Finite Group Databasebeta

← C2×#13072377 #14921667

Subgroups — C2×#13072377 #14921667

Order 2816.

4110 conjugacy classes of subgroups.

The subgroup lattice has 664 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66988C212yesmaximal, complemented
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3#13072377C2116yesmaximal, direct product factor
4C2×#10622835C212yesmaximal, complemented
5C2×#10622835C212yesmaximal, complemented
6C2×#10622834C211yesmaximal, characteristic, complemented
7C2×#10622834C211yesmaximal, characteristic, complemented
8C2×#10622834C211yesmaximal, characteristic, complemented
9C2×#10622541C211yesmaximal, characteristic, complemented
10C2×#10622833C212yesmaximal, complemented
11C2×C4×Dic11⋊C4C211yesmaximal, characteristic, complemented
12C22×C11×#127C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C23×D4×C11C2212yes—
15C23×D4×C11C2212yes—
16C23×D4×C11C2211yescharacteristic
17C24×Dic11C2212yes—
18C2×C11×#127—28no—
19C2×C11×#127C2218yes—
20C22×C42×C11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C22×C22⋊Dic11C2212yes—
28C2×#66988—216no—
29C2×#66988C22116yescomplemented
30C2×D4×Dic11—28no—
31C2×D4×Dic11C2218yescomplemented
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4⋊Dic11C2211yescharacteristic
34C22×Dic11⋊C4C2211yescharacteristic
35C22×Dic11⋊C4C2212yes—
36C22×Dic11⋊C4C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38C22×C4×Dic11C2211yescharacteristic
39#10622835C22116yescomplemented
40#10622835C22116yescomplemented
41#10622834C2218yescomplemented
42#10622834C2218yescomplemented
43#10622834C2218yescomplemented
44#10622833C22116yescomplemented
45C2×C11⋊#95C2211yescharacteristic
46C2×C11⋊#95C2211yescharacteristic
47C2×C11⋊#95C2212yes—
48C4×Dic11⋊C4C2218yescomplemented
49#10622541C2218yescomplemented
50C25×C11C2312yes—
51C25×C11C2312yes—
52C22×D4×C11—28no—
53C22×D4×C11—28no—
54C22×D4×C11—28no—
55C22×D4×C11—24no—
56C22×D4×C11—24no—
57C22×D4×C11—24no—
58C22×D4×C11—28no—
59C22×D4×C11—24no—
60C22×D4×C11—24no—
61C22×D4×C11—44no—
62C22×D4×C11—44no—
63C22×D4×C11D418yes—
64C22×D4×C11C2314yes—
65C22×D4×C11C2318yes—
66C22×D4×C11C2318yes—
67C22×D4×C11C2314yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×Dic11—28no—
72C23×Dic11—28no—
73C23×Dic11—44no—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2312yes—
77C23×Dic11C2312yes—
78C23×Dic11C2318yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C11×#127—232no—
82C2×C42×C11—24no—
83C2×C42×C11C2314yes—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—28no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11—28no—
88C2×C22⋊Dic11—44no—
89C2×C22⋊Dic11—44no—
90C2×C22⋊Dic11—44no—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2318yes—
93C2×C22⋊Dic11C2318yes—
94C2×C22⋊Dic11C2318yes—
95C2×C22⋊Dic11C2318yes—
96C2×C22⋊Dic11C2318yes—
97C2×C22⋊Dic11C2318yes—
98#66988—264no—
99D4×Dic11—232no—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11—24no—
102C2×C4⋊Dic11C2314yes—
103C2×C4⋊Dic11C2314yes—
104C2×Dic11⋊C4—28no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4D418yescomplemented
107C2×Dic11⋊C4C2318yes—
108C2×Dic11⋊C4C2314yes—
109C2×Dic11⋊C4C2314yes—
110C2×C4×Dic11—24no—
111C2×C4×Dic11—24no—
112C2×C4×Dic11C2314yes—
113C2×C4×Dic11C2314yes—
114C11⋊#95C2318yes—
115C11⋊#95C2314yes—
116C11⋊#95C2314yes—
117C2×#2445—111nomaximal, Sylow
118C24×C11—24no—
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11—24no—
127C24×C11—24no—
128C24×C11—24no—
129C24×C11—24no—
130C24×C11—24no—
131C24×C11C2×D418yes—
132C24×C11C2414yes—
133C24×C11C2414yes—
134C24×C11C2411yescharacteristic
135C2×D4×C11—216no—
136C2×D4×C11—216no—
137C2×D4×C11—232no—
138C2×D4×C11—216no—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11—28no—
142C2×D4×C11—216no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—48no—
146C2×D4×C11—48no—
147C2×D4×C11—432no—
148C2×D4×C11—432no—
149C2×D4×C11—416no—
150C2×D4×C11C2×D4116yes—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11#4114yes—
158C22×C4×C11#4114yes—
159C22×C4×C11#4114yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×Dic11—216no—
164C22×Dic11—22no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—216no—
170C22×Dic11—22no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—22no—
174C22×Dic11—24no—
175C22×Dic11—22no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—24no—
180C22×Dic11—24no—
181C22×Dic11—48no—
182C22×Dic11—432no—
183C22×Dic11C2×D414yes—
184C22×Dic11C2×D414yes—
185C22×Dic11C2412yes—
186C22×Dic11C2412yes—
187C22×Dic11C2414yes—
188C22×Dic11C2414yes—
189C22×Dic11C2412yes—
190C22×Dic11C2412yes—
191C42×C11—28no—
192C22⋊Dic11—216no—
193C22⋊Dic11—216no—
194C22⋊Dic11—216no—
195C22⋊Dic11—216no—
196C22⋊Dic11—48no—
197C22⋊Dic11—48no—
198C22⋊Dic11—48no—
199C4⋊Dic11—28no—
200C4⋊Dic11—28no—
201Dic11⋊C4—216no—
202Dic11⋊C4—28no—
203Dic11⋊C4C2×D4116yescomplemented
204C4×Dic11—28no—
205C4×Dic11—28no—
206C22×#127D1111yescharacteristic
207C22×#123—112no—
208C22×C4×D4—111no—
209#2445—1116no—
210C2×#394—112no—
211C2×#394—112no—
212C2×#390—111no—
213C2×#390—111no—
214C2×#390—111no—
215C2×#389—111no—
216C2×#386—112no—
217C2×C4×C4⋊C4—111no—
218C23×C11—216no—
219C23×C11—216no—
220C23×C11—216no—
221C23×C11—24no—
222C23×C11—24no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—24no—
227C23×C11—24no—
228C23×C11—24no—
229C23×C11—24no—
230C23×C11—24no—
231C23×C11—24no—
232C23×C11—24no—
233C23×C11—24no—
234C23×C11—48no—
235C23×C11—48no—
236C23×C11—48no—
237C23×C11—48no—
238C23×C11—48no—
239C23×C11—48no—
240C23×C11—48no—
241C23×C11—48no—
242C23×C11—48no—
243C23×C11—48no—
244C23×C11—48no—
245C23×C11C22×D412yes—
246C23×C11C22×D418yes—
247C23×C11C22×D412yes—
248C23×C11C2×#4112yes—
249C23×C11C2×#4112yes—
250C23×C11C2×#4112yes—
251C23×C11H(5,𝔽2)12yes—
252C23×C11H(5,𝔽2)12yes—
253C23×C11C2511yescharacteristic
254D4×C11—232no—
255D4×C11—432no—
256D4×C11—432no—
257D4×C11—416no—
258C2×C4×C11—28no—
259C2×C4×C11—28no—
260C2×C4×C11—22no—
261C2×C4×C11—22no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11#123116yescomplemented
265C2×C4×C11C22×D414yes—
266C2×C4×C11C22×D414yes—
267C2×C4×C11C2×#4114yes—
268C2×C4×C11C2×#4114yes—
269C2×C4×C11C2×#4114yes—
270C2×Dic11—28no—
271C2×Dic11—28no—
272C2×Dic11—22no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—22no—
276C2×Dic11—22no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—22no—
281C2×Dic11—22no—
282C2×Dic11—24no—
283C2×Dic11—22no—
284C2×Dic11—22no—
285C2×Dic11—22no—
286C2×Dic11—24no—
287C2×Dic11—24no—
288C2×Dic11—432no—
289C2×Dic11—44no—
290C2×Dic11—48no—
291C2×Dic11—44no—
292C2×Dic11—48no—
293C2×Dic11C22×D414yes—
294C2×Dic11C22×D414yes—
295C23×D4C2×D1111yescharacteristic
296C23×D4C2×D1112yes—
297C23×D4C2×D1112yes—
298C23×D4C2×D1111yescharacteristic
299C24×C4—112no—
300C2×#127—28no—
301C2×#127C2×D1118yes—
302C2×#123—1116no—
303C2×#123—2216no—
304C2×C4×D4—118no—
305C2×C4×D4—228no—
306C22×C4⋊C4—111no—
307C22×C4⋊C4—111no—
308C22×C4⋊C4—112no—
309C22×C4⋊C4—111no—
310C22×C4⋊C4—111no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C22⋊C4—112no—
314C22×C22⋊C4—112no—
315C22×C22⋊C4—112no—
316C22×C22⋊C4—112no—
317C22×C22⋊C4—112no—
318C22×C42—111no—
319C22×C42—111no—
320C22×C42C2×D1111yescharacteristic
321#394—1116no—
322#394—1116no—
323#390—118no—
324#390—118no—
325#390—118no—
326#389—118no—
327#386—1116no—
328C4×C4⋊C4—118no—
329C2×#95—111no—
330C2×#95—112no—
331C2×#95—111no—
332C22×C11—28no—
333C22×C11—28no—
334C22×C11—28no—
335C22×C11—44no—
336C22×C11—44no—
337C22×C11—44no—
338C22×C11—432no—
339C22×C11—44no—
340C22×C11—44no—
341C22×C11—44no—
342C22×C11—44no—
343C22×C11—44no—
344C22×C11—44no—
345C22×C11—44no—
346C22×C11—44no—
347C22×C11—816no—
348C22×C11C2×#12314yes—
349C22×C11#53214yes—
350C22×C11#54014yes—
351C22×C11D4214yes—
352C22×C11#54614yes—
353C22×C11#55014yes—
354C22×C11#55914yes—
355C22×C11C23×D411yescharacteristic
356C22×C11C23×D411yescharacteristic
357C22×C11C22×#4111yescharacteristic
358C22×C11C22×#4111yescharacteristic
359C22×C11C22×#4111yescharacteristic
360C22×C11C2×H(5,𝔽2)11yescharacteristic
361C22×C11C2×H(5,𝔽2)11yescharacteristic
362C4×C11—24no—
363C4×C11—24no—
364C4×C11C2×#12318yescomplemented
365Dic11—24no—
366Dic11—24no—
367Dic11—42no—
368Dic11—44no—
369Dic11—42no—
370Dic11—44no—
371C25C22×D1112yes—
372C25C22×D1112yes—
373C22×D4—28no—
374C22×D4—28no—
375C22×D4—28no—
376C22×D4—24no—
377C22×D4—24no—
378C22×D4—28no—
379C22×D4—24no—
380C22×D4—24no—
381C22×D4—24no—
382C22×D4—44no—
383C22×D4—44no—
384C22×D4C22⋊D1118yes—
385C22×D4C22×D1114yes—
386C22×D4C22×D1118yes—
387C22×D4C22×D1118yes—
388C22×D4C22×D1114yes—
389C23×C4—111no—
390C23×C4—111no—
391C23×C4—112no—
392C23×C4—111no—
393C23×C4—111no—
394C23×C4—112no—
395C23×C4—118no—
396C23×C4—228no—
397C23×C4—228no—
398C23×C4—444no—
399C23×C4C22×D1111yescharacteristic
400C23×C4C22×D1111yescharacteristic
401C23×C4C22×D1111yescharacteristic
402#127—232no—
403#123—2264no—
404C4×D4—2232no—
405C2×C4⋊C4—118no—
406C2×C4⋊C4—114no—
407C2×C4⋊C4—114no—
408C2×C4⋊C4—118no—
409C2×C4⋊C4—114no—
410C2×C4⋊C4—114no—
411C2×C4⋊C4—228no—
412C2×C4⋊C4—224no—
413C2×C4⋊C4—224no—
414C2×C4⋊C4—224no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—118no—
418C2×C22⋊C4—118no—
419C2×C22⋊C4—118no—
420C2×C22⋊C4—118no—
421C2×C22⋊C4—118no—
422C2×C22⋊C4—228no—
423C2×C22⋊C4—228no—
424C2×C22⋊C4—228no—
425C2×C22⋊C4—228no—
426C2×C22⋊C4—444no—
427C2×C22⋊C4—444no—
428C2×C22⋊C4—444no—
429C2×C42—24no—
430C2×C42—114no—
431C2×C42—114no—
432C2×C42—224no—
433C2×C42—224no—
434C2×C42C22×D1114yes—
435#95—114no—
436#95—114no—
437#95—118no—
438C2×C11—48no—
439C2×C11—84no—
440C2×C11#244518yescomplemented
441C2×C11C22×#12311yescharacteristic
442C2×C11C2×#53211yescharacteristic
443C2×C11C2×#54011yescharacteristic
444C2×C11C2×D4211yescharacteristic
445C2×C11C2×#54611yescharacteristic
446C2×C11C2×#55011yescharacteristic
447C2×C11C2×#55911yescharacteristic
448C24—24no—
449C24—24no—
450C24—24no—
451C24—24no—
452C24—24no—
453C24—24no—
454C24—24no—
455C24—24no—
456C24—24no—
457C24—24no—
458C24—24no—
459C24—24no—
460C24—24no—
461C24C2×C22⋊D1118yes—
462C24C23×D1114yes—
463C24C23×D1114yes—
464C24C23×D1111yescharacteristic
465C2×D4—216no—
466C2×D4—216no—
467C2×D4—232no—
468C2×D4—216no—
469C2×D4—28no—
470C2×D4—28no—
471C2×D4—216no—
472C2×D4—28no—
473C2×D4—28no—
474C2×D4—28no—
475C2×D4—48no—
476C2×D4—48no—
477C2×D4—432no—
478C2×D4—432no—
479C2×D4—416no—
480C2×D4C2×C22⋊D11116yes—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—22no—
484C22×C4—22no—
485C22×C4—114no—
486C22×C4—114no—
487C22×C4—112no—
488C22×C4—112no—
489C22×C4—112no—
490C22×C4—112no—
491C22×C4—114no—
492C22×C4—114no—
493C22×C4—2216no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—222no—
497C22×C4—222no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—222no—
501C22×C4—224no—
502C22×C4—222no—
503C22×C4—224no—
504C22×C4—222no—
505C22×C4—222no—
506C22×C4—222no—
507C22×C4—224no—
508C22×C4—222no—
509C22×C4—224no—
510C22×C4—2216no—
511C22×C4—448no—
512C22×C4—4432no—
513C22×C4D4×D1114yes—
514C22×C4#434114yes—
515C22×C4#434114yes—
516C22×C4#434114yes—
517C22×C4C2×C22⋊D1114yes—
518C22×C4C23×D1112yes—
519C22×C4C23×D1112yes—
520C22×C4C23×D1112yes—
521C4⋊C4—1116no—
522C4⋊C4—2216no—
523C4⋊C4—228no—
524C4⋊C4—228no—
525C4⋊C4—228no—
526C22⋊C4—2216no—
527C22⋊C4—2216no—
528C22⋊C4—2216no—
529C22⋊C4—2216no—
530C22⋊C4—448no—
531C22⋊C4—448no—
532C22⋊C4—448no—
533C42—28no—
534C42—228no—
535C42—228no—
536C11C2×#244511yescharacteristic, complemented, Sylow
537C23—216no—
538C23—216no—
539C23—216no—
540C23—24no—
541C23—24no—
542C23—24no—
543C23—24no—
544C23—24no—
545C23—24no—
546C23—24no—
547C23—24no—
548C23—24no—
549C23—24no—
550C23—24no—
551C23—24no—
552C23—24no—
553C23—48no—
554C23—48no—
555C23—48no—
556C23—48no—
557C23—48no—
558C23—48no—
559C23—48no—
560C23—48no—
561C23—48no—
562C23—48no—
563C23—48no—
564C23C2×D4×D1112yes—
565C23C2×#434112yes—
566C23C2×#434112yes—
567C23C2×#434112yes—
568C23#6703712yes—
569C23#6703712yes—
570C23C22×C22⋊D1118yes—
571C23C22×C22⋊D1112yes—
572C23C24×D1111yescharacteristic
573D4—232no—
574D4—432no—
575D4—432no—
576D4—416no—
577C2×C4—28no—
578C2×C4—28no—
579C2×C4—22no—
580C2×C4—22no—
581C2×C4—22no—
582C2×C4—22no—
583C2×C4—114no—
584C2×C4—114no—
585C2×C4—228no—
586C2×C4—228no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—222no—
590C2×C4—222no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—222no—
594C2×C4—222no—
595C2×C4—224no—
596C2×C4—222no—
597C2×C4—222no—
598C2×C4—222no—
599C2×C4—224no—
600C2×C4—224no—
601C2×C4—222no—
602C2×C4—224no—
603C2×C4—4432no—
604C2×C4—448no—
605C2×C4—444no—
606C2×C4—448no—
607C2×C4—444no—
608C2×C4#66988116yescomplemented
609C2×C4C2×D4×D1114yes—
610C2×C4C2×#434114yes—
611C2×C4C2×#434114yes—
612C2×C4C2×#434114yes—
613C2×C4C22×C22⋊D1114yes—
614C22—28no—
615C22—28no—
616C22—28no—
617C22—44no—
618C22—44no—
619C22—44no—
620C22—44no—
621C22—432no—
622C22—44no—
623C22—44no—
624C22—44no—
625C22—44no—
626C22—44no—
627C22—44no—
628C22—44no—
629C22—816no—
630C22#1062324414yes—
631C22#1062324714yes—
632C22#1062324914yes—
633C22#1062325014yes—
634C22C2×#6698814yes—
635C22D4×C22⋊D1114yes—
636C22#1062333714yes—
637C22C22×D4×D1111yescharacteristic
638C22C22×#434111yescharacteristic
639C22C22×#434111yescharacteristic
640C22C22×#434111yescharacteristic
641C22C2×#6703711yescharacteristic
642C22C2×#6703711yescharacteristic
643C22C23×C22⋊D1111yescharacteristic
644C4—24no—
645C4—24no—
646C4—224no—
647C4—224no—
648C4—442no—
649C4—444no—
650C4—442no—
651C4—444no—
652C4C2×#6698818yescomplemented
653C2—48no—
654C2—84no—
655C2#1307237718yesdirect product factor
656C2C22×#6698811yescharacteristic
657C2C2×#1062324711yescharacteristic
658C2C2×#1062325011yescharacteristic
659C2C2×D4×C22⋊D1111yescharacteristic
660C2C2×#1062333711yescharacteristic
661C2C2×#1062324911yescharacteristic
662C2C2×#1062324411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#127C2
socleC24×C11C24
hypercenterC22×#127D11
hypocenterC11C2×#2445
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#127

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13072377C2direct (N × H)
4. C2×#10622835C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622834C2semidirect
7. C2×#10622834C2semidirect
8. C2×#10622834C2semidirect
9. C2×#10622541C2semidirect
10. C2×#10622833C2semidirect
11. C2×C4×Dic11⋊C4C2semidirect
29. C2×#66988C22semidirect
31. C2×D4×Dic11C22semidirect
39. #10622835C22semidirect
40. #10622835C22semidirect
41. #10622834C22semidirect
42. #10622834C22semidirect
43. #10622834C22semidirect
44. #10622833C22semidirect
48. C4×Dic11⋊C4C22semidirect
49. #10622541C22semidirect
106. C2×Dic11⋊C4D4semidirect
203. Dic11⋊C4C2×D4semidirect
264. C2×C4×C11#123semidirect
364. C4×C11C2×#123semidirect
440. C2×C11#2445semidirect
536. C11C2×#2445semidirect
608. C2×C4#66988semidirect
652. C4C2×#66988semidirect
655. C2#13072377direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669882
C22×D4×Dic112
#130723772
C2×#106228352
C2×#106228342
C2×#106225412
C2×#106228332
C2×C4×Dic11⋊C42
C22×C11×#1272
C2×#244511