Finite Group Databasebeta

← C2×#13073082 #14922829

Subgroups — C2×#13073082 #14922829

Order 2816.

4222 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66947C212yesmaximal, complemented
2C22×#66936C212yesmaximal, complemented
3C22×#66937C211yesmaximal, characteristic
4C22×C4⋊C4×D11C211yesmaximal, characteristic, complemented
5#13073082C2116yesmaximal, direct product factor
6C2×#10622290C211yesmaximal, characteristic, complemented
7C2×#10622562C211yesmaximal, characteristic, complemented
8C2×#10622605C211yesmaximal, characteristic, complemented
9C2×#10622570C212yesmaximal, complemented
10C2×#10622589C212yesmaximal, complemented
11C2×#10622279C211yesmaximal, characteristic, complemented
12C2×C11×#399C211yesmaximal, characteristic, complemented
13C23×C22⋊D11C2211yescharacteristic
14C23×C22⋊D11C2211yescharacteristic
15C23×D44C2211yescharacteristic
16C23×C4×D11C2212yes—
17C23×C4×D11C2211yescharacteristic
18C22×C11×C4⋊C4C2212yes—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C22×C4⋊Dic11C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×Dic11⋊C4C2211yescharacteristic
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×Dic11⋊C4C2212yes—
33C22×C4×Dic11C2212yes—
34C2×#66947—216no—
35C2×#66947C22116yescomplemented
36C2×C4⋊C4×D11—28no—
37C2×C4⋊C4×D11C2218yescomplemented
38C2×#66937—28no—
39C2×#66937C2218yes—
40C2×#66936—216no—
41C2×#66936C22116yescomplemented
42C11×#399C2218yescomplemented
43C2×C11×#95C2211yescharacteristic
44C2×C11⋊#95C2211yescharacteristic
45#10622605C2218yescomplemented
46#10622589C22116yescomplemented
47#10622570C22116yescomplemented
48#10622562C2218yescomplemented
49#10622290C2218yescomplemented
50#10622279C2218yescomplemented
51C25×C11C2311yescharacteristic
52C24×D11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C23×C4×C11C2311yescharacteristic
55C23×C4×C11C2312yes—
56C23×C4×C11C2312yes—
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—28no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—28no—
62C22×C22⋊D11C2314yes—
63C22×C22⋊D11C2314yes—
64C23×Dic11C2311yescharacteristic
65C23×Dic11C2312yes—
66C23×Dic11C2312yes—
67C23×Dic11C2311yescharacteristic
68C22×D44—24no—
69C22×D44—28no—
70C22×D44C2314yes—
71C22×C4×D11—28no—
72C22×C4×D11—28no—
73C22×C4×D11—28no—
74C22×C4×D11—28no—
75C22×C4×D11D418yes—
76C22×C4×D11C2318yes—
77C22×C4×D11C2314yes—
78C2×C11×C4⋊C4—24no—
79C2×C11×C4⋊C4—28no—
80C2×C11×C4⋊C4C2314yes—
81C2×C11×C4⋊C4C2318yes—
82C2×C11×C22⋊C4—28no—
83C2×C11×C22⋊C4—24no—
84C2×C11×C22⋊C4C2318yes—
85C2×C11×C22⋊C4C2314yes—
86C2×C22⋊Dic11—28no—
87C2×C22⋊Dic11C2318yes—
88C2×(C2×D11)⋊C4—24no—
89C2×(C2×D11)⋊C4—28no—
90C2×(C2×D11)⋊C4—28no—
91C2×(C2×D11)⋊C4D4116yescomplemented
92C2×(C2×D11)⋊C4C2314yes—
93C2×(C2×D11)⋊C4C2318yes—
94C2×(C2×D11)⋊C4C2318yes—
95C2×(C2×D11)⋊C4C2318yes—
96C2×C4⋊Dic11—28no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2318yes—
99C2×C4⋊Dic11C2314yes—
100C2×Dic11⋊C4—28no—
101C2×Dic11⋊C4—24no—
102C2×Dic11⋊C4—28no—
103C2×Dic11⋊C4—28no—
104C2×Dic11⋊C4C2318yes—
105C2×Dic11⋊C4C2314yes—
106C2×Dic11⋊C4C2318yes—
107C2×Dic11⋊C4C2318yes—
108C2×C4×Dic11—28no—
109C2×C4×Dic11C2318yes—
110#66947—264no—
111C4⋊C4×D11—232no—
112#66937—232no—
113#66936—264no—
114C11×#95C2314yes—
115C11⋊#95C2314yes—
116C2×#2501—111nomaximal, Sylow
117C24×C11—24no—
118C24×C11—22no—
119C24×C11—24no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11C2412yes—
123C24×C11C2411yescharacteristic
124C23×D11—24no—
125C23×D11—22no—
126C23×D11—22no—
127C23×D11—24no—
128C23×D11—22no—
129C23×D11—24no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11C2×D418yes—
133C23×D11C2×D414yes—
134C23×D11C2412yes—
135C23×D11C2412yes—
136C22×C4×C11—24no—
137C22×C4×C11—24no—
138C22×C4×C11—24no—
139C22×C4×C11—24no—
140C22×C4×C11—22no—
141C22×C4×C11—24no—
142C22×C4×C11—24no—
143C22×C4×C11—24no—
144C22×C4×C11C2×D418yes—
145C22×C4×C11C2×D414yes—
146C22×C4×C11C2412yes—
147C22×C4×C11C2414yes—
148C22×C4×C11C2412yes—
149C22×C4×C11C2414yes—
150C2×C22⋊D11—28no—
151C2×C22⋊D11—216no—
152C2×C22⋊D11—216no—
153C2×C22⋊D11—28no—
154C2×C22⋊D11—416no—
155C2×C22⋊D11—416no—
156C22×Dic11—24no—
157C22×Dic11—24no—
158C22×Dic11—24no—
159C22×Dic11—22no—
160C22×Dic11—24no—
161C22×Dic11—24no—
162C22×Dic11—24no—
163C22×Dic11C2×D418yes—
164C22×Dic11C2×D414yes—
165C22×Dic11#4118yes—
166C22×Dic11C2412yes—
167C22×Dic11C2414yes—
168C22×Dic11C2414yes—
169C22×Dic11C2412yes—
170C2×D44—28no—
171C2×D44—216no—
172C2×D44—416no—
173C2×C4×D11—232no—
174C2×C4×D11—216no—
175C2×C4×D11—216no—
176C2×C4×D11—216no—
177C2×C4×D11—216no—
178C2×C4×D11—432no—
179C2×C4×D11C2×D4116yes—
180C11×C4⋊C4—28no—
181C11×C4⋊C4—216no—
182C11×C22⋊C4—216no—
183C11×C22⋊C4—28no—
184C22⋊Dic11—216no—
185(C2×D11)⋊C4—216no—
186(C2×D11)⋊C4—28no—
187(C2×D11)⋊C4—216no—
188(C2×D11)⋊C4C2×D4132yescomplemented
189C4⋊Dic11—216no—
190C4⋊Dic11—28no—
191Dic11⋊C4—216no—
192Dic11⋊C4—28no—
193Dic11⋊C4—216no—
194Dic11⋊C4—216no—
195C4×Dic11—216no—
196C22×#123—112no—
197C22×#123—112no—
198C22×#121—111no—
199C23×C4⋊C4—111no—
200#2501—1116no—
201C2×#399—111no—
202C2×#399—111no—
203C2×#399—111no—
204C2×#399D1111yescharacteristic, complemented
205C2×#390—112no—
206C2×#384—112no—
207C2×C4×C22⋊C4—111no—
208C23×C11—24no—
209C23×C11—22no—
210C23×C11—24no—
211C23×C11—22no—
212C23×C11—22no—
213C23×C11—44no—
214C23×C11—44no—
215C23×C11—44no—
216C23×C11—48no—
217C23×C11—48no—
218C23×C11C22×D412yes—
219C23×C11C22×D414yes—
220C23×C11C2×#4114yes—
221C23×C112−1+412yes—
222C23×C112−1+412yes—
223C23×C11C2511yescharacteristic
224C22×D11—28no—
225C22×D11—28no—
226C22×D11—216no—
227C22×D11—216no—
228C22×D11—24no—
229C22×D11—22no—
230C22×D11—22no—
231C22×D11—24no—
232C22×D11—22no—
233C22×D11—24no—
234C22×D11—22no—
235C22×D11—22no—
236C22×D11—44no—
237C22×D11—44no—
238C22×D11—44no—
239C22×D11—48no—
240C22×D11—48no—
241C22×D11#127116yes—
242C22×D11C22×D418yes—
243C22×D11C22×D414yes—
244C2×C4×C11—28no—
245C2×C4×C11—216no—
246C2×C4×C11—24no—
247C2×C4×C11—24no—
248C2×C4×C11—24no—
249C2×C4×C11—24no—
250C2×C4×C11—22no—
251C2×C4×C11—24no—
252C2×C4×C11—24no—
253C2×C4×C11—24no—
254C2×C4×C11—48no—
255C2×C4×C11—44no—
256C2×C4×C11C22×D418yes—
257C2×C4×C11C22×D414yes—
258C22⋊D11—416no—
259C22⋊D11—416no—
260C2×Dic11—216no—
261C2×Dic11—24no—
262C2×Dic11—24no—
263C2×Dic11—24no—
264C2×Dic11—24no—
265C2×Dic11—24no—
266C2×Dic11—22no—
267C2×Dic11—24no—
268C2×Dic11—48no—
269C2×Dic11—44no—
270C2×Dic11#123116yescomplemented
271C2×Dic11C22×D418yes—
272C2×Dic11C22×D414yes—
273C2×Dic11C2×#4118yes—
274D44—416no—
275C4×D11—232no—
276C4×D11—432no—
277C23×D4—111no—
278C23×D4—111no—
279C23×D4—111no—
280C24×C4—111no—
281C24×C4—112no—
282C2×#123—1116no—
283C2×#123—1116no—
284C2×#123—2216no—
285C2×#123—2216no—
286C2×#121—118no—
287C2×#121—228no—
288C22×C4⋊C4—112no—
289C22×C4⋊C4—112no—
290C22×C4⋊C4—112no—
291C22×C4⋊C4—111no—
292C22×C4⋊C4—111no—
293C22×C4⋊C4—112no—
294C22×C4⋊C4—118no—
295C22×C4⋊C4—228no—
296C22×C4⋊C4C2×D1111yescharacteristic
297C22×C4⋊C4C2×D1112yes—
298C22×C22⋊C4—112no—
299C22×C22⋊C4—112no—
300C22×C22⋊C4—111no—
301C22×C22⋊C4—112no—
302C22×C22⋊C4—112no—
303C22×C22⋊C4C2×D1111yescharacteristic
304C22×C22⋊C4C2×D1112yes—
305C22×C42—112no—
306#399—118no—
307#399—118no—
308#399—118no—
309#399C2×D1118yescomplemented
310#390—1116no—
311#384—1116no—
312C4×C22⋊C4—118no—
313C2×#95—111no—
314C2×#95C2×D1111yescharacteristic
315C22×C11—42no—
316C22×C11—42no—
317C22×C11—42no—
318C22×C11—44no—
319C22×C11—44no—
320C22×C11—88no—
321C22×C11C2×#12314yes—
322C22×C11C2×#12714yes—
323C22×C11#53614yes—
324C22×C11#54718yes—
325C22×C11#54718yes—
326C22×C11C23×D411yescharacteristic
327C22×C11C23×D412yes—
328C22×C11C22×#4112yes—
329C22×C11C2×2−1+411yescharacteristic
330C22×C11C2×2−1+411yescharacteristic
331C2×D11—24no—
332C2×D11—24no—
333C2×D11—28no—
334C2×D11—28no—
335C2×D11—232no—
336C2×D11—42no—
337C2×D11—42no—
338C2×D11—42no—
339C2×D11—44no—
340C2×D11—44no—
341C2×D11—88no—
342C2×D11C2×#12718yes—
343C4×C11—24no—
344C4×C11—28no—
345C4×C11—44no—
346C4×C11—42no—
347Dic11—28no—
348Dic11—44no—
349Dic11—42no—
350Dic11C2×#12318yescomplemented
351C25—111no—
352C25—111no—
353C25C22×D1111yescharacteristic
354C22×D4—114no—
355C22×D4—114no—
356C22×D4—114no—
357C22×D4—224no—
358C22×D4—228no—
359C22×D4—224no—
360C22×D4—228no—
361C22×D4—224no—
362C22×D4—228no—
363C23×C4—111no—
364C23×C4—112no—
365C23×C4—118no—
366C23×C4—114no—
367C23×C4—112no—
368C23×C4—111no—
369C23×C4—118no—
370C23×C4—228no—
371C23×C4—228no—
372C23×C4—228no—
373C23×C4—228no—
374C23×C4C22×D1112yes—
375C23×C4C22×D1111yescharacteristic
376C23×C4C22×D1112yes—
377C23×C4C22×D1111yescharacteristic
378#123—2264no—
379#123—2264no—
380#121—2232no—
381C2×C4⋊C4—24no—
382C2×C4⋊C4—28no—
383C2×C4⋊C4—118no—
384C2×C4⋊C4—114no—
385C2×C4⋊C4—114no—
386C2×C4⋊C4—118no—
387C2×C4⋊C4—118no—
388C2×C4⋊C4—118no—
389C2×C4⋊C4—2232no—
390C2×C4⋊C4—228no—
391C2×C4⋊C4—224no—
392C2×C4⋊C4—228no—
393C2×C4⋊C4—228no—
394C2×C4⋊C4—224no—
395C2×C4⋊C4—228no—
396C2×C4⋊C4C22×D1114yes—
397C2×C4⋊C4C22×D1118yes—
398C2×C22⋊C4—24no—
399C2×C22⋊C4—28no—
400C2×C22⋊C4—1116no—
401C2×C22⋊C4—118no—
402C2×C22⋊C4—118no—
403C2×C22⋊C4—114no—
404C2×C22⋊C4—118no—
405C2×C22⋊C4—118no—
406C2×C22⋊C4—228no—
407C2×C22⋊C4—228no—
408C2×C22⋊C4—224no—
409C2×C22⋊C4—228no—
410C2×C22⋊C4C22×D1114yes—
411C2×C22⋊C4C22×D1118yes—
412C2×C42—118no—
413C2×C42—228no—
414#95—114no—
415#95C22×D1114yes—
416C2×C11—82no—
417C2×C11#250118yescomplemented
418C2×C11C22×#12311yescharacteristic
419C2×C11C22×#12711yescharacteristic
420C2×C11C2×#53611yescharacteristic
421C2×C11C2×#54712yes—
422C2×C11C2×#54712yes—
423D11—28no—
424D11—82no—
425C24—24no—
426C24—22no—
427C24—22no—
428C24—24no—
429C24—22no—
430C24—118no—
431C24—114no—
432C24—112no—
433C24—112no—
434C24—222no—
435C24—224no—
436C24—222no—
437C24—224no—
438C24—222no—
439C24—222no—
440C24—224no—
441C24—222no—
442C24C23×D1112yes—
443C24C23×D1111yescharacteristic
444C2×D4—228no—
445C2×D4—2216no—
446C2×D4—228no—
447C2×D4—2216no—
448C2×D4—228no—
449C2×D4—2216no—
450C2×D4—4416no—
451C2×D4—4416no—
452C2×D4—4416no—
453C22×C4—24no—
454C22×C4—24no—
455C22×C4—24no—
456C22×C4—24no—
457C22×C4—22no—
458C22×C4—24no—
459C22×C4—24no—
460C22×C4—24no—
461C22×C4—114no—
462C22×C4—118no—
463C22×C4—112no—
464C22×C4—118no—
465C22×C4—114no—
466C22×C4—1116no—
467C22×C4—114no—
468C22×C4—112no—
469C22×C4—2232no—
470C22×C4—2216no—
471C22×C4—2216no—
472C22×C4—2216no—
473C22×C4—2216no—
474C22×C4—224no—
475C22×C4—224no—
476C22×C4—224no—
477C22×C4—224no—
478C22×C4—222no—
479C22×C4—224no—
480C22×C4—224no—
481C22×C4—4432no—
482C22×C4D4×D1118yes—
483C22×C4D4×D1114yes—
484C22×C4C23×D1114yes—
485C22×C4C23×D1112yes—
486C22×C4C23×D1112yes—
487C22×C4C23×D1114yes—
488C4⋊C4—28no—
489C4⋊C4—216no—
490C4⋊C4—2216no—
491C4⋊C4—228no—
492C4⋊C4—2216no—
493C4⋊C4—2216no—
494C4⋊C4—228no—
495C4⋊C4—2216no—
496C22⋊C4—28no—
497C22⋊C4—216no—
498C22⋊C4—1132no—
499C22⋊C4—2216no—
500C22⋊C4—2216no—
501C22⋊C4—228no—
502C22⋊C4—2216no—
503C42—2216no—
504C11C2×#250111yescharacteristic, complemented, Sylow
505C23—24no—
506C23—22no—
507C23—22no—
508C23—24no—
509C23—22no—
510C23—44no—
511C23—44no—
512C23—48no—
513C23—44no—
514C23—48no—
515C23—1116no—
516C23—118no—
517C23—114no—
518C23—228no—
519C23—2216no—
520C23—228no—
521C23—2216no—
522C23—222no—
523C23—224no—
524C23—222no—
525C23—224no—
526C23—222no—
527C23—222no—
528C23—224no—
529C23—222no—
530C23—444no—
531C23—444no—
532C23—448no—
533C23—444no—
534C23—448no—
535C23C2×D4×D1112yes—
536C23C2×D4×D1114yes—
537C23#6704012yes—
538C23#41×D1114yes—
539C23#6704312yes—
540C23C24×D1111yescharacteristic
541D4—4416no—
542D4—4416no—
543D4—4416no—
544C2×C4—28no—
545C2×C4—216no—
546C2×C4—24no—
547C2×C4—24no—
548C2×C4—24no—
549C2×C4—24no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—48no—
555C2×C4—44no—
556C2×C4—1116no—
557C2×C4—114no—
558C2×C4—118no—
559C2×C4—118no—
560C2×C4—2232no—
561C2×C4—2216no—
562C2×C4—224no—
563C2×C4—224no—
564C2×C4—224no—
565C2×C4—224no—
566C2×C4—222no—
567C2×C4—224no—
568C2×C4—224no—
569C2×C4—4432no—
570C2×C4—448no—
571C2×C4—444no—
572C2×C4C2×D4×D1118yes—
573C2×C4C2×D4×D1114yes—
574C22—42no—
575C22—42no—
576C22—44no—
577C22—44no—
578C22—42no—
579C22—88no—
580C22—118no—
581C22—224no—
582C22—2232no—
583C22—228no—
584C22—228no—
585C22—224no—
586C22—442no—
587C22—442no—
588C22—444no—
589C22—444no—
590C22—442no—
591C22—888no—
592C22#1062315914yes—
593C22#1062316218yes—
594C22D11×#12314yes—
595C22#1062318618yes—
596C22D11×#12714yes—
597C22C22×D4×D1111yescharacteristic
598C22C22×D4×D1112yes—
599C22C2×#6704011yescharacteristic
600C22C2×#41×D1112yes—
601C22C2×#6704311yescharacteristic
602C4—28no—
603C4—24no—
604C4—44no—
605C4—42no—
606C4—118no—
607C4—228no—
608C4—444no—
609C4—442no—
610C2—82no—
611C2—228no—
612C2—882no—
613C2#1307308218yesdirect product factor
614C2C2×D11×#12311yescharacteristic
615C2C2×D11×#12711yescharacteristic
616C2C2×#1062315911yescharacteristic
617C2C2×#1062318612yes—
618C2C2×#1062316212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C11×#399C2
socleC24×C11C24
prime radicalC22×#66937C2
hypercenterC2×#399D11
hypocenterC11C2×#2501
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#399

Complements

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

NH ≅ G/Ntype
1. C22×#66947C2semidirect
2. C22×#66936C2semidirect
4. C22×C4⋊C4×D11C2semidirect
5. #13073082C2direct (N × H)
6. C2×#10622290C2semidirect
7. C2×#10622562C2semidirect
8. C2×#10622605C2semidirect
9. C2×#10622570C2semidirect
10. C2×#10622589C2semidirect
11. C2×#10622279C2semidirect
12. C2×C11×#399C2semidirect
35. C2×#66947C22semidirect
37. C2×C4⋊C4×D11C22semidirect
41. C2×#66936C22semidirect
42. C11×#399C22semidirect
45. #10622605C22semidirect
46. #10622589C22semidirect
47. #10622570C22semidirect
48. #10622562C22semidirect
49. #10622290C22semidirect
50. #10622279C22semidirect
91. C2×(C2×D11)⋊C4D4semidirect
188. (C2×D11)⋊C4C2×D4semidirect
204. C2×#399D11semidirect
270. C2×Dic11#123semidirect
309. #399C2×D11semidirect
350. Dic11C2×#123semidirect
417. C2×C11#2501semidirect
504. C11C2×#2501semidirect
613. C2#13073082direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669472
C22×#669362
C22×#669372
C22×C4⋊C4×D112
#130730822
C2×#106222902
C2×#106225622
C2×#106226052
C2×#106225702
C2×#106225892
C2×#106222792
C2×C11×#3992
C2×#250111