Finite Group Databasebeta

← #14676581

Subgroups — #14676581

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
2C22×D4×Dic11C211yesmaximal, characteristic, complemented
3C2×#10622571C212yesmaximal, 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#13066838C212yesmaximal, complemented
11C2×C11×#390C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C24×Dic11C2212yes—
15C23×C4×D11C2211yescharacteristic
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C22⋊C4C2212yes—
18C22×C11×C22⋊C4C2212yes—
19C22×C42×C11C2211yescharacteristic
20C22×C22⋊Dic11C2212yes—
21C22×C22⋊Dic11C2212yes—
22C2×#66991—24no—
23C2×#66991—24no—
24C2×#66991C418yescomplemented
25C2×D4×Dic11—24no—
26C2×D4×Dic11—24no—
27C2×D4×Dic11—24no—
28C22×(C2×D11)⋊C4C2211yescharacteristic
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4⋊Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34C11×#390—24no—
35C2×C11⋊#95C2211yescharacteristic
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622600—24no—
43#10622571—28no—
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×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2311yescharacteristic
57C23×C4×C11C2311yescharacteristic
58C22×C22⋊D11—24no—
59C22×C22⋊D11—24no—
60C22×C22⋊D11—24no—
61C22×C22⋊D11—24no—
62C22×C22⋊D11—42no—
63C22×C22⋊D11—42no—
64C22×C22⋊D11C2×C418yescomplemented
65C23×Dic11—24no—
66C23×Dic11—24no—
67C23×Dic11—24no—
68C23×Dic11—24no—
69C23×Dic11—24no—
70C23×Dic11—42no—
71C23×Dic11—42no—
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—22no—
81C22×C4×D11—22no—
82C22×C4×D11—22no—
83C22×C4×D11C2×C414yescomplemented
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C22⋊C4—24no—
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—42no—
92C2×C11×C22⋊C4—42no—
93C2×C42×C11—22no—
94C2×C42×C11—22no—
95C2×C42×C11—22no—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11C2×C418yescomplemented
102#66991—232no—
103D4×Dic11—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⋊Dic11C2×C414yescomplemented
118C2×C4⋊Dic11D414yescomplemented
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11D414yescomplemented
122C11⋊#95—24no—
123C11⋊#95—22no—
124C11⋊#95—22no—
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—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—22no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11#4112yes—
194C22×C4×C11#4112yes—
195C22×C4×C11#4112yes—
196C2×C22⋊D11—216no—
197C2×C22⋊D11—216no—
198C2×C22⋊D11—48no—
199C2×C22⋊D11—48no—
200C2×C22⋊D11—48no—
201C2×C22⋊D11—48no—
202C2×C22⋊D11—48no—
203C22×Dic11—216no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—22no—
209C22×Dic11—22no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—22no—
223C22×Dic11—22no—
224C22×Dic11—21no—
225C22×Dic11—21no—
226C22×Dic11—21no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—21no—
232C22×Dic11—48no—
233C22×Dic11—48no—
234C22×Dic11—48no—
235C22×Dic11—48no—
236C22×Dic11—48no—
237C22×Dic11—48no—
238C22×Dic11C22×C414yes—
239C22×Dic11C22×C412yes—
240C22×Dic11C2×D412yes—
241C22×Dic11C2×D414yes—
242C22×Dic11C2×D412yes—
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—44no—
253C11×C22⋊C4—48no—
254C11×C22⋊C4—48no—
255C42×C11—44no—
256C22⋊Dic11—216no—
257C22⋊Dic11—216no—
258(C2×D11)⋊C4—28no—
259(C2×D11)⋊C4—28no—
260(C2×D11)⋊C4—48no—
261C4⋊Dic11—28no—
262C4⋊Dic11—28no—
263C4×Dic11—28no—
264C22×#121—111no—
265C22×C4×D4—111no—
266C2×#390D1111yescharacteristic, complemented
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—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—42no—
376C2×C4×C11—42no—
377C2×C4×C11—42no—
378C2×C4×C11—42no—
379C2×C4×C11—42no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
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#12314yes—
389C22⋊D11—432no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—24no—
397C2×Dic11—22no—
398C2×Dic11—22no—
399C2×Dic11—22no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11—22no—
403C2×Dic11—24no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—24no—
407C2×Dic11—24no—
408C2×Dic11—432no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—42no—
413C2×Dic11—41no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11—41no—
419C2×Dic11—42no—
420C2×Dic11—42no—
421C2×Dic11—42no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11—41no—
425C2×Dic11#12114yescomplemented
426C4×D11—416no—
427C23×D4—112no—
428C23×D4C2×D1111yescharacteristic
429C24×C4—111no—
430C24×C4—112no—
431C2×#121—118no—
432C2×#121—224no—
433C2×#121—224no—
434C2×C4×D4—224no—
435C2×C4×D4—224no—
436C2×C4×D4—224no—
437C22×C4⋊C4—111no—
438C22×C4⋊C4—111no—
439C22×C4⋊C4C2×D1111yescharacteristic
440C22×C22⋊C4—112no—
441C22×C22⋊C4—111no—
442C22×C22⋊C4—112no—
443C22×C22⋊C4—111no—
444C22×C22⋊C4—112no—
445C22×C22⋊C4C2×D1112yes—
446C22×C22⋊C4C2×D1112yes—
447C22×C42—111no—
448C22×C42C2×D1111yescharacteristic
449#390—24no—
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—42no—
526C4×C11—42no—
527C4×C11—82no—
528C4×C11#38618yescomplemented
529Dic11—24no—
530Dic11—44no—
531Dic11—42no—
532Dic11—44no—
533Dic11—42no—
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—111no—
551C23×C4—111no—
552C23×C4—112no—
553C23×C4—111no—
554C23×C4—112no—
555C23×C4—114no—
556C23×C4—224no—
557C23×C4—224no—
558C23×C4—224no—
559C23×C4—224no—
560C23×C4—224no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—222no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—222no—
567C23×C4—442no—
568C23×C4—442no—
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1111yescharacteristic
572C23×C4C22×D1111yescharacteristic
573#121—2232no—
574C4×D4—2232no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—114no—
579C2×C4⋊C4—114no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4—222no—
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—24no—
587C2×C22⋊C4—24no—
588C2×C22⋊C4—42no—
589C2×C22⋊C4—42no—
590C2×C22⋊C4—118no—
591C2×C22⋊C4—114no—
592C2×C22⋊C4—222no—
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—222no—
602C2×C22⋊C4—224no—
603C2×C22⋊C4—224no—
604C2×C22⋊C4—442no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—114no—
609C2×C42—222no—
610C2×C42—222no—
611#95—222no—
612#95—222no—
613#95—224no—
614#95—224no—
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—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—21no—
691C22×C4—21no—
692C22×C4—22no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—114no—
704C22×C4—112no—
705C22×C4—114no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—221no—
710C22×C4—2216no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—222no—
714C22×C4—222no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—221no—
720C22×C4—222no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—221no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—222no—
735C22×C4—228no—
736C22×C4—228no—
737C22×C4—228no—
738C22×C4—448no—
739C22×C4—448no—
740C22×C4—448no—
741C22×C4—448no—
742C22×C4—448no—
743C22×C4—448no—
744C22×C4—444no—
745C22×C4—444no—
746C22×C4—444no—
747C22×C4—444no—
748C22×C4C2×C4×D1112yes—
749C22×C4C2×D4412yes—
750C22×C4D4×D1112yes—
751C22×C4D4×D1112yes—
752C22×C4D4×D1112yes—
753C22×C4#434112yes—
754C22×C4#434112yes—
755C22×C4#434112yes—
756C22×C4C2×C22⋊D1112yes—
757C4⋊C4—44no—
758C4⋊C4—228no—
759C4⋊C4—228no—
760C22⋊C4—48no—
761C22⋊C4—48no—
762C22⋊C4—228no—
763C22⋊C4—228no—
764C22⋊C4—2216no—
765C22⋊C4—2216no—
766C22⋊C4—448no—
767C42—44no—
768C42—228no—
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×D4×D1111yescharacteristic
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×#434111yescharacteristic
846C23C2×#434111yescharacteristic
847C23C2×#434111yescharacteristic
848C23#6703711yescharacteristic
849C23#6703711yescharacteristic
850C23#41×D1111yescharacteristic
851C23#41×D1111yescharacteristic
852C23#6704211yescharacteristic
853C23#6704311yescharacteristic
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—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—41no—
870C2×C4—41no—
871C2×C4—42no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—114no—
879C2×C4—222no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—224no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—224no—
890C2×C4—222no—
891C2×C4—224no—
892C2×C4—224no—
893C2×C4—224no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—224no—
897C2×C4—4432no—
898C2×C4—441no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—442no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—442no—
905C2×C4—442no—
906C2×C4—442no—
907C2×C4—442no—
908C2×C4—441no—
909C2×C4—441no—
910C2×C4—442no—
911C2×C4—442no—
912C2×C4—442no—
913C2×C4—441no—
914C2×C4—4416no—
915C2×C4(C22⋊D11)⋊C414yes—
916C2×C4(C22⋊D11)⋊C414yes—
917C2×C4#6693514yes—
918C2×C4#6693914yes—
919C2×C4C2×(C2×D11)⋊C414yes—
920C2×C4#6699214yes—
921C2×C4#6699214yes—
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—
952C22C2×(C22⋊D11)⋊C411yescharacteristic
953C22C2×(C22⋊D11)⋊C411yescharacteristic
954C22C2×#6693511yescharacteristic
955C22C2×#6693911yescharacteristic
956C22C4×#434111yescharacteristic
957C22C4×D4×D1111yescharacteristic
958C22#1062307611yescharacteristic
959C22#1062307711yescharacteristic
960C22D4×D4411yescharacteristic
961C22#1062308511yescharacteristic
962C22#1062308511yescharacteristic
963C22#1062308611yescharacteristic
964C22D11×#12111yescharacteristic
965C22#1062313711yescharacteristic
966C22#1062313811yescharacteristic
967C22#1062313911yescharacteristic
968C22#1062314211yescharacteristic
969C22#1062314511yescharacteristic
970C22#1062314711yescharacteristic
971C22#1062314911yescharacteristic
972C22#1062320711yescharacteristic
973C22#1062320811yescharacteristic
974C22#1062321111yescharacteristic
975C22#1062321311yescharacteristic
976C22#1062324711yescharacteristic
977C22#1062324811yescharacteristic
978C22#1062324911yescharacteristic
979C22#1062325011yescharacteristic
980C22C22×(C2×D11)⋊C411yescharacteristic
981C22D4×C22⋊D1111yescharacteristic
982C22C2×#6699211yescharacteristic
983C22C2×#6699211yescharacteristic
984C22#1062333711yescharacteristic
985C22#1062335511yescharacteristic
986C22#1062336011yescharacteristic
987C4—42no—
988C4—42no—
989C4—82no—
990C4—224no—
991C4—444no—
992C4—442no—
993C4—444no—
994C4—442no—
995C4#1062257118yescomplemented
996C2—48no—
997C2—444no—
998C2C2×#1062257111yescharacteristic
999C2#1307113211yescharacteristic
1000C2#1307131211yescharacteristic
1001C2D4×(C2×D11)⋊C411yescharacteristic
1002C2#1307144111yescharacteristic
1003C2#1307163711yescharacteristic
1004C2#1307165911yescharacteristic
1005C2#1307195911yescharacteristic
1006C2#1307197011yescharacteristic
1007C2#1307210611yescharacteristic
1008C2#1307212811yescharacteristic
1009C2#1307219611yescharacteristic
1010C2#1307220711yescharacteristic
1011C2#1307351511yescharacteristic
1012C2#1307353011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#390C2
socle, cosocleC24×C11C24
prime radicalC22×#66991C2
hypercenterC2×#390D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#390

Complements

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

NH ≅ G/Ntype
2. C22×D4×Dic11C2semidirect
3. C2×#10622571C2semidirect
4. C2×#10622600C2semidirect
5. C2×C4×(C2×D11)⋊C4C2semidirect
6. #13066863C2semidirect
7. #13066855C2semidirect
8. #13066846C2semidirect
9. #13066845C2semidirect
10. #13066838C2semidirect
11. C2×C11×#390C2semidirect
24. C2×#66991C4semidirect
64. C22×C22⋊D11C2×C4semidirect
83. C22×C4×D11C2×C4semidirect
101. C2×C22⋊Dic11C2×C4semidirect
112. C2×(C2×D11)⋊C4D4semidirect
117. C2×C4⋊Dic11C2×C4semidirect
118. C2×C4⋊Dic11D4semidirect
121. C2×C4×Dic11D4semidirect
167. C2×D4×C11C22⋊C4semidirect
266. C2×#390D11semidirect
359. C22×D11C4×D4semidirect
425. C2×Dic11#121semidirect
528. C4×C11#386semidirect
679. C2×D4(C2×D11)⋊C4semidirect
769. C11#13970semidirect
995. C4#10622571semidirect

Maximal subgroups

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

subgroupindex
C22×#669912
C22×D4×Dic112
C2×#106225712
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668632
#130668552
#130668462
#130668452
#130668382
C2×C11×#3902
#1397011