Finite Group Databasebeta

← C2×#13074362 #14920135

Subgroups — C2×#13074362 #14920135

Order 2816.

3718 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic
3C23×C4⋊Dic11C211yesmaximal, characteristic, complemented
4#13074362C2116yesmaximal, direct product factor
5C2×#10622597C212yesmaximal, complemented
6C2×#10622561C212yesmaximal, complemented
7C2×#10622607C212yesmaximal, complemented
8C2×#10622574C212yesmaximal, complemented
9C2×#10622833C211yesmaximal, characteristic, complemented
10C2×#10622571C211yesmaximal, characteristic, complemented
11C2×#10622555C211yesmaximal, characteristic, complemented
12C22×C11×#123C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C24×Dic11C2211yescharacteristic
18C24×Dic11C2211yescharacteristic
19C2×C11×#123—28no—
20C2×C11×#123C2218yescomplemented
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C2×#66992—28no—
28C2×#66992C2218yes—
29C2×#66982—28no—
30C2×#66982C2218yescomplemented
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2211yescharacteristic
33C22×(C2×D11)⋊C4C2212yes—
34C22×C4⋊Dic11—28no—
35C22×C4⋊Dic11C2212yes—
36C22×C4⋊Dic11C2212yes—
37C22×C4⋊Dic11C2218yescomplemented
38C22×Dic11⋊C4C2212yes—
39C22×Dic11⋊C4C2211yescharacteristic
40C22×Dic11⋊C4C2212yes—
41#10622833C2218yescomplemented
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45#10622607C22116yescomplemented
46#10622597C22116yescomplemented
47#10622574C22116yescomplemented
48#10622571C2218yescomplemented
49#10622561C22116yescomplemented
50#10622555C2218yescomplemented
51C25×C11C2311yescharacteristic
52C25×C11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C22×D4×C11—24no—
55C22×D4×C11—24no—
56C22×D4×C11—24no—
57C22×D4×C11C2314yes—
58C23×C4×C11—24no—
59C23×C4×C11—24no—
60C23×C4×C11D418yescomplemented
61C23×C4×C11C2312yes—
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2312yes—
64C23×C4×C11C2314yes—
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—24no—
68C22×C22⋊D11—24no—
69C22×C22⋊D11—44no—
70C22×C22⋊D11C2314yes—
71C22×C22⋊D11C2314yes—
72C23×Dic11—24no—
73C23×Dic11—44no—
74C23×Dic11—44no—
75C23×Dic11D418yes—
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2312yes—
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2314yes—
82C23×Dic11C2314yes—
83C11×#123—232no—
84C2×C11×C4⋊C4—28no—
85C2×C11×C4⋊C4C2318yes—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4—28no—
88C2×C11×C22⋊C4C2314yes—
89C2×C11×C22⋊C4C2318yes—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—44no—
93C2×C22⋊Dic11C2314yes—
94C2×C22⋊Dic11C2314yes—
95C2×C22⋊Dic11C2318yes—
96#66992—232no—
97#66982—232no—
98C2×(C2×D11)⋊C4—28no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—44no—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2314yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×C4⋊Dic11—28no—
105C2×C4⋊Dic11—28no—
106C2×C4⋊Dic11—232no—
107C2×C4⋊Dic11C2318yes—
108C2×C4⋊Dic11C2318yes—
109C2×Dic11⋊C4—28no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—44no—
112C2×Dic11⋊C4C2318yes—
113C2×Dic11⋊C4C2314yes—
114C2×Dic11⋊C4C2318yes—
115C11⋊#95C2318yes—
116C11⋊#95C2318yes—
117C11⋊#95C2318yes—
118C2×#2618—111nomaximal, Sylow
119C24×C11—24no—
120C24×C11—24no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—24no—
125C24×C11—24no—
126C24×C11C2×D414yes—
127C24×C11C2×D414yes—
128C24×C11#4114yes—
129C24×C11C2412yes—
130C24×C11C2412yes—
131C24×C11C2411yescharacteristic
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11C2412yes—
138C2×D4×C11—28no—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11—416no—
142C22×C4×C11—232no—
143C22×C4×C11—24no—
144C22×C4×C11—28no—
145C22×C4×C11—24no—
146C22×C4×C11—28no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—24no—
152C22×C4×C11—24no—
153C22×C4×C11C2×D418yes—
154C22×C4×C11C2×D4116yescomplemented
155C22×C4×C11C2414yes—
156C22×C4×C11C2412yes—
157C22×C4×C11C2414yes—
158C2×C22⋊D11—28no—
159C2×C22⋊D11—28no—
160C2×C22⋊D11—28no—
161C2×C22⋊D11—28no—
162C2×C22⋊D11—48no—
163C2×C22⋊D11—416no—
164C2×C22⋊D11—416no—
165C22×Dic11—22no—
166C22×Dic11—24no—
167C22×Dic11—22no—
168C22×Dic11—28no—
169C22×Dic11—24no—
170C22×Dic11—22no—
171C22×Dic11—24no—
172C22×Dic11—24no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—416no—
178C22×Dic11—48no—
179C22×Dic11—48no—
180C22×Dic11—416no—
181C22×Dic11C2×D414yes—
182C22×Dic11C2×D414yes—
183C22×Dic11C2×D4116yes—
184C22×Dic11C2412yes—
185C22×Dic11C2414yes—
186C22×Dic11C2414yes—
187C22×Dic11C2412yes—
188C22×Dic11C2412yes—
189C11×C4⋊C4—216no—
190C11×C22⋊C4—28no—
191C11×C22⋊C4—216no—
192C22⋊Dic11—28no—
193C22⋊Dic11—28no—
194C22⋊Dic11—48no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—48no—
198C4⋊Dic11—216no—
199C4⋊Dic11—216no—
200Dic11⋊C4—28no—
201Dic11⋊C4—216no—
202Dic11⋊C4—48no—
203C22×#123—111no—
204C22×#123D1111yescharacteristic, complemented
205C22×#121—111no—
206C23×C4⋊C4—111no—
207#2618—1116no—
208C2×#398—112no—
209C2×#396—112no—
210C2×#396—112no—
211C2×#394—112no—
212C2×#386—111no—
213C2×#386—111no—
214C2×#380—111no—
215C23×C11—28no—
216C23×C11—28no—
217C23×C11—216no—
218C23×C11—216no—
219C23×C11—24no—
220C23×C11—24no—
221C23×C11—22no—
222C23×C11—22no—
223C23×C11—22no—
224C23×C11—24no—
225C23×C11—24no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—44no—
229C23×C11—48no—
230C23×C11—48no—
231C23×C11#121116yes—
232C23×C11C22×D414yes—
233C23×C11C22×D412yes—
234C23×C11C22×D414yes—
235C23×C11C22×D412yes—
236C23×C11C2×#4114yes—
237C23×C11C2×#4112yes—
238C23×C11H(5,𝔽2)14yes—
239C23×C112−1+414yes—
240C23×C11C2511yescharacteristic
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—44no—
247C22×D11—44no—
248C22×D11—44no—
249C22×D11—48no—
250C22×D11—48no—
251D4×C11—416no—
252C2×C4×C11—216no—
253C2×C4×C11—232no—
254C2×C4×C11—24no—
255C2×C4×C11—24no—
256C2×C4×C11—22no—
257C2×C4×C11—24no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—44no—
263C2×C4×C11—48no—
264C2×C4×C11C22×D418yes—
265C22⋊D11—416no—
266C22⋊D11—416no—
267C2×Dic11—28no—
268C2×Dic11—28no—
269C2×Dic11—24no—
270C2×Dic11—24no—
271C2×Dic11—22no—
272C2×Dic11—24no—
273C2×Dic11—22no—
274C2×Dic11—24no—
275C2×Dic11—22no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—416no—
281C2×Dic11—416no—
282C2×Dic11—44no—
283C2×Dic11—48no—
284C2×Dic11—48no—
285C2×Dic11C22×D414yes—
286C2×Dic11C22×D414yes—
287C23×D4—111no—
288C23×D4—111no—
289C23×D4C2×D1111yescharacteristic
290C24×C4—111no—
291C24×C4—111no—
292C24×C4C2×D1111yescharacteristic
293C2×#123—28no—
294C2×#123—118no—
295C2×#123—228no—
296C2×#123C2×D1118yescomplemented
297C2×#121—118no—
298C2×#121—228no—
299C22×C4⋊C4—118no—
300C22×C4⋊C4—112no—
301C22×C4⋊C4—112no—
302C22×C4⋊C4—111no—
303C22×C4⋊C4—112no—
304C22×C4⋊C4—112no—
305C22×C4⋊C4—228no—
306C22×C4⋊C4C2×D1112yes—
307C22×C22⋊C4—111no—
308C22×C22⋊C4—111no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4—111no—
311C22×C22⋊C4—112no—
312C22×C22⋊C4—112no—
313C22×C22⋊C4C2×D1112yes—
314C22×C22⋊C4C2×D1111yescharacteristic
315#398—1116no—
316#396—1116no—
317#396—1116no—
318#394—1116no—
319#386—118no—
320#386—118no—
321#380—118no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C22×C11—232no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—28no—
329C22×C11—28no—
330C22×C11—42no—
331C22×C11—42no—
332C22×C11—42no—
333C22×C11—44no—
334C22×C11—44no—
335C22×C11—88no—
336C22×C11C2×#12118yes—
337C22×C11C2×#12114yes—
338C22×C11#53414yes—
339C22×C11#53614yes—
340C22×C11#53718yes—
341C22×C11#53918yes—
342C22×C11C23×D411yescharacteristic
343C22×C11C23×D411yescharacteristic
344C22×C11C22×#4111yescharacteristic
345C22×C11C2×H(5,𝔽2)12yes—
346C22×C11C2×2−1+412yes—
347C2×D11—42no—
348C2×D11—42no—
349C2×D11—42no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—88no—
353C4×C11—28no—
354C4×C11—42no—
355C4×C11—44no—
356Dic11—24no—
357Dic11—24no—
358Dic11—42no—
359Dic11—44no—
360Dic11—44no—
361C25—111no—
362C25C22×D1111yescharacteristic
363C25C22×D1111yescharacteristic
364C22×D4—24no—
365C22×D4—24no—
366C22×D4—24no—
367C22×D4—114no—
368C22×D4—114no—
369C22×D4—224no—
370C22×D4—224no—
371C22×D4—224no—
372C22×D4—224no—
373C22×D4—444no—
374C22×D4C22×D1114yes—
375C23×C4—24no—
376C23×C4—24no—
377C23×C4—111no—
378C23×C4—111no—
379C23×C4—118no—
380C23×C4—114no—
381C23×C4—112no—
382C23×C4—112no—
383C23×C4—111no—
384C23×C4—114no—
385C23×C4—224no—
386C23×C4—444no—
387C23×C4—444no—
388C23×C4C22⋊D1118yescomplemented
389C23×C4C22×D1112yes—
390C23×C4C22×D1111yescharacteristic
391C23×C4C22×D1112yes—
392C23×C4C22×D1114yes—
393#123—232no—
394#123—2232no—
395#121—2232no—
396C2×C4⋊C4—28no—
397C2×C4⋊C4—118no—
398C2×C4⋊C4—118no—
399C2×C4⋊C4—114no—
400C2×C4⋊C4—118no—
401C2×C4⋊C4—118no—
402C2×C4⋊C4—228no—
403C2×C4⋊C4—228no—
404C2×C4⋊C4—2232no—
405C2×C4⋊C4—224no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—444no—
408C2×C4⋊C4C22×D1118yes—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—28no—
411C2×C22⋊C4—114no—
412C2×C22⋊C4—114no—
413C2×C22⋊C4—114no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—118no—
417C2×C22⋊C4—224no—
418C2×C22⋊C4—224no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—444no—
422C2×C22⋊C4—444no—
423C2×C22⋊C4C22×D1114yes—
424C2×C22⋊C4C22×D1118yes—
425#95—118no—
426#95—118no—
427#95—118no—
428C2×C11—28no—
429C2×C11—82no—
430C2×C11#261818yescomplemented
431C2×C11C22×#12111yescharacteristic
432C2×C11C2×#53411yescharacteristic
433C2×C11C2×#53611yescharacteristic
434C2×C11C2×#53712yes—
435C2×C11C2×#53912yes—
436D11—82no—
437C24—24no—
438C24—24no—
439C24—22no—
440C24—22no—
441C24—24no—
442C24—24no—
443C24—22no—
444C24—112no—
445C24—222no—
446C24—222no—
447C24—224no—
448C24—224no—
449C24—222no—
450C24D4×D1114yes—
451C24#434114yes—
452C24C2×C22⋊D1114yes—
453C24C23×D1112yes—
454C24C23×D1112yes—
455C24C23×D1111yescharacteristic
456C2×D4—28no—
457C2×D4—28no—
458C2×D4—28no—
459C2×D4—416no—
460C2×D4—228no—
461C2×D4—228no—
462C2×D4—228no—
463C2×D4—228no—
464C2×D4—448no—
465C2×D4—4416no—
466C2×D4—4416no—
467C22×C4—232no—
468C22×C4—24no—
469C22×C4—28no—
470C22×C4—24no—
471C22×C4—28no—
472C22×C4—22no—
473C22×C4—22no—
474C22×C4—24no—
475C22×C4—24no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—114no—
479C22×C4—114no—
480C22×C4—112no—
481C22×C4—112no—
482C22×C4—1116no—
483C22×C4—114no—
484C22×C4—114no—
485C22×C4—112no—
486C22×C4—224no—
487C22×C4—224no—
488C22×C4—222no—
489C22×C4—228no—
490C22×C4—224no—
491C22×C4—222no—
492C22×C4—224no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—222no—
498C22×C4—4416no—
499C22×C4—448no—
500C22×C4—448no—
501C22×C4—4416no—
502C22×C4C2×C22⋊D1118yes—
503C22×C4C2×C22⋊D11116yescomplemented
504C22×C4C23×D1114yes—
505C22×C4C23×D1112yes—
506C22×C4C23×D1114yes—
507C4⋊C4—216no—
508C4⋊C4—2216no—
509C4⋊C4—2216no—
510C4⋊C4—228no—
511C4⋊C4—2216no—
512C4⋊C4—448no—
513C22⋊C4—28no—
514C22⋊C4—216no—
515C22⋊C4—228no—
516C22⋊C4—228no—
517C22⋊C4—228no—
518C22⋊C4—2216no—
519C22⋊C4—448no—
520C22⋊C4—448no—
521C11C2×#261811yescharacteristic, complemented, Sylow
522C23—216no—
523C23—28no—
524C23—28no—
525C23—24no—
526C23—216no—
527C23—24no—
528C23—22no—
529C23—22no—
530C23—24no—
531C23—24no—
532C23—22no—
533C23—44no—
534C23—48no—
535C23—44no—
536C23—44no—
537C23—48no—
538C23—222no—
539C23—222no—
540C23—224no—
541C23—224no—
542C23—222no—
543C23—444no—
544C23—448no—
545C23—444no—
546C23—444no—
547C23—448no—
548C23#66992116yes—
549C23C2×D4×D1114yes—
550C23C2×D4×D1112yes—
551C23C2×#434114yes—
552C23C2×#434112yes—
553C23#6704214yes—
554C23#6704314yes—
555C23C22×C22⋊D1114yes—
556C23C22×C22⋊D1112yes—
557C23C24×D1111yescharacteristic
558D4—416no—
559D4—4416no—
560D4—4416no—
561C2×C4—216no—
562C2×C4—232no—
563C2×C4—24no—
564C2×C4—24no—
565C2×C4—22no—
566C2×C4—22no—
567C2×C4—24no—
568C2×C4—24no—
569C2×C4—24no—
570C2×C4—22no—
571C2×C4—44no—
572C2×C4—48no—
573C2×C4—114no—
574C2×C4—114no—
575C2×C4—228no—
576C2×C4—228no—
577C2×C4—224no—
578C2×C4—224no—
579C2×C4—222no—
580C2×C4—224no—
581C2×C4—222no—
582C2×C4—224no—
583C2×C4—224no—
584C2×C4—224no—
585C2×C4—224no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—4416no—
589C2×C4—4416no—
590C2×C4—444no—
591C2×C4—448no—
592C2×C4—448no—
593C2×C4C22×C22⋊D1118yes—
594C22—24no—
595C22—24no—
596C22—28no—
597C22—28no—
598C22—232no—
599C22—42no—
600C22—42no—
601C22—44no—
602C22—44no—
603C22—42no—
604C22—88no—
605C22—442no—
606C22—442no—
607C22—444no—
608C22—444no—
609C22—442no—
610C22—888no—
611C22#1062317914yes—
612C22#1062318414yes—
613C22#1062319618yes—
614C22C2×#6699218yes—
615C22C2×#6699214yes—
616C22#1062336418yes—
617C22C22×D4×D1111yescharacteristic
618C22C22×#434111yescharacteristic
619C22C2×#6704212yes—
620C22C2×#6704312yes—
621C22C23×C22⋊D1111yescharacteristic
622C4—28no—
623C4—44no—
624C4—42no—
625C4—224no—
626C4—224no—
627C4—444no—
628C4—444no—
629C4—442no—
630C2—28no—
631C2—82no—
632C2—882no—
633C2#1307436218yesdirect product factor
634C2C22×#6699211yescharacteristic
635C2C2×#1062318411yescharacteristic
636C2C2×#1062317911yescharacteristic
637C2C2×#1062336412yes—
638C2C2×#1062319612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
prime radicalC22×#66992C2
hypercenterC22×#123D11
hypocenterC11C2×#2618
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#123

Complements

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

NH ≅ G/Ntype
1. C22×#66982C2semidirect
3. C23×C4⋊Dic11C2semidirect
4. #13074362C2direct (N × H)
5. C2×#10622597C2semidirect
6. C2×#10622561C2semidirect
7. C2×#10622607C2semidirect
8. C2×#10622574C2semidirect
9. C2×#10622833C2semidirect
10. C2×#10622571C2semidirect
11. C2×#10622555C2semidirect
12. C22×C11×#123C2semidirect
20. C2×C11×#123C22semidirect
30. C2×#66982C22semidirect
37. C22×C4⋊Dic11C22semidirect
41. #10622833C22semidirect
45. #10622607C22semidirect
46. #10622597C22semidirect
47. #10622574C22semidirect
48. #10622571C22semidirect
49. #10622561C22semidirect
50. #10622555C22semidirect
60. C23×C4×C11D4semidirect
154. C22×C4×C11C2×D4semidirect
204. C22×#123D11semidirect
296. C2×#123C2×D11semidirect
388. C23×C4C22⋊D11semidirect
430. C2×C11#2618semidirect
503. C22×C4C2×C22⋊D11semidirect
521. C11C2×#2618semidirect
633. C2#13074362direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669822
C22×#669922
C23×C4⋊Dic112
#130743622
C2×#106225972
C2×#106225612
C2×#106226072
C2×#106225742
C2×#106228332
C2×#106225712
C2×#106225552
C22×C11×#1232
C2×#261811