Finite Group Databasebeta

← C2×#13082326 #15661715

Subgroups — C2×#13082326 #15661715

Order 2816.

7910 conjugacy classes of subgroups.

The subgroup lattice has 608 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082326C2132yesmaximal, direct product factor
2C2×#10623261C214yesmaximal, complemented
3C2×#10623226C214yesmaximal, complemented
4C2×#10623225C214yesmaximal, complemented
5C2×#10623257C214yesmaximal, complemented
6C2×#10623176C214yesmaximal, complemented
7C2×#10623041C211yesmaximal, characteristic, complemented
8C2×#10623158C214yesmaximal, complemented
9C2×#10623055C212yesmaximal, complemented
10C2×#10623054C212yesmaximal, complemented
11C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
12C2×C11×#544C211yesmaximal, characteristic, complemented
13C22×#4343C2214yes—
14C22×#4339C2212yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C11×#544C22116yescomplemented
18C2×C11×C4⋊Q8C2214yescomplemented
19C2×C11×#125C2214yescomplemented
20C2×C11×C22⋊Q8C2214yes—
21C2×C11×#117C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C2×#66999C2214yes—
24C2×#66999C2218yescomplemented
25C2×#66983C2214yes—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28#10623261C22164yescomplemented
29#10623257C22164yescomplemented
30#10623226C22164yescomplemented
31#10623225C22164yescomplemented
32#10623176C22164yescomplemented
33#10623158C22164yescomplemented
34#10623055C22132yescomplemented
35#10623054C22132yescomplemented
36C2×#66951C2218yescomplemented
37#10623041C22116yescomplemented
38C2×#66950C2212yes—
39C2×#66950C2212yes—
40C2×#66950C2214yescomplemented
41C2×#66948C2212yes—
42C2×#66948C2212yes—
43C2×#66948C2214yes—
44C2×#66948C2214yescomplemented
45C2×#66947C2218yes—
46C2×#66947C2218yescomplemented
47C2×#66946C2218yes—
48C2×#66945C2214yes—
49C2×#66945C2214yescomplemented
50C2×C4⋊C4×D11C2214yes—
51C2×C4⋊C4×D11C2214yes—
52C2×C4⋊C4×D11C22116yescomplemented
53C2×C4⋊C4×D11C2214yescomplemented
54C2×#66943C2218yescomplemented
55C2×#66939C2214yes—
56C2×#66935C2214yes—
57C2×(C22⋊D11)⋊C4C2218yes—
58C2×C4×D44C2214yes—
59C2×C4×D44C2214yes—
60C2×C4×D44C2214yescomplemented
61C2×C4×Dic22C2214yescomplemented
62C24×D11C2311yescharacteristic
63C22×Q8×C11C2314yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2314yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2312yes—
69C2×#4343—416no—
70C2×#4343C23132yes—
71C2×#4339—216no—
72C2×#4339C23116yes—
73C22×D44C2314yes—
74C22×D44C2314yes—
75C22×D44C2312yes—
76C22×D44C2314yes—
77C22×C4×D11—28no—
78C22×C4×D11—48no—
79C22×C4×D11C2312yes—
80C22×C4×D11C2312yes—
81C22×C4×D11C2314yes—
82C22×C4×D11C2314yes—
83C22×C4×D11C2318yes—
84C22×C4×D11C2318yes—
85C22×C4×D11C2314yes—
86C22×C4×D11C23116yes—
87C22×Dic22C2312yes—
88C11×C4⋊Q8C23132yescomplemented
89C11×#125C23132yescomplemented
90C11×C22⋊Q8C23132yes—
91C11×#117C23116yes—
92C2×C11×C4⋊C4C2318yes—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C4⋊C4C2312yes—
95C2×C11×C4⋊C4C2318yes—
96C2×C11×C4⋊C4C2314yes—
97C2×C11×C4⋊C4C2312yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C42×C11C2314yes—
100#66999C23132yes—
101#66999C23164yescomplemented
102#66983C23132yes—
103C2×(C2×D11)⋊C4C2314yes—
104C2×(C2×D11)⋊C4C2314yes—
105C2×(C2×D11)⋊C4C2314yes—
106C2×(C2×D11)⋊C4C2314yes—
107C2×(C2×D11)⋊C4C2318yes—
108C2×(C2×D11)⋊C4C2318yes—
109C2×C4⋊Dic11C2314yes—
110C2×C4⋊Dic11C2314yes—
111C2×C4⋊Dic11C2314yes—
112C2×C4⋊Dic11C2314yes—
113C2×C4⋊Dic11C2318yes—
114C2×Dic11⋊C4C2318yes—
115C2×Dic11⋊C4C2318yes—
116C2×Dic11⋊C4C23116yes—
117C2×C4×Dic11C2318yes—
118#66951C23164yescomplemented
119#66950C23116yes—
120#66950C23116yes—
121#66950C23132yescomplemented
122#66948C23116yes—
123#66948C23116yes—
124#66948C23132yes—
125#66948C23132yescomplemented
126#66947C23164yes—
127#66947C23164yescomplemented
128#66946C23164yes—
129#66945C23132yes—
130#66945C23132yescomplemented
131C4⋊C4×D11C23132yes—
132C4⋊C4×D11C23132yes—
133C4⋊C4×D11C23132yescomplemented
134#66943C23164yescomplemented
135#66939C23132yes—
136#66935C23132yes—
137(C22⋊D11)⋊C4C23164yes—
138C4×D44C23132yes—
139C4×D44C23132yes—
140C4×D44C23132yescomplemented
141C4×Dic22C23132yescomplemented
142C2×#3492—111nomaximal, Sylow
143C24×C11C2411yescharacteristic
144C23×D11—24no—
145C23×D11—24no—
146C23×D11—24no—
147C23×D11C2414yes—
148C23×D11C2414yes—
149C23×D11C2411yescharacteristic
150C23×D11C2411yescharacteristic
151C2×Q8×C11—48no—
152C2×Q8×C11C24116yes—
153C22×C4×C11—44no—
154C22×C4×C11#4118yescomplemented
155C22×C4×C11C2414yes—
156C22×C4×C11C2414yes—
157C22×C4×C11C2414yes—
158C22×C4×C11C2418yes—
159C22×C4×C11C2412yes—
160C22×C4×C11C2414yes—
161C2×C22⋊D11—216no—
162C2×C22⋊D11C24116yes—
163C22×Dic11—24no—
164C22×Dic11—44no—
165C22×Dic11C2414yes—
166C22×Dic11C2414yes—
167C22×Dic11C2414yes—
168C22×Dic11C2412yes—
169C22×Dic11C2418yes—
170#4343—464no—
171#4339—264no—
172C2×D44—216no—
173C2×D44—216no—
174C2×D44—28no—
175C2×D44—48no—
176C2×D44C24116yes—
177C2×D44C24116yes—
178C2×D44C2418yes—
179C2×D44C24116yes—
180C2×C4×D11—216no—
181C2×C4×D11—28no—
182C2×C4×D11—28no—
183C2×C4×D11—216no—
184C2×C4×D11—232no—
185C2×C4×D11—48no—
186C2×C4×D11—416no—
187C2×C4×D11—432no—
188C2×C4×D11C2418yes—
189C2×C4×D11C2418yes—
190C2×C4×D11C24116yes—
191C2×C4×D11C24116yes—
192C2×C4×D11C24132yes—
193C2×C4×D11C24116yes—
194C2×Dic22—28no—
195C2×Dic22C2418yes—
196C11×C4⋊C4C24132yes—
197C11×C4⋊C4C24116yes—
198C11×C4⋊C4C2418yes—
199C11×C4⋊C4C24116yes—
200C11×C4⋊C4C2418yes—
201C11×C22⋊C4C24116yes—
202C42×C11C24116yes—
203(C2×D11)⋊C4C24116yes—
204(C2×D11)⋊C4C24116yes—
205(C2×D11)⋊C4C24116yes—
206(C2×D11)⋊C4C24116yes—
207(C2×D11)⋊C4C24132yes—
208(C2×D11)⋊C4C24132yes—
209C4⋊Dic11C24116yes—
210C4⋊Dic11C24116yes—
211C4⋊Dic11C24116yes—
212C4⋊Dic11C24116yes—
213Dic11⋊C4C24132yes—
214Dic11⋊C4C24132yes—
215C4×Dic11C24132yes—
216#3492—1132no—
217C2×#554—114no—
218C2×#553—114no—
219C2×#552—114no—
220C2×#547—114no—
221C2×#544D1111yescharacteristic, complemented
222C2×#539—114no—
223C2×#537—111no—
224C2×#525—114no—
225C2×#525—112no—
226C2×#520—112no—
227C23×C4⋊C4—111no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11C2×#4114yes—
231C23×C11C2512yes—
232C23×C11C2511yescharacteristic
233C22×D11—232no—
234C22×D11—28no—
235C22×D11—22no—
236C22×D11—22no—
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—28no—
240C22×D11—28no—
241C22×D11—28no—
242C22×D11—28no—
243C22×D11—28no—
244C22×D11H(5,𝔽2)14yes—
245C22×D112−1+414yes—
246C22×D11C2518yes—
247C22×D11C2512yes—
248C22×D11C2512yes—
249Q8×C11—416no—
250C2×C4×C11—28no—
251C2×C4×C11—28no—
252C2×C4×C11—28no—
253C2×C4×C11—48no—
254C2×C4×C11C2×#4118yes—
255C2×C4×C11C2×#41116yescomplemented
256C2×C4×C11C2518yes—
257C2×C4×C11C2518yes—
258C2×C4×C11C2518yes—
259C2×C4×C11C2514yes—
260C22⋊D11—232no—
261C2×Dic11—28no—
262C2×Dic11—28no—
263C2×Dic11—24no—
264C2×Dic11—28no—
265C2×Dic11—48no—
266C2×Dic11C2518yes—
267C2×Dic11C2518yes—
268C2×Dic11C2514yes—
269D44—232no—
270D44—232no—
271D44—216no—
272D44—416no—
273C4×D11—232no—
274C4×D11—216no—
275C4×D11—216no—
276C4×D11—232no—
277C4×D11—416no—
278C4×D11—432no—
279Dic22—216no—
280C22×#41—114no—
281C22×#41—112no—
282C24×C4—111no—
283C24×C4—112no—
284#554—1164no—
285#553—1164no—
286#552—1164no—
287#547—1164no—
288#544C2×D11116yescomplemented
289#539—1164no—
290#537—1116no—
291C2×C4⋊Q8C2×D1114yescomplemented
292C2×#126—118no—
293C2×#125—118no—
294C2×#125C2×D1114yescomplemented
295#525—1164no—
296#525—1132no—
297C2×#123—118no—
298C2×#123—118no—
299C2×#123—114no—
300C2×C22⋊Q8—114no—
301C2×C22⋊Q8—118no—
302C2×C22⋊Q8—112no—
303C2×C22⋊Q8—112no—
304C2×C22⋊Q8—114no—
305C2×C22⋊Q8C2×D1114yes—
306C2×#121—114no—
307C2×#121—112no—
308C2×#121—114no—
309C2×#121—112no—
310C2×#121—114no—
311C2×#120—114no—
312#520—1132no—
313C2×C4×Q8—114no—
314C2×C4×D4—118no—
315C2×C4×D4—118no—
316C2×C4×D4—114no—
317C2×C4×D4—114no—
318C2×C4×D4—114no—
319C2×#117—114no—
320C2×#117—114no—
321C2×#117C2×D1112yes—
322C22×C4⋊C4—112no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—114no—
325C22×C4⋊C4—114no—
326C22×C4⋊C4—1116no—
327C22×C4⋊C4—114no—
328C22×C4⋊C4C2×D1111yescharacteristic
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—28no—
332C22×C11C22×#4114yes—
333C22×C11C22×#4112yes—
334C22×C11C2×H(5,𝔽2)12yes—
335C22×C11C2×2−1+412yes—
336C22×C11C2611yescharacteristic
337C2×D11—232no—
338C2×D11—22no—
339C2×D11—22no—
340C2×D11—22no—
341C2×D11—22no—
342C2×D11—28no—
343C2×D11—28no—
344C2×D11—28no—
345C2×D11—28no—
346C2×D11—28no—
347C2×D11—416no—
348C2×D11C2×H(5,𝔽2)14yes—
349C2×D11C2×2−1+414yes—
350C4×C11—28no—
351C4×C11—28no—
352C4×C11—28no—
353C4×C11C22×#4118yes—
354Dic11—28no—
355Dic11—24no—
356Dic11—28no—
357C25—111no—
358C2×#41—1132no—
359C2×#41—1116no—
360C2×#41—2216no—
361C2×#41—4416no—
362C22×Q8—112no—
363C22×Q8C22×D1114yes—
364C22×D4—114no—
365C22×D4—114no—
366C22×D4—112no—
367C22×D4—114no—
368C22×D4—114no—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—114no—
372C23×C4—112no—
373C23×C4—112no—
374C23×C4—118no—
375C23×C4—114no—
376C23×C4—114no—
377C23×C4—1116no—
378C23×C4—118no—
379C23×C4—228no—
380C23×C4—448no—
381C23×C4C22×D1112yes—
382C23×C4C22×D1111yescharacteristic
383C4⋊Q8C22×D11132yescomplemented
384#126—1164no—
385#125—1164no—
386#125C22×D11132yescomplemented
387#123—1164no—
388#123—1164no—
389#123—1132no—
390C22⋊Q8—1132no—
391C22⋊Q8—1164no—
392C22⋊Q8—1116no—
393C22⋊Q8—1116no—
394C22⋊Q8—1132no—
395C22⋊Q8C22×D11132yes—
396#121—1132no—
397#121—1116no—
398#121—1132no—
399#121—1116no—
400#121—1132no—
401#120—1132no—
402C4×Q8—1132no—
403C4×D4—1164no—
404C4×D4—1164no—
405C4×D4—1132no—
406C4×D4—1132no—
407C4×D4—1132no—
408#117—1132no—
409#117—1132no—
410#117C22×D11116yes—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—118no—
413C2×C4⋊C4—118no—
414C2×C4⋊C4—1116no—
415C2×C4⋊C4—118no—
416C2×C4⋊C4—114no—
417C2×C4⋊C4—114no—
418C2×C4⋊C4—114no—
419C2×C4⋊C4—1132no—
420C2×C4⋊C4—1132no—
421C2×C4⋊C4—1132no—
422C2×C4⋊C4C22×D1114yes—
423C2×C4⋊C4C22×D1118yes—
424C2×C4⋊C4C22×D1112yes—
425C2×C4⋊C4C22×D1112yes—
426C2×C4⋊C4C22×D1114yes—
427C2×C4⋊C4C22×D1118yes—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—118no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4C22×D1114yes—
435C2×C42—118no—
436C2×C42C22×D1114yes—
437C2×C11—24no—
438C2×C11#349214yescomplemented
439C2×C11C23×#4111yescharacteristic
440C2×C11C22×H(5,𝔽2)11yescharacteristic
441C2×C11C22×2−1+411yescharacteristic
442D11—24no—
443D11—24no—
444D11—48no—
445C24—111no—
446C24—111no—
447C24—114no—
448C24—114no—
449C24—224no—
450C24—224no—
451C24—224no—
452C24C23×D1111yescharacteristic
453#41—2264no—
454#41—4464no—
455C2×Q8—48no—
456C2×Q8—118no—
457C2×Q8—228no—
458C2×Q8C23×D11116yes—
459C2×D4—1116no—
460C2×D4—1116no—
461C2×D4—118no—
462C2×D4—1116no—
463C2×D4—1116no—
464C2×D4—2216no—
465C2×D4—2216no—
466C2×D4—2216no—
467C2×D4—228no—
468C2×D4—448no—
469C22×C4—44no—
470C22×C4—114no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—112no—
474C22×C4—118no—
475C22×C4—1116no—
476C22×C4—118no—
477C22×C4—118no—
478C22×C4—1116no—
479C22×C4—1116no—
480C22×C4—1132no—
481C22×C4—2216no—
482C22×C4—224no—
483C22×C4—228no—
484C22×C4—228no—
485C22×C4—2216no—
486C22×C4—2232no—
487C22×C4—448no—
488C22×C4—4416no—
489C22×C4—4432no—
490C22×C4—444no—
491C22×C4#434318yescomplemented
492C22×C4C23×D1114yes—
493C22×C4C23×D1114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1118yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1114yes—
498C4⋊C4—1116no—
499C4⋊C4—1132no—
500C4⋊C4—1132no—
501C4⋊C4—1116no—
502C4⋊C4—1116no—
503C4⋊C4—1116no—
504C4⋊C4C23×D11116yes—
505C4⋊C4C23×D1118yes—
506C4⋊C4C23×D1118yes—
507C4⋊C4C23×D11116yes—
508C4⋊C4C23×D11132yes—
509C22⋊C4—1116no—
510C22⋊C4—1132no—
511C22⋊C4—1116no—
512C22⋊C4—1132no—
513C22⋊C4—1116no—
514C22⋊C4—1116no—
515C22⋊C4C23×D11116yes—
516C42—1132no—
517C42C23×D11116yes—
518C11C2×#349211yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—114no—
522C23—114no—
523C23—112no—
524C23—112no—
525C23—118no—
526C23—228no—
527C23—228no—
528C23—2232no—
529C23—228no—
530C23—222no—
531C23—222no—
532C23—222no—
533C23—222no—
534C23—228no—
535C23—228no—
536C23—228no—
537C23C2×#434314yes—
538C23C24×D1112yes—
539C23C24×D1111yescharacteristic
540Q8—416no—
541Q8—2216no—
542D4—2232no—
543D4—2232no—
544D4—2232no—
545D4—2216no—
546D4—4416no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—28no—
550C2×C4—48no—
551C2×C4—118no—
552C2×C4—118no—
553C2×C4—114no—
554C2×C4—2232no—
555C2×C4—228no—
556C2×C4—224no—
557C2×C4—228no—
558C2×C4—228no—
559C2×C4—2216no—
560C2×C4—2216no—
561C2×C4—2232no—
562C2×C4—4416no—
563C2×C4—4432no—
564C2×C4—448no—
565C2×C4C2×#434318yes—
566C2×C4C2×#4343116yescomplemented
567C2×C4C24×D1118yes—
568C2×C4C24×D1118yes—
569C2×C4C24×D1118yes—
570C2×C4C24×D1114yes—
571C22—22no—
572C22—22no—
573C22—28no—
574C22—114no—
575C22—114no—
576C22—2232no—
577C22—222no—
578C22—222no—
579C22—222no—
580C22—222no—
581C22—228no—
582C22—228no—
583C22—228no—
584C22—228no—
585C22—228no—
586C22—4416no—
587C22C22×#434314yes—
588C22C22×#434312yes—
589C22D11×H(5,𝔽2)12yes—
590C22D11×2−1+412yes—
591C22C25×D1111yescharacteristic
592C4—28no—
593C4—28no—
594C4—28no—
595C4—224no—
596C4—228no—
597C4—228no—
598C4C22×#434318yes—
599C2—24no—
600C2—224no—
601C2—224no—
602C2—448no—
603C2#1308232614yesdirect product factor
604C2C23×#434311yescharacteristic
605C2C2×D11×H(5,𝔽2)11yescharacteristic
606C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#544C2
socleC23×C11C25
hypercenterC2×#544D11
hypocenterC11C2×#3492
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#544

Complements

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

NH ≅ G/Ntype
1. #13082326C2direct (N × H)
2. C2×#10623261C2semidirect
3. C2×#10623226C2semidirect
4. C2×#10623225C2semidirect
5. C2×#10623257C2semidirect
6. C2×#10623176C2semidirect
7. C2×#10623041C2semidirect
8. C2×#10623158C2semidirect
9. C2×#10623055C2semidirect
10. C2×#10623054C2semidirect
11. C22×C4⋊C4×D11C2semidirect
12. C2×C11×#544C2semidirect
17. C11×#544C22semidirect
18. C2×C11×C4⋊Q8C22semidirect
19. C2×C11×#125C22semidirect
24. C2×#66999C22semidirect
28. #10623261C22semidirect
29. #10623257C22semidirect
30. #10623226C22semidirect
31. #10623225C22semidirect
32. #10623176C22semidirect
33. #10623158C22semidirect
34. #10623055C22semidirect
35. #10623054C22semidirect
36. C2×#66951C22semidirect
37. #10623041C22semidirect
40. C2×#66950C22semidirect
44. C2×#66948C22semidirect
46. C2×#66947C22semidirect
49. C2×#66945C22semidirect
52. C2×C4⋊C4×D11C22semidirect
53. C2×C4⋊C4×D11C22semidirect
54. C2×#66943C22semidirect
60. C2×C4×D44C22semidirect
61. C2×C4×Dic22C22semidirect
88. C11×C4⋊Q8C23semidirect
89. C11×#125C23semidirect
101. #66999C23semidirect
118. #66951C23semidirect
121. #66950C23semidirect
125. #66948C23semidirect
127. #66947C23semidirect
130. #66945C23semidirect
133. C4⋊C4×D11C23semidirect
134. #66943C23semidirect
140. C4×D44C23semidirect
141. C4×Dic22C23semidirect
154. C22×C4×C11#41semidirect
221. C2×#544D11semidirect
255. C2×C4×C11C2×#41semidirect
288. #544C2×D11semidirect
291. C2×C4⋊Q8C2×D11semidirect
294. C2×#125C2×D11semidirect
383. C4⋊Q8C22×D11semidirect
386. #125C22×D11semidirect
438. C2×C11#3492semidirect
491. C22×C4#4343semidirect
518. C11C2×#3492semidirect
566. C2×C4C2×#4343semidirect
603. C2#13082326direct (N × H)

Maximal subgroups

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

subgroupindex
#130823262
C2×#106232612
C2×#106232262
C2×#106232252
C2×#106232572
C2×#106231762
C2×#106230412
C2×#106231582
C2×#106230552
C2×#106230542
C22×C4⋊C4×D112
C2×C11×#5442
C2×#349211