Finite Group Databasebeta

← #14676574

Subgroups — #14676574

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×#66983C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3C2×#10622601C211yesmaximal, characteristic, complemented
4C2×#10622569C212yesmaximal, complemented
5C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
6#13066864C212yesmaximal, complemented
7#13066855C212yesmaximal, complemented
8#13066845C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C2×C11×#380C211yesmaximal, characteristic, complemented
12C24×C4×C11C2211yescharacteristic
13C23×C22⋊D11C2212yes—
14C23×D44C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C11×C22⋊C4C2212yes—
19C22×C22⋊Dic11C2211yescharacteristic
20C22×C22⋊Dic11C2211yescharacteristic
21C2×#66983—24no—
22C2×#66983—24no—
23C2×#66983C418yescomplemented
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2212yes—
26C22×(C2×D11)⋊C4C2212yes—
27C22×(C2×D11)⋊C4C2212yes—
28C22×C4⋊Dic11C2211yescharacteristic
29C22×C4×Dic11C2211yescharacteristic
30C22×C4×Dic11C2211yescharacteristic
31C2×#66946—24no—
32C2×#66946—24no—
33C2×#66946—24no—
34C11×#380—24no—
35C2×C11×#95C2212yes—
36C4×C22⋊Dic11—24no—
37C2×C11⋊#95C2211yescharacteristic
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2212yes—
40C2×C11⋊#95C2211yescharacteristic
41C2×C11⋊#95C2212yes—
42C2×C11⋊#95C2212yes—
43#10622601—24no—
44#10622569—28no—
45C25×C11C2311yescharacteristic
46C24×D11C2312yes—
47C23×C4×C11—22no—
48C23×C4×C11—22no—
49C23×C4×C11—22no—
50C23×C4×C11—22no—
51C23×C4×C11—22no—
52C23×C4×C11—22no—
53C23×C4×C11C2×C414yescomplemented
54C23×C4×C11C2312yes—
55C23×C4×C11C2311yescharacteristic
56C23×C4×C11C2312yes—
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×Dic11C2312yes—
66C23×Dic11C2311yescharacteristic
67C23×Dic11C2311yescharacteristic
68C23×Dic11C2311yescharacteristic
69C23×Dic11C2311yescharacteristic
70C22×D44—22no—
71C22×D44—22no—
72C22×D44—22no—
73C22×D44—22no—
74C22×D44C2×C414yes—
75C22×D44D414yes—
76C22×D44D414yes—
77C22×C4×D11—24no—
78C22×C4×D11—24no—
79C22×C4×D11—24no—
80C22×C4×D11—24no—
81C22×C4×D11—24no—
82C22×C4×D11—42no—
83C22×C4×D11—42no—
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4—22no—
89C2×C11×C4⋊C4D414yescomplemented
90C2×C11×C22⋊C4—24no—
91C2×C11×C22⋊C4—24no—
92C2×C11×C22⋊C4—42no—
93C2×C22⋊Dic11—22no—
94C2×C22⋊Dic11—22no—
95C2×C22⋊Dic11—22no—
96C2×C22⋊Dic11—22no—
97C2×C22⋊Dic11—22no—
98C2×C22⋊Dic11D414yescomplemented
99#66983—232no—
100C2×(C2×D11)⋊C4—24no—
101C2×(C2×D11)⋊C4—24no—
102C2×(C2×D11)⋊C4—24no—
103C2×(C2×D11)⋊C4—24no—
104C2×(C2×D11)⋊C4—24no—
105C2×(C2×D11)⋊C4—24no—
106C2×(C2×D11)⋊C4—24no—
107C2×(C2×D11)⋊C4—24no—
108C2×(C2×D11)⋊C4—24no—
109C2×(C2×D11)⋊C4—42no—
110C2×(C2×D11)⋊C4—42no—
111C2×(C2×D11)⋊C4C2×C418yescomplemented
112C2×C4⋊Dic11—22no—
113C2×C4⋊Dic11—22no—
114C2×C4⋊Dic11C2×C414yescomplemented
115C2×C4×Dic11—22no—
116C2×C4×Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11—22no—
120C2×C4×Dic11D414yescomplemented
121#66946—232no—
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—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—21no—
142C24×C11C22×C412yes—
143C24×C11C2×D412yes—
144C24×C11#4112yes—
145C24×C11C2411yescharacteristic
146C23×D11—22no—
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—22no—
152C23×D11—22no—
153C23×D11—22no—
154C23×D11—22no—
155C23×D11—22no—
156C23×D11—22no—
157C23×D11—22no—
158C23×D11C22×C414yes—
159C23×D11C2×D414yes—
160C23×D11C2×D414yes—
161C22×C4×C11—21no—
162C22×C4×C11—22no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—22no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—22no—
172C22×C4×C11—22no—
173C22×C4×C11—28no—
174C22×C4×C11—28no—
175C22×C4×C11—28no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—22no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—22no—
182C22×C4×C11—22no—
183C22×C4×C11—44no—
184C22×C4×C11—44no—
185C22×C4×C11—44no—
186C22×C4×C11—44no—
187C22×C4×C11C22×C412yes—
188C22×C4×C11C22×C412yes—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2×D412yes—
191C22×C4×C11C2×D412yes—
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D412yes—
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—21no—
204C22×Dic11—21no—
205C22×Dic11—22no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—21no—
212C22×Dic11—22no—
213C22×Dic11—22no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—21no—
217C22×Dic11—21no—
218C22×Dic11—21no—
219C22×Dic11—21no—
220C22×Dic11—22no—
221C22×Dic11—21no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—21no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C22×C414yes—
232C22×Dic11C2×D412yes—
233C22×Dic11C2×D412yes—
234C22×Dic11C2×D412yes—
235C22×Dic11C2×D412yes—
236C22×Dic11#4112yes—
237C22×Dic11#4112yes—
238C2×D44—28no—
239C2×D44—28no—
240C2×D44—28no—
241C2×D44—28no—
242C2×D44—28no—
243C2×D44—28no—
244C2×D44C22⋊C4116yescomplemented
245C2×C4×D11—216no—
246C2×C4×D11—48no—
247C2×C4×D11—48no—
248C2×C4×D11—48no—
249C2×C4×D11—48no—
250C2×C4×D11—48no—
251C2×C4×D11—48no—
252C11×C4⋊C4—28no—
253C11×C4⋊C4—44no—
254C11×C22⋊C4—48no—
255C22⋊Dic11—28no—
256C22⋊Dic11—28no—
257(C2×D11)⋊C4—216no—
258(C2×D11)⋊C4—216no—
259(C2×D11)⋊C4—48no—
260(C2×D11)⋊C4—48no—
261C4⋊Dic11—28no—
262C4×Dic11—28no—
263C4×Dic11—44no—
264C22×#121—111no—
265C22×C4×D4—111no—
266C2×#390—111no—
267C2×#386—112no—
268C2×#380D1111yescharacteristic, complemented
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—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—22no—
289C23×C11—22no—
290C23×C11—22no—
291C23×C11—22no—
292C23×C11—22no—
293C23×C11—41no—
294C23×C11—41no—
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×C11C4×D414yescomplemented
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—24no—
326C22×D11—24no—
327C22×D11—24no—
328C22×D11—24no—
329C22×D11—24no—
330C22×D11—24no—
331C22×D11—24no—
332C22×D11—24no—
333C22×D11—24no—
334C22×D11—24no—
335C22×D11—24no—
336C22×D11—24no—
337C22×D11—24no—
338C22×D11—24no—
339C22×D11—24no—
340C22×D11—24no—
341C22×D11—24no—
342C22×D11—24no—
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×D11C2×C22⋊C418yes—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—24no—
364C2×C4×C11—24no—
365C2×C4×C11—24no—
366C2×C4×C11—41no—
367C2×C4×C11—42no—
368C2×C4×C11—41no—
369C2×C4×C11—41no—
370C2×C4×C11—41no—
371C2×C4×C11—42no—
372C2×C4×C11—42no—
373C2×C4×C11—42no—
374C2×C4×C11—416no—
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—24no—
398C2×Dic11—24no—
399C2×Dic11—22no—
400C2×Dic11—22no—
401C2×Dic11—22no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—42no—
413C2×Dic11—42no—
414C2×Dic11—41no—
415C2×Dic11—41no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11—41no—
419C2×Dic11—41no—
420C2×Dic11—41no—
421C2×Dic11—41no—
422C2×Dic11—41no—
423C2×Dic11—41no—
424C2×Dic11#12114yescomplemented
425D44—232no—
426C4×D11—432no—
427C23×D4—112no—
428C23×D4—111no—
429C24×C4—112no—
430C24×C4C2×D1111yescharacteristic
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⋊C4C2×D1111yescharacteristic
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—24no—
452C4×C22⋊C4—224no—
453C2×#95—111no—
454C2×#95—112no—
455C2×#95—112no—
456C2×#95—111no—
457C2×#95—112no—
458C2×#95—112no—
459C2×#95C2×D1112yes—
460C22×C11—24no—
461C22×C11—24no—
462C22×C11—24no—
463C22×C11—42no—
464C22×C11—42no—
465C22×C11—42no—
466C22×C11—42no—
467C22×C11—42no—
468C22×C11—42no—
469C22×C11—42no—
470C22×C11—42no—
471C22×C11—42no—
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
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—28no—
511C2×D11—28no—
512C2×D11—28no—
513C2×D11—44no—
514C2×D11—44no—
515C2×D11—44no—
516C2×D11—44no—
517C2×D11—44no—
518C2×D11—44no—
519C2×D11—44no—
520C2×D11—44no—
521C2×D11—44no—
522C2×D11—44no—
523C2×D11—44no—
524C2×D11—44no—
525C4×C11—44no—
526C4×C11—42no—
527C4×C11—82no—
528C4×C11#38618yescomplemented
529Dic11—24no—
530Dic11—44no—
531Dic11—42no—
532Dic11—42no—
533Dic11—42no—
534C25—112no—
535C25C22×D1111yescharacteristic
536C22×D4—118no—
537C22×D4—114no—
538C22×D4—114no—
539C22×D4—114no—
540C22×D4—224no—
541C22×D4—224no—
542C22×D4—224no—
543C22×D4—224no—
544C22×D4—222no—
545C22×D4—222no—
546C22×D4—222no—
547C22×D4—222no—
548C22×D4—442no—
549C22×D4—442no—
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—224no—
562C23×C4—224no—
563C23×C4—224no—
564C23×C4—224no—
565C23×C4—224no—
566C23×C4—442no—
567C23×C4—442no—
568C23×C4C4×D1114yescomplemented
569C23×C4C22×D1112yes—
570C23×C4C22×D1111yescharacteristic
571C23×C4C22×D1112yes—
572C23×C4C22×D1111yescharacteristic
573#121—2232no—
574C4×D4—2232no—
575C2×C4⋊C4—22no—
576C2×C4⋊C4—22no—
577C2×C4⋊C4—22no—
578C2×C4⋊C4—22no—
579C2×C4⋊C4—22no—
580C2×C4⋊C4—114no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4—222no—
583C2×C4⋊C4C22⋊D1114yescomplemented
584C2×C22⋊C4—24no—
585C2×C22⋊C4—24no—
586C2×C22⋊C4—42no—
587C2×C22⋊C4—114no—
588C2×C22⋊C4—118no—
589C2×C22⋊C4—224no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—222no—
595C2×C22⋊C4—222no—
596C2×C22⋊C4—222no—
597C2×C22⋊C4—222no—
598C2×C22⋊C4—224no—
599C2×C22⋊C4—224no—
600C2×C22⋊C4—224no—
601C2×C22⋊C4—224no—
602C2×C22⋊C4—224no—
603C2×C22⋊C4—442no—
604C2×C22⋊C4—442no—
605C2×C42—114no—
606C2×C42—222no—
607C2×C42—222no—
608C2×C42—222no—
609C2×C42—222no—
610C2×C42—222no—
611#95—24no—
612#95—222no—
613#95—222no—
614#95—224no—
615#95—224no—
616#95—442no—
617#95—442no—
618C2×C11—44no—
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—48no—
635C24—21no—
636C24—21no—
637C24—21no—
638C24—21no—
639C24—21no—
640C24—21no—
641C24—21no—
642C24—21no—
643C24—21no—
644C24—21no—
645C24—21no—
646C24—21no—
647C24—114no—
648C24—114no—
649C24—114no—
650C24—222no—
651C24—222no—
652C24—222no—
653C24—222no—
654C24—222no—
655C24—222no—
656C24—222no—
657C24—222no—
658C24—222no—
659C24—222no—
660C24—222no—
661C24—222no—
662C24C2×C4×D1112yes—
663C24D4×D1112yes—
664C24#434312yes—
665C24C23×D1111yescharacteristic
666C2×D4—1116no—
667C2×D4—2216no—
668C2×D4—2216no—
669C2×D4—228no—
670C2×D4—228no—
671C2×D4—228no—
672C2×D4—228no—
673C2×D4—228no—
674C2×D4—228no—
675C2×D4—448no—
676C2×D4—448no—
677C2×D4—448no—
678C2×D4—448no—
679C2×D4—448no—
680C22×C4—21no—
681C22×C4—21no—
682C22×C4—22no—
683C22×C4—21no—
684C22×C4—21no—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—21no—
692C22×C4—28no—
693C22×C4—28no—
694C22×C4—28no—
695C22×C4—22no—
696C22×C4—22no—
697C22×C4—22no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—22no—
702C22×C4—44no—
703C22×C4—44no—
704C22×C4—44no—
705C22×C4—44no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—114no—
710C22×C4—112no—
711C22×C4—112no—
712C22×C4—112no—
713C22×C4—2216no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—222no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—222no—
727C22×C4—222no—
728C22×C4—221no—
729C22×C4—221no—
730C22×C4—221no—
731C22×C4—222no—
732C22×C4—221no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—221no—
736C22×C4—221no—
737C22×C4—221no—
738C22×C4—222no—
739C22×C4—222no—
740C22×C4—221no—
741C22×C4—221no—
742C22×C4—448no—
743C22×C4—448no—
744C22×C4—448no—
745C22×C4—448no—
746C22×C4—448no—
747C22×C4—448no—
748C22×C4C2×C4×D1112yes—
749C22×C4C2×C4×D1112yes—
750C22×C4#433912yes—
751C22×C4D4×D1112yes—
752C22×C4D4×D1112yes—
753C22×C4D4×D1112yes—
754C22×C4#434112yes—
755C22×C4C2×C22⋊D1114yes—
756C22×C4C2×C22⋊D1112yes—
757C4⋊C4—28no—
758C4⋊C4—44no—
759C4⋊C4—228no—
760C22⋊C4—48no—
761C22⋊C4—2216no—
762C22⋊C4—2216no—
763C22⋊C4—228no—
764C22⋊C4—228no—
765C22⋊C4—448no—
766C22⋊C4—448no—
767C42—228no—
768C42—444no—
769C11#1397011yescharacteristic, complemented, Sylow
770C23—22no—
771C23—22no—
772C23—22no—
773C23—22no—
774C23—22no—
775C23—22no—
776C23—22no—
777C23—22no—
778C23—22no—
779C23—22no—
780C23—22no—
781C23—22no—
782C23—22no—
783C23—22no—
784C23—22no—
785C23—22no—
786C23—22no—
787C23—22no—
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—41no—
801C23—41no—
802C23—41no—
803C23—41no—
804C23—118no—
805C23—224no—
806C23—224no—
807C23—224no—
808C23—224no—
809C23—224no—
810C23—224no—
811C23—224no—
812C23—224no—
813C23—224no—
814C23—224no—
815C23—224no—
816C23—224no—
817C23—224no—
818C23—224no—
819C23—224no—
820C23—224no—
821C23—224no—
822C23—224no—
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—442no—
837C23—442no—
838C23—442no—
839C23#6694614yescomplemented
840C23C22×C4×D1111yescharacteristic
841C23C2×#433911yescharacteristic
842C23C2×D4×D1111yescharacteristic
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×D4×D1111yescharacteristic
846C23C2×#434111yescharacteristic
847C23#6703711yescharacteristic
848C23C2×#434311yescharacteristic
849C23#6704011yescharacteristic
850C23#41×D1111yescharacteristic
851C23#41×D1111yescharacteristic
852C23#6704211yescharacteristic
853C23#6704211yescharacteristic
854C23C22×C22⋊D1111yescharacteristic
855D4—2232no—
856D4—4432no—
857C2×C4—22no—
858C2×C4—22no—
859C2×C4—22no—
860C2×C4—24no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—41no—
864C2×C4—41no—
865C2×C4—41no—
866C2×C4—41no—
867C2×C4—42no—
868C2×C4—42no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—416no—
872C2×C4—42no—
873C2×C4—42no—
874C2×C4—42no—
875C2×C4—42no—
876C2×C4—42no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—114no—
880C2×C4—222no—
881C2×C4—222no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—222no—
885C2×C4—222no—
886C2×C4—224no—
887C2×C4—224no—
888C2×C4—222no—
889C2×C4—224no—
890C2×C4—222no—
891C2×C4—222no—
892C2×C4—222no—
893C2×C4—222no—
894C2×C4—222no—
895C2×C4—222no—
896C2×C4—222no—
897C2×C4—222no—
898C2×C4—4432no—
899C2×C4—441no—
900C2×C4—441no—
901C2×C4—441no—
902C2×C4—441no—
903C2×C4—441no—
904C2×C4—441no—
905C2×C4—441no—
906C2×C4—442no—
907C2×C4—442no—
908C2×C4—441no—
909C2×C4—442no—
910C2×C4—442no—
911C2×C4—441no—
912C2×C4—441no—
913C2×C4—441no—
914C2×C4—441no—
915C2×C4C22⋊C4×D1114yes—
916C2×C4(C22⋊D11)⋊C414yes—
917C2×C4#6693614yes—
918C2×C4#6693714yes—
919C2×C4C4×C22⋊D1114yes—
920C2×C4#6699014yes—
921C2×C4#6699114yes—
922C22—24no—
923C22—24no—
924C22—24no—
925C22—42no—
926C22—42no—
927C22—42no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—42no—
935C22—42no—
936C22—42no—
937C22—228no—
938C22—228no—
939C22—228no—
940C22—444no—
941C22—444no—
942C22—444no—
943C22—444no—
944C22—444no—
945C22—444no—
946C22—444no—
947C22—444no—
948C22—444no—
949C22—444no—
950C22—444no—
951C22—444no—
952C22C2×C22⋊C4×D1111yescharacteristic
953C22C2×(C22⋊D11)⋊C411yescharacteristic
954C22C2×#6693611yescharacteristic
955C22C2×#6693711yescharacteristic
956C22C2×#6694611yescharacteristic
957C22#1062303511yescharacteristic
958C22#1062303811yescharacteristic
959C22#1062304511yescharacteristic
960C22#1062305211yescharacteristic
961C22#1062305311yescharacteristic
962C22#1062306111yescharacteristic
963C22#1062306311yescharacteristic
964C22#1062312711yescharacteristic
965C22D11×#12111yescharacteristic
966C22#1062313811yescharacteristic
967C22#1062314011yescharacteristic
968C22#1062314011yescharacteristic
969C22#1062314311yescharacteristic
970C22#1062314311yescharacteristic
971C22#1062315011yescharacteristic
972C22#1062315511yescharacteristic
973C22#1062315811yescharacteristic
974C22#1062316011yescharacteristic
975C22#1062316111yescharacteristic
976C22#1062316111yescharacteristic
977C22#1062316211yescharacteristic
978C22#1062316211yescharacteristic
979C22#1062317411yescharacteristic
980C22C2×C4×C22⋊D1111yescharacteristic
981C22C2×#6699011yescharacteristic
982C22C2×#6699111yescharacteristic
983C22D4×C22⋊D1111yescharacteristic
984C22#1062334811yescharacteristic
985C22#1062336011yescharacteristic
986C22#1062336511yescharacteristic
987C4—44no—
988C4—42no—
989C4—82no—
990C4—224no—
991C4—444no—
992C4—442no—
993C4—442no—
994C4—442no—
995C4#1062256918yescomplemented
996C2—44no—
997C2—448no—
998C2C2×#1062256911yescharacteristic
999C2#1307112211yescharacteristic
1000C2#1307130511yescharacteristic
1001C2#1307143611yescharacteristic
1002C2#1307144411yescharacteristic
1003C2#1307163211yescharacteristic
1004C2#1307165411yescharacteristic
1005C2#1307196311yescharacteristic
1006C2#1307196811yescharacteristic
1007C2#1307211011yescharacteristic
1008C2#1307213211yescharacteristic
1009C2#1307218911yescharacteristic
1010C2#1307220011yescharacteristic
1011C2#1307351911yescharacteristic
1012C2#1307353111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C11×#380C2
socle, cosocleC24×C11C24
prime radicalC22×#66983C2
hypercenterC2×#380D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×#380

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. C2×#10622601C2semidirect
4. C2×#10622569C2semidirect
5. C2×C4×C22⋊Dic11C2semidirect
6. #13066864C2semidirect
7. #13066855C2semidirect
8. #13066845C2semidirect
9. #13066845C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C2×C11×#380C2semidirect
23. C2×#66983C4semidirect
53. C23×C4×C11C2×C4semidirect
64. C22×C22⋊D11C2×C4semidirect
89. C2×C11×C4⋊C4D4semidirect
98. C2×C22⋊Dic11D4semidirect
111. C2×(C2×D11)⋊C4C2×C4semidirect
114. C2×C4⋊Dic11C2×C4semidirect
120. C2×C4×Dic11D4semidirect
244. C2×D44C22⋊C4semidirect
268. C2×#380D11semidirect
309. C23×C11C4×D4semidirect
424. C2×Dic11#121semidirect
528. C4×C11#386semidirect
568. C23×C4C4×D11semidirect
583. C2×C4⋊C4C22⋊D11semidirect
769. C11#13970semidirect
839. C23#66946semidirect
995. C4#10622569semidirect

Maximal subgroups

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

subgroupindex
C22×#669832
C22×#669462
C2×#106226012
C2×#106225692
C2×C4×C22⋊Dic112
#130668642
#130668552
#130668452
(C2×D11)⋊#952
C2×C11×#3802
#1397011