Finite Group Databasebeta

← C2×#13072102 #14921900

Subgroups — C2×#13072102 #14921900

Order 2816.

3438 conjugacy classes of subgroups.

The subgroup lattice has 636 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2#13072102C2116yesmaximal, direct product factor
3C2×#10622565C212yesmaximal, complemented
4C2×#10622572C212yesmaximal, complemented
5C2×#10622834C211yesmaximal, characteristic, complemented
6C2×#10622541C211yesmaximal, characteristic, complemented
7C2×#10622826C212yesmaximal, complemented
8C2×#10622590C211yesmaximal, characteristic, complemented
9C2×#10622824C212yesmaximal, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C2×C4×D4×C11—28no—
18C2×C4×D4×C11C2218yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—28no—
26C2×#66991C2218yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×Dic11⋊C4C2212yes—
33C22×C4×Dic11C2211yescharacteristic
34#10622834C2218yescomplemented
35#10622826C22116yescomplemented
36#10622824C22116yescomplemented
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622600C2218yescomplemented
44#10622590C2218yescomplemented
45#10622572C22116yescomplemented
46#10622565C22116yescomplemented
47C4×(C2×D11)⋊C4C2218yescomplemented
48#10622541C2218yescomplemented
49C25×C11C2312yes—
50C24×D11C2311yescharacteristic
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11D418yes—
54C22×D4×C11C2314yes—
55C23×C4×C11—28no—
56C23×C4×C11—28no—
57C23×C4×C11—44no—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2312yes—
60C23×C4×C11C2318yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C22×C22⋊D11—28no—
64C22×C22⋊D11—28no—
65C22×C22⋊D11—44no—
66C22×C22⋊D11C2318yes—
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2312yes—
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11C2314yes—
76C4×D4×C11—232no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4C2314yes—
79C2×C11×C22⋊C4—28no—
80C2×C11×C22⋊C4C2318yes—
81C2×C42×C11—24no—
82C2×C42×C11C2314yes—
83C2×C22⋊Dic11—28no—
84C2×C22⋊Dic11—44no—
85C2×C22⋊Dic11—44no—
86C2×C22⋊Dic11C2318yes—
87C2×C22⋊Dic11C2318yes—
88C2×C22⋊Dic11C2318yes—
89#66991—232no—
90C2×(C2×D11)⋊C4—24no—
91C2×(C2×D11)⋊C4—24no—
92C2×(C2×D11)⋊C4—44no—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—24no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2314yes—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—44no—
101C2×Dic11⋊C4C2318yes—
102C2×C4×Dic11—24no—
103C2×C4×Dic11C2314yes—
104C11⋊#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2314yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2318yes—
110C2×#2420—111nomaximal, Sylow
111C24×C11—24no—
112C24×C11—24no—
113C24×C11—24no—
114C24×C11—24no—
115C24×C11—24no—
116C24×C11—24no—
117C24×C11C2×D418yes—
118C24×C11C2414yes—
119C24×C11C2411yescharacteristic
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—22no—
123C23×D11—22no—
124C23×D11—22no—
125C23×D11—22no—
126C23×D11#4114yes—
127C23×D11C2412yes—
128C2×D4×C11—232no—
129C2×D4×C11—28no—
130C2×D4×C11—28no—
131C2×D4×C11C2×D4116yes—
132C22×C4×C11—22no—
133C22×C4×C11—22no—
134C22×C4×C11—22no—
135C22×C4×C11—24no—
136C22×C4×C11—216no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11—22no—
140C22×C4×C11—24no—
141C22×C4×C11—216no—
142C22×C4×C11—48no—
143C22×C4×C11—432no—
144C22×C4×C11C2×D414yes—
145C22×C4×C11#4114yes—
146C22×C4×C11#4114yes—
147C22×C4×C11#4114yes—
148C22×C4×C11C2414yes—
149C22×C4×C11C2412yes—
150C22×C4×C11C2412yes—
151C22×C4×C11C2412yes—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—216no—
154C2×C22⋊D11—48no—
155C2×C22⋊D11—432no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—22no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—22no—
165C22×Dic11—24no—
166C22×Dic11—24no—
167C22×Dic11—24no—
168C22×Dic11—24no—
169C22×Dic11—22no—
170C22×Dic11—22no—
171C22×Dic11C2412yes—
172C22×Dic11C2412yes—
173C22×Dic11C2412yes—
174C22×Dic11C2414yes—
175C22×Dic11C2414yes—
176C2×C4×D11—28no—
177C2×C4×D11—28no—
178C2×C4×D11—28no—
179C2×C4×D11—416no—
180C11×C4⋊C4—28no—
181C11×C22⋊C4—216no—
182C42×C11—28no—
183C22⋊Dic11—216no—
184C22⋊Dic11—48no—
185C22⋊Dic11—48no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—48no—
189C4⋊Dic11—28no—
190C4⋊Dic11—28no—
191Dic11⋊C4—48no—
192C4×Dic11—28no—
193C22×#121—111no—
194C22×C4×D4D1111yescharacteristic, complemented
195#2420—1116no—
196C2×#397—112no—
197C2×#394—112no—
198C2×#390—111no—
199C2×#389—111no—
200C2×#386—112no—
201C2×#382—111no—
202C2×#381—112no—
203C2×#380—111no—
204C2×C4×C22⋊C4—111no—
205C23×C11—216no—
206C23×C11—216no—
207C23×C11—216no—
208C23×C11—24no—
209C23×C11—24no—
210C23×C11—24no—
211C23×C11—24no—
212C23×C11—24no—
213C23×C11—24no—
214C23×C11—48no—
215C23×C11—48no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11C22×D418yes—
219C23×C11C22×D412yes—
220C23×C11C2×#4112yes—
221C23×C11C2×#4112yes—
222C23×C11C2×#4112yes—
223C23×C11C2×#4112yes—
224C23×C11H(5,𝔽2)12yes—
225C23×C11H(5,𝔽2)12yes—
226C23×C11C2511yescharacteristic
227C22×D11—28no—
228C22×D11—28no—
229C22×D11—28no—
230C22×D11—22no—
231C22×D11—22no—
232C22×D11—22no—
233C22×D11—22no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—44no—
240C22×D11C2×#4114yes—
241D4×C11—232no—
242C2×C4×C11—28no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—22no—
246C2×C4×C11—24no—
247C2×C4×C11—22no—
248C2×C4×C11—24no—
249C2×C4×C11—22no—
250C2×C4×C11—24no—
251C2×C4×C11—432no—
252C2×C4×C11—44no—
253C2×C4×C11—48no—
254C2×C4×C11#123116yes—
255C2×C4×C11C22×D414yes—
256C2×C4×C11C2×#4114yes—
257C2×C4×C11C2×#4114yes—
258C2×C4×C11C2×#4114yes—
259C22⋊D11—432no—
260C2×Dic11—24no—
261C2×Dic11—22no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—24no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—24no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—22no—
275C2×Dic11—44no—
276C2×Dic11—48no—
277C2×Dic11—48no—
278C2×Dic11—44no—
279C2×Dic11—44no—
280C4×D11—416no—
281C23×D4—112no—
282C23×D4C2×D1111yescharacteristic
283C24×C4—111no—
284C24×C4C2×D1112yes—
285C2×#121—118no—
286C2×#121—228no—
287C2×C4×D4—28no—
288C2×C4×D4C2×D1118yescomplemented
289C22×C4⋊C4—111no—
290C22×C4⋊C4—111no—
291C22×C4⋊C4—112no—
292C22×C4⋊C4C2×D1111yescharacteristic
293C22×C22⋊C4—112no—
294C22×C22⋊C4—111no—
295C22×C22⋊C4—111no—
296C22×C22⋊C4—112no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4C2×D1112yes—
300C22×C42—111no—
301C22×C42C2×D1111yescharacteristic
302#397—1116no—
303#394—1116no—
304#390—118no—
305#389—118no—
306#386—1116no—
307#382—118no—
308#381—1116no—
309#380—118no—
310C4×C22⋊C4—118no—
311C2×#95—112no—
312C2×#95—111no—
313C2×#95—112no—
314C2×#95—112no—
315C2×#95—111no—
316C2×#95—112no—
317C22×C11—28no—
318C22×C11—28no—
319C22×C11—28no—
320C22×C11—44no—
321C22×C11—432no—
322C22×C11—44no—
323C22×C11—44no—
324C22×C11—44no—
325C22×C11C2×#12314yes—
326C22×C11#52914yes—
327C22×C11#54014yes—
328C22×C11#54614yes—
329C22×C11#54614yes—
330C22×C11#55314yes—
331C22×C11#55514yes—
332C22×C11C23×D411yescharacteristic
333C22×C11C22×#4111yescharacteristic
334C22×C11C22×#4111yescharacteristic
335C22×C11C22×#4111yescharacteristic
336C22×C11C22×#4111yescharacteristic
337C22×C11C2×H(5,𝔽2)11yescharacteristic
338C22×C11C2×H(5,𝔽2)11yescharacteristic
339C2×D11—24no—
340C2×D11—24no—
341C2×D11—24no—
342C2×D11—42no—
343C2×D11—416no—
344C2×D11—42no—
345C2×D11—42no—
346C2×D11—42no—
347C4×C11—24no—
348C4×C11—42no—
349C4×C11—44no—
350C4×C11C2×#12318yes—
351Dic11—42no—
352Dic11—44no—
353Dic11—44no—
354Dic11—42no—
355Dic11—42no—
356C25—111no—
357C25C22×D1112yes—
358C22×D4—24no—
359C22×D4—24no—
360C22×D4—118no—
361C22×D4—228no—
362C22×D4—228no—
363C22×D4—444no—
364C22×D4C22⋊D1118yes—
365C22×D4C22×D1114yes—
366C23×C4—28no—
367C23×C4—28no—
368C23×C4—44no—
369C23×C4—112no—
370C23×C4—111no—
371C23×C4—111no—
372C23×C4—111no—
373C23×C4—112no—
374C23×C4—114no—
375C23×C4—224no—
376C23×C4—224no—
377C23×C4—224no—
378C23×C4C22×D1111yescharacteristic
379C23×C4C22×D1112yes—
380C23×C4C22×D1118yes—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383#121—2232no—
384C4×D4—232no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—114no—
387C2×C4⋊C4—114no—
388C2×C4⋊C4—118no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4—224no—
391C2×C4⋊C4—444no—
392C2×C4⋊C4C22×D1114yes—
393C2×C22⋊C4—28no—
394C2×C22⋊C4—118no—
395C2×C22⋊C4—114no—
396C2×C22⋊C4—114no—
397C2×C22⋊C4—118no—
398C2×C22⋊C4—118no—
399C2×C22⋊C4—118no—
400C2×C22⋊C4—224no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—444no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4C22×D1118yes—
407C2×C42—24no—
408C2×C42—114no—
409C2×C42—224no—
410C2×C42C22×D1114yes—
411#95—114no—
412#95—114no—
413#95—118no—
414#95—118no—
415#95—118no—
416#95—118no—
417C2×C11—48no—
418C2×C11#242018yescomplemented
419C2×C11C22×#12311yescharacteristic
420C2×C11C2×#52911yescharacteristic
421C2×C11C2×#54011yescharacteristic
422C2×C11C2×#54611yescharacteristic
423C2×C11C2×#54611yescharacteristic
424C2×C11C2×#55311yescharacteristic
425C2×C11C2×#55511yescharacteristic
426D11—44no—
427C24—24no—
428C24—24no—
429C24—24no—
430C24—24no—
431C24—24no—
432C24—24no—
433C24—114no—
434C24—112no—
435C24—222no—
436C24—222no—
437C24—222no—
438C24—222no—
439C24—222no—
440C24—222no—
441C24C2×C22⋊D1118yes—
442C24C23×D1114yes—
443C24C23×D1111yescharacteristic
444C2×D4—232no—
445C2×D4—28no—
446C2×D4—28no—
447C2×D4—2216no—
448C2×D4—2216no—
449C2×D4—448no—
450C2×D4—4432no—
451C2×D4C2×C22⋊D11116yes—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—22no—
457C22×C4—22no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—216no—
461C22×C4—216no—
462C22×C4—48no—
463C22×C4—432no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—112no—
467C22×C4—114no—
468C22×C4—114no—
469C22×C4—222no—
470C22×C4—222no—
471C22×C4—224no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—224no—
479C22×C4—222no—
480C22×C4—224no—
481C22×C4—224no—
482C22×C4—222no—
483C22×C4—224no—
484C22×C4—228no—
485C22×C4—228no—
486C22×C4—228no—
487C22×C4—4416no—
488C22×C4#433914yes—
489C22×C4#433914yes—
490C22×C4#434114yes—
491C22×C4C2×C22⋊D1114yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1112yes—
495C22×C4C23×D1112yes—
496C4⋊C4—28no—
497C4⋊C4—228no—
498C4⋊C4—228no—
499C4⋊C4—448no—
500C22⋊C4—216no—
501C22⋊C4—228no—
502C22⋊C4—2216no—
503C22⋊C4—228no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C42—28no—
508C42—228no—
509C11C2×#242011yescharacteristic, complemented, Sylow
510C23—216no—
511C23—216no—
512C23—216no—
513C23—24no—
514C23—24no—
515C23—24no—
516C23—24no—
517C23—24no—
518C23—24no—
519C23—48no—
520C23—48no—
521C23—48no—
522C23—48no—
523C23—114no—
524C23—228no—
525C23—228no—
526C23—228no—
527C23—222no—
528C23—222no—
529C23—222no—
530C23—222no—
531C23—222no—
532C23—222no—
533C23—444no—
534C23—444no—
535C23—444no—
536C23—444no—
537C23C2×#433912yes—
538C23C2×#433912yes—
539C23C2×#434112yes—
540C23#6703712yes—
541C23#41×D1112yes—
542C23#6704212yes—
543C23C22×C22⋊D1118yes—
544C23C22×C22⋊D1112yes—
545C23C24×D1111yescharacteristic
546D4—232no—
547D4—4432no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—22no—
554C2×C4—22no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—432no—
558C2×C4—48no—
559C2×C4—44no—
560C2×C4—222no—
561C2×C4—222no—
562C2×C4—224no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—222no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—222no—
569C2×C4—224no—
570C2×C4—222no—
571C2×C4—224no—
572C2×C4—224no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—444no—
576C2×C4—444no—
577C2×C4—448no—
578C2×C4—444no—
579C2×C4—448no—
580C2×C4—4416no—
581C2×C4#66982116yes—
582C2×C4C2×#433914yes—
583C2×C4C2×#433914yes—
584C2×C4C2×#434114yes—
585C2×C4C22×C22⋊D1114yes—
586C22—28no—
587C22—28no—
588C22—28no—
589C22—44no—
590C22—44no—
591C22—44no—
592C22—44no—
593C22—432no—
594C22—224no—
595C22—224no—
596C22—224no—
597C22—442no—
598C22—442no—
599C22—442no—
600C22—4416no—
601C22—442no—
602C22#1062308814yes—
603C22#1062308914yes—
604C22#1062309314yes—
605C22#1062309414yes—
606C22C2×#6698214yes—
607C22#1062333714yes—
608C22#1062336014yes—
609C22C22×#433911yescharacteristic
610C22C22×#433911yescharacteristic
611C22C22×#434111yescharacteristic
612C22C2×#6703711yescharacteristic
613C22C2×#41×D1111yescharacteristic
614C22C2×#6704211yescharacteristic
615C22C23×C22⋊D1111yescharacteristic
616C4—24no—
617C4—42no—
618C4—44no—
619C4—442no—
620C4—442no—
621C4—444no—
622C4—444no—
623C4—442no—
624C4C2×#6698218yes—
625C2—48no—
626C2—444no—
627C2#1307210218yesdirect product factor
628C2C22×#6698211yescharacteristic
629C2C2×#1062308811yescharacteristic
630C2C2×#1062309311yescharacteristic
631C2C2×#1062336011yescharacteristic
632C2C2×#1062333711yescharacteristic
633C2C2×#1062308911yescharacteristic
634C2C2×#1062309411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC22×#66991C2
hypercenterC22×C4×D4D11
hypocenterC11C2×#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. #13072102C2direct (N × H)
3. C2×#10622565C2semidirect
4. C2×#10622572C2semidirect
5. C2×#10622834C2semidirect
6. C2×#10622541C2semidirect
7. C2×#10622826C2semidirect
8. C2×#10622590C2semidirect
9. C2×#10622824C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C22×C4×D4×C11C2semidirect
18. C2×C4×D4×C11C22semidirect
34. #10622834C22semidirect
35. #10622826C22semidirect
36. #10622824C22semidirect
43. #10622600C22semidirect
44. #10622590C22semidirect
45. #10622572C22semidirect
46. #10622565C22semidirect
47. C4×(C2×D11)⋊C4C22semidirect
48. #10622541C22semidirect
194. C22×C4×D4D11semidirect
288. C2×C4×D4C2×D11semidirect
418. C2×C11#2420semidirect
509. C11C2×#2420semidirect
627. C2#13072102direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669912
#130721022
C2×#106225652
C2×#106225722
C2×#106228342
C2×#106225412
C2×#106228262
C2×#106225902
C2×#106228242
C2×#106226002
C2×C4×(C2×D11)⋊C42
C22×C4×D4×C112
C2×#242011