Finite Group Databasebeta

← C2×#13069104 #14755656

Subgroups — C2×#13069104 #14755656

Order 2816.

1894 conjugacy classes of subgroups.

The subgroup lattice has 804 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic
2C2×#10623052C211yesmaximal, characteristic, complemented
3C2×#10622618C211yesmaximal, characteristic, complemented
4C2×#10622614C211yesmaximal, characteristic, complemented
5C2×#10622619C211yesmaximal, characteristic, complemented
6#13069104C218yesmaximal, direct product factor
7C2×#10622194C211yesmaximal, characteristic, complemented
8C2×C11×H(3,ℤ/4)C211yesmaximal, characteristic, complemented
9C22×#4339C2211yescharacteristic
10C23×D44C2211yescharacteristic
11C22×C11×M16C2211yescharacteristic
12C2×C11×#117C2211yescharacteristic
13C2×C11×#117C2211yescharacteristic
14C2×#66979C2211yescharacteristic
15C22×#4318C2211yescharacteristic
16C2×#66961—22no—
17C2×#66961—22no—
18C2×#66961—22no—
19C2×#66961—22no—
20C2×#66961C414yescomplemented
21C2×#66961C2214yes—
22C22×D88C412yescomplemented
23C22×#4314C412yescomplemented
24#10623052—22no—
25#10623052—22no—
26#10623052—22no—
27#10623052C2214yescomplemented
28C2×#66946—22no—
29C2×C22⋊C4×D11—22no—
30C2×C4×D44—22no—
31#10622619—22no—
32#10622619C2214yescomplemented
33#10622618—22no—
34#10622618C2214yescomplemented
35#10622614—22no—
36#10622614C2214yescomplemented
37C2×#66873—22no—
38C2×#66870—22no—
39C2×#66869—22no—
40C11×H(3,ℤ/4)C2214yescomplemented
41#10622194C2214yescomplemented
42C24×D11—21no—
43C23×C4×C11C2311yescharacteristic
44C22×C22⋊D11—21no—
45C2×#4339—21no—
46C2×#4339—21no—
47C2×#4339—21no—
48C2×#4339—21no—
49C2×#4339—21no—
50C2×#4339—21no—
51C2×#4339—21no—
52C2×#4339—21no—
53C2×#4339—21no—
54C2×#4339—21no—
55C2×#4339C2×C412yescomplemented
56C2×#4339C2312yes—
57C22×D44—21no—
58C22×D44—21no—
59C22×D44—21no—
60C22×D44—21no—
61C22×D44—21no—
62C22×D44—21no—
63C22×D44—21no—
64C22×D44C2×C412yes—
65C22×D44C2×C412yes—
66C22×D44C2×C411yescharacteristic, complemented
67C22×D44D412yes—
68C22×D44D412yes—
69C22×D44D412yes—
70C22×D44D412yes—
71C22×D44C2312yes—
72C22×C4×D11—21no—
73C22×C4×D11—24no—
74C22×Dic22C2×C411yescharacteristic, complemented
75C2×C11×M16—21no—
76C2×C11×M16—21no—
77C2×C11×M16—21no—
78C2×C11×M16—21no—
79C2×C11×M16C2×C412yescomplemented
80C2×C11×M16C2312yes—
81C22×C8×C11C2×C412yescomplemented
82C11×#117—21no—
83C11×#117—21no—
84C11×#117—21no—
85C11×#117—21no—
86C11×#117—21no—
87C11×#117D412yes—
88C11×#117C2312yes—
89C11×#117C2312yes—
90C2×C11×C4⋊C4—21no—
91C2×C11×C4⋊C4—21no—
92C2×C11×C22⋊C4—21no—
93C2×C11×C22⋊C4—21no—
94C2×C42×C11—21no—
95C2×C42×C11D412yes—
96C2×C22⋊Dic11D412yes—
97C2×(C2×D11)⋊C4—24no—
98#66979—21no—
99#66979—21no—
100#66979D412yes—
101#66979C2312yes—
102C2×C4⋊Dic11—21no—
103C2×C4×Dic11—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106C2×#4318—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109C2×#4318C2312yes—
110C22×C11⋊C8—21no—
111#66961—28no—
112#66961—28no—
113#66961—28no—
114#66961—28no—
115C2×D88—24no—
116C2×D88—24no—
117C2×D88C2×C418yescomplemented
118C2×#4314—24no—
119C2×#4314—24no—
120C2×#4314C2×C418yescomplemented
121#66946—28no—
122#66946—28no—
123C22⋊C4×D11—28no—
124C22⋊C4×D11—28no—
125C4×D44—28no—
126C4×D44—28no—
127#66873—28no—
128#66870—28no—
129#66869—28no—
130C2×#1904—111nomaximal, Sylow
131C24×C11C2×D411yescharacteristic
132C23×D11—22no—
133C23×D11—22no—
134C23×D11—22no—
135C23×D11—22no—
136C23×D11—22no—
137C23×D11—22no—
138C23×D11—22no—
139C23×D11—21no—
140C23×D11—84no—
141C22×C4×C11—22no—
142C22×C4×C11—41no—
143C22×C4×C11C22×C411yescharacteristic
144C22×C4×C11C22×C411yescharacteristic
145C22×C4×C11C2×D411yescharacteristic
146C22×C4×C11C2×D411yescharacteristic
147C22×C4×C11C2×D411yescharacteristic
148C22×C4×C11C2×D411yescharacteristic
149C22×C4×C11C2×D411yescharacteristic
150C22×C4×C11C2×D411yescharacteristic
151C22×C4×C11C2×D411yescharacteristic
152C22×C4×C11#4111yescharacteristic
153C22×C4×C11#4111yescharacteristic
154C22×C4×C11#4111yescharacteristic
155C22×C4×C11#4111yescharacteristic
156C22×C4×C11C2411yescharacteristic
157C2×C22⋊D11—22no—
158C2×C22⋊D11—22no—
159C2×C22⋊D11—41no—
160C2×C22⋊D11—41no—
161C2×C22⋊D11—41no—
162C2×C22⋊D11—41no—
163C22×Dic11—21no—
164C22×Dic11—22no—
165#4339—22no—
166#4339—22no—
167#4339—22no—
168#4339—22no—
169#4339—22no—
170#4339—22no—
171#4339—22no—
172#4339—22no—
173#4339—41no—
174#4339—41no—
175#4339—41no—
176#4339—41no—
177#4339—41no—
178#4339—41no—
179#4339—41no—
180#4339—41no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—22no—
184C2×D44—22no—
185C2×D44—22no—
186C2×D44—22no—
187C2×D44—22no—
188C2×D44—22no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—22no—
193C2×D44—22no—
194C2×D44—22no—
195C2×D44—22no—
196C2×D44—22no—
197C2×D44—22no—
198C2×D44—22no—
199C2×D44—22no—
200C2×D44—22no—
201C2×D44—22no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44C22⋊C414yes—
208C2×D44C22⋊C414yes—
209C2×D44C22⋊C414yes—
210C2×D44C22⋊C414yes—
211C2×D44C22×C414yes—
212C2×D44C22×C412yescomplemented
213C2×D44C2×D414yes—
214C2×D44C2×D414yes—
215C2×C4×D11—216no—
216C2×C4×D11—22no—
217C2×C4×D11—22no—
218C2×C4×D11—41no—
219C2×C4×D11—41no—
220C2×C4×D11—41no—
221C2×C4×D11—41no—
222C2×C4×D11—88no—
223C2×Dic22—21no—
224C2×Dic22—21no—
225C2×Dic22—21no—
226C2×Dic22—21no—
227C2×Dic22—21no—
228C2×Dic22C22×C412yescomplemented
229C11×M16—22no—
230C11×M16—22no—
231C11×M16—22no—
232C11×M16—22no—
233C2×C8×C11—22no—
234C2×C8×C11—22no—
235C2×C8×C11C22×C414yescomplemented
236C11×C4⋊C4—22no—
237C11×C4⋊C4—22no—
238C11×C4⋊C4—22no—
239C11×C4⋊C4—41no—
240C11×C22⋊C4—22no—
241C11×C22⋊C4—22no—
242C11×C22⋊C4—22no—
243C11×C22⋊C4—41no—
244C42×C11—22no—
245C42×C11—22no—
246C42×C11—41no—
247C42×C11C2×D414yes—
248C22⋊Dic11—22no—
249C22⋊Dic11C2×D414yes—
250(C2×D11)⋊C4—216no—
251C4⋊Dic11—22no—
252C4⋊Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255#4318—22no—
256#4318—22no—
257#4318—41no—
258#4318—41no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8—41no—
261C2×C11⋊C8—41no—
262D88—216no—
263#4314—216no—
264C22×AGL(1,ℤ/8)—111no—
265C2×#518—111no—
266C2×#421—111no—
267C2×#418—111no—
268C2×#410—111no—
269#1904—118no—
270C2×#344—111no—
271C2×H(3,ℤ/4)D1111yescharacteristic, complemented
272C23×C11—42no—
273C23×C11C4×D411yescharacteristic
274C23×C11C4×D411yescharacteristic
275C23×C11#12011yescharacteristic
276C23×C11#12011yescharacteristic
277C23×C11#12111yescharacteristic
278C23×C11#12111yescharacteristic
279C23×C11C22×D411yescharacteristic
280C22×D11—24no—
281C22×D11—24no—
282C22×D11—24no—
283C22×D11—24no—
284C22×D11—24no—
285C22×D11—24no—
286C22×D11—24no—
287C22×D11—22no—
288C22×D11—48no—
289C22×D11—41no—
290C22×D11—41no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294C22×D11—84no—
295C22×D11—84no—
296C22×D11—84no—
297C22×D11—82no—
298C2×C4×C11—24no—
299C2×C4×C11—44no—
300C2×C4×C11—42no—
301C2×C4×C11—82no—
302C2×C4×C11C2×C22⋊C411yescharacteristic
303C2×C4×C11C2×C22⋊C411yescharacteristic
304C2×C4×C11C2×C22⋊C411yescharacteristic
305C2×C4×C11C2×C22⋊C411yescharacteristic
306C2×C4×C11C4×D411yescharacteristic
307C2×C4×C11C4×D411yescharacteristic
308C2×C4×C11C4×D411yescharacteristic
309C2×C4×C11C4×D411yescharacteristic
310C2×C4×C11C4×D411yescharacteristic
311C2×C4×C11C4×D411yescharacteristic
312C2×C4×C11#12011yescharacteristic
313C2×C4×C11#12011yescharacteristic
314C2×C4×C11#12111yescharacteristic
315C2×C4×C11#12111yescharacteristic
316C2×C4×C11#12111yescharacteristic
317C2×C4×C11#12111yescharacteristic
318C2×C4×C11#12111yescharacteristic
319C2×C4×C11#12111yescharacteristic
320C2×C4×C11#12311yescharacteristic
321C2×C4×C11#12311yescharacteristic
322C2×C4×C11#12311yescharacteristic
323C2×C4×C11#12311yescharacteristic
324C2×C4×C11C23×C411yescharacteristic
325C2×C4×C11C22×D411yescharacteristic
326C2×C4×C11C22×D411yescharacteristic
327C2×C4×C11C22×D411yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11C2×#4111yescharacteristic
330C22⋊D11—42no—
331C22⋊D11—42no—
332C22⋊D11—42no—
333C22⋊D11—42no—
334C2×Dic11—22no—
335C2×Dic11—24no—
336C2×Dic11—44no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339D44—22no—
340D44—24no—
341D44—22no—
342D44—24no—
343D44—24no—
344D44—24no—
345D44—24no—
346D44—24no—
347D44—24no—
348D44—41no—
349D44—41no—
350D44C2×C22⋊C418yes—
351C4×D11—42no—
352C4×D11—42no—
353C4×D11—42no—
354C4×D11—42no—
355C4×D11—816no—
356Dic22—22no—
357Dic22—22no—
358Dic22—41no—
359Dic22—41no—
360C8×C11—24no—
361C11⋊C8—42no—
362C22×#41—111no—
363C23×D4—111no—
364C2×AGL(1,ℤ/8)—114no—
365C2×AGL(1,ℤ/8)—114no—
366C2×AGL(1,ℤ/8)—222no—
367C2×AGL(1,ℤ/8)—222no—
368C2×AGL(1,ℤ/8)—222no—
369C2×AGL(1,ℤ/8)—222no—
370C22×SD16—112no—
371C22×D8—112no—
372C22×M16—111no—
373C22×M16C2×D1111yescharacteristic
374#518—114no—
375#518—222no—
376#518—222no—
377#518—222no—
378C2×C4×D4—222no—
379C2×C4×D4—222no—
380C2×#117—111no—
381C2×#117C2×D1111yescharacteristic
382C2×#117C2×D1111yescharacteristic
383C22×C22⋊C4—222no—
384#421—114no—
385#421—222no—
386C2×#104—222no—
387#418—114no—
388#418—222no—
389C2×#102—222no—
390#410—114no—
391#410—222no—
392C2×#99—222no—
393#344—114no—
394H(3,ℤ/4)C2×D1114yescomplemented
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—41no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11#38611yescharacteristic
403C22×C11#38611yescharacteristic
404C22×C11#38611yescharacteristic
405C22×C11#38611yescharacteristic
406C22×C11C2×C4×D411yescharacteristic
407C22×C11C2×#12011yescharacteristic
408C22×C11C2×#12111yescharacteristic
409C2×D11—28no—
410C2×D11—48no—
411C2×D11—48no—
412C2×D11—48no—
413C2×D11—42no—
414C2×D11—84no—
415C2×D11—84no—
416C2×D11—84no—
417C2×D11—84no—
418C2×D11—82no—
419C2×D11—82no—
420C2×D11—82no—
421C4×C11—44no—
422C4×C11—82no—
423C4×C11#38611yescharacteristic
424C4×C11#38611yescharacteristic
425C4×C11#38611yescharacteristic
426C4×C11#38611yescharacteristic
427C4×C11C22×C22⋊C411yescharacteristic
428C4×C11C2×C4×D411yescharacteristic
429C4×C11C2×#12111yescharacteristic
430C4×C11C2×#12311yescharacteristic
431Dic11—44no—
432Dic11—42no—
433C25—221no—
434C2×#41—112no—
435C2×#41—112no—
436C2×#41—221no—
437C2×#41—221no—
438C2×#41—221no—
439C2×#41—221no—
440C2×#41—221no—
441C2×#41—221no—
442C2×#41—221no—
443C2×#41—221no—
444C2×#41—221no—
445C2×#41—221no—
446C22×Q8—111no—
447C22×D4—112no—
448C22×D4—112no—
449C22×D4—111no—
450C22×D4—112no—
451C22×D4—112no—
452C22×D4—112no—
453C22×D4—112no—
454C22×D4—112no—
455C22×D4—221no—
456C22×D4—221no—
457C22×D4—221no—
458C22×D4—221no—
459C22×D4—221no—
460C22×D4—221no—
461C22×D4—221no—
462C22×D4—221no—
463C23×C4—224no—
464C23×C4—221no—
465C23×C4C22×D1111yescharacteristic
466AGL(1,ℤ/8)—228no—
467AGL(1,ℤ/8)—228no—
468AGL(1,ℤ/8)—228no—
469AGL(1,ℤ/8)—228no—
470C2×SD16—118no—
471C2×SD16—224no—
472C2×SD16—224no—
473C2×D8—118no—
474C2×D8—224no—
475C2×D8—224no—
476C2×M16—21no—
477C2×M16—21no—
478C2×M16—21no—
479C2×M16—21no—
480C2×M16—112no—
481C2×M16—221no—
482C2×M16—221no—
483C2×M16—221no—
484C2×M16—221no—
485C2×M16—221no—
486C2×M16C4×D1112yescomplemented
487C2×M16C22×D1112yes—
488C22×C8—221no—
489C22×C8C4×D1112yescomplemented
490C4×D4—228no—
491C4×D4—228no—
492C4×D4—228no—
493C4×D4—228no—
494#117—21no—
495#117—21no—
496#117—21no—
497#117—21no—
498#117—21no—
499#117—112no—
500#117—112no—
501#117—221no—
502#117—221no—
503#117D4412yes—
504#117C22×D1112yes—
505#117C22×D1112yes—
506C2×C4⋊C4—21no—
507C2×C4⋊C4—21no—
508C2×C4⋊C4—221no—
509C2×C22⋊C4—21no—
510C2×C22⋊C4—21no—
511C2×C22⋊C4—112no—
512C2×C22⋊C4—228no—
513C2×C22⋊C4—228no—
514C2×C22⋊C4—224no—
515C2×C42—21no—
516C2×C42—221no—
517C2×C42D4412yes—
518#104—228no—
519#102—228no—
520#99—228no—
521C2×C11—21no—
522C2×C11—21no—
523C2×C11—21no—
524C2×C11—21no—
525C2×C11—21no—
526C2×C11—21no—
527C2×C11#190412yescomplemented
528C2×C11C2×#38611yescharacteristic
529D11—48no—
530D11—82no—
531C24—222no—
532C24—222no—
533C24—222no—
534C24—222no—
535C24—222no—
536C24—222no—
537C24—222no—
538C24—221no—
539C24—884no—
540C24D4×D1111yescharacteristic
541#41—222no—
542#41—222no—
543#41—222no—
544#41—222no—
545#41—222no—
546#41—222no—
547#41—222no—
548#41—222no—
549#41—441no—
550#41—441no—
551#41—441no—
552#41—441no—
553#41—441no—
554#41—441no—
555#41—441no—
556#41—441no—
557C2×Q8—112no—
558C2×Q8—221no—
559C2×Q8—221no—
560C2×Q8—221no—
561C2×Q8—221no—
562C2×Q8—221no—
563C2×D4—114no—
564C2×D4—114no—
565C2×D4—114no—
566C2×D4—114no—
567C2×D4—114no—
568C2×D4—112no—
569C2×D4—114no—
570C2×D4—114no—
571C2×D4—222no—
572C2×D4—222no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—222no—
582C2×D4—222no—
583C2×D4—222no—
584C2×D4—222no—
585C2×D4—222no—
586C2×D4—222no—
587C2×D4—221no—
588C2×D4—222no—
589C2×D4—222no—
590C2×D4—222no—
591C2×D4—222no—
592C2×D4—222no—
593C2×D4—222no—
594C2×D4—222no—
595C2×D4—222no—
596C2×D4—222no—
597C2×D4—222no—
598C2×D4—222no—
599C2×D4—441no—
600C2×D4—441no—
601C2×D4—441no—
602C2×D4—441no—
603C22×C4—22no—
604C22×C4—41no—
605C22×C4—2216no—
606C22×C4—222no—
607C22×C4—221no—
608C22×C4—222no—
609C22×C4—222no—
610C22×C4—441no—
611C22×C4—441no—
612C22×C4—441no—
613C22×C4—441no—
614C22×C4—888no—
615C22×C4C2×C4×D1111yescharacteristic
616C22×C4C2×C4×D1111yescharacteristic
617C22×C4C2×D4411yescharacteristic
618C22×C4C2×D4411yescharacteristic
619C22×C4#433911yescharacteristic
620C22×C4#433911yescharacteristic
621C22×C4D4×D1111yescharacteristic
622C22×C4D4×D1111yescharacteristic
623C22×C4D4×D1111yescharacteristic
624C22×C4D4×D1111yescharacteristic
625C22×C4D4×D1111yescharacteristic
626C22×C4#434311yescharacteristic
627C22×C4#434311yescharacteristic
628C22×C4C23×D1111yescharacteristic
629SD16—2216no—
630D8—2216no—
631M16—22no—
632M16—22no—
633M16—22no—
634M16—22no—
635M16—222no—
636M16—222no—
637M16—441no—
638M16—441no—
639C2×C8—22no—
640C2×C8—22no—
641C2×C8—222no—
642C2×C8—441no—
643C2×C8—441no—
644C2×C8C2×C4×D1114yescomplemented
645C4⋊C4—22no—
646C4⋊C4—22no—
647C4⋊C4—22no—
648C4⋊C4—41no—
649C4⋊C4—222no—
650C4⋊C4—222no—
651C22⋊C4—22no—
652C22⋊C4—22no—
653C22⋊C4—22no—
654C22⋊C4—41no—
655C22⋊C4—114no—
656C22⋊C4—2216no—
657C22⋊C4—222no—
658C42—22no—
659C42—22no—
660C42—41no—
661C42—222no—
662C42—222no—
663C42C2×D4414yes—
664C11C2×#190411yescharacteristic, complemented, Sylow
665C23—42no—
666C23—224no—
667C23—224no—
668C23—224no—
669C23—224no—
670C23—224no—
671C23—224no—
672C23—224no—
673C23—222no—
674C23—448no—
675C23—441no—
676C23—441no—
677C23—884no—
678C23—884no—
679C23—882no—
680C23—884no—
681C23—884no—
682C23—884no—
683C23—884no—
684C23#6693511yescharacteristic
685C23#6693511yescharacteristic
686C23#6693711yescharacteristic
687C23#6693711yescharacteristic
688C23#6694611yescharacteristic
689C23#6694611yescharacteristic
690C23C2×D4×D1111yescharacteristic
691Q8—222no—
692Q8—222no—
693Q8—441no—
694Q8—441no—
695D4—118no—
696D4—224no—
697D4—222no—
698D4—222no—
699D4—224no—
700D4—224no—
701D4—224no—
702D4—224no—
703D4—224no—
704D4—224no—
705D4—442no—
706D4—442no—
707D4—442no—
708D4—442no—
709D4—441no—
710D4—441no—
711C2×C4—24no—
712C2×C4—44no—
713C2×C4—42no—
714C2×C4—82no—
715C2×C4—224no—
716C2×C4—222no—
717C2×C4—444no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—442no—
721C2×C4—442no—
722C2×C4—442no—
723C2×C4—442no—
724C2×C4—8816no—
725C2×C4C4×D4411yescharacteristic
726C2×C4C4×D4411yescharacteristic
727C2×C4C4×D4411yescharacteristic
728C2×C4C4×D4411yescharacteristic
729C2×C4C22⋊C4×D1111yescharacteristic
730C2×C4C22⋊C4×D1111yescharacteristic
731C2×C4C22⋊C4×D1111yescharacteristic
732C2×C4C22⋊C4×D1111yescharacteristic
733C2×C4#6693511yescharacteristic
734C2×C4#6693511yescharacteristic
735C2×C4#6693711yescharacteristic
736C2×C4#6693711yescharacteristic
737C2×C4#6694611yescharacteristic
738C2×C4#6694611yescharacteristic
739C2×C4#6694711yescharacteristic
740C2×C4#6694711yescharacteristic
741C2×C4#6694711yescharacteristic
742C2×C4#6694711yescharacteristic
743C2×C4#6694811yescharacteristic
744C2×C4#6694811yescharacteristic
745C2×C4#6694811yescharacteristic
746C2×C4#6694811yescharacteristic
747C2×C4C22×C4×D1111yescharacteristic
748C2×C4C22×D4411yescharacteristic
749C2×C4C2×#433911yescharacteristic
750C2×C4C2×D4×D1111yescharacteristic
751C2×C4C2×D4×D1111yescharacteristic
752C2×C4C2×#434311yescharacteristic
753C8—24no—
754C8—442no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—41no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—228no—
763C22—448no—
764C22—448no—
765C22—448no—
766C22—442no—
767C22—884no—
768C22—884no—
769C22—884no—
770C22—884no—
771C22—882no—
772C22—882no—
773C22—882no—
774C22#1062227811yescharacteristic
775C22#1062227811yescharacteristic
776C22#1062227811yescharacteristic
777C22#1062227811yescharacteristic
778C22C2×#6693511yescharacteristic
779C22C2×#6693711yescharacteristic
780C22C2×#6694611yescharacteristic
781C4—44no—
782C4—82no—
783C4—444no—
784C4—442no—
785C4#1062227811yescharacteristic
786C4#1062227811yescharacteristic
787C4#1062227811yescharacteristic
788C4#1062227811yescharacteristic
789C4C2×C4×D4411yescharacteristic
790C4C2×C22⋊C4×D1111yescharacteristic
791C4C2×#6694711yescharacteristic
792C4C2×#6694811yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—448no—
800C2—882no—
801C2#1306910412yesdirect product factor
802C2C2×#1062227811yescharacteristic
subgroupG/H
centerC22#10622278
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×H(3,ℤ/4)C2
socleC22×C11#386
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenterC2×H(3,ℤ/4)D11
hypocenterC11C2×#1904
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C2×H(3,ℤ/4)

Complements

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

NH ≅ G/Ntype
2. C2×#10623052C2semidirect
3. C2×#10622618C2semidirect
4. C2×#10622614C2semidirect
5. C2×#10622619C2semidirect
6. #13069104C2direct (N × H)
7. C2×#10622194C2semidirect
8. C2×C11×H(3,ℤ/4)C2semidirect
20. C2×#66961C4semidirect
22. C22×D88C4semidirect
23. C22×#4314C4semidirect
27. #10623052C22semidirect
32. #10622619C22semidirect
34. #10622618C22semidirect
36. #10622614C22semidirect
40. C11×H(3,ℤ/4)C22semidirect
41. #10622194C22semidirect
55. C2×#4339C2×C4semidirect
66. C22×D44C2×C4semidirect
74. C22×Dic22C2×C4semidirect
79. C2×C11×M16C2×C4semidirect
81. C22×C8×C11C2×C4semidirect
117. C2×D88C2×C4semidirect
120. C2×#4314C2×C4semidirect
212. C2×D44C22×C4semidirect
228. C2×Dic22C22×C4semidirect
235. C2×C8×C11C22×C4semidirect
271. C2×H(3,ℤ/4)D11semidirect
394. H(3,ℤ/4)C2×D11semidirect
486. C2×M16C4×D11semidirect
489. C22×C8C4×D11semidirect
527. C2×C11#1904semidirect
644. C2×C8C2×C4×D11semidirect
664. C11C2×#1904semidirect
801. C2#13069104direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106230522
C2×#106226182
C2×#106226142
C2×#106226192
#130691042
C2×#106221942
C2×C11×H(3,ℤ/4)2
C2×#190411