Finite Group Databasebeta

← #14719955

Subgroups — #14719955

Order 2816.

1424 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623360C211yesmaximal, characteristic
2#13077065C211yesmaximal, characteristic, complemented
3#13066977C211yesmaximal, characteristic, complemented
4#13066975C211yesmaximal, characteristic, complemented
5#13066965C212yesmaximal, complemented
6#13066962C212yesmaximal, complemented
7#13066952C211yesmaximal, characteristic, complemented
8#13066942C212yesmaximal, complemented
9#13066932C211yesmaximal, characteristic, complemented
10C2×#10622106C212yesmaximal, complemented
11C11×#2880C211yesmaximal, characteristic, complemented
12C22×C11×#41C2211yescharacteristic
13C22×D4×D11C411yescharacteristic
14C2×C11×#131—21no—
15#10623360—21no—
16#10623360—22no—
17#10623360—21no—
18#10623360—21no—
19#10623360—22no—
20#10623360—21no—
21C2×#67001—21no—
22C2×#67000C411yescharacteristic
23C2×#66999C411yescharacteristic
24C2×#66992C412yes—
25C2×#66990C412yes—
26C2×D4×Dic11C411yescharacteristic
27C2×#66983C2211yescharacteristic
28C2×#66982C2212yes—
29C2×C4×C22⋊D11C2211yescharacteristic
30C22×(C2×D11)⋊C4C2212yes—
31C11×#408—21no—
32C11×#408—22no—
33C11×#407C2212yescomplemented
34C11×#407C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2212yescomplemented
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37#10622847—21no—
38#10622847—22no—
39#10622820C2212yescomplemented
40#10622820C2211yescharacteristic, complemented
41C2×C22⋊(C11⋊C8)C2212yescomplemented
42C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
43#10622107C2211yescharacteristic, complemented
44#10622107C2211yescharacteristic, complemented
45#10622107C2212yescomplemented
46#10622106C2211yescharacteristic
47#10622106C2212yes—
48#10622106C2211yescharacteristic
49#10622106C2212yescomplemented
50#10622106C2212yescomplemented
51#10622106C2212yescomplemented
52#10622106C2212yescomplemented
53C24×D11C2×C412yes—
54C2×C11×#41—44no—
55C2×C11×#41D411yescharacteristic
56C2×C11×#41D412yes—
57C2×C11×#41D411yescharacteristic
58C2×C11×#41D411yescharacteristic
59C2×C11×#41D412yes—
60C2×C11×#41D411yescharacteristic
61C22×Q8×C11C2×C411yescharacteristic
62C22×D4×C11C2×C411yescharacteristic
63C22×D4×C11C2×C412yes—
64C23×C4×C11C2312yes—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11C2×C411yescharacteristic
67C22×C22⋊D11C2×C412yes—
68C22×C22⋊D11C2×C412yes—
69C23×Dic11C2×C412yes—
70C2×D4×D11—22no—
71C2×D4×D11—21no—
72C2×D4×D11—21no—
73C2×D4×D11—44no—
74C22×D44C2×C411yescharacteristic
75C22×C4×D11C2×C411yescharacteristic
76C11×#131—44no—
77C2×C11×M16—22no—
78C2×C11×M16—21no—
79C22×C8×C11—22no—
80C22×C8×C11—21no—
81C2×C22⋊Dic11C2×C411yescharacteristic
82C2×C22⋊Dic11C2×C412yes—
83#67001—44no—
84#67000—21no—
85#67000—21no—
86#67000—22no—
87#66999—21no—
88#66999—21no—
89#66999—22no—
90#66992—22no—
91#66992—22no—
92#66992—22no—
93#66992—22no—
94#66990—22no—
95#66990—22no—
96#66990—22no—
97#66990—22no—
98D4×Dic11—22no—
99D4×Dic11—21no—
100D4×Dic11—21no—
101#66983—21no—
102#66983—21no—
103#66983—21no—
104#66983—21no—
105#66982—22no—
106#66982—22no—
107#66982—22no—
108#66982—22no—
109C4×C22⋊D11—21no—
110C4×C22⋊D11—21no—
111C4×C22⋊D11—21no—
112C4×C22⋊D11—21no—
113C2×(C2×D11)⋊C4—22no—
114C2×(C2×D11)⋊C4—22no—
115C2×(C2×D11)⋊C4—22no—
116C2×(C2×D11)⋊C4—22no—
117C2×(C2×D11)⋊C4C2×C412yes—
118C2×(C2×D11)⋊C4C2×C412yes—
119C2×(C2×D11)⋊C4C2×C412yes—
120C2×(C2×D11)⋊C4C2311yescharacteristic
121C2×(C2×D11)⋊C4C2312yes—
122C2×C4⋊Dic11C2×C411yescharacteristic
123C2×Dic11⋊C4C2×C412yes—
124C2×Dic11⋊C4C2311yescharacteristic
125C2×C4×Dic11C2×C411yescharacteristic
126C2×#4318—22no—
127C2×#4318—21no—
128C22×C11⋊C8—22no—
129C22×C11⋊C8—21no—
130C11×C22⋊C8—22no—
131C11×C22⋊C8—21no—
132C11×C22⋊C8—22no—
133C11×C22⋊C8—21no—
134C11×C22⋊C8C2311yescharacteristic
135C11×C22⋊C8C2312yes—
136C11×C22⋊C8C2311yescharacteristic
137C22⋊(C11⋊C8)—22no—
138C22⋊(C11⋊C8)—21no—
139C22⋊(C11⋊C8)—22no—
140C22⋊(C11⋊C8)—21no—
141C22⋊(C11⋊C8)C2311yescharacteristic
142C22⋊(C11⋊C8)C2312yes—
143C22⋊(C11⋊C8)C2311yescharacteristic
144#17411—111nomaximal, Sylow
145C24×C11C22×C412yes—
146C24×C11C22×C411yescharacteristic
147C23×D11—22no—
148C23×D11—22no—
149C23×D11—24no—
150C23×D11—42no—
151C23×D11—44no—
152C23×D11—82no—
153C23×D11C22×C412yes—
154C23×D11C22×C411yescharacteristic
155C11×#41—24no—
156C11×#41—24no—
157C11×#41—44no—
158C11×#41—44no—
159C11×#41—42no—
160C11×#41—42no—
161C2×Q8×C11—42no—
162C2×Q8×C11C22⋊C411yescharacteristic
163C2×Q8×C11C22⋊C411yescharacteristic
164C2×Q8×C11C22⋊C412yes—
165C2×D4×C11—24no—
166C2×D4×C11—44no—
167C2×D4×C11C22⋊C412yes—
168C2×D4×C11C22⋊C411yescharacteristic
169C2×D4×C11C22⋊C412yes—
170C2×D4×C11C22⋊C412yes—
171C2×D4×C11C22⋊C412yes—
172C2×D4×C11C22⋊C412yes—
173C2×D4×C11C22⋊C411yescharacteristic
174C22×C4×C11—42no—
175C22×C4×C11—44no—
176C22×C4×C11C22×C411yescharacteristic
177C22×C4×C11C22×C412yes—
178C22×C4×C11C2×D412yes—
179C22×C4×C11C2×D411yescharacteristic
180C22×C4×C11C2×D412yes—
181C22×C4×C11C2×D411yescharacteristic
182C22×C4×C11C2×D412yes—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2×D412yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2411yescharacteristic
187C2×C22⋊D11—21no—
188C2×C22⋊D11—21no—
189C2×C22⋊D11—22no—
190C2×C22⋊D11—22no—
191C2×C22⋊D11—22no—
192C2×C22⋊D11—22no—
193C2×C22⋊D11—22no—
194C2×C22⋊D11—41no—
195C2×C22⋊D11—44no—
196C2×C22⋊D11—82no—
197C22×Dic11—22no—
198C22×Dic11—22no—
199C22×Dic11—82no—
200C22×Dic11C22×C411yescharacteristic
201C22×Dic11C22×C411yescharacteristic
202C22×Dic11C22×C411yescharacteristic
203C22×Dic11C22×C412yes—
204D4×D11—48no—
205D4×D11—44no—
206D4×D11—44no—
207C2×D44—21no—
208C2×D44—21no—
209C2×D44—42no—
210C2×C4×D11—21no—
211C2×C4×D11—21no—
212C2×C4×D11—42no—
213C11×M16—44no—
214C11×M16—42no—
215C2×C8×C11—21no—
216C2×C8×C11—22no—
217C2×C8×C11—21no—
218C2×C8×C11—44no—
219C2×C8×C11—42no—
220C22⋊Dic11—21no—
221C22⋊Dic11—21no—
222C22⋊Dic11—22no—
223C22⋊Dic11—22no—
224(C2×D11)⋊C4—22no—
225(C2×D11)⋊C4—22no—
226(C2×D11)⋊C4—22no—
227(C2×D11)⋊C4—22no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—21no—
231(C2×D11)⋊C4—21no—
232(C2×D11)⋊C4—22no—
233(C2×D11)⋊C4—22no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236Dic11⋊C4—22no—
237Dic11⋊C4—22no—
238Dic11⋊C4—21no—
239Dic11⋊C4—21no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242#4318—44no—
243#4318—42no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—22no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—44no—
248C2×C11⋊C8—42no—
249C2×#546—111no—
250#2880—111no—
251#2880D1111yescharacteristic, complemented
252#1471—111no—
253#1471—111no—
254#1468—112no—
255#1468—112no—
256#1465—111no—
257#1462—112no—
258#1459—111no—
259C2×#323—112no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—24no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—42no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11C2×C22⋊C412yes—
269C23×C11C2×C22⋊C411yescharacteristic
270C23×C11C2×C22⋊C411yescharacteristic
271C23×C11C2×C22⋊C412yes—
272C23×C11C23×C411yescharacteristic
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—22no—
278C22×D11—44no—
279C22×D11—44no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—44no—
283C22×D11—44no—
284C22×D11—42no—
285C22×D11—42no—
286C22×D11—82no—
287C22×D11—82no—
288C22×D11—88no—
289C22×D11—88no—
290C22×D11#13112yescomplemented
291Q8×C11—22no—
292Q8×C11—22no—
293Q8×C11—42no—
294D4×C11—24no—
295D4×C11—24no—
296D4×C11—24no—
297D4×C11—22no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11#9914yes—
301C2×C4×C11—24no—
302C2×C4×C11—24no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—41no—
307C2×C4×C11—42no—
308C2×C4×C11—41no—
309C2×C4×C11—42no—
310C2×C4×C11—41no—
311C2×C4×C11—42no—
312C2×C4×C11C2×C22⋊C411yescharacteristic
313C2×C4×C11C2×C22⋊C412yes—
314C2×C4×C11C2×C22⋊C412yes—
315C2×C4×C11C2×C22⋊C411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C22×D411yescharacteristic
318C22⋊D11—42no—
319C22⋊D11—42no—
320C22⋊D11—44no—
321C22⋊D11—44no—
322C22⋊D11—82no—
323C22⋊D11—82no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—42no—
333C2×Dic11—82no—
334C2×Dic11—82no—
335D44—42no—
336D44—42no—
337C4×D11—42no—
338C4×D11—42no—
339C8×C11—41no—
340C8×C11—42no—
341C8×C11—41no—
342C11⋊C8—41no—
343C11⋊C8—42no—
344C11⋊C8—41no—
345C22×#41C2×D1111yescharacteristic
346C23×D4—111no—
347C2×#131—21no—
348C2×#131—221no—
349#546—221no—
350#546—222no—
351#546—221no—
352#546—221no—
353#546—222no—
354#546—221no—
355C2×#124—111no—
356C2×#123—112no—
357C2×C22⋊Q8—111no—
358C2×#121—112no—
359C2×#121—111no—
360C2×#120—112no—
361C2×C4×D4—111no—
362C2×C4×D4—111no—
363C22×C22⋊C4—112no—
364#408—21no—
365#408—22no—
366#408—221no—
367#408—222no—
368#407—112no—
369#407—111no—
370#407C2×D1112yescomplemented
371#407C2×D1111yescharacteristic, complemented
372C2×C22⋊C8—112no—
373C2×C22⋊C8—111no—
374C2×C22⋊C8C2×D1112yescomplemented
375C2×C22⋊C8C2×D1111yescharacteristic, complemented
376#324—111no—
377#324—111no—
378#324—112no—
379#323—111no—
380#323—112no—
381#323—111no—
382#323—112no—
383#323—112no—
384#323—112no—
385#323—112no—
386C22×C11—22no—
387C22×C11—21no—
388C22×C11—21no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—21no—
392C22×C11—21no—
393C22×C11—21no—
394C22×C11—21no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—21no—
398C22×C11—21no—
399C22×C11—44no—
400C22×C11—44no—
401C22×C11—81no—
402C22×C11—81no—
403C22×C11C2×#9914yes—
404C22×C11C22×C22⋊C411yescharacteristic
405C22×C11C2×#13111yescharacteristic
406C22×C11#56811yescharacteristic
407C2×D11—22no—
408C2×D11—42no—
409C2×D11—41no—
410C2×D11—41no—
411C2×D11—42no—
412C2×D11—42no—
413C2×D11—42no—
414C2×D11—42no—
415C2×D11—88no—
416C2×D11—88no—
417C2×D11—82no—
418C2×D11—82no—
419C4×C11—21no—
420C4×C11—21no—
421C4×C11—21no—
422C4×C11—22no—
423C4×C11—22no—
424C4×C11C2×#9912yes—
425Dic11—41no—
426Dic11—41no—
427Dic11—41no—
428Dic11—42no—
429C25—112no—
430C2×#41—44no—
431C2×#41D4411yescharacteristic
432C2×#41D4412yes—
433C2×#41D4411yescharacteristic
434C2×#41C22⋊D1111yescharacteristic
435C2×#41C22⋊D1112yes—
436C2×#41C22⋊D1111yescharacteristic
437C22×Q8C4×D1111yescharacteristic
438C22×D4—111no—
439C22×D4—112no—
440C22×D4—112no—
441C22×D4—111no—
442C22×D4—222no—
443C22×D4—221no—
444C22×D4—221no—
445C22×D4—444no—
446C22×D4C4×D1111yescharacteristic
447C22×D4C4×D1112yes—
448C23×C4—112no—
449C23×C4—111no—
450C23×C4C22×D1112yes—
451C23×C4C22×D1111yescharacteristic
452#131—44no—
453#131—444no—
454C2×M16—22no—
455C2×M16—21no—
456C2×M16—222no—
457C2×M16—221no—
458C22×C8—22no—
459C22×C8—21no—
460C22×C8—222no—
461C22×C8—221no—
462#124—221no—
463#124—221no—
464#124—222no—
465#123—222no—
466#123—222no—
467#123—222no—
468#123—222no—
469C22⋊Q8—221no—
470C22⋊Q8—221no—
471C22⋊Q8—222no—
472#121—222no—
473#121—222no—
474#121—222no—
475#121—222no—
476#121—221no—
477#121—221no—
478#121—221no—
479#121—221no—
480#120—222no—
481#120—222no—
482#120—222no—
483#120—222no—
484C4×D4—222no—
485C4×D4—221no—
486C4×D4—221no—
487C4×D4—221no—
488C4×D4—221no—
489C4×D4—221no—
490C4×D4—221no—
491C2×C4⋊C4—111no—
492C2×C4⋊C4—112no—
493C2×C4⋊C4—111no—
494C2×C22⋊C4—112no—
495C2×C22⋊C4—111no—
496C2×C22⋊C4—112no—
497C2×C22⋊C4—112no—
498C2×C22⋊C4—112no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—112no—
501C2×C22⋊C4—222no—
502C2×C22⋊C4—222no—
503C2×C22⋊C4—222no—
504C2×C22⋊C4—222no—
505C2×C42—111no—
506C22⋊C8—22no—
507C22⋊C8—21no—
508C22⋊C8—22no—
509C22⋊C8—21no—
510C22⋊C8—111no—
511C22⋊C8—112no—
512C22⋊C8—111no—
513C22⋊C8—222no—
514C22⋊C8—221no—
515C22⋊C8—222no—
516C22⋊C8—221no—
517C22⋊C8C22×D1111yescharacteristic
518C22⋊C8C22×D1112yes—
519C22⋊C8C22×D1111yescharacteristic
520C2×C11—21no—
521C2×C11—21no—
522C2×C11—24no—
523C2×C11—42no—
524C2×C11—41no—
525C2×C11—41no—
526C2×C11#288011yescharacteristic
527C2×C11C22×#9911yescharacteristic
528C2×C11#288811yescharacteristic
529D11—42no—
530D11—82no—
531C24—111no—
532C24—112no—
533C24—224no—
534C24—222no—
535C24—222no—
536C24—442no—
537C24—444no—
538C24—882no—
539C24C2×C4×D1112yes—
540C24C2×C4×D1111yescharacteristic
541#41—24no—
542#41—24no—
543#41—44no—
544#41—44no—
545#41—42no—
546#41—42no—
547C2×Q8—42no—
548C2×Q8(C2×D11)⋊C411yescharacteristic
549C2×Q8(C2×D11)⋊C411yescharacteristic
550C2×Q8(C2×D11)⋊C412yes—
551C2×D4—24no—
552C2×D4—44no—
553C2×D4—222no—
554C2×D4—221no—
555C2×D4—221no—
556C2×D4—222no—
557C2×D4—222no—
558C2×D4—222no—
559C2×D4—222no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—442no—
563C2×D4—441no—
564C2×D4—448no—
565C2×D4—444no—
566C2×D4—444no—
567C2×D4—444no—
568C2×D4—882no—
569C2×D4(C2×D11)⋊C412yes—
570C2×D4(C2×D11)⋊C411yescharacteristic
571C2×D4(C2×D11)⋊C412yes—
572C2×D4(C2×D11)⋊C412yes—
573C2×D4(C2×D11)⋊C412yes—
574C2×D4(C2×D11)⋊C412yes—
575C2×D4(C2×D11)⋊C411yescharacteristic
576C22×C4—42no—
577C22×C4—44no—
578C22×C4—111no—
579C22×C4—111no—
580C22×C4—112no—
581C22×C4—111no—
582C22×C4—222no—
583C22×C4—222no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—442no—
587C22×C4—882no—
588C22×C4C2×C4×D1111yescharacteristic
589C22×C4C2×C4×D1112yes—
590C22×C4C2×D4412yes—
591C22×C4C2×D4411yescharacteristic
592C22×C4C2×D4412yes—
593C22×C4C2×D4411yescharacteristic
594C22×C4C2×C22⋊D1112yes—
595C22×C4C2×C22⋊D1111yescharacteristic
596C22×C4C2×C22⋊D1112yes—
597C22×C4C2×C22⋊D1111yescharacteristic
598C22×C4C23×D1111yescharacteristic
599M16—44no—
600M16—42no—
601M16—444no—
602M16—442no—
603C2×C8—21no—
604C2×C8—22no—
605C2×C8—21no—
606C2×C8—44no—
607C2×C8—42no—
608C2×C8—221no—
609C2×C8—222no—
610C2×C8—221no—
611C2×C8—444no—
612C2×C8—442no—
613C4⋊C4—221no—
614C4⋊C4—221no—
615C4⋊C4—222no—
616C4⋊C4—222no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C22⋊C4—222no—
620C22⋊C4—222no—
621C22⋊C4—221no—
622C22⋊C4—221no—
623C22⋊C4—222no—
624C22⋊C4—222no—
625C22⋊C4—222no—
626C22⋊C4—222no—
627C22⋊C4—222no—
628C22⋊C4—222no—
629C22⋊C4—221no—
630C22⋊C4—222no—
631C22⋊C4—221no—
632C22⋊C4—222no—
633C42—221no—
634C42—221no—
635C11#1741111yescharacteristic, complemented, Sylow
636C23—22no—
637C23—22no—
638C23—24no—
639C23—21no—
640C23—21no—
641C23—42no—
642C23—41no—
643C23—41no—
644C23—112no—
645C23—221no—
646C23—221no—
647C23—222no—
648C23—222no—
649C23—222no—
650C23—444no—
651C23—444no—
652C23—441no—
653C23—441no—
654C23—444no—
655C23—442no—
656C23—442no—
657C23—444no—
658C23—882no—
659C23—882no—
660C23—888no—
661C23—888no—
662C23C2×(C2×D11)⋊C412yes—
663C23C2×(C2×D11)⋊C411yescharacteristic
664C23C2×(C2×D11)⋊C411yescharacteristic
665C23C2×(C2×D11)⋊C412yes—
666C23C22×C4×D1111yescharacteristic
667Q8—22no—
668Q8—22no—
669Q8—42no—
670D4—24no—
671D4—24no—
672D4—24no—
673D4—22no—
674D4—42no—
675D4—42no—
676D4—442no—
677D4—442no—
678D4—442no—
679D4—444no—
680D4—444no—
681D4—442no—
682D4—882no—
683D4—882no—
684D4#6687014yes—
685C2×C4—24no—
686C2×C4—24no—
687C2×C4—22no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—41no—
693C2×C4—42no—
694C2×C4—41no—
695C2×C4—42no—
696C2×C4—221no—
697C2×C4—221no—
698C2×C4—221no—
699C2×C4—221no—
700C2×C4—222no—
701C2×C4—221no—
702C2×C4—442no—
703C2×C4—442no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—442no—
707C2×C4—882no—
708C2×C4—882no—
709C2×C4C2×(C2×D11)⋊C411yescharacteristic
710C2×C4C2×(C2×D11)⋊C412yes—
711C2×C4C2×(C2×D11)⋊C412yes—
712C2×C4C2×(C2×D11)⋊C411yescharacteristic
713C2×C4C22×D4411yescharacteristic
714C2×C4C22×C22⋊D1111yescharacteristic
715C8—41no—
716C8—42no—
717C8—41no—
718C8—441no—
719C8—442no—
720C8—441no—
721C22—22no—
722C22—21no—
723C22—21no—
724C22—22no—
725C22—21no—
726C22—21no—
727C22—22no—
728C22—21no—
729C22—21no—
730C22—22no—
731C22—22no—
732C22—21no—
733C22—21no—
734C22—44no—
735C22—44no—
736C22—81no—
737C22—81no—
738C22—222no—
739C22—442no—
740C22—442no—
741C22—441no—
742C22—441no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—888no—
747C22—882no—
748C22—882no—
749C22—888no—
750C22C2×#6687014yes—
751C22D11×#13111yescharacteristic
752C22#1062328111yescharacteristic
753C22C22×(C2×D11)⋊C411yescharacteristic
754C4—21no—
755C4—21no—
756C4—21no—
757C4—22no—
758C4—22no—
759C4—441no—
760C4—441no—
761C4—441no—
762C4—442no—
763C4C2×#6687012yes—
764C2—21no—
765C2—21no—
766C2—24no—
767C2—42no—
768C2—41no—
769C2—41no—
770C2—442no—
771C2—882no—
772C2#1307706311yescharacteristic
773C2C22×#6687011yescharacteristic
774C2#1307709411yescharacteristic
subgroupG/H
centerC22C22×(C2×D11)⋊C4
commutatorC23×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#2880C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623360C2
cosocleC22×C4×C11C24
hypercenter#2880D11
hypocenterC11#17411
LCSG ▷ C23×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C22×#41 ◁ #2880

Complements

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

NH ≅ G/Ntype
2. #13077065C2semidirect
3. #13066977C2semidirect
4. #13066975C2semidirect
5. #13066965C2semidirect
6. #13066962C2semidirect
7. #13066952C2semidirect
8. #13066942C2semidirect
9. #13066932C2semidirect
10. C2×#10622106C2semidirect
11. C11×#2880C2semidirect
33. C11×#407C22semidirect
34. C11×#407C22semidirect
35. C2×C11×C22⋊C8C22semidirect
36. C2×C11×C22⋊C8C22semidirect
39. #10622820C22semidirect
40. #10622820C22semidirect
41. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×C22⋊(C11⋊C8)C22semidirect
43. #10622107C22semidirect
44. #10622107C22semidirect
45. #10622107C22semidirect
49. #10622106C22semidirect
50. #10622106C22semidirect
51. #10622106C22semidirect
52. #10622106C22semidirect
251. #2880D11semidirect
290. C22×D11#131semidirect
370. #407C2×D11semidirect
371. #407C2×D11semidirect
374. C2×C22⋊C8C2×D11semidirect
375. C2×C22⋊C8C2×D11semidirect
635. C11#17411semidirect

Maximal subgroups

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

subgroupindex
C2×#106233602
#130770652
#130669772
#130669752
#130669652
#130669622
#130669522
#130669422
#130669322
C2×#106221062
C11×#28802
#1741111