Finite Group Databasebeta

← #14676491

Subgroups — #14676491

Order 2816.

2590 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
1C22×D4×Dic11C211yesmaximal, characteristic
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622555C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066868C212yesmaximal, complemented
6#13066859C212yesmaximal, complemented
7#13066842C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066838C212yesmaximal, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C2×C11×#386C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2211yescharacteristic
23C2×D4×Dic11—24no—
24C2×D4×Dic11—24no—
25C2×D4×Dic11C418yescomplemented
26C22×C4⋊Dic11C2211yescharacteristic
27C22×Dic11⋊C4C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C11×#386—24no—
30C2×C11×#95C2212yes—
31#10622833—24no—
32C2×C11⋊#95—24no—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41#10622555—24no—
42C25×C11C2311yescharacteristic
43C25×C11C2311yescharacteristic
44C22×D4×C11—22no—
45C22×D4×C11—22no—
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11C2×C414yes—
49C22×D4×C11D414yes—
50C22×D4×C11Q814yes—
51C23×C4×C11—22no—
52C23×C4×C11—24no—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—42no—
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—24no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—42no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11—42no—
69C23×Dic11—42no—
70C23×Dic11C2×C414yes—
71C23×Dic11C2×C414yescomplemented
72C23×Dic11D414yes—
73C23×Dic11D414yes—
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2312yes—
78C23×Dic11C2311yescharacteristic
79C23×Dic11C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—24no—
85C2×C11×C22⋊C4—42no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—42no—
96C2×C22⋊Dic11C2×C414yes—
97C2×C22⋊Dic11C2×C414yescomplemented
98D4×Dic11—232no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11C2×C414yescomplemented
102C2×Dic11⋊C4—24no—
103C2×Dic11⋊C4—42no—
104C2×Dic11⋊C4—42no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11C2×C414yescomplemented
108C11×#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—24no—
115C11⋊#95—42no—
116C11⋊#95—42no—
117#13960—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11—21no—
123C24×C11—21no—
124C24×C11—22no—
125C24×C11—22no—
126C24×C11—21no—
127C24×C11—21no—
128C24×C11—22no—
129C24×C11—22no—
130C24×C11C22×C412yes—
131C24×C11C22×C412yes—
132C24×C11C2×D412yes—
133C24×C11C2×D412yes—
134C24×C11C2×D412yes—
135C24×C11C2×D412yes—
136C24×C11C2×Q812yes—
137C24×C11C2×Q812yes—
138C24×C11#4112yes—
139C24×C11#4112yes—
140C24×C11C2411yescharacteristic
141C2×D4×C11—28no—
142C2×D4×C11—28no—
143C2×D4×C11—28no—
144C2×D4×C11—28no—
145C2×D4×C11—28no—
146C2×D4×C11—28no—
147C2×D4×C11C4⋊C4116yescomplemented
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—21no—
151C22×C4×C11—21no—
152C22×C4×C11—28no—
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—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—48no—
167C22×C4×C11—48no—
168C22×C4×C11—44no—
169C22×C4×C11—44no—
170C22×C4×C11C22×C412yes—
171C22×C4×C11C2×D412yes—
172C22×C4×C11C2×Q812yes—
173C22×C4×C11#4114yes—
174C22×Dic11—28no—
175C22×Dic11—28no—
176C22×Dic11—22no—
177C22×Dic11—22no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—22no—
186C22×Dic11—22no—
187C22×Dic11—22no—
188C22×Dic11—22no—
189C22×Dic11—22no—
190C22×Dic11—22no—
191C22×Dic11—22no—
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—48no—
202C22×Dic11—48no—
203C22×Dic11—44no—
204C22×Dic11—44no—
205C22×Dic11—48no—
206C22×Dic11—48no—
207C22×Dic11—48no—
208C22×Dic11—44no—
209C22×Dic11—44no—
210C22×Dic11—48no—
211C22×Dic11—44no—
212C22×Dic11—44no—
213C22×Dic11C22⋊C4116yescomplemented
214C22×Dic11C22×C412yes—
215C22×Dic11C22×C412yes—
216C22×Dic11C22×C412yes—
217C22×Dic11C22×C412yes—
218C22×Dic11C2×D412yes—
219C22×Dic11C2×D412yes—
220C22×Dic11C2×D412yes—
221C22×Dic11C2×D412yes—
222C22×Dic11#4114yes—
223C11×C22⋊C4—48no—
224C11×C22⋊C4—44no—
225C22⋊Dic11—28no—
226C22⋊Dic11—28no—
227C22⋊Dic11—48no—
228C22⋊Dic11—44no—
229C4⋊Dic11—28no—
230Dic11⋊C4—48no—
231C4×Dic11—28no—
232C22×C4×D4—111no—
233C2×#386—111no—
234C2×#386D1111yescharacteristic
235C2×#380—111no—
236C22×#95—111no—
237#1441—112no—
238#1439—112no—
239#1434—112no—
240C22⋊#95—111no—
241C22⋊#95—111no—
242C22⋊#95—112no—
243C23×C11—24no—
244C23×C11—24no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—24no—
251C23×C11—24no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—24no—
255C23×C11—24no—
256C23×C11—24no—
257C23×C11—24no—
258C23×C11—24no—
259C23×C11—22no—
260C23×C11—22no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—22no—
267C23×C11—24no—
268C23×C11—24no—
269C23×C11—24no—
270C23×C11—24no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—42no—
274C23×C11—41no—
275C23×C11—42no—
276C23×C11—41no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11C2×C22⋊C414yes—
282C23×C11C2×C4⋊C414yes—
283C23×C11C2×C4⋊C414yes—
284C23×C11#11714yes—
285C23×C11#12114yes—
286C23×C11#12114yes—
287C23×C11C22⋊Q814yes—
288C23×C11C22⋊Q814yes—
289C23×C11C23×C411yescharacteristic
290C23×C11C22×D411yescharacteristic
291C23×C11C22×D411yescharacteristic
292C23×C11C22×D411yescharacteristic
293C23×C11C22×Q811yescharacteristic
294C23×C11C2×#4111yescharacteristic
295C23×C11C2×#4111yescharacteristic
296C23×C11C2×#4112yes—
297C23×C11C2×#4112yes—
298C23×C11H(5,𝔽2)12yes—
299C23×C11H(5,𝔽2)12yes—
300D4×C11—232no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—416no—
311C2×C4×C11—42no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11—42no—
319C2×C4×C11—42no—
320C2×C4×C11—42no—
321C2×C4×C11—42no—
322C2×C4×C11C2×C4⋊C414yes—
323C2×Dic11—24no—
324C2×Dic11—24no—
325C2×Dic11—24no—
326C2×Dic11—22no—
327C2×Dic11—24no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—416no—
339C2×Dic11—416no—
340C2×Dic11—416no—
341C2×Dic11—42no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—42no—
345C2×Dic11—41no—
346C2×Dic11—42no—
347C2×Dic11—41no—
348C2×Dic11—42no—
349C2×Dic11—42no—
350C2×Dic11—42no—
351C2×Dic11—42no—
352C2×Dic11—42no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11C2×C22⋊C414yes—
359C2×Dic11C2×C22⋊C414yes—
360C23×D4C2×D1111yescharacteristic
361C24×C4—111no—
362C24×C4—111no—
363C24×C4—111no—
364C24×C4C2×D1111yescharacteristic
365C2×C4×D4—118no—
366C2×C4×D4—224no—
367C2×C4×D4—224no—
368C22×C4⋊C4—111no—
369C22×C4⋊C4—112no—
370C22×C22⋊C4—111no—
371C22×C22⋊C4—111no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1112yes—
376C22×C42—111no—
377#386—24no—
378#386—224no—
379#380—224no—
380C2×#95—112no—
381C2×#95—112no—
382C2×#95—112no—
383C2×#95—112no—
384C2×#95—112no—
385C2×#95—112no—
386C2×#95—112no—
387C2×#95—112no—
388C2×#95—224no—
389C2×#95C2×D1112yes—
390C22×C11—24no—
391C22×C11—28no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—28no—
395C22×C11—28no—
396C22×C11—24no—
397C22×C11—24no—
398C22×C11—28no—
399C22×C11—24no—
400C22×C11—28no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—44no—
404C22×C11—42no—
405C22×C11—42no—
406C22×C11—44no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—44no—
410C22×C11—42no—
411C22×C11#38018yes—
412C22×C11C22×C22⋊C411yescharacteristic
413C22×C11C22×C4⋊C411yescharacteristic
414C22×C11C2×#11711yescharacteristic
415C22×C11C4×#4112yes—
416C22×C11#51812yes—
417C22×C11C2×#12111yescharacteristic
418C22×C11C2×#12111yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×C22⋊Q811yescharacteristic
421C22×C11#52511yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#53212yes—
424C22×C11#53411yescharacteristic
425C22×C11#53412yes—
426C22×C11#53411yescharacteristic
427C22×C11#54612yes—
428C22×C11#54612yes—
429C22×C11#55112yes—
430C22×C11#55112yes—
431C22×C11#55312yes—
432C22×C11#55312yes—
433C22×C11#55412yes—
434C22×C11#55412yes—
435C4×C11—24no—
436C4×C11—44no—
437C4×C11—82no—
438Dic11—24no—
439Dic11—24no—
440Dic11—42no—
441Dic11—44no—
442Dic11—42no—
443Dic11—82no—
444C25C22×D1111yescharacteristic
445C25C22×D1111yescharacteristic
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4Dic2214yes—
451C22×D4C4×D1114yes—
452C22×D4C22⋊D1114yes—
453C23×C4—22no—
454C23×C4—24no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—42no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—114no—
461C23×C4—114no—
462C23×C4—114no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—112no—
466C23×C4—114no—
467C23×C4—112no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—224no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4—222no—
474C23×C4—442no—
475C23×C4—442no—
476C23×C4—442no—
477C23×C4—442no—
478C23×C4—442no—
479C23×C4C22×D1112yes—
480C23×C4C22×D1112yes—
481C23×C4C22×D1111yescharacteristic
482C4×D4—2232no—
483C2×C4⋊C4—114no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—442no—
488C2×C4⋊C4—442no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—24no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—24no—
494C2×C22⋊C4—42no—
495C2×C22⋊C4—114no—
496C2×C22⋊C4—114no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—222no—
504C2×C22⋊C4—224no—
505C2×C22⋊C4—222no—
506C2×C22⋊C4—442no—
507C2×C42—114no—
508C2×C42—222no—
509C2×C42—222no—
510#95—24no—
511#95—224no—
512#95—224no—
513#95—224no—
514#95—224no—
515#95—224no—
516#95—224no—
517#95—442no—
518#95—442no—
519C2×C11—28no—
520C2×C11—44no—
521C2×C11C2×#38011yescharacteristic
522C2×C11#229711yescharacteristic
523C2×C11#230811yescharacteristic
524C2×C11#234912yes—
525C2×C11#235312yes—
526C2×C11#253411yescharacteristic
527C2×C11#253411yescharacteristic
528C2×C11#254312yes—
529C2×C11#256412yes—
530C2×C11#257911yescharacteristic
531C2×C11#257911yescharacteristic
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—22no—
539C24—21no—
540C24—21no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic2212yes—
545C24C2×Dic2212yes—
546C24C2×C4×D1112yes—
547C24C2×C4×D1112yes—
548C24D4×D1112yes—
549C24D4×D1112yes—
550C24#434112yes—
551C24#434112yes—
552C24C2×C22⋊D1112yes—
553C24C2×C22⋊D1112yes—
554C24C23×D1111yescharacteristic
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4Dic11⋊C4116yescomplemented
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—28no—
567C22×C4—22no—
568C22×C4—22no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—22no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—48no—
581C22×C4—48no—
582C22×C4—44no—
583C22×C4—44no—
584C22×C4—112no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—1116no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—114no—
594C22×C4—228no—
595C22×C4—222no—
596C22×C4—222no—
597C22×C4—222no—
598C22×C4—222no—
599C22×C4—228no—
600C22×C4—222no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—222no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—448no—
622C22×C4—448no—
623C22×C4—444no—
624C22×C4—448no—
625C22×C4—444no—
626C22×C4—448no—
627C22×C4—448no—
628C22×C4—444no—
629C22×C4—448no—
630C22×C4—444no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4C2×Dic2212yes—
634C22×C4C2×C4×D1112yes—
635C22×C4#434114yes—
636C22×C4C2×C22⋊D1112yes—
637C4⋊C4—228no—
638C4⋊C4—448no—
639C22⋊C4—48no—
640C22⋊C4—44no—
641C22⋊C4—228no—
642C22⋊C4—228no—
643C22⋊C4—448no—
644C22⋊C4—444no—
645C42—228no—
646C11#1396011yescharacteristic, complemented, Sylow
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—42no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—41no—
683C23—41no—
684C23—42no—
685C23#6693014yes—
686C23#6693114yes—
687C23#6693114yes—
688C23C22⋊C4×D1114yes—
689C23C2×Dic11⋊C414yes—
690C23C2×Dic11⋊C414yes—
691C23#6699214yes—
692C23#6699214yes—
693C23C22×Dic2211yescharacteristic
694C23C22×C4×D1111yescharacteristic
695C23C2×D4×D1111yescharacteristic
696C23C2×D4×D1111yescharacteristic
697C23C2×#434111yescharacteristic
698C23C2×#434111yescharacteristic
699C23C2×#434112yes—
700C23#6703712yes—
701C23#41×D1112yes—
702C23#6704212yes—
703C23C22×C22⋊D1111yescharacteristic
704D4—232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—22no—
710C2×C4—22no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—24no—
714C2×C4—416no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—42no—
719C2×C4—42no—
720C2×C4—42no—
721C2×C4—42no—
722C2×C4—42no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—42no—
726C2×C4—114no—
727C2×C4—114no—
728C2×C4—224no—
729C2×C4—224no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—224no—
733C2×C4—224no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—224no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—4416no—
744C2×C4—4416no—
745C2×C4—4416no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—442no—
751C2×C4—442no—
752C2×C4—441no—
753C2×C4—442no—
754C2×C4—441no—
755C2×C4—442no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4C2×Dic11⋊C414yes—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—24no—
768C22—24no—
769C22—28no—
770C22—28no—
771C22—28no—
772C22—28no—
773C22—24no—
774C22—24no—
775C22—28no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—44no—
782C22—44no—
783C22—44no—
784C22—42no—
785C22#1062255518yes—
786C22C2×#6693011yescharacteristic
787C22C2×#6693111yescharacteristic
788C22C2×#6693111yescharacteristic
789C22C2×C22⋊C4×D1111yescharacteristic
790C22C4×#434112yes—
791C22#1062307012yes—
792C22#1062307412yes—
793C22#1062307612yes—
794C22#1062311711yescharacteristic
795C22#1062311812yes—
796C22#1062312011yescharacteristic
797C22#1062312712yes—
798C22#1062313212yes—
799C22#1062313612yes—
800C22#1062314912yes—
801C22#1062318411yescharacteristic
802C22#1062318711yescharacteristic
803C22#1062318912yes—
804C22C22×Dic11⋊C411yescharacteristic
805C22C2×#6699211yescharacteristic
806C22C2×#6699211yescharacteristic
807C22#1062333712yes—
808C22#1062336012yes—
809C4—24no—
810C4—44no—
811C4—82no—
812C4—224no—
813C4—224no—
814C4—442no—
815C4—444no—
816C4—442no—
817C4—882no—
818C2—28no—
819C2—44no—
820C2C2×#1062255511yescharacteristic
821C2#1307110111yescharacteristic
822C2#1307119011yescharacteristic
823C2#1307152112yes—
824C2#1307155412yes—
825C2#1307350311yescharacteristic
826C2#1307350511yescharacteristic
827C2#1307357412yes—
828C2#1307380012yes—
829C2#1307396011yescharacteristic
830C2#1307396211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#13960
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#10622555C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066868C2semidirect
6. #13066859C2semidirect
7. #13066842C2semidirect
8. #13066839C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
25. C2×D4×Dic11C4semidirect
71. C23×Dic11C2×C4semidirect
97. C2×C22⋊Dic11C2×C4semidirect
101. C2×C4⋊Dic11C2×C4semidirect
107. C2×C4×Dic11C2×C4semidirect
147. C2×D4×C11C4⋊C4semidirect
213. C22×Dic11C22⋊C4semidirect
561. C2×D4Dic11⋊C4semidirect
646. C11#13960semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228332
C2×#106225552
C22×C11⋊#952
#130668682
#130668592
#130668422
#130668392
#130668382
C2×C11×#3862
#1396011