Finite Group Databasebeta

← #15620298

Subgroups — #15620298

Order 2816.

5126 conjugacy classes of subgroups.

The subgroup lattice has 1220 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#67037C211yesmaximal, characteristic, complemented
2C2×#10623288C212yesmaximal, complemented
3#13082281C211yesmaximal, characteristic, complemented
4#13077925C212yesmaximal, complemented
5#13077915C214yesmaximal, complemented
6#13077880C212yesmaximal, complemented
7#13077879C214yesmaximal, complemented
8#13077866C211yesmaximal, characteristic, complemented
9#13077863C212yesmaximal, complemented
10#13077843C211yesmaximal, characteristic, complemented
11#13077840C212yesmaximal, complemented
12#13077838C211yesmaximal, characteristic, complemented
13#13077829C212yesmaximal, complemented
14D11×#447C212yesmaximal, complemented
15#13077137C212yesmaximal, complemented
16#13077062C211yesmaximal, characteristic, complemented
17C2×C11×#447C211yesmaximal, characteristic, complemented
18C23×D4×C11C2211yescharacteristic, complemented
19C23×C22⋊D11—22no—
20C2×#67037—216no—
21C2×#67037—22no—
22C2×#67037—21no—
23C2×#67037—21no—
24C2×#67037C2212yes—
25C2×#67037C2214yescomplemented
26C2×#67037C2212yescomplemented
27C2×#67037C2211yescharacteristic, complemented
28C22×#4341—21no—
29C22×#4341C2212yescomplemented
30C22×D4×D11—21no—
31C22×D4×D11C2212yescomplemented
32C22×#4339C2211yescharacteristic
33C22×#4339C2211yescharacteristic, complemented
34C22×C11×D8C2212yescomplemented
35C2×C11×#121C2211yescharacteristic, complemented
36#10623336C2211yescharacteristic, complemented
37D4×C22⋊D11—22no—
38C2×#66985C2212yescomplemented
39C2×#66985C2212yescomplemented
40#10623322C2211yescharacteristic, complemented
41#10623288—216no—
42C2×#66965C2214yescomplemented
43C2×#66964C2214yescomplemented
44C2×#66964C2214yescomplemented
45C2×D8×D11C2214yescomplemented
46C2×#66957C2212yescomplemented
47C2×#66954C2212yescomplemented
48#10623143—21no—
49#10623140—21no—
50#10623139C2212yescomplemented
51#10623138C2212yescomplemented
52#10623137C2212yescomplemented
53D11×#121C2212yescomplemented
54#10623130—21no—
55#10623129—21no—
56#10623041C2211yescharacteristic, complemented
57#10623035C2211yescharacteristic, complemented
58#10623021—22no—
59C11×#447C2212yescomplemented
60C11×#447C2212yescomplemented
61C11×#447C2214yescomplemented
62C2×C11×#102C2212yescomplemented
63C2×C11×C22⋊C8C2211yescharacteristic, complemented
64#10622831C2212yescomplemented
65#10622831C2212yescomplemented
66#10622830C2212yescomplemented
67#10622830C2212yescomplemented
68#10622828C2212yescomplemented
69#10622820C2211yescharacteristic, complemented
70#10622771C2214yescomplemented
71#10622771C2214yescomplemented
72#10622769C2214yescomplemented
73#10622769C2214yescomplemented
74#10622726C2212yescomplemented
75#10622723C2212yescomplemented
76#10622653C2212yescomplemented
77#10622650C2214yescomplemented
78#10622649C2212yescomplemented
79#10622579C2212yescomplemented
80#10622396C2214yescomplemented
81#10622394C2214yescomplemented
82#10622389C2214yescomplemented
83#10622386C2214yescomplemented
84#10622385C2214yescomplemented
85#10622384C2214yescomplemented
86#10622383C2214yescomplemented
87D11×#102C2214yescomplemented
88#10622352C2211yescharacteristic, complemented
89#10622351C2211yescharacteristic, complemented
90#10622347C2212yescomplemented
91#10622346C2212yescomplemented
92#10622345C2211yescharacteristic, complemented
93#10622344C2211yescharacteristic, complemented
94#10622340C2214yescomplemented
95#10622339C2212yescomplemented
96D11×C22⋊C8C2212yescomplemented
97C25×C11—21no—
98C24×D11—22no—
99C22×D4×C11—28no—
100C22×D4×C11—21no—
101C22×D4×C11—21no—
102C22×D4×C11—21no—
103C22×D4×C11—21no—
104C22×D4×C11C2312yes—
105C22×D4×C11C2312yes—
106C22×D4×C11C2312yes—
107C22×D4×C11C2311yescharacteristic, complemented
108C23×C4×C11C2311yescharacteristic
109C22×C22⋊D11—232no—
110C22×C22⋊D11—21no—
111C22×C22⋊D11—22no—
112C22×C22⋊D11—24no—
113C22×C22⋊D11—24no—
114C22×C22⋊D11—24no—
115C22×C22⋊D11—24no—
116C22×C22⋊D11—22no—
117C22×C22⋊D11—22no—
118C22×C22⋊D11D412yes—
119C23×Dic11—22no—
120#67037—232no—
121#67037—216no—
122#67037—216no—
123#67037—28no—
124#67037—216no—
125#67037—216no—
126#67037—28no—
127#67037—28no—
128#67037—28no—
129#67037D4116yescomplemented
130C2×#4341—216no—
131C2×#4341—216no—
132C2×#4341—22no—
133C2×#4341—22no—
134C2×#4341—22no—
135C2×#4341—24no—
136C2×#4341—22no—
137C2×#4341—21no—
138C2×#4341C2314yes—
139C2×#4341C2314yes—
140C2×#4341C2312yescomplemented
141C2×D4×D11—216no—
142C2×D4×D11—216no—
143C2×D4×D11—22no—
144C2×D4×D11—22no—
145C2×D4×D11—24no—
146C2×D4×D11—22no—
147C2×D4×D11—21no—
148C2×D4×D11—22no—
149C2×D4×D11—22no—
150C2×D4×D11C2314yes—
151C2×D4×D11C2314yes—
152C2×D4×D11C2312yescomplemented
153C2×#4339—21no—
154C2×#4339—21no—
155C2×#4339—28no—
156C2×#4339—28no—
157C2×#4339D412yes—
158C2×#4339D411yescharacteristic
159C2×#4339D411yescharacteristic
160C2×#4339C2311yescharacteristic
161C2×#4339C2312yes—
162C2×#4339C2311yescharacteristic
163C2×#4339C2312yes—
164C2×#4339C2312yes—
165C2×#4339C2311yescharacteristic, complemented
166C22×D44D411yescharacteristic
167C22×D44C2311yescharacteristic
168C22×C4×D11—21no—
169C22×C4×D11C2312yes—
170C22×Dic22D411yescharacteristic
171C22×Dic22C2311yescharacteristic
172C2×C11×D8—28no—
173C2×C11×D8C2314yescomplemented
174C2×C11×D8C2314yescomplemented
175C22×C8×C11C2312yescomplemented
176C11×#121—21no—
177C11×#121—21no—
178C11×#121C2312yes—
179C11×#121C2312yescomplemented
180C2×C11×C4⋊C4C2311yescharacteristic, complemented
181C2×C11×C22⋊C4—21no—
182#67006—21no—
183#67006—22no—
184#66993—22no—
185#66993—21no—
186#66992—22no—
187#66992—22no—
188#66991—22no—
189#66991C2312yescomplemented
190#66991C2312yescomplemented
191#66990—22no—
192#66990—22no—
193#66989—21no—
194D4×Dic11—22no—
195C2×#4324C2314yescomplemented
196C2×#4324C2314yescomplemented
197#66985—28no—
198#66985—28no—
199C2×#4323C2314yescomplemented
200C2×#4323C2314yescomplemented
201#66983—22no—
202#66983C2311yescharacteristic
203#66983C2311yescharacteristic, complemented
204#66982—21no—
205C4×C22⋊D11—21no—
206C4×C22⋊D11—21no—
207C4×C22⋊D11—22no—
208#66979C2311yescharacteristic, complemented
209#66977C2311yescharacteristic
210#66977C2311yescharacteristic, complemented
211C2×#4318C2312yescomplemented
212#66965—216no—
213#66964—216no—
214#66964—216no—
215D8×D11—216no—
216C2×Dic44C2312yescomplemented
217#66957—28no—
218C2×D88C2312yescomplemented
219C2×#4314C2312yescomplemented
220C2×#4314C2312yescomplemented
221#66954—28no—
222C2×#4313C2314yescomplemented
223C2×C8×D11C2314yescomplemented
224#66950—21no—
225#66950C2312yescomplemented
226#66948—21no—
227#66948C2312yescomplemented
228#66946—21no—
229#66945C2312yescomplemented
230C4⋊C4×D11C2312yescomplemented
231#66940—21no—
232#66938—22no—
233#66937—22no—
234#66937—22no—
235#66936—22no—
236#66935—22no—
237(C22⋊D11)⋊C4—22no—
238C22⋊C4×D11—22no—
239#66931—22no—
240C11×#102C2314yescomplemented
241C11×#102C2314yescomplemented
242C11×C22⋊C8C2311yescharacteristic
243C11×C22⋊C8C2311yescharacteristic
244C11×C22⋊C8C2312yescomplemented
245#66896C2314yescomplemented
246#66896C2314yescomplemented
247C22⋊(C11⋊C8)C2312yes—
248C22⋊(C11⋊C8)C2312yescomplemented
249#66885C2312yescomplemented
250#66885C2312yescomplemented
251(C2×D11)⋊C8C2314yescomplemented
252(C2×D11)⋊C8C2314yescomplemented
253#66880C2312yescomplemented
254#66880C2312yescomplemented
255#66874C2314yescomplemented
256#66873C2314yescomplemented
257#60372—111nomaximal, Sylow
258C24×C11—28no—
259C24×C11—22no—
260C24×C11—22no—
261C24×C11—22no—
262C24×C11—21no—
263C24×C11—82no—
264C24×C11—82no—
265C24×C11C2×D411yescharacteristic
266C23×D11—21no—
267C23×D11—216no—
268C23×D11—24no—
269C23×D11—24no—
270C23×D11—22no—
271C23×D11—84no—
272C23×D11—84no—
273C23×D11C2×D412yes—
274C2×D4×C11—28no—
275C2×D4×C11—28no—
276C2×D4×C11—28no—
277C2×D4×C11—28no—
278C2×D4×C11—28no—
279C2×D4×C11—22no—
280C2×D4×C11—22no—
281C2×D4×C11—22no—
282C2×D4×C11—22no—
283C2×D4×C11—22no—
284C2×D4×C11—24no—
285C2×D4×C11—24no—
286C2×D4×C11—21no—
287C2×D4×C11—82no—
288C2×D4×C11C2×D418yescomplemented
289C2×D4×C11C2412yes—
290C2×D4×C11C2414yes—
291C22×C4×C11—24no—
292C22×C4×C11—21no—
293C22×C4×C11C2×D411yescharacteristic
294C22×C4×C11C2×D411yescharacteristic
295C22×C4×C11C2×D411yescharacteristic
296C22×C4×C11C2411yescharacteristic
297C22×C4×C11C2411yescharacteristic
298C22×C4×C11C2411yescharacteristic
299C2×C22⋊D11—28no—
300C2×C22⋊D11—216no—
301C2×C22⋊D11—216no—
302C2×C22⋊D11—232no—
303C2×C22⋊D11—232no—
304C2×C22⋊D11—232no—
305C2×C22⋊D11—28no—
306C2×C22⋊D11—232no—
307C2×C22⋊D11—24no—
308C2×C22⋊D11—24no—
309C2×C22⋊D11—22no—
310C2×C22⋊D11—22no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—21no—
313C2×C22⋊D11—21no—
314C2×C22⋊D11—21no—
315C2×C22⋊D11—24no—
316C2×C22⋊D11—24no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—22no—
319C2×C22⋊D11—22no—
320C2×C22⋊D11—48no—
321C2×C22⋊D11C2×D412yes—
322C2×C22⋊D11C2×D412yes—
323C2×C22⋊D11C2×D412yes—
324C2×C22⋊D11C2×D412yes—
325C22×Dic11—216no—
326C22×Dic11—24no—
327C22×Dic11—24no—
328C22×Dic11—22no—
329C22×Dic11—21no—
330C22×Dic11C2×D412yes—
331#4341—216no—
332#4341—216no—
333#4341—232no—
334#4341—216no—
335#4341—28no—
336#4341—28no—
337#4341—216no—
338#4341—28no—
339#4341—28no—
340#4341—44no—
341#4341C2×D4116yescomplemented
342D4×D11—216no—
343D4×D11—232no—
344D4×D11—216no—
345D4×D11—216no—
346D4×D11—216no—
347D4×D11—28no—
348D4×D11—28no—
349D4×D11—28no—
350D4×D11—28no—
351D4×D11—44no—
352D4×D11—84no—
353D4×D11C2×D4116yescomplemented
354#4339—28no—
355#4339—28no—
356#4339—28no—
357#4339—24no—
358#4339—24no—
359#4339—28no—
360#4339—24no—
361#4339—24no—
362#4339—24no—
363#4339—24no—
364#4339—24no—
365#4339C2×D418yes—
366#4339C2×D418yescomplemented
367C2×D44—24no—
368C2×D44—24no—
369C2×D44—22no—
370C2×D44—21no—
371C2×D44C2×D412yes—
372C2×D44C2×D411yescharacteristic
373C2×D44C2×D411yescharacteristic
374C2×D44C2411yescharacteristic
375C2×D44C2412yes—
376C2×C4×D11—28no—
377C2×C4×D11—28no—
378C2×C4×D11—22no—
379C2×C4×D11—22no—
380C2×C4×D11—22no—
381C2×C4×D11—21no—
382C2×C4×D11C2×D412yes—
383C2×C4×D11C2×D412yes—
384C2×C4×D11C2412yes—
385C2×C4×D11C2412yes—
386C2×Dic22—24no—
387C2×Dic22—24no—
388C2×Dic22—21no—
389C2×Dic22C2×D412yes—
390C2×Dic22C2×D411yescharacteristic
391C2×Dic22C2×D411yescharacteristic
392C2×Dic22C2411yescharacteristic
393C2×Dic22C2412yes—
394C11×D8—28no—
395C11×D8—28no—
396C2×C8×C11—24no—
397C2×C8×C11C2412yes—
398C2×C8×C11C2412yes—
399C11×C4⋊C4—21no—
400C11×C4⋊C4C2412yes—
401C11×C22⋊C4—22no—
402C11×C22⋊C4—22no—
403C22⋊Dic11—22no—
404C22⋊Dic11—22no—
405C22⋊Dic11—21no—
406C22⋊Dic11—21no—
407C22⋊Dic11—21no—
408#4324—28no—
409#4324—28no—
410#4323—28no—
411#4323—28no—
412(C2×D11)⋊C4—22no—
413(C2×D11)⋊C4—22no—
414(C2×D11)⋊C4—22no—
415(C2×D11)⋊C4—21no—
416(C2×D11)⋊C4—21no—
417C4⋊Dic11—22no—
418C4⋊Dic11C2411yescharacteristic
419C4⋊Dic11C2411yescharacteristic
420Dic11⋊C4—22no—
421Dic11⋊C4—21no—
422Dic11⋊C4—21no—
423C4×Dic11—22no—
424C4×Dic11—21no—
425#4318—24no—
426C2×C11⋊C8C2414yes—
427Dic44—24no—
428D88—24no—
429#4314—24no—
430#4314—24no—
431#4313—28no—
432C8×D11—28no—
433C22×H(5,𝔽2)—111no—
434C2×#576—112no—
435#3488—111no—
436#3012—114no—
437#3012—112no—
438#3008—114no—
439#3008—112no—
440#3006—112no—
441#3006—111no—
442#3003—112no—
443#3003—111no—
444#3002—112no—
445#3002—111no—
446C2×#447—112no—
447C2×#447D1111yescharacteristic, complemented
448#2897—112no—
449#2880—111no—
450C23×C11—28no—
451C23×C11—28no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—24no—
455C23×C11—28no—
456C23×C11—22no—
457C23×C11—41no—
458C23×C11—44no—
459C23×C11—44no—
460C23×C11—42no—
461C23×C11—82no—
462C23×C11—82no—
463C23×C11—82no—
464C23×C11—82no—
465C23×C11—81no—
466C23×C11—81no—
467C23×C11—816no—
468C23×C11C22×D411yescharacteristic
469C23×C11C22×D411yescharacteristic
470C23×C11C22×D411yescharacteristic
471C22×D11—24no—
472C22×D11—24no—
473C22×D11—22no—
474C22×D11—216no—
475C22×D11—24no—
476C22×D11—216no—
477C22×D11—21no—
478C22×D11—42no—
479C22×D11—42no—
480C22×D11—42no—
481C22×D11—44no—
482C22×D11—84no—
483C22×D11—84no—
484C22×D11—84no—
485C22×D11—84no—
486C22×D11—82no—
487C22×D11—82no—
488C22×D11—832no—
489C22×D11C22×D412yes—
490C22×D11C22×D412yes—
491D4×C11—28no—
492D4×C11—28no—
493D4×C11—28no—
494D4×C11—24no—
495D4×C11—24no—
496D4×C11—44no—
497D4×C11—42no—
498D4×C11—82no—
499D4×C11C22×D418yes—
500C2×C4×C11—22no—
501C2×C4×C11—22no—
502C2×C4×C11—22no—
503C2×C4×C11—22no—
504C2×C4×C11—22no—
505C2×C4×C11—22no—
506C2×C4×C11—81no—
507C2×C4×C11C22×D411yescharacteristic
508C2×C4×C11C22×D411yescharacteristic
509C2×C4×C11C22×D411yescharacteristic
510C2×C4×C11C22×D414yes—
511C2×C4×C11C2511yescharacteristic
512C22⋊D11—28no—
513C22⋊D11—216no—
514C22⋊D11—216no—
515C22⋊D11—24no—
516C22⋊D11—28no—
517C22⋊D11—24no—
518C22⋊D11—216no—
519C22⋊D11—24no—
520C22⋊D11—216no—
521C22⋊D11—42no—
522C22⋊D11—42no—
523C22⋊D11—44no—
524C22⋊D11—44no—
525C22⋊D11—82no—
526C22⋊D11—82no—
527C22⋊D11—81no—
528C22⋊D11#12018yes—
529C2×Dic11—24no—
530C2×Dic11—216no—
531C2×Dic11—22no—
532C2×Dic11—24no—
533C2×Dic11—216no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—21no—
537C2×Dic11—44no—
538C2×Dic11C22×D412yes—
539C2×Dic11C22×D412yes—
540D44—24no—
541D44—24no—
542D44—22no—
543D44—22no—
544D44—22no—
545D44—82no—
546D44#12014yes—
547D44C22×D414yes—
548C4×D11—28no—
549C4×D11—24no—
550C4×D11—28no—
551C4×D11—24no—
552C4×D11—24no—
553C4×D11—42no—
554C4×D11—82no—
555C4×D11C22×D418yes—
556Dic22—24no—
557Dic22—22no—
558Dic22—22no—
559Dic22—24no—
560Dic22—22no—
561Dic22#12014yes—
562Dic22C22×D414yes—
563C8×C11—22no—
564C8×C11—22no—
565C11⋊C8—24no—
566C2×H(5,𝔽2)—112no—
567C2×H(5,𝔽2)—114no—
568C2×H(5,𝔽2)—112no—
569C2×H(5,𝔽2)—111no—
570C2×H(5,𝔽2)—222no—
571C2×H(5,𝔽2)—221no—
572C2×H(5,𝔽2)—221no—
573C2×H(5,𝔽2)—2216no—
574C22×#41—111no—
575C22×#41—112no—
576C22×#41—111no—
577C22×#41—221no—
578C23×D4—112no—
579C23×D4—221no—
580C23×D4—222no—
581C23×D4C2×D1111yescharacteristic, complemented
582#576—2216no—
583C2×AGL(1,ℤ/8)—112no—
584C2×AGL(1,ℤ/8)—112no—
585C2×AGL(1,ℤ/8)—114no—
586C2×AGL(1,ℤ/8)—114no—
587C2×#135—114no—
588C2×#135—112no—
589C22×D8—114no—
590C22×D8C2×D1112yescomplemented
591C2×#131—112no—
592#550—221no—
593#548—221no—
594#546—222no—
595#546—221no—
596D42—221no—
597D42—222no—
598#537—112no—
599#537—111no—
600#535—111no—
601#535—112no—
602#525—111no—
603#525—112no—
604C2×#121—112no—
605C2×#121C2×D1111yescharacteristic, complemented
606#520—111no—
607#452—114no—
608#452—112no—
609#451—111no—
610#450—112no—
611#450—112no—
612#450—114no—
613#450—111no—
614#449—114no—
615#449—114no—
616#449—114no—
617#449—114no—
618#449—112no—
619#448—112no—
620#448—111no—
621#447—112no—
622#447—112no—
623#447—114no—
624#447—114no—
625#447—112no—
626#447—114no—
627#447—111no—
628#447C2×D1112yescomplemented
629#447C2×D1112yescomplemented
630#447C2×D1114yescomplemented
631#418—112no—
632#418—114no—
633#417—112no—
634#417—114no—
635#416—112no—
636#416—114no—
637C2×#102—114no—
638C2×#102C2×D1112yescomplemented
639#408—112no—
640#408—114no—
641#407—111no—
642#407—112no—
643C2×C22⋊C8—112no—
644C2×C22⋊C8C2×D1111yescharacteristic, complemented
645C22×C11—21no—
646C22×C11—21no—
647C22×C11—21no—
648C22×C11—21no—
649C22×C11—21no—
650C22×C11—21no—
651C22×C11—28no—
652C22×C11—21no—
653C22×C11—44no—
654C22×C11—416no—
655C22×C11—44no—
656C22×C11—44no—
657C22×C11—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—88no—
661C22×C11—88no—
662C22×C11—162no—
663C22×C11C2×#12012yes—
664C22×C11#57612yescomplemented
665C22×C11C23×D411yescharacteristic
666C2×D11—22no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—24no—
670C2×D11—22no—
671C2×D11—22no—
672C2×D11—48no—
673C2×D11—48no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—41no—
677C2×D11—41no—
678C2×D11—41no—
679C2×D11—816no—
680C2×D11—816no—
681C2×D11—164no—
682C2×D11C2×#12014yes—
683C4×C11—21no—
684C4×C11—21no—
685C4×C11—42no—
686C4×C11C2×#12012yes—
687C4×C11C23×D412yes—
688Dic11—22no—
689Dic11—24no—
690Dic11—41no—
691Dic11—41no—
692Dic11—41no—
693Dic11C2×#12014yes—
694C25—21no—
695C25—222no—
696H(5,𝔽2)—1116no—
697H(5,𝔽2)—2216no—
698H(5,𝔽2)—2216no—
699H(5,𝔽2)—228no—
700H(5,𝔽2)—228no—
701H(5,𝔽2)—2216no—
702H(5,𝔽2)—2232no—
703H(5,𝔽2)—2216no—
704H(5,𝔽2)—228no—
705H(5,𝔽2)—228no—
706C2×#41—111no—
707C2×#41—112no—
708C2×#41—111no—
709C2×#41—111no—
710C2×#41—112no—
711C2×#41—111no—
712C2×#41—114no—
713C2×#41—112no—
714C2×#41—114no—
715C2×#41—112no—
716C2×#41—111no—
717C2×#41—112no—
718C2×#41—228no—
719C2×#41—228no—
720C2×#41—222no—
721C2×#41—222no—
722C2×#41—222no—
723C2×#41—224no—
724C2×#41—222no—
725C2×#41—221no—
726C2×#41—2216no—
727C2×#41—2216no—
728C2×#41—221no—
729C2×#41—221no—
730C22×Q8—111no—
731C22×Q8—111no—
732C22×D4—28no—
733C22×D4—21no—
734C22×D4—21no—
735C22×D4—21no—
736C22×D4—21no—
737C22×D4—114no—
738C22×D4—112no—
739C22×D4—112no—
740C22×D4—114no—
741C22×D4—111no—
742C22×D4—111no—
743C22×D4—222no—
744C22×D4—222no—
745C22×D4—222no—
746C22×D4—2216no—
747C22×D4—222no—
748C22×D4—224no—
749C22×D4—222no—
750C22×D4—221no—
751C22×D4—2216no—
752C22×D4—222no—
753C22×D4—224no—
754C22×D4—224no—
755C22×D4—224no—
756C22×D4—224no—
757C22×D4—222no—
758C22×D4—222no—
759C22×D4—2232no—
760C22×D4—221no—
761C22×D4C22×D1112yes—
762C22×D4C22×D1112yes—
763C22×D4C22×D1112yes—
764C22×D4C22×D1111yescharacteristic, complemented
765C23×C4—112no—
766C23×C4—222no—
767C23×C4—221no—
768C23×C4C22×D1111yescharacteristic
769AGL(1,ℤ/8)—2216no—
770AGL(1,ℤ/8)—2216no—
771AGL(1,ℤ/8)—228no—
772AGL(1,ℤ/8)—228no—
773#135—228no—
774#135—2216no—
775C2×Q16—112no—
776C2×SD16—114no—
777C2×SD16—114no—
778C2×SD16—112no—
779C2×SD16—112no—
780C2×D8—28no—
781C2×D8—114no—
782C2×D8—114no—
783C2×D8—112no—
784C2×D8—2216no—
785C2×D8C22×D1114yescomplemented
786C2×D8C22×D1114yescomplemented
787#131—228no—
788C2×M16—112no—
789C2×M16—114no—
790C22×C8—114no—
791C22×C8C22×D1112yescomplemented
792#127—222no—
793#127—221no—
794#124—222no—
795#124—221no—
796#123—222no—
797#123—221no—
798C22⋊Q8—111no—
799C22⋊Q8—111no—
800C22⋊Q8—112no—
801C22⋊Q8—222no—
802C22⋊Q8—221no—
803#121—21no—
804#121—21no—
805#121—112no—
806#121—112no—
807#121—111no—
808#121—111no—
809#121—112no—
810#121—222no—
811#121—222no—
812#121—221no—
813#121—222no—
814#121—222no—
815#121—222no—
816#121—222no—
817#121C22×D1112yes—
818#121C22×D1112yescomplemented
819#120—222no—
820#120—222no—
821#120—222no—
822#120—222no—
823#120—221no—
824C4×Q8—221no—
825C4×D4—222no—
826C4×D4—221no—
827C4×D4—222no—
828C4×D4—222no—
829C4×D4—221no—
830C4×D4—221no—
831#117—111no—
832#117—112no—
833C2×C4⋊C4—112no—
834C2×C4⋊C4C22×D1111yescharacteristic, complemented
835C2×C22⋊C4—21no—
836C2×C22⋊C4—222no—
837#103—112no—
838#103—112no—
839#103—114no—
840#102—114no—
841#102—114no—
842#102—112no—
843#102—112no—
844#102—114no—
845#102C22×D1114yescomplemented
846#102C22×D1114yescomplemented
847C22⋊C8—112no—
848C22⋊C8—112no—
849C22⋊C8—114no—
850C22⋊C8—114no—
851C22⋊C8C22×D1111yescharacteristic
852C22⋊C8C22×D1111yescharacteristic
853C22⋊C8C22×D1112yescomplemented
854C2×C11—22no—
855C2×C11—22no—
856C2×C11—48no—
857C2×C11—41no—
858C2×C11—82no—
859C2×C11C22×#12011yescharacteristic
860C2×C11C2×#57611yescharacteristic
861C2×C11#358511yescharacteristic
862D11—24no—
863D11—42no—
864D11—44no—
865D11—81no—
866C24—28no—
867C24—22no—
868C24—22no—
869C24—22no—
870C24—21no—
871C24—82no—
872C24—82no—
873C24—112no—
874C24—224no—
875C24—224no—
876C24—222no—
877C24—2216no—
878C24—221no—
879C24—884no—
880C24—884no—
881C24D4×D1111yescharacteristic
882#41—118no—
883#41—1116no—
884#41—118no—
885#41—228no—
886#41—228no—
887#41—224no—
888#41—224no—
889#41—224no—
890#41—224no—
891#41—228no—
892#41—228no—
893#41—228no—
894#41—228no—
895#41—228no—
896#41—2216no—
897#41—2216no—
898#41—2216no—
899#41—2232no—
900#41—2216no—
901#41—228no—
902#41—224no—
903#41—224no—
904#41—224no—
905#41—444no—
906C2×Q8—111no—
907C2×Q8—112no—
908C2×Q8—111no—
909C2×Q8—112no—
910C2×Q8—111no—
911C2×Q8—224no—
912C2×Q8—224no—
913C2×Q8—221no—
914C2×D4—28no—
915C2×D4—28no—
916C2×D4—28no—
917C2×D4—28no—
918C2×D4—28no—
919C2×D4—22no—
920C2×D4—22no—
921C2×D4—22no—
922C2×D4—22no—
923C2×D4—22no—
924C2×D4—24no—
925C2×D4—24no—
926C2×D4—21no—
927C2×D4—82no—
928C2×D4—112no—
929C2×D4—1116no—
930C2×D4—112no—
931C2×D4—112no—
932C2×D4—112no—
933C2×D4—111no—
934C2×D4—112no—
935C2×D4—111no—
936C2×D4—112no—
937C2×D4—111no—
938C2×D4—224no—
939C2×D4—224no—
940C2×D4—222no—
941C2×D4—228no—
942C2×D4—228no—
943C2×D4—224no—
944C2×D4—224no—
945C2×D4—222no—
946C2×D4—228no—
947C2×D4—2216no—
948C2×D4—2216no—
949C2×D4—2216no—
950C2×D4—2232no—
951C2×D4—2216no—
952C2×D4—228no—
953C2×D4—2232no—
954C2×D4—224no—
955C2×D4—224no—
956C2×D4—2216no—
957C2×D4—2216no—
958C2×D4—228no—
959C2×D4—2232no—
960C2×D4—2232no—
961C2×D4—2232no—
962C2×D4—222no—
963C2×D4—222no—
964C2×D4—228no—
965C2×D4—222no—
966C2×D4—221no—
967C2×D4—221no—
968C2×D4—222no—
969C2×D4—222no—
970C2×D4—221no—
971C2×D4—221no—
972C2×D4—444no—
973C2×D4—448no—
974C2×D4—884no—
975C2×D4D4×D1118yescomplemented
976C2×D4C23×D1112yes—
977C2×D4C23×D1114yes—
978C22×C4—24no—
979C22×C4—21no—
980C22×C4—112no—
981C22×C4—112no—
982C22×C4—112no—
983C22×C4—112no—
984C22×C4—112no—
985C22×C4—228no—
986C22×C4—228no—
987C22×C4—222no—
988C22×C4—224no—
989C22×C4—224no—
990C22×C4—222no—
991C22×C4—2216no—
992C22×C4—221no—
993C22×C4—222no—
994C22×C4—222no—
995C22×C4—221no—
996C22×C4D4×D1111yescharacteristic
997C22×C4D4×D1111yescharacteristic
998C22×C4D4×D1111yescharacteristic
999C22×C4C23×D1111yescharacteristic
1000C22×C4C23×D1111yescharacteristic
1001C22×C4C23×D1111yescharacteristic
1002Q16—224no—
1003SD16—224no—
1004SD16—224no—
1005SD16—228no—
1006SD16—228no—
1007D8—28no—
1008D8—28no—
1009D8—224no—
1010D8—228no—
1011D8—228no—
1012M16—228no—
1013M16—224no—
1014C2×C8—24no—
1015C2×C8—114no—
1016C2×C8—228no—
1017C2×C8C23×D1112yes—
1018C2×C8C23×D1112yes—
1019C4⋊C4—21no—
1020C4⋊C4—111no—
1021C4⋊C4—111no—
1022C4⋊C4—222no—
1023C4⋊C4—222no—
1024C4⋊C4—221no—
1025C4⋊C4—221no—
1026C4⋊C4C23×D1112yes—
1027C22⋊C4—22no—
1028C22⋊C4—22no—
1029C22⋊C4—222no—
1030C22⋊C4—222no—
1031C22⋊C4—222no—
1032C22⋊C4—222no—
1033C22⋊C4—222no—
1034C22⋊C4—221no—
1035C22⋊C4—221no—
1036C22⋊C4—221no—
1037C22⋊C4—221no—
1038C22⋊C4—221no—
1039C42—222no—
1040C42—221no—
1041C11#6037211yescharacteristic, complemented, Sylow
1042C23—28no—
1043C23—28no—
1044C23—22no—
1045C23—22no—
1046C23—24no—
1047C23—28no—
1048C23—22no—
1049C23—41no—
1050C23—44no—
1051C23—44no—
1052C23—42no—
1053C23—82no—
1054C23—82no—
1055C23—82no—
1056C23—82no—
1057C23—81no—
1058C23—81no—
1059C23—816no—
1060C23—112no—
1061C23—112no—
1062C23—224no—
1063C23—2216no—
1064C23—224no—
1065C23—2216no—
1066C23—224no—
1067C23—222no—
1068C23—221no—
1069C23—442no—
1070C23—442no—
1071C23—444no—
1072C23—442no—
1073C23—884no—
1074C23—884no—
1075C23—884no—
1076C23—884no—
1077C23—882no—
1078C23—882no—
1079C23—8832no—
1080C23C2×D4×D1111yescharacteristic
1081C23C2×D4×D1111yescharacteristic
1082C23C2×D4×D1111yescharacteristic
1083Q8—114no—
1084Q8—114no—
1085Q8—224no—
1086Q8—224no—
1087Q8—222no—
1088Q8—222no—
1089Q8—222no—
1090D4—28no—
1091D4—28no—
1092D4—28no—
1093D4—24no—
1094D4—24no—
1095D4—44no—
1096D4—42no—
1097D4—82no—
1098D4—118no—
1099D4—114no—
1100D4—114no—
1101D4—224no—
1102D4—224no—
1103D4—224no—
1104D4—2216no—
1105D4—224no—
1106D4—2216no—
1107D4—2216no—
1108D4—228no—
1109D4—2216no—
1110D4—224no—
1111D4—228no—
1112D4—222no—
1113D4—222no—
1114D4—222no—
1115D4—444no—
1116D4—444no—
1117D4—442no—
1118D4—442no—
1119D4—882no—
1120D4—881no—
1121D4—882no—
1122D4—882no—
1123D4C2×D4×D1118yes—
1124C2×C4—22no—
1125C2×C4—22no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—22no—
1130C2×C4—81no—
1131C2×C4—112no—
1132C2×C4—118no—
1133C2×C4—112no—
1134C2×C4—224no—
1135C2×C4—224no—
1136C2×C4—228no—
1137C2×C4—224no—
1138C2×C4—2216no—
1139C2×C4—224no—
1140C2×C4—2216no—
1141C2×C4—222no—
1142C2×C4—228no—
1143C2×C4—224no—
1144C2×C4—221no—
1145C2×C4—221no—
1146C2×C4—221no—
1147C2×C4—444no—
1148C2×C4—442no—
1149C2×C4—882no—
1150C2×C4C2×D4×D1111yescharacteristic
1151C2×C4C2×D4×D1111yescharacteristic
1152C2×C4C2×D4×D1111yescharacteristic
1153C2×C4C2×D4×D1114yes—
1154C2×C4C24×D1111yescharacteristic
1155C8—22no—
1156C8—22no—
1157C8—224no—
1158C22—21no—
1159C22—21no—
1160C22—21no—
1161C22—21no—
1162C22—21no—
1163C22—21no—
1164C22—21no—
1165C22—28no—
1166C22—44no—
1167C22—416no—
1168C22—44no—
1169C22—44no—
1170C22—42no—
1171C22—42no—
1172C22—42no—
1173C22—88no—
1174C22—88no—
1175C22—114no—
1176C22—162no—
1177C22—222no—
1178C22—222no—
1179C22—222no—
1180C22—222no—
1181C22—224no—
1182C22—222no—
1183C22—448no—
1184C22—448no—
1185C22—442no—
1186C22—442no—
1187C22—441no—
1188C22—441no—
1189C22—441no—
1190C22—8816no—
1191C22—8816no—
1192C22—1764no—
1193C22D11×#12012yes—
1194C22#1062328812yescomplemented
1195C22C22×D4×D1111yescharacteristic
1196C4—21no—
1197C4—21no—
1198C4—42no—
1199C4—114no—
1200C4—222no—
1201C4—224no—
1202C4—441no—
1203C4—441no—
1204C4—441no—
1205C4D11×#12012yes—
1206C4C22×D4×D1112yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—48no—
1211C2—82no—
1212C2—224no—
1213C2—442no—
1214C2—444no—
1215C2—881no—
1216C2C2×D11×#12011yescharacteristic
1217C2C2×#1062328811yescharacteristic
1218C2#1308339211yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#447C2
socleC22×C11C23×D4
hypercenterC2×#447D11
hypocenterC11#60372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×#447

Complements

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

NH ≅ G/Ntype
1. C22×#67037C2semidirect
2. C2×#10623288C2semidirect
3. #13082281C2semidirect
4. #13077925C2semidirect
5. #13077915C2semidirect
6. #13077880C2semidirect
7. #13077879C2semidirect
8. #13077866C2semidirect
9. #13077863C2semidirect
10. #13077843C2semidirect
11. #13077840C2semidirect
12. #13077838C2semidirect
13. #13077829C2semidirect
14. D11×#447C2semidirect
15. #13077137C2semidirect
16. #13077062C2semidirect
17. C2×C11×#447C2semidirect
18. C23×D4×C11C22semidirect
25. C2×#67037C22semidirect
26. C2×#67037C22semidirect
27. C2×#67037C22semidirect
29. C22×#4341C22semidirect
31. C22×D4×D11C22semidirect
33. C22×#4339C22semidirect
34. C22×C11×D8C22semidirect
35. C2×C11×#121C22semidirect
36. #10623336C22semidirect
38. C2×#66985C22semidirect
39. C2×#66985C22semidirect
40. #10623322C22semidirect
42. C2×#66965C22semidirect
43. C2×#66964C22semidirect
44. C2×#66964C22semidirect
45. C2×D8×D11C22semidirect
46. C2×#66957C22semidirect
47. C2×#66954C22semidirect
50. #10623139C22semidirect
51. #10623138C22semidirect
52. #10623137C22semidirect
53. D11×#121C22semidirect
56. #10623041C22semidirect
57. #10623035C22semidirect
59. C11×#447C22semidirect
60. C11×#447C22semidirect
61. C11×#447C22semidirect
62. C2×C11×#102C22semidirect
63. C2×C11×C22⋊C8C22semidirect
64. #10622831C22semidirect
65. #10622831C22semidirect
66. #10622830C22semidirect
67. #10622830C22semidirect
68. #10622828C22semidirect
69. #10622820C22semidirect
70. #10622771C22semidirect
71. #10622771C22semidirect
72. #10622769C22semidirect
73. #10622769C22semidirect
74. #10622726C22semidirect
75. #10622723C22semidirect
76. #10622653C22semidirect
77. #10622650C22semidirect
78. #10622649C22semidirect
79. #10622579C22semidirect
80. #10622396C22semidirect
81. #10622394C22semidirect
82. #10622389C22semidirect
83. #10622386C22semidirect
84. #10622385C22semidirect
85. #10622384C22semidirect
86. #10622383C22semidirect
87. D11×#102C22semidirect
88. #10622352C22semidirect
89. #10622351C22semidirect
90. #10622347C22semidirect
91. #10622346C22semidirect
92. #10622345C22semidirect
93. #10622344C22semidirect
94. #10622340C22semidirect
95. #10622339C22semidirect
96. D11×C22⋊C8C22semidirect
107. C22×D4×C11C23semidirect
129. #67037D4semidirect
140. C2×#4341C23semidirect
152. C2×D4×D11C23semidirect
165. C2×#4339C23semidirect
173. C2×C11×D8C23semidirect
174. C2×C11×D8C23semidirect
175. C22×C8×C11C23semidirect
179. C11×#121C23semidirect
180. C2×C11×C4⋊C4C23semidirect
189. #66991C23semidirect
190. #66991C23semidirect
195. C2×#4324C23semidirect
196. C2×#4324C23semidirect
199. C2×#4323C23semidirect
200. C2×#4323C23semidirect
203. #66983C23semidirect
208. #66979C23semidirect
210. #66977C23semidirect
211. C2×#4318C23semidirect
216. C2×Dic44C23semidirect
218. C2×D88C23semidirect
219. C2×#4314C23semidirect
220. C2×#4314C23semidirect
222. C2×#4313C23semidirect
223. C2×C8×D11C23semidirect
225. #66950C23semidirect
227. #66948C23semidirect
229. #66945C23semidirect
230. C4⋊C4×D11C23semidirect
240. C11×#102C23semidirect
241. C11×#102C23semidirect
244. C11×C22⋊C8C23semidirect
245. #66896C23semidirect
246. #66896C23semidirect
248. C22⋊(C11⋊C8)C23semidirect
249. #66885C23semidirect
250. #66885C23semidirect
251. (C2×D11)⋊C8C23semidirect
252. (C2×D11)⋊C8C23semidirect
253. #66880C23semidirect
254. #66880C23semidirect
255. #66874C23semidirect
256. #66873C23semidirect
288. C2×D4×C11C2×D4semidirect
341. #4341C2×D4semidirect
353. D4×D11C2×D4semidirect
366. #4339C2×D4semidirect
447. C2×#447D11semidirect
581. C23×D4C2×D11semidirect
590. C22×D8C2×D11semidirect
605. C2×#121C2×D11semidirect
628. #447C2×D11semidirect
629. #447C2×D11semidirect
630. #447C2×D11semidirect
638. C2×#102C2×D11semidirect
644. C2×C22⋊C8C2×D11semidirect
664. C22×C11#576semidirect
764. C22×D4C22×D11semidirect
785. C2×D8C22×D11semidirect
786. C2×D8C22×D11semidirect
791. C22×C8C22×D11semidirect
818. #121C22×D11semidirect
834. C2×C4⋊C4C22×D11semidirect
845. #102C22×D11semidirect
846. #102C22×D11semidirect
853. C22⋊C8C22×D11semidirect
975. C2×D4D4×D11semidirect
1041. C11#60372semidirect
1194. C22#10623288semidirect

Maximal subgroups

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

subgroupindex
C22×#670372
C2×#106232882
#130822812
#130779252
#130779152
#130778802
#130778792
#130778662
#130778632
#130778432
#130778402
#130778382
#130778292
D11×#4472
#130771372
#130770622
C2×C11×#4472
#6037211