Finite Group Databasebeta

← C2×#13079568 #15624979

Subgroups — C2×#13079568 #15624979

Order 2816.

2186 conjugacy classes of subgroups.

The subgroup lattice has 502 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic
2#13079568C2116yesmaximal, direct product factor
3C2×#10622705C211yesmaximal, characteristic, complemented
4C2×#10622698C211yesmaximal, characteristic, complemented
5C2×#10622706C211yesmaximal, characteristic, complemented
6C2×#10622701C211yesmaximal, characteristic, complemented
7C2×#10622641C214yesmaximal, complemented
8C2×#10622660C214yesmaximal, complemented
9C2×#10622538C211yesmaximal, characteristic, complemented
10C2×C11×#533C211yesmaximal, characteristic, complemented
11C22×#4339C2212yes—
12C11×#533—24no—
13C11×#533C2218yescomplemented
14C2×C11×C4⋊Q8C2211yescharacteristic
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#125—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C4×Q8×C11—21no—
20C2×C4×Q8×C11C2212yes—
21C2×C11×#117—21no—
22C22×C42×C11C2211yescharacteristic
23C22×#4326C2214yes—
24C22×#4325C2214yes—
25C2×#66983—21no—
26C2×#66983—21no—
27#10623008—24no—
28#10623008C2218yes—
29C2×#66928C2212yes—
30C2×#66927C2211yescharacteristic
31C2×C4×D44—21no—
32C2×C4×D44—21no—
33C2×#66922C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2212yes—
35#10622706C2218yescomplemented
36#10622705C2218yescomplemented
37#10622701C2218yescomplemented
38#10622698C2218yescomplemented
39#10622660C22132yescomplemented
40#10622641C22132yescomplemented
41C2×#66874C2214yes—
42C2×#66873C2214yes—
43#10622538C2218yescomplemented
44C2×C4⋊(C11⋊C8)C2212yes—
45C2×C4×C11⋊C8C2211yescharacteristic
46C2×C4×C11⋊C8C2211yescharacteristic
47C22×Q8×C11—21no—
48C22×Q8×C11C2312yes—
49C23×C4×C11D411yescharacteristic
50C23×C4×C11D411yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C22×C22⋊D11—22no—
53C2×#4339—24no—
54C2×#4339—48no—
55C2×#4339C2318yes—
56C22×D44—21no—
57C22×D44—21no—
58C22×D44C2312yes—
59C22×C4×D11—22no—
60C22×Dic22C2312yes—
61C11×C4⋊Q8—22no—
62C11×C4⋊Q8—22no—
63C11×C4⋊Q8C2314yes—
64C11×C4⋊Q8C2314yes—
65C11×#125—28no—
66C11×C22⋊Q8—28no—
67C11×C22⋊Q8—24no—
68C11×C22⋊Q8C2318yes—
69C4×Q8×C11—28no—
70C4×Q8×C11—24no—
71C4×Q8×C11C2318yes—
72C11×#117—28no—
73C2×C11×C4⋊C4—21no—
74C2×C11×C4⋊C4—21no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—22no—
77C2×C11×C4⋊C4—22no—
78C2×C11×C4⋊C4C2312yes—
79C2×C11×C22⋊C4—22no—
80C2×C42×C11—22no—
81C2×C42×C11D411yescharacteristic
82C2×C42×C11D411yescharacteristic
83C2×C42×C11D414yes—
84C2×C42×C11C2311yescharacteristic
85C2×C42×C11C2311yescharacteristic
86C2×C42×C11C2314yes—
87C2×#4326—48no—
88C2×#4326C23116yes—
89C2×#4325—48no—
90C2×#4325C23116yes—
91#66983—28no—
92#66983—28no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C22×C11⋊C8C2312yes—
98C22×C11⋊C8C2312yes—
99#66928—24no—
100#66928C2318yes—
101#66927—22no—
102#66927C2314yes—
103C4×D44—28no—
104C4×D44—28no—
105#66922—22no—
106#66922C2314yes—
107C22⋊(C11⋊C8)C2318yes—
108#66874C23116yes—
109#66873C23116yes—
110C4⋊(C11⋊C8)C2318yes—
111C4×C11⋊C8C2314yes—
112C4×C11⋊C8C2314yes—
113C2×#3210—111nomaximal, Sylow
114C24×C11C2×D411yescharacteristic
115C23×D11—22no—
116C2×Q8×C11—22no—
117C2×Q8×C11—24no—
118C2×Q8×C11—28no—
119C2×Q8×C11—44no—
120C2×Q8×C11C2414yes—
121C22×C4×C11—24no—
122C22×C4×C11—24no—
123C22×C4×C11—24no—
124C22×C4×C11—22no—
125C22×C4×C11—22no—
126C22×C4×C11C2×D411yescharacteristic
127C22×C4×C11C2×D411yescharacteristic
128C22×C4×C11C2×D414yes—
129C22×C4×C11C2×D414yes—
130C22×C4×C11C2×D411yescharacteristic
131C22×C4×C11C2×D412yes—
132C22×C4×C11C2×D411yescharacteristic
133C22×C4×C11C2×D411yescharacteristic
134C22×C4×C11C2412yes—
135C22×C4×C11C2411yescharacteristic
136C2×C22⋊D11—28no—
137C2×C22⋊D11—48no—
138C22×Dic11—22no—
139#4339—416no—
140#4339—416no—
141C2×D44—24no—
142C2×D44—24no—
143C2×D44—22no—
144C2×D44—28no—
145C2×D44—44no—
146C2×D44—44no—
147C2×D44C2414yes—
148C2×C4×D11—28no—
149C2×C4×D11—48no—
150C2×Dic22—22no—
151C2×Dic22—28no—
152C2×Dic22C2414yes—
153C11×C4⋊C4—24no—
154C11×C4⋊C4—24no—
155C11×C4⋊C4—24no—
156C11×C4⋊C4—28no—
157C11×C4⋊C4—28no—
158C11×C4⋊C4—22no—
159C11×C4⋊C4C2414yes—
160C11×C22⋊C4—28no—
161C42×C11—28no—
162C42×C11C2×D412yes—
163C42×C11C2×D414yes—
164C42×C11C2×D414yes—
165C42×C11C2×D412yes—
166C42×C11C2412yes—
167C42×C11C2412yes—
168#4326—416no—
169#4325—416no—
170(C2×D11)⋊C4—28no—
171(C2×D11)⋊C4—28no—
172C4⋊Dic11—24no—
173C4⋊Dic11—24no—
174C2×C11⋊C8—24no—
175C2×C11⋊C8—24no—
176C2×C11⋊C8C2414yes—
177C2×C11⋊C8C2414yes—
178C2×#533D1111yescharacteristic, complemented
179C2×#532—111no—
180#3210—1116no—
181C2×#494—111no—
182C2×#492—111no—
183C2×#487—111no—
184C2×#486—111no—
185C2×#464—114no—
186C2×#452—114no—
187C2×#431—111no—
188C23×C11—22no—
189C23×C11—22no—
190C23×C11—22no—
191C23×C11C22×D412yes—
192C23×C11C22×D411yescharacteristic
193C22×D11—24no—
194C22×D11—44no—
195C22×D11—44no—
196C22×D11—44no—
197Q8×C11—28no—
198Q8×C11—44no—
199Q8×C11—48no—
200C2×C4×C11—22no—
201C2×C4×C11—22no—
202C2×C4×C11—22no—
203C2×C4×C11—24no—
204C2×C4×C11—28no—
205C2×C4×C11—28no—
206C2×C4×C11—24no—
207C2×C4×C11—24no—
208C2×C4×C11—24no—
209C2×C4×C11—44no—
210C2×C4×C11—44no—
211C2×C4×C11#13514yes—
212C2×C4×C11#13714yes—
213C2×C4×C11C22×D412yes—
214C2×C4×C11C22×D412yes—
215C2×C4×C11C22×D412yes—
216C2×C4×C11C22×D411yescharacteristic
217C2×C4×C11C22×D412yes—
218C2×C4×C11C22×D412yes—
219C2×C4×C11H(5,𝔽2)14yes—
220C2×C4×C11C2511yescharacteristic
221C22⋊D11—416no—
222C2×Dic11—24no—
223C2×Dic11—44no—
224D44—28no—
225D44—44no—
226D44—48no—
227D44—48no—
228C4×D11—416no—
229Dic22—28no—
230Dic22—44no—
231C11⋊C8—24no—
232C11⋊C8—24no—
233C22×#41—112no—
234C22×Q16—114no—
235C22×SD16—114no—
236#533—24no—
237#533C2×D1118yescomplemented
238#532—118no—
239#532—224no—
240C2×C4⋊Q8—111no—
241C2×C4⋊Q8C2×D1111yescharacteristic
242C2×C4⋊Q8C2×D1111yescharacteristic
243C2×#127—111no—
244C2×#125—21no—
245C2×#124—112no—
246C2×C22⋊Q8—21no—
247C2×C22⋊Q8C2×D1112yes—
248C2×#121—221no—
249C2×#121—221no—
250C2×C4×Q8—21no—
251C2×C4×Q8C2×D1112yes—
252C2×C4×D4—221no—
253C2×C4×D4—221no—
254C2×#117—21no—
255C22×C42C2×D1111yescharacteristic
256#494—118no—
257#492—118no—
258#487—118no—
259#486—118no—
260#464—1132no—
261#452—1132no—
262#431—118no—
263C2×C4⋊C8—112no—
264C2×#103—114no—
265C2×#102—114no—
266C2×C22⋊C8—112no—
267C2×C4×C8—111no—
268C2×C4×C8—111no—
269C22×C11—22no—
270C22×C11—22no—
271C22×C11—22no—
272C22×C11—44no—
273C22×C11#53512yes—
274C22×C11C2×#13512yes—
275C22×C11C2×#13712yes—
276C22×C11C23×D411yescharacteristic
277C2×D11—44no—
278C2×D11—44no—
279C2×D11—44no—
280C2×D11—88no—
281C4×C11—22no—
282C4×C11—22no—
283C4×C11—22no—
284C4×C11—44no—
285C4×C11—44no—
286C4×C11#53512yes—
287C4×C11C2×#13514yes—
288C4×C11C2×#13714yes—
289C4×C11C2×H(5,𝔽2)12yes—
290Dic11—44no—
291C2×#41—118no—
292C2×#41—224no—
293C2×#41—448no—
294C22×Q8—21no—
295C22×Q8—112no—
296C22×Q8C22×D1112yes—
297C22×D4—112no—
298C22×D4—222no—
299C22×D4—221no—
300C22×D4—221no—
301C23×C4—222no—
302C23×C4C22⋊D1111yescharacteristic
303C23×C4C22⋊D1111yescharacteristic
304C23×C4C22×D1111yescharacteristic
305C2×Q16—1116no—
306C2×Q16—448no—
307C2×SD16—1116no—
308C2×SD16—448no—
309C22×C8—112no—
310C22×C8—112no—
311C4⋊Q8—22no—
312C4⋊Q8—22no—
313C4⋊Q8—114no—
314C4⋊Q8—222no—
315C4⋊Q8C22×D1114yes—
316C4⋊Q8C22×D1114yes—
317#127—114no—
318#127—222no—
319#125—28no—
320#124—118no—
321#124—224no—
322C22⋊Q8—28no—
323C22⋊Q8—24no—
324C22⋊Q8C22×D1118yes—
325#121—228no—
326#121—228no—
327C4×Q8—28no—
328C4×Q8—24no—
329C4×Q8C22×D1118yes—
330C4×D4—228no—
331C4×D4—228no—
332#117—28no—
333C2×C4⋊C4—21no—
334C2×C4⋊C4—21no—
335C2×C4⋊C4—21no—
336C2×C4⋊C4—22no—
337C2×C4⋊C4—22no—
338C2×C4⋊C4—221no—
339C2×C4⋊C4—221no—
340C2×C4⋊C4C22×D1112yes—
341C2×C22⋊C4—22no—
342C2×C22⋊C4—222no—
343C2×C22⋊C4—222no—
344C2×C42—22no—
345C2×C42C22⋊D1111yescharacteristic
346C2×C42C22⋊D1111yescharacteristic
347C2×C42C22⋊D1114yes—
348C2×C42C22×D1111yescharacteristic
349C2×C42C22×D1111yescharacteristic
350C2×C42C22×D1114yes—
351C4⋊C8—118no—
352#103—1116no—
353#102—1116no—
354C22⋊C8—118no—
355C4×C8—114no—
356C4×C8—114no—
357C2×C11—42no—
358C2×C11#321014yescomplemented
359C2×C11C2×#53511yescharacteristic
360C2×C11C22×#13511yescharacteristic
361C2×C11C22×#13711yescharacteristic
362D11—84no—
363C24—222no—
364C24C2×C22⋊D1111yescharacteristic
365#41—4416no—
366#41—4416no—
367C2×Q8—22no—
368C2×Q8—24no—
369C2×Q8—28no—
370C2×Q8—44no—
371C2×Q8—114no—
372C2×Q8—222no—
373C2×Q8—228no—
374C2×Q8C23×D1114yes—
375C2×D4—114no—
376C2×D4—228no—
377C2×D4—228no—
378C2×D4—224no—
379C2×D4—224no—
380C2×D4—222no—
381C2×D4—448no—
382C2×D4—444no—
383C2×D4—444no—
384C22×C4—24no—
385C22×C4—24no—
386C22×C4—24no—
387C22×C4—22no—
388C22×C4—22no—
389C22×C4—222no—
390C22×C4—228no—
391C22×C4—448no—
392C22×C4C2×C22⋊D1114yes—
393C22×C4C2×C22⋊D1114yes—
394C22×C4C2×C22⋊D1112yes—
395C22×C4C2×C22⋊D1111yescharacteristic
396C22×C4C2×C22⋊D1111yescharacteristic
397C22×C4C2×C22⋊D1111yescharacteristic
398C22×C4C2×C22⋊D1111yescharacteristic
399C22×C4C2×C22⋊D1111yescharacteristic
400C22×C4C23×D1112yes—
401C22×C4C23×D1111yescharacteristic
402Q16—4416no—
403SD16—4416no—
404C2×C8—114no—
405C2×C8—114no—
406C2×C8—224no—
407C2×C8—224no—
408C4⋊C4—24no—
409C4⋊C4—24no—
410C4⋊C4—24no—
411C4⋊C4—28no—
412C4⋊C4—28no—
413C4⋊C4—22no—
414C4⋊C4—224no—
415C4⋊C4—224no—
416C4⋊C4C23×D1114yes—
417C22⋊C4—28no—
418C22⋊C4—228no—
419C22⋊C4—228no—
420C42—28no—
421C42C2×C22⋊D1114yes—
422C42C2×C22⋊D1114yes—
423C42C2×C22⋊D1112yes—
424C42C2×C22⋊D1112yes—
425C42C23×D1112yes—
426C42C23×D1112yes—
427C11C2×#321011yescharacteristic, complemented, Sylow
428C23—22no—
429C23—22no—
430C23—22no—
431C23—224no—
432C23—444no—
433C23—444no—
434C23—444no—
435C23C22×C22⋊D1112yes—
436C23C22×C22⋊D1111yescharacteristic
437Q8—28no—
438Q8—48no—
439Q8—44no—
440Q8—228no—
441Q8—444no—
442D4—228no—
443D4—4416no—
444D4—448no—
445D4—448no—
446D4—444no—
447C2×C4—22no—
448C2×C4—22no—
449C2×C4—22no—
450C2×C4—28no—
451C2×C4—28no—
452C2×C4—24no—
453C2×C4—24no—
454C2×C4—24no—
455C2×C4—24no—
456C2×C4—44no—
457C2×C4—44no—
458C2×C4—224no—
459C2×C4—4416no—
460C2×C4—444no—
461C2×C4#6699514yes—
462C2×C4#6700314yes—
463C2×C4#6704214yes—
464C2×C4C22×C22⋊D1112yes—
465C2×C4C22×C22⋊D1112yes—
466C2×C4C22×C22⋊D1112yes—
467C2×C4C22×C22⋊D1112yes—
468C2×C4C22×C22⋊D1112yes—
469C2×C4C22×C22⋊D1111yescharacteristic
470C2×C4C24×D1111yescharacteristic
471C8—224no—
472C8—224no—
473C22—22no—
474C22—22no—
475C22—22no—
476C22—44no—
477C22—444no—
478C22—444no—
479C22—444no—
480C22—888no—
481C22C2×#6699512yes—
482C22C2×#6700312yes—
483C22#1062336112yes—
484C22C23×C22⋊D1111yescharacteristic
485C4—22no—
486C4—22no—
487C4—22no—
488C4—44no—
489C4—44no—
490C4—444no—
491C4C2×#6699514yes—
492C4C2×#6700314yes—
493C4#1062336112yes—
494C4C2×#6704212yes—
495C2—42no—
496C2—884no—
497C2#1307956814yesdirect product factor
498C2C2×#1062336111yescharacteristic
499C2C22×#6700311yescharacteristic
500C2C22×#6699511yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#533C2
socleC23×C11C22×D4
prime radicalC2×#10623008C2
hypercenterC2×#533D11
hypocenterC11C2×#3210
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#533

Complements

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

NH ≅ G/Ntype
2. #13079568C2direct (N × H)
3. C2×#10622705C2semidirect
4. C2×#10622698C2semidirect
5. C2×#10622706C2semidirect
6. C2×#10622701C2semidirect
7. C2×#10622641C2semidirect
8. C2×#10622660C2semidirect
9. C2×#10622538C2semidirect
10. C2×C11×#533C2semidirect
13. C11×#533C22semidirect
35. #10622706C22semidirect
36. #10622705C22semidirect
37. #10622701C22semidirect
38. #10622698C22semidirect
39. #10622660C22semidirect
40. #10622641C22semidirect
43. #10622538C22semidirect
178. C2×#533D11semidirect
237. #533C2×D11semidirect
358. C2×C11#3210semidirect
427. C11C2×#3210semidirect
497. C2#13079568direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
#130795682
C2×#106227052
C2×#106226982
C2×#106227062
C2×#106227012
C2×#106226412
C2×#106226602
C2×#106225382
C2×C11×#5332
C2×#321011