Finite Group Databasebeta

← #15622233

Subgroups — #15622233

Order 2816.

2180 conjugacy classes of subgroups.

The subgroup lattice has 1316 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1D11×#529C211yesmaximal, characteristic, complemented
2C2×C4×#4343C211yesmaximal, characteristic, complemented
3#13078788C211yesmaximal, characteristic, complemented
4#13078782C211yesmaximal, characteristic, complemented
5#13078757C211yesmaximal, characteristic, complemented
6#13078751C211yesmaximal, characteristic, complemented
7#13078732C212yesmaximal, complemented
8#13078724C212yesmaximal, complemented
9#13078696C211yesmaximal, characteristic, complemented
10#13078665C211yesmaximal, characteristic, complemented
11#13078659C211yesmaximal, characteristic, complemented
12#13078640C212yesmaximal, complemented
13#13078632C212yesmaximal, complemented
14#13078559C211yesmaximal, characteristic, complemented
15#13078551C211yesmaximal, characteristic, complemented
16#13078435C212yesmaximal, complemented
17#13078107C212yesmaximal, complemented
18#13077875C211yesmaximal, characteristic, complemented
19#13077867C211yesmaximal, characteristic
20C4×#66971C212yesmaximal, complemented
21C4×#66967C212yesmaximal, complemented
22#13077244C211yesmaximal, characteristic, complemented
23C11×#3108C211yesmaximal, characteristic, complemented
24C22×#4343C2211yescharacteristic
25C11×#529C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic, complemented
27C2×Q8×Dic11C2211yescharacteristic, complemented
28C2×#66971C2212yes—
29C2×#66967C2212yes—
30#10623237—21no—
31D11×#126—21no—
32#10623222C2211yescharacteristic, complemented
33D11×#125C2211yescharacteristic, complemented
34#10623211C2211yescharacteristic, complemented
35D11×#124C2211yescharacteristic, complemented
36D11×#123—21no—
37#10623180—21no—
38D11×C22⋊Q8C2211yescharacteristic
39#10623155C2211yescharacteristic
40D11×#121C2211yescharacteristic
41#10623131C2211yescharacteristic
42#10623111C2211yescharacteristic, complemented
43C4×#4343—21no—
44C4×#4343—21no—
45C4×#4343—21no—
46C4×#4343—21no—
47C4×#4343C2212yes—
48C4×#4343C2212yes—
49C4×#4343C2212yescomplemented
50C4×#4343C2212yescomplemented
51C4×Q8×D11C2211yescharacteristic, complemented
52#10623088C2211yescharacteristic, complemented
53C4×D4×D11—21no—
54C4×D4×D11C2211yescharacteristic, complemented
55#10623069—21no—
56#10623059—21no—
57D11×#117—21no—
58C2×#66946—21no—
59C2×#66946C2211yescharacteristic, complemented
60C2×#66945—21no—
61C2×#66945C2211yescharacteristic
62#10623010C2211yescharacteristic
63C2×C4×D44—21no—
64C2×C4×D44C2211yescharacteristic, complemented
65C2×C42×D11—21no—
66C2×C42×D11C2211yescharacteristic
67C11×#483C2211yescharacteristic, complemented
68C11×#480C2211yescharacteristic
69C11×#479C2212yescomplemented
70C11×#464C2212yescomplemented
71C11×#451C2211yescharacteristic, complemented
72C11×#448C2211yescharacteristic
73C4×C11×Q16C2212yescomplemented
74C4×C11×SD16C2212yescomplemented
75C11×#431C2211yescharacteristic, complemented
76#10622841C2211yescharacteristic, complemented
77#10622840C2211yescharacteristic
78#10622800C2212yescomplemented
79#10622798C2212yescomplemented
80#10622797C2212yescomplemented
81#10622785C2212yes—
82#10622779C2212yescomplemented
83#10622777C2212yescomplemented
84#10622679C2212yescomplemented
85#10622670C2212yescomplemented
86#10622659C2211yescharacteristic, complemented
87#10622657C2211yescharacteristic, complemented
88#10622649C2211yescharacteristic
89#10622647C2211yescharacteristic
90C4×#4326C2212yescomplemented
91#10622641C2212yescomplemented
92C4×#4325C2212yescomplemented
93C4×#4325C2212yescomplemented
94#10622635C2212yescomplemented
95C4×#4323C2212yescomplemented
96#10622584C2211yescharacteristic, complemented
97#10622580C2211yescharacteristic
98#10622538C2211yescharacteristic, complemented
99#10622504C2212yescomplemented
100#10622502C2212yescomplemented
101#10622498C2212yescomplemented
102#10622494C2212yescomplemented
103#10622484C2212yescomplemented
104#10622482C2212yescomplemented
105#10622480C2212yescomplemented
106#10622474C2212yescomplemented
107#10622460C2212yescomplemented
108#10622457C2212yescomplemented
109#10622450C2212yescomplemented
110#10622448C2212yescomplemented
111#10622432C2212yescomplemented
112#10622430C2212yescomplemented
113#10622430C2212yescomplemented
114#10622427C2212yescomplemented
115#10622424C2212yes—
116#10622423C2212yescomplemented
117#10622416C2212yes—
118#10622416C2212yes—
119#10622415C2212yescomplemented
120#10622412C2212yescomplemented
121#10622409C2212yescomplemented
122#10622402C2212yescomplemented
123#10622400C2212yescomplemented
124#10622398C2212yescomplemented
125#10622392C2212yescomplemented
126#10622383C2212yescomplemented
127#10622348C2211yescharacteristic
128#10622345C2211yescharacteristic
129#10622344C2211yescharacteristic, complemented
130#10622339C2211yescharacteristic
131#10622339C2211yescharacteristic
132#10622335C2211yescharacteristic, complemented
133#10622332C2211yescharacteristic, complemented
134#10622332C2211yescharacteristic, complemented
135C4×D88C2212yescomplemented
136C4×#4314C2212yescomplemented
137C4×#4313C2212yescomplemented
138#10622298C2212yescomplemented
139C22×Q8×C11C2311yescharacteristic
140C2×#4343—28no—
141C2×#4343—21no—
142C2×#4343—21no—
143C2×#4343C2312yes—
144C2×#4343C2312yes—
145C2×Q8×D11C2311yescharacteristic
146C2×D4×D11—21no—
147C2×D4×D11C2311yescharacteristic
148C22×D44—21no—
149C22×D44C2311yescharacteristic
150C22×C4×D11—21no—
151C22×C4×D11—21no—
152C22×C4×D11—21no—
153C22×C4×D11—21no—
154C22×C4×D11D411yescharacteristic
155C22×C4×D11D411yescharacteristic
156C22×C4×D11C2311yescharacteristic
157C2×C11×Q16C2312yes—
158C2×C11×SD16C2312yes—
159C11×#126—21no—
160C11×#125C2311yescharacteristic
161C11×#124C2311yescharacteristic
162C11×#123—21no—
163C11×C22⋊Q8C2311yescharacteristic
164C11×#121C2311yescharacteristic
165C4×Q8×C11—21no—
166C4×Q8×C11—21no—
167C4×Q8×C11C2311yescharacteristic
168C4×Q8×C11C2312yes—
169C4×Q8×C11C2312yes—
170C4×D4×C11—21no—
171C4×D4×C11C2311yescharacteristic
172C11×#117—21no—
173C2×C11×C4⋊C4—21no—
174C2×C11×C4⋊C4C2311yescharacteristic
175C2×C42×C11—21no—
176C2×C42×C11C2311yescharacteristic
177#67000C2311yescharacteristic
178#66999C2311yescharacteristic
179Q8×Dic11—21no—
180Q8×Dic11—21no—
181Q8×Dic11C2312yes—
182Q8×Dic11C2312yes—
183Q8×Dic11C2311yescharacteristic
184C2×#4326C2312yes—
185C2×#4325C2312yes—
186C2×#4325C2312yes—
187#66992—21no—
188#66991C2311yescharacteristic
189#66989C2311yescharacteristic
190#66988—21no—
191D4×Dic11—21no—
192D4×Dic11C2311yescharacteristic
193C2×#4323C2312yes—
194#66983C2311yescharacteristic
195#66982—21no—
196C4×C22⋊D11—21no—
197C4×C22⋊D11—21no—
198C4×C22⋊D11—21no—
199C2×(C2×D11)⋊C4—21no—
200C2×(C2×D11)⋊C4—21no—
201C2×(C2×D11)⋊C4—21no—
202#66979—21no—
203C2×C4⋊Dic11—21no—
204C2×C4⋊Dic11C2311yescharacteristic
205#66977C2311yescharacteristic
206C2×C4×Dic11—21no—
207C2×C4×Dic11—21no—
208C2×C4×Dic11D411yescharacteristic
209C2×C4×Dic11D411yescharacteristic
210C2×C4×Dic11C2311yescharacteristic
211#66971—28no—
212#66967—28no—
213C2×D88C2312yes—
214C2×#4314C2312yes—
215C2×#4313C2312yes—
216C2×#4313C2312yes—
217#66951—21no—
218#66951—21no—
219#66951—21no—
220#66950C2311yescharacteristic
221#66949—21no—
222#66948C2311yescharacteristic
223#66947—21no—
224#66947—21no—
225#66946—21no—
226#66946—22no—
227#66946—22no—
228#66946—22no—
229#66946—22no—
230#66946—21no—
231#66946—21no—
232#66946C2311yescharacteristic
233#66946C2312yes—
234#66946C2312yes—
235#66945—21no—
236#66945—21no—
237#66945—21no—
238#66945—22no—
239#66945—22no—
240#66945—22no—
241#66945—22no—
242#66945—21no—
243#66945C2312yes—
244#66945C2312yes—
245C4⋊C4×D11—21no—
246C4⋊C4×D11—21no—
247C4⋊C4×D11—21no—
248C4⋊C4×D11—21no—
249C4⋊C4×D11C2311yescharacteristic
250C4⋊C4×D11C2311yescharacteristic
251#66943C2311yescharacteristic
252#66943C2311yescharacteristic
253#66942—21no—
254#66942—21no—
255#66940—21no—
256#66940C2311yescharacteristic
257#66939—21no—
258#66938—21no—
259#66938—21no—
260#66937—21no—
261#66936—21no—
262#66936—21no—
263(C22⋊D11)⋊C4—21no—
264(C22⋊D11)⋊C4—21no—
265(C22⋊D11)⋊C4—21no—
266C22⋊C4×D11—21no—
267C22⋊C4×D11—21no—
268C22⋊C4×D11—21no—
269C22⋊C4×D11—21no—
270C22⋊C4×D11—21no—
271#66932—21no—
272#66932—21no—
273#66932—21no—
274#66931—21no—
275#66930—21no—
276#66930—21no—
277#66929—21no—
278#66928C2311yescharacteristic
279C4×D44—22no—
280C4×D44—22no—
281C4×D44—22no—
282C4×D44—22no—
283C4×D44—21no—
284C4×D44—21no—
285C4×D44—21no—
286C4×D44C2312yes—
287C4×D44C2312yes—
288C4×D44C2311yescharacteristic
289#66925—21no—
290#66925—21no—
291C42×D11—21no—
292C42×D11—22no—
293C42×D11—22no—
294C42×D11—22no—
295C42×D11—22no—
296C42×D11D411yescharacteristic
297C42×D11D411yescharacteristic
298C42×D11D411yescharacteristic
299C42×D11D411yescharacteristic
300C42×D11C2311yescharacteristic
301C42×D11C2311yescharacteristic
302C42×D11C2311yescharacteristic
303C42×D11C2311yescharacteristic
304#66923C2311yescharacteristic
305C4×Dic22—21no—
306C4×Dic22C2311yescharacteristic
307C11×#107C2312yes—
308C11×#106C2312yes—
309C11×C4⋊C8C2312yes—
310C11×#103C2312yes—
311C11×#103C2312yes—
312C11×#103C2312yes—
313C11×#102C2312yes—
314C11×C22⋊C8C2311yescharacteristic
315C11×C22⋊C8C2311yescharacteristic
316C4×C8×C11C2312yes—
317#66899C2312yes—
318#66899C2312yes—
319#66899C2312yes—
320#66896C2312yes—
321C22⋊(C11⋊C8)C2311yescharacteristic
322C22⋊(C11⋊C8)C2311yescharacteristic
323#66885C2312yes—
324#66885C2312yes—
325#66885C2312yes—
326(C2×D11)⋊C8C2312yes—
327(C2×D11)⋊C8C2312yes—
328#66882C2312yes—
329#66881C2312yes—
330#66880C2312yes—
331#66879C2312yes—
332#66879C2312yes—
333Dic11⋊C8C2312yes—
334Dic11⋊C8C2312yes—
335#66874C2312yes—
336#66873C2312yes—
337#66873C2312yes—
338#66873C2312yes—
339#66872C2312yes—
340#66872C2312yes—
341#66871C2312yes—
342#66871C2312yes—
343C4⋊(C11⋊C8)C2312yes—
344C4×C11⋊C8C2312yes—
345#60563—111nomaximal, Sylow
346C23×D11—21no—
347C23×D11—21no—
348C23×D11C2×D411yescharacteristic
349C2×Q8×C11—24no—
350C2×Q8×C11—21no—
351C2×Q8×C11C2411yescharacteristic
352C2×Q8×C11C2412yes—
353C2×D4×C11—21no—
354C2×D4×C11C2411yescharacteristic
355C22×C4×C11—21no—
356C22×C4×C11—21no—
357C22×C4×C11—21no—
358C22×C4×C11C2×D411yescharacteristic
359C22×C4×C11C2×D411yescharacteristic
360C22×C4×C11C2411yescharacteristic
361C2×C22⋊D11—21no—
362C2×C22⋊D11—21no—
363C2×C22⋊D11—21no—
364C22×Dic11—21no—
365C22×Dic11—21no—
366C22×Dic11C2×D411yescharacteristic
367C22×Dic11C2×D411yescharacteristic
368C22×Dic11C2×D411yescharacteristic
369#4343—28no—
370#4343—28no—
371#4343—24no—
372#4343—24no—
373#4343—24no—
374#4343#4118yes—
375Q8×D11—24no—
376D4×D11—24no—
377D4×D11—44no—
378C2×D44—28no—
379C2×D44—24no—
380C2×D44—22no—
381C2×D44—22no—
382C2×D44—21no—
383C2×D44—21no—
384C2×D44C2411yescharacteristic
385C2×D44C2412yes—
386C2×C4×D11—28no—
387C2×C4×D11—22no—
388C2×C4×D11—22no—
389C2×C4×D11—24no—
390C2×C4×D11—22no—
391C2×C4×D11—22no—
392C2×C4×D11—21no—
393C2×C4×D11—21no—
394C2×C4×D11—21no—
395C2×C4×D11—21no—
396C2×C4×D11—22no—
397C2×C4×D11—22no—
398C2×C4×D11—21no—
399C2×C4×D11—42no—
400C2×C4×D11—42no—
401C2×C4×D11—44no—
402C2×C4×D11—44no—
403C2×C4×D11—44no—
404C2×C4×D11C2×D411yescharacteristic
405C2×C4×D11C2×D411yescharacteristic
406C2×C4×D11C2×D411yescharacteristic
407C2×C4×D11C2×D411yescharacteristic
408C2×C4×D11C2×D411yescharacteristic
409C2×C4×D11C2×D411yescharacteristic
410C2×C4×D11C2×D411yescharacteristic
411C2×C4×D11C2×D411yescharacteristic
412C2×C4×D11C2×D411yescharacteristic
413C2×C4×D11C2×D411yescharacteristic
414C2×C4×D11C2411yescharacteristic
415C2×C4×D11C2411yescharacteristic
416C2×Dic22—21no—
417C2×Dic22C2411yescharacteristic
418C11×Q16—24no—
419C11×SD16—24no—
420C2×C8×C11C2412yes—
421C2×C8×C11C2412yes—
422C11×C4⋊C4—21no—
423C11×C4⋊C4—21no—
424C11×C4⋊C4—21no—
425C11×C4⋊C4—21no—
426C11×C4⋊C4—22no—
427C11×C4⋊C4—22no—
428C11×C4⋊C4—21no—
429C11×C4⋊C4C2411yescharacteristic
430C11×C4⋊C4C2412yes—
431C11×C4⋊C4C2411yescharacteristic
432C11×C22⋊C4—21no—
433C11×C22⋊C4—21no—
434C11×C22⋊C4—21no—
435C11×C22⋊C4—21no—
436C11×C22⋊C4—21no—
437C42×C11—21no—
438C42×C11—22no—
439C42×C11—22no—
440C42×C11C2×D411yescharacteristic
441C42×C11C2×D411yescharacteristic
442C42×C11C2411yescharacteristic
443C42×C11C2411yescharacteristic
444C22⋊Dic11—21no—
445C22⋊Dic11—21no—
446C22⋊Dic11—21no—
447C22⋊Dic11—21no—
448C22⋊Dic11—21no—
449#4326—24no—
450#4325—24no—
451#4325—24no—
452#4323—24no—
453(C2×D11)⋊C4—21no—
454(C2×D11)⋊C4—21no—
455(C2×D11)⋊C4—22no—
456(C2×D11)⋊C4—22no—
457(C2×D11)⋊C4—21no—
458(C2×D11)⋊C4—21no—
459(C2×D11)⋊C4—22no—
460(C2×D11)⋊C4—22no—
461(C2×D11)⋊C4—21no—
462(C2×D11)⋊C4—21no—
463(C2×D11)⋊C4—21no—
464(C2×D11)⋊C4—21no—
465(C2×D11)⋊C4—22no—
466(C2×D11)⋊C4—22no—
467(C2×D11)⋊C4—21no—
468(C2×D11)⋊C4—21no—
469C4⋊Dic11—21no—
470C4⋊Dic11—22no—
471C4⋊Dic11—22no—
472C4⋊Dic11—21no—
473C4⋊Dic11—21no—
474C4⋊Dic11—21no—
475C4⋊Dic11—21no—
476C4⋊Dic11C2411yescharacteristic
477C4⋊Dic11C2412yes—
478C4⋊Dic11C2411yescharacteristic
479Dic11⋊C4—21no—
480Dic11⋊C4—21no—
481Dic11⋊C4—21no—
482Dic11⋊C4—21no—
483Dic11⋊C4—21no—
484Dic11⋊C4—21no—
485Dic11⋊C4—21no—
486Dic11⋊C4—21no—
487Dic11⋊C4—21no—
488Dic11⋊C4—21no—
489C4×Dic11—22no—
490C4×Dic11—22no—
491C4×Dic11—22no—
492C4×Dic11—22no—
493C4×Dic11—21no—
494C4×Dic11—21no—
495C4×Dic11—21no—
496C4×Dic11C2×D411yescharacteristic
497C4×Dic11C2×D411yescharacteristic
498C4×Dic11C2×D411yescharacteristic
499C4×Dic11C2×D411yescharacteristic
500C4×Dic11C2×D411yescharacteristic
501C4×Dic11C2×D411yescharacteristic
502C4×Dic11C2×D411yescharacteristic
503C4×Dic11C2×D411yescharacteristic
504C4×Dic11C2×D411yescharacteristic
505C4×Dic11C2×D411yescharacteristic
506C4×Dic11C2411yescharacteristic
507C4×Dic11C2411yescharacteristic
508C2×C11⋊C8C2412yes—
509C2×C11⋊C8C2412yes—
510D88—24no—
511#4314—24no—
512#4313—24no—
513#4313—24no—
514C2×#529—111no—
515C2×C4×#41—111no—
516#3117—111no—
517#3117—111no—
518#3114—111no—
519#3114—111no—
520#3111—112no—
521#3111—112no—
522#3108—111no—
523#3108D1111yescharacteristic, complemented
524#3105—111no—
525#3105—111no—
526#3102—112no—
527#3102—112no—
528#3095—111no—
529#3094—111no—
530#3080—112no—
531#3040—112no—
532#3007—111no—
533#3006—111no—
534C4×#137—112no—
535C4×AGL(1,ℤ/8)—112no—
536#2920—111no—
537C23×C11—21no—
538C23×C11C22×D411yescharacteristic
539C22×D11—24no—
540C22×D11—22no—
541C22×D11—22no—
542C22×D11—22no—
543C22×D11—21no—
544C22×D11—41no—
545C22×D11—42no—
546C22×D11—42no—
547C22×D11—42no—
548C22×D11—42no—
549C22×D11—42no—
550C22×D11C22×D411yescharacteristic
551C22×D11C22×D411yescharacteristic
552Q8×C11—24no—
553Q8×C11—22no—
554Q8×C11—22no—
555Q8×C11C2×#4114yes—
556D4×C11—22no—
557D4×C11—42no—
558C2×C4×C11—24no—
559C2×C4×C11—22no—
560C2×C4×C11—22no—
561C2×C4×C11—22no—
562C2×C4×C11—22no—
563C2×C4×C11—22no—
564C2×C4×C11—21no—
565C2×C4×C11—21no—
566C2×C4×C11—21no—
567C2×C4×C11—42no—
568C2×C4×C11—42no—
569C2×C4×C11C22×D411yescharacteristic
570C2×C4×C11C22×D411yescharacteristic
571C2×C4×C11C22×D411yescharacteristic
572C2×C4×C11C22×D411yescharacteristic
573C2×C4×C11C22×D411yescharacteristic
574C2×C4×C11C2511yescharacteristic
575C22⋊D11—42no—
576C22⋊D11—42no—
577C22⋊D11—42no—
578C2×Dic11—22no—
579C2×Dic11—22no—
580C2×Dic11—22no—
581C2×Dic11—21no—
582C2×Dic11—21no—
583C2×Dic11—21no—
584C2×Dic11—41no—
585C2×Dic11—42no—
586C2×Dic11—42no—
587C2×Dic11C22×D411yescharacteristic
588C2×Dic11C22×D411yescharacteristic
589C2×Dic11C22×D411yescharacteristic
590C2×Dic11C22×D411yescharacteristic
591C2×Dic11C22×D411yescharacteristic
592C2×Dic11C22×D411yescharacteristic
593D44—28no—
594D44—24no—
595D44—28no—
596D44—22no—
597D44—22no—
598D44—42no—
599D44C2×#4114yes—
600C4×D11—28no—
601C4×D11—22no—
602C4×D11—22no—
603C4×D11—22no—
604C4×D11—22no—
605C4×D11—28no—
606C4×D11—22no—
607C4×D11—41no—
608C4×D11—41no—
609C4×D11—41no—
610C4×D11—41no—
611C4×D11—41no—
612C4×D11—41no—
613C4×D11—42no—
614C4×D11—44no—
615C4×D11—44no—
616C4×D11—44no—
617C4×D11—42no—
618C4×D11—42no—
619C4×D11—42no—
620C4×D11—44no—
621C4×D11—42no—
622C4×D11C2×#4114yes—
623Dic22—22no—
624Dic22—42no—
625C8×C11—22no—
626C8×C11—22no—
627C11⋊C8—22no—
628C11⋊C8—22no—
629C22×#41—111no—
630C2×#137—112no—
631C2×AGL(1,ℤ/8)—112no—
632#529—111no—
633#529—111no—
634#529—111no—
635#529—111no—
636#529—111no—
637#529—111no—
638#529—111no—
639#529—221no—
640#529—221no—
641#529—221no—
642#529—221no—
643#529C2×D1111yescharacteristic
644C2×#126—221no—
645C2×#125—111no—
646C2×#124—111no—
647C2×#123—221no—
648C2×C22⋊Q8—111no—
649C2×#121—111no—
650C4×#41—112no—
651C4×#41—112no—
652C4×#41—112no—
653C4×#41—112no—
654C4×#41—221no—
655C4×#41—221no—
656C4×#41—221no—
657C4×#41—221no—
658C2×C4×Q8—111no—
659C2×C4×Q8—111no—
660C2×C4×Q8C2×D1111yescharacteristic, complemented
661C2×C4×D4—111no—
662C2×C4×D4—111no—
663C2×C4×D4—111no—
664C2×C4×D4—221no—
665C2×C4×D4—221no—
666C2×C4×D4—221no—
667C2×#117—111no—
668C2×#117—221no—
669C2×#117—221no—
670C22×C42—111no—
671C22×C42—221no—
672#485—112no—
673#485—112no—
674#484—111no—
675#484—111no—
676#483—111no—
677#483C2×D1111yescharacteristic, complemented
678#482—112no—
679#482—112no—
680#481—111no—
681#481—111no—
682#480—111no—
683#480C2×D1111yescharacteristic
684#479—112no—
685#479—112no—
686#479—112no—
687#479C2×D1112yescomplemented
688#478—112no—
689#478—112no—
690#478—112no—
691#478—112no—
692#464—112no—
693#464—112no—
694#464—112no—
695#464C2×D1112yescomplemented
696#463—112no—
697#463—112no—
698#463—112no—
699#463—112no—
700#452—112no—
701#452—112no—
702#451—111no—
703#451C2×D1111yescharacteristic, complemented
704#450—111no—
705#450—111no—
706#449—112no—
707#449—112no—
708#448—111no—
709#448C2×D1111yescharacteristic
710#447—111no—
711#447—111no—
712#442—112no—
713#442—112no—
714#441—112no—
715#441—112no—
716#440—112no—
717#440—112no—
718#440—112no—
719#440—112no—
720C4×Q16—112no—
721C4×Q16C2×D1112yescomplemented
722C4×SD16—112no—
723C4×SD16—112no—
724C4×SD16—112no—
725C4×SD16C2×D1112yescomplemented
726C4×D8—112no—
727C4×D8—112no—
728#432—112no—
729#432—111no—
730#432—111no—
731#431—111no—
732#431—112no—
733#431C2×D1111yescharacteristic, complemented
734#428—112no—
735#428—112no—
736#423—112no—
737#419—112no—
738#418—112no—
739#417—112no—
740#417—112no—
741#407—111no—
742#407—111no—
743C4×M16—112no—
744C22×C11—21no—
745C22×C11—21no—
746C22×C11—41no—
747C22×C11—41no—
748C22×C11—41no—
749C22×C11#57512yes—
750C22×C11C23×D411yescharacteristic
751C2×D11—21no—
752C2×D11—21no—
753C2×D11—24no—
754C2×D11—21no—
755C2×D11—21no—
756C2×D11—21no—
757C2×D11—44no—
758C2×D11—48no—
759C2×D11—42no—
760C2×D11—42no—
761C2×D11—41no—
762C2×D11—41no—
763C2×D11—41no—
764C2×D11—84no—
765C2×D11#52512yes—
766C4×C11—24no—
767C4×C11—21no—
768C4×C11—21no—
769C4×C11—21no—
770C4×C11—21no—
771C4×C11—41no—
772C4×C11—42no—
773C4×C11—41no—
774C4×C11—41no—
775C4×C11#57512yes—
776C4×C11C22×#4112yes—
777Dic11—21no—
778Dic11—21no—
779Dic11—21no—
780Dic11—21no—
781Dic11—21no—
782Dic11—41no—
783Dic11—42no—
784Dic11—41no—
785Dic11—41no—
786Dic11#52512yes—
787C2×#41—112no—
788C2×#41—112no—
789C2×#41—221no—
790C2×#41—221no—
791C2×#41—228no—
792C22×Q8—111no—
793C22×Q8C22×D1111yescharacteristic
794C22×D4—111no—
795C22×D4—111no—
796C22×D4—221no—
797C22×D4—221no—
798C23×C4—111no—
799C23×C4—111no—
800C23×C4—111no—
801C23×C4—221no—
802C23×C4—221no—
803C23×C4—221no—
804C23×C4—221no—
805#137—228no—
806AGL(1,ℤ/8)—228no—
807C2×Q16—112no—
808C2×Q16C22×D1112yes—
809C2×SD16—112no—
810C2×SD16—112no—
811C2×SD16—112no—
812C2×SD16C22×D1112yes—
813C2×D8—112no—
814C2×D8—112no—
815C2×M16—112no—
816C2×M16—112no—
817#126—21no—
818#126—221no—
819#126—221no—
820#126—221no—
821#126—221no—
822#126—221no—
823#126—221no—
824#126—221no—
825#125—111no—
826#125—111no—
827#125—111no—
828#125—221no—
829#125—221no—
830#125C22×D1111yescharacteristic
831#124—111no—
832#124—111no—
833#124—111no—
834#124—221no—
835#124—221no—
836#124C22×D1111yescharacteristic
837#123—21no—
838#123—221no—
839#123—221no—
840#123—221no—
841#123—221no—
842#123—221no—
843#123—221no—
844#123—221no—
845C22⋊Q8—111no—
846C22⋊Q8—111no—
847C22⋊Q8—111no—
848C22⋊Q8—221no—
849C22⋊Q8—221no—
850C22⋊Q8C22×D1111yescharacteristic
851#121—111no—
852#121—111no—
853#121—111no—
854#121—221no—
855#121—221no—
856#121C22×D1111yescharacteristic
857C4×Q8—21no—
858C4×Q8—21no—
859C4×Q8—112no—
860C4×Q8—112no—
861C4×Q8—111no—
862C4×Q8—111no—
863C4×Q8—111no—
864C4×Q8—221no—
865C4×Q8—221no—
866C4×Q8—221no—
867C4×Q8—221no—
868C4×Q8C22×D1111yescharacteristic
869C4×Q8C22×D1112yes—
870C4×Q8C22×D1112yes—
871C4×D4—21no—
872C4×D4—111no—
873C4×D4—112no—
874C4×D4—112no—
875C4×D4—111no—
876C4×D4—112no—
877C4×D4—112no—
878C4×D4—111no—
879C4×D4—222no—
880C4×D4—222no—
881C4×D4—222no—
882C4×D4—222no—
883C4×D4—221no—
884C4×D4—221no—
885C4×D4—221no—
886C4×D4—221no—
887C4×D4—221no—
888C4×D4—221no—
889C4×D4—221no—
890C4×D4—222no—
891C4×D4—222no—
892C4×D4—222no—
893C4×D4—222no—
894C4×D4—221no—
895C4×D4—221no—
896C4×D4—221no—
897C4×D4—221no—
898C4×D4—221no—
899C4×D4—221no—
900C4×D4C22×D1111yescharacteristic
901#117—21no—
902#117—112no—
903#117—112no—
904#117—221no—
905#117—221no—
906#117—221no—
907#117—222no—
908#117—222no—
909#117—222no—
910#117—222no—
911#117—221no—
912#117—221no—
913#117—221no—
914#117—221no—
915#117—221no—
916#117—221no—
917C2×C4⋊C4—21no—
918C2×C4⋊C4—111no—
919C2×C4⋊C4—111no—
920C2×C4⋊C4—111no—
921C2×C4⋊C4—221no—
922C2×C4⋊C4—221no—
923C2×C4⋊C4—221no—
924C2×C4⋊C4—221no—
925C2×C4⋊C4—221no—
926C2×C4⋊C4C22×D1111yescharacteristic
927C2×C22⋊C4—221no—
928C2×C22⋊C4—221no—
929C2×C22⋊C4—221no—
930C2×C22⋊C4—221no—
931C2×C22⋊C4—221no—
932C2×C22⋊C4—221no—
933C2×C22⋊C4—221no—
934C2×C22⋊C4—221no—
935C2×C42—21no—
936C2×C42—111no—
937C2×C42—111no—
938C2×C42—111no—
939C2×C42—111no—
940C2×C42—111no—
941C2×C42—111no—
942C2×C42—111no—
943C2×C42—111no—
944C2×C42—111no—
945C2×C42—111no—
946C2×C42—111no—
947C2×C42—222no—
948C2×C42—222no—
949C2×C42—222no—
950C2×C42—222no—
951C2×C42—221no—
952C2×C42—221no—
953C2×C42—221no—
954C2×C42C22×D1111yescharacteristic
955#107—112no—
956#107—112no—
957#107—112no—
958#107C22×D1112yes—
959#106—112no—
960#106—112no—
961#106—112no—
962#106C22×D1112yes—
963C4⋊C8—112no—
964C4⋊C8—112no—
965C4⋊C8—112no—
966C4⋊C8C22×D1112yes—
967#103—112no—
968#103—112no—
969#103—112no—
970#103—112no—
971#103—112no—
972#103C22×D1112yes—
973#103C22×D1112yes—
974#103C22×D1112yes—
975#102—112no—
976#102—112no—
977#102—112no—
978#102—112no—
979#102—112no—
980#102—112no—
981#102—112no—
982#102C22×D1112yes—
983C22⋊C8—111no—
984C22⋊C8—111no—
985C22⋊C8—112no—
986C22⋊C8—112no—
987C22⋊C8C22×D1111yescharacteristic
988C22⋊C8C22×D1111yescharacteristic
989#97—112no—
990#97—112no—
991C4×C8—112no—
992C4×C8C22×D1112yes—
993C2×C11—22no—
994C2×C11—81no—
995C2×C11C2×#52511yescharacteristic
996C2×C11C2×#57511yescharacteristic
997C2×C11C2×#57511yescharacteristic
998D11—22no—
999D11—41no—
1000D11—44no—
1001D11—81no—
1002C24—111no—
1003C24—221no—
1004C24—221no—
1005#41—118no—
1006#41—224no—
1007#41—224no—
1008#41—228no—
1009#41—228no—
1010#41—224no—
1011C2×Q8—24no—
1012C2×Q8—21no—
1013C2×Q8—111no—
1014C2×Q8—221no—
1015C2×Q8—224no—
1016C2×Q8C23×D1111yescharacteristic
1017C2×Q8C23×D1112yes—
1018C2×D4—21no—
1019C2×D4—112no—
1020C2×D4—111no—
1021C2×D4—224no—
1022C2×D4—222no—
1023C2×D4—222no—
1024C2×D4—228no—
1025C2×D4—221no—
1026C2×D4—224no—
1027C2×D4—221no—
1028C2×D4—221no—
1029C2×D4—221no—
1030C2×D4—221no—
1031C2×D4—444no—
1032C2×D4C23×D1111yescharacteristic
1033C22×C4—21no—
1034C22×C4—21no—
1035C22×C4—21no—
1036C22×C4—111no—
1037C22×C4—111no—
1038C22×C4—111no—
1039C22×C4—111no—
1040C22×C4—111no—
1041C22×C4—111no—
1042C22×C4—111no—
1043C22×C4—111no—
1044C22×C4—111no—
1045C22×C4—111no—
1046C22×C4—111no—
1047C22×C4—111no—
1048C22×C4—111no—
1049C22×C4—111no—
1050C22×C4—111no—
1051C22×C4—222no—
1052C22×C4—222no—
1053C22×C4—224no—
1054C22×C4—222no—
1055C22×C4—222no—
1056C22×C4—221no—
1057C22×C4—228no—
1058C22×C4—221no—
1059C22×C4—221no—
1060C22×C4—221no—
1061C22×C4—221no—
1062C22×C4—221no—
1063C22×C4—222no—
1064C22×C4—222no—
1065C22×C4—221no—
1066C22×C4—442no—
1067C22×C4—442no—
1068C22×C4—444no—
1069C22×C4—444no—
1070C22×C4—444no—
1071C22×C4D4×D1111yescharacteristic
1072C22×C4D4×D1111yescharacteristic
1073C22×C4C23×D1111yescharacteristic
1074Q16—24no—
1075Q16—224no—
1076SD16—24no—
1077SD16—224no—
1078SD16—224no—
1079SD16—224no—
1080D8—224no—
1081D8—224no—
1082M16—224no—
1083M16—224no—
1084C2×C8—112no—
1085C2×C8—112no—
1086C2×C8C23×D1112yes—
1087C2×C8C23×D1112yes—
1088C4⋊C4—22no—
1089C4⋊C4—22no—
1090C4⋊C4—21no—
1091C4⋊C4—21no—
1092C4⋊C4—21no—
1093C4⋊C4—21no—
1094C4⋊C4—21no—
1095C4⋊C4—112no—
1096C4⋊C4—111no—
1097C4⋊C4—111no—
1098C4⋊C4—221no—
1099C4⋊C4—221no—
1100C4⋊C4—222no—
1101C4⋊C4—222no—
1102C4⋊C4—221no—
1103C4⋊C4—221no—
1104C4⋊C4—221no—
1105C4⋊C4—221no—
1106C4⋊C4—221no—
1107C4⋊C4—221no—
1108C4⋊C4—221no—
1109C4⋊C4—221no—
1110C4⋊C4—221no—
1111C4⋊C4—221no—
1112C4⋊C4—221no—
1113C4⋊C4—221no—
1114C4⋊C4—221no—
1115C4⋊C4C23×D1111yescharacteristic
1116C4⋊C4C23×D1111yescharacteristic
1117C4⋊C4C23×D1112yes—
1118C22⋊C4—21no—
1119C22⋊C4—21no—
1120C22⋊C4—21no—
1121C22⋊C4—21no—
1122C22⋊C4—21no—
1123C22⋊C4—222no—
1124C22⋊C4—222no—
1125C22⋊C4—221no—
1126C22⋊C4—221no—
1127C22⋊C4—221no—
1128C22⋊C4—221no—
1129C22⋊C4—222no—
1130C22⋊C4—222no—
1131C22⋊C4—221no—
1132C22⋊C4—221no—
1133C22⋊C4—221no—
1134C22⋊C4—221no—
1135C22⋊C4—221no—
1136C22⋊C4—221no—
1137C22⋊C4—221no—
1138C22⋊C4—222no—
1139C22⋊C4—222no—
1140C22⋊C4—221no—
1141C22⋊C4—221no—
1142C22⋊C4—221no—
1143C22⋊C4—221no—
1144C42—22no—
1145C42—22no—
1146C42—21no—
1147C42—111no—
1148C42—111no—
1149C42—111no—
1150C42—111no—
1151C42—111no—
1152C42—111no—
1153C42—111no—
1154C42—111no—
1155C42—111no—
1156C42—111no—
1157C42—111no—
1158C42—111no—
1159C42—222no—
1160C42—222no—
1161C42—222no—
1162C42—222no—
1163C42—221no—
1164C42—221no—
1165C42—221no—
1166C42D4×D1111yescharacteristic
1167C42D4×D1111yescharacteristic
1168C42C23×D1111yescharacteristic
1169C42C23×D1111yescharacteristic
1170C11#6056311yescharacteristic, complemented, Sylow
1171C23—21no—
1172C23—111no—
1173C23—111no—
1174C23—222no—
1175C23—224no—
1176C23—222no—
1177C23—222no—
1178C23—221no—
1179C23—441no—
1180C23—442no—
1181C23—442no—
1182C23—442no—
1183C23—442no—
1184C23—442no—
1185C23C2×D4×D1111yescharacteristic
1186Q8—24no—
1187Q8—22no—
1188Q8—22no—
1189Q8—222no—
1190Q8—442no—
1191Q8#41×D1114yes—
1192D4—22no—
1193D4—42no—
1194D4—114no—
1195D4—228no—
1196D4—228no—
1197D4—224no—
1198D4—222no—
1199D4—222no—
1200D4—442no—
1201D4—442no—
1202D4—442no—
1203D4—442no—
1204C2×C4—24no—
1205C2×C4—22no—
1206C2×C4—22no—
1207C2×C4—22no—
1208C2×C4—22no—
1209C2×C4—22no—
1210C2×C4—21no—
1211C2×C4—21no—
1212C2×C4—21no—
1213C2×C4—42no—
1214C2×C4—42no—
1215C2×C4—111no—
1216C2×C4—114no—
1217C2×C4—111no—
1218C2×C4—111no—
1219C2×C4—111no—
1220C2×C4—111no—
1221C2×C4—111no—
1222C2×C4—222no—
1223C2×C4—228no—
1224C2×C4—222no—
1225C2×C4—228no—
1226C2×C4—222no—
1227C2×C4—222no—
1228C2×C4—222no—
1229C2×C4—222no—
1230C2×C4—222no—
1231C2×C4—222no—
1232C2×C4—221no—
1233C2×C4—221no—
1234C2×C4—221no—
1235C2×C4—441no—
1236C2×C4—441no—
1237C2×C4—441no—
1238C2×C4—441no—
1239C2×C4—441no—
1240C2×C4—441no—
1241C2×C4—444no—
1242C2×C4—444no—
1243C2×C4—444no—
1244C2×C4—442no—
1245C2×C4—442no—
1246C2×C4—442no—
1247C2×C4—442no—
1248C2×C4—441no—
1249C2×C4—442no—
1250C2×C4—442no—
1251C2×C4—444no—
1252C2×C4—442no—
1253C2×C4C2×D4×D1111yescharacteristic
1254C2×C4C2×D4×D1111yescharacteristic
1255C2×C4C2×D4×D1111yescharacteristic
1256C2×C4C2×D4×D1111yescharacteristic
1257C2×C4C2×D4×D1111yescharacteristic
1258C2×C4C24×D1111yescharacteristic
1259C8—22no—
1260C8—22no—
1261C8—222no—
1262C8—222no—
1263C22—21no—
1264C22—21no—
1265C22—41no—
1266C22—41no—
1267C22—41no—
1268C22—112no—
1269C22—221no—
1270C22—221no—
1271C22—221no—
1272C22—221no—
1273C22—224no—
1274C22—221no—
1275C22—444no—
1276C22—448no—
1277C22—442no—
1278C22—442no—
1279C22—441no—
1280C22—441no—
1281C22—441no—
1282C22—884no—
1283C22#1062329912yes—
1284C22C22×D4×D1111yescharacteristic
1285C4—21no—
1286C4—21no—
1287C4—21no—
1288C4—24no—
1289C4—21no—
1290C4—42no—
1291C4—41no—
1292C4—41no—
1293C4—41no—
1294C4—112no—
1295C4—221no—
1296C4—221no—
1297C4—221no—
1298C4—221no—
1299C4—221no—
1300C4—441no—
1301C4—442no—
1302C4—441no—
1303C4—441no—
1304C4#1062330812yes—
1305C4C2×#41×D1112yes—
1306C2—22no—
1307C2—81no—
1308C2—222no—
1309C2—441no—
1310C2—444no—
1311C2—881no—
1312C2D11×#52511yescharacteristic
1313C2C2×#1062329911yescharacteristic
1314C2C2×#1062330811yescharacteristic
subgroupG/H
centerC2×C4C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3108C2
socleC22×C11C23×D4
prime radical#13077867C2
hypercenter#3108D11
hypocenterC11#60563
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C2×C4 ◁ C2×C42 ◁ #3108

Complements

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

NH ≅ G/Ntype
1. D11×#529C2semidirect
2. C2×C4×#4343C2semidirect
3. #13078788C2semidirect
4. #13078782C2semidirect
5. #13078757C2semidirect
6. #13078751C2semidirect
7. #13078732C2semidirect
8. #13078724C2semidirect
9. #13078696C2semidirect
10. #13078665C2semidirect
11. #13078659C2semidirect
12. #13078640C2semidirect
13. #13078632C2semidirect
14. #13078559C2semidirect
15. #13078551C2semidirect
16. #13078435C2semidirect
17. #13078107C2semidirect
18. #13077875C2semidirect
20. C4×#66971C2semidirect
21. C4×#66967C2semidirect
22. #13077244C2semidirect
23. C11×#3108C2semidirect
26. C2×C4×Q8×C11C22semidirect
27. C2×Q8×Dic11C22semidirect
32. #10623222C22semidirect
33. D11×#125C22semidirect
34. #10623211C22semidirect
35. D11×#124C22semidirect
42. #10623111C22semidirect
49. C4×#4343C22semidirect
50. C4×#4343C22semidirect
51. C4×Q8×D11C22semidirect
52. #10623088C22semidirect
54. C4×D4×D11C22semidirect
59. C2×#66946C22semidirect
64. C2×C4×D44C22semidirect
67. C11×#483C22semidirect
69. C11×#479C22semidirect
70. C11×#464C22semidirect
71. C11×#451C22semidirect
73. C4×C11×Q16C22semidirect
74. C4×C11×SD16C22semidirect
75. C11×#431C22semidirect
76. #10622841C22semidirect
78. #10622800C22semidirect
79. #10622798C22semidirect
80. #10622797C22semidirect
82. #10622779C22semidirect
83. #10622777C22semidirect
84. #10622679C22semidirect
85. #10622670C22semidirect
86. #10622659C22semidirect
87. #10622657C22semidirect
90. C4×#4326C22semidirect
91. #10622641C22semidirect
92. C4×#4325C22semidirect
93. C4×#4325C22semidirect
94. #10622635C22semidirect
95. C4×#4323C22semidirect
96. #10622584C22semidirect
98. #10622538C22semidirect
99. #10622504C22semidirect
100. #10622502C22semidirect
101. #10622498C22semidirect
102. #10622494C22semidirect
103. #10622484C22semidirect
104. #10622482C22semidirect
105. #10622480C22semidirect
106. #10622474C22semidirect
107. #10622460C22semidirect
108. #10622457C22semidirect
109. #10622450C22semidirect
110. #10622448C22semidirect
111. #10622432C22semidirect
112. #10622430C22semidirect
113. #10622430C22semidirect
114. #10622427C22semidirect
116. #10622423C22semidirect
119. #10622415C22semidirect
120. #10622412C22semidirect
121. #10622409C22semidirect
122. #10622402C22semidirect
123. #10622400C22semidirect
124. #10622398C22semidirect
125. #10622392C22semidirect
126. #10622383C22semidirect
129. #10622344C22semidirect
132. #10622335C22semidirect
133. #10622332C22semidirect
134. #10622332C22semidirect
135. C4×D88C22semidirect
136. C4×#4314C22semidirect
137. C4×#4313C22semidirect
138. #10622298C22semidirect
523. #3108D11semidirect
660. C2×C4×Q8C2×D11semidirect
677. #483C2×D11semidirect
687. #479C2×D11semidirect
695. #464C2×D11semidirect
703. #451C2×D11semidirect
721. C4×Q16C2×D11semidirect
725. C4×SD16C2×D11semidirect
733. #431C2×D11semidirect
1170. C11#60563semidirect

Maximal subgroups

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

subgroupindex
D11×#5292
C2×C4×#43432
#130787882
#130787822
#130787572
#130787512
#130787322
#130787242
#130786962
#130786652
#130786592
#130786402
#130786322
#130785592
#130785512
#130784352
#130781072
#130778752
#130778672
C4×#669712
C4×#669672
#130772442
C11×#31082
#6056311