Finite Group Databasebeta

← C2×#13072109 #14921906

Subgroups — C2×#13072109 #14921906

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×#66948C211yesmaximal, characteristic
2C22×C4×D44C211yesmaximal, characteristic, complemented
3#13072109C2116yesmaximal, direct product factor
4C2×#10622606C212yesmaximal, complemented
5C2×#10622604C212yesmaximal, complemented
6C2×#10622601C211yesmaximal, characteristic, complemented
7C2×#10622278C212yesmaximal, complemented
8C2×#10622590C211yesmaximal, characteristic, complemented
9C2×#10622277C212yesmaximal, complemented
10C2×#10622600C211yesmaximal, characteristic, complemented
11C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
12C2×C11×#389C211yesmaximal, characteristic, complemented
13C23×D44C2212yes—
14C23×D44C2211yescharacteristic
15C23×C4×D11C2211yescharacteristic
16C23×C4×D11C2212yes—
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C4⋊C4C2212yes—
20C22×C42×C11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C2×#66948—28no—
31C2×#66948C2218yes—
32C2×C4×D44—28no—
33C2×C4×D44C2218yescomplemented
34C11×#389C2218yescomplemented
35C2×C11×#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622606C22116yescomplemented
42#10622604C22116yescomplemented
43#10622601C2218yescomplemented
44#10622600C2218yescomplemented
45#10622590C2218yescomplemented
46C4×(C2×D11)⋊C4C2218yescomplemented
47#10622278C22116yescomplemented
48#10622277C22116yescomplemented
49C24×D11C2312yes—
50C24×D11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2311yescharacteristic
56C23×Dic11C2311yescharacteristic
57C23×Dic11C2311yescharacteristic
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C22×D44—24no—
61C22×D44—24no—
62C22×D44—28no—
63C22×D44—28no—
64C22×D44—44no—
65C22×D44D418yes—
66C22×D44C2318yes—
67C22×D44C2314yes—
68C22×C4×D11—28no—
69C22×C4×D11—24no—
70C22×C4×D11—24no—
71C22×C4×D11—28no—
72C22×C4×D11—24no—
73C22×C4×D11—44no—
74C22×C4×D11C2314yes—
75C22×C4×D11C2318yes—
76C2×C11×C4⋊C4—24no—
77C2×C11×C4⋊C4—24no—
78C2×C11×C4⋊C4—44no—
79C2×C11×C4⋊C4C2314yes—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C42×C11—24no—
83C2×C42×C11C2314yes—
84C2×(C2×D11)⋊C4—28no—
85C2×(C2×D11)⋊C4—28no—
86C2×(C2×D11)⋊C4—24no—
87C2×(C2×D11)⋊C4—24no—
88C2×(C2×D11)⋊C4—44no—
89C2×(C2×D11)⋊C4—44no—
90C2×(C2×D11)⋊C4—44no—
91C2×(C2×D11)⋊C4C2318yes—
92C2×(C2×D11)⋊C4C2318yes—
93C2×(C2×D11)⋊C4C2314yes—
94C2×(C2×D11)⋊C4C2314yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×(C2×D11)⋊C4C2318yes—
97C2×(C2×D11)⋊C4C2318yes—
98C2×C4⋊Dic11—24no—
99C2×C4⋊Dic11C2314yes—
100C2×C4×Dic11—24no—
101C2×C4×Dic11C2314yes—
102#66948—232no—
103C4×D44—232no—
104C11×#95C2318yes—
105C11⋊#95C2314yes—
106C11⋊#95C2318yes—
107C11⋊#95C2318yes—
108C11⋊#95C2318yes—
109C11⋊#95C2314yes—
110C2×#2420—111nomaximal, Sylow
111C24×C11C2411yescharacteristic
112C23×D11—22no—
113C23×D11—22no—
114C23×D11—22no—
115C23×D11—24no—
116C23×D11—22no—
117C23×D11—24no—
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—24no—
122C23×D11—24no—
123C23×D11—22no—
124C23×D11C2×D418yes—
125C23×D11#4114yes—
126C23×D11C2414yes—
127C23×D11C2412yes—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—24no—
132C22×C4×C11—22no—
133C22×C4×C11—24no—
134C22×C4×C11—24no—
135C22×C4×C11—24no—
136C22×C4×C11—24no—
137C22×C4×C11—22no—
138C22×C4×C11—24no—
139C22×C4×C11C2×D414yes—
140C22×C4×C11#4114yes—
141C22×C4×C11#4114yes—
142C22×C4×C11#4114yes—
143C22×C4×C11C2414yes—
144C22×C4×C11C2414yes—
145C22×C4×C11C2412yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2412yes—
148C22×Dic11—24no—
149C22×Dic11—22no—
150C22×Dic11—22no—
151C22×Dic11—22no—
152C22×Dic11—22no—
153C22×Dic11—22no—
154C22×Dic11—22no—
155C22×Dic11—22no—
156C22×Dic11—24no—
157C22×Dic11—22no—
158C22×Dic11—22no—
159C22×Dic11—24no—
160C22×Dic11C2412yes—
161C22×Dic11C2412yes—
162C22×Dic11C2412yes—
163C22×Dic11C2414yes—
164C2×D44—216no—
165C2×D44—216no—
166C2×D44—232no—
167C2×D44—28no—
168C2×D44—28no—
169C2×D44—48no—
170C2×D44—432no—
171C2×D44C2×D4116yes—
172C2×C4×D11—216no—
173C2×C4×D11—28no—
174C2×C4×D11—28no—
175C2×C4×D11—216no—
176C2×C4×D11—28no—
177C2×C4×D11—48no—
178C2×C4×D11—432no—
179C2×C4×D11—416no—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—28no—
182C11×C4⋊C4—48no—
183C42×C11—28no—
184(C2×D11)⋊C4—216no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—28no—
188(C2×D11)⋊C4—48no—
189(C2×D11)⋊C4—48no—
190(C2×D11)⋊C4—48no—
191C4⋊Dic11—28no—
192C4×Dic11—28no—
193C22×#121—111no—
194C22×C4×D4—111no—
195#2420—1116no—
196C2×#397—112no—
197C2×#394—112no—
198C2×#390—111no—
199C2×#389D1111yescharacteristic, complemented
200C2×#386—112no—
201C2×#382—111no—
202C2×#381—112no—
203C2×#380—111no—
204C2×C4×C22⋊C4—111no—
205C23×C11C22×D412yes—
206C23×C11C2×#4112yes—
207C23×C11C2×#4112yes—
208C23×C11C2×#4112yes—
209C23×C11C2×#4112yes—
210C23×C11H(5,𝔽2)12yes—
211C23×C11H(5,𝔽2)12yes—
212C23×C11C2511yescharacteristic
213C22×D11—216no—
214C22×D11—28no—
215C22×D11—216no—
216C22×D11—28no—
217C22×D11—216no—
218C22×D11—28no—
219C22×D11—22no—
220C22×D11—22no—
221C22×D11—22no—
222C22×D11—24no—
223C22×D11—22no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—24no—
227C22×D11—22no—
228C22×D11—24no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—44no—
232C22×D11—48no—
233C22×D11—44no—
234C22×D11—48no—
235C22×D11—44no—
236C22×D11—48no—
237C22×D11—44no—
238C22×D11—48no—
239C22×D11C22×D418yes—
240C22×D11C2×#4114yes—
241C2×C4×C11—28no—
242C2×C4×C11—22no—
243C2×C4×C11—22no—
244C2×C4×C11—22no—
245C2×C4×C11—24no—
246C2×C4×C11—22no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—24no—
251C2×C4×C11—22no—
252C2×C4×C11—24no—
253C2×C4×C11—48no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11#123116yes—
257C2×C4×C11C22×D414yes—
258C2×C4×C11C2×#4114yes—
259C2×C4×C11C2×#4114yes—
260C2×C4×C11C2×#4114yes—
261C2×Dic11—24no—
262C2×Dic11—22no—
263C2×Dic11—22no—
264C2×Dic11—22no—
265C2×Dic11—22no—
266C2×Dic11—22no—
267C2×Dic11—22no—
268C2×Dic11—22no—
269C2×Dic11—24no—
270C2×Dic11—22no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—44no—
274C2×Dic11—48no—
275C2×Dic11—44no—
276C2×Dic11—44no—
277D44—232no—
278D44—432no—
279C4×D11—432no—
280C4×D11—416no—
281C23×D4—111no—
282C23×D4—112no—
283C24×C4—111no—
284C24×C4—112no—
285C2×#121—118no—
286C2×#121—228no—
287C2×C4×D4—118no—
288C2×C4×D4—228no—
289C22×C4⋊C4—111no—
290C22×C4⋊C4C2×D1111yescharacteristic
291C22×C4⋊C4C2×D1111yescharacteristic
292C22×C4⋊C4C2×D1112yes—
293C22×C22⋊C4—111no—
294C22×C22⋊C4—112no—
295C22×C22⋊C4—112no—
296C22×C22⋊C4—111no—
297C22×C22⋊C4—112no—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C42—111no—
301C22×C42C2×D1111yescharacteristic
302#397—1116no—
303#394—1116no—
304#390—118no—
305#389C2×D1118yescomplemented
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×#95C2×D1112yes—
317C22×C11C2×#12314yes—
318C22×C11#52914yes—
319C22×C11#54014yes—
320C22×C11#54614yes—
321C22×C11#54614yes—
322C22×C11#55314yes—
323C22×C11#55514yes—
324C22×C11C23×D411yescharacteristic
325C22×C11C22×#4111yescharacteristic
326C22×C11C22×#4111yescharacteristic
327C22×C11C22×#4111yescharacteristic
328C22×C11C22×#4111yescharacteristic
329C22×C11C2×H(5,𝔽2)11yescharacteristic
330C22×C11C2×H(5,𝔽2)11yescharacteristic
331C2×D11—28no—
332C2×D11—24no—
333C2×D11—28no—
334C2×D11—28no—
335C2×D11—24no—
336C2×D11—24no—
337C2×D11—42no—
338C2×D11—44no—
339C2×D11—432no—
340C2×D11—416no—
341C2×D11—42no—
342C2×D11—44no—
343C2×D11—42no—
344C2×D11—44no—
345C2×D11—42no—
346C2×D11—44no—
347C4×C11—24no—
348C4×C11—44no—
349C4×C11—42no—
350C4×C11—44no—
351C4×C11C2×#12318yes—
352Dic11—42no—
353Dic11—44no—
354Dic11—42no—
355Dic11—42no—
356C25—112no—
357C25—111no—
358C22×D4—118no—
359C22×D4—114no—
360C22×D4—118no—
361C22×D4—228no—
362C22×D4—228no—
363C22×D4—224no—
364C22×D4—224no—
365C22×D4—444no—
366C23×C4—111no—
367C23×C4—111no—
368C23×C4—112no—
369C23×C4—111no—
370C23×C4—114no—
371C23×C4—118no—
372C23×C4—228no—
373C23×C4—224no—
374C23×C4—224no—
375C23×C4—228no—
376C23×C4—224no—
377C23×C4—444no—
378C23×C4C22×D1112yes—
379C23×C4C22×D1111yescharacteristic
380C23×C4C22×D1112yes—
381C23×C4C22×D1111yescharacteristic
382C23×C4C22×D1111yescharacteristic
383#121—2232no—
384C4×D4—2232no—
385C2×C4⋊C4—24no—
386C2×C4⋊C4—24no—
387C2×C4⋊C4—44no—
388C2×C4⋊C4—114no—
389C2×C4⋊C4—224no—
390C2×C4⋊C4C22×D1114yes—
391C2×C4⋊C4C22×D1114yes—
392C2×C4⋊C4C22×D1118yes—
393C2×C22⋊C4—118no—
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—228no—
401C2×C22⋊C4—228no—
402C2×C22⋊C4—224no—
403C2×C22⋊C4—224no—
404C2×C22⋊C4—444no—
405C2×C22⋊C4—444no—
406C2×C22⋊C4—444no—
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#95C22×D1118yes—
417C2×C11#242018yescomplemented
418C2×C11C22×#12311yescharacteristic
419C2×C11C2×#52911yescharacteristic
420C2×C11C2×#54011yescharacteristic
421C2×C11C2×#54611yescharacteristic
422C2×C11C2×#54611yescharacteristic
423C2×C11C2×#55311yescharacteristic
424C2×C11C2×#55511yescharacteristic
425D11—48no—
426D11—44no—
427C24—118no—
428C24—114no—
429C24—114no—
430C24—112no—
431C24—222no—
432C24—224no—
433C24—222no—
434C24—224no—
435C24—222no—
436C24—222no—
437C24—224no—
438C24—222no—
439C24—224no—
440C24—224no—
441C24—222no—
442C24—224no—
443C24C23×D1111yescharacteristic
444C2×D4—1116no—
445C2×D4—2216no—
446C2×D4—2216no—
447C2×D4—2232no—
448C2×D4—228no—
449C2×D4—228no—
450C2×D4—448no—
451C2×D4—4432no—
452C22×C4—22no—
453C22×C4—22no—
454C22×C4—24no—
455C22×C4—22no—
456C22×C4—24no—
457C22×C4—24no—
458C22×C4—22no—
459C22×C4—24no—
460C22×C4—22no—
461C22×C4—24no—
462C22×C4—24no—
463C22×C4—112no—
464C22×C4—112no—
465C22×C4—112no—
466C22×C4—114no—
467C22×C4—2216no—
468C22×C4—222no—
469C22×C4—222no—
470C22×C4—224no—
471C22×C4—222no—
472C22×C4—222no—
473C22×C4—222no—
474C22×C4—222no—
475C22×C4—222no—
476C22×C4—224no—
477C22×C4—222no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—228no—
481C22×C4—228no—
482C22×C4—2216no—
483C22×C4—228no—
484C22×C4—448no—
485C22×C4—4432no—
486C22×C4—4416no—
487C22×C4#433914yes—
488C22×C4D4×D1114yes—
489C22×C4#434314yes—
490C22×C4#434314yes—
491C22×C4C23×D1114yes—
492C22×C4C23×D1114yes—
493C22×C4C23×D1112yes—
494C22×C4C23×D1112yes—
495C22×C4C23×D1112yes—
496C4⋊C4—28no—
497C4⋊C4—28no—
498C4⋊C4—48no—
499C4⋊C4—228no—
500C22⋊C4—2216no—
501C22⋊C4—2216no—
502C22⋊C4—228no—
503C22⋊C4—228no—
504C22⋊C4—448no—
505C22⋊C4—448no—
506C22⋊C4—448no—
507C42—28no—
508C42—228no—
509C11C2×#242011yescharacteristic, complemented, Sylow
510C23—118no—
511C23—114no—
512C23—2216no—
513C23—228no—
514C23—228no—
515C23—2216no—
516C23—2216no—
517C23—222no—
518C23—224no—
519C23—222no—
520C23—224no—
521C23—222no—
522C23—222no—
523C23—222no—
524C23—224no—
525C23—224no—
526C23—224no—
527C23—222no—
528C23—224no—
529C23—228no—
530C23—448no—
531C23—444no—
532C23—444no—
533C23—444no—
534C23—448no—
535C23—448no—
536C23—444no—
537C23—448no—
538C23C2×#433912yes—
539C23C2×D4×D1112yes—
540C23#6703712yes—
541C23C2×#434312yes—
542C23C2×#434312yes—
543C23#41×D1112yes—
544C23#6704212yes—
545C23C24×D1111yescharacteristic
546D4—2232no—
547D4—4432no—
548C2×C4—28no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—22no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—22no—
556C2×C4—24no—
557C2×C4—22no—
558C2×C4—24no—
559C2×C4—24no—
560C2×C4—48no—
561C2×C4—44no—
562C2×C4—48no—
563C2×C4—222no—
564C2×C4—222no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—222no—
568C2×C4—222no—
569C2×C4—222no—
570C2×C4—224no—
571C2×C4—222no—
572C2×C4—222no—
573C2×C4—222no—
574C2×C4—224no—
575C2×C4—4432no—
576C2×C4—444no—
577C2×C4—444no—
578C2×C4—448no—
579C2×C4—444no—
580C2×C4—4416no—
581C2×C4#66947116yes—
582C2×C4C2×#433914yes—
583C2×C4C2×D4×D1114yes—
584C2×C4C2×#434314yes—
585C2×C4C2×#434314yes—
586C22—224no—
587C22—224no—
588C22—228no—
589C22—224no—
590C22—228no—
591C22—228no—
592C22—444no—
593C22—444no—
594C22—444no—
595C22—442no—
596C22—442no—
597C22—444no—
598C22—442no—
599C22—4432no—
600C22—4416no—
601C22—442no—
602C22C2×#6694714yes—
603C22#1062309314yes—
604C22#1062311114yes—
605C22#1062314314yes—
606C22#1062316114yes—
607C22#1062322614yes—
608C22#1062326514yes—
609C22C22×#433911yescharacteristic
610C22C22×D4×D1111yescharacteristic
611C22C2×#6703711yescharacteristic
612C22C22×#434311yescharacteristic
613C22C22×#434311yescharacteristic
614C22C2×#41×D1111yescharacteristic
615C22C2×#6704211yescharacteristic
616C4—24no—
617C4—44no—
618C4—44no—
619C4—42no—
620C4—442no—
621C4—442no—
622C4—444no—
623C4—442no—
624C4C2×#6694718yes—
625C2—444no—
626C2—448no—
627C2#1307210918yesdirect product factor
628C2C22×#6694711yescharacteristic
629C2C2×#1062311111yescharacteristic
630C2C2×#1062309311yescharacteristic
631C2C2×#1062316111yescharacteristic
632C2C2×#1062314311yescharacteristic
633C2C2×#1062322611yescharacteristic
634C2C2×#1062326511yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#389C2
socleC24×C11C24
prime radicalC22×#66948C2
hypercenterC2×#389D11
hypocenterC11C2×#2420
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#389

Complements

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

NH ≅ G/Ntype
2. C22×C4×D44C2semidirect
3. #13072109C2direct (N × H)
4. C2×#10622606C2semidirect
5. C2×#10622604C2semidirect
6. C2×#10622601C2semidirect
7. C2×#10622278C2semidirect
8. C2×#10622590C2semidirect
9. C2×#10622277C2semidirect
10. C2×#10622600C2semidirect
11. C2×C4×(C2×D11)⋊C4C2semidirect
12. C2×C11×#389C2semidirect
33. C2×C4×D44C22semidirect
34. C11×#389C22semidirect
41. #10622606C22semidirect
42. #10622604C22semidirect
43. #10622601C22semidirect
44. #10622600C22semidirect
45. #10622590C22semidirect
46. C4×(C2×D11)⋊C4C22semidirect
47. #10622278C22semidirect
48. #10622277C22semidirect
199. C2×#389D11semidirect
305. #389C2×D11semidirect
417. C2×C11#2420semidirect
509. C11C2×#2420semidirect
627. C2#13072109direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669482
C22×C4×D442
#130721092
C2×#106226062
C2×#106226042
C2×#106226012
C2×#106222782
C2×#106225902
C2×#106222772
C2×#106226002
C2×C4×(C2×D11)⋊C42
C2×C11×#3892
C2×#242011