Finite Group Databasebeta

← #14685022

Subgroups — #14685022

Order 2816.

3366 conjugacy classes of subgroups.

The subgroup lattice has 866 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66937C211yesmaximal, characteristic
2C22×C42×D11C211yesmaximal, characteristic, complemented
3C2×#10622570C212yesmaximal, complemented
4C2×#10622278C212yesmaximal, complemented
5C2×#10622569C212yesmaximal, complemented
6C2×#10622280C211yesmaximal, characteristic, complemented
7#13066854C211yesmaximal, characteristic, complemented
8#13066853C211yesmaximal, characteristic, complemented
9#13066852C211yesmaximal, characteristic, complemented
10Dic11⋊#95C212yesmaximal, complemented
11C11×#1437C211yesmaximal, characteristic, complemented
12C23×C22⋊D11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C23×C4×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×Dic11⋊C4C2212yes—
26C22×Dic11⋊C4C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C22×C4×Dic11C2212yes—
29C2×#66937—24no—
30C2×#66937—24no—
31C2×#66937C418yescomplemented
32C2×C42×D11—24no—
33C2×C42×D11—28no—
34C2×C11×#95C2212yes—
35C2×C11×#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40#10622570—28no—
41#10622569—28no—
42#10622280—24no—
43#10622278—28no—
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C24×D11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2311yescharacteristic
50C23×C4×C11C2312yes—
51C22×C22⋊D11—22no—
52C22×C22⋊D11—22no—
53C22×C22⋊D11—24no—
54C22×C22⋊D11—24no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—24no—
58C22×C22⋊D11—24no—
59C22×C22⋊D11C2×C414yes—
60C22×C22⋊D11C2×C414yescomplemented
61C23×Dic11C2312yes—
62C23×Dic11C2311yescharacteristic
63C23×Dic11C2312yes—
64C23×Dic11C2311yescharacteristic
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—24no—
68C22×D44—24no—
69C22×D44C2×C414yes—
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11—24no—
74C22×C4×D11—24no—
75C22×C4×D11—24no—
76C22×C4×D11—24no—
77C22×C4×D11—24no—
78C22×C4×D11C2×C414yes—
79C22×C4×D11D414yes—
80C22×C4×D11D414yes—
81C22×C4×D11D418yescomplemented
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—24no—
86C2×C11×C22⋊C4—24no—
87C2×C11×C22⋊C4C2×C414yescomplemented
88C2×C42×C11—22no—
89C2×C42×C11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—24no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4C2×C414yescomplemented
105C2×Dic11⋊C4—22no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—24no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4C2×C414yescomplemented
111C2×C4×Dic11—22no—
112C2×C4×Dic11—24no—
113C2×C4×Dic11—24no—
114C2×C4×Dic11—24no—
115C2×C4×Dic11D418yescomplemented
116#66937—232no—
117C42×D11—232no—
118C11×#95—24no—
119C11×#95—22no—
120C11⋊#95—22no—
121C11⋊#95—24no—
122C11⋊#95—24no—
123C11⋊#95—24no—
124#14698—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—21no—
128C24×C11—21no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11C22×C412yes—
134C24×C11C2411yescharacteristic
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—22no—
140C23×D11—22no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11C22×C412yes—
148C23×D11C22×C412yes—
149C23×D11C2×D412yes—
150C23×D11C2×D412yes—
151C23×D11C2×D414yes—
152C23×D11#4114yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C22×C412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×D412yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D414yes—
176C22×C4×C11#4114yes—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—216no—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—216no—
181C2×C22⋊D11—44no—
182C2×C22⋊D11—48no—
183C2×C22⋊D11—44no—
184C2×C22⋊D11—48no—
185C2×C22⋊D11—44no—
186C2×C22⋊D11—44no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—21no—
191C22×Dic11—21no—
192C22×Dic11—22no—
193C22×Dic11—22no—
194C22×Dic11—22no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11C22×C412yes—
203C22×Dic11C22×C412yes—
204C22×Dic11C2×D414yes—
205C22×Dic11C2×D414yes—
206C22×Dic11C2×D412yes—
207C22×Dic11C2×D412yes—
208C22×Dic11C2×D414yes—
209C22×Dic11#4114yes—
210C22×Dic11#4114yes—
211C2×D44—28no—
212C2×D44—216no—
213C2×D44—48no—
214C2×D44—44no—
215C2×D44—44no—
216C2×C4×D11—216no—
217C2×C4×D11—216no—
218C2×C4×D11—216no—
219C2×C4×D11—216no—
220C2×C4×D11—216no—
221C2×C4×D11—28no—
222C2×C4×D11—216no—
223C2×C4×D11—216no—
224C2×C4×D11—28no—
225C2×C4×D11—216no—
226C2×C4×D11—216no—
227C2×C4×D11C22⋊C4116yescomplemented
228C11×C22⋊C4—28no—
229C11×C22⋊C4—48no—
230C42×C11—28no—
231C22⋊Dic11—48no—
232(C2×D11)⋊C4—28no—
233(C2×D11)⋊C4—48no—
234(C2×D11)⋊C4—48no—
235(C2×D11)⋊C4—48no—
236Dic11⋊C4—28no—
237Dic11⋊C4—48no—
238C4×Dic11—28no—
239C4×Dic11—216no—
240C22×#121—111no—
241C23×C42—111no—
242C2×#390—112no—
243C2×#386—112no—
244C2×#386—112no—
245C2×#380—111no—
246#1437—111no—
247#1437—111no—
248#1437—111no—
249#1437D1111yescharacteristic, complemented
250C4⋊#95—112no—
251C23×C11—22no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—41no—
257C23×C11—42no—
258C23×C11—42no—
259C23×C11—42no—
260C23×C11—42no—
261C23×C11—41no—
262C23×C11—42no—
263C23×C11—42no—
264C23×C11—42no—
265C23×C11—41no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—41no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11C23×C411yescharacteristic
273C23×C11C22×D411yescharacteristic
274C23×C11C22×D411yescharacteristic
275C23×C11C22×D412yes—
276C23×C11C22×D412yes—
277C23×C11C2×#4112yes—
278C23×C11C2×#4112yes—
279C23×C11C2×#4112yes—
280C23×C11C2×#4112yes—
281C22×D11—24no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—22no—
289C22×D11—24no—
290C22×D11—24no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—22no—
298C22×D11—24no—
299C22×D11—24no—
300C22×D11—22no—
301C22×D11—22no—
302C22×D11—41no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—41no—
308C22×D11—42no—
309C22×D11—42no—
310C22×D11—42no—
311C22×D11—41no—
312C22×D11—42no—
313C22×D11—42no—
314C22×D11—41no—
315C22×D11—42no—
316C22×D11—42no—
317C22×D11—42no—
318C22×D11C2×C22⋊C414yes—
319C22×D11C4×D418yes—
320C22×D11#12118yes—
321C22×D11#12414yes—
322C22×D11#12714yes—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—22no—
326C2×C4×C11—24no—
327C2×C4×C11—24no—
328C2×C4×C11—24no—
329C2×C4×C11—22no—
330C2×C4×C11—24no—
331C2×C4×C11—24no—
332C2×C4×C11—24no—
333C2×C4×C11—22no—
334C2×C4×C11—24no—
335C2×C4×C11—42no—
336C2×C4×C11—41no—
337C2×C4×C11—41no—
338C2×C4×C11—42no—
339C2×C4×C11—42no—
340C2×C4×C11—42no—
341C2×C4×C11—42no—
342C2×C4×C11—42no—
343C2×C4×C11—42no—
344C2×C4×C11—42no—
345C2×C4×C11C2×C22⋊C414yes—
346C2×C4×C11#12118yescomplemented
347C22⋊D11—416no—
348C22⋊D11—416no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—22no—
356C2×Dic11—24no—
357C2×Dic11—42no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11C2×C22⋊C414yes—
368C2×Dic11C4×D418yes—
369C2×Dic11#12014yes—
370C2×Dic11#12118yes—
371C2×Dic11#12118yescomplemented
372C2×Dic11#12314yes—
373D44—416no—
374C4×D11—264no—
375C4×D11—232no—
376C23×D4—111no—
377C23×D4—111no—
378C23×D4—111no—
379C24×C4—111no—
380C24×C4—112no—
381C2×#121—118no—
382C2×#121—224no—
383C2×#121—224no—
384C22×C4⋊C4—111no—
385C22×C4⋊C4—112no—
386C22×C22⋊C4—111no—
387C22×C22⋊C4—112no—
388C22×C22⋊C4—112no—
389C22×C22⋊C4—112no—
390C22×C22⋊C4—112no—
391C22×C22⋊C4C2×D1112yes—
392C22×C22⋊C4C2×D1111yescharacteristic
393C22×C42—112no—
394C22×C42—111no—
395C22×C42—228no—
396C22×C42—224no—
397C22×C42C2×D1111yescharacteristic
398#390—228no—
399#386—228no—
400#386—228no—
401#380—224no—
402C2×#95—112no—
403C2×#95—112no—
404C2×#95—112no—
405C2×#95—111no—
406C2×#95C2×D1112yes—
407C2×#95C2×D1111yescharacteristic
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—44no—
412C22×C11—44no—
413C22×C11—82no—
414C22×C11—82no—
415C22×C11—82no—
416C22×C11—82no—
417C22×C11C22×C22⋊C411yescharacteristic
418C22×C11C2×C4×D412yes—
419C22×C11C2×C4×D412yes—
420C22×C11C4×#4111yescharacteristic
421C22×C11C4×#4111yescharacteristic
422C22×C11C2×#12011yescharacteristic
423C22×C11C2×#12112yes—
424C22×C11C2×#12112yes—
425C22×C11C2×#12112yes—
426C22×C11C2×#12112yes—
427C22×C11C2×#12311yescharacteristic
428C22×C11#52512yes—
429C22×C11#52512yes—
430C22×C11#52512yes—
431C22×C11C2×#12411yescharacteristic
432C22×C11#52912yes—
433C22×C11#52912yes—
434C22×C11C2×#12711yescharacteristic
435C22×C11#53212yes—
436C22×C11#53212yes—
437C22×C11#53212yes—
438C2×D11—28no—
439C2×D11—28no—
440C2×D11—28no—
441C2×D11—28no—
442C2×D11—24no—
443C2×D11—24no—
444C2×D11—28no—
445C2×D11—28no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—42no—
449C2×D11—44no—
450C2×D11—44no—
451C2×D11—82no—
452C2×D11—82no—
453C2×D11—82no—
454C2×D11—82no—
455C2×D11#39018yescomplemented
456C4×C11—28no—
457C4×C11—24no—
458C4×C11—42no—
459C4×C11—82no—
460Dic11—28no—
461Dic11—42no—
462Dic11—82no—
463Dic11#38618yescomplemented
464C25—111no—
465C25—111no—
466C25C22×D1111yescharacteristic
467C22×D4—114no—
468C22×D4—114no—
469C22×D4—114no—
470C22×D4—222no—
471C22×D4—222no—
472C22×D4—224no—
473C22×D4—224no—
474C22×D4—222no—
475C22×D4—222no—
476C22×D4—224no—
477C22×D4—224no—
478C22×D4—222no—
479C22×D4—222no—
480C22×D4—224no—
481C22×D4—224no—
482C23×C4—111no—
483C23×C4—112no—
484C23×C4—114no—
485C23×C4—114no—
486C23×C4—114no—
487C23×C4—111no—
488C23×C4—118no—
489C23×C4—112no—
490C23×C4—224no—
491C23×C4—224no—
492C23×C4—224no—
493C23×C4—224no—
494C23×C4—224no—
495C23×C4—224no—
496C23×C4—224no—
497C23×C4—224no—
498C23×C4C22×D1112yes—
499C23×C4C22×D1111yescharacteristic
500C23×C4C22×D1111yescharacteristic
501C23×C4C22×D1112yes—
502#121—2232no—
503C2×C4⋊C4—114no—
504C2×C4⋊C4—222no—
505C2×C4⋊C4—222no—
506C2×C4⋊C4—224no—
507C2×C4⋊C4—224no—
508C2×C4⋊C4—224no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—24no—
512C2×C22⋊C4—24no—
513C2×C22⋊C4—24no—
514C2×C22⋊C4—114no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—224no—
520C2×C22⋊C4—224no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—224no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—224no—
525C2×C22⋊C4—224no—
526C2×C22⋊C4—224no—
527C2×C22⋊C4—224no—
528C2×C22⋊C4—224no—
529C2×C22⋊C4C4×D1114yescomplemented
530C2×C42—22no—
531C2×C42—24no—
532C2×C42—118no—
533C2×C42—2232no—
534C2×C42—224no—
535C2×C42—224no—
536C2×C42—224no—
537C2×C42—222no—
538#95—22no—
539#95—24no—
540#95—224no—
541#95—224no—
542#95—222no—
543#95—224no—
544C2×C11—82no—
545C2×C11C2×#38611yescharacteristic
546C2×C11C2×#39011yescharacteristic
547C2×C11#229711yescharacteristic
548C2×C11C4×#12112yes—
549C2×C11C4×#12112yes—
550C2×C11#284712yes—
551C2×C11#285012yes—
552C2×C11#285412yes—
553C2×C11#285612yes—
554D11—28no—
555D11—82no—
556C24—22no—
557C24—22no—
558C24—22no—
559C24—21no—
560C24—21no—
561C24—22no—
562C24—22no—
563C24—22no—
564C24—112no—
565C24—112no—
566C24—114no—
567C24—112no—
568C24—114no—
569C24—112no—
570C24—222no—
571C24—222no—
572C24—222no—
573C24—222no—
574C24—222no—
575C24—222no—
576C24—222no—
577C24—221no—
578C24—221no—
579C24—222no—
580C24—222no—
581C24—222no—
582C24C2×C4×D1112yes—
583C24C23×D1111yescharacteristic
584C2×D4—228no—
585C2×D4—2216no—
586C2×D4—228no—
587C2×D4—2216no—
588C2×D4—228no—
589C2×D4—2216no—
590C2×D4—444no—
591C2×D4—448no—
592C2×D4—444no—
593C2×D4—444no—
594C2×D4—448no—
595C2×D4—444no—
596C2×D4—444no—
597C2×D4—448no—
598C2×D4—444no—
599C22×C4—22no—
600C22×C4—22no—
601C22×C4—22no—
602C22×C4—22no—
603C22×C4—22no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—21no—
607C22×C4—21no—
608C22×C4—22no—
609C22×C4—22no—
610C22×C4—22no—
611C22×C4—22no—
612C22×C4—22no—
613C22×C4—22no—
614C22×C4—22no—
615C22×C4—22no—
616C22×C4—112no—
617C22×C4—114no—
618C22×C4—112no—
619C22×C4—112no—
620C22×C4—114no—
621C22×C4—114no—
622C22×C4—114no—
623C22×C4—114no—
624C22×C4—1116no—
625C22×C4—112no—
626C22×C4—228no—
627C22×C4—2216no—
628C22×C4—2216no—
629C22×C4—2216no—
630C22×C4—228no—
631C22×C4—2216no—
632C22×C4—2216no—
633C22×C4—2216no—
634C22×C4—2216no—
635C22×C4—2216no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—2216no—
641C22×C4—222no—
642C22×C4—221no—
643C22×C4—221no—
644C22×C4—222no—
645C22×C4—222no—
646C22×C4—222no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—222no—
651C22×C4—222no—
652C22×C4C2×C4×D1112yes—
653C22×C4C2×C4×D1112yes—
654C22×C4#433914yes—
655C22×C4D4×D1112yes—
656C22×C4D4×D1112yes—
657C22×C4D4×D1114yes—
658C22×C4D4×D1114yes—
659C4⋊C4—228no—
660C4⋊C4—448no—
661C22⋊C4—28no—
662C22⋊C4—48no—
663C22⋊C4—228no—
664C22⋊C4—448no—
665C22⋊C4—448no—
666C22⋊C4—448no—
667C22⋊C4—448no—
668C42—28no—
669C42—2216no—
670C42—228no—
671C11#1469811yescharacteristic, complemented, Sylow
672C23—22no—
673C23—22no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—42no—
678C23—41no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—42no—
684C23—42no—
685C23—41no—
686C23—42no—
687C23—42no—
688C23—42no—
689C23—41no—
690C23—42no—
691C23—42no—
692C23—41no—
693C23—114no—
694C23—114no—
695C23—118no—
696C23—118no—
697C23—114no—
698C23—224no—
699C23—222no—
700C23—224no—
701C23—222no—
702C23—224no—
703C23—224no—
704C23—224no—
705C23—224no—
706C23—224no—
707C23—224no—
708C23—222no—
709C23—224no—
710C23—224no—
711C23—222no—
712C23—224no—
713C23—224no—
714C23—222no—
715C23—222no—
716C23—222no—
717C23—224no—
718C23—224no—
719C23—442no—
720C23—441no—
721C23—442no—
722C23—442no—
723C23—442no—
724C23—442no—
725C23—442no—
726C23—442no—
727C23—441no—
728C23—442no—
729C23—442no—
730C23—442no—
731C23—441no—
732C23—442no—
733C23—442no—
734C23—441no—
735C23C22×C4×D1111yescharacteristic
736C23C2×#433912yes—
737C23C2×D4×D1111yescharacteristic
738C23C2×D4×D1112yes—
739C23C2×D4×D1111yescharacteristic
740C23C2×D4×D1112yes—
741C23#41×D1112yes—
742C23#41×D1112yes—
743C23#41×D1112yes—
744D4—4416no—
745D4—4416no—
746D4—4416no—
747C2×C4—24no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—24no—
751C2×C4—22no—
752C2×C4—24no—
753C2×C4—24no—
754C2×C4—24no—
755C2×C4—22no—
756C2×C4—24no—
757C2×C4—22no—
758C2×C4—24no—
759C2×C4—41no—
760C2×C4—42no—
761C2×C4—41no—
762C2×C4—42no—
763C2×C4—42no—
764C2×C4—42no—
765C2×C4—42no—
766C2×C4—42no—
767C2×C4—42no—
768C2×C4—42no—
769C2×C4—114no—
770C2×C4—118no—
771C2×C4—114no—
772C2×C4—118no—
773C2×C4—114no—
774C2×C4—118no—
775C2×C4—2232no—
776C2×C4—2264no—
777C2×C4—224no—
778C2×C4—224no—
779C2×C4—224no—
780C2×C4—224no—
781C2×C4—224no—
782C2×C4—224no—
783C2×C4—222no—
784C2×C4—224no—
785C2×C4—441no—
786C2×C4—442no—
787C2×C4—441no—
788C2×C4—442no—
789C2×C4—442no—
790C2×C4—442no—
791C2×C4—442no—
792C2×C4—442no—
793C2×C4—442no—
794C2×C4—442no—
795C2×C4C22⋊C4×D1114yes—
796C2×C4#6693718yescomplemented
797C22—44no—
798C22—44no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—82no—
803C22—82no—
804C22—82no—
805C22—82no—
806C22—118no—
807C22—228no—
808C22—228no—
809C22—228no—
810C22—228no—
811C22—224no—
812C22—228no—
813C22—228no—
814C22—224no—
815C22—444no—
816C22—444no—
817C22—442no—
818C22—442no—
819C22—442no—
820C22—882no—
821C22—882no—
822C22—882no—
823C22—882no—
824C22C4×#433911yescharacteristic
825C22C2×C22⋊C4×D1111yescharacteristic
826C22C2×#6693712yes—
827C22#1062305311yescharacteristic
828C22#1062305912yes—
829C22C4×D4×D1112yes—
830C22C4×D4×D1112yes—
831C22#1062307812yes—
832C22#1062307812yes—
833C22#1062307912yes—
834C22#1062307912yes—
835C22D11×#12011yescharacteristic
836C22D11×#12112yes—
837C22D11×#12112yes—
838C22D11×#12112yes—
839C22D11×#12311yescharacteristic
840C22#1062318712yes—
841C22#1062319912yes—
842C22D11×#12411yescharacteristic
843C22#1062323712yes—
844C22D11×#12711yescharacteristic
845C4—28no—
846C4—24no—
847C4—42no—
848C4—82no—
849C4—118no—
850C4—228no—
851C4—442no—
852C4—882no—
853C2—82no—
854C2—228no—
855C2—882no—
856C2D11×#38611yescharacteristic
857C2D11×#39011yescharacteristic
858C2#1307110211yescharacteristic
859C2C4×#6693712yes—
860C2#1307112812yes—
861C2#1307689712yes—
862C2#1307691412yes—
863C2#1307694312yes—
864C2#1307696012yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1437C2
socle, cosocleC24×C11C24
prime radicalC22×#66937C2
hypercenter#1437D11
hypocenterC11#14698
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1437

Complements

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

NH ≅ G/Ntype
2. C22×C42×D11C2semidirect
3. C2×#10622570C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622569C2semidirect
6. C2×#10622280C2semidirect
7. #13066854C2semidirect
8. #13066853C2semidirect
9. #13066852C2semidirect
10. Dic11⋊#95C2semidirect
11. C11×#1437C2semidirect
31. C2×#66937C4semidirect
60. C22×C22⋊D11C2×C4semidirect
81. C22×C4×D11D4semidirect
87. C2×C11×C22⋊C4C2×C4semidirect
104. C2×(C2×D11)⋊C4C2×C4semidirect
110. C2×Dic11⋊C4C2×C4semidirect
115. C2×C4×Dic11D4semidirect
227. C2×C4×D11C22⋊C4semidirect
249. #1437D11semidirect
346. C2×C4×C11#121semidirect
371. C2×Dic11#121semidirect
455. C2×D11#390semidirect
463. Dic11#386semidirect
529. C2×C22⋊C4C4×D11semidirect
671. C11#14698semidirect
796. C2×C4#66937semidirect

Maximal subgroups

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

subgroupindex
C22×#669372
C22×C42×D112
C2×#106225702
C2×#106222782
C2×#106225692
C2×#106222802
#130668542
#130668532
#130668522
Dic11⋊#952
C11×#14372
#1469811