Finite Group Databasebeta

← C2×#13072126 #14921643

Subgroups — C2×#13072126 #14921643

Order 2816.

3830 conjugacy classes of subgroups.

The subgroup lattice has 648 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#13072126C2116yesmaximal, direct product factor
4C2×#10622565C212yesmaximal, complemented
5C2×#10622835C212yesmaximal, complemented
6C2×#10622834C211yesmaximal, characteristic, complemented
7C2×#10622586C211yesmaximal, characteristic, complemented
8C2×#10622559C212yesmaximal, complemented
9C2×#10622589C211yesmaximal, characteristic, complemented
10C2×#10622825C211yesmaximal, characteristic, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
12C22×C11×#121C211yesmaximal, characteristic
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×Dic11C2212yes—
17C2×C11×#121—28no—
18C2×C11×#121C2218yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C2×#66988—216no—
28C2×#66988C22116yescomplemented
29C2×D4×Dic11—28no—
30C2×D4×Dic11C2218yescomplemented
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×Dic11⋊C4C2212yes—
34C22×Dic11⋊C4C2212yes—
35C22×Dic11⋊C4C2212yes—
36C22×C4×Dic11C2211yescharacteristic
37C22×C4×Dic11C2211yescharacteristic
38#10622835C22116yescomplemented
39#10622834C2218yescomplemented
40#10622825C2218yescomplemented
41C4×C22⋊Dic11C2218yescomplemented
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2211yescharacteristic
44C2×C11⋊#95C2212yes—
45C2×C11⋊#95C2212yes—
46#10622589C2218yescomplemented
47#10622586C2218yescomplemented
48#10622565C22116yescomplemented
49#10622559C22116yescomplemented
50C25×C11C2311yescharacteristic
51C25×C11C2312yes—
52C22×D4×C11—28no—
53C22×D4×C11—28no—
54C22×D4×C11—24no—
55C22×D4×C11—24no—
56C22×D4×C11—44no—
57C22×D4×C11D418yes—
58C22×D4×C11C2318yes—
59C22×D4×C11C2314yes—
60C23×C4×C11—24no—
61C23×C4×C11—24no—
62C23×C4×C11—24no—
63C23×C4×C11C2312yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C23×C4×C11C2311yescharacteristic
67C23×Dic11—28no—
68C23×Dic11—28no—
69C23×Dic11—44no—
70C23×Dic11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2312yes—
73C23×Dic11C2318yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C11×#121—232no—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C22⋊C4—28no—
81C2×C11×C22⋊C4C2318yes—
82C2×C22⋊Dic11—28no—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11—28no—
85C2×C22⋊Dic11—24no—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11D418yescomplemented
88C2×C22⋊Dic11C2318yes—
89C2×C22⋊Dic11C2318yes—
90C2×C22⋊Dic11C2318yes—
91C2×C22⋊Dic11C2318yes—
92C2×C22⋊Dic11C2314yes—
93C2×C22⋊Dic11C2314yes—
94#66988—264no—
95D4×Dic11—232no—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—28no—
102C2×Dic11⋊C4—44no—
103C2×Dic11⋊C4C2318yes—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2318yes—
106C2×C4×Dic11—24no—
107C2×C4×Dic11—24no—
108C2×C4×Dic11C2314yes—
109C2×C4×Dic11C2314yes—
110C11⋊#95C2314yes—
111C11⋊#95C2318yes—
112C11⋊#95C2314yes—
113C11⋊#95C2318yes—
114C2×#2422—111nomaximal, Sylow
115C24×C11—24no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—24no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—24no—
122C24×C11—24no—
123C24×C11—24no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—24no—
127C24×C11C2×D414yes—
128C24×C11C2×D418yes—
129C24×C11C2412yes—
130C24×C11C2414yes—
131C24×C11C2411yescharacteristic
132C2×D4×C11—216no—
133C2×D4×C11—216no—
134C2×D4×C11—232no—
135C2×D4×C11—28no—
136C2×D4×C11—28no—
137C2×D4×C11—48no—
138C2×D4×C11—432no—
139C2×D4×C11C2×D4116yes—
140C22×C4×C11—24no—
141C22×C4×C11—22no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—24no—
146C22×C4×C11—28no—
147C22×C4×C11—28no—
148C22×C4×C11—28no—
149C22×C4×C11—416no—
150C22×C4×C11C2×D414yes—
151C22×C4×C11#4114yes—
152C22×C4×C11#4114yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2414yes—
155C22×C4×C11C2412yes—
156C22×Dic11—216no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—216no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—22no—
169C22×Dic11—22no—
170C22×Dic11—24no—
171C22×Dic11—22no—
172C22×Dic11—22no—
173C22×Dic11—48no—
174C22×Dic11—432no—
175C22×Dic11C2×D414yes—
176C22×Dic11C2×D414yes—
177C22×Dic11#4114yes—
178C22×Dic11C2412yes—
179C22×Dic11C2414yes—
180C22×Dic11C2414yes—
181C22×Dic11C2412yes—
182C22×Dic11C2412yes—
183C22×Dic11C2412yes—
184C11×C4⋊C4—28no—
185C11×C22⋊C4—216no—
186C22⋊Dic11—216no—
187C22⋊Dic11—216no—
188C22⋊Dic11—28no—
189C22⋊Dic11—216no—
190C22⋊Dic11—216no—
191C22⋊Dic11C2×D4116yescomplemented
192C4⋊Dic11—28no—
193C4⋊Dic11—28no—
194Dic11⋊C4—216no—
195Dic11⋊C4—216no—
196Dic11⋊C4—48no—
197C4×Dic11—28no—
198C4×Dic11—28no—
199C22×#123—112no—
200C22×#121D1111yescharacteristic
201C22×C4×D4—111no—
202#2422—1116no—
203C2×#397—112no—
204C2×#394—112no—
205C2×#390—111no—
206C2×#389—111no—
207C2×#385—112no—
208C2×#384—111no—
209C2×#380—111no—
210C2×C4×C22⋊C4—111no—
211C23×C11—216no—
212C23×C11—28no—
213C23×C11—216no—
214C23×C11—28no—
215C23×C11—216no—
216C23×C11—28no—
217C23×C11—24no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—24no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—22no—
227C23×C11—22no—
228C23×C11—24no—
229C23×C11—44no—
230C23×C11—48no—
231C23×C11—44no—
232C23×C11—48no—
233C23×C11—44no—
234C23×C11—48no—
235C23×C11—44no—
236C23×C11—48no—
237C23×C11C22×D414yes—
238C23×C11C22×D412yes—
239C23×C11C22×D418yes—
240C23×C11C22×D412yes—
241C23×C11C2×#4112yes—
242C23×C11C2×#4112yes—
243C23×C11C2×#4112yes—
244C23×C11H(5,𝔽2)12yes—
245C23×C112−1+412yes—
246C23×C11C2511yescharacteristic
247D4×C11—232no—
248D4×C11—432no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—22no—
253C2×C4×C11—22no—
254C2×C4×C11—24no—
255C2×C4×C11—44no—
256C2×C4×C11—48no—
257C2×C4×C11—416no—
258C2×C4×C11#123116yescomplemented
259C2×C4×C11C22×D414yes—
260C2×C4×C11C2×#4114yes—
261C2×C4×C11C2×#4114yes—
262C2×Dic11—28no—
263C2×Dic11—28no—
264C2×Dic11—28no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—22no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—24no—
274C2×Dic11—24no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—22no—
278C2×Dic11—24no—
279C2×Dic11—22no—
280C2×Dic11—432no—
281C2×Dic11—48no—
282C2×Dic11—48no—
283C2×Dic11—44no—
284C2×Dic11C22×D414yes—
285C2×Dic11C22×D414yes—
286C2×Dic11C2×#4114yes—
287C23×D4C2×D1112yes—
288C23×D4C2×D1111yescharacteristic
289C24×C4—112no—
290C24×C4C2×D1111yescharacteristic
291C2×#123—1116no—
292C2×#123—2216no—
293C2×#121—28no—
294C2×#121C2×D1118yes—
295C2×C4×D4—118no—
296C2×C4×D4—228no—
297C22×C4⋊C4—112no—
298C22×C4⋊C4—112no—
299C22×C4⋊C4—111no—
300C22×C4⋊C4—111no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C22⋊C4—111no—
304C22×C22⋊C4—111no—
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4C2×D1112yes—
310C22×C42—111no—
311C22×C42—111no—
312#397—1116no—
313#394—1116no—
314#390—118no—
315#389—118no—
316#385—1116no—
317#384—118no—
318#380—118no—
319C4×C22⋊C4—118no—
320C2×#95—112no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—111no—
324C22×C11—28no—
325C22×C11—24no—
326C22×C11—24no—
327C22×C11—28no—
328C22×C11—28no—
329C22×C11—24no—
330C22×C11—42no—
331C22×C11—44no—
332C22×C11—432no—
333C22×C11—416no—
334C22×C11—42no—
335C22×C11—44no—
336C22×C11—42no—
337C22×C11—44no—
338C22×C11—42no—
339C22×C11—44no—
340C22×C11C2×#12314yes—
341C22×C11#53214yes—
342C22×C11#54214yes—
343C22×C11D4214yes—
344C22×C11#54714yes—
345C22×C11#54714yes—
346C22×C11#55314yes—
347C22×C11C23×D411yescharacteristic
348C22×C11C23×D411yescharacteristic
349C22×C11C22×#4111yescharacteristic
350C22×C11C22×#4111yescharacteristic
351C22×C11C22×#4111yescharacteristic
352C22×C11C2×H(5,𝔽2)11yescharacteristic
353C22×C11C2×2−1+411yescharacteristic
354C4×C11—42no—
355C4×C11—44no—
356C4×C11C2×#12318yescomplemented
357Dic11—24no—
358Dic11—24no—
359Dic11—24no—
360Dic11—44no—
361Dic11—44no—
362Dic11—42no—
363C25C22×D1111yescharacteristic
364C25C22×D1112yes—
365C22×D4—28no—
366C22×D4—28no—
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—44no—
370C22×D4C22⋊D1118yes—
371C22×D4C22×D1118yes—
372C22×D4C22×D1114yes—
373C23×C4—24no—
374C23×C4—24no—
375C23×C4—24no—
376C23×C4—111no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—112no—
380C23×C4—111no—
381C23×C4—112no—
382C23×C4—118no—
383C23×C4—228no—
384C23×C4—228no—
385C23×C4—444no—
386C23×C4C22×D1114yes—
387C23×C4C22×D1111yescharacteristic
388C23×C4C22×D1112yes—
389C23×C4C22×D1111yescharacteristic
390#123—2264no—
391#121—232no—
392C4×D4—2232no—
393C2×C4⋊C4—24no—
394C2×C4⋊C4—114no—
395C2×C4⋊C4—118no—
396C2×C4⋊C4—118no—
397C2×C4⋊C4—114no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—228no—
400C2×C4⋊C4—228no—
401C2×C4⋊C4—224no—
402C2×C4⋊C4—224no—
403C2×C4⋊C4—444no—
404C2×C4⋊C4C22×D1114yes—
405C2×C22⋊C4—28no—
406C2×C22⋊C4—118no—
407C2×C22⋊C4—114no—
408C2×C22⋊C4—118no—
409C2×C22⋊C4—118no—
410C2×C22⋊C4—118no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—228no—
414C2×C22⋊C4—224no—
415C2×C22⋊C4—228no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4C22×D1118yes—
419C2×C42—114no—
420C2×C42—114no—
421C2×C42—224no—
422C2×C42—224no—
423#95—114no—
424#95—114no—
425#95—118no—
426#95—118no—
427C2×C11—48no—
428C2×C11—44no—
429C2×C11#242218yescomplemented
430C2×C11C22×#12311yescharacteristic
431C2×C11C2×#53211yescharacteristic
432C2×C11C2×#54211yescharacteristic
433C2×C11C2×D4211yescharacteristic
434C2×C11C2×#54711yescharacteristic
435C2×C11C2×#54711yescharacteristic
436C2×C11C2×#55311yescharacteristic
437C24—24no—
438C24—22no—
439C24—22no—
440C24—24no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—24no—
445C24—22no—
446C24—24no—
447C24—22no—
448C24—22no—
449C24D4×D1114yes—
450C24C2×C22⋊D1118yes—
451C24C23×D1112yes—
452C24C23×D1114yes—
453C24C23×D1111yescharacteristic
454C2×D4—216no—
455C2×D4—216no—
456C2×D4—232no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—48no—
460C2×D4—432no—
461C2×D4C2×C22⋊D11116yes—
462C22×C4—24no—
463C22×C4—22no—
464C22×C4—22no—
465C22×C4—24no—
466C22×C4—22no—
467C22×C4—24no—
468C22×C4—28no—
469C22×C4—28no—
470C22×C4—28no—
471C22×C4—416no—
472C22×C4—114no—
473C22×C4—114no—
474C22×C4—114no—
475C22×C4—112no—
476C22×C4—112no—
477C22×C4—112no—
478C22×C4—112no—
479C22×C4—114no—
480C22×C4—114no—
481C22×C4—2216no—
482C22×C4—222no—
483C22×C4—222no—
484C22×C4—222no—
485C22×C4—222no—
486C22×C4—222no—
487C22×C4—222no—
488C22×C4—224no—
489C22×C4—224no—
490C22×C4—224no—
491C22×C4—224no—
492C22×C4—222no—
493C22×C4—224no—
494C22×C4—222no—
495C22×C4—222no—
496C22×C4—224no—
497C22×C4—2216no—
498C22×C4—448no—
499C22×C4—4432no—
500C22×C4#434114yes—
501C22×C4#434114yes—
502C22×C4C2×C22⋊D1114yes—
503C22×C4C23×D1112yes—
504C22×C4C23×D1114yes—
505C22×C4C23×D1112yes—
506C4⋊C4—28no—
507C4⋊C4—2216no—
508C4⋊C4—2216no—
509C4⋊C4—228no—
510C4⋊C4—228no—
511C4⋊C4—448no—
512C22⋊C4—216no—
513C22⋊C4—1116no—
514C22⋊C4—2216no—
515C22⋊C4—228no—
516C22⋊C4—2216no—
517C22⋊C4—2216no—
518C22⋊C4—2216no—
519C42—228no—
520C42—228no—
521C11C2×#242211yescharacteristic, complemented, Sylow
522C23—216no—
523C23—216no—
524C23—28no—
525C23—216no—
526C23—28no—
527C23—28no—
528C23—24no—
529C23—22no—
530C23—22no—
531C23—24no—
532C23—24no—
533C23—24no—
534C23—22no—
535C23—22no—
536C23—24no—
537C23—24no—
538C23—22no—
539C23—22no—
540C23—44no—
541C23—44no—
542C23—48no—
543C23—44no—
544C23—48no—
545C23—48no—
546C23—44no—
547C23—48no—
548C23C2×D4×D1114yes—
549C23C2×D4×D1112yes—
550C23C2×#434112yes—
551C23C2×#434112yes—
552C23#6703712yes—
553C23#41×D1112yes—
554C23#6704312yes—
555C23C22×C22⋊D1118yes—
556C23C22×C22⋊D1112yes—
557C23C24×D1111yescharacteristic
558D4—232no—
559D4—432no—
560C2×C4—24no—
561C2×C4—22no—
562C2×C4—22no—
563C2×C4—24no—
564C2×C4—22no—
565C2×C4—24no—
566C2×C4—44no—
567C2×C4—48no—
568C2×C4—416no—
569C2×C4—114no—
570C2×C4—114no—
571C2×C4—114no—
572C2×C4—228no—
573C2×C4—228no—
574C2×C4—228no—
575C2×C4—222no—
576C2×C4—222no—
577C2×C4—222no—
578C2×C4—222no—
579C2×C4—222no—
580C2×C4—222no—
581C2×C4—224no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—222no—
587C2×C4—222no—
588C2×C4—222no—
589C2×C4—224no—
590C2×C4—4432no—
591C2×C4—448no—
592C2×C4—444no—
593C2×C4—448no—
594C2×C4#66988116yescomplemented
595C2×C4C2×#434114yes—
596C2×C4C2×#434114yes—
597C2×C4C22×C22⋊D1114yes—
598C22—24no—
599C22—28no—
600C22—24no—
601C22—28no—
602C22—24no—
603C22—28no—
604C22—42no—
605C22—44no—
606C22—44no—
607C22—42no—
608C22—44no—
609C22—42no—
610C22—44no—
611C22—42no—
612C22—432no—
613C22—416no—
614C22#1062312714yes—
615C22#1062313414yes—
616C22#1062314214yes—
617C22#1062314514yes—
618C22C2×#6698814yes—
619C22D4×C22⋊D1114yes—
620C22#1062335514yes—
621C22C22×D4×D1111yescharacteristic
622C22C22×#434111yescharacteristic
623C22C22×#434111yescharacteristic
624C22C2×#6703711yescharacteristic
625C22C2×#41×D1111yescharacteristic
626C22C2×#6704311yescharacteristic
627C22C23×C22⋊D1111yescharacteristic
628C4—44no—
629C4—42no—
630C4—224no—
631C4—224no—
632C4—224no—
633C4—444no—
634C4—444no—
635C4—442no—
636C4C2×#6698818yescomplemented
637C2—44no—
638C2—48no—
639C2#1307212618yesdirect product factor
640C2C22×#6698811yescharacteristic
641C2C2×#1062312711yescharacteristic
642C2C2×#1062313411yescharacteristic
643C2C2×D4×C22⋊D1111yescharacteristic
644C2C2×#1062335511yescharacteristic
645C2C2×#1062314211yescharacteristic
646C2C2×#1062314511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
Fitting, prime radicalC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2422
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66988C2semidirect
2. C22×D4×Dic11C2semidirect
3. #13072126C2direct (N × H)
4. C2×#10622565C2semidirect
5. C2×#10622835C2semidirect
6. C2×#10622834C2semidirect
7. C2×#10622586C2semidirect
8. C2×#10622559C2semidirect
9. C2×#10622589C2semidirect
10. C2×#10622825C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
28. C2×#66988C22semidirect
30. C2×D4×Dic11C22semidirect
38. #10622835C22semidirect
39. #10622834C22semidirect
40. #10622825C22semidirect
41. C4×C22⋊Dic11C22semidirect
46. #10622589C22semidirect
47. #10622586C22semidirect
48. #10622565C22semidirect
49. #10622559C22semidirect
87. C2×C22⋊Dic11D4semidirect
191. C22⋊Dic11C2×D4semidirect
258. C2×C4×C11#123semidirect
356. C4×C11C2×#123semidirect
429. C2×C11#2422semidirect
521. C11C2×#2422semidirect
594. C2×C4#66988semidirect
636. C4C2×#66988semidirect
639. C2#13072126direct (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
#130721262
C2×#106225652
C2×#106228352
C2×#106228342
C2×#106225862
C2×#106225592
C2×#106225892
C2×#106228252
C2×C4×C22⋊Dic112
C22×C11×#1212
C2×#242211