Finite Group Databasebeta

← #14676580

Subgroups — #14676580

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×D4×Dic11C211yesmaximal, characteristic, complemented
2C2×#10622834C211yesmaximal, characteristic, complemented
3C2×#10622833C212yesmaximal, complemented
4C2×#10622825C211yesmaximal, characteristic, complemented
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13066865C212yesmaximal, complemented
7#13066857C212yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066838C212yesmaximal, complemented
11C22×C11×#121C211yesmaximal, characteristic
12C23×D4×C11C2212yes—
13C23×D4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C24×Dic11C2212yes—
16C2×C11×#121—24no—
17C2×C11×#121—24no—
18C2×C11×#121C418yescomplemented
19C22×C11×C4⋊C4C2211yescharacteristic
20C22×C11×C22⋊C4C2212yes—
21C22×C22⋊Dic11C2211yescharacteristic
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2211yescharacteristic
27C2×D4×Dic11—24no—
28C2×D4×Dic11—24no—
29C2×D4×Dic11—24no—
30C22×C4⋊Dic11C2211yescharacteristic
31C22×C4⋊Dic11C2211yescharacteristic
32C22×C4×Dic11C2211yescharacteristic
33C22×C4×Dic11C2211yescharacteristic
34#10622834—24no—
35#10622833—28no—
36#10622825—24no—
37C4×C22⋊Dic11—24no—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2211yescharacteristic
43C2×C11⋊#95C2212yes—
44C2×C11⋊#95C2212yes—
45C25×C11C2312yes—
46C25×C11C2311yescharacteristic
47C22×D4×C11—24no—
48C22×D4×C11—24no—
49C22×D4×C11—24no—
50C22×D4×C11—24no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—42no—
56C22×D4×C11—42no—
57C22×D4×C11C2×C414yes—
58C22×D4×C11C2×C418yescomplemented
59C22×D4×C11D414yes—
60C22×D4×C11D414yes—
61C23×C4×C11—22no—
62C23×C4×C11—22no—
63C23×C4×C11—22no—
64C23×C4×C11—22no—
65C23×C4×C11—22no—
66C23×C4×C11—22no—
67C23×C4×C11C2×C414yescomplemented
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C23×C4×C11C2311yescharacteristic
71C23×Dic11—24no—
72C23×Dic11—24no—
73C23×Dic11—24no—
74C23×Dic11—24no—
75C23×Dic11—24no—
76C23×Dic11—42no—
77C23×Dic11—42no—
78C23×Dic11C2312yes—
79C23×Dic11C2311yescharacteristic
80C23×Dic11C2311yescharacteristic
81C23×Dic11C2312yes—
82C23×Dic11C2311yescharacteristic
83C23×Dic11C2311yescharacteristic
84C11×#121—232no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4C2×C414yescomplemented
88C2×C11×C22⋊C4—24no—
89C2×C11×C22⋊C4—24no—
90C2×C11×C22⋊C4C2×C418yescomplemented
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—22no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11—22no—
99C2×C22⋊Dic11—24no—
100C2×C22⋊Dic11—24no—
101C2×C22⋊Dic11—24no—
102C2×C22⋊Dic11—24no—
103C2×C22⋊Dic11—24no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—42no—
106C2×C22⋊Dic11—42no—
107C2×C22⋊Dic11—42no—
108C2×C22⋊Dic11D414yescomplemented
109D4×Dic11—232no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—22no—
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11D414yescomplemented
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—22no—
121C2×C4×Dic11D414yescomplemented
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—21no—
131C24×C11—21no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—22no—
140C24×C11—22no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—21no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—21no—
151C24×C11—21no—
152C24×C11—22no—
153C24×C11—21no—
154C24×C11C22×C414yes—
155C24×C11C22×C412yes—
156C24×C11C2×D414yes—
157C24×C11C2×D414yes—
158C24×C11C2×D412yes—
159C24×C11#4112yes—
160C24×C11C2411yescharacteristic
161C2×D4×C11—216no—
162C2×D4×C11—216no—
163C2×D4×C11—28no—
164C2×D4×C11—28no—
165C2×D4×C11—28no—
166C2×D4×C11—28no—
167C2×D4×C11—28no—
168C2×D4×C11—28no—
169C2×D4×C11—48no—
170C2×D4×C11—48no—
171C2×D4×C11—48no—
172C2×D4×C11—48no—
173C2×D4×C11—48no—
174C2×D4×C11C22⋊C4116yescomplemented
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—22no—
185C22×C4×C11—22no—
186C22×C4×C11—22no—
187C22×C4×C11—28no—
188C22×C4×C11—28no—
189C22×C4×C11—28no—
190C22×C4×C11—44no—
191C22×C4×C11—44no—
192C22×C4×C11—44no—
193C22×C4×C11—44no—
194C22×C4×C11C22×C412yes—
195C22×C4×C11C22×C414yes—
196C22×C4×C11C22×C412yes—
197C22×C4×C11C2×D412yes—
198C22×C4×C11C2×D412yes—
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2×D412yes—
201C22×C4×C11#4112yes—
202C22×C4×C11#4112yes—
203C22×Dic11—216no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—22no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—21no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—22no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—22no—
232C22×Dic11—21no—
233C22×Dic11—21no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—21no—
238C22×Dic11—21no—
239C22×Dic11—48no—
240C22×Dic11—48no—
241C22×Dic11—48no—
242C22×Dic11—48no—
243C22×Dic11—48no—
244C22×Dic11—48no—
245C22×Dic11C2×D412yes—
246C22×Dic11C2×D412yes—
247C22×Dic11C2×D414yes—
248C22×Dic11C2×D412yes—
249C22×Dic11C2×D412yes—
250C22×Dic11#4112yes—
251C22×Dic11#4112yes—
252C11×C4⋊C4—28no—
253C11×C22⋊C4—216no—
254C22⋊Dic11—216no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257C22⋊Dic11—48no—
258C22⋊Dic11—48no—
259C22⋊Dic11—48no—
260C4⋊Dic11—28no—
261C4⋊Dic11—44no—
262C4×Dic11—28no—
263C4×Dic11—44no—
264C22×#121D1111yescharacteristic
265C22×C4×D4—111no—
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—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—24no—
279C23×C11—24no—
280C23×C11—24no—
281C23×C11—24no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—24no—
285C23×C11—24no—
286C23×C11—22no—
287C23×C11—24no—
288C23×C11—22no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—22no—
293C23×C11—22no—
294C23×C11—22no—
295C23×C11—22no—
296C23×C11—24no—
297C23×C11—24no—
298C23×C11—22no—
299C23×C11—22no—
300C23×C11—24no—
301C23×C11—24no—
302C23×C11—22no—
303C23×C11—22no—
304C23×C11—24no—
305C23×C11—24no—
306C23×C11—24no—
307C23×C11—24no—
308C23×C11—22no—
309C23×C11—22no—
310C23×C11—22no—
311C23×C11—41no—
312C23×C11—42no—
313C23×C11—41no—
314C23×C11—41no—
315C23×C11—41no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—41no—
321C23×C11—41no—
322C23×C11—42no—
323C23×C11—41no—
324C23×C11—42no—
325C23×C11—41no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—41no—
330C23×C11—41no—
331C23×C11—41no—
332C23×C11—41no—
333C23×C11—41no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—41no—
337C23×C11—42no—
338C23×C11—41no—
339C23×C11—42no—
340C23×C11—42no—
341C23×C11—41no—
342C23×C11—42no—
343C23×C11C2×C22⋊C418yes—
344C23×C11C4×D414yescomplemented
345C23×C11C23×C411yescharacteristic
346C23×C11C22×D411yescharacteristic
347C23×C11C22×D411yescharacteristic
348C23×C11C22×D411yescharacteristic
349C23×C11C22×D411yescharacteristic
350C23×C11C22×D411yescharacteristic
351C23×C11C2×#4111yescharacteristic
352C23×C11C2×#4111yescharacteristic
353C23×C11C2×#4111yescharacteristic
354C23×C11C2×#4111yescharacteristic
355C23×C11C2×#4111yescharacteristic
356C23×C11H(5,𝔽2)11yescharacteristic
357C23×C11H(5,𝔽2)11yescharacteristic
358C23×C11H(5,𝔽2)11yescharacteristic
359C23×C112−1+411yescharacteristic
360D4×C11—232no—
361D4×C11—432no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—24no—
367C2×C4×C11—24no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—41no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—416no—
377C2×C4×C11C2×C22⋊C414yes—
378C2×C4×C11C4×D414yes—
379C2×C4×C11C4×D414yes—
380C2×C4×C11#12014yes—
381C2×C4×C11#12114yes—
382C2×C4×C11#12114yes—
383C2×C4×C11#12314yes—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—22no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—24no—
392C2×Dic11—22no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—24no—
398C2×Dic11—22no—
399C2×Dic11—24no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—432no—
403C2×Dic11—41no—
404C2×Dic11—41no—
405C2×Dic11—42no—
406C2×Dic11—41no—
407C2×Dic11—42no—
408C2×Dic11—41no—
409C2×Dic11—42no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—42no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—41no—
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—
426C2×Dic11#12114yescomplemented
427C23×D4C2×D1112yes—
428C23×D4C2×D1111yescharacteristic
429C24×C4—112no—
430C24×C4C2×D1111yescharacteristic
431C2×#121—24no—
432C2×#121—24no—
433C2×#121Dic1118yescomplemented
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—111no—
441C22×C22⋊C4—112no—
442C22×C22⋊C4—111no—
443C22×C22⋊C4—112no—
444C22×C22⋊C4—112no—
445C22×C22⋊C4—112no—
446C22×C22⋊C4C2×D1112yes—
447C22×C42—111no—
448C22×C42—111no—
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—24no—
461C22×C11—28no—
462C22×C11—28no—
463C22×C11—24no—
464C22×C11—28no—
465C22×C11—24no—
466C22×C11—42no—
467C22×C11—44no—
468C22×C11—42no—
469C22×C11—44no—
470C22×C11—42no—
471C22×C11—44no—
472C22×C11—44no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—44no—
476C22×C11—44no—
477C22×C11—42no—
478C22×C11—44no—
479C22×C11—42no—
480C22×C11—44no—
481C22×C11—42no—
482C22×C11—44no—
483C22×C11—42no—
484C22×C11—44no—
485C22×C11—42no—
486C22×C11—42no—
487C22×C11—44no—
488C22×C11—42no—
489C22×C11—44no—
490C22×C11C22×C22⋊C411yescharacteristic
491C22×C11C2×C4×D411yescharacteristic
492C22×C11C2×C4×D411yescharacteristic
493C22×C11C2×C4×D411yescharacteristic
494C22×C11C4×#4111yescharacteristic
495C22×C11#51811yescharacteristic
496C22×C11#52011yescharacteristic
497C22×C11C2×#12011yescharacteristic
498C22×C11C2×#12111yescharacteristic
499C22×C11C2×#12111yescharacteristic
500C22×C11C2×#12111yescharacteristic
501C22×C11C2×#12311yescharacteristic
502C22×C11#52511yescharacteristic
503C22×C11#52911yescharacteristic
504C22×C11#53211yescharacteristic
505C22×C11#53511yescharacteristic
506C22×C11#53711yescharacteristic
507C22×C11#54011yescharacteristic
508C22×C11#54211yescharacteristic
509C22×C11D4211yescharacteristic
510C22×C11D4211yescharacteristic
511C22×C11D4211yescharacteristic
512C22×C11#54611yescharacteristic
513C22×C11#54611yescharacteristic
514C22×C11#54611yescharacteristic
515C22×C11#54611yescharacteristic
516C22×C11#54611yescharacteristic
517C22×C11#54711yescharacteristic
518C22×C11#54711yescharacteristic
519C22×C11#54711yescharacteristic
520C22×C11#54811yescharacteristic
521C22×C11#55011yescharacteristic
522C22×C11#55311yescharacteristic
523C22×C11#55311yescharacteristic
524C22×C11#55511yescharacteristic
525C4×C11—44no—
526C4×C11—42no—
527C4×C11#38618yescomplemented
528Dic11—24no—
529Dic11—42no—
530Dic11—44no—
531Dic11—42no—
532Dic11—42no—
533Dic11—82no—
534C25C22×D1111yescharacteristic
535C25C22×D1112yes—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—24no—
539C22×D4—24no—
540C22×D4—22no—
541C22×D4—22no—
542C22×D4—22no—
543C22×D4—22no—
544C22×D4—42no—
545C22×D4—42no—
546C22×D4C2×Dic1114yes—
547C22×D4C2×Dic1118yescomplemented
548C22×D4C22⋊D1114yes—
549C22×D4C22⋊D1114yes—
550C23×C4—22no—
551C23×C4—22no—
552C23×C4—22no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—111no—
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—111no—
560C23×C4—112no—
561C23×C4—112no—
562C23×C4—224no—
563C23×C4—224no—
564C23×C4—224no—
565C23×C4—224no—
566C23×C4—224no—
567C23×C4—442no—
568C23×C4—442no—
569C23×C4C2×Dic1114yescomplemented
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1112yes—
572C23×C4C22×D1111yescharacteristic
573#121—232no—
574C4×D4—2232no—
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⋊C4C2×Dic1114yescomplemented
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—114no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—222no—
591C2×C22⋊C4—222no—
592C2×C22⋊C4—222no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—224no—
595C2×C22⋊C4—224no—
596C2×C22⋊C4—224no—
597C2×C22⋊C4—224no—
598C2×C22⋊C4—224no—
599C2×C22⋊C4—224no—
600C2×C22⋊C4—224no—
601C2×C22⋊C4—442no—
602C2×C22⋊C4—442no—
603C2×C22⋊C4—442no—
604C2×C22⋊C4C2×Dic1118yescomplemented
605C2×C42—114no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—222no—
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—44no—
619C2×C11—48no—
620C2×C11C2×#38611yescharacteristic
621C2×C11C4×#12111yescharacteristic
622C2×C11#232411yescharacteristic
623C2×C11D4×C22⋊C411yescharacteristic
624C2×C11#233911yescharacteristic
625C2×C11#236111yescharacteristic
626C2×C11#236311yescharacteristic
627C2×C11#240711yescharacteristic
628C2×C11#240811yescharacteristic
629C2×C11#242011yescharacteristic
630C2×C11#242211yescharacteristic
631C2×C11#242711yescharacteristic
632C2×C11#242811yescharacteristic
633C2×C11#253511yescharacteristic
634C2×C11#253711yescharacteristic
635C24—21no—
636C24—21no—
637C24—22no—
638C24—22no—
639C24—22no—
640C24—21no—
641C24—21no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—21no—
648C24—21no—
649C24—22no—
650C24—21no—
651C24—21no—
652C24—22no—
653C24—21no—
654C24—22no—
655C24—22no—
656C24—21no—
657C24—21no—
658C24—21no—
659C24D4×D1112yes—
660C24#434112yes—
661C24C22×Dic1112yes—
662C24C22×Dic1114yes—
663C24C2×C22⋊D1114yes—
664C24C2×C22⋊D1114yes—
665C24C23×D1111yescharacteristic
666C2×D4—216no—
667C2×D4—216no—
668C2×D4—28no—
669C2×D4—28no—
670C2×D4—28no—
671C2×D4—28no—
672C2×D4—28no—
673C2×D4—28no—
674C2×D4—48no—
675C2×D4—48no—
676C2×D4—48no—
677C2×D4—48no—
678C2×D4—48no—
679C2×D4C22⋊Dic11116yescomplemented
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—44no—
696C22×C4—44no—
697C22×C4—44no—
698C22×C4—44no—
699C22×C4—112no—
700C22×C4—112no—
701C22×C4—112no—
702C22×C4—112no—
703C22×C4—112no—
704C22×C4—114no—
705C22×C4—112no—
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—221no—
715C22×C4—222no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—222no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—222no—
727C22×C4—221no—
728C22×C4—222no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—221no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—222no—
737C22×C4—222no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—222no—
741C22×C4—222no—
742C22×C4—448no—
743C22×C4—448no—
744C22×C4—448no—
745C22×C4—448no—
746C22×C4—448no—
747C22×C4—448no—
748C22×C4D4×D1112yes—
749C22×C4D4×D1112yes—
750C22×C4#434112yes—
751C22×C4#434112yes—
752C22×C4C22×Dic1112yes—
753C22×C4C22×Dic1114yes—
754C22×C4C22×Dic1112yes—
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—228no—
768C42—444no—
769C11#1397011yescharacteristic, complemented, Sylow
770C23—22no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—22no—
782C23—22no—
783C23—24no—
784C23—24no—
785C23—22no—
786C23—22no—
787C23—24no—
788C23—24no—
789C23—24no—
790C23—24no—
791C23—22no—
792C23—24no—
793C23—22no—
794C23—24no—
795C23—24no—
796C23—24no—
797C23—22no—
798C23—22no—
799C23—22no—
800C23—22no—
801C23—22no—
802C23—22no—
803C23—22no—
804C23—22no—
805C23—22no—
806C23—41no—
807C23—41no—
808C23—41no—
809C23—41no—
810C23—41no—
811C23—41no—
812C23—41no—
813C23—41no—
814C23—42no—
815C23—42no—
816C23—41no—
817C23—42no—
818C23—42no—
819C23—41no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—41no—
825C23—41no—
826C23—42no—
827C23—42no—
828C23—42no—
829C23—42no—
830C23—41no—
831C23—41no—
832C23—42no—
833C23—41no—
834C23—42no—
835C23—42no—
836C23—41no—
837C23—42no—
838C23D4×Dic1114yescomplemented
839C23C2×C22⋊Dic1118yes—
840C23C2×D4×D1111yescharacteristic
841C23C2×D4×D1111yescharacteristic
842C23C2×D4×D1111yescharacteristic
843C23C2×#434111yescharacteristic
844C23C2×#434111yescharacteristic
845C23C2×#434111yescharacteristic
846C23#6703711yescharacteristic
847C23#6703711yescharacteristic
848C23#41×D1111yescharacteristic
849C23#41×D1111yescharacteristic
850C23#6704211yescharacteristic
851C23#6704311yescharacteristic
852C23C23×Dic1111yescharacteristic
853C23C22×C22⋊D1111yescharacteristic
854C23C22×C22⋊D1111yescharacteristic
855D4—232no—
856D4—432no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—22no—
862C2×C4—24no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—42no—
866C2×C4—42no—
867C2×C4—41no—
868C2×C4—41no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—416no—
872C2×C4—114no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—222no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—222no—
879C2×C4—222no—
880C2×C4—224no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—222no—
887C2×C4—224no—
888C2×C4—222no—
889C2×C4—224no—
890C2×C4—222no—
891C2×C4—4432no—
892C2×C4—442no—
893C2×C4—441no—
894C2×C4—441no—
895C2×C4—441no—
896C2×C4—441no—
897C2×C4—441no—
898C2×C4—441no—
899C2×C4—442no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—442no—
903C2×C4—442no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—441no—
907C2×C4—441no—
908C2×C4—442no—
909C2×C4—442no—
910C2×C4—442no—
911C2×C4—442no—
912C2×C4—442no—
913C2×C4—442no—
914C2×C4—442no—
915C2×C4D4×Dic1114yes—
916C2×C4D4×Dic1114yes—
917C2×C4#6698814yes—
918C2×C4#6699014yes—
919C2×C4#6699214yes—
920C2×C4#6699214yes—
921C2×C4C2×C22⋊Dic1114yes—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—28no—
926C22—28no—
927C22—28no—
928C22—44no—
929C22—44no—
930C22—42no—
931C22—44no—
932C22—44no—
933C22—42no—
934C22—44no—
935C22—42no—
936C22—44no—
937C22—42no—
938C22—42no—
939C22—44no—
940C22—42no—
941C22—44no—
942C22—42no—
943C22—44no—
944C22—42no—
945C22—42no—
946C22—42no—
947C22—44no—
948C22—44no—
949C22—42no—
950C22—44no—
951C22—42no—
952C22#1062312711yescharacteristic
953C22#1062312911yescharacteristic
954C22#1062313011yescharacteristic
955C22#1062313111yescharacteristic
956C22#1062313411yescharacteristic
957C22D11×#12111yescharacteristic
958C22#1062313711yescharacteristic
959C22#1062313811yescharacteristic
960C22#1062313911yescharacteristic
961C22#1062314011yescharacteristic
962C22#1062314211yescharacteristic
963C22#1062314311yescharacteristic
964C22#1062314511yescharacteristic
965C22#1062314711yescharacteristic
966C22#1062314911yescharacteristic
967C22#1062315011yescharacteristic
968C22C2×D4×Dic1111yescharacteristic
969C22C2×D4×Dic1111yescharacteristic
970C22C2×D4×Dic1111yescharacteristic
971C22C2×#6698811yescharacteristic
972C22#1062332911yescharacteristic
973C22C2×#6699011yescharacteristic
974C22D4×C22⋊D1111yescharacteristic
975C22D4×C22⋊D1111yescharacteristic
976C22C2×#6699211yescharacteristic
977C22C2×#6699211yescharacteristic
978C22#1062333711yescharacteristic
979C22#1062333711yescharacteristic
980C22#1062335511yescharacteristic
981C22#1062335511yescharacteristic
982C22#41×Dic1111yescharacteristic
983C22#1062335811yescharacteristic
984C22#1062336011yescharacteristic
985C22#1062336011yescharacteristic
986C22C22×C22⋊Dic1111yescharacteristic
987C4—44no—
988C4—42no—
989C4—224no—
990C4—442no—
991C4—444no—
992C4—442no—
993C4—442no—
994C4—882no—
995C4#1062283318yescomplemented
996C2—44no—
997C2—48no—
998C2C2×#1062283311yescharacteristic
999C2#121×Dic1111yescharacteristic
1000C2#1307131111yescharacteristic
1001C2D4×C22⋊Dic1111yescharacteristic
1002C2#1307144611yescharacteristic
1003C2#1307163611yescharacteristic
1004C2#1307165811yescharacteristic
1005C2#1307195711yescharacteristic
1006C2#1307196811yescharacteristic
1007C2#1307210411yescharacteristic
1008C2#1307212611yescharacteristic
1009C2#1307219511yescharacteristic
1010C2#1307220611yescharacteristic
1011C2#1307351511yescharacteristic
1012C2#1307353011yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#121C2
socle, cosocleC24×C11C24
hypercenterC22×#121D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C22×D4×Dic11C2semidirect
2. C2×#10622834C2semidirect
3. C2×#10622833C2semidirect
4. C2×#10622825C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. #13066865C2semidirect
7. #13066857C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. #13066838C2semidirect
18. C2×C11×#121C4semidirect
58. C22×D4×C11C2×C4semidirect
67. C23×C4×C11C2×C4semidirect
87. C2×C11×C4⋊C4C2×C4semidirect
90. C2×C11×C22⋊C4C2×C4semidirect
108. C2×C22⋊Dic11D4semidirect
115. C2×C4⋊Dic11D4semidirect
121. C2×C4×Dic11D4semidirect
174. C2×D4×C11C22⋊C4semidirect
344. C23×C11C4×D4semidirect
426. C2×Dic11#121semidirect
433. C2×#121Dic11semidirect
527. C4×C11#386semidirect
547. C22×D4C2×Dic11semidirect
569. C23×C4C2×Dic11semidirect
583. C2×C4⋊C4C2×Dic11semidirect
604. C2×C22⋊C4C2×Dic11semidirect
679. C2×D4C22⋊Dic11semidirect
769. C11#13970semidirect
838. C23D4×Dic11semidirect
995. C4#10622833semidirect

Maximal subgroups

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

subgroupindex
C22×D4×Dic112
C2×#106228342
C2×#106228332
C2×#106228252
C2×C4×C22⋊Dic112
#130668652
#130668572
#130668452
#130668382
C22×C11×#1212
#1397011