Finite Group Databasebeta

← C2×#13079588 #15624989

Subgroups — C2×#13079588 #15624989

Order 2816.

2218 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623008C211yesmaximal, characteristic, complemented
2#13079588C2116yesmaximal, direct product factor
3C2×#10622672C212yesmaximal, complemented
4C2×#10622681C212yesmaximal, complemented
5C2×#10622644C211yesmaximal, characteristic, complemented
6C2×#10622640C211yesmaximal, characteristic, complemented
7C2×#10622632C211yesmaximal, characteristic, complemented
8C2×#10622628C211yesmaximal, characteristic, complemented
9C2×#10622660C212yesmaximal, complemented
10C2×#10622650C212yesmaximal, complemented
11C2×#10622538C211yesmaximal, characteristic, complemented
12C2×C11×#529C211yesmaximal, characteristic, complemented
13C22×#4339C2212yes—
14C11×#529—24no—
15C11×#529C2218yescomplemented
16C2×C11×#126—21no—
17C2×C11×#125C2211yescharacteristic
18C2×C11×#124C2211yescharacteristic
19C2×C11×#123—21no—
20C2×C11×C22⋊Q8C2211yescharacteristic
21C2×C11×#121C2211yescharacteristic
22C2×C4×Q8×C11C2211yescharacteristic
23C2×C4×D4×C11—21no—
24C2×C4×D4×C11C2211yescharacteristic
25C2×C11×#117—21no—
26C22×C42×C11C2211yescharacteristic
27C22×#4326C2212yes—
28C22×#4325C2212yes—
29C22×#4324C2212yes—
30C22×#4323C2212yes—
31C2×#66983—21no—
32C2×#66983—21no—
33#10623008—24no—
34#10623008C2218yescomplemented
35C2×#66928C2212yes—
36C2×#66927C2211yescharacteristic
37C2×C4×D44—21no—
38C2×C4×D44—21no—
39C2×#66922C2211yescharacteristic
40C2×C22⋊(C11⋊C8)C2212yes—
41#10622681C22116yescomplemented
42#10622672C22116yescomplemented
43#10622660C22116yescomplemented
44#10622650C22116yescomplemented
45#10622644C2218yescomplemented
46#10622640C2218yescomplemented
47#10622632C2218yescomplemented
48#10622628C2218yescomplemented
49C2×#66874C2212yes—
50C2×#66874C2212yes—
51C2×#66873C2212yes—
52C2×#66873C2212yes—
53#10622538C2218yescomplemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4×C11⋊C8C2212yes—
57C22×Q8×C11C2311yescharacteristic
58C22×D4×C11—21no—
59C22×D4×C11C2311yescharacteristic
60C23×C4×C11—21no—
61C23×C4×C11D411yescharacteristic
62C23×C4×C11D411yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×C22⋊D11—22no—
65C2×#4339—24no—
66C2×#4339—44no—
67C2×#4339—44no—
68C2×#4339C2318yes—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44C2312yes—
72C22×C4×D11—22no—
73C22×Dic22C2312yes—
74C11×#126—28no—
75C11×#125—22no—
76C11×#125C2314yes—
77C11×#124—22no—
78C11×#124C2314yes—
79C11×#123—28no—
80C11×C22⋊Q8—22no—
81C11×C22⋊Q8C2314yes—
82C11×#121—22no—
83C11×#121C2314yes—
84C4×Q8×C11—22no—
85C4×Q8×C11C2314yes—
86C4×D4×C11—28no—
87C4×D4×C11—22no—
88C4×D4×C11C2314yes—
89C11×#117—28no—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4—21no—
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C22⋊C4—21no—
97C2×C11×C22⋊C4—21no—
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C11×C22⋊C4—21no—
101C2×C42×C11—21no—
102C2×C42×C11D411yescharacteristic
103C2×C42×C11D411yescharacteristic
104C2×C42×C11D414yes—
105C2×C42×C11C2311yescharacteristic
106C2×C42×C11C2311yescharacteristic
107C2×C42×C11C2314yes—
108C2×#4326—44no—
109C2×#4326C2318yes—
110C2×#4325—44no—
111C2×#4325C2318yes—
112C2×#4324—44no—
113C2×#4324C2318yes—
114C2×#4323—44no—
115C2×#4323C2318yes—
116#66983—28no—
117#66983—28no—
118C2×(C2×D11)⋊C4—22no—
119C2×(C2×D11)⋊C4—22no—
120C2×C4⋊Dic11—21no—
121C2×C4⋊Dic11—21no—
122C22×C11⋊C8C2312yes—
123C22×C11⋊C8C2312yes—
124#66928—24no—
125#66928C2318yes—
126#66927—22no—
127#66927C2314yes—
128C4×D44—28no—
129C4×D44—28no—
130#66922—22no—
131#66922C2314yes—
132C22⋊(C11⋊C8)C2318yes—
133#66874C2318yes—
134#66874C2318yes—
135#66873C2318yes—
136#66873C2318yes—
137C4⋊(C11⋊C8)C2314yes—
138C4⋊(C11⋊C8)C2314yes—
139C4×C11⋊C8C2318yes—
140C2×#3212—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11C2×D411yescharacteristic
143C23×D11—22no—
144C2×Q8×C11—21no—
145C2×Q8×C11—22no—
146C2×Q8×C11—22no—
147C2×Q8×C11C2412yes—
148C2×D4×C11—24no—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—22no—
152C2×D4×C11—44no—
153C2×D4×C11C2412yes—
154C22×C4×C11—24no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—24no—
161C22×C4×C11—42no—
162C22×C4×C11—44no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2412yes—
172C22×C4×C11C2411yescharacteristic
173C2×C22⋊D11—28no—
174C2×C22⋊D11—48no—
175C22×Dic11—22no—
176#4339—48no—
177#4339—48no—
178#4339—416no—
179C2×D44—24no—
180C2×D44—24no—
181C2×D44—22no—
182C2×D44—24no—
183C2×D44—24no—
184C2×D44—44no—
185C2×D44—44no—
186C2×D44C2414yes—
187C2×C4×D11—28no—
188C2×C4×D11—48no—
189C2×Dic22—22no—
190C2×Dic22—24no—
191C2×Dic22—24no—
192C2×Dic22C2414yes—
193C11×C4⋊C4—24no—
194C11×C4⋊C4—24no—
195C11×C4⋊C4—24no—
196C11×C4⋊C4—24no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4C2412yes—
200C11×C4⋊C4C2412yes—
201C11×C22⋊C4—24no—
202C11×C22⋊C4—24no—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—24no—
205C11×C22⋊C4—24no—
206C42×C11—24no—
207C42×C11C2×D412yes—
208C42×C11C2×D414yes—
209C42×C11C2×D414yes—
210C42×C11C2×D412yes—
211C42×C11C2412yes—
212C42×C11C2412yes—
213#4326—48no—
214#4325—48no—
215#4324—48no—
216#4323—48no—
217(C2×D11)⋊C4—28no—
218(C2×D11)⋊C4—28no—
219C4⋊Dic11—24no—
220C4⋊Dic11—24no—
221C2×C11⋊C8—24no—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224C2×C11⋊C8C2414yes—
225C2×#532—111no—
226C2×#529D1111yescharacteristic, complemented
227#3212—1116no—
228C2×#495—112no—
229C2×#488—112no—
230C2×#462—111no—
231C2×#460—111no—
232C2×#461—111no—
233C2×#459—111no—
234C2×#452—112no—
235C2×#449—112no—
236C2×#431—111no—
237C23×C11—22no—
238C23×C11—22no—
239C23×C11—22no—
240C23×C11—22no—
241C23×C11—42no—
242C23×C11—42no—
243C23×C11—42no—
244C23×C11C22×D412yes—
245C23×C11C22×D411yescharacteristic
246C22×D11—24no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—44no—
250Q8×C11—22no—
251Q8×C11—22no—
252Q8×C11—42no—
253D4×C11—22no—
254D4×C11—22no—
255D4×C11—48no—
256D4×C11—42no—
257C2×C4×C11—22no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—28no—
263C2×C4×C11—22no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—22no—
267C2×C4×C11—22no—
268C2×C4×C11—44no—
269C2×C4×C11—42no—
270C2×C4×C11—42no—
271C2×C4×C11—42no—
272C2×C4×C11—48no—
273C2×C4×C11#13514yes—
274C2×C4×C11C22×D412yes—
275C2×C4×C11C22×D412yes—
276C2×C4×C11C22×D412yes—
277C2×C4×C11C22×D412yes—
278C2×C4×C11C22×D411yescharacteristic
279C2×C4×C11C22×D412yes—
280C2×C4×C11H(5,𝔽2)12yes—
281C2×C4×C11H(5,𝔽2)12yes—
282C2×C4×C11C2511yescharacteristic
283C22⋊D11—416no—
284C2×Dic11—24no—
285C2×Dic11—44no—
286D44—24no—
287D44—24no—
288D44—48no—
289D44—44no—
290D44—48no—
291C4×D11—416no—
292Dic22—24no—
293Dic22—24no—
294Dic22—44no—
295C11⋊C8—24no—
296C11⋊C8—24no—
297C22×#41—112no—
298C22×Q16—112no—
299C22×SD16—112no—
300C22×SD16—112no—
301C22×D8—112no—
302#532—118no—
303#532—224no—
304C2×C4⋊Q8—111no—
305C2×#127—111no—
306#529—24no—
307#529C2×D1118yescomplemented
308C2×#126—21no—
309C2×#125C2×D1111yescharacteristic
310C2×#124—112no—
311C2×#124C2×D1111yescharacteristic
312C2×#123—21no—
313C2×C22⋊Q8C2×D1111yescharacteristic
314C2×#121—221no—
315C2×#121—221no—
316C2×#121C2×D1111yescharacteristic
317C2×C4×Q8C2×D1111yescharacteristic
318C2×C4×D4—21no—
319C2×C4×D4—221no—
320C2×C4×D4—221no—
321C2×C4×D4C2×D1111yescharacteristic
322C2×#117—21no—
323C22×C42C2×D1111yescharacteristic
324#495—1116no—
325#488—1116no—
326#462—118no—
327#461—118no—
328#460—118no—
329#459—118no—
330#452—1116no—
331#449—1116no—
332#431—118no—
333C2×C4⋊C8—111no—
334C2×C4⋊C8—111no—
335C2×#103—112no—
336C2×#103—112no—
337C2×#102—112no—
338C2×#102—112no—
339C2×C22⋊C8—112no—
340C2×C4×C8—112no—
341C22×C11—22no—
342C22×C11—22no—
343C22×C11—22no—
344C22×C11—44no—
345C22×C11—42no—
346C22×C11—42no—
347C22×C11—42no—
348C22×C11—84no—
349C22×C11#53512yes—
350C22×C11C2×#13512yes—
351C22×C11#57512yes—
352C22×C11C23×D411yescharacteristic
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—44no—
356C2×D11—88no—
357C4×C11—22no—
358C4×C11—22no—
359C4×C11—22no—
360C4×C11—22no—
361C4×C11—42no—
362C4×C11—42no—
363C4×C11—42no—
364C4×C11#53512yes—
365C4×C11C2×#13514yes—
366C4×C11C2×H(5,𝔽2)11yescharacteristic
367C4×C11C2×H(5,𝔽2)11yescharacteristic
368Dic11—44no—
369C2×#41—118no—
370C2×#41—224no—
371C2×#41—444no—
372C2×#41—444no—
373C22×Q8—112no—
374C22×Q8C22×D1111yescharacteristic
375C22×D4—21no—
376C22×D4—112no—
377C22×D4—222no—
378C22×D4—221no—
379C22×D4—221no—
380C22×D4C22×D1111yescharacteristic
381C23×C4—21no—
382C23×C4—222no—
383C23×C4C22⋊D1111yescharacteristic
384C23×C4C22⋊D1111yescharacteristic
385C23×C4C22×D1111yescharacteristic
386C2×Q16—118no—
387C2×Q16—444no—
388C2×SD16—118no—
389C2×SD16—118no—
390C2×SD16—444no—
391C2×SD16—444no—
392C2×D8—118no—
393C2×D8—444no—
394C22×C8—112no—
395C22×C8—112no—
396C4⋊Q8—114no—
397C4⋊Q8—222no—
398#127—114no—
399#127—222no—
400#126—28no—
401#125—22no—
402#125C22×D1114yes—
403#124—22no—
404#124—118no—
405#124—224no—
406#124C22×D1114yes—
407#123—28no—
408C22⋊Q8—22no—
409C22⋊Q8C22×D1114yes—
410#121—22no—
411#121—228no—
412#121—228no—
413#121C22×D1114yes—
414C4×Q8—22no—
415C4×Q8C22×D1114yes—
416C4×D4—28no—
417C4×D4—22no—
418C4×D4—228no—
419C4×D4—228no—
420C4×D4C22×D1114yes—
421#117—28no—
422C2×C4⋊C4—21no—
423C2×C4⋊C4—21no—
424C2×C4⋊C4—21no—
425C2×C4⋊C4—21no—
426C2×C4⋊C4—221no—
427C2×C4⋊C4—221no—
428C2×C4⋊C4C22×D1111yescharacteristic
429C2×C4⋊C4C22×D1111yescharacteristic
430C2×C22⋊C4—21no—
431C2×C22⋊C4—21no—
432C2×C22⋊C4—21no—
433C2×C22⋊C4—21no—
434C2×C22⋊C4—21no—
435C2×C22⋊C4—222no—
436C2×C22⋊C4—222no—
437C2×C42—21no—
438C2×C42C22⋊D1111yescharacteristic
439C2×C42C22⋊D1111yescharacteristic
440C2×C42C22⋊D1114yes—
441C2×C42C22×D1111yescharacteristic
442C2×C42C22×D1111yescharacteristic
443C2×C42C22×D1114yes—
444C4⋊C8—114no—
445C4⋊C8—114no—
446#103—118no—
447#103—118no—
448#102—118no—
449#102—118no—
450C22⋊C8—118no—
451C4×C8—118no—
452C2×C11—42no—
453C2×C11—82no—
454C2×C11#321214yescomplemented
455C2×C11C2×#53511yescharacteristic
456C2×C11C22×#13511yescharacteristic
457C2×C11C2×#57511yescharacteristic
458D11—84no—
459C24—21no—
460C24—222no—
461C24C2×C22⋊D1111yescharacteristic
462#41—448no—
463#41—448no—
464#41—4416no—
465C2×Q8—21no—
466C2×Q8—22no—
467C2×Q8—22no—
468C2×Q8—114no—
469C2×Q8—222no—
470C2×Q8—224no—
471C2×Q8—224no—
472C2×Q8C23×D1112yes—
473C2×D4—24no—
474C2×D4—22no—
475C2×D4—22no—
476C2×D4—21no—
477C2×D4—44no—
478C2×D4—114no—
479C2×D4—228no—
480C2×D4—224no—
481C2×D4—224no—
482C2×D4—224no—
483C2×D4—224no—
484C2×D4—222no—
485C2×D4—444no—
486C2×D4—448no—
487C2×D4—444no—
488C2×D4C23×D1112yes—
489C22×C4—24no—
490C22×C4—22no—
491C22×C4—22no—
492C22×C4—21no—
493C22×C4—21no—
494C22×C4—21no—
495C22×C4—24no—
496C22×C4—42no—
497C22×C4—44no—
498C22×C4—222no—
499C22×C4—228no—
500C22×C4—448no—
501C22×C4C2×C22⋊D1114yes—
502C22×C4C2×C22⋊D1112yes—
503C22×C4C2×C22⋊D1111yescharacteristic
504C22×C4C2×C22⋊D1111yescharacteristic
505C22×C4C2×C22⋊D1111yescharacteristic
506C22×C4C2×C22⋊D1111yescharacteristic
507C22×C4C2×C22⋊D1114yes—
508C22×C4C2×C22⋊D1111yescharacteristic
509C22×C4C23×D1112yes—
510C22×C4C23×D1111yescharacteristic
511Q16—448no—
512SD16—448no—
513SD16—448no—
514D8—448no—
515C2×C8—114no—
516C2×C8—114no—
517C2×C8—224no—
518C2×C8—224no—
519C4⋊C4—24no—
520C4⋊C4—24no—
521C4⋊C4—24no—
522C4⋊C4—24no—
523C4⋊C4—21no—
524C4⋊C4—21no—
525C4⋊C4—224no—
526C4⋊C4—224no—
527C4⋊C4C23×D1112yes—
528C4⋊C4C23×D1112yes—
529C22⋊C4—24no—
530C22⋊C4—24no—
531C22⋊C4—24no—
532C22⋊C4—24no—
533C22⋊C4—24no—
534C22⋊C4—228no—
535C22⋊C4—228no—
536C42—24no—
537C42C2×C22⋊D1114yes—
538C42C2×C22⋊D1112yes—
539C42C2×C22⋊D1114yes—
540C42C2×C22⋊D1112yes—
541C42C23×D1112yes—
542C42C23×D1112yes—
543C11C2×#321211yescharacteristic, complemented, Sylow
544C23—22no—
545C23—22no—
546C23—22no—
547C23—22no—
548C23—42no—
549C23—42no—
550C23—42no—
551C23—224no—
552C23—444no—
553C23—444no—
554C23—444no—
555C23C22×C22⋊D1112yes—
556C23C22×C22⋊D1111yescharacteristic
557Q8—22no—
558Q8—22no—
559Q8—42no—
560Q8—224no—
561Q8—224no—
562Q8—444no—
563D4—22no—
564D4—22no—
565D4—48no—
566D4—42no—
567D4—224no—
568D4—224no—
569D4—448no—
570D4—4416no—
571D4—448no—
572D4—444no—
573C2×C4—22no—
574C2×C4—22no—
575C2×C4—22no—
576C2×C4—22no—
577C2×C4—28no—
578C2×C4—24no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—22no—
584C2×C4—44no—
585C2×C4—42no—
586C2×C4—42no—
587C2×C4—42no—
588C2×C4—48no—
589C2×C4—224no—
590C2×C4—4416no—
591C2×C4—444no—
592C2×C4#6700314yes—
593C2×C4#6704212yes—
594C2×C4#6704212yes—
595C2×C4C22×C22⋊D1112yes—
596C2×C4C22×C22⋊D1112yes—
597C2×C4C22×C22⋊D1112yes—
598C2×C4C22×C22⋊D1112yes—
599C2×C4C22×C22⋊D1112yes—
600C2×C4C22×C22⋊D1111yescharacteristic
601C2×C4C24×D1111yescharacteristic
602C8—224no—
603C8—224no—
604C22—22no—
605C22—22no—
606C22—22no—
607C22—44no—
608C22—42no—
609C22—42no—
610C22—42no—
611C22—84no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—888no—
616C22C2×#6700312yes—
617C22#1062335312yes—
618C22#1062336112yes—
619C22C23×C22⋊D1111yescharacteristic
620C4—22no—
621C4—22no—
622C4—22no—
623C4—22no—
624C4—42no—
625C4—42no—
626C4—42no—
627C4—444no—
628C4C2×#6700314yes—
629C4#1062336112yes—
630C4C2×#6704211yescharacteristic
631C4C2×#6704211yescharacteristic
632C2—42no—
633C2—82no—
634C2—884no—
635C2#1307958814yesdirect product factor
636C2C2×#1062336111yescharacteristic
637C2C22×#6700311yescharacteristic
638C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#529C2
socleC23×C11C22×D4
hypercenterC2×#529D11
hypocenterC11C2×#3212
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C42 ◁ C2×#529

Complements

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

NH ≅ G/Ntype
1. C2×#10623008C2semidirect
2. #13079588C2direct (N × H)
3. C2×#10622672C2semidirect
4. C2×#10622681C2semidirect
5. C2×#10622644C2semidirect
6. C2×#10622640C2semidirect
7. C2×#10622632C2semidirect
8. C2×#10622628C2semidirect
9. C2×#10622660C2semidirect
10. C2×#10622650C2semidirect
11. C2×#10622538C2semidirect
12. C2×C11×#529C2semidirect
15. C11×#529C22semidirect
34. #10623008C22semidirect
41. #10622681C22semidirect
42. #10622672C22semidirect
43. #10622660C22semidirect
44. #10622650C22semidirect
45. #10622644C22semidirect
46. #10622640C22semidirect
47. #10622632C22semidirect
48. #10622628C22semidirect
53. #10622538C22semidirect
226. C2×#529D11semidirect
307. #529C2×D11semidirect
454. C2×C11#3212semidirect
543. C11C2×#3212semidirect
635. C2#13079588direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230082
#130795882
C2×#106226722
C2×#106226812
C2×#106226442
C2×#106226402
C2×#106226322
C2×#106226282
C2×#106226602
C2×#106226502
C2×#106225382
C2×C11×#5292
C2×#321211