Finite Group Databasebeta

← #14676868

Subgroups — #14676868

Order 2816.

1802 conjugacy classes of subgroups.

The subgroup lattice has 816 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622586C211yesmaximal, characteristic, complemented
2C2×#10622553C212yesmaximal
3C2×#10622600C211yesmaximal, characteristic
4C2×#10622600C211yesmaximal, characteristic
5C2×C4×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13066871C212yesmaximal, complemented
7#13066864C212yesmaximal
8#13066846C211yesmaximal, characteristic, complemented
9#13066845C211yesmaximal, characteristic, complemented
10#13066843C212yesmaximal, complemented
11C2×C4×C11×C4⋊C4C211yesmaximal, characteristic, complemented
12C23×C4×D11C2211yescharacteristic
13C22×C11×C4⋊C4C2211yescharacteristic
14C22×C11×C4⋊C4C2211yescharacteristic
15C22×C42×C11C2212yes—
16C22×C42×C11C2211yescharacteristic
17C22×(C2×D11)⋊C4C2211yescharacteristic
18C22×(C2×D11)⋊C4C2212yes—
19C22×(C2×D11)⋊C4C2212yes—
20C22×(C2×D11)⋊C4C2211yescharacteristic
21C22×C4⋊Dic11C2211yescharacteristic
22C22×C4⋊Dic11C2211yescharacteristic
23C22×Dic11⋊C4C2212yes—
24C22×C4×Dic11C2211yescharacteristic
25C4×C11×C4⋊C4—24no—
26C2×C11×#95C2212yes—
27C2×C11⋊#95C2211yescharacteristic
28C2×C11⋊#95C2212yes—
29C2×C11⋊#95C2212yes—
30C2×C11⋊#95C2212yes—
31C2×C11⋊#95C2212yes—
32C2×C11⋊#95C2212yes—
33C2×C11⋊#95C2211yescharacteristic
34C2×C11⋊#95C2212yes—
35C2×C11⋊#95C2212yes—
36#10622600—24no—
37#10622600C418yescomplemented
38#10622586—24no—
39#10622553—28no—
40C4×(C2×D11)⋊C4—24no—
41C24×D11C2311yescharacteristic
42C23×C4×C11C2312yes—
43C23×C4×C11C2312yes—
44C23×C4×C11C2311yescharacteristic
45C23×C4×C11C2311yescharacteristic
46C23×C4×C11C2311yescharacteristic
47C23×Dic11C2312yes—
48C23×Dic11C2312yes—
49C23×Dic11C2311yescharacteristic
50C23×Dic11C2311yescharacteristic
51C23×Dic11C2311yescharacteristic
52C22×C4×D11—22no—
53C22×C4×D11—22no—
54C22×C4×D11—22no—
55C22×C4×D11—22no—
56C22×C4×D11—22no—
57C22×C4×D11—22no—
58C22×C4×D11C2×C414yes—
59C2×C11×C4⋊C4—22no—
60C2×C11×C4⋊C4—22no—
61C2×C11×C4⋊C4—22no—
62C2×C11×C4⋊C4—22no—
63C2×C11×C4⋊C4C2×C414yes—
64C2×C11×C4⋊C4D414yes—
65C2×C42×C11—22no—
66C2×C42×C11—22no—
67C2×C42×C11—24no—
68C2×C42×C11—24no—
69C2×C42×C11—24no—
70C2×C42×C11D414yes—
71C2×(C2×D11)⋊C4—24no—
72C2×(C2×D11)⋊C4—22no—
73C2×(C2×D11)⋊C4—24no—
74C2×(C2×D11)⋊C4—22no—
75C2×(C2×D11)⋊C4—22no—
76C2×(C2×D11)⋊C4—22no—
77C2×(C2×D11)⋊C4—22no—
78C2×(C2×D11)⋊C4—24no—
79C2×(C2×D11)⋊C4—24no—
80C2×(C2×D11)⋊C4—42no—
81C2×(C2×D11)⋊C4C2×C418yes—
82C2×(C2×D11)⋊C4D414yes—
83C2×C4⋊Dic11—22no—
84C2×C4⋊Dic11—22no—
85C2×C4⋊Dic11—22no—
86C2×C4⋊Dic11—22no—
87C2×C4⋊Dic11—22no—
88C2×C4⋊Dic11C2×C414yes—
89C2×Dic11⋊C4—24no—
90C2×Dic11⋊C4—24no—
91C2×Dic11⋊C4—42no—
92C2×C4×Dic11—22no—
93C2×C4×Dic11—22no—
94C2×C4×Dic11—22no—
95C11×#95—24no—
96C11⋊#95—22no—
97C11⋊#95—22no—
98C11⋊#95—24no—
99C11⋊#95—24no—
100C11⋊#95—24no—
101C11⋊#95—24no—
102C11⋊#95—24no—
103C11⋊#95—42no—
104C11⋊#95C2×C418yes—
105#13994—111nomaximal, Sylow
106C24×C11C2411yescharacteristic
107C23×D11—21no—
108C23×D11—21no—
109C23×D11—21no—
110C23×D11—21no—
111C23×D11—21no—
112C23×D11—21no—
113C23×D11—21no—
114C23×D11—21no—
115C23×D11—21no—
116C23×D11—21no—
117C23×D11—21no—
118C23×D11—21no—
119C23×D11C22×C412yes—
120C23×D11C2×D412yes—
121C23×D11#4112yes—
122C22×C4×C11—21no—
123C22×C4×C11—21no—
124C22×C4×C11—21no—
125C22×C4×C11—21no—
126C22×C4×C11—22no—
127C22×C4×C11—22no—
128C22×C4×C11—22no—
129C22×C4×C11—22no—
130C22×C4×C11—22no—
131C22×C4×C11—22no—
132C22×C4×C11—21no—
133C22×C4×C11—21no—
134C22×C4×C11—22no—
135C22×C4×C11—21no—
136C22×C4×C11—21no—
137C22×C4×C11—22no—
138C22×C4×C11—22no—
139C22×C4×C11—22no—
140C22×C4×C11—21no—
141C22×C4×C11—22no—
142C22×C4×C11—21no—
143C22×C4×C11—22no—
144C22×C4×C11C22×C414yes—
145C22×C4×C11C22×C412yes—
146C22×C4×C11C2×D414yes—
147C22×C4×C11C2×D412yes—
148C22×C4×C11C2×D412yes—
149C22×C4×C11C2×D412yes—
150C22×C4×C11C2×D412yes—
151C22×C4×C11C2×D412yes—
152C22×C4×C11#4112yes—
153C22×C4×C11#4112yes—
154C22×C4×C11#4112yes—
155C22×C4×C11#4112yes—
156C22×C4×C11#4112yes—
157C22×Dic11—21no—
158C22×Dic11—21no—
159C22×Dic11—21no—
160C22×Dic11—21no—
161C22×Dic11—21no—
162C22×Dic11—22no—
163C22×Dic11—22no—
164C22×Dic11—21no—
165C22×Dic11—22no—
166C22×Dic11—22no—
167C22×Dic11—21no—
168C22×Dic11—21no—
169C22×Dic11—22no—
170C22×Dic11—21no—
171C22×Dic11—22no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11—21no—
176C22×Dic11—21no—
177C22×Dic11—22no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—22no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—21no—
184C22×Dic11—22no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—22no—
188C22×Dic11C22×C412yes—
189C22×Dic11C22×C414yes—
190C22×Dic11C2×D412yes—
191C22×Dic11#4112yes—
192C2×C4×D11—28no—
193C2×C4×D11—28no—
194C2×C4×D11—28no—
195C2×C4×D11—44no—
196C2×C4×D11—44no—
197C2×C4×D11—44no—
198C2×C4×D11—44no—
199C11×C4⋊C4—28no—
200C11×C4⋊C4—28no—
201C42×C11—28no—
202C42×C11—48no—
203(C2×D11)⋊C4—28no—
204(C2×D11)⋊C4—216no—
205(C2×D11)⋊C4—28no—
206(C2×D11)⋊C4—48no—
207C4⋊Dic11—28no—
208C4⋊Dic11—44no—
209Dic11⋊C4—48no—
210C4×Dic11—44no—
211C2×#389—111no—
212C2×#388—112no—
213C2×#380—111no—
214C2×#380—111no—
215C2×C4×C4⋊C4D1111yescharacteristic, complemented
216C2×C4×C22⋊C4—111no—
217#1442—112no—
218#1440—112no—
219C4⋊#95—111no—
220C4⋊#95—111no—
221#1434—112no—
222C23×C11C23×C411yescharacteristic
223C23×C11C22×D411yescharacteristic
224C23×C11C22×D411yescharacteristic
225C23×C11C22×D411yescharacteristic
226C23×C11C2×#4111yescharacteristic
227C23×C11C2×#4111yescharacteristic
228C23×C11C2×#4111yescharacteristic
229C23×C11C2×#4111yescharacteristic
230C23×C11C2×#4111yescharacteristic
231C23×C11C2×#4111yescharacteristic
232C23×C11C2×#4111yescharacteristic
233C23×C11H(5,𝔽2)11yescharacteristic
234C23×C112−1+411yescharacteristic
235C23×C112−1+411yescharacteristic
236C23×C112−1+411yescharacteristic
237C22×D11—22no—
238C22×D11—22no—
239C22×D11—22no—
240C22×D11—22no—
241C22×D11—22no—
242C22×D11—22no—
243C22×D11—22no—
244C22×D11—22no—
245C22×D11—22no—
246C22×D11—22no—
247C22×D11—22no—
248C22×D11—22no—
249C22×D11—22no—
250C22×D11—22no—
251C22×D11—22no—
252C22×D11—22no—
253C22×D11—22no—
254C22×D11—22no—
255C22×D11—41no—
256C22×D11—41no—
257C22×D11—41no—
258C22×D11—41no—
259C22×D11—41no—
260C22×D11—41no—
261C22×D11—41no—
262C22×D11—41no—
263C22×D11—41no—
264C22×D11—41no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11C4×D414yes—
272C2×C4×C11—22no—
273C2×C4×C11—22no—
274C2×C4×C11—22no—
275C2×C4×C11—22no—
276C2×C4×C11—22no—
277C2×C4×C11—22no—
278C2×C4×C11—24no—
279C2×C4×C11—24no—
280C2×C4×C11—24no—
281C2×C4×C11—24no—
282C2×C4×C11—22no—
283C2×C4×C11—22no—
284C2×C4×C11—22no—
285C2×C4×C11—24no—
286C2×C4×C11—24no—
287C2×C4×C11—42no—
288C2×C4×C11—42no—
289C2×C4×C11—42no—
290C2×C4×C11—42no—
291C2×C4×C11—42no—
292C2×C4×C11—42no—
293C2×C4×C11—42no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—42no—
298C2×C4×C11—41no—
299C2×C4×C11#11714yes—
300C2×C4×C11C4×D414yes—
301C2×C4×C11C4×D414yes—
302C2×C4×C11#12114yes—
303C2×C4×C11#12114yes—
304C2×C4×C11#12314yes—
305C2×C4×C11#12414yes—
306C2×C4×C11#12614yes—
307C2×Dic11—22no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—22no—
311C2×Dic11—22no—
312C2×Dic11—24no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329C2×Dic11—41no—
330C2×Dic11—42no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—42no—
334C2×Dic11—41no—
335C2×Dic11—42no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—42no—
341C2×Dic11—42no—
342C4×D11—416no—
343C24×C4—111no—
344C22×C4⋊C4—111no—
345C22×C4⋊C4—111no—
346C22×C4⋊C4—112no—
347C22×C4⋊C4C2×D1111yescharacteristic
348C22×C4⋊C4C2×D1111yescharacteristic
349C22×C22⋊C4—112no—
350C22×C22⋊C4—111no—
351C22×C22⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C42—111no—
354C22×C42C2×D1112yes—
355C22×C42C2×D1111yescharacteristic
356#389—224no—
357#388—228no—
358#380—118no—
359#380—224no—
360C4×C4⋊C4—24no—
361C4×C22⋊C4—224no—
362C2×#95—112no—
363C2×#95—111no—
364C2×#95—112no—
365C2×#95—112no—
366C2×#95—112no—
367C2×#95—112no—
368C2×#95—112no—
369C2×#95—111no—
370C2×#95—112no—
371C2×#95C2×D1112yes—
372C22×C11C2×#11711yescharacteristic
373C22×C11C2×C4×D411yescharacteristic
374C22×C11C2×C4×D411yescharacteristic
375C22×C11C2×C4×D411yescharacteristic
376C22×C11C4×#4111yescharacteristic
377C22×C11#51911yescharacteristic
378C22×C11#52011yescharacteristic
379C22×C11C2×#12111yescharacteristic
380C22×C11C2×#12111yescharacteristic
381C22×C11C2×#12311yescharacteristic
382C22×C11#52511yescharacteristic
383C22×C11C2×#12411yescharacteristic
384C22×C11C2×#12611yescharacteristic
385C22×C11#52911yescharacteristic
386C22×C11#53211yescharacteristic
387C22×C11#53611yescharacteristic
388C22×C11#53711yescharacteristic
389C22×C11#54111yescharacteristic
390C22×C11#54211yescharacteristic
391C22×C11D4211yescharacteristic
392C22×C11#54711yescharacteristic
393C22×C11#54711yescharacteristic
394C22×C11#54711yescharacteristic
395C22×C11#54711yescharacteristic
396C22×C11#54811yescharacteristic
397C22×C11#54811yescharacteristic
398C22×C11#55211yescharacteristic
399C22×C11#55211yescharacteristic
400C22×C11#55211yescharacteristic
401C22×C11#55211yescharacteristic
402C22×C11#55211yescharacteristic
403C22×C11#55311yescharacteristic
404C22×C11#55511yescharacteristic
405C22×C11#55511yescharacteristic
406C22×C11#55611yescharacteristic
407C2×D11—24no—
408C2×D11—24no—
409C2×D11—24no—
410C2×D11—42no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—42no—
416C2×D11—42no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C4×C11—24no—
423C4×C11—42no—
424C4×C11—44no—
425C4×C11—44no—
426C4×C11#38818yescomplemented
427Dic11—44no—
428Dic11—42no—
429Dic11—42no—
430Dic11—42no—
431Dic11—82no—
432C25—111no—
433C23×C4—112no—
434C23×C4—111no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—114no—
438C23×C4—112no—
439C23×C4—222no—
440C23×C4—222no—
441C23×C4—222no—
442C23×C4—222no—
443C23×C4—222no—
444C23×C4—222no—
445C23×C4C22×D1112yes—
446C23×C4C22×D1112yes—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C2×C4⋊C4—22no—
451C2×C4⋊C4—22no—
452C2×C4⋊C4—22no—
453C2×C4⋊C4—22no—
454C2×C4⋊C4—114no—
455C2×C4⋊C4—222no—
456C2×C4⋊C4—222no—
457C2×C4⋊C4—224no—
458C2×C4⋊C4—222no—
459C2×C4⋊C4—224no—
460C2×C4⋊C4—222no—
461C2×C4⋊C4—222no—
462C2×C4⋊C4—442no—
463C2×C4⋊C4C4×D1114yes—
464C2×C4⋊C4D4414yes—
465C2×C22⋊C4—118no—
466C2×C22⋊C4—114no—
467C2×C22⋊C4—222no—
468C2×C22⋊C4—224no—
469C2×C22⋊C4—224no—
470C2×C22⋊C4—222no—
471C2×C22⋊C4—222no—
472C2×C22⋊C4—222no—
473C2×C22⋊C4—222no—
474C2×C22⋊C4—224no—
475C2×C22⋊C4—224no—
476C2×C22⋊C4—442no—
477C2×C42—22no—
478C2×C42—22no—
479C2×C42—24no—
480C2×C42—24no—
481C2×C42—24no—
482C2×C42—222no—
483C2×C42—222no—
484C2×C42—222no—
485C2×C42C22⋊D1114yes—
486#95—24no—
487#95—118no—
488#95—224no—
489#95—224no—
490#95—224no—
491#95—224no—
492#95—224no—
493#95—222no—
494#95—222no—
495#95—442no—
496C2×C11C2×#38811yescharacteristic
497C2×C11C4×#12111yescharacteristic
498C2×C11#232311yescharacteristic
499C2×C11#234411yescharacteristic
500C2×C11#234611yescharacteristic
501C2×C11#236111yescharacteristic
502C2×C11#236211yescharacteristic
503C2×C11#248511yescharacteristic
504C2×C11#248611yescharacteristic
505C2×C11#248911yescharacteristic
506C2×C11#249111yescharacteristic
507C2×C11#249511yescharacteristic
508C2×C11#249611yescharacteristic
509C2×C11#253611yescharacteristic
510C2×C11#253711yescharacteristic
511D11—44no—
512C24—112no—
513C24—112no—
514C24—112no—
515C24—221no—
516C24—221no—
517C24—221no—
518C24—221no—
519C24—221no—
520C24—221no—
521C24—221no—
522C24—221no—
523C24—221no—
524C24—221no—
525C24—221no—
526C24—221no—
527C24C23×D1111yescharacteristic
528C22×C4—21no—
529C22×C4—21no—
530C22×C4—21no—
531C22×C4—21no—
532C22×C4—21no—
533C22×C4—21no—
534C22×C4—22no—
535C22×C4—22no—
536C22×C4—22no—
537C22×C4—22no—
538C22×C4—22no—
539C22×C4—22no—
540C22×C4—22no—
541C22×C4—22no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—22no—
546C22×C4—22no—
547C22×C4—21no—
548C22×C4—22no—
549C22×C4—22no—
550C22×C4—112no—
551C22×C4—114no—
552C22×C4—112no—
553C22×C4—112no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—222no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—222no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—221no—
565C22×C4—222no—
566C22×C4—221no—
567C22×C4—222no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—222no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—228no—
579C22×C4—228no—
580C22×C4—228no—
581C22×C4—222no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—222no—
585C22×C4—222no—
586C22×C4—222no—
587C22×C4—222no—
588C22×C4—444no—
589C22×C4—444no—
590C22×C4—444no—
591C22×C4—444no—
592C22×C4C2×C4×D1114yes—
593C22×C4C2×C4×D1112yes—
594C22×C4C2×D4414yes—
595C22×C4C2×D4412yes—
596C22×C4#433912yes—
597C22×C4#433912yes—
598C22×C4#433912yes—
599C22×C4#433912yes—
600C22×C4D4×D1112yes—
601C22×C4#434112yes—
602C22×C4C2×C22⋊D1112yes—
603C22×C4C2×C22⋊D1112yes—
604C22×C4C2×C22⋊D1112yes—
605C4⋊C4—28no—
606C4⋊C4—28no—
607C4⋊C4—228no—
608C4⋊C4—448no—
609C4⋊C4—444no—
610C22⋊C4—2216no—
611C22⋊C4—228no—
612C22⋊C4—228no—
613C22⋊C4—448no—
614C42—28no—
615C42—48no—
616C42—444no—
617C11#1399411yescharacteristic, complemented, Sylow
618C23—114no—
619C23—222no—
620C23—222no—
621C23—222no—
622C23—222no—
623C23—222no—
624C23—222no—
625C23—222no—
626C23—222no—
627C23—222no—
628C23—222no—
629C23—222no—
630C23—222no—
631C23—222no—
632C23—222no—
633C23—222no—
634C23—222no—
635C23—222no—
636C23—222no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—441no—
642C23—441no—
643C23—441no—
644C23—441no—
645C23—441no—
646C23—441no—
647C23—441no—
648C23—441no—
649C23—441no—
650C23—441no—
651C23—441no—
652C23—441no—
653C23C22×C4×D1111yescharacteristic
654C23C22×D4411yescharacteristic
655C23C2×#433911yescharacteristic
656C23C2×#433911yescharacteristic
657C23C2×#433911yescharacteristic
658C23C2×#433911yescharacteristic
659C23C2×D4×D1111yescharacteristic
660C23C2×#434111yescharacteristic
661C23#6704011yescharacteristic
662C23#6704011yescharacteristic
663C23#41×D1111yescharacteristic
664C23#41×D1111yescharacteristic
665C23#6704211yescharacteristic
666C23#6704311yescharacteristic
667C23C22×C22⋊D1111yescharacteristic
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—24no—
675C2×C4—22no—
676C2×C4—24no—
677C2×C4—24no—
678C2×C4—24no—
679C2×C4—24no—
680C2×C4—24no—
681C2×C4—22no—
682C2×C4—22no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—42no—
688C2×C4—42no—
689C2×C4—42no—
690C2×C4—42no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—222no—
696C2×C4—224no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—224no—
700C2×C4—222no—
701C2×C4—222no—
702C2×C4—222no—
703C2×C4—222no—
704C2×C4—224no—
705C2×C4—222no—
706C2×C4—222no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—442no—
710C2×C4—442no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4—442no—
716C2×C4—441no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—442no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—4416no—
724C2×C4—442no—
725C2×C4—442no—
726C2×C4—442no—
727C2×C4—442no—
728C2×C4—442no—
729C2×C4—442no—
730C2×C4—442no—
731C2×C4#6692514yes—
732C2×C4C4×D4414yes—
733C2×C4#6692814yes—
734C2×C4#6692914yes—
735C2×C4C4×C22⋊D1114yes—
736C2×C4#6698214yes—
737C2×C4#6698314yes—
738C2×C4#6699114yes—
739C22—224no—
740C22—224no—
741C22—224no—
742C22—442no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—442no—
753C22—442no—
754C22C2×#6692511yescharacteristic
755C22C2×C4×D4411yescharacteristic
756C22C2×#6692811yescharacteristic
757C22C2×#6692911yescharacteristic
758C22#1062303811yescharacteristic
759C22#1062303811yescharacteristic
760C22#1062304411yescharacteristic
761C22#1062304411yescharacteristic
762C22#1062306011yescharacteristic
763C22#1062306111yescharacteristic
764C22#1062306311yescharacteristic
765C22#1062306411yescharacteristic
766C22C4×#434111yescharacteristic
767C22C4×D4×D1111yescharacteristic
768C22#1062307911yescharacteristic
769C22D4×D4411yescharacteristic
770C22#1062308211yescharacteristic
771C22#1062308611yescharacteristic
772C22#1062308811yescharacteristic
773C22#1062309411yescharacteristic
774C22#1062310311yescharacteristic
775C22#1062310511yescharacteristic
776C22#1062310711yescharacteristic
777C22#1062310711yescharacteristic
778C22#1062311211yescharacteristic
779C22#1062311211yescharacteristic
780C22#1062311311yescharacteristic
781C22#1062311411yescharacteristic
782C22C2×C4×C22⋊D1111yescharacteristic
783C22C2×#6698211yescharacteristic
784C22C2×#6698311yescharacteristic
785C22C2×#6699111yescharacteristic
786C22#1062334711yescharacteristic
787C22#1062335911yescharacteristic
788C22#1062336411yescharacteristic
789C4—24no—
790C4—42no—
791C4—44no—
792C4—44no—
793C4—444no—
794C4—442no—
795C4—442no—
796C4—442no—
797C4—882no—
798C4#1062255318yescomplemented
799C2—444no—
800C2C2×#1062255311yescharacteristic
801C2C4×#6699111yescharacteristic
802C2#1307129211yescharacteristic
803C2#1307148111yescharacteristic
804C2#1307149711yescharacteristic
805C2#1307163411yescharacteristic
806C2#1307164511yescharacteristic
807C2#1307290711yescharacteristic
808C2#1307291811yescharacteristic
809C2#1307295111yescharacteristic
810C2#1307297311yescharacteristic
811C2#1307302111yescharacteristic
812C2#1307303211yescharacteristic
813C2#1307352111yescharacteristic
814C2#1307352911yescharacteristic
subgroupG/H
center, FrattiniC24C23×D11
commutatorC23×C11C23×C4
FittingC2×C4×C11×C4⋊C4C2
socle, cosocleC24×C11C24
prime radicalC24×D11C23
hypercenterC2×C4×C4⋊C4D11
hypocenterC11#13994
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C4⋊C4

Complements

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

NH ≅ G/Ntype
1. C2×#10622586C2semidirect
6. #13066871C2semidirect
8. #13066846C2semidirect
9. #13066845C2semidirect
10. #13066843C2semidirect
11. C2×C4×C11×C4⋊C4C2semidirect
37. #10622600C4semidirect
215. C2×C4×C4⋊C4D11semidirect
426. C4×C11#388semidirect
617. C11#13994semidirect
798. C4#10622553semidirect

Maximal subgroups

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

subgroupindex
C2×#106225862
C2×#106225532
C2×#106226002
C2×C4×(C2×D11)⋊C42
#130668712
#130668642
#130668462
#130668452
#130668432
C2×C4×C11×C4⋊C42
#1399411