Finite Group Databasebeta

← C2×#10623026 #13082113

Subgroups — C2×#10623026 #13082113

Order 1408.

1328 conjugacy classes of subgroups.

The subgroup lattice has 444 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C11×C22⋊C4C211yesmaximal, characteristic, complemented
2C2×#67006C211yesmaximal, characteristic
3C22×C22⋊Dic11C211yesmaximal, characteristic, complemented
4C2×#66982C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊D11C211yesmaximal, characteristic, complemented
6C2×#66979C211yesmaximal, characteristic, complemented
7C2×#66977C211yesmaximal, characteristic, complemented
8#10623026C2116yesmaximal, direct product factor
9C2×#66939C211yesmaximal, characteristic, complemented
10C2×#66938C211yesmaximal, characteristic, complemented
11C2×#66936C211yesmaximal, characteristic, complemented
12C2×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
13C2×#66932C211yesmaximal, characteristic, complemented
14C2×#66932C211yesmaximal, characteristic, complemented
15C2×#66931C211yesmaximal, characteristic, complemented
16C2×#66930C211yesmaximal, characteristic, complemented
17C25×C11C2211yescharacteristic
18C23×C4×C11C2211yescharacteristic
19C23×C4×C11C2211yescharacteristic
20C22×C22⋊D11C2211yescharacteristic
21C22×C22⋊D11C2211yescharacteristic
22C22×C22⋊D11C2211yescharacteristic
23C23×Dic11C2211yescharacteristic
24C23×Dic11C2211yescharacteristic
25C22×C4×D11C2211yescharacteristic, complemented
26C22×Dic22C2211yescharacteristic, complemented
27C2×C11×C22⋊C4C2211yescharacteristic
28C2×C11×C22⋊C4C2211yescharacteristic
29C2×C11×C22⋊C4C2211yescharacteristic
30C2×C11×C22⋊C4C2211yescharacteristic
31C2×C11×C22⋊C4C2218yescomplemented
32#67006C2218yes—
33C2×C22⋊Dic11C2211yescharacteristic
34C2×C22⋊Dic11C2211yescharacteristic
35C2×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊Dic11C2211yescharacteristic
37C2×C22⋊Dic11C2211yescharacteristic
38C2×C22⋊Dic11C2211yescharacteristic
39C2×C22⋊Dic11C2211yescharacteristic
40C2×C22⋊Dic11C2218yescomplemented
41#66982C2218yescomplemented
42C4×C22⋊D11C2218yescomplemented
43C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
44C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
45C2×(C2×D11)⋊C4C2211yescharacteristic, complemented
46#66979C2218yescomplemented
47C2×C4⋊Dic11C2211yescharacteristic, complemented
48C2×C4⋊Dic11C2211yescharacteristic, complemented
49C2×C4⋊Dic11C2211yescharacteristic, complemented
50#66977C2218yescomplemented
51C2×Dic11⋊C4C2211yescharacteristic, complemented
52C2×Dic11⋊C4C2211yescharacteristic, complemented
53C2×Dic11⋊C4C2211yescharacteristic, complemented
54C2×Dic11⋊C4C2211yescharacteristic, complemented
55C2×Dic11⋊C4C2211yescharacteristic, complemented
56C2×C4×Dic11C2211yescharacteristic, complemented
57C2×C4×Dic11C2211yescharacteristic, complemented
58C2×C4×Dic11C2211yescharacteristic, complemented
59#66939C2218yescomplemented
60#66938C2218yescomplemented
61#66936C2218yescomplemented
62(C22⋊D11)⋊C4C2218yescomplemented
63#66932C2218yescomplemented
64#66932C2218yescomplemented
65#66931C2218yescomplemented
66#66930C2218yescomplemented
67C24×C11—24no—
68C24×C11—24no—
69C24×C11—42no—
70C24×C11C2311yescharacteristic
71C24×C11C2314yes—
72C24×C11C2311yescharacteristic
73C24×C11C2311yescharacteristic
74C23×D11C2311yescharacteristic
75C22×C4×C11—24no—
76C22×C4×C11—42no—
77C22×C4×C11C2311yescharacteristic
78C22×C4×C11C2311yescharacteristic
79C22×C4×C11C2311yescharacteristic
80C22×C4×C11C2311yescharacteristic
81C22×C4×C11C2314yes—
82C22×C4×C11C2314yes—
83C2×C22⋊D11—24no—
84C2×C22⋊D11—24no—
85C2×C22⋊D11—42no—
86C2×C22⋊D11C2314yes—
87C2×C22⋊D11C2314yes—
88C2×C22⋊D11C2314yes—
89C22×Dic11—24no—
90C22×Dic11—42no—
91C22×Dic11C2314yes—
92C22×Dic11C2311yescharacteristic
93C22×Dic11C2311yescharacteristic
94C22×Dic11C2311yescharacteristic
95C22×Dic11C2311yescharacteristic
96C22×Dic11C2311yescharacteristic
97C22×Dic11C2311yescharacteristic
98C22×Dic11C2311yescharacteristic
99C22×Dic11C2314yes—
100C2×C4×D11—42no—
101C2×C4×D11C2314yescomplemented
102C2×Dic22—42no—
103C2×Dic22C2314yescomplemented
104C11×C22⋊C4C2314yes—
105C11×C22⋊C4C2314yes—
106C11×C22⋊C4C2314yes—
107C11×C22⋊C4C2314yes—
108C22⋊Dic11C2314yes—
109C22⋊Dic11C2314yes—
110C22⋊Dic11C2314yes—
111C22⋊Dic11C2314yes—
112C22⋊Dic11C2314yes—
113C22⋊Dic11C2314yes—
114C22⋊Dic11C2314yes—
115(C2×D11)⋊C4C2314yescomplemented
116(C2×D11)⋊C4C2314yescomplemented
117(C2×D11)⋊C4C2314yescomplemented
118C4⋊Dic11C2314yescomplemented
119C4⋊Dic11C2314yescomplemented
120C4⋊Dic11C2314yescomplemented
121Dic11⋊C4C2314yescomplemented
122Dic11⋊C4C2314yescomplemented
123Dic11⋊C4C2314yescomplemented
124Dic11⋊C4C2314yescomplemented
125Dic11⋊C4C2314yescomplemented
126C4×Dic11C2314yescomplemented
127C4×Dic11C2314yescomplemented
128C4×Dic11C2314yescomplemented
129C2×#551—111nomaximal, Sylow
130C23×C11—22no—
131C23×C11—22no—
132C23×C11—22no—
133C23×C11—22no—
134C23×C11—28no—
135C23×C11—22no—
136C23×C11—28no—
137C23×C11—22no—
138C23×C11—22no—
139C23×C11—44no—
140C23×C11—416no—
141C23×C11#4114yes—
142C23×C11#4114yes—
143C23×C11C2412yes—
144C23×C11C2412yes—
145C23×C11C2412yes—
146C23×C11C2411yescharacteristic
147C22×D11—22no—
148C22×D11—22no—
149C22×D11—22no—
150C22×D11C2412yes—
151C2×C4×C11—28no—
152C2×C4×C11—22no—
153C2×C4×C11—22no—
154C2×C4×C11—22no—
155C2×C4×C11—22no—
156C2×C4×C11—44no—
157C2×C4×C11C2412yes—
158C2×C4×C11C2412yes—
159C2×C4×C11C2412yes—
160C2×C4×C11C2412yes—
161C22⋊D11—28no—
162C22⋊D11—28no—
163C22⋊D11—44no—
164C2×Dic11—28no—
165C2×Dic11—22no—
166C2×Dic11—22no—
167C2×Dic11—22no—
168C2×Dic11—22no—
169C2×Dic11—22no—
170C2×Dic11—22no—
171C2×Dic11—22no—
172C2×Dic11—44no—
173C2×Dic11C2412yes—
174C2×Dic11C2412yes—
175C2×Dic11C2412yes—
176C2×Dic11C2412yes—
177C2×Dic11C2412yes—
178C2×Dic11C2412yes—
179C2×Dic11C2412yes—
180C4×D11—44no—
181Dic22—44no—
182#551—1116no—
183C2×#126—111no—
184C2×#126—111no—
185C2×#124—111no—
186C2×#123—111no—
187C2×#123—111no—
188C2×#123—111no—
189C2×C22⋊Q8—111no—
190C2×C22⋊Q8—111no—
191C2×#120—111no—
192C2×C4×D4—111no—
193C2×C4×D4—111no—
194C2×#117—111no—
195C2×#117—111no—
196C22×C22⋊C4—111no—
197C22×C22⋊C4D1111yescharacteristic, complemented
198C22×C11—28no—
199C22×C11—28no—
200C22×C11—22no—
201C22×C11—22no—
202C22×C11—22no—
203C22×C11—22no—
204C22×C11—22no—
205C22×C11—22no—
206C22×C11—22no—
207C22×C11—416no—
208C22×C11—44no—
209C22×C11C2×#4114yes—
210C22×C11C2×#4112yes—
211C22×C11C2×#4114yes—
212C22×C11C2×#4112yes—
213C22×C11H(5,𝔽2)12yes—
214C22×C11C2511yescharacteristic
215C2×D11—22no—
216C2×D11—22no—
217C2×D11—22no—
218C2×D11—44no—
219C4×C11—22no—
220C4×C11—22no—
221C4×C11—22no—
222C4×C11—22no—
223Dic11—22no—
224Dic11—22no—
225Dic11—22no—
226Dic11—22no—
227Dic11—22no—
228Dic11—22no—
229Dic11—22no—
230C25C2×D1111yescharacteristic
231C22×Q8—111no—
232C22×D4—111no—
233C22×D4—111no—
234C22×D4—111no—
235C23×C4—111no—
236C23×C4—111no—
237C23×C4—111no—
238C23×C4C2×D1111yescharacteristic
239C23×C4C2×D1111yescharacteristic
240#126—118no—
241#126—118no—
242#124—118no—
243#123—118no—
244#123—118no—
245#123—118no—
246C22⋊Q8—118no—
247C22⋊Q8—118no—
248#120—118no—
249C4×D4—118no—
250C4×D4—118no—
251#117—118no—
252#117—118no—
253C2×C4⋊C4—111no—
254C2×C4⋊C4—111no—
255C2×C4⋊C4—111no—
256C2×C4⋊C4—111no—
257C2×C4⋊C4—111no—
258C2×C4⋊C4—111no—
259C2×C4⋊C4—111no—
260C2×C4⋊C4—111no—
261C2×C22⋊C4—111no—
262C2×C22⋊C4—111no—
263C2×C22⋊C4—111no—
264C2×C22⋊C4—111no—
265C2×C22⋊C4—118no—
266C2×C22⋊C4—111no—
267C2×C22⋊C4—111no—
268C2×C22⋊C4—111no—
269C2×C22⋊C4—111no—
270C2×C22⋊C4—111no—
271C2×C22⋊C4—111no—
272C2×C22⋊C4C2×D1111yescharacteristic
273C2×C22⋊C4C2×D1111yescharacteristic
274C2×C22⋊C4C2×D1111yescharacteristic
275C2×C22⋊C4C2×D1111yescharacteristic
276C2×C22⋊C4C2×D1118yescomplemented
277C2×C42—111no—
278C2×C42—111no—
279C2×C42—111no—
280C2×C11—24no—
281C2×C11—24no—
282C2×C11—42no—
283C2×C11#55114yescomplemented
284C2×C11C22×#4111yescharacteristic
285C2×C11C22×#4111yescharacteristic
286C2×C11C2×H(5,𝔽2)11yescharacteristic
287D11—42no—
288C24—24no—
289C24—24no—
290C24—42no—
291C24—111no—
292C24C22×D1111yescharacteristic
293C24C22×D1114yes—
294C24C22×D1111yescharacteristic
295C24C22×D1111yescharacteristic
296C2×Q8—114no—
297C2×Q8—442no—
298C2×D4—114no—
299C2×D4—114no—
300C2×D4—114no—
301C2×D4—224no—
302C2×D4—224no—
303C2×D4—442no—
304C22×C4—24no—
305C22×C4—42no—
306C22×C4—114no—
307C22×C4—111no—
308C22×C4—111no—
309C22×C4—111no—
310C22×C4—111no—
311C22×C4—111no—
312C22×C4—111no—
313C22×C4—111no—
314C22×C4—114no—
315C22×C4—114no—
316C22×C4—224no—
317C22×C4—442no—
318C22×C4—442no—
319C22×C4C22×D1114yes—
320C22×C4C22×D1111yescharacteristic
321C22×C4C22×D1111yescharacteristic
322C22×C4C22×D1111yescharacteristic
323C22×C4C22×D1111yescharacteristic
324C22×C4C22×D1114yes—
325C4⋊C4—114no—
326C4⋊C4—114no—
327C4⋊C4—114no—
328C4⋊C4—114no—
329C4⋊C4—114no—
330C4⋊C4—114no—
331C4⋊C4—114no—
332C4⋊C4—114no—
333C22⋊C4—114no—
334C22⋊C4—114no—
335C22⋊C4—114no—
336C22⋊C4—114no—
337C22⋊C4—114no—
338C22⋊C4—114no—
339C22⋊C4—114no—
340C22⋊C4—114no—
341C22⋊C4—114no—
342C22⋊C4—114no—
343C22⋊C4C22×D1114yes—
344C22⋊C4C22×D1114yes—
345C22⋊C4C22×D1114yes—
346C22⋊C4C22×D1114yes—
347C42—114no—
348C42—114no—
349C42—114no—
350C11C2×#55111yescharacteristic, complemented, Sylow
351C23—22no—
352C23—22no—
353C23—22no—
354C23—22no—
355C23—28no—
356C23—22no—
357C23—28no—
358C23—22no—
359C23—22no—
360C23—44no—
361C23—416no—
362C23—112no—
363C23—222no—
364C23—222no—
365C23—222no—
366C23#433914yes—
367C23#434114yes—
368C23C23×D1112yes—
369C23C23×D1112yes—
370C23C23×D1112yes—
371C23C23×D1111yescharacteristic
372Q8—444no—
373D4—228no—
374D4—228no—
375D4—444no—
376C2×C4—28no—
377C2×C4—22no—
378C2×C4—22no—
379C2×C4—22no—
380C2×C4—22no—
381C2×C4—44no—
382C2×C4—112no—
383C2×C4—112no—
384C2×C4—112no—
385C2×C4—112no—
386C2×C4—112no—
387C2×C4—112no—
388C2×C4—112no—
389C2×C4—228no—
390C2×C4—222no—
391C2×C4—222no—
392C2×C4—222no—
393C2×C4—222no—
394C2×C4—222no—
395C2×C4—222no—
396C2×C4—222no—
397C2×C4—444no—
398C2×C4—444no—
399C2×C4C23×D1112yes—
400C2×C4C23×D1112yes—
401C2×C4C23×D1112yes—
402C2×C4C23×D1112yes—
403C22—28no—
404C22—28no—
405C22—22no—
406C22—22no—
407C22—22no—
408C22—22no—
409C22—22no—
410C22—22no—
411C22—22no—
412C22—416no—
413C22—44no—
414C22—222no—
415C22—222no—
416C22—222no—
417C22—444no—
418C22C2×#433914yes—
419C22C2×#433912yes—
420C22C2×#434114yes—
421C22C2×#434112yes—
422C22#6703712yes—
423C22C24×D1111yescharacteristic
424C4—22no—
425C4—22no—
426C4—22no—
427C4—22no—
428C4—222no—
429C4—222no—
430C4—222no—
431C4—222no—
432C4—222no—
433C4—222no—
434C4—222no—
435C2—24no—
436C2—24no—
437C2—42no—
438C2—442no—
439C2#1062302614yesdirect product factor
440C2C22×#433911yescharacteristic
441C2C22×#434111yescharacteristic
442C2C2×#6703711yescharacteristic
subgroupG/H
centerC23C23×D11
commutator, cosocleC22×C11C25
FrattiniC22C24×D11
FittingC22×C11×C22⋊C4C2
socleC23×C11C24
prime radicalC2×#67006C2
hypercenterC22×C22⋊C4D11
hypocenterC11C2×#551
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×C11×C22⋊C4C2semidirect
3. C22×C22⋊Dic11C2semidirect
4. C2×#66982C2semidirect
5. C2×C4×C22⋊D11C2semidirect
6. C2×#66979C2semidirect
7. C2×#66977C2semidirect
8. #10623026C2direct (N × H)
9. C2×#66939C2semidirect
10. C2×#66938C2semidirect
11. C2×#66936C2semidirect
12. C2×(C22⋊D11)⋊C4C2semidirect
13. C2×#66932C2semidirect
14. C2×#66932C2semidirect
15. C2×#66931C2semidirect
16. C2×#66930C2semidirect
25. C22×C4×D11C22semidirect
26. C22×Dic22C22semidirect
31. C2×C11×C22⋊C4C22semidirect
40. C2×C22⋊Dic11C22semidirect
41. #66982C22semidirect
42. C4×C22⋊D11C22semidirect
43. C2×(C2×D11)⋊C4C22semidirect
44. C2×(C2×D11)⋊C4C22semidirect
45. C2×(C2×D11)⋊C4C22semidirect
46. #66979C22semidirect
47. C2×C4⋊Dic11C22semidirect
48. C2×C4⋊Dic11C22semidirect
49. C2×C4⋊Dic11C22semidirect
50. #66977C22semidirect
51. C2×Dic11⋊C4C22semidirect
52. C2×Dic11⋊C4C22semidirect
53. C2×Dic11⋊C4C22semidirect
54. C2×Dic11⋊C4C22semidirect
55. C2×Dic11⋊C4C22semidirect
56. C2×C4×Dic11C22semidirect
57. C2×C4×Dic11C22semidirect
58. C2×C4×Dic11C22semidirect
59. #66939C22semidirect
60. #66938C22semidirect
61. #66936C22semidirect
62. (C22⋊D11)⋊C4C22semidirect
63. #66932C22semidirect
64. #66932C22semidirect
65. #66931C22semidirect
66. #66930C22semidirect
101. C2×C4×D11C23semidirect
103. C2×Dic22C23semidirect
115. (C2×D11)⋊C4C23semidirect
116. (C2×D11)⋊C4C23semidirect
117. (C2×D11)⋊C4C23semidirect
118. C4⋊Dic11C23semidirect
119. C4⋊Dic11C23semidirect
120. C4⋊Dic11C23semidirect
121. Dic11⋊C4C23semidirect
122. Dic11⋊C4C23semidirect
123. Dic11⋊C4C23semidirect
124. Dic11⋊C4C23semidirect
125. Dic11⋊C4C23semidirect
126. C4×Dic11C23semidirect
127. C4×Dic11C23semidirect
128. C4×Dic11C23semidirect
197. C22×C22⋊C4D11semidirect
276. C2×C22⋊C4C2×D11semidirect
283. C2×C11#551semidirect
350. C11C2×#551semidirect
439. C2#10623026direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C11×C22⋊C42
C2×#670062
C22×C22⋊Dic112
C2×#669822
C2×C4×C22⋊D112
C2×#669792
C2×#669772
#106230262
C2×#669392
C2×#669382
C2×#669362
C2×(C22⋊D11)⋊C42
C2×#669322
C2×#669312
C2×#669302
C2×#55111