Finite Group Databasebeta

← C2×#13071986 #14921184

Subgroups — C2×#13071986 #14921184

Order 2816.

8730 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊D11C211yesmaximal, characteristic, complemented
2C22×#66991C212yesmaximal, complemented
3C22×#66990C211yesmaximal, characteristic, complemented
4C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
5#13071986C2116yesmaximal, direct product factor
6C2×#10622574C212yesmaximal, complemented
7C2×#10622836C212yesmaximal, complemented
8C2×#10622833C211yesmaximal, characteristic, complemented
9C2×#10622569C212yesmaximal, complemented
10C2×#10622563C211yesmaximal, characteristic, complemented
11C2×#10622860C211yesmaximal, characteristic, complemented
12C22×C11×#120C211yesmaximal, characteristic, complemented
13C26×C11C2211yescharacteristic
14C25×D11C2211yescharacteristic
15C23×D4×C11C2211yescharacteristic
16C23×D4×C11C2212yescomplemented
17C23×C22⋊D11—28no—
18C23×C22⋊D11—216no—
19C23×C22⋊D11C2212yes—
20C23×C22⋊D11C2212yes—
21C23×C22⋊D11C2218yescomplemented
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×C22⋊D11C2211yescharacteristic, complemented
24C24×Dic11C2211yescharacteristic
25C23×C4×D11C2212yescomplemented
26C2×C11×#120—28no—
27C2×C11×#120C2218yescomplemented
28C22×C11×C22⋊C4C2211yescharacteristic
29C22×C11×C22⋊C4C2212yescomplemented
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2212yescomplemented
33C22×C22⋊Dic11C2212yescomplemented
34C22×C22⋊Dic11C2212yescomplemented
35C2×#66991—216no—
36C2×#66991C22116yescomplemented
37C2×#66990—28no—
38C2×#66990C2218yescomplemented
39C22×(C2×D11)⋊C4C2212yescomplemented
40C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
41C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
42C22×C4⋊Dic11C2212yescomplemented
43C2×C22⋊C4×D11—28no—
44C2×C22⋊C4×D11C2218yescomplemented
45#10622860C2218yescomplemented
46#10622836C22116yescomplemented
47#10622833C2218yescomplemented
48C2×C11⋊#95C2212yescomplemented
49C2×C11⋊#95C2212yescomplemented
50#10622574C22116yescomplemented
51#10622569C22116yescomplemented
52#10622563C2218yescomplemented
53C25×C11—28no—
54C25×C11—24no—
55C25×C11—24no—
56C25×C11—24no—
57C25×C11—44no—
58C25×C11C2311yescharacteristic
59C25×C11C2312yes—
60C25×C11C2314yes—
61C25×C11C2311yescharacteristic
62C24×D11—24no—
63C24×D11—24no—
64C24×D11—28no—
65C24×D11—44no—
66C24×D11D418yescomplemented
67C24×D11C2311yescharacteristic
68C24×D11C2314yes—
69C24×D11C2311yescharacteristic
70C22×D4×C11—24no—
71C22×D4×C11—28no—
72C22×D4×C11—24no—
73C22×D4×C11—24no—
74C22×D4×C11—28no—
75C22×D4×C11—44no—
76C22×D4×C11C2314yes—
77C22×D4×C11C2318yescomplemented
78C23×C4×C11C2311yescharacteristic
79C23×C4×C11C2312yes—
80C22×C22⋊D11—2128no—
81C22×C22⋊D11—28no—
82C22×C22⋊D11—28no—
83C22×C22⋊D11—28no—
84C22×C22⋊D11—28no—
85C22×C22⋊D11—232no—
86C22×C22⋊D11—264no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—28no—
90C22×C22⋊D11—28no—
91C22×C22⋊D11—44no—
92C22×C22⋊D11D4116yescomplemented
93C22×C22⋊D11C2318yes—
94C22×C22⋊D11C2318yes—
95C22×C22⋊D11C2314yescomplemented
96C22×C22⋊D11C2314yescomplemented
97C23×Dic11—24no—
98C23×Dic11—28no—
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2312yes—
102C23×Dic11C2314yes—
103C23×Dic11C2312yes—
104C22×C4×D11—28no—
105C22×C4×D11—28no—
106C22×C4×D11—44no—
107C22×C4×D11C2318yescomplemented
108C11×#120—232no—
109C2×C11×C22⋊C4—28no—
110C2×C11×C22⋊C4D418yescomplemented
111C2×C11×C22⋊C4C2314yes—
112C2×C11×C22⋊C4C2318yescomplemented
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—28no—
116C2×C22⋊Dic11—28no—
117C2×C22⋊Dic11—44no—
118C2×C22⋊Dic11C2314yes—
119C2×C22⋊Dic11C2314yes—
120C2×C22⋊Dic11C2318yescomplemented
121C2×C22⋊Dic11C2318yescomplemented
122C2×C22⋊Dic11C2318yescomplemented
123#66991—264no—
124#66990—232no—
125C2×(C2×D11)⋊C4—24no—
126C2×(C2×D11)⋊C4—24no—
127C2×(C2×D11)⋊C4—28no—
128C2×(C2×D11)⋊C4C2318yescomplemented
129C2×(C2×D11)⋊C4C2314yescomplemented
130C2×(C2×D11)⋊C4C2314yescomplemented
131C2×C4⋊Dic11—28no—
132C2×C4⋊Dic11C2318yescomplemented
133C22⋊C4×D11—232no—
134C11⋊#95C2318yescomplemented
135C11⋊#95C2318yescomplemented
136C2×#2410—111nomaximal, Sylow
137C24×C11—24no—
138C24×C11—24no—
139C24×C11—232no—
140C24×C11—24no—
141C24×C11—216no—
142C24×C11—28no—
143C24×C11—24no—
144C24×C11—24no—
145C24×C11—24no—
146C24×C11—24no—
147C24×C11—24no—
148C24×C11—24no—
149C24×C11—28no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—28no—
154C24×C11—24no—
155C24×C11—48no—
156C24×C11—432no—
157C24×C11—432no—
158C24×C11—416no—
159C24×C11—416no—
160C24×C11C2×D418yes—
161C24×C11C2×D414yes—
162C24×C11C2×D414yes—
163C24×C11#4114yes—
164C24×C11C2412yes—
165C24×C11C2414yes—
166C24×C11C2412yes—
167C24×C11C2411yescharacteristic
168C23×D11—22no—
169C23×D11—22no—
170C23×D11—24no—
171C23×D11—232no—
172C23×D11—28no—
173C23×D11—22no—
174C23×D11—24no—
175C23×D11—28no—
176C23×D11—22no—
177C23×D11—24no—
178C23×D11—232no—
179C23×D11—216no—
180C23×D11—416no—
181C23×D11—48no—
182C23×D11—432no—
183C23×D11—432no—
184C23×D11C2×D414yes—
185C23×D11C2×D414yes—
186C23×D11C2×D418yes—
187C23×D11C2×D4116yescomplemented
188C23×D11C2412yes—
189C23×D11C2412yes—
190C2×D4×C11—28no—
191C2×D4×C11—216no—
192C2×D4×C11—28no—
193C2×D4×C11—28no—
194C2×D4×C11—216no—
195C2×D4×C11—48no—
196C2×D4×C11—432no—
197C2×D4×C11—416no—
198C22×C4×C11—24no—
199C22×C4×C11—24no—
200C22×C4×C11—22no—
201C22×C4×C11—22no—
202C22×C4×C11—22no—
203C22×C4×C11C2×D418yescomplemented
204C22×C4×C11C2412yes—
205C22×C4×C11C2414yes—
206C2×C22⋊D11—264no—
207C2×C22⋊D11—2256no—
208C2×C22⋊D11—216no—
209C2×C22⋊D11—216no—
210C2×C22⋊D11—264no—
211C2×C22⋊D11—216no—
212C2×C22⋊D11—216no—
213C2×C22⋊D11—216no—
214C2×C22⋊D11—28no—
215C2×C22⋊D11—28no—
216C2×C22⋊D11—216no—
217C2×C22⋊D11—48no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
220C2×C22⋊D11C2×D4132yescomplemented
221C22×Dic11—232no—
222C22×Dic11—216no—
223C22×Dic11—28no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—24no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—24no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11C2×D418yes—
234C22×Dic11C2412yes—
235C22×Dic11C2414yes—
236C22×Dic11C2412yes—
237C22×Dic11C2414yes—
238C2×C4×D11—216no—
239C2×C4×D11—216no—
240C2×C4×D11—48no—
241C2×C4×D11—432no—
242C11×C22⋊C4—216no—
243C11×C22⋊C4C2×D4116yescomplemented
244C22⋊Dic11—216no—
245C22⋊Dic11—28no—
246C22⋊Dic11—28no—
247C22⋊Dic11—216no—
248C22⋊Dic11—48no—
249(C2×D11)⋊C4—28no—
250(C2×D11)⋊C4—28no—
251(C2×D11)⋊C4—216no—
252C4⋊Dic11—216no—
253C24×D4—111no—
254C22×#121—112no—
255C22×#120—111no—
256C22×#120D1111yescharacteristic, complemented
257C23×C22⋊C4—111no—
258#2410—1116no—
259C2×#394—112no—
260C2×#392—112no—
261C2×#386—111no—
262C2×#386—112no—
263C2×#385—111no—
264C2×#379—111no—
265C23×C11—28no—
266C23×C11—28no—
267C23×C11—216no—
268C23×C11—216no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—232no—
272C23×C11—216no—
273C23×C11—216no—
274C23×C11—216no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—24no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—24no—
286C23×C11—432no—
287C23×C11—432no—
288C23×C11—4128no—
289C23×C11—416no—
290C23×C11—48no—
291C23×C11—416no—
292C23×C11—48no—
293C23×C11—48no—
294C23×C11—48no—
295C23×C11—44no—
296C23×C11—44no—
297C23×C11—44no—
298C23×C11—48no—
299C23×C11—48no—
300C23×C11#121116yescomplemented
301C23×C11C22×D418yes—
302C23×C11C22×D414yes—
303C23×C11C22×D412yes—
304C23×C11C22×D414yes—
305C23×C11C22×D414yes—
306C23×C11C22×D412yes—
307C23×C11C2×#4114yes—
308C23×C11C2×#4112yes—
309C23×C11H(5,𝔽2)14yes—
310C23×C11C2511yescharacteristic
311C22×D11—28no—
312C22×D11—28no—
313C22×D11—216no—
314C22×D11—216no—
315C22×D11—22no—
316C22×D11—22no—
317C22×D11—24no—
318C22×D11—28no—
319C22×D11—28no—
320C22×D11—232no—
321C22×D11—28no—
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—22no—
325C22×D11—24no—
326C22×D11—232no—
327C22×D11—416no—
328C22×D11—4128no—
329C22×D11—432no—
330C22×D11—432no—
331C22×D11—48no—
332C22×D11—48no—
333C22×D11#120116yescomplemented
334C22×D11C22×D414yes—
335C22×D11C22×D414yes—
336C22×D11C22×D418yes—
337D4×C11—432no—
338D4×C11—416no—
339C2×C4×C11—216no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—44no—
346C2×C4×C11C22×D418yescomplemented
347C22⋊D11—264no—
348C22⋊D11—264no—
349C22⋊D11—416no—
350C22⋊D11—416no—
351C2×Dic11—232no—
352C2×Dic11—216no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—24no—
356C2×Dic11—24no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—24no—
362C2×Dic11—44no—
363C2×Dic11—44no—
364C2×Dic11—48no—
365C2×Dic11C22×D418yes—
366C4×D11—432no—
367C26—111no—
368C26C2×D1111yescharacteristic
369C23×D4—112no—
370C23×D4—112no—
371C23×D4—118no—
372C23×D4—111no—
373C23×D4—111no—
374C23×D4—2216no—
375C23×D4—228no—
376C23×D4C2×D1111yescharacteristic
377C23×D4C2×D1112yescomplemented
378C24×C4—111no—
379C24×C4—112no—
380C2×#121—1116no—
381C2×#121—2216no—
382C2×#120—28no—
383C2×#120—118no—
384C2×#120—228no—
385C2×#120C2×D1118yescomplemented
386C22×C4⋊C4—112no—
387C22×C22⋊C4—112no—
388C22×C22⋊C4—112no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—111no—
391C22×C22⋊C4—112no—
392C22×C22⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—118no—
396C22×C22⋊C4—228no—
397C22×C22⋊C4C2×D1111yescharacteristic
398C22×C22⋊C4C2×D1112yescomplemented
399#394—1116no—
400#392—1116no—
401#386—118no—
402#386—1116no—
403#385—118no—
404#379—118no—
405C2×#95—112no—
406C2×#95—112no—
407C22×C11—24no—
408C22×C11—232no—
409C22×C11—24no—
410C22×C11—28no—
411C22×C11—28no—
412C22×C11—28no—
413C22×C11—28no—
414C22×C11—28no—
415C22×C11—464no—
416C22×C11—44no—
417C22×C11—432no—
418C22×C11—44no—
419C22×C11—44no—
420C22×C11—44no—
421C22×C11—42no—
422C22×C11—42no—
423C22×C11—42no—
424C22×C11—44no—
425C22×C11—44no—
426C22×C11—88no—
427C22×C11C2×#12014yes—
428C22×C11C2×#12114yes—
429C22×C11C2×#12118yescomplemented
430C22×C11#53414yes—
431C22×C11D4218yes—
432C22×C11#54618yes—
433C22×C11C23×D411yescharacteristic
434C22×C11C23×D412yes—
435C22×C11C23×D411yescharacteristic
436C22×C11C22×#4111yescharacteristic
437C22×C11C2×H(5,𝔽2)12yes—
438C2×D11—24no—
439C2×D11—232no—
440C2×D11—24no—
441C2×D11—28no—
442C2×D11—28no—
443C2×D11—24no—
444C2×D11—24no—
445C2×D11—24no—
446C2×D11—464no—
447C2×D11—416no—
448C2×D11—44no—
449C2×D11—44no—
450C2×D11C2×#12018yescomplemented
451C4×C11—28no—
452C4×C11—42no—
453Dic11—28no—
454Dic11—42no—
455Dic11—42no—
456Dic11—44no—
457C25—28no—
458C25—24no—
459C25—24no—
460C25—24no—
461C25—44no—
462C25—111no—
463C25—111no—
464C25—118no—
465C25—114no—
466C25—228no—
467C25—224no—
468C25—224no—
469C25—444no—
470C25C22×D1111yescharacteristic
471C25C22×D1112yes—
472C25C22×D1114yes—
473C25C22×D1111yescharacteristic
474C22×D4—24no—
475C22×D4—28no—
476C22×D4—24no—
477C22×D4—24no—
478C22×D4—28no—
479C22×D4—44no—
480C22×D4—1116no—
481C22×D4—118no—
482C22×D4—114no—
483C22×D4—118no—
484C22×D4—114no—
485C22×D4—228no—
486C22×D4—2264no—
487C22×D4—228no—
488C22×D4—228no—
489C22×D4—228no—
490C22×D4—2232no—
491C22×D4—22128no—
492C22×D4—228no—
493C22×D4—224no—
494C22×D4—224no—
495C22×D4—228no—
496C22×D4—444no—
497C22×D4C22×D1114yes—
498C22×D4C22×D1118yescomplemented
499C23×C4—112no—
500C23×C4—114no—
501C23×C4—112no—
502C23×C4—111no—
503C23×C4—111no—
504C23×C4—118no—
505C23×C4—228no—
506C23×C4—228no—
507C23×C4—224no—
508C23×C4—228no—
509C23×C4—444no—
510C23×C4C22×D1111yescharacteristic
511C23×C4C22×D1112yes—
512#121—2264no—
513#120—232no—
514#120—2232no—
515C2×C4⋊C4—118no—
516C2×C4⋊C4—228no—
517C2×C22⋊C4—28no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—118no—
522C2×C22⋊C4—118no—
523C2×C22⋊C4—114no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—118no—
526C2×C22⋊C4—224no—
527C2×C22⋊C4—224no—
528C2×C22⋊C4—228no—
529C2×C22⋊C4—224no—
530C2×C22⋊C4—228no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—228no—
533C2×C22⋊C4—2232no—
534C2×C22⋊C4—444no—
535C2×C22⋊C4C22⋊D1118yescomplemented
536C2×C22⋊C4C22×D1114yes—
537C2×C22⋊C4C22×D1118yescomplemented
538#95—118no—
539#95—118no—
540C2×C11—28no—
541C2×C11—48no—
542C2×C11—82no—
543C2×C11#241018yescomplemented
544C2×C11C22×#12011yescharacteristic
545C2×C11C22×#12111yescharacteristic
546C2×C11C2×#53411yescharacteristic
547C2×C11C2×D4212yes—
548C2×C11C2×#54612yes—
549D11—28no—
550D11—44no—
551C24—24no—
552C24—24no—
553C24—232no—
554C24—216no—
555C24—28no—
556C24—24no—
557C24—24no—
558C24—24no—
559C24—24no—
560C24—24no—
561C24—24no—
562C24—24no—
563C24—22no—
564C24—22no—
565C24—28no—
566C24—24no—
567C24—28no—
568C24—22no—
569C24—48no—
570C24—432no—
571C24—432no—
572C24—416no—
573C24—416no—
574C24—114no—
575C24—118no—
576C24—112no—
577C24—114no—
578C24—112no—
579C24—1116no—
580C24—2232no—
581C24—2216no—
582C24—222no—
583C24—224no—
584C24—222no—
585C24—2232no—
586C24—224no—
587C24—228no—
588C24—222no—
589C24—224no—
590C24—228no—
591C24—222no—
592C24—4416no—
593C24—448no—
594C24—4432no—
595C24—4432no—
596C24D4×D1118yes—
597C24D4×D1114yes—
598C24#434114yes—
599C24C2×C22⋊D1114yes—
600C24C23×D1112yes—
601C24C23×D1114yes—
602C24C23×D1112yes—
603C24C23×D1111yescharacteristic
604C2×D4—28no—
605C2×D4—216no—
606C2×D4—28no—
607C2×D4—28no—
608C2×D4—216no—
609C2×D4—48no—
610C2×D4—432no—
611C2×D4—416no—
612C2×D4—1132no—
613C2×D4—2216no—
614C2×D4—2264no—
615C2×D4—2216no—
616C2×D4—2216no—
617C2×D4—2216no—
618C2×D4—22256no—
619C2×D4—2264no—
620C2×D4—2216no—
621C2×D4—228no—
622C2×D4—228no—
623C2×D4—2216no—
624C2×D4—448no—
625C2×D4—4416no—
626C2×D4—4416no—
627C22×C4—24no—
628C22×C4—24no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—118no—
633C22×C4—114no—
634C22×C4—112no—
635C22×C4—114no—
636C22×C4—112no—
637C22×C4—2216no—
638C22×C4—2216no—
639C22×C4—2232no—
640C22×C4—228no—
641C22×C4—224no—
642C22×C4—224no—
643C22×C4—224no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—224no—
647C22×C4—224no—
648C22×C4—224no—
649C22×C4—224no—
650C22×C4—2216no—
651C22×C4—448no—
652C22×C4—4432no—
653C22×C4C2×C22⋊D1118yescomplemented
654C22×C4C23×D1112yes—
655C22×C4C23×D1114yes—
656C4⋊C4—2216no—
657C22⋊C4—216no—
658C22⋊C4—228no—
659C22⋊C4—228no—
660C22⋊C4—2216no—
661C22⋊C4—228no—
662C22⋊C4—2216no—
663C22⋊C4—228no—
664C22⋊C4—2216no—
665C22⋊C4—448no—
666C22⋊C4C2×C22⋊D11116yescomplemented
667C11C2×#241011yescharacteristic, complemented, Sylow
668C23—216no—
669C23—28no—
670C23—28no—
671C23—216no—
672C23—24no—
673C23—24no—
674C23—232no—
675C23—216no—
676C23—216no—
677C23—216no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—24no—
682C23—24no—
683C23—24no—
684C23—24no—
685C23—22no—
686C23—22no—
687C23—24no—
688C23—22no—
689C23—432no—
690C23—432no—
691C23—416no—
692C23—4128no—
693C23—48no—
694C23—416no—
695C23—48no—
696C23—48no—
697C23—48no—
698C23—44no—
699C23—48no—
700C23—44no—
701C23—44no—
702C23—48no—
703C23—1116no—
704C23—114no—
705C23—118no—
706C23—114no—
707C23—2232no—
708C23—228no—
709C23—2216no—
710C23—228no—
711C23—2216no—
712C23—222no—
713C23—224no—
714C23—222no—
715C23—228no—
716C23—2232no—
717C23—228no—
718C23—228no—
719C23—224no—
720C23—222no—
721C23—224no—
722C23—222no—
723C23—4416no—
724C23—44128no—
725C23—4432no—
726C23—4432no—
727C23—448no—
728C23—448no—
729C23#66991116yescomplemented
730C23C2×D4×D1118yes—
731C23C2×D4×D1114yes—
732C23C2×D4×D1112yes—
733C23C2×D4×D1114yes—
734C23C2×#434114yes—
735C23C2×#434112yes—
736C23#6703714yes—
737C23C22×C22⋊D1114yes—
738C23C22×C22⋊D1112yes—
739C23C24×D1111yescharacteristic
740D4—432no—
741D4—416no—
742D4—2264no—
743D4—2264no—
744D4—4416no—
745D4—4416no—
746C2×C4—216no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—22no—
750C2×C4—22no—
751C2×C4—22no—
752C2×C4—44no—
753C2×C4—118no—
754C2×C4—2232no—
755C2×C4—2216no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—222no—
760C2×C4—222no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—224no—
765C2×C4—4432no—
766C2×C4—448no—
767C2×C4—444no—
768C2×C4—444no—
769C2×C4C22×C22⋊D1118yescomplemented
770C22—24no—
771C22—232no—
772C22—28no—
773C22—28no—
774C22—24no—
775C22—28no—
776C22—28no—
777C22—28no—
778C22—464no—
779C22—44no—
780C22—432no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22—44no—
786C22—44no—
787C22—42no—
788C22—42no—
789C22—88no—
790C22—118no—
791C22—224no—
792C22—2232no—
793C22—228no—
794C22—228no—
795C22—224no—
796C22—224no—
797C22—224no—
798C22—224no—
799C22—4464no—
800C22—4416no—
801C22—444no—
802C22—444no—
803C22D11×#12014yes—
804C22#1062312014yes—
805C22#1062312218yes—
806C22C2×#6699114yes—
807C22C2×#6699118yescomplemented
808C22D4×C22⋊D1118yes—
809C22C22×D4×D1111yescharacteristic
810C22C22×D4×D1112yes—
811C22C22×#434111yescharacteristic
812C22C2×#6703712yes—
813C22C23×C22⋊D1111yescharacteristic
814C4—28no—
815C4—42no—
816C4—228no—
817C4—442no—
818C4—444no—
819C4—442no—
820C2—28no—
821C2—48no—
822C2—82no—
823C2—228no—
824C2—444no—
825C2#1307198618yesdirect product factor
826C2C2×D11×#12011yescharacteristic
827C2C22×#6699111yescharacteristic
828C2C2×#1062312011yescharacteristic
829C2C2×D4×C22⋊D1112yes—
830C2C2×#1062312212yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC22×C11×#120C2
socleC24×C11C24
hypercenterC22×#120D11
hypocenterC11C2×#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#120

Complements

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

NH ≅ G/Ntype
1. C24×C22⋊D11C2semidirect
2. C22×#66991C2semidirect
3. C22×#66990C2semidirect
4. C22×C22⋊C4×D11C2semidirect
5. #13071986C2direct (N × H)
6. C2×#10622574C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622569C2semidirect
10. C2×#10622563C2semidirect
11. C2×#10622860C2semidirect
12. C22×C11×#120C2semidirect
16. C23×D4×C11C22semidirect
21. C23×C22⋊D11C22semidirect
22. C23×C22⋊D11C22semidirect
23. C23×C22⋊D11C22semidirect
25. C23×C4×D11C22semidirect
27. C2×C11×#120C22semidirect
29. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C22⋊Dic11C22semidirect
34. C22×C22⋊Dic11C22semidirect
36. C2×#66991C22semidirect
38. C2×#66990C22semidirect
39. C22×(C2×D11)⋊C4C22semidirect
40. C22×(C2×D11)⋊C4C22semidirect
41. C22×(C2×D11)⋊C4C22semidirect
42. C22×C4⋊Dic11C22semidirect
44. C2×C22⋊C4×D11C22semidirect
45. #10622860C22semidirect
46. #10622836C22semidirect
47. #10622833C22semidirect
48. C2×C11⋊#95C22semidirect
49. C2×C11⋊#95C22semidirect
50. #10622574C22semidirect
51. #10622569C22semidirect
52. #10622563C22semidirect
66. C24×D11D4semidirect
77. C22×D4×C11C23semidirect
92. C22×C22⋊D11D4semidirect
95. C22×C22⋊D11C23semidirect
96. C22×C22⋊D11C23semidirect
107. C22×C4×D11C23semidirect
110. C2×C11×C22⋊C4D4semidirect
112. C2×C11×C22⋊C4C23semidirect
120. C2×C22⋊Dic11C23semidirect
121. C2×C22⋊Dic11C23semidirect
122. C2×C22⋊Dic11C23semidirect
128. C2×(C2×D11)⋊C4C23semidirect
129. C2×(C2×D11)⋊C4C23semidirect
130. C2×(C2×D11)⋊C4C23semidirect
132. C2×C4⋊Dic11C23semidirect
134. C11⋊#95C23semidirect
135. C11⋊#95C23semidirect
187. C23×D11C2×D4semidirect
203. C22×C4×C11C2×D4semidirect
220. C2×C22⋊D11C2×D4semidirect
243. C11×C22⋊C4C2×D4semidirect
256. C22×#120D11semidirect
300. C23×C11#121semidirect
333. C22×D11#120semidirect
346. C2×C4×C11C22×D4semidirect
377. C23×D4C2×D11semidirect
385. C2×#120C2×D11semidirect
398. C22×C22⋊C4C2×D11semidirect
429. C22×C11C2×#121semidirect
450. C2×D11C2×#120semidirect
498. C22×D4C22×D11semidirect
535. C2×C22⋊C4C22⋊D11semidirect
537. C2×C22⋊C4C22×D11semidirect
543. C2×C11#2410semidirect
653. C22×C4C2×C22⋊D11semidirect
666. C22⋊C4C2×C22⋊D11semidirect
667. C11C2×#2410semidirect
729. C23#66991semidirect
769. C2×C4C22×C22⋊D11semidirect
807. C22C2×#66991semidirect
825. C2#13071986direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊D112
C22×#669912
C22×#669902
C22×C22⋊C4×D112
#130719862
C2×#106225742
C2×#106228362
C2×#106228332
C2×#106225692
C2×#106225632
C2×#106228602
C22×C11×#1202
C2×#241011