Finite Group Databasebeta

← C2×#13079925 #15626547

Subgroups — C2×#13079925 #15626547

Order 2816.

2458 conjugacy classes of subgroups.

The subgroup lattice has 660 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623256C211yesmaximal, characteristic, complemented
2C2×#10623079C211yesmaximal, characteristic, complemented
3#13079925C2116yesmaximal, direct product factor
4C2×#10622503C212yesmaximal, complemented
5C2×#10622700C211yesmaximal, characteristic, complemented
6C2×#10622496C212yesmaximal, complemented
7C2×#10622388C212yesmaximal, complemented
8C2×#10622456C211yesmaximal, characteristic, complemented
9C2×#10622628C211yesmaximal, characteristic, complemented
10C2×#10622399C212yesmaximal, complemented
11C2×D11×C4⋊C8C211yesmaximal, characteristic, complemented
12C2×C11×#474C211yesmaximal, characteristic, complemented
13C22×#4343—21no—
14C22×#4339—21no—
15C2×C11×C4⋊Q8C2211yescharacteristic
16C2×C4×D4×C11C2211yescharacteristic
17C2×#67000—21no—
18C2×#66993C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C22×#4323C2212yes—
21C2×C4×C22⋊D11—21no—
22C22×D88C2212yes—
23C22×C8×D11C2212yes—
24#10623256—24no—
25#10623256C2218yescomplemented
26#10623079—24no—
27#10623079C2218yescomplemented
28C2×#66948—21no—
29C2×#66948C2211yescharacteristic
30C2×#66948C2212yes—
31C2×#66946—21no—
32C2×#66946C2212yes—
33C2×#66941C2211yescharacteristic
34C2×#66938—21no—
35C2×#66937—21no—
36C2×#66927C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×C42×D11C2211yescharacteristic
39C11×#474C2218yescomplemented
40C2×C11×#107C2212yes—
41C2×C11×C4⋊C8C2211yescharacteristic
42C2×C11×#102C2212yes—
43C2×#66885C2212yes—
44C2×Dic11⋊C8C2212yes—
45#10622700C2218yescomplemented
46#10622628C2218yescomplemented
47C2×#66873C2212yes—
48C2×#66873C2212yes—
49C2×#66871C2212yes—
50C2×C4⋊(C11⋊C8)C2211yescharacteristic
51#10622503C22116yescomplemented
52#10622496C22116yescomplemented
53#10622456C2218yescomplemented
54D11×C4⋊C8C2218yescomplemented
55#10622399C22116yescomplemented
56#10622388C22116yescomplemented
57C22×Q8×C11—21no—
58C22×D4×C11C2311yescharacteristic
59C23×C4×C11—21no—
60C22×C22⋊D11—21no—
61C22×C22⋊D11—21no—
62C22×C22⋊D11—21no—
63C2×#4343—28no—
64C2×#4343—48no—
65C2×#4339—28no—
66C2×#4339—48no—
67C22×D44—21no—
68C22×D44—22no—
69C22×D44—21no—
70C22×D44—21no—
71C22×D44C2312yes—
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11—22no—
75C22×C4×D11D411yescharacteristic
76C22×C4×D11D411yescharacteristic
77C22×C4×D11C2311yescharacteristic
78C22×Dic22—21no—
79C22×C8×C11C2312yes—
80C11×C4⋊Q8—22no—
81C11×C4⋊Q8C2314yes—
82C4×D4×C11—22no—
83C4×D4×C11C2314yes—
84C2×C11×C4⋊C4—21no—
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2312yes—
87C2×C11×C22⋊C4—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90#67000—28no—
91#66993—22no—
92#66993C2314yes—
93#66991—22no—
94#66991C2314yes—
95C2×#4323—44no—
96C2×#4323C2318yes—
97C4×C22⋊D11—28no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×C4⋊Dic11C2311yescharacteristic
103C2×Dic11⋊C4—21no—
104C2×C4×Dic11D411yescharacteristic
105C2×C4×Dic11D411yescharacteristic
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2312yes—
108C2×D88—44no—
109C2×D88C2318yes—
110C2×C8×D11—44no—
111C2×C8×D11C2318yes—
112#66948—24no—
113#66948—28no—
114#66948—22no—
115#66948C2318yes—
116#66948C2314yes—
117#66946—24no—
118#66946—28no—
119#66946C2318yes—
120#66941—22no—
121#66941C2314yes—
122#66938—28no—
123#66937—28no—
124#66927—22no—
125#66927C2314yes—
126C4×D44—22no—
127C4×D44C2314yes—
128C42×D11D414yes—
129C42×D11C2314yes—
130C11×#107C2318yes—
131C11×C4⋊C8C2314yes—
132C11×#102C2318yes—
133#66885C2318yes—
134Dic11⋊C8C2318yes—
135#66873C2318yes—
136#66873C2318yes—
137#66871C2318yes—
138C4⋊(C11⋊C8)C2314yes—
139C2×#3245—111nomaximal, Sylow
140C24×C11—21no—
141C23×D11—22no—
142C23×D11—21no—
143C23×D11C2×D411yescharacteristic
144C2×Q8×C11—24no—
145C2×Q8×C11—44no—
146C2×D4×C11—21no—
147C2×D4×C11—22no—
148C2×D4×C11—22no—
149C2×D4×C11C2412yes—
150C22×C4×C11—21no—
151C22×C4×C11—22no—
152C22×C4×C11—24no—
153C22×C4×C11—44no—
154C22×C4×C11C2×D411yescharacteristic
155C22×C4×C11C2×D411yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—24no—
158C2×C22⋊D11—24no—
159C2×C22⋊D11—24no—
160C2×C22⋊D11—44no—
161C2×C22⋊D11—44no—
162C2×C22⋊D11—44no—
163C22×Dic11—21no—
164C22×Dic11C2×D411yescharacteristic
165C22×Dic11C2×D411yescharacteristic
166C22×Dic11C2×D411yescharacteristic
167#4343—432no—
168#4339—432no—
169C2×D44—24no—
170C2×D44—28no—
171C2×D44—21no—
172C2×D44—22no—
173C2×D44—24no—
174C2×D44—24no—
175C2×D44—22no—
176C2×D44—24no—
177C2×D44—24no—
178C2×D44—22no—
179C2×D44—44no—
180C2×D44—44no—
181C2×D44—48no—
182C2×D44—44no—
183C2×D44C2412yes—
184C2×D44C2414yes—
185C2×C4×D11—28no—
186C2×C4×D11—24no—
187C2×C4×D11—22no—
188C2×C4×D11—22no—
189C2×C4×D11—42no—
190C2×C4×D11—48no—
191C2×C4×D11—44no—
192C2×C4×D11D818yescomplemented
193C2×C4×D11C2×D412yes—
194C2×C4×D11C2×D414yes—
195C2×C4×D11C2×D414yes—
196C2×C4×D11C2412yes—
197C2×Dic22—24no—
198C2×Dic22—44no—
199C2×C8×C11—24no—
200C2×C8×C11C2414yes—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—24no—
203C11×C4⋊C4—22no—
204C11×C4⋊C4C2414yes—
205C11×C4⋊C4C2412yes—
206C11×C22⋊C4—24no—
207C42×C11C2×D412yes—
208C42×C11C2412yes—
209C22⋊Dic11—24no—
210#4323—48no—
211(C2×D11)⋊C4—24no—
212(C2×D11)⋊C4—28no—
213(C2×D11)⋊C4—28no—
214(C2×D11)⋊C4—24no—
215C4⋊Dic11—21no—
216C4⋊Dic11C2412yes—
217Dic11⋊C4—24no—
218C4×Dic11C2×D412yes—
219C4×Dic11C2×D414yes—
220C4×Dic11C2×D414yes—
221C4×Dic11C2412yes—
222C2×C11⋊C8—24no—
223C2×C11⋊C8C2414yes—
224D88—48no—
225C8×D11—48no—
226C2×#532—111no—
227C2×#532—111no—
228#3245—1116no—
229C2×#474—112no—
230C2×#474—111no—
231C2×#474D1111yescharacteristic, complemented
232C2×#466—112no—
233C2×#466—112no—
234C2×#459—111no—
235C2×#459—112no—
236C2×#459—111no—
237C22×C4⋊C8—111no—
238C23×C11—22no—
239C23×C11—42no—
240C23×C11—42no—
241C23×C11—42no—
242C23×C11C22×D411yescharacteristic
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—24no—
246C22×D11—22no—
247C22×D11—42no—
248C22×D11—44no—
249C22×D11—44no—
250C22×D11—42no—
251C22×D11—44no—
252C22×D11—42no—
253C22×D11C2×D814yes—
254C22×D11C22×D412yes—
255Q8×C11—48no—
256D4×C11—22no—
257D4×C11—22no—
258D4×C11—42no—
259C2×C4×C11—22no—
260C2×C4×C11—22no—
261C2×C4×C11—24no—
262C2×C4×C11—42no—
263C2×C4×C11—44no—
264C2×C4×C11—48no—
265C2×C4×C11C2×D814yes—
266C2×C4×C11C22×D412yes—
267C2×C4×C11C22×D411yescharacteristic
268C2×C4×C11C22×D412yes—
269C2×C4×C11H(5,𝔽2)12yes—
270C2×C4×C112−1+412yes—
271C2×C4×C11C2511yescharacteristic
272C22⋊D11—48no—
273C22⋊D11—48no—
274C22⋊D11—48no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—22no—
278C2×Dic11—42no—
279C2×Dic11C2×D814yes—
280C2×Dic11C22×D412yes—
281C2×Dic11C22×D412yes—
282C2×Dic11C22×D412yes—
283D44—22no—
284D44—24no—
285D44—22no—
286D44—24no—
287D44—48no—
288D44—48no—
289D44—416no—
290D44—42no—
291D44—44no—
292D44—48no—
293C4×D11—24no—
294C4×D11—22no—
295C4×D11—22no—
296C4×D11—44no—
297C4×D11—48no—
298C4×D11—416no—
299C4×D11C2×D8116yescomplemented
300Dic22—48no—
301C8×C11—24no—
302C11⋊C8—24no—
303C22×#41—221no—
304C22×#41—221no—
305C22×D8—112no—
306C22×D8—112no—
307C23×C8—112no—
308#532—118no—
309#532—118no—
310#532—224no—
311#532—224no—
312C2×C4⋊Q8—111no—
313C2×C4⋊Q8C2×D1111yescharacteristic
314C2×#127—111no—
315C2×#127—111no—
316C2×#124—221no—
317C2×#124—221no—
318C2×#121—111no—
319C2×#121—112no—
320C2×#121—111no—
321C2×#121—221no—
322C2×#121—221no—
323C2×C4×D4—112no—
324C2×C4×D4—111no—
325C2×C4×D4—221no—
326C2×C4×D4—221no—
327C2×C4×D4C2×D1111yescharacteristic
328C22×C42—111no—
329#474—118no—
330#474—1116no—
331#474C2×D1118yescomplemented
332#466—1116no—
333#466—1116no—
334#459—118no—
335#459—118no—
336#459—1116no—
337C2×#107—112no—
338C2×#107C2×D1112yes—
339C2×C4⋊C8—112no—
340C2×C4⋊C8—111no—
341C2×C4⋊C8—118no—
342C2×C4⋊C8C2×D1111yescharacteristic
343C2×#102—112no—
344C2×#102—112no—
345C2×#102—112no—
346C2×#102C2×D1112yes—
347C22×C11—42no—
348C22×C11—42no—
349C22×C11—42no—
350C22×C11—84no—
351C22×C11#53712yes—
352C22×C11C22×D812yes—
353C22×C11#57512yes—
354C22×C11C23×D411yescharacteristic
355C2×D11—22no—
356C2×D11—28no—
357C2×D11—22no—
358C2×D11—44no—
359C2×D11—42no—
360C2×D11—44no—
361C2×D11—42no—
362C2×D11—44no—
363C2×D11—42no—
364C2×D11—88no—
365C2×D11—84no—
366C2×D11C22×D814yes—
367C4×C11—22no—
368C4×C11—42no—
369C4×C11—44no—
370C4×C11#53712yes—
371C4×C11C22×D814yes—
372C4×C11C2×H(5,𝔽2)11yescharacteristic
373C4×C11C2×2−1+411yescharacteristic
374Dic11—22no—
375Dic11—22no—
376Dic11—42no—
377Dic11C22×D814yes—
378C2×#41—228no—
379C2×#41—228no—
380C2×#41—448no—
381C2×#41—448no—
382C22×Q8—21no—
383C22×Q8—221no—
384C22×D4—112no—
385C22×D4—111no—
386C22×D4—221no—
387C22×D4—222no—
388C22×D4—221no—
389C22×D4—221no—
390C22×D4—221no—
391C22×D4—221no—
392C22×D4—221no—
393C22×D4C22×D1111yescharacteristic
394C23×C4—21no—
395C23×C4—111no—
396C23×C4—111no—
397C23×C4—111no—
398C23×C4—222no—
399C23×C4—221no—
400C2×D8—118no—
401C2×D8—118no—
402C2×D8—444no—
403C2×D8—444no—
404C22×C8—112no—
405C22×C8—118no—
406C22×C8—444no—
407C22×C8C22×D1112yes—
408C4⋊Q8—22no—
409C4⋊Q8—114no—
410C4⋊Q8—222no—
411C4⋊Q8C22×D1114yes—
412#127—114no—
413#127—114no—
414#127—222no—
415#127—222no—
416#124—228no—
417#124—228no—
418#121—114no—
419#121—114no—
420#121—118no—
421#121—228no—
422#121—222no—
423#121—224no—
424#121—228no—
425#121—222no—
426C4×D4—22no—
427C4×D4—118no—
428C4×D4—114no—
429C4×D4—224no—
430C4×D4—228no—
431C4×D4—228no—
432C4×D4—222no—
433C4×D4C22×D1114yes—
434C2×C4⋊C4—21no—
435C2×C4⋊C4—111no—
436C2×C4⋊C4—221no—
437C2×C4⋊C4C22×D1112yes—
438C2×C4⋊C4C22×D1111yescharacteristic
439C2×C22⋊C4—21no—
440C2×C22⋊C4—222no—
441C2×C22⋊C4—221no—
442C2×C22⋊C4—222no—
443C2×C22⋊C4—221no—
444C2×C22⋊C4—221no—
445C2×C42—111no—
446C2×C42—111no—
447C2×C42—111no—
448C2×C42—114no—
449C2×C42—114no—
450C2×C42C22×D1111yescharacteristic
451#107—118no—
452#107C22×D1118yes—
453C4⋊C8—118no—
454C4⋊C8—114no—
455C4⋊C8C22×D1114yes—
456#102—118no—
457#102—118no—
458#102—118no—
459#102C22×D1118yes—
460C2×C11—82no—
461C2×C11#324514yescomplemented
462C2×C11C2×#53711yescharacteristic
463C2×C11C23×D811yescharacteristic
464C2×C11C2×#57511yescharacteristic
465D11—24no—
466D11—84no—
467D11—82no—
468C24—21no—
469C24—111no—
470C24—222no—
471C24—221no—
472#41—4432no—
473#41—4432no—
474C2×Q8—24no—
475C2×Q8—44no—
476C2×Q8—224no—
477C2×Q8—444no—
478C2×D4—21no—
479C2×D4—22no—
480C2×D4—22no—
481C2×D4—114no—
482C2×D4—112no—
483C2×D4—224no—
484C2×D4—228no—
485C2×D4—224no—
486C2×D4—224no—
487C2×D4—224no—
488C2×D4—224no—
489C2×D4—222no—
490C2×D4—221no—
491C2×D4—224no—
492C2×D4—224no—
493C2×D4—222no—
494C2×D4—222no—
495C2×D4—224no—
496C2×D4—444no—
497C2×D4—444no—
498C2×D4—448no—
499C2×D4—444no—
500C2×D4—444no—
501C2×D4—444no—
502C2×D4—444no—
503C2×D4C23×D1112yes—
504C22×C4—21no—
505C22×C4—22no—
506C22×C4—24no—
507C22×C4—44no—
508C22×C4—111no—
509C22×C4—118no—
510C22×C4—114no—
511C22×C4—111no—
512C22×C4—111no—
513C22×C4—112no—
514C22×C4—112no—
515C22×C4—114no—
516C22×C4—228no—
517C22×C4—222no—
518C22×C4—222no—
519C22×C4—221no—
520C22×C4—224no—
521C22×C4—442no—
522C22×C4—448no—
523C22×C4—444no—
524C22×C4D4×D1111yescharacteristic
525C22×C4D4×D1111yescharacteristic
526C22×C4C23×D1111yescharacteristic
527D8—448no—
528D8—448no—
529C2×C8—24no—
530C2×C8—114no—
531C2×C8—224no—
532C2×C8—448no—
533C2×C8C23×D1114yes—
534C4⋊C4—24no—
535C4⋊C4—21no—
536C4⋊C4—22no—
537C4⋊C4—112no—
538C4⋊C4—224no—
539C4⋊C4—221no—
540C4⋊C4C23×D1112yes—
541C4⋊C4C23×D1114yes—
542C22⋊C4—24no—
543C22⋊C4—228no—
544C22⋊C4—224no—
545C22⋊C4—228no—
546C22⋊C4—224no—
547C22⋊C4—224no—
548C42—114no—
549C42—114no—
550C42—112no—
551C42—112no—
552C42D4×D1112yes—
553C42C23×D1112yes—
554C11C2×#324511yescharacteristic, complemented, Sylow
555C23—22no—
556C23—42no—
557C23—42no—
558C23—42no—
559C23—114no—
560C23—112no—
561C23—222no—
562C23—222no—
563C23—224no—
564C23—222no—
565C23—444no—
566C23—442no—
567C23—444no—
568C23—442no—
569C23—442no—
570C23—444no—
571C23C2×D4×D1111yescharacteristic
572Q8—48no—
573Q8—448no—
574D4—22no—
575D4—22no—
576D4—42no—
577D4—224no—
578D4—222no—
579D4—222no—
580D4—224no—
581D4—448no—
582D4—448no—
583D4—4416no—
584D4—448no—
585D4—448no—
586D4—448no—
587D4—448no—
588D4—444no—
589D4—442no—
590C2×C4—22no—
591C2×C4—22no—
592C2×C4—24no—
593C2×C4—42no—
594C2×C4—44no—
595C2×C4—48no—
596C2×C4—114no—
597C2×C4—112no—
598C2×C4—1116no—
599C2×C4—112no—
600C2×C4—112no—
601C2×C4—222no—
602C2×C4—222no—
603C2×C4—224no—
604C2×C4—222no—
605C2×C4—222no—
606C2×C4—222no—
607C2×C4—444no—
608C2×C4—4416no—
609C2×C4—442no—
610C2×C4—448no—
611C2×C4D8×D1114yes—
612C2×C4C2×D4×D1112yes—
613C2×C4C2×D4×D1112yes—
614C2×C4C2×D4×D1111yescharacteristic
615C2×C4#6704012yes—
616C2×C4#6704212yes—
617C2×C4C24×D1111yescharacteristic
618C8—24no—
619C8—224no—
620C22—42no—
621C22—42no—
622C22—42no—
623C22—84no—
624C22—114no—
625C22—222no—
626C22—228no—
627C22—222no—
628C22—442no—
629C22—444no—
630C22—444no—
631C22—442no—
632C22—444no—
633C22—442no—
634C22—888no—
635C22—884no—
636C22#1062316012yes—
637C22C2×D8×D1112yes—
638C22#1062330812yes—
639C22C22×D4×D1111yescharacteristic
640C4—22no—
641C4—42no—
642C4—44no—
643C4—114no—
644C4—222no—
645C4—222no—
646C4—442no—
647C4#1062316012yes—
648C4C2×D8×D1114yes—
649C4C2×#6704011yescharacteristic
650C4C2×#6704211yescharacteristic
651C2—82no—
652C2—224no—
653C2—884no—
654C2—882no—
655C2#1307992514yesdirect product factor
656C2C2×#1062316011yescharacteristic
657C2C22×D8×D1111yescharacteristic
658C2C2×#1062330811yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#474C2
socleC23×C11C22×D4
hypercenterC2×#474D11
hypocenterC11C2×#3245
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#474

Complements

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

NH ≅ G/Ntype
1. C2×#10623256C2semidirect
2. C2×#10623079C2semidirect
3. #13079925C2direct (N × H)
4. C2×#10622503C2semidirect
5. C2×#10622700C2semidirect
6. C2×#10622496C2semidirect
7. C2×#10622388C2semidirect
8. C2×#10622456C2semidirect
9. C2×#10622628C2semidirect
10. C2×#10622399C2semidirect
11. C2×D11×C4⋊C8C2semidirect
12. C2×C11×#474C2semidirect
25. #10623256C22semidirect
27. #10623079C22semidirect
39. C11×#474C22semidirect
45. #10622700C22semidirect
46. #10622628C22semidirect
51. #10622503C22semidirect
52. #10622496C22semidirect
53. #10622456C22semidirect
54. D11×C4⋊C8C22semidirect
55. #10622399C22semidirect
56. #10622388C22semidirect
192. C2×C4×D11D8semidirect
231. C2×#474D11semidirect
299. C4×D11C2×D8semidirect
331. #474C2×D11semidirect
461. C2×C11#3245semidirect
554. C11C2×#3245semidirect
655. C2#13079925direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232562
C2×#106230792
#130799252
C2×#106225032
C2×#106227002
C2×#106224962
C2×#106223882
C2×#106224562
C2×#106226282
C2×#106223992
C2×D11×C4⋊C82
C2×C11×#4742
C2×#324511