Finite Group Databasebeta

← C2×#13082961 #15661458

Subgroups — C2×#13082961 #15661458

Order 2816.

7086 conjugacy classes of subgroups.

The subgroup lattice has 536 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082961C2132yesmaximal, direct product factor
2C2×#10623266C214yesmaximal, complemented
3C2×#10623265C211yesmaximal, characteristic, complemented
4C2×#10623110C212yesmaximal, complemented
5C2×#10623112C214yesmaximal, complemented
6C2×#10623257C214yesmaximal, complemented
7C2×#10623260C214yesmaximal, complemented
8C2×#10623113C214yesmaximal, complemented
9C2×#10623255C214yesmaximal, complemented
10C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
11C2×#10623111C212yesmaximal, complemented
12C2×Q82×C11C211yesmaximal, characteristic, complemented
13C22×#4343C2214yes—
14C22×Q8×D11C2212yes—
15Q82×C11C22116yescomplemented
16C2×C11×C4⋊Q8C2211yescharacteristic
17C2×C11×C4⋊Q8C2214yes—
18C2×C11×C4⋊Q8C2214yes—
19C2×C4×Q8×C11C2214yes—
20C2×C4×Q8×C11C2212yes—
21C2×#67000C2212yes—
22C2×#67000C2214yes—
23C2×#66999C2212yes—
24C2×#66999C2214yes—
25C2×#66999C2218yes—
26C2×#66997C2212yes—
27C2×#66997C2214yes—
28#10623266C22164yescomplemented
29#10623265C22116yescomplemented
30#10623260C22164yescomplemented
31#10623257C22164yescomplemented
32#10623255C22164yescomplemented
33D11×C4⋊Q8C22116yescomplemented
34#10623113C22164yescomplemented
35#10623112C22164yescomplemented
36#10623111C22132yescomplemented
37#10623110C22132yescomplemented
38C2×#66951C2214yes—
39C2×#66949C2218yes—
40C2×#66949C2218yes—
41C2×#66948C2212yes—
42C2×#66948C2214yes—
43C2×#66947C2218yes—
44C2×#66947C2214yes—
45C2×#66947C2218yes—
46C2×#66945C2214yes—
47C2×C4⋊C4×D11C2214yes—
48C2×C4⋊C4×D11C2214yes—
49C2×#66943C2212yes—
50C2×#66942C2218yes—
51C2×#66941C2214yes—
52C2×#66929C2218yes—
53C2×#66928C2214yes—
54C2×C4×D44C2214yes—
55C2×C4×D44C2212yes—
56C2×C4×D44C2214yes—
57C2×#66925C2214yes—
58C2×#66925C2214yes—
59C2×C42×D11C2211yescharacteristic
60C2×#66923C2214yes—
61C2×#66922C2211yescharacteristic
62C22×Q8×C11C2312yes—
63C22×Q8×C11C2314yes—
64C22×Q8×C11C2312yes—
65C2×#4343—416no—
66C2×#4343C23132yes—
67C2×Q8×D11—48no—
68C2×Q8×D11C23116yes—
69C22×D44C2312yes—
70C22×D44C2314yes—
71C22×D44C2314yes—
72C22×C4×D11C2312yes—
73C22×C4×D11C2311yescharacteristic
74C22×C4×D11C2314yes—
75C22×C4×D11C2314yes—
76C22×C4×D11C2318yes—
77C22×Dic22C2312yes—
78C22×Dic22C2314yes—
79C11×C4⋊Q8C2318yes—
80C11×C4⋊Q8C23132yes—
81C11×C4⋊Q8C23132yes—
82C4×Q8×C11C23116yes—
83C4×Q8×C11C23132yes—
84C2×C11×C4⋊C4C2314yes—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C42×C11C2311yescharacteristic
89C2×C42×C11C2314yes—
90C2×C42×C11C2314yes—
91#67000C23132yes—
92#67000C23116yes—
93#66999C23164yes—
94#66999C23132yes—
95#66999C23116yes—
96#66997C23116yes—
97#66997C23132yes—
98C2×(C2×D11)⋊C4C2314yes—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×C4⋊Dic11C2314yes—
106C2×C4⋊Dic11C2312yes—
107C2×C4⋊Dic11C2314yes—
108C2×Dic11⋊C4C2318yes—
109C2×Dic11⋊C4C2318yes—
110C2×Dic11⋊C4C2314yes—
111C2×Dic11⋊C4C2314yes—
112C2×Dic11⋊C4C2318yes—
113C2×C4×Dic11C2312yes—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2314yes—
116#66951C23132yes—
117#66949C23164yes—
118#66949C23164yes—
119#66948C23116yes—
120#66948C23132yes—
121#66947C23132yes—
122#66947C23164yes—
123#66947C23164yes—
124#66945C23132yes—
125C4⋊C4×D11C23132yes—
126C4⋊C4×D11C23132yes—
127#66943C23116yes—
128#66942C23164yes—
129#66941C23132yes—
130#66929C23164yes—
131#66928C23132yes—
132C4×D44C23132yes—
133C4×D44C23132yes—
134C4×D44C23116yes—
135#66925C23132yes—
136#66925C23132yes—
137C42×D11C2318yes—
138#66923C23132yes—
139#66922C2318yes—
140C2×#3544—111nomaximal, Sylow
141C23×D11C2414yes—
142C23×D11C2411yescharacteristic
143C2×Q8×C11—28no—
144C2×Q8×C11—44no—
145C2×Q8×C11—48no—
146C2×Q8×C11C2418yes—
147C2×Q8×C11C24116yes—
148C2×Q8×C11C2418yes—
149C22×C4×C11C2414yes—
150C22×C4×C11C2411yescharacteristic
151C22×C4×C11C2414yes—
152C22×C4×C11C2414yes—
153C22×C4×C11C2412yes—
154C22×Dic11C2412yes—
155C22×Dic11C2414yes—
156C22×Dic11C2411yescharacteristic
157C22×Dic11C2414yes—
158#4343—464no—
159Q8×D11—432no—
160C2×D44—216no—
161C2×D44—28no—
162C2×D44—48no—
163C2×D44C2418yes—
164C2×D44C24116yes—
165C2×D44C24116yes—
166C2×C4×D11—24no—
167C2×C4×D11—216no—
168C2×C4×D11—28no—
169C2×C4×D11—216no—
170C2×C4×D11—416no—
171C2×C4×D11C2418yes—
172C2×C4×D11C2414yes—
173C2×C4×D11C24116yes—
174C2×C4×D11C24116yes—
175C2×C4×D11C24132yes—
176C2×Dic22—44no—
177C2×Dic22—48no—
178C2×Dic22C2418yes—
179C2×Dic22C24116yes—
180C11×C4⋊C4C24116yes—
181C11×C4⋊C4C24132yes—
182C11×C4⋊C4C2418yes—
183C11×C4⋊C4C24116yes—
184C42×C11C2414yes—
185C42×C11C24116yes—
186C42×C11C24116yes—
187(C2×D11)⋊C4C24116yes—
188(C2×D11)⋊C4C24116yes—
189(C2×D11)⋊C4C24116yes—
190(C2×D11)⋊C4C24132yes—
191(C2×D11)⋊C4C24116yes—
192(C2×D11)⋊C4C24116yes—
193(C2×D11)⋊C4C24132yes—
194C4⋊Dic11C24116yes—
195C4⋊Dic11C2418yes—
196C4⋊Dic11C24116yes—
197Dic11⋊C4C24132yes—
198Dic11⋊C4C24132yes—
199Dic11⋊C4C24116yes—
200Dic11⋊C4C24116yes—
201Dic11⋊C4C24132yes—
202C4×Dic11C2418yes—
203C4×Dic11C2414yes—
204C4×Dic11C24116yes—
205#3544—1132no—
206C2×#563—114no—
207C2×Q82D1111yescharacteristic, complemented
208C2×#555—111no—
209C2×#554—112no—
210C2×#552—114no—
211C2×#547—114no—
212C2×#544—114no—
213C2×#542—114no—
214C2×#536—114no—
215C22×C4⋊Q8—111no—
216C2×#529—112no—
217C23×C11C2511yescharacteristic
218C22×D11—24no—
219C22×D11—28no—
220C22×D11—28no—
221C22×D11—28no—
222C22×D11H(5,𝔽2)14yes—
223C22×D11C2518yes—
224C22×D11C2512yes—
225Q8×C11—216no—
226Q8×C11—48no—
227Q8×C11—416no—
228C2×C4×C11—22no—
229C2×C4×C11—28no—
230C2×C4×C11—28no—
231C2×C4×C11—28no—
232C2×C4×C112−1+418yes—
233C2×C4×C11C2518yes—
234C2×C4×C11C2512yes—
235C2×C4×C11C2518yes—
236C2×C4×C11C2518yes—
237C2×C4×C11C2514yes—
238C2×Dic11—22no—
239C2×Dic11—28no—
240C2×Dic11—24no—
241C2×Dic11—28no—
242C2×Dic11C2514yes—
243C2×Dic11C2518yes—
244C2×Dic11C2512yes—
245C2×Dic11C2518yes—
246D44—232no—
247D44—216no—
248D44—416no—
249C4×D11—28no—
250C4×D11—232no—
251C4×D11—216no—
252C4×D11—232no—
253C4×D11—432no—
254Dic22—416no—
255Dic22—48no—
256C22×#41—114no—
257C23×Q8—112no—
258#563—1164no—
259Q82C2×D11116yescomplemented
260#555—1116no—
261#554—1132no—
262#552—1164no—
263#547—1164no—
264#544—1164no—
265#542—1164no—
266#536—1164no—
267C2×C4⋊Q8—112no—
268C2×C4⋊Q8—114no—
269C2×C4⋊Q8—1116no—
270C2×C4⋊Q8—114no—
271C2×C4⋊Q8—111no—
272C2×C4⋊Q8C2×D1111yescharacteristic
273C2×C4⋊Q8C2×D1114yes—
274C2×C4⋊Q8C2×D1114yes—
275#529—1132no—
276C2×#126—114no—
277C2×#126—118no—
278C2×#125—118no—
279C2×#125—112no—
280C2×#125—114no—
281C2×#124—112no—
282C2×#124—114no—
283C2×#124—114no—
284C2×#123—114no—
285C2×#123—118no—
286C2×#123—118no—
287C2×C22⋊Q8—112no—
288C2×C22⋊Q8—114no—
289C2×C22⋊Q8—118no—
290C2×C22⋊Q8—118no—
291C2×C22⋊Q8—118no—
292C2×#121—112no—
293C2×#121—114no—
294C2×C4×Q8C2×D1112yes—
295C2×C4×Q8C2×D1114yes—
296C2×C4×D4—114no—
297C2×C4×D4—112no—
298C2×C4×D4—114no—
299C2×#117—114no—
300C2×#117—114no—
301C2×#117—114no—
302C22×C4⋊C4—114no—
303C22×C4⋊C4—114no—
304C22×C42—111no—
305C22×C11C2×H(5,𝔽2)12yes—
306C22×C11C2×2−1+414yes—
307C22×C11C2611yescharacteristic
308C2×D11—24no—
309C2×D11—28no—
310C2×D11—28no—
311C2×D11—28no—
312C2×D11—28no—
313C2×D11—416no—
314C2×D11C2×H(5,𝔽2)14yes—
315C4×C11—22no—
316C4×C11—28no—
317C4×C11—28no—
318C4×C11—28no—
319C4×C11C2×2−1+418yes—
320Dic11—22no—
321Dic11—28no—
322Dic11—24no—
323Dic11—28no—
324C2×#41—1132no—
325C2×#41—4416no—
326C22×Q8—1116no—
327C22×Q8—112no—
328C22×Q8—114no—
329C22×Q8—448no—
330C22×Q8C22×D1112yes—
331C22×Q8C22×D1114yes—
332C22×Q8C22×D1112yes—
333C22×D4—112no—
334C22×D4—114no—
335C22×D4—114no—
336C23×C4—114no—
337C23×C4—112no—
338C23×C4—114no—
339C23×C4—111no—
340C23×C4—118no—
341C4⋊Q8—1116no—
342C4⋊Q8—1132no—
343C4⋊Q8—1132no—
344C4⋊Q8—118no—
345C4⋊Q8C22×D1118yes—
346C4⋊Q8C22×D11132yes—
347C4⋊Q8C22×D11132yes—
348#126—1132no—
349#126—1164no—
350#125—1116no—
351#125—1164no—
352#125—1132no—
353#124—1116no—
354#124—1132no—
355#124—1132no—
356#123—1132no—
357#123—1164no—
358#123—1164no—
359C22⋊Q8—1116no—
360C22⋊Q8—1132no—
361C22⋊Q8—1164no—
362C22⋊Q8—1164no—
363C22⋊Q8—1164no—
364#121—1116no—
365#121—1132no—
366C4×Q8C22×D11116yes—
367C4×Q8C22×D11132yes—
368C4×D4—1132no—
369C4×D4—1116no—
370C4×D4—1132no—
371#117—1132no—
372#117—1132no—
373#117—1132no—
374C2×C4⋊C4—114no—
375C2×C4⋊C4—118no—
376C2×C4⋊C4—118no—
377C2×C4⋊C4—112no—
378C2×C4⋊C4—118no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—1132no—
383C2×C4⋊C4—1132no—
384C2×C4⋊C4C22×D1112yes—
385C2×C4⋊C4C22×D1114yes—
386C2×C4⋊C4C22×D1114yes—
387C2×C4⋊C4C22×D1118yes—
388C2×C22⋊C4—114no—
389C2×C22⋊C4—114no—
390C2×C22⋊C4—118no—
391C2×C22⋊C4—114no—
392C2×C22⋊C4—118no—
393C2×C22⋊C4—114no—
394C2×C22⋊C4—114no—
395C2×C42—114no—
396C2×C42—112no—
397C2×C42—111no—
398C2×C42—118no—
399C2×C42C22×D1114yes—
400C2×C42C22×D1114yes—
401C2×C42C22×D1111yescharacteristic
402C2×C11#354414yescomplemented
403C2×C11C22×H(5,𝔽2)11yescharacteristic
404C2×C11C22×2−1+412yes—
405D11—24no—
406D11—48no—
407C24—111no—
408C24—114no—
409#41—4464no—
410C2×Q8—28no—
411C2×Q8—44no—
412C2×Q8—48no—
413C2×Q8—118no—
414C2×Q8—1116no—
415C2×Q8—448no—
416C2×Q8—444no—
417C2×Q8—4432no—
418C2×Q8C23×D1118yes—
419C2×Q8C23×D11116yes—
420C2×Q8C23×D1118yes—
421C2×D4—118no—
422C2×D4—1116no—
423C2×D4—1116no—
424C2×D4—2216no—
425C2×D4—228no—
426C2×D4—448no—
427C22×C4—114no—
428C22×C4—112no—
429C22×C4—111no—
430C22×C4—114no—
431C22×C4—118no—
432C22×C4—114no—
433C22×C4—1116no—
434C22×C4—1116no—
435C22×C4—1132no—
436C22×C4—224no—
437C22×C4—2216no—
438C22×C4—228no—
439C22×C4—2216no—
440C22×C4—4416no—
441C22×C4C23×D1111yescharacteristic
442C22×C4C23×D1114yes—
443C22×C4C23×D1114yes—
444C22×C4C23×D1114yes—
445C22×C4C23×D1112yes—
446C4⋊C4—1116no—
447C4⋊C4—1132no—
448C4⋊C4—1132no—
449C4⋊C4—118no—
450C4⋊C4—1132no—
451C4⋊C4—1116no—
452C4⋊C4—1116no—
453C4⋊C4—1116no—
454C4⋊C4C23×D1118yes—
455C4⋊C4C23×D11116yes—
456C4⋊C4C23×D11116yes—
457C4⋊C4C23×D11132yes—
458C22⋊C4—1116no—
459C22⋊C4—1116no—
460C22⋊C4—1132no—
461C22⋊C4—1116no—
462C22⋊C4—1132no—
463C22⋊C4—1116no—
464C22⋊C4—1116no—
465C42—118no—
466C42—114no—
467C42—1116no—
468C42C23×D1114yes—
469C42C23×D11116yes—
470C42C23×D11116yes—
471C11C2×#354411yescharacteristic, complemented, Sylow
472C23—114no—
473C23—112no—
474C23—118no—
475C23—224no—
476C23—228no—
477C23—228no—
478C23—228no—
479C23C24×D1111yescharacteristic
480Q8—216no—
481Q8—48no—
482Q8—416no—
483Q8—4416no—
484Q8—448no—
485D4—2232no—
486D4—2216no—
487D4—4416no—
488C2×C4—28no—
489C2×C4—28no—
490C2×C4—22no—
491C2×C4—28no—
492C2×C4—114no—
493C2×C4—118no—
494C2×C4—112no—
495C2×C4—118no—
496C2×C4—228no—
497C2×C4—2232no—
498C2×C4—228no—
499C2×C4—224no—
500C2×C4—228no—
501C2×C4—222no—
502C2×C4—2216no—
503C2×C4—2232no—
504C2×C4—4432no—
505C2×C4#6704018yes—
506C2×C4C24×D1112yes—
507C2×C4C24×D1118yes—
508C2×C4C24×D1118yes—
509C2×C4C24×D1118yes—
510C2×C4C24×D1114yes—
511C22—114no—
512C22—224no—
513C22—228no—
514C22—228no—
515C22—228no—
516C22—228no—
517C22—4416no—
518C22C2×#6704014yes—
519C22D11×H(5,𝔽2)12yes—
520C22C25×D1111yescharacteristic
521C4—28no—
522C4—22no—
523C4—28no—
524C4—28no—
525C4—228no—
526C4—222no—
527C4—224no—
528C4—228no—
529C4C2×#6704018yes—
530C2—224no—
531C2—448no—
532C2#1308296114yesdirect product factor
533C2C2×D11×H(5,𝔽2)11yescharacteristic
534C2C22×#6704012yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×Q82×C11C2
socleC23×C11C25
hypercenterC2×Q82D11
hypocenterC11C2×#3544
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×Q82

Complements

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

NH ≅ G/Ntype
1. #13082961C2direct (N × H)
2. C2×#10623266C2semidirect
3. C2×#10623265C2semidirect
4. C2×#10623110C2semidirect
5. C2×#10623112C2semidirect
6. C2×#10623257C2semidirect
7. C2×#10623260C2semidirect
8. C2×#10623113C2semidirect
9. C2×#10623255C2semidirect
10. C2×D11×C4⋊Q8C2semidirect
11. C2×#10623111C2semidirect
12. C2×Q82×C11C2semidirect
15. Q82×C11C22semidirect
28. #10623266C22semidirect
29. #10623265C22semidirect
30. #10623260C22semidirect
31. #10623257C22semidirect
32. #10623255C22semidirect
33. D11×C4⋊Q8C22semidirect
34. #10623113C22semidirect
35. #10623112C22semidirect
36. #10623111C22semidirect
37. #10623110C22semidirect
207. C2×Q82D11semidirect
259. Q82C2×D11semidirect
402. C2×C11#3544semidirect
471. C11C2×#3544semidirect
532. C2#13082961direct (N × H)

Maximal subgroups

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

subgroupindex
#130829612
C2×#106232662
C2×#106232652
C2×#106231102
C2×#106231122
C2×#106232572
C2×#106232602
C2×#106231132
C2×#106232552
C2×D11×C4⋊Q82
C2×#106231112
C2×Q82×C112
C2×#354411