Finite Group Databasebeta

← C2×#13082501 #15662215

Subgroups — C2×#13082501 #15662215

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#13082501C2132yesmaximal, direct product factor
2C2×#10623252C214yesmaximal, complemented
3C2×#10623202C214yesmaximal, complemented
4C2×#10623181C218yesmaximal, complemented
5C2×#10623156C214yesmaximal, complemented
6C2×#10623356C211yesmaximal, characteristic
7C2×#10623048C211yesmaximal, characteristic, complemented
8C2×#10623153C214yesmaximal, complemented
9C22×#66997C211yesmaximal, characteristic, complemented
10C2×#10623343C211yesmaximal, characteristic, complemented
11C2×#10623047C211yesmaximal, characteristic, complemented
12C2×#41×Dic11C211yesmaximal, characteristic
13C2×C11×#536C211yesmaximal, characteristic
14C22×C11×#41C2211yescharacteristic
15C23×Q8×C11C2211yescharacteristic
16C23×Dic22C2211yescharacteristic
17C11×#536C22116yes—
18C2×C11×C4⋊Q8C2212yes—
19C2×C11×#124C2212yes—
20C2×C11×#123C2214yes—
21C2×C11×C22⋊Q8C2214yes—
22C2×C11×#117C2211yescharacteristic
23#41×Dic11C22116yes—
24#10623356C22116yes—
25#10623343C22116yescomplemented
26C2×Q8×Dic11C2214yes—
27C2×Q8×Dic11C2214yes—
28C2×Q8×Dic11C2212yes—
29C2×#66997C2212yes—
30C2×#66997C2214yes—
31C2×#66997C2212yes—
32C2×#66997C2212yes—
33C2×#66997C22116yescomplemented
34C2×#66989C2212yes—
35C2×#66988C2214yes—
36C2×D4×Dic11C2214yes—
37C2×D4×Dic11C2212yes—
38C2×#66979C2214yes—
39C2×#66979C2211yescharacteristic
40C2×#66979C2212yes—
41C2×#66979C2211yescharacteristic
42C2×#66977C2214yes—
43C22×Dic11⋊C4C2214yes—
44C22×C4×Dic11C2211yescharacteristic
45C22×C4×Dic11C2212yes—
46#10623252C22164yescomplemented
47#10623202C22164yescomplemented
48#10623181C221128yescomplemented
49#10623156C22164yescomplemented
50#10623153C22164yescomplemented
51#10623048C22116yescomplemented
52#10623047C22116yescomplemented
53C2×#66943C2218yes—
54C2×#66943C2212yes—
55C2×#66942C2218yes—
56C2×#66942C2218yes—
57C2×#66941C2212yes—
58C2×#66940C2218yes—
59C2×#66940C2214yes—
60C2×#66932C2218yes—
61C2×#66932C2218yes—
62C2×#66931C2214yes—
63C2×#66931C2218yes—
64C2×#66930C2214yes—
65C2×#66930C2218yes—
66C2×C4×Dic22C2214yes—
67C2×C4×Dic22C2214yes—
68C2×C11×#41—28no—
69C2×C11×#41C2318yes—
70C22×Q8×C11—28no—
71C22×Q8×C11C2312yes—
72C22×Q8×C11C2312yes—
73C22×Q8×C11C2311yescharacteristic
74C22×Q8×C11C2318yes—
75C22×D4×C11C2312yes—
76C22×D4×C11C2311yescharacteristic
77C23×C4×C11C2312yes—
78C23×C4×C11C2312yes—
79C23×C4×C11C2311yescharacteristic
80C23×Dic11C2314yes—
81C23×Dic11C2312yes—
82C23×Dic11C2312yes—
83C22×Dic22—28no—
84C22×Dic22C2312yes—
85C22×Dic22C2314yes—
86C22×Dic22C2312yes—
87C22×Dic22C2318yes—
88C11×C4⋊Q8C23116yes—
89C11×#124C23116yes—
90C11×#123C23132yes—
91C11×C22⋊Q8C23132yes—
92C11×#117C2318yes—
93C2×C11×C4⋊C4C2312yes—
94C2×C11×C4⋊C4C2318yes—
95C2×C11×C22⋊C4C2312yes—
96C2×C11×C22⋊C4C2318yes—
97C2×C42×C11C2312yes—
98C2×C22⋊Dic11C2312yes—
99C2×C22⋊Dic11C2318yes—
100C2×C22⋊Dic11C2312yes—
101C2×C22⋊Dic11C2314yes—
102Q8×Dic11C23116yes—
103Q8×Dic11C23132yes—
104Q8×Dic11C23132yes—
105#66997C23116yes—
106#66997C23132yes—
107#66997C23116yes—
108#66997C23116yes—
109#66989C23116yes—
110#66988C23132yes—
111D4×Dic11C23132yes—
112D4×Dic11C23116yes—
113#66979C2318yes—
114#66979C2318yes—
115#66979C23132yes—
116#66979C23116yes—
117C2×C4⋊Dic11C2312yes—
118C2×C4⋊Dic11C2314yes—
119C2×C4⋊Dic11C2318yes—
120C2×C4⋊Dic11C2312yes—
121C2×C4⋊Dic11C2314yes—
122#66977C23132yes—
123C2×Dic11⋊C4C2314yes—
124C2×Dic11⋊C4C2318yes—
125C2×Dic11⋊C4C2314yes—
126C2×Dic11⋊C4C2318yes—
127C2×Dic11⋊C4C2318yes—
128C2×Dic11⋊C4C2318yes—
129C2×Dic11⋊C4C23132yes—
130C2×C4×Dic11C2312yes—
131C2×C4×Dic11C2312yes—
132C2×C4×Dic11C2318yes—
133C2×C4×Dic11C2318yes—
134C2×C4×Dic11C2314yes—
135C2×C4×Dic11C2312yes—
136C2×C4×Dic11C2311yescharacteristic
137C2×C4×Dic11C2311yescharacteristic
138C2×C4×Dic11C2318yes—
139C2×C4×Dic11C23116yes—
140#66943C23164yes—
141#66943C23116yes—
142#66942C23164yes—
143#66942C23164yes—
144#66941C23116yes—
145#66940C23164yes—
146#66940C23132yes—
147#66932C23164yes—
148#66932C23164yes—
149#66931C23132yes—
150#66931C23164yes—
151#66930C23132yes—
152#66930C23164yes—
153C4×Dic22C23132yes—
154C4×Dic22C23132yes—
155C2×#3509—111nomaximal, Sylow
156C24×C11C2412yes—
157C24×C11C2411yescharacteristic
158C11×#41—232no—
159C2×Q8×C11—28no—
160C2×Q8×C11—28no—
161C2×Q8×C11—232no—
162C2×Q8×C11—24no—
163C2×Q8×C11C2418yes—
164C2×Q8×C11C2418yes—
165C2×Q8×C11C2414yes—
166C2×D4×C11—28no—
167C2×D4×C11—24no—
168C2×D4×C11C2418yes—
169C2×D4×C11C2414yes—
170C22×C4×C11—28no—
171C22×C4×C11—28no—
172C22×C4×C11#4118yes—
173C22×C4×C11C2414yes—
174C22×C4×C11C2412yes—
175C22×C4×C11C2414yes—
176C22×C4×C11C2418yes—
177C22×C4×C11C2418yes—
178C22×C4×C11C2411yescharacteristic
179C22×C4×C11C2411yescharacteristic
180C22×C4×C11C2414yes—
181C22×Dic11—28no—
182C22×Dic11—216no—
183C22×Dic11—28no—
184C22×Dic11C24116yes—
185C22×Dic11C2418yes—
186C22×Dic11C2418yes—
187C22×Dic11C2414yes—
188C22×Dic11C2414yes—
189C22×Dic11C2414yes—
190C22×Dic11C2412yes—
191C22×Dic11C2412yes—
192C2×Dic22—216no—
193C2×Dic22—28no—
194C2×Dic22—28no—
195C2×Dic22—232no—
196C2×Dic22C2418yes—
197C2×Dic22C24116yes—
198C2×Dic22C2418yes—
199C11×C4⋊C4C2418yes—
200C11×C4⋊C4C24132yes—
201C11×C22⋊C4C2418yes—
202C11×C22⋊C4C24132yes—
203C42×C11C2418yes—
204C22⋊Dic11C2418yes—
205C22⋊Dic11C24132yes—
206C22⋊Dic11C2418yes—
207C22⋊Dic11C24116yes—
208C4⋊Dic11C2418yes—
209C4⋊Dic11C24116yes—
210C4⋊Dic11C24132yes—
211C4⋊Dic11C2418yes—
212C4⋊Dic11C24116yes—
213Dic11⋊C4C24116yes—
214Dic11⋊C4C24132yes—
215Dic11⋊C4C24116yes—
216Dic11⋊C4C24132yes—
217Dic11⋊C4C24132yes—
218Dic11⋊C4C24132yes—
219C4×Dic11C2418yes—
220C4×Dic11C2418yes—
221C4×Dic11C24132yes—
222C4×Dic11C24132yes—
223C4×Dic11C24116yes—
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×#536D1111yescharacteristic
234C2×#533—114no—
235C2×#533—111no—
236C22×C4⋊Q8—111no—
237C2×#519—111no—
238C2×#519—111no—
239C2×C4×#41—111no—
240C23×C11—24no—
241C23×C11—24no—
242C23×C11—28no—
243C23×C11C2×#4114yes—
244C23×C11C2514yes—
245C23×C11C2512yes—
246C23×C11C2511yescharacteristic
247Q8×C11—216no—
248Q8×C11—216no—
249Q8×C11—28no—
250D4×C11—216no—
251D4×C11—28no—
252C2×C4×C11—24no—
253C2×C4×C11—216no—
254C2×C4×C11—28no—
255C2×C4×C11—28no—
256C2×C4×C11—216no—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2×#41116yes—
260C2×C4×C11C2518yes—
261C2×C4×C11C2514yes—
262C2×C4×C11C2518yes—
263C2×C4×C11C2512yes—
264C2×C4×C11C2512yes—
265C2×Dic11—216no—
266C2×Dic11—28no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—24no—
270C2×Dic11—216no—
271C2×Dic11—232no—
272C2×Dic112−1+418yes—
273C2×Dic11C2518yes—
274C2×Dic11C2518yes—
275C2×Dic11C2518yes—
276C2×Dic11C2514yes—
277C2×Dic11C2514yes—
278Dic22—216no—
279Dic22—216no—
280Dic22—232no—
281C22×#41C2×D1111yescharacteristic
282C23×Q8—111no—
283C23×Q8C2×D1111yescharacteristic
284#557—1164no—
285#556—1164no—
286#552—11128no—
287#541—1164no—
288#536—1116no—
289#536C2×D11116yes—
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⋊Q8C2×D1112yes—
299C2×#126—118no—
300C2×#126—118no—
301C2×#125—118no—
302C2×#125—118no—
303C2×#125—112no—
304C2×#125—118no—
305C2×#124—112no—
306C2×#124C2×D1112yes—
307C2×#123—114no—
308C2×#123C2×D1114yes—
309C2×C22⋊Q8—114no—
310C2×C22⋊Q8—114no—
311C2×C22⋊Q8—118no—
312C2×C22⋊Q8C2×D1114yes—
313#519—1116no—
314#519—1116no—
315C4×#41—1116no—
316C2×C4×Q8—112no—
317C2×C4×Q8—114no—
318C2×C4×Q8—114no—
319C2×C4×Q8—114no—
320C2×C4×Q8—118no—
321C2×C4×Q8—114no—
322C2×C4×Q8—114no—
323C2×C4×D4—114no—
324C2×C4×D4—112no—
325C2×#117—111no—
326C2×#117—112no—
327C2×#117—111no—
328C2×#117—114no—
329C2×#117—114no—
330C2×#117—118no—
331C2×#117C2×D1111yescharacteristic
332C22×C4⋊C4—114no—
333C22×C42—111no—
334C22×C42—112no—
335C22×C11—24no—
336C22×C11—28no—
337C22×C11—24no—
338C22×C11—28no—
339C22×C11—48no—
340C22×C11C22×#4114yes—
341C22×C11C22×#4112yes—
342C22×C11C2×2−1+414yes—
343C22×C11C2611yescharacteristic
344C4×C11—24no—
345C4×C11—28no—
346C4×C11—28no—
347C4×C11C22×#4114yes—
348C4×C11C22×#4114yes—
349Dic11—28no—
350Dic11—28no—
351Dic11—28no—
352Dic11—24no—
353Dic11C2×2−1+418yes—
354C2×#41—28no—
355C2×#41C22×D1118yes—
356C22×Q8—28no—
357C22×Q8—114no—
358C22×Q8—112no—
359C22×Q8—112no—
360C22×Q8—118no—
361C22×Q8—228no—
362C22×Q8C22×D1112yes—
363C22×Q8C22×D1112yes—
364C22×Q8C22×D1111yescharacteristic
365C22×Q8C22×D1118yes—
366C22×D4C22×D1112yes—
367C22×D4C22×D1111yescharacteristic
368C23×C4—112no—
369C23×C4—112no—
370C23×C4—114no—
371C23×C4C22×D1112yes—
372C23×C4C22×D1112yes—
373C23×C4C22×D1111yescharacteristic
374C4⋊Q8—1116no—
375C4⋊Q8—1116no—
376C4⋊Q8—1132no—
377C4⋊Q8—1116no—
378C4⋊Q8—1116no—
379C4⋊Q8C22×D11116yes—
380#126—1164no—
381#126—1164no—
382#125—1116no—
383#125—1164no—
384#125—1164no—
385#125—1164no—
386#124—1116no—
387#124C22×D11116yes—
388#123—1132no—
389#123C22×D11132yes—
390C22⋊Q8—1132no—
391C22⋊Q8—1132no—
392C22⋊Q8—1164no—
393C22⋊Q8C22×D11132yes—
394C4×Q8—1116no—
395C4×Q8—1132no—
396C4×Q8—1132no—
397C4×Q8—1132no—
398C4×Q8—1164no—
399C4×Q8—1132no—
400C4×Q8—1132no—
401C4×D4—1132no—
402C4×D4—1116no—
403#117—118no—
404#117—1116no—
405#117—118no—
406#117—1132no—
407#117—1132no—
408#117—1164no—
409#117C22×D1118yes—
410C2×C4⋊C4—118no—
411C2×C4⋊C4—118no—
412C2×C4⋊C4—1132no—
413C2×C4⋊C4—114no—
414C2×C4⋊C4—112no—
415C2×C4⋊C4—114no—
416C2×C4⋊C4—112no—
417C2×C4⋊C4—118no—
418C2×C4⋊C4—118no—
419C2×C4⋊C4—118no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4—114no—
422C2×C4⋊C4C22×D1112yes—
423C2×C4⋊C4C22×D1118yes—
424C2×C22⋊C4—112no—
425C2×C22⋊C4—112no—
426C2×C22⋊C4—114no—
427C2×C22⋊C4—118no—
428C2×C22⋊C4C22×D1112yes—
429C2×C22⋊C4C22×D1118yes—
430C2×C42—112no—
431C2×C42—118no—
432C2×C42—118no—
433C2×C42—111no—
434C2×C42—112no—
435C2×C42—114no—
436C2×C42—112no—
437C2×C42—118no—
438C2×C42—1116no—
439C2×C42—111no—
440C2×C42C22×D1112yes—
441C2×C11—24no—
442C2×C11—44no—
443C2×C11#350914yescomplemented
444C2×C11C23×#4111yescharacteristic
445C2×C11C22×2−1+412yes—
446C24C23×D1112yes—
447C24C23×D1111yescharacteristic
448#41—232no—
449C2×Q8—28no—
450C2×Q8—28no—
451C2×Q8—232no—
452C2×Q8—24no—
453C2×Q8—1116no—
454C2×Q8—118no—
455C2×Q8—118no—
456C2×Q8—2216no—
457C2×Q8—228no—
458C2×Q8—228no—
459C2×Q8—2232no—
460C2×Q8C23×D1118yes—
461C2×Q8C23×D1118yes—
462C2×Q8C23×D1114yes—
463C2×D4—28no—
464C2×D4—24no—
465C2×D4C23×D1118yes—
466C2×D4C23×D1114yes—
467C22×C4—28no—
468C22×C4—28no—
469C22×C4—112no—
470C22×C4—118no—
471C22×C4—1116no—
472C22×C4—118no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—112no—
476C22×C4—114no—
477C22×C4—228no—
478C22×C4—2216no—
479C22×C4—228no—
480C22×C4#434118yes—
481C22×C4C23×D1118yes—
482C22×C4C23×D1118yes—
483C22×C4C23×D1114yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1114yes—
487C22×C4C23×D1111yescharacteristic
488C22×C4C23×D1111yescharacteristic
489C4⋊C4—1132no—
490C4⋊C4—1132no—
491C4⋊C4—1116no—
492C4⋊C4—118no—
493C4⋊C4—1116no—
494C4⋊C4—118no—
495C4⋊C4—1132no—
496C4⋊C4—1132no—
497C4⋊C4—1132no—
498C4⋊C4—1116no—
499C4⋊C4—1116no—
500C4⋊C4C23×D1118yes—
501C4⋊C4C23×D11132yes—
502C22⋊C4—118no—
503C22⋊C4—118no—
504C22⋊C4—1116no—
505C22⋊C4—1132no—
506C22⋊C4C23×D1118yes—
507C22⋊C4C23×D11132yes—
508C42—114no—
509C42—118no—
510C42—114no—
511C42—1116no—
512C42—118no—
513C42—1132no—
514C42—1132no—
515C42—118no—
516C42C23×D1118yes—
517C11C2×#350911yescharacteristic, complemented, Sylow
518C23—24no—
519C23—24no—
520C23—28no—
521C23C2×#434114yes—
522C23C24×D1114yes—
523C23C24×D1112yes—
524C23C24×D1111yescharacteristic
525Q8—216no—
526Q8—216no—
527Q8—28no—
528Q8—2232no—
529Q8—2216no—
530Q8—2216no—
531D4—216no—
532D4—28no—
533C2×C4—24no—
534C2×C4—216no—
535C2×C4—28no—
536C2×C4—28no—
537C2×C4—216no—
538C2×C4—118no—
539C2×C4—114no—
540C2×C4—118no—
541C2×C4—118no—
542C2×C4—114no—
543C2×C4—118no—
544C2×C4—2216no—
545C2×C4—2232no—
546C2×C4—2216no—
547C2×C4—228no—
548C2×C4—228no—
549C2×C4—224no—
550C2×C4—228no—
551C2×C4C2×#434114yes—
552C2×C4C2×#434114yes—
553C2×C4C2×#4341116yes—
554C2×C4C24×D1118yes—
555C2×C4C24×D1118yes—
556C2×C4C24×D1114yes—
557C2×C4C24×D1112yes—
558C2×C4C24×D1112yes—
559C22—24no—
560C22—28no—
561C22—24no—
562C22—28no—
563C22—48no—
564C22C22×#434114yes—
565C22C22×#434112yes—
566C22D11×2−1+414yes—
567C22C25×D1111yescharacteristic
568C4—24no—
569C4—28no—
570C4—28no—
571C4—118no—
572C4—228no—
573C4—228no—
574C4—224no—
575C4—228no—
576C4C22×#434114yes—
577C4C22×#434114yes—
578C2—24no—
579C2—44no—
580C2#1308250114yesdirect product factor
581C2C23×#434111yescharacteristic
582C2C2×D11×2−1+412yes—
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#536C2
socleC23×C11C25
prime radicalC22×C11×#41C22
hypercenterC2×#536D11
hypocenterC11C2×#3509
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
1. #13082501C2direct (N × H)
2. C2×#10623252C2semidirect
3. C2×#10623202C2semidirect
4. C2×#10623181C2semidirect
5. C2×#10623156C2semidirect
7. C2×#10623048C2semidirect
8. C2×#10623153C2semidirect
9. C22×#66997C2semidirect
10. C2×#10623343C2semidirect
11. C2×#10623047C2semidirect
25. #10623343C22semidirect
33. C2×#66997C22semidirect
46. #10623252C22semidirect
47. #10623202C22semidirect
48. #10623181C22semidirect
49. #10623156C22semidirect
50. #10623153C22semidirect
51. #10623048C22semidirect
52. #10623047C22semidirect
443. C2×C11#3509semidirect
517. C11C2×#3509semidirect
580. C2#13082501direct (N × H)

Maximal subgroups

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

subgroupindex
#130825012
C2×#106232522
C2×#106232022
C2×#106231812
C2×#106231562
C2×#106233562
C2×#106230482
C2×#106231532
C22×#669972
C2×#106233432
C2×#106230472
C2×#41×Dic112
C2×C11×#5362
C2×#350911