Finite Group Databasebeta

← #14677148

Subgroups — #14677148

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×C4×C22⋊D11C211yesmaximal, characteristic
2C2×#10622571C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C2×#10622563C211yesmaximal, characteristic, complemented
5C22×C11⋊#95C211yesmaximal, characteristic, complemented
6#13066871C212yesmaximal, complemented
7#13066862C212yesmaximal, complemented
8#13066850C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×C22⋊#95C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C22⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C22⋊Dic11C2211yescharacteristic
20C2×C4×C22⋊D11—24no—
21C2×C4×C22⋊D11—24no—
22C2×C4×C22⋊D11—24no—
23C22×(C2×D11)⋊C4C2211yescharacteristic
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×C4⋊Dic11C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×C4×Dic11C2211yescharacteristic
29C2×C11×#95C2212yes—
30C2×C11×#95C2212yes—
31C2×C11⋊#95—24no—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2212yes—
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39#10622571—24no—
40#10622571C418yescomplemented
41#10622563—24no—
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—22no—
46C23×C4×C11—24no—
47C23×C4×C11—42no—
48C23×C4×C11D414yes—
49C23×C4×C11C2312yes—
50C23×C4×C11C2312yes—
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—22no—
54C22×C22⋊D11—22no—
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11C2×C414yes—
58C22×C22⋊D11D414yes—
59C22×C22⋊D11Q814yes—
60C23×Dic11—22no—
61C23×Dic11—22no—
62C23×Dic11—22no—
63C23×Dic11—24no—
64C23×Dic11—22no—
65C23×Dic11—22no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11—42no—
69C23×Dic11C2×C414yescomplemented
70C23×Dic11C2312yes—
71C23×Dic11C2311yescharacteristic
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—24no—
79C22×C4×D11—42no—
80C2×C11×C22⋊C4—22no—
81C2×C11×C22⋊C4—22no—
82C2×C11×C22⋊C4—22no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4C2×C414yescomplemented
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11D414yes—
89C4×C22⋊D11—232no—
90C2×(C2×D11)⋊C4—22no—
91C2×(C2×D11)⋊C4—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—42no—
96C2×(C2×D11)⋊C4—42no—
97C2×(C2×D11)⋊C4—42no—
98C2×(C2×D11)⋊C4C2×C418yescomplemented
99C2×C4⋊Dic11—24no—
100C2×C4⋊Dic11—24no—
101C2×C4⋊Dic11—42no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×Dic11⋊C4—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107C2×C4×Dic11—22no—
108C11×#95—24no—
109C11×#95—42no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—24no—
114C11⋊#95—42no—
115C11⋊#95—42no—
116C11⋊#95C2×C418yescomplemented
117#14016—111nomaximal, Sylow
118C24×C11—22no—
119C24×C11—22no—
120C24×C11—22no—
121C24×C11—22no—
122C24×C11C22×C412yes—
123C24×C11C2×D412yes—
124C24×C11C2×D412yes—
125C24×C11C2×D412yes—
126C24×C11C2×Q812yes—
127C24×C11#4112yes—
128C24×C11#4112yes—
129C24×C11C2411yescharacteristic
130C23×D11—21no—
131C23×D11—21no—
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—21no—
135C23×D11—21no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11C22×C412yes—
139C23×D11C2×D412yes—
140C23×D11C2×Q812yes—
141C22×C4×C11—21no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11—28no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—22no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—28no—
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—44no—
164C22×C4×C11—48no—
165C22×C4×C11—48no—
166C22×C4×C11C22×C414yes—
167C22×C4×C11C2×D412yes—
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4114yes—
170C2×C22⋊D11—28no—
171C2×C22⋊D11—28no—
172C2×C22⋊D11—28no—
173C2×C22⋊D11—28no—
174C2×C22⋊D11—28no—
175C2×C22⋊D11—28no—
176C2×C22⋊D11C4⋊C4116yescomplemented
177C22×Dic11—28no—
178C22×Dic11—28no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—22no—
182C22×Dic11—22no—
183C22×Dic11—22no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—21no—
190C22×Dic11—21no—
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—48no—
204C22×Dic11—48no—
205C22×Dic11—48no—
206C22×Dic11—44no—
207C22×Dic11—44no—
208C22×Dic11—44no—
209C22×Dic11—48no—
210C22×Dic11—44no—
211C22×Dic11C22×C414yes—
212C22×Dic11C22×C412yes—
213C22×Dic11C2×D412yes—
214C22×Dic11C2×D412yes—
215C22×Dic11C2×D412yes—
216C22×Dic11C2×Q812yes—
217C22×Dic11#4114yes—
218C2×C4×D11—28no—
219C2×C4×D11—48no—
220C2×C4×D11—48no—
221C2×C4×D11—44no—
222C2×C4×D11—44no—
223C11×C22⋊C4—28no—
224C11×C22⋊C4—44no—
225C22⋊Dic11—28no—
226(C2×D11)⋊C4—28no—
227(C2×D11)⋊C4—48no—
228(C2×D11)⋊C4—48no—
229C4⋊Dic11—48no—
230Dic11⋊C4—28no—
231C4×Dic11—28no—
232C22×C4×D4—111no—
233C2×#386—111no—
234C2×#386—111no—
235C2×#385—111no—
236C22×#95—111no—
237#1442—112no—
238#1439—112no—
239#1436—112no—
240C22⋊#95—112no—
241C22⋊#95—111no—
242C22⋊#95D1111yescharacteristic, complemented
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×C11C2×C4⋊C414yes—
260C23×C11C4×D414yes—
261C23×C11C4×D414yes—
262C23×C11#12014yes—
263C23×C11C22⋊Q814yes—
264C23×C11C22⋊Q814yes—
265C23×C11#12314yes—
266C23×C11C23×C411yescharacteristic
267C23×C11C22×D411yescharacteristic
268C23×C11C22×D411yescharacteristic
269C23×C11C22×D411yescharacteristic
270C23×C11C22×Q811yescharacteristic
271C23×C11C2×#4111yescharacteristic
272C23×C11C2×#4111yescharacteristic
273C23×C11C2×#4112yes—
274C23×C11C2×#4112yes—
275C23×C11H(5,𝔽2)12yes—
276C23×C11H(5,𝔽2)12yes—
277C22×D11—22no—
278C22×D11—22no—
279C22×D11—24no—
280C22×D11—24no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—24no—
288C22×D11—24no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—42no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11C2×C4⋊C414yes—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—24no—
303C2×C4×C11—24no—
304C2×C4×C11—24no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
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×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11#12314yes—
325C22⋊D11—232no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—24no—
333C2×Dic11—24no—
334C2×Dic11—24no—
335C2×Dic11—22no—
336C2×Dic11—22no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—416no—
343C2×Dic11—416no—
344C2×Dic11—42no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—42no—
349C2×Dic11—41no—
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×C4⋊C414yes—
359C4×D11—416no—
360C23×D4—111no—
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—112no—
372C22×C22⋊C4—111no—
373C22×C22⋊C4—112no—
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376C22×C42—111no—
377#386—118no—
378#386—224no—
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—224no—
388C2×#95C2×D1112yes—
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#38518yes—
401C22×C11C22×C4⋊C411yescharacteristic
402C22×C11C2×C4×D411yescharacteristic
403C22×C11C2×C4×D411yescharacteristic
404C22×C11C4×#4112yes—
405C22×C11#51812yes—
406C22×C11C2×#12011yescharacteristic
407C22×C11C2×C22⋊Q811yescharacteristic
408C22×C11C2×C22⋊Q811yescharacteristic
409C22×C11C2×#12311yescharacteristic
410C22×C11C2×#12311yescharacteristic
411C22×C11#52511yescharacteristic
412C22×C11#52912yes—
413C22×C11#53411yescharacteristic
414C22×C11#53511yescharacteristic
415C22×C11#53812yes—
416C22×C11#54612yes—
417C22×C11#54612yes—
418C22×C11#54612yes—
419C22×C11#54612yes—
420C22×C11#55312yes—
421C22×C11#55312yes—
422C22×C11#55412yes—
423C22×C11#55412yes—
424C2×D11—28no—
425C2×D11—24no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—44no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—44no—
432C2×D11—44no—
433C2×D11—42no—
434C2×D11—42no—
435C4×C11—24no—
436C4×C11—44no—
437C4×C11—42no—
438C4×C11—82no—
439Dic11—24no—
440Dic11—44no—
441Dic11—42no—
442Dic11—44no—
443Dic11—42no—
444C25—111no—
445C25C22×D1111yescharacteristic
446C22×D4—114no—
447C22×D4—114no—
448C22×D4—114no—
449C22×D4—222no—
450C22×D4—222no—
451C22×D4—222no—
452C22×D4—222no—
453C23×C4—22no—
454C23×C4—22no—
455C23×C4—24no—
456C23×C4—42no—
457C23×C4—111no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—112no—
461C23×C4—112no—
462C23×C4—114no—
463C23×C4—222no—
464C23×C4—222no—
465C23×C4—224no—
466C23×C4—222no—
467C23×C4—222no—
468C23×C4—222no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—224no—
473C23×C4—442no—
474C23×C4—442no—
475C23×C4—442no—
476C23×C4—442no—
477C23×C4D4414yes—
478C23×C4C22×D1112yes—
479C23×C4C22×D1112yes—
480C23×C4C22×D1111yescharacteristic
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—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—22no—
494C2×C22⋊C4—114no—
495C2×C22⋊C4—118no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—222no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—224no—
503C2×C22⋊C4—442no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4—442no—
506C2×C22⋊C4C4×D1114yescomplemented
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—222no—
510#95—24no—
511#95—42no—
512#95—118no—
513#95—224no—
514#95—224no—
515#95—224no—
516#95—224no—
517#95—442no—
518#95—442no—
519C2×C11—28no—
520C2×C11C2×#38511yescharacteristic
521C2×C11C4×#12311yescharacteristic
522C2×C11#232111yescharacteristic
523C2×C11#234912yes—
524C2×C11#236412yes—
525C2×C11#240411yescharacteristic
526C2×C11#240511yescharacteristic
527C2×C11#244412yes—
528C2×C11#245012yes—
529C2×C11#248711yescharacteristic
530C2×C11#257911yescharacteristic
531D11—44no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—112no—
537C24—112no—
538C24—112no—
539C24—221no—
540C24—221no—
541C24—221no—
542C24—222no—
543C24—221no—
544C24—222no—
545C24—222no—
546C24—222no—
547C24C2×C4×D1112yes—
548C24C2×D4412yes—
549C24#433912yes—
550C24D4×D1112yes—
551C24D4×D1112yes—
552C24#434112yes—
553C24Q8×D1112yes—
554C24C23×D1111yescharacteristic
555C2×D4—1116no—
556C2×D4—228no—
557C2×D4—228no—
558C2×D4—228no—
559C2×D4—228no—
560C2×D4—228no—
561C2×D4—228no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—22no—
565C22×C4—28no—
566C22×C4—22no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—22no—
570C22×C4—22no—
571C22×C4—22no—
572C22×C4—22no—
573C22×C4—22no—
574C22×C4—22no—
575C22×C4—22no—
576C22×C4—28no—
577C22×C4—22no—
578C22×C4—22no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—22no—
584C22×C4—44no—
585C22×C4—48no—
586C22×C4—48no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—114no—
591C22×C4—112no—
592C22×C4—112no—
593C22×C4—114no—
594C22×C4—228no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—228no—
600C22×C4—228no—
601C22×C4—222no—
602C22×C4—222no—
603C22×C4—221no—
604C22×C4—221no—
605C22×C4—222no—
606C22×C4—222no—
607C22×C4—222no—
608C22×C4—221no—
609C22×C4—221no—
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—448no—
626C22×C4—448no—
627C22×C4—444no—
628C22×C4—444no—
629C22×C4—444no—
630C22×C4—448no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4C2×C4×D1114yes—
634C22×C4C2×D4412yes—
635C22×C4C2×D4412yes—
636C22×C4#434114yes—
637C4⋊C4—228no—
638C4⋊C4—448no—
639C22⋊C4—28no—
640C22⋊C4—44no—
641C22⋊C4—228no—
642C22⋊C4—228no—
643C22⋊C4—448no—
644C22⋊C4—448no—
645C42—228no—
646C11#1401611yescharacteristic, complemented, Sylow
647C23—22no—
648C23—22no—
649C23—22no—
650C23—22no—
651C23—24no—
652C23—24no—
653C23—24no—
654C23—24no—
655C23—24no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—24no—
661C23—24no—
662C23—24no—
663C23—114no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—222no—
669C23—222no—
670C23—224no—
671C23—224no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—441no—
677C23—441no—
678C23—441no—
679C23—441no—
680C23—442no—
681C23—442no—
682C23—442no—
683C23—442no—
684C23—442no—
685C23—442no—
686C23C4×D4414yes—
687C23(C22⋊D11)⋊C414yes—
688C23#6693514yes—
689C23#6693614yes—
690C23C4⋊C4×D1114yes—
691C23#6694914yes—
692C23#6695014yes—
693C23C22×C4×D1111yescharacteristic
694C23C22×D4411yescharacteristic
695C23C2×#433911yescharacteristic
696C23C2×D4×D1111yescharacteristic
697C23C2×D4×D1111yescharacteristic
698C23C2×#434111yescharacteristic
699C23C2×#434112yes—
700C23#6703712yes—
701C23C2×Q8×D1111yescharacteristic
702C23#41×D1112yes—
703C23#6704212yes—
704D4—2232no—
705C2×C4—22no—
706C2×C4—22no—
707C2×C4—24no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—22no—
711C2×C4—22no—
712C2×C4—22no—
713C2×C4—24no—
714C2×C4—24no—
715C2×C4—416no—
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—42no—
727C2×C4—42no—
728C2×C4—42no—
729C2×C4—114no—
730C2×C4—222no—
731C2×C4—222no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—224no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—224no—
740C2×C4—224no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—224no—
744C2×C4—224no—
745C2×C4—224no—
746C2×C4—4416no—
747C2×C4—4416no—
748C2×C4—4416no—
749C2×C4—442no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—442no—
753C2×C4—441no—
754C2×C4—442no—
755C2×C4—442no—
756C2×C4—441no—
757C2×C4—442no—
758C2×C4—442no—
759C2×C4—442no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4#6693914yes—
764C22—24no—
765C22—24no—
766C22—24no—
767C22—28no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—24no—
773C22—28no—
774C22—228no—
775C22—224no—
776C22—442no—
777C22—442no—
778C22—442no—
779C22—444no—
780C22—444no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—444no—
785C22#1062228118yes—
786C22C2×C4×D4411yescharacteristic
787C22C2×(C22⋊D11)⋊C411yescharacteristic
788C22C2×#6693511yescharacteristic
789C22C2×#6693611yescharacteristic
790C22C2×#6693911yescharacteristic
791C22#1062302411yescharacteristic
792C22C2×C4⋊C4×D1111yescharacteristic
793C22C2×#6694911yescharacteristic
794C22C2×#6695011yescharacteristic
795C22#1062305511yescharacteristic
796C22#1062305611yescharacteristic
797C22C4×#434112yes—
798C22#1062306912yes—
799C22#1062307612yes—
800C22#1062309112yes—
801C22#1062312212yes—
802C22#1062312212yes—
803C22#1062313212yes—
804C22#1062314912yes—
805C22#1062316612yes—
806C22#1062316712yes—
807C22#1062318512yes—
808C22#1062318512yes—
809C4—24no—
810C4—44no—
811C4—42no—
812C4—82no—
813C4—224no—
814C4—444no—
815C4—442no—
816C4—442no—
817C4—444no—
818C2—28no—
819C2—444no—
820C2C2×#1062228111yescharacteristic
821C2C4×#6693911yescharacteristic
822C2#1307127611yescharacteristic
823C2#1307152212yes—
824C2#1307166412yes—
825C2#1307193711yescharacteristic
826C2#1307194411yescharacteristic
827C2#1307236812yes—
828C2#1307244212yes—
829C2#1307293411yescharacteristic
830C2#1307396511yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C22⋊#95C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC22⋊#95D11
hypocenterC11#14016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22⋊#95

Complements

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

NH ≅ G/Ntype
4. C2×#10622563C2semidirect
5. C22×C11⋊#95C2semidirect
6. #13066871C2semidirect
7. #13066862C2semidirect
8. #13066850C2semidirect
9. #13066838C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C22⋊#95C2semidirect
40. #10622571C4semidirect
69. C23×Dic11C2×C4semidirect
85. C2×C11×C22⋊C4C2×C4semidirect
98. C2×(C2×D11)⋊C4C2×C4semidirect
116. C11⋊#95C2×C4semidirect
176. C2×C22⋊D11C4⋊C4semidirect
242. C22⋊#95D11semidirect
506. C2×C22⋊C4C4×D11semidirect
646. C11#14016semidirect

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D112
C2×#106225712
C2×#106225632
C22×C11⋊#952
#130668712
#130668622
#130668502
#130668382
(C2×D11)⋊#952
C11×C22⋊#952
#1401611