Finite Group Databasebeta

← #14676572

Subgroups — #14676572

Order 2816.

3058 conjugacy classes of subgroups.

The subgroup lattice has 1014 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66991C211yesmaximal, characteristic
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622826C212yesmaximal, complemented
4C2×#10622600C211yesmaximal, characteristic, complemented
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
6#13066863C212yesmaximal, complemented
7#13066855C212yesmaximal, complemented
8#13066846C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066839C212yesmaximal, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2212yes—
14C23×C22⋊D11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C2×C4×D4×C11—24no—
17C2×C4×D4×C11—24no—
18C2×C4×D4×C11—24no—
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C42×C11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C2×#66991—24no—
26C2×#66991—24no—
27C2×#66991C418yescomplemented
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34#10622834—24no—
35#10622826—28no—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622600—24no—
44C4×(C2×D11)⋊C4—24no—
45C25×C11C2312yes—
46C24×D11C2311yescharacteristic
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11C2×C414yes—
52C22×D4×C11D414yes—
53C22×D4×C11D414yes—
54C23×C4×C11—24no—
55C23×C4×C11—24no—
56C23×C4×C11—24no—
57C23×C4×C11—24no—
58C23×C4×C11—24no—
59C23×C4×C11—42no—
60C23×C4×C11—42no—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2312yes—
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—24no—
66C22×C22⋊D11—24no—
67C22×C22⋊D11—24no—
68C22×C22⋊D11—24no—
69C22×C22⋊D11—42no—
70C22×C22⋊D11—42no—
71C22×C22⋊D11C2×C418yescomplemented
72C23×Dic11C2312yes—
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C22×C4×D11—22no—
78C22×C4×D11—22no—
79C22×C4×D11—22no—
80C22×C4×D11—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11C2×C414yescomplemented
84C4×D4×C11—232no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4D414yescomplemented
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—24no—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×C42×C11D414yescomplemented
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—42no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11C2×C418yescomplemented
103#66991—232no—
104C2×(C2×D11)⋊C4—22no—
105C2×(C2×D11)⋊C4—22no—
106C2×(C2×D11)⋊C4—22no—
107C2×(C2×D11)⋊C4—22no—
108C2×(C2×D11)⋊C4—22no—
109C2×(C2×D11)⋊C4—24no—
110C2×(C2×D11)⋊C4—24no—
111C2×(C2×D11)⋊C4—42no—
112C2×(C2×D11)⋊C4D414yescomplemented
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—22no—
117C2×C4⋊Dic11—22no—
118C2×C4⋊Dic11C2×C414yescomplemented
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11—22no—
122C11⋊#95—22no—
123C11⋊#95—22no—
124C11⋊#95—24no—
125C11⋊#95—24no—
126C11⋊#95—24no—
127C11⋊#95—42no—
128C11⋊#95—42no—
129#13970—111nomaximal, Sylow
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—22no—
142C24×C11C22×C414yes—
143C24×C11C2×D414yes—
144C24×C11C2×D414yes—
145C24×C11C2411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—21no—
149C23×D11—21no—
150C23×D11—21no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—21no—
154C23×D11—21no—
155C23×D11—21no—
156C23×D11—21no—
157C23×D11—21no—
158C23×D11C22×C412yes—
159C23×D11C2×D412yes—
160C23×D11#4112yes—
161C2×D4×C11—28no—
162C2×D4×C11—28no—
163C2×D4×C11—28no—
164C2×D4×C11—28no—
165C2×D4×C11—28no—
166C2×D4×C11—28no—
167C2×D4×C11C22⋊C4116yescomplemented
168C22×C4×C11—21no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—216no—
173C22×C4×C11—22no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—21no—
185C22×C4×C11—48no—
186C22×C4×C11—48no—
187C22×C4×C11—48no—
188C22×C4×C11—48no—
189C22×C4×C11—48no—
190C22×C4×C11—48no—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D414yes—
194C22×C4×C11C2×D412yes—
195C22×C4×C11C2×D412yes—
196C22×C4×C11C2×D412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11#4112yes—
201C22×C4×C11#4112yes—
202C22×C4×C11#4112yes—
203C2×C22⋊D11—216no—
204C2×C22⋊D11—216no—
205C2×C22⋊D11—48no—
206C2×C22⋊D11—48no—
207C2×C22⋊D11—48no—
208C2×C22⋊D11—48no—
209C2×C22⋊D11—48no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—22no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—22no—
218C22×Dic11—22no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—22no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—21no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—21no—
237C22×Dic11—21no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—21no—
241C22×Dic11C22×C414yes—
242C22×Dic11C22×C412yes—
243C22×Dic11C2×D412yes—
244C22×Dic11#4112yes—
245C2×C4×D11—28no—
246C2×C4×D11—28no—
247C2×C4×D11—28no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C11×C4⋊C4—28no—
253C11×C22⋊C4—216no—
254C42×C11—28no—
255C22⋊Dic11—216no—
256C22⋊Dic11—48no—
257C22⋊Dic11—48no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—48no—
261C4⋊Dic11—28no—
262C4⋊Dic11—44no—
263C4×Dic11—44no—
264C22×#121—111no—
265C22×C4×D4D1111yescharacteristic, complemented
266C2×#390—111no—
267C2×#386—112no—
268C2×#380—111no—
269C2×C4×C22⋊C4—111no—
270#1440—112no—
271#1438—112no—
272C4⋊#95—111no—
273C4⋊#95—111no—
274C22⋊#95—112no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—24no—
282C23×C11—24no—
283C23×C11—24no—
284C23×C11—24no—
285C23×C11—24no—
286C23×C11—24no—
287C23×C11—24no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11—42no—
294C23×C11—42no—
295C23×C11—42no—
296C23×C11—42no—
297C23×C11—42no—
298C23×C11—42no—
299C23×C11—42no—
300C23×C11—42no—
301C23×C11—42no—
302C23×C11—42no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—42no—
307C23×C11—42no—
308C23×C11—42no—
309C23×C11C2×C22⋊C418yes—
310C23×C11C23×C411yescharacteristic
311C23×C11C22×D411yescharacteristic
312C23×C11C22×D411yescharacteristic
313C23×C11C22×D411yescharacteristic
314C23×C11C22×D411yescharacteristic
315C23×C11C22×D411yescharacteristic
316C23×C11C2×#4111yescharacteristic
317C23×C11C2×#4111yescharacteristic
318C23×C11C2×#4111yescharacteristic
319C23×C11C2×#4111yescharacteristic
320C23×C11C2×#4111yescharacteristic
321C23×C11H(5,𝔽2)11yescharacteristic
322C23×C11H(5,𝔽2)11yescharacteristic
323C23×C11H(5,𝔽2)11yescharacteristic
324C23×C112−1+411yescharacteristic
325C22×D11—22no—
326C22×D11—22no—
327C22×D11—22no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—22no—
332C22×D11—22no—
333C22×D11—22no—
334C22×D11—22no—
335C22×D11—22no—
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—22no—
341C22×D11—22no—
342C22×D11—22no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—41no—
349C22×D11—41no—
350C22×D11—41no—
351C22×D11—41no—
352C22×D11—41no—
353C22×D11—41no—
354C22×D11—41no—
355C22×D11—41no—
356C22×D11—41no—
357C22×D11—41no—
358C22×D11—41no—
359C22×D11C4×D414yescomplemented
360D4×C11—232no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—22no—
368C2×C4×C11—24no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—24no—
372C2×C4×C11—24no—
373C2×C4×C11—432no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—41no—
378C2×C4×C11—42no—
379C2×C4×C11—41no—
380C2×C4×C11—41no—
381C2×C4×C11—41no—
382C2×C4×C11C2×C22⋊C414yes—
383C2×C4×C11C4×D414yes—
384C2×C4×C11C4×D414yes—
385C2×C4×C11#12014yes—
386C2×C4×C11#12114yes—
387C2×C4×C11#12114yes—
388C2×C4×C11#12114yescomplemented
389C2×C4×C11#12314yes—
390C22⋊D11—432no—
391C2×Dic11—24no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—24no—
396C2×Dic11—24no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413C2×Dic11—41no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—41no—
417C2×Dic11—41no—
418C2×Dic11—41no—
419C2×Dic11—42no—
420C2×Dic11—42no—
421C2×Dic11—42no—
422C2×Dic11—42no—
423C2×Dic11—42no—
424C2×Dic11—42no—
425C2×Dic11—42no—
426C4×D11—416no—
427C23×D4—112no—
428C23×D4C2×D1111yescharacteristic
429C24×C4—111no—
430C24×C4C2×D1112yes—
431C2×#121—118no—
432C2×#121—224no—
433C2×#121—224no—
434C2×C4×D4—24no—
435C2×C4×D4—24no—
436C2×C4×D4—24no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4—112no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—112no—
444C22×C22⋊C4—112no—
445C22×C22⋊C4—112no—
446C22×C22⋊C4C2×D1112yes—
447C22×C42—111no—
448C22×C42C2×D1111yescharacteristic
449#390—224no—
450#386—228no—
451#380—224no—
452C4×C22⋊C4—224no—
453C2×#95—111no—
454C2×#95—112no—
455C2×#95—112no—
456C2×#95—112no—
457C2×#95—111no—
458C2×#95—112no—
459C2×#95—112no—
460C22×C11—28no—
461C22×C11—28no—
462C22×C11—28no—
463C22×C11—44no—
464C22×C11—44no—
465C22×C11—44no—
466C22×C11—44no—
467C22×C11—44no—
468C22×C11—44no—
469C22×C11—44no—
470C22×C11—44no—
471C22×C11—44no—
472C22×C11—44no—
473C22×C11—44no—
474C22×C11—44no—
475C22×C11C22×C22⋊C411yescharacteristic
476C22×C11C2×C4×D411yescharacteristic
477C22×C11C2×C4×D411yescharacteristic
478C22×C11C2×C4×D411yescharacteristic
479C22×C11C4×#4111yescharacteristic
480C22×C11#51811yescharacteristic
481C22×C11#52011yescharacteristic
482C22×C11C2×#12011yescharacteristic
483C22×C11C2×#12111yescharacteristic
484C22×C11C2×#12111yescharacteristic
485C22×C11C2×#12111yescharacteristic
486C22×C11C2×#12311yescharacteristic
487C22×C11#52511yescharacteristic
488C22×C11#52911yescharacteristic
489C22×C11#53211yescharacteristic
490C22×C11#53511yescharacteristic
491C22×C11#53711yescharacteristic
492C22×C11#54011yescharacteristic
493C22×C11#54211yescharacteristic
494C22×C11D4211yescharacteristic
495C22×C11D4211yescharacteristic
496C22×C11D4211yescharacteristic
497C22×C11#54611yescharacteristic
498C22×C11#54611yescharacteristic
499C22×C11#54611yescharacteristic
500C22×C11#54611yescharacteristic
501C22×C11#54611yescharacteristic
502C22×C11#54711yescharacteristic
503C22×C11#54711yescharacteristic
504C22×C11#54711yescharacteristic
505C22×C11#54811yescharacteristic
506C22×C11#55011yescharacteristic
507C22×C11#55311yescharacteristic
508C22×C11#55311yescharacteristic
509C22×C11#55511yescharacteristic
510C2×D11—24no—
511C2×D11—24no—
512C2×D11—24no—
513C2×D11—42no—
514C2×D11—42no—
515C2×D11—42no—
516C2×D11—42no—
517C2×D11—42no—
518C2×D11—42no—
519C2×D11—42no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C4×C11—24no—
526C4×C11—42no—
527C4×C11—44no—
528C4×C11#38618yescomplemented
529Dic11—44no—
530Dic11—42no—
531Dic11—42no—
532Dic11—42no—
533Dic11—82no—
534C25—111no—
535C25C22×D1112yes—
536C22×D4—22no—
537C22×D4—22no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—118no—
541C22×D4—224no—
542C22×D4—224no—
543C22×D4—224no—
544C22×D4—224no—
545C22×D4—442no—
546C22×D4—442no—
547C22×D4C4×D1114yes—
548C22×D4D4414yes—
549C22×D4C22⋊D1114yes—
550C23×C4—24no—
551C23×C4—24no—
552C23×C4—24no—
553C23×C4—24no—
554C23×C4—24no—
555C23×C4—42no—
556C23×C4—42no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—112no—
561C23×C4—114no—
562C23×C4—112no—
563C23×C4—222no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—222no—
568C23×C4—222no—
569C23×C4C22×D1111yescharacteristic
570C23×C4C22×D1112yes—
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573#121—2232no—
574C4×D4—232no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—114no—
578C2×C4⋊C4—222no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4C22⋊D1114yescomplemented
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—118no—
588C2×C22⋊C4—114no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—224no—
598C2×C22⋊C4—224no—
599C2×C22⋊C4—224no—
600C2×C22⋊C4—224no—
601C2×C22⋊C4—224no—
602C2×C22⋊C4—442no—
603C2×C22⋊C4—442no—
604C2×C22⋊C4—442no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—222no—
608C2×C42—222no—
609C2×C42—222no—
610C2×C42C22⋊D1114yescomplemented
611#95—224no—
612#95—224no—
613#95—222no—
614#95—222no—
615#95—224no—
616#95—442no—
617#95—442no—
618C2×C11—48no—
619C2×C11C2×#38611yescharacteristic
620C2×C11C4×#12111yescharacteristic
621C2×C11#232411yescharacteristic
622C2×C11D4×C22⋊C411yescharacteristic
623C2×C11#233911yescharacteristic
624C2×C11#236111yescharacteristic
625C2×C11#236311yescharacteristic
626C2×C11#240711yescharacteristic
627C2×C11#240811yescharacteristic
628C2×C11#242011yescharacteristic
629C2×C11#242211yescharacteristic
630C2×C11#242711yescharacteristic
631C2×C11#242811yescharacteristic
632C2×C11#253511yescharacteristic
633C2×C11#253711yescharacteristic
634D11—44no—
635C24—22no—
636C24—22no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—112no—
648C24—112no—
649C24—112no—
650C24—221no—
651C24—221no—
652C24—221no—
653C24—221no—
654C24—221no—
655C24—221no—
656C24—221no—
657C24—221no—
658C24—221no—
659C24—221no—
660C24—221no—
661C24—221no—
662C24C2×C4×D1114yes—
663C24C2×D4414yes—
664C24C2×C22⋊D1114yes—
665C24C23×D1111yescharacteristic
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—2216no—
673C2×D4—2216no—
674C2×D4—448no—
675C2×D4—448no—
676C2×D4—448no—
677C2×D4—448no—
678C2×D4—448no—
679C2×D4(C2×D11)⋊C4116yescomplemented
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—21no—
684C22×C4—216no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—48no—
698C22×C4—48no—
699C22×C4—48no—
700C22×C4—48no—
701C22×C4—48no—
702C22×C4—48no—
703C22×C4—112no—
704C22×C4—114no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—222no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—222no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—222no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—221no—
727C22×C4—221no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—222no—
731C22×C4—228no—
732C22×C4—228no—
733C22×C4—228no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—444no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4—444no—
745C22×C4C2×C4×D1112yes—
746C22×C4C2×D4412yes—
747C22×C4#433912yes—
748C22×C4#433912yes—
749C22×C4D4×D1112yes—
750C22×C4#434112yes—
751C22×C4C2×C22⋊D1112yes—
752C22×C4C2×C22⋊D1114yes—
753C22×C4C2×C22⋊D1112yes—
754C22×C4C2×C22⋊D1112yes—
755C22×C4C2×C22⋊D1112yes—
756C22×C4C2×C22⋊D1112yes—
757C4⋊C4—28no—
758C4⋊C4—228no—
759C4⋊C4—444no—
760C22⋊C4—216no—
761C22⋊C4—228no—
762C22⋊C4—2216no—
763C22⋊C4—228no—
764C22⋊C4—448no—
765C22⋊C4—448no—
766C22⋊C4—448no—
767C42—28no—
768C42—444no—
769C11#1397011yescharacteristic, complemented, Sylow
770C23—24no—
771C23—24no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—24no—
785C23—24no—
786C23—24no—
787C23—24no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—42no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—42no—
798C23—42no—
799C23—42no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—114no—
805C23—222no—
806C23—222no—
807C23—222no—
808C23—222no—
809C23—222no—
810C23—222no—
811C23—222no—
812C23—222no—
813C23—222no—
814C23—222no—
815C23—222no—
816C23—222no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—441no—
824C23—441no—
825C23—441no—
826C23—441no—
827C23—441no—
828C23—441no—
829C23—441no—
830C23—441no—
831C23—441no—
832C23—441no—
833C23—441no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—441no—
838C23—441no—
839C23C2×(C2×D11)⋊C418yes—
840C23C22×C4×D1111yescharacteristic
841C23C22×D4411yescharacteristic
842C23C2×#433911yescharacteristic
843C23C2×#433911yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×#434111yescharacteristic
846C23#6703711yescharacteristic
847C23#6703711yescharacteristic
848C23#41×D1111yescharacteristic
849C23#41×D1111yescharacteristic
850C23#6704211yescharacteristic
851C23#6704311yescharacteristic
852C23C22×C22⋊D1111yescharacteristic
853C23C22×C22⋊D1111yescharacteristic
854C23C22×C22⋊D1111yescharacteristic
855D4—232no—
856D4—4432no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—22no—
862C2×C4—22no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—24no—
869C2×C4—432no—
870C2×C4—42no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—41no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—222no—
879C2×C4—224no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—224no—
883C2×C4—222no—
884C2×C4—224no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—442no—
896C2×C4—442no—
897C2×C4—441no—
898C2×C4—442no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—442no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—4416no—
907C2×C4—442no—
908C2×C4—442no—
909C2×C4—442no—
910C2×C4—442no—
911C2×C4—442no—
912C2×C4—442no—
913C2×C4—442no—
914C2×C4C2×(C2×D11)⋊C414yes—
915C2×C4C4×C22⋊D1114yes—
916C2×C4C4×C22⋊D1114yes—
917C2×C4#6698214yes—
918C2×C4#6698314yes—
919C2×C4#6698314yes—
920C2×C4#6699114yescomplemented
921C2×C4#6700614yes—
922C22—28no—
923C22—28no—
924C22—28no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—44no—
933C22—44no—
934C22—44no—
935C22—44no—
936C22—44no—
937C22—224no—
938C22—224no—
939C22—224no—
940C22—442no—
941C22—442no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—442no—
951C22—442no—
952C22C4×#434111yescharacteristic
953C22C4×D4×D1111yescharacteristic
954C22#1062307611yescharacteristic
955C22#1062307711yescharacteristic
956C22#1062307911yescharacteristic
957C22D4×D4411yescharacteristic
958C22#1062308211yescharacteristic
959C22#1062308511yescharacteristic
960C22#1062308511yescharacteristic
961C22#1062308611yescharacteristic
962C22#1062308811yescharacteristic
963C22#1062308911yescharacteristic
964C22#1062308911yescharacteristic
965C22#1062309211yescharacteristic
966C22#1062309311yescharacteristic
967C22#1062309411yescharacteristic
968C22C22×(C2×D11)⋊C411yescharacteristic
969C22C2×C4×C22⋊D1111yescharacteristic
970C22C2×C4×C22⋊D1111yescharacteristic
971C22C2×#6698211yescharacteristic
972C22C2×#6698311yescharacteristic
973C22C2×#6698311yescharacteristic
974C22C2×#6699111yescharacteristic
975C22D4×C22⋊D1111yescharacteristic
976C22D4×C22⋊D1111yescharacteristic
977C22#1062333611yescharacteristic
978C22#1062333711yescharacteristic
979C22#1062333711yescharacteristic
980C22#1062335511yescharacteristic
981C22#1062335911yescharacteristic
982C22#1062336011yescharacteristic
983C22#1062336211yescharacteristic
984C22#1062336411yescharacteristic
985C22#1062336511yescharacteristic
986C22C2×#6700611yescharacteristic
987C4—24no—
988C4—42no—
989C4—44no—
990C4—444no—
991C4—442no—
992C4—442no—
993C4—442no—
994C4—882no—
995C4#1062282618yescomplemented
996C2—48no—
997C2—444no—
998C2C2×#1062282611yescharacteristic
999C2C4×#6699111yescharacteristic
1000C2#1307130311yescharacteristic
1001C2D4×(C2×D11)⋊C411yescharacteristic
1002C2#1307144111yescharacteristic
1003C2#1307162811yescharacteristic
1004C2#1307165011yescharacteristic
1005C2#1307195511yescharacteristic
1006C2#1307196611yescharacteristic
1007C2#1307210211yescharacteristic
1008C2#1307212411yescharacteristic
1009C2#1307218711yescharacteristic
1010C2#1307219811yescharacteristic
1011C2#1307351311yescharacteristic
1012C2#1307352911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC22×C4×D4×C11C2
socle, cosocleC24×C11C24
prime radicalC22×#66991C2
hypercenterC22×C4×D4D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
2. C2×#10622834C2semidirect
3. C2×#10622826C2semidirect
4. C2×#10622600C2semidirect
5. C2×C4×(C2×D11)⋊C4C2semidirect
6. #13066863C2semidirect
7. #13066855C2semidirect
8. #13066846C2semidirect
9. #13066845C2semidirect
10. #13066839C2semidirect
11. C22×C4×D4×C11C2semidirect
27. C2×#66991C4semidirect
71. C22×C22⋊D11C2×C4semidirect
83. C22×C4×D11C2×C4semidirect
87. C2×C11×C4⋊C4D4semidirect
93. C2×C42×C11D4semidirect
102. C2×C22⋊Dic11C2×C4semidirect
112. C2×(C2×D11)⋊C4D4semidirect
118. C2×C4⋊Dic11C2×C4semidirect
167. C2×D4×C11C22⋊C4semidirect
265. C22×C4×D4D11semidirect
359. C22×D11C4×D4semidirect
388. C2×C4×C11#121semidirect
528. C4×C11#386semidirect
583. C2×C4⋊C4C22⋊D11semidirect
610. C2×C42C22⋊D11semidirect
679. C2×D4(C2×D11)⋊C4semidirect
769. C11#13970semidirect
920. C2×C4#66991semidirect
995. C4#10622826semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C2×#106228342
C2×#106228262
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668632
#130668552
#130668462
#130668452
#130668392
C22×C4×D4×C112
#1397011