Finite Group Databasebeta

← #14677131

Subgroups — #14677131

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
1C23×Dic11⋊C4C211yesmaximal, characteristic, complemented
2C2×#10622833C211yesmaximal, characteristic
3C2×#10622833C211yesmaximal, characteristic
4C2×#10622823C212yesmaximal, complemented
5C2×#10622559C211yesmaximal, characteristic, complemented
6#13066879C212yesmaximal, complemented
7#13066859C212yesmaximal, complemented
8#13066849C212yesmaximal, complemented
9#13066839C211yesmaximal, characteristic, complemented
10#13066838C211yesmaximal, characteristic, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2211yescharacteristic
16C24×Dic11C2211yescharacteristic
17C2×C4×D4×C11—24no—
18C2×C4×D4×C11—24no—
19C2×C4×D4×C11—24no—
20C22×C11×C4⋊C4C2211yescharacteristic
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C22⋊Dic11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C22×C22⋊Dic11C2212yes—
28C22×Dic11⋊C4—24no—
29C22×Dic11⋊C4—28no—
30C22×Dic11⋊C4C2212yes—
31C22×Dic11⋊C4C2212yes—
32C22×Dic11⋊C4C2212yes—
33#10622833—24no—
34#10622833C418yescomplemented
35#10622823—28no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622559—24no—
44C25×C11C2311yescharacteristic
45C25×C11C2311yescharacteristic
46C22×D4×C11—22no—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11C2×C414yes—
51C22×D4×C11D414yes—
52C22×D4×C11Q814yes—
53C23×C4×C11—22no—
54C23×C4×C11—22no—
55C23×C4×C11—22no—
56C23×C4×C11—24no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—24no—
60C23×C4×C11—42no—
61C23×C4×C11—42no—
62C23×C4×C11D414yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×Dic11—22no—
69C23×Dic11—22no—
70C23×Dic11—24no—
71C23×Dic11—24no—
72C23×Dic11—22no—
73C23×Dic11—24no—
74C23×Dic11—22no—
75C23×Dic11—22no—
76C23×Dic11—42no—
77C23×Dic11C2×C414yescomplemented
78C23×Dic11C2312yes—
79C23×Dic11C2312yes—
80C23×Dic11C2312yes—
81C23×Dic11C2312yes—
82C4×D4×C11—232no—
83C2×C11×C4⋊C4—22no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C22⋊C4—22no—
87C2×C11×C22⋊C4—22no—
88C2×C11×C22⋊C4—22no—
89C2×C11×C22⋊C4—22no—
90C2×C11×C22⋊C4—22no—
91C2×C11×C22⋊C4D414yes—
92C2×C42×C11—22no—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—22no—
101C2×C22⋊Dic11—22no—
102C2×C22⋊Dic11—22no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—42no—
105C2×C22⋊Dic11C2×C418yescomplemented
106C2×C22⋊Dic11C2×C414yescomplemented
107C2×Dic11⋊C4—232no—
108C2×Dic11⋊C4—24no—
109C2×Dic11⋊C4—24no—
110C2×Dic11⋊C4—24no—
111C2×Dic11⋊C4—24no—
112C2×Dic11⋊C4—24no—
113C2×Dic11⋊C4—24no—
114C2×Dic11⋊C4—24no—
115C2×Dic11⋊C4—42no—
116C2×Dic11⋊C4D418yescomplemented
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×C11—22no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—22no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11C22×C412yes—
138C24×C11C22×C412yes—
139C24×C11C2×D412yes—
140C24×C11C2×D412yes—
141C24×C11C2×D412yes—
142C24×C11C2×D412yes—
143C24×C11C2×Q812yes—
144C24×C11C2×Q812yes—
145C24×C11#4112yes—
146C24×C11#4112yes—
147C24×C11C2411yescharacteristic
148C2×D4×C11—28no—
149C2×D4×C11—28no—
150C2×D4×C11—28no—
151C2×D4×C11—28no—
152C2×D4×C11—28no—
153C2×D4×C11—28no—
154C2×D4×C11C4⋊C4116yescomplemented
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—22no—
162C22×C4×C11—28no—
163C22×C4×C11—28no—
164C22×C4×C11—22no—
165C22×C4×C11—22no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—22no—
173C22×C4×C11—22no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—28no—
177C22×C4×C11—44no—
178C22×C4×C11—48no—
179C22×C4×C11—48no—
180C22×C4×C11—48no—
181C22×C4×C11—48no—
182C22×C4×C11—44no—
183C22×C4×C11—44no—
184C22×C4×C11C22×C412yes—
185C22×C4×C11C2×D412yes—
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×Q812yes—
192C22×Dic11—28no—
193C22×Dic11—28no—
194C22×Dic11—216no—
195C22×Dic11—216no—
196C22×Dic11—28no—
197C22×Dic11—28no—
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—22no—
207C22×Dic11—22no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—22no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—22no—
220C22×Dic11—22no—
221C22×Dic11—48no—
222C22×Dic11—48no—
223C22×Dic11—44no—
224C22×Dic11—44no—
225C22×Dic11C22×C414yes—
226C22×Dic11C22×C414yes—
227C22×Dic11C2×D414yes—
228C22×Dic11C2×D414yes—
229C22×Dic11#4114yes—
230C11×C4⋊C4—28no—
231C11×C22⋊C4—28no—
232C11×C22⋊C4—28no—
233C42×C11—28no—
234C22⋊Dic11—216no—
235C22⋊Dic11—28no—
236C22⋊Dic11—48no—
237C22⋊Dic11—44no—
238Dic11⋊C4—216no—
239Dic11⋊C4—216no—
240Dic11⋊C4—48no—
241C22×C4×D4D1111yescharacteristic
242C23×C4⋊C4—111no—
243C2×#386—111no—
244C2×#386—111no—
245C2×#385—112no—
246C2×#385—111no—
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×C11—24no—
269C23×C11—22no—
270C23×C11—22no—
271C23×C11—24no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—41no—
281C23×C11—42no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—41no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11—42no—
290C23×C11C2×C4⋊C414yes—
291C23×C11C2×C4⋊C414yescomplemented
292C23×C11C4×D414yes—
293C23×C11C4×D414yes—
294C23×C11#12014yes—
295C23×C11C22⋊Q814yes—
296C23×C11C22⋊Q814yes—
297C23×C11#12314yes—
298C23×C11C23×C411yescharacteristic
299C23×C11C22×D412yes—
300C23×C11C22×D411yescharacteristic
301C23×C11C22×D411yescharacteristic
302C23×C11C22×D411yescharacteristic
303C23×C11C22×Q811yescharacteristic
304C23×C11C2×#4111yescharacteristic
305C23×C11C2×#4111yescharacteristic
306C23×C11C2×#4112yes—
307C23×C11H(5,𝔽2)12yes—
308C23×C112−1+412yes—
309D4×C11—232no—
310C2×C4×C11—22no—
311C2×C4×C11—22no—
312C2×C4×C11—22no—
313C2×C4×C11—22no—
314C2×C4×C11—22no—
315C2×C4×C11—22no—
316C2×C4×C11—22no—
317C2×C4×C11—22no—
318C2×C4×C11—24no—
319C2×C4×C11—24no—
320C2×C4×C11—22no—
321C2×C4×C11—22no—
322C2×C4×C11—22no—
323C2×C4×C11—22no—
324C2×C4×C11—22no—
325C2×C4×C11—24no—
326C2×C4×C11—24no—
327C2×C4×C11—416no—
328C2×C4×C11—416no—
329C2×C4×C11—41no—
330C2×C4×C11—41no—
331C2×C4×C11—41no—
332C2×C4×C11—41no—
333C2×C4×C11—42no—
334C2×C4×C11—42no—
335C2×C4×C11—42no—
336C2×C4×C11—42no—
337C2×C4×C11C2×C4⋊C414yescomplemented
338C2×C4×C11#12014yes—
339C2×Dic11—232no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—24no—
343C2×Dic11—24no—
344C2×Dic11—24no—
345C2×Dic11—24no—
346C2×Dic11—24no—
347C2×Dic11—24no—
348C2×Dic11—24no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—416no—
353C2×Dic11—42no—
354C2×Dic11—42no—
355C2×Dic11—42no—
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×Dic11—42no—
366C2×Dic11—42no—
367C2×Dic11—42no—
368C2×Dic11C4×D418yescomplemented
369C23×D4C2×D1111yescharacteristic
370C24×C4—111no—
371C24×C4—111no—
372C24×C4C2×D1111yescharacteristic
373C24×C4C2×D1111yescharacteristic
374C2×C4×D4—24no—
375C2×C4×D4—24no—
376C2×C4×D4—24no—
377C22×C4⋊C4—112no—
378C22×C4⋊C4—112no—
379C22×C4⋊C4—112no—
380C22×C4⋊C4—228no—
381C22×C4⋊C4—224no—
382C22×C4⋊C4C2×D1111yescharacteristic
383C22×C22⋊C4—111no—
384C22×C22⋊C4—112no—
385C22×C22⋊C4—111no—
386C22×C22⋊C4—112no—
387C22×C22⋊C4C2×D1111yescharacteristic
388C22×C22⋊C4C2×D1111yescharacteristic
389C22×C42C2×D1111yescharacteristic
390#386—118no—
391#386—224no—
392#385—228no—
393#385—224no—
394C2×#95—112no—
395C2×#95—112no—
396C2×#95—112no—
397C2×#95—112no—
398C2×#95—112no—
399C2×#95—112no—
400C2×#95—112no—
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—28no—
412C22×C11—24no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—44no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—42no—
419C22×C11—44no—
420C22×C11—44no—
421C22×C11—42no—
422C22×C11#38518yescomplemented
423C22×C11C22×C4⋊C411yescharacteristic
424C22×C11C2×C4×D411yescharacteristic
425C22×C11C2×C4×D411yescharacteristic
426C22×C11C2×C4×D412yes—
427C22×C11#52012yes—
428C22×C11C2×#12011yescharacteristic
429C22×C11C2×#12011yescharacteristic
430C22×C11C2×C22⋊Q811yescharacteristic
431C22×C11C2×C22⋊Q811yescharacteristic
432C22×C11C2×#12311yescharacteristic
433C22×C11#52512yes—
434C22×C11#52511yescharacteristic
435C22×C11#53411yescharacteristic
436C22×C11#53611yescharacteristic
437C22×C11#53912yes—
438C22×C11D4212yes—
439C22×C11D4212yes—
440C22×C11#54712yes—
441C22×C11#54712yes—
442C22×C11#54812yes—
443C22×C11D4×Q812yes—
444C22×C11#55312yes—
445C22×C11#55412yes—
446C4×C11—24no—
447C4×C11—24no—
448C4×C11—42no—
449C4×C11—42no—
450C4×C11—42no—
451Dic11—28no—
452Dic11—44no—
453Dic11—44no—
454Dic11—82no—
455C25C22×D1111yescharacteristic
456C25C22×D1111yescharacteristic
457C22×D4—22no—
458C22×D4—22no—
459C22×D4—22no—
460C22×D4—22no—
461C22×D4Dic2214yes—
462C22×D4C4×D1114yes—
463C22×D4C22⋊D1114yes—
464C23×C4—22no—
465C23×C4—22no—
466C23×C4—22no—
467C23×C4—24no—
468C23×C4—22no—
469C23×C4—22no—
470C23×C4—24no—
471C23×C4—42no—
472C23×C4—42no—
473C23×C4—112no—
474C23×C4—114no—
475C23×C4—112no—
476C23×C4—112no—
477C23×C4—112no—
478C23×C4—224no—
479C23×C4—224no—
480C23×C4—224no—
481C23×C4—222no—
482C23×C4—222no—
483C23×C4—222no—
484C23×C4—222no—
485C23×C4—222no—
486C23×C4—442no—
487C23×C4C22⋊D1114yes—
488C23×C4C22×D1111yescharacteristic
489C23×C4C22×D1111yescharacteristic
490C23×C4C22×D1111yescharacteristic
491C23×C4C22×D1111yescharacteristic
492C23×C4C22×D1111yescharacteristic
493C4×D4—232no—
494C2×C4⋊C4—22no—
495C2×C4⋊C4—22no—
496C2×C4⋊C4—22no—
497C2×C4⋊C4—118no—
498C2×C4⋊C4—224no—
499C2×C4⋊C4—224no—
500C2×C4⋊C4—2232no—
501C2×C4⋊C4—224no—
502C2×C4⋊C4—224no—
503C2×C4⋊C4—224no—
504C2×C4⋊C4—224no—
505C2×C4⋊C4—224no—
506C2×C4⋊C4—442no—
507C2×C22⋊C4—22no—
508C2×C22⋊C4—22no—
509C2×C22⋊C4—22no—
510C2×C22⋊C4—22no—
511C2×C22⋊C4—22no—
512C2×C22⋊C4—118no—
513C2×C22⋊C4—114no—
514C2×C22⋊C4—224no—
515C2×C22⋊C4—224no—
516C2×C22⋊C4—222no—
517C2×C22⋊C4—222no—
518C2×C22⋊C4—224no—
519C2×C22⋊C4—222no—
520C2×C22⋊C4—222no—
521C2×C22⋊C4—224no—
522C2×C22⋊C4—222no—
523C2×C22⋊C4—442no—
524C2×C22⋊C4C22⋊D1114yes—
525C2×C42—22no—
526C2×C42—22no—
527C2×C42—22no—
528#95—118no—
529#95—224no—
530#95—224no—
531#95—224no—
532#95—224no—
533#95—224no—
534#95—442no—
535C2×C11—28no—
536C2×C11—44no—
537C2×C11C2×#38511yescharacteristic
538C2×C11C4×#12011yescharacteristic
539C2×C11#232211yescharacteristic
540C2×C11D4×C4⋊C412yes—
541C2×C11#236112yes—
542C2×C11#240311yescharacteristic
543C2×C11#240611yescharacteristic
544C2×C11#240911yescharacteristic
545C2×C11#244312yes—
546C2×C11#244912yes—
547C2×C11#257911yescharacteristic
548C24—22no—
549C24—22no—
550C24—22no—
551C24—22no—
552C24—21no—
553C24—21no—
554C24—22no—
555C24—22no—
556C24—22no—
557C24—22no—
558C24—21no—
559C24—21no—
560C24C2×Dic2212yes—
561C24C2×Dic2212yes—
562C24C2×C4×D1112yes—
563C24C2×C4×D1112yes—
564C24#433912yes—
565C24#433912yes—
566C24C2×C22⋊D1112yes—
567C24C2×C22⋊D1112yes—
568C24C2×C22⋊D1112yes—
569C24C2×C22⋊D1112yes—
570C24C23×D1111yescharacteristic
571C2×D4—28no—
572C2×D4—28no—
573C2×D4—28no—
574C2×D4—28no—
575C2×D4—28no—
576C2×D4—28no—
577C2×D4Dic11⋊C4116yescomplemented
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—22no—
581C22×C4—21no—
582C22×C4—21no—
583C22×C4—21no—
584C22×C4—21no—
585C22×C4—28no—
586C22×C4—28no—
587C22×C4—22no—
588C22×C4—22no—
589C22×C4—22no—
590C22×C4—22no—
591C22×C4—22no—
592C22×C4—22no—
593C22×C4—21no—
594C22×C4—21no—
595C22×C4—21no—
596C22×C4—21no—
597C22×C4—21no—
598C22×C4—21no—
599C22×C4—28no—
600C22×C4—44no—
601C22×C4—48no—
602C22×C4—48no—
603C22×C4—48no—
604C22×C4—48no—
605C22×C4—44no—
606C22×C4—44no—
607C22×C4—114no—
608C22×C4—114no—
609C22×C4—114no—
610C22×C4—114no—
611C22×C4—114no—
612C22×C4—2216no—
613C22×C4—228no—
614C22×C4—2216no—
615C22×C4—228no—
616C22×C4—228no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—222no—
620C22×C4—222no—
621C22×C4—228no—
622C22×C4—222no—
623C22×C4—222no—
624C22×C4—222no—
625C22×C4—222no—
626C22×C4—222no—
627C22×C4—222no—
628C22×C4—222no—
629C22×C4—222no—
630C22×C4—222no—
631C22×C4—222no—
632C22×C4—222no—
633C22×C4—222no—
634C22×C4—222no—
635C22×C4—222no—
636C22×C4—222no—
637C22×C4—222no—
638C22×C4—222no—
639C22×C4—222no—
640C22×C4—222no—
641C22×C4—448no—
642C22×C4—448no—
643C22×C4—444no—
644C22×C4—444no—
645C22×C4C2×Dic2212yes—
646C22×C4C2×C4×D1112yes—
647C22×C4D4×D1114yes—
648C22×C4C2×C22⋊D1112yes—
649C22×C4C2×C22⋊D1112yes—
650C22×C4C2×C22⋊D1112yes—
651C22×C4C2×C22⋊D1112yes—
652C22×C4C2×C22⋊D1112yes—
653C4⋊C4—28no—
654C4⋊C4—2216no—
655C4⋊C4—2216no—
656C4⋊C4—448no—
657C22⋊C4—28no—
658C22⋊C4—28no—
659C22⋊C4—2216no—
660C22⋊C4—228no—
661C22⋊C4—448no—
662C22⋊C4—444no—
663C42—28no—
664C11#1401511yescharacteristic, complemented, Sylow
665C23—24no—
666C23—24no—
667C23—24no—
668C23—22no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—24no—
673C23—24no—
674C23—22no—
675C23—24no—
676C23—24no—
677C23—24no—
678C23—24no—
679C23—22no—
680C23—22no—
681C23—22no—
682C23—22no—
683C23—22no—
684C23—22no—
685C23—22no—
686C23—24no—
687C23—24no—
688C23—24no—
689C23—24no—
690C23—24no—
691C23—24no—
692C23—22no—
693C23—42no—
694C23—41no—
695C23—42no—
696C23—42no—
697C23—41no—
698C23—42no—
699C23—42no—
700C23—42no—
701C23—41no—
702C23—41no—
703C23C2×Dic11⋊C414yes—
704C23C2×Dic11⋊C414yescomplemented
705C23#6697714yes—
706C23#6697714yes—
707C23C4×C22⋊D1114yes—
708C23C4×C22⋊D1114yes—
709C23#6698214yes—
710C23#6700614yes—
711C23C22×Dic2211yescharacteristic
712C23C22×C4×D1111yescharacteristic
713C23C2×#433911yescharacteristic
714C23C2×#433911yescharacteristic
715C23C2×D4×D1112yes—
716C23#6703712yes—
717C23#41×D1112yes—
718C23#6704312yes—
719C23C22×C22⋊D1111yescharacteristic
720C23C22×C22⋊D1111yescharacteristic
721C23C22×C22⋊D1111yescharacteristic
722D4—232no—
723C2×C4—22no—
724C2×C4—22no—
725C2×C4—22no—
726C2×C4—22no—
727C2×C4—22no—
728C2×C4—24no—
729C2×C4—24no—
730C2×C4—22no—
731C2×C4—22no—
732C2×C4—22no—
733C2×C4—22no—
734C2×C4—24no—
735C2×C4—22no—
736C2×C4—24no—
737C2×C4—22no—
738C2×C4—22no—
739C2×C4—22no—
740C2×C4—416no—
741C2×C4—416no—
742C2×C4—41no—
743C2×C4—42no—
744C2×C4—42no—
745C2×C4—42no—
746C2×C4—41no—
747C2×C4—42no—
748C2×C4—41no—
749C2×C4—41no—
750C2×C4—118no—
751C2×C4—2232no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—224no—
756C2×C4—224no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—224no—
761C2×C4—224no—
762C2×C4—224no—
763C2×C4—224no—
764C2×C4—4416no—
765C2×C4—442no—
766C2×C4—442no—
767C2×C4—442no—
768C2×C4—442no—
769C2×C4—442no—
770C2×C4—442no—
771C2×C4—442no—
772C2×C4—442no—
773C2×C4—442no—
774C2×C4—442no—
775C2×C4—442no—
776C2×C4—442no—
777C2×C4—442no—
778C2×C4—442no—
779C2×C4—442no—
780C2×C4C2×Dic11⋊C414yescomplemented
781C2×C4#6699014yes—
782C22—24no—
783C22—28no—
784C22—28no—
785C22—24no—
786C22—24no—
787C22—24no—
788C22—24no—
789C22—28no—
790C22—24no—
791C22—28no—
792C22—28no—
793C22—24no—
794C22—42no—
795C22—44no—
796C22—44no—
797C22—42no—
798C22—42no—
799C22—42no—
800C22—42no—
801C22—42no—
802C22—44no—
803C22#1062282318yescomplemented
804C22D4×Dic2212yes—
805C22#1062307012yes—
806C22#1062307112yes—
807C22C4×D4×D1112yes—
808C22#1062307712yes—
809C22#1062307812yes—
810C22#1062308312yes—
811C22#1062309512yes—
812C22C22×Dic11⋊C411yescharacteristic
813C22C2×#6697711yescharacteristic
814C22C2×#6697711yescharacteristic
815C22C2×C4×C22⋊D1111yescharacteristic
816C22C2×C4×C22⋊D1111yescharacteristic
817C22C2×#6698211yescharacteristic
818C22C2×#6699011yescharacteristic
819C22D4×C22⋊D1112yes—
820C22D4×C22⋊D1112yes—
821C22#1062333511yescharacteristic
822C22#1062335512yes—
823C22#1062335512yes—
824C22#1062335611yescharacteristic
825C22#1062335911yescharacteristic
826C22C2×#6700611yescharacteristic
827C4—24no—
828C4—24no—
829C4—42no—
830C4—42no—
831C4—42no—
832C4—228no—
833C4—444no—
834C4—444no—
835C4—882no—
836C2—28no—
837C2—44no—
838C2C2×#1062282311yescharacteristic
839C2C4×#6699011yescharacteristic
840C2#1307128111yescharacteristic
841C2D4×Dic11⋊C412yes—
842C2#1307163312yes—
843C2#1307192611yescharacteristic
844C2#1307194711yescharacteristic
845C2#1307198111yescharacteristic
846C2#1307234512yes—
847C2#1307241912yes—
848C2#1307395911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC23×D4×C11C22
hypercenterC22×C4×D4D11
hypocenterC11#14015
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C23×Dic11⋊C4C2semidirect
4. C2×#10622823C2semidirect
5. C2×#10622559C2semidirect
6. #13066879C2semidirect
7. #13066859C2semidirect
8. #13066849C2semidirect
9. #13066839C2semidirect
10. #13066838C2semidirect
34. #10622833C4semidirect
77. C23×Dic11C2×C4semidirect
105. C2×C22⋊Dic11C2×C4semidirect
106. C2×C22⋊Dic11C2×C4semidirect
116. C2×Dic11⋊C4D4semidirect
123. C11⋊#95C2×C4semidirect
154. C2×D4×C11C4⋊C4semidirect
291. C23×C11C2×C4⋊C4semidirect
337. C2×C4×C11C2×C4⋊C4semidirect
368. C2×Dic11C4×D4semidirect
422. C22×C11#385semidirect
577. C2×D4Dic11⋊C4semidirect
664. C11#14015semidirect
704. C23C2×Dic11⋊C4semidirect
780. C2×C4C2×Dic11⋊C4semidirect
803. C22#10622823semidirect

Maximal subgroups

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

subgroupindex
C23×Dic11⋊C42
C2×#106228332
C2×#106228232
C2×#106225592
#130668792
#130668592
#130668492
#130668392
#130668382
C22×C4×D4×C112
#1401511