋊C4—111no—
253C2×C4⋊C4C2×D1111yescharacteristic
254C2×C4⋊C4C2×D1111yescharacteristic
255C2×C22⋊C4—111no—
256C2×C22⋊C4—111no—
257C2×C22⋊C4—111no—
258C2×C22⋊C4—111no—
259C2×C22⋊C4—111no—
260C2×C22⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4C2×D1111yescharacteristic
263C2×C22⋊C4C2×D1111yescharacteristic
264C2×C22⋊C4C2×D1111yescharacteristic
265C2×C42—111no—
266C2×C42—111no—
267C2×C11—24no—
268C2×C11—42no—
269C2×C11#53914yescomplemented
270C2×C11C22×#4111yescharacteristic
271C2×C11C2×H(5,𝔽2)11yescharacteristic
272C2×C11C2×2−1+411yescharacteristic
273D11—42no—
274C24—111no—
275C24C22×D1111yescharacteristic
276C24C22×D1111yescharacteristic
277C2×Q8—114no—
278C2×Q8—442no—
279C2×D4—24no—
280C2×D4—114no—
281C2×D4—114no—
282C2×D4—224no—
283C2×D4—442no—
284C2×D4C22×D1114yes—
285C22×C4—24no—
286C22×C4—111no—
287C22×C4—111no—
288C22×C4—111no—
289C22×C4—111no—
290C22×C4—111no—
291C22×C4—111no—
292C22×C4—111no—
293C22×C4—114no—
294C22×C4—114no—
295C22×C4—114no—
296C22×C4—114no—
297C22×C4—442no—
298C22×C4—442no—
299C22×C4—442no—
300C22×C4—442no—
301C22×C4C22×D1114yes—
302C22×C4C22×D1111yescharacteristic
303C22×C4C22×D1111yescharacteristic
304C22×C4C22×D1111yescharacteristic
305C22×C4C22×D1111yescharacteristic
306C22×C4C22×D1111yescharacteristic
307C4⋊C4—114no—
308C4⋊C4—114no—
309C4⋊C4—114no—
310C4⋊C4—114no—
311C4⋊C4—114no—
312C4⋊C4—114no—
313C4⋊C4—114no—
314C4⋊C4—114no—
315C4⋊C4—114no—
316C4⋊C4—114no—
317C4⋊C4—114no—
318C4⋊C4—114no—
319C4⋊C4C22×D1114yes—
320C4⋊C4C22×D1114yes—
321C22⋊C4—114no—
322C22⋊C4—114no—
323C22⋊C4—114no—
324C22⋊C4—114no—
325C22⋊C4—114no—
326C22⋊C4—114no—
327C22⋊C4—114no—
328C22⋊C4C22×D1114yes—
329C22⋊C4C22×D1114yes—
330C22⋊C4C22×D1114yes—
331C42—114no—
332C42—114no—
333C11C2×#53911yescharacteristic, complemented, Sylow
334C23—22no—
335C23—22no—
336C23—22no—
337C23—22no—
338C23—22no—
339C23—112no—
340C23—222no—
341C23—222no—
342C23—222no—
343C23#434114yes—
344C23C23×D1112yes—
345C23C23×D1112yes—
346C23C23×D1111yescharacteristic
347Q8—444no—
348D4—28no—
349D4—228no—
350D4—444no—
351C2×C4—28no—
352C2×C4—22no—
353C2×C4—22no—
354C2×C4—22no—
355C2×C4—22no—
356C2×C4—22no—
357C2×C4—112no—
358C2×C4—112no—
359C2×C4—112no—
360C2×C4—112no—
361C2×C4—112no—
362C2×C4—112no—
363C2×C4—112no—
364C2×C4—222no—
365C2×C4—222no—
366C2×C4—222no—
367C2×C4—222no—
368C2×C4—222no—
369C2×C4—222no—
370C2×C4—222no—
371C2×C4—444no—
372C2×C4—444no—
373C2×C4—444no—
374C2×C4—444no—
375C2×C4C23×D1112yes—
376C2×C4C23×D1112yes—
377C2×C4C23×D1112yes—
378C2×C4C23×D1112yes—
379C2×C4C23×D1112yes—
380C22—22no—
381C22—28no—
382C22—22no—
383C22—22no—
384C22—22no—
385C22—22no—
386C22—44no—
387C22—222no—
388C22—222no—
389C22—222no—
390C22—444no—
391C22C2×#434114yes—
392C22C2×#434112yes—
393C22#6704212yes—
394C22#6704312yes—
395C22C24×D1111yescharacteristic
396C4—22no—
397C4—22no—
398C4—22no—
399C4—22no—
400C4—22no—
401C4—222no—
402C4—222no—
403C4—222no—
404C4—222no—
405C4—222no—
406C4—222no—
407C4—222no—
408C2—24no—
409C2—42no—
410C2—442no—
411C2#1062319614yesdirect product factor
412C2C22×#434111yescharacteristic
413C2C2×#6704211yescharacteristic
414C2C2×#6704311yescharacteristic
subgroupG/H
centerC23C23×D11
commutator, cosocleC22×C11C25
FrattiniC22C24×D11
FittingC2×C11×#123C2
socleC23×C11C24
prime radicalC2×#66992C2
hypercenterC2×#123D11
hypocenterC11C2×#539
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#123

Complements

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

NH ≅ G/Ntype
1. C2×C11×#123C2semidirect
3. C2×D4×Dic11C2semidirect
4. C2×#66982C2semidirect
5. C22×C4⋊Dic11C2semidirect
6. #10623196C2direct (N × H)
7. C2×#66951C2semidirect
8. C2×#66950C2semidirect
9. C2×#66943C2semidirect
10. C2×#66942C2semidirect
11. C2×#66939C2semidirect
12. C2×#66936C2semidirect
13. C2×(C22⋊D11)⋊C4C2semidirect
14. C2×#66932C2semidirect
15. C2×#66931C2semidirect
16. C2×#66931C2semidirect
26. C11×#123C22semidirect
36. D4×Dic11C22semidirect
37. #66982C22semidirect
48. C2×C4⋊Dic11C22semidirect
57. #66951C22semidirect
58. #66950C22semidirect
59. #66943C22semidirect
60. #66942C22semidirect
61. #66939C22semidirect
62. #66936C22semidirect
63. (C22⋊D11)⋊C4C22semidirect
64. #66932C22semidirect
65. #66931C22semidirect
66. #66931C22semidirect
181. C2×#123D11semidirect
233. #123C2×D11semidirect
269. C2×C11#539semidirect
333. C11C2×#539semidirect
411. C2#10623196direct (N × H)

Maximal subgroups

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

subgroupindex
C2×C11×#1232
C2×#669922
C2×D4×Dic112
C2×#669822
C22×C4⋊Dic112
#106231962
C2×#669512
C2×#669502
C2×#669432
C2×#669422
C2×#669392
C2×#669362
C2×(C22⋊D11)⋊C42
C2×#669322
C2×#669312
C2×#53911