Finite Group Databasebeta

← #14677149

Subgroups — #14677149

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×#10622563C211yesmaximal, characteristic, complemented
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066873C212yesmaximal, complemented
6#13066861C212yesmaximal, complemented
7#13066850C212yesmaximal, complemented
8#13066839C211yesmaximal, characteristic, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C212yesmaximal, 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⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2211yescharacteristic
23C2×D4×Dic11—24no—
24C2×D4×Dic11—24no—
25C2×D4×Dic11—24no—
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4⋊Dic11C2212yes—
28C22×C4×Dic11C2211yescharacteristic
29C11×#386C418yescomplemented
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#10622563—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—22no—
53C23×C4×C11—42no—
54C23×C4×C11—42no—
55C23×C4×C11C2×C414yescomplemented
56C23×C4×C11C2312yes—
57C23×C4×C11C2312yes—
58C23×C4×C11C2311yescharacteristic
59C23×Dic11—22no—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—22no—
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—22no—
68C23×Dic11—22no—
69C23×Dic11—24no—
70C23×Dic11—42no—
71C23×Dic11—42no—
72C23×Dic11—42no—
73C23×Dic11D414yes—
74C23×Dic11C2312yes—
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C23×Dic11C2311yescharacteristic
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—42no—
83C2×C11×C22⋊C4—42no—
84C2×C11×C22⋊C4C2×C414yescomplemented
85C2×C11×C22⋊C4C2×C418yescomplemented
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—22no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—42no—
97C2×C22⋊Dic11D414yes—
98D4×Dic11—232no—
99C2×C4⋊Dic11—22no—
100C2×C4⋊Dic11—22no—
101C2×C4⋊Dic11—22no—
102C2×C4⋊Dic11—24no—
103C2×C4⋊Dic11—24no—
104C2×C4⋊Dic11—42no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C11×#95C2×C418yescomplemented
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—42no—
115C11⋊#95—42no—
116C11⋊#95—42no—
117#14016—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—48no—
166C22×C4×C11—44no—
167C22×C4×C11—44no—
168C22×C4×C11—48no—
169C22×C4×C11C22×C414yes—
170C22×C4×C11C22×C414yes—
171C22×C4×C11C22×C412yes—
172C22×C4×C11C2×D412yes—
173C22×C4×C11C2×Q812yes—
174C22×Dic11—28no—
175C22×Dic11—28no—
176C22×Dic11—28no—
177C22×Dic11—28no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—22no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
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—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—44no—
207C22×Dic11—48no—
208C22×Dic11—48no—
209C22×Dic11—48no—
210C22×Dic11—48no—
211C22×Dic11—48no—
212C22×Dic11—44no—
213C22×Dic11—48no—
214C22×Dic11—44no—
215C22×Dic11—44no—
216C22×Dic11—44no—
217C22×Dic11C2×D412yes—
218C22×Dic11C2×D412yes—
219C22×Dic11C2×D412yes—
220C22×Dic11C2×D412yes—
221C22×Dic11#4114yes—
222C22×Dic11#4114yes—
223C11×C22⋊C4—28no—
224C11×C22⋊C4—48no—
225C22⋊Dic11—28no—
226C22⋊Dic11—28no—
227C22⋊Dic11—48no—
228C22⋊Dic11—44no—
229C4⋊Dic11—28no—
230C4⋊Dic11—48no—
231C4×Dic11—28no—
232C22×C4×D4—111no—
233C2×#386—111no—
234C2×#386D1111yescharacteristic
235C2×#385—111no—
236C22×#95—111no—
237#1442—112no—
238#1439—112no—
239#1436—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—41no—
276C23×C11—42no—
277C23×C11—42no—
278C23×C11—42no—
279C23×C11—42no—
280C23×C11—42no—
281C23×C11C2×C4⋊C414yes—
282C23×C11C2×C4⋊C414yes—
283C23×C11C4×D414yes—
284C23×C11C4×D414yes—
285C23×C11#12014yes—
286C23×C11C22⋊Q814yes—
287C23×C11C22⋊Q814yes—
288C23×C11#12314yes—
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—24no—
311C2×C4×C11—24no—
312C2×C4×C11—24no—
313C2×C4×C11—416no—
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—22no—
324C2×Dic11—22no—
325C2×Dic11—24no—
326C2×Dic11—24no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—24no—
332C2×Dic11—22no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—416no—
338C2×Dic11—416no—
339C2×Dic11—416no—
340C2×Dic11—42no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—42no—
346C2×Dic11—42no—
347C2×Dic11—42no—
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×Dic11—42no—
359C2×Dic11#12314yes—
360C23×D4C2×D1111yescharacteristic
361C24×C4—111no—
362C24×C4—111no—
363C24×C4—111no—
364C24×C4C2×D1111yescharacteristic
365C2×C4×D4—224no—
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—224no—
378#386Dic1118yescomplemented
379#385—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—24no—
392C22×C11—28no—
393C22×C11—28no—
394C22×C11—24no—
395C22×C11—24no—
396C22×C11—28no—
397C22×C11—28no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—28no—
401C22×C11—24no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—44no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—44no—
408C22×C11—44no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11#38518yes—
412C22×C11C22×C4⋊C411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C4×#4112yes—
416C22×C11#51812yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×C22⋊Q811yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×#12311yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52511yescharacteristic
423C22×C11#52912yes—
424C22×C11#53411yescharacteristic
425C22×C11#53511yescharacteristic
426C22×C11#53812yes—
427C22×C11#54612yes—
428C22×C11#54612yes—
429C22×C11#54612yes—
430C22×C11#54612yes—
431C22×C11#55312yes—
432C22×C11#55312yes—
433C22×C11#55412yes—
434C22×C11#55412yes—
435C4×C11—24no—
436C4×C11—44no—
437C4×C11—44no—
438Dic11—24no—
439Dic11—42no—
440Dic11—44no—
441Dic11—42no—
442Dic11—42no—
443Dic11—82no—
444C25C22×D1111yescharacteristic
445C25C22×D1111yescharacteristic
446C22×D4—22no—
447C22×D4—22no—
448C22×D4—22no—
449C22×D4—22no—
450C22×D4Dic2214yes—
451C22×D4D4414yes—
452C22×D4C2×Dic1114yes—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—42no—
456C23×C4—42no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—112no—
462C23×C4—114no—
463C23×C4—112no—
464C23×C4—222no—
465C23×C4—222no—
466C23×C4—224no—
467C23×C4—224no—
468C23×C4—224no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4—222no—
474C23×C4—222no—
475C23×C4—442no—
476C23×C4—442no—
477C23×C4—442no—
478C23×C4C2×Dic1114yescomplemented
479C23×C4C22×D1112yes—
480C23×C4C22×D1112yes—
481C23×C4C22×D1111yescharacteristic
482C4×D4—2232no—
483C2×C4⋊C4—222no—
484C2×C4⋊C4—222no—
485C2×C4⋊C4—222no—
486C2×C4⋊C4—224no—
487C2×C4⋊C4—224no—
488C2×C4⋊C4—442no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—42no—
492C2×C22⋊C4—42no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—222no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—224no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—222no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4C2×Dic1114yescomplemented
506C2×C22⋊C4C2×Dic1118yescomplemented
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—222no—
510#95—224no—
511#95—224no—
512#95—224no—
513#95—224no—
514#95—224no—
515#95—442no—
516#95—442no—
517#95—442no—
518#95C2×Dic1118yescomplemented
519C2×C11—28no—
520C2×C11—44no—
521C2×C11C2×#38511yescharacteristic
522C2×C11C4×#12311yescharacteristic
523C2×C11#232111yescharacteristic
524C2×C11#234912yes—
525C2×C11#236412yes—
526C2×C11#240411yescharacteristic
527C2×C11#240511yescharacteristic
528C2×C11#244412yes—
529C2×C11#245012yes—
530C2×C11#248711yescharacteristic
531C2×C11#257911yescharacteristic
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—21no—
537C24—21no—
538C24—21no—
539C24—21no—
540C24—22no—
541C24—22no—
542C24—22no—
543C24—22no—
544C24C2×Dic2212yes—
545C24C2×Dic2212yes—
546C24C2×D4412yes—
547C24C2×D4412yes—
548C24D4×D1112yes—
549C24D4×D1112yes—
550C24#434112yes—
551C24#434112yes—
552C24C22×Dic1112yes—
553C24C22×Dic1112yes—
554C24C23×D1111yescharacteristic
555C2×D4—28no—
556C2×D4—28no—
557C2×D4—28no—
558C2×D4—28no—
559C2×D4—28no—
560C2×D4—28no—
561C2×D4C4⋊Dic11116yescomplemented
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—48no—
580C22×C4—44no—
581C22×C4—44no—
582C22×C4—48no—
583C22×C4—112no—
584C22×C4—114no—
585C22×C4—112no—
586C22×C4—112no—
587C22×C4—112no—
588C22×C4—114no—
589C22×C4—228no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—222no—
593C22×C4—228no—
594C22×C4—228no—
595C22×C4—228no—
596C22×C4—222no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—222no—
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—444no—
622C22×C4—444no—
623C22×C4—448no—
624C22×C4—448no—
625C22×C4—448no—
626C22×C4—448no—
627C22×C4—448no—
628C22×C4—448no—
629C22×C4—444no—
630C22×C4—444no—
631C22×C4—444no—
632C22×C4C2×Dic2212yes—
633C22×C4C2×D4412yes—
634C22×C4C22×Dic1114yes—
635C22×C4C22×Dic1114yes—
636C22×C4C22×Dic1112yes—
637C4⋊C4—228no—
638C4⋊C4—448no—
639C22⋊C4—28no—
640C22⋊C4—48no—
641C22⋊C4—228no—
642C22⋊C4—228no—
643C22⋊C4—448no—
644C22⋊C4—444no—
645C42—228no—
646C11#1401611yescharacteristic, complemented, Sylow
647C23—24no—
648C23—24no—
649C23—24no—
650C23—24no—
651C23—24no—
652C23—24no—
653C23—22no—
654C23—22no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—22no—
662C23—22no—
663C23—22no—
664C23—22no—
665C23—22no—
666C23—22no—
667C23—24no—
668C23—24no—
669C23—22no—
670C23—22no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—24no—
675C23—41no—
676C23—41no—
677C23—42no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—42no—
682C23—42no—
683C23—41no—
684C23—41no—
685C23#6693114yes—
686C23#6693114yes—
687C23#6693514yes—
688C23#6693914yes—
689C23C2×C4⋊Dic1114yes—
690C23C2×C4⋊Dic1114yes—
691C23D4×Dic1114yes—
692C23D4×Dic1114yes—
693C23C22×Dic2211yescharacteristic
694C23C22×D4411yescharacteristic
695C23C2×D4×D1111yescharacteristic
696C23C2×D4×D1111yescharacteristic
697C23C2×#434111yescharacteristic
698C23C2×#434111yescharacteristic
699C23#6703712yes—
700C23#6703712yes—
701C23#41×D1112yes—
702C23#41×D1112yes—
703C23C23×Dic1111yescharacteristic
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—24no—
715C2×C4—24no—
716C2×C4—24no—
717C2×C4—416no—
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—222no—
728C2×C4—224no—
729C2×C4—222no—
730C2×C4—224no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—224no—
735C2×C4—222no—
736C2×C4—224no—
737C2×C4—224no—
738C2×C4—224no—
739C2×C4—222no—
740C2×C4—224no—
741C2×C4—4416no—
742C2×C4—4416no—
743C2×C4—4416no—
744C2×C4—442no—
745C2×C4—442no—
746C2×C4—442no—
747C2×C4—442no—
748C2×C4—442no—
749C2×C4—441no—
750C2×C4—442no—
751C2×C4—441no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—441no—
755C2×C4—441no—
756C2×C4—442no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4C2×C4⋊Dic1114yes—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—24no—
769C22—28no—
770C22—24no—
771C22—28no—
772C22—24no—
773C22—28no—
774C22—28no—
775C22—24no—
776C22—42no—
777C22—42no—
778C22—42no—
779C22—44no—
780C22—42no—
781C22—44no—
782C22—42no—
783C22—42no—
784C22—44no—
785C22#1062256318yes—
786C22C2×#6693111yescharacteristic
787C22C2×#6693111yescharacteristic
788C22C2×#6693511yescharacteristic
789C22C2×#6693911yescharacteristic
790C22#1062307012yes—
791C22#1062307012yes—
792C22#1062308512yes—
793C22#1062308512yes—
794C22#1062312011yescharacteristic
795C22#1062312311yescharacteristic
796C22#1062312412yes—
797C22#1062313212yes—
798C22#1062313212yes—
799C22#1062314112yes—
800C22#1062314112yes—
801C22#1062318012yes—
802C22D11×#12311yescharacteristic
803C22#1062318711yescharacteristic
804C22C22×C4⋊Dic1111yescharacteristic
805C22C2×D4×Dic1111yescharacteristic
806C22C2×D4×Dic1111yescharacteristic
807C22#1062332912yes—
808C22#41×Dic1112yes—
809C4—24no—
810C4—44no—
811C4—44no—
812C4—224no—
813C4—444no—
814C4—442no—
815C4—442no—
816C4—442no—
817C4—882no—
818C2—28no—
819C2—44no—
820C2C2×#1062256311yescharacteristic
821C2#123×Dic1111yescharacteristic
822C2#1307127711yescharacteristic
823C2#1307152612yes—
824C2#1307166812yes—
825C2#1307193411yescharacteristic
826C2#1307194211yescharacteristic
827C2#1307236412yes—
828C2#1307244612yes—
829C2#1307293011yescharacteristic
830C2#1307396211yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#386C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC2×#386D11
hypocenterC11#14016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#386

Complements

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

NH ≅ G/Ntype
3. C2×#10622563C2semidirect
4. C22×C11⋊#95C2semidirect
5. #13066873C2semidirect
6. #13066861C2semidirect
7. #13066850C2semidirect
8. #13066839C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
29. C11×#386C4semidirect
55. C23×C4×C11C2×C4semidirect
84. C2×C11×C22⋊C4C2×C4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
108. C11×#95C2×C4semidirect
147. C2×D4×C11C4⋊C4semidirect
378. #386Dic11semidirect
478. C23×C4C2×Dic11semidirect
505. C2×C22⋊C4C2×Dic11semidirect
506. C2×C22⋊C4C2×Dic11semidirect
518. #95C2×Dic11semidirect
561. C2×D4C4⋊Dic11semidirect
646. C11#14016semidirect

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×#106225632
C22×C11⋊#952
#130668732
#130668612
#130668502
#130668392
#130668382
C2×C11×#3862
#1401611