Finite Group Databasebeta

← C2×#13073577 #14923794

Subgroups — C2×#13073577 #14923794

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×#66948C212yesmaximal, complemented
2C22×#66948C211yesmaximal, characteristic, complemented
3C22×#66946C211yesmaximal, characteristic, complemented
4#13073577C2116yesmaximal, direct product factor
5C2×#10622606C211yesmaximal, characteristic, complemented
6C2×#10622604C211yesmaximal, characteristic, complemented
7C2×#10622284C211yesmaximal, characteristic, complemented
8C2×#10622603C212yesmaximal, complemented
9C2×#10622278C212yesmaximal, complemented
10C2×#10622278C212yesmaximal, complemented
11C2×D11×#95C211yesmaximal, characteristic, complemented
12C2×C11×#398C211yesmaximal, characteristic, complemented
13C23×D44C2212yes—
14C23×D44C2212yes—
15C23×D44C2211yescharacteristic
16C23×D44C2211yescharacteristic
17C23×C4×D11C2212yes—
18C23×C4×D11C2211yescharacteristic
19C23×C4×D11C2211yescharacteristic
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C4⋊C4C2212yes—
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2211yescharacteristic
28C22×(C2×D11)⋊C4C2212yes—
29C22×(C2×D11)⋊C4C2212yes—
30C22×C4×Dic11C2211yescharacteristic
31C2×#66948—216no—
32C2×#66948—28no—
33C2×#66948C22116yescomplemented
34C2×#66948C2218yescomplemented
35C2×#66946—28no—
36C2×#66946C2218yescomplemented
37C11×#398C2218yescomplemented
38C2×C11×#95C2211yescharacteristic
39C2×C11×#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2211yescharacteristic
42C2×C11⋊#95C2212yes—
43#10622606C2218yescomplemented
44#10622604C2218yescomplemented
45#10622603C22116yescomplemented
46#10622284C2218yescomplemented
47#10622278C22116yescomplemented
48#10622278C22116yescomplemented
49D11×#95C2218yescomplemented
50C24×D11C2312yes—
51C24×D11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C23×C4×C11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×Dic11C2311yescharacteristic
59C23×Dic11C2312yes—
60C23×Dic11C2311yescharacteristic
61C22×D44—24no—
62C22×D44—24no—
63C22×D44—28no—
64C22×D44—28no—
65C22×D44—28no—
66C22×D44—28no—
67C22×D44—24no—
68C22×D44—28no—
69C22×D44—44no—
70C22×D44—44no—
71C22×D44D418yescomplemented
72C22×D44C2318yes—
73C22×D44C2318yes—
74C22×D44C2314yes—
75C22×D44C2314yes—
76C22×C4×D11—28no—
77C22×C4×D11—28no—
78C22×C4×D11—24no—
79C22×C4×D11—44no—
80C22×C4×D11—44no—
81C22×C4×D11—44no—
82C22×C4×D11D418yescomplemented
83C22×C4×D11C2318yes—
84C22×C4×D11C2314yes—
85C22×C4×D11C2314yes—
86C2×C11×C4⋊C4—24no—
87C2×C11×C4⋊C4—28no—
88C2×C11×C4⋊C4—24no—
89C2×C11×C4⋊C4C2314yes—
90C2×C11×C4⋊C4C2318yes—
91C2×C11×C4⋊C4C2314yes—
92C2×(C2×D11)⋊C4—24no—
93C2×(C2×D11)⋊C4—28no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—28no—
96C2×(C2×D11)⋊C4—28no—
97C2×(C2×D11)⋊C4—28no—
98C2×(C2×D11)⋊C4—44no—
99C2×(C2×D11)⋊C4C2314yes—
100C2×(C2×D11)⋊C4C2314yes—
101C2×(C2×D11)⋊C4C2318yes—
102C2×(C2×D11)⋊C4C2318yes—
103C2×(C2×D11)⋊C4C2318yes—
104C2×(C2×D11)⋊C4C2318yes—
105C2×(C2×D11)⋊C4C2318yes—
106C2×C4×Dic11—24no—
107C2×C4×Dic11C2314yes—
108#66948—264no—
109#66948—232no—
110#66946—232no—
111C11×#95C2314yes—
112C11×#95C2318yes—
113C11⋊#95C2318yes—
114C11⋊#95C2314yes—
115C11⋊#95C2318yes—
116C2×#2543—111nomaximal, Sylow
117C24×C11C2411yescharacteristic
118C23×D11—24no—
119C23×D11—24no—
120C23×D11—22no—
121C23×D11—22no—
122C23×D11—24no—
123C23×D11—24no—
124C23×D11—24no—
125C23×D11—24no—
126C23×D11—24no—
127C23×D11—24no—
128C23×D11—24no—
129C23×D11—24no—
130C23×D11—24no—
131C23×D11C2×D414yes—
132C23×D11C2×D414yes—
133C23×D11C2×D414yes—
134C23×D11#4114yes—
135C23×D11C2414yes—
136C23×D11C2412yes—
137C23×D11C2412yes—
138C22×C4×C11—22no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—22no—
144C22×C4×C11—24no—
145C22×C4×C11—24no—
146C22×C4×C11—24no—
147C22×C4×C11—24no—
148C22×C4×C11C2×D414yes—
149C22×C4×C11C2×D414yes—
150C22×C4×C11#4118yes—
151C22×C4×C11C2414yes—
152C22×C4×C11C2412yes—
153C22×C4×C11C2412yes—
154C22×C4×C11C2412yes—
155C22×C4×C11C2414yes—
156C22×Dic11—22no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—24no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11C2×D414yes—
163C22×Dic11C2414yes—
164C22×Dic11C2412yes—
165C22×Dic11C2412yes—
166C2×D44—232no—
167C2×D44—28no—
168C2×D44—216no—
169C2×D44—216no—
170C2×D44—216no—
171C2×D44—28no—
172C2×D44—216no—
173C2×D44—28no—
174C2×D44—216no—
175C2×D44—48no—
176C2×D44—48no—
177C2×D44—432no—
178C2×D44—416no—
179C2×D44—432no—
180C2×D44C2×D4116yescomplemented
181C2×C4×D11—28no—
182C2×C4×D11—216no—
183C2×C4×D11—216no—
184C2×C4×D11—416no—
185C2×C4×D11—48no—
186C2×C4×D11—48no—
187C2×C4×D11—48no—
188C2×C4×D11—432no—
189C2×C4×D11—416no—
190C2×C4×D11C2×D4116yescomplemented
191C11×C4⋊C4—28no—
192C11×C4⋊C4—216no—
193C11×C4⋊C4—28no—
194(C2×D11)⋊C4—216no—
195(C2×D11)⋊C4—28no—
196(C2×D11)⋊C4—216no—
197(C2×D11)⋊C4—28no—
198(C2×D11)⋊C4—216no—
199(C2×D11)⋊C4—216no—
200(C2×D11)⋊C4—48no—
201C4×Dic11—28no—
202C22×#121—112no—
203C22×#121—111no—
204C22×C4×D4—111no—
205#2543—1116no—
206C2×#398D1111yescharacteristic, complemented
207C2×#397—111no—
208C2×#394—111no—
209C2×#392—111no—
210C2×#388—112no—
211C2×#386—112no—
212C2×#386—112no—
213C22×#95—111no—
214C23×C11C22×D412yes—
215C23×C11C22×D412yes—
216C23×C11C2×#4114yes—
217C23×C11C2×#4112yes—
218C23×C11H(5,𝔽2)14yes—
219C23×C11C2511yescharacteristic
220C22×D11—28no—
221C22×D11—28no—
222C22×D11—216no—
223C22×D11—216no—
224C22×D11—24no—
225C22×D11—24no—
226C22×D11—28no—
227C22×D11—216no—
228C22×D11—22no—
229C22×D11—24no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—24no—
233C22×D11—24no—
234C22×D11—24no—
235C22×D11—24no—
236C22×D11—24no—
237C22×D11—24no—
238C22×D11—24no—
239C22×D11—44no—
240C22×D11—44no—
241C22×D11—48no—
242C22×D11—48no—
243C22×D11—48no—
244C22×D11—48no—
245C22×D11—48no—
246C22×D11—48no—
247C22×D11—48no—
248C22×D11—48no—
249C22×D11#121116yes—
250C22×D11C22×D414yes—
251C22×D11C22×D414yes—
252C22×D11C22×D414yes—
253C22×D11C2×#4114yes—
254C2×C4×C11—28no—
255C2×C4×C11—28no—
256C2×C4×C11—216no—
257C2×C4×C11—22no—
258C2×C4×C11—24no—
259C2×C4×C11—22no—
260C2×C4×C11—24no—
261C2×C4×C11—24no—
262C2×C4×C11—22no—
263C2×C4×C11—24no—
264C2×C4×C11—24no—
265C2×C4×C11—24no—
266C2×C4×C11—24no—
267C2×C4×C11—48no—
268C2×C4×C11—44no—
269C2×C4×C11C22×D414yes—
270C2×C4×C11C22×D414yes—
271C2×C4×C11C2×#4118yes—
272C2×Dic11—28no—
273C2×Dic11—24no—
274C2×Dic11—22no—
275C2×Dic11—24no—
276C2×Dic11—24no—
277C2×Dic11—24no—
278C2×Dic11—24no—
279C2×Dic11—44no—
280C2×Dic11—48no—
281C2×Dic11C22×D414yes—
282D44—232no—
283D44—432no—
284D44—416no—
285D44—432no—
286C4×D11—416no—
287C4×D11—416no—
288C4×D11—432no—
289C23×D4—111no—
290C23×D4—112no—
291C23×D4—112no—
292C23×D4—111no—
293C24×C4—111no—
294C24×C4—112no—
295C24×C4—111no—
296C2×#121—118no—
297C2×#121—1116no—
298C2×#121—228no—
299C2×#121—2216no—
300C2×C4×D4—118no—
301C2×C4×D4—228no—
302C22×C4⋊C4C2×D1111yescharacteristic
303C22×C4⋊C4C2×D1111yescharacteristic
304C22×C4⋊C4C2×D1112yes—
305C22×C22⋊C4—111no—
306C22×C22⋊C4—112no—
307C22×C22⋊C4—112no—
308C22×C22⋊C4—112no—
309C22×C22⋊C4—111no—
310C22×C22⋊C4—112no—
311C22×C22⋊C4—112no—
312C22×C42—111no—
313#398C2×D1118yescomplemented
314#397—118no—
315#394—118no—
316#392—118no—
317#388—1116no—
318#386—1116no—
319#386—1116no—
320C2×#95—111no—
321C2×#95—112no—
322C2×#95—112no—
323C2×#95—118no—
324C2×#95C2×D1111yescharacteristic
325C2×#95C2×D1112yes—
326C22×C11C2×#12114yes—
327C22×C11#53214yes—
328C22×C11#53414yes—
329C22×C11#54618yes—
330C22×C11#55318yes—
331C22×C11C23×D411yescharacteristic
332C22×C11C23×D411yescharacteristic
333C22×C11C22×#4112yes—
334C22×C11C22×#4111yescharacteristic
335C22×C11C2×H(5,𝔽2)12yes—
336C2×D11—24no—
337C2×D11—24no—
338C2×D11—28no—
339C2×D11—28no—
340C2×D11—232no—
341C2×D11—24no—
342C2×D11—28no—
343C2×D11—42no—
344C2×D11—42no—
345C2×D11—44no—
346C2×D11—416no—
347C2×D11—44no—
348C2×D11—44no—
349C2×D11—44no—
350C2×D11—44no—
351C2×D11—44no—
352C2×D11—44no—
353C2×D11—44no—
354C2×D11—816no—
355C2×D11C2×#12118yes—
356C4×C11—24no—
357C4×C11—24no—
358C4×C11—28no—
359C4×C11—44no—
360C4×C11—42no—
361Dic11—24no—
362Dic11—42no—
363Dic11—44no—
364C25—111no—
365C25—111no—
366C25—112no—
367C22×D4—118no—
368C22×D4—114no—
369C22×D4—118no—
370C22×D4—118no—
371C22×D4—114no—
372C22×D4—224no—
373C22×D4—224no—
374C22×D4—228no—
375C22×D4—228no—
376C22×D4—228no—
377C22×D4—228no—
378C22×D4—224no—
379C22×D4—228no—
380C22×D4—444no—
381C22×D4—444no—
382C23×C4—111no—
383C23×C4—118no—
384C23×C4—114no—
385C23×C4—111no—
386C23×C4—112no—
387C23×C4—118no—
388C23×C4—114no—
389C23×C4—224no—
390C23×C4—228no—
391C23×C4—228no—
392C23×C4—444no—
393C23×C4—444no—
394C23×C4—444no—
395C23×C4C22×D1111yescharacteristic
396C23×C4C22×D1112yes—
397C23×C4C22×D1111yescharacteristic
398C23×C4C22×D1111yescharacteristic
399C23×C4C22×D1112yes—
400#121—2232no—
401#121—2264no—
402C4×D4—2232no—
403C2×C4⋊C4—24no—
404C2×C4⋊C4—28no—
405C2×C4⋊C4—24no—
406C2×C4⋊C4C22×D1114yes—
407C2×C4⋊C4C22×D1118yes—
408C2×C4⋊C4C22×D1114yes—
409C2×C22⋊C4—114no—
410C2×C22⋊C4—114no—
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—224no—
418C2×C22⋊C4—228no—
419C2×C22⋊C4—224no—
420C2×C22⋊C4—228no—
421C2×C22⋊C4—228no—
422C2×C22⋊C4—444no—
423C2×C42—114no—
424C2×C42—224no—
425#95—118no—
426#95—114no—
427#95—118no—
428#95C22×D1114yes—
429#95C22×D1118yes—
430C2×C11#254318yescomplemented
431C2×C11C22×#12111yescharacteristic
432C2×C11C2×#53211yescharacteristic
433C2×C11C2×#53411yescharacteristic
434C2×C11C2×#54612yes—
435C2×C11C2×#55312yes—
436D11—28no—
437D11—44no—
438D11—84no—
439C24—114no—
440C24—114no—
441C24—114no—
442C24—112no—
443C24—114no—
444C24—112no—
445C24—114no—
446C24—224no—
447C24—224no—
448C24—222no—
449C24—224no—
450C24—222no—
451C24—224no—
452C24—224no—
453C24—224no—
454C24—224no—
455C24—224no—
456C24—224no—
457C24—224no—
458C24—224no—
459C24C23×D1111yescharacteristic
460C2×D4—1116no—
461C2×D4—228no—
462C2×D4—2232no—
463C2×D4—228no—
464C2×D4—2216no—
465C2×D4—2216no—
466C2×D4—2216no—
467C2×D4—2216no—
468C2×D4—228no—
469C2×D4—2216no—
470C2×D4—448no—
471C2×D4—448no—
472C2×D4—4432no—
473C2×D4—4416no—
474C2×D4—4432no—
475C22×C4—22no—
476C22×C4—24no—
477C22×C4—22no—
478C22×C4—24no—
479C22×C4—24no—
480C22×C4—22no—
481C22×C4—24no—
482C22×C4—24no—
483C22×C4—24no—
484C22×C4—24no—
485C22×C4—114no—
486C22×C4—112no—
487C22×C4—1116no—
488C22×C4—114no—
489C22×C4—112no—
490C22×C4—228no—
491C22×C4—2216no—
492C22×C4—224no—
493C22×C4—222no—
494C22×C4—224no—
495C22×C4—224no—
496C22×C4—224no—
497C22×C4—224no—
498C22×C4—2216no—
499C22×C4—4416no—
500C22×C4—448no—
501C22×C4—448no—
502C22×C4—448no—
503C22×C4—4432no—
504C22×C4—4416no—
505C22×C4D4×D1114yes—
506C22×C4D4×D1114yes—
507C22×C4#434318yes—
508C22×C4C23×D1114yes—
509C22×C4C23×D1112yes—
510C22×C4C23×D1112yes—
511C22×C4C23×D1112yes—
512C22×C4C23×D1114yes—
513C4⋊C4—28no—
514C4⋊C4—216no—
515C4⋊C4—28no—
516C22⋊C4—2216no—
517C22⋊C4—228no—
518C22⋊C4—2216no—
519C22⋊C4—228no—
520C22⋊C4—2216no—
521C22⋊C4—2216no—
522C22⋊C4—448no—
523C42—228no—
524C11C2×#254311yescharacteristic, complemented, Sylow
525C23—1116no—
526C23—114no—
527C23—114no—
528C23—114no—
529C23—114no—
530C23—228no—
531C23—2216no—
532C23—228no—
533C23—224no—
534C23—224no—
535C23—2216no—
536C23—228no—
537C23—2216no—
538C23—222no—
539C23—224no—
540C23—222no—
541C23—224no—
542C23—224no—
543C23—224no—
544C23—224no—
545C23—224no—
546C23—224no—
547C23—224no—
548C23—224no—
549C23—444no—
550C23—444no—
551C23—448no—
552C23—448no—
553C23—448no—
554C23—448no—
555C23—448no—
556C23—448no—
557C23—448no—
558C23—448no—
559C23C2×D4×D1112yes—
560C23C2×D4×D1112yes—
561C23C2×#434314yes—
562C23#41×D1112yes—
563C23#6704214yes—
564C23C24×D1111yescharacteristic
565D4—2232no—
566D4—4432no—
567D4—4416no—
568D4—4432no—
569C2×C4—28no—
570C2×C4—216no—
571C2×C4—28no—
572C2×C4—22no—
573C2×C4—24no—
574C2×C4—22no—
575C2×C4—24no—
576C2×C4—24no—
577C2×C4—22no—
578C2×C4—24no—
579C2×C4—24no—
580C2×C4—24no—
581C2×C4—24no—
582C2×C4—48no—
583C2×C4—44no—
584C2×C4—114no—
585C2×C4—228no—
586C2×C4—224no—
587C2×C4—222no—
588C2×C4—224no—
589C2×C4—224no—
590C2×C4—224no—
591C2×C4—224no—
592C2×C4—4416no—
593C2×C4—4432no—
594C2×C4—4416no—
595C2×C4—444no—
596C2×C4—448no—
597C2×C4C2×D4×D1114yes—
598C2×C4C2×D4×D1114yes—
599C2×C4C2×#434318yes—
600C22—118no—
601C22—228no—
602C22—224no—
603C22—224no—
604C22—2232no—
605C22—228no—
606C22—228no—
607C22—224no—
608C22—444no—
609C22—442no—
610C22—442no—
611C22—4416no—
612C22—444no—
613C22—444no—
614C22—444no—
615C22—444no—
616C22—444no—
617C22—444no—
618C22—444no—
619C22—8816no—
620C22D11×#12114yes—
621C22#1062316118yes—
622C22#1062318414yes—
623C22#1062322618yes—
624C22#1062325614yes—
625C22C22×D4×D1111yescharacteristic
626C22C22×D4×D1111yescharacteristic
627C22C22×#434312yes—
628C22C2×#41×D1111yescharacteristic
629C22C2×#6704212yes—
630C4—24no—
631C4—28no—
632C4—24no—
633C4—42no—
634C4—44no—
635C4—224no—
636C4—442no—
637C4—444no—
638C2—228no—
639C2—444no—
640C2—884no—
641C2#1307357718yesdirect product factor
642C2C2×D11×#12111yescharacteristic
643C2C2×#1062325611yescharacteristic
644C2C2×#1062318411yescharacteristic
645C2C2×#1062316112yes—
646C2C2×#1062322612yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#398C2
socleC24×C11C24
hypercenterC2×#398D11
hypocenterC11C2×#2543
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#398

Complements

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

NH ≅ G/Ntype
1. C22×#66948C2semidirect
2. C22×#66948C2semidirect
3. C22×#66946C2semidirect
4. #13073577C2direct (N × H)
5. C2×#10622606C2semidirect
6. C2×#10622604C2semidirect
7. C2×#10622284C2semidirect
8. C2×#10622603C2semidirect
9. C2×#10622278C2semidirect
10. C2×#10622278C2semidirect
11. C2×D11×#95C2semidirect
12. C2×C11×#398C2semidirect
33. C2×#66948C22semidirect
34. C2×#66948C22semidirect
36. C2×#66946C22semidirect
37. C11×#398C22semidirect
43. #10622606C22semidirect
44. #10622604C22semidirect
45. #10622603C22semidirect
46. #10622284C22semidirect
47. #10622278C22semidirect
48. #10622278C22semidirect
49. D11×#95C22semidirect
71. C22×D44D4semidirect
82. C22×C4×D11D4semidirect
180. C2×D44C2×D4semidirect
190. C2×C4×D11C2×D4semidirect
206. C2×#398D11semidirect
313. #398C2×D11semidirect
430. C2×C11#2543semidirect
524. C11C2×#2543semidirect
641. C2#13073577direct (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×#669462
#130735772
C2×#106226062
C2×#106226042
C2×#106222842
C2×#106226032
C2×#106222782
C2×D11×#952
C2×C11×#3982
C2×#254311