Finite Group Databasebeta

← #15618027

Subgroups — #15618027

Order 2816.

2734 conjugacy classes of subgroups.

The subgroup lattice has 1232 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623309C211yesmaximal, characteristic
2#13081825C211yesmaximal, characteristic, complemented
3#13081822C211yesmaximal, characteristic, complemented
4#13077491C212yesmaximal, complemented
5#13077489C211yesmaximal, characteristic, complemented
6#13077475C211yesmaximal, characteristic, complemented
7#13077470C212yesmaximal, complemented
8#13077458C212yesmaximal, complemented
9#13077450C211yesmaximal, characteristic, complemented
10#13077447C212yesmaximal, complemented
11#137×Dic11C211yesmaximal, characteristic, complemented
12C4×#66971C212yesmaximal, complemented
13C4×#66967C212yesmaximal, complemented
14#13077423C211yesmaximal, characteristic, complemented
15#13077415C212yesmaximal, complemented
16#13077412C211yesmaximal, characteristic, complemented
17C2×#10622430C211yesmaximal, characteristic, complemented
18D11×#440C212yesmaximal, complemented
19#13077215C211yesmaximal, characteristic, complemented
20#13077144C211yesmaximal, characteristic, complemented
21#13077138C211yesmaximal, characteristic, complemented
22#13077043C211yesmaximal, characteristic, complemented
23C11×#2947C211yesmaximal, characteristic, complemented
24C2×#67042C2211yescharacteristic
25C2×#67040C2211yescharacteristic
26C2×C11×#137C2211yescharacteristic
27C11×#520C2211yescharacteristic
28C11×#519C2211yescharacteristic, complemented
29#41×Dic11C2211yescharacteristic
30C2×#67003C2211yescharacteristic
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C22×#4325C2211yescharacteristic
33#10623309C4116yescomplemented
34C2×#66972C2212yes—
35C2×#66971C2212yes—
36C2×#66967C2212yes—
37C2×SD16×D11C2212yes—
38C2×#66961C2211yescharacteristic
39C2×#66960C2211yescharacteristic
40C2×#66954C2211yescharacteristic
41#10623105—21no—
42#10623105C2212yes—
43#10623105C2212yescomplemented
44C4×#4343—21no—
45C4×#4343C2212yes—
46C4×#4343C2212yescomplemented
47#10623103—21no—
48#10623103C2212yescomplemented
49C4×Q8×D11—21no—
50C4×Q8×D11C2212yescomplemented
51#10623076—22no—
52#10623076C2212yes—
53C4×D4×D11—22no—
54C4×D4×D11C2212yes—
55#10623054—22no—
56#10623054C2211yescharacteristic
57#10623054C2211yescharacteristic, complemented
58#10623053—21no—
59#10623053—22no—
60#10623053C2211yescharacteristic
61#10623053C2211yescharacteristic, complemented
62#10623052—21no—
63#10623052C2211yescharacteristic
64#10623035—21no—
65#10623035C2211yescharacteristic
66C2×#66946—21no—
67C2×#66946C2211yescharacteristic
68C11×#441C2212yescomplemented
69C11×#440C2212yescomplemented
70C4×C11×Q16C2212yescomplemented
71C4×C11×SD16C2212yescomplemented
72C11×#428C2211yescharacteristic, complemented
73C11×#416C2211yescharacteristic
74C2×C11×#103C2211yescharacteristic, complemented
75C11×#405C2211yescharacteristic, complemented
76#10622845C2211yescharacteristic
77#10622838C2211yescharacteristic, complemented
78#10622797C2212yescomplemented
79Q16×Dic11C2212yescomplemented
80#10622777C2212yescomplemented
81SD16×Dic11C2212yescomplemented
82#10622734C2211yescharacteristic, complemented
83M16×Dic11C2211yescharacteristic, complemented
84#10622726C2211yescharacteristic, complemented
85C2×#66885C2211yescharacteristic
86C2×#66879C2211yescharacteristic, complemented
87C4×#4326C2212yescomplemented
88#10622639C2212yescomplemented
89#10622639C2212yescomplemented
90#10622639C2212yescomplemented
91C4×#4325C2212yescomplemented
92C4×#4325C2212yescomplemented
93#10622631C2212yescomplemented
94C4×#4323C2212yescomplemented
95#10622614C2211yescharacteristic
96#10622611C2211yescharacteristic, complemented
97#10622610C2211yescharacteristic, complemented
98#10622579C2211yescharacteristic, complemented
99C2×#66871C2211yescharacteristic, complemented
100#10622502C2212yescomplemented
101#10622494C2212yescomplemented
102D11×#107C2212yescomplemented
103#10622485C2212yescomplemented
104#10622482C2212yescomplemented
105#10622474C2212yescomplemented
106#10622473C2212yescomplemented
107#10622465C2212yescomplemented
108#10622430C2212yescomplemented
109#10622430C2212yescomplemented
110#10622430C2212yescomplemented
111#10622430C2212yescomplemented
112#10622430C2211yescharacteristic, complemented
113#10622430C2211yescharacteristic, complemented
114#10622417C2212yes—
115#10622417C2212yescomplemented
116#10622416C2212yes—
117#10622416C2212yescomplemented
118#10622415C2212yescomplemented
119D11×#103C2212yescomplemented
120#10622402C2211yescharacteristic, complemented
121#10622402C2211yescharacteristic, complemented
122#10622398C2211yescharacteristic, complemented
123#10622398C2211yescharacteristic, complemented
124#10622383C2212yes—
125D11×#102C2212yes—
126#10622370C2211yescharacteristic, complemented
127#10622370C2211yescharacteristic, complemented
128#10622324C2212yescomplemented
129#10622323C2212yescomplemented
130#10622321C2212yescomplemented
131D11×#97C2212yescomplemented
132C4×D88C2212yescomplemented
133C4×#4314C2212yescomplemented
134#10622302C2212yescomplemented
135C4×#4313C2212yescomplemented
136C2×C11×#41C2311yescharacteristic
137C22×Q8×C11C2311yescharacteristic
138#67042—24no—
139#67042C2×C418yescomplemented
140#67040—24no—
141#67040C2×C418yescomplemented
142C2×#4343—21no—
143C2×#4343C2312yes—
144C2×#4343C2312yes—
145C2×Q8×D11—21no—
146C2×Q8×D11C2312yes—
147C2×D4×D11—22no—
148C2×D4×D11C2312yes—
149C2×#4339—22no—
150C2×#4339—21no—
151C2×#4339C2311yescharacteristic
152C2×#4339C2311yescharacteristic
153C22×D44—21no—
154C22×D44C2311yescharacteristic
155C22×C4×D11—21no—
156C22×C4×D11—22no—
157C11×#137C2×C418yescomplemented
158C2×C11×Q16C2312yes—
159C2×C11×SD16C2312yes—
160C2×C11×M16C2311yescharacteristic
161C22×C8×C11C2311yescharacteristic
162C4×Q8×C11—21no—
163C4×Q8×C11—21no—
164C4×Q8×C11C2312yes—
165C4×Q8×C11C2312yes—
166C4×Q8×C11C2312yes—
167C4×D4×C11—22no—
168C4×D4×C11C2312yes—
169C11×#117—21no—
170C11×#117—22no—
171C11×#117C2311yescharacteristic
172C11×#117C2311yescharacteristic
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4C2311yescharacteristic
175#67003C2×C418yescomplemented
176Q8×Dic11—21no—
177Q8×Dic11—21no—
178Q8×Dic11C2312yes—
179Q8×Dic11C2312yes—
180Q8×Dic11C2311yescharacteristic
181Q8×Dic11C2311yescharacteristic
182C2×#4326C2311yescharacteristic
183C2×#4325C2×C418yescomplemented
184C2×#4325C2312yes—
185C2×#4325C2312yes—
186C2×#4325C2311yescharacteristic
187D4×Dic11—21no—
188D4×Dic11—21no—
189D4×Dic11C2311yescharacteristic
190D4×Dic11C2311yescharacteristic
191C2×#4324C2311yescharacteristic
192C2×#4323C2311yescharacteristic
193C4×C22⋊D11—22no—
194C4×C22⋊D11—22no—
195C4×C22⋊D11—22no—
196C2×(C2×D11)⋊C4—21no—
197C2×(C2×D11)⋊C4—22no—
198#66979—21no—
199#66979C2311yescharacteristic
200C2×C4⋊Dic11—21no—
201C2×C4⋊Dic11C2311yescharacteristic
202C2×C4×Dic11—21no—
203C2×C4×Dic11—21no—
204C2×C4×Dic11C2311yescharacteristic
205C2×#4318C2311yescharacteristic
206C22×C11⋊C8C2311yescharacteristic
207#66972C2×C4116yescomplemented
208#66971C2×C4116yescomplemented
209#66967C2×C4116yescomplemented
210SD16×D11C2×C4116yescomplemented
211#66961C2×C418yescomplemented
212#66960C2×C418yescomplemented
213C2×D88C2312yes—
214C2×#4314C2312yes—
215#66954—24no—
216C2×#4313C2312yes—
217C2×#4313C2312yes—
218C2×C8×D11C2312yes—
219C2×C8×D11C2312yes—
220#66946—21no—
221#66946—22no—
222#66946—22no—
223#66946—21no—
224#66946—21no—
225#66946—22no—
226#66946—22no—
227#66946—21no—
228#66946—21no—
229#66946D411yescharacteristic
230#66946D411yescharacteristic
231#66946C2312yes—
232#66946C2311yescharacteristic
233#66946C2312yes—
234#66946C2311yescharacteristic
235#66945—21no—
236#66945—22no—
237#66945—22no—
238#66945—22no—
239#66945C2312yes—
240#66945C2312yes—
241C4⋊C4×D11—22no—
242C4⋊C4×D11—21no—
243C4⋊C4×D11—22no—
244C4⋊C4×D11—22no—
245C4⋊C4×D11C2312yes—
246C4⋊C4×D11C2312yes—
247#66940—21no—
248#66940—22no—
249#66940—22no—
250#66940D411yescharacteristic
251#66940D411yescharacteristic
252#66940C2311yescharacteristic
253#66940C2311yescharacteristic
254(C22⋊D11)⋊C4—22no—
255(C22⋊D11)⋊C4—21no—
256(C22⋊D11)⋊C4—21no—
257(C22⋊D11)⋊C4—22no—
258(C22⋊D11)⋊C4—22no—
259(C22⋊D11)⋊C4—22no—
260(C22⋊D11)⋊C4D412yes—
261(C22⋊D11)⋊C4D412yes—
262C22⋊C4×D11—22no—
263C22⋊C4×D11—22no—
264C22⋊C4×D11—22no—
265C4×D44—21no—
266C4×D44—22no—
267C4×D44—22no—
268C4×D44—22no—
269C4×D44—22no—
270C4×D44C2312yes—
271C4×D44C2312yes—
272C4×D44C2312yes—
273#66925—22no—
274#66925—22no—
275#66925—22no—
276#66925—21no—
277#66925C2312yes—
278C42×D11—22no—
279C42×D11—22no—
280C42×D11—22no—
281C42×D11—21no—
282C42×D11C2312yes—
283C4×Dic22—21no—
284C4×Dic22—22no—
285C4×Dic22—22no—
286C4×Dic22C2312yes—
287C11×#107C2312yes—
288C11×#106C2312yes—
289C11×#103C2312yes—
290C11×#103C2312yes—
291C11×#103C2311yescharacteristic
292C11×#103C2311yescharacteristic
293C11×#102C2311yescharacteristic
294C11×#102C2311yescharacteristic
295C11×#97C2312yes—
296C4×C8×C11C2312yes—
297#66899C2312yes—
298#66899C2312yes—
299#66899C2312yes—
300#66896C2312yes—
301#66885C2312yes—
302#66885C2312yes—
303#66885C2311yescharacteristic
304#66885C2311yescharacteristic
305#66882C2312yes—
306#66881C2312yes—
307#66880C2311yescharacteristic
308#66880C2311yescharacteristic
309#66879C2312yes—
310#66879C2311yescharacteristic
311#66879C2311yescharacteristic
312#66879C2311yescharacteristic
313#66879C2311yescharacteristic
314C8×Dic11C2312yes—
315#66874C2312yes—
316#66873C2312yes—
317#66873C2312yes—
318#66873C2312yes—
319#66872C2311yescharacteristic
320#66872C2311yescharacteristic
321#66871C2311yescharacteristic
322#66871C2312yes—
323#66871C2312yes—
324#66871C2311yescharacteristic
325#66867C2312yes—
326C4×C11⋊C8C2312yes—
327#60174—111nomaximal, Sylow
328C23×D11—21no—
329C23×D11—22no—
330C11×#41—22no—
331C11×#41C22×C414yes—
332C2×Q8×C11—21no—
333C2×Q8×C11—22no—
334C2×Q8×C11C22×C414yescomplemented
335C2×Q8×C11C2412yes—
336C2×Q8×C11C2411yescharacteristic
337C2×D4×C11—21no—
338C2×D4×C11C2411yescharacteristic
339C22×C4×C11—21no—
340C22×C4×C11—21no—
341C22×C4×C11—21no—
342C22×C4×C11—22no—
343C22×C4×C11C2411yescharacteristic
344C2×C22⋊D11—22no—
345C2×C22⋊D11—21no—
346C2×C22⋊D11C2×D412yes—
347C22×Dic11—21no—
348C22×Dic11—21no—
349C22×Dic11—21no—
350C22×Dic11C2×D411yescharacteristic
351C22×Dic11C2×D411yescharacteristic
352#4343—28no—
353#4343—24no—
354#4343—24no—
355#4343C22×C418yes—
356#4343C22×C418yescomplemented
357Q8×D11—24no—
358Q8×D11—28no—
359Q8×D11C22×C418yescomplemented
360D4×D11—216no—
361D4×D11—24no—
362D4×D11C22×C418yes—
363#4339—216no—
364#4339—28no—
365#4339—22no—
366#4339C22×C414yes—
367#4339C22×C414yescomplemented
368#4339#4114yes—
369C2×D44—28no—
370C2×D44—22no—
371C2×D44—22no—
372C2×D44—21no—
373C2×D44—22no—
374C2×D44C22×C414yes—
375C2×D44C2×D411yescharacteristic
376C2×D44C2412yes—
377C2×D44C2411yescharacteristic
378C2×C4×D11—22no—
379C2×C4×D11—22no—
380C2×C4×D11—21no—
381C2×C4×D11—22no—
382C2×C4×D11—21no—
383C2×C4×D11—22no—
384C2×C4×D11—22no—
385C2×C4×D11—22no—
386C2×C4×D11—22no—
387C2×C4×D11—21no—
388C2×C4×D11—22no—
389C2×C4×D11—22no—
390C2×C4×D11—22no—
391C2×C4×D11—84no—
392C2×C4×D11—82no—
393C2×C4×D11C2×D412yes—
394C2×C4×D11C2×D412yes—
395C2×C4×D11C2412yes—
396C2×Dic22—22no—
397C2×Dic22C2×D411yescharacteristic
398C2×Dic22C2411yescharacteristic
399C11×Q16C22×C418yescomplemented
400C11×SD16C22×C418yescomplemented
401C11×M16C22×C414yescomplemented
402C2×C8×C11—22no—
403C2×C8×C11C2411yescharacteristic
404C2×C8×C11C2411yescharacteristic
405C2×C8×C11C2412yes—
406C11×C4⋊C4—22no—
407C11×C4⋊C4—22no—
408C11×C4⋊C4—21no—
409C11×C4⋊C4—22no—
410C11×C4⋊C4C2×D411yescharacteristic
411C11×C4⋊C4C2×D411yescharacteristic
412C11×C4⋊C4C2412yes—
413C11×C4⋊C4C2411yescharacteristic
414C11×C4⋊C4C2411yescharacteristic
415C11×C22⋊C4—21no—
416C11×C22⋊C4—22no—
417C11×C22⋊C4C2×D412yes—
418C42×C11—22no—
419C42×C11—22no—
420C42×C11—21no—
421C42×C11—22no—
422C42×C11C2412yes—
423C22⋊Dic11—21no—
424C22⋊Dic11—21no—
425C22⋊Dic11—21no—
426#4326C22×C414yescomplemented
427#4325C22×C418yescomplemented
428#4325C22×C418yescomplemented
429#4325C22×C414yescomplemented
430#4324C22×C414yescomplemented
431#4323C22×C414yescomplemented
432(C2×D11)⋊C4—21no—
433(C2×D11)⋊C4—21no—
434(C2×D11)⋊C4—22no—
435(C2×D11)⋊C4—22no—
436(C2×D11)⋊C4—22no—
437(C2×D11)⋊C4—22no—
438(C2×D11)⋊C4—22no—
439(C2×D11)⋊C4—22no—
440(C2×D11)⋊C4—22no—
441(C2×D11)⋊C4C2×D412yes—
442(C2×D11)⋊C4C2×D412yes—
443C4⋊Dic11—22no—
444C4⋊Dic11—22no—
445C4⋊Dic11—21no—
446C4⋊Dic11—21no—
447C4⋊Dic11—21no—
448C4⋊Dic11C2412yes—
449C4⋊Dic11C2411yescharacteristic
450C4⋊Dic11C2411yescharacteristic
451Dic11⋊C4—22no—
452Dic11⋊C4—21no—
453Dic11⋊C4—21no—
454Dic11⋊C4—22no—
455Dic11⋊C4—22no—
456Dic11⋊C4C2×D412yes—
457Dic11⋊C4C2×D412yes—
458C4×Dic11—22no—
459C4×Dic11—21no—
460C4×Dic11—21no—
461C4×Dic11—22no—
462C4×Dic11—21no—
463C4×Dic11—22no—
464C4×Dic11—22no—
465C4×Dic11—21no—
466C4×Dic11—22no—
467C4×Dic11—21no—
468C4×Dic11C2×D412yes—
469C4×Dic11C2×D412yes—
470C4×Dic11C2×D411yescharacteristic
471C4×Dic11C2×D411yescharacteristic
472C4×Dic11C2411yescharacteristic
473C4×Dic11C2411yescharacteristic
474#4318—22no—
475C2×C11⋊C8C22×C414yescomplemented
476C2×C11⋊C8C2412yes—
477C2×C11⋊C8C2411yescharacteristic
478C2×C11⋊C8C2411yescharacteristic
479D88C22×C418yescomplemented
480#4314C22×C418yescomplemented
481#4313—24no—
482#4313C22×C418yescomplemented
483C8×D11—24no—
484C8×D11C22×C418yescomplemented
485C2×#577—111no—
486C4×2−1+4—111no—
487C4×H(5,𝔽2)—111no—
488#2951—112no—
489#2951—111no—
490#2949—112no—
491#2949—111no—
492#2947—112no—
493#2947D1111yescharacteristic, complemented
494#2946—112no—
495#2946—111no—
496C4×#137—112no—
497C4×#137—111no—
498C4×AGL(1,ℤ/8)—112no—
499C4×AGL(1,ℤ/8)—111no—
500#2943—112no—
501#2943—111no—
502C2×#440—112no—
503C2×#440—111no—
504#2913—111no—
505#2898—111no—
506#2897—111no—
507#2875—111no—
508C23×C11—21no—
509C23×C11C22×D411yescharacteristic
510C22×D11—21no—
511C22×D11—22no—
512C22×D11—24no—
513C22×D11—28no—
514C22×D11—82no—
515C22×D11—82no—
516C22×D11—81no—
517C22×D11—81no—
518C22×D11C22×D412yes—
519Q8×C11—24no—
520Q8×C11—22no—
521Q8×C11—21no—
522Q8×C11C23×C414yes—
523Q8×C11C23×C412yes—
524D4×C11—24no—
525D4×C11—21no—
526D4×C11C23×C412yes—
527C2×C4×C11—24no—
528C2×C4×C11—22no—
529C2×C4×C11—21no—
530C2×C4×C11—24no—
531C2×C4×C11—21no—
532C2×C4×C11—21no—
533C2×C4×C11—22no—
534C2×C4×C11—82no—
535C2×C4×C11—81no—
536C2×C4×C11C23×C412yes—
537C2×C4×C11C22×D412yes—
538C2×C4×C11C22×D412yes—
539C2×C4×C11C22×D411yescharacteristic
540C2×C4×C11C2×#4112yes—
541C2×C4×C11C2511yescharacteristic
542C22⋊D11—24no—
543C22⋊D11—28no—
544C22⋊D11C4×D418yes—
545C2×Dic11—21no—
546C2×Dic11—22no—
547C2×Dic11—21no—
548C2×Dic11—21no—
549C2×Dic11—41no—
550C2×Dic11—41no—
551C2×Dic11—42no—
552C2×Dic11—81no—
553C2×Dic11—81no—
554C2×Dic11C22×D411yescharacteristic
555C2×Dic11C22×D411yescharacteristic
556C2×Dic11C22×D411yescharacteristic
557C2×Dic11C22×D411yescharacteristic
558C2×Dic11C22×D412yes—
559D44—28no—
560D44—28no—
561D44—24no—
562D44—22no—
563D44—21no—
564D44C4×D414yes—
565D44C23×C414yes—
566D44C23×C412yes—
567C4×D11—28no—
568C4×D11—24no—
569C4×D11—28no—
570C4×D11—28no—
571C4×D11—42no—
572C4×D11—42no—
573C4×D11—42no—
574C4×D11—44no—
575C4×D11—81no—
576C4×D11—82no—
577C4×D11—82no—
578C4×D11—82no—
579C4×D11—82no—
580C4×D11—82no—
581C4×D11—82no—
582C4×D11C23×C414yes—
583C4×D11C2×#4114yes—
584Dic22—21no—
585Dic22—28no—
586Dic22C4×D414yes—
587Dic22C23×C412yes—
588C8×C11—21no—
589C8×C11—21no—
590C8×C11C23×C414yes—
591C11⋊C8—22no—
592C11⋊C8C23×C412yes—
593C11⋊C8C23×C412yes—
594C2×2−1+4—111no—
595C2×H(5,𝔽2)—111no—
596#577—1116no—
597C2×#137—112no—
598C2×#137C2×D1111yescharacteristic
599C2×AGL(1,ℤ/8)—112no—
600C2×AGL(1,ℤ/8)—111no—
601C2×#135—111no—
602C2×#135—112no—
603C22×SD16—111no—
604C22×SD16—112no—
605C2×#131—111no—
606C2×#131—111no—
607#520—111no—
608#520—111no—
609#520—112no—
610#520—112no—
611#520—111no—
612#520—221no—
613#520—222no—
614#520—221no—
615#520C2×D1111yescharacteristic
616#519—112no—
617#519—221no—
618#519C2×D1111yescharacteristic, complemented
619#518—112no—
620#518—111no—
621#518—221no—
622#518—222no—
623C4×#41—111no—
624C4×#41—111no—
625C4×#41—112no—
626C4×#41—112no—
627C4×#41—111no—
628C4×#41—222no—
629C4×#41—221no—
630C4×#41—221no—
631C2×C4×Q8—111no—
632C2×C4×Q8—112no—
633C2×C4×Q8—221no—
634C2×C4×D4—112no—
635C2×C4×D4—111no—
636C2×C4×D4—221no—
637C2×C4×D4—222no—
638#442—112no—
639#442—111no—
640#442—111no—
641#442—112no—
642#441—112no—
643#441—111no—
644#441—111no—
645#441C2×D1112yescomplemented
646#440—112no—
647#440—112no—
648#440—112no—
649#440—112no—
650#440—112no—
651#440—112no—
652#440—112no—
653#440—112no—
654#440—112no—
655#440—112no—
656#440—111no—
657#440—111no—
658#440—111no—
659#440—111no—
660#440—112no—
661#440C2×D1112yescomplemented
662C4×Q16—112no—
663C4×Q16—112no—
664C4×Q16C2×D1112yescomplemented
665C4×SD16—112no—
666C4×SD16—112no—
667C4×SD16—112no—
668C4×SD16—112no—
669C4×SD16—112no—
670C4×SD16C2×D1112yescomplemented
671C4×D8—112no—
672C4×D8—112no—
673C4×D8—112no—
674#428—111no—
675#428—112no—
676#428—112no—
677#428C2×D1111yescharacteristic, complemented
678#427—111no—
679#427—112no—
680C2×#107—111no—
681C2×#107—112no—
682#419—111no—
683#419—112no—
684#418—111no—
685#418—112no—
686#417—111no—
687#417—111no—
688#417—112no—
689#417—112no—
690#416—111no—
691#416—112no—
692#416—112no—
693#416C2×D1111yescharacteristic
694C2×#103—112no—
695C2×#103C2×D1111yescharacteristic, complemented
696C2×#102—111no—
697C2×#102—112no—
698#405—111no—
699#405—112no—
700#405—112no—
701#405C2×D1111yescharacteristic, complemented
702C4×M16—111no—
703C4×M16—112no—
704C2×#97—111no—
705C2×#97—112no—
706C22×C11—21no—
707C22×C11—21no—
708C22×C11—22no—
709C22×C11—41no—
710C22×C11—41no—
711C22×C11C2×C4×D412yes—
712C22×C11C23×D411yescharacteristic
713C2×D11—22no—
714C2×D11—22no—
715C2×D11—24no—
716C2×D11—22no—
717C2×D11—42no—
718C2×D11—41no—
719C2×D11—42no—
720C2×D11—41no—
721C2×D11—88no—
722C2×D11—84no—
723C2×D11C2×C4×D414yes—
724C4×C11—22no—
725C4×C11—22no—
726C4×C11—22no—
727C4×C11—24no—
728C4×C11—42no—
729C4×C11—41no—
730C4×C11—41no—
731C4×C11C2×C4×D412yes—
732C4×C11C24×C411yescharacteristic
733C4×C11C22×#4111yescharacteristic
734Dic11—21no—
735Dic11—21no—
736Dic11—21no—
737Dic11—21no—
738Dic11—22no—
739Dic11—41no—
740Dic11—42no—
741Dic11—41no—
742Dic11C2×C4×D414yes—
7432−1+4—118no—
7442−1+4—224no—
745H(5,𝔽2)—118no—
746H(5,𝔽2)—224no—
747C2×#41—111no—
748C2×#41—112no—
749C2×#41—112no—
750C2×#41—111no—
751C2×#41—222no—
752C2×#41—221no—
753C2×#41—221no—
754C2×#41C22×D1111yescharacteristic
755C22×Q8—112no—
756C22×Q8—221no—
757C22×Q8C22×D1111yescharacteristic
758C22×D4—112no—
759C22×D4—111no—
760C22×D4—221no—
761C22×D4—222no—
762C23×C4—221no—
763C23×C4—222no—
764#137—1116no—
765#137C4×D1118yescomplemented
766AGL(1,ℤ/8)—1116no—
767AGL(1,ℤ/8)—118no—
768#135—118no—
769#135—1116no—
770C2×Q16—111no—
771C2×Q16C22×D1112yes—
772C2×SD16—118no—
773C2×SD16—112no—
774C2×SD16—112no—
775C2×SD16—111no—
776C2×SD16—111no—
777C2×SD16—1116no—
778C2×SD16—112no—
779C2×SD16C22×D1112yes—
780C2×D8—111no—
781C2×D8—112no—
782#131—118no—
783#131—224no—
784C2×M16—111no—
785C2×M16—112no—
786C2×M16—112no—
787C2×M16C22×D1111yescharacteristic
788C22×C8—111no—
789C22×C8—112no—
790C22×C8—112no—
791C22×C8C22×D1111yescharacteristic
792C4×Q8—21no—
793C4×Q8—21no—
794C4×Q8—111no—
795C4×Q8—111no—
796C4×Q8—112no—
797C4×Q8—112no—
798C4×Q8—111no—
799C4×Q8—111no—
800C4×Q8—111no—
801C4×Q8—111no—
802C4×Q8—112no—
803C4×Q8—222no—
804C4×Q8—222no—
805C4×Q8—221no—
806C4×Q8—222no—
807C4×Q8—221no—
808C4×Q8—221no—
809C4×Q8—222no—
810C4×Q8—221no—
811C4×Q8C22×D1112yes—
812C4×Q8C22×D1112yes—
813C4×Q8C22×D1112yes—
814C4×D4—22no—
815C4×D4—111no—
816C4×D4—111no—
817C4×D4—112no—
818C4×D4—112no—
819C4×D4—111no—
820C4×D4—111no—
821C4×D4—112no—
822C4×D4—112no—
823C4×D4—111no—
824C4×D4—111no—
825C4×D4—112no—
826C4×D4—112no—
827C4×D4—112no—
828C4×D4—222no—
829C4×D4—222no—
830C4×D4—222no—
831C4×D4—222no—
832C4×D4—221no—
833C4×D4—222no—
834C4×D4—221no—
835C4×D4—221no—
836C4×D4—222no—
837C4×D4—222no—
838C4×D4—221no—
839C4×D4—221no—
840C4×D4—222no—
841C4×D4—222no—
842C4×D4—222no—
843C4×D4—222no—
844C4×D4—222no—
845C4×D4—221no—
846C4×D4—222no—
847C4×D4—222no—
848C4×D4—221no—
849C4×D4—221no—
850C4×D4—221no—
851C4×D4—221no—
852C4×D4—222no—
853C4×D4C22×D1112yes—
854#117—21no—
855#117—22no—
856#117—112no—
857#117—111no—
858#117—112no—
859#117—112no—
860#117—221no—
861#117—222no—
862#117—222no—
863#117—222no—
864#117—222no—
865#117—222no—
866#117—221no—
867#117—222no—
868#117—221no—
869#117C22×D1111yescharacteristic
870#117C22×D1111yescharacteristic
871C2×C4⋊C4—21no—
872C2×C4⋊C4—111no—
873C2×C4⋊C4—112no—
874C2×C4⋊C4—112no—
875C2×C4⋊C4—222no—
876C2×C4⋊C4—222no—
877C2×C4⋊C4—222no—
878C2×C4⋊C4—221no—
879C2×C4⋊C4—221no—
880C2×C4⋊C4C22×D1111yescharacteristic
881C2×C22⋊C4—222no—
882C2×C22⋊C4—222no—
883C2×C22⋊C4—222no—
884C2×C22⋊C4—221no—
885C2×C22⋊C4—222no—
886C2×C42—111no—
887C2×C42—112no—
888C2×C42—222no—
889C2×C42—222no—
890C2×C42—221no—
891C2×C42—222no—
892C2×C42—221no—
893C2×C42—221no—
894#107—112no—
895#107—112no—
896#107—111no—
897#107—112no—
898#107—111no—
899#107C22×D1112yes—
900#106—112no—
901#106—111no—
902#106—111no—
903#106C22×D1112yes—
904#103—112no—
905#103—112no—
906#103—112no—
907#103—111no—
908#103—111no—
909#103—112no—
910#103C22×D1112yes—
911#103C22×D1112yes—
912#103C22×D1111yescharacteristic
913#103C22×D1111yescharacteristic
914#102—112no—
915#102—112no—
916#102—112no—
917#102—111no—
918#102—111no—
919#102—112no—
920#102—112no—
921#102—112no—
922#102C22×D1111yescharacteristic
923#102C22×D1111yescharacteristic
924#97—111no—
925#97—111no—
926#97—112no—
927#97—111no—
928#97—111no—
929#97—112no—
930#97C22×D1112yes—
931C4×C8—112no—
932C4×C8—112no—
933C4×C8C22×D1112yes—
934C2×C11—22no—
935C2×C11—42no—
936C2×C11C22×C4×D411yescharacteristic
937C2×C11#358511yescharacteristic
938C2×C11#358611yescharacteristic
939D11—24no—
940D11—42no—
941D11—44no—
942C24—222no—
943C24—221no—
944#41—22no—
945#41—114no—
946#41—114no—
947#41—118no—
948#41—118no—
949#41—114no—
950#41—2216no—
951#41—228no—
952#41—224no—
953#41—224no—
954#41—228no—
955#41—222no—
956#41C2×C4×D1114yes—
957C2×Q8—21no—
958C2×Q8—22no—
959C2×Q8—111no—
960C2×Q8—118no—
961C2×Q8—111no—
962C2×Q8—222no—
963C2×Q8—224no—
964C2×Q8—228no—
965C2×Q8C2×C4×D1114yescomplemented
966C2×Q8C23×D1112yes—
967C2×Q8C23×D1111yescharacteristic
968C2×D4—21no—
969C2×D4—112no—
970C2×D4—118no—
971C2×D4—114no—
972C2×D4—111no—
973C2×D4—111no—
974C2×D4—112no—
975C2×D4—228no—
976C2×D4—222no—
977C2×D4—222no—
978C2×D4—224no—
979C2×D4—222no—
980C2×D4—2216no—
981C2×D4—221no—
982C2×D4—221no—
983C2×D4—222no—
984C2×D4C23×D1111yescharacteristic
985C22×C4—21no—
986C22×C4—21no—
987C22×C4—21no—
988C22×C4—22no—
989C22×C4—112no—
990C22×C4—111no—
991C22×C4—111no—
992C22×C4—112no—
993C22×C4—112no—
994C22×C4—222no—
995C22×C4—222no—
996C22×C4—221no—
997C22×C4—222no—
998C22×C4—221no—
999C22×C4—222no—
1000C22×C4—222no—
1001C22×C4—222no—
1002C22×C4—222no—
1003C22×C4—221no—
1004C22×C4—221no—
1005C22×C4—221no—
1006C22×C4—221no—
1007C22×C4—222no—
1008C22×C4—222no—
1009C22×C4—222no—
1010C22×C4—884no—
1011C22×C4—882no—
1012C22×C4C23×D1111yescharacteristic
1013Q16—114no—
1014Q16C2×C4×D1118yescomplemented
1015SD16—118no—
1016SD16—118no—
1017SD16—114no—
1018SD16—114no—
1019SD16—118no—
1020SD16C2×C4×D1118yescomplemented
1021D8—114no—
1022D8—118no—
1023M16—118no—
1024M16—224no—
1025M16—222no—
1026M16C2×C4×D1114yescomplemented
1027C2×C8—22no—
1028C2×C8—114no—
1029C2×C8—111no—
1030C2×C8—111no—
1031C2×C8—118no—
1032C2×C8—112no—
1033C2×C8—224no—
1034C2×C8C23×D1111yescharacteristic
1035C2×C8C23×D1111yescharacteristic
1036C2×C8C23×D1112yes—
1037C4⋊C4—22no—
1038C4⋊C4—21no—
1039C4⋊C4—22no—
1040C4⋊C4—22no—
1041C4⋊C4—112no—
1042C4⋊C4—112no—
1043C4⋊C4—112no—
1044C4⋊C4—111no—
1045C4⋊C4—111no—
1046C4⋊C4—222no—
1047C4⋊C4—222no—
1048C4⋊C4—221no—
1049C4⋊C4—221no—
1050C4⋊C4—222no—
1051C4⋊C4—222no—
1052C4⋊C4—221no—
1053C4⋊C4—221no—
1054C4⋊C4—221no—
1055C4⋊C4—222no—
1056C4⋊C4D4×D1111yescharacteristic
1057C4⋊C4D4×D1111yescharacteristic
1058C4⋊C4C23×D1111yescharacteristic
1059C4⋊C4C23×D1111yescharacteristic
1060C4⋊C4C23×D1112yes—
1061C22⋊C4—21no—
1062C22⋊C4—22no—
1063C22⋊C4—112no—
1064C22⋊C4—112no—
1065C22⋊C4—222no—
1066C22⋊C4—222no—
1067C22⋊C4—221no—
1068C22⋊C4—221no—
1069C22⋊C4—222no—
1070C22⋊C4—222no—
1071C22⋊C4—221no—
1072C22⋊C4—221no—
1073C22⋊C4—221no—
1074C22⋊C4—222no—
1075C22⋊C4—222no—
1076C22⋊C4—222no—
1077C22⋊C4D4×D1112yes—
1078C42—22no—
1079C42—22no—
1080C42—22no—
1081C42—21no—
1082C42—112no—
1083C42—112no—
1084C42—111no—
1085C42—111no—
1086C42—111no—
1087C42—111no—
1088C42—221no—
1089C42—222no—
1090C42—221no—
1091C42—222no—
1092C42—222no—
1093C42—221no—
1094C42—222no—
1095C42—221no—
1096C42—221no—
1097C42—222no—
1098C42C23×D1112yes—
1099C11#6017411yescharacteristic, complemented, Sylow
1100C23—21no—
1101C23—112no—
1102C23—228no—
1103C23—221no—
1104C23—222no—
1105C23—224no—
1106C23—881no—
1107C23—881no—
1108C23—882no—
1109C23—882no—
1110C23C2×D4×D1111yescharacteristic
1111Q8—24no—
1112Q8—22no—
1113Q8—21no—
1114Q8—114no—
1115Q8—112no—
1116Q8—228no—
1117Q8—221no—
1118Q8C22×C4×D1114yes—
1119Q8C22×C4×D1112yes—
1120D4—24no—
1121D4—21no—
1122D4—118no—
1123D4—114no—
1124D4—112no—
1125D4—114no—
1126D4—228no—
1127D4—228no—
1128D4—228no—
1129D4—224no—
1130D4—224no—
1131D4—222no—
1132D4—221no—
1133D4C22×C4×D1112yes—
1134C2×C4—24no—
1135C2×C4—21no—
1136C2×C4—22no—
1137C2×C4—24no—
1138C2×C4—21no—
1139C2×C4—21no—
1140C2×C4—22no—
1141C2×C4—82no—
1142C2×C4—81no—
1143C2×C4—112no—
1144C2×C4—114no—
1145C2×C4—114no—
1146C2×C4—111no—
1147C2×C4—111no—
1148C2×C4—111no—
1149C2×C4—111no—
1150C2×C4—228no—
1151C2×C4—228no—
1152C2×C4—228no—
1153C2×C4—221no—
1154C2×C4—224no—
1155C2×C4—221no—
1156C2×C4—222no—
1157C2×C4—221no—
1158C2×C4—442no—
1159C2×C4—442no—
1160C2×C4—444no—
1161C2×C4—442no—
1162C2×C4—441no—
1163C2×C4—441no—
1164C2×C4—442no—
1165C2×C4—882no—
1166C2×C4—882no—
1167C2×C4—882no—
1168C2×C4—882no—
1169C2×C4—881no—
1170C2×C4—882no—
1171C2×C4—882no—
1172C2×C4—881no—
1173C2×C4—881no—
1174C2×C4C22×C4×D1112yes—
1175C2×C4C2×D4×D1112yes—
1176C2×C4C2×D4×D1112yes—
1177C2×C4C2×D4×D1111yescharacteristic
1178C2×C4#41×D1112yes—
1179C2×C4C24×D1111yescharacteristic
1180C8—21no—
1181C8—21no—
1182C8—112no—
1183C8—112no—
1184C8—222no—
1185C8C22×C4×D1114yes—
1186C22—21no—
1187C22—21no—
1188C22—22no—
1189C22—41no—
1190C22—41no—
1191C22—114no—
1192C22—222no—
1193C22—222no—
1194C22—222no—
1195C22—224no—
1196C22—442no—
1197C22—441no—
1198C22—441no—
1199C22—442no—
1200C22—884no—
1201C22—888no—
1202C22C4×D4×D1112yes—
1203C22C22×D4×D1111yescharacteristic
1204C4—22no—
1205C4—22no—
1206C4—22no—
1207C4—24no—
1208C4—42no—
1209C4—41no—
1210C4—41no—
1211C4—114no—
1212C4—221no—
1213C4—221no—
1214C4—221no—
1215C4—221no—
1216C4—222no—
1217C4—441no—
1218C4—442no—
1219C4—441no—
1220C4C4×D4×D1112yes—
1221C4C23×C4×D1111yescharacteristic
1222C4C2×#41×D1111yescharacteristic
1223C2—22no—
1224C2—42no—
1225C2—224no—
1226C2—444no—
1227C2—442no—
1228C2C2×C4×D4×D1111yescharacteristic
1229C2#1308339411yescharacteristic
1230C2#1308340111yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutatorC4×C11C24×C4
FrattiniC2×C4C24×D11
FittingC11×#2947C2
socleC22×C11C23×D4
prime radicalC2×#10623309C2
cosocleC2×C4×C11C25
hypercenter#2947D11
hypocenterC11#60174
LCSG ▷ C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ #117 ◁ #2947

Complements

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

NH ≅ G/Ntype
2. #13081825C2semidirect
3. #13081822C2semidirect
4. #13077491C2semidirect
5. #13077489C2semidirect
6. #13077475C2semidirect
7. #13077470C2semidirect
8. #13077458C2semidirect
9. #13077450C2semidirect
10. #13077447C2semidirect
11. #137×Dic11C2semidirect
12. C4×#66971C2semidirect
13. C4×#66967C2semidirect
14. #13077423C2semidirect
15. #13077415C2semidirect
16. #13077412C2semidirect
17. C2×#10622430C2semidirect
18. D11×#440C2semidirect
19. #13077215C2semidirect
20. #13077144C2semidirect
21. #13077138C2semidirect
22. #13077043C2semidirect
23. C11×#2947C2semidirect
28. C11×#519C22semidirect
31. C2×Q8×Dic11C22semidirect
33. #10623309C4semidirect
43. #10623105C22semidirect
46. C4×#4343C22semidirect
48. #10623103C22semidirect
50. C4×Q8×D11C22semidirect
57. #10623054C22semidirect
61. #10623053C22semidirect
68. C11×#441C22semidirect
69. C11×#440C22semidirect
70. C4×C11×Q16C22semidirect
71. C4×C11×SD16C22semidirect
72. C11×#428C22semidirect
74. C2×C11×#103C22semidirect
75. C11×#405C22semidirect
77. #10622838C22semidirect
78. #10622797C22semidirect
79. Q16×Dic11C22semidirect
80. #10622777C22semidirect
81. SD16×Dic11C22semidirect
82. #10622734C22semidirect
83. M16×Dic11C22semidirect
84. #10622726C22semidirect
86. C2×#66879C22semidirect
87. C4×#4326C22semidirect
88. #10622639C22semidirect
89. #10622639C22semidirect
90. #10622639C22semidirect
91. C4×#4325C22semidirect
92. C4×#4325C22semidirect
93. #10622631C22semidirect
94. C4×#4323C22semidirect
96. #10622611C22semidirect
97. #10622610C22semidirect
98. #10622579C22semidirect
99. C2×#66871C22semidirect
100. #10622502C22semidirect
101. #10622494C22semidirect
102. D11×#107C22semidirect
103. #10622485C22semidirect
104. #10622482C22semidirect
105. #10622474C22semidirect
106. #10622473C22semidirect
107. #10622465C22semidirect
108. #10622430C22semidirect
109. #10622430C22semidirect
110. #10622430C22semidirect
111. #10622430C22semidirect
112. #10622430C22semidirect
113. #10622430C22semidirect
115. #10622417C22semidirect
117. #10622416C22semidirect
118. #10622415C22semidirect
119. D11×#103C22semidirect
120. #10622402C22semidirect
121. #10622402C22semidirect
122. #10622398C22semidirect
123. #10622398C22semidirect
126. #10622370C22semidirect
127. #10622370C22semidirect
128. #10622324C22semidirect
129. #10622323C22semidirect
130. #10622321C22semidirect
131. D11×#97C22semidirect
132. C4×D88C22semidirect
133. C4×#4314C22semidirect
134. #10622302C22semidirect
135. C4×#4313C22semidirect
139. #67042C2×C4semidirect
141. #67040C2×C4semidirect
157. C11×#137C2×C4semidirect
175. #67003C2×C4semidirect
183. C2×#4325C2×C4semidirect
207. #66972C2×C4semidirect
208. #66971C2×C4semidirect
209. #66967C2×C4semidirect
210. SD16×D11C2×C4semidirect
211. #66961C2×C4semidirect
212. #66960C2×C4semidirect
334. C2×Q8×C11C22×C4semidirect
356. #4343C22×C4semidirect
359. Q8×D11C22×C4semidirect
367. #4339C22×C4semidirect
399. C11×Q16C22×C4semidirect
400. C11×SD16C22×C4semidirect
401. C11×M16C22×C4semidirect
426. #4326C22×C4semidirect
427. #4325C22×C4semidirect
428. #4325C22×C4semidirect
429. #4325C22×C4semidirect
430. #4324C22×C4semidirect
431. #4323C22×C4semidirect
475. C2×C11⋊C8C22×C4semidirect
479. D88C22×C4semidirect
480. #4314C22×C4semidirect
482. #4313C22×C4semidirect
484. C8×D11C22×C4semidirect
493. #2947D11semidirect
618. #519C2×D11semidirect
645. #441C2×D11semidirect
661. #440C2×D11semidirect
664. C4×Q16C2×D11semidirect
670. C4×SD16C2×D11semidirect
677. #428C2×D11semidirect
695. C2×#103C2×D11semidirect
701. #405C2×D11semidirect
765. #137C4×D11semidirect
965. C2×Q8C2×C4×D11semidirect
1014. Q16C2×C4×D11semidirect
1020. SD16C2×C4×D11semidirect
1026. M16C2×C4×D11semidirect
1099. C11#60174semidirect

Maximal subgroups

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

subgroupindex
C2×#106233092
#130818252
#130818222
#130774912
#130774892
#130774752
#130774702
#130774582
#130774502
#130774472
#137×Dic112
C4×#669712
C4×#669672
#130774232
#130774152
#130774122
C2×#106224302
D11×#4402
#130772152
#130771442
#130771382
#130770432
C11×#29472
#6017411