Finite Group Databasebeta

← #15625290

Subgroups — #15625290

Order 2816.

2222 conjugacy classes of subgroups.

The subgroup lattice has 1002 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082004C211yesmaximal, characteristic, complemented
2C2×#10623361C211yesmaximal, characteristic, complemented
3#13079716C214yesmaximal, complemented
4#13079708C214yesmaximal, complemented
5#13079686C214yesmaximal, complemented
6#13079664C214yesmaximal, complemented
7#13079083C211yesmaximal, characteristic, complemented
8#13079064C211yesmaximal, characteristic, complemented
9#13079004C211yesmaximal, characteristic, complemented
10#13078988C211yesmaximal, characteristic, complemented
11#13078113C211yesmaximal, characteristic, complemented
12#13078112C211yesmaximal, characteristic, complemented
13#13078095C211yesmaximal, characteristic, complemented
14#13078094C211yesmaximal, characteristic, complemented
15#13077858C211yesmaximal, characteristic, complemented
16#13077846C211yesmaximal, characteristic, complemented
17#13077842C211yesmaximal, characteristic, complemented
18#13077251C211yesmaximal, characteristic, complemented
19C11×#3005C211yesmaximal, characteristic, complemented
20C22×C11×#41C2211yescharacteristic
21C23×D44C2211yescharacteristic
22C2×C11×#137C2211yescharacteristic, complemented
23C2×C11×AGL(1,ℤ/8)C2211yescharacteristic, complemented
24C11×#525C2211yescharacteristic
25#10623363C2211yescharacteristic, complemented
26#10623361—22no—
27#10623361—22no—
28#10623361C2214yes—
29#10623361C2214yes—
30#41×Dic11C2211yescharacteristic, complemented
31C2×#67002C2211yescharacteristic
32C2×#67002C2211yescharacteristic
33C2×#67000C2211yescharacteristic
34C2×#67000C2211yescharacteristic
35C2×#66995C2211yescharacteristic, complemented
36C2×#66993C2211yescharacteristic
37C2×#66993C2211yescharacteristic
38C2×#66990—22no—
39C2×#66985C2211yescharacteristic, complemented
40#10623322C2211yescharacteristic
41C2×#66983—22no—
42C2×#66979C2211yescharacteristic
43C2×#66961C2211yescharacteristic
44C2×#66961C2211yescharacteristic
45#10623196—22no—
46#10623174C2212yescomplemented
47#10623156C2212yescomplemented
48#10623150C2212yescomplemented
49#10623134C2212yescomplemented
50#10623124—22no—
51#10623088—22no—
52#10623069—22no—
53#10623053C2211yescharacteristic, complemented
54#10623048C2211yescharacteristic, complemented
55C11×#452C2214yescomplemented
56C11×#449C2214yescomplemented
57C11×#419C2211yescharacteristic, complemented
58C11×#418C2211yescharacteristic, complemented
59C11×#407C2211yescharacteristic
60#10622852C2214yescomplemented
61#10622851C2214yescomplemented
62#10622838C2211yescharacteristic, complemented
63#10622828C2211yescharacteristic, complemented
64#10622820C2211yescharacteristic
65#10622804C2212yescomplemented
66#10622803C2212yescomplemented
67#10622798C2214yescomplemented
68#10622789C2212yescomplemented
69#10622789C2212yescomplemented
70#10622788C2212yescomplemented
71#10622781C2212yescomplemented
72#10622778C2214yescomplemented
73#10622776C2214yescomplemented
74#10622767C2212yescomplemented
75#10622764C2212yescomplemented
76#10622763C2214yescomplemented
77#10622744C2211yescharacteristic
78#10622744C2211yescharacteristic
79#10622731C2211yescharacteristic, complemented
80#10622731C2211yescharacteristic, complemented
81M16×Dic11C2211yescharacteristic, complemented
82M16×Dic11C2211yescharacteristic, complemented
83#10622659C2214yescomplemented
84#10622649C2214yescomplemented
85#10622614C2211yescharacteristic
86#10622614C2211yescharacteristic
87#10622432C2214yescomplemented
88#10622413C2214yescomplemented
89#10622411C2214yescomplemented
90#10622408C2214yescomplemented
91#10622399C2214yescomplemented
92#10622377C2214yescomplemented
93#10622375C2214yescomplemented
94#10622373C2214yescomplemented
95#10622345C2214yescomplemented
96#10622344C2214yescomplemented
97#10622333C2214yescomplemented
98#10622333C2214yescomplemented
99C24×D11—21no—
100C2×C11×#41—22no—
101C2×C11×#41—42no—
102C2×C11×#41—42no—
103C2×C11×#41C2311yescharacteristic
104C2×C11×#41C2314yes—
105C22×Q8×C11C2311yescharacteristic
106C22×D4×C11—21no—
107C22×D4×C11C2311yescharacteristic
108C23×C4×C11—21no—
109C23×C4×C11C2311yescharacteristic
110C22×C22⋊D11—22no—
111C22×C22⋊D11—22no—
112C2×#4339C2311yescharacteristic
113C22×D44—21no—
114C22×D44—22no—
115C22×D44—42no—
116C22×D44—42no—
117C22×D44C2311yescharacteristic
118C22×D44C2311yescharacteristic
119C22×D44C2314yes—
120C11×#137—42no—
121C11×AGL(1,ℤ/8)—42no—
122C2×C11×Q16C2312yescomplemented
123C2×C11×SD16C2312yescomplemented
124C2×C11×SD16C2312yescomplemented
125C2×C11×D8C2312yescomplemented
126C2×C11×M16C2311yescharacteristic
127C2×C11×M16C2311yescharacteristic
128C11×#123—21no—
129C11×C22⋊Q8C2312yes—
130C11×#121C2312yes—
131C11×#120—21no—
132C4×D4×C11—22no—
133C11×#117C2311yescharacteristic
134#67006—21no—
135C2×C22⋊Dic11D412yes—
136#67002—42no—
137#67002—42no—
138#67000—22no—
139#67000—21no—
140#67000—21no—
141#67000C2314yes—
142#67000C2312yes—
143#67000C2312yes—
144#67000C2311yescharacteristic, complemented
145Q8×Dic11C2312yescomplemented
146#66997C2311yescharacteristic, complemented
147C2×#4326C2312yescomplemented
148#66995—42no—
149C2×#4325C2312yes—
150C2×#4325C2312yes—
151C2×#4325C2312yescomplemented
152#66993—22no—
153#66993—21no—
154#66993—21no—
155#66993C2314yes—
156#66993C2312yes—
157#66993C2312yes—
158#66993C2311yescharacteristic, complemented
159#66992—22no—
160#66992—22no—
161#66991—22no—
162#66990—24no—
163#66990—24no—
164#66990—24no—
165#66990—24no—
166#66989—22no—
167#66989C2311yescharacteristic, complemented
168#66988—22no—
169D4×Dic11—22no—
170D4×Dic11C2312yescomplemented
171C2×#4324C2312yescomplemented
172#66985—42no—
173C2×#4323C2312yes—
174C2×#4323C2312yes—
175C2×#4323C2312yescomplemented
176#66983—24no—
177#66983—24no—
178#66983—24no—
179#66983—24no—
180#66983C2312yes—
181#66982—21no—
182C4×C22⋊D11—22no—
183C4×C22⋊D11—22no—
184C2×(C2×D11)⋊C4—22no—
185C2×(C2×D11)⋊C4—22no—
186#66979—21no—
187#66979D412yes—
188#66979D412yes—
189#66979C2311yescharacteristic
190#66979C2312yes—
191#66979C2312yes—
192C2×C4⋊Dic11D412yes—
193#66977C2312yes—
194C2×C4×Dic11—21no—
195C2×C4×Dic11C2311yescharacteristic
196C2×C4×Dic11C2311yescharacteristic
197C2×#4318C2311yescharacteristic
198C2×#4318C2311yescharacteristic
199#66961—42no—
200#66961—42no—
201C2×D88C2312yes—
202C2×D88C2312yes—
203C2×#4314C2312yes—
204C2×#4314C2312yes—
205#66951—22no—
206#66950—22no—
207#66946C2312yescomplemented
208#66943—22no—
209#66943C2312yescomplemented
210#66942—22no—
211#66941C2312yescomplemented
212#66940C2312yescomplemented
213#66939—22no—
214#66938—22no—
215#66936—22no—
216#66936—22no—
217(C22⋊D11)⋊C4—22no—
218#66932—22no—
219#66932—22no—
220#66932—22no—
221#66931—22no—
222#66931—22no—
223#66925—21no—
224C42×D11—21no—
225C4×Dic22—22no—
226C11×#103C2314yescomplemented
227C11×#102C2314yescomplemented
228C11×C22⋊C8C2314yes—
229#66899C2314yescomplemented
230#66896C2314yescomplemented
231C22⋊(C11⋊C8)C2314yes—
232#66885C2314yes—
233#66885C2314yes—
234#66879C2312yescomplemented
235#66879C2312yescomplemented
236Dic11⋊C8C2314yescomplemented
237Dic11⋊C8C2314yescomplemented
238C8×Dic11C2312yescomplemented
239C8×Dic11C2312yescomplemented
240#66873C2314yes—
241#66873C2314yes—
242#60806—111nomaximal, Sylow
243C24×C11—21no—
244C24×C11C2×D411yescharacteristic
245C23×D11—21no—
246C23×D11—21no—
247C23×D11—24no—
248C23×D11—44no—
249C23×D11—84no—
250C11×#41—22no—
251C11×#41—22no—
252C11×#41—44no—
253C11×#41—44no—
254C11×#41—48no—
255C2×Q8×C11—21no—
256C2×Q8×C11—22no—
257C2×Q8×C11—22no—
258C2×Q8×C11C2412yes—
259C2×Q8×C11C2411yescharacteristic
260C2×D4×C11—21no—
261C2×D4×C11—24no—
262C2×D4×C11—22no—
263C2×D4×C11—21no—
264C2×D4×C11—22no—
265C2×D4×C11—22no—
266C2×D4×C11—44no—
267C2×D4×C11C2412yes—
268C2×D4×C11C2411yescharacteristic
269C22×C4×C11—22no—
270C22×C4×C11—22no—
271C22×C4×C11—21no—
272C22×C4×C11—21no—
273C22×C4×C11—24no—
274C22×C4×C11—44no—
275C22×C4×C11C2×D411yescharacteristic
276C22×C4×C11C2×D412yes—
277C22×C4×C11C2412yes—
278C22×C4×C11C2411yescharacteristic
279C2×C22⋊D11—22no—
280C2×C22⋊D11—24no—
281C2×C22⋊D11—24no—
282C2×C22⋊D11—24no—
283C2×C22⋊D11—24no—
284C2×C22⋊D11—21no—
285C2×C22⋊D11—22no—
286C2×C22⋊D11—84no—
287C2×C22⋊D11—84no—
288C22×Dic11—22no—
289C22×Dic11C2×D412yes—
290C22×Dic11C2×D412yes—
291#4339—22no—
292#4339—22no—
293C2×D44—24no—
294C2×D44—21no—
295C2×D44—21no—
296C2×D44—22no—
297C2×D44—22no—
298C2×D44—22no—
299C2×D44—22no—
300C2×D44—44no—
301C2×D44—44no—
302C2×D44—44no—
303C2×D44—48no—
304C2×D44C2412yes—
305C2×D44C2412yes—
306C2×D44C2411yescharacteristic
307C2×C4×D11—22no—
308C2×C4×D11—21no—
309C2×Dic22—22no—
310C2×Dic22C2411yescharacteristic
311C11×Q16—42no—
312C11×SD16—42no—
313C11×SD16—42no—
314C11×D8—42no—
315C11×M16—22no—
316C11×M16—22no—
317C2×C8×C11C2412yes—
318C2×C8×C11C2412yes—
319C11×C4⋊C4—22no—
320C11×C4⋊C4C2412yes—
321C11×C22⋊C4—21no—
322C11×C22⋊C4—22no—
323C11×C22⋊C4—22no—
324C42×C11—21no—
325C22⋊Dic11—22no—
326C22⋊Dic11—22no—
327C22⋊Dic11—21no—
328C22⋊Dic11—22no—
329C22⋊Dic11C2×D412yes—
330C22⋊Dic11C2×D412yes—
331C22⋊Dic11C2×D412yes—
332C22⋊Dic11C2×D412yes—
333#4326—42no—
334#4325—42no—
335#4325—42no—
336#4325—42no—
337#4324—42no—
338#4323—42no—
339#4323—42no—
340#4323—42no—
341(C2×D11)⋊C4—22no—
342(C2×D11)⋊C4—22no—
343(C2×D11)⋊C4—24no—
344(C2×D11)⋊C4—24no—
345(C2×D11)⋊C4—24no—
346(C2×D11)⋊C4—24no—
347(C2×D11)⋊C4—22no—
348C4⋊Dic11—22no—
349C4⋊Dic11—22no—
350C4⋊Dic11C2×D412yes—
351C4⋊Dic11C2×D412yes—
352C4⋊Dic11C2×D412yes—
353C4⋊Dic11C2×D412yes—
354C4⋊Dic11C2412yes—
355Dic11⋊C4—22no—
356Dic11⋊C4—22no—
357Dic11⋊C4—22no—
358Dic11⋊C4—22no—
359Dic11⋊C4—22no—
360C4×Dic11—22no—
361C4×Dic11—22no—
362C4×Dic11—21no—
363C4×Dic11C2×D412yes—
364C4×Dic11C2×D411yescharacteristic
365C4×Dic11C2×D411yescharacteristic
366C4×Dic11C2411yescharacteristic
367C4×Dic11C2411yescharacteristic
368C4×Dic11C2412yes—
369#4318—22no—
370#4318—22no—
371C2×C11⋊C8C2412yes—
372C2×C11⋊C8C2412yes—
373D88—42no—
374D88—42no—
375#4314—42no—
376#4314—42no—
377#3455—111no—
378C2×#535—111no—
379#3224—114no—
380#3224—114no—
381#3222—114no—
382#3220—114no—
383#3153—111no—
384#3151—111no—
385#3140—111no—
386#3138—111no—
387#3040—111no—
388#3040—111no—
389#3038—111no—
390#3038—111no—
391#3005—111no—
392#3005D1111yescharacteristic, complemented
393#3003—111no—
394#3003—111no—
395#2921—111no—
396C23×C11—22no—
397C23×C11—21no—
398C23×C11—22no—
399C23×C11—42no—
400C23×C11—44no—
401C23×C11—42no—
402C23×C11C22×D412yes—
403C23×C11C22×D411yescharacteristic
404C22×D11—21no—
405C22×D11—22no—
406C22×D11—22no—
407C22×D11—48no—
408C22×D11—44no—
409C22×D11—44no—
410C22×D11—42no—
411C22×D11—42no—
412C22×D11—84no—
413C22×D11—84no—
414C22×D11—816no—
415Q8×C11—21no—
416Q8×C11—21no—
417Q8×C11—22no—
418Q8×C11—22no—
419Q8×C11—42no—
420D4×C11—21no—
421D4×C11—21no—
422D4×C11—22no—
423D4×C11—22no—
424D4×C11—48no—
425D4×C11—42no—
426D4×C11—42no—
427D4×C11—82no—
428C2×C4×C11—22no—
429C2×C4×C11—24no—
430C2×C4×C11—22no—
431C2×C4×C11—22no—
432C2×C4×C11—21no—
433C2×C4×C11—22no—
434C2×C4×C11—22no—
435C2×C4×C11—48no—
436C2×C4×C11—42no—
437C2×C4×C11—42no—
438C2×C4×C11C22×D412yes—
439C2×C4×C11C22×D411yescharacteristic
440C2×C4×C11H(5,𝔽2)12yes—
441C2×C4×C11H(5,𝔽2)12yes—
442C2×C4×C11C2511yescharacteristic
443C22⋊D11—42no—
444C22⋊D11—82no—
445C22⋊D11—84no—
446C22⋊D11—84no—
447C22⋊D11—84no—
448C22⋊D11—84no—
449C22⋊D11—82no—
450C2×Dic11—21no—
451C2×Dic11—22no—
452C2×Dic11—42no—
453C2×Dic11—42no—
454C2×Dic11—82no—
455C2×Dic11C22×D412yes—
456C2×Dic11C22×D412yes—
457C2×Dic11C22×D412yes—
458C2×Dic11C22×D412yes—
459D44—22no—
460D44—22no—
461D44—21no—
462D44—21no—
463D44—22no—
464D44—22no—
465D44—48no—
466D44—42no—
467D44—42no—
468C4×D11—42no—
469C4×D11—82no—
470Dic22—21no—
471Dic22—21no—
472Dic22—82no—
473C8×C11—22no—
474C8×C11—22no—
475C11⋊C8—22no—
476C11⋊C8—22no—
477C22×#41C2×D1111yescharacteristic
478C23×D4—111no—
479C2×#137—111no—
480C2×#137C2×D1111yescharacteristic, complemented
481C2×AGL(1,ℤ/8)—111no—
482C2×AGL(1,ℤ/8)—111no—
483C2×AGL(1,ℤ/8)—111no—
484C2×AGL(1,ℤ/8)—111no—
485C2×AGL(1,ℤ/8)—111no—
486C2×AGL(1,ℤ/8)C2×D1111yescharacteristic, complemented
487#542—112no—
488#542—112no—
489#541—112no—
490#540—112no—
491#539—222no—
492#538—222no—
493#535—114no—
494#535—114no—
495#535—222no—
496#535—222no—
497#533—111no—
498#532—111no—
499C2×#127—111no—
500C2×#127—111no—
501#529—222no—
502#529—222no—
503C2×#124—111no—
504C2×#124—111no—
505#525—111no—
506#525C2×D1111yescharacteristic
507C2×#121—222no—
508C2×#120—222no—
509C4×#41—111no—
510C4×#41—111no—
511C2×#117—111no—
512#497—112no—
513#496—112no—
514#496—112no—
515#496—112no—
516#495—112no—
517#495—112no—
518#493—112no—
519#492—112no—
520#490—114no—
521#489—114no—
522#488—114no—
523#486—114no—
524#464—114no—
525#464—114no—
526#463—114no—
527#463—114no—
528#460—114no—
529#460—114no—
530#459—114no—
531#459—114no—
532#452—114no—
533#452C2×D1114yescomplemented
534#450—114no—
535#450—114no—
536#449—114no—
537#449C2×D1114yescomplemented
538#447—114no—
539#447—114no—
540#433—114no—
541#433—114no—
542#423—111no—
543#423—111no—
544#419—111no—
545#419C2×D1111yescharacteristic, complemented
546#418—111no—
547#418—111no—
548#418—111no—
549#418—111no—
550#418—111no—
551#418C2×D1111yescharacteristic, complemented
552#407—111no—
553#407C2×D1111yescharacteristic
554C4×M16—111no—
555C4×M16—111no—
556C22×C11—22no—
557C22×C11—22no—
558C22×C11—22no—
559C22×C11—22no—
560C22×C11—44no—
561C22×C11—42no—
562C22×C11—44no—
563C22×C11—42no—
564C22×C11—41no—
565C22×C11—84no—
566C22×C11#53512yes—
567C22×C11C23×D411yescharacteristic
568C2×D11—44no—
569C2×D11—44no—
570C2×D11—42no—
571C2×D11—42no—
572C2×D11—42no—
573C2×D11—41no—
574C2×D11—84no—
575C2×D11—84no—
576C2×D11—816no—
577C4×C11—22no—
578C4×C11—42no—
579C4×C11—42no—
580C4×C11—41no—
581C4×C11#53512yes—
582C4×C11C2×H(5,𝔽2)11yescharacteristic
583C4×C11C2×H(5,𝔽2)11yescharacteristic
584Dic11—22no—
585Dic11—22no—
586Dic11—22no—
587Dic11—22no—
588Dic11—42no—
589Dic11—41no—
590C25—221no—
591C2×#41—22no—
592C2×#41—42no—
593C2×#41—42no—
594C2×#41—111no—
595C2×#41C22×D1111yescharacteristic
596C2×#41C22×D1114yes—
597C22×Q8C22×D1111yescharacteristic
598C22×D4—21no—
599C22×D4—111no—
600C22×D4—111no—
601C22×D4—114no—
602C22×D4—222no—
603C22×D4—222no—
604C22×D4—221no—
605C22×D4—222no—
606C22×D4—442no—
607C22×D4—442no—
608C22×D4C22×D1111yescharacteristic
609C23×C4—21no—
610C23×C4C22×D1111yescharacteristic
611#137—42no—
612#137—442no—
613AGL(1,ℤ/8)—42no—
614AGL(1,ℤ/8)—442no—
615AGL(1,ℤ/8)—442no—
616AGL(1,ℤ/8)—442no—
617AGL(1,ℤ/8)—442no—
618AGL(1,ℤ/8)—442no—
619C2×Q16—112no—
620C2×Q16C22×D1112yescomplemented
621C2×SD16—112no—
622C2×SD16—112no—
623C2×SD16—112no—
624C2×SD16—112no—
625C2×SD16—112no—
626C2×SD16—112no—
627C2×SD16C22×D1112yescomplemented
628C2×SD16C22×D1112yescomplemented
629C2×D8—112no—
630C2×D8—112no—
631C2×D8—112no—
632C2×D8—112no—
633C2×D8—112no—
634C2×D8C22×D1112yescomplemented
635C2×M16—111no—
636C2×M16—111no—
637C2×M16C22×D1111yescharacteristic
638C2×M16C22×D1111yescharacteristic
639C4⋊Q8—112no—
640C4⋊Q8—111no—
641#127—114no—
642#127—112no—
643#127—112no—
644#127—111no—
645#127—221no—
646#127—221no—
647#127—222no—
648#126—222no—
649#126—222no—
650#126—222no—
651#126—222no—
652#125—112no—
653#125—222no—
654#125—222no—
655#124—114no—
656#124—112no—
657#124—112no—
658#124—111no—
659#124—111no—
660#124—221no—
661#124—221no—
662#124—222no—
663#124—222no—
664#124—222no—
665#123—21no—
666#123—222no—
667#123—222no—
668#123—222no—
669#123—222no—
670#123—221no—
671C22⋊Q8—112no—
672C22⋊Q8—222no—
673C22⋊Q8—222no—
674C22⋊Q8—222no—
675C22⋊Q8C22×D1112yes—
676#121—112no—
677#121—222no—
678#121—222no—
679#121—224no—
680#121—224no—
681#121—224no—
682#121—224no—
683#121—222no—
684#121C22×D1112yes—
685#120—21no—
686#120—224no—
687#120—224no—
688#120—224no—
689#120—224no—
690#120—221no—
691C4×Q8—112no—
692C4×Q8—112no—
693C4×Q8—222no—
694C4×D4—22no—
695C4×D4—112no—
696C4×D4—112no—
697C4×D4—222no—
698C4×D4—222no—
699C4×D4—222no—
700C4×D4—222no—
701#117—112no—
702#117—112no—
703#117—112no—
704#117—112no—
705#117—111no—
706#117—221no—
707#117—221no—
708#117C22×D1111yescharacteristic
709C2×C4⋊C4—112no—
710C2×C22⋊C4—112no—
711C2×C22⋊C4—222no—
712C2×C22⋊C4—222no—
713C2×C42—111no—
714C2×C42—111no—
715C2×C42—221no—
716C2×C42—221no—
717C4⋊C8—114no—
718C4⋊C8—114no—
719#103—114no—
720#103C22×D1114yescomplemented
721#102—114no—
722#102—114no—
723#102—114no—
724#102—114no—
725#102—114no—
726#102C22×D1114yescomplemented
727C22⋊C8—114no—
728C22⋊C8C22×D1114yes—
729#97—112no—
730#97—112no—
731C4×C8—112no—
732C4×C8—112no—
733C2×C11—22no—
734C2×C11—42no—
735C2×C11—81no—
736C2×C11—82no—
737C2×C11C2×#53511yescharacteristic
738C2×C11#358512yes—
739D11—81no—
740D11—82no—
741D11—82no—
742C24—21no—
743C24—221no—
744C24—221no—
745C24—224no—
746C24—444no—
747C24—884no—
748C24D4×D1111yescharacteristic
749#41—22no—
750#41—22no—
751#41—44no—
752#41—44no—
753#41—48no—
754#41—222no—
755#41—222no—
756C2×Q8—21no—
757C2×Q8—22no—
758C2×Q8—22no—
759C2×Q8—111no—
760C2×Q8—222no—
761C2×Q8C23×D1112yes—
762C2×Q8C23×D1111yescharacteristic
763C2×D4—21no—
764C2×D4—24no—
765C2×D4—22no—
766C2×D4—21no—
767C2×D4—22no—
768C2×D4—22no—
769C2×D4—44no—
770C2×D4—112no—
771C2×D4—112no—
772C2×D4—111no—
773C2×D4—222no—
774C2×D4—224no—
775C2×D4—224no—
776C2×D4—224no—
777C2×D4—224no—
778C2×D4—221no—
779C2×D4—222no—
780C2×D4—224no—
781C2×D4—221no—
782C2×D4—221no—
783C2×D4—222no—
784C2×D4—222no—
785C2×D4—222no—
786C2×D4—222no—
787C2×D4—444no—
788C2×D4—444no—
789C2×D4—444no—
790C2×D4—448no—
791C2×D4—884no—
792C2×D4—884no—
793C2×D4C23×D1112yes—
794C2×D4C23×D1111yescharacteristic
795C22×C4—22no—
796C22×C4—22no—
797C22×C4—21no—
798C22×C4—21no—
799C22×C4—24no—
800C22×C4—44no—
801C22×C4—112no—
802C22×C4—112no—
803C22×C4—222no—
804C22×C4—222no—
805C22×C4—221no—
806C22×C4D4×D1111yescharacteristic
807C22×C4D4×D1112yes—
808C22×C4C23×D1112yes—
809C22×C4C23×D1111yescharacteristic
810Q16—42no—
811Q16—442no—
812SD16—42no—
813SD16—42no—
814SD16—442no—
815SD16—442no—
816SD16—442no—
817SD16—442no—
818SD16—442no—
819SD16—442no—
820D8—42no—
821D8—442no—
822D8—442no—
823D8—442no—
824D8—442no—
825D8—442no—
826M16—22no—
827M16—22no—
828M16—222no—
829M16—222no—
830C2×C8—112no—
831C2×C8—112no—
832C2×C8C23×D1112yes—
833C2×C8C23×D1112yes—
834C4⋊C4—22no—
835C4⋊C4—112no—
836C4⋊C4—112no—
837C4⋊C4—112no—
838C4⋊C4—112no—
839C4⋊C4—112no—
840C4⋊C4—222no—
841C4⋊C4—222no—
842C4⋊C4—222no—
843C4⋊C4—222no—
844C4⋊C4—222no—
845C4⋊C4—222no—
846C4⋊C4—222no—
847C4⋊C4C23×D1112yes—
848C22⋊C4—21no—
849C22⋊C4—22no—
850C22⋊C4—22no—
851C22⋊C4—112no—
852C22⋊C4—112no—
853C22⋊C4—112no—
854C22⋊C4—112no—
855C22⋊C4—224no—
856C22⋊C4—224no—
857C22⋊C4—224no—
858C22⋊C4—224no—
859C22⋊C4—222no—
860C22⋊C4—222no—
861C22⋊C4—222no—
862C22⋊C4—222no—
863C22⋊C4—221no—
864C22⋊C4—222no—
865C22⋊C4—222no—
866C42—21no—
867C42—111no—
868C42—111no—
869C42—112no—
870C42—111no—
871C42—111no—
872C42—112no—
873C42—222no—
874C42—222no—
875C42—221no—
876C11#6080611yescharacteristic, complemented, Sylow
877C23—22no—
878C23—21no—
879C23—22no—
880C23—42no—
881C23—44no—
882C23—42no—
883C23—221no—
884C23—222no—
885C23—222no—
886C23—448no—
887C23—444no—
888C23—444no—
889C23—442no—
890C23—442no—
891C23—884no—
892C23—884no—
893C23—8816no—
894C23C2×D4×D1112yes—
895C23C2×D4×D1111yescharacteristic
896Q8—21no—
897Q8—22no—
898Q8—21no—
899Q8—22no—
900Q8—42no—
901Q8—221no—
902Q8—221no—
903Q8—882no—
904D4—21no—
905D4—22no—
906D4—21no—
907D4—22no—
908D4—48no—
909D4—42no—
910D4—42no—
911D4—82no—
912D4—221no—
913D4—221no—
914D4—222no—
915D4—222no—
916D4—222no—
917D4—222no—
918D4—448no—
919D4—442no—
920D4—442no—
921D4—442no—
922D4—884no—
923D4—884no—
924D4—884no—
925D4—884no—
926D4—882no—
927D4—882no—
928C2×C4—22no—
929C2×C4—24no—
930C2×C4—22no—
931C2×C4—22no—
932C2×C4—22no—
933C2×C4—21no—
934C2×C4—22no—
935C2×C4—48no—
936C2×C4—42no—
937C2×C4—42no—
938C2×C4—112no—
939C2×C4—112no—
940C2×C4—112no—
941C2×C4—112no—
942C2×C4—222no—
943C2×C4—221no—
944C2×C4—442no—
945C2×C4—442no—
946C2×C4—442no—
947C2×C4—882no—
948C2×C4—882no—
949C2×C4C2×D4×D1112yes—
950C2×C4C2×D4×D1111yescharacteristic
951C2×C4#6703712yes—
952C2×C4#6703712yes—
953C2×C4C24×D1111yescharacteristic
954C8—22no—
955C8—22no—
956C8—222no—
957C8—222no—
958C22—22no—
959C22—22no—
960C22—22no—
961C22—22no—
962C22—44no—
963C22—42no—
964C22—44no—
965C22—42no—
966C22—41no—
967C22—84no—
968C22—442no—
969C22—444no—
970C22—444no—
971C22—441no—
972C22—442no—
973C22—442no—
974C22—884no—
975C22—884no—
976C22—8816no—
977C22#1062312312yes—
978C22C22×D4×D1111yescharacteristic
979C4—22no—
980C4—42no—
981C4—42no—
982C4—41no—
983C4—222no—
984C4—222no—
985C4—222no—
986C4—222no—
987C4—442no—
988C4—441no—
989C4#1062312312yes—
990C4C2×#6703711yescharacteristic
991C4C2×#6703711yescharacteristic
992C2—22no—
993C2—42no—
994C2—82no—
995C2—81no—
996C2—882no—
997C2—882no—
998C2—881no—
999C2C2×#1062312311yescharacteristic
1000C2#1308339312yes—
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3005C2
socleC22×C11C23×D4
hypercenter#3005D11
hypocenterC11#60806
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ #3005

Complements

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

NH ≅ G/Ntype
1. #13082004C2semidirect
2. C2×#10623361C2semidirect
3. #13079716C2semidirect
4. #13079708C2semidirect
5. #13079686C2semidirect
6. #13079664C2semidirect
7. #13079083C2semidirect
8. #13079064C2semidirect
9. #13079004C2semidirect
10. #13078988C2semidirect
11. #13078113C2semidirect
12. #13078112C2semidirect
13. #13078095C2semidirect
14. #13078094C2semidirect
15. #13077858C2semidirect
16. #13077846C2semidirect
17. #13077842C2semidirect
18. #13077251C2semidirect
19. C11×#3005C2semidirect
22. C2×C11×#137C22semidirect
23. C2×C11×AGL(1,ℤ/8)C22semidirect
25. #10623363C22semidirect
30. #41×Dic11C22semidirect
35. C2×#66995C22semidirect
39. C2×#66985C22semidirect
46. #10623174C22semidirect
47. #10623156C22semidirect
48. #10623150C22semidirect
49. #10623134C22semidirect
53. #10623053C22semidirect
54. #10623048C22semidirect
55. C11×#452C22semidirect
56. C11×#449C22semidirect
57. C11×#419C22semidirect
58. C11×#418C22semidirect
60. #10622852C22semidirect
61. #10622851C22semidirect
62. #10622838C22semidirect
63. #10622828C22semidirect
65. #10622804C22semidirect
66. #10622803C22semidirect
67. #10622798C22semidirect
68. #10622789C22semidirect
69. #10622789C22semidirect
70. #10622788C22semidirect
71. #10622781C22semidirect
72. #10622778C22semidirect
73. #10622776C22semidirect
74. #10622767C22semidirect
75. #10622764C22semidirect
76. #10622763C22semidirect
79. #10622731C22semidirect
80. #10622731C22semidirect
81. M16×Dic11C22semidirect
82. M16×Dic11C22semidirect
83. #10622659C22semidirect
84. #10622649C22semidirect
87. #10622432C22semidirect
88. #10622413C22semidirect
89. #10622411C22semidirect
90. #10622408C22semidirect
91. #10622399C22semidirect
92. #10622377C22semidirect
93. #10622375C22semidirect
94. #10622373C22semidirect
95. #10622345C22semidirect
96. #10622344C22semidirect
97. #10622333C22semidirect
98. #10622333C22semidirect
122. C2×C11×Q16C23semidirect
123. C2×C11×SD16C23semidirect
124. C2×C11×SD16C23semidirect
125. C2×C11×D8C23semidirect
144. #67000C23semidirect
145. Q8×Dic11C23semidirect
146. #66997C23semidirect
147. C2×#4326C23semidirect
151. C2×#4325C23semidirect
158. #66993C23semidirect
167. #66989C23semidirect
170. D4×Dic11C23semidirect
171. C2×#4324C23semidirect
175. C2×#4323C23semidirect
207. #66946C23semidirect
209. #66943C23semidirect
211. #66941C23semidirect
212. #66940C23semidirect
226. C11×#103C23semidirect
227. C11×#102C23semidirect
229. #66899C23semidirect
230. #66896C23semidirect
234. #66879C23semidirect
235. #66879C23semidirect
236. Dic11⋊C8C23semidirect
237. Dic11⋊C8C23semidirect
238. C8×Dic11C23semidirect
239. C8×Dic11C23semidirect
392. #3005D11semidirect
480. C2×#137C2×D11semidirect
486. C2×AGL(1,ℤ/8)C2×D11semidirect
533. #452C2×D11semidirect
537. #449C2×D11semidirect
545. #419C2×D11semidirect
551. #418C2×D11semidirect
620. C2×Q16C22×D11semidirect
627. C2×SD16C22×D11semidirect
628. C2×SD16C22×D11semidirect
634. C2×D8C22×D11semidirect
720. #103C22×D11semidirect
726. #102C22×D11semidirect
876. C11#60806semidirect

Maximal subgroups

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

subgroupindex
#130820042
C2×#106233612
#130797162
#130797082
#130796862
#130796642
#130790832
#130790642
#130790042
#130789882
#130781132
#130781122
#130780952
#130780942
#130778582
#130778462
#130778422
#130772512
C11×#30052
#6080611