Finite Group Databasebeta

← #15622197

Subgroups — #15622197

Order 2816.

2428 conjugacy classes of subgroups.

The subgroup lattice has 1082 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623127C211yesmaximal, characteristic, complemented
2C2×#41×Dic11C211yesmaximal, characteristic, complemented
3#13078760C214yesmaximal, complemented
4#13078733C212yesmaximal, complemented
5#13078702C212yesmaximal, complemented
6#13078669C214yesmaximal, complemented
7#13078642C212yesmaximal, complemented
8#13078611C212yesmaximal, complemented
9#13078557C211yesmaximal, characteristic, complemented
10#13078552C211yesmaximal, characteristic, complemented
11#13078427C212yesmaximal, complemented
12#13078094C212yesmaximal, complemented
13#13077868C211yesmaximal, characteristic, complemented
14#13077429C212yesmaximal, complemented
15AGL(1,ℤ/8)×Dic11C212yesmaximal, complemented
16#13077245C211yesmaximal, characteristic, complemented
17C11×#3006C211yesmaximal, characteristic, complemented
18C22×C11×#41C2211yescharacteristic
19C22×#4341—21no—
20C2×C11×AGL(1,ℤ/8)C2212yes—
21C2×C11×#121C2211yescharacteristic
22#41×Dic11—21no—
23#41×Dic11—21no—
24#41×Dic11—21no—
25#41×Dic11—21no—
26#41×Dic11C2212yes—
27#41×Dic11C2212yes—
28#41×Dic11C2212yescomplemented
29#41×Dic11C2212yescomplemented
30C2×#67002C2212yes—
31C2×Q8×Dic11C2211yescharacteristic, complemented
32C2×Q8×Dic11C2211yescharacteristic, complemented
33C2×#66993C2211yescharacteristic, complemented
34C2×#66992—21no—
35C2×D4×Dic11—21no—
36C2×D4×Dic11—21no—
37C2×D4×Dic11C2211yescharacteristic, complemented
38C2×D4×Dic11C2211yescharacteristic, complemented
39C2×D4×Dic11C2211yescharacteristic, complemented
40C2×#66983C2211yescharacteristic
41C2×#66979—21no—
42C2×#66979C2211yescharacteristic
43C22×C4×Dic11—21no—
44C22×C4×Dic11C2211yescharacteristic
45#10623127—21no—
46#10623127—21no—
47#10623127—21no—
48#10623127—21no—
49#10623127C2212yes—
50#10623127C2212yes—
51#10623127C2212yescomplemented
52#10623127C2212yescomplemented
53C2×#66946C2211yescharacteristic, complemented
54C2×#66941C2211yescharacteristic, complemented
55C2×#66938—21no—
56C2×(C22⋊D11)⋊C4—21no—
57C11×#449C2214yescomplemented
58C11×#448C2212yescomplemented
59C11×#447C2212yescomplemented
60C11×#417C2212yes—
61C11×#407C2211yescharacteristic
62#10622851C2214yescomplemented
63#10622845C2212yes—
64#10622840C2212yescomplemented
65#10622830C2212yescomplemented
66#10622828C2212yescomplemented
67#10622820C2211yescharacteristic
68#10622777C2214yescomplemented
69#10622776C2214yescomplemented
70#10622776C2214yescomplemented
71SD16×Dic11C2214yescomplemented
72#10622765C2214yescomplemented
73#10622763C2214yescomplemented
74#10622763C2214yescomplemented
75D8×Dic11C2214yescomplemented
76#10622744C2212yescomplemented
77#10622734C2212yescomplemented
78#10622731C2212yescomplemented
79M16×Dic11C2212yescomplemented
80#10622648C2214yescomplemented
81#10622647C2212yescomplemented
82#10622646C2212yescomplemented
83#10622577C2212yescomplemented
84#10622430C2214yescomplemented
85#10622407C2214yescomplemented
86#10622404C2214yescomplemented
87#10622401C2214yescomplemented
88#10622398C2214yescomplemented
89#10622374C2214yescomplemented
90#10622372C2214yescomplemented
91#10622369C2214yescomplemented
92#10622350C2214yescomplemented
93#10622349C2212yescomplemented
94#10622348C2212yescomplemented
95#10622332C2212yescomplemented
96#10622332C2212yescomplemented
97#10622331C2212yescomplemented
98#10622331C2212yescomplemented
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
109C23×C4×C11—21no—
110C23×C4×C11C2311yescharacteristic
111C22×C22⋊D11—21no—
112C22×C22⋊D11—21no—
113C22×C22⋊D11—21no—
114C23×Dic11—21no—
115C23×Dic11—21no—
116C23×Dic11—21no—
117C23×Dic11D411yescharacteristic
118C23×Dic11D411yescharacteristic
119C2×#4341—22no—
120C2×#4341—22no—
121C2×#4341—22no—
122C2×#4341—22no—
123C2×#4341—48no—
124C22×D44C2311yescharacteristic
125C22×C4×D11—21no—
126C22×Dic22—21no—
127C11×AGL(1,ℤ/8)—28no—
128C2×C11×SD16C2314yes—
129C2×C11×D8C2314yes—
130C2×C11×M16C2312yes—
131C11×#121—21no—
132C11×#121—21no—
133C11×#121C2312yes—
134C11×#121C2312yes—
135C2×C11×C4⋊C4C2311yescharacteristic
136C2×C11×C22⋊C4—21no—
137C2×C22⋊Dic11—21no—
138C2×C22⋊Dic11—21no—
139C2×C22⋊Dic11—21no—
140C2×C22⋊Dic11—21no—
141#67002—28no—
142Q8×Dic11—21no—
143Q8×Dic11—21no—
144Q8×Dic11—21no—
145Q8×Dic11—21no—
146Q8×Dic11C2312yes—
147Q8×Dic11C2312yes—
148Q8×Dic11C2312yes—
149Q8×Dic11C2312yes—
150C2×#4325C2314yes—
151#66993—21no—
152#66993—21no—
153#66993C2312yes—
154#66993C2312yes—
155#66992—22no—
156#66992—22no—
157#66992—22no—
158#66992—22no—
159D4×Dic11—22no—
160D4×Dic11—22no—
161D4×Dic11—22no—
162D4×Dic11—22no—
163D4×Dic11—22no—
164D4×Dic11—22no—
165D4×Dic11—22no—
166D4×Dic11—22no—
167D4×Dic11—21no—
168D4×Dic11—21no—
169D4×Dic11—21no—
170D4×Dic11—21no—
171D4×Dic11—21no—
172D4×Dic11—21no—
173D4×Dic11C2312yes—
174D4×Dic11C2312yes—
175D4×Dic11C2312yes—
176D4×Dic11C2312yes—
177D4×Dic11C2312yes—
178D4×Dic11C2312yes—
179C2×#4323C2314yes—
180#66983—21no—
181#66983—21no—
182#66983C2312yes—
183#66983C2312yes—
184C2×(C2×D11)⋊C4—21no—
185C2×(C2×D11)⋊C4—21no—
186#66979—21no—
187#66979—21no—
188#66979—22no—
189#66979—22no—
190#66979—22no—
191#66979—22no—
192#66979C2312yes—
193#66979C2312yes—
194C2×C4⋊Dic11—21no—
195C2×C4⋊Dic11—21no—
196C2×C4⋊Dic11C2311yescharacteristic
197C2×C4⋊Dic11C2311yescharacteristic
198C2×C4⋊Dic11C2311yescharacteristic
199C2×Dic11⋊C4—21no—
200C2×C4×Dic11—21no—
201C2×C4×Dic11—21no—
202C2×C4×Dic11—21no—
203C2×C4×Dic11—22no—
204C2×C4×Dic11—22no—
205C2×C4×Dic11—22no—
206C2×C4×Dic11—22no—
207C2×C4×Dic11D411yescharacteristic
208C2×C4×Dic11D411yescharacteristic
209C2×C4×Dic11D411yescharacteristic
210C2×C4×Dic11D411yescharacteristic
211C2×C4×Dic11D411yescharacteristic
212C2×C4×Dic11D411yescharacteristic
213C2×C4×Dic11C2311yescharacteristic
214C2×C4×Dic11C2311yescharacteristic
215C2×C4×Dic11C2311yescharacteristic
216C2×C4×Dic11C2311yescharacteristic
217C2×C4×Dic11C2311yescharacteristic
218C2×C4×Dic11C2311yescharacteristic
219C2×#4318C2312yes—
220#66946—21no—
221#66946—21no—
222#66946C2312yes—
223#66946C2312yes—
224#66941—21no—
225#66941—21no—
226#66941C2312yes—
227#66941C2312yes—
228#66938—22no—
229#66938—22no—
230#66938—22no—
231#66938—22no—
232(C22⋊D11)⋊C4—22no—
233(C22⋊D11)⋊C4—22no—
234(C22⋊D11)⋊C4—22no—
235(C22⋊D11)⋊C4—22no—
236C11×#103C2314yes—
237C11×#102C2314yes—
238C11×C22⋊C8C2312yes—
239C11×C22⋊C8C2312yes—
240#66899C2314yes—
241#66896C2314yes—
242#66896C2314yes—
243#66896C2314yes—
244C22⋊(C11⋊C8)C2312yes—
245C22⋊(C11⋊C8)C2312yes—
246#66885C2314yes—
247#66885C2314yes—
248#66882C2314yes—
249#66881C2314yes—
250#66879C2314yes—
251Dic11⋊C8C2314yes—
252Dic11⋊C8C2314yes—
253C8×Dic11C2314yes—
254#66872C2314yes—
255#66871C2314yes—
256#60561—111nomaximal, Sylow
257C24×C11—21no—
258C24×C11—21no—
259C24×C11C2×D411yescharacteristic
260C23×D11—21no—
261C11×#41—28no—
262C11×#41—28no—
263C11×#41—24no—
264C11×#41—24no—
265C11×#41—24no—
266C11×#41#4118yescomplemented
267C2×Q8×C11—24no—
268C2×Q8×C11—21no—
269C2×Q8×C11C2412yes—
270C2×D4×C11—28no—
271C2×D4×C11—22no—
272C2×D4×C11—22no—
273C2×D4×C11—24no—
274C2×D4×C11—22no—
275C2×D4×C11—22no—
276C2×D4×C11—21no—
277C2×D4×C11—21no—
278C2×D4×C11—24no—
279C2×D4×C11—44no—
280C2×D4×C11C2412yes—
281C2×D4×C11C2412yes—
282C22×C4×C11—28no—
283C22×C4×C11—21no—
284C22×C4×C11—22no—
285C22×C4×C11—22no—
286C22×C4×C11—24no—
287C22×C4×C11—21no—
288C22×C4×C11C2×D411yescharacteristic
289C22×C4×C11C2×D411yescharacteristic
290C22×C4×C11C2×D411yescharacteristic
291C22×C4×C11C2411yescharacteristic
292C22×C4×C11C2411yescharacteristic
293C22×C4×C11C2411yescharacteristic
294C2×C22⋊D11—22no—
295C2×C22⋊D11—22no—
296C2×C22⋊D11—22no—
297C2×C22⋊D11—22no—
298C2×C22⋊D11—22no—
299C2×C22⋊D11—22no—
300C2×C22⋊D11—44no—
301C2×C22⋊D11—44no—
302C2×C22⋊D11—44no—
303C22×Dic11—24no—
304C22×Dic11—22no—
305C22×Dic11—22no—
306C22×Dic11—22no—
307C22×Dic11—22no—
308C22×Dic11—22no—
309C22×Dic11—22no—
310C22×Dic11—21no—
311C22×Dic11—21no—
312C22×Dic11—21no—
313C22×Dic11—42no—
314C22×Dic11—44no—
315C22×Dic11—44no—
316C22×Dic11—44no—
317C22×Dic11C2×D411yescharacteristic
318C22×Dic11C2×D411yescharacteristic
319C22×Dic11C2×D411yescharacteristic
320C22×Dic11C2×D411yescharacteristic
321C22×Dic11C2×D411yescharacteristic
322C22×Dic11C2×D411yescharacteristic
323C22×Dic11C2×D411yescharacteristic
324C22×Dic11C2×D411yescharacteristic
325C22×Dic11C2×D411yescharacteristic
326C22×Dic11C2×D411yescharacteristic
327C22×Dic11C2×D411yescharacteristic
328C22×Dic11C2×D411yescharacteristic
329#4341—48no—
330#4341—48no—
331#4341—48no—
332#4341—48no—
333C2×D44—21no—
334C2×D44—24no—
335C2×D44C2412yes—
336C2×C4×D11—22no—
337C2×C4×D11—22no—
338C2×C4×D11—44no—
339C2×Dic22—22no—
340C2×Dic22—22no—
341C2×Dic22—44no—
342C11×SD16—28no—
343C11×D8—28no—
344C11×M16—24no—
345C2×C8×C11C2414yes—
346C11×C4⋊C4—21no—
347C11×C4⋊C4C2412yes—
348C11×C22⋊C4—22no—
349C11×C22⋊C4—22no—
350C22⋊Dic11—22no—
351C22⋊Dic11—22no—
352C22⋊Dic11—22no—
353C22⋊Dic11—22no—
354C22⋊Dic11—22no—
355C22⋊Dic11—22no—
356C22⋊Dic11—22no—
357C22⋊Dic11—22no—
358#4325—28no—
359#4323—28no—
360(C2×D11)⋊C4—22no—
361(C2×D11)⋊C4—22no—
362(C2×D11)⋊C4—22no—
363(C2×D11)⋊C4—22no—
364C4⋊Dic11—22no—
365C4⋊Dic11—22no—
366C4⋊Dic11—22no—
367C4⋊Dic11—22no—
368C4⋊Dic11—21no—
369C4⋊Dic11—21no—
370C4⋊Dic11—21no—
371C4⋊Dic11C2412yes—
372C4⋊Dic11C2412yes—
373C4⋊Dic11C2412yes—
374Dic11⋊C4—22no—
375Dic11⋊C4—22no—
376C4×Dic11—22no—
377C4×Dic11—22no—
378C4×Dic11—22no—
379C4×Dic11—22no—
380C4×Dic11—22no—
381C4×Dic11—22no—
382C4×Dic11C2×D411yescharacteristic
383C4×Dic11C2×D411yescharacteristic
384C4×Dic11C2×D411yescharacteristic
385C4×Dic11C2×D411yescharacteristic
386C4×Dic11C2×D411yescharacteristic
387C4×Dic11C2×D411yescharacteristic
388C4×Dic11C2×D411yescharacteristic
389C4×Dic11C2×D411yescharacteristic
390C4×Dic11C2×D411yescharacteristic
391C4×Dic11C2×D411yescharacteristic
392C4×Dic11C2×D411yescharacteristic
393C4×Dic11C2×D411yescharacteristic
394C4×Dic11C2411yescharacteristic
395C4×Dic11C2411yescharacteristic
396C4×Dic11C2411yescharacteristic
397C4×Dic11C2411yescharacteristic
398#4318—24no—
399C2×C11⋊C8C2414yes—
400C2×#532—111no—
401C2×C4×#41—111no—
402#3115—114no—
403#3112—112no—
404#3109—112no—
405#3106—114no—
406#3103—112no—
407#3100—112no—
408#3094—111no—
409#3094—111no—
410#3079—112no—
411#3038—112no—
412#3006—111no—
413#3006D1111yescharacteristic, complemented
414C4×AGL(1,ℤ/8)—112no—
415C4×AGL(1,ℤ/8)—112no—
416#2920—111no—
417C23×C11—24no—
418C23×C11—22no—
419C23×C11—22no—
420C23×C11—22no—
421C23×C11—22no—
422C23×C11—41no—
423C23×C11—42no—
424C23×C11—42no—
425C23×C11—42no—
426C23×C11—42no—
427C23×C11—42no—
428C23×C11C22×D411yescharacteristic
429C23×C11C22×D411yescharacteristic
430C23×C11C22×D411yescharacteristic
431C22×D11—22no—
432C22×D11—42no—
433C22×D11—42no—
434C22×D11—42no—
435Q8×C11—24no—
436Q8×C11—22no—
437Q8×C11C2×#4114yescomplemented
438D4×C11—28no—
439D4×C11—24no—
440D4×C11—28no—
441D4×C11—22no—
442D4×C11—24no—
443D4×C11—44no—
444D4×C11—44no—
445D4×C11—42no—
446D4×C11C2×#4114yescomplemented
447C2×C4×C11—24no—
448C2×C4×C11—28no—
449C2×C4×C11—22no—
450C2×C4×C11—22no—
451C2×C4×C11—22no—
452C2×C4×C11—28no—
453C2×C4×C11—22no—
454C2×C4×C11—22no—
455C2×C4×C11—22no—
456C2×C4×C11—22no—
457C2×C4×C11—42no—
458C2×C4×C11C22×D411yescharacteristic
459C2×C4×C11C22×D411yescharacteristic
460C2×C4×C11C22×D411yescharacteristic
461C2×C4×C11C2×#4114yes—
462C2×C4×C11C2511yescharacteristic
463C22⋊D11—44no—
464C22⋊D11—44no—
465C22⋊D11—44no—
466C22⋊D11—44no—
467C22⋊D11—44no—
468C22⋊D11—44no—
469C2×Dic11—22no—
470C2×Dic11—22no—
471C2×Dic11—22no—
472C2×Dic11—22no—
473C2×Dic11—22no—
474C2×Dic11—22no—
475C2×Dic11—22no—
476C2×Dic11—22no—
477C2×Dic11—22no—
478C2×Dic11—22no—
479C2×Dic11—22no—
480C2×Dic11—41no—
481C2×Dic11—41no—
482C2×Dic11—41no—
483C2×Dic11—44no—
484C2×Dic11—44no—
485C2×Dic11—42no—
486C2×Dic11—42no—
487C2×Dic11—42no—
488C2×Dic11—44no—
489C2×Dic11—44no—
490C2×Dic11—44no—
491C2×Dic11—44no—
492C2×Dic11AGL(1,ℤ/8)14yescomplemented
493C2×Dic11C22×D411yescharacteristic
494C2×Dic11C22×D411yescharacteristic
495C2×Dic11C22×D411yescharacteristic
496C2×Dic11C22×D411yescharacteristic
497C2×Dic11C22×D411yescharacteristic
498C2×Dic11C22×D411yescharacteristic
499C2×Dic11C22×D411yescharacteristic
500C2×Dic11C22×D411yescharacteristic
501D44—24no—
502D44—42no—
503C4×D11—44no—
504C4×D11—44no—
505Dic22—44no—
506Dic22—44no—
507C8×C11—24no—
508C11⋊C8—24no—
509C22×#41—221no—
510C22×#41C2×D1111yescharacteristic
511C2×AGL(1,ℤ/8)—112no—
512C2×AGL(1,ℤ/8)C2×D1112yes—
513#532—112no—
514#532—112no—
515#532—112no—
516#532—112no—
517#532—221no—
518#532—221no—
519#532—221no—
520#532—221no—
521C2×C4⋊Q8—111no—
522C2×#127—111no—
523C2×#124—221no—
524C2×#121—111no—
525C2×#121—221no—
526C2×#121C2×D1111yescharacteristic
527C4×#41—112no—
528C4×#41—112no—
529C4×#41—112no—
530C4×#41—112no—
531C4×#41—221no—
532C4×#41—221no—
533C4×#41—221no—
534C4×#41—221no—
535C2×C4×Q8—111no—
536C2×C4×Q8—111no—
537C2×C4×D4—111no—
538C2×C4×D4—111no—
539C2×C4×D4—111no—
540C2×C4×D4—111no—
541C2×C4×D4—221no—
542C2×C4×D4—221no—
543C2×C4×D4—221no—
544C2×#117—111no—
545C2×#117—221no—
546C22×C42—111no—
547C22×C42—221no—
548#482—114no—
549#482—114no—
550#481—112no—
551#481—112no—
552#480—112no—
553#480—112no—
554#477—114no—
555#476—114no—
556#475—114no—
557#474—114no—
558#460—114no—
559#460—114no—
560#459—114no—
561#459—114no—
562#449—114no—
563#449C2×D1114yescomplemented
564#448—112no—
565#448C2×D1112yescomplemented
566#447—112no—
567#447C2×D1112yescomplemented
568#442—114no—
569#442—114no—
570#440—114no—
571#440—114no—
572C4×SD16—114no—
573C4×SD16—114no—
574C4×D8—114no—
575C4×D8—114no—
576#432—112no—
577#432—112no—
578#431—112no—
579#431—112no—
580#428—112no—
581#428—112no—
582#423—112no—
583#418—112no—
584#418—112no—
585#417—112no—
586#417C2×D1112yes—
587#407—111no—
588#407C2×D1111yescharacteristic
589C4×M16—112no—
590C22×C11—21no—
591C22×C11—21no—
592C22×C11—21no—
593C22×C11—21no—
594C22×C11—21no—
595C22×C11—24no—
596C22×C11—21no—
597C22×C11—21no—
598C22×C11—44no—
599C22×C11—48no—
600C22×C11—42no—
601C22×C11—42no—
602C22×C11—42no—
603C22×C11—42no—
604C22×C11—42no—
605C22×C11—84no—
606C22×C11#52512yes—
607C22×C11C2×AGL(1,ℤ/8)12yes—
608C22×C11C23×D411yescharacteristic
609C2×D11—42no—
610C2×D11—42no—
611C2×D11—42no—
612C2×D11—84no—
613C4×C11—21no—
614C4×C11—24no—
615C4×C11—21no—
616C4×C11—42no—
617C4×C11#52512yes—
618C4×C11C22×#4112yes—
619Dic11—21no—
620Dic11—21no—
621Dic11—21no—
622Dic11—21no—
623Dic11—21no—
624Dic11—42no—
625Dic11—42no—
626Dic11—42no—
627Dic11C2×AGL(1,ℤ/8)12yes—
628Dic11C2×AGL(1,ℤ/8)12yes—
629Dic11#57512yes—
630C2×#41—28no—
631C2×#41—21no—
632C2×#41—21no—
633C2×#41—222no—
634C2×#41—222no—
635C2×#41—222no—
636C2×#41—222no—
637C2×#41—448no—
638C2×#41C22×D1112yes—
639C2×#41C22×D1112yes—
640C22×Q8—221no—
641C22×Q8C22×D1111yescharacteristic
642C22×D4—21no—
643C22×D4—21no—
644C22×D4—111no—
645C22×D4—221no—
646C22×D4—221no—
647C22×D4—221no—
648C22×D4C22×D1111yescharacteristic
649C22×D4C22×D1111yescharacteristic
650C23×C4—21no—
651C23×C4—111no—
652C23×C4—111no—
653C23×C4—221no—
654C23×C4—221no—
655C23×C4—221no—
656C23×C4—221no—
657C23×C4C22×D1111yescharacteristic
658AGL(1,ℤ/8)—28no—
659AGL(1,ℤ/8)—228no—
660C2×SD16—114no—
661C2×SD16C22×D1114yes—
662C2×D8—114no—
663C2×D8C22×D1114yes—
664C2×M16—112no—
665C2×M16C22×D1112yes—
666C4⋊Q8—112no—
667C4⋊Q8—112no—
668C4⋊Q8—221no—
669C4⋊Q8—221no—
670#127—112no—
671#127—112no—
672#127—221no—
673#127—221no—
674#124—222no—
675#124—222no—
676#124—222no—
677#124—222no—
678#121—21no—
679#121—21no—
680#121—112no—
681#121—112no—
682#121—222no—
683#121—222no—
684#121—222no—
685#121—222no—
686#121—221no—
687#121—221no—
688#121C22×D1112yes—
689#121C22×D1112yes—
690C4×Q8—112no—
691C4×Q8—112no—
692C4×Q8—112no—
693C4×Q8—112no—
694C4×Q8—221no—
695C4×Q8—221no—
696C4×Q8—221no—
697C4×Q8—221no—
698C4×D4—112no—
699C4×D4—112no—
700C4×D4—112no—
701C4×D4—112no—
702C4×D4—112no—
703C4×D4—112no—
704C4×D4—112no—
705C4×D4—112no—
706C4×D4—222no—
707C4×D4—222no—
708C4×D4—222no—
709C4×D4—222no—
710C4×D4—221no—
711C4×D4—221no—
712C4×D4—221no—
713C4×D4—221no—
714C4×D4—221no—
715C4×D4—221no—
716C4×D4—221no—
717C4×D4—221no—
718C4×D4—222no—
719C4×D4—222no—
720C4×D4—222no—
721C4×D4—222no—
722C4×D4—222no—
723C4×D4—222no—
724C4×D4—222no—
725C4×D4—222no—
726#117—112no—
727#117—112no—
728#117—222no—
729#117—222no—
730#117—222no—
731#117—222no—
732#117—221no—
733#117—221no—
734C2×C4⋊C4—111no—
735C2×C4⋊C4—111no—
736C2×C4⋊C4—111no—
737C2×C4⋊C4—221no—
738C2×C4⋊C4—221no—
739C2×C4⋊C4—221no—
740C2×C4⋊C4C22×D1111yescharacteristic
741C2×C22⋊C4—21no—
742C2×C22⋊C4—221no—
743C2×C22⋊C4—221no—
744C2×C22⋊C4—221no—
745C2×C22⋊C4—221no—
746C2×C22⋊C4—221no—
747C2×C22⋊C4—221no—
748C2×C42—111no—
749C2×C42—111no—
750C2×C42—111no—
751C2×C42—111no—
752C2×C42—111no—
753C2×C42—111no—
754C2×C42—111no—
755C2×C42—111no—
756C2×C42—111no—
757C2×C42—111no—
758C2×C42—111no—
759C2×C42—111no—
760C2×C42—222no—
761C2×C42—222no—
762C2×C42—222no—
763C2×C42—222no—
764C2×C42—221no—
765C2×C42—221no—
766C2×C42—221no—
767#107—114no—
768#107—114no—
769#106—114no—
770#106—114no—
771C4⋊C8—114no—
772C4⋊C8—114no—
773#103—114no—
774#103C22×D1114yes—
775#102—114no—
776#102—114no—
777#102—114no—
778#102—114no—
779#102—114no—
780#102C22×D1114yes—
781C22⋊C8—112no—
782C22⋊C8—112no—
783C22⋊C8C22×D1112yes—
784C22⋊C8C22×D1112yes—
785#97—114no—
786C4×C8—114no—
787C2×C11—22no—
788C2×C11—22no—
789C2×C11—41no—
790C2×C11—44no—
791C2×C11—82no—
792C2×C11C2×#52511yescharacteristic
793C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
794C2×C11C2×#57511yescharacteristic
795D11—82no—
796C24—21no—
797C24—21no—
798C24—221no—
799C24D4×D1111yescharacteristic
800#41—28no—
801#41—28no—
802#41—24no—
803#41—24no—
804#41—24no—
805#41—448no—
806#41—448no—
807#41—448no—
808#41—448no—
809#41#434118yescomplemented
810C2×Q8—24no—
811C2×Q8—21no—
812C2×Q8—222no—
813C2×Q8—222no—
814C2×Q8—444no—
815C2×Q8C23×D1112yes—
816C2×D4—28no—
817C2×D4—22no—
818C2×D4—22no—
819C2×D4—24no—
820C2×D4—22no—
821C2×D4—22no—
822C2×D4—21no—
823C2×D4—21no—
824C2×D4—24no—
825C2×D4—44no—
826C2×D4—112no—
827C2×D4—222no—
828C2×D4—222no—
829C2×D4—222no—
830C2×D4—222no—
831C2×D4—222no—
832C2×D4—222no—
833C2×D4—221no—
834C2×D4—224no—
835C2×D4—444no—
836C2×D4—444no—
837C2×D4—444no—
838C2×D4C23×D1112yes—
839C2×D4C23×D1112yes—
840C22×C4—28no—
841C22×C4—21no—
842C22×C4—22no—
843C22×C4—22no—
844C22×C4—24no—
845C22×C4—21no—
846C22×C4—111no—
847C22×C4—111no—
848C22×C4—111no—
849C22×C4—111no—
850C22×C4—111no—
851C22×C4—111no—
852C22×C4—111no—
853C22×C4—111no—
854C22×C4—111no—
855C22×C4—111no—
856C22×C4—111no—
857C22×C4—111no—
858C22×C4—222no—
859C22×C4—222no—
860C22×C4—224no—
861C22×C4—222no—
862C22×C4—222no—
863C22×C4—222no—
864C22×C4—222no—
865C22×C4—222no—
866C22×C4—222no—
867C22×C4—221no—
868C22×C4—221no—
869C22×C4—221no—
870C22×C4—444no—
871C22×C4—444no—
872C22×C4—442no—
873C22×C4—444no—
874C22×C4—444no—
875C22×C4D4×D1111yescharacteristic
876C22×C4D4×D1111yescharacteristic
877C22×C4D4×D1111yescharacteristic
878C22×C4C23×D1111yescharacteristic
879C22×C4C23×D1111yescharacteristic
880C22×C4C23×D1111yescharacteristic
881SD16—28no—
882SD16—228no—
883D8—28no—
884D8—228no—
885M16—24no—
886M16—224no—
887C2×C8—114no—
888C2×C8C23×D1114yes—
889C4⋊C4—21no—
890C4⋊C4—112no—
891C4⋊C4—112no—
892C4⋊C4—112no—
893C4⋊C4—222no—
894C4⋊C4—222no—
895C4⋊C4—222no—
896C4⋊C4—222no—
897C4⋊C4—222no—
898C4⋊C4—222no—
899C4⋊C4—221no—
900C4⋊C4—221no—
901C4⋊C4—221no—
902C4⋊C4C23×D1112yes—
903C22⋊C4—22no—
904C22⋊C4—22no—
905C22⋊C4—222no—
906C22⋊C4—222no—
907C22⋊C4—222no—
908C22⋊C4—222no—
909C22⋊C4—222no—
910C22⋊C4—222no—
911C22⋊C4—222no—
912C22⋊C4—222no—
913C22⋊C4—222no—
914C22⋊C4—222no—
915C22⋊C4—222no—
916C22⋊C4—222no—
917C42—111no—
918C42—111no—
919C42—111no—
920C42—111no—
921C42—111no—
922C42—111no—
923C42—111no—
924C42—111no—
925C42—111no—
926C42—111no—
927C42—111no—
928C42—111no—
929C42—111no—
930C42—111no—
931C42—111no—
932C42—111no—
933C42—222no—
934C42—222no—
935C42—222no—
936C42—222no—
937C42—222no—
938C42—222no—
939C11#6056111yescharacteristic, complemented, Sylow
940C23—24no—
941C23—22no—
942C23—22no—
943C23—22no—
944C23—22no—
945C23—41no—
946C23—42no—
947C23—42no—
948C23—42no—
949C23—42no—
950C23—42no—
951C23—222no—
952C23—442no—
953C23—442no—
954C23—442no—
955C23C2×D4×D1111yescharacteristic
956C23C2×D4×D1111yescharacteristic
957C23C2×D4×D1111yescharacteristic
958Q8—24no—
959Q8—22no—
960Q8—444no—
961Q8—444no—
962Q8C2×#434114yescomplemented
963D4—28no—
964D4—24no—
965D4—28no—
966D4—22no—
967D4—24no—
968D4—44no—
969D4—44no—
970D4—42no—
971D4—224no—
972D4—444no—
973D4—444no—
974D4—444no—
975D4—444no—
976D4—444no—
977D4—444no—
978D4—442no—
979D4C2×#434114yescomplemented
980C2×C4—24no—
981C2×C4—28no—
982C2×C4—22no—
983C2×C4—22no—
984C2×C4—22no—
985C2×C4—28no—
986C2×C4—22no—
987C2×C4—22no—
988C2×C4—22no—
989C2×C4—22no—
990C2×C4—42no—
991C2×C4—114no—
992C2×C4—111no—
993C2×C4—111no—
994C2×C4—111no—
995C2×C4—111no—
996C2×C4—111no—
997C2×C4—111no—
998C2×C4—111no—
999C2×C4—111no—
1000C2×C4—222no—
1001C2×C4—222no—
1002C2×C4—222no—
1003C2×C4—222no—
1004C2×C4—222no—
1005C2×C4—222no—
1006C2×C4—222no—
1007C2×C4—222no—
1008C2×C4—222no—
1009C2×C4—222no—
1010C2×C4—222no—
1011C2×C4—444no—
1012C2×C4—444no—
1013C2×C4—444no—
1014C2×C4—444no—
1015C2×C4—444no—
1016C2×C4—444no—
1017C2×C4—441no—
1018C2×C4—441no—
1019C2×C4—441no—
1020C2×C4—444no—
1021C2×C4—444no—
1022C2×C4—442no—
1023C2×C4—442no—
1024C2×C4—442no—
1025C2×C4C2×D4×D1111yescharacteristic
1026C2×C4C2×D4×D1111yescharacteristic
1027C2×C4C2×D4×D1111yescharacteristic
1028C2×C4C2×#434114yes—
1029C2×C4C24×D1111yescharacteristic
1030C8—24no—
1031C8—224no—
1032C22—21no—
1033C22—21no—
1034C22—21no—
1035C22—21no—
1036C22—21no—
1037C22—21no—
1038C22—21no—
1039C22—24no—
1040C22—44no—
1041C22—48no—
1042C22—42no—
1043C22—42no—
1044C22—42no—
1045C22—42no—
1046C22—42no—
1047C22—84no—
1048C22—442no—
1049C22—442no—
1050C22—442no—
1051C22—884no—
1052C22#1062311712yes—
1053C22D11×AGL(1,ℤ/8)12yes—
1054C22C22×D4×D1111yescharacteristic
1055C4—21no—
1056C4—24no—
1057C4—21no—
1058C4—42no—
1059C4—112no—
1060C4—112no—
1061C4—112no—
1062C4—221no—
1063C4—221no—
1064C4—221no—
1065C4—221no—
1066C4—221no—
1067C4—442no—
1068C4—442no—
1069C4—442no—
1070C4#1062311712yes—
1071C4C22×#434112yes—
1072C2—22no—
1073C2—22no—
1074C2—41no—
1075C2—44no—
1076C2—82no—
1077C2—882no—
1078C2C2×#1062311711yescharacteristic
1079C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
1080C2D11×#57511yescharacteristic
subgroupG/H
centerC22C22×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC11×#3006C2
socleC22×C11C23×D4
hypercenter#3006D11
hypocenterC11#60561
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. C2×#10623127C2semidirect
2. C2×#41×Dic11C2semidirect
3. #13078760C2semidirect
4. #13078733C2semidirect
5. #13078702C2semidirect
6. #13078669C2semidirect
7. #13078642C2semidirect
8. #13078611C2semidirect
9. #13078557C2semidirect
10. #13078552C2semidirect
11. #13078427C2semidirect
12. #13078094C2semidirect
13. #13077868C2semidirect
14. #13077429C2semidirect
15. AGL(1,ℤ/8)×Dic11C2semidirect
16. #13077245C2semidirect
17. C11×#3006C2semidirect
28. #41×Dic11C22semidirect
29. #41×Dic11C22semidirect
31. C2×Q8×Dic11C22semidirect
32. C2×Q8×Dic11C22semidirect
33. C2×#66993C22semidirect
37. C2×D4×Dic11C22semidirect
38. C2×D4×Dic11C22semidirect
39. C2×D4×Dic11C22semidirect
51. #10623127C22semidirect
52. #10623127C22semidirect
53. C2×#66946C22semidirect
54. C2×#66941C22semidirect
57. C11×#449C22semidirect
58. C11×#448C22semidirect
59. C11×#447C22semidirect
62. #10622851C22semidirect
64. #10622840C22semidirect
65. #10622830C22semidirect
66. #10622828C22semidirect
68. #10622777C22semidirect
69. #10622776C22semidirect
70. #10622776C22semidirect
71. SD16×Dic11C22semidirect
72. #10622765C22semidirect
73. #10622763C22semidirect
74. #10622763C22semidirect
75. D8×Dic11C22semidirect
76. #10622744C22semidirect
77. #10622734C22semidirect
78. #10622731C22semidirect
79. M16×Dic11C22semidirect
80. #10622648C22semidirect
81. #10622647C22semidirect
82. #10622646C22semidirect
83. #10622577C22semidirect
84. #10622430C22semidirect
85. #10622407C22semidirect
86. #10622404C22semidirect
87. #10622401C22semidirect
88. #10622398C22semidirect
89. #10622374C22semidirect
90. #10622372C22semidirect
91. #10622369C22semidirect
92. #10622350C22semidirect
93. #10622349C22semidirect
94. #10622348C22semidirect
95. #10622332C22semidirect
96. #10622332C22semidirect
97. #10622331C22semidirect
98. #10622331C22semidirect
266. C11×#41#41semidirect
413. #3006D11semidirect
437. Q8×C11C2×#41semidirect
446. D4×C11C2×#41semidirect
492. C2×Dic11AGL(1,ℤ/8)semidirect
563. #449C2×D11semidirect
565. #448C2×D11semidirect
567. #447C2×D11semidirect
809. #41#4341semidirect
939. C11#60561semidirect
962. Q8C2×#4341semidirect
979. D4C2×#4341semidirect

Maximal subgroups

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

subgroupindex
C2×#106231272
C2×#41×Dic112
#130787602
#130787332
#130787022
#130786692
#130786422
#130786112
#130785572
#130785522
#130784272
#130780942
#130778682
#130774292
AGL(1,ℤ/8)×Dic112
#130772452
C11×#30062
#6056111