Finite Group Databasebeta

← C2×#13077460 #15617883

Subgroups — C2×#13077460 #15617883

Order 2816.

2730 conjugacy classes of subgroups.

The subgroup lattice has 578 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic
2C2×#10623343C211yesmaximal, characteristic, complemented
3#13077460C2116yesmaximal, direct product factor
4C2×#10622797C212yesmaximal, complemented
5C2×#10622777C212yesmaximal, complemented
6C2×Q16×Dic11C212yesmaximal, complemented
7C2×SD16×Dic11C212yesmaximal, complemented
8C2×#10622734C211yesmaximal, characteristic, complemented
9C2×#10622846C211yesmaximal, characteristic
10C22×#66899C211yesmaximal, characteristic, complemented
11C2×#10622735C211yesmaximal, characteristic, complemented
12C22×C11×#137C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C23×Q8×C11C2211yescharacteristic
15C2×C11×#137C4116yescomplemented
16C2×C11×#137C2218yes—
17C22×C11×Q16C2212yes—
18C22×C11×SD16C2212yes—
19C22×C11×M16C2211yescharacteristic
20#10623358—24no—
21#10623358C2218yes—
22#10623343—24no—
23#10623343C2218yescomplemented
24C2×Q8×Dic11—21no—
25C2×Q8×Dic11—21no—
26C2×Q8×Dic11C2212yes—
27C2×Q8×Dic11C2212yes—
28C2×Q8×Dic11C2212yes—
29C2×D4×Dic11—22no—
30C2×D4×Dic11C2212yes—
31C2×#66979—22no—
32C2×#66979—21no—
33C2×#66979C2211yescharacteristic
34C2×#66979C2211yescharacteristic
35C22×C4⋊Dic11—21no—
36C22×C4⋊Dic11C2211yescharacteristic
37C23×C11⋊C8C2211yescharacteristic
38#10622846C2218yes—
39C2×#66899C2212yes—
40C2×#66899C2212yes—
41C2×#66899C2211yescharacteristic
42C2×#66899C2211yescharacteristic
43C2×#66899C2218yescomplemented
44C2×#66896C2211yescharacteristic
45C2×#66896C2211yescharacteristic
46#10622797C22116yescomplemented
47Q16×Dic11C22116yescomplemented
48#10622777C22116yescomplemented
49SD16×Dic11C22116yescomplemented
50#10622735C2218yescomplemented
51#10622734C2218yescomplemented
52C2×#66882C2212yes—
53C2×#66881C2212yes—
54C2×#66879C2212yes—
55C2×C8×Dic11C2212yes—
56C2×C11×#41—22no—
57C2×C11×#41—24no—
58C2×C11×#41C2×C418yes—
59C2×C11×#41C2314yes—
60C22×Q8×C11—21no—
61C22×Q8×C11—22no—
62C22×Q8×C11—24no—
63C22×Q8×C11C2×C418yescomplemented
64C22×Q8×C11C2312yes—
65C22×Q8×C11C2311yescharacteristic
66C22×Q8×C11C2314yes—
67C22×D4×C11—21no—
68C22×D4×C11C2311yescharacteristic
69C23×C4×C11—21no—
70C23×C4×C11—21no—
71C23×C4×C11C2311yescharacteristic
72C23×Dic11—21no—
73C23×Dic11—22no—
74C11×#137C2×C4164yescomplemented
75C2×C11×Q16C2×C4116yescomplemented
76C2×C11×Q16C2318yes—
77C2×C11×SD16C2×C4116yescomplemented
78C2×C11×SD16C2318yes—
79C2×C11×M16C2×C418yescomplemented
80C2×C11×M16C2314yes—
81C22×C8×C11C2312yes—
82C2×C22⋊Dic11—21no—
83C2×C22⋊Dic11—22no—
84C2×C22⋊Dic11D412yes—
85Q8×Dic11—28no—
86Q8×Dic11—28no—
87Q8×Dic11—24no—
88Q8×Dic11—24no—
89Q8×Dic11—24no—
90Q8×Dic11C2318yes—
91Q8×Dic11C2318yes—
92Q8×Dic11C2318yes—
93D4×Dic11—216no—
94D4×Dic11—24no—
95D4×Dic11C2318yes—
96#66979—22no—
97#66979—216no—
98#66979—28no—
99#66979D414yes—
100#66979C2314yes—
101#66979C2314yes—
102C2×C4⋊Dic11—21no—
103C2×C4⋊Dic11—22no—
104C2×C4⋊Dic11—22no—
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—28no—
108C2×C4⋊Dic11D411yescharacteristic
109C2×C4⋊Dic11D411yescharacteristic
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2312yes—
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114C2×C4×Dic11—21no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11C2312yes—
119C22×C11⋊C8—24no—
120C22×C11⋊C8C2314yes—
121C22×C11⋊C8C2311yescharacteristic
122C22×C11⋊C8C2311yescharacteristic
123#66899C2318yes—
124#66899C2318yes—
125#66899C2314yes—
126#66899C2314yes—
127#66896C2314yes—
128#66896C2314yes—
129#66882C2318yes—
130#66881C2318yes—
131#66879C2318yes—
132C8×Dic11C2318yes—
133C2×#2947—111nomaximal, Sylow
134C24×C11—21no—
135C24×C11C2×D411yescharacteristic
136C11×#41—216no—
137C11×#41—28no—
138C11×#41C22×C4116yes—
139C2×Q8×C11—28no—
140C2×Q8×C11—216no—
141C2×Q8×C11—24no—
142C2×Q8×C11—22no—
143C2×Q8×C11—21no—
144C2×Q8×C11—24no—
145C2×Q8×C11—28no—
146C2×Q8×C11—22no—
147C2×Q8×C11C22×C418yes—
148C2×Q8×C11C22×C414yes—
149C2×Q8×C11C22×C4116yescomplemented
150C2×Q8×C11C2414yes—
151C2×Q8×C11C2412yes—
152C2×D4×C11—28no—
153C2×D4×C11—24no—
154C2×D4×C11—21no—
155C2×D4×C11—22no—
156C2×D4×C11C22×C414yes—
157C2×D4×C11C2412yes—
158C22×C4×C11—28no—
159C22×C4×C11—21no—
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—28no—
163C22×C4×C11—24no—
164C22×C4×C11C22×C414yes—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D412yes—
167C22×C4×C11#4114yes—
168C22×C4×C11C2411yescharacteristic
169C22×C4×C11C2412yes—
170C22×Dic11—28no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—82no—
176C22×Dic11—84no—
177C22×Dic11C2×D412yes—
178C22×Dic11C2×D412yes—
179C11×Q16C22×C4132yescomplemented
180C11×SD16C22×C4132yescomplemented
181C11×M16C22×C4116yescomplemented
182C2×C8×C11C22×C418yes—
183C2×C8×C11C2414yes—
184C22⋊Dic11—28no—
185C22⋊Dic11—24no—
186C22⋊Dic11C2×D418yes—
187C4⋊Dic11—28no—
188C4⋊Dic11—28no—
189C4⋊Dic11—28no—
190C4⋊Dic11—24no—
191C4⋊Dic11—22no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2×D414yes—
195C4⋊Dic11C2×D414yes—
196C4⋊Dic11C2412yes—
197C4⋊Dic11C2414yes—
198C4⋊Dic11C2412yes—
199C4×Dic11—28no—
200C4×Dic11—28no—
201C4×Dic11—28no—
202C4×Dic11—24no—
203C4×Dic11C2×D414yes—
204C4×Dic11C2414yes—
205C2×C11⋊C8—22no—
206C2×C11⋊C8—22no—
207C2×C11⋊C8—28no—
208C2×C11⋊C8C2412yes—
209C2×C11⋊C8C2412yes—
210C22×#137D1111yescharacteristic
211C2×#520—111no—
212C2×#519—111no—
213#2947—1116no—
214C2×#441—112no—
215C2×#440—112no—
216C2×C4×Q16—112no—
217C2×C4×SD16—112no—
218C2×#428—111no—
219C2×#416—111no—
220C22×#103—111no—
221C2×#405—111no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—22no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11C4×D414yes—
229C23×C11C22×D412yes—
230C23×C11C22×D411yescharacteristic
231Q8×C11—28no—
232Q8×C11—216no—
233Q8×C11—24no—
234Q8×C11—24no—
235Q8×C11—22no—
236Q8×C11C23×C418yes—
237Q8×C11C23×C414yes—
238D4×C11—216no—
239D4×C11—24no—
240D4×C11—22no—
241D4×C11C23×C414yes—
242C2×C4×C11—24no—
243C2×C4×C11—28no—
244C2×C4×C11—216no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—216no—
248C2×C4×C11C4×D414yes—
249C2×C4×C11C4×D418yes—
250C2×C4×C11C23×C412yes—
251C2×C4×C11C23×C414yes—
252C2×C4×C11C22×D412yes—
253C2×C4×C11C22×D411yescharacteristic
254C2×C4×C11C2×#4112yes—
255C2×C4×C11C2×#4114yes—
256C2×C4×C11C2511yescharacteristic
257C2×Dic11—24no—
258C2×Dic11—24no—
259C2×Dic11—22no—
260C2×Dic11—22no—
261C2×Dic11—24no—
262C2×Dic11—42no—
263C2×Dic11—44no—
264C2×Dic11—42no—
265C2×Dic11—88no—
266C2×Dic11—84no—
267C2×Dic11C22×D414yes—
268C2×Dic11C22×D414yes—
269C8×C11C23×C418yes—
270C11⋊C8—22no—
271C11⋊C8—22no—
272C22×#41C2×D1111yescharacteristic
273C23×Q8C2×D1111yescharacteristic
274C2×#137Dic11116yescomplemented
275C2×#137C2×D1118yes—
276C22×Q16C2×D1112yes—
277C22×SD16C2×D1112yes—
278C22×M16C2×D1111yescharacteristic
279C23×C8—111no—
280#520—118no—
281#520—224no—
282#519—118no—
283#519—224no—
284C2×C4×Q8—112no—
285C2×C4×Q8—112no—
286C2×C4×Q8—112no—
287C2×C4×Q8—221no—
288C2×C4×Q8—221no—
289C2×C4×D4—112no—
290C2×C4×D4—222no—
291C2×#117—111no—
292C2×#117—111no—
293C2×#117—222no—
294C2×#117—221no—
295C22×C4⋊C4—111no—
296C22×C4⋊C4—221no—
297#441—1116no—
298#440—1116no—
299C4×Q16—1116no—
300C4×SD16—1116no—
301#428—118no—
302C2×#107—112no—
303C2×#106—112no—
304#416—118no—
305C2×#103—112no—
306C2×#103—112no—
307C2×#103—118no—
308C2×#103—111no—
309C2×#103—111no—
310C2×#102—111no—
311C2×#102—111no—
312#405—118no—
313C2×#97—112no—
314C2×C4×C8—112no—
315C22×C11—28no—
316C22×C11—22no—
317C22×C11—22no—
318C22×C11—24no—
319C22×C11—48no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11C2×C4×D414yes—
323C22×C11C2×C4×D412yes—
324C22×C11#57712yes—
325C22×C11#57812yes—
326C22×C11C23×D411yescharacteristic
327C4×C11—24no—
328C4×C11—28no—
329C4×C11C2×C4×D414yes—
330C4×C11C2×C4×D412yes—
331C4×C11C24×C411yescharacteristic
332C4×C11C22×#4111yescharacteristic
333Dic11—24no—
334Dic11—24no—
335Dic11—42no—
336Dic11—44no—
337Dic11—42no—
338C2×#41—22no—
339C2×#41—24no—
340C2×#41C2×Dic1118yes—
341C2×#41C22×D1114yes—
342C22×Q8—21no—
343C22×Q8—22no—
344C22×Q8—24no—
345C22×Q8C2×Dic1118yescomplemented
346C22×Q8C22×D1112yes—
347C22×Q8C22×D1111yescharacteristic
348C22×Q8C22×D1114yes—
349C22×D4—21no—
350C22×D4C22×D1111yescharacteristic
351C23×C4—21no—
352C23×C4—21no—
353C23×C4—222no—
354C23×C4—221no—
355C23×C4C22×D1111yescharacteristic
356#137C2×Dic11164yescomplemented
357C2×Q16C2×Dic11116yescomplemented
358C2×Q16C22×D1118yes—
359C2×SD16C2×Dic11116yescomplemented
360C2×SD16C22×D1118yes—
361C2×M16C2×Dic1118yescomplemented
362C2×M16C22×D1114yes—
363C22×C8—111no—
364C22×C8—111no—
365C22×C8—114no—
366C22×C8—224no—
367C22×C8C22×D1112yes—
368C4×Q8—118no—
369C4×Q8—118no—
370C4×Q8—118no—
371C4×Q8—224no—
372C4×Q8—224no—
373C4×Q8—224no—
374C4×Q8—228no—
375C4×Q8—228no—
376C4×D4—118no—
377C4×D4—224no—
378C4×D4—2216no—
379#117—114no—
380#117—114no—
381#117—114no—
382#117—2216no—
383#117—228no—
384#117—222no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—111no—
390C2×C4⋊C4—111no—
391C2×C4⋊C4—228no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—222no—
394C2×C4⋊C4—222no—
395C2×C4⋊C4—221no—
396C2×C4⋊C4—222no—
397C2×C22⋊C4—112no—
398C2×C22⋊C4—222no—
399C2×C22⋊C4—221no—
400C2×C42—112no—
401C2×C42—222no—
402C2×C42—222no—
403C2×C42—222no—
404C2×C42—221no—
405#107—118no—
406#106—118no—
407#103—118no—
408#103—118no—
409#103—114no—
410#103—114no—
411#102—114no—
412#102—114no—
413#97—118no—
414C4×C8—118no—
415C2×C11—24no—
416C2×C11—44no—
417C2×C11#294714yescomplemented
418C2×C11C22×C4×D411yescharacteristic
419C2×C11C2×#57711yescharacteristic
420C2×C11C2×#57811yescharacteristic
421C24—21no—
422C24D4×D1111yescharacteristic
423#41—216no—
424#41—28no—
425#41C22×Dic11116yes—
426C2×Q8—28no—
427C2×Q8—216no—
428C2×Q8—22no—
429C2×Q8—24no—
430C2×Q8—21no—
431C2×Q8—24no—
432C2×Q8—28no—
433C2×Q8—22no—
434C2×Q8C22×Dic1118yes—
435C2×Q8C22×Dic1114yes—
436C2×Q8C22×Dic11116yescomplemented
437C2×Q8C23×D1114yes—
438C2×Q8C23×D1112yes—
439C2×D4—28no—
440C2×D4—24no—
441C2×D4—21no—
442C2×D4—22no—
443C2×D4C22×Dic1114yes—
444C2×D4C23×D1112yes—
445C22×C4—28no—
446C22×C4—24no—
447C22×C4—21no—
448C22×C4—22no—
449C22×C4—28no—
450C22×C4—24no—
451C22×C4—112no—
452C22×C4—112no—
453C22×C4—228no—
454C22×C4—221no—
455C22×C4—221no—
456C22×C4—222no—
457C22×C4—224no—
458C22×C4—884no—
459C22×C4—882no—
460C22×C4D4×D1112yes—
461C22×C4D4×D1111yescharacteristic
462C22×C4#434114yes—
463C22×C4C22×Dic1114yes—
464C22×C4C23×D1112yes—
465C22×C4C23×D1111yescharacteristic
466Q16C22×Dic11132yescomplemented
467SD16C22×Dic11132yescomplemented
468M16C22×Dic11116yescomplemented
469C2×C8—112no—
470C2×C8—112no—
471C2×C8—222no—
472C2×C8—222no—
473C2×C8—228no—
474C2×C8C22×Dic1118yes—
475C2×C8C23×D1114yes—
476C4⋊C4—114no—
477C4⋊C4—114no—
478C4⋊C4—112no—
479C4⋊C4—112no—
480C4⋊C4—114no—
481C4⋊C4—228no—
482C4⋊C4—228no—
483C4⋊C4—228no—
484C4⋊C4—224no—
485C4⋊C4—222no—
486C4⋊C4—221no—
487C4⋊C4—221no—
488C22⋊C4—118no—
489C22⋊C4—228no—
490C22⋊C4—224no—
491C42—114no—
492C42—114no—
493C42—228no—
494C42—228no—
495C42—228no—
496C42—224no—
497C11C2×#294711yescharacteristic, complemented, Sylow
498C23—22no—
499C23—22no—
500C23—24no—
501C23—22no—
502C23—42no—
503C23—42no—
504C23D4×Dic1114yes—
505C23C2×D4×D1112yes—
506C23C2×D4×D1111yescharacteristic
507Q8—28no—
508Q8—216no—
509Q8—24no—
510Q8—24no—
511Q8—22no—
512Q8C23×Dic1118yes—
513Q8C23×Dic1114yes—
514D4—216no—
515D4—24no—
516D4—22no—
517D4C23×Dic1114yes—
518C2×C4—24no—
519C2×C4—28no—
520C2×C4—216no—
521C2×C4—22no—
522C2×C4—24no—
523C2×C4—216no—
524C2×C4—114no—
525C2×C4—114no—
526C2×C4—224no—
527C2×C4—224no—
528C2×C4—222no—
529C2×C4—222no—
530C2×C4—224no—
531C2×C4—444no—
532C2×C4—442no—
533C2×C4—442no—
534C2×C4—888no—
535C2×C4—884no—
536C2×C4D4×Dic1114yes—
537C2×C4D4×Dic1118yes—
538C2×C4C2×D4×D1111yescharacteristic
539C2×C4C2×D4×D1112yes—
540C2×C4C2×#434112yes—
541C2×C4C2×#434114yes—
542C2×C4C23×Dic1112yes—
543C2×C4C23×Dic1114yes—
544C2×C4C24×D1111yescharacteristic
545C8—222no—
546C8—222no—
547C8C23×Dic1118yes—
548C22—28no—
549C22—22no—
550C22—22no—
551C22—24no—
552C22—48no—
553C22—42no—
554C22—42no—
555C22#1062330912yes—
556C22#1062331012yes—
557C22C2×D4×Dic1114yes—
558C22C2×D4×Dic1112yes—
559C22C22×D4×D1111yescharacteristic
560C4—24no—
561C4—28no—
562C4—224no—
563C4—224no—
564C4—444no—
565C4—442no—
566C4—442no—
567C4C2×D4×Dic1114yes—
568C4C2×D4×Dic1112yes—
569C4C22×#434111yescharacteristic
570C4C24×Dic1111yescharacteristic
571C2—24no—
572C2—44no—
573C2#1307746014yesdirect product factor
574C2C22×D4×Dic1111yescharacteristic
575C2C2×#1062330911yescharacteristic
576C2C2×#1062331011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
prime radicalC22×C11×#41C22
cosocleC2×C4×C11C25
hypercenterC22×#137D11
hypocenterC11C2×#2947
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
2. C2×#10623343C2semidirect
3. #13077460C2direct (N × H)
4. C2×#10622797C2semidirect
5. C2×#10622777C2semidirect
6. C2×Q16×Dic11C2semidirect
7. C2×SD16×Dic11C2semidirect
8. C2×#10622734C2semidirect
10. C22×#66899C2semidirect
11. C2×#10622735C2semidirect
15. C2×C11×#137C4semidirect
23. #10623343C22semidirect
43. C2×#66899C22semidirect
46. #10622797C22semidirect
47. Q16×Dic11C22semidirect
48. #10622777C22semidirect
49. SD16×Dic11C22semidirect
50. #10622735C22semidirect
51. #10622734C22semidirect
63. C22×Q8×C11C2×C4semidirect
74. C11×#137C2×C4semidirect
75. C2×C11×Q16C2×C4semidirect
77. C2×C11×SD16C2×C4semidirect
79. C2×C11×M16C2×C4semidirect
149. C2×Q8×C11C22×C4semidirect
179. C11×Q16C22×C4semidirect
180. C11×SD16C22×C4semidirect
181. C11×M16C22×C4semidirect
274. C2×#137Dic11semidirect
345. C22×Q8C2×Dic11semidirect
356. #137C2×Dic11semidirect
357. C2×Q16C2×Dic11semidirect
359. C2×SD16C2×Dic11semidirect
361. C2×M16C2×Dic11semidirect
417. C2×C11#2947semidirect
436. C2×Q8C22×Dic11semidirect
466. Q16C22×Dic11semidirect
467. SD16C22×Dic11semidirect
468. M16C22×Dic11semidirect
497. C11C2×#2947semidirect
573. C2#13077460direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233582
C2×#106233432
#130774602
C2×#106227972
C2×#106227772
C2×Q16×Dic112
C2×SD16×Dic112
C2×#106227342
C2×#106228462
C22×#668992
C2×#106227352
C22×C11×#1372
C2×#294711