Finite Group Databasebeta

← C2×#13073530 #14925510

Subgroups — C2×#13073530 #14925510

Order 2816.

4782 conjugacy classes of subgroups.

The subgroup lattice has 744 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C212yesmaximal, complemented
2C22×#66991C211yesmaximal, characteristic, complemented
3C22×D4×Dic11C211yesmaximal, characteristic, complemented
4C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
5#13073530C2116yesmaximal, direct product factor
6C2×#10622572C212yesmaximal, complemented
7C2×#10622835C212yesmaximal, complemented
8C2×#10622589C211yesmaximal, characteristic, complemented
9C2×#10622825C211yesmaximal, characteristic, complemented
10C2×#10622555C212yesmaximal, complemented
11C2×#10622600C211yesmaximal, characteristic, complemented
12C22×C11×#121C211yesmaximal, characteristic, complemented
13C23×D4×C11C2212yes—
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C23×C22⋊D11C2212yes—
17C23×C22⋊D11C2211yescharacteristic
18C24×Dic11C2212yes—
19C23×C4×D11C2211yescharacteristic
20C2×C11×#121—28no—
21C2×C11×#121C2218yescomplemented
22C22×C11×C4⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C2×#66992—216no—
29C2×#66992C22116yescomplemented
30C2×#66991—28no—
31C2×#66991C2218yescomplemented
32C2×D4×Dic11—28no—
33C2×D4×Dic11C2218yescomplemented
34C2×C4×C22⋊D11—28no—
35C2×C4×C22⋊D11C2218yescomplemented
36C22×(C2×D11)⋊C4C2212yes—
37C22×(C2×D11)⋊C4C2211yescharacteristic
38C22×C4⋊Dic11C2211yescharacteristic
39C22×C4⋊Dic11C2211yescharacteristic
40C22×Dic11⋊C4C2211yescharacteristic
41C22×Dic11⋊C4C2212yes—
42C22×Dic11⋊C4C2212yes—
43C22×C4×Dic11C2211yescharacteristic
44#10622835C22116yescomplemented
45#10622825C2218yescomplemented
46C2×C11⋊#95C2212yes—
47C2×C11⋊#95C2212yes—
48#10622600C2218yescomplemented
49#10622589C2218yescomplemented
50#10622572C22116yescomplemented
51#10622555C22116yescomplemented
52C25×C11C2311yescharacteristic
53C25×C11C2312yes—
54C24×D11C2311yescharacteristic
55C22×D4×C11—28no—
56C22×D4×C11—28no—
57C22×D4×C11—24no—
58C22×D4×C11—24no—
59C22×D4×C11—44no—
60C22×D4×C11D418yescomplemented
61C22×D4×C11C2318yes—
62C22×D4×C11C2314yes—
63C23×C4×C11—24no—
64C23×C4×C11—24no—
65C23×C4×C11—24no—
66C23×C4×C11C2312yes—
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2314yes—
69C23×C4×C11C2311yescharacteristic
70C22×C22⋊D11—28no—
71C22×C22⋊D11—28no—
72C22×C22⋊D11—24no—
73C22×C22⋊D11—24no—
74C22×C22⋊D11—44no—
75C22×C22⋊D11D418yescomplemented
76C22×C22⋊D11C2318yes—
77C22×C22⋊D11C2314yes—
78C23×Dic11—28no—
79C23×Dic11—28no—
80C23×Dic11—28no—
81C23×Dic11C2312yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2312yes—
84C23×Dic11C2318yes—
85C23×Dic11C2311yescharacteristic
86C23×Dic11C2311yescharacteristic
87C22×C4×D11—24no—
88C22×C4×D11—24no—
89C22×C4×D11—24no—
90C22×C4×D11C2314yes—
91C11×#121—232no—
92C2×C11×C4⋊C4—24no—
93C2×C11×C4⋊C4C2314yes—
94C2×C11×C22⋊C4—28no—
95C2×C11×C22⋊C4C2318yes—
96C2×C22⋊Dic11—28no—
97C2×C22⋊Dic11—28no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—28no—
100C2×C22⋊Dic11C2314yes—
101C2×C22⋊Dic11C2318yes—
102C2×C22⋊Dic11C2318yes—
103C2×C22⋊Dic11C2318yes—
104#66992—264no—
105#66991—232no—
106D4×Dic11—232no—
107C4×C22⋊D11—232no—
108C2×(C2×D11)⋊C4—28no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4C2314yes—
111C2×(C2×D11)⋊C4C2318yes—
112C2×C4⋊Dic11—24no—
113C2×C4⋊Dic11—24no—
114C2×C4⋊Dic11C2314yes—
115C2×C4⋊Dic11C2314yes—
116C2×Dic11⋊C4—24no—
117C2×Dic11⋊C4—28no—
118C2×Dic11⋊C4—44no—
119C2×Dic11⋊C4C2314yes—
120C2×Dic11⋊C4C2318yes—
121C2×Dic11⋊C4C2318yes—
122C2×C4×Dic11D418yescomplemented
123C2×C4×Dic11C2314yes—
124C11⋊#95C2318yes—
125C11⋊#95C2318yes—
126C2×#2537—111nomaximal, Sylow
127C24×C11—24no—
128C24×C11—22no—
129C24×C11—24no—
130C24×C11—22no—
131C24×C11—24no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—24no—
135C24×C11—24no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—24no—
139C24×C11C2×D414yes—
140C24×C11C2×D418yes—
141C24×C11C2412yes—
142C24×C11C2414yes—
143C24×C11C2411yescharacteristic
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11C2×D414yes—
151C23×D11C2412yes—
152C2×D4×C11—216no—
153C2×D4×C11—216no—
154C2×D4×C11—232no—
155C2×D4×C11—28no—
156C2×D4×C11—28no—
157C2×D4×C11—48no—
158C2×D4×C11—432no—
159C2×D4×C11C2×D4116yescomplemented
160C22×C4×C11—22no—
161C22×C4×C11—24no—
162C22×C4×C11—22no—
163C22×C4×C11—24no—
164C22×C4×C11—22no—
165C22×C4×C11—24no—
166C22×C4×C11—28no—
167C22×C4×C11—28no—
168C22×C4×C11—28no—
169C22×C4×C11—416no—
170C22×C4×C11C2×D414yes—
171C22×C4×C11C2×D414yes—
172C22×C4×C11#4114yes—
173C22×C4×C11C2412yes—
174C22×C4×C11C2414yes—
175C22×C4×C11C2412yes—
176C2×C22⋊D11—232no—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—216no—
180C2×C22⋊D11—216no—
181C2×C22⋊D11—48no—
182C2×C22⋊D11—432no—
183C2×C22⋊D11C2×D4116yescomplemented
184C22×Dic11—216no—
185C22×Dic11—216no—
186C22×Dic11—216no—
187C22×Dic11—22no—
188C22×Dic11—24no—
189C22×Dic11—24no—
190C22×Dic11—24no—
191C22×Dic11—24no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—24no—
195C22×Dic11—22no—
196C22×Dic11—24no—
197C22×Dic11—22no—
198C22×Dic11—432no—
199C22×Dic11C2×D414yes—
200C22×Dic11C2×D414yes—
201C22×Dic11C2×D414yes—
202C22×Dic11#4114yes—
203C22×Dic11C2412yes—
204C22×Dic11C2414yes—
205C22×Dic11C2414yes—
206C22×Dic11C2412yes—
207C22×Dic11C2412yes—
208C2×C4×D11—28no—
209C2×C4×D11—28no—
210C2×C4×D11—28no—
211C2×C4×D11—416no—
212C11×C4⋊C4—28no—
213C11×C22⋊C4—216no—
214C22⋊Dic11—28no—
215C22⋊Dic11—216no—
216C22⋊Dic11—216no—
217C22⋊Dic11—216no—
218(C2×D11)⋊C4—28no—
219(C2×D11)⋊C4—216no—
220C4⋊Dic11—28no—
221C4⋊Dic11—28no—
222Dic11⋊C4—28no—
223Dic11⋊C4—216no—
224Dic11⋊C4—48no—
225C4×Dic11C2×D4116yescomplemented
226C22×#121—111no—
227C22×#121—112no—
228C22×#121D1111yescharacteristic, complemented
229C22×C4×D4—111no—
230C22×C4×D4—111no—
231#2537—1116no—
232C2×#394—112no—
233C2×#394—112no—
234C2×#384—111no—
235C2×#380—111no—
236C2×#380—111no—
237C2×#380—112no—
238C23×C11—28no—
239C23×C11—216no—
240C23×C11—216no—
241C23×C11—28no—
242C23×C11—216no—
243C23×C11—28no—
244C23×C11—24no—
245C23×C11—22no—
246C23×C11—24no—
247C23×C11—22no—
248C23×C11—24no—
249C23×C11—22no—
250C23×C11—22no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—22no—
254C23×C11—22no—
255C23×C11—24no—
256C23×C11—48no—
257C23×C11—44no—
258C23×C11—48no—
259C23×C11—44no—
260C23×C11—44no—
261C23×C11—48no—
262C23×C11—48no—
263C23×C11—44no—
264C23×C11C22×D414yes—
265C23×C11C22×D412yes—
266C23×C11C22×D412yes—
267C23×C11C22×D418yes—
268C23×C11C22×D412yes—
269C23×C11C2×#4112yes—
270C23×C11C2×#4112yes—
271C23×C11H(5,𝔽2)12yes—
272C23×C112−1+412yes—
273C23×C11C2511yescharacteristic
274C22×D11—28no—
275C22×D11—28no—
276C22×D11—28no—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—44no—
284C22×D11—44no—
285C22×D11—44no—
286C22×D11—44no—
287C22×D11C22×D414yes—
288D4×C11—232no—
289D4×C11—432no—
290C2×C4×C11—22no—
291C2×C4×C11—24no—
292C2×C4×C11—22no—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—24no—
296C2×C4×C11—44no—
297C2×C4×C11—48no—
298C2×C4×C11—416no—
299C2×C4×C11#121116yescomplemented
300C2×C4×C11C22×D414yes—
301C2×C4×C11C22×D414yes—
302C2×C4×C11C2×#4114yes—
303C22⋊D11—232no—
304C22⋊D11—432no—
305C2×Dic11—28no—
306C2×Dic11—22no—
307C2×Dic11—22no—
308C2×Dic11—22no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—24no—
316C2×Dic11—24no—
317C2×Dic11—44no—
318C2×Dic11—48no—
319C2×Dic11—48no—
320C2×Dic11—432no—
321C2×Dic11#121116yescomplemented
322C2×Dic11C22×D414yes—
323C2×Dic11C22×D414yes—
324C2×Dic11C22×D414yes—
325C2×Dic11C2×#4114yes—
326C4×D11—416no—
327C23×D4—111no—
328C23×D4—112no—
329C23×D4C2×D1112yes—
330C23×D4C2×D1111yescharacteristic
331C24×C4—112no—
332C24×C4—111no—
333C24×C4C2×D1111yescharacteristic
334C2×#121—28no—
335C2×#121—118no—
336C2×#121—1116no—
337C2×#121—2216no—
338C2×#121—228no—
339C2×#121C2×D1118yescomplemented
340C2×C4×D4—118no—
341C2×C4×D4—118no—
342C2×C4×D4—228no—
343C2×C4×D4—228no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—112no—
346C22×C4⋊C4—111no—
347C22×C4⋊C4—111no—
348C22×C4⋊C4—112no—
349C22×C4⋊C4C2×D1111yescharacteristic
350C22×C22⋊C4—111no—
351C22×C22⋊C4—112no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—111no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4C2×D1112yes—
357C22×C42—111no—
358#394—1116no—
359#394—1116no—
360#384—118no—
361#380—118no—
362#380—118no—
363#380—1116no—
364C2×#95—112no—
365C2×#95—112no—
366C22×C11—28no—
367C22×C11—24no—
368C22×C11—24no—
369C22×C11—28no—
370C22×C11—28no—
371C22×C11—24no—
372C22×C11—42no—
373C22×C11—44no—
374C22×C11—44no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—44no—
378C22×C11—44no—
379C22×C11—42no—
380C22×C11—416no—
381C22×C11—432no—
382C22×C11C2×#12114yes—
383C22×C11C2×#12114yes—
384C22×C11#53714yes—
385C22×C11D4214yes—
386C22×C11#54714yes—
387C22×C11#54714yes—
388C22×C11#55514yes—
389C22×C11C23×D411yescharacteristic
390C22×C11C23×D411yescharacteristic
391C22×C11C23×D411yescharacteristic
392C22×C11C22×#4111yescharacteristic
393C22×C11C22×#4111yescharacteristic
394C22×C11C2×H(5,𝔽2)11yescharacteristic
395C22×C11C2×2−1+411yescharacteristic
396C2×D11—24no—
397C2×D11—24no—
398C2×D11—24no—
399C2×D11—42no—
400C2×D11—42no—
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—416no—
404C4×C11—42no—
405C4×C11—44no—
406C4×C11C2×#12118yescomplemented
407Dic11—24no—
408Dic11—42no—
409Dic11—44no—
410Dic11—44no—
411Dic11C2×#12118yescomplemented
412C25—111no—
413C25C22×D1111yescharacteristic
414C25C22×D1112yes—
415C22×D4—28no—
416C22×D4—28no—
417C22×D4—24no—
418C22×D4—24no—
419C22×D4—44no—
420C22×D4—118no—
421C22×D4—114no—
422C22×D4—118no—
423C22×D4—224no—
424C22×D4—224no—
425C22×D4—228no—
426C22×D4—228no—
427C22×D4—444no—
428C22×D4C22⋊D1118yescomplemented
429C22×D4C22×D1118yes—
430C22×D4C22×D1114yes—
431C23×C4—24no—
432C23×C4—24no—
433C23×C4—24no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—118no—
437C23×C4—112no—
438C23×C4—111no—
439C23×C4—112no—
440C23×C4—114no—
441C23×C4—228no—
442C23×C4—228no—
443C23×C4—228no—
444C23×C4—224no—
445C23×C4—224no—
446C23×C4—224no—
447C23×C4C22×D1114yes—
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1112yes—
450C23×C4C22×D1111yescharacteristic
451#121—232no—
452#121—2264no—
453#121—2232no—
454C4×D4—2232no—
455C4×D4—2232no—
456C2×C4⋊C4—24no—
457C2×C4⋊C4—114no—
458C2×C4⋊C4—114no—
459C2×C4⋊C4—118no—
460C2×C4⋊C4—114no—
461C2×C4⋊C4—118no—
462C2×C4⋊C4—224no—
463C2×C4⋊C4—228no—
464C2×C4⋊C4—224no—
465C2×C4⋊C4—224no—
466C2×C4⋊C4—444no—
467C2×C4⋊C4C22×D1114yes—
468C2×C22⋊C4—28no—
469C2×C22⋊C4—114no—
470C2×C22⋊C4—118no—
471C2×C22⋊C4—118no—
472C2×C22⋊C4—118no—
473C2×C22⋊C4—114no—
474C2×C22⋊C4—118no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—228no—
477C2×C22⋊C4—224no—
478C2×C22⋊C4—228no—
479C2×C22⋊C4—228no—
480C2×C22⋊C4—228no—
481C2×C22⋊C4C22×D1118yes—
482C2×C42—118no—
483C2×C42—114no—
484#95—118no—
485#95—118no—
486C2×C11—48no—
487C2×C11—44no—
488C2×C11#253718yescomplemented
489C2×C11C22×#12111yescharacteristic
490C2×C11C22×#12111yescharacteristic
491C2×C11C2×#53711yescharacteristic
492C2×C11C2×D4211yescharacteristic
493C2×C11C2×#54711yescharacteristic
494C2×C11C2×#54711yescharacteristic
495C2×C11C2×#55511yescharacteristic
496D11—44no—
497C24—22no—
498C24—24no—
499C24—24no—
500C24—22no—
501C24—24no—
502C24—22no—
503C24—24no—
504C24—24no—
505C24—22no—
506C24—24no—
507C24—22no—
508C24—22no—
509C24—114no—
510C24—112no—
511C24—222no—
512C24—222no—
513C24—222no—
514C24—222no—
515C24—222no—
516C24—222no—
517C24D4×D1114yes—
518C24C2×C22⋊D1118yes—
519C24C23×D1112yes—
520C24C23×D1114yes—
521C24C23×D1111yescharacteristic
522C2×D4—216no—
523C2×D4—216no—
524C2×D4—232no—
525C2×D4—28no—
526C2×D4—28no—
527C2×D4—48no—
528C2×D4—432no—
529C2×D4—1116no—
530C2×D4—228no—
531C2×D4—2232no—
532C2×D4—228no—
533C2×D4—2216no—
534C2×D4—2216no—
535C2×D4—448no—
536C2×D4—4432no—
537C2×D4C2×C22⋊D11116yescomplemented
538C22×C4—22no—
539C22×C4—24no—
540C22×C4—22no—
541C22×C4—24no—
542C22×C4—22no—
543C22×C4—24no—
544C22×C4—28no—
545C22×C4—28no—
546C22×C4—28no—
547C22×C4—416no—
548C22×C4—114no—
549C22×C4—114no—
550C22×C4—114no—
551C22×C4—112no—
552C22×C4—114no—
553C22×C4—112no—
554C22×C4—114no—
555C22×C4—112no—
556C22×C4—114no—
557C22×C4—2216no—
558C22×C4—2216no—
559C22×C4—2216no—
560C22×C4—222no—
561C22×C4—222no—
562C22×C4—224no—
563C22×C4—222no—
564C22×C4—224no—
565C22×C4—224no—
566C22×C4—222no—
567C22×C4—224no—
568C22×C4—224no—
569C22×C4—222no—
570C22×C4—224no—
571C22×C4—228no—
572C22×C4—228no—
573C22×C4—228no—
574C22×C4—4432no—
575C22×C4—4416no—
576C22×C4D4×D1114yes—
577C22×C4#434114yes—
578C22×C4C2×C22⋊D1114yes—
579C22×C4C23×D1112yes—
580C22×C4C23×D1114yes—
581C22×C4C23×D1112yes—
582C4⋊C4—28no—
583C4⋊C4—228no—
584C4⋊C4—2216no—
585C4⋊C4—228no—
586C4⋊C4—228no—
587C4⋊C4—448no—
588C22⋊C4—216no—
589C22⋊C4—228no—
590C22⋊C4—2216no—
591C22⋊C4—228no—
592C22⋊C4—2216no—
593C22⋊C4—2216no—
594C22⋊C4—2216no—
595C42—1116no—
596C11C2×#253711yescharacteristic, complemented, Sylow
597C23—28no—
598C23—216no—
599C23—216no—
600C23—216no—
601C23—28no—
602C23—28no—
603C23—22no—
604C23—24no—
605C23—24no—
606C23—22no—
607C23—24no—
608C23—22no—
609C23—24no—
610C23—24no—
611C23—22no—
612C23—24no—
613C23—22no—
614C23—22no—
615C23—44no—
616C23—44no—
617C23—48no—
618C23—44no—
619C23—48no—
620C23—48no—
621C23—44no—
622C23—48no—
623C23—114no—
624C23—228no—
625C23—228no—
626C23—228no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—444no—
634C23—444no—
635C23—444no—
636C23—444no—
637C23C2×D4×D1114yes—
638C23C2×D4×D1112yes—
639C23C2×D4×D1112yes—
640C23C2×#434112yes—
641C23#6703712yes—
642C23#41×D1112yes—
643C23#6704312yes—
644C23C22×C22⋊D1118yes—
645C23C22×C22⋊D1112yes—
646C23C24×D1111yescharacteristic
647D4—232no—
648D4—432no—
649D4—2232no—
650D4—4432no—
651C2×C4—22no—
652C2×C4—24no—
653C2×C4—22no—
654C2×C4—24no—
655C2×C4—22no—
656C2×C4—24no—
657C2×C4—48no—
658C2×C4—44no—
659C2×C4—416no—
660C2×C4—1116no—
661C2×C4—114no—
662C2×C4—114no—
663C2×C4—114no—
664C2×C4—114no—
665C2×C4—228no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—224no—
669C2×C4—224no—
670C2×C4—222no—
671C2×C4—224no—
672C2×C4—222no—
673C2×C4—224no—
674C2×C4—224no—
675C2×C4—222no—
676C2×C4—224no—
677C2×C4—4432no—
678C2×C4—448no—
679C2×C4—444no—
680C2×C4—448no—
681C2×C4—4416no—
682C2×C4#66992116yescomplemented
683C2×C4C2×D4×D1114yes—
684C2×C4C2×#434114yes—
685C2×C4C22×C22⋊D1114yes—
686C22—24no—
687C22—28no—
688C22—28no—
689C22—24no—
690C22—24no—
691C22—28no—
692C22—42no—
693C22—44no—
694C22—42no—
695C22—44no—
696C22—416no—
697C22—432no—
698C22—42no—
699C22—44no—
700C22—44no—
701C22—42no—
702C22—224no—
703C22—224no—
704C22—224no—
705C22—442no—
706C22—442no—
707C22—4416no—
708C22—442no—
709C22—442no—
710C22D11×#12114yes—
711C22#1062313914yes—
712C22#1062314214yes—
713C22#1062314714yes—
714C22D4×C22⋊D1114yes—
715C22C2×#6699214yes—
716C22#1062335514yes—
717C22C22×D4×D1111yescharacteristic
718C22C22×D4×D1111yescharacteristic
719C22C22×#434111yescharacteristic
720C22C2×#6703711yescharacteristic
721C22C2×#41×D1111yescharacteristic
722C22C2×#6704311yescharacteristic
723C22C23×C22⋊D1111yescharacteristic
724C4—44no—
725C4—42no—
726C4—118no—
727C4—224no—
728C4—444no—
729C4—444no—
730C4—442no—
731C4C2×#6699218yescomplemented
732C2—44no—
733C2—48no—
734C2—444no—
735C2#1307353018yesdirect product factor
736C2C2×D11×#12111yescharacteristic
737C2C22×#6699211yescharacteristic
738C2C2×#1062313911yescharacteristic
739C2C2×D4×C22⋊D1111yescharacteristic
740C2C2×#1062335511yescharacteristic
741C2C2×#1062314211yescharacteristic
742C2C2×#1062314711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C2×#2537
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×#66991C2semidirect
3. C22×D4×Dic11C2semidirect
4. C22×C4×C22⋊D11C2semidirect
5. #13073530C2direct (N × H)
6. C2×#10622572C2semidirect
7. C2×#10622835C2semidirect
8. C2×#10622589C2semidirect
9. C2×#10622825C2semidirect
10. C2×#10622555C2semidirect
11. C2×#10622600C2semidirect
12. C22×C11×#121C2semidirect
21. C2×C11×#121C22semidirect
29. C2×#66992C22semidirect
31. C2×#66991C22semidirect
33. C2×D4×Dic11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
44. #10622835C22semidirect
45. #10622825C22semidirect
48. #10622600C22semidirect
49. #10622589C22semidirect
50. #10622572C22semidirect
51. #10622555C22semidirect
60. C22×D4×C11D4semidirect
75. C22×C22⋊D11D4semidirect
122. C2×C4×Dic11D4semidirect
159. C2×D4×C11C2×D4semidirect
183. C2×C22⋊D11C2×D4semidirect
225. C4×Dic11C2×D4semidirect
228. C22×#121D11semidirect
299. C2×C4×C11#121semidirect
321. C2×Dic11#121semidirect
339. C2×#121C2×D11semidirect
406. C4×C11C2×#121semidirect
411. Dic11C2×#121semidirect
428. C22×D4C22⋊D11semidirect
488. C2×C11#2537semidirect
537. C2×D4C2×C22⋊D11semidirect
596. C11C2×#2537semidirect
682. C2×C4#66992semidirect
731. C4C2×#66992semidirect
735. C2#13073530direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×#669912
C22×D4×Dic112
C22×C4×C22⋊D112
#130735302
C2×#106225722
C2×#106228352
C2×#106225892
C2×#106228252
C2×#106225552
C2×#106226002
C22×C11×#1212
C2×#253711