Finite Group Databasebeta

← C2×#13078590 #15621618

Subgroups — C2×#13078590 #15621618

Order 2816.

2234 conjugacy classes of subgroups.

The subgroup lattice has 590 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623358C211yesmaximal, characteristic, complemented
2#13078590C2116yesmaximal, direct product factor
3C2×#10622657C212yesmaximal, complemented
4C2×#10622658C212yesmaximal, complemented
5C2×#10622648C212yesmaximal, complemented
6C2×#10622646C212yesmaximal, complemented
7C2×#10622577C211yesmaximal, characteristic, complemented
8C22×#66871C211yesmaximal, characteristic, complemented
9C2×#10622845C211yesmaximal, characteristic, complemented
10C2×#10622846C211yesmaximal, characteristic, complemented
11C2×#10622847C211yesmaximal, characteristic, complemented
12C2×C11×#537C211yesmaximal, characteristic
13C22×C11×#41C2211yescharacteristic
14C22×C11×#41C2211yescharacteristic
15C11×#537—24no—
16C11×#537C2218yes—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8C2212yes—
19C2×C11×#121—21no—
20C2×C11×#121—22no—
21C2×C11×#121C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23#10623358—24no—
24#10623358C2218yescomplemented
25C2×Q8×Dic11—21no—
26C2×D4×Dic11—22no—
27C2×D4×Dic11—21no—
28C2×#66979C2211yescharacteristic
29C2×#66979C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2212yes—
32C22×#4318C2211yescharacteristic
33C23×C11⋊C8C2211yescharacteristic
34#10622847C2218yescomplemented
35#10622846C2218yescomplemented
36#10622845C2218yescomplemented
37C2×#66899C2211yescharacteristic
38C2×#66899C2211yescharacteristic
39C2×#66899C2212yes—
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2212yes—
43C2×C22⋊(C11⋊C8)C2212yes—
44C2×C22⋊(C11⋊C8)C2212yes—
45#10622658C22116yescomplemented
46#10622657C22116yescomplemented
47#10622648C22116yescomplemented
48#10622646C22116yescomplemented
49#10622577C2218yescomplemented
50C2×#66872C2212yes—
51C2×#66871C2212yes—
52C2×#66871C2212yes—
53C2×#66871C2212yes—
54C2×#66871C2218yescomplemented
55C2×C11×#41—22no—
56C2×C11×#41—24no—
57C2×C11×#41—24no—
58C2×C11×#41—24no—
59C2×C11×#41—24no—
60C2×C11×#41D414yes—
61C2×C11×#41C2314yes—
62C2×C11×#41C2314yes—
63C22×Q8×C11D411yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11D412yes—
68C22×D4×C11D411yescharacteristic
69C22×D4×C11C2311yescharacteristic
70C23×C4×C11—21no—
71C23×C4×C11—21no—
72C23×C4×C11C2312yes—
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—22no—
75C23×Dic11—21no—
76C11×C22⋊Q8—28no—
77C11×C22⋊Q8—24no—
78C11×C22⋊Q8C2318yes—
79C11×#121—28no—
80C11×#121—216no—
81C11×#121—24no—
82C11×#121C2318yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C4⋊C4C2314yes—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—21no—
92Q8×Dic11—28no—
93D4×Dic11—216no—
94D4×Dic11—28no—
95#66979—24no—
96#66979—22no—
97#66979C2314yes—
98#66979C2318yes—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11—22no—
103C2×C4⋊Dic11C2312yes—
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2314yes—
106C2×C4⋊Dic11C2318yes—
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4×Dic11—22no—
109C2×C4×Dic11—21no—
110C2×#4318—24no—
111C2×#4318C2314yes—
112C22×C11⋊C8—24no—
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2314yes—
116C22×C11⋊C8C2312yes—
117#66899C2318yes—
118#66899C2314yes—
119#66899C2314yes—
120#66896C2318yes—
121#66896C2314yes—
122#66896C2314yes—
123C22⋊(C11⋊C8)C2318yes—
124C22⋊(C11⋊C8)C2318yes—
125#66872C2318yes—
126#66871C2318yes—
127#66871C2318yes—
128#66871C2318yes—
129C2×#3098—111nomaximal, Sylow
130C24×C11—21no—
131C24×C11C2×D412yes—
132C24×C11C2×D411yescharacteristic
133C11×#41—216no—
134C11×#41—28no—
135C11×#41—28no—
136C11×#41—28no—
137C11×#41—28no—
138C11×#41—48no—
139C2×Q8×C11—24no—
140C2×Q8×C11—21no—
141C2×Q8×C11—22no—
142C2×Q8×C11—22no—
143C2×Q8×C11C2×D414yes—
144C2×Q8×C11C2412yes—
145C2×D4×C11—28no—
146C2×D4×C11—24no—
147C2×D4×C11—28no—
148C2×D4×C11—24no—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—44no—
153C2×D4×C11—84no—
154C2×D4×C11C2×D418yes—
155C2×D4×C11C2×D414yes—
156C2×D4×C11C2412yes—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—24no—
162C22×C4×C11—24no—
163C22×C4×C11—44no—
164C22×C4×C11—82no—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4114yes—
170C22×C4×C11#4114yes—
171C22×C4×C11C2414yes—
172C22×C4×C11C2411yescharacteristic
173C22×C4×C11C2412yes—
174C22×Dic11—21no—
175C22×Dic11—22no—
176C22×Dic11—21no—
177C22×Dic11—28no—
178C22×Dic11—24no—
179C22×Dic11—82no—
180C22×Dic11—84no—
181C11×C4⋊C4—24no—
182C11×C4⋊C4—22no—
183C11×C4⋊C4—28no—
184C11×C4⋊C4C2414yes—
185C11×C22⋊C4—28no—
186C11×C22⋊C4—28no—
187C22⋊Dic11—28no—
188C22⋊Dic11—24no—
189C4⋊Dic11—21no—
190C4⋊Dic11—22no—
191C4⋊Dic11—28no—
192C4⋊Dic11—24no—
193C4⋊Dic11—21no—
194C4⋊Dic11C2414yes—
195C4⋊Dic11C2412yes—
196C4⋊Dic11C2412yes—
197C4×Dic11—28no—
198C4×Dic11—24no—
199#4318—28no—
200C2×C11⋊C8—22no—
201C2×C11⋊C8—22no—
202C2×C11⋊C8—28no—
203C2×C11⋊C8—24no—
204C2×C11⋊C8C2412yes—
205C2×C11⋊C8C2412yes—
206C2×C11⋊C8C2414yes—
207C2×#537D1111yescharacteristic
208C2×#520—111no—
209#3098—1116no—
210C2×#484—112no—
211C2×#485—112no—
212C2×#482—112no—
213C2×#480—112no—
214C2×#428—111no—
215C22×#107—111no—
216C2×#417—111no—
217C2×#416—111no—
218C2×#408—111no—
219C23×C11—22no—
220C23×C11—22no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—42no—
226C23×C11—42no—
227C23×C11—42no—
228C23×C11#12314yes—
229C23×C11C22×D414yes—
230C23×C11C22×D412yes—
231C23×C11C22×D411yescharacteristic
232Q8×C11—28no—
233Q8×C11—22no—
234Q8×C11—22no—
235Q8×C11—42no—
236D4×C11—216no—
237D4×C11—28no—
238D4×C11—22no—
239D4×C11—22no—
240D4×C11—48no—
241D4×C11—42no—
242D4×C11—88no—
243C2×C4×C11—24no—
244C2×C4×C11—28no—
245C2×C4×C11—24no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—22no—
249C2×C4×C11—42no—
250C2×C4×C11—44no—
251C2×C4×C11—48no—
252C2×C4×C11—84no—
253C2×C4×C11#12314yes—
254C2×C4×C11#12318yes—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C22×D412yes—
257C2×C4×C11C22×D411yescharacteristic
258C2×C4×C11C2×#4112yes—
259C2×C4×C11C2×#4112yes—
260C2×C4×C11C2×#4114yes—
261C2×C4×C11C2×#4114yes—
262C2×C4×C11C2511yescharacteristic
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—44no—
267C2×Dic11—42no—
268C2×Dic11—42no—
269C2×Dic11—84no—
270C2×Dic11—88no—
271C11⋊C8—22no—
272C11⋊C8—22no—
273C11⋊C8—24no—
274C22×#41C2×D1111yescharacteristic
275C22×#41C2×D1111yescharacteristic
276C22×M16—111no—
277C23×C8—111no—
278#537—24no—
279#537C2×D1118yes—
280C2×C22⋊Q8—21no—
281C2×C22⋊Q8C2×D1112yes—
282C2×#121—21no—
283C2×#121—22no—
284C2×#121C2×D1112yes—
285#520—118no—
286#520—224no—
287C2×C4×Q8—221no—
288C2×C4×D4—222no—
289C2×C4×D4—221no—
290C2×#117—112no—
291C2×#117—111no—
292C22×C4⋊C4—112no—
293C22×C4⋊C4—111no—
294C22×C4⋊C4C2×D1111yescharacteristic
295#485—1116no—
296#484—1116no—
297#482—1116no—
298#480—1116no—
299#428—118no—
300C2×#107—112no—
301C2×#107—112no—
302C2×#107—112no—
303C2×#107—118no—
304C2×#106—112no—
305#417—118no—
306#416—118no—
307C2×#103—111no—
308C2×#103—112no—
309C2×#103—111no—
310C2×#102—111no—
311C2×#102—112no—
312C2×#102—111no—
313#408—118no—
314C2×C22⋊C8—112no—
315C2×C22⋊C8—112no—
316C22×C11—28no—
317C22×C11—22no—
318C22×C11—22no—
319C22×C11—24no—
320C22×C11—24no—
321C22×C11—24no—
322C22×C11—48no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—84no—
327C22×C11C2×#12314yes—
328C22×C11C2×#12312yes—
329C22×C11#57612yes—
330C22×C11#57812yes—
331C22×C11C23×D411yescharacteristic
332C4×C11—24no—
333C4×C11—42no—
334C4×C11—44no—
335C4×C11C2×#12312yes—
336C4×C11C2×#12314yes—
337C4×C11C22×#4111yescharacteristic
338C4×C11C22×#4111yescharacteristic
339Dic11—44no—
340Dic11—42no—
341Dic11—42no—
342C2×#41—24no—
343C2×#41—24no—
344C2×#41—22no—
345C2×#41—24no—
346C2×#41—24no—
347C2×#41C22⋊D1114yes—
348C2×#41C22×D1114yes—
349C2×#41C22×D1114yes—
350C22×Q8C22⋊D1111yescharacteristic
351C22×Q8C22×D1111yescharacteristic
352C22×D4—21no—
353C22×D4—22no—
354C22×D4C22⋊D1112yes—
355C22×D4C22⋊D1111yescharacteristic
356C22×D4C22×D1111yescharacteristic
357C23×C4—21no—
358C23×C4—21no—
359C23×C4—222no—
360C23×C4—221no—
361C23×C4C22×D1112yes—
362C23×C4C22×D1111yescharacteristic
363C2×M16—114no—
364C2×M16—224no—
365C22×C8—111no—
366C22×C8—111no—
367C22×C8—114no—
368C22×C8—112no—
369C22×C8—224no—
370C22⋊Q8—28no—
371C22⋊Q8—24no—
372C22⋊Q8C22×D1118yes—
373#121—28no—
374#121—216no—
375#121—24no—
376#121C22×D1118yes—
377C4×Q8—228no—
378C4×D4—2216no—
379C4×D4—228no—
380#117—114no—
381#117—118no—
382#117—224no—
383#117—222no—
384C2×C4⋊C4—21no—
385C2×C4⋊C4—22no—
386C2×C4⋊C4—22no—
387C2×C4⋊C4—111no—
388C2×C4⋊C4—112no—
389C2×C4⋊C4—114no—
390C2×C4⋊C4—118no—
391C2×C4⋊C4—111no—
392C2×C4⋊C4—222no—
393C2×C4⋊C4—221no—
394C2×C4⋊C4—224no—
395C2×C4⋊C4—222no—
396C2×C4⋊C4C22×D1112yes—
397C2×C4⋊C4C22×D1114yes—
398C2×C22⋊C4—22no—
399C2×C22⋊C4—22no—
400C2×C22⋊C4—222no—
401C2×C22⋊C4—221no—
402C2×C42—222no—
403C2×C42—221no—
404#107—118no—
405#107—118no—
406#107—118no—
407#106—118no—
408#103—114no—
409#103—114no—
410#103—118no—
411#102—114no—
412#102—114no—
413#102—118no—
414C22⋊C8—118no—
415C22⋊C8—118no—
416C2×C11—24no—
417C2×C11—44no—
418C2×C11—82no—
419C2×C11#309814yescomplemented
420C2×C11C22×#12311yescharacteristic
421C2×C11C2×#57611yescharacteristic
422C2×C11C2×#57811yescharacteristic
423C24—21no—
424C24C2×C22⋊D1112yes—
425C24C2×C22⋊D1111yescharacteristic
426#41—216no—
427#41—28no—
428#41—28no—
429#41—28no—
430#41—28no—
431#41—48no—
432C2×Q8—24no—
433C2×Q8—21no—
434C2×Q8—22no—
435C2×Q8—22no—
436C2×Q8C2×C22⋊D1114yes—
437C2×Q8C23×D1112yes—
438C2×D4—28no—
439C2×D4—24no—
440C2×D4—28no—
441C2×D4—24no—
442C2×D4—22no—
443C2×D4—22no—
444C2×D4—21no—
445C2×D4—44no—
446C2×D4—84no—
447C2×D4C2×C22⋊D1118yes—
448C2×D4C2×C22⋊D1114yes—
449C2×D4C23×D1112yes—
450C22×C4—24no—
451C22×C4—24no—
452C22×C4—22no—
453C22×C4—21no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—44no—
457C22×C4—82no—
458C22×C4—221no—
459C22×C4—222no—
460C22×C4—221no—
461C22×C4—228no—
462C22×C4—224no—
463C22×C4—882no—
464C22×C4—884no—
465C22×C4#434114yes—
466C22×C4#434114yes—
467C22×C4C2×C22⋊D1114yes—
468C22×C4C2×C22⋊D1112yes—
469C22×C4C2×C22⋊D1112yes—
470C22×C4C2×C22⋊D1111yescharacteristic
471C22×C4C23×D1114yes—
472C22×C4C23×D1112yes—
473C22×C4C23×D1111yescharacteristic
474M16—228no—
475C2×C8—114no—
476C2×C8—112no—
477C2×C8—112no—
478C2×C8—222no—
479C2×C8—222no—
480C2×C8—228no—
481C2×C8—224no—
482C4⋊C4—24no—
483C4⋊C4—22no—
484C4⋊C4—28no—
485C4⋊C4—112no—
486C4⋊C4—112no—
487C4⋊C4—114no—
488C4⋊C4—221no—
489C4⋊C4—222no—
490C4⋊C4—228no—
491C4⋊C4—224no—
492C4⋊C4—221no—
493C4⋊C4C23×D1114yes—
494C22⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—228no—
497C22⋊C4—224no—
498C42—228no—
499C42—224no—
500C11C2×#309811yescharacteristic, complemented, Sylow
501C23—22no—
502C23—22no—
503C23—24no—
504C23—24no—
505C23—24no—
506C23—22no—
507C23—42no—
508C23—42no—
509C23—42no—
510C23#6698814yes—
511C23C22×C22⋊D1114yes—
512C23C22×C22⋊D1112yes—
513C23C22×C22⋊D1111yescharacteristic
514Q8—28no—
515Q8—22no—
516Q8—22no—
517Q8—42no—
518D4—216no—
519D4—28no—
520D4—22no—
521D4—22no—
522D4—48no—
523D4—42no—
524D4—88no—
525C2×C4—24no—
526C2×C4—28no—
527C2×C4—24no—
528C2×C4—24no—
529C2×C4—24no—
530C2×C4—22no—
531C2×C4—42no—
532C2×C4—44no—
533C2×C4—48no—
534C2×C4—84no—
535C2×C4—222no—
536C2×C4—224no—
537C2×C4—222no—
538C2×C4—444no—
539C2×C4—442no—
540C2×C4—442no—
541C2×C4—884no—
542C2×C4—888no—
543C2×C4#6698814yes—
544C2×C4#6698818yes—
545C2×C4C2×#434112yes—
546C2×C4C2×#434112yes—
547C2×C4C2×#434114yes—
548C2×C4C2×#434114yes—
549C2×C4C22×C22⋊D1114yes—
550C2×C4C22×C22⋊D1112yes—
551C2×C4C22×C22⋊D1111yescharacteristic
552C2×C4C24×D1111yescharacteristic
553C8—222no—
554C8—222no—
555C8—224no—
556C22—28no—
557C22—22no—
558C22—22no—
559C22—24no—
560C22—24no—
561C22—24no—
562C22—48no—
563C22—42no—
564C22—42no—
565C22—42no—
566C22—84no—
567C22C2×#6698814yes—
568C22C2×#6698812yes—
569C22#1062336612yes—
570C22#1062336912yes—
571C22C23×C22⋊D1111yescharacteristic
572C4—24no—
573C4—44no—
574C4—42no—
575C4—444no—
576C4—442no—
577C4—442no—
578C4C2×#6698812yes—
579C4C2×#6698814yes—
580C4C22×#434111yescharacteristic
581C4C22×#434111yescharacteristic
582C2—24no—
583C2—44no—
584C2—82no—
585C2#1307859014yesdirect product factor
586C2C22×#6698811yescharacteristic
587C2C2×#1062336611yescharacteristic
588C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
Fitting, prime radicalC2×C11×#537C2
socleC23×C11C22×D4
hypercenterC2×#537D11
hypocenterC11C2×#3098
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×#41 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. C2×#10623358C2semidirect
2. #13078590C2direct (N × H)
3. C2×#10622657C2semidirect
4. C2×#10622658C2semidirect
5. C2×#10622648C2semidirect
6. C2×#10622646C2semidirect
7. C2×#10622577C2semidirect
8. C22×#66871C2semidirect
9. C2×#10622845C2semidirect
10. C2×#10622846C2semidirect
11. C2×#10622847C2semidirect
24. #10623358C22semidirect
34. #10622847C22semidirect
35. #10622846C22semidirect
36. #10622845C22semidirect
45. #10622658C22semidirect
46. #10622657C22semidirect
47. #10622648C22semidirect
48. #10622646C22semidirect
49. #10622577C22semidirect
54. C2×#66871C22semidirect
419. C2×C11#3098semidirect
500. C11C2×#3098semidirect
585. C2#13078590direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233582
#130785902
C2×#106226572
C2×#106226582
C2×#106226482
C2×#106226462
C2×#106225772
C22×#668712
C2×#106228452
C2×#106228462
C2×#106228472
C2×C11×#5372
C2×#309811