Finite Group Databasebeta

← #14677145

Subgroups — #14677145

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×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C2×#10622826C211yesmaximal, characteristic
3C2×#10622571C211yesmaximal, characteristic
4C22×C11⋊#95C211yesmaximal, characteristic, complemented
5#13066874C212yesmaximal, complemented
6#13066858C212yesmaximal, complemented
7#13066848C212yesmaximal, complemented
8#13066838C211yesmaximal, characteristic, complemented
9#13066838C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C11×#385C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2211yescharacteristic
14C24×Dic11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C23×C4×D11C2211yescharacteristic
17C22×C11×C4⋊C4C2212yes—
18C22×C11×C22⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C22×(C2×D11)⋊C4C2211yescharacteristic
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×Dic11⋊C4C2211yescharacteristic
25C22×C4×Dic11C2211yescharacteristic
26C2×(C22⋊D11)⋊C4—24no—
27C2×(C22⋊D11)⋊C4—24no—
28C2×(C22⋊D11)⋊C4—24no—
29C11×#385—24no—
30C2×C11×#95C2212yes—
31#10622826—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#10622571C418yescomplemented
42C25×C11C2311yescharacteristic
43C24×D11C2311yescharacteristic
44C23×C4×C11—22no—
45C23×C4×C11—24no—
46C23×C4×C11—22no—
47C23×C4×C11—22no—
48C23×C4×C11—42no—
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×C4×C11C2312yes—
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—22no—
64C23×Dic11—24no—
65C23×Dic11—42no—
66C23×Dic11—42no—
67C23×Dic11—42no—
68C23×Dic11C2×C414yescomplemented
69C23×Dic11D414yes—
70C23×Dic11C2312yes—
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—24no—
79C22×C4×D11—42no—
80C2×C11×C4⋊C4—24no—
81C2×C11×C4⋊C4—24no—
82C2×C11×C4⋊C4—42no—
83C2×C11×C22⋊C4—22no—
84C2×C11×C22⋊C4—22no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4C2×C414yescomplemented
88C2×C11×C22⋊C4D414yes—
89C2×C22⋊Dic11—22no—
90C2×C22⋊Dic11—22no—
91C2×C22⋊Dic11—22no—
92C2×(C2×D11)⋊C4—22no—
93C2×(C2×D11)⋊C4—22no—
94C2×(C2×D11)⋊C4—22no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—24no—
97C2×(C2×D11)⋊C4—42no—
98C2×(C2×D11)⋊C4—42no—
99C2×(C2×D11)⋊C4—42no—
100C2×(C2×D11)⋊C4C2×C418yescomplemented
101C2×Dic11⋊C4—22no—
102C2×Dic11⋊C4—22no—
103C2×Dic11⋊C4—22no—
104C2×C4×Dic11—22no—
105C2×C4×Dic11—22no—
106C2×C4×Dic11—22no—
107(C22⋊D11)⋊C4—232no—
108C11×#95—24no—
109C11⋊#95—24no—
110C11⋊#95—24no—
111C11⋊#95—24no—
112C11⋊#95—24no—
113C11⋊#95—42no—
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—28no—
142C22×C4×C11—22no—
143C22×C4×C11—22no—
144C22×C4×C11—22no—
145C22×C4×C11—22no—
146C22×C4×C11—21no—
147C22×C4×C11—21no—
148C22×C4×C11—21no—
149C22×C4×C11—21no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
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—48no—
163C22×C4×C11—48no—
164C22×C4×C11—44no—
165C22×C4×C11—44no—
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—28no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—21no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11—21no—
189C22×Dic11—21no—
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—48no—
205C22×Dic11—44no—
206C22×Dic11—48no—
207C22×Dic11—48no—
208C22×Dic11—44no—
209C22×Dic11—44no—
210C22×Dic11—48no—
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×C4⋊C4—48no—
224C11×C22⋊C4—28no—
225C11×C22⋊C4—28no—
226C22⋊Dic11—44no—
227(C2×D11)⋊C4—28no—
228(C2×D11)⋊C4—48no—
229(C2×D11)⋊C4—48no—
230Dic11⋊C4—28no—
231C4×Dic11—28no—
232C22×C4×D4—111no—
233C2×#386—111no—
234C2×#386—111no—
235C2×#385D1111yescharacteristic, complemented
236C22×#95—111no—
237#1442—112no—
238#1439—112no—
239#1436—112no—
240C22⋊#95—112no—
241C22⋊#95—111no—
242C22⋊#95—111no—
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×#4112yes—
273C23×C11C2×#4111yescharacteristic
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—24no—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—24no—
306C2×C4×C11—24no—
307C2×C4×C11—24no—
308C2×C4×C11—24no—
309C2×C4×C11—24no—
310C2×C4×C11—416no—
311C2×C4×C11—42no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—41no—
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—42no—
325C22⋊D11—232no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—22no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—22no—
333C2×Dic11—22no—
334C2×Dic11—24no—
335C2×Dic11—24no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—416no—
343C2×Dic11—416no—
344C2×Dic11—42no—
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×Dic11C2×C4⋊C414yes—
358C2×Dic11#12314yes—
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⋊C4C2×D1112yes—
370C22×C22⋊C4—112no—
371C22×C22⋊C4—111no—
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—24no—
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#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—44no—
436C4×C11—42no—
437C4×C11—44no—
438C4×C11—42no—
439Dic11—24no—
440Dic11—24no—
441Dic11—44no—
442Dic11—42no—
443Dic11—82no—
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—24no—
455C23×C4—22no—
456C23×C4—22no—
457C23×C4—42no—
458C23×C4—111no—
459C23×C4—111no—
460C23×C4—111no—
461C23×C4—112no—
462C23×C4—114no—
463C23×C4—114no—
464C23×C4—112no—
465C23×C4—222no—
466C23×C4—224no—
467C23×C4—222no—
468C23×C4—224no—
469C23×C4—222no—
470C23×C4—222no—
471C23×C4—222no—
472C23×C4—222no—
473C23×C4—222no—
474C23×C4—442no—
475C23×C4—442no—
476C23×C4—442no—
477C23×C4—442no—
478C23×C4C22×D1112yes—
479C23×C4C22×D1112yes—
480C23×C4C22×D1111yescharacteristic
481C23×C4C22×D1111yescharacteristic
482C4×D4—2232no—
483C2×C4⋊C4—24no—
484C2×C4⋊C4—24no—
485C2×C4⋊C4—42no—
486C2×C4⋊C4—222no—
487C2×C4⋊C4—222no—
488C2×C4⋊C4—222no—
489C2×C22⋊C4—22no—
490C2×C22⋊C4—22no—
491C2×C22⋊C4—22no—
492C2×C22⋊C4—22no—
493C2×C22⋊C4—118no—
494C2×C22⋊C4—222no—
495C2×C22⋊C4—222no—
496C2×C22⋊C4—222no—
497C2×C22⋊C4—224no—
498C2×C22⋊C4—222no—
499C2×C22⋊C4—222no—
500C2×C22⋊C4—222no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—442no—
503C2×C22⋊C4—442no—
504C2×C22⋊C4—442no—
505C2×C22⋊C4C4×D1114yescomplemented
506C2×C22⋊C4C22⋊D1114yes—
507C2×C42—222no—
508C2×C42—222no—
509C2×C42—222no—
510#95—24no—
511#95—118no—
512#95—224no—
513#95—224no—
514#95—224no—
515#95—224no—
516#95—442no—
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—222no—
542C24—222no—
543C24—221no—
544C24—222no—
545C24—222no—
546C24—221no—
547C24C2×C4×D1112yes—
548C24#433912yes—
549C24D4×D1112yes—
550C24D4×D1112yes—
551C24Q8×D1112yes—
552C24#434312yes—
553C24C2×C22⋊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—28no—
563C22×C4—22no—
564C22×C4—22no—
565C22×C4—22no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
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—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—48no—
584C22×C4—48no—
585C22×C4—44no—
586C22×C4—44no—
587C22×C4—112no—
588C22×C4—112no—
589C22×C4—112no—
590C22×C4—112no—
591C22×C4—114no—
592C22×C4—114no—
593C22×C4—112no—
594C22×C4—228no—
595C22×C4—228no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—222no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—228no—
604C22×C4—228no—
605C22×C4—222no—
606C22×C4—221no—
607C22×C4—222no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—222no—
613C22×C4—222no—
614C22×C4—221no—
615C22×C4—222no—
616C22×C4—222no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—222no—
622C22×C4—448no—
623C22×C4—444no—
624C22×C4—448no—
625C22×C4—444no—
626C22×C4—444no—
627C22×C4—448no—
628C22×C4—448no—
629C22×C4—448no—
630C22×C4—444no—
631C22×C4—448no—
632C22×C4—444no—
633C22×C4C2×C4×D1114yes—
634C22×C4#434114yes—
635C22×C4C2×C22⋊D1112yes—
636C22×C4C2×C22⋊D1112yes—
637C4⋊C4—48no—
638C4⋊C4—228no—
639C22⋊C4—28no—
640C22⋊C4—28no—
641C22⋊C4—228no—
642C22⋊C4—448no—
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—24no—
655C23—22no—
656C23—24no—
657C23—24no—
658C23—24no—
659C23—24no—
660C23—22no—
661C23—22no—
662C23—24no—
663C23—114no—
664C23—222no—
665C23—222no—
666C23—222no—
667C23—222no—
668C23—224no—
669C23—222no—
670C23—224no—
671C23—222no—
672C23—224no—
673C23—224no—
674C23—224no—
675C23—224no—
676C23—442no—
677C23—442no—
678C23—442no—
679C23—442no—
680C23—441no—
681C23—441no—
682C23—442no—
683C23—442no—
684C23—441no—
685C23—441no—
686C23C4⋊C4×D1114yes—
687C23#6694614yes—
688C23#6694714yes—
689C23#6694914yes—
690C23C4×C22⋊D1114yes—
691C23#6699014yes—
692C23#6699914yes—
693C23C22×C4×D1111yescharacteristic
694C23C2×#433911yescharacteristic
695C23C2×D4×D1111yescharacteristic
696C23C2×D4×D1111yescharacteristic
697C23C2×#434112yes—
698C23#6703712yes—
699C23C2×Q8×D1111yescharacteristic
700C23C2×#434311yescharacteristic
701C23#41×D1112yes—
702C23#6704212yes—
703C23C22×C22⋊D1111yescharacteristic
704D4—2232no—
705C2×C4—24no—
706C2×C4—24no—
707C2×C4—22no—
708C2×C4—22no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
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—41no—
723C2×C4—42no—
724C2×C4—42no—
725C2×C4—41no—
726C2×C4—42no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—42no—
730C2×C4—114no—
731C2×C4—114no—
732C2×C4—222no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—224no—
740C2×C4—222no—
741C2×C4—224no—
742C2×C4—224no—
743C2×C4—222no—
744C2×C4—224no—
745C2×C4—224no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—4416no—
749C2×C4—4416no—
750C2×C4—4416no—
751C2×C4—442no—
752C2×C4—442no—
753C2×C4—442no—
754C2×C4—442no—
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×C4—442no—
764C22—24no—
765C22—24no—
766C22—28no—
767C22—24no—
768C22—28no—
769C22—24no—
770C22—24no—
771C22—28no—
772C22—24no—
773C22—28no—
774C22—228no—
775C22—224no—
776C22—442no—
777C22—442no—
778C22—444no—
779C22—442no—
780C22—444no—
781C22—442no—
782C22—442no—
783C22—442no—
784C22—444no—
785C22#1062260218yes—
786C22C2×C4⋊C4×D1111yescharacteristic
787C22C2×#6694611yescharacteristic
788C22C2×#6694711yescharacteristic
789C22C2×#6694911yescharacteristic
790C22C4×#434112yes—
791C22#1062307112yes—
792C22#1062307612yes—
793C22#1062309612yes—
794C22#1062311711yescharacteristic
795C22#1062312212yes—
796C22#1062312311yescharacteristic
797C22#1062315512yes—
798C22#1062316612yes—
799C22#1062316712yes—
800C22#1062317512yes—
801C22D11×#12311yescharacteristic
802C22#1062318411yescharacteristic
803C22#1062318512yes—
804C22C2×C4×C22⋊D1111yescharacteristic
805C22C2×#6699011yescharacteristic
806C22#1062333712yes—
807C22C2×#6699911yescharacteristic
808C22#1062336012yes—
809C4—44no—
810C4—44no—
811C4—42no—
812C4—42no—
813C4—224no—
814C4—224no—
815C4—442no—
816C4—444no—
817C4—882no—
818C2—28no—
819C2—444no—
820C2C2×#1062260211yescharacteristic
821C2#1307113511yescharacteristic
822C2#1307127311yescharacteristic
823C2#1307152212yes—
824C2#1307166112yes—
825C2#1307193211yescharacteristic
826C2#1307194011yescharacteristic
827C2#1307237012yes—
828C2#1307243612yes—
829C2#1307293211yescharacteristic
830C2#1307396611yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#14016
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
4. C22×C11⋊#95C2semidirect
5. #13066874C2semidirect
6. #13066858C2semidirect
7. #13066848C2semidirect
8. #13066838C2semidirect
9. #13066838C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#385C2semidirect
41. #10622571C4semidirect
68. C23×Dic11C2×C4semidirect
87. C2×C11×C22⋊C4C2×C4semidirect
100. C2×(C2×D11)⋊C4C2×C4semidirect
116. C11⋊#95C2×C4semidirect
176. C2×C22⋊D11C4⋊C4semidirect
235. C2×#385D11semidirect
505. 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×(C22⋊D11)⋊C42
C2×#106228262
C2×#106225712
C22×C11⋊#952
#130668742
#130668582
#130668482
#130668382
(C2×D11)⋊#952
C2×C11×#3852
#1401611