Finite Group Databasebeta

← C2×#13079322 #15623693

Subgroups — C2×#13079322 #15623693

Order 2816.

1998 conjugacy classes of subgroups.

The subgroup lattice has 576 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623259C211yesmaximal, characteristic, complemented
2C2×#10623211C211yesmaximal, characteristic
3#13079322C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622695C211yesmaximal, characteristic, complemented
6C2×#10622668C211yesmaximal, characteristic, complemented
7C2×#10622801C212yesmaximal, complemented
8C2×#10622784C212yesmaximal
9C2×#10622797C212yesmaximal, complemented
10C2×#10622777C212yesmaximal, complemented
11C2×D11×#97C211yesmaximal, characteristic, complemented
12C2×C11×#497C211yesmaximal, characteristic, complemented
13C22×C11×Q16C2212yes—
14C22×C11×SD16C2212yes—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C11×#124C2211yescharacteristic
17C2×#66999C2211yescharacteristic
18C2×#66999C2212yes—
19C2×Q8×Dic11C2211yescharacteristic
20C2×Q8×Dic11C2212yes—
21C2×#66991C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C22×C8×D11C2212yes—
24#10623259—24no—
25#10623259C2218yescomplemented
26#10623211—24no—
27#10623211C2218yes—
28C2×#66950—21no—
29C2×#66945—21no—
30C2×#66943—21no—
31C2×#66940—21no—
32C2×#66936—21no—
33C2×(C22⋊D11)⋊C4—21no—
34C2×#66932—21no—
35C2×#66930—21no—
36C2×C42×D11C2211yescharacteristic
37C2×#66923C2211yescharacteristic
38C2×#66922C2211yescharacteristic
39C11×#497C2218yescomplemented
40C2×C11×#97C2211yescharacteristic
41C2×#66899C2212yes—
42C2×#66899C2212yes—
43C2×#66899C2212yes—
44C2×#66896C2212yes—
45#10622801C22116yescomplemented
46#10622797C22116yescomplemented
47#10622784C22116yes—
48#10622777C22116yescomplemented
49C2×#66882C2212yes—
50C2×#66881C2212yes—
51C2×#66879C2212yes—
52#10622695C2218yescomplemented
53#10622668C2218yescomplemented
54C2×#66867C2211yescharacteristic
55D11×#97C2218yescomplemented
56#10622315C2218yescomplemented
57C22×Q8×C11C2311yescharacteristic
58C22×Q8×C11C2312yes—
59C22×D4×C11C2311yescharacteristic
60C22×C22⋊D11—21no—
61C23×Dic11—21no—
62C22×C4×D11D411yescharacteristic
63C22×C4×D11D411yescharacteristic
64C22×C4×D11C2311yescharacteristic
65C22×Dic22—21no—
66C2×C11×Q16—28no—
67C2×C11×Q16C2318yes—
68C2×C11×SD16—28no—
69C2×C11×SD16C2318yes—
70C22×C8×C11C2312yes—
71C11×C4⋊Q8—22no—
72C11×C4⋊Q8C2314yes—
73C11×#124—22no—
74C11×#124C2314yes—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4—21no—
77C2×C11×C22⋊C4—21no—
78C2×C11×C22⋊C4—21no—
79C2×C42×C11C2311yescharacteristic
80C2×C22⋊Dic11—21no—
81C2×C22⋊Dic11—21no—
82#66999—24no—
83#66999—22no—
84#66999C2318yes—
85#66999C2314yes—
86Q8×Dic11—24no—
87Q8×Dic11—22no—
88Q8×Dic11C2318yes—
89Q8×Dic11C2314yes—
90#66991—22no—
91#66991C2314yes—
92D4×Dic11—22no—
93D4×Dic11C2314yes—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—22no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—22no—
99C2×C4⋊Dic11C2312yes—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—22no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—22no—
108C2×C4×Dic11D411yescharacteristic
109C2×C4×Dic11D411yescharacteristic
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2312yes—
112C2×C8×D11—28no—
113C2×C8×D11C2318yes—
114#66950—28no—
115#66945—28no—
116#66943—28no—
117#66940—28no—
118#66936—28no—
119(C22⋊D11)⋊C4—28no—
120#66932—28no—
121#66930—28no—
122C42×D11D414yes—
123C42×D11C2314yes—
124#66923—22no—
125#66923C2314yes—
126#66922—22no—
127#66922C2314yes—
128C11×#97C2314yes—
129#66899C2318yes—
130#66899C2318yes—
131#66899C2318yes—
132#66896C2318yes—
133#66882C2318yes—
134#66881C2318yes—
135#66879C2318yes—
136#66867C2314yes—
137C2×#3181—111nomaximal, Sylow
138C24×C11—21no—
139C23×D11C2×D411yescharacteristic
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—24no—
143C2×Q8×C11—24no—
144C2×Q8×C11—24no—
145C2×Q8×C11C2412yes—
146C2×Q8×C11C2414yes—
147C2×D4×C11—21no—
148C2×D4×C11—24no—
149C2×D4×C11C2412yes—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11C2×D411yescharacteristic
153C22×C4×C11C2×D411yescharacteristic
154C22×C4×C11C2411yescharacteristic
155C2×C22⋊D11—24no—
156C2×C22⋊D11—44no—
157C22×Dic11—24no—
158C22×Dic11—21no—
159C22×Dic11—22no—
160C22×Dic11—21no—
161C22×Dic11—44no—
162C22×Dic11C2×D411yescharacteristic
163C22×Dic11C2×D411yescharacteristic
164C22×Dic11C2×D411yescharacteristic
165C2×C4×D11—24no—
166C2×C4×D11—24no—
167C2×C4×D11—42no—
168C2×C4×D11C2×D412yes—
169C2×C4×D11C2×D414yes—
170C2×C4×D11C2×D414yes—
171C2×C4×D11C2412yes—
172C2×Dic22—24no—
173C2×Dic22—44no—
174C11×Q16—216no—
175C11×SD16—216no—
176C2×C8×C11#4118yes—
177C2×C8×C11C2414yes—
178C11×C4⋊C4—24no—
179C11×C4⋊C4—24no—
180C11×C22⋊C4—24no—
181C11×C22⋊C4—24no—
182C42×C11C2×D412yes—
183C42×C11C2412yes—
184C22⋊Dic11—24no—
185C22⋊Dic11—24no—
186(C2×D11)⋊C4—24no—
187(C2×D11)⋊C4—28no—
188C4⋊Dic11—24no—
189C4⋊Dic11—28no—
190C4⋊Dic11—22no—
191C4⋊Dic11—24no—
192C4⋊Dic11—21no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2412yes—
195C4⋊Dic11C2414yes—
196C4⋊Dic11C2412yes—
197Dic11⋊C4—24no—
198Dic11⋊C4—28no—
199Dic11⋊C4—24no—
200Dic11⋊C4—24no—
201C4×Dic11—24no—
202C4×Dic11—28no—
203C4×Dic11C2×D412yes—
204C4×Dic11C2×D414yes—
205C4×Dic11C2×D414yes—
206C4×Dic11C2412yes—
207C2×C11⋊C8—24no—
208C2×C11⋊C8C2414yes—
209C8×D11—216no—
210C2×#533—111no—
211C2×#529—111no—
212#3181—1116no—
213C2×#501—111no—
214C2×#497D1111yescharacteristic, complemented
215C2×#491—111no—
216C2×#489—111no—
217C2×#467—112no—
218C2×#465—112no—
219C2×#441—112no—
220C2×#440—112no—
221C22×#97—111no—
222C23×C11—22no—
223C23×C11—42no—
224C23×C11—42no—
225C23×C11—42no—
226C23×C11C22×D411yescharacteristic
227C22×D11—22no—
228C22×D11—22no—
229C22×D11#13714yes—
230C22×D11C22×D412yes—
231Q8×C11—24no—
232Q8×C11—24no—
233Q8×C11—24no—
234Q8×C11—42no—
235Q8×C11—44no—
236D4×C11—24no—
237D4×C11—42no—
238C2×C4×C11—22no—
239C2×C4×C11—22no—
240C2×C4×C11—22no—
241C2×C4×C11—24no—
242C2×C4×C11—42no—
243C2×C4×C11—44no—
244C2×C4×C11C22×D412yes—
245C2×C4×C11C22×D412yes—
246C2×C4×C11C22×D411yescharacteristic
247C2×C4×C11C2×#4114yes—
248C2×C4×C11C2511yescharacteristic
249C22⋊D11—48no—
250C2×Dic11—22no—
251C2×Dic11—22no—
252C2×Dic11—22no—
253C2×Dic11—22no—
254C2×Dic11—24no—
255C2×Dic11—22no—
256C2×Dic11—48no—
257C2×Dic11—42no—
258C2×Dic11—44no—
259C2×Dic11—42no—
260C2×Dic11C22×D412yes—
261C2×Dic11C22×D412yes—
262C2×Dic11C22×D412yes—
263C4×D11—28no—
264C4×D11—24no—
265C4×D11—24no—
266C4×D11—44no—
267Dic22—48no—
268C8×C11C2×#4118yes—
269C11⋊C8—24no—
270C22×Q16C2×D1112yes—
271C22×SD16C2×D1112yes—
272C23×C8—112no—
273#533—118no—
274#533—224no—
275C2×C4⋊Q8—111no—
276C2×C4⋊Q8C2×D1111yescharacteristic
277#529—118no—
278#529—224no—
279C2×#126—221no—
280C2×#125—111no—
281C2×#125—221no—
282C2×#124C2×D1111yescharacteristic
283C2×#123—221no—
284C2×C22⋊Q8—111no—
285C2×C22⋊Q8—112no—
286C2×C22⋊Q8—221no—
287C2×#121—111no—
288C2×C4×Q8—111no—
289C2×C4×Q8—112no—
290C2×C4×Q8—221no—
291C2×C4×D4—111no—
292C2×C4×D4—221no—
293C2×#117—221no—
294C2×#117—221no—
295C22×C42—111no—
296#501—118no—
297#497C2×D1118yescomplemented
298#491—118no—
299#489—118no—
300#467—1116no—
301#465—1116no—
302#441—1116no—
303#440—1116no—
304C2×#107—112no—
305C2×#106—112no—
306C2×#103—112no—
307C2×#103—112no—
308C2×#103—112no—
309C2×#102—112no—
310C2×#97—112no—
311C2×#97—111no—
312C2×#97—118no—
313C2×#97C2×D1111yescharacteristic
314C22×C11—42no—
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—84no—
318C22×C11#53212yes—
319C22×C11C2×#13712yes—
320C22×C11#57512yes—
321C22×C11C23×D411yescharacteristic
322C2×D11—28no—
323C2×D11—22no—
324C2×D11—22no—
325C2×D11C2×#13714yes—
326C4×C11—22no—
327C4×C11—22no—
328C4×C11—42no—
329C4×C11—44no—
330C4×C11#53212yes—
331C4×C11C22×#4112yes—
332Dic11—22no—
333Dic11—22no—
334Dic11—22no—
335Dic11—42no—
336Dic11—44no—
337Dic11—42no—
338C22×Q8—221no—
339C22×Q8C22×D1111yescharacteristic
340C22×Q8C22×D1112yes—
341C22×D4—221no—
342C22×D4C22×D1111yescharacteristic
343C23×C4—111no—
344C23×C4—111no—
345C23×C4—111no—
346C23×C4—221no—
347C2×Q16—28no—
348C2×Q16C22×D1118yes—
349C2×SD16—28no—
350C2×SD16C22×D1118yes—
351C22×C8—112no—
352C22×C8—118no—
353C22×C8—228no—
354C22×C8C22×D1112yes—
355C4⋊Q8—22no—
356C4⋊Q8—114no—
357C4⋊Q8—222no—
358C4⋊Q8C22×D1114yes—
359#126—228no—
360#125—114no—
361#125—228no—
362#125—222no—
363#124—22no—
364#124C22×D1114yes—
365#123—228no—
366C22⋊Q8—114no—
367C22⋊Q8—118no—
368C22⋊Q8—228no—
369C22⋊Q8—222no—
370C22⋊Q8—224no—
371#121—114no—
372#121—222no—
373C4×Q8—114no—
374C4×Q8—118no—
375C4×Q8—228no—
376C4×Q8—222no—
377C4×Q8—224no—
378C4×D4—114no—
379C4×D4—222no—
380C4×D4—228no—
381#117—228no—
382#117—228no—
383C2×C4⋊C4—21no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—111no—
386C2×C4⋊C4—111no—
387C2×C4⋊C4—112no—
388C2×C4⋊C4—221no—
389C2×C4⋊C4—222no—
390C2×C4⋊C4—221no—
391C2×C4⋊C4—222no—
392C2×C4⋊C4—221no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—221no—
395C2×C22⋊C4—21no—
396C2×C22⋊C4—21no—
397C2×C22⋊C4—222no—
398C2×C22⋊C4—221no—
399C2×C22⋊C4—221no—
400C2×C22⋊C4—221no—
401C2×C42—111no—
402C2×C42—111no—
403C2×C42—111no—
404C2×C42—114no—
405C2×C42—114no—
406C2×C42—221no—
407C2×C42—222no—
408C2×C42C22×D1111yescharacteristic
409#107—118no—
410#106—118no—
411#103—118no—
412#103—118no—
413#103—118no—
414#102—118no—
415#97—118no—
416#97—114no—
417#97C22×D1114yes—
418C2×C11—82no—
419C2×C11#318114yescomplemented
420C2×C11C2×#53211yescharacteristic
421C2×C11C22×#13711yescharacteristic
422C2×C11C2×#57511yescharacteristic
423D11—24no—
424C24—21no—
425C24—111no—
426C2×Q8—21no—
427C2×Q8—22no—
428C2×Q8—24no—
429C2×Q8—24no—
430C2×Q8—24no—
431C2×Q8—224no—
432C2×Q8—444no—
433C2×Q8C23×D1112yes—
434C2×Q8C23×D1114yes—
435C2×D4—21no—
436C2×D4—24no—
437C2×D4—224no—
438C2×D4—444no—
439C2×D4C23×D1112yes—
440C22×C4—21no—
441C22×C4—22no—
442C22×C4—111no—
443C22×C4—111no—
444C22×C4—111no—
445C22×C4—114no—
446C22×C4—112no—
447C22×C4—112no—
448C22×C4—114no—
449C22×C4—224no—
450C22×C4—224no—
451C22×C4—224no—
452C22×C4—221no—
453C22×C4—222no—
454C22×C4—221no—
455C22×C4—442no—
456C22×C4—444no—
457C22×C4D4×D1111yescharacteristic
458C22×C4D4×D1111yescharacteristic
459C22×C4C23×D1111yescharacteristic
460Q16—216no—
461SD16—216no—
462C2×C8—114no—
463C2×C8—224no—
464C2×C8—2216no—
465C2×C8#434118yes—
466C2×C8C23×D1114yes—
467C4⋊C4—24no—
468C4⋊C4—24no—
469C4⋊C4—114no—
470C4⋊C4—112no—
471C4⋊C4—112no—
472C4⋊C4—224no—
473C4⋊C4—228no—
474C4⋊C4—224no—
475C4⋊C4—228no—
476C4⋊C4—221no—
477C4⋊C4—221no—
478C4⋊C4—222no—
479C4⋊C4—224no—
480C4⋊C4—224no—
481C4⋊C4—224no—
482C22⋊C4—24no—
483C22⋊C4—24no—
484C22⋊C4—228no—
485C22⋊C4—224no—
486C22⋊C4—224no—
487C22⋊C4—224no—
488C42—114no—
489C42—112no—
490C42—114no—
491C42—112no—
492C42—224no—
493C42—228no—
494C42D4×D1112yes—
495C42C23×D1112yes—
496C11C2×#318111yescharacteristic, complemented, Sylow
497C23—22no—
498C23—42no—
499C23—42no—
500C23—42no—
501C23—114no—
502C23—112no—
503C23—222no—
504C23—222no—
505C23C2×D4×D1111yescharacteristic
506Q8—24no—
507Q8—24no—
508Q8—24no—
509Q8—42no—
510Q8—44no—
511Q8—448no—
512D4—24no—
513D4—42no—
514D4—448no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—24no—
519C2×C4—42no—
520C2×C4—44no—
521C2×C4—112no—
522C2×C4—112no—
523C2×C4—112no—
524C2×C4—228no—
525C2×C4—222no—
526C2×C4—222no—
527C2×C4—222no—
528C2×C4—224no—
529C2×C4—224no—
530C2×C4—222no—
531C2×C4—224no—
532C2×C4—222no—
533C2×C4—444no—
534C2×C4—448no—
535C2×C4—442no—
536C2×C4—442no—
537C2×C4—444no—
538C2×C4C2×D4×D1112yes—
539C2×C4C2×D4×D1112yes—
540C2×C4C2×D4×D1111yescharacteristic
541C2×C4C2×#434114yes—
542C2×C4C24×D1111yescharacteristic
543C8—224no—
544C8C2×#434118yes—
545C22—42no—
546C22—42no—
547C22—42no—
548C22—84no—
549C22—114no—
550C22—228no—
551C22—222no—
552C22—222no—
553C22#1062324712yes—
554C22D11×#13712yes—
555C22#1062330812yes—
556C22C22×D4×D1111yescharacteristic
557C4—22no—
558C4—22no—
559C4—42no—
560C4—44no—
561C4—222no—
562C4—222no—
563C4—222no—
564C4—442no—
565C4—442no—
566C4—444no—
567C4#1062324712yes—
568C4C22×#434112yes—
569C2—82no—
570C2—224no—
571C2#1307932214yesdirect product factor
572C2C2×#1062324711yescharacteristic
573C2C2×D11×#13711yescharacteristic
574C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#497C2
socleC23×C11C22×D4
prime radicalC2×#66991C22
hypercenterC2×#497D11
hypocenterC11C2×#3181
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#497

Complements

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

NH ≅ G/Ntype
1. C2×#10623259C2semidirect
3. #13079322C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622695C2semidirect
6. C2×#10622668C2semidirect
7. C2×#10622801C2semidirect
9. C2×#10622797C2semidirect
10. C2×#10622777C2semidirect
11. C2×D11×#97C2semidirect
12. C2×C11×#497C2semidirect
25. #10623259C22semidirect
39. C11×#497C22semidirect
45. #10622801C22semidirect
46. #10622797C22semidirect
48. #10622777C22semidirect
52. #10622695C22semidirect
53. #10622668C22semidirect
55. D11×#97C22semidirect
56. #10622315C22semidirect
214. C2×#497D11semidirect
297. #497C2×D11semidirect
419. C2×C11#3181semidirect
496. C11C2×#3181semidirect
571. C2#13079322direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232592
C2×#106232112
#130793222
C2×#106223152
C2×#106226952
C2×#106226682
C2×#106228012
C2×#106227842
C2×#106227972
C2×#106227772
C2×D11×#972
C2×C11×#4972
C2×#318111