Finite Group Databasebeta

← C2×#13073546 #14923808

Subgroups — C2×#13073546 #14923808

Order 2816.

5726 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66982C211yesmaximal, characteristic, complemented
2C22×#66992C211yesmaximal, characteristic, complemented
3C22×#66935C211yesmaximal, characteristic, complemented
4C22×#66990C211yesmaximal, characteristic, complemented
5C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13073546C2116yesmaximal, direct product factor
7C2×#10622605C212yesmaximal, complemented
8C2×#10622573C212yesmaximal, complemented
9C2×#10622601C212yesmaximal, complemented
10C2×#10622570C212yesmaximal, complemented
11C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C22×C11×#123C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2211yescharacteristic
17C23×C22⋊D11C2212yes—
18C23×C22⋊D11C2211yescharacteristic, complemented
19C24×Dic11C2211yescharacteristic
20C23×D44C2212yes—
21C2×C11×#123—28no—
22C2×C11×#123C2218yescomplemented
23C22×C11×C4⋊C4C2212yescomplemented
24C22×C11×C22⋊C4C2211yescharacteristic
25C22×C11×C22⋊C4C2212yescomplemented
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2211yescharacteristic, complemented
28C2×#66992—28no—
29C2×#66992C2218yescomplemented
30C2×#66990—28no—
31C2×#66990C2218yescomplemented
32C2×#66982—28no—
33C2×#66982C2218yescomplemented
34C22×(C2×D11)⋊C4—28no—
35C22×(C2×D11)⋊C4C2212yes—
36C22×(C2×D11)⋊C4C2212yes—
37C22×(C2×D11)⋊C4C2212yes—
38C22×(C2×D11)⋊C4C2212yes—
39C22×(C2×D11)⋊C4C2218yescomplemented
40C22×(C2×D11)⋊C4C2212yescomplemented
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×Dic11⋊C4C2212yescomplemented
43C22×Dic11⋊C4C2211yescharacteristic, complemented
44C22×C4×Dic11C2212yescomplemented
45C2×#66935—28no—
46C2×#66935C2218yescomplemented
47C2×C11⋊#95C2212yescomplemented
48#10622605C22116yescomplemented
49#10622601C22116yescomplemented
50#10622573C22116yescomplemented
51#10622570C22116yescomplemented
52C22⋊C4×Dic11C2218yescomplemented
53C25×C11C2311yescharacteristic
54C25×C11C2311yescharacteristic
55C24×D11—24no—
56C24×D11—28no—
57C24×D11—24no—
58C24×D11—24no—
59C24×D11—44no—
60C24×D11C2311yescharacteristic
61C24×D11C2312yes—
62C24×D11C2314yes—
63C22×D4×C11—24no—
64C22×D4×C11—24no—
65C22×D4×C11—24no—
66C22×D4×C11C2314yes—
67C23×C4×C11—24no—
68C23×C4×C11—24no—
69C23×C4×C11—24no—
70C23×C4×C11C2312yes—
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2314yes—
73C23×C4×C11C2312yes—
74C22×C22⋊D11—24no—
75C22×C22⋊D11—24no—
76C22×C22⋊D11—24no—
77C22×C22⋊D11—28no—
78C22×C22⋊D11—28no—
79C22×C22⋊D11—24no—
80C22×C22⋊D11—44no—
81C22×C22⋊D11—44no—
82C22×C22⋊D11C2314yes—
83C22×C22⋊D11C2318yes—
84C22×C22⋊D11C2314yescomplemented
85C23×Dic11—44no—
86C23×Dic11D418yescomplemented
87C23×Dic11C2311yescharacteristic
88C23×Dic11C2311yescharacteristic
89C23×Dic11C2312yes—
90C23×Dic11C2311yescharacteristic
91C23×Dic11C2314yes—
92C22×D44—28no—
93C22×D44—28no—
94C22×D44—44no—
95C22×D44C2318yes—
96C11×#123—232no—
97C2×C11×C4⋊C4—28no—
98C2×C11×C4⋊C4C2318yescomplemented
99C2×C11×C22⋊C4—28no—
100C2×C11×C22⋊C4D418yescomplemented
101C2×C11×C22⋊C4C2314yes—
102C2×C11×C22⋊C4C2318yescomplemented
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11D418yescomplemented
105C2×C22⋊Dic11C2314yes—
106C2×C22⋊Dic11C2314yescomplemented
107#66992—232no—
108#66990—232no—
109#66982—232no—
110C2×(C2×D11)⋊C4—28no—
111C2×(C2×D11)⋊C4—28no—
112C2×(C2×D11)⋊C4—28no—
113C2×(C2×D11)⋊C4—28no—
114C2×(C2×D11)⋊C4—28no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—232no—
117C2×(C2×D11)⋊C4C2318yes—
118C2×(C2×D11)⋊C4C2318yes—
119C2×(C2×D11)⋊C4C2318yes—
120C2×(C2×D11)⋊C4C2318yes—
121C2×(C2×D11)⋊C4C2318yescomplemented
122C2×(C2×D11)⋊C4C2314yescomplemented
123C2×Dic11⋊C4—28no—
124C2×Dic11⋊C4—24no—
125C2×Dic11⋊C4C2318yescomplemented
126C2×Dic11⋊C4C2314yescomplemented
127C2×C4×Dic11—44no—
128C2×C4×Dic11C2318yescomplemented
129#66935—232no—
130C11⋊#95C2318yescomplemented
131C2×#2539—111nomaximal, Sylow
132C24×C11—24no—
133C24×C11—24no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—24no—
138C24×C11—24no—
139C24×C11C2×D414yes—
140C24×C11C2×D414yes—
141C24×C11C2×D414yes—
142C24×C11C2412yes—
143C24×C11C2412yes—
144C24×C11C2411yescharacteristic
145C23×D11—232no—
146C23×D11—28no—
147C23×D11—24no—
148C23×D11—24no—
149C23×D11—24no—
150C23×D11—24no—
151C23×D11—24no—
152C23×D11—24no—
153C23×D11—216no—
154C23×D11—28no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—28no—
158C23×D11—22no—
159C23×D11—24no—
160C23×D11—24no—
161C23×D11—48no—
162C23×D11—432no—
163C23×D11—432no—
164C23×D11—416no—
165C23×D11—416no—
166C23×D11#4118yes—
167C23×D11C2412yes—
168C23×D11C2414yes—
169C2×D4×C11—28no—
170C2×D4×C11—28no—
171C2×D4×C11—28no—
172C2×D4×C11—416no—
173C22×C4×C11—24no—
174C22×C4×C11—24no—
175C22×C4×C11—24no—
176C22×C4×C11—22no—
177C22×C4×C11—28no—
178C22×C4×C11—24no—
179C22×C4×C11—22no—
180C22×C4×C11—28no—
181C22×C4×C11—24no—
182C22×C4×C11—22no—
183C22×C4×C11—28no—
184C22×C4×C11—416no—
185C22×C4×C11C2×D418yes—
186C22×C4×C11C2414yes—
187C22×C4×C11C2412yes—
188C22×C4×C11C2414yes—
189C2×C22⋊D11—216no—
190C2×C22⋊D11—28no—
191C2×C22⋊D11—28no—
192C2×C22⋊D11—28no—
193C2×C22⋊D11—28no—
194C2×C22⋊D11—216no—
195C2×C22⋊D11—48no—
196C2×C22⋊D11—48no—
197C2×C22⋊D11—432no—
198C2×C22⋊D11—416no—
199C2×C22⋊D11—416no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—24no—
204C22×Dic11—24no—
205C22×Dic11—24no—
206C22×Dic11—24no—
207C22×Dic11—416no—
208C22×Dic11—48no—
209C22×Dic11C2×D418yes—
210C22×Dic11C2×D414yes—
211C22×Dic11C2×D414yes—
212C22×Dic11C2×D4116yescomplemented
213C22×Dic11C2412yes—
214C22×Dic11C2412yes—
215C22×Dic11C2414yes—
216C22×Dic11C2412yes—
217C2×D44—216no—
218C2×D44—216no—
219C2×D44—48no—
220C2×D44—432no—
221C11×C4⋊C4—216no—
222C11×C22⋊C4—216no—
223C11×C22⋊C4C2×D4116yescomplemented
224C22⋊Dic11—28no—
225C22⋊Dic11C2×D4116yescomplemented
226(C2×D11)⋊C4—216no—
227(C2×D11)⋊C4—216no—
228(C2×D11)⋊C4—216no—
229(C2×D11)⋊C4—216no—
230(C2×D11)⋊C4—28no—
231(C2×D11)⋊C4—216no—
232Dic11⋊C4—216no—
233Dic11⋊C4—28no—
234C4×Dic11—48no—
235C22×#123—111no—
236C22×#123D1111yescharacteristic, complemented
237C22×#121—111no—
238C22×#120—111no—
239C22×#120—111no—
240C23×C22⋊C4—111no—
241#2539—1116no—
242C2×#399—112no—
243C2×#392—112no—
244C2×#390—112no—
245C2×#390—112no—
246C2×C4×C22⋊C4—111no—
247C23×C11—28no—
248C23×C11—28no—
249C23×C11—216no—
250C23×C11—216no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—44no—
259C23×C11—44no—
260C23×C11—44no—
261C23×C11—48no—
262C23×C11—48no—
263C23×C11#127116yes—
264C23×C11C22×D414yes—
265C23×C11C22×D414yes—
266C23×C11C22×D412yes—
267C23×C11C22×D412yes—
268C23×C11C22×D414yes—
269C23×C11C22×D412yes—
270C23×C11C2×#4114yes—
271C23×C11H(5,𝔽2)14yes—
272C23×C11C2511yescharacteristic
273C22×D11—232no—
274C22×D11—216no—
275C22×D11—216no—
276C22×D11—216no—
277C22×D11—24no—
278C22×D11—24no—
279C22×D11—24no—
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—24no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—432no—
289C22×D11—432no—
290C22×D11—416no—
291C22×D11—4128no—
292C22×D11—416no—
293C22×D11—48no—
294C22×D11—48no—
295C22×D11—48no—
296C22×D11—48no—
297C22×D11—44no—
298C22×D11—44no—
299C22×D11—44no—
300C22×D11—48no—
301C22×D11—48no—
302C22×D11C2×#4118yes—
303D4×C11—416no—
304C2×C4×C11—216no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—22no—
309C2×C4×C11—24no—
310C2×C4×C11—22no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—416no—
314C2×C4×C11—48no—
315C2×C4×C11—44no—
316C2×C4×C11C22×D418yes—
317C22⋊D11—432no—
318C22⋊D11—416no—
319C22⋊D11—416no—
320C2×Dic11—28no—
321C2×Dic11—28no—
322C2×Dic11—216no—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—416no—
331C2×Dic11—44no—
332C2×Dic11C22×D418yes—
333C2×Dic11C22×D414yes—
334C2×Dic11C22×D414yes—
335D44—432no—
336C26—111no—
337C23×D4—111no—
338C23×D4—112no—
339C23×D4—111no—
340C23×D4—112no—
341C23×D4C2×D1111yescharacteristic
342C24×C4—111no—
343C24×C4C2×D1111yescharacteristic
344C2×#123—28no—
345C2×#123—118no—
346C2×#123—228no—
347C2×#123C2×D1118yescomplemented
348C2×#121—118no—
349C2×#121—228no—
350C2×#120—118no—
351C2×#120—118no—
352C2×#120—228no—
353C2×#120—228no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4—112no—
356C22×C4⋊C4C2×D1112yescomplemented
357C22×C22⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—112no—
360C22×C22⋊C4—112no—
361C22×C22⋊C4—112no—
362C22×C22⋊C4—112no—
363C22×C22⋊C4—112no—
364C22×C22⋊C4—118no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—228no—
367C22×C22⋊C4C2×D1111yescharacteristic
368C22×C22⋊C4C2×D1112yescomplemented
369C22×C42—112no—
370#399—1116no—
371#392—1116no—
372#390—1116no—
373#390—1116no—
374C4×C22⋊C4—118no—
375C2×#95—112no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—28no—
379C22×C11—28no—
380C22×C11—232no—
381C22×C11—42no—
382C22×C11—42no—
383C22×C11—42no—
384C22×C11—44no—
385C22×C11—44no—
386C22×C11—88no—
387C22×C11#52514yes—
388C22×C11C2×#12718yes—
389C22×C11C2×#12714yes—
390C22×C11#53414yes—
391C22×C11#54618yes—
392C22×C11#54618yes—
393C22×C11C23×D411yescharacteristic
394C22×C11C23×D411yescharacteristic
395C22×C11C23×D411yescharacteristic
396C22×C11C22×#4112yes—
397C22×C11C2×H(5,𝔽2)12yes—
398C2×D11—28no—
399C2×D11—28no—
400C2×D11—28no—
401C2×D11—464no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—432no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—44no—
411C2×D11—44no—
412C2×D11—88no—
413C4×C11—28no—
414C4×C11—44no—
415C4×C11—42no—
416Dic11—24no—
417Dic11—24no—
418Dic11—28no—
419Dic11—42no—
420C25—112no—
421C25—111no—
422C25—114no—
423C25—228no—
424C25—224no—
425C25—224no—
426C25—224no—
427C25—444no—
428C25C22×D1111yescharacteristic
429C25C22×D1111yescharacteristic
430C22×D4—24no—
431C22×D4—24no—
432C22×D4—24no—
433C22×D4—114no—
434C22×D4—118no—
435C22×D4—114no—
436C22×D4—118no—
437C22×D4—228no—
438C22×D4—228no—
439C22×D4—224no—
440C22×D4—228no—
441C22×D4—224no—
442C22×D4—224no—
443C22×D4—224no—
444C22×D4—228no—
445C22×D4—444no—
446C22×D4—444no—
447C22×D4—444no—
448C22×D4C22×D1114yes—
449C23×C4—24no—
450C23×C4—24no—
451C23×C4—24no—
452C23×C4—111no—
453C23×C4—112no—
454C23×C4—111no—
455C23×C4—118no—
456C23×C4—114no—
457C23×C4—111no—
458C23×C4—444no—
459C23×C4C22×D1114yes—
460C23×C4C22×D1112yes—
461C23×C4C22×D1111yescharacteristic
462C23×C4C22×D1112yes—
463#123—232no—
464#123—2232no—
465#121—2232no—
466#120—2232no—
467#120—2232no—
468C2×C4⋊C4—28no—
469C2×C4⋊C4—114no—
470C2×C4⋊C4—118no—
471C2×C4⋊C4—224no—
472C2×C4⋊C4—228no—
473C2×C4⋊C4C22×D1118yescomplemented
474C2×C22⋊C4—28no—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—114no—
477C2×C22⋊C4—114no—
478C2×C22⋊C4—118no—
479C2×C22⋊C4—118no—
480C2×C22⋊C4—118no—
481C2×C22⋊C4—118no—
482C2×C22⋊C4—114no—
483C2×C22⋊C4—118no—
484C2×C22⋊C4—228no—
485C2×C22⋊C4—228no—
486C2×C22⋊C4—2232no—
487C2×C22⋊C4—228no—
488C2×C22⋊C4—224no—
489C2×C22⋊C4—228no—
490C2×C22⋊C4—224no—
491C2×C22⋊C4—228no—
492C2×C22⋊C4C22⋊D1118yescomplemented
493C2×C22⋊C4C22×D1114yes—
494C2×C22⋊C4C22×D1118yescomplemented
495C2×C42—118no—
496C2×C42—444no—
497#95—118no—
498C2×C11—28no—
499C2×C11—82no—
500C2×C11#253918yescomplemented
501C2×C11C2×#52511yescharacteristic
502C2×C11C22×#12711yescharacteristic
503C2×C11C2×#53411yescharacteristic
504C2×C11C2×#54612yes—
505C2×C11C2×#54612yes—
506D11—48no—
507D11—82no—
508C24—24no—
509C24—24no—
510C24—22no—
511C24—22no—
512C24—24no—
513C24—24no—
514C24—22no—
515C24—118no—
516C24—114no—
517C24—112no—
518C24—2216no—
519C24—2232no—
520C24—228no—
521C24—224no—
522C24—224no—
523C24—224no—
524C24—224no—
525C24—224no—
526C24—224no—
527C24—222no—
528C24—222no—
529C24—228no—
530C24—224no—
531C24—224no—
532C24—228no—
533C24—222no—
534C24—448no—
535C24—4432no—
536C24—4432no—
537C24—4416no—
538C24—4416no—
539C24D4×D1114yes—
540C24D4×D1114yes—
541C24C2×C22⋊D1114yes—
542C24C23×D1112yes—
543C24C23×D1112yes—
544C24C23×D1111yescharacteristic
545C2×D4—28no—
546C2×D4—28no—
547C2×D4—28no—
548C2×D4—416no—
549C2×D4—2216no—
550C2×D4—2216no—
551C2×D4—228no—
552C2×D4—2216no—
553C2×D4—228no—
554C2×D4—228no—
555C2×D4—228no—
556C2×D4—2216no—
557C2×D4—448no—
558C2×D4—4432no—
559C2×D4—448no—
560C2×D4—448no—
561C2×D4—4432no—
562C2×D4—4416no—
563C2×D4—4416no—
564C22×C4—24no—
565C22×C4—24no—
566C22×C4—28no—
567C22×C4—24no—
568C22×C4—22no—
569C22×C4—24no—
570C22×C4—22no—
571C22×C4—28no—
572C22×C4—24no—
573C22×C4—22no—
574C22×C4—28no—
575C22×C4—416no—
576C22×C4—118no—
577C22×C4—114no—
578C22×C4—114no—
579C22×C4—112no—
580C22×C4—114no—
581C22×C4—112no—
582C22×C4—1116no—
583C22×C4—112no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—222no—
589C22×C4—222no—
590C22×C4—222no—
591C22×C4—4416no—
592C22×C4—448no—
593C22×C4C2×C22⋊D1118yes—
594C22×C4C23×D1114yes—
595C22×C4C23×D1112yes—
596C22×C4C23×D1114yes—
597C4⋊C4—216no—
598C4⋊C4—228no—
599C4⋊C4—2216no—
600C22⋊C4—216no—
601C22⋊C4—1116no—
602C22⋊C4—2216no—
603C22⋊C4—2216no—
604C22⋊C4—2216no—
605C22⋊C4—228no—
606C22⋊C4—2216no—
607C22⋊C4—228no—
608C22⋊C4—2216no—
609C22⋊C4C2×C22⋊D11116yescomplemented
610C42—448no—
611C11C2×#253911yescharacteristic, complemented, Sylow
612C23—216no—
613C23—28no—
614C23—216no—
615C23—28no—
616C23—24no—
617C23—24no—
618C23—22no—
619C23—22no—
620C23—24no—
621C23—24no—
622C23—22no—
623C23—44no—
624C23—48no—
625C23—44no—
626C23—48no—
627C23—44no—
628C23—118no—
629C23—2232no—
630C23—2216no—
631C23—2216no—
632C23—2216no—
633C23—224no—
634C23—224no—
635C23—224no—
636C23—224no—
637C23—224no—
638C23—224no—
639C23—222no—
640C23—222no—
641C23—224no—
642C23—224no—
643C23—222no—
644C23—4432no—
645C23—4432no—
646C23—4416no—
647C23—44128no—
648C23—4416no—
649C23—448no—
650C23—448no—
651C23—448no—
652C23—448no—
653C23—444no—
654C23—448no—
655C23—444no—
656C23—448no—
657C23—444no—
658C23#66993116yes—
659C23C2×D4×D1114yes—
660C23C2×D4×D1114yes—
661C23C2×D4×D1112yes—
662C23C2×D4×D1112yes—
663C23#41×D1114yes—
664C23#6704214yes—
665C23C22×C22⋊D1114yes—
666C23C22×C22⋊D1112yes—
667C23C24×D1111yescharacteristic
668D4—416no—
669D4—4432no—
670D4—4432no—
671D4—4416no—
672D4—4416no—
673C2×C4—216no—
674C2×C4—24no—
675C2×C4—24no—
676C2×C4—24no—
677C2×C4—22no—
678C2×C4—24no—
679C2×C4—22no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—416no—
683C2×C4—48no—
684C2×C4—44no—
685C2×C4—118no—
686C2×C4—114no—
687C2×C4—114no—
688C2×C4—228no—
689C2×C4—228no—
690C2×C4—2216no—
691C2×C4—224no—
692C2×C4—224no—
693C2×C4—224no—
694C2×C4—224no—
695C2×C4—222no—
696C2×C4—222no—
697C2×C4—222no—
698C2×C4—4416no—
699C2×C4—444no—
700C2×C4C22×C22⋊D1118yes—
701C22—24no—
702C22—232no—
703C22—28no—
704C22—28no—
705C22—24no—
706C22—42no—
707C22—42no—
708C22—44no—
709C22—44no—
710C22—42no—
711C22—88no—
712C22—228no—
713C22—228no—
714C22—228no—
715C22—4464no—
716C22—444no—
717C22—444no—
718C22—4432no—
719C22—444no—
720C22—444no—
721C22—442no—
722C22—442no—
723C22—444no—
724C22—444no—
725C22—442no—
726C22—888no—
727C22#1062318414yes—
728C22#1062318518yes—
729C22#1062318714yes—
730C22C2×#6699318yes—
731C22C2×#6699314yes—
732C22#1062336018yes—
733C22C22×D4×D1111yescharacteristic
734C22C22×D4×D1111yescharacteristic
735C22C2×#41×D1112yes—
736C22C2×#6704212yes—
737C22C23×C22⋊D1111yescharacteristic
738C4—28no—
739C4—44no—
740C4—42no—
741C4—224no—
742C4—224no—
743C4—228no—
744C4—442no—
745C2—28no—
746C2—82no—
747C2—448no—
748C2—882no—
749C2#1307354618yesdirect product factor
750C2C2×#1062318711yescharacteristic
751C2C22×#6699311yescharacteristic
752C2C2×#1062318411yescharacteristic
753C2C2×#1062336012yes—
754C2C2×#1062318512yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#123C2
socleC24×C11C24
hypercenterC22×#123D11
hypocenterC11C2×#2539
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
2. C22×#66992C2semidirect
3. C22×#66935C2semidirect
4. C22×#66990C2semidirect
5. C23×(C2×D11)⋊C4C2semidirect
6. #13073546C2direct (N × H)
7. C2×#10622605C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622601C2semidirect
10. C2×#10622570C2semidirect
11. C2×C22⋊C4×Dic11C2semidirect
12. C22×C11×#123C2semidirect
18. C23×C22⋊D11C22semidirect
22. C2×C11×#123C22semidirect
23. C22×C11×C4⋊C4C22semidirect
25. C22×C11×C22⋊C4C22semidirect
27. C22×C22⋊Dic11C22semidirect
29. C2×#66992C22semidirect
31. C2×#66990C22semidirect
33. C2×#66982C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×Dic11⋊C4C22semidirect
43. C22×Dic11⋊C4C22semidirect
44. C22×C4×Dic11C22semidirect
46. C2×#66935C22semidirect
47. C2×C11⋊#95C22semidirect
48. #10622605C22semidirect
49. #10622601C22semidirect
50. #10622573C22semidirect
51. #10622570C22semidirect
52. C22⋊C4×Dic11C22semidirect
84. C22×C22⋊D11C23semidirect
86. C23×Dic11D4semidirect
98. C2×C11×C4⋊C4C23semidirect
100. C2×C11×C22⋊C4D4semidirect
102. C2×C11×C22⋊C4C23semidirect
104. C2×C22⋊Dic11D4semidirect
106. C2×C22⋊Dic11C23semidirect
121. C2×(C2×D11)⋊C4C23semidirect
122. C2×(C2×D11)⋊C4C23semidirect
125. C2×Dic11⋊C4C23semidirect
126. C2×Dic11⋊C4C23semidirect
128. C2×C4×Dic11C23semidirect
130. C11⋊#95C23semidirect
212. C22×Dic11C2×D4semidirect
223. C11×C22⋊C4C2×D4semidirect
225. C22⋊Dic11C2×D4semidirect
236. C22×#123D11semidirect
347. C2×#123C2×D11semidirect
356. C22×C4⋊C4C2×D11semidirect
368. C22×C22⋊C4C2×D11semidirect
473. C2×C4⋊C4C22×D11semidirect
492. C2×C22⋊C4C22⋊D11semidirect
494. C2×C22⋊C4C22×D11semidirect
500. C2×C11#2539semidirect
609. C22⋊C4C2×C22⋊D11semidirect
611. C11C2×#2539semidirect
749. C2#13073546direct (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
C22×#669352
C22×#669902
C23×(C2×D11)⋊C42
#130735462
C2×#106226052
C2×#106225732
C2×#106226012
C2×#106225702
C2×C22⋊C4×Dic112
C22×C11×#1232
C2×#253911