Finite Group Databasebeta

← C2×#13074527 #14920718

Subgroups — C2×#13074527 #14920718

Order 2816.

2482 conjugacy classes of subgroups.

The subgroup lattice has 500 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66951C211yesmaximal, characteristic
2C22×#66940C211yesmaximal, characteristic, complemented
3#13074527C2116yesmaximal, direct product factor
4C2×#10622593C212yesmaximal, complemented
5C2×#10622606C211yesmaximal, characteristic
6C2×#10622289C212yesmaximal
7C2×#10622592C211yesmaximal, characteristic, complemented
8C2×#10622286C211yesmaximal, characteristic
9C2×#10622603C212yesmaximal
10C2×#10622268C212yesmaximal, complemented
11C2×#10622263C211yesmaximal, characteristic, complemented
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×Dic22C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C11×C4⋊C4C2211yescharacteristic
16C22×C11×C4⋊C4C2212yes—
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2211yescharacteristic
24C22×Dic11⋊C4C2212yes—
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2212yes—
27C22×C4×Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C2×#66951—28no—
30C2×#66951C2218yes—
31C2×#66940—28no—
32C2×#66940C2218yescomplemented
33C11×#398C2218yescomplemented
34C2×C11×#95C2211yescharacteristic
35C2×C11×#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C2218yes—
42#10622603C22116yes—
43#10622593C22116yescomplemented
44#10622592C2218yescomplemented
45#10622289C22116yes—
46#10622286C2218yes—
47#10622268C22116yescomplemented
48#10622263C2218yescomplemented
49C24×D11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×Dic11C2312yes—
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C22×Dic22—24no—
61C22×Dic22—28no—
62C22×Dic22C2314yes—
63C2×C11×C4⋊C4—24no—
64C2×C11×C4⋊C4—24no—
65C2×C11×C4⋊C4—44no—
66C2×C11×C4⋊C4C2314yes—
67C2×C11×C4⋊C4C2314yes—
68C2×C11×C4⋊C4C2318yes—
69C2×(C2×D11)⋊C4—24no—
70C2×(C2×D11)⋊C4—24no—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—28no—
73C2×(C2×D11)⋊C4—44no—
74C2×(C2×D11)⋊C4C2314yes—
75C2×(C2×D11)⋊C4C2314yes—
76C2×(C2×D11)⋊C4C2314yes—
77C2×(C2×D11)⋊C4C2318yes—
78C2×(C2×D11)⋊C4C2318yes—
79C2×C4⋊Dic11—24no—
80C2×C4⋊Dic11C2314yes—
81C2×Dic11⋊C4—28no—
82C2×Dic11⋊C4—24no—
83C2×Dic11⋊C4—28no—
84C2×Dic11⋊C4—44no—
85C2×Dic11⋊C4C2318yes—
86C2×Dic11⋊C4C2318yes—
87C2×Dic11⋊C4C2314yes—
88C2×Dic11⋊C4C2318yes—
89C2×C4×Dic11—28no—
90C2×C4×Dic11D418yes—
91C2×C4×Dic11C2318yes—
92C2×C4×Dic11C2314yes—
93#66951—232no—
94#66940—232no—
95C11×#95C2314yes—
96C11×#95C2318yes—
97C11⋊#95C2318yes—
98C11⋊#95C2314yes—
99C11⋊#95C2318yes—
100C11⋊#95C2318yes—
101C11⋊#95C2318yes—
102C2×#2637—111nomaximal, Sylow
103C24×C11C2411yescharacteristic
104C23×D11—22no—
105C23×D11—24no—
106C23×D11—22no—
107C23×D11—24no—
108C23×D11—22no—
109C23×D11C2412yes—
110C22×C4×C11—24no—
111C22×C4×C11—24no—
112C22×C4×C11—22no—
113C22×C4×C11—22no—
114C22×C4×C11—24no—
115C22×C4×C11—24no—
116C22×C4×C11—24no—
117C22×C4×C11—24no—
118C22×C4×C11—22no—
119C22×C4×C11—24no—
120C22×C4×C11—22no—
121C22×C4×C11—24no—
122C22×C4×C11C2×D414yes—
123C22×C4×C11C2414yes—
124C22×C4×C11C2412yes—
125C22×C4×C11C2414yes—
126C22×C4×C11C2412yes—
127C22×C4×C11C2412yes—
128C22×Dic11—24no—
129C22×Dic11—22no—
130C22×Dic11—24no—
131C22×Dic11—24no—
132C22×Dic11—22no—
133C22×Dic11—24no—
134C22×Dic11—24no—
135C22×Dic11—22no—
136C22×Dic11—24no—
137C22×Dic11—24no—
138C22×Dic11C2×D414yes—
139C22×Dic11C2×D414yes—
140C22×Dic11#4118yes—
141C22×Dic11C2414yes—
142C22×Dic11C2412yes—
143C22×Dic11C2412yes—
144C22×Dic11C2412yes—
145C22×Dic11C2414yes—
146C2×Dic22—232no—
147C2×Dic22—216no—
148C2×Dic22—28no—
149C11×C4⋊C4—28no—
150C11×C4⋊C4—28no—
151C11×C4⋊C4—48no—
152(C2×D11)⋊C4—28no—
153(C2×D11)⋊C4—28no—
154(C2×D11)⋊C4—216no—
155(C2×D11)⋊C4—28no—
156(C2×D11)⋊C4—48no—
157C4⋊Dic11—28no—
158Dic11⋊C4—216no—
159Dic11⋊C4—28no—
160Dic11⋊C4—216no—
161Dic11⋊C4—48no—
162C4×Dic11—216no—
163C4×Dic11C2×D4116yes—
164C22×#126—111no—
165C22×C4×Q8—111no—
166#2637—1116no—
167C2×#398—112no—
168C2×#398D1111yescharacteristic, complemented
169C2×#397—111no—
170C2×#396—112no—
171C2×#395—111no—
172C2×#393—111no—
173C2×#388—112no—
174C2×#387—112no—
175C2×#382—111no—
176C23×C11C22×D412yes—
177C23×C11C2×#4114yes—
178C23×C11H(5,𝔽2)12yes—
179C23×C112−1+414yes—
180C23×C112−1+412yes—
181C23×C11C2511yescharacteristic
182C22×D11—22no—
183C22×D11—24no—
184C22×D11—22no—
185C22×D11—24no—
186C22×D11—22no—
187C22×D11—44no—
188C22×D11—44no—
189C22×D11—44no—
190C22×D11—48no—
191C22×D11—48no—
192C2×C4×C11—28no—
193C2×C4×C11—24no—
194C2×C4×C11—24no—
195C2×C4×C11—22no—
196C2×C4×C11—22no—
197C2×C4×C11—24no—
198C2×C4×C11—24no—
199C2×C4×C11—24no—
200C2×C4×C11—24no—
201C2×C4×C11—22no—
202C2×C4×C11—24no—
203C2×C4×C11—22no—
204C2×C4×C11—24no—
205C2×C4×C11—44no—
206C2×C4×C11—48no—
207C2×C4×C11—44no—
208C2×C4×C11—48no—
209C2×C4×C11C22×D414yes—
210C2×Dic11—216no—
211C2×Dic11—28no—
212C2×Dic11—28no—
213C2×Dic11—24no—
214C2×Dic11—24no—
215C2×Dic11—22no—
216C2×Dic11—24no—
217C2×Dic11—22no—
218C2×Dic11—22no—
219C2×Dic11—24no—
220C2×Dic11—24no—
221C2×Dic11—24no—
222C2×Dic11—24no—
223C2×Dic11—44no—
224C2×Dic11—48no—
225C2×Dic11C22×D414yes—
226C2×Dic11C22×D414yes—
227C2×Dic11C2×#4118yes—
228Dic22—232no—
229C23×Q8—111no—
230C2×#126—118no—
231C2×#126—228no—
232C2×C4×Q8—118no—
233C2×C4×Q8—228no—
234C22×C4⋊C4—112no—
235C22×C4⋊C4—112no—
236C22×C4⋊C4—111no—
237C22×C4⋊C4—111no—
238C22×C4⋊C4—112no—
239C22×C4⋊C4C2×D1111yescharacteristic
240C22×C4⋊C4C2×D1111yescharacteristic
241C22×C4⋊C4C2×D1112yes—
242C22×C22⋊C4—112no—
243C22×C22⋊C4—111no—
244C22×C22⋊C4—111no—
245C22×C22⋊C4—111no—
246C22×C22⋊C4—112no—
247C22×C42—111no—
248C22×C42—112no—
249#398—1116no—
250#398C2×D1118yescomplemented
251#397—118no—
252#396—1116no—
253#395—118no—
254#393—118no—
255#388—1116no—
256#387—1116no—
257#382—118no—
258C2×#95—112no—
259C2×#95—111no—
260C2×#95—112no—
261C2×#95—112no—
262C2×#95—112no—
263C2×#95C2×D1111yescharacteristic
264C2×#95C2×D1112yes—
265C22×C11#52514yes—
266C22×C11#53614yes—
267C22×C11#53714yes—
268C22×C11#54118yes—
269C22×C11#54218yes—
270C22×C11C23×D411yescharacteristic
271C22×C11C22×#4112yes—
272C22×C11C2×H(5,𝔽2)11yescharacteristic
273C22×C11C2×2−1+412yes—
274C22×C11C2×2−1+411yescharacteristic
275C2×D11—42no—
276C2×D11—42no—
277C2×D11—42no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—88no—
281C4×C11—24no—
282C4×C11—42no—
283C4×C11—44no—
284C4×C11—42no—
285C4×C11—44no—
286Dic11—28no—
287Dic11—24no—
288Dic11—24no—
289Dic11—42no—
290Dic11—44no—
291C25—111no—
292C22×Q8—114no—
293C22×Q8—228no—
294C22×Q8—224no—
295C23×C4—111no—
296C23×C4—112no—
297C23×C4—111no—
298C23×C4—111no—
299C23×C4—112no—
300C23×C4C22×D1111yescharacteristic
301C23×C4C22×D1111yescharacteristic
302C23×C4C22×D1112yes—
303C23×C4C22×D1112yes—
304C23×C4C22×D1111yescharacteristic
305#126—2232no—
306C4×Q8—2232no—
307C2×C4⋊C4—24no—
308C2×C4⋊C4—24no—
309C2×C4⋊C4—44no—
310C2×C4⋊C4—118no—
311C2×C4⋊C4—114no—
312C2×C4⋊C4—114no—
313C2×C4⋊C4—118no—
314C2×C4⋊C4—118no—
315C2×C4⋊C4—228no—
316C2×C4⋊C4—224no—
317C2×C4⋊C4—224no—
318C2×C4⋊C4—228no—
319C2×C4⋊C4—444no—
320C2×C4⋊C4C22×D1114yes—
321C2×C4⋊C4C22×D1114yes—
322C2×C4⋊C4C22×D1118yes—
323C2×C22⋊C4—114no—
324C2×C22⋊C4—114no—
325C2×C22⋊C4—114no—
326C2×C22⋊C4—118no—
327C2×C22⋊C4—118no—
328C2×C22⋊C4—224no—
329C2×C22⋊C4—224no—
330C2×C22⋊C4—228no—
331C2×C22⋊C4—224no—
332C2×C22⋊C4—444no—
333C2×C42—118no—
334C2×C42—114no—
335C2×C42—118no—
336C2×C42—228no—
337#95—118no—
338#95—114no—
339#95—118no—
340#95—118no—
341#95—118no—
342#95C22×D1114yes—
343#95C22×D1118yes—
344C2×C11#263718yescomplemented
345C2×C11C2×#52511yescharacteristic
346C2×C11C2×#53611yescharacteristic
347C2×C11C2×#53711yescharacteristic
348C2×C11C2×#54112yes—
349C2×C11C2×#54212yes—
350D11—82no—
351C24—112no—
352C24—222no—
353C24—222no—
354C24—224no—
355C24—224no—
356C24—222no—
357C24C23×D1111yescharacteristic
358C2×Q8—2216no—
359C2×Q8—2232no—
360C2×Q8—228no—
361C22×C4—24no—
362C22×C4—24no—
363C22×C4—22no—
364C22×C4—22no—
365C22×C4—24no—
366C22×C4—22no—
367C22×C4—24no—
368C22×C4—24no—
369C22×C4—24no—
370C22×C4—24no—
371C22×C4—22no—
372C22×C4—24no—
373C22×C4—114no—
374C22×C4—114no—
375C22×C4—118no—
376C22×C4—112no—
377C22×C4—114no—
378C22×C4—112no—
379C22×C4—112no—
380C22×C4—114no—
381C22×C4—224no—
382C22×C4—222no—
383C22×C4—224no—
384C22×C4—224no—
385C22×C4—222no—
386C22×C4—222no—
387C22×C4—224no—
388C22×C4—224no—
389C22×C4—224no—
390C22×C4—224no—
391C22×C4D4×D1114yes—
392C22×C4C23×D1114yes—
393C22×C4C23×D1112yes—
394C22×C4C23×D1114yes—
395C22×C4C23×D1112yes—
396C22×C4C23×D1112yes—
397C4⋊C4—28no—
398C4⋊C4—28no—
399C4⋊C4—48no—
400C4⋊C4—2216no—
401C4⋊C4—228no—
402C4⋊C4—228no—
403C4⋊C4—2216no—
404C4⋊C4—448no—
405C22⋊C4—228no—
406C22⋊C4—228no—
407C22⋊C4—2216no—
408C22⋊C4—228no—
409C22⋊C4—448no—
410C42—1116no—
411C42—2216no—
412C11C2×#263711yescharacteristic, complemented, Sylow
413C23—222no—
414C23—222no—
415C23—224no—
416C23—224no—
417C23—222no—
418C23—444no—
419C23—444no—
420C23—448no—
421C23—444no—
422C23—448no—
423C23C2×D4×D1112yes—
424C23#6703712yes—
425C23#6704014yes—
426C23#41×D1114yes—
427C23#6704312yes—
428C23C24×D1111yescharacteristic
429Q8—2232no—
430C2×C4—28no—
431C2×C4—24no—
432C2×C4—24no—
433C2×C4—22no—
434C2×C4—22no—
435C2×C4—24no—
436C2×C4—22no—
437C2×C4—24no—
438C2×C4—24no—
439C2×C4—24no—
440C2×C4—24no—
441C2×C4—22no—
442C2×C4—24no—
443C2×C4—48no—
444C2×C4—44no—
445C2×C4—48no—
446C2×C4—44no—
447C2×C4—114no—
448C2×C4—114no—
449C2×C4—118no—
450C2×C4—228no—
451C2×C4—228no—
452C2×C4—2216no—
453C2×C4—224no—
454C2×C4—222no—
455C2×C4—224no—
456C2×C4—224no—
457C2×C4—222no—
458C2×C4—222no—
459C2×C4—224no—
460C2×C4—224no—
461C2×C4—224no—
462C2×C4—224no—
463C2×C4—444no—
464C2×C4—448no—
465C2×C4C2×D4×D1114yes—
466C22—442no—
467C22—442no—
468C22—444no—
469C22—444no—
470C22—442no—
471C22—888no—
472C22#1062313914yes—
473C22#1062317118yes—
474C22#1062318714yes—
475C22#1062322718yes—
476C22#1062325514yes—
477C22C22×D4×D1111yescharacteristic
478C22C2×#6703711yescharacteristic
479C22C2×#6704012yes—
480C22C2×#41×D1112yes—
481C22C2×#6704311yescharacteristic
482C4—24no—
483C4—44no—
484C4—42no—
485C4—44no—
486C4—42no—
487C4—224no—
488C4—224no—
489C4—228no—
490C4—442no—
491C4—444no—
492C2—882no—
493C2#1307452718yesdirect product factor
494C2C2×#1062318711yescharacteristic
495C2C2×#1062325511yescharacteristic
496C2C2×#1062313911yescharacteristic
497C2C2×#1062322712yes—
498C2C2×#1062317112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×#398D11
hypocenterC11C2×#2637
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
2. C22×#66940C2semidirect
3. #13074527C2direct (N × H)
4. C2×#10622593C2semidirect
7. C2×#10622592C2semidirect
10. C2×#10622268C2semidirect
11. C2×#10622263C2semidirect
12. C2×C11×#398C2semidirect
32. C2×#66940C22semidirect
33. C11×#398C22semidirect
43. #10622593C22semidirect
44. #10622592C22semidirect
47. #10622268C22semidirect
48. #10622263C22semidirect
168. C2×#398D11semidirect
250. #398C2×D11semidirect
344. C2×C11#2637semidirect
412. C11C2×#2637semidirect
493. C2#13074527direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669512
C22×#669402
#130745272
C2×#106225932
C2×#106226062
C2×#106222892
C2×#106225922
C2×#106222862
C2×#106226032
C2×#106222682
C2×#106222632
C2×C11×#3982
C2×#263711