Finite Group Databasebeta

← #15620299

Subgroups — #15620299

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×#67042C211yesmaximal, characteristic, complemented
2C2×#10623300C212yesmaximal, complemented
3#13082277C211yesmaximal, characteristic, complemented
4#13077924C214yesmaximal, complemented
5#13077916C212yesmaximal, complemented
6#13077887C212yesmaximal, complemented
7#13077881C214yesmaximal, complemented
8#13077868C211yesmaximal, characteristic, complemented
9#13077867C212yesmaximal, complemented
10#13077844C212yesmaximal, complemented
11#13077842C211yesmaximal, characteristic, complemented
12#13077839C212yesmaximal, complemented
13C2×#10622345C211yesmaximal, characteristic, complemented
14D11×#447C212yesmaximal, complemented
15#13077138C212yesmaximal, complemented
16#13077062C211yesmaximal, characteristic, complemented
17C11×#3002C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic, complemented
19C2×#67042—216no—
20C2×#67042—21no—
21C2×#67042—21no—
22C2×#67042—22no—
23C2×#67042C2212yes—
24C2×#67042C2214yescomplemented
25C2×#67042C2212yescomplemented
26C2×#67042C2211yescharacteristic, complemented
27C22×#4343C2212yescomplemented
28C22×D4×D11—22no—
29C22×D4×D11C2212yescomplemented
30C22×#4339—21no—
31C22×#4339C2211yescharacteristic
32C23×D44—21no—
33C23×D44C2211yescharacteristic, complemented
34C2×C11×#135C2212yescomplemented
35C11×#525C2211yescharacteristic, complemented
36#10623364C2211yescharacteristic, complemented
37C2×#67002C2212yescomplemented
38C2×#67002C2212yescomplemented
39C2×#66983C2211yescharacteristic, complemented
40#10623300—216no—
41C2×#66972C2214yescomplemented
42C2×#66967C2214yescomplemented
43C2×#66967C2214yescomplemented
44C2×D8×D11C2214yescomplemented
45C22×D88C2212yescomplemented
46C2×#66954C2212yescomplemented
47#10623185—22no—
48#10623160C2212yescomplemented
49#10623158C2212yescomplemented
50#10623138C2212yescomplemented
51D11×#121C2212yescomplemented
52#10623121—22no—
53#10623084—21no—
54#10623083—21no—
55#10623081—21no—
56D4×D44—21no—
57#10623056C2211yescharacteristic, complemented
58#10623054C2211yescharacteristic, complemented
59C11×#452C2212yescomplemented
60C11×#451C2211yescharacteristic, complemented
61C11×#450C2211yescharacteristic, complemented
62C11×#449C2212yescomplemented
63C11×#448C2211yescharacteristic, complemented
64C11×#447C2211yescharacteristic, complemented
65C11×#416C2212yescomplemented
66C2×C11×C22⋊C8C2211yescharacteristic, complemented
67#10622851C2214yescomplemented
68#10622845C2212yescomplemented
69#10622840C2212yescomplemented
70#10622830C2212yescomplemented
71#10622820C2211yescharacteristic, complemented
72#10622800C2214yescomplemented
73#10622785C2214yescomplemented
74#10622782C2214yescomplemented
75#10622769C2214yescomplemented
76C2×#66885C2212yescomplemented
77#10622723C2212yescomplemented
78#10622659C2212yescomplemented
79#10622659C2212yescomplemented
80#10622649C2212yescomplemented
81#10622649C2212yescomplemented
82#10622614C2212yescomplemented
83#10622424C2214yescomplemented
84#10622424C2214yescomplemented
85#10622417C2214yescomplemented
86#10622416C2214yescomplemented
87#10622386C2214yescomplemented
88#10622386C2214yescomplemented
89#10622383C2214yescomplemented
90D11×#102C2214yescomplemented
91#10622345C2212yescomplemented
92#10622345C2212yescomplemented
93#10622345C2214yescomplemented
94#10622340C2214yescomplemented
95#10622339C2212yescomplemented
96D11×C22⋊C8C2212yescomplemented
97C24×D11—21no—
98C24×D11—22no—
99C2×C11×#41—28no—
100C2×C11×#41—21no—
101C2×C11×#41—21no—
102C2×C11×#41C2312yes—
103C2×C11×#41C2312yes—
104C2×C11×#41C2311yescharacteristic, complemented
105C22×Q8×C11C2311yescharacteristic
106C22×D4×C11—21no—
107C22×D4×C11C2311yescharacteristic
108C23×C4×C11—21no—
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11—21no—
111C22×C22⋊D11—22no—
112C22×C22⋊D11D412yes—
113#67042—232no—
114#67042—216no—
115#67042—216no—
116#67042—28no—
117#67042—216no—
118#67042—216no—
119#67042—28no—
120#67042—28no—
121#67042—28no—
122#67042D4116yescomplemented
123C2×#4343—216no—
124C2×#4343—22no—
125C2×#4343—22no—
126C2×#4343C2314yes—
127C2×#4343C2314yes—
128C2×#4343C2312yescomplemented
129C2×D4×D11—232no—
130C2×D4×D11—24no—
131C2×D4×D11—24no—
132C2×D4×D11—24no—
133C2×D4×D11—24no—
134C2×D4×D11—216no—
135C2×D4×D11—22no—
136C2×D4×D11—22no—
137C2×D4×D11—22no—
138C2×D4×D11—22no—
139C2×D4×D11C2314yes—
140C2×D4×D11C2314yes—
141C2×D4×D11C2312yescomplemented
142C2×#4339—216no—
143C2×#4339—28no—
144C2×#4339—22no—
145C2×#4339—22no—
146C2×#4339—24no—
147C2×#4339—21no—
148C2×#4339D411yescharacteristic
149C2×#4339D411yescharacteristic
150C2×#4339D412yes—
151C2×#4339C2311yescharacteristic
152C2×#4339C2312yes—
153C2×#4339C2311yescharacteristic
154C22×D44—216no—
155C22×D44—22no—
156C22×D44—21no—
157C22×D44—21no—
158C22×D44—21no—
159C22×D44—22no—
160C22×D44—22no—
161C22×D44—24no—
162C22×D44—28no—
163C22×D44—21no—
164C22×D44D411yescharacteristic
165C22×D44C2312yes—
166C22×D44C2312yes—
167C22×D44C2312yes—
168C22×D44C2311yescharacteristic, complemented
169C22×C4×D11—22no—
170C22×C4×D11C2312yes—
171C22×Dic22D411yescharacteristic
172C11×#135—28no—
173C2×C11×Q16C2312yescomplemented
174C2×C11×SD16C2312yescomplemented
175C2×C11×SD16C2312yescomplemented
176C2×C11×D8C2312yescomplemented
177C22×C8×C11C2312yescomplemented
178C11×#123—21no—
179C11×C22⋊Q8C2311yescharacteristic
180C11×C22⋊Q8C2311yescharacteristic, complemented
181C11×#121C2311yescharacteristic
182C11×#121C2311yescharacteristic, complemented
183C11×#120—21no—
184C4×D4×C11—21no—
185C4×D4×C11—21no—
186C11×#117C2311yescharacteristic, complemented
187#67002—28no—
188#67002—28no—
189#66999C2312yescomplemented
190C2×#4325C2314yescomplemented
191C2×#4325C2314yescomplemented
192#66993—22no—
193#66992—22no—
194#66992—22no—
195#66991C2312yescomplemented
196#66990—22no—
197C2×#4323C2314yescomplemented
198C2×#4323C2314yescomplemented
199#66983—21no—
200#66983—21no—
201#66983—21no—
202#66983C2312yes—
203#66983C2312yescomplemented
204C2×(C2×D11)⋊C4—21no—
205C2×C4⋊Dic11C2311yescharacteristic, complemented
206#66977—21no—
207C2×#4318C2312yescomplemented
208#66972—216no—
209#66967—216no—
210#66967—216no—
211D8×D11—216no—
212C2×D88—28no—
213C2×D88C2314yescomplemented
214C2×D88C2314yescomplemented
215#66954—28no—
216C2×#4313C2314yescomplemented
217C2×C8×D11C2314yescomplemented
218#66949—22no—
219#66948—22no—
220#66948C2312yescomplemented
221#66948C2312yescomplemented
222#66947—22no—
223#66946—22no—
224#66945C2312yescomplemented
225C4⋊C4×D11C2312yescomplemented
226#66938—22no—
227#66937—22no—
228#66937—22no—
229#66937—22no—
230#66935—22no—
231#66935—22no—
232#66935—22no—
233(C22⋊D11)⋊C4—22no—
234(C22⋊D11)⋊C4—22no—
235C22⋊C4×D11—22no—
236#66928—21no—
237#66927—21no—
238C4×D44—21no—
239C4×Dic22—21no—
240C11×#103C2312yescomplemented
241C11×#103C2312yescomplemented
242C11×#102C2312yescomplemented
243C11×#102C2312yescomplemented
244C11×C22⋊C8C2311yescharacteristic
245C11×C22⋊C8C2311yescharacteristic
246C11×C22⋊C8C2312yescomplemented
247#66899C2314yescomplemented
248#66896C2314yescomplemented
249C22⋊(C11⋊C8)C2312yes—
250C22⋊(C11⋊C8)C2312yescomplemented
251#66885C2314yescomplemented
252#66885C2314yescomplemented
253(C2×D11)⋊C8C2314yescomplemented
254(C2×D11)⋊C8C2314yescomplemented
255#66873C2314yescomplemented
256#66873C2314yescomplemented
257#60372—111nomaximal, Sylow
258C24×C11—21no—
259C24×C11C2×D411yescharacteristic
260C23×D11—22no—
261C23×D11—28no—
262C23×D11—216no—
263C23×D11—22no—
264C23×D11—22no—
265C23×D11—24no—
266C23×D11—24no—
267C23×D11—21no—
268C23×D11—22no—
269C23×D11—84no—
270C23×D11—82no—
271C23×D11—84no—
272C23×D11—82no—
273C23×D11C2×D412yes—
274C11×#41—28no—
275C11×#41—28no—
276C11×#41—24no—
277C11×#41—24no—
278C11×#41—24no—
279C11×#41—24no—
280C11×#41C2×D418yescomplemented
281C2×Q8×C11—24no—
282C2×Q8×C11—21no—
283C2×Q8×C11C2411yescharacteristic
284C2×Q8×C11C2412yes—
285C2×D4×C11—28no—
286C2×D4×C11—22no—
287C2×D4×C11—22no—
288C2×D4×C11—24no—
289C2×D4×C11—21no—
290C2×D4×C11—21no—
291C2×D4×C11—21no—
292C2×D4×C11—21no—
293C2×D4×C11C2411yescharacteristic
294C2×D4×C11C2412yes—
295C22×C4×C11—28no—
296C22×C4×C11—21no—
297C22×C4×C11—22no—
298C22×C4×C11—22no—
299C22×C4×C11—24no—
300C22×C4×C11—21no—
301C22×C4×C11C2×D411yescharacteristic
302C22×C4×C11C2×D411yescharacteristic
303C22×C4×C11C2×D411yescharacteristic
304C22×C4×C11C2411yescharacteristic
305C22×C4×C11C2411yescharacteristic
306C22×C4×C11C2411yescharacteristic
307C2×C22⋊D11—216no—
308C2×C22⋊D11—28no—
309C2×C22⋊D11—24no—
310C2×C22⋊D11—24no—
311C2×C22⋊D11—22no—
312C2×C22⋊D11—22no—
313C2×C22⋊D11—22no—
314C2×C22⋊D11—22no—
315C2×C22⋊D11—82no—
316C2×C22⋊D11C2×D412yes—
317C2×C22⋊D11C2×D412yes—
318C2×C22⋊D11C2×D412yes—
319C2×C22⋊D11C2×D412yes—
320C22×Dic11—21no—
321C22×Dic11C2×D412yes—
322#4343—216no—
323#4343—216no—
324#4343—28no—
325#4343—28no—
326#4343—28no—
327#4343—28no—
328#4343C2×D4116yescomplemented
329D4×D11—232no—
330D4×D11—216no—
331D4×D11—232no—
332D4×D11—216no—
333D4×D11—232no—
334D4×D11—232no—
335D4×D11—28no—
336D4×D11—28no—
337D4×D11—28no—
338D4×D11—28no—
339D4×D11—48no—
340D4×D11—84no—
341D4×D11C2×D4116yescomplemented
342#4339—232no—
343#4339—216no—
344#4339—28no—
345#4339—24no—
346#4339—28no—
347#4339—216no—
348#4339—24no—
349#4339—24no—
350#4339—44no—
351#4339C2×D418yes—
352C2×D44—28no—
353C2×D44—216no—
354C2×D44—232no—
355C2×D44—28no—
356C2×D44—216no—
357C2×D44—28no—
358C2×D44—24no—
359C2×D44—216no—
360C2×D44—28no—
361C2×D44—28no—
362C2×D44—24no—
363C2×D44—24no—
364C2×D44—22no—
365C2×D44—22no—
366C2×D44—22no—
367C2×D44—22no—
368C2×D44—22no—
369C2×D44—22no—
370C2×D44—24no—
371C2×D44—21no—
372C2×D44—24no—
373C2×D44—44no—
374C2×D44C2×D411yescharacteristic
375C2×D44C2×D412yes—
376C2×D44C2×D411yescharacteristic
377C2×D44C2×D418yescomplemented
378C2×D44C2412yes—
379C2×D44C2414yes—
380C2×C4×D11—216no—
381C2×C4×D11—24no—
382C2×C4×D11—24no—
383C2×C4×D11—28no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11C2×D412yes—
387C2×C4×D11C2×D412yes—
388C2×C4×D11C2412yes—
389C2×C4×D11C2412yes—
390C2×Dic22—24no—
391C2×Dic22C2×D411yescharacteristic
392C2×Dic22C2×D412yes—
393C2×Dic22C2×D411yescharacteristic
394C11×Q16—24no—
395C11×SD16—24no—
396C11×SD16—24no—
397C11×D8—24no—
398C2×C8×C11—24no—
399C2×C8×C11C2412yes—
400C2×C8×C11C2412yes—
401C11×C4⋊C4—21no—
402C11×C4⋊C4—21no—
403C11×C4⋊C4C2411yescharacteristic
404C11×C4⋊C4C2411yescharacteristic
405C11×C22⋊C4—21no—
406C11×C22⋊C4—21no—
407C11×C22⋊C4—21no—
408C11×C22⋊C4—21no—
409C11×C22⋊C4—21no—
410C42×C11—21no—
411C22⋊Dic11—22no—
412#4325—28no—
413#4325—28no—
414#4323—28no—
415#4323—28no—
416(C2×D11)⋊C4—22no—
417(C2×D11)⋊C4—22no—
418(C2×D11)⋊C4—22no—
419(C2×D11)⋊C4—22no—
420(C2×D11)⋊C4—22no—
421(C2×D11)⋊C4—22no—
422C4⋊Dic11—21no—
423C4⋊Dic11C2412yes—
424Dic11⋊C4—22no—
425Dic11⋊C4—22no—
426C4×Dic11—22no—
427#4318—24no—
428C2×C11⋊C8C2414yes—
429D88—28no—
430D88—28no—
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#3002D1111yescharacteristic, complemented
446C2×#447—112no—
447C2×#447—111no—
448#2897—112no—
449#2880—111no—
450C23×C11—24no—
451C23×C11—22no—
452C23×C11—22no—
453C23×C11—22no—
454C23×C11—21no—
455C23×C11—41no—
456C23×C11—42no—
457C23×C11—42no—
458C23×C11C22×D411yescharacteristic
459C23×C11C22×D411yescharacteristic
460C23×C11C22×D411yescharacteristic
461C22×D11—28no—
462C22×D11—24no—
463C22×D11—24no—
464C22×D11—28no—
465C22×D11—216no—
466C22×D11—28no—
467C22×D11—24no—
468C22×D11—216no—
469C22×D11—22no—
470C22×D11—42no—
471C22×D11—44no—
472C22×D11—44no—
473C22×D11—42no—
474C22×D11—44no—
475C22×D11—84no—
476C22×D11—84no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11—82no—
480C22×D11—82no—
481C22×D11—82no—
482C22×D11—82no—
483C22×D11—82no—
484C22×D11—82no—
485C22×D11—832no—
486C22×D11—816no—
487C22×D11—81no—
488C22×D11—81no—
489C22×D11C22×D412yes—
490C22×D11C22×D412yes—
491Q8×C11—24no—
492Q8×C11—22no—
493Q8×C11—22no—
494Q8×C11C22×D414yes—
495D4×C11—28no—
496D4×C11—24no—
497D4×C11—28no—
498D4×C11—22no—
499D4×C11—22no—
500D4×C11—42no—
501D4×C11—42no—
502D4×C11—81no—
503D4×C11C22×D414yes—
504C2×C4×C11—24no—
505C2×C4×C11—28no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—22no—
509C2×C4×C11—28no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—21no—
514C2×C4×C11—21no—
515C2×C4×C11—21no—
516C2×C4×C11—42no—
517C2×C4×C11C22×D411yescharacteristic
518C2×C4×C11C22×D411yescharacteristic
519C2×C4×C11C22×D411yescharacteristic
520C2×C4×C11C22×D414yes—
521C2×C4×C11C2511yescharacteristic
522C22⋊D11—216no—
523C22⋊D11—24no—
524C22⋊D11—24no—
525C22⋊D11—24no—
526C22⋊D11—216no—
527C22⋊D11—44no—
528C22⋊D11—44no—
529C22⋊D11—82no—
530C22⋊D11—82no—
531C22⋊D11#12018yes—
532C2×Dic11—24no—
533C2×Dic11—22no—
534C2×Dic11—81no—
535C2×Dic11C22×D412yes—
536C2×Dic11C22×D412yes—
537D44—28no—
538D44—216no—
539D44—28no—
540D44—24no—
541D44—216no—
542D44—22no—
543D44—28no—
544D44—24no—
545D44—24no—
546D44—44no—
547D44—42no—
548D44—82no—
549D44—82no—
550D44#12014yes—
551D44C22×D418yes—
552C4×D11—216no—
553C4×D11—24no—
554C4×D11—24no—
555C4×D11—216no—
556C4×D11—24no—
557C4×D11—44no—
558C4×D11—82no—
559C4×D11C22×D418yes—
560Dic22—22no—
561Dic22—24no—
562Dic22#12014yes—
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)—221no—
571C2×H(5,𝔽2)—222no—
572C2×H(5,𝔽2)—221no—
573C2×H(5,𝔽2)—2216no—
574C22×#41—111no—
575C22×#41—112no—
576C22×#41—221no—
577C22×#41C2×D1111yescharacteristic, complemented
578C23×D4—112no—
579C23×D4—111no—
580C23×D4—221no—
581C23×D4—222no—
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×#135C2×D1112yescomplemented
589C22×D8—114no—
590C22×D8—112no—
591C2×#131—112no—
592#550—221no—
593#548—221no—
594#546—221no—
595#546—222no—
596D42—221no—
597D42—222no—
598#537—111no—
599#537—112no—
600#535—112no—
601#535—111no—
602#525—112no—
603#525C2×D1111yescharacteristic, complemented
604C2×#121—111no—
605C2×#121—112no—
606#520—111no—
607#452—114no—
608#452C2×D1112yescomplemented
609#451C2×D1111yescharacteristic, complemented
610#450—114no—
611#450—112no—
612#450—112no—
613#450C2×D1111yescharacteristic, complemented
614#449—114no—
615#449—114no—
616#449—114no—
617#449—114no—
618#449C2×D1112yescomplemented
619#448—112no—
620#448C2×D1111yescharacteristic, complemented
621#447—112no—
622#447—114no—
623#447—112no—
624#447—112no—
625#447—114no—
626#447—114no—
627#447—112no—
628#447—112no—
629#447—114no—
630#447C2×D1111yescharacteristic, complemented
631#418—112no—
632#418—114no—
633#417—112no—
634#417—114no—
635#416—114no—
636#416C2×D1112yescomplemented
637C2×#102—112no—
638C2×#102—114no—
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—24no—
652C22×C11—21no—
653C22×C11—44no—
654C22×C11—48no—
655C22×C11—42no—
656C22×C11—42no—
657C22×C11—41no—
658C22×C11—41no—
659C22×C11—41no—
660C22×C11C2×#12012yes—
661C22×C11#57612yescomplemented
662C22×C11C23×D411yescharacteristic
663C2×D11—22no—
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—28no—
667C2×D11—22no—
668C2×D11—22no—
669C2×D11—48no—
670C2×D11—416no—
671C2×D11—44no—
672C2×D11—44no—
673C2×D11—42no—
674C2×D11—42no—
675C2×D11—42no—
676C2×D11—816no—
677C2×D11—88no—
678C2×D11—816no—
679C2×D11—88no—
680C2×D11—164no—
681C2×D11—162no—
682C2×D11C2×#12014yes—
683C4×C11—21no—
684C4×C11—24no—
685C4×C11—21no—
686C4×C11—41no—
687C4×C11—41no—
688C4×C11—41no—
689C4×C11C2×#12012yes—
690C4×C11C23×D412yes—
691Dic11—22no—
692Dic11—42no—
693Dic11C2×#12014yes—
694C25—222no—
695C25—221no—
696H(5,𝔽2)—1116no—
697H(5,𝔽2)—2216no—
698H(5,𝔽2)—228no—
699H(5,𝔽2)—2216no—
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—28no—
707C2×#41—21no—
708C2×#41—21no—
709C2×#41—111no—
710C2×#41—112no—
711C2×#41—111no—
712C2×#41—111no—
713C2×#41—112no—
714C2×#41—111no—
715C2×#41—114no—
716C2×#41—112no—
717C2×#41—114no—
718C2×#41—222no—
719C2×#41—224no—
720C2×#41—222no—
721C2×#41—221no—
722C2×#41—228no—
723C2×#41—2216no—
724C2×#41—222no—
725C2×#41—222no—
726C2×#41—2216no—
727C2×#41C22×D1112yes—
728C2×#41C22×D1112yes—
729C2×#41C22×D1111yescharacteristic, complemented
730C22×Q8—111no—
731C22×Q8C22×D1111yescharacteristic
732C22×D4—21no—
733C22×D4—114no—
734C22×D4—112no—
735C22×D4—112no—
736C22×D4—114no—
737C22×D4—111no—
738C22×D4—112no—
739C22×D4—111no—
740C22×D4—112no—
741C22×D4—112no—
742C22×D4—228no—
743C22×D4—222no—
744C22×D4—224no—
745C22×D4—222no—
746C22×D4—221no—
747C22×D4—222no—
748C22×D4—2216no—
749C22×D4—222no—
750C22×D4—222no—
751C22×D4—222no—
752C22×D4—2216no—
753C22×D4—224no—
754C22×D4—224no—
755C22×D4—224no—
756C22×D4—224no—
757C22×D4—222no—
758C22×D4—2232no—
759C22×D4—222no—
760C22×D4—221no—
761C22×D4—221no—
762C22×D4—221no—
763C22×D4—221no—
764C22×D4C22×D1111yescharacteristic
765C23×C4—21no—
766C23×C4—112no—
767C23×C4—222no—
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—28no—
774#135—2216no—
775C2×Q16C22×D1112yescomplemented
776C2×SD16—114no—
777C2×SD16—114no—
778C2×SD16C22×D1112yescomplemented
779C2×SD16C22×D1112yescomplemented
780C2×D8—114no—
781C2×D8—114no—
782C2×D8—114no—
783C2×D8—114no—
784C2×D8—228no—
785C2×D8—2216no—
786C2×D8C22×D1112yescomplemented
787#131—228no—
788C2×M16—112no—
789C2×M16—114no—
790C22×C8—114no—
791C22×C8C22×D1112yescomplemented
792#127—221no—
793#127—222no—
794#124—221no—
795#124—222no—
796#123—21no—
797#123—222no—
798C22⋊Q8—112no—
799C22⋊Q8—222no—
800C22⋊Q8—221no—
801C22⋊Q8C22×D1111yescharacteristic
802C22⋊Q8C22×D1111yescharacteristic, complemented
803#121—112no—
804#121—112no—
805#121—112no—
806#121—112no—
807#121—112no—
808#121—222no—
809#121—222no—
810#121—222no—
811#121—222no—
812#121—221no—
813#121—222no—
814#121—222no—
815#121—221no—
816#121—221no—
817#121C22×D1111yescharacteristic
818#121C22×D1111yescharacteristic, complemented
819#120—21no—
820#120—222no—
821#120—222no—
822#120—222no—
823#120—222no—
824C4×Q8—221no—
825C4×D4—21no—
826C4×D4—21no—
827C4×D4—221no—
828C4×D4—222no—
829C4×D4—222no—
830C4×D4—222no—
831#117—112no—
832#117C22×D1111yescharacteristic, complemented
833C2×C4⋊C4—111no—
834C2×C4⋊C4—112no—
835C2×C22⋊C4—222no—
836C2×C22⋊C4—221no—
837#103—114no—
838#103C22×D1112yescomplemented
839#103C22×D1112yescomplemented
840#102—114no—
841#102—114no—
842#102—114no—
843#102—114no—
844#102—114no—
845#102C22×D1112yescomplemented
846#102C22×D1112yescomplemented
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—41no—
857C2×C11—44no—
858C2×C11—81no—
859C2×C11C22×#12011yescharacteristic
860C2×C11C2×#57611yescharacteristic
861C2×C11#358511yescharacteristic
862D11—24no—
863D11—42no—
864D11—48no—
865D11—82no—
866C24—21no—
867C24—112no—
868C24—224no—
869C24—224no—
870C24—222no—
871C24—2216no—
872C24—228no—
873C24—222no—
874C24—222no—
875C24—222no—
876C24—221no—
877C24—882no—
878C24—884no—
879C24—882no—
880C24—884no—
881C24D4×D1111yescharacteristic
882#41—28no—
883#41—28no—
884#41—24no—
885#41—24no—
886#41—24no—
887#41—24no—
888#41—118no—
889#41—1116no—
890#41—228no—
891#41—228no—
892#41—224no—
893#41—224no—
894#41—2216no—
895#41—2232no—
896#41—2216no—
897#41—228no—
898#41—228no—
899#41—228no—
900#41—2216no—
901#41—2216no—
902#41—228no—
903#41—224no—
904#41—444no—
905#41D4×D1118yescomplemented
906C2×Q8—24no—
907C2×Q8—21no—
908C2×Q8—111no—
909C2×Q8—112no—
910C2×Q8—111no—
911C2×Q8—224no—
912C2×Q8C23×D1111yescharacteristic
913C2×Q8C23×D1112yes—
914C2×D4—28no—
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—24no—
918C2×D4—21no—
919C2×D4—21no—
920C2×D4—21no—
921C2×D4—21no—
922C2×D4—112no—
923C2×D4—1116no—
924C2×D4—112no—
925C2×D4—112no—
926C2×D4—112no—
927C2×D4—111no—
928C2×D4—118no—
929C2×D4—112no—
930C2×D4—111no—
931C2×D4—114no—
932C2×D4—112no—
933C2×D4—224no—
934C2×D4—228no—
935C2×D4—228no—
936C2×D4—2216no—
937C2×D4—224no—
938C2×D4—224no—
939C2×D4—2216no—
940C2×D4—228no—
941C2×D4—2232no—
942C2×D4—228no—
943C2×D4—2216no—
944C2×D4—228no—
945C2×D4—222no—
946C2×D4—222no—
947C2×D4—222no—
948C2×D4—228no—
949C2×D4—228no—
950C2×D4—224no—
951C2×D4—224no—
952C2×D4—222no—
953C2×D4—228no—
954C2×D4—2232no—
955C2×D4—2216no—
956C2×D4—2232no—
957C2×D4—2216no—
958C2×D4—2232no—
959C2×D4—2232no—
960C2×D4—228no—
961C2×D4—2216no—
962C2×D4—228no—
963C2×D4—222no—
964C2×D4—222no—
965C2×D4—222no—
966C2×D4—222no—
967C2×D4—222no—
968C2×D4—222no—
969C2×D4—224no—
970C2×D4—224no—
971C2×D4—221no—
972C2×D4—444no—
973C2×D4—448no—
974C2×D4—884no—
975C2×D4—882no—
976C2×D4C23×D1111yescharacteristic
977C2×D4C23×D1112yes—
978C22×C4—28no—
979C22×C4—21no—
980C22×C4—22no—
981C22×C4—22no—
982C22×C4—24no—
983C22×C4—21no—
984C22×C4—112no—
985C22×C4—112no—
986C22×C4—112no—
987C22×C4—112no—
988C22×C4—112no—
989C22×C4—228no—
990C22×C4—224no—
991C22×C4—224no—
992C22×C4—222no—
993C22×C4—2216no—
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—24no—
1003SD16—24no—
1004SD16—24no—
1005SD16—228no—
1006SD16—228no—
1007D8—24no—
1008D8—228no—
1009D8—228no—
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—21no—
1021C4⋊C4—112no—
1022C4⋊C4—222no—
1023C4⋊C4—222no—
1024C4⋊C4—221no—
1025C4⋊C4C23×D1111yescharacteristic
1026C4⋊C4C23×D1111yescharacteristic
1027C22⋊C4—21no—
1028C22⋊C4—21no—
1029C22⋊C4—21no—
1030C22⋊C4—21no—
1031C22⋊C4—21no—
1032C22⋊C4—222no—
1033C22⋊C4—222no—
1034C22⋊C4—222no—
1035C22⋊C4—222no—
1036C22⋊C4—222no—
1037C22⋊C4—222no—
1038C22⋊C4—222no—
1039C42—21no—
1040C42—222no—
1041C11#6037211yescharacteristic, complemented, Sylow
1042C23—24no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—21no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—112no—
1051C23—112no—
1052C23—224no—
1053C23—2216no—
1054C23—228no—
1055C23—228no—
1056C23—2216no—
1057C23—224no—
1058C23—224no—
1059C23—228no—
1060C23—222no—
1061C23—442no—
1062C23—444no—
1063C23—444no—
1064C23—444no—
1065C23—442no—
1066C23—882no—
1067C23—882no—
1068C23—882no—
1069C23—882no—
1070C23—881no—
1071C23—881no—
1072C23—884no—
1073C23—884no—
1074C23—884no—
1075C23—884no—
1076C23—882no—
1077C23—882no—
1078C23—8816no—
1079C23—8832no—
1080C23C2×D4×D1111yescharacteristic
1081C23C2×D4×D1111yescharacteristic
1082C23C2×D4×D1111yescharacteristic
1083Q8—24no—
1084Q8—22no—
1085Q8—22no—
1086Q8—114no—
1087Q8—224no—
1088Q8—222no—
1089Q8C2×D4×D1114yes—
1090D4—28no—
1091D4—24no—
1092D4—28no—
1093D4—22no—
1094D4—22no—
1095D4—42no—
1096D4—42no—
1097D4—81no—
1098D4—118no—
1099D4—114no—
1100D4—118no—
1101D4—224no—
1102D4—2216no—
1103D4—228no—
1104D4—2216no—
1105D4—228no—
1106D4—224no—
1107D4—2216no—
1108D4—224no—
1109D4—2216no—
1110D4—224no—
1111D4—228no—
1112D4—222no—
1113D4—224no—
1114D4—224no—
1115D4—444no—
1116D4—444no—
1117D4—444no—
1118D4—442no—
1119D4—882no—
1120D4—882no—
1121D4—882no—
1122D4—882no—
1123D4C2×D4×D1114yes—
1124C2×C4—24no—
1125C2×C4—28no—
1126C2×C4—22no—
1127C2×C4—22no—
1128C2×C4—22no—
1129C2×C4—28no—
1130C2×C4—22no—
1131C2×C4—22no—
1132C2×C4—22no—
1133C2×C4—21no—
1134C2×C4—21no—
1135C2×C4—21no—
1136C2×C4—42no—
1137C2×C4—112no—
1138C2×C4—118no—
1139C2×C4—112no—
1140C2×C4—224no—
1141C2×C4—2216no—
1142C2×C4—224no—
1143C2×C4—2216no—
1144C2×C4—224no—
1145C2×C4—224no—
1146C2×C4—222no—
1147C2×C4—444no—
1148C2×C4—882no—
1149C2×C4—881no—
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—24no—
1165C22—21no—
1166C22—44no—
1167C22—48no—
1168C22—42no—
1169C22—42no—
1170C22—41no—
1171C22—41no—
1172C22—41no—
1173C22—114no—
1174C22—222no—
1175C22—222no—
1176C22—222no—
1177C22—228no—
1178C22—222no—
1179C22—222no—
1180C22—448no—
1181C22—4416no—
1182C22—444no—
1183C22—444no—
1184C22—442no—
1185C22—442no—
1186C22—442no—
1187C22—888no—
1188C22—8816no—
1189C22—888no—
1190C22—8816no—
1191C22—1762no—
1192C22—1764no—
1193C22D11×#12012yes—
1194C22#1062330012yescomplemented
1195C22C22×D4×D1111yescharacteristic
1196C4—21no—
1197C4—24no—
1198C4—21no—
1199C4—41no—
1200C4—41no—
1201C4—41no—
1202C4—114no—
1203C4—222no—
1204C4—442no—
1205C4D11×#12012yes—
1206C4C22×D4×D1112yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—44no—
1211C2—81no—
1212C2—224no—
1213C2—442no—
1214C2—448no—
1215C2—882no—
1216C2C2×D11×#12011yescharacteristic
1217C2C2×#1062330011yescharacteristic
1218C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3002C2
socleC22×C11C23×D4
hypercenter#3002D11
hypocenterC11#60372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3002

Complements

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

NH ≅ G/Ntype
1. C22×#67042C2semidirect
2. C2×#10623300C2semidirect
3. #13082277C2semidirect
4. #13077924C2semidirect
5. #13077916C2semidirect
6. #13077887C2semidirect
7. #13077881C2semidirect
8. #13077868C2semidirect
9. #13077867C2semidirect
10. #13077844C2semidirect
11. #13077842C2semidirect
12. #13077839C2semidirect
13. C2×#10622345C2semidirect
14. D11×#447C2semidirect
15. #13077138C2semidirect
16. #13077062C2semidirect
17. C11×#3002C2semidirect
18. C22×C11×#41C22semidirect
24. C2×#67042C22semidirect
25. C2×#67042C22semidirect
26. C2×#67042C22semidirect
27. C22×#4343C22semidirect
29. C22×D4×D11C22semidirect
33. C23×D44C22semidirect
34. C2×C11×#135C22semidirect
35. C11×#525C22semidirect
36. #10623364C22semidirect
37. C2×#67002C22semidirect
38. C2×#67002C22semidirect
39. C2×#66983C22semidirect
41. C2×#66972C22semidirect
42. C2×#66967C22semidirect
43. C2×#66967C22semidirect
44. C2×D8×D11C22semidirect
45. C22×D88C22semidirect
46. C2×#66954C22semidirect
48. #10623160C22semidirect
49. #10623158C22semidirect
50. #10623138C22semidirect
51. D11×#121C22semidirect
57. #10623056C22semidirect
58. #10623054C22semidirect
59. C11×#452C22semidirect
60. C11×#451C22semidirect
61. C11×#450C22semidirect
62. C11×#449C22semidirect
63. C11×#448C22semidirect
64. C11×#447C22semidirect
65. C11×#416C22semidirect
66. C2×C11×C22⋊C8C22semidirect
67. #10622851C22semidirect
68. #10622845C22semidirect
69. #10622840C22semidirect
70. #10622830C22semidirect
71. #10622820C22semidirect
72. #10622800C22semidirect
73. #10622785C22semidirect
74. #10622782C22semidirect
75. #10622769C22semidirect
76. C2×#66885C22semidirect
77. #10622723C22semidirect
78. #10622659C22semidirect
79. #10622659C22semidirect
80. #10622649C22semidirect
81. #10622649C22semidirect
82. #10622614C22semidirect
83. #10622424C22semidirect
84. #10622424C22semidirect
85. #10622417C22semidirect
86. #10622416C22semidirect
87. #10622386C22semidirect
88. #10622386C22semidirect
89. #10622383C22semidirect
90. D11×#102C22semidirect
91. #10622345C22semidirect
92. #10622345C22semidirect
93. #10622345C22semidirect
94. #10622340C22semidirect
95. #10622339C22semidirect
96. D11×C22⋊C8C22semidirect
104. C2×C11×#41C23semidirect
122. #67042D4semidirect
128. C2×#4343C23semidirect
141. C2×D4×D11C23semidirect
168. C22×D44C23semidirect
173. C2×C11×Q16C23semidirect
174. C2×C11×SD16C23semidirect
175. C2×C11×SD16C23semidirect
176. C2×C11×D8C23semidirect
177. C22×C8×C11C23semidirect
180. C11×C22⋊Q8C23semidirect
182. C11×#121C23semidirect
186. C11×#117C23semidirect
189. #66999C23semidirect
190. C2×#4325C23semidirect
191. C2×#4325C23semidirect
195. #66991C23semidirect
197. C2×#4323C23semidirect
198. C2×#4323C23semidirect
203. #66983C23semidirect
205. C2×C4⋊Dic11C23semidirect
207. C2×#4318C23semidirect
213. C2×D88C23semidirect
214. C2×D88C23semidirect
216. C2×#4313C23semidirect
217. C2×C8×D11C23semidirect
220. #66948C23semidirect
221. #66948C23semidirect
224. #66945C23semidirect
225. C4⋊C4×D11C23semidirect
240. C11×#103C23semidirect
241. C11×#103C23semidirect
242. C11×#102C23semidirect
243. C11×#102C23semidirect
246. C11×C22⋊C8C23semidirect
247. #66899C23semidirect
248. #66896C23semidirect
250. C22⋊(C11⋊C8)C23semidirect
251. #66885C23semidirect
252. #66885C23semidirect
253. (C2×D11)⋊C8C23semidirect
254. (C2×D11)⋊C8C23semidirect
255. #66873C23semidirect
256. #66873C23semidirect
280. C11×#41C2×D4semidirect
328. #4343C2×D4semidirect
341. D4×D11C2×D4semidirect
377. C2×D44C2×D4semidirect
445. #3002D11semidirect
577. C22×#41C2×D11semidirect
588. C2×#135C2×D11semidirect
603. #525C2×D11semidirect
608. #452C2×D11semidirect
609. #451C2×D11semidirect
613. #450C2×D11semidirect
618. #449C2×D11semidirect
620. #448C2×D11semidirect
630. #447C2×D11semidirect
636. #416C2×D11semidirect
644. C2×C22⋊C8C2×D11semidirect
661. C22×C11#576semidirect
729. C2×#41C22×D11semidirect
775. C2×Q16C22×D11semidirect
778. C2×SD16C22×D11semidirect
779. C2×SD16C22×D11semidirect
786. C2×D8C22×D11semidirect
791. C22×C8C22×D11semidirect
802. C22⋊Q8C22×D11semidirect
818. #121C22×D11semidirect
832. #117C22×D11semidirect
838. #103C22×D11semidirect
839. #103C22×D11semidirect
845. #102C22×D11semidirect
846. #102C22×D11semidirect
853. C22⋊C8C22×D11semidirect
905. #41D4×D11semidirect
1041. C11#60372semidirect
1194. C22#10623300semidirect

Maximal subgroups

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

subgroupindex
C22×#670422
C2×#106233002
#130822772
#130779242
#130779162
#130778872
#130778812
#130778682
#130778672
#130778442
#130778422
#130778392
C2×#106223452
D11×#4472
#130771382
#130770622
C11×#30022
#6037211