Finite Group Databasebeta

← #14685218

Subgroups — #14685218

Order 2816.

3246 conjugacy classes of subgroups.

The subgroup lattice has 986 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66983C211yesmaximal, characteristic, complemented
2C2×#10622604C211yesmaximal, characteristic, complemented
3C2×#10622573C211yesmaximal, characteristic, complemented
4C2×#10622836C212yesmaximal, complemented
5C2×#10622826C212yesmaximal, complemented
6#13066869C211yesmaximal, characteristic, complemented
7#13066861C211yesmaximal, characteristic, complemented
8#13066855C212yesmaximal, complemented
9#13066854C212yesmaximal, complemented
10#13066839C211yesmaximal, characteristic, complemented
11C22×C4×D4×C11C211yesmaximal, characteristic, complemented
12C23×D4×C11C2211yescharacteristic
13C24×C4×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C23×C22⋊D11C2212yes—
16C23×C22⋊D11C2212yes—
17C23×D44C2211yescharacteristic
18C2×C4×D4×C11—24no—
19C2×C4×D4×C11—24no—
20C2×C4×D4×C11—24no—
21C22×C11×C4⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C11×C22⋊C4C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C22×C22⋊Dic11C2212yes—
26C22×C22⋊Dic11C2212yes—
27C2×#66983—24no—
28C2×#66983—28no—
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×C4⋊Dic11C2211yescharacteristic
34#10622836—28no—
35#10622826—28no—
36C2×C11⋊#95C2212yes—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2211yescharacteristic
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2212yes—
41C2×C11⋊#95C2212yes—
42#10622604—24no—
43#10622573—24no—
44C25×C11C2311yescharacteristic
45C25×C11C2311yescharacteristic
46C24×D11C2312yes—
47C22×D4×C11—22no—
48C22×D4×C11—22no—
49C22×D4×C11—22no—
50C22×D4×C11—22no—
51C22×D4×C11—22no—
52C22×D4×C11—22no—
53C22×D4×C11D414yescomplemented
54C23×C4×C11—22no—
55C23×C4×C11—24no—
56C23×C4×C11—22no—
57C23×C4×C11—22no—
58C23×C4×C11—22no—
59C23×C4×C11—22no—
60C23×C4×C11—24no—
61C23×C4×C11—42no—
62C23×C4×C11—42no—
63C23×C4×C11D414yescomplemented
64C23×C4×C11C2311yescharacteristic
65C23×C4×C11C2311yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—24no—
70C22×C22⋊D11—24no—
71C22×C22⋊D11—24no—
72C22×C22⋊D11—24no—
73C22×C22⋊D11—24no—
74C22×C22⋊D11—24no—
75C22×C22⋊D11—24no—
76C22×C22⋊D11—24no—
77C22×C22⋊D11—24no—
78C22×C22⋊D11—24no—
79C22×C22⋊D11—42no—
80C22×C22⋊D11—42no—
81C22×C22⋊D11—42no—
82C22×C22⋊D11—42no—
83C23×Dic11C2312yes—
84C23×Dic11C2312yes—
85C23×Dic11C2312yes—
86C22×D44—24no—
87C22×D44—22no—
88C22×D44—22no—
89C22×D44—22no—
90C22×D44—42no—
91C4×D4×C11—232no—
92C2×C11×C4⋊C4—22no—
93C2×C11×C4⋊C4—22no—
94C2×C11×C4⋊C4D414yescomplemented
95C2×C11×C22⋊C4—22no—
96C2×C11×C22⋊C4—22no—
97C2×C11×C22⋊C4—22no—
98C2×C11×C22⋊C4—22no—
99C2×C11×C22⋊C4—22no—
100C2×C11×C22⋊C4D414yescomplemented
101C2×C42×C11—22no—
102C2×C42×C11—22no—
103C2×C42×C11—22no—
104C2×C22⋊Dic11—24no—
105C2×C22⋊Dic11—24no—
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—24no—
108C2×C22⋊Dic11—42no—
109C2×C22⋊Dic11—42no—
110#66983—232no—
111C2×(C2×D11)⋊C4—24no—
112C2×(C2×D11)⋊C4—24no—
113C2×(C2×D11)⋊C4—24no—
114C2×(C2×D11)⋊C4—24no—
115C2×(C2×D11)⋊C4—24no—
116C2×(C2×D11)⋊C4—24no—
117C2×(C2×D11)⋊C4—24no—
118C2×(C2×D11)⋊C4—24no—
119C2×(C2×D11)⋊C4—24no—
120C2×(C2×D11)⋊C4—42no—
121C2×(C2×D11)⋊C4—42no—
122C2×(C2×D11)⋊C4D418yescomplemented
123C2×C4⋊Dic11—22no—
124C2×C4⋊Dic11—24no—
125C11⋊#95—24no—
126C11⋊#95—22no—
127C11⋊#95—24no—
128C11⋊#95—22no—
129C11⋊#95—24no—
130C11⋊#95—42no—
131#14722—111nomaximal, Sylow
132C24×C11—22no—
133C24×C11—21no—
134C24×C11—21no—
135C24×C11—21no—
136C24×C11—21no—
137C24×C11—22no—
138C24×C11—22no—
139C24×C11—22no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—21no—
143C24×C11—21no—
144C24×C11—22no—
145C24×C11—22no—
146C24×C11—22no—
147C24×C11—22no—
148C24×C11C2×D412yes—
149C24×C11C2×D412yes—
150C24×C11C2×D412yes—
151C24×C11C2×D412yes—
152C24×C11#4112yes—
153C24×C11#4112yes—
154C24×C11C2411yescharacteristic
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11—22no—
159C23×D11—22no—
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—22no—
163C23×D11—22no—
164C23×D11—22no—
165C23×D11—22no—
166C23×D11—22no—
167C23×D11—22no—
168C23×D11—22no—
169C23×D11C2×D414yes—
170C2×D4×C11—28no—
171C2×D4×C11—28no—
172C2×D4×C11—28no—
173C2×D4×C11—28no—
174C2×D4×C11—28no—
175C2×D4×C11—28no—
176C2×D4×C11—28no—
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—22no—
185C22×C4×C11—22no—
186C22×C4×C11—28no—
187C22×C4×C11—22no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—22no—
193C22×C4×C11—22no—
194C22×C4×C11—22no—
195C22×C4×C11—28no—
196C22×C4×C11—28no—
197C22×C4×C11—44no—
198C22×C4×C11—48no—
199C22×C4×C11—48no—
200C22×C4×C11—48no—
201C22×C4×C11—48no—
202C22×C4×C11—44no—
203C22×C4×C11—44no—
204C22×C4×C11C2×D412yes—
205C22×C4×C11C2×D412yes—
206C22×C4×C11C2×D414yes—
207C22×C4×C11C2×D412yes—
208C22×C4×C11C2×D412yes—
209C22×C4×C11C2×D412yes—
210C22×C4×C11C2×D412yes—
211C22×C4×C11C2×D412yes—
212C22×C4×C11C2×D412yes—
213C22×C4×C11#4112yes—
214C2×C22⋊D11—216no—
215C2×C22⋊D11—216no—
216C2×C22⋊D11—48no—
217C2×C22⋊D11—48no—
218C2×C22⋊D11—48no—
219C2×C22⋊D11—48no—
220C2×C22⋊D11—48no—
221C2×C22⋊D11—48no—
222C2×C22⋊D11—48no—
223C2×C22⋊D11—48no—
224C2×C22⋊D11—48no—
225C2×C22⋊D11—48no—
226C2×C22⋊D11—48no—
227C2×C22⋊D11—48no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—22no—
232C22×Dic11—22no—
233C22×Dic11—22no—
234C22×Dic11—22no—
235C22×Dic11—22no—
236C22×Dic11—22no—
237C22×Dic11—22no—
238C22×Dic11—22no—
239C22×Dic11—22no—
240C22×Dic11—22no—
241C22×Dic11—22no—
242C22×Dic11—22no—
243C22×Dic11—22no—
244C22×Dic11—22no—
245C22×Dic11—22no—
246C22×Dic11—22no—
247C22×Dic11C2×D414yes—
248C22×Dic11#4114yes—
249C2×D44—28no—
250C2×D44—48no—
251C2×D44—48no—
252C2×D44—44no—
253C2×D44—44no—
254C11×C4⋊C4—28no—
255C11×C22⋊C4—28no—
256C11×C22⋊C4—28no—
257C42×C11—28no—
258C22⋊Dic11—48no—
259C22⋊Dic11—48no—
260(C2×D11)⋊C4—216no—
261(C2×D11)⋊C4—48no—
262(C2×D11)⋊C4—48no—
263(C2×D11)⋊C4—48no—
264C4⋊Dic11—28no—
265C22×#121—111no—
266C22×C4×D4D1111yescharacteristic, complemented
267C2×#394—111no—
268C2×#392—112no—
269C2×#392—111no—
270C2×#386—112no—
271#1441—111no—
272#1439—111no—
273#1438—112no—
274#1437—112no—
275C22⋊#95—111no—
276C23×C11—22no—
277C23×C11—22no—
278C23×C11—22no—
279C23×C11—22no—
280C23×C11—22no—
281C23×C11—22no—
282C23×C11—22no—
283C23×C11—24no—
284C23×C11—22no—
285C23×C11—22no—
286C23×C11—22no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—24no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—24no—
297C23×C11—24no—
298C23×C11—24no—
299C23×C11—24no—
300C23×C11—24no—
301C23×C11—24no—
302C23×C11—41no—
303C23×C11—42no—
304C23×C11—42no—
305C23×C11—42no—
306C23×C11—41no—
307C23×C11—41no—
308C23×C11—41no—
309C23×C11—42no—
310C23×C11—42no—
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#12114yes—
321C23×C11#12114yescomplemented
322C23×C11C22×D411yescharacteristic
323C23×C11C22×D412yes—
324C23×C11C22×D411yescharacteristic
325C23×C11C22×D411yescharacteristic
326C23×C11C22×D411yescharacteristic
327C23×C11C2×#4111yescharacteristic
328C23×C11C2×#4111yescharacteristic
329C23×C11C2×#4111yescharacteristic
330C23×C11C2×#4112yes—
331C23×C11H(5,𝔽2)12yes—
332C23×C11H(5,𝔽2)12yes—
333C22×D11—24no—
334C22×D11—24no—
335C22×D11—24no—
336C22×D11—24no—
337C22×D11—24no—
338C22×D11—24no—
339C22×D11—24no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—42no—
347C22×D11—42no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351C22×D11—42no—
352C22×D11—42no—
353C22×D11—42no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—42no—
357C22×D11—42no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—42no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368D4×C11—232no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—22no—
373C2×C4×C11—22no—
374C2×C4×C11—22no—
375C2×C4×C11—22no—
376C2×C4×C11—22no—
377C2×C4×C11—22no—
378C2×C4×C11—22no—
379C2×C4×C11—24no—
380C2×C4×C11—24no—
381C2×C4×C11—24no—
382C2×C4×C11—24no—
383C2×C4×C11—22no—
384C2×C4×C11—22no—
385C2×C4×C11—24no—
386C2×C4×C11—24no—
387C2×C4×C11—416no—
388C2×C4×C11—416no—
389C2×C4×C11—41no—
390C2×C4×C11—41no—
391C2×C4×C11—41no—
392C2×C4×C11—41no—
393C2×C4×C11—42no—
394C2×C4×C11—42no—
395C2×C4×C11#12014yes—
396C2×C4×C11#12014yes—
397C2×C4×C11#12114yescomplemented
398C22⋊D11—432no—
399C22⋊D11—432no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11—24no—
403C2×Dic11—24no—
404C2×Dic11—24no—
405C2×Dic11—24no—
406C2×Dic11—42no—
407C2×Dic11—42no—
408C2×Dic11—42no—
409C2×Dic11—42no—
410C2×Dic11—42no—
411C2×Dic11—42no—
412C2×Dic11—42no—
413C2×Dic11—42no—
414C2×Dic11—42no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420C2×Dic11—42no—
421D44—416no—
422C23×D4—112no—
423C23×D4—112no—
424C23×D4—111no—
425C23×D4C2×D1111yescharacteristic
426C24×C4C2×D1111yescharacteristic
427C24×C4C2×D1111yescharacteristic
428C2×#121—228no—
429C2×#121—224no—
430C2×C4×D4—24no—
431C2×C4×D4—24no—
432C2×C4×D4—24no—
433C22×C4⋊C4—111no—
434C22×C4⋊C4C2×D1111yescharacteristic
435C22×C22⋊C4—112no—
436C22×C22⋊C4—112no—
437C22×C22⋊C4—112no—
438C22×C22⋊C4—112no—
439C22×C22⋊C4—112no—
440C22×C22⋊C4—112no—
441C22×C22⋊C4C2×D1111yescharacteristic
442C22×C22⋊C4C2×D1111yescharacteristic
443C22×C42C2×D1111yescharacteristic
444#394—224no—
445#392—228no—
446#392—224no—
447#386—228no—
448C2×#95—111no—
449C2×#95—112no—
450C2×#95—111no—
451C2×#95—112no—
452C2×#95—112no—
453C2×#95—112no—
454C22×C11—24no—
455C22×C11—24no—
456C22×C11—24no—
457C22×C11—28no—
458C22×C11—24no—
459C22×C11—42no—
460C22×C11—42no—
461C22×C11—42no—
462C22×C11—42no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—44no—
467C22×C11—44no—
468C22×C11—44no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—44no—
472C22×C11—44no—
473C22×C11—44no—
474C22×C11—44no—
475C22×C11—42no—
476C22×C11C2×#12011yescharacteristic
477C22×C11C2×#12011yescharacteristic
478C22×C11C2×#12111yescharacteristic
479C22×C11C2×#12111yescharacteristic
480C22×C11C2×#12111yescharacteristic
481C22×C11#52511yescharacteristic
482C22×C11#52511yescharacteristic
483C22×C11#52511yescharacteristic
484C22×C11#52512yes—
485C22×C11#53212yes—
486C22×C11#53211yescharacteristic
487C22×C11#53411yescharacteristic
488C22×C11#53511yescharacteristic
489C22×C11#53812yes—
490C22×C11#54012yes—
491C22×C11D4212yes—
492C22×C11D4212yes—
493C22×C11D4212yes—
494C22×C11#54612yes—
495C22×C11#54612yes—
496C22×C11#54612yes—
497C22×C11#55012yes—
498C22×C11#55312yes—
499C2×D11—44no—
500C2×D11—44no—
501C2×D11—44no—
502C2×D11—44no—
503C2×D11—44no—
504C2×D11—44no—
505C2×D11—44no—
506C2×D11—82no—
507C2×D11—82no—
508C2×D11—82no—
509C2×D11—82no—
510C2×D11—82no—
511C2×D11—82no—
512C2×D11—82no—
513C2×D11—82no—
514C4×C11—24no—
515C4×C11—24no—
516C4×C11—24no—
517C4×C11—42no—
518C4×C11—42no—
519Dic11—44no—
520Dic11—44no—
521Dic11—82no—
522C25—112no—
523C25C22×D1111yescharacteristic
524C25C22×D1111yescharacteristic
525C22×D4—22no—
526C22×D4—22no—
527C22×D4—22no—
528C22×D4—22no—
529C22×D4—22no—
530C22×D4—22no—
531C22×D4—224no—
532C22×D4—224no—
533C22×D4—224no—
534C22×D4—224no—
535C22×D4—224no—
536C22×D4—224no—
537C22×D4—224no—
538C22×D4—224no—
539C22×D4—224no—
540C22×D4—224no—
541C22×D4—224no—
542C22×D4—222no—
543C22×D4—222no—
544C22×D4—222no—
545C22×D4—442no—
546C22×D4—442no—
547C22×D4—442no—
548C22×D4—442no—
549C22×D4—442no—
550C22×D4D4414yescomplemented
551C23×C4—22no—
552C23×C4—24no—
553C23×C4—22no—
554C23×C4—22no—
555C23×C4—22no—
556C23×C4—22no—
557C23×C4—24no—
558C23×C4—42no—
559C23×C4—42no—
560C23×C4—112no—
561C23×C4—112no—
562C23×C4—112no—
563C23×C4C22⋊D1114yescomplemented
564C23×C4C22×D1111yescharacteristic
565C23×C4C22×D1111yescharacteristic
566C23×C4C22×D1111yescharacteristic
567C23×C4C22×D1111yescharacteristic
568C23×C4C22×D1111yescharacteristic
569#121—2232no—
570C4×D4—232no—
571C2×C4⋊C4—22no—
572C2×C4⋊C4—22no—
573C2×C4⋊C4—224no—
574C2×C4⋊C4—222no—
575C2×C4⋊C4C22⋊D1114yescomplemented
576C2×C22⋊C4—22no—
577C2×C22⋊C4—22no—
578C2×C22⋊C4—22no—
579C2×C22⋊C4—22no—
580C2×C22⋊C4—22no—
581C2×C22⋊C4—118no—
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—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—224no—
594C2×C22⋊C4—224no—
595C2×C22⋊C4—442no—
596C2×C22⋊C4—442no—
597C2×C22⋊C4—442no—
598C2×C22⋊C4—442no—
599C2×C22⋊C4C22⋊D1114yescomplemented
600C2×C42—22no—
601C2×C42—22no—
602C2×C42—22no—
603#95—224no—
604#95—224no—
605#95—224no—
606#95—222no—
607#95—222no—
608#95—442no—
609C2×C11—44no—
610C2×C11—44no—
611C2×C11#238811yescharacteristic
612C2×C11#240311yescharacteristic
613C2×C11#240811yescharacteristic
614C2×C11#242412yes—
615C2×C11#242812yes—
616C2×C11#243111yescharacteristic
617C2×C11#245612yes—
618C2×C11#246412yes—
619C2×C11#254311yescharacteristic
620C2×C11#263511yescharacteristic
621C2×C11#284711yescharacteristic
622D11—84no—
623C24—21no—
624C24—21no—
625C24—21no—
626C24—21no—
627C24—22no—
628C24—22no—
629C24—22no—
630C24—22no—
631C24—22no—
632C24—22no—
633C24—22no—
634C24—22no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—114no—
640C24—222no—
641C24—222no—
642C24—222no—
643C24—222no—
644C24—222no—
645C24—222no—
646C24—222no—
647C24—222no—
648C24—222no—
649C24—222no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24C2×D4412yes—
655C24C2×D4412yes—
656C24#433912yes—
657C24#433912yes—
658C24C2×C22⋊D1112yes—
659C24C2×C22⋊D1112yes—
660C24C23×D1111yescharacteristic
661C2×D4—28no—
662C2×D4—28no—
663C2×D4—28no—
664C2×D4—28no—
665C2×D4—28no—
666C2×D4—28no—
667C2×D4—28no—
668C2×D4—228no—
669C2×D4—2216no—
670C2×D4—2216no—
671C2×D4—448no—
672C2×D4—448no—
673C2×D4—444no—
674C2×D4—448no—
675C2×D4—448no—
676C2×D4—448no—
677C2×D4—448no—
678C2×D4—448no—
679C2×D4—448no—
680C2×D4—448no—
681C2×D4—448no—
682C2×D4—448no—
683C2×D4—448no—
684C2×D4—448no—
685C2×D4—448no—
686C2×D4—444no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—21no—
694C22×C4—21no—
695C22×C4—21no—
696C22×C4—28no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—21no—
704C22×C4—21no—
705C22×C4—28no—
706C22×C4—28no—
707C22×C4—44no—
708C22×C4—48no—
709C22×C4—48no—
710C22×C4—48no—
711C22×C4—48no—
712C22×C4—44no—
713C22×C4—44no—
714C22×C4—114no—
715C22×C4—114no—
716C22×C4—222no—
717C22×C4—222no—
718C22×C4—222no—
719C22×C4—222no—
720C22×C4—222no—
721C22×C4—222no—
722C22×C4—222no—
723C22×C4—222no—
724C22×C4—222no—
725C22×C4—222no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—222no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4C2×D4412yes—
736C22×C4#433912yes—
737C22×C4D4×D1114yes—
738C22×C4C2×C22⋊D1112yes—
739C22×C4C2×C22⋊D1112yes—
740C22×C4C2×C22⋊D1112yes—
741C22×C4C2×C22⋊D1112yes—
742C22×C4C2×C22⋊D1112yes—
743C22×C4C2×C22⋊D1112yes—
744C22×C4C2×C22⋊D1112yes—
745C4⋊C4—28no—
746C4⋊C4—228no—
747C22⋊C4—28no—
748C22⋊C4—28no—
749C22⋊C4—2216no—
750C22⋊C4—448no—
751C22⋊C4—448no—
752C22⋊C4—448no—
753C22⋊C4—448no—
754C22⋊C4—448no—
755C42—28no—
756C11#1472211yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—22no—
763C23—22no—
764C23—22no—
765C23—22no—
766C23—22no—
767C23—24no—
768C23—22no—
769C23—24no—
770C23—24no—
771C23—22no—
772C23—24no—
773C23—24no—
774C23—24no—
775C23—24no—
776C23—24no—
777C23—24no—
778C23—24no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—42no—
784C23—41no—
785C23—42no—
786C23—42no—
787C23—42no—
788C23—42no—
789C23—42no—
790C23—42no—
791C23—41no—
792C23—42no—
793C23—42no—
794C23—42no—
795C23—42no—
796C23—42no—
797C23—41no—
798C23—41no—
799C23—42no—
800C23—42no—
801C23—224no—
802C23—224no—
803C23—224no—
804C23—224no—
805C23—224no—
806C23—224no—
807C23—224no—
808C23—442no—
809C23—442no—
810C23—442no—
811C23—442no—
812C23—442no—
813C23—442no—
814C23—442no—
815C23—442no—
816C23—442no—
817C23—442no—
818C23—442no—
819C23—442no—
820C23—442no—
821C23—442no—
822C23—442no—
823C23—442no—
824C23—442no—
825C23—442no—
826C23—442no—
827C23—442no—
828C23—442no—
829C23—442no—
830C23—442no—
831C23—442no—
832C23—442no—
833C23—442no—
834C23—442no—
835C23—442no—
836C23#6698314yes—
837C23#6698314yescomplemented
838C23C22×D4411yescharacteristic
839C23C2×#433911yescharacteristic
840C23C2×#433911yescharacteristic
841C23C2×#433911yescharacteristic
842C23C2×D4×D1112yes—
843C23#6703712yes—
844C23#41×D1112yes—
845C23#6704212yes—
846C23C22×C22⋊D1111yescharacteristic
847C23C22×C22⋊D1111yescharacteristic
848C23C22×C22⋊D1111yescharacteristic
849D4—232no—
850D4—4416no—
851D4—4432no—
852D4—4432no—
853C2×C4—22no—
854C2×C4—22no—
855C2×C4—22no—
856C2×C4—22no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—24no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—22no—
864C2×C4—22no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—24no—
868C2×C4—24no—
869C2×C4—22no—
870C2×C4—22no—
871C2×C4—416no—
872C2×C4—416no—
873C2×C4—41no—
874C2×C4—42no—
875C2×C4—41no—
876C2×C4—41no—
877C2×C4—41no—
878C2×C4—42no—
879C2×C4—224no—
880C2×C4—224no—
881C2×C4—224no—
882C2×C4—224no—
883C2×C4—224no—
884C2×C4—224no—
885C2×C4—442no—
886C2×C4—442no—
887C2×C4—442no—
888C2×C4—442no—
889C2×C4—442no—
890C2×C4—442no—
891C2×C4—442no—
892C2×C4—442no—
893C2×C4—442no—
894C2×C4—442no—
895C2×C4—442no—
896C2×C4—442no—
897C2×C4—442no—
898C2×C4—442no—
899C2×C4—442no—
900C2×C4#6698314yescomplemented
901C2×C4#6699014yes—
902C2×C4#6700614yes—
903C22—28no—
904C22—24no—
905C22—24no—
906C22—24no—
907C22—24no—
908C22—44no—
909C22—42no—
910C22—42no—
911C22—42no—
912C22—42no—
913C22—44no—
914C22—44no—
915C22—42no—
916C22—42no—
917C22—42no—
918C22—44no—
919C22—44no—
920C22—42no—
921C22—42no—
922C22—42no—
923C22—44no—
924C22—44no—
925C22—444no—
926C22—444no—
927C22—444no—
928C22—444no—
929C22—444no—
930C22—444no—
931C22—444no—
932C22—882no—
933C22—882no—
934C22—882no—
935C22—882no—
936C22—882no—
937C22—882no—
938C22—882no—
939C22—882no—
940C22#1062307112yes—
941C22#1062307812yes—
942C22#1062307912yes—
943C22D4×D4412yes—
944C22#1062308112yes—
945C22#1062308512yes—
946C22#1062309112yes—
947C22#1062309312yes—
948C22C2×#6698311yescharacteristic
949C22C2×#6698311yescharacteristic
950C22C2×#6698311yescharacteristic
951C22#1062332211yescharacteristic
952C22#1062332211yescharacteristic
953C22#1062332211yescharacteristic
954C22C2×#6699011yescharacteristic
955C22D4×C22⋊D1112yes—
956C22D4×C22⋊D1112yes—
957C22#1062333511yescharacteristic
958C22#1062336012yes—
959C22#1062336111yescharacteristic
960C22#1062336311yescharacteristic
961C22#1062336512yes—
962C22C2×#6700611yescharacteristic
963C4—24no—
964C4—24no—
965C4—24no—
966C4—42no—
967C4—42no—
968C4—444no—
969C4—444no—
970C4—882no—
971C2—44no—
972C2—44no—
973C2—884no—
974C2#1307183111yescharacteristic
975C2#1307192611yescharacteristic
976C2#1307197211yescharacteristic
977C2#1307214612yes—
978C2#1307219812yes—
979C2#1307223111yescharacteristic
980C2#1307250212yes—
981C2#1307261612yes—
982C2#1307357211yescharacteristic
983C2#1307450011yescharacteristic
984C2#1307689811yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutator, socle, cosocleC24×C11C24
FittingC22×C4×D4×C11C2
hypercenterC22×C4×D4D11
hypocenterC11#14722
LCSG ▷ C24×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66983C2semidirect
2. C2×#10622604C2semidirect
3. C2×#10622573C2semidirect
4. C2×#10622836C2semidirect
5. C2×#10622826C2semidirect
6. #13066869C2semidirect
7. #13066861C2semidirect
8. #13066855C2semidirect
9. #13066854C2semidirect
10. #13066839C2semidirect
11. C22×C4×D4×C11C2semidirect
53. C22×D4×C11D4semidirect
63. C23×C4×C11D4semidirect
94. C2×C11×C4⋊C4D4semidirect
100. C2×C11×C22⋊C4D4semidirect
122. C2×(C2×D11)⋊C4D4semidirect
266. C22×C4×D4D11semidirect
321. C23×C11#121semidirect
397. C2×C4×C11#121semidirect
550. C22×D4D44semidirect
563. C23×C4C22⋊D11semidirect
575. C2×C4⋊C4C22⋊D11semidirect
599. C2×C22⋊C4C22⋊D11semidirect
756. C11#14722semidirect
837. C23#66983semidirect
900. C2×C4#66983semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C2×#106226042
C2×#106225732
C2×#106228362
C2×#106228262
#130668692
#130668612
#130668552
#130668542
#130668392
C22×C4×D4×C112
#1472211