Finite Group Databasebeta

← #14676920

Subgroups — #14676920

Order 2816.

2682 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622834C211yesmaximal, characteristic, complemented
2C2×#10622834C212yesmaximal, complemented
3C2×#10622834C211yesmaximal, characteristic, complemented
4C2×#10622598C211yesmaximal, characteristic, complemented
5C2×#10622825C211yesmaximal, characteristic, complemented
6C2×C4⋊C4×Dic11C211yesmaximal, characteristic, complemented
7C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
8#13066861C212yesmaximal, complemented
9#13066857C212yesmaximal, complemented
10#13066853C212yesmaximal, complemented
11C22×C11×#121C211yesmaximal, characteristic
12C23×D4×C11C2211yescharacteristic
13C23×D4×C11C2212yes—
14C24×C4×C11C2211yescharacteristic
15C2×C11×#121—24no—
16C2×C11×#121—24no—
17C2×C11×#121C418yescomplemented
18C22×C11×C4⋊C4C2211yescharacteristic
19C22×C11×C22⋊C4C2212yes—
20C22×C22⋊Dic11C2211yescharacteristic
21C22×C22⋊Dic11C2212yes—
22C22×C22⋊Dic11C2212yes—
23C22×C22⋊Dic11C2212yes—
24C22×C22⋊Dic11C2212yes—
25C22×C22⋊Dic11C2211yescharacteristic
26C22×C22⋊Dic11C2212yes—
27C22×C4⋊Dic11C2211yescharacteristic
28C22×C4⋊Dic11C2212yes—
29C22×C4⋊Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C22×C4×Dic11C2212yes—
32C22×C4×Dic11C2211yescharacteristic
33#10622834—28no—
34#10622834—24no—
35#10622834—24no—
36#10622825—24no—
37C4×C22⋊Dic11—24no—
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622598—24no—
44C4⋊C4×Dic11—24no—
45C25×C11C2312yes—
46C25×C11C2311yescharacteristic
47C22×D4×C11—24no—
48C22×D4×C11—24no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—24no—
52C22×D4×C11—24no—
53C22×D4×C11—22no—
54C22×D4×C11—22no—
55C22×D4×C11—22no—
56C22×D4×C11—22no—
57C22×D4×C11—42no—
58C22×D4×C11—42no—
59C22×D4×C11C2×C414yes—
60C22×D4×C11C2×C418yes—
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×C414yes—
68C23×C4×C11C2311yescharacteristic
69C23×C4×C11C2312yes—
70C23×C4×C11C2311yescharacteristic
71C23×Dic11C2312yes—
72C23×Dic11C2311yescharacteristic
73C23×Dic11C2312yes—
74C23×Dic11C2311yescharacteristic
75C23×Dic11C2311yescharacteristic
76C23×Dic11C2311yescharacteristic
77C11×#121—232no—
78C2×C11×C4⋊C4C2×C414yes—
79C2×C11×C4⋊C4D414yes—
80C2×C11×C4⋊C4D414yes—
81C2×C11×C22⋊C4—24no—
82C2×C11×C22⋊C4—24no—
83C2×C11×C22⋊C4C2×C418yes—
84C2×C22⋊Dic11—22no—
85C2×C22⋊Dic11—22no—
86C2×C22⋊Dic11—22no—
87C2×C22⋊Dic11—22no—
88C2×C22⋊Dic11—22no—
89C2×C22⋊Dic11—24no—
90C2×C22⋊Dic11—24no—
91C2×C22⋊Dic11—24no—
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—24no—
94C2×C22⋊Dic11—24no—
95C2×C22⋊Dic11—24no—
96C2×C22⋊Dic11—24no—
97C2×C22⋊Dic11—24no—
98C2×C22⋊Dic11—24no—
99C2×C22⋊Dic11—42no—
100C2×C22⋊Dic11—42no—
101C2×C22⋊Dic11—42no—
102C2×C22⋊Dic11—42no—
103C2×C22⋊Dic11—42no—
104C2×C22⋊Dic11D414yescomplemented
105C2×C4⋊Dic11—22no—
106C2×C4⋊Dic11—22no—
107C2×C4⋊Dic11—22no—
108C2×C4⋊Dic11—22no—
109C2×C4⋊Dic11—24no—
110C2×C4⋊Dic11—22no—
111C2×C4⋊Dic11—24no—
112C2×C4⋊Dic11—42no—
113C2×C4⋊Dic11D414yescomplemented
114C2×C4×Dic11—22no—
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—24no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11—24no—
121C2×C4×Dic11—42no—
122C2×C4×Dic11D414yescomplemented
123C11⋊#95—24no—
124C11⋊#95—24no—
125C11⋊#95—22no—
126C11⋊#95—22no—
127C11⋊#95—24no—
128#13998—111nomaximal, Sylow
129C24×C11—21no—
130C24×C11—21no—
131C24×C11—21no—
132C24×C11—21no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—21no—
138C24×C11—21no—
139C24×C11—21no—
140C24×C11—21no—
141C24×C11—22no—
142C24×C11—22no—
143C24×C11—22no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11—22no—
149C24×C11—22no—
150C24×C11—22no—
151C24×C11—22no—
152C24×C11—22no—
153C24×C11—22no—
154C24×C11—22no—
155C24×C11C22×C414yes—
156C24×C11C22×C412yes—
157C24×C11C2×D412yes—
158C24×C11#4112yes—
159C24×C11C2411yescharacteristic
160C2×D4×C11—216no—
161C2×D4×C11—216no—
162C2×D4×C11—28no—
163C2×D4×C11—28no—
164C2×D4×C11—28no—
165C2×D4×C11—48no—
166C2×D4×C11—48no—
167C2×D4×C11—48no—
168C2×D4×C11—48no—
169C2×D4×C11—48no—
170C2×D4×C11—44no—
171C2×D4×C11—44no—
172C2×D4×C11—44no—
173C2×D4×C11—44no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—21no—
184C22×C4×C11—28no—
185C22×C4×C11—28no—
186C22×C4×C11—28no—
187C22×C4×C11—44no—
188C22×C4×C11—44no—
189C22×C4×C11—44no—
190C22×C4×C11—44no—
191C22×C4×C11C22×C412yes—
192C22×C4×C11C22×C414yes—
193C22×C4×C11C22×C412yes—
194C22×C4×C11C2×D414yes—
195C22×C4×C11C2×D414yes—
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×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—22no—
215C22×Dic11—22no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—22no—
219C22×Dic11—21no—
220C22×Dic11—21no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—22no—
224C22×Dic11—22no—
225C22×Dic11—21no—
226C22×Dic11—22no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—21no—
236C22×Dic11—21no—
237C22×Dic11C2×D412yes—
238C22×Dic11C2×D414yes—
239C22×Dic11C2×D412yes—
240C22×Dic11C2×D412yes—
241C22×Dic11C2×D412yes—
242C22×Dic11#4112yes—
243C22×Dic11#4112yes—
244C11×C4⋊C4C22⋊C4116yescomplemented
245C11×C22⋊C4—216no—
246C22⋊Dic11—28no—
247C22⋊Dic11—28no—
248C22⋊Dic11—48no—
249C22⋊Dic11—48no—
250C22⋊Dic11—48no—
251C22⋊Dic11—48no—
252C22⋊Dic11—48no—
253C4⋊Dic11—28no—
254C4⋊Dic11—48no—
255C4⋊Dic11—44no—
256C4×Dic11—28no—
257C4×Dic11—48no—
258C4×Dic11—44no—
259C22×#121D1111yescharacteristic
260C2×#390—112no—
261C2×#390—111no—
262C2×#390—111no—
263C2×#389—111no—
264C2×#380—111no—
265C2×C4×C4⋊C4—111no—
266C2×C4×C22⋊C4—111no—
267#1439—112no—
268#1438—112no—
269#1437—112no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—22no—
274C23×C11—22no—
275C23×C11—22no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—22no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—24no—
293C23×C11—24no—
294C23×C11—24no—
295C23×C11—41no—
296C23×C11—41no—
297C23×C11—41no—
298C23×C11—41no—
299C23×C11—41no—
300C23×C11—41no—
301C23×C11—41no—
302C23×C11—41no—
303C23×C11—41no—
304C23×C11—41no—
305C23×C11—41no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—41no—
310C23×C11—41no—
311C23×C11—42no—
312C23×C11—42no—
313C23×C11—42no—
314C23×C11—42no—
315C23×C11—42no—
316C23×C11—42no—
317C23×C11—42no—
318C23×C11—42no—
319C23×C11—42no—
320C23×C11—42no—
321C23×C11—42no—
322C23×C11—42no—
323C23×C11—42no—
324C23×C11—42no—
325C23×C11—42no—
326C23×C11—42no—
327C23×C11—42no—
328C23×C11—42no—
329C23×C11—42no—
330C23×C11—42no—
331C23×C11—42no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11—42no—
336C23×C11—42no—
337C23×C11—42no—
338C23×C11—42no—
339C23×C11C4×D414yes—
340C23×C11C23×C411yescharacteristic
341C23×C11C22×D411yescharacteristic
342C23×C11C22×D411yescharacteristic
343C23×C11C22×D411yescharacteristic
344C23×C11C22×D411yescharacteristic
345C23×C11C22×D411yescharacteristic
346C23×C11C2×#4111yescharacteristic
347C23×C11C2×#4111yescharacteristic
348C23×C11C2×#4111yescharacteristic
349C23×C11C2×#4111yescharacteristic
350C23×C11C2×#4111yescharacteristic
351C23×C11H(5,𝔽2)11yescharacteristic
352C23×C11H(5,𝔽2)11yescharacteristic
353C23×C11H(5,𝔽2)11yescharacteristic
354C23×C112−1+411yescharacteristic
355D4×C11—432no—
356D4×C11—416no—
357C2×C4×C11—24no—
358C2×C4×C11—24no—
359C2×C4×C11—24no—
360C2×C4×C11—24no—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—41no—
367C2×C4×C11—41no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—416no—
371C2×C4×C11C2×C22⋊C418yes—
372C2×C4×C11C2×C22⋊C414yes—
373C2×C4×C11C4×D414yes—
374C2×C4×C11C4×D414yes—
375C2×C4×C11#12114yes—
376C2×C4×C11#12114yes—
377C2×C4×C11#12414yes—
378C2×C4×C11#12714yes—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—22no—
385C2×Dic11—22no—
386C2×Dic11—24no—
387C2×Dic11—22no—
388C2×Dic11—22no—
389C2×Dic11—22no—
390C2×Dic11—22no—
391C2×Dic11—22no—
392C2×Dic11—24no—
393C2×Dic11—22no—
394C2×Dic11—22no—
395C2×Dic11—24no—
396C2×Dic11—22no—
397C2×Dic11—41no—
398C2×Dic11—41no—
399C2×Dic11—42no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—42no—
403C2×Dic11—42no—
404C2×Dic11—41no—
405C2×Dic11—41no—
406C2×Dic11—41no—
407C2×Dic11—41no—
408C2×Dic11—42no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420C2×Dic11#12114yescomplemented
421C23×D4C2×D1111yescharacteristic
422C23×D4C2×D1112yes—
423C24×C4C2×D1111yescharacteristic
424C2×#121—24no—
425C2×#121—24no—
426C2×#121Dic1118yescomplemented
427C22×C4⋊C4—111no—
428C22×C4⋊C4—111no—
429C22×C4⋊C4—112no—
430C22×C4⋊C4C2×D1111yescharacteristic
431C22×C22⋊C4—111no—
432C22×C22⋊C4—112no—
433C22×C22⋊C4—111no—
434C22×C22⋊C4—112no—
435C22×C22⋊C4—112no—
436C22×C22⋊C4—112no—
437C22×C22⋊C4—112no—
438C22×C22⋊C4C2×D1112yes—
439C22×C42—111no—
440C22×C42—111no—
441C22×C42—112no—
442#390—224no—
443#390—228no—
444#390—224no—
445#389—224no—
446#380—224no—
447C4×C4⋊C4—224no—
448C4×C22⋊C4—224no—
449C2×#95—111no—
450C2×#95—112no—
451C2×#95—112no—
452C2×#95—112no—
453C2×#95—111no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—42no—
458C22×C11—42no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—44no—
470C22×C11—44no—
471C22×C11—44no—
472C22×C11—44no—
473C22×C11—44no—
474C22×C11—44no—
475C22×C11—44no—
476C22×C11—82no—
477C22×C11—82no—
478C22×C11—82no—
479C22×C11—82no—
480C22×C11—82no—
481C22×C11—82no—
482C22×C11—82no—
483C22×C11—82no—
484C22×C11C22×C22⋊C411yescharacteristic
485C22×C11C2×C4×D411yescharacteristic
486C22×C11C2×C4×D411yescharacteristic
487C22×C11C2×C4×D411yescharacteristic
488C22×C11C4×#4111yescharacteristic
489C22×C11#51811yescharacteristic
490C22×C11#52011yescharacteristic
491C22×C11C2×#12111yescharacteristic
492C22×C11C2×#12111yescharacteristic
493C22×C11C2×#12111yescharacteristic
494C22×C11#52511yescharacteristic
495C22×C11C2×#12411yescharacteristic
496C22×C11#52911yescharacteristic
497C22×C11C2×#12711yescharacteristic
498C22×C11#53211yescharacteristic
499C22×C11#53511yescharacteristic
500C22×C11#53711yescharacteristic
501C22×C11#54011yescharacteristic
502C22×C11#54211yescharacteristic
503C22×C11D4211yescharacteristic
504C22×C11D4211yescharacteristic
505C22×C11D4211yescharacteristic
506C22×C11#54611yescharacteristic
507C22×C11#54611yescharacteristic
508C22×C11#54611yescharacteristic
509C22×C11#54711yescharacteristic
510C22×C11#54811yescharacteristic
511C22×C11#54811yescharacteristic
512C22×C11#54811yescharacteristic
513C22×C11#55011yescharacteristic
514C22×C11#55011yescharacteristic
515C22×C11#55011yescharacteristic
516C22×C11#55311yescharacteristic
517C22×C11#55311yescharacteristic
518C22×C11#55511yescharacteristic
519C4×C11—28no—
520C4×C11—42no—
521C4×C11#39018yescomplemented
522Dic11—24no—
523Dic11—42no—
524Dic11—44no—
525Dic11—42no—
526Dic11—42no—
527Dic11—82no—
528C25C22×D1112yes—
529C25C22×D1111yescharacteristic
530C22×D4—24no—
531C22×D4—24no—
532C22×D4—22no—
533C22×D4—22no—
534C22×D4—22no—
535C22×D4—22no—
536C22×D4—24no—
537C22×D4—24no—
538C22×D4—22no—
539C22×D4—22no—
540C22×D4—42no—
541C22×D4—42no—
542C22×D4C2×Dic1114yes—
543C22×D4C2×Dic1118yes—
544C23×C4—22no—
545C23×C4—22no—
546C23×C4—22no—
547C23×C4—22no—
548C23×C4—22no—
549C23×C4—22no—
550C23×C4—111no—
551C23×C4—111no—
552C23×C4—112no—
553C23×C4—111no—
554C23×C4—111no—
555C23×C4—112no—
556C23×C4C2×Dic1114yes—
557C23×C4C22×D1111yescharacteristic
558C23×C4C22×D1112yes—
559C23×C4C22×D1111yescharacteristic
560#121—232no—
561C2×C4⋊C4—114no—
562C2×C4⋊C4—222no—
563C2×C4⋊C4—222no—
564C2×C4⋊C4—224no—
565C2×C4⋊C4—222no—
566C2×C4⋊C4—222no—
567C2×C4⋊C4—224no—
568C2×C4⋊C4—222no—
569C2×C4⋊C4—442no—
570C2×C4⋊C4C2×Dic1114yes—
571C2×C4⋊C4C22⋊D1114yes—
572C2×C4⋊C4C22⋊D1114yes—
573C2×C22⋊C4—24no—
574C2×C22⋊C4—24no—
575C2×C22⋊C4—114no—
576C2×C22⋊C4—222no—
577C2×C22⋊C4—222no—
578C2×C22⋊C4—222no—
579C2×C22⋊C4—222no—
580C2×C22⋊C4—222no—
581C2×C22⋊C4—224no—
582C2×C22⋊C4—224no—
583C2×C22⋊C4—224no—
584C2×C22⋊C4—224no—
585C2×C22⋊C4—224no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—224no—
588C2×C22⋊C4—224no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—442no—
592C2×C22⋊C4—442no—
593C2×C22⋊C4—442no—
594C2×C22⋊C4—442no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4C2×Dic1118yes—
597C2×C42—114no—
598C2×C42—222no—
599C2×C42—222no—
600C2×C42—224no—
601C2×C42—222no—
602C2×C42—222no—
603C2×C42—224no—
604C2×C42—222no—
605C2×C42—442no—
606#95—222no—
607#95—222no—
608#95—224no—
609#95—224no—
610#95—224no—
611C2×C11—44no—
612C2×C11—84no—
613C2×C11C2×#39011yescharacteristic
614C2×C11C4×#12111yescharacteristic
615C2×C11#232411yescharacteristic
616C2×C11D4×C22⋊C411yescharacteristic
617C2×C11#234111yescharacteristic
618C2×C11#236111yescharacteristic
619C2×C11#236311yescharacteristic
620C2×C11#241411yescharacteristic
621C2×C11#241611yescharacteristic
622C2×C11#242611yescharacteristic
623C2×C11#242811yescharacteristic
624C2×C11#249011yescharacteristic
625C2×C11#249111yescharacteristic
626C2×C11#254011yescharacteristic
627C2×C11#254111yescharacteristic
628C24—21no—
629C24—21no—
630C24—21no—
631C24—21no—
632C24—21no—
633C24—21no—
634C24—21no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—22no—
641C24—22no—
642C24—22no—
643C24—22no—
644C24—22no—
645C24—22no—
646C24—22no—
647C24—22no—
648C24—22no—
649C24—22no—
650C24—22no—
651C24—22no—
652C24—22no—
653C24—22no—
654C24D4×D1112yes—
655C24#434112yes—
656C24C22×Dic1114yes—
657C24C22×Dic1112yes—
658C24C23×D1111yescharacteristic
659C2×D4—216no—
660C2×D4—28no—
661C2×D4—28no—
662C2×D4—216no—
663C2×D4—28no—
664C2×D4—48no—
665C2×D4—48no—
666C2×D4—48no—
667C2×D4—48no—
668C2×D4—48no—
669C2×D4—44no—
670C2×D4—44no—
671C2×D4—44no—
672C2×D4—44no—
673C22×C4—22no—
674C22×C4—22no—
675C22×C4—22no—
676C22×C4—22no—
677C22×C4—21no—
678C22×C4—21no—
679C22×C4—21no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—21no—
683C22×C4—28no—
684C22×C4—28no—
685C22×C4—28no—
686C22×C4—44no—
687C22×C4—44no—
688C22×C4—44no—
689C22×C4—44no—
690C22×C4—112no—
691C22×C4—112no—
692C22×C4—112no—
693C22×C4—112no—
694C22×C4—114no—
695C22×C4—112no—
696C22×C4—112no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—221no—
702C22×C4—221no—
703C22×C4—222no—
704C22×C4—221no—
705C22×C4—221no—
706C22×C4—221no—
707C22×C4—221no—
708C22×C4—221no—
709C22×C4—222no—
710C22×C4—222no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—222no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—222no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—222no—
724C22×C4—221no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4D4×D1112yes—
733C22×C4D4×D1112yes—
734C22×C4#434112yes—
735C22×C4#434112yes—
736C22×C4C22×Dic1112yes—
737C22×C4C22×Dic1114yes—
738C22×C4C22×Dic1112yes—
739C22×C4C2×C22⋊D1114yes—
740C22×C4C2×C22⋊D1114yes—
741C22×C4C2×C22⋊D1112yes—
742C22×C4C2×C22⋊D1112yes—
743C4⋊C4—228no—
744C4⋊C4—448no—
745C4⋊C4—444no—
746C4⋊C4C22⋊Dic11116yescomplemented
747C22⋊C4—216no—
748C22⋊C4—228no—
749C22⋊C4—228no—
750C22⋊C4—448no—
751C22⋊C4—448no—
752C22⋊C4—448no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C42—228no—
756C42—448no—
757C42—444no—
758C11#1399811yescharacteristic, complemented, Sylow
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—22no—
768C23—22no—
769C23—22no—
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—24no—
778C23—24no—
779C23—24no—
780C23—24no—
781C23—24no—
782C23—24no—
783C23—24no—
784C23—41no—
785C23—41no—
786C23—41no—
787C23—41no—
788C23—41no—
789C23—41no—
790C23—41no—
791C23—41no—
792C23—41no—
793C23—41no—
794C23—41no—
795C23—41no—
796C23—41no—
797C23—41no—
798C23—41no—
799C23—41no—
800C23—42no—
801C23—42no—
802C23—42no—
803C23—42no—
804C23—42no—
805C23—42no—
806C23—42no—
807C23—42no—
808C23—42no—
809C23—42no—
810C23—42no—
811C23—42no—
812C23—42no—
813C23—42no—
814C23—42no—
815C23—42no—
816C23—42no—
817C23—42no—
818C23—42no—
819C23—42no—
820C23—42no—
821C23—42no—
822C23—42no—
823C23—42no—
824C23—42no—
825C23—42no—
826C23—42no—
827C23—42no—
828C23D4×Dic1114yes—
829C23C2×D4×D1111yescharacteristic
830C23C2×D4×D1111yescharacteristic
831C23C2×D4×D1111yescharacteristic
832C23C2×#434111yescharacteristic
833C23C2×#434111yescharacteristic
834C23C2×#434111yescharacteristic
835C23#6703711yescharacteristic
836C23#6703711yescharacteristic
837C23#41×D1111yescharacteristic
838C23#41×D1111yescharacteristic
839C23#6704211yescharacteristic
840C23#6704311yescharacteristic
841C23C23×Dic1111yescharacteristic
842C23C22×C22⋊D1111yescharacteristic
843C23C22×C22⋊D1111yescharacteristic
844D4—432no—
845D4—416no—
846C2×C4—24no—
847C2×C4—24no—
848C2×C4—24no—
849C2×C4—24no—
850C2×C4—24no—
851C2×C4—24no—
852C2×C4—22no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—41no—
859C2×C4—416no—
860C2×C4—114no—
861C2×C4—222no—
862C2×C4—222no—
863C2×C4—222no—
864C2×C4—222no—
865C2×C4—222no—
866C2×C4—222no—
867C2×C4—222no—
868C2×C4—224no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—222no—
873C2×C4—222no—
874C2×C4—222no—
875C2×C4—224no—
876C2×C4—222no—
877C2×C4—222no—
878C2×C4—224no—
879C2×C4—442no—
880C2×C4—441no—
881C2×C4—441no—
882C2×C4—441no—
883C2×C4—441no—
884C2×C4—442no—
885C2×C4—441no—
886C2×C4—441no—
887C2×C4—442no—
888C2×C4—441no—
889C2×C4—441no—
890C2×C4—441no—
891C2×C4—441no—
892C2×C4—441no—
893C2×C4—441no—
894C2×C4—442no—
895C2×C4—442no—
896C2×C4—442no—
897C2×C4—442no—
898C2×C4—442no—
899C2×C4—442no—
900C2×C4—442no—
901C2×C4—442no—
902C2×C4D4×Dic1114yes—
903C2×C4D4×Dic1114yes—
904C2×C4#6698914yes—
905C2×C4#6699114yes—
906C2×C4#6699114yes—
907C2×C4#6699314yes—
908C2×C4C2×C22⋊Dic1118yes—
909C2×C4C2×C22⋊Dic1114yes—
910C22—24no—
911C22—24no—
912C22—24no—
913C22—42no—
914C22—42no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—42no—
919C22—42no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—42no—
924C22—42no—
925C22—44no—
926C22—44no—
927C22—44no—
928C22—44no—
929C22—44no—
930C22—44no—
931C22—44no—
932C22—82no—
933C22—82no—
934C22—82no—
935C22—82no—
936C22—82no—
937C22—82no—
938C22—82no—
939C22—82no—
940C22#1062312711yescharacteristic
941C22#1062312911yescharacteristic
942C22#1062313011yescharacteristic
943C22#1062313111yescharacteristic
944C22#1062313411yescharacteristic
945C22D11×#12111yescharacteristic
946C22#1062313711yescharacteristic
947C22#1062313811yescharacteristic
948C22#1062313911yescharacteristic
949C22#1062314011yescharacteristic
950C22#1062314211yescharacteristic
951C22#1062314311yescharacteristic
952C22#1062314511yescharacteristic
953C22#1062314711yescharacteristic
954C22#1062314911yescharacteristic
955C22#1062315011yescharacteristic
956C22C2×D4×Dic1111yescharacteristic
957C22C2×D4×Dic1111yescharacteristic
958C22C2×D4×Dic1111yescharacteristic
959C22C2×#6698911yescharacteristic
960C22#1062332911yescharacteristic
961C22C2×#6699111yescharacteristic
962C22C2×#6699111yescharacteristic
963C22D4×C22⋊D1111yescharacteristic
964C22D4×C22⋊D1111yescharacteristic
965C22C2×#6699311yescharacteristic
966C22#1062333711yescharacteristic
967C22#1062333711yescharacteristic
968C22#41×Dic1111yescharacteristic
969C22#1062335811yescharacteristic
970C22#1062336211yescharacteristic
971C22#1062336211yescharacteristic
972C22#1062336511yescharacteristic
973C22#1062336511yescharacteristic
974C22C22×C22⋊Dic1111yescharacteristic
975C4—28no—
976C4—42no—
977C4—224no—
978C4—444no—
979C4—442no—
980C4—442no—
981C4—442no—
982C4—882no—
983C4#1062283418yescomplemented
984C2—44no—
985C2—84no—
986C2C2×#1062283411yescharacteristic
987C2#121×Dic1111yescharacteristic
988C2#1307131111yescharacteristic
989C2D4×C22⋊Dic1111yescharacteristic
990C2#1307145711yescharacteristic
991C2#1307163611yescharacteristic
992C2#1307165811yescharacteristic
993C2#1307203011yescharacteristic
994C2#1307205211yescharacteristic
995C2#1307217811yescharacteristic
996C2#1307220011yescharacteristic
997C2#1307297011yescharacteristic
998C2#1307298111yescharacteristic
999C2#1307355211yescharacteristic
1000C2#1307355911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
Fitting, prime radicalC22×C11×#121C2
socle, cosocleC24×C11C24
hypercenterC22×#121D11
hypocenterC11#13998
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10622834C2semidirect
2. C2×#10622834C2semidirect
3. C2×#10622834C2semidirect
4. C2×#10622598C2semidirect
5. C2×#10622825C2semidirect
6. C2×C4⋊C4×Dic11C2semidirect
7. C2×C4×C22⋊Dic11C2semidirect
8. #13066861C2semidirect
9. #13066857C2semidirect
10. #13066853C2semidirect
17. C2×C11×#121C4semidirect
104. C2×C22⋊Dic11D4semidirect
113. C2×C4⋊Dic11D4semidirect
122. C2×C4×Dic11D4semidirect
244. C11×C4⋊C4C22⋊C4semidirect
420. C2×Dic11#121semidirect
426. C2×#121Dic11semidirect
521. C4×C11#390semidirect
746. C4⋊C4C22⋊Dic11semidirect
758. C11#13998semidirect
983. C4#10622834semidirect

Maximal subgroups

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

subgroupindex
C2×#106228342
C2×#106225982
C2×#106228252
C2×C4⋊C4×Dic112
C2×C4×C22⋊Dic112
#130668612
#130668572
#130668532
C22×C11×#1212
#1399811