Finite Group Databasebeta

← C2×#13082323 #15661713

Subgroups — C2×#13082323 #15661713

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#13082323C2132yesmaximal, direct product factor
2C2×#10623166C214yesmaximal, complemented
3C2×#10623145C214yesmaximal, complemented
4C2×#10623170C214yesmaximal, complemented
5C2×#10623142C214yesmaximal, complemented
6C2×#10623031C211yesmaximal, characteristic, complemented
7C2×#10623133C214yesmaximal, complemented
8C2×#10623137C214yesmaximal, complemented
9C2×#10623359C212yesmaximal, complemented
10C2×#10623358C212yesmaximal, complemented
11C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
12C2×C11×#537C211yesmaximal, characteristic, complemented
13C22×C11×#41C2212yes—
14C22×#4341C2214yes—
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C11×#537C22116yescomplemented
18C2×C11×C22⋊Q8C2214yescomplemented
19C2×C11×#121C2214yes—
20C2×C11×#121C2214yescomplemented
21C22×C11×C4⋊C4C2211yescharacteristic
22#10623359C22132yescomplemented
23#10623358C22132yescomplemented
24C2×#66999C2212yes—
25C2×#66999C2212yes—
26C2×Q8×Dic11C2214yescomplemented
27C2×#66991C2214yes—
28C2×#66991C2212yes—
29C2×#66991C2212yes—
30C2×#66990C2214yes—
31C2×#66988C2214yes—
32C2×#66988C2218yescomplemented
33C2×D4×Dic11C2218yes—
34C2×D4×Dic11C2214yescomplemented
35C2×C4×C22⋊D11C2214yes—
36C2×C4×C22⋊D11C2214yes—
37C2×#66979C2212yes—
38C2×#66979C2214yescomplemented
39C22×C4⋊Dic11C2211yescharacteristic
40C22×C4⋊Dic11C2214yescomplemented
41C2×#66977C2214yes—
42C22×Dic11⋊C4C2212yes—
43#10623170C22164yescomplemented
44#10623166C22164yescomplemented
45#10623145C22164yescomplemented
46#10623142C22164yescomplemented
47#10623137C22164yescomplemented
48#10623133C22164yescomplemented
49C2×#66950C2214yes—
50C2×#66945C2214yes—
51C2×C4⋊C4×D11C2214yes—
52C2×C4⋊C4×D11C2214yes—
53C2×C4⋊C4×D11C22116yescomplemented
54#10623031C22116yescomplemented
55C2×#66943C2214yescomplemented
56C2×#66942C2218yescomplemented
57C2×#66941C2214yescomplemented
58C2×#66936C2218yes—
59C2×(C22⋊D11)⋊C4C2218yes—
60C2×#66932C2218yescomplemented
61C2×#66931C2218yescomplemented
62C24×D11C2311yescharacteristic
63C2×C11×#41—216no—
64C2×C11×#41C23116yes—
65C22×Q8×C11C2312yes—
66C22×D4×C11C2314yes—
67C22×D4×C11C2312yes—
68C22×D4×C11C2314yes—
69C23×C4×C11C2314yes—
70C23×C4×C11C2312yes—
71C23×C4×C11C2311yescharacteristic
72C22×C22⋊D11C2314yes—
73C22×C22⋊D11C2314yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2318yes—
76C23×Dic11C2312yes—
77C2×#4341—416no—
78C2×#4341C23132yes—
79C22×C4×D11—28no—
80C22×C4×D11—48no—
81C22×C4×D11C2314yes—
82C22×C4×D11C2312yes—
83C22×C4×D11C2312yes—
84C22×C4×D11C2318yes—
85C22×C4×D11C2314yes—
86C22×C4×D11C23116yes—
87C22×Dic22C2314yes—
88C11×C22⋊Q8C23132yescomplemented
89C11×#121C23132yes—
90C11×#121C23132yescomplemented
91C2×C11×C4⋊C4C2314yes—
92C2×C11×C4⋊C4C2314yes—
93C2×C11×C4⋊C4C2318yes—
94C2×C11×C22⋊C4C2318yes—
95C2×C22⋊Dic11C2314yes—
96C2×C22⋊Dic11C2314yes—
97C2×C22⋊Dic11C2318yes—
98C2×C22⋊Dic11C2314yes—
99#66999C23116yes—
100#66999C23116yes—
101Q8×Dic11C23132yescomplemented
102#66991C23116yes—
103#66991C23116yes—
104#66991C23132yes—
105#66990C23132yes—
106#66988C23132yes—
107#66988C23164yescomplemented
108D4×Dic11C23164yes—
109D4×Dic11C23132yescomplemented
110C4×C22⋊D11C23132yes—
111C4×C22⋊D11C23132yes—
112C2×(C2×D11)⋊C4C2314yes—
113C2×(C2×D11)⋊C4C2314yes—
114#66979C23116yes—
115#66979C23132yescomplemented
116C2×C4⋊Dic11C2318yes—
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2312yes—
119C2×C4⋊Dic11C2312yes—
120C2×C4⋊Dic11C2314yes—
121C2×C4⋊Dic11C2318yes—
122C2×C4⋊Dic11C23132yescomplemented
123#66977C23132yes—
124C2×Dic11⋊C4C2314yes—
125C2×Dic11⋊C4C2318yes—
126C2×Dic11⋊C4C2314yes—
127C2×Dic11⋊C4C2318yes—
128C2×Dic11⋊C4C23116yes—
129C2×C4×Dic11C2318yes—
130C2×C4×Dic11C2314yes—
131#66950C23132yes—
132#66945C23132yes—
133C4⋊C4×D11C23132yes—
134C4⋊C4×D11C23132yes—
135#66943C23132yescomplemented
136#66942C23164yescomplemented
137#66941C23132yescomplemented
138#66936C23164yes—
139(C22⋊D11)⋊C4C23164yes—
140#66932C23164yescomplemented
141#66931C23164yescomplemented
142C2×#3492—111nomaximal, Sylow
143C24×C11C2414yes—
144C24×C11C2411yescharacteristic
145C23×D11—24no—
146C23×D11—24no—
147C23×D11—24no—
148C23×D11C2414yes—
149C23×D11C2411yescharacteristic
150C23×D11C2411yescharacteristic
151C11×#41—264no—
152C2×Q8×C11—28no—
153C2×Q8×C11C2418yes—
154C2×D4×C11—216no—
155C2×D4×C11—28no—
156C2×D4×C11—48no—
157C2×D4×C11C24116yes—
158C2×D4×C11C2418yes—
159C2×D4×C11C24116yes—
160C22×C4×C11—216no—
161C22×C4×C11—44no—
162C22×C4×C11#4118yescomplemented
163C22×C4×C11C2414yes—
164C22×C4×C11C2414yes—
165C22×C4×C11C24116yes—
166C22×C4×C11C2418yes—
167C22×C4×C11C2412yes—
168C22×C4×C11C2414yes—
169C2×C22⋊D11—216no—
170C2×C22⋊D11—216no—
171C2×C22⋊D11C24116yes—
172C2×C22⋊D11C24116yes—
173C22×Dic11—24no—
174C22×Dic11—44no—
175C22×Dic11—416no—
176C22×Dic11C2414yes—
177C22×Dic11C2414yes—
178C22×Dic11C2414yes—
179C22×Dic11C2412yes—
180C22×Dic11C2414yes—
181C22×Dic11C24132yes—
182C22×Dic11C2418yes—
183#4341—464no—
184C2×C4×D11—216no—
185C2×C4×D11—28no—
186C2×C4×D11—28no—
187C2×C4×D11—232no—
188C2×C4×D11—48no—
189C2×C4×D11—432no—
190C2×C4×D11C24116yes—
191C2×C4×D11C2418yes—
192C2×C4×D11C2418yes—
193C2×C4×D11C24116yes—
194C2×Dic22—48no—
195C2×Dic22C24116yes—
196C11×C4⋊C4C24116yes—
197C11×C4⋊C4C24116yes—
198C11×C22⋊C4C24132yes—
199C22⋊Dic11C24116yes—
200C22⋊Dic11C24116yes—
201C22⋊Dic11C24132yes—
202C22⋊Dic11C24116yes—
203(C2×D11)⋊C4C24116yes—
204(C2×D11)⋊C4C24116yes—
205C4⋊Dic11C24132yes—
206C4⋊Dic11C24116yes—
207C4⋊Dic11C2418yes—
208C4⋊Dic11C2418yes—
209C4⋊Dic11C24116yes—
210Dic11⋊C4C24116yes—
211Dic11⋊C4C24132yes—
212Dic11⋊C4C24116yes—
213Dic11⋊C4C24132yes—
214C4×Dic11C24132yes—
215C4×Dic11C24116yes—
216#3492—1132no—
217C2×#554—114no—
218C2×#553—114no—
219C2×#552—114no—
220C2×#547—114no—
221C2×#544—111no—
222C2×#539—114no—
223C2×#537D1111yescharacteristic, complemented
224C2×#525—112no—
225C2×#525—114no—
226C2×#520—112no—
227C23×C4⋊C4—111no—
228C23×C11—22no—
229C23×C11—22no—
230C23×C11—28no—
231C23×C11—28no—
232C23×C11—28no—
233C23×C11C2×#4114yes—
234C23×C11C2518yes—
235C23×C11C2512yes—
236C23×C11C2511yescharacteristic
237C22×D11—232no—
238C22×D11—28no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—28no—
244C22×D11—28no—
245C22×D11H(5,𝔽2)14yes—
246C22×D112−1+414yes—
247C22×D11C2512yes—
248C22×D11C2512yes—
249Q8×C11—216no—
250D4×C11—232no—
251D4×C11—216no—
252D4×C11—416no—
253C2×C4×C11—28no—
254C2×C4×C11—28no—
255C2×C4×C11—232no—
256C2×C4×C11—48no—
257C2×C4×C11C2×#4118yes—
258C2×C4×C11C2×#41116yescomplemented
259C2×C4×C11C2518yes—
260C2×C4×C11C2518yes—
261C2×C4×C11C2514yes—
262C22⋊D11—232no—
263C22⋊D11—232no—
264C2×Dic11—28no—
265C2×Dic11—24no—
266C2×Dic11—28no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—48no—
270C2×Dic11—432no—
271C2×Dic11C2518yes—
272C2×Dic11C2518yes—
273C2×Dic11C2518yes—
274C2×Dic11C2514yes—
275C4×D11—232no—
276C4×D11—216no—
277C4×D11—216no—
278C4×D11—416no—
279Dic22—416no—
280C22×#41—114no—
281C22×#41C2×D1112yes—
282C24×C4—111no—
283C24×C4—112no—
284#554—1164no—
285#553—1164no—
286#552—1164no—
287#547—1164no—
288#544—1116no—
289#539—1164no—
290#537C2×D11116yescomplemented
291C2×C4⋊Q8—114no—
292C2×#126—118no—
293C2×#125—118no—
294C2×#125—114no—
295#525—1132no—
296#525—1164no—
297C2×#123—114no—
298C2×#123—118no—
299C2×#123—118no—
300C2×C22⋊Q8—112no—
301C2×C22⋊Q8—112no—
302C2×C22⋊Q8—114no—
303C2×C22⋊Q8—114no—
304C2×C22⋊Q8—118no—
305C2×C22⋊Q8C2×D1114yescomplemented
306C2×#121—112no—
307C2×#121—114no—
308C2×#121—112no—
309C2×#121C2×D1114yes—
310C2×#121C2×D1114yescomplemented
311C2×#120—114no—
312#520—1132no—
313C2×C4×Q8—114no—
314C2×C4×D4—118no—
315C2×C4×D4—114no—
316C2×C4×D4—114no—
317C2×C4×D4—114no—
318C2×C4×D4—118no—
319C2×#117—112no—
320C2×#117—114no—
321C2×#117—114no—
322C22×C4⋊C4—112no—
323C22×C4⋊C4—111no—
324C22×C4⋊C4—114no—
325C22×C4⋊C4—114no—
326C22×C4⋊C4—114no—
327C22×C4⋊C4—1116no—
328C22×C4⋊C4C2×D1111yescharacteristic
329C22×C11—22no—
330C22×C11—22no—
331C22×C11—28no—
332C22×C11—28no—
333C22×C11—28no—
334C22×C11—28no—
335C22×C11—416no—
336C22×C11C22×#4114yes—
337C22×C11C22×#4112yes—
338C22×C11C2×H(5,𝔽2)12yes—
339C22×C11C2×2−1+412yes—
340C22×C11C2611yescharacteristic
341C2×D11—232no—
342C2×D11—22no—
343C2×D11—22no—
344C2×D11—22no—
345C2×D11—22no—
346C2×D11—28no—
347C2×D11—28no—
348C2×D11C2×H(5,𝔽2)14yes—
349C2×D11C2×2−1+414yes—
350C4×C11—28no—
351C4×C11—28no—
352C4×C11C22×#4118yes—
353Dic11—24no—
354Dic11—28no—
355Dic11—28no—
356Dic11—28no—
357C25—111no—
358C2×#41—216no—
359C2×#41—1132no—
360C2×#41—4416no—
361C2×#41C22×D11116yes—
362C22×Q8—114no—
363C22×Q8C22×D1112yes—
364C22×D4—114no—
365C22×D4—114no—
366C22×D4C22×D1114yes—
367C22×D4C22×D1112yes—
368C22×D4C22×D1114yes—
369C23×C4—111no—
370C23×C4—112no—
371C23×C4—118no—
372C23×C4—114no—
373C23×C4—112no—
374C23×C4—112no—
375C23×C4—118no—
376C23×C4—114no—
377C23×C4—1116no—
378C23×C4—228no—
379C23×C4—448no—
380C23×C4C22×D1114yes—
381C23×C4C22×D1112yes—
382C23×C4C22×D1111yescharacteristic
383C4⋊Q8—1132no—
384#126—1164no—
385#125—1164no—
386#125—1132no—
387#123—1132no—
388#123—1164no—
389#123—1164no—
390C22⋊Q8—1116no—
391C22⋊Q8—1116no—
392C22⋊Q8—1132no—
393C22⋊Q8—1132no—
394C22⋊Q8—1164no—
395C22⋊Q8C22×D11132yescomplemented
396#121—1116no—
397#121—1132no—
398#121—1116no—
399#121C22×D11132yes—
400#121C22×D11132yescomplemented
401#120—1132no—
402C4×Q8—1132no—
403C4×D4—1164no—
404C4×D4—1132no—
405C4×D4—1132no—
406C4×D4—1132no—
407C4×D4—1164no—
408#117—1116no—
409#117—1132no—
410#117—1132no—
411C2×C4⋊C4—114no—
412C2×C4⋊C4—118no—
413C2×C4⋊C4—118no—
414C2×C4⋊C4—1116no—
415C2×C4⋊C4—112no—
416C2×C4⋊C4—118no—
417C2×C4⋊C4—1132no—
418C2×C4⋊C4—112no—
419C2×C4⋊C4—114no—
420C2×C4⋊C4—114no—
421C2×C4⋊C4—118no—
422C2×C4⋊C4—114no—
423C2×C4⋊C4—1132no—
424C2×C4⋊C4—1132no—
425C2×C4⋊C4C22×D1114yes—
426C2×C4⋊C4C22×D1118yes—
427C2×C4⋊C4C22×D1114yes—
428C2×C22⋊C4—114no—
429C2×C22⋊C4—118no—
430C2×C22⋊C4—114no—
431C2×C22⋊C4—114no—
432C2×C22⋊C4—114no—
433C2×C22⋊C4—114no—
434C2×C22⋊C4C22×D1118yes—
435C2×C42—118no—
436C2×C42—114no—
437C2×C11—24no—
438C2×C11—48no—
439C2×C11#349214yescomplemented
440C2×C11C23×#4111yescharacteristic
441C2×C11C22×H(5,𝔽2)11yescharacteristic
442C2×C11C22×2−1+411yescharacteristic
443D11—24no—
444D11—24no—
445C24—111no—
446C24—111no—
447C24—114no—
448C24—224no—
449C24—224no—
450C24—224no—
451C24C23×D1114yes—
452C24C23×D1111yescharacteristic
453#41—264no—
454#41—4464no—
455C2×Q8—28no—
456C2×Q8—1116no—
457C2×Q8—448no—
458C2×Q8C23×D1118yes—
459C2×D4—216no—
460C2×D4—28no—
461C2×D4—48no—
462C2×D4—1116no—
463C2×D4—1116no—
464C2×D4—2216no—
465C2×D4—2216no—
466C2×D4C23×D11116yes—
467C2×D4C23×D1118yes—
468C2×D4C23×D11116yes—
469C22×C4—216no—
470C22×C4—44no—
471C22×C4—114no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—112no—
476C22×C4—118no—
477C22×C4—1132no—
478C22×C4—1116no—
479C22×C4—118no—
480C22×C4—118no—
481C22×C4—1116no—
482C22×C4—2216no—
483C22×C4—224no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—2232no—
487C22×C4—448no—
488C22×C4—4432no—
489C22×C4—444no—
490C22×C4—4416no—
491C22×C4#434118yescomplemented
492C22×C4C23×D11116yes—
493C22×C4C23×D1114yes—
494C22×C4C23×D1114yes—
495C22×C4C23×D1118yes—
496C22×C4C23×D1112yes—
497C22×C4C23×D1114yes—
498C4⋊C4—1116no—
499C4⋊C4—1132no—
500C4⋊C4—118no—
501C4⋊C4—1132no—
502C4⋊C4—118no—
503C4⋊C4—1116no—
504C4⋊C4—1116no—
505C4⋊C4—1132no—
506C4⋊C4—1116no—
507C4⋊C4C23×D11116yes—
508C4⋊C4C23×D11116yes—
509C22⋊C4—1116no—
510C22⋊C4—1132no—
511C22⋊C4—1116no—
512C22⋊C4—1116no—
513C22⋊C4—1116no—
514C22⋊C4—1116no—
515C22⋊C4C23×D11132yes—
516C42—1132no—
517C42—1116no—
518C11C2×#349211yescharacteristic, complemented, Sylow
519C23—22no—
520C23—22no—
521C23—28no—
522C23—28no—
523C23—28no—
524C23—114no—
525C23—114no—
526C23—112no—
527C23—112no—
528C23—228no—
529C23—228no—
530C23—2232no—
531C23—228no—
532C23—222no—
533C23—222no—
534C23—222no—
535C23—222no—
536C23C2×#434114yes—
537C23C24×D1118yes—
538C23C24×D1112yes—
539C23C24×D1111yescharacteristic
540Q8—216no—
541Q8—4416no—
542D4—232no—
543D4—216no—
544D4—416no—
545D4—2232no—
546D4—2232no—
547C2×C4—28no—
548C2×C4—28no—
549C2×C4—232no—
550C2×C4—48no—
551C2×C4—118no—
552C2×C4—118no—
553C2×C4—118no—
554C2×C4—114no—
555C2×C4—2232no—
556C2×C4—228no—
557C2×C4—224no—
558C2×C4—228no—
559C2×C4—228no—
560C2×C4—228no—
561C2×C4—2216no—
562C2×C4—2216no—
563C2×C4—4416no—
564C2×C4—448no—
565C2×C4—4432no—
566C2×C4C2×#434118yes—
567C2×C4C2×#4341116yescomplemented
568C2×C4C24×D1118yes—
569C2×C4C24×D1118yes—
570C2×C4C24×D1114yes—
571C22—22no—
572C22—22no—
573C22—28no—
574C22—28no—
575C22—28no—
576C22—28no—
577C22—416no—
578C22—114no—
579C22—114no—
580C22—2232no—
581C22—222no—
582C22—222no—
583C22—222no—
584C22—222no—
585C22—228no—
586C22—228no—
587C22C22×#434114yes—
588C22C22×#434112yes—
589C22D11×H(5,𝔽2)12yes—
590C22D11×2−1+412yes—
591C22C25×D1111yescharacteristic
592C4—28no—
593C4—28no—
594C4—224no—
595C4—228no—
596C4—228no—
597C4—228no—
598C4C22×#434118yes—
599C2—24no—
600C2—48no—
601C2—224no—
602C2—224no—
603C2#1308232314yesdirect product factor
604C2C23×#434111yescharacteristic
605C2C2×D11×H(5,𝔽2)11yescharacteristic
606C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#537C2
socleC23×C11C25
hypercenterC2×#537D11
hypocenterC11C2×#3492
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#537

Complements

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

NH ≅ G/Ntype
1. #13082323C2direct (N × H)
2. C2×#10623166C2semidirect
3. C2×#10623145C2semidirect
4. C2×#10623170C2semidirect
5. C2×#10623142C2semidirect
6. C2×#10623031C2semidirect
7. C2×#10623133C2semidirect
8. C2×#10623137C2semidirect
9. C2×#10623359C2semidirect
10. C2×#10623358C2semidirect
11. C22×C4⋊C4×D11C2semidirect
12. C2×C11×#537C2semidirect
17. C11×#537C22semidirect
18. C2×C11×C22⋊Q8C22semidirect
20. C2×C11×#121C22semidirect
22. #10623359C22semidirect
23. #10623358C22semidirect
26. C2×Q8×Dic11C22semidirect
32. C2×#66988C22semidirect
34. C2×D4×Dic11C22semidirect
38. C2×#66979C22semidirect
40. C22×C4⋊Dic11C22semidirect
43. #10623170C22semidirect
44. #10623166C22semidirect
45. #10623145C22semidirect
46. #10623142C22semidirect
47. #10623137C22semidirect
48. #10623133C22semidirect
53. C2×C4⋊C4×D11C22semidirect
54. #10623031C22semidirect
55. C2×#66943C22semidirect
56. C2×#66942C22semidirect
57. C2×#66941C22semidirect
60. C2×#66932C22semidirect
61. C2×#66931C22semidirect
88. C11×C22⋊Q8C23semidirect
90. C11×#121C23semidirect
101. Q8×Dic11C23semidirect
107. #66988C23semidirect
109. D4×Dic11C23semidirect
115. #66979C23semidirect
122. C2×C4⋊Dic11C23semidirect
135. #66943C23semidirect
136. #66942C23semidirect
137. #66941C23semidirect
140. #66932C23semidirect
141. #66931C23semidirect
162. C22×C4×C11#41semidirect
223. C2×#537D11semidirect
258. C2×C4×C11C2×#41semidirect
290. #537C2×D11semidirect
305. C2×C22⋊Q8C2×D11semidirect
310. C2×#121C2×D11semidirect
395. C22⋊Q8C22×D11semidirect
400. #121C22×D11semidirect
439. C2×C11#3492semidirect
491. C22×C4#4341semidirect
518. C11C2×#3492semidirect
567. C2×C4C2×#4341semidirect
603. C2#13082323direct (N × H)

Maximal subgroups

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

subgroupindex
#130823232
C2×#106231662
C2×#106231452
C2×#106231702
C2×#106231422
C2×#106230312
C2×#106231332
C2×#106231372
C2×#106233592
C2×#106233582
C22×C4⋊C4×D112
C2×C11×#5372
C2×#349211