Finite Group Databasebeta

← #14677134

Subgroups — #14677134

Order 2816.

2950 conjugacy classes of subgroups.

The subgroup lattice has 850 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic
2C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
3C2×#10622826C211yesmaximal, characteristic
4C2×#10622571C211yesmaximal, characteristic
5C2×#10622602C212yesmaximal, complemented
6#13066879C212yesmaximal, complemented
7#13066860C212yesmaximal, complemented
8#13066847C212yesmaximal, complemented
9#13066838C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, 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⋊C4—24no—
25C22×Dic11⋊C4—28no—
26C22×Dic11⋊C4C2212yes—
27C22×Dic11⋊C4C2211yescharacteristic
28C22×Dic11⋊C4C2212yes—
29C22×C4×Dic11C2211yescharacteristic
30C2×(C22⋊D11)⋊C4—24no—
31C2×(C22⋊D11)⋊C4—24no—
32C2×(C22⋊D11)⋊C4—24no—
33C11×#385—24no—
34C2×C11×#95C2212yes—
35#10622826—24no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622602—28no—
43#10622571C418yescomplemented
44C25×C11C2311yescharacteristic
45C24×D11C2311yescharacteristic
46C23×C4×C11—22no—
47C23×C4×C11—24no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—42no—
51C23×C4×C11C2312yes—
52C23×C4×C11C2311yescharacteristic
53C23×C4×C11C2312yes—
54C23×C4×C11C2311yescharacteristic
55C22×C22⋊D11—22no—
56C22×C22⋊D11—22no—
57C22×C22⋊D11—22no—
58C22×C22⋊D11—22no—
59C22×C22⋊D11C2×C414yes—
60C22×C22⋊D11D414yes—
61C22×C22⋊D11Q814yes—
62C23×Dic11—22no—
63C23×Dic11—22no—
64C23×Dic11—24no—
65C23×Dic11—24no—
66C23×Dic11—22no—
67C23×Dic11—22no—
68C23×Dic11—24no—
69C23×Dic11—42no—
70C23×Dic11C2×C414yescomplemented
71C23×Dic11D414yes—
72C23×Dic11C2312yes—
73C23×Dic11C2311yescharacteristic
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2312yes—
76C23×Dic11C2311yescharacteristic
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—24no—
81C22×C4×D11—42no—
82C2×C11×C4⋊C4—24no—
83C2×C11×C4⋊C4—24no—
84C2×C11×C4⋊C4—42no—
85C2×C11×C22⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4C2×C414yescomplemented
90C2×C11×C22⋊C4D414yes—
91C2×C22⋊Dic11—22no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—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—42no—
102C2×(C2×D11)⋊C4C2×C418yescomplemented
103C2×Dic11⋊C4—232no—
104C2×Dic11⋊C4—22no—
105C2×Dic11⋊C4—24no—
106C2×Dic11⋊C4—22no—
107C2×Dic11⋊C4—22no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4D418yescomplemented
113C2×C4×Dic11—22no—
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116(C22⋊D11)⋊C4—232no—
117C11×#95—24no—
118C11⋊#95—24no—
119C11⋊#95—24no—
120C11⋊#95—24no—
121C11⋊#95—24no—
122C11⋊#95—42no—
123C11⋊#95C2×C418yescomplemented
124#14015—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—22no—
128C24×C11—22no—
129C24×C11C22×C412yes—
130C24×C11C2×D412yes—
131C24×C11C2×D412yes—
132C24×C11C2×D412yes—
133C24×C11C2×Q812yes—
134C24×C11#4112yes—
135C24×C11#4112yes—
136C24×C11C2411yescharacteristic
137C23×D11—22no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—22no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11C22×C412yes—
146C23×D11C2×D412yes—
147C23×D11C2×Q812yes—
148C22×C4×C11—28no—
149C22×C4×C11—22no—
150C22×C4×C11—22no—
151C22×C4×C11—22no—
152C22×C4×C11—22no—
153C22×C4×C11—22no—
154C22×C4×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
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—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—48no—
170C22×C4×C11—48no—
171C22×C4×C11—44no—
172C22×C4×C11—44no—
173C22×C4×C11C22×C414yes—
174C22×C4×C11C2×D414yes—
175C22×C4×C11C2×D412yes—
176C22×C4×C11C2×D412yes—
177C2×C22⋊D11—28no—
178C2×C22⋊D11—28no—
179C2×C22⋊D11—28no—
180C2×C22⋊D11—28no—
181C2×C22⋊D11—28no—
182C2×C22⋊D11—28no—
183C2×C22⋊D11C4⋊C4116yescomplemented
184C22×Dic11—28no—
185C22×Dic11—28no—
186C22×Dic11—216no—
187C22×Dic11—216no—
188C22×Dic11—28no—
189C22×Dic11—28no—
190C22×Dic11—28no—
191C22×Dic11—21no—
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—22no—
196C22×Dic11—22no—
197C22×Dic11—22no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—22no—
201C22×Dic11—22no—
202C22×Dic11—22no—
203C22×Dic11—22no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—44no—
214C22×Dic11—48no—
215C22×Dic11—48no—
216C22×Dic11C22×C412yes—
217C22×Dic11C22×C414yes—
218C22×Dic11C2×D412yes—
219C22×Dic11C2×D412yes—
220C22×Dic11C2×D414yes—
221C22×Dic11C2×D414yes—
222C22×Dic11C2×D412yes—
223C22×Dic11C2×Q812yes—
224C22×Dic11#4114yes—
225C2×C4×D11—28no—
226C2×C4×D11—48no—
227C2×C4×D11—48no—
228C2×C4×D11—44no—
229C2×C4×D11—44no—
230C11×C4⋊C4—48no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C22⋊Dic11—44no—
234(C2×D11)⋊C4—28no—
235(C2×D11)⋊C4—216no—
236(C2×D11)⋊C4—48no—
237Dic11⋊C4—28no—
238Dic11⋊C4—216no—
239Dic11⋊C4—216no—
240C4×Dic11—28no—
241C22×C4×D4—111no—
242C23×C4⋊C4—111no—
243C2×#386—111no—
244C2×#386—111no—
245C2×#385—112no—
246C2×#385D1111yescharacteristic, complemented
247#1444—112no—
248#1439—112no—
249#1436—112no—
250C22⋊#95—111no—
251C22⋊#95—111no—
252C23×C11—24no—
253C23×C11—24no—
254C23×C11—22no—
255C23×C11—22no—
256C23×C11—24no—
257C23×C11—22no—
258C23×C11—22no—
259C23×C11—24no—
260C23×C11—24no—
261C23×C11—24no—
262C23×C11—24no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—24no—
266C23×C11—24no—
267C23×C11—24no—
268C23×C11C2×C4⋊C414yes—
269C23×C11C4×D414yes—
270C23×C11C4×D414yes—
271C23×C11#12014yes—
272C23×C11C22⋊Q814yes—
273C23×C11C22⋊Q814yes—
274C23×C11#12314yes—
275C23×C11C23×C411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D412yes—
279C23×C11C22×D411yescharacteristic
280C23×C11C22×Q811yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4112yes—
284C23×C11H(5,𝔽2)12yes—
285C23×C112−1+412yes—
286C22×D11—24no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—24no—
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—24no—
298C22×D11—41no—
299C22×D11—42no—
300C22×D11—41no—
301C22×D11—41no—
302C22×D11—41no—
303C22×D11—42no—
304C22×D11—42no—
305C22×D11—42no—
306C22×D11—42no—
307C22×D11—42no—
308C22×D11C2×C4⋊C414yescomplemented
309C2×C4×C11—24no—
310C2×C4×C11—24no—
311C2×C4×C11—24no—
312C2×C4×C11—22no—
313C2×C4×C11—24no—
314C2×C4×C11—22no—
315C2×C4×C11—24no—
316C2×C4×C11—24no—
317C2×C4×C11—24no—
318C2×C4×C11—24no—
319C2×C4×C11—416no—
320C2×C4×C11—41no—
321C2×C4×C11—42no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—42no—
325C2×C4×C11—41no—
326C2×C4×C11—42no—
327C2×C4×C11—42no—
328C2×C4×C11—42no—
329C2×C4×C11—42no—
330C2×C4×C11—42no—
331C2×C4×C11—42no—
332C2×C4×C11—42no—
333C2×C4×C11—42no—
334C22⋊D11—232no—
335C2×Dic11—232no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—22no—
339C2×Dic11—22no—
340C2×Dic11—22no—
341C2×Dic11—22no—
342C2×Dic11—24no—
343C2×Dic11—22no—
344C2×Dic11—22no—
345C2×Dic11—22no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—22no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—22no—
353C2×Dic11—22no—
354C2×Dic11—22no—
355C2×Dic11—416no—
356C2×Dic11—42no—
357C2×Dic11—42no—
358C2×Dic11—42no—
359C2×Dic11—42no—
360C2×Dic11—42no—
361C2×Dic11—42no—
362C2×Dic11—42no—
363C2×Dic11—42no—
364C2×Dic11—42no—
365C2×Dic11C2×C4⋊C414yescomplemented
366C2×Dic11C4×D418yescomplemented
367C2×Dic11#12014yes—
368C4×D11—416no—
369C23×D4—111no—
370C24×C4—111no—
371C24×C4—111no—
372C24×C4—111no—
373C24×C4C2×D1111yescharacteristic
374C2×C4×D4—224no—
375C2×C4×D4—224no—
376C2×C4×D4—224no—
377C22×C4⋊C4—112no—
378C22×C4⋊C4—112no—
379C22×C4⋊C4—111no—
380C22×C4⋊C4—228no—
381C22×C4⋊C4—224no—
382C22×C4⋊C4C2×D1112yes—
383C22×C22⋊C4—112no—
384C22×C22⋊C4—111no—
385C22×C22⋊C4—111no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389C22×C42—111no—
390#386—118no—
391#386—224no—
392#385—24no—
393#385—228no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—112no—
399C2×#95—112no—
400C2×#95C2×D1112yes—
401C22×C11—24no—
402C22×C11—24no—
403C22×C11—28no—
404C22×C11—28no—
405C22×C11—24no—
406C22×C11—24no—
407C22×C11—24no—
408C22×C11—28no—
409C22×C11—28no—
410C22×C11—24no—
411C22×C11#38518yescomplemented
412C22×C11C22×C4⋊C411yescharacteristic
413C22×C11C2×C4×D411yescharacteristic
414C22×C11C2×C4×D411yescharacteristic
415C22×C11C2×C4×D412yes—
416C22×C11#52012yes—
417C22×C11C2×#12011yescharacteristic
418C22×C11C2×#12011yescharacteristic
419C22×C11C2×C22⋊Q811yescharacteristic
420C22×C11C2×C22⋊Q811yescharacteristic
421C22×C11C2×#12311yescharacteristic
422C22×C11#52512yes—
423C22×C11#52511yescharacteristic
424C22×C11#53411yescharacteristic
425C22×C11#53611yescharacteristic
426C22×C11#53912yes—
427C22×C11D4212yes—
428C22×C11D4212yes—
429C22×C11#54712yes—
430C22×C11#54712yes—
431C22×C11#54812yes—
432C22×C11D4×Q812yes—
433C22×C11#55312yes—
434C22×C11#55412yes—
435C2×D11—28no—
436C2×D11—24no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—44no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—42no—
443C2×D11—44no—
444C2×D11—44no—
445C2×D11—42no—
446C4×C11—44no—
447C4×C11—44no—
448C4×C11—42no—
449C4×C11—42no—
450Dic11—24no—
451Dic11—24no—
452Dic11—28no—
453Dic11—42no—
454Dic11—82no—
455C25—111no—
456C25C22×D1111yescharacteristic
457C22×D4—114no—
458C22×D4—114no—
459C22×D4—114no—
460C22×D4—222no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C23×C4—22no—
465C23×C4—24no—
466C23×C4—22no—
467C23×C4—22no—
468C23×C4—42no—
469C23×C4—112no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—114no—
473C23×C4—111no—
474C23×C4—114no—
475C23×C4—112no—
476C23×C4—222no—
477C23×C4—224no—
478C23×C4—222no—
479C23×C4—224no—
480C23×C4—224no—
481C23×C4—224no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—222no—
486C23×C4—222no—
487C23×C4—442no—
488C23×C4—442no—
489C23×C4C22×D1112yes—
490C23×C4C22×D1112yes—
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C4×D4—2232no—
494C2×C4⋊C4—24no—
495C2×C4⋊C4—24no—
496C2×C4⋊C4—42no—
497C2×C4⋊C4—118no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—224no—
501C2×C4⋊C4—224no—
502C2×C4⋊C4—222no—
503C2×C4⋊C4—222no—
504C2×C4⋊C4—2232no—
505C2×C4⋊C4—224no—
506C2×C4⋊C4—222no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—118no—
512C2×C22⋊C4—222no—
513C2×C22⋊C4—224no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—222no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—224no—
518C2×C22⋊C4—222no—
519C2×C22⋊C4—222no—
520C2×C22⋊C4—222no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—442no—
523C2×C22⋊C4C4×D1114yescomplemented
524C2×C22⋊C4C22⋊D1114yes—
525C2×C42—222no—
526C2×C42—222no—
527C2×C42—222no—
528#95—24no—
529#95—118no—
530#95—224no—
531#95—224no—
532#95—224no—
533#95—224no—
534#95—442no—
535C2×C11—28no—
536C2×C11C2×#38511yescharacteristic
537C2×C11C4×#12011yescharacteristic
538C2×C11#232211yescharacteristic
539C2×C11D4×C4⋊C412yes—
540C2×C11#236112yes—
541C2×C11#240311yescharacteristic
542C2×C11#240611yescharacteristic
543C2×C11#240911yescharacteristic
544C2×C11#244312yes—
545C2×C11#244912yes—
546C2×C11#257911yescharacteristic
547D11—44no—
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—112no—
553C24—112no—
554C24—112no—
555C24—221no—
556C24—222no—
557C24—221no—
558C24—222no—
559C24—221no—
560C24—222no—
561C24—222no—
562C24—221no—
563C24C2×C4×D1112yes—
564C24#433912yes—
565C24D4×D1112yes—
566C24D4×D1112yes—
567C24Q8×D1112yes—
568C24#434312yes—
569C24C2×C22⋊D1112yes—
570C24C23×D1111yescharacteristic
571C2×D4—1116no—
572C2×D4—228no—
573C2×D4—228no—
574C2×D4—228no—
575C2×D4—228no—
576C2×D4—228no—
577C2×D4—228no—
578C22×C4—28no—
579C22×C4—22no—
580C22×C4—22no—
581C22×C4—22no—
582C22×C4—22no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—21no—
586C22×C4—21no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—22no—
594C22×C4—22no—
595C22×C4—22no—
596C22×C4—22no—
597C22×C4—22no—
598C22×C4—22no—
599C22×C4—48no—
600C22×C4—48no—
601C22×C4—44no—
602C22×C4—44no—
603C22×C4—112no—
604C22×C4—114no—
605C22×C4—112no—
606C22×C4—114no—
607C22×C4—114no—
608C22×C4—112no—
609C22×C4—112no—
610C22×C4—114no—
611C22×C4—112no—
612C22×C4—228no—
613C22×C4—2216no—
614C22×C4—228no—
615C22×C4—228no—
616C22×C4—2216no—
617C22×C4—228no—
618C22×C4—228no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—221no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—221no—
627C22×C4—222no—
628C22×C4—221no—
629C22×C4—221no—
630C22×C4—228no—
631C22×C4—221no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—221no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—222no—
642C22×C4—448no—
643C22×C4—444no—
644C22×C4—448no—
645C22×C4—444no—
646C22×C4—444no—
647C22×C4—448no—
648C22×C4—448no—
649C22×C4C2×C4×D1114yes—
650C22×C4D4×D1114yes—
651C22×C4C2×C22⋊D1112yes—
652C22×C4C2×C22⋊D1112yes—
653C4⋊C4—48no—
654C4⋊C4—2216no—
655C4⋊C4—2216no—
656C4⋊C4—228no—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—2216no—
660C22⋊C4—228no—
661C22⋊C4—448no—
662C22⋊C4—444no—
663C42—228no—
664C11#1401511yescharacteristic, complemented, Sylow
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—22no—
672C23—22no—
673C23—24no—
674C23—24no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—22no—
679C23—24no—
680C23—22no—
681C23—114no—
682C23—222no—
683C23—222no—
684C23—222no—
685C23—222no—
686C23—222no—
687C23—224no—
688C23—224no—
689C23—222no—
690C23—224no—
691C23—224no—
692C23—224no—
693C23—224no—
694C23—442no—
695C23—442no—
696C23—442no—
697C23—442no—
698C23—441no—
699C23—441no—
700C23—442no—
701C23—442no—
702C23—441no—
703C23—441no—
704C23C4⋊C4×D1114yes—
705C23#6694614yes—
706C23#6694714yes—
707C23#6694914yes—
708C23C4×C22⋊D1114yes—
709C23#6699014yes—
710C23#6699914yes—
711C23C22×C4×D1111yescharacteristic
712C23C2×#433911yescharacteristic
713C23C2×D4×D1111yescharacteristic
714C23C2×D4×D1111yescharacteristic
715C23C2×D4×D1112yes—
716C23#6703712yes—
717C23C2×Q8×D1111yescharacteristic
718C23C2×#434311yescharacteristic
719C23#41×D1112yes—
720C23#6704312yes—
721C23C22×C22⋊D1111yescharacteristic
722D4—2232no—
723C2×C4—24no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—24no—
727C2×C4—24no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—24no—
731C2×C4—24no—
732C2×C4—24no—
733C2×C4—416no—
734C2×C4—42no—
735C2×C4—42no—
736C2×C4—42no—
737C2×C4—42no—
738C2×C4—42no—
739C2×C4—42no—
740C2×C4—41no—
741C2×C4—42no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—41no—
746C2×C4—42no—
747C2×C4—41no—
748C2×C4—114no—
749C2×C4—118no—
750C2×C4—114no—
751C2×C4—2232no—
752C2×C4—224no—
753C2×C4—222no—
754C2×C4—222no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—222no—
758C2×C4—222no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—222no—
762C2×C4—224no—
763C2×C4—222no—
764C2×C4—224no—
765C2×C4—224no—
766C2×C4—224no—
767C2×C4—224no—
768C2×C4—222no—
769C2×C4—222no—
770C2×C4—222no—
771C2×C4—4416no—
772C2×C4—4416no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4—442no—
781C2×C4—442no—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—228no—
793C22—224no—
794C22—442no—
795C22—444no—
796C22—444no—
797C22—442no—
798C22—442no—
799C22—442no—
800C22—442no—
801C22—442no—
802C22—444no—
803C22#1062260218yescomplemented
804C22C2×C4⋊C4×D1111yescharacteristic
805C22C2×#6694611yescharacteristic
806C22C2×#6694711yescharacteristic
807C22C2×#6694911yescharacteristic
808C22#1062307112yes—
809C22C4×D4×D1112yes—
810C22#1062307712yes—
811C22#1062308312yes—
812C22D11×#12011yescharacteristic
813C22#1062312011yescharacteristic
814C22#1062312112yes—
815C22#1062315812yes—
816C22#1062316312yes—
817C22#1062316712yes—
818C22#1062317612yes—
819C22#1062317911yescharacteristic
820C22#1062318612yes—
821C22#1062318711yescharacteristic
822C22C2×C4×C22⋊D1111yescharacteristic
823C22C2×#6699011yescharacteristic
824C22D4×C22⋊D1112yes—
825C22C2×#6699911yescharacteristic
826C22#1062335512yes—
827C4—44no—
828C4—44no—
829C4—42no—
830C4—42no—
831C4—228no—
832C4—224no—
833C4—224no—
834C4—442no—
835C4—882no—
836C2—28no—
837C2—444no—
838C2C2×#1062260211yescharacteristic
839C2#1307111711yescharacteristic
840C2#1307128411yescharacteristic
841C2#1307151412yes—
842C2#1307163312yes—
843C2#1307192711yescharacteristic
844C2#1307194811yescharacteristic
845C2#1307198011yescharacteristic
846C2#1307235512yes—
847C2#1307242112yes—
848C2#1307396811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#385C2
socle, cosocleC24×C11C24
prime radicalC23×C22⋊D11C22
hypercenterC2×#385D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#385

Complements

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

NH ≅ G/Ntype
2. C23×Dic11⋊C4C2semidirect
5. C2×#10622602C2semidirect
6. #13066879C2semidirect
7. #13066860C2semidirect
8. #13066847C2semidirect
9. #13066838C2semidirect
10. #13066838C2semidirect
11. C2×C11×#385C2semidirect
43. #10622571C4semidirect
70. C23×Dic11C2×C4semidirect
89. C2×C11×C22⋊C4C2×C4semidirect
102. C2×(C2×D11)⋊C4C2×C4semidirect
112. C2×Dic11⋊C4D4semidirect
123. C11⋊#95C2×C4semidirect
183. C2×C22⋊D11C4⋊C4semidirect
246. C2×#385D11semidirect
308. C22×D11C2×C4⋊C4semidirect
365. C2×Dic11C2×C4⋊C4semidirect
366. C2×Dic11C4×D4semidirect
411. C22×C11#385semidirect
523. C2×C22⋊C4C4×D11semidirect
664. C11#14015semidirect
803. C22#10622602semidirect

Maximal subgroups

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

subgroupindex
C22×(C22⋊D11)⋊C42
C23×Dic11⋊C42
C2×#106228262
C2×#106225712
C2×#106226022
#130668792
#130668602
#130668472
#130668382
C2×C11×#3852
#1401511