Finite Group Databasebeta

← #15620304

Subgroups — #15620304

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×#10623305C212yesmaximal, complemented
3#13082281C211yesmaximal, characteristic, complemented
4#13077922C212yesmaximal, complemented
5#13077918C214yesmaximal, complemented
6#13077883C212yesmaximal, complemented
7#13077881C214yesmaximal, complemented
8#13077867C212yesmaximal, complemented
9#13077846C211yesmaximal, characteristic, complemented
10#13077840C212yesmaximal, complemented
11#13077834C211yesmaximal, characteristic, complemented
12#13077833C212yesmaximal, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14D11×#447C212yesmaximal, complemented
15#13077140C212yesmaximal, complemented
16#13077066C211yesmaximal, characteristic, complemented
17C11×#3006C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic, complemented
19C2×#67042—216no—
20C2×#67042—21no—
21C2×#67042—21no—
22C2×#67042—22no—
23C2×#67042C2212yes—
24C2×#67042C2214yescomplemented
25C2×#67042C2212yescomplemented
26C22×#4343C2212yescomplemented
27C2×#67037C2211yescharacteristic, complemented
28C22×D4×D11—22no—
29C22×D4×D11C2212yescomplemented
30C22×#4339—21no—
31C22×#4339C2211yescharacteristic
32C23×D44—21no—
33C23×D44C2211yescharacteristic, complemented
34C2×C11×AGL(1,ℤ/8)C2212yescomplemented
35C2×C11×#121C2211yescharacteristic, complemented
36C2×#67003C2212yescomplemented
37#10623336C2211yescharacteristic, complemented
38D4×C22⋊D11—22no—
39C22×#4323C2212yescomplemented
40#10623322C2211yescharacteristic, complemented
41#10623305—216no—
42C2×#66969C2214yescomplemented
43C2×#66967C2214yescomplemented
44C2×#66964C2214yescomplemented
45C2×D8×D11C2214yescomplemented
46C2×#66961C2212yescomplemented
47C2×#66960C2212yescomplemented
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×#449C2214yescomplemented
60C11×#448C2212yescomplemented
61C11×#447C2212yescomplemented
62C11×#417C2212yescomplemented
63C11×#407C2211yescharacteristic, complemented
64#10622852C2212yescomplemented
65#10622851C2212yescomplemented
66#10622846C2212yescomplemented
67#10622841C2211yescharacteristic, complemented
68#10622840C2211yescharacteristic, complemented
69#10622831C2211yescharacteristic, complemented
70#10622830C2211yescharacteristic, complemented
71C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
72#10622785C2214yescomplemented
73#10622785C2214yescomplemented
74#10622769C2214yescomplemented
75#10622769C2214yescomplemented
76#10622744C2212yescomplemented
77#10622742C2212yescomplemented
78#10622649C2212yescomplemented
79#10622649C2212yescomplemented
80#10622649C2214yescomplemented
81C2×#66873C2212yescomplemented
82#10622424C2214yescomplemented
83#10622423C2214yescomplemented
84#10622417C2214yescomplemented
85#10622416C2214yescomplemented
86#10622389C2214yescomplemented
87#10622386C2214yescomplemented
88#10622383C2214yescomplemented
89D11×#102C2214yescomplemented
90#10622345C2212yescomplemented
91#10622345C2212yescomplemented
92#10622344C2212yescomplemented
93#10622344C2212yescomplemented
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—
104C22×Q8×C11C2311yescharacteristic
105C22×D4×C11—21no—
106C22×D4×C11—21no—
107C22×D4×C11C2311yescharacteristic
108C22×D4×C11C2311yescharacteristic, complemented
109C23×C4×C11—21no—
110C23×C4×C11C2311yescharacteristic
111C22×C22⋊D11—22no—
112C22×C22⋊D11—22no—
113C22×C22⋊D11D412yes—
114#67042—232no—
115#67042—216no—
116#67042—216no—
117#67042—28no—
118#67042—216no—
119#67042—216no—
120#67042—28no—
121#67042—28no—
122#67042D4116yescomplemented
123C2×#4343—216no—
124C2×#4343—22no—
125C2×#4343—22no—
126C2×#4343C2314yes—
127C2×#4343C2314yes—
128#67037—28no—
129C2×#4341—21no—
130C2×#4341C2312yescomplemented
131C2×D4×D11—232no—
132C2×D4×D11—24no—
133C2×D4×D11—24no—
134C2×D4×D11—24no—
135C2×D4×D11—24no—
136C2×D4×D11—216no—
137C2×D4×D11—22no—
138C2×D4×D11—21no—
139C2×D4×D11—22no—
140C2×D4×D11—22no—
141C2×D4×D11C2314yes—
142C2×D4×D11C2314yes—
143C2×D4×D11C2312yescomplemented
144C2×#4339—216no—
145C2×#4339—28no—
146C2×#4339—22no—
147C2×#4339—24no—
148C2×#4339—22no—
149C2×#4339D412yes—
150C2×#4339D411yescharacteristic
151C2×#4339D411yescharacteristic
152C2×#4339C2311yescharacteristic
153C2×#4339C2312yes—
154C2×#4339C2311yescharacteristic
155C2×#4339C2311yescharacteristic, complemented
156C22×D44—216no—
157C22×D44—22no—
158C22×D44—21no—
159C22×D44—21no—
160C22×D44—21no—
161C22×D44—22no—
162C22×D44—24no—
163C22×D44—22no—
164C22×D44—28no—
165C22×D44D411yescharacteristic
166C22×D44C2312yes—
167C22×D44C2312yes—
168C22×D44C2312yes—
169C22×C4×D11—22no—
170C22×C4×D11C2312yes—
171C22×Dic22D411yescharacteristic
172C11×AGL(1,ℤ/8)—28no—
173C2×C11×SD16C2314yescomplemented
174C2×C11×D8C2314yescomplemented
175C2×C11×M16C2312yescomplemented
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#67003—28no—
185C2×#4326C2312yescomplemented
186C2×#4325C2312yescomplemented
187#66993—22no—
188#66993—21no—
189#66992—22no—
190#66992—22no—
191#66991—22no—
192#66991C2312yescomplemented
193#66991C2312yescomplemented
194#66990—22no—
195#66990—22no—
196#66989—21no—
197D4×Dic11—22no—
198C2×#4324C2312yescomplemented
199C2×#4323—28no—
200C2×#4323C2314yescomplemented
201C2×#4323C2314yescomplemented
202C2×#4323C2312yescomplemented
203#66983—22no—
204#66983C2311yescharacteristic
205#66983C2311yescharacteristic, complemented
206#66982—21no—
207C4×C22⋊D11—21no—
208C4×C22⋊D11—21no—
209C4×C22⋊D11—22no—
210#66979C2311yescharacteristic, complemented
211#66977C2311yescharacteristic
212#66977C2311yescharacteristic, complemented
213C22×C11⋊C8C2312yescomplemented
214#66969—216no—
215#66967—216no—
216#66964—216no—
217D8×D11—216no—
218#66961—28no—
219#66960—28no—
220C2×D88C2314yescomplemented
221C2×#4314C2314yescomplemented
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×#103C2314yescomplemented
241C11×#102C2314yescomplemented
242C11×C22⋊C8C2312yes—
243C11×C22⋊C8C2312yescomplemented
244#66899C2312yescomplemented
245#66899C2312yescomplemented
246#66896C2312yescomplemented
247#66896C2312yescomplemented
248C22⋊(C11⋊C8)C2311yescharacteristic
249C22⋊(C11⋊C8)C2311yescharacteristic
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×C11—21no—
260C24×C11C2×D411yescharacteristic
261C23×D11—22no—
262C23×D11—28no—
263C23×D11—216no—
264C23×D11—22no—
265C23×D11—22no—
266C23×D11—24no—
267C23×D11—24no—
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×#41C2×D418yescomplemented
280C2×Q8×C11—24no—
281C2×Q8×C11—21no—
282C2×Q8×C11C2412yes—
283C2×D4×C11—28no—
284C2×D4×C11—22no—
285C2×D4×C11—22no—
286C2×D4×C11—24no—
287C2×D4×C11—22no—
288C2×D4×C11—22no—
289C2×D4×C11—21no—
290C2×D4×C11—24no—
291C2×D4×C11—21no—
292C2×D4×C11—82no—
293C2×D4×C11C2412yes—
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—21no—
313C2×C22⋊D11—21no—
314C2×C22⋊D11—21no—
315C2×C22⋊D11—22no—
316C2×C22⋊D11—22no—
317C2×C22⋊D11—22no—
318C2×C22⋊D11—48no—
319C2×C22⋊D11C2×D412yes—
320C2×C22⋊D11C2×D412yes—
321C2×C22⋊D11C2×D412yes—
322C2×C22⋊D11C2×D412yes—
323C22×Dic11—22no—
324C22×Dic11C2×D412yes—
325#4343—216no—
326#4343—216no—
327#4343—28no—
328#4343—28no—
329#4343—28no—
330#4343C2×D4116yescomplemented
331#4341—28no—
332#4341—44no—
333D4×D11—232no—
334D4×D11—216no—
335D4×D11—232no—
336D4×D11—216no—
337D4×D11—232no—
338D4×D11—232no—
339D4×D11—28no—
340D4×D11—28no—
341D4×D11—28no—
342D4×D11—28no—
343D4×D11—44no—
344D4×D11—84no—
345D4×D11C2×D4116yescomplemented
346#4339—232no—
347#4339—216no—
348#4339—28no—
349#4339—24no—
350#4339—28no—
351#4339—216no—
352#4339—24no—
353#4339—24no—
354#4339—24no—
355#4339C2×D418yes—
356C2×D44—28no—
357C2×D44—216no—
358C2×D44—232no—
359C2×D44—28no—
360C2×D44—216no—
361C2×D44—28no—
362C2×D44—24no—
363C2×D44—216no—
364C2×D44—28no—
365C2×D44—28no—
366C2×D44—24no—
367C2×D44—24no—
368C2×D44—22no—
369C2×D44—22no—
370C2×D44—22no—
371C2×D44—22no—
372C2×D44—24no—
373C2×D44C2×D412yes—
374C2×D44C2×D411yescharacteristic
375C2×D44C2×D411yescharacteristic
376C2×D44C2×D418yescomplemented
377C2×D44C2411yescharacteristic
378C2×D44C2414yes—
379C2×C4×D11—216no—
380C2×C4×D11—24no—
381C2×C4×D11—24no—
382C2×C4×D11—28no—
383C2×C4×D11—22no—
384C2×C4×D11—21no—
385C2×C4×D11C2×D412yes—
386C2×C4×D11C2×D412yes—
387C2×C4×D11C2412yes—
388C2×C4×D11C2412yes—
389C2×Dic22—24no—
390C2×Dic22C2×D412yes—
391C2×Dic22C2×D411yescharacteristic
392C2×Dic22C2×D411yescharacteristic
393C2×Dic22C2411yescharacteristic
394C11×SD16—28no—
395C11×D8—28no—
396C11×M16—24no—
397C2×C8×C11C2414yes—
398C11×C4⋊C4—21no—
399C11×C4⋊C4C2412yes—
400C11×C22⋊C4—22no—
401C11×C22⋊C4—22no—
402C22⋊Dic11—22no—
403C22⋊Dic11—22no—
404C22⋊Dic11—21no—
405C22⋊Dic11—21no—
406C22⋊Dic11—21no—
407#4326—24no—
408#4325—24no—
409#4324—24no—
410#4323—28no—
411#4323—28no—
412#4323—24no—
413(C2×D11)⋊C4—22no—
414(C2×D11)⋊C4—22no—
415(C2×D11)⋊C4—22no—
416(C2×D11)⋊C4—21no—
417(C2×D11)⋊C4—21no—
418C4⋊Dic11—22no—
419C4⋊Dic11C2411yescharacteristic
420C4⋊Dic11C2411yescharacteristic
421Dic11⋊C4—22no—
422Dic11⋊C4—21no—
423Dic11⋊C4—21no—
424C4×Dic11—22no—
425C4×Dic11—21no—
426C2×C11⋊C8—24no—
427C2×C11⋊C8C2412yes—
428C2×C11⋊C8C2412yes—
429D88—28no—
430#4314—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#3006D1111yescharacteristic, complemented
442#3003—112no—
443#3003—111no—
444#3002—112no—
445#3002—111no—
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—22no—
455C23×C11—41no—
456C23×C11—42no—
457C23×C11—42no—
458C23×C11—42no—
459C23×C11—81no—
460C23×C11—81no—
461C23×C11C22×D411yescharacteristic
462C23×C11C22×D411yescharacteristic
463C23×C11C22×D411yescharacteristic
464C22×D11—28no—
465C22×D11—24no—
466C22×D11—24no—
467C22×D11—28no—
468C22×D11—216no—
469C22×D11—28no—
470C22×D11—24no—
471C22×D11—216no—
472C22×D11—21no—
473C22×D11—42no—
474C22×D11—44no—
475C22×D11—44no—
476C22×D11—44no—
477C22×D11—84no—
478C22×D11—84no—
479C22×D11—84no—
480C22×D11—84no—
481C22×D11—82no—
482C22×D11—82no—
483C22×D11—82no—
484C22×D11—82no—
485C22×D11—82no—
486C22×D11—82no—
487C22×D11—832no—
488C22×D11—816no—
489C22×D11C22×D412yes—
490C22×D11C22×D412yes—
491Q8×C11—24no—
492Q8×C11—22no—
493Q8×C11C22×D414yes—
494D4×C11—28no—
495D4×C11—24no—
496D4×C11—28no—
497D4×C11—22no—
498D4×C11—24no—
499D4×C11—44no—
500D4×C11—42no—
501D4×C11—82no—
502D4×C11C22×D414yes—
503C2×C4×C11—24no—
504C2×C4×C11—28no—
505C2×C4×C11—22no—
506C2×C4×C11—22no—
507C2×C4×C11—22no—
508C2×C4×C11—28no—
509C2×C4×C11—22no—
510C2×C4×C11—22no—
511C2×C4×C11—22no—
512C2×C4×C11—22no—
513C2×C4×C11—81no—
514C2×C4×C11C22×D411yescharacteristic
515C2×C4×C11C22×D411yescharacteristic
516C2×C4×C11C22×D411yescharacteristic
517C2×C4×C11C22×D414yes—
518C2×C4×C11C2511yescharacteristic
519C22⋊D11—216no—
520C22⋊D11—24no—
521C22⋊D11—24no—
522C22⋊D11—24no—
523C22⋊D11—216no—
524C22⋊D11—42no—
525C22⋊D11—42no—
526C22⋊D11—44no—
527C22⋊D11—44no—
528C22⋊D11—82no—
529C22⋊D11—82no—
530C22⋊D11—81no—
531C22⋊D11#12018yes—
532C2×Dic11—24no—
533C2×Dic11—21no—
534C2×Dic11—21no—
535C2×Dic11—21no—
536C2×Dic11—44no—
537C2×Dic11C22×D412yes—
538C2×Dic11C22×D412yes—
539D44—28no—
540D44—216no—
541D44—28no—
542D44—24no—
543D44—216no—
544D44—22no—
545D44—28no—
546D44—24no—
547D44—22no—
548D44—82no—
549D44#12014yes—
550D44C22×D418yes—
551C4×D11—216no—
552C4×D11—24no—
553C4×D11—24no—
554C4×D11—216no—
555C4×D11—24no—
556C4×D11—42no—
557C4×D11—82no—
558C4×D11C22×D418yes—
559Dic22—22no—
560Dic22—24no—
561Dic22—22no—
562Dic22#12014yes—
563C8×C11—24no—
564C11⋊C8—22no—
565C11⋊C8—22no—
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)—114no—
584C2×AGL(1,ℤ/8)—114no—
585C2×AGL(1,ℤ/8)—112no—
586C2×AGL(1,ℤ/8)C2×D1112yescomplemented
587C2×#135—112no—
588C2×#135—114no—
589C22×D8—112no—
590C22×D8—114no—
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—112no—
608#452—114no—
609#451—111no—
610#450—111no—
611#450—114no—
612#450—112no—
613#450—112no—
614#449—112no—
615#449—114no—
616#449—114no—
617#449—114no—
618#449C2×D1114yescomplemented
619#448—111no—
620#448C2×D1112yescomplemented
621#447—111no—
622#447—114no—
623#447—114no—
624#447—112no—
625#447—112no—
626#447—114no—
627#447—114no—
628#447—112no—
629#447—112no—
630#447C2×D1112yescomplemented
631#418—112no—
632#418—114no—
633#417—114no—
634#417C2×D1112yescomplemented
635#416—112no—
636#416—114no—
637C2×#102—112no—
638C2×#102—114no—
639#408—112no—
640#408—114no—
641#407—112no—
642#407C2×D1111yescharacteristic, complemented
643C2×C22⋊C8—111no—
644C2×C22⋊C8—112no—
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—42no—
658C22×C11—42no—
659C22×C11—42no—
660C22×C11—162no—
661C22×C11C2×#12012yes—
662C22×C11#57612yescomplemented
663C22×C11C23×D411yescharacteristic
664C2×D11—22no—
665C2×D11—22no—
666C2×D11—22no—
667C2×D11—28no—
668C2×D11—22no—
669C2×D11—22no—
670C2×D11—48no—
671C2×D11—416no—
672C2×D11—44no—
673C2×D11—44no—
674C2×D11—41no—
675C2×D11—41no—
676C2×D11—41no—
677C2×D11—816no—
678C2×D11—88no—
679C2×D11—816no—
680C2×D11—88no—
681C2×D11—164no—
682C2×D11C2×#12014yes—
683C4×C11—21no—
684C4×C11—24no—
685C4×C11—21no—
686C4×C11—42no—
687C4×C11C2×#12012yes—
688C4×C11C23×D412yes—
689Dic11—22no—
690Dic11—41no—
691Dic11—41no—
692Dic11—41no—
693Dic11C2×#12014yes—
694C25—222no—
695C25—221no—
696H(5,𝔽2)—1116no—
697H(5,𝔽2)—228no—
698H(5,𝔽2)—2216no—
699H(5,𝔽2)—228no—
700H(5,𝔽2)—2216no—
701H(5,𝔽2)—228no—
702H(5,𝔽2)—2216no—
703H(5,𝔽2)—2232no—
704H(5,𝔽2)—2216no—
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—114no—
717C2×#41—112no—
718C2×#41—111no—
719C2×#41—222no—
720C2×#41—224no—
721C2×#41—222no—
722C2×#41—228no—
723C2×#41—2216no—
724C2×#41—222no—
725C2×#41—222no—
726C2×#41—221no—
727C2×#41—2216no—
728C2×#41C22×D1112yes—
729C2×#41C22×D1112yes—
730C22×Q8—111no—
731C22×Q8C22×D1111yescharacteristic
732C22×D4—21no—
733C22×D4—21no—
734C22×D4—114no—
735C22×D4—112no—
736C22×D4—112no—
737C22×D4—114no—
738C22×D4—111no—
739C22×D4—112no—
740C22×D4—112no—
741C22×D4—112no—
742C22×D4—228no—
743C22×D4—222no—
744C22×D4—224no—
745C22×D4—222no—
746C22×D4—222no—
747C22×D4—2216no—
748C22×D4—222no—
749C22×D4—222no—
750C22×D4—222no—
751C22×D4—2216no—
752C22×D4—224no—
753C22×D4—224no—
754C22×D4—224no—
755C22×D4—224no—
756C22×D4—221no—
757C22×D4—2232no—
758C22×D4—222no—
759C22×D4—222no—
760C22×D4—221no—
761C22×D4—221no—
762C22×D4—221no—
763C22×D4C22×D1111yescharacteristic
764C22×D4C22×D1111yescharacteristic, complemented
765C23×C4—21no—
766C23×C4—112no—
767C23×C4—222no—
768C23×C4C22×D1111yescharacteristic
769AGL(1,ℤ/8)—28no—
770AGL(1,ℤ/8)—228no—
771AGL(1,ℤ/8)—2216no—
772AGL(1,ℤ/8)—2216no—
773#135—2216no—
774#135—228no—
775C2×Q16—112no—
776C2×SD16—112no—
777C2×SD16—112no—
778C2×SD16—114no—
779C2×SD16C22×D1114yescomplemented
780C2×D8—114no—
781C2×D8—112no—
782C2×D8—114no—
783C2×D8—114no—
784C2×D8—2216no—
785C2×D8—228no—
786C2×D8C22×D1114yescomplemented
787#131—228no—
788C2×M16—114no—
789C2×M16C22×D1112yescomplemented
790C22×C8—112no—
791C22×C8—114no—
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#103C22×D1114yescomplemented
840#102—112no—
841#102—112no—
842#102—114no—
843#102—114no—
844#102—114no—
845#102—114no—
846#102C22×D1114yescomplemented
847C22⋊C8—111no—
848C22⋊C8—111no—
849C22⋊C8—112no—
850C22⋊C8—114no—
851C22⋊C8—114no—
852C22⋊C8C22×D1112yes—
853C22⋊C8C22×D1112yescomplemented
854C2×C11—22no—
855C2×C11—22no—
856C2×C11—41no—
857C2×C11—44no—
858C2×C11—82no—
859C2×C11C22×#12011yescharacteristic
860C2×C11C2×#57611yescharacteristic
861C2×C11#358511yescharacteristic
862D11—24no—
863D11—42no—
864D11—48no—
865D11—81no—
866C24—21no—
867C24—21no—
868C24—112no—
869C24—224no—
870C24—224no—
871C24—222no—
872C24—2216no—
873C24—228no—
874C24—222no—
875C24—222no—
876C24—222no—
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—118no—
888#41—1116no—
889#41—228no—
890#41—228no—
891#41—224no—
892#41—224no—
893#41—2216no—
894#41—2232no—
895#41—2216no—
896#41—228no—
897#41—228no—
898#41—228no—
899#41—2216no—
900#41—2216no—
901#41—228no—
902#41—224no—
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—111no—
912C2×Q8—224no—
913C2×Q8C23×D1112yes—
914C2×D4—28no—
915C2×D4—22no—
916C2×D4—22no—
917C2×D4—24no—
918C2×D4—22no—
919C2×D4—22no—
920C2×D4—21no—
921C2×D4—24no—
922C2×D4—21no—
923C2×D4—82no—
924C2×D4—112no—
925C2×D4—1116no—
926C2×D4—112no—
927C2×D4—112no—
928C2×D4—112no—
929C2×D4—111no—
930C2×D4—118no—
931C2×D4—112no—
932C2×D4—111no—
933C2×D4—114no—
934C2×D4—111no—
935C2×D4—224no—
936C2×D4—228no—
937C2×D4—228no—
938C2×D4—2216no—
939C2×D4—224no—
940C2×D4—224no—
941C2×D4—2216no—
942C2×D4—228no—
943C2×D4—2232no—
944C2×D4—228no—
945C2×D4—2216no—
946C2×D4—228no—
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—221no—
965C2×D4—221no—
966C2×D4—222no—
967C2×D4—222no—
968C2×D4—221no—
969C2×D4—222no—
970C2×D4—222no—
971C2×D4—222no—
972C2×D4—224no—
973C2×D4—444no—
974C2×D4—448no—
975C2×D4—884no—
976C2×D4C23×D1112yes—
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—2216no—
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—28no—
1004SD16—228no—
1005SD16—224no—
1006SD16—224no—
1007D8—28no—
1008D8—228no—
1009D8—228no—
1010D8—228no—
1011D8—224no—
1012M16—24no—
1013M16—228no—
1014C2×C8—112no—
1015C2×C8—112no—
1016C2×C8—228no—
1017C2×C8—224no—
1018C2×C8C23×D1114yes—
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—24no—
1043C23—22no—
1044C23—22no—
1045C23—22no—
1046C23—22no—
1047C23—41no—
1048C23—42no—
1049C23—42no—
1050C23—42no—
1051C23—81no—
1052C23—81no—
1053C23—112no—
1054C23—112no—
1055C23—224no—
1056C23—2216no—
1057C23—228no—
1058C23—228no—
1059C23—2216no—
1060C23—224no—
1061C23—224no—
1062C23—228no—
1063C23—221no—
1064C23—442no—
1065C23—444no—
1066C23—444no—
1067C23—444no—
1068C23—882no—
1069C23—882no—
1070C23—882no—
1071C23—882no—
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—114no—
1086Q8—224no—
1087Q8—222no—
1088Q8—222no—
1089Q8C2×D4×D1114yes—
1090D4—28no—
1091D4—24no—
1092D4—28no—
1093D4—22no—
1094D4—24no—
1095D4—44no—
1096D4—42no—
1097D4—82no—
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—222no—
1115D4—444no—
1116D4—444no—
1117D4—442no—
1118D4—442no—
1119D4—882no—
1120D4—881no—
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—22no—
1134C2×C4—81no—
1135C2×C4—112no—
1136C2×C4—118no—
1137C2×C4—112no—
1138C2×C4—224no—
1139C2×C4—2216no—
1140C2×C4—224no—
1141C2×C4—2216no—
1142C2×C4—224no—
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—24no—
1156C8—222no—
1157C8—222no—
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—42no—
1171C22—42no—
1172C22—42no—
1173C22—114no—
1174C22—162no—
1175C22—222no—
1176C22—222no—
1177C22—222no—
1178C22—228no—
1179C22—222no—
1180C22—222no—
1181C22—448no—
1182C22—4416no—
1183C22—444no—
1184C22—444no—
1185C22—441no—
1186C22—441no—
1187C22—441no—
1188C22—888no—
1189C22—8816no—
1190C22—888no—
1191C22—8816no—
1192C22—1764no—
1193C22D11×#12012yes—
1194C22#1062330512yescomplemented
1195C22C22×D4×D1111yescharacteristic
1196C4—21no—
1197C4—24no—
1198C4—21no—
1199C4—42no—
1200C4—114no—
1201C4—222no—
1202C4—441no—
1203C4—441no—
1204C4—441no—
1205C4D11×#12012yes—
1206C4C22×D4×D1112yes—
1207C2—22no—
1208C2—22no—
1209C2—41no—
1210C2—44no—
1211C2—82no—
1212C2—224no—
1213C2—442no—
1214C2—448no—
1215C2—881no—
1216C2C2×D11×#12011yescharacteristic
1217C2C2×#1062330511yescharacteristic
1218C2#1308339311yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#60372
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3006

Complements

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

NH ≅ G/Ntype
1. C22×#67042C2semidirect
2. C2×#10623305C2semidirect
3. #13082281C2semidirect
4. #13077922C2semidirect
5. #13077918C2semidirect
6. #13077883C2semidirect
7. #13077881C2semidirect
8. #13077867C2semidirect
9. #13077846C2semidirect
10. #13077840C2semidirect
11. #13077834C2semidirect
12. #13077833C2semidirect
13. C2×#10622649C2semidirect
14. D11×#447C2semidirect
15. #13077140C2semidirect
16. #13077066C2semidirect
17. C11×#3006C2semidirect
18. C22×C11×#41C22semidirect
24. C2×#67042C22semidirect
25. C2×#67042C22semidirect
26. C22×#4343C22semidirect
27. C2×#67037C22semidirect
29. C22×D4×D11C22semidirect
33. C23×D44C22semidirect
34. C2×C11×AGL(1,ℤ/8)C22semidirect
35. C2×C11×#121C22semidirect
36. C2×#67003C22semidirect
37. #10623336C22semidirect
39. C22×#4323C22semidirect
40. #10623322C22semidirect
42. C2×#66969C22semidirect
43. C2×#66967C22semidirect
44. C2×#66964C22semidirect
45. C2×D8×D11C22semidirect
46. C2×#66961C22semidirect
47. C2×#66960C22semidirect
50. #10623139C22semidirect
51. #10623138C22semidirect
52. #10623137C22semidirect
53. D11×#121C22semidirect
56. #10623041C22semidirect
57. #10623035C22semidirect
59. C11×#449C22semidirect
60. C11×#448C22semidirect
61. C11×#447C22semidirect
62. C11×#417C22semidirect
63. C11×#407C22semidirect
64. #10622852C22semidirect
65. #10622851C22semidirect
66. #10622846C22semidirect
67. #10622841C22semidirect
68. #10622840C22semidirect
69. #10622831C22semidirect
70. #10622830C22semidirect
71. C2×C22⋊(C11⋊C8)C22semidirect
72. #10622785C22semidirect
73. #10622785C22semidirect
74. #10622769C22semidirect
75. #10622769C22semidirect
76. #10622744C22semidirect
77. #10622742C22semidirect
78. #10622649C22semidirect
79. #10622649C22semidirect
80. #10622649C22semidirect
81. C2×#66873C22semidirect
82. #10622424C22semidirect
83. #10622423C22semidirect
84. #10622417C22semidirect
85. #10622416C22semidirect
86. #10622389C22semidirect
87. #10622386C22semidirect
88. #10622383C22semidirect
89. D11×#102C22semidirect
90. #10622345C22semidirect
91. #10622345C22semidirect
92. #10622344C22semidirect
93. #10622344C22semidirect
94. #10622340C22semidirect
95. #10622339C22semidirect
96. D11×C22⋊C8C22semidirect
108. C22×D4×C11C23semidirect
122. #67042D4semidirect
130. C2×#4341C23semidirect
143. C2×D4×D11C23semidirect
155. C2×#4339C23semidirect
173. C2×C11×SD16C23semidirect
174. C2×C11×D8C23semidirect
175. C2×C11×M16C23semidirect
179. C11×#121C23semidirect
180. C2×C11×C4⋊C4C23semidirect
185. C2×#4326C23semidirect
186. C2×#4325C23semidirect
192. #66991C23semidirect
193. #66991C23semidirect
198. C2×#4324C23semidirect
200. C2×#4323C23semidirect
201. C2×#4323C23semidirect
202. C2×#4323C23semidirect
205. #66983C23semidirect
210. #66979C23semidirect
212. #66977C23semidirect
213. C22×C11⋊C8C23semidirect
220. C2×D88C23semidirect
221. C2×#4314C23semidirect
222. C2×#4313C23semidirect
223. C2×C8×D11C23semidirect
225. #66950C23semidirect
227. #66948C23semidirect
229. #66945C23semidirect
230. C4⋊C4×D11C23semidirect
240. C11×#103C23semidirect
241. C11×#102C23semidirect
243. C11×C22⋊C8C23semidirect
244. #66899C23semidirect
245. #66899C23semidirect
246. #66896C23semidirect
247. #66896C23semidirect
250. C22⋊(C11⋊C8)C23semidirect
251. #66885C23semidirect
252. #66885C23semidirect
253. (C2×D11)⋊C8C23semidirect
254. (C2×D11)⋊C8C23semidirect
255. #66873C23semidirect
256. #66873C23semidirect
279. C11×#41C2×D4semidirect
330. #4343C2×D4semidirect
345. D4×D11C2×D4semidirect
376. C2×D44C2×D4semidirect
441. #3006D11semidirect
577. C22×#41C2×D11semidirect
586. C2×AGL(1,ℤ/8)C2×D11semidirect
605. C2×#121C2×D11semidirect
618. #449C2×D11semidirect
620. #448C2×D11semidirect
630. #447C2×D11semidirect
634. #417C2×D11semidirect
642. #407C2×D11semidirect
662. C22×C11#576semidirect
764. C22×D4C22×D11semidirect
779. C2×SD16C22×D11semidirect
786. C2×D8C22×D11semidirect
789. C2×M16C22×D11semidirect
818. #121C22×D11semidirect
834. C2×C4⋊C4C22×D11semidirect
839. #103C22×D11semidirect
846. #102C22×D11semidirect
853. C22⋊C8C22×D11semidirect
905. #41D4×D11semidirect
1041. C11#60372semidirect
1194. C22#10623305semidirect

Maximal subgroups

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

subgroupindex
C22×#670422
C2×#106233052
#130822812
#130779222
#130779182
#130778832
#130778812
#130778672
#130778462
#130778402
#130778342
#130778332
C2×#106226492
D11×#4472
#130771402
#130770662
C11×#30062
#6037211