Finite Group Databasebeta

← C2×#13078021 #15620511

Subgroups — C2×#13078021 #15620511

Order 2816.

4790 conjugacy classes of subgroups.

The subgroup lattice has 670 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623453C211yesmaximal, characteristic
2C2×#10623347C212yesmaximal, complemented
3#13078021C2116yesmaximal, direct product factor
4C2×#10622666C218yesmaximal, complemented
5C2×#10622853C211yesmaximal, characteristic, complemented
6C2×#10622619C212yesmaximal, complemented
7C2×C11×#536C211yesmaximal, characteristic, complemented
8C22×C11×#41C2211yescharacteristic
9C23×Q8×C11C2211yescharacteristic, complemented
10#10623453—24no—
11#10623453—28no—
12#10623453C2218yes—
13C2×#67043—22no—
14C2×#67042—22no—
15C2×#41×D11—24no—
16C2×#67040—21no—
17C2×#67037—21no—
18C2×#67037C2214yes—
19C22×#4339—22no—
20C22×#4339C2212yes—
21C11×#536—24no—
22C11×#536C2218yescomplemented
23C2×C11×C4⋊Q8—21no—
24C2×C11×#124—21no—
25C2×C11×#123C2214yescomplemented
26C2×C11×C22⋊Q8—22no—
27C2×C11×#117C2211yescharacteristic, complemented
28#10623347—28no—
29#10623347C22116yescomplemented
30C2×#67000—22no—
31C2×#66999—24no—
32C2×#66997—22no—
33C2×#66982C2218yescomplemented
34C2×#66979C2212yescomplemented
35#10622853C2218yescomplemented
36C2×#66898C2214yescomplemented
37#10622666C22164yescomplemented
38#10622619C22116yescomplemented
39C2×#66870C2218yescomplemented
40C2×C11×#41—22no—
41C2×C11×#41—22no—
42C2×C11×#41—24no—
43C2×C11×#41D414yes—
44C2×C11×#41C2314yes—
45C22×Q8×C11—22no—
46C22×Q8×C11—22no—
47C22×Q8×C11—24no—
48C22×Q8×C11—21no—
49C22×Q8×C11—21no—
50C22×Q8×C11—22no—
51C22×Q8×C11D411yescharacteristic
52C22×Q8×C11C2314yescomplemented
53C22×D4×C11D411yescharacteristic
54C22×D4×C11C2312yes—
55C23×C4×C11D412yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11C2314yes—
60#67043—216no—
61#67043—216no—
62#67042—216no—
63#67042—216no—
64#41×D11—232no—
65#41×D11—232no—
66#67040—28no—
67#67040—28no—
68C2×#4343—24no—
69C2×Q8×D11—24no—
70#67037—28no—
71#67037—28no—
72#67037—28no—
73#67037—216no—
74#67037C23116yes—
75C2×#4341—24no—
76C2×#4341—28no—
77C2×D4×D11—24no—
78C2×D4×D11—28no—
79C2×#4339—24no—
80C2×#4339—24no—
81C2×#4339—216no—
82C2×#4339—22no—
83C2×#4339—24no—
84C2×#4339—216no—
85C2×#4339—22no—
86C2×#4339—22no—
87C2×#4339—22no—
88C2×#4339—24no—
89C2×#4339—24no—
90C2×#4339D418yes—
91C2×#4339C2318yes—
92C22×D44—22no—
93C22×D44D412yes—
94C22×C4×D11—24no—
95C22×C4×D11D414yes—
96C22×Dic22—22no—
97C22×Dic22D412yes—
98C11×C4⋊Q8—28no—
99C11×#124—28no—
100C11×#123—28no—
101C11×#123C23116yescomplemented
102C11×C22⋊Q8—216no—
103C11×#117—22no—
104C11×#117C2314yescomplemented
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—24no—
107C2×C11×C22⋊C4—24no—
108C2×C11×C22⋊C4C2312yes—
109C2×C42×C11—21no—
110C2×C22⋊Dic11C2314yes—
111#67000—216no—
112#66999—232no—
113#66997—216no—
114#66982—216no—
115#66982C23132yescomplemented
116C2×(C2×D11)⋊C4—28no—
117#66979—24no—
118#66979C2318yescomplemented
119C2×C4⋊Dic11—22no—
120C2×Dic11⋊C4—28no—
121C2×C4×Dic11—22no—
122#66898C23116yescomplemented
123#66870C23132yescomplemented
124C2×#3028—111nomaximal, Sylow
125C24×C11C2×D412yes—
126C24×C11C2411yescharacteristic
127C23×D11—24no—
128C23×D11C2×D414yes—
129C11×#41—28no—
130C11×#41—28no—
131C11×#41—28no—
132C11×#41—28no—
133C2×Q8×C11—22no—
134C2×Q8×C11—22no—
135C2×Q8×C11—28no—
136C2×Q8×C11—28no—
137C2×Q8×C11—24no—
138C2×Q8×C11—24no—
139C2×Q8×C11—41no—
140C2×Q8×C11—42no—
141C2×Q8×C11—44no—
142C2×Q8×C11—41no—
143C2×Q8×C11—44no—
144C2×Q8×C11—42no—
145C2×Q8×C11—42no—
146C2×Q8×C11C2×D414yes—
147C2×D4×C11—24no—
148C2×D4×C11—24no—
149C2×D4×C11—22no—
150C2×D4×C11—22no—
151C2×D4×C11C2×D414yes—
152C2×D4×C11C2×D414yes—
153C2×D4×C11C2414yes—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—24no—
158C22×C4×C11—24no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11C2×D412yes—
163C22×C4×C11C2×D418yes—
164C22×C4×C11C2×D412yes—
165C22×C4×C11C2×D412yes—
166C22×C4×C11C2×D414yes—
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D412yes—
170C22×C4×C11C2414yes—
171C22×C4×C11C2412yes—
172C2×C22⋊D11—28no—
173C2×C22⋊D11—216no—
174C2×C22⋊D11—24no—
175C2×C22⋊D11—24no—
176C2×C22⋊D11—24no—
177C2×C22⋊D11—24no—
178C2×C22⋊D11—216no—
179C2×C22⋊D11C2×D418yes—
180C2×C22⋊D11C2418yes—
181C22×Dic11—24no—
182C22×Dic11—24no—
183C22×Dic11C2×D414yes—
184#4343—232no—
185Q8×D11—232no—
186#4341—232no—
187#4341—232no—
188#4341—232no—
189D4×D11—232no—
190D4×D11—232no—
191D4×D11—232no—
192#4339—216no—
193#4339—232no—
194#4339—232no—
195#4339—28no—
196#4339—28no—
197#4339—28no—
198#4339—28no—
199#4339—28no—
200#4339—216no—
201#4339—28no—
202#4339—28no—
203#4339—28no—
204C2×D44—24no—
205C2×D44—216no—
206C2×D44—22no—
207C2×D44—22no—
208C2×D44—24no—
209C2×D44C2×D418yes—
210C2×C4×D11—28no—
211C2×C4×D11—232no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—28no—
215C2×C4×D11C2×D4116yes—
216C2×Dic22—24no—
217C2×Dic22—216no—
218C2×Dic22—22no—
219C2×Dic22—22no—
220C2×Dic22—24no—
221C2×Dic22C2×D418yes—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—216no—
224C11×C22⋊C4—216no—
225C11×C22⋊C4—22no—
226C11×C22⋊C4C2414yes—
227C42×C11—24no—
228C22⋊Dic11—24no—
229C22⋊Dic11C2418yes—
230(C2×D11)⋊C4—232no—
231C4⋊Dic11—28no—
232Dic11⋊C4—232no—
233C4×Dic11—28no—
234C2×#585—111no—
235C2×#536—112no—
236C2×#536D1111yescharacteristic, complemented
237#3028—1116no—
238C2×#458—118no—
239C2×#410—111no—
240C2×#410—112no—
241C23×C11—22no—
242C23×C11—22no—
243C23×C11—42no—
244C23×C11—44no—
245C23×C11C22×D412yes—
246C23×C11C22×D412yes—
247C23×C11C22×D411yescharacteristic
248C23×C11C22×D414yes—
249C23×C11C22×D411yescharacteristic
250C23×C11C2511yescharacteristic
251C22×D11—24no—
252C22×D11—216no—
253C22×D11—24no—
254C22×D11—48no—
255C22×D11—88no—
256C22×D11C22×D418yes—
257Q8×C11—28no—
258Q8×C11—44no—
259Q8×C11—44no—
260Q8×C11—48no—
261D4×C11—28no—
262D4×C11—28no—
263D4×C11—28no—
264C2×C4×C11—22no—
265C2×C4×C11—22no—
266C2×C4×C11—28no—
267C2×C4×C11—28no—
268C2×C4×C11—28no—
269C2×C4×C11—24no—
270C2×C4×C11—24no—
271C2×C4×C11—44no—
272C2×C4×C11—42no—
273C2×C4×C11—44no—
274C2×C4×C11—42no—
275C2×C4×C11#12011yescharacteristic
276C2×C4×C11#12012yes—
277C2×C4×C11#12014yes—
278C2×C4×C11#12011yescharacteristic
279C2×C4×C11#12014yes—
280C2×C4×C11#12012yes—
281C2×C4×C11#12012yes—
282C2×C4×C11C22×D414yes—
283C2×C4×C11C22×D414yes—
284C2×C4×C11C22×D414yes—
285C2×C4×C11C22×D412yes—
286C2×C4×C11C22×D412yes—
287C22⋊D11—232no—
288C22⋊D11—28no—
289C22⋊D11—28no—
290C22⋊D11—28no—
291C22⋊D11—28no—
292C2×Dic11—216no—
293C2×Dic11—24no—
294C2×Dic11—24no—
295C2×Dic11—28no—
296C2×Dic11—48no—
297C2×Dic11C22×D418yes—
298D44—216no—
299D44—28no—
300D44—28no—
301C4×D11—232no—
302C4×D11—216no—
303C4×D11—216no—
304Dic22—216no—
305Dic22—28no—
306Dic22—28no—
307#585—118no—
308#585—228no—
309#585—224no—
310C2×2−1+4—222no—
311C2×2−1+4—221no—
312C2×H(5,𝔽2)—114no—
313C2×H(5,𝔽2)—222no—
314C2×H(5,𝔽2)—221no—
315C22×#41—112no—
316C22×#41—224no—
317C22×#41—222no—
318C22×#41C2×D1111yescharacteristic
319C23×Q8C2×D1111yescharacteristic, complemented
320#536—24no—
321#536—1116no—
322#536—228no—
323#536C2×D1118yescomplemented
324C2×C4⋊Q8—21no—
325C2×C4⋊Q8—222no—
326C2×#124—21no—
327C2×#124—222no—
328C2×#123—118no—
329C2×#123C2×D1114yescomplemented
330C2×C22⋊Q8—22no—
331C2×C22⋊Q8—224no—
332C2×#117—112no—
333C2×#117C2×D1111yescharacteristic, complemented
334#458—1164no—
335#410—118no—
336#410—1116no—
337C2×#99—114no—
338C2×#99—118no—
339C22×C11—22no—
340C22×C11—24no—
341C22×C11—24no—
342C22×C11—42no—
343C22×C11—41no—
344C22×C11—41no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—82no—
348C22×C11C2×#12011yescharacteristic
349C22×C11C2×#12012yes—
350C22×C11C2×#12011yescharacteristic
351C22×C11C23×D412yes—
352C22×C11C23×D411yescharacteristic
353C2×D11—28no—
354C2×D11—48no—
355C2×D11—48no—
356C2×D11—84no—
357C2×D11—816no—
358C4×C11—24no—
359C4×C11—44no—
360C4×C11—44no—
361C4×C11C2×#12012yes—
362C4×C11C2×#12012yes—
363C4×C11C2×#12014yes—
364Dic11—28no—
365Dic11—48no—
3662−1+4—228no—
3672−1+4—2216no—
3682−1+4—2216no—
3692−1+4—228no—
370H(5,𝔽2)—1116no—
371H(5,𝔽2)—2216no—
372H(5,𝔽2)—228no—
373H(5,𝔽2)—2216no—
374H(5,𝔽2)—2216no—
375H(5,𝔽2)—228no—
376H(5,𝔽2)—228no—
377C2×#41—22no—
378C2×#41—22no—
379C2×#41—24no—
380C2×#41—118no—
381C2×#41—118no—
382C2×#41—224no—
383C2×#41—224no—
384C2×#41—2216no—
385C2×#41—228no—
386C2×#41—2232no—
387C2×#41—224no—
388C2×#41—224no—
389C2×#41—2232no—
390C2×#41—222no—
391C2×#41—222no—
392C2×#41—224no—
393C2×#41—222no—
394C2×#41—222no—
395C2×#41—224no—
396C2×#41—224no—
397C2×#41—2216no—
398C2×#41C22⋊D1114yes—
399C2×#41C22×D1114yes—
400C22×Q8—22no—
401C22×Q8—22no—
402C22×Q8—24no—
403C22×Q8—21no—
404C22×Q8—21no—
405C22×Q8—22no—
406C22×Q8—112no—
407C22×Q8—222no—
408C22×Q8—224no—
409C22×Q8C22⋊D1111yescharacteristic
410C22×Q8C22×D1114yescomplemented
411C22×D4—114no—
412C22×D4—112no—
413C22×D4—222no—
414C22×D4—228no—
415C22×D4—224no—
416C22×D4—224no—
417C22×D4C22⋊D1111yescharacteristic
418C22×D4C22×D1112yes—
419C23×C4—114no—
420C23×C4—224no—
421C23×C4C22⋊D1112yes—
422C23×C4C22×D1112yes—
423C23×C4C22×D1111yescharacteristic
424C4⋊Q8—28no—
425C4⋊Q8—2216no—
426#124—28no—
427#124—2216no—
428#123—28no—
429#123—1132no—
430#123—2216no—
431#123C22×D11116yescomplemented
432C22⋊Q8—216no—
433C22⋊Q8—2232no—
434#117—22no—
435#117—118no—
436#117—224no—
437#117C22×D1114yescomplemented
438C2×C4⋊C4—21no—
439C2×C4⋊C4—24no—
440C2×C4⋊C4—228no—
441C2×C4⋊C4—222no—
442C2×C22⋊C4—24no—
443C2×C22⋊C4—114no—
444C2×C22⋊C4—228no—
445C2×C22⋊C4C22×D1112yes—
446C2×C42—21no—
447C2×C42—222no—
448#99—1116no—
449#99—1132no—
450C2×C11—22no—
451C2×C11—21no—
452C2×C11—22no—
453C2×C11—21no—
454C2×C11—44no—
455C2×C11#302812yescomplemented
456C2×C11C22×#12011yescharacteristic
457D11—48no—
458C24—114no—
459C24—224no—
460C24C2×C22⋊D1112yes—
461C24C23×D1111yescharacteristic
462#41—28no—
463#41—28no—
464#41—28no—
465#41—28no—
466#41—2232no—
467#41—2216no—
468#41—2232no—
469#41—2232no—
470#41—2232no—
471#41—2232no—
472#41—2232no—
473#41—228no—
474#41—228no—
475#41—228no—
476#41—228no—
477#41—228no—
478#41—228no—
479#41—228no—
480#41—228no—
481#41—2216no—
482C2×Q8—22no—
483C2×Q8—22no—
484C2×Q8—28no—
485C2×Q8—28no—
486C2×Q8—24no—
487C2×Q8—24no—
488C2×Q8—42no—
489C2×Q8—44no—
490C2×Q8—42no—
491C2×Q8—44no—
492C2×Q8—41no—
493C2×Q8—41no—
494C2×Q8—42no—
495C2×Q8—118no—
496C2×Q8—224no—
497C2×Q8—2216no—
498C2×Q8—2232no—
499C2×Q8—222no—
500C2×Q8—222no—
501C2×Q8—224no—
502C2×Q8C2×C22⋊D1114yes—
503C2×D4—24no—
504C2×D4—24no—
505C2×D4—22no—
506C2×D4—22no—
507C2×D4—118no—
508C2×D4—118no—
509C2×D4—118no—
510C2×D4—224no—
511C2×D4—2216no—
512C2×D4—2232no—
513C2×D4—2232no—
514C2×D4—2232no—
515C2×D4—228no—
516C2×D4—2216no—
517C2×D4—224no—
518C2×D4—224no—
519C2×D4—224no—
520C2×D4—224no—
521C2×D4—2216no—
522C2×D4—222no—
523C2×D4—222no—
524C2×D4—224no—
525C2×D4C2×C22⋊D1114yes—
526C2×D4C2×C22⋊D1114yes—
527C2×D4C23×D1114yes—
528C22×C4—22no—
529C22×C4—22no—
530C22×C4—24no—
531C22×C4—24no—
532C22×C4—24no—
533C22×C4—22no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—114no—
537C22×C4—1116no—
538C22×C4—228no—
539C22×C4—2232no—
540C22×C4—224no—
541C22×C4—224no—
542C22×C4—224no—
543C22×C4—228no—
544C22×C4—224no—
545C22×C4D4×D1112yes—
546C22×C4D4×D1112yes—
547C22×C4D4×D1114yes—
548C22×C4C2×C22⋊D1112yes—
549C22×C4C2×C22⋊D1118yes—
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C2×C22⋊D1111yescharacteristic
552C22×C4C2×C22⋊D1112yes—
553C22×C4C23×D1114yes—
554C22×C4C23×D1112yes—
555C4⋊C4—24no—
556C4⋊C4—216no—
557C4⋊C4—2232no—
558C4⋊C4—228no—
559C22⋊C4—216no—
560C22⋊C4—22no—
561C22⋊C4—118no—
562C22⋊C4—2232no—
563C22⋊C4—224no—
564C22⋊C4C23×D1114yes—
565C42—24no—
566C42—228no—
567C11C2×#302811yescharacteristic, complemented, Sylow
568C23—22no—
569C23—22no—
570C23—42no—
571C23—44no—
572C23—118no—
573C23—2216no—
574C23—224no—
575C23—224no—
576C23—448no—
577C23—888no—
578C23C2×D4×D1112yes—
579C23C2×D4×D1112yes—
580C23C22×C22⋊D1111yescharacteristic
581C23C22×C22⋊D1114yes—
582C23C22×C22⋊D1111yescharacteristic
583C23C24×D1111yescharacteristic
584Q8—28no—
585Q8—44no—
586Q8—44no—
587Q8—48no—
588Q8—2216no—
589Q8—228no—
590Q8—228no—
591D4—28no—
592D4—28no—
593D4—28no—
594D4—2216no—
595D4—2232no—
596D4—228no—
597D4—228no—
598D4—228no—
599D4—228no—
600D4—228no—
601D4—228no—
602C2×C4—22no—
603C2×C4—22no—
604C2×C4—28no—
605C2×C4—28no—
606C2×C4—28no—
607C2×C4—24no—
608C2×C4—24no—
609C2×C4—44no—
610C2×C4—42no—
611C2×C4—44no—
612C2×C4—42no—
613C2×C4—118no—
614C2×C4—2232no—
615C2×C4—2216no—
616C2×C4—224no—
617C2×C4—224no—
618C2×C4—2216no—
619C2×C4—2216no—
620C2×C4—228no—
621C2×C4—448no—
622C2×C4#6699012yes—
623C2×C4#6699014yes—
624C2×C4#6699012yes—
625C2×C4#6699014yes—
626C2×C4#6699011yescharacteristic
627C2×C4#6699011yescharacteristic
628C2×C4#6699012yes—
629C2×C4C2×D4×D1114yes—
630C2×C4C2×D4×D1114yes—
631C2×C4C22×C22⋊D1114yes—
632C2×C4C22×C22⋊D1112yes—
633C2×C4C22×C22⋊D1112yes—
634C22—22no—
635C22—24no—
636C22—24no—
637C22—42no—
638C22—41no—
639C22—41no—
640C22—44no—
641C22—44no—
642C22—82no—
643C22—228no—
644C22—448no—
645C22—448no—
646C22—884no—
647C22—8816no—
648C22C2×#6699011yescharacteristic
649C22C2×#6699012yes—
650C22C2×#6699011yescharacteristic
651C22C22×D4×D1112yes—
652C22C23×C22⋊D1111yescharacteristic
653C4—24no—
654C4—44no—
655C4—44no—
656C4—228no—
657C4—448no—
658C4C2×#6699012yes—
659C4C2×#6699012yes—
660C4C2×#6699014yes—
661C2—21no—
662C2—22no—
663C2—21no—
664C2—22no—
665C2—44no—
666C2—448no—
667C2#1307802112yesdirect product factor
668C2C22×#6699011yescharacteristic
subgroupG/H
centerC22C2×#66990
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#536C2
socleC22×C11C2×#120
prime radicalC2×#10623453C2
hypercenterC2×#536D11
hypocenterC11C2×#3028
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#536

Complements

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

NH ≅ G/Ntype
2. C2×#10623347C2semidirect
3. #13078021C2direct (N × H)
4. C2×#10622666C2semidirect
5. C2×#10622853C2semidirect
6. C2×#10622619C2semidirect
7. C2×C11×#536C2semidirect
9. C23×Q8×C11C22semidirect
22. C11×#536C22semidirect
25. C2×C11×#123C22semidirect
27. C2×C11×#117C22semidirect
29. #10623347C22semidirect
33. C2×#66982C22semidirect
34. C2×#66979C22semidirect
35. #10622853C22semidirect
36. C2×#66898C22semidirect
37. #10622666C22semidirect
38. #10622619C22semidirect
39. C2×#66870C22semidirect
52. C22×Q8×C11C23semidirect
101. C11×#123C23semidirect
104. C11×#117C23semidirect
115. #66982C23semidirect
118. #66979C23semidirect
122. #66898C23semidirect
123. #66870C23semidirect
236. C2×#536D11semidirect
319. C23×Q8C2×D11semidirect
323. #536C2×D11semidirect
329. C2×#123C2×D11semidirect
333. C2×#117C2×D11semidirect
410. C22×Q8C22×D11semidirect
431. #123C22×D11semidirect
437. #117C22×D11semidirect
455. C2×C11#3028semidirect
567. C11C2×#3028semidirect
667. C2#13078021direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106234532
C2×#106233472
#130780212
C2×#106226662
C2×#106228532
C2×#106226192
C2×C11×#5362
C2×#302811