Finite Group Databasebeta

← #14755017

Subgroups — #14755017

Order 2816.

2278 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×D11×#121C211yesmaximal, characteristic
2C22×#66945C211yesmaximal, characteristic, complemented
3C2×#10622383C212yesmaximal, complemented
4C2×#10622339C211yesmaximal, characteristic, complemented
5#13068937C212yesmaximal, complemented
6#13068935C212yesmaximal, complemented
7#13068934C211yesmaximal, characteristic, complemented
8#13068933C211yesmaximal, characteristic, complemented
9#13068931C211yesmaximal, characteristic, complemented
10#13068334C212yesmaximal, complemented
11C11×#1874C211yesmaximal, characteristic, complemented
12C22×D4×D11—21no—
13C22×D4×D11C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C2×C11×#121C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic, complemented
17C2×#66992—21no—
18C2×#66991C2211yescharacteristic
19C2×#66983C2211yescharacteristic
20C22×(C2×D11)⋊C4—21no—
21C22×C4⋊Dic11C2211yescharacteristic, complemented
22C22×C4×Dic11—21no—
23C22×#4313C2212yes—
24D11×#121—24no—
25D11×#121C418yescomplemented
26C2×#66948C2211yescharacteristic
27C2×#66945—21no—
28C2×#66945—21no—
29C2×#66945—28no—
30C2×#66945C2212yes—
31C2×#66945C2212yescomplemented
32C2×C4⋊C4×D11C2211yescharacteristic
33C2×#66937—21no—
34C2×C22⋊C4×D11—21no—
35C2×C11×#102C2212yescomplemented
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37C2×#66896C2212yescomplemented
38C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
39C2×#66885C2212yescomplemented
40C2×(C2×D11)⋊C8C2212yescomplemented
41C2×#66873C2212yescomplemented
42#10622383—28no—
43#10622339—24no—
44C11×#340C2212yescomplemented
45#10622189C2212yescomplemented
46#10622167C2212yescomplemented
47#10622167C2212yescomplemented
48C24×D11—21no—
49C24×D11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2311yescharacteristic
52C23×C4×C11—21no—
53C23×C4×C11C2311yescharacteristic
54C22×C22⋊D11—21no—
55C22×C22⋊D11—21no—
56C22×C22⋊D11—21no—
57C23×Dic11—21no—
58C23×Dic11D411yescharacteristic
59C2×D4×D11—28no—
60C2×D4×D11—24no—
61C2×D4×D11—22no—
62C2×D4×D11—24no—
63C2×D4×D11—44no—
64C2×D4×D11—44no—
65C2×D4×D11C2×C414yescomplemented
66C22×D44—21no—
67C22×D44C2311yescharacteristic
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—21no—
71C22×C4×D11C2×C414yes—
72C22×C4×D11D411yescharacteristic
73C22×C4×D11D411yescharacteristic
74C22×C4×D11D414yes—
75C22×C4×D11C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C22×C8×C11C2312yes—
78C11×#121—22no—
79C11×#121C2×C414yes—
80C2×C11×C4⋊C4—21no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2312yes—
84C2×C11×C22⋊C4—21no—
85C2×C22⋊Dic11—21no—
86#66992—28no—
87#66991—22no—
88#66991C2×C414yescomplemented
89#66983—22no—
90#66983C2×C414yes—
91C2×(C2×D11)⋊C4—28no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4—21no—
96C2×C4⋊Dic11—21no—
97C2×C4⋊Dic11—24no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2312yes—
100C2×Dic11⋊C4—21no—
101C2×C4×Dic11—28no—
102C2×C4×Dic11—22no—
103C2×C4×Dic11—22no—
104C22×C11⋊C8C2312yes—
105C2×#4313—24no—
106C2×#4313—24no—
107C2×#4313—24no—
108#66948—22no—
109#66948C2×C414yescomplemented
110#66945—28no—
111#66945—28no—
112#66945—24no—
113#66945—24no—
114#66945—24no—
115#66945D418yescomplemented
116C4⋊C4×D11—22no—
117C4⋊C4×D11C2×C414yescomplemented
118#66937—28no—
119C22⋊C4×D11—28no—
120C11×#102—24no—
121C11×C22⋊C8—22no—
122#66896—24no—
123C22⋊(C11⋊C8)—22no—
124#66885—24no—
125(C2×D11)⋊C8—24no—
126#66873—24no—
127#20912—111nomaximal, Sylow
128C24×C11—21no—
129C24×C11C2×D411yescharacteristic
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—21no—
135C23×D11—24no—
136C23×D11—41no—
137C23×D11—41no—
138C23×D11—42no—
139C23×D11—42no—
140C23×D11—42no—
141C23×D11—42no—
142C23×D11—42no—
143C23×D11—42no—
144C23×D11C22⋊C414yes—
145C23×D11C2×D411yescharacteristic
146C23×D11C2×D411yescharacteristic
147C2×D4×C11—24no—
148C2×D4×C11—22no—
149C2×D4×C11—21no—
150C2×D4×C11—22no—
151C2×D4×C11—42no—
152C2×D4×C11—42no—
153C2×D4×C11C22×C412yes—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—24no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—42no—
160C22×C4×C11—42no—
161C22×C4×C11C22×C412yes—
162C22×C4×C11C2×D411yescharacteristic
163C22×C4×C11C2×D412yes—
164C22×C4×C11C2411yescharacteristic
165C2×C22⋊D11—24no—
166C2×C22⋊D11—24no—
167C2×C22⋊D11—24no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C2×C22⋊D11—42no—
172C2×C22⋊D11—42no—
173C2×C22⋊D11—42no—
174C22×Dic11—22no—
175C22×Dic11—22no—
176C22×Dic11—24no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—42no—
180C22×Dic11—42no—
181C22×Dic11C22⋊C414yes—
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184D4×D11—216no—
185D4×D11—432no—
186D4×D11—48no—
187C2×D44—24no—
188C2×D44—21no—
189C2×D44—22no—
190C2×D44—22no—
191C2×D44—42no—
192C2×D44—42no—
193C2×D44C22×C412yes—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—216no—
197C2×C4×D11—216no—
198C2×C4×D11—24no—
199C2×C4×D11—22no—
200C2×C4×D11—22no—
201C2×C4×D11—22no—
202C2×C4×D11—22no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11C22⋊C414yes—
206C2×C4×D11C22⋊C414yes—
207C2×C4×D11C22×C412yes—
208C2×C4×D11C22×C412yes—
209C2×C4×D11C2×D412yes—
210C2×C4×D11C2×D412yes—
211C2×C4×D11C2×D414yes—
212C2×C4×D11#4114yes—
213C2×C8×C11—22no—
214C2×C8×C11—22no—
215C2×C8×C11—22no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—22no—
219C11×C4⋊C4C22×C412yes—
220C11×C4⋊C4C2×D414yescomplemented
221C11×C22⋊C4—24no—
222C22⋊Dic11—24no—
223(C2×D11)⋊C4—28no—
224(C2×D11)⋊C4—24no—
225(C2×D11)⋊C4—28no—
226(C2×D11)⋊C4—24no—
227C4⋊Dic11—24no—
228C4⋊Dic11—21no—
229C4⋊Dic11—22no—
230C4⋊Dic11C22×C412yes—
231C4⋊Dic11C2×D414yescomplemented
232Dic11⋊C4—24no—
233C4×Dic11—28no—
234C4×Dic11—28no—
235C2×C11⋊C8—22no—
236C2×C11⋊C8—22no—
237C2×C11⋊C8—22no—
238#4313—48no—
239C22×#121—111no—
240C22×#117—111no—
241C2×#418—112no—
242C2×#407—111no—
243#1875—112no—
244#1875—112no—
245#1874—111no—
246#1874—111no—
247#1874—111no—
248#1874D1111yescharacteristic, complemented
249#1736—112no—
250C23×C11—21no—
251C23×C11—21no—
252C23×C11—21no—
253C23×C11—21no—
254C23×C11—22no—
255C23×C11—41no—
256C23×C11—41no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11C2×C22⋊C412yes—
262C23×C11AGL(1,ℤ/8)12yes—
263C23×C11AGL(1,ℤ/8)12yes—
264C23×C11C22×D411yescharacteristic
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—21no—
271C22×D11—21no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—28no—
276C22×D11—28no—
277C22×D11—22no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—44no—
281C22×D11—44no—
282C22×D11—44no—
283C22×D11—48no—
284C22×D11—48no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—48no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11C2×C22⋊C412yes—
297C22×D11C2×C22⋊C412yes—
298C22×D11#12012yes—
299C22×D11#12312yes—
300D4×C11—24no—
301D4×C11—48no—
302D4×C11—42no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—24no—
309C2×C4×C11—48no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11C2×C22⋊C412yes—
315C2×C4×C11C23×C411yescharacteristic
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C2×#4112yes—
319C22⋊D11—48no—
320C22⋊D11—48no—
321C22⋊D11—48no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—28no—
325C2×Dic11—22no—
326C2×Dic11—24no—
327C2×Dic11—48no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—42no—
331C2×Dic11—42no—
332C2×Dic11C2×C22⋊C412yes—
333C2×Dic11C2×C22⋊C412yes—
334C2×Dic11#12012yes—
335C2×Dic11#12312yes—
336D44—24no—
337D44—48no—
338D44—42no—
339C4×D11—28no—
340C4×D11—24no—
341C4×D11—24no—
342C4×D11—28no—
343C4×D11—48no—
344C4×D11C4×D418yes—
345C4×D11#12118yes—
346C8×C11—42no—
347C11⋊C8—42no—
348C23×D4—111no—
349C23×D4—221no—
350C24×C4—111no—
351C22×M16—112no—
352C2×#121—111no—
353C2×#121—111no—
354C2×#121—118no—
355C2×#121—111no—
356C2×#121—221no—
357C2×#121—224no—
358C2×#121—221no—
359C2×#121C2×D1111yescharacteristic
360C2×#117—112no—
361C2×#117—112no—
362C2×#117—228no—
363C2×#117—221no—
364C2×#117—221no—
365C22×C4⋊C4—111no—
366C22×C4⋊C4—111no—
367C22×C4⋊C4C2×D1111yescharacteristic, complemented
368C22×C22⋊C4—221no—
369C22×C22⋊C4—221no—
370C22×C42—221no—
371#418—228no—
372C2×#102—112no—
373C2×#102—112no—
374C2×#102—112no—
375C2×#102C2×D1112yescomplemented
376#407—224no—
377C2×C22⋊C8—111no—
378C2×C22⋊C8—112no—
379C2×C22⋊C8C2×D1111yescharacteristic, complemented
380#340—112no—
381#340—112no—
382#340—112no—
383#340C2×D1112yescomplemented
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—42no—
391C22×C11—42no—
392C22×C11—42no—
393C22×C11—81no—
394C22×C11—81no—
395C22×C11—81no—
396C22×C11—81no—
397C22×C11#41814yescomplemented
398C22×C11C22×C22⋊C411yescharacteristic
399C22×C11C2×#12011yescharacteristic
400C22×C11C2×#12311yescharacteristic
401C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
402C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
403C22×C11#57511yescharacteristic
404C22×C11#57511yescharacteristic
405C2×D11—22no—
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—22no—
414C2×D11—416no—
415C2×D11—41no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—41no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—816no—
423C2×D11—81no—
424C2×D11—81no—
425C2×D11—81no—
426C2×D11—81no—
427C2×D11#38614yes—
428C4×C11—22no—
429C4×C11—42no—
430C4×C11—44no—
431C4×C11C2×C4×D412yes—
432C4×C11C2×#12112yes—
433Dic11—22no—
434Dic11—42no—
435Dic11—44no—
436Dic11#38614yes—
437C25—111no—
438C25—221no—
439C22×D4—21no—
440C22×D4—114no—
441C22×D4—111no—
442C22×D4—221no—
443C22×D4—224no—
444C22×D4—224no—
445C22×D4—222no—
446C22×D4—221no—
447C22×D4—228no—
448C22×D4—221no—
449C22×D4—221no—
450C22×D4—444no—
451C22×D4—444no—
452C22×D4C22×D1111yescharacteristic
453C23×C4—21no—
454C23×C4—111no—
455C23×C4—111no—
456C23×C4—114no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—114no—
460C23×C4—111no—
461C23×C4—224no—
462C23×C4—224no—
463C23×C4—221no—
464C23×C4—221no—
465C23×C4C22×D1111yescharacteristic
466C2×M16—224no—
467C2×M16—224no—
468C2×M16—224no—
469C22×C8—112no—
470C22×C8C22×D1112yes—
471#121—22no—
472#121—114no—
473#121—114no—
474#121—114no—
475#121—228no—
476#121—222no—
477#121—222no—
478#121—228no—
479#121—222no—
480#121C4×D1114yes—
481#117—118no—
482#117—224no—
483#117—224no—
484#117—228no—
485#117—228no—
486#117—224no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—24no—
489C2×C4⋊C4—112no—
490C2×C4⋊C4—111no—
491C2×C4⋊C4—114no—
492C2×C4⋊C4—222no—
493C2×C4⋊C4—224no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4C22×D1111yescharacteristic
497C2×C4⋊C4C22×D1112yes—
498C2×C22⋊C4—21no—
499C2×C22⋊C4—228no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—228no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C42—222no—
507C2×C42—222no—
508C2×C42—228no—
509#102—24no—
510#102—224no—
511#102—224no—
512#102—224no—
513C22⋊C8—22no—
514C22⋊C8—224no—
515C22⋊C8—222no—
516C2×C11—24no—
517C2×C11—82no—
518C2×C11C2×#38611yescharacteristic
519C2×C11C2×#41811yescharacteristic
520C2×C11#289611yescharacteristic
521C2×C11#300611yescharacteristic
522C2×C11#300611yescharacteristic
523C2×C11#309411yescharacteristic
524C2×C11#309411yescharacteristic
525D11—24no—
526D11—42no—
527D11—82no—
528C24—21no—
529C24—111no—
530C24—111no—
531C24—114no—
532C24—222no—
533C24—222no—
534C24—224no—
535C24—222no—
536C24—222no—
537C24—221no—
538C24—441no—
539C24—441no—
540C24—442no—
541C24—442no—
542C24—442no—
543C24—442no—
544C24—442no—
545C24—442no—
546C24D4×D1111yescharacteristic
547C2×D4—24no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—22no—
551C2×D4—42no—
552C2×D4—42no—
553C2×D4—112no—
554C2×D4—224no—
555C2×D4—2216no—
556C2×D4—224no—
557C2×D4—224no—
558C2×D4—224no—
559C2×D4—222no—
560C2×D4—221no—
561C2×D4—222no—
562C2×D4—442no—
563C2×D4—442no—
564C2×D4—448no—
565C2×D4—442no—
566C2×D4—442no—
567C2×D4—4432no—
568C2×D4—442no—
569C2×D4—442no—
570C2×D4—442no—
571C2×D4—442no—
572C2×D4C2×C4×D1112yes—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—24no—
576C22×C4—22no—
577C22×C4—21no—
578C22×C4—42no—
579C22×C4—42no—
580C22×C4—111no—
581C22×C4—112no—
582C22×C4—112no—
583C22×C4—114no—
584C22×C4—114no—
585C22×C4—114no—
586C22×C4—111no—
587C22×C4—114no—
588C22×C4—114no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—222no—
592C22×C4—222no—
593C22×C4—2216no—
594C22×C4—2216no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—224no—
598C22×C4—222no—
599C22×C4—222no—
600C22×C4—222no—
601C22×C4—222no—
602C22×C4—224no—
603C22×C4—222no—
604C22×C4—221no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—442no—
609C22×C4C2×C4×D1112yes—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1112yes—
612C22×C4C23×D1111yescharacteristic
613M16—448no—
614C2×C8—22no—
615C2×C8—22no—
616C2×C8—22no—
617C2×C8—222no—
618C2×C8—222no—
619C2×C8—222no—
620C4⋊C4—24no—
621C4⋊C4—22no—
622C4⋊C4—21no—
623C4⋊C4—112no—
624C4⋊C4—114no—
625C4⋊C4—224no—
626C4⋊C4—224no—
627C4⋊C4—222no—
628C4⋊C4—221no—
629C4⋊C4C2×C4×D1112yes—
630C4⋊C4D4×D1114yescomplemented
631C22⋊C4—24no—
632C22⋊C4—224no—
633C22⋊C4—228no—
634C22⋊C4—228no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C42—228no—
638C42—228no—
639C11#2091211yescharacteristic, complemented, Sylow
640C23—21no—
641C23—21no—
642C23—21no—
643C23—21no—
644C23—22no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—112no—
652C23—112no—
653C23—112no—
654C23—112no—
655C23—228no—
656C23—221no—
657C23—221no—
658C23—221no—
659C23—221no—
660C23—221no—
661C23—221no—
662C23—221no—
663C23—221no—
664C23—221no—
665C23—228no—
666C23—221no—
667C23—222no—
668C23—444no—
669C23—444no—
670C23—444no—
671C23—444no—
672C23—444no—
673C23—448no—
674C23—448no—
675C23—448no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—441no—
681C23—441no—
682C23—884no—
683C23—884no—
684C23—884no—
685C23—884no—
686C23C22⋊C4×D1112yes—
687C23#6696412yes—
688C23#6696712yes—
689C23C2×D4×D1111yescharacteristic
690D4—24no—
691D4—48no—
692D4—42no—
693D4—224no—
694D4—448no—
695D4—448no—
696D4—448no—
697D4—448no—
698D4—442no—
699C2×C4—21no—
700C2×C4—21no—
701C2×C4—24no—
702C2×C4—24no—
703C2×C4—22no—
704C2×C4—24no—
705C2×C4—48no—
706C2×C4—42no—
707C2×C4—41no—
708C2×C4—41no—
709C2×C4—42no—
710C2×C4—112no—
711C2×C4—112no—
712C2×C4—112no—
713C2×C4—118no—
714C2×C4—118no—
715C2×C4—112no—
716C2×C4—228no—
717C2×C4—228no—
718C2×C4—228no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—222no—
724C2×C4—224no—
725C2×C4—448no—
726C2×C4—448no—
727C2×C4—441no—
728C2×C4—441no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4C22⋊C4×D1112yes—
732C2×C4C22×C4×D1111yescharacteristic
733C2×C4C2×D4×D1112yes—
734C2×C4C2×D4×D1111yescharacteristic
735C2×C4#41×D1112yes—
736C8—42no—
737C8—442no—
738C22—22no—
739C22—22no—
740C22—22no—
741C22—22no—
742C22—22no—
743C22—22no—
744C22—42no—
745C22—42no—
746C22—42no—
747C22—81no—
748C22—81no—
749C22—81no—
750C22—81no—
751C22—114no—
752C22—222no—
753C22—222no—
754C22—222no—
755C22—222no—
756C22—222no—
757C22—222no—
758C22—222no—
759C22—222no—
760C22—222no—
761C22—4416no—
762C22—441no—
763C22—441no—
764C22—441no—
765C22—441no—
766C22—442no—
767C22—442no—
768C22—442no—
769C22—8816no—
770C22—881no—
771C22—881no—
772C22—881no—
773C22—881no—
774C22#1062238314yescomplemented
775C22C2×C22⋊C4×D1111yescharacteristic
776C22D11×#12011yescharacteristic
777C22D11×#12311yescharacteristic
778C22C2×#6696411yescharacteristic
779C22C2×#6696711yescharacteristic
780C22#1062330411yescharacteristic
781C22#1062330811yescharacteristic
782C4—22no—
783C4—44no—
784C4—42no—
785C4—114no—
786C4—222no—
787C4—444no—
788C4—442no—
789C4C4×D4×D1112yes—
790C4D11×#12112yes—
791C2—24no—
792C2—82no—
793C2—224no—
794C2—442no—
795C2—882no—
796C2D11×#38611yescharacteristic
797C2C2×#1062238311yescharacteristic
798C2#1307713211yescharacteristic
799C2#1307786311yescharacteristic
800C2#1307786711yescharacteristic
801C2#1307855111yescharacteristic
802C2#1307855311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1874C2
socleC23×C11C22×D4
prime radicalC2×D11×#121C2
cosocleC22×C4×C11C24
hypercenter#1874D11
hypocenterC11#20912
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1874

Complements

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

NH ≅ G/Ntype
2. C22×#66945C2semidirect
3. C2×#10622383C2semidirect
4. C2×#10622339C2semidirect
5. #13068937C2semidirect
6. #13068935C2semidirect
7. #13068934C2semidirect
8. #13068933C2semidirect
9. #13068931C2semidirect
10. #13068334C2semidirect
11. C11×#1874C2semidirect
16. C22×C11×C4⋊C4C22semidirect
21. C22×C4⋊Dic11C22semidirect
25. D11×#121C4semidirect
31. C2×#66945C22semidirect
35. C2×C11×#102C22semidirect
36. C2×C11×C22⋊C8C22semidirect
37. C2×#66896C22semidirect
38. C2×C22⋊(C11⋊C8)C22semidirect
39. C2×#66885C22semidirect
40. C2×(C2×D11)⋊C8C22semidirect
41. C2×#66873C22semidirect
44. C11×#340C22semidirect
45. #10622189C22semidirect
46. #10622167C22semidirect
47. #10622167C22semidirect
65. C2×D4×D11C2×C4semidirect
88. #66991C2×C4semidirect
109. #66948C2×C4semidirect
115. #66945D4semidirect
117. C4⋊C4×D11C2×C4semidirect
220. C11×C4⋊C4C2×D4semidirect
231. C4⋊Dic11C2×D4semidirect
248. #1874D11semidirect
367. C22×C4⋊C4C2×D11semidirect
375. C2×#102C2×D11semidirect
379. C2×C22⋊C8C2×D11semidirect
383. #340C2×D11semidirect
397. C22×C11#418semidirect
630. C4⋊C4D4×D11semidirect
639. C11#20912semidirect
774. C22#10622383semidirect

Maximal subgroups

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

subgroupindex
C2×D11×#1212
C22×#669452
C2×#106223832
C2×#106223392
#130689372
#130689352
#130689342
#130689332
#130689312
#130683342
C11×#18742
#2091211