Finite Group Databasebeta

← #14676576

Subgroups — #14676576

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×#66948C211yesmaximal, characteristic
2C22×#66946C211yesmaximal, characteristic, complemented
3C2×#10622552C211yesmaximal, characteristic, complemented
4C2×#10622278C212yesmaximal, complemented
5C2×#10622600C211yesmaximal, characteristic, complemented
6C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
7#13066864C212yesmaximal, complemented
8#13066856C212yesmaximal, complemented
9#13066845C211yesmaximal, characteristic, complemented
10(C2×D11)⋊#95C212yesmaximal, complemented
11C11×C4⋊#95C211yesmaximal, characteristic, complemented
12C23×D44C2212yes—
13C23×D44C2211yescharacteristic
14C23×C4×D11C2211yescharacteristic
15C23×C4×D11C2212yes—
16C22×C11×C4⋊C4C2211yescharacteristic
17C22×C11×C4⋊C4C2211yescharacteristic
18C22×C42×C11C2211yescharacteristic
19C22×(C2×D11)⋊C4C2211yescharacteristic
20C22×(C2×D11)⋊C4C2212yes—
21C22×(C2×D11)⋊C4C2212yes—
22C22×(C2×D11)⋊C4C2212yes—
23C22×(C2×D11)⋊C4C2212yes—
24C22×(C2×D11)⋊C4C2212yes—
25C22×(C2×D11)⋊C4C2211yescharacteristic
26C22×C4⋊Dic11C2211yescharacteristic
27C22×C4×Dic11C2211yescharacteristic
28C2×#66948—24no—
29C2×#66948—24no—
30C2×#66948C418yescomplemented
31C2×#66946—24no—
32C2×#66946—24no—
33C2×#66946—24no—
34C2×C11×#95C2212yes—
35C2×C11×#95C2212yes—
36C2×C11⋊#95C2211yescharacteristic
37C2×C11⋊#95C2212yes—
38C2×C11⋊#95C2212yes—
39C2×C11⋊#95C2211yescharacteristic
40C2×C11⋊#95C2212yes—
41#10622600—24no—
42#10622552—24no—
43C4×(C2×D11)⋊C4—24no—
44#10622278—28no—
45C24×D11C2312yes—
46C24×D11C2311yescharacteristic
47C23×C4×C11C2312yes—
48C23×C4×C11C2311yescharacteristic
49C23×C4×C11C2312yes—
50C23×C4×C11C2311yescharacteristic
51C23×C4×C11C2311yescharacteristic
52C23×Dic11C2312yes—
53C23×Dic11C2311yescharacteristic
54C23×Dic11C2311yescharacteristic
55C23×Dic11C2311yescharacteristic
56C22×D44—22no—
57C22×D44—22no—
58C22×D44—22no—
59C22×D44—22no—
60C22×D44—24no—
61C22×D44—24no—
62C22×D44—24no—
63C22×D44—24no—
64C22×D44—42no—
65C22×D44—42no—
66C22×D44C2×C414yes—
67C22×D44C2×C418yescomplemented
68C22×D44D414yes—
69C22×D44D414yes—
70C22×C4×D11—24no—
71C22×C4×D11—24no—
72C22×C4×D11—22no—
73C22×C4×D11—22no—
74C22×C4×D11—22no—
75C22×C4×D11—22no—
76C22×C4×D11—22no—
77C22×C4×D11—22no—
78C22×C4×D11—24no—
79C22×C4×D11—24no—
80C22×C4×D11—24no—
81C22×C4×D11—42no—
82C22×C4×D11—42no—
83C22×C4×D11C2×C414yescomplemented
84C2×C11×C4⋊C4—22no—
85C2×C11×C4⋊C4—22no—
86C2×C11×C4⋊C4—22no—
87C2×C11×C4⋊C4—22no—
88C2×C11×C4⋊C4C2×C414yescomplemented
89C2×C11×C4⋊C4D414yescomplemented
90C2×C42×C11—22no—
91C2×C42×C11—22no—
92C2×C42×C11—22no—
93C2×(C2×D11)⋊C4—24no—
94C2×(C2×D11)⋊C4—24no—
95C2×(C2×D11)⋊C4—24no—
96C2×(C2×D11)⋊C4—22no—
97C2×(C2×D11)⋊C4—24no—
98C2×(C2×D11)⋊C4—22no—
99C2×(C2×D11)⋊C4—24no—
100C2×(C2×D11)⋊C4—22no—
101C2×(C2×D11)⋊C4—22no—
102C2×(C2×D11)⋊C4—22no—
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)⋊C4—42no—
112C2×(C2×D11)⋊C4C2×C418yescomplemented
113C2×(C2×D11)⋊C4D414yescomplemented
114C2×C4⋊Dic11—22no—
115C2×C4⋊Dic11—22no—
116C2×C4⋊Dic11—22no—
117C2×C4×Dic11—22no—
118C2×C4×Dic11—22no—
119C2×C4×Dic11D414yescomplemented
120#66948—232no—
121#66946—232no—
122C11×#95—24no—
123C11×#95—42no—
124C11⋊#95—24no—
125C11⋊#95—24no—
126C11⋊#95—22no—
127C11⋊#95—22no—
128C11⋊#95—42no—
129#13970—111nomaximal, Sylow
130C24×C11C2411yescharacteristic
131C23×D11—21no—
132C23×D11—21no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—21no—
137C23×D11—21no—
138C23×D11—21no—
139C23×D11—21no—
140C23×D11—22no—
141C23×D11—21no—
142C23×D11—21no—
143C23×D11—22no—
144C23×D11—22no—
145C23×D11—22no—
146C23×D11—22no—
147C23×D11—21no—
148C23×D11—22no—
149C23×D11—22no—
150C23×D11—22no—
151C23×D11—21no—
152C23×D11—21no—
153C23×D11—22no—
154C23×D11—21no—
155C23×D11C22×C414yes—
156C23×D11C22×C412yes—
157C23×D11C2×D414yes—
158C23×D11C2×D414yes—
159C23×D11C2×D412yes—
160C23×D11#4112yes—
161C22×C4×C11—22no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—22no—
168C22×C4×C11—22no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—22no—
178C22×C4×C11—21no—
179C22×C4×C11—22no—
180C22×C4×C11—22no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11—22no—
184C22×C4×C11—21no—
185C22×C4×C11C22×C414yes—
186C22×C4×C11C22×C412yes—
187C22×C4×C11C2×D414yes—
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—
196C22×Dic11—21no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—22no—
205C22×Dic11—22no—
206C22×Dic11—22no—
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C22×Dic11—22no—
212C22×Dic11—22no—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—21no—
216C22×Dic11—22no—
217C22×Dic11—22no—
218C22×Dic11—21no—
219C22×Dic11C22×C412yes—
220C22×Dic11C2×D412yes—
221C22×Dic11C2×D412yes—
222C22×Dic11C2×D412yes—
223C22×Dic11#4112yes—
224C2×D44—216no—
225C2×D44—216no—
226C2×D44—28no—
227C2×D44—28no—
228C2×D44—28no—
229C2×D44—28no—
230C2×D44—28no—
231C2×D44—28no—
232C2×D44—48no—
233C2×D44—48no—
234C2×D44—48no—
235C2×D44—48no—
236C2×D44—48no—
237C2×D44C22⋊C4116yescomplemented
238C2×C4×D11—216no—
239C2×C4×D11—28no—
240C2×C4×D11—28no—
241C2×C4×D11—28no—
242C2×C4×D11—48no—
243C2×C4×D11—48no—
244C2×C4×D11—48no—
245C2×C4×D11—48no—
246C2×C4×D11—48no—
247C2×C4×D11—48no—
248C2×C4×D11—44no—
249C2×C4×D11—44no—
250C2×C4×D11—44no—
251C2×C4×D11—44no—
252C11×C4⋊C4—28no—
253C11×C4⋊C4—28no—
254C42×C11—44no—
255(C2×D11)⋊C4—216no—
256(C2×D11)⋊C4—28no—
257(C2×D11)⋊C4—28no—
258(C2×D11)⋊C4—216no—
259(C2×D11)⋊C4—48no—
260(C2×D11)⋊C4—48no—
261(C2×D11)⋊C4—48no—
262C4⋊Dic11—44no—
263C4×Dic11—28no—
264C22×#121—111no—
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⋊#95D1111yescharacteristic, complemented
274C22⋊#95—112no—
275C23×C11C23×C411yescharacteristic
276C23×C11C22×D411yescharacteristic
277C23×C11C22×D411yescharacteristic
278C23×C11C22×D411yescharacteristic
279C23×C11C22×D411yescharacteristic
280C23×C11C22×D411yescharacteristic
281C23×C11C2×#4111yescharacteristic
282C23×C11C2×#4111yescharacteristic
283C23×C11C2×#4111yescharacteristic
284C23×C11C2×#4111yescharacteristic
285C23×C11C2×#4111yescharacteristic
286C23×C11H(5,𝔽2)11yescharacteristic
287C23×C11H(5,𝔽2)11yescharacteristic
288C23×C11H(5,𝔽2)11yescharacteristic
289C23×C112−1+411yescharacteristic
290C22×D11—22no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—24no—
294C22×D11—24no—
295C22×D11—24no—
296C22×D11—24no—
297C22×D11—22no—
298C22×D11—22no—
299C22×D11—24no—
300C22×D11—24no—
301C22×D11—22no—
302C22×D11—24no—
303C22×D11—22no—
304C22×D11—24no—
305C22×D11—24no—
306C22×D11—24no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—22no—
311C22×D11—24no—
312C22×D11—24no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—24no—
316C22×D11—24no—
317C22×D11—22no—
318C22×D11—22no—
319C22×D11—24no—
320C22×D11—24no—
321C22×D11—24no—
322C22×D11—22no—
323C22×D11—24no—
324C22×D11—22no—
325C22×D11—22no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—41no—
329C22×D11—42no—
330C22×D11—41no—
331C22×D11—42no—
332C22×D11—42no—
333C22×D11—42no—
334C22×D11—42no—
335C22×D11—41no—
336C22×D11—41no—
337C22×D11—42no—
338C22×D11—41no—
339C22×D11—42no—
340C22×D11—41no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—42no—
349C22×D11—41no—
350C22×D11—42no—
351C22×D11—41no—
352C22×D11—42no—
353C22×D11—41no—
354C22×D11—42no—
355C22×D11—42no—
356C22×D11—41no—
357C22×D11—42no—
358C22×D11C2×C22⋊C418yes—
359C22×D11C4×D414yescomplemented
360C2×C4×C11—24no—
361C2×C4×C11—24no—
362C2×C4×C11—24no—
363C2×C4×C11—24no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—24no—
368C2×C4×C11—22no—
369C2×C4×C11—24no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—42no—
375C2×C4×C11—42no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—42no—
379C2×C4×C11—42no—
380C2×C4×C11—42no—
381C2×C4×C11—42no—
382C2×C4×C11—42no—
383C2×C4×C11—42no—
384C2×C4×C11—41no—
385C2×C4×C11—41no—
386C2×C4×C11—41no—
387C2×C4×C11—41no—
388C2×C4×C11C2×C22⋊C414yes—
389C2×C4×C11C4×D414yes—
390C2×C4×C11C4×D414yes—
391C2×C4×C11#12014yes—
392C2×C4×C11#12114yes—
393C2×C4×C11#12114yes—
394C2×C4×C11#12314yes—
395C2×Dic11—22no—
396C2×Dic11—22no—
397C2×Dic11—22no—
398C2×Dic11—22no—
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—41no—
408C2×Dic11—41no—
409C2×Dic11—41no—
410C2×Dic11—41no—
411C2×Dic11—41no—
412C2×Dic11—41no—
413C2×Dic11—41no—
414C2×Dic11—41no—
415C2×Dic11—42no—
416C2×Dic11—42no—
417C2×Dic11—42no—
418C2×Dic11—42no—
419C2×Dic11—42no—
420C2×Dic11—42no—
421C2×Dic11—42no—
422C2×Dic11#12114yescomplemented
423D44—232no—
424D44—432no—
425C4×D11—432no—
426C4×D11—416no—
427C23×D4—111no—
428C23×D4—112no—
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⋊C4C2×D1111yescharacteristic
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⋊C4—112no—
446C22×C22⋊C4—112no—
447C22×C42—111no—
448C22×C42C2×D1111yescharacteristic
449#390—224no—
450#386—228no—
451#380—224no—
452C4×C22⋊C4—224no—
453C2×#95—111no—
454C2×#95—112no—
455C2×#95—112no—
456C2×#95—111no—
457C2×#95—112no—
458C2×#95C2×D1112yes—
459C2×#95C2×D1112yes—
460C22×C11C22×C22⋊C411yescharacteristic
461C22×C11C2×C4×D411yescharacteristic
462C22×C11C2×C4×D411yescharacteristic
463C22×C11C2×C4×D411yescharacteristic
464C22×C11C4×#4111yescharacteristic
465C22×C11#51811yescharacteristic
466C22×C11#52011yescharacteristic
467C22×C11C2×#12011yescharacteristic
468C22×C11C2×#12111yescharacteristic
469C22×C11C2×#12111yescharacteristic
470C22×C11C2×#12111yescharacteristic
471C22×C11C2×#12311yescharacteristic
472C22×C11#52511yescharacteristic
473C22×C11#52911yescharacteristic
474C22×C11#53211yescharacteristic
475C22×C11#53511yescharacteristic
476C22×C11#53711yescharacteristic
477C22×C11#54011yescharacteristic
478C22×C11#54211yescharacteristic
479C22×C11D4211yescharacteristic
480C22×C11D4211yescharacteristic
481C22×C11D4211yescharacteristic
482C22×C11#54611yescharacteristic
483C22×C11#54611yescharacteristic
484C22×C11#54611yescharacteristic
485C22×C11#54611yescharacteristic
486C22×C11#54611yescharacteristic
487C22×C11#54711yescharacteristic
488C22×C11#54711yescharacteristic
489C22×C11#54711yescharacteristic
490C22×C11#54811yescharacteristic
491C22×C11#55011yescharacteristic
492C22×C11#55311yescharacteristic
493C22×C11#55311yescharacteristic
494C22×C11#55511yescharacteristic
495C2×D11—28no—
496C2×D11—24no—
497C2×D11—28no—
498C2×D11—24no—
499C2×D11—28no—
500C2×D11—24no—
501C2×D11—42no—
502C2×D11—44no—
503C2×D11—42no—
504C2×D11—44no—
505C2×D11—42no—
506C2×D11—44no—
507C2×D11—44no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—44no—
511C2×D11—44no—
512C2×D11—42no—
513C2×D11—44no—
514C2×D11—42no—
515C2×D11—44no—
516C2×D11—42no—
517C2×D11—44no—
518C2×D11—42no—
519C2×D11—44no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—44no—
523C2×D11—42no—
524C2×D11—44no—
525C4×C11—44no—
526C4×C11—44no—
527C4×C11—42no—
528C4×C11—42no—
529C4×C11#38618yescomplemented
530Dic11—24no—
531Dic11—42no—
532Dic11—42no—
533Dic11—82no—
534C25—112no—
535C25—111no—
536C22×D4—114no—
537C22×D4—118no—
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—111no—
551C23×C4—111no—
552C23×C4—111no—
553C23×C4—114no—
554C23×C4—112no—
555C23×C4—224no—
556C23×C4—224no—
557C23×C4—224no—
558C23×C4—224no—
559C23×C4—224no—
560C23×C4—222no—
561C23×C4—222no—
562C23×C4—222no—
563C23×C4—222no—
564C23×C4—222no—
565C23×C4—222no—
566C23×C4—442no—
567C23×C4—442no—
568C23×C4C22×D1112yes—
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—22no—
579C2×C4⋊C4—222no—
580C2×C4⋊C4—222no—
581C2×C4⋊C4—222no—
582C2×C4⋊C4C4×D1114yescomplemented
583C2×C4⋊C4D4414yescomplemented
584C2×C22⋊C4—118no—
585C2×C22⋊C4—114no—
586C2×C22⋊C4—224no—
587C2×C22⋊C4—222no—
588C2×C22⋊C4—222no—
589C2×C22⋊C4—222no—
590C2×C22⋊C4—224no—
591C2×C22⋊C4—224no—
592C2×C22⋊C4—224no—
593C2×C22⋊C4—222no—
594C2×C22⋊C4—224no—
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—224no—
602C2×C22⋊C4—442no—
603C2×C22⋊C4—442no—
604C2×C22⋊C4—442no—
605C2×C42—22no—
606C2×C42—22no—
607C2×C42—22no—
608C2×C42—114no—
609C2×C42—222no—
610C2×C42—222no—
611#95—24no—
612#95—42no—
613#95—222no—
614#95—222no—
615#95—224no—
616#95—224no—
617#95—442no—
618C2×C11C2×#38611yescharacteristic
619C2×C11C4×#12111yescharacteristic
620C2×C11#232411yescharacteristic
621C2×C11D4×C22⋊C411yescharacteristic
622C2×C11#233911yescharacteristic
623C2×C11#236111yescharacteristic
624C2×C11#236311yescharacteristic
625C2×C11#240711yescharacteristic
626C2×C11#240811yescharacteristic
627C2×C11#242011yescharacteristic
628C2×C11#242211yescharacteristic
629C2×C11#242711yescharacteristic
630C2×C11#242811yescharacteristic
631C2×C11#253511yescharacteristic
632C2×C11#253711yescharacteristic
633D11—48no—
634D11—44no—
635C24—114no—
636C24—112no—
637C24—112no—
638C24—114no—
639C24—114no—
640C24—112no—
641C24—221no—
642C24—222no—
643C24—221no—
644C24—222no—
645C24—221no—
646C24—222no—
647C24—222no—
648C24—221no—
649C24—221no—
650C24—222no—
651C24—221no—
652C24—221no—
653C24—222no—
654C24—221no—
655C24—222no—
656C24—222no—
657C24—221no—
658C24—221no—
659C24—222no—
660C24—222no—
661C24—221no—
662C24—222no—
663C24—222no—
664C24—221no—
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—22no—
684C22×C4—21no—
685C22×C4—21no—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—22no—
689C22×C4—22no—
690C22×C4—22no—
691C22×C4—22no—
692C22×C4—21no—
693C22×C4—22no—
694C22×C4—22no—
695C22×C4—21no—
696C22×C4—21no—
697C22×C4—21no—
698C22×C4—22no—
699C22×C4—22no—
700C22×C4—22no—
701C22×C4—21no—
702C22×C4—21no—
703C22×C4—22no—
704C22×C4—112no—
705C22×C4—112no—
706C22×C4—112no—
707C22×C4—112no—
708C22×C4—112no—
709C22×C4—2216no—
710C22×C4—221no—
711C22×C4—221no—
712C22×C4—221no—
713C22×C4—221no—
714C22×C4—221no—
715C22×C4—221no—
716C22×C4—221no—
717C22×C4—221no—
718C22×C4—221no—
719C22×C4—221no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—228no—
727C22×C4—228no—
728C22×C4—228no—
729C22×C4—222no—
730C22×C4—222no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—222no—
734C22×C4—222no—
735C22×C4—222no—
736C22×C4—448no—
737C22×C4—448no—
738C22×C4—448no—
739C22×C4—448no—
740C22×C4—448no—
741C22×C4—448no—
742C22×C4—444no—
743C22×C4—444no—
744C22×C4—444no—
745C22×C4—444no—
746C22×C4C2×C4×D1114yes—
747C22×C4C2×C4×D1112yes—
748C22×C4C2×D4414yes—
749C22×C4C2×D4412yes—
750C22×C4#433912yes—
751C22×C4D4×D1112yes—
752C22×C4D4×D1112yes—
753C22×C4D4×D1112yes—
754C22×C4D4×D1112yes—
755C22×C4#434312yes—
756C22×C4#434312yes—
757C4⋊C4—28no—
758C4⋊C4—28no—
759C4⋊C4—444no—
760C22⋊C4—228no—
761C22⋊C4—2216no—
762C22⋊C4—2216no—
763C22⋊C4—228no—
764C22⋊C4—448no—
765C22⋊C4—448no—
766C22⋊C4—448no—
767C42—44no—
768C42—228no—
769C11#1397011yescharacteristic, complemented, Sylow
770C23—118no—
771C23—114no—
772C23—224no—
773C23—222no—
774C23—222no—
775C23—224no—
776C23—222no—
777C23—224no—
778C23—222no—
779C23—224no—
780C23—224no—
781C23—222no—
782C23—224no—
783C23—224no—
784C23—224no—
785C23—222no—
786C23—222no—
787C23—224no—
788C23—222no—
789C23—224no—
790C23—222no—
791C23—222no—
792C23—224no—
793C23—222no—
794C23—224no—
795C23—222no—
796C23—222no—
797C23—224no—
798C23—222no—
799C23—222no—
800C23—224no—
801C23—222no—
802C23—224no—
803C23—224no—
804C23—224no—
805C23—222no—
806C23—224no—
807C23—222no—
808C23—442no—
809C23—441no—
810C23—442no—
811C23—441no—
812C23—441no—
813C23—441no—
814C23—441no—
815C23—441no—
816C23—442no—
817C23—441no—
818C23—442no—
819C23—442no—
820C23—441no—
821C23—442no—
822C23—442no—
823C23—442no—
824C23—441no—
825C23—442no—
826C23—441no—
827C23—442no—
828C23—442no—
829C23—442no—
830C23—441no—
831C23—442no—
832C23—441no—
833C23—442no—
834C23—441no—
835C23—441no—
836C23—441no—
837C23—442no—
838C23—441no—
839C23—442no—
840C23C22×C4×D1111yescharacteristic
841C23C22×D4411yescharacteristic
842C23C2×#433911yescharacteristic
843C23C2×D4×D1111yescharacteristic
844C23C2×D4×D1111yescharacteristic
845C23C2×D4×D1111yescharacteristic
846C23C2×D4×D1111yescharacteristic
847C23#6703711yescharacteristic
848C23C2×#434311yescharacteristic
849C23C2×#434311yescharacteristic
850C23#6704011yescharacteristic
851C23#41×D1111yescharacteristic
852C23#41×D1111yescharacteristic
853C23#6704211yescharacteristic
854C23#6704211yescharacteristic
855D4—2232no—
856D4—4432no—
857C2×C4—24no—
858C2×C4—24no—
859C2×C4—22no—
860C2×C4—22no—
861C2×C4—24no—
862C2×C4—24no—
863C2×C4—24no—
864C2×C4—24no—
865C2×C4—22no—
866C2×C4—22no—
867C2×C4—22no—
868C2×C4—22no—
869C2×C4—42no—
870C2×C4—42no—
871C2×C4—41no—
872C2×C4—41no—
873C2×C4—41no—
874C2×C4—41no—
875C2×C4—42no—
876C2×C4—41no—
877C2×C4—42no—
878C2×C4—42no—
879C2×C4—41no—
880C2×C4—42no—
881C2×C4—41no—
882C2×C4—41no—
883C2×C4—42no—
884C2×C4—42no—
885C2×C4—114no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
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—441no—
907C2×C4—4416no—
908C2×C4—442no—
909C2×C4—442no—
910C2×C4—442no—
911C2×C4—442no—
912C2×C4—442no—
913C2×C4—442no—
914C2×C4—442no—
915C2×C4C4×D4414yes—
916C2×C4C22⋊C4×D1114yes—
917C2×C4#6693514yes—
918C2×C4#6693714yes—
919C2×C4#6694614yes—
920C2×C4#6694714yes—
921C2×C4#6694814yes—
922C22—224no—
923C22—224no—
924C22—224no—
925C22—228no—
926C22—228no—
927C22—228no—
928C22—444no—
929C22—442no—
930C22—444no—
931C22—444no—
932C22—442no—
933C22—444no—
934C22—444no—
935C22—442no—
936C22—442no—
937C22—444no—
938C22—442no—
939C22—444no—
940C22—442no—
941C22—444no—
942C22—442no—
943C22—444no—
944C22—442no—
945C22—444no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—444no—
950C22—444no—
951C22—442no—
952C22C2×C4×D4411yescharacteristic
953C22C2×C22⋊C4×D1111yescharacteristic
954C22C2×#6693511yescharacteristic
955C22C2×#6693711yescharacteristic
956C22C2×#6694611yescharacteristic
957C22C2×#6694711yescharacteristic
958C22C2×#6694811yescharacteristic
959C22#1062303811yescharacteristic
960C22#1062304511yescharacteristic
961C22#1062306111yescharacteristic
962C22#1062306311yescharacteristic
963C22C4×D4×D1111yescharacteristic
964C22#1062307611yescharacteristic
965C22D4×D4411yescharacteristic
966C22#1062308511yescharacteristic
967C22C4×#434311yescharacteristic
968C22#1062310511yescharacteristic
969C22#1062310711yescharacteristic
970C22#1062310811yescharacteristic
971C22D11×#12111yescharacteristic
972C22#1062313811yescharacteristic
973C22#1062314011yescharacteristic
974C22#1062314311yescharacteristic
975C22#1062315811yescharacteristic
976C22#1062316011yescharacteristic
977C22#1062316111yescharacteristic
978C22#1062316211yescharacteristic
979C22#1062320711yescharacteristic
980C22#1062320711yescharacteristic
981C22#1062322211yescharacteristic
982C22#1062322911yescharacteristic
983C22#1062324811yescharacteristic
984C22#1062325611yescharacteristic
985C22#1062325711yescharacteristic
986C22#1062326411yescharacteristic
987C4—44no—
988C4—44no—
989C4—42no—
990C4—42no—
991C4—224no—
992C4—442no—
993C4—442no—
994C4—882no—
995C4#1062227818yescomplemented
996C2—444no—
997C2—448no—
998C2C2×#1062227811yescharacteristic
999C2#1307112411yescharacteristic
1000C2#1307130711yescharacteristic
1001C2#1307143711yescharacteristic
1002C2#1307144511yescharacteristic
1003C2#1307163411yescharacteristic
1004C2#1307165611yescharacteristic
1005C2#1307196411yescharacteristic
1006C2#1307197011yescharacteristic
1007C2#1307211111yescharacteristic
1008C2#1307213311yescharacteristic
1009C2#1307219111yescharacteristic
1010C2#1307220211yescharacteristic
1011C2#1307351911yescharacteristic
1012C2#1307353111yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC11×C4⋊#95C2
socle, cosocleC24×C11C24
prime radicalC22×#66948C2
hypercenterC4⋊#95D11
hypocenterC11#13970
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C4⋊#95

Complements

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

NH ≅ G/Ntype
2. C22×#66946C2semidirect
3. C2×#10622552C2semidirect
4. C2×#10622278C2semidirect
5. C2×#10622600C2semidirect
6. C2×C4×(C2×D11)⋊C4C2semidirect
7. #13066864C2semidirect
8. #13066856C2semidirect
9. #13066845C2semidirect
10. (C2×D11)⋊#95C2semidirect
11. C11×C4⋊#95C2semidirect
30. C2×#66948C4semidirect
67. C22×D44C2×C4semidirect
83. C22×C4×D11C2×C4semidirect
88. C2×C11×C4⋊C4C2×C4semidirect
89. C2×C11×C4⋊C4D4semidirect
112. C2×(C2×D11)⋊C4C2×C4semidirect
113. C2×(C2×D11)⋊C4D4semidirect
119. C2×C4×Dic11D4semidirect
237. C2×D44C22⋊C4semidirect
273. C4⋊#95D11semidirect
359. C22×D11C4×D4semidirect
422. C2×Dic11#121semidirect
529. C4×C11#386semidirect
582. C2×C4⋊C4C4×D11semidirect
583. C2×C4⋊C4D44semidirect
769. C11#13970semidirect
995. C4#10622278semidirect

Maximal subgroups

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

subgroupindex
C22×#669482
C22×#669462
C2×#106225522
C2×#106222782
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668642
#130668562
#130668452
(C2×D11)⋊#952
C11×C4⋊#952
#1397011