Finite Group Databasebeta

← C2×#13082497 #15662213

Subgroups — C2×#13082497 #15662213

Order 2816.

7022 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082497C2132yesmaximal, direct product factor
2C2×#10623098C214yesmaximal, complemented
3C2×#10623099C214yesmaximal, complemented
4C2×#10623062C218yesmaximal, complemented
5C2×#10623114C214yesmaximal, complemented
6C2×#10623057C211yesmaximal, characteristic
7C2×#10623347C211yesmaximal, characteristic
8C2×#10623109C214yesmaximal, complemented
9C2×#10623048C211yesmaximal, characteristic, complemented
10C22×#66997C211yesmaximal, characteristic, complemented
11C2×#10623047C211yesmaximal, characteristic, complemented
12C2×#10623053C211yesmaximal, characteristic
13C2×C11×#519C211yesmaximal, characteristic, complemented
14C23×Q8×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C11×#519C22116yescomplemented
18C2×C4×Q8×C11C2214yes—
19C2×C4×Q8×C11C2214yes—
20C2×C11×#117C2214yes—
21C2×C11×#117C2211yescharacteristic
22C2×C11×#117C2211yescharacteristic
23#10623347C22116yes—
24C2×#67000C2212yes—
25C2×#66999C2214yes—
26C2×#66997C2212yes—
27C2×#66997C2214yes—
28C2×#66997C2212yes—
29C2×#66997C2212yes—
30C2×#66997C22116yescomplemented
31C2×#66982C2214yes—
32C2×#66979C2211yescharacteristic
33C22×Dic11⋊C4C2214yes—
34C22×C4×Dic11C2211yescharacteristic
35#10623114C22164yescomplemented
36#10623109C22164yescomplemented
37#10623099C22164yescomplemented
38#10623098C22164yescomplemented
39#10623062C221128yescomplemented
40#10623057C22116yes—
41#10623053C22116yes—
42#10623048C22116yescomplemented
43#10623047C22116yescomplemented
44C2×#66951C2218yes—
45C2×#66950C2214yes—
46C2×#66949C2218yes—
47C2×#66946C2212yes—
48C2×#66943C2212yes—
49C2×#66942C2218yes—
50C2×#66942C2218yes—
51C2×#66941C2212yes—
52C2×#66940C2214yes—
53C2×#66940C2212yes—
54C2×#66939C2214yes—
55C2×(C22⋊D11)⋊C4C2214yes—
56C2×#66931C2214yes—
57C2×#66930C2214yes—
58C2×#66929C2218yes—
59C2×#66928C2212yes—
60C2×#66925C2218yes—
61C2×#66925C2212yes—
62C2×C42×D11C2212yes—
63C2×#66923C2218yes—
64C2×#66922C2212yes—
65C2×C4×Dic22C2218yes—
66C2×C4×Dic22C2214yes—
67C2×C4×Dic22C2214yes—
68C22×Q8×C11—28no—
69C22×Q8×C11C2312yes—
70C22×Q8×C11C2312yes—
71C22×Q8×C11C2318yes—
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C22×C22⋊D11C2312yes—
75C23×Dic11C2312yes—
76C23×Dic11C2312yes—
77C2×#4339—28no—
78C2×#4339C2318yes—
79C22×D44C2311yescharacteristic
80C22×C4×D11C2314yes—
81C22×C4×D11C2312yes—
82C22×Dic22—28no—
83C22×Dic22C2314yes—
84C22×Dic22C2312yes—
85C22×Dic22C2311yescharacteristic
86C22×Dic22C2312yes—
87C22×Dic22C2318yes—
88C4×Q8×C11C23132yes—
89C4×Q8×C11C23132yes—
90C11×#117C2318yes—
91C11×#117C2318yes—
92C11×#117C23132yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2318yes—
96C2×C11×C22⋊C4C2312yes—
97C2×C11×C22⋊C4C2312yes—
98C2×C42×C11C2312yes—
99C2×C42×C11C2312yes—
100C2×C42×C11C2318yes—
101C2×C22⋊Dic11C2312yes—
102#67000C23116yes—
103#66999C23132yes—
104#66997C23132yes—
105#66997C23116yes—
106#66997C23116yes—
107#66997C23116yes—
108#66982C23132yes—
109C2×(C2×D11)⋊C4C2318yes—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2318yes—
112#66979C2318yes—
113C2×C4⋊Dic11C2312yes—
114C2×C4⋊Dic11C2318yes—
115C2×C4⋊Dic11C2314yes—
116C2×Dic11⋊C4C2318yes—
117C2×Dic11⋊C4C2318yes—
118C2×Dic11⋊C4C2314yes—
119C2×Dic11⋊C4C2318yes—
120C2×Dic11⋊C4C2314yes—
121C2×Dic11⋊C4C2314yes—
122C2×Dic11⋊C4C2318yes—
123C2×Dic11⋊C4C23132yes—
124C2×C4×Dic11C2314yes—
125C2×C4×Dic11C2318yes—
126C2×C4×Dic11C2312yes—
127C2×C4×Dic11C2312yes—
128C2×C4×Dic11C2311yescharacteristic
129C2×C4×Dic11C2311yescharacteristic
130C2×C4×Dic11C2318yes—
131#66951C23164yes—
132#66950C23132yes—
133#66949C23164yes—
134#66946C23116yes—
135#66943C23116yes—
136#66942C23164yes—
137#66942C23164yes—
138#66941C23116yes—
139#66940C23132yes—
140#66940C23116yes—
141#66939C23132yes—
142(C22⋊D11)⋊C4C23132yes—
143#66931C23132yes—
144#66930C23132yes—
145#66929C23164yes—
146#66928C23116yes—
147#66925C23116yes—
148#66925C23164yes—
149C42×D11C23116yes—
150#66923C23164yes—
151#66922C23116yes—
152C4×Dic22C23132yes—
153C4×Dic22C23132yes—
154C4×Dic22C23164yes—
155C2×#3509—111nomaximal, Sylow
156C24×C11C2411yescharacteristic
157C23×D11C2412yes—
158C2×Q8×C11—28no—
159C2×Q8×C11—28no—
160C2×Q8×C11—232no—
161C2×Q8×C11C2418yes—
162C2×Q8×C11C2418yes—
163C22×C4×C11—28no—
164C22×C4×C11#4118yes—
165C22×C4×C11C2414yes—
166C22×C4×C11C2414yes—
167C22×C4×C11C2418yes—
168C22×C4×C11C2414yes—
169C22×C4×C11C2411yescharacteristic
170C22×C4×C11C2411yescharacteristic
171C22×C4×C11C2414yes—
172C2×C22⋊D11—28no—
173C2×C22⋊D11C2418yes—
174C22×Dic11—28no—
175C22×Dic11—28no—
176C22×Dic11C2418yes—
177C22×Dic11C2418yes—
178C22×Dic11C2414yes—
179C22×Dic11C2412yes—
180C22×Dic11C2412yes—
181C22×Dic11C2414yes—
182C22×Dic11C2412yes—
183#4339—232no—
184C2×D44—24no—
185C2×D44C2414yes—
186C2×C4×D11—216no—
187C2×C4×D11—28no—
188C2×C4×D11C24116yes—
189C2×C4×D11C2418yes—
190C2×Dic22—216no—
191C2×Dic22—28no—
192C2×Dic22—28no—
193C2×Dic22—232no—
194C2×Dic22—24no—
195C2×Dic22C24116yes—
196C2×Dic22C2418yes—
197C2×Dic22C2414yes—
198C2×Dic22C2418yes—
199C11×C4⋊C4C2418yes—
200C11×C4⋊C4C2418yes—
201C11×C4⋊C4C24132yes—
202C11×C22⋊C4C2418yes—
203C11×C22⋊C4C2418yes—
204C42×C11C2418yes—
205C42×C11C2418yes—
206C42×C11C24132yes—
207C22⋊Dic11C2418yes—
208(C2×D11)⋊C4C24132yes—
209(C2×D11)⋊C4C24116yes—
210(C2×D11)⋊C4C24132yes—
211C4⋊Dic11C2418yes—
212C4⋊Dic11C24132yes—
213C4⋊Dic11C24116yes—
214Dic11⋊C4C24132yes—
215Dic11⋊C4C24132yes—
216Dic11⋊C4C24116yes—
217Dic11⋊C4C24132yes—
218Dic11⋊C4C24116yes—
219Dic11⋊C4C24116yes—
220Dic11⋊C4C24132yes—
221C4×Dic11C24116yes—
222C4×Dic11C24132yes—
223C4×Dic11C2418yes—
224C4×Dic11C2418yes—
225C4×Dic11C2414yes—
226C4×Dic11C2414yes—
227#3509—1132no—
228C2×#557—114no—
229C2×#556—114no—
230C2×#552—118no—
231C2×#541—114no—
232C2×#536—111no—
233C2×#536—111no—
234C2×#533—114no—
235C2×#533—111no—
236C22×C4⋊Q8—111no—
237C2×#519—111no—
238C2×#519D1111yescharacteristic, complemented
239C2×C4×#41—111no—
240C23×C11—24no—
241C23×C11C2×#4114yes—
242C23×C11C2512yes—
243C23×C11C2511yescharacteristic
244C22×D11—24no—
245C22×D11—28no—
246C22×D11C2514yes—
247Q8×C11—216no—
248Q8×C11—216no—
249C2×C4×C11—216no—
250C2×C4×C11—28no—
251C2×C4×C11—28no—
252C2×C4×C11—28no—
253C2×C4×C11C2×#4114yes—
254C2×C4×C11C2×#4114yes—
255C2×C4×C11C2×#41116yes—
256C2×C4×C11C2518yes—
257C2×C4×C11C2518yes—
258C2×C4×C11C2518yes—
259C2×C4×C11C2512yes—
260C2×C4×C11C2512yes—
261C22⋊D11—216no—
262C2×Dic11—216no—
263C2×Dic11—28no—
264C2×Dic11—24no—
265C2×Dic11—28no—
266C2×Dic11—24no—
267C2×Dic11—216no—
268C2×Dic112−1+418yes—
269C2×Dic11C2518yes—
270C2×Dic11C2514yes—
271C2×Dic11C2514yes—
272C2×Dic11C2518yes—
273C2×Dic11C2514yes—
274D44—28no—
275C4×D11—216no—
276C4×D11—232no—
277Dic22—216no—
278Dic22—216no—
279Dic22—28no—
280Dic22—232no—
281C22×#41—111no—
282C23×Q8—111no—
283C23×Q8C2×D1111yescharacteristic
284#557—1164no—
285#556—1164no—
286#552—11128no—
287#541—1164no—
288#536—1116no—
289#536—1116no—
290#533—1164no—
291#533—1116no—
292C2×C4⋊Q8—112no—
293C2×C4⋊Q8—112no—
294C2×C4⋊Q8—114no—
295C2×C4⋊Q8—112no—
296C2×C4⋊Q8—1116no—
297C2×C4⋊Q8—112no—
298C2×C4⋊Q8—112no—
299C2×#126—118no—
300C2×#126—118no—
301C2×#125—118no—
302C2×#125—118no—
303C2×#125—112no—
304C2×#125—118no—
305C2×#124—112no—
306C2×#124—112no—
307C2×#123—114no—
308C2×#123—114no—
309C2×C22⋊Q8—114no—
310C2×C22⋊Q8—118no—
311C2×C22⋊Q8—114no—
312C2×C22⋊Q8—114no—
313#519—1116no—
314#519C2×D11116yescomplemented
315C4×#41—1116no—
316C2×C4×Q8—112no—
317C2×C4×Q8—114no—
318C2×C4×Q8—114no—
319C2×C4×Q8—118no—
320C2×C4×Q8—114no—
321C2×C4×Q8C2×D1114yes—
322C2×C4×Q8C2×D1114yes—
323C2×C4×D4—112no—
324C2×C4×D4—114no—
325C2×#117—111no—
326C2×#117—114no—
327C2×#117—112no—
328C2×#117—118no—
329C2×#117C2×D1111yescharacteristic
330C2×#117C2×D1111yescharacteristic
331C2×#117C2×D1114yes—
332C22×C4⋊C4—114no—
333C22×C42—111no—
334C22×C42—112no—
335C22×C11—24no—
336C22×C11—28no—
337C22×C11C22×#4114yes—
338C22×C11C22×#4112yes—
339C22×C11C2×2−1+414yes—
340C22×C11C2611yescharacteristic
341C2×D11—24no—
342C2×D11—28no—
343C2×D11—48no—
344C4×C11—28no—
345C4×C11—28no—
346C4×C11—28no—
347C4×C11C22×#4114yes—
348C4×C11C22×#4114yes—
349Dic11—28no—
350Dic11—24no—
351Dic11—28no—
352Dic11—24no—
353Dic11C2×2−1+418yes—
354C2×#41—118no—
355C2×#41—228no—
356C22×Q8—28no—
357C22×Q8—114no—
358C22×Q8—112no—
359C22×Q8—112no—
360C22×Q8—111no—
361C22×Q8—118no—
362C22×Q8—228no—
363C22×Q8C22×D1112yes—
364C22×Q8C22×D1112yes—
365C22×Q8C22×D1118yes—
366C22×D4—112no—
367C22×D4—111no—
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—114no—
371C23×C4—112no—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C4⋊Q8—1116no—
375C4⋊Q8—1116no—
376C4⋊Q8—1132no—
377C4⋊Q8—1116no—
378C4⋊Q8—1116no—
379C4⋊Q8—1116no—
380#126—1164no—
381#126—1164no—
382#125—1116no—
383#125—1164no—
384#125—1164no—
385#125—1164no—
386#124—1116no—
387#124—1116no—
388#123—1132no—
389#123—1132no—
390C22⋊Q8—1132no—
391C22⋊Q8—1132no—
392C22⋊Q8—1164no—
393C22⋊Q8—1132no—
394C4×Q8—1116no—
395C4×Q8—1132no—
396C4×Q8—1132no—
397C4×Q8—1164no—
398C4×Q8—1132no—
399C4×Q8C22×D11132yes—
400C4×Q8C22×D11132yes—
401C4×D4—1116no—
402C4×D4—1132no—
403#117—118no—
404#117—1132no—
405#117—1116no—
406#117—1164no—
407#117C22×D1118yes—
408#117C22×D1118yes—
409#117C22×D11132yes—
410C2×C4⋊C4—118no—
411C2×C4⋊C4—118no—
412C2×C4⋊C4—1132no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—114no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—118no—
417C2×C4⋊C4—118no—
418C2×C4⋊C4—118no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4C22×D1112yes—
422C2×C4⋊C4C22×D1112yes—
423C2×C4⋊C4C22×D1118yes—
424C2×C22⋊C4—112no—
425C2×C22⋊C4—114no—
426C2×C22⋊C4—118no—
427C2×C22⋊C4—118no—
428C2×C22⋊C4C22×D1112yes—
429C2×C22⋊C4C22×D1112yes—
430C2×C42—118no—
431C2×C42—111no—
432C2×C42—112no—
433C2×C42—114no—
434C2×C42—112no—
435C2×C42—118no—
436C2×C42—111no—
437C2×C42—1116no—
438C2×C42C22×D1112yes—
439C2×C42C22×D1118yes—
440C2×C42C22×D1112yes—
441C2×C11—24no—
442C2×C11#350914yescomplemented
443C2×C11C23×#4111yescharacteristic
444C2×C11C22×2−1+412yes—
445D11—44no—
446C24—112no—
447C24C23×D1111yescharacteristic
448#41—2232no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—232no—
452C2×Q8—1116no—
453C2×Q8—118no—
454C2×Q8—118no—
455C2×Q8—114no—
456C2×Q8—2216no—
457C2×Q8—228no—
458C2×Q8—228no—
459C2×Q8—2232no—
460C2×Q8—224no—
461C2×Q8C23×D1118yes—
462C2×Q8C23×D1118yes—
463C2×D4—118no—
464C2×D4—114no—
465C2×D4—228no—
466C2×D4—224no—
467C22×C4—28no—
468C22×C4—112no—
469C22×C4—118no—
470C22×C4—118no—
471C22×C4—114no—
472C22×C4—112no—
473C22×C4—114no—
474C22×C4—112no—
475C22×C4—1116no—
476C22×C4—118no—
477C22×C4—2216no—
478C22×C4—228no—
479C22×C4—228no—
480C22×C4—228no—
481C22×C4#433918yes—
482C22×C4C23×D1118yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1114yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C4⋊C4—1132no—
490C4⋊C4—1132no—
491C4⋊C4—1116no—
492C4⋊C4—1116no—
493C4⋊C4—118no—
494C4⋊C4—1132no—
495C4⋊C4—1132no—
496C4⋊C4—1132no—
497C4⋊C4—1116no—
498C4⋊C4—1116no—
499C4⋊C4C23×D1118yes—
500C4⋊C4C23×D1118yes—
501C4⋊C4C23×D11132yes—
502C22⋊C4—118no—
503C22⋊C4—1116no—
504C22⋊C4—1132no—
505C22⋊C4—1132no—
506C22⋊C4C23×D1118yes—
507C22⋊C4C23×D1118yes—
508C42—114no—
509C42—114no—
510C42—1116no—
511C42—118no—
512C42—1132no—
513C42—118no—
514C42C23×D1118yes—
515C42C23×D11132yes—
516C42C23×D1118yes—
517C11C2×#350911yescharacteristic, complemented, Sylow
518C23—24no—
519C23—114no—
520C23—224no—
521C23—228no—
522C23C2×#433914yes—
523C23C24×D1112yes—
524C23C24×D1111yescharacteristic
525Q8—216no—
526Q8—216no—
527Q8—2232no—
528Q8—2216no—
529Q8—2216no—
530Q8—228no—
531D4—2216no—
532D4—228no—
533C2×C4—216no—
534C2×C4—28no—
535C2×C4—28no—
536C2×C4—28no—
537C2×C4—118no—
538C2×C4—114no—
539C2×C4—118no—
540C2×C4—114no—
541C2×C4—118no—
542C2×C4—114no—
543C2×C4—2232no—
544C2×C4—2216no—
545C2×C4—224no—
546C2×C4—2216no—
547C2×C4—228no—
548C2×C4—224no—
549C2×C4—228no—
550C2×C4—2216no—
551C2×C4C2×#433914yes—
552C2×C4C2×#433914yes—
553C2×C4C2×#4339116yes—
554C2×C4C24×D1118yes—
555C2×C4C24×D1118yes—
556C2×C4C24×D1118yes—
557C2×C4C24×D1112yes—
558C2×C4C24×D1112yes—
559C22—24no—
560C22—28no—
561C22—224no—
562C22—228no—
563C22—448no—
564C22C22×#433914yes—
565C22C22×#433912yes—
566C22D11×2−1+414yes—
567C22C25×D1111yescharacteristic
568C4—28no—
569C4—28no—
570C4—28no—
571C4—118no—
572C4—224no—
573C4—228no—
574C4—224no—
575C4—228no—
576C4C22×#433914yes—
577C4C22×#433914yes—
578C2—24no—
579C2—444no—
580C2#1308249714yesdirect product factor
581C2C23×#433911yescharacteristic
582C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#519C2
socleC23×C11C25
prime radicalC22×#4339C22
hypercenterC2×#519D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#519

Complements

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

NH ≅ G/Ntype
1. #13082497C2direct (N × H)
2. C2×#10623098C2semidirect
3. C2×#10623099C2semidirect
4. C2×#10623062C2semidirect
5. C2×#10623114C2semidirect
8. C2×#10623109C2semidirect
9. C2×#10623048C2semidirect
10. C22×#66997C2semidirect
11. C2×#10623047C2semidirect
13. C2×C11×#519C2semidirect
17. C11×#519C22semidirect
30. C2×#66997C22semidirect
35. #10623114C22semidirect
36. #10623109C22semidirect
37. #10623099C22semidirect
38. #10623098C22semidirect
39. #10623062C22semidirect
42. #10623048C22semidirect
43. #10623047C22semidirect
238. C2×#519D11semidirect
314. #519C2×D11semidirect
442. C2×C11#3509semidirect
517. C11C2×#3509semidirect
580. C2#13082497direct (N × H)

Maximal subgroups

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

subgroupindex
#130824972
C2×#106230982
C2×#106230992
C2×#106230622
C2×#106231142
C2×#106230572
C2×#106233472
C2×#106231092
C2×#106230482
C22×#669972
C2×#106230472
C2×#106230532
C2×C11×#5192
C2×#350911