Finite Group Databasebeta

← C2×#13072913 #14923290

Subgroups — C2×#13072913 #14923290

Order 2816.

3070 conjugacy classes of subgroups.

The subgroup lattice has 628 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66979C211yesmaximal, characteristic, complemented
2#13072913C2116yesmaximal, direct product factor
3C2×#10622565C212yesmaximal, complemented
4C2×#10622835C212yesmaximal
5C2×#10622541C211yesmaximal, characteristic, complemented
6C2×#10622541C211yesmaximal, characteristic, complemented
7C2×#10622557C212yesmaximal, complemented
8C2×#10622591C212yesmaximal, complemented
9C2×#10622825C211yesmaximal, characteristic, complemented
10C2×#10622825C211yesmaximal, characteristic, complemented
11C2×#10622825C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C2×C4×D4×C11—28no—
17C2×C4×D4×C11C2218yes—
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2211yescharacteristic
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C2×#66979—28no—
27C2×#66979C2218yescomplemented
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×Dic11⋊C4C2212yes—
34C22×C4×Dic11C2212yes—
35#10622835C22116yes—
36#10622825C2218yescomplemented
37#10622825C2218yescomplemented
38#10622825C2218yescomplemented
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44#10622591C22116yescomplemented
45#10622565C22116yescomplemented
46#10622557C22116yescomplemented
47#10622541C2218yescomplemented
48#10622541C2218yescomplemented
49C25×C11C2311yescharacteristic
50C25×C11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11—24no—
54C22×D4×C11C2314yes—
55C23×C4×C11—24no—
56C23×C4×C11—24no—
57C23×C4×C11—24no—
58C23×C4×C11—24no—
59C23×C4×C11—24no—
60C23×C4×C11D418yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2314yes—
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2314yes—
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11C2312yes—
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C4×D4×C11—232no—
73C2×C11×C4⋊C4—24no—
74C2×C11×C4⋊C4C2314yes—
75C2×C11×C22⋊C4—24no—
76C2×C11×C22⋊C4—24no—
77C2×C11×C22⋊C4C2314yes—
78C2×C11×C22⋊C4C2314yes—
79C2×C42×C11—24no—
80C2×C42×C11C2314yes—
81C2×C22⋊Dic11—28no—
82C2×C22⋊Dic11—28no—
83C2×C22⋊Dic11—44no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11C2318yes—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89#66979—232no—
90C2×C4⋊Dic11—24no—
91C2×C4⋊Dic11—24no—
92C2×C4⋊Dic11—24no—
93C2×C4⋊Dic11—24no—
94C2×C4⋊Dic11C2314yes—
95C2×C4⋊Dic11C2314yes—
96C2×C4⋊Dic11C2314yes—
97C2×C4⋊Dic11C2314yes—
98C2×Dic11⋊C4—28no—
99C2×Dic11⋊C4—44no—
100C2×Dic11⋊C4C2318yes—
101C2×Dic11⋊C4C2318yes—
102C2×C4×Dic11—28no—
103C2×C4×Dic11C2318yes—
104C11⋊#95C2318yes—
105C11⋊#95C2318yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C2×#2485—111nomaximal, Sylow
110C24×C11—22no—
111C24×C11—22no—
112C24×C11—22no—
113C24×C11—22no—
114C24×C11—22no—
115C24×C11—22no—
116C24×C11—22no—
117C24×C11—22no—
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11C2×D414yes—
123C24×C11#4114yes—
124C24×C11C2412yes—
125C24×C11C2412yes—
126C24×C11C2411yescharacteristic
127C2×D4×C11—232no—
128C2×D4×C11—28no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C22×C4×C11—22no—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—232no—
136C22×C4×C11—28no—
137C22×C4×C11—28no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—22no—
141C22×C4×C11—22no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—28no—
146C22×C4×C11—28no—
147C22×C4×C11—416no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D4116yes—
150C22×C4×C11C2×D414yes—
151C22×C4×C11#4114yes—
152C22×C4×C11#4114yes—
153C22×C4×C11#4114yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2412yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2412yes—
158C22×C4×C11C2412yes—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11—24no—
164C22×Dic11—24no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—24no—
170C22×Dic11—24no—
171C22×Dic11C2414yes—
172C22×Dic11C2414yes—
173C22×Dic11C2414yes—
174C22×Dic11C2414yes—
175C11×C4⋊C4—28no—
176C11×C22⋊C4—28no—
177C11×C22⋊C4—28no—
178C42×C11—28no—
179C22⋊Dic11—216no—
180C22⋊Dic11—216no—
181C22⋊Dic11—48no—
182C22⋊Dic11—48no—
183C4⋊Dic11—28no—
184C4⋊Dic11—28no—
185C4⋊Dic11—28no—
186C4⋊Dic11—28no—
187Dic11⋊C4—216no—
188Dic11⋊C4—48no—
189C4×Dic11—216no—
190C22×C4×D4D1111yescharacteristic
191C22×#117—111no—
192#2485—1116no—
193C2×#397—112no—
194C2×#394—112no—
195C2×#389—111no—
196C2×#389—111no—
197C2×#388—112no—
198C2×#387—112no—
199C2×#380—111no—
200C2×#380—111no—
201C2×#380—111no—
202C23×C11—28no—
203C23×C11—28no—
204C23×C11—28no—
205C23×C11—28no—
206C23×C11—28no—
207C23×C11—28no—
208C23×C11—22no—
209C23×C11—22no—
210C23×C11—22no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—22no—
214C23×C11—22no—
215C23×C11—22no—
216C23×C11—22no—
217C23×C11—22no—
218C23×C11—22no—
219C23×C11—22no—
220C23×C11—44no—
221C23×C11—44no—
222C23×C11—44no—
223C23×C11—44no—
224C23×C11—44no—
225C23×C11—44no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11C22×D414yes—
229C23×C11C22×D412yes—
230C23×C11C2×#4114yes—
231C23×C11C2×#4112yes—
232C23×C11C2×#4112yes—
233C23×C11C2×#4112yes—
234C23×C11C2×#4112yes—
235C23×C11H(5,𝔽2)12yes—
236C23×C112−1+412yes—
237C23×C11C2511yescharacteristic
238D4×C11—232no—
239C2×C4×C11—28no—
240C2×C4×C11—28no—
241C2×C4×C11—22no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—232no—
246C2×C4×C11—22no—
247C2×C4×C11—22no—
248C2×C4×C11—22no—
249C2×C4×C11—22no—
250C2×C4×C11—22no—
251C2×C4×C11—22no—
252C2×C4×C11—44no—
253C2×C4×C11—44no—
254C2×C4×C11—416no—
255C2×C4×C11#123116yes—
256C2×C4×C11C22×D414yes—
257C2×C4×C11C22×D414yes—
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2×#4114yes—
260C2×C4×C11C2×#4114yes—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—24no—
267C2×Dic11—24no—
268C2×Dic11—24no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—48no—
274C2×Dic11—48no—
275C2×Dic11—48no—
276C2×Dic11—48no—
277C23×D4C2×D1111yescharacteristic
278C24×C4C2×D1111yescharacteristic
279C24×C4C2×D1111yescharacteristic
280C2×C4×D4—28no—
281C2×C4×D4C2×D1118yes—
282C2×#117—118no—
283C2×#117—228no—
284C22×C4⋊C4—112no—
285C22×C4⋊C4—111no—
286C22×C4⋊C4—111no—
287C22×C4⋊C4—111no—
288C22×C4⋊C4—111no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C22⋊C4—112no—
292C22×C22⋊C4—112no—
293C22×C22⋊C4—112no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4C2×D1111yescharacteristic
296C22×C22⋊C4C2×D1111yescharacteristic
297C22×C42—112no—
298C22×C42C2×D1111yescharacteristic
299#397—1116no—
300#394—1116no—
301#389—118no—
302#389—118no—
303#388—1116no—
304#387—1116no—
305#380—118no—
306#380—118no—
307#380—118no—
308C2×#95—112no—
309C2×#95—112no—
310C2×#95—112no—
311C2×#95—112no—
312C2×#95—112no—
313C22×C11—24no—
314C22×C11—24no—
315C22×C11—24no—
316C22×C11—24no—
317C22×C11—24no—
318C22×C11—24no—
319C22×C11—42no—
320C22×C11—42no—
321C22×C11—42no—
322C22×C11—42no—
323C22×C11—42no—
324C22×C11—42no—
325C22×C11—42no—
326C22×C11—42no—
327C22×C11—416no—
328C22×C11—416no—
329C22×C11C2×#12314yes—
330C22×C11#52514yes—
331C22×C11#53714yes—
332C22×C11#55214yes—
333C22×C11#55314yes—
334C22×C11#55514yes—
335C22×C11#55614yes—
336C22×C11C23×D411yescharacteristic
337C22×C11C22×#4111yescharacteristic
338C22×C11C22×#4111yescharacteristic
339C22×C11C22×#4111yescharacteristic
340C22×C11C22×#4111yescharacteristic
341C22×C11C2×H(5,𝔽2)11yescharacteristic
342C22×C11C2×2−1+411yescharacteristic
343C4×C11—24no—
344C4×C11—24no—
345C4×C11—42no—
346C4×C11—42no—
347C4×C11C2×#12318yes—
348Dic11—44no—
349Dic11—44no—
350Dic11—44no—
351Dic11—44no—
352C25C22×D1111yescharacteristic
353C25C22×D1111yescharacteristic
354C22×D4—24no—
355C22×D4—24no—
356C22×D4—24no—
357C22×D4C22×D1114yes—
358C23×C4—24no—
359C23×C4—24no—
360C23×C4—24no—
361C23×C4—24no—
362C23×C4—24no—
363C23×C4—112no—
364C23×C4—112no—
365C23×C4—112no—
366C23×C4—112no—
367C23×C4C22⋊D1118yes—
368C23×C4C22×D1114yes—
369C23×C4C22×D1111yescharacteristic
370C23×C4C22×D1111yescharacteristic
371C23×C4C22×D1111yescharacteristic
372C23×C4C22×D1114yes—
373C23×C4C22×D1111yescharacteristic
374C23×C4C22×D1111yescharacteristic
375C4×D4—232no—
376#117—2232no—
377C2×C4⋊C4—24no—
378C2×C4⋊C4—114no—
379C2×C4⋊C4—114no—
380C2×C4⋊C4—114no—
381C2×C4⋊C4—114no—
382C2×C4⋊C4—118no—
383C2×C4⋊C4—118no—
384C2×C4⋊C4—228no—
385C2×C4⋊C4—224no—
386C2×C4⋊C4—224no—
387C2×C4⋊C4—224no—
388C2×C4⋊C4—224no—
389C2×C4⋊C4—444no—
390C2×C4⋊C4C22×D1114yes—
391C2×C22⋊C4—24no—
392C2×C22⋊C4—24no—
393C2×C22⋊C4—118no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—118no—
396C2×C22⋊C4—118no—
397C2×C22⋊C4—228no—
398C2×C22⋊C4—228no—
399C2×C22⋊C4—444no—
400C2×C22⋊C4—444no—
401C2×C22⋊C4C22×D1114yes—
402C2×C22⋊C4C22×D1114yes—
403C2×C42—24no—
404C2×C42—118no—
405C2×C42—228no—
406C2×C42C22×D1114yes—
407#95—118no—
408#95—118no—
409#95—118no—
410#95—118no—
411#95—118no—
412C2×C11—44no—
413C2×C11—44no—
414C2×C11#248518yescomplemented
415C2×C11C22×#12311yescharacteristic
416C2×C11C2×#52511yescharacteristic
417C2×C11C2×#53711yescharacteristic
418C2×C11C2×#55211yescharacteristic
419C2×C11C2×#55311yescharacteristic
420C2×C11C2×#55511yescharacteristic
421C2×C11C2×#55611yescharacteristic
422C24—22no—
423C24—22no—
424C24—22no—
425C24—22no—
426C24—22no—
427C24—22no—
428C24—22no—
429C24—22no—
430C24—22no—
431C24—22no—
432C24—22no—
433C24—22no—
434C24#433914yes—
435C24C2×C22⋊D1114yes—
436C24C23×D1112yes—
437C24C23×D1112yes—
438C24C23×D1111yescharacteristic
439C2×D4—232no—
440C2×D4—28no—
441C2×D4—28no—
442C2×D4—28no—
443C22×C4—22no—
444C22×C4—22no—
445C22×C4—22no—
446C22×C4—22no—
447C22×C4—232no—
448C22×C4—28no—
449C22×C4—28no—
450C22×C4—22no—
451C22×C4—22no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—22no—
455C22×C4—22no—
456C22×C4—28no—
457C22×C4—28no—
458C22×C4—28no—
459C22×C4—416no—
460C22×C4—114no—
461C22×C4—114no—
462C22×C4—114no—
463C22×C4—114no—
464C22×C4—224no—
465C22×C4—224no—
466C22×C4—224no—
467C22×C4—224no—
468C22×C4—224no—
469C22×C4—224no—
470C22×C4—224no—
471C22×C4—224no—
472C22×C4—224no—
473C22×C4—224no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4#433914yes—
477C22×C4#434114yes—
478C22×C4#434114yes—
479C22×C4C2×C22⋊D1114yes—
480C22×C4C2×C22⋊D11116yes—
481C22×C4C2×C22⋊D1114yes—
482C22×C4C23×D1112yes—
483C22×C4C23×D1112yes—
484C22×C4C23×D1112yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C4⋊C4—28no—
488C4⋊C4—2216no—
489C4⋊C4—228no—
490C4⋊C4—228no—
491C4⋊C4—228no—
492C4⋊C4—228no—
493C4⋊C4—448no—
494C22⋊C4—28no—
495C22⋊C4—28no—
496C22⋊C4—2216no—
497C22⋊C4—2216no—
498C22⋊C4—448no—
499C22⋊C4—448no—
500C42—28no—
501C42—2216no—
502C11C2×#248511yescharacteristic, complemented, Sylow
503C23—28no—
504C23—28no—
505C23—28no—
506C23—28no—
507C23—28no—
508C23—28no—
509C23—22no—
510C23—22no—
511C23—22no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—22no—
521C23—44no—
522C23—44no—
523C23—44no—
524C23—44no—
525C23—44no—
526C23—44no—
527C23—44no—
528C23—44no—
529C23C2×#433914yes—
530C23C2×#433912yes—
531C23C2×#433912yes—
532C23C2×#434112yes—
533C23C2×#434112yes—
534C23#6704212yes—
535C23#6704312yes—
536C23C22×C22⋊D1114yes—
537C23C22×C22⋊D1112yes—
538C23C24×D1111yescharacteristic
539D4—232no—
540C2×C4—28no—
541C2×C4—28no—
542C2×C4—22no—
543C2×C4—22no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—232no—
547C2×C4—22no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—22no—
552C2×C4—22no—
553C2×C4—44no—
554C2×C4—44no—
555C2×C4—416no—
556C2×C4—224no—
557C2×C4—224no—
558C2×C4—224no—
559C2×C4—224no—
560C2×C4—224no—
561C2×C4—224no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—224no—
567C2×C4—224no—
568C2×C4—448no—
569C2×C4—448no—
570C2×C4—448no—
571C2×C4—448no—
572C2×C4#66988116yes—
573C2×C4C2×#433914yes—
574C2×C4C2×#434114yes—
575C2×C4C2×#434114yes—
576C2×C4C22×C22⋊D1114yes—
577C2×C4C22×C22⋊D1114yes—
578C22—24no—
579C22—24no—
580C22—24no—
581C22—24no—
582C22—24no—
583C22—24no—
584C22—42no—
585C22—416no—
586C22—416no—
587C22—42no—
588C22—42no—
589C22—42no—
590C22—42no—
591C22—42no—
592C22—42no—
593C22—42no—
594C22#1062307214yes—
595C22#1062307314yes—
596C22#1062309414yes—
597C22#1062309614yes—
598C22#1062332214yes—
599C22C2×#6698814yes—
600C22#1062336414yes—
601C22C22×#433911yescharacteristic
602C22C22×#433911yescharacteristic
603C22C22×#434111yescharacteristic
604C22C22×#434111yescharacteristic
605C22C2×#6704211yescharacteristic
606C22C2×#6704311yescharacteristic
607C22C23×C22⋊D1111yescharacteristic
608C4—24no—
609C4—24no—
610C4—42no—
611C4—42no—
612C4—444no—
613C4—444no—
614C4—444no—
615C4—444no—
616C4C2×#6698818yes—
617C2—44no—
618C2—44no—
619C2#1307291318yesdirect product factor
620C2C22×#6698811yescharacteristic
621C2C2×#1062332211yescharacteristic
622C2C2×#1062336411yescharacteristic
623C2C2×#1062307211yescharacteristic
624C2C2×#1062309611yescharacteristic
625C2C2×#1062309411yescharacteristic
626C2C2×#1062307311yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11C2×#2485
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66979C2semidirect
2. #13072913C2direct (N × H)
3. C2×#10622565C2semidirect
5. C2×#10622541C2semidirect
6. C2×#10622541C2semidirect
7. C2×#10622557C2semidirect
8. C2×#10622591C2semidirect
9. C2×#10622825C2semidirect
10. C2×#10622825C2semidirect
11. C2×#10622825C2semidirect
27. C2×#66979C22semidirect
36. #10622825C22semidirect
37. #10622825C22semidirect
38. #10622825C22semidirect
44. #10622591C22semidirect
45. #10622565C22semidirect
46. #10622557C22semidirect
47. #10622541C22semidirect
48. #10622541C22semidirect
414. C2×C11#2485semidirect
502. C11C2×#2485semidirect
619. C2#13072913direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669792
#130729132
C2×#106225652
C2×#106228352
C2×#106225412
C2×#106225572
C2×#106225912
C2×#106228252
C22×C4×D4×C112
C2×#248511