Finite Group Databasebeta

← C2×#13073572 #14923797

Subgroups — C2×#13073572 #14923797

Order 2816.

4326 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×#66983C211yesmaximal, characteristic, complemented
2C22×#66992C212yesmaximal, complemented
3#13073572C2116yesmaximal, direct product factor
4C2×#10622596C211yesmaximal, characteristic, complemented
5C2×#10622566C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622573C211yesmaximal, characteristic, complemented
8C2×#10622553C212yesmaximal, complemented
9C2×#10622826C212yesmaximal, complemented
10C2×#10622571C212yesmaximal, complemented
11C22×C11⋊#95C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic, complemented
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C22⋊D11C2212yes—
18C24×Dic11C2212yes—
19C23×D44C2211yescharacteristic
20C2×C4×D4×C11—28no—
21C2×C4×D4×C11C2218yescomplemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C42×C11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C2×#66992—216no—
28C2×#66992C22116yescomplemented
29C2×#66983—28no—
30C2×#66983C2218yescomplemented
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×(C2×D11)⋊C4C2212yes—
34C22×(C2×D11)⋊C4C2212yes—
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2212yes—
37#10622826C22116yescomplemented
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43C2×C11⋊#95C2218yescomplemented
44#10622604C2218yescomplemented
45#10622596C2218yescomplemented
46#10622573C2218yescomplemented
47#10622571C22116yescomplemented
48#10622566C2218yescomplemented
49#10622553C22116yescomplemented
50C25×C11C2311yescharacteristic
51C25×C11C2311yescharacteristic
52C24×D11C2312yes—
53C22×D4×C11—24no—
54C22×D4×C11—24no—
55C22×D4×C11D418yescomplemented
56C22×D4×C11C2314yes—
57C23×C4×C11—24no—
58C23×C4×C11—44no—
59C23×C4×C11—44no—
60C23×C4×C11D418yescomplemented
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2314yes—
67C23×C4×C11C2314yes—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—28no—
70C22×C22⋊D11—28no—
71C22×C22⋊D11—28no—
72C22×C22⋊D11—28no—
73C22×C22⋊D11—44no—
74C22×C22⋊D11C2318yes—
75C22×C22⋊D11C2318yes—
76C23×Dic11—28no—
77C23×Dic11—28no—
78C23×Dic11—44no—
79C23×Dic11C2312yes—
80C23×Dic11C2312yes—
81C23×Dic11C2318yes—
82C23×Dic11C2312yes—
83C22×D44—24no—
84C22×D44—44no—
85C22×D44C2314yes—
86C4×D4×C11—232no—
87C2×C11×C4⋊C4—24no—
88C2×C11×C4⋊C4C2314yes—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4C2314yes—
92C2×C11×C22⋊C4C2314yes—
93C2×C42×C11—24no—
94C2×C42×C11C2314yes—
95C2×C22⋊Dic11—28no—
96C2×C22⋊Dic11C2318yes—
97#66992—264no—
98#66983—232no—
99C2×(C2×D11)⋊C4—28no—
100C2×(C2×D11)⋊C4—28no—
101C2×(C2×D11)⋊C4—28no—
102C2×(C2×D11)⋊C4—44no—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×(C2×D11)⋊C4C2318yes—
107C2×C4⋊Dic11—24no—
108C2×C4⋊Dic11C2314yes—
109C2×Dic11⋊C4—28no—
110C2×Dic11⋊C4C2318yes—
111C11⋊#95C2318yes—
112C11⋊#95C2318yes—
113C11⋊#95C2314yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C2×#2543—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—24no—
119C24×C11—22no—
120C24×C11—24no—
121C24×C11—22no—
122C24×C11—24no—
123C24×C11C2×D414yes—
124C24×C11C2×D414yes—
125C24×C11C2×D414yes—
126C24×C11#4114yes—
127C24×C11C2412yes—
128C24×C11C2412yes—
129C24×C11C2411yescharacteristic
130C23×D11—24no—
131C23×D11—24no—
132C23×D11—24no—
133C23×D11—24no—
134C23×D11—24no—
135C23×D11—24no—
136C23×D11—24no—
137C23×D11C2414yes—
138C2×D4×C11—232no—
139C2×D4×C11—28no—
140C2×D4×C11—28no—
141C2×D4×C11C2×D4116yescomplemented
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—22no—
147C22×C4×C11—22no—
148C22×C4×C11—24no—
149C22×C4×C11—24no—
150C22×C4×C11—28no—
151C22×C4×C11—416no—
152C22×C4×C11—48no—
153C22×C4×C11—48no—
154C22×C4×C11—416no—
155C22×C4×C11C2×D414yes—
156C22×C4×C11C2×D414yes—
157C22×C4×C11C2×D414yes—
158C22×C4×C11C2×D4116yescomplemented
159C22×C4×C11C2412yes—
160C22×C4×C11C2412yes—
161C22×C4×C11C2412yes—
162C22×C4×C11C2412yes—
163C22×C4×C11C2412yes—
164C2×C22⋊D11—216no—
165C2×C22⋊D11—216no—
166C2×C22⋊D11—216no—
167C2×C22⋊D11—216no—
168C2×C22⋊D11—216no—
169C2×C22⋊D11—48no—
170C2×C22⋊D11—432no—
171C2×C22⋊D11—432no—
172C22×Dic11—216no—
173C22×Dic11—24no—
174C22×Dic11—24no—
175C22×Dic11—24no—
176C22×Dic11—24no—
177C22×Dic11—216no—
178C22×Dic11—24no—
179C22×Dic11—24no—
180C22×Dic11—24no—
181C22×Dic11—24no—
182C22×Dic11—48no—
183C22×Dic11—432no—
184C22×Dic11#4118yes—
185C22×Dic11C2414yes—
186C22×Dic11C2414yes—
187C22×Dic11C2414yes—
188C2×D44—28no—
189C2×D44—48no—
190C2×D44—416no—
191C11×C4⋊C4—28no—
192C11×C22⋊C4—28no—
193C11×C22⋊C4—28no—
194C42×C11—28no—
195C22⋊Dic11—216no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—216no—
198(C2×D11)⋊C4—216no—
199(C2×D11)⋊C4—48no—
200C4⋊Dic11—28no—
201Dic11⋊C4—216no—
202C22×#121—112no—
203C22×#121—111no—
204C22×C4×D4D1111yescharacteristic, complemented
205#2543—1116no—
206C2×#398—111no—
207C2×#397—111no—
208C2×#394—111no—
209C2×#392—111no—
210C2×#388—112no—
211C2×#386—112no—
212C2×#386—112no—
213C22×#95—111no—
214C23×C11—28no—
215C23×C11—28no—
216C23×C11—216no—
217C23×C11—216no—
218C23×C11—24no—
219C23×C11—24no—
220C23×C11—28no—
221C23×C11—216no—
222C23×C11—22no—
223C23×C11—24no—
224C23×C11—22no—
225C23×C11—24no—
226C23×C11—44no—
227C23×C11—44no—
228C23×C11—48no—
229C23×C11#121116yes—
230C23×C11C22×D414yes—
231C23×C11C22×D414yes—
232C23×C11C22×D412yes—
233C23×C11C22×D414yes—
234C23×C11C22×D412yes—
235C23×C11C2×#4114yes—
236C23×C11C2×#4112yes—
237C23×C11C2×#4114yes—
238C23×C11H(5,𝔽2)14yes—
239C23×C11C2511yescharacteristic
240C22×D11—24no—
241C22×D11—24no—
242C22×D11—24no—
243C22×D11—24no—
244C22×D11—24no—
245C22×D11—24no—
246C22×D11—24no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11—48no—
250C22×D11—48no—
251C22×D11—48no—
252C22×D11—48no—
253C22×D11—48no—
254D4×C11—232no—
255C2×C4×C11—28no—
256C2×C4×C11—28no—
257C2×C4×C11—28no—
258C2×C4×C11—22no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—22no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—416no—
267C2×C4×C11—416no—
268C2×C4×C11—44no—
269C2×C4×C11—44no—
270C2×C4×C11C22×D414yes—
271C2×C4×C11C22×D414yes—
272C2×C4×C11C22×D414yes—
273C22⋊D11—432no—
274C22⋊D11—432no—
275C2×Dic11—216no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—24no—
280C2×Dic11—24no—
281C2×Dic11—24no—
282C2×Dic11—24no—
283C2×Dic11—24no—
284C2×Dic11—432no—
285C2×Dic11—48no—
286C2×Dic11—48no—
287C2×Dic11C2×#4118yes—
288D44—416no—
289C23×D4—112no—
290C23×D4—112no—
291C23×D4—111no—
292C23×D4C2×D1111yescharacteristic
293C24×C4—112no—
294C24×C4C2×D1111yescharacteristic
295C24×C4C2×D1111yescharacteristic
296C2×#121—1116no—
297C2×#121—118no—
298C2×#121—2216no—
299C2×#121—228no—
300C2×C4×D4—28no—
301C2×C4×D4C2×D1118yescomplemented
302C22×C4⋊C4—112no—
303C22×C4⋊C4—111no—
304C22×C4⋊C4C2×D1111yescharacteristic
305C22×C22⋊C4—112no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—112no—
310C22×C22⋊C4C2×D1111yescharacteristic
311C22×C22⋊C4C2×D1111yescharacteristic
312C22×C42C2×D1111yescharacteristic
313#398—118no—
314#397—118no—
315#394—118no—
316#392—118no—
317#388—1116no—
318#386—1116no—
319#386—1116no—
320C2×#95—111no—
321C2×#95—111no—
322C2×#95—112no—
323C2×#95—112no—
324C2×#95—112no—
325C2×#95—118no—
326C22×C11—24no—
327C22×C11—24no—
328C22×C11—28no—
329C22×C11—28no—
330C22×C11—232no—
331C22×C11—24no—
332C22×C11—28no—
333C22×C11—42no—
334C22×C11—42no—
335C22×C11—44no—
336C22×C11—416no—
337C22×C11C2×#12118yes—
338C22×C11C2×#12114yes—
339C22×C11#53214yes—
340C22×C11#53414yes—
341C22×C11#54618yes—
342C22×C11#55318yes—
343C22×C11C23×D411yescharacteristic
344C22×C11C23×D411yescharacteristic
345C22×C11C22×#4111yescharacteristic
346C22×C11C22×#4112yes—
347C22×C11C2×H(5,𝔽2)12yes—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—44no—
355C2×D11—816no—
356C4×C11—24no—
357C4×C11—24no—
358C4×C11—24no—
359C4×C11—42no—
360C4×C11—42no—
361Dic11—28no—
362Dic11—44no—
363Dic11—44no—
364C25—112no—
365C25C22×D1111yescharacteristic
366C25C22×D1111yescharacteristic
367C22×D4—24no—
368C22×D4—24no—
369C22×D4—118no—
370C22×D4—118no—
371C22×D4—114no—
372C22×D4—228no—
373C22×D4—228no—
374C22×D4—228no—
375C22×D4—228no—
376C22×D4—228no—
377C22×D4—224no—
378C22×D4—444no—
379C22×D4—444no—
380C22×D4D4418yescomplemented
381C22×D4C22×D1114yes—
382C23×C4—24no—
383C23×C4—44no—
384C23×C4—44no—
385C23×C4—112no—
386C23×C4—112no—
387C23×C4—112no—
388C23×C4—118no—
389C23×C4—228no—
390C23×C4—228no—
391C23×C4—444no—
392C23×C4C22⋊D1118yescomplemented
393C23×C4C22×D1111yescharacteristic
394C23×C4C22×D1111yescharacteristic
395C23×C4C22×D1111yescharacteristic
396C23×C4C22×D1111yescharacteristic
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1114yes—
399C23×C4C22×D1114yes—
400#121—2264no—
401#121—2232no—
402C4×D4—232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—118no—
405C2×C4⋊C4—114no—
406C2×C4⋊C4—228no—
407C2×C4⋊C4—224no—
408C2×C4⋊C4C22×D1114yes—
409C2×C22⋊C4—24no—
410C2×C22⋊C4—24no—
411C2×C22⋊C4—118no—
412C2×C22⋊C4—118no—
413C2×C22⋊C4—118no—
414C2×C22⋊C4—118no—
415C2×C22⋊C4—118no—
416C2×C22⋊C4—228no—
417C2×C22⋊C4—228no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—228no—
420C2×C22⋊C4—444no—
421C2×C22⋊C4C22×D1114yes—
422C2×C22⋊C4C22×D1114yes—
423C2×C42—24no—
424C2×C42C22×D1114yes—
425#95—118no—
426#95—114no—
427#95—114no—
428#95—118no—
429#95—118no—
430C2×C11—28no—
431C2×C11—44no—
432C2×C11#254318yescomplemented
433C2×C11C22×#12111yescharacteristic
434C2×C11C2×#53211yescharacteristic
435C2×C11C2×#53411yescharacteristic
436C2×C11C2×#54612yes—
437C2×C11C2×#55312yes—
438D11—84no—
439C24—24no—
440C24—24no—
441C24—22no—
442C24—24no—
443C24—24no—
444C24—22no—
445C24—114no—
446C24—224no—
447C24—224no—
448C24—224no—
449C24—224no—
450C24—224no—
451C24—224no—
452C24—224no—
453C24C2×D4414yes—
454C24C2×D4414yes—
455C24#433914yes—
456C24C2×C22⋊D1114yes—
457C24C23×D1112yes—
458C24C23×D1112yes—
459C24C23×D1111yescharacteristic
460C2×D4—232no—
461C2×D4—28no—
462C2×D4—28no—
463C2×D4—2216no—
464C2×D4—2216no—
465C2×D4—2216no—
466C2×D4—2216no—
467C2×D4—2216no—
468C2×D4—228no—
469C2×D4—448no—
470C2×D4—4416no—
471C2×D4—448no—
472C2×D4—4432no—
473C2×D4—4432no—
474C2×D4C2×D44116yescomplemented
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—24no—
478C22×C4—22no—
479C22×C4—24no—
480C22×C4—24no—
481C22×C4—22no—
482C22×C4—22no—
483C22×C4—28no—
484C22×C4—48no—
485C22×C4—48no—
486C22×C4—416no—
487C22×C4—416no—
488C22×C4—118no—
489C22×C4—114no—
490C22×C4—114no—
491C22×C4—114no—
492C22×C4—2216no—
493C22×C4—224no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—2216no—
498C22×C4—224no—
499C22×C4—224no—
500C22×C4—224no—
501C22×C4—224no—
502C22×C4—448no—
503C22×C4—4432no—
504C22×C4C2×D4414yes—
505C22×C4C2×C22⋊D1114yes—
506C22×C4C2×C22⋊D1114yes—
507C22×C4C2×C22⋊D11116yescomplemented
508C22×C4C23×D1112yes—
509C22×C4C23×D1112yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1112yes—
513C4⋊C4—28no—
514C4⋊C4—2216no—
515C4⋊C4—228no—
516C22⋊C4—28no—
517C22⋊C4—28no—
518C22⋊C4—2216no—
519C22⋊C4—2216no—
520C22⋊C4—2216no—
521C22⋊C4—2216no—
522C22⋊C4—448no—
523C42—28no—
524C11C2×#254311yescharacteristic, complemented, Sylow
525C23—216no—
526C23—28no—
527C23—216no—
528C23—28no—
529C23—24no—
530C23—24no—
531C23—28no—
532C23—216no—
533C23—22no—
534C23—24no—
535C23—24no—
536C23—22no—
537C23—48no—
538C23—44no—
539C23—44no—
540C23—224no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—448no—
548C23—448no—
549C23—448no—
550C23—448no—
551C23—448no—
552C23—448no—
553C23—448no—
554C23#66983116yes—
555C23C22×D4414yes—
556C23C22×D4414yes—
557C23C22×D4412yes—
558C23C2×#433914yes—
559C23C2×#433912yes—
560C23#6703714yes—
561C23#41×D1114yes—
562C23C22×C22⋊D1114yes—
563C23C22×C22⋊D1112yes—
564C23C24×D1111yescharacteristic
565D4—232no—
566D4—4416no—
567D4—4432no—
568D4—4432no—
569C2×C4—28no—
570C2×C4—28no—
571C2×C4—28no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—24no—
575C2×C4—22no—
576C2×C4—24no—
577C2×C4—24no—
578C2×C4—22no—
579C2×C4—22no—
580C2×C4—416no—
581C2×C4—416no—
582C2×C4—44no—
583C2×C4—44no—
584C2×C4—118no—
585C2×C4—2216no—
586C2×C4—224no—
587C2×C4—224no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—224no—
593C2×C4—224no—
594C2×C4—4432no—
595C2×C4—448no—
596C2×C4—448no—
597C2×C4C22×D4414yes—
598C2×C4C22×C22⋊D1114yes—
599C2×C4C22×C22⋊D1114yes—
600C22—28no—
601C22—24no—
602C22—24no—
603C22—232no—
604C22—28no—
605C22—28no—
606C22—24no—
607C22—44no—
608C22—42no—
609C22—42no—
610C22—416no—
611C22—444no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—8816no—
619C22#1062307118yes—
620C22#1062308518yes—
621C22C2×#6698318yes—
622C22C2×#6698314yes—
623C22#1062333514yes—
624C22#1062336314yes—
625C22C23×D4411yescharacteristic
626C22C22×#433911yescharacteristic
627C22C2×#6703712yes—
628C22C2×#41×D1112yes—
629C22C23×C22⋊D1111yescharacteristic
630C4—24no—
631C4—24no—
632C4—24no—
633C4—42no—
634C4—42no—
635C4—228no—
636C4—444no—
637C4—444no—
638C2—28no—
639C2—44no—
640C2—884no—
641C2#1307357218yesdirect product factor
642C2C22×#6698311yescharacteristic
643C2C2×#1062336311yescharacteristic
644C2C2×#1062333511yescharacteristic
645C2C2×#1062308512yes—
646C2C2×#1062307112yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C2×#2543
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×#66983C2semidirect
2. C22×#66992C2semidirect
3. #13073572C2direct (N × H)
4. C2×#10622596C2semidirect
5. C2×#10622566C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622573C2semidirect
8. C2×#10622553C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622571C2semidirect
11. C22×C11⋊#95C2semidirect
12. C22×C4×D4×C11C2semidirect
21. C2×C4×D4×C11C22semidirect
28. C2×#66992C22semidirect
30. C2×#66983C22semidirect
37. #10622826C22semidirect
43. C2×C11⋊#95C22semidirect
44. #10622604C22semidirect
45. #10622596C22semidirect
46. #10622573C22semidirect
47. #10622571C22semidirect
48. #10622566C22semidirect
49. #10622553C22semidirect
55. C22×D4×C11D4semidirect
60. C23×C4×C11D4semidirect
141. C2×D4×C11C2×D4semidirect
158. C22×C4×C11C2×D4semidirect
204. C22×C4×D4D11semidirect
301. C2×C4×D4C2×D11semidirect
380. C22×D4D44semidirect
392. C23×C4C22⋊D11semidirect
432. C2×C11#2543semidirect
474. C2×D4C2×D44semidirect
507. C22×C4C2×C22⋊D11semidirect
524. C11C2×#2543semidirect
641. C2#13073572direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669832
C22×#669922
#130735722
C2×#106225962
C2×#106225662
C2×#106226042
C2×#106225732
C2×#106225532
C2×#106228262
C2×#106225712
C22×C11⋊#952
C22×C4×D4×C112
C2×#254311