Finite Group Databasebeta

← #14720932

Subgroups — #14720932

Order 2816.

1574 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623137C211yesmaximal, characteristic
2D11×#407C211yesmaximal, characteristic, complemented
3C4×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4#13067137C211yesmaximal, characteristic, complemented
5#13067135C211yesmaximal, characteristic, complemented
6#13067132C211yesmaximal, characteristic, complemented
7#13067117C214yesmaximal, complemented
8#13067104C214yesmaximal, complemented
9C11×#1507C211yesmaximal, characteristic, complemented
10C22×#4341C411yescharacteristic, complemented
11C23×C4×D11C2211yescharacteristic
12C2×C11×#121C2211yescharacteristic
13C2×#66991C411yescharacteristic, complemented
14C2×#66990—21no—
15C2×D4×Dic11—21no—
16C2×#66977C2211yescharacteristic
17C2×M16×D11—21no—
18#10623137—21no—
19#10623137—21no—
20#10623137—21no—
21#10623137—21no—
22#10623137C412yescomplemented
23#10623137C412yescomplemented
24#10623137C2212yes—
25#10623137C2212yes—
26C2×#66950C411yescharacteristic, complemented
27C2×#66945C411yescharacteristic, complemented
28C2×#66936—21no—
29C2×(C22⋊D11)⋊C4—21no—
30C2×C22⋊C4×D11—21no—
31C2×C42×D11—21no—
32C11×#407C2211yescharacteristic
33C4×C11×C22⋊C4C2211yescharacteristic
34C4×C22⋊Dic11C2211yescharacteristic
35#10622820C2211yescharacteristic
36#10622739—21no—
37C22⋊C4×Dic11—21no—
38C4×(C2×D11)⋊C4—21no—
39#10622339—21no—
40#10622339C2212yescomplemented
41D11×C22⋊C8—21no—
42D11×C22⋊C8C2212yescomplemented
43#10622279C2212yescomplemented
44D11×#95C2212yescomplemented
45C11×#327C2214yescomplemented
46#10622175C2214yescomplemented
47#10622105C2214yescomplemented
48#10622090C2214yescomplemented
49C24×D11D411yescharacteristic
50C22×D4×C11—21no—
51C22×D4×C11C2×C411yescharacteristic, complemented
52C23×C4×C11C2311yescharacteristic
53C22×C22⋊D11—21no—
54C22×C22⋊D11—21no—
55C23×Dic11—21no—
56C23×Dic11D411yescharacteristic
57C2×#4341—21no—
58C2×#4341—21no—
59C2×#4341—44no—
60C2×#4341C2×C412yes—
61C2×#4341C2×C412yescomplemented
62C22×C4×D11—22no—
63C22×C4×D11—44no—
64C22×C4×D11C2×C411yescharacteristic
65C22×C4×D11C2×C411yescharacteristic
66C22×C4×D11C2×C411yescharacteristic
67C22×C4×D11C2×C411yescharacteristic
68C22×C4×D11D411yescharacteristic
69C22×C4×D11D411yescharacteristic
70C22×C4×D11D411yescharacteristic
71C22×C4×D11D411yescharacteristic
72C22×C4×D11D411yescharacteristic
73C22×C4×D11D411yescharacteristic
74C22×C4×D11C2311yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×Dic22C2×C411yescharacteristic, complemented
77C2×C11×M16—21no—
78C11×#121—21no—
79C11×#121—21no—
80C11×#121C2×C412yescomplemented
81C11×#121C2312yes—
82C2×C11×C4⋊C4C2×C411yescharacteristic, complemented
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×C22⋊Dic11—21no—
89#66991—21no—
90#66991—21no—
91#66991C2×C412yes—
92#66991C2×C412yescomplemented
93#66990—22no—
94#66990—22no—
95#66990—22no—
96#66990—22no—
97D4×Dic11—22no—
98D4×Dic11—22no—
99D4×Dic11—22no—
100D4×Dic11—22no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—22no—
104C2×C4⋊Dic11—21no—
105C2×C4⋊Dic11C2×C411yescharacteristic, complemented
106#66977—21no—
107#66977—21no—
108#66977C2×C412yescomplemented
109#66977C2312yes—
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11—21no—
113C2×C4×Dic11—22no—
114C2×#4318—21no—
115M16×D11—44no—
116C2×#4313—22no—
117C2×C8×D11—22no—
118#66950—21no—
119#66950—21no—
120#66950C2×C412yes—
121#66950C2×C412yescomplemented
122#66945—21no—
123#66945—21no—
124#66945C2×C412yes—
125#66945C2×C412yescomplemented
126#66936—22no—
127#66936—22no—
128#66936—22no—
129#66936—22no—
130(C22⋊D11)⋊C4—22no—
131(C22⋊D11)⋊C4—22no—
132(C22⋊D11)⋊C4—22no—
133(C22⋊D11)⋊C4—22no—
134C22⋊C4×D11—28no—
135C42×D11—44no—
136C11×C22⋊C8—21no—
137C11×C22⋊C8C2312yes—
138C11×#95C2312yes—
139C11⋊#95—22no—
140C11⋊#95C2312yes—
141C22⋊(C11⋊C8)—21no—
142C22⋊(C11⋊C8)C2312yes—
143(C2×D11)⋊C8—22no—
144(C2×D11)⋊C8—22no—
145#17542—111nomaximal, Sylow
146C24×C11—21no—
147C24×C11C2×D411yescharacteristic
148C23×D11—24no—
149C23×D11—42no—
150C23×D11—42no—
151C23×D11C22⋊C411yescharacteristic
152C23×D11C22⋊C411yescharacteristic
153C23×D11C22⋊C411yescharacteristic
154C23×D11C22⋊C411yescharacteristic
155C23×D11C2×D411yescharacteristic
156C23×D11C2×D411yescharacteristic
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—42no—
161C2×D4×C11—44no—
162C2×D4×C11C22×C412yes—
163C22×C4×C11—21no—
164C22×C4×C11—22no—
165C22×C4×C11—42no—
166C22×C4×C11C22×C411yescharacteristic
167C22×C4×C11C22×C411yescharacteristic
168C22×C4×C11C2×D411yescharacteristic
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—22no—
173C2×C22⋊D11—22no—
174C2×C22⋊D11—22no—
175C2×C22⋊D11—22no—
176C2×C22⋊D11—44no—
177C2×C22⋊D11—44no—
178C22×Dic11—22no—
179C22×Dic11—22no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C22×Dic11—22no—
183C22×Dic11—42no—
184C22×Dic11—44no—
185C22×Dic11C22⋊C411yescharacteristic
186C22×Dic11C22⋊C411yescharacteristic
187C22×Dic11C22⋊C411yescharacteristic
188C22×Dic11C22⋊C411yescharacteristic
189C22×Dic11C2×D411yescharacteristic
190C22×Dic11C2×D411yescharacteristic
191#4341—44no—
192#4341—44no—
193#4341—44no—
194#4341—44no—
195C2×C4×D11—24no—
196C2×C4×D11—24no—
197C2×C4×D11—24no—
198C2×C4×D11—28no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—42no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—44no—
206C2×C4×D11—44no—
207C2×C4×D11—42no—
208C2×C4×D11—42no—
209C2×C4×D11—42no—
210C2×C4×D11C22⋊C411yescharacteristic
211C2×C4×D11C22⋊C411yescharacteristic
212C2×C4×D11C22⋊C411yescharacteristic
213C2×C4×D11C22⋊C411yescharacteristic
214C2×C4×D11C22⋊C411yescharacteristic
215C2×C4×D11C22⋊C411yescharacteristic
216C2×C4×D11C22⋊C411yescharacteristic
217C2×C4×D11C22⋊C411yescharacteristic
218C2×C4×D11C22×C411yescharacteristic
219C2×C4×D11C22×C411yescharacteristic
220C2×C4×D11C22×C411yescharacteristic
221C2×C4×D11C22×C411yescharacteristic
222C2×C4×D11C2×D411yescharacteristic
223C2×C4×D11C2×D411yescharacteristic
224C2×C4×D11C2×D411yescharacteristic
225C2×C4×D11C2×D411yescharacteristic
226C2×Dic22—21no—
227C2×Dic22—42no—
228C2×Dic22C22×C412yes—
229C11×M16—42no—
230C2×C8×C11—22no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4C22×C412yes—
233C11×C22⋊C4—24no—
234C11×C22⋊C4—22no—
235C11×C22⋊C4—22no—
236C42×C11—42no—
237C22⋊Dic11—24no—
238C22⋊Dic11—22no—
239C22⋊Dic11—22no—
240C22⋊Dic11—22no—
241C22⋊Dic11—22no—
242(C2×D11)⋊C4—28no—
243(C2×D11)⋊C4—22no—
244(C2×D11)⋊C4—22no—
245(C2×D11)⋊C4—22no—
246(C2×D11)⋊C4—22no—
247C4⋊Dic11—22no—
248C4⋊Dic11—22no—
249C4⋊Dic11—21no—
250C4⋊Dic11C22×C412yes—
251Dic11⋊C4—22no—
252Dic11⋊C4—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255C4×Dic11—42no—
256C4×Dic11—44no—
257#4318—42no—
258C2×C11⋊C8—22no—
259#4313—44no—
260C8×D11—44no—
261C2×#525—111no—
262C2×#407—111no—
263C2×C4×C22⋊C4—111no—
264#1508—111no—
265#1508—111no—
266#1507—111no—
267#1507D1111yescharacteristic, complemented
268#1504—114no—
269#1501—114no—
270C23×C11—22no—
271C23×C11—22no—
272C23×C11—22no—
273C23×C11—41no—
274C23×C11—42no—
275C23×C11—42no—
276C23×C11—42no—
277C23×C11C2×C22⋊C411yescharacteristic
278C23×C11C2×C22⋊C411yescharacteristic
279C23×C11C22×D411yescharacteristic
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—22no—
283C22×D11—22no—
284C22×D11—22no—
285C22×D11—22no—
286C22×D11—22no—
287C22×D11—22no—
288C22×D11—22no—
289C22×D11—22no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—416no—
298C22×D11#10414yes—
299C22×D11C2×C22⋊C411yescharacteristic
300C22×D11C2×C22⋊C411yescharacteristic
301C22×D11C2×C22⋊C411yescharacteristic
302C22×D11C2×C22⋊C411yescharacteristic
303D4×C11—42no—
304D4×C11—44no—
305D4×C11—44no—
306D4×C11—42no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11—22no—
310C2×C4×C11—24no—
311C2×C4×C11—22no—
312C2×C4×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11—41no—
315C2×C4×C11—42no—
316C2×C4×C11—42no—
317C2×C4×C11—42no—
318C2×C4×C11C2×C22⋊C411yescharacteristic
319C2×C4×C11C2×C22⋊C411yescharacteristic
320C2×C4×C11C23×C411yescharacteristic
321C2×C4×C11C22×D411yescharacteristic
322C22⋊D11—44no—
323C22⋊D11—44no—
324C22⋊D11—44no—
325C22⋊D11—44no—
326C2×Dic11—22no—
327C2×Dic11—22no—
328C2×Dic11—22no—
329C2×Dic11—24no—
330C2×Dic11—22no—
331C2×Dic11—22no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—44no—
336C2×Dic11—42no—
337C2×Dic11—42no—
338C2×Dic11—42no—
339C2×Dic11—42no—
340C2×Dic11—44no—
341C2×Dic11C2×C22⋊C411yescharacteristic
342C2×Dic11C2×C22⋊C411yescharacteristic
343C2×Dic11C2×C22⋊C411yescharacteristic
344C2×Dic11C2×C22⋊C411yescharacteristic
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—22no—
349C4×D11—22no—
350C4×D11—22no—
351C4×D11—22no—
352C4×D11—22no—
353C4×D11—22no—
354C4×D11—41no—
355C4×D11—41no—
356C4×D11—41no—
357C4×D11—41no—
358C4×D11—41no—
359C4×D11—41no—
360C4×D11—416no—
361C4×D11#9914yes—
362Dic22—42no—
363Dic22—42no—
364C8×C11—42no—
365C11⋊C8—42no—
366C22×#41—111no—
367C24×C4—111no—
368C22×M16—221no—
369#525—112no—
370#525—112no—
371#525—112no—
372#525—112no—
373#525—221no—
374#525—221no—
375#525—221no—
376#525—221no—
377C2×#123—221no—
378C2×C22⋊Q8—111no—
379C2×C22⋊Q8—111no—
380C2×#121—111no—
381C2×#121C2×D1111yescharacteristic
382C2×#120—221no—
383C2×C4×D4—221no—
384C2×C4×D4—221no—
385C2×#117—111no—
386C22×C22⋊C4—221no—
387C22×C42—221no—
388#407—111no—
389#407—112no—
390#407—221no—
391#407—221no—
392#407C2×D1111yescharacteristic
393C2×C22⋊C8—112no—
394C2×C22⋊C8—221no—
395C4×C22⋊C4—111no—
396C4×C22⋊C4—112no—
397C4×C22⋊C4—221no—
398C4×C22⋊C4—221no—
399C4×C22⋊C4C2×D1111yescharacteristic
400C2×#95—112no—
401#328—114no—
402#328—114no—
403#327—114no—
404#327C2×D1114yescomplemented
405C22×C11—21no—
406C22×C11—21no—
407C22×C11—21no—
408C22×C11—21no—
409C22×C11—21no—
410C22×C11—21no—
411C22×C11—21no—
412C22×C11—44no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—84no—
417C22×C11C2×#10412yes—
418C22×C11C22×C22⋊C411yescharacteristic
419C22×C11#57512yes—
420C2×D11—28no—
421C2×D11—21no—
422C2×D11—21no—
423C2×D11—21no—
424C2×D11—21no—
425C2×D11—21no—
426C2×D11—21no—
427C2×D11—21no—
428C2×D11—21no—
429C2×D11—21no—
430C2×D11—44no—
431C2×D11—44no—
432C2×D11—44no—
433C2×D11—44no—
434C2×D11—44no—
435C2×D11C2×#9912yes—
436C2×D11C2×#10412yes—
437C2×D11C2×#10412yes—
438C4×C11—21no—
439C4×C11—21no—
440C4×C11—21no—
441C4×C11—44no—
442C4×C11—42no—
443C4×C11C2×#9912yes—
444Dic11—21no—
445Dic11—21no—
446Dic11—21no—
447Dic11—44no—
448Dic11—42no—
449Dic11—42no—
450Dic11C2×#9912yes—
451C25—111no—
452C2×#41—112no—
453C2×#41—112no—
454C2×#41—221no—
455C2×#41—221no—
456C2×#41—444no—
457C22×Q8—111no—
458C22×D4—21no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4C4×D1111yescharacteristic, complemented
462C23×C4—111no—
463C23×C4—111no—
464C23×C4—111no—
465C23×C4—111no—
466C23×C4—111no—
467C23×C4—111no—
468C23×C4—111no—
469C23×C4—111no—
470C23×C4—111no—
471C23×C4—111no—
472C23×C4—111no—
473C23×C4—111no—
474C23×C4—111no—
475C23×C4—222no—
476C23×C4—221no—
477C23×C4—444no—
478C23×C4C22×D1111yescharacteristic
479C2×M16—21no—
480C2×M16—222no—
481C2×M16—221no—
482C2×M16—444no—
483C22×C8—222no—
484#123—222no—
485#123—222no—
486#123—222no—
487#123—222no—
488C22⋊Q8—112no—
489C22⋊Q8—112no—
490C22⋊Q8—112no—
491C22⋊Q8—112no—
492C22⋊Q8—221no—
493C22⋊Q8—221no—
494C22⋊Q8—221no—
495C22⋊Q8—221no—
496#121—21no—
497#121—21no—
498#121—112no—
499#121—112no—
500#121—221no—
501#121—221no—
502#121C4×D1112yescomplemented
503#121C22×D1112yes—
504#120—222no—
505#120—222no—
506#120—222no—
507#120—222no—
508C4×D4—222no—
509C4×D4—222no—
510C4×D4—222no—
511C4×D4—222no—
512C4×D4—222no—
513C4×D4—222no—
514C4×D4—222no—
515C4×D4—222no—
516#117—112no—
517#117—112no—
518#117—221no—
519#117—221no—
520C2×C4⋊C4—111no—
521C2×C4⋊C4—221no—
522C2×C4⋊C4—221no—
523C2×C4⋊C4C4×D1111yescharacteristic, complemented
524C2×C22⋊C4—21no—
525C2×C22⋊C4—21no—
526C2×C22⋊C4—228no—
527C2×C22⋊C4—222no—
528C2×C22⋊C4—221no—
529C2×C22⋊C4—221no—
530C2×C22⋊C4—221no—
531C2×C22⋊C4—221no—
532C2×C22⋊C4—221no—
533C2×C42—21no—
534C2×C42—221no—
535C2×C42—222no—
536C2×C42—221no—
537C2×C42—444no—
538C22⋊C8—21no—
539C22⋊C8—112no—
540C22⋊C8—222no—
541C22⋊C8—222no—
542C22⋊C8—221no—
543C22⋊C8C22×D1112yes—
544#95—112no—
545#95—222no—
546#95C22×D1112yes—
547C2×C11—22no—
548C2×C11—22no—
549C2×C11—41no—
550C2×C11—82no—
551C2×C11C22×#9911yescharacteristic
552C2×C11#289611yescharacteristic
553C2×C11C22×#10411yescharacteristic
554D11—22no—
555D11—22no—
556D11—22no—
557D11—41no—
558C24—21no—
559C24—111no—
560C24—111no—
561C24—111no—
562C24—111no—
563C24—111no—
564C24—111no—
565C24—224no—
566C24—442no—
567C24—442no—
568C24D4×D1111yescharacteristic
569#41—444no—
570#41—444no—
571#41—444no—
572#41—444no—
573C2×Q8—112no—
574C2×Q8—221no—
575C2×Q8—442no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—21no—
579C2×D4—42no—
580C2×D4—44no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—444no—
586C2×D4—444no—
587C2×D4C2×C4×D1112yes—
588C22×C4—21no—
589C22×C4—22no—
590C22×C4—42no—
591C22×C4—111no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—111no—
596C22×C4—111no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—111no—
601C22×C4—111no—
602C22×C4—111no—
603C22×C4—111no—
604C22×C4—111no—
605C22×C4—111no—
606C22×C4—111no—
607C22×C4—111no—
608C22×C4—111no—
609C22×C4—111no—
610C22×C4—111no—
611C22×C4—111no—
612C22×C4—111no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—228no—
617C22×C4—222no—
618C22×C4—222no—
619C22×C4—221no—
620C22×C4—221no—
621C22×C4—222no—
622C22×C4—442no—
623C22×C4—442no—
624C22×C4—442no—
625C22×C4—442no—
626C22×C4—442no—
627C22×C4—442no—
628C22×C4—442no—
629C22×C4—442no—
630C22×C4—442no—
631C22×C4—444no—
632C22×C4—444no—
633C22×C4—442no—
634C22×C4—444no—
635C22×C4C2×C4×D1111yescharacteristic
636C22×C4C2×C4×D1111yescharacteristic
637C22×C4D4×D1111yescharacteristic
638C22×C4D4×D1111yescharacteristic
639C22×C4D4×D1111yescharacteristic
640C22×C4C23×D1111yescharacteristic
641M16—42no—
642M16—444no—
643M16—442no—
644C2×C8—22no—
645C2×C8—222no—
646C2×C8—444no—
647C4⋊C4—21no—
648C4⋊C4—112no—
649C4⋊C4—222no—
650C4⋊C4—222no—
651C4⋊C4—221no—
652C4⋊C4—222no—
653C4⋊C4—222no—
654C4⋊C4C2×C4×D1112yes—
655C22⋊C4—24no—
656C22⋊C4—22no—
657C22⋊C4—22no—
658C22⋊C4—222no—
659C22⋊C4—222no—
660C22⋊C4—222no—
661C22⋊C4—222no—
662C22⋊C4—228no—
663C22⋊C4—222no—
664C22⋊C4—222no—
665C22⋊C4—224no—
666C22⋊C4—222no—
667C22⋊C4—222no—
668C42—42no—
669C42—222no—
670C42—222no—
671C42—442no—
672C42—444no—
673C11#1754211yescharacteristic, complemented, Sylow
674C23—22no—
675C23—22no—
676C23—22no—
677C23—41no—
678C23—42no—
679C23—42no—
680C23—42no—
681C23—111no—
682C23—111no—
683C23—111no—
684C23—114no—
685C23—111no—
686C23—222no—
687C23—222no—
688C23—222no—
689C23—222no—
690C23—222no—
691C23—222no—
692C23—222no—
693C23—222no—
694C23—222no—
695C23—222no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—441no—
700C23—441no—
701C23—441no—
702C23—441no—
703C23—4416no—
704C23C22⋊C4×D1111yescharacteristic
705C23C22⋊C4×D1111yescharacteristic
706C23C2×D4×D1111yescharacteristic
707Q8—442no—
708Q8—442no—
709D4—42no—
710D4—44no—
711D4—44no—
712D4—42no—
713D4—444no—
714D4—444no—
715D4—444no—
716D4—444no—
717C2×C4—22no—
718C2×C4—22no—
719C2×C4—22no—
720C2×C4—24no—
721C2×C4—22no—
722C2×C4—41no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—42no—
726C2×C4—42no—
727C2×C4—42no—
728C2×C4—111no—
729C2×C4—114no—
730C2×C4—111no—
731C2×C4—111no—
732C2×C4—111no—
733C2×C4—222no—
734C2×C4—222no—
735C2×C4—222no—
736C2×C4—222no—
737C2×C4—222no—
738C2×C4—222no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—222no—
745C2×C4—224no—
746C2×C4—222no—
747C2×C4—222no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—4416no—
755C2×C4—444no—
756C2×C4—441no—
757C2×C4—441no—
758C2×C4—441no—
759C2×C4—444no—
760C2×C4—442no—
761C2×C4—442no—
762C2×C4—442no—
763C2×C4—442no—
764C2×C4C22⋊C4×D1111yescharacteristic
765C2×C4C22⋊C4×D1111yescharacteristic
766C2×C4C22×C4×D1111yescharacteristic
767C2×C4C2×D4×D1111yescharacteristic
768C8—42no—
769C8—442no—
770C22—21no—
771C22—21no—
772C22—21no—
773C22—21no—
774C22—21no—
775C22—21no—
776C22—21no—
777C22—44no—
778C22—42no—
779C22—42no—
780C22—42no—
781C22—84no—
782C22—112no—
783C22—112no—
784C22—112no—
785C22—228no—
786C22—221no—
787C22—221no—
788C22—221no—
789C22—221no—
790C22—221no—
791C22—221no—
792C22—221no—
793C22—221no—
794C22—221no—
795C22—444no—
796C22—444no—
797C22—444no—
798C22—444no—
799C22—444no—
800C22D11×#10412yes—
801C22C2×C22⋊C4×D1111yescharacteristic
802C22#1062330412yes—
803C4—21no—
804C4—21no—
805C4—21no—
806C4—44no—
807C4—42no—
808C4—112no—
809C4—221no—
810C4—221no—
811C4—221no—
812C4—444no—
813C4—442no—
814C4—442no—
815C4D11×#9912yes—
816C2—22no—
817C2—22no—
818C2—41no—
819C2—82no—
820C2—222no—
821C2—222no—
822C2—222no—
823C2—441no—
824C2C2×D11×#9911yescharacteristic
825C2#1307713011yescharacteristic
826C2C2×D11×#10411yescharacteristic
subgroupG/H
centerC22C2×C22⋊C4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1507C2
socleC22×C11C22×C22⋊C4
prime radicalC2×#10623137C2
cosocleC22×C4×C11C24
hypercenter#1507D11
hypocenterC11#17542
LCSG ▷ C2×C4×C11 ▷ C22×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #1507

Complements

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

NH ≅ G/Ntype
2. D11×#407C2semidirect
3. C4×C22⋊C4×D11C2semidirect
4. #13067137C2semidirect
5. #13067135C2semidirect
6. #13067132C2semidirect
7. #13067117C2semidirect
8. #13067104C2semidirect
9. C11×#1507C2semidirect
10. C22×#4341C4semidirect
13. C2×#66991C4semidirect
22. #10623137C4semidirect
23. #10623137C4semidirect
26. C2×#66950C4semidirect
27. C2×#66945C4semidirect
40. #10622339C22semidirect
42. D11×C22⋊C8C22semidirect
43. #10622279C22semidirect
44. D11×#95C22semidirect
45. C11×#327C22semidirect
46. #10622175C22semidirect
47. #10622105C22semidirect
48. #10622090C22semidirect
51. C22×D4×C11C2×C4semidirect
61. C2×#4341C2×C4semidirect
76. C22×Dic22C2×C4semidirect
80. C11×#121C2×C4semidirect
82. C2×C11×C4⋊C4C2×C4semidirect
92. #66991C2×C4semidirect
105. C2×C4⋊Dic11C2×C4semidirect
108. #66977C2×C4semidirect
121. #66950C2×C4semidirect
125. #66945C2×C4semidirect
267. #1507D11semidirect
404. #327C2×D11semidirect
461. C22×D4C4×D11semidirect
502. #121C4×D11semidirect
523. C2×C4⋊C4C4×D11semidirect
673. C11#17542semidirect

Maximal subgroups

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

subgroupindex
C2×#106231372
D11×#4072
C4×C22⋊C4×D112
#130671372
#130671352
#130671322
#130671172
#130671042
C11×#15072
#1754211