Finite Group Databasebeta

← C2×#13081616 #15634695

Subgroups — C2×#13081616 #15634695

Order 2816.

2022 conjugacy classes of subgroups.

The subgroup lattice has 554 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623244C211yesmaximal, characteristic, complemented
2C2×#10623073C211yesmaximal, characteristic, complemented
3#13081616C2116yesmaximal, direct product factor
4C2×#10622768C212yesmaximal, complemented
5C2×#10622689C211yesmaximal, characteristic, complemented
6C2×#10622380C212yesmaximal, complemented
7C2×#10622462C211yesmaximal, characteristic, complemented
8C2×#10622766C212yesmaximal, complemented
9C2×#10622443C211yesmaximal, characteristic, complemented
10C2×#10622371C212yesmaximal, complemented
11C2×C4×#4324C211yesmaximal, characteristic, complemented
12C2×C11×#459C211yesmaximal, characteristic
13C22×C11×D8C2212yes—
14C2×C11×#127C2211yescharacteristic
15C2×C4×D4×C11C2211yescharacteristic
16C2×#66989—21no—
17C2×#66989C2212yes—
18C2×#66989C2212yes—
19C2×#66988—22no—
20C2×D4×Dic11—21no—
21C2×D4×Dic11C2212yes—
22C22×#4324C2211yescharacteristic
23C22×#4324C2212yes—
24C22×#4324C2212yes—
25C2×#66979—21no—
26C2×#66977—21no—
27C22×Dic44C2212yes—
28#10623244—24no—
29#10623244C2218yescomplemented
30#10623073—24no—
31#10623073C2218yescomplemented
32C2×#66940C2212yes—
33C2×#66932—22no—
34C2×#66922C2211yescharacteristic
35C2×C4×Dic22C2211yescharacteristic
36C2×C4×Dic22C2211yescharacteristic
37C11×#459C2218yes—
38C2×C11×C4⋊C8C2211yescharacteristic
39C2×C11×#102C2212yes—
40C2×#66896C2211yescharacteristic
41#10622768C22116yescomplemented
42#10622766C22116yescomplemented
43C2×#66880C2212yes—
44C2×Dic11⋊C8C2212yes—
45C2×C8×Dic11C2212yes—
46#10622689C2218yescomplemented
47C4×#4324C2218yescomplemented
48C2×#66874C2211yescharacteristic
49C2×#66872C2211yescharacteristic
50C2×C4×C11⋊C8C2211yescharacteristic
51#10622462C2218yescomplemented
52#10622443C2218yescomplemented
53#10622380C22116yescomplemented
54#10622371C22116yescomplemented
55C22×D4×C11—21no—
56C22×D4×C11—21no—
57C22×D4×C11C2312yes—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C23×Dic11—22no—
61C22×Dic22D411yescharacteristic
62C22×Dic22C2311yescharacteristic
63C22×Dic22C2312yes—
64C2×C11×D8—44no—
65C2×C11×D8C2318yes—
66C22×C8×C11C2312yes—
67C11×#127—22no—
68C11×#127C2314yes—
69C4×D4×C11—22no—
70C4×D4×C11C2314yes—
71C2×C11×C4⋊C4C2311yescharacteristic
72C2×C11×C22⋊C4—21no—
73C2×C42×C11C2311yescharacteristic
74C2×C22⋊Dic11—22no—
75C2×C22⋊Dic11—22no—
76C2×C22⋊Dic11—22no—
77C2×C22⋊Dic11—22no—
78C2×C22⋊Dic11—22no—
79#66989—28no—
80#66989—24no—
81#66989—24no—
82#66989C2318yes—
83#66989C2318yes—
84#66988—216no—
85D4×Dic11—28no—
86D4×Dic11—24no—
87D4×Dic11C2318yes—
88C2×#4324—24no—
89C2×#4324—28no—
90C2×#4324—44no—
91C2×#4324C2314yes—
92C2×#4324C2318yes—
93C2×#4324C2318yes—
94#66979—28no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11D411yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99#66977—28no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4D412yes—
103C2×C4×Dic11—21no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11C2312yes—
106C22×C11⋊C8C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C2×Dic44—44no—
109C2×Dic44C2318yes—
110#66940—24no—
111#66940C2318yes—
112#66932—216no—
113#66922—22no—
114#66922C2314yes—
115C4×Dic22—22no—
116C4×Dic22D414yes—
117C4×Dic22C2314yes—
118C4×Dic22C2314yes—
119C11×C4⋊C8C2314yes—
120C11×#102C2318yes—
121#66896C2314yes—
122#66880C2318yes—
123Dic11⋊C8C2318yes—
124C8×Dic11C2318yes—
125#66874C2314yes—
126#66872C2314yes—
127C4×C11⋊C8C2314yes—
128C2×#3394—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—22no—
131C2×D4×C11—22no—
132C2×D4×C11—24no—
133C2×D4×C11—21no—
134C2×D4×C11—24no—
135C2×D4×C11—24no—
136C2×D4×C11—22no—
137C2×D4×C11—24no—
138C2×D4×C11—22no—
139C2×D4×C11—44no—
140C2×D4×C11—82no—
141C2×D4×C11C2412yes—
142C2×D4×C11C2414yes—
143C22×C4×C11—21no—
144C22×C4×C11—24no—
145C22×C4×C11—44no—
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2411yescharacteristic
149C22×Dic11—28no—
150C22×Dic11—22no—
151C22×Dic11—21no—
152C22×Dic11—21no—
153C22×Dic11—84no—
154C22×Dic11C2×D412yes—
155C22×Dic11C2×D412yes—
156C2×Dic22—24no—
157C2×Dic22—21no—
158C2×Dic22—22no—
159C2×Dic22—22no—
160C2×Dic22—24no—
161C2×Dic22—22no—
162C2×Dic22—24no—
163C2×Dic22C2×D414yes—
164C2×Dic22C2412yes—
165C2×Dic22C2414yes—
166C11×D8—48no—
167C2×C8×C11—24no—
168C2×C8×C11C2414yes—
169C11×C4⋊C4—21no—
170C11×C4⋊C4C2412yes—
171C11×C22⋊C4—24no—
172C42×C11C2×D412yes—
173C42×C11C2412yes—
174C22⋊Dic11—28no—
175C22⋊Dic11—28no—
176C22⋊Dic11—28no—
177C22⋊Dic11—28no—
178C22⋊Dic11—28no—
179#4324—28no—
180#4324—216no—
181#4324—48no—
182C4⋊Dic11—21no—
183C4⋊Dic11—24no—
184C4⋊Dic11—24no—
185C4⋊Dic11C2×D414yes—
186C4⋊Dic11C2412yes—
187Dic11⋊C4—28no—
188Dic11⋊C4—24no—
189Dic11⋊C4C2×D418yes—
190C4×Dic11—28no—
191C4×Dic11—24no—
192C4×Dic11C2×D414yes—
193C4×Dic11C2414yes—
194C2×C11⋊C8—22no—
195C2×C11⋊C8#4114yes—
196C2×C11⋊C8C2412yes—
197C2×C11⋊C8C2412yes—
198Dic44—48no—
199C2×#559—111no—
200C2×#556—111no—
201#3394—1116no—
202C2×#495—112no—
203C2×#492—111no—
204C2×#464—112no—
205C2×#462—111no—
206C2×#463—112no—
207C2×#459D1111yescharacteristic
208C2×C8×Q8—111no—
209C2×C4×SD16—112no—
210C2×C4×SD16—111no—
211C23×C11—22no—
212C23×C11—24no—
213C23×C11—44no—
214C23×C11—42no—
215C23×C11—42no—
216C23×C11—44no—
217C23×C11—44no—
218C23×C11—42no—
219C23×C11C22×D411yescharacteristic
220D4×C11—22no—
221D4×C11—24no—
222D4×C11—24no—
223D4×C11—22no—
224D4×C11—44no—
225D4×C11—42no—
226D4×C11—48no—
227D4×C11—84no—
228C2×C4×C11—22no—
229C2×C4×C11—22no—
230C2×C4×C11—42no—
231C2×C4×C11—48no—
232C2×C4×C11#13514yes—
233C2×C4×C11C22×D412yes—
234C2×C4×C11C22×D411yescharacteristic
235C2×C4×C11C22×D412yes—
236C2×C4×C11C2×#4112yes—
237C2×C4×C11H(5,𝔽2)12yes—
238C2×C4×C11C2511yescharacteristic
239C2×Dic11—24no—
240C2×Dic11—24no—
241C2×Dic11—24no—
242C2×Dic11—22no—
243C2×Dic11—22no—
244C2×Dic11—42no—
245C2×Dic11—44no—
246C2×Dic11—42no—
247C2×Dic11—88no—
248C2×Dic11C22×D414yes—
249C2×Dic11C22×D414yes—
250Dic22—28no—
251Dic22—22no—
252Dic22—24no—
253Dic22—22no—
254Dic22—24no—
255Dic22—42no—
256Dic22—44no—
257C8×C11—24no—
258C11⋊C8—22no—
259C11⋊C8C2×#4114yes—
260C22×Q16—112no—
261C22×SD16—112no—
262C22×SD16—111no—
263C22×SD16—112no—
264C22×D8C2×D1112yes—
265#559—118no—
266#559—224no—
267#556—118no—
268#556—224no—
269C2×C4⋊Q8—111no—
270C2×#127C2×D1111yescharacteristic
271C2×#126—222no—
272C2×#124—112no—
273C2×#124—112no—
274C2×#124—221no—
275C2×#123—222no—
276C2×C22⋊Q8—221no—
277C2×C4×Q8—111no—
278C2×C4×Q8—112no—
279C2×C4×Q8—111no—
280C2×C4×D4—112no—
281C2×C4×D4—221no—
282C2×C4×D4C2×D1111yescharacteristic
283C2×#117—221no—
284#495—1116no—
285#492—118no—
286#464—1116no—
287#463—1116no—
288#462—118no—
289#459C2×D1118yes—
290C8×Q8—118no—
291C4×SD16—118no—
292C4×SD16—1116no—
293C2×#106—111no—
294C2×C4⋊C8—112no—
295C2×C4⋊C8C2×D1111yescharacteristic
296C2×#103—112no—
297C2×#103—111no—
298C2×#102—111no—
299C2×#102C2×D1112yes—
300C2×C4×C8—112no—
301C2×C4×C8—111no—
302C22×C11—44no—
303C22×C11—42no—
304C22×C11—42no—
305C22×C11—44no—
306C22×C11—44no—
307C22×C11—42no—
308C22×C11—84no—
309C22×C11—88no—
310C22×C11#55012yes—
311C22×C11C2×#13512yes—
312C22×C11#57712yes—
313C22×C11C23×D411yescharacteristic
314C4×C11—22no—
315C4×C11—42no—
316C4×C11#55012yes—
317C4×C11C2×#13514yes—
318C4×C11C22×#4111yescharacteristic
319C4×C11C2×H(5,𝔽2)11yescharacteristic
320Dic11—24no—
321Dic11—24no—
322Dic11—42no—
323Dic11—44no—
324Dic11—42no—
325C22×Q8—111no—
326C22×Q8—111no—
327C22×Q8—112no—
328C22×D4—21no—
329C22×D4—21no—
330C22×D4C22×D1112yes—
331C22×D4C22×D1111yescharacteristic
332C23×C4—21no—
333C23×C4—222no—
334C2×Q16—118no—
335C2×Q16—444no—
336C2×SD16—118no—
337C2×SD16—114no—
338C2×SD16—118no—
339C2×SD16—228no—
340C2×SD16—224no—
341C2×SD16—444no—
342C2×D8—44no—
343C2×D8C22×D1118yes—
344C22×C8—111no—
345C22×C8—111no—
346C22×C8C22×D1112yes—
347C4⋊Q8—114no—
348C4⋊Q8—222no—
349#127—22no—
350#127C22×D1114yes—
351#126—2216no—
352#124—118no—
353#124—118no—
354#124—224no—
355#124—224no—
356#124—228no—
357#123—2216no—
358C22⋊Q8—228no—
359C4×Q8—114no—
360C4×Q8—114no—
361C4×Q8—118no—
362C4×Q8—114no—
363C4×Q8—224no—
364C4×Q8—222no—
365C4×D4—22no—
366C4×D4—118no—
367C4×D4—224no—
368C4×D4—228no—
369C4×D4C22×D1114yes—
370#117—228no—
371C2×C4⋊C4—111no—
372C2×C4⋊C4—112no—
373C2×C4⋊C4—111no—
374C2×C4⋊C4—222no—
375C2×C4⋊C4—221no—
376C2×C4⋊C4—221no—
377C2×C4⋊C4—221no—
378C2×C4⋊C4C22×D1111yescharacteristic
379C2×C22⋊C4—21no—
380C2×C22⋊C4—222no—
381C2×C22⋊C4—222no—
382C2×C22⋊C4—222no—
383C2×C22⋊C4—222no—
384C2×C22⋊C4—222no—
385C2×C42—112no—
386C2×C42—222no—
387C2×C42—221no—
388C2×C42C22×D1111yescharacteristic
389#106—114no—
390C4⋊C8—118no—
391C4⋊C8C22×D1114yes—
392#103—118no—
393#103—114no—
394#102—114no—
395#102C22×D1118yes—
396C4×C8—118no—
397C4×C8—114no—
398C2×C11—82no—
399C2×C11—84no—
400C2×C11#339414yescomplemented
401C2×C11C2×#55011yescharacteristic
402C2×C11C22×#13511yescharacteristic
403C2×C11C2×#57711yescharacteristic
404C24—21no—
405C24—22no—
406C2×Q8—114no—
407C2×Q8—112no—
408C2×Q8—114no—
409C2×Q8—224no—
410C2×Q8—221no—
411C2×Q8—222no—
412C2×Q8—224no—
413C2×Q8—222no—
414C2×Q8—222no—
415C2×Q8—224no—
416C2×D4—21no—
417C2×D4—22no—
418C2×D4—24no—
419C2×D4—24no—
420C2×D4—22no—
421C2×D4—24no—
422C2×D4—24no—
423C2×D4—22no—
424C2×D4—44no—
425C2×D4—82no—
426C2×D4C23×D1112yes—
427C2×D4C23×D1114yes—
428C22×C4—21no—
429C22×C4—24no—
430C22×C4—44no—
431C22×C4—112no—
432C22×C4—112no—
433C22×C4—228no—
434C22×C4—221no—
435C22×C4—221no—
436C22×C4—222no—
437C22×C4—884no—
438C22×C4D4×D1111yescharacteristic
439C22×C4D4×D1111yescharacteristic
440C22×C4C23×D1111yescharacteristic
441Q16—448no—
442SD16—2216no—
443SD16—228no—
444SD16—448no—
445D8—48no—
446C2×C8—24no—
447C2×C8—114no—
448C2×C8—112no—
449C2×C8—112no—
450C2×C8—222no—
451C2×C8C23×D1114yes—
452C4⋊C4—21no—
453C4⋊C4—114no—
454C4⋊C4—118no—
455C4⋊C4—112no—
456C4⋊C4—228no—
457C4⋊C4—221no—
458C4⋊C4—224no—
459C4⋊C4—224no—
460C4⋊C4—224no—
461C4⋊C4C23×D1112yes—
462C22⋊C4—24no—
463C22⋊C4—228no—
464C22⋊C4—228no—
465C22⋊C4—228no—
466C22⋊C4—228no—
467C22⋊C4—228no—
468C42—114no—
469C42—114no—
470C42—228no—
471C42—224no—
472C42D4×D1112yes—
473C42C23×D1112yes—
474C11C2×#339411yescharacteristic, complemented, Sylow
475C23—22no—
476C23—24no—
477C23—42no—
478C23—44no—
479C23—44no—
480C23—42no—
481C23—42no—
482C23—44no—
483C23C2×D4×D1111yescharacteristic
484Q8—228no—
485Q8—224no—
486Q8—222no—
487Q8—222no—
488Q8—224no—
489Q8—442no—
490Q8—444no—
491D4—22no—
492D4—24no—
493D4—22no—
494D4—24no—
495D4—48no—
496D4—42no—
497D4—44no—
498D4—84no—
499C2×C4—22no—
500C2×C4—22no—
501C2×C4—42no—
502C2×C4—48no—
503C2×C4—114no—
504C2×C4—114no—
505C2×C4—224no—
506C2×C4—224no—
507C2×C4—222no—
508C2×C4—222no—
509C2×C4—224no—
510C2×C4—442no—
511C2×C4—442no—
512C2×C4—444no—
513C2×C4—888no—
514C2×C4#6696514yes—
515C2×C4C2×D4×D1112yes—
516C2×C4C2×D4×D1112yes—
517C2×C4C2×D4×D1111yescharacteristic
518C2×C4#6703712yes—
519C2×C4#41×D1112yes—
520C2×C4C24×D1111yescharacteristic
521C8—24no—
522C8—114no—
523C8—222no—
524C22—42no—
525C22—44no—
526C22—42no—
527C22—44no—
528C22—44no—
529C22—42no—
530C22—84no—
531C22—88no—
532C22#1062313012yes—
533C22C2×#6696512yes—
534C22#1062330612yes—
535C22C22×D4×D1111yescharacteristic
536C4—22no—
537C4—42no—
538C4—224no—
539C4—224no—
540C4—442no—
541C4—444no—
542C4—442no—
543C4#1062313012yes—
544C4C2×#6696514yes—
545C4C2×#6703711yescharacteristic
546C4C2×#41×D1111yescharacteristic
547C2—82no—
548C2—84no—
549C2#1308161614yesdirect product factor
550C2C2×#1062313011yescharacteristic
551C2C22×#6696511yescharacteristic
552C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#459C2
socleC23×C11C22×D4
hypercenterC2×#459D11
hypocenterC11C2×#3394
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#459

Complements

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

NH ≅ G/Ntype
1. C2×#10623244C2semidirect
2. C2×#10623073C2semidirect
3. #13081616C2direct (N × H)
4. C2×#10622768C2semidirect
5. C2×#10622689C2semidirect
6. C2×#10622380C2semidirect
7. C2×#10622462C2semidirect
8. C2×#10622766C2semidirect
9. C2×#10622443C2semidirect
10. C2×#10622371C2semidirect
11. C2×C4×#4324C2semidirect
29. #10623244C22semidirect
31. #10623073C22semidirect
41. #10622768C22semidirect
42. #10622766C22semidirect
46. #10622689C22semidirect
47. C4×#4324C22semidirect
51. #10622462C22semidirect
52. #10622443C22semidirect
53. #10622380C22semidirect
54. #10622371C22semidirect
400. C2×C11#3394semidirect
474. C11C2×#3394semidirect
549. C2#13081616direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232442
C2×#106230732
#130816162
C2×#106227682
C2×#106226892
C2×#106223802
C2×#106224622
C2×#106227662
C2×#106224432
C2×#106223712
C2×C4×#43242
C2×C11×#4592
C2×#339411