Finite Group Databasebeta

← #14675652

Subgroups — #14675652

Order 2816.

3902 conjugacy classes of subgroups.

The subgroup lattice has 890 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C22⋊C4×D11C211yesmaximal, characteristic
2C22×C22⋊C4×D11C211yesmaximal, characteristic
3C2×#10622277C212yesmaximal, complemented
4C2×#10622568C211yesmaximal, characteristic
5#13066865C211yesmaximal, characteristic, complemented
6#13066863C211yesmaximal, characteristic, complemented
7#13066863C211yesmaximal, characteristic, complemented
8(C2×D11)⋊#95C212yesmaximal, complemented
9(C2×D11)⋊#95C212yesmaximal, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×#1440C211yesmaximal, characteristic, complemented
12C25×D11C2211yescharacteristic
13C23×C4×D11C2211yescharacteristic
14C23×C4×D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C22×C11×C22⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2211yescharacteristic
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×(C2×D11)⋊C4C2212yes—
27C2×C22⋊C4×D11—24no—
28C2×C22⋊C4×D11—24no—
29C2×C22⋊C4×D11—24no—
30C2×C22⋊C4×D11—28no—
31C2×C22⋊C4×D11C418yescomplemented
32C2×C11×#95C2212yescomplemented
33C2×C11×#95C2212yescomplemented
34C2×C11⋊#95C2212yescomplemented
35C2×C11⋊#95C2212yescomplemented
36C2×C11⋊#95C2212yescomplemented
37C2×C11⋊#95C2212yescomplemented
38C2×C11⋊#95C2212yescomplemented
39C2×C11⋊#95C2212yescomplemented
40#10622568—24no—
41#10622277—28no—
42C25×C11C2311yescharacteristic
43C24×D11—24no—
44C24×D11—24no—
45C24×D11—24no—
46C24×D11—24no—
47C24×D11—42no—
48C24×D11—42no—
49C24×D11C2×C414yes—
50C24×D11D414yes—
51C24×D11D414yes—
52C24×D11C2311yescharacteristic
53C24×D11C2311yescharacteristic
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2312yes—
58C23×Dic11C2312yes—
59C23×Dic11C2311yescharacteristic
60C23×Dic11C2311yescharacteristic
61C23×Dic11C2312yes—
62C22×C4×D11—24no—
63C22×C4×D11—22no—
64C22×C4×D11—22no—
65C22×C4×D11—22no—
66C22×C4×D11—22no—
67C22×C4×D11—24no—
68C22×C4×D11—24no—
69C22×C4×D11—24no—
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11—24no—
73C22×C4×D11—42no—
74C22×C4×D11—42no—
75C22×C4×D11—42no—
76C22×C4×D11—42no—
77C22×C4×D11C2×C414yescomplemented
78C22×C4×D11C2×C414yescomplemented
79C2×C11×C22⋊C4—22no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—42no—
85C2×C11×C22⋊C4C2×C414yescomplemented
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—42no—
92C2×C22⋊Dic11C2×C414yescomplemented
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—22no—
96C2×(C2×D11)⋊C4—22no—
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)⋊C4—24no—
105C2×(C2×D11)⋊C4C2×C414yes—
106C2×(C2×D11)⋊C4C2×C414yes—
107C2×(C2×D11)⋊C4D418yes—
108C22⋊C4×D11—232no—
109C22⋊C4×D11—232no—
110C11×#95—24no—
111C11×#95—42no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—42no—
116C11⋊#95—42no—
117C11⋊#95—42no—
118#13869—111nomaximal, Sylow
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—22no—
123C24×C11—22no—
124C24×C11—22no—
125C24×C11C22×C412yes—
126C24×C11C2×D412yes—
127C24×C11C2×D412yes—
128C24×C11C2411yescharacteristic
129C23×D11—22no—
130C23×D11—22no—
131C23×D11—22no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—28no—
138C23×D11—28no—
139C23×D11—216no—
140C23×D11—28no—
141C23×D11—216no—
142C23×D11—216no—
143C23×D11—216no—
144C23×D11—28no—
145C23×D11—48no—
146C23×D11—48no—
147C23×D11—44no—
148C23×D11—44no—
149C23×D11—48no—
150C23×D11—48no—
151C23×D11—48no—
152C23×D11—48no—
153C23×D11—48no—
154C23×D11—48no—
155C23×D11—48no—
156C23×D11—48no—
157C23×D11C22⋊C4116yes—
158C23×D11C22×C412yes—
159C23×D11C22×C412yes—
160C23×D11C2×D412yes—
161C23×D11C2×D412yes—
162C23×D11C2×D412yes—
163C23×D11C2×D412yes—
164C23×D11C2×D414yes—
165C23×D11#4114yes—
166C23×D11#4114yes—
167C23×D11#4114yes—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—22no—
188C22×C4×C11—22no—
189C22×C4×C11C22×C412yes—
190C22×C4×C11C22×C412yes—
191C22×C4×C11C2×D414yes—
192C22×Dic11—22no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—22no—
199C22×Dic11—22no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11C22×C412yes—
214C22×Dic11C22×C412yes—
215C22×Dic11C2×D414yes—
216C2×C4×D11—216no—
217C2×C4×D11—28no—
218C2×C4×D11—28no—
219C2×C4×D11—216no—
220C2×C4×D11—48no—
221C2×C4×D11—48no—
222C2×C4×D11—48no—
223C2×C4×D11—48no—
224C2×C4×D11—48no—
225C2×C4×D11—44no—
226C2×C4×D11—48no—
227C2×C4×D11—48no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C2×C4×D11—48no—
231C2×C4×D11—48no—
232C2×C4×D11—44no—
233C11×C22⋊C4—28no—
234C11×C22⋊C4—28no—
235C11×C22⋊C4—44no—
236C22⋊Dic11—28no—
237C22⋊Dic11—28no—
238C22⋊Dic11—44no—
239(C2×D11)⋊C4—28no—
240(C2×D11)⋊C4—28no—
241(C2×D11)⋊C4—216no—
242(C2×D11)⋊C4—48no—
243(C2×D11)⋊C4—48no—
244C23×C22⋊C4—111no—
245C23×C22⋊C4—111no—
246C2×#381—112no—
247C2×#379—111no—
248#1440—111no—
249#1440—111no—
250#1440—111no—
251#1440D1111yescharacteristic, complemented
252C22⋊#95—112no—
253C22⋊#95—112no—
254C22⋊#95—112no—
255C23×C11—22no—
256C23×C11—22no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—22no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—24no—
267C23×C11—42no—
268C23×C11—42no—
269C23×C11—42no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—42no—
275C23×C11C2×C22⋊C414yes—
276C23×C11C23×C411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×D412yes—
280C23×C11C2×#4112yes—
281C23×C11C2×#4112yes—
282C23×C11C2×#4112yes—
283C23×C11H(5,𝔽2)12yes—
284C23×C11H(5,𝔽2)12yes—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—24no—
288C22×D11—24no—
289C22×D11—24no—
290C22×D11—22no—
291C22×D11—24no—
292C22×D11—24no—
293C22×D11—24no—
294C22×D11—22no—
295C22×D11—22no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—22no—
301C22×D11—24no—
302C22×D11—24no—
303C22×D11—24no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—24no—
308C22×D11—24no—
309C22×D11—24no—
310C22×D11—24no—
311C22×D11—24no—
312C22×D11—24no—
313C22×D11—24no—
314C22×D11—24no—
315C22×D11—24no—
316C22×D11—24no—
317C22×D11—232no—
318C22×D11—232no—
319C22×D11—416no—
320C22×D11—432no—
321C22×D11—432no—
322C22×D11—432no—
323C22×D11—432no—
324C22×D11—432no—
325C22×D11—432no—
326C22×D11C2×C22⋊C414yes—
327C22×D11C2×C22⋊C414yes—
328C22×D11#11714yes—
329C22×D11#11714yes—
330C22×D11C4×D418yes—
331C22×D11#12014yes—
332C22×D11#12118yes—
333C22×D11#12318yes—
334C22×D11#12318yes—
335C22×D11#12314yes—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—24no—
339C2×C4×C11—24no—
340C2×C4×C11—24no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11—41no—
344C2×C4×C11—42no—
345C2×C4×C11—42no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—42no—
349C2×C4×C11—42no—
350C2×C4×C11—41no—
351C2×C4×C11—42no—
352C2×C4×C11—42no—
353C2×C4×C11—42no—
354C2×C4×C11—42no—
355C2×C4×C11—42no—
356C2×C4×C11—42no—
357C2×C4×C11—42no—
358C2×C4×C11—42no—
359C2×C4×C11—42no—
360C2×Dic11—22no—
361C2×Dic11—22no—
362C2×Dic11—24no—
363C2×Dic11—24no—
364C2×Dic11—24no—
365C2×Dic11—24no—
366C2×Dic11—24no—
367C2×Dic11—41no—
368C2×Dic11—42no—
369C2×Dic11—42no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—42no—
373C2×Dic11—42no—
374C2×Dic11—41no—
375C2×Dic11—42no—
376C2×Dic11—42no—
377C2×Dic11—42no—
378C2×Dic11—42no—
379C2×Dic11—42no—
380C2×Dic11—42no—
381C2×Dic11—42no—
382C2×Dic11—42no—
383C2×Dic11—42no—
384C4×D11—416no—
385C4×D11—432no—
386C4×D11—416no—
387C26—111no—
388C24×C4—111no—
389C24×C4—111no—
390C24×C4—112no—
391C22×C22⋊C4—111no—
392C22×C22⋊C4—111no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—112no—
395C22×C22⋊C4—118no—
396C22×C22⋊C4—111no—
397C22×C22⋊C4—112no—
398C22×C22⋊C4—112no—
399C22×C22⋊C4—111no—
400C22×C22⋊C4—228no—
401C22×C22⋊C4—224no—
402C22×C22⋊C4—224no—
403C22×C22⋊C4—224no—
404C22×C22⋊C4C2×D1111yescharacteristic
405C22×C22⋊C4C2×D1111yescharacteristic
406C22×C22⋊C4C2×D1111yescharacteristic
407#381—228no—
408#379—224no—
409C2×#95—112no—
410C2×#95—112no—
411C2×#95—112no—
412C2×#95—112no—
413C2×#95—112no—
414C2×#95—112no—
415C2×#95C2×D1112yescomplemented
416C2×#95C2×D1112yescomplemented
417C22×C11—24no—
418C22×C11—24no—
419C22×C11—24no—
420C22×C11—44no—
421C22×C11—44no—
422C22×C11—44no—
423C22×C11—44no—
424C22×C11—44no—
425C22×C11—44no—
426C22×C11C22×C22⋊C411yescharacteristic
427C22×C11C2×#11711yescharacteristic
428C22×C11C2×#11711yescharacteristic
429C22×C11C2×C4×D412yes—
430C22×C11#51812yes—
431C22×C11C2×#12011yescharacteristic
432C22×C11C2×#12112yes—
433C22×C11C2×#12312yes—
434C22×C11C2×#12312yes—
435C22×C11C2×#12311yescharacteristic
436C22×C11#53411yescharacteristic
437C22×C11#53412yes—
438C22×C11#53411yescharacteristic
439C22×C11#54612yes—
440C22×C11#54612yes—
441C22×C11#54612yes—
442C22×C11#54612yes—
443C22×C11#55112yes—
444C22×C11#55112yes—
445C22×C11#55112yes—
446C22×C11#55112yes—
447C2×D11—24no—
448C2×D11—24no—
449C2×D11—28no—
450C2×D11—28no—
451C2×D11—28no—
452C2×D11—28no—
453C2×D11—28no—
454C2×D11—28no—
455C2×D11—28no—
456C2×D11—28no—
457C2×D11—28no—
458C2×D11—28no—
459C2×D11—28no—
460C2×D11—28no—
461C2×D11—24no—
462C2×D11—24no—
463C2×D11—464no—
464C2×D11#38118yescomplemented
465C2×D11#38618yes—
466C4×C11—42no—
467C4×C11—44no—
468C4×C11—42no—
469C4×C11—82no—
470Dic11—42no—
471Dic11—44no—
472Dic11—42no—
473Dic11—82no—
474C25—111no—
475C25—111no—
476C25—114no—
477C25—114no—
478C25—114no—
479C25—224no—
480C25—224no—
481C25—224no—
482C25—224no—
483C25—442no—
484C25—442no—
485C25C22×D1111yescharacteristic
486C23×C4—111no—
487C23×C4—111no—
488C23×C4—112no—
489C23×C4—114no—
490C23×C4—114no—
491C23×C4—112no—
492C23×C4—224no—
493C23×C4—222no—
494C23×C4—222no—
495C23×C4—222no—
496C23×C4—222no—
497C23×C4—224no—
498C23×C4—224no—
499C23×C4—224no—
500C23×C4—224no—
501C23×C4—224no—
502C23×C4—224no—
503C23×C4—442no—
504C23×C4—442no—
505C23×C4—442no—
506C23×C4—442no—
507C23×C4C22×D1112yes—
508C23×C4C22×D1111yescharacteristic
509C23×C4C22×D1111yescharacteristic
510C23×C4C22×D1112yes—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—22no—
513C2×C22⋊C4—22no—
514C2×C22⋊C4—24no—
515C2×C22⋊C4—22no—
516C2×C22⋊C4—42no—
517C2×C22⋊C4—114no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—2232no—
522C2×C22⋊C4—2232no—
523C2×C22⋊C4—224no—
524C2×C22⋊C4—222no—
525C2×C22⋊C4—222no—
526C2×C22⋊C4—222no—
527C2×C22⋊C4—222no—
528C2×C22⋊C4—224no—
529C2×C22⋊C4—224no—
530C2×C22⋊C4—222no—
531C2×C22⋊C4—222no—
532C2×C22⋊C4—222no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—224no—
536C2×C22⋊C4—224no—
537C2×C22⋊C4—224no—
538C2×C22⋊C4—224no—
539C2×C22⋊C4—222no—
540C2×C22⋊C4—442no—
541C2×C22⋊C4C4×D1114yescomplemented
542#95—24no—
543#95—42no—
544#95—224no—
545#95—224no—
546#95—224no—
547#95—442no—
548#95—442no—
549#95—442no—
550C2×C11—44no—
551C2×C11C2×#38111yescharacteristic
552C2×C11C2×#38611yescharacteristic
553C2×C11#230811yescharacteristic
554C2×C11#234212yes—
555C2×C11#234212yes—
556C2×C11#240512yes—
557C2×C11#241212yes—
558C2×C11#241212yes—
559C2×C11#248312yes—
560D11—28no—
561D11—28no—
562C24—22no—
563C24—22no—
564C24—22no—
565C24—22no—
566C24—22no—
567C24—22no—
568C24—112no—
569C24—112no—
570C24—114no—
571C24—112no—
572C24—112no—
573C24—112no—
574C24—112no—
575C24—114no—
576C24—114no—
577C24—114no—
578C24—1116no—
579C24—228no—
580C24—228no—
581C24—228no—
582C24—2216no—
583C24—2216no—
584C24—2216no—
585C24—2216no—
586C24—228no—
587C24—222no—
588C24—222no—
589C24—222no—
590C24—222no—
591C24—222no—
592C24—222no—
593C24—222no—
594C24—222no—
595C24—448no—
596C24—444no—
597C24—448no—
598C24—444no—
599C24—448no—
600C24—448no—
601C24—448no—
602C24—448no—
603C24—448no—
604C24—448no—
605C24—448no—
606C24—448no—
607C24C2×C4×D1112yes—
608C24D4×D1112yes—
609C24D4×D1112yes—
610C24C23×D1111yescharacteristic
611C22×C4—22no—
612C22×C4—21no—
613C22×C4—21no—
614C22×C4—21no—
615C22×C4—21no—
616C22×C4—22no—
617C22×C4—22no—
618C22×C4—22no—
619C22×C4—22no—
620C22×C4—22no—
621C22×C4—22no—
622C22×C4—22no—
623C22×C4—22no—
624C22×C4—22no—
625C22×C4—22no—
626C22×C4—22no—
627C22×C4—22no—
628C22×C4—22no—
629C22×C4—22no—
630C22×C4—22no—
631C22×C4—22no—
632C22×C4—112no—
633C22×C4—112no—
634C22×C4—114no—
635C22×C4—228no—
636C22×C4—228no—
637C22×C4—2216no—
638C22×C4—2216no—
639C22×C4—222no—
640C22×C4—221no—
641C22×C4—221no—
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×C4—222no—
653C22×C4—222no—
654C22×C4—222no—
655C22×C4—222no—
656C22×C4—222no—
657C22×C4—222no—
658C22×C4—222no—
659C22×C4—222no—
660C22×C4—448no—
661C22×C4—448no—
662C22×C4—448no—
663C22×C4—448no—
664C22×C4—448no—
665C22×C4—444no—
666C22×C4—448no—
667C22×C4—444no—
668C22×C4—448no—
669C22×C4—444no—
670C22×C4—448no—
671C22×C4—448no—
672C22×C4—444no—
673C22×C4C2×C4×D1112yes—
674C22×C4C2×C4×D1112yes—
675C22×C4D4×D1114yes—
676C22⋊C4—28no—
677C22⋊C4—28no—
678C22⋊C4—44no—
679C22⋊C4—228no—
680C22⋊C4—228no—
681C22⋊C4—2216no—
682C22⋊C4—228no—
683C22⋊C4—228no—
684C22⋊C4—448no—
685C22⋊C4—448no—
686C22⋊C4—444no—
687C11#1386911yescharacteristic, complemented, Sylow
688C23—22no—
689C23—22no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—22no—
699C23—22no—
700C23—42no—
701C23—42no—
702C23—42no—
703C23—42no—
704C23—42no—
705C23—42no—
706C23—42no—
707C23—42no—
708C23—114no—
709C23—114no—
710C23—114no—
711C23—114no—
712C23—118no—
713C23—114no—
714C23—118no—
715C23—118no—
716C23—118no—
717C23—114no—
718C23—2232no—
719C23—2232no—
720C23—224no—
721C23—224no—
722C23—224no—
723C23—224no—
724C23—222no—
725C23—222no—
726C23—224no—
727C23—224no—
728C23—224no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—224no—
733C23—224no—
734C23—224no—
735C23—224no—
736C23—224no—
737C23—224no—
738C23—224no—
739C23—224no—
740C23—224no—
741C23—222no—
742C23—222no—
743C23—222no—
744C23—224no—
745C23—224no—
746C23—224no—
747C23—224no—
748C23—224no—
749C23—224no—
750C23—224no—
751C23—224no—
752C23—4416no—
753C23—4432no—
754C23—4432no—
755C23—4432no—
756C23—4432no—
757C23—4432no—
758C23—4432no—
759C23C22⋊C4×D1114yes—
760C23C22×C4×D1111yescharacteristic
761C23C2×D4×D1111yescharacteristic
762C23C2×D4×D1111yescharacteristic
763C23C2×D4×D1112yes—
764C23#6703712yes—
765C23#41×D1112yes—
766C23#41×D1112yes—
767C23#41×D1112yes—
768C23#6704212yes—
769C2×C4—22no—
770C2×C4—22no—
771C2×C4—24no—
772C2×C4—24no—
773C2×C4—24no—
774C2×C4—24no—
775C2×C4—24no—
776C2×C4—41no—
777C2×C4—41no—
778C2×C4—42no—
779C2×C4—42no—
780C2×C4—42no—
781C2×C4—42no—
782C2×C4—42no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—42no—
786C2×C4—42no—
787C2×C4—42no—
788C2×C4—42no—
789C2×C4—42no—
790C2×C4—42no—
791C2×C4—42no—
792C2×C4—42no—
793C2×C4—222no—
794C2×C4—222no—
795C2×C4—224no—
796C2×C4—224no—
797C2×C4—224no—
798C2×C4—224no—
799C2×C4—224no—
800C2×C4—4416no—
801C2×C4—4432no—
802C2×C4—4416no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—442no—
806C2×C4—442no—
807C2×C4—442no—
808C2×C4—442no—
809C2×C4—442no—
810C2×C4—441no—
811C2×C4—441no—
812C2×C4—442no—
813C2×C4—442no—
814C2×C4—442no—
815C2×C4—442no—
816C2×C4—442no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4—442no—
820C22—24no—
821C22—24no—
822C22—24no—
823C22—44no—
824C22—44no—
825C22—44no—
826C22—44no—
827C22—44no—
828C22—44no—
829C22—118no—
830C22—118no—
831C22—228no—
832C22—228no—
833C22—224no—
834C22—224no—
835C22—228no—
836C22—228no—
837C22—228no—
838C22—228no—
839C22—228no—
840C22—228no—
841C22—228no—
842C22—228no—
843C22—224no—
844C22—224no—
845C22—228no—
846C22—228no—
847C22—4464no—
848C22C2×C22⋊C4×D1111yescharacteristic
849C22D11×#11711yescharacteristic
850C22D11×#11711yescharacteristic
851C22C4×D4×D1112yes—
852C22#1062307612yes—
853C22D11×#12011yescharacteristic
854C22#1062312011yescharacteristic
855C22D11×#12112yes—
856C22#1062313612yes—
857C22#1062314112yes—
858C22#1062314312yes—
859C22D11×#12312yes—
860C22D11×#12312yes—
861C22D11×#12311yescharacteristic
862C22#1062318411yescharacteristic
863C22#1062318512yes—
864C22#1062319012yes—
865C22#1062320712yes—
866C22#1062321012yes—
867C22#1062323612yes—
868C22#1062323612yes—
869C4—44no—
870C4—42no—
871C4—42no—
872C4—82no—
873C4—444no—
874C4—442no—
875C4—442no—
876C4—882no—
877C2—44no—
878C2—228no—
879C2—228no—
880C2D11×#38111yescharacteristic
881C2D11×#38611yescharacteristic
882C2#1307119011yescharacteristic
883C2#1307146012yes—
884C2#1307146412yes—
885C2#1307193812yes—
886C2#1307200512yes—
887C2#1307200712yes—
888C2#1307289312yes—
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×#1440C2
socle, cosocleC24×C11C24
prime radicalC25×D11C22
hypercenter#1440D11
hypocenterC11#13869
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ #1440

Complements

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

NH ≅ G/Ntype
3. C2×#10622277C2semidirect
5. #13066865C2semidirect
6. #13066863C2semidirect
7. #13066863C2semidirect
8. (C2×D11)⋊#95C2semidirect
9. (C2×D11)⋊#95C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×#1440C2semidirect
31. C2×C22⋊C4×D11C4semidirect
32. C2×C11×#95C22semidirect
33. C2×C11×#95C22semidirect
34. C2×C11⋊#95C22semidirect
35. C2×C11⋊#95C22semidirect
36. C2×C11⋊#95C22semidirect
37. C2×C11⋊#95C22semidirect
38. C2×C11⋊#95C22semidirect
39. C2×C11⋊#95C22semidirect
77. C22×C4×D11C2×C4semidirect
78. C22×C4×D11C2×C4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
92. C2×C22⋊Dic11C2×C4semidirect
251. #1440D11semidirect
415. C2×#95C2×D11semidirect
416. C2×#95C2×D11semidirect
464. C2×D11#381semidirect
541. C2×C22⋊C4C4×D11semidirect
687. C11#13869semidirect

Maximal subgroups

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

subgroupindex
C22×C22⋊C4×D112
C2×#106222772
C2×#106225682
#130668652
#130668632
(C2×D11)⋊#952
C11×#14402
#1386911