Finite Group Databasebeta

← C2×#13069105 #14755657

Subgroups — C2×#13069105 #14755657

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
1C2×#10623329C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622853C211yesmaximal, characteristic, complemented
5#13069105C218yesmaximal, direct product factor
6C2×#10622194C211yesmaximal, characteristic, complemented
7C2×#10622195C211yesmaximal, characteristic, complemented
8C22×C11×AGL(1,ℤ/8)C211yesmaximal, characteristic
9C22×C11×#41C2211yescharacteristic
10C23×D4×C11C2211yescharacteristic
11C2×C11×AGL(1,ℤ/8)—22no—
12C2×C11×AGL(1,ℤ/8)—22no—
13C2×C11×AGL(1,ℤ/8)—22no—
14C2×C11×AGL(1,ℤ/8)—22no—
15C2×C11×AGL(1,ℤ/8)C414yescomplemented
16C2×C11×AGL(1,ℤ/8)C2214yes—
17C22×C11×SD16C412yescomplemented
18C22×C11×D8C412yescomplemented
19C22×C11×M16C2211yescharacteristic
20C22×C22⋊Dic11—22no—
21#10623329—22no—
22#10623329—22no—
23#10623329—22no—
24#10623329C2214yescomplemented
25C2×D4×Dic11—22no—
26C2×D4×Dic11—22no—
27C2×#66979C2211yescharacteristic
28C2×#66979C2211yescharacteristic
29C2×#66979C2211yescharacteristic
30C22×#4318C2211yescharacteristic
31#10622853—22no—
32#10622853C2214yescomplemented
33#10622849—22no—
34#10622849C2214yescomplemented
35C2×#66901—22no—
36C2×#66898—22no—
37#10622828—22no—
38#10622828C2214yescomplemented
39C2×#66896—22no—
40#10622195C2214yescomplemented
41#10622194C2214yescomplemented
42C25×C11—21no—
43C2×C11×#41—21no—
44C2×C11×#41—21no—
45C2×C11×#41—21no—
46C2×C11×#41—21no—
47C2×C11×#41—21no—
48C2×C11×#41—21no—
49C2×C11×#41—21no—
50C2×C11×#41—21no—
51C2×C11×#41—21no—
52C2×C11×#41—21no—
53C2×C11×#41C2×C412yescomplemented
54C2×C11×#41C2312yes—
55C22×Q8×C11C2×C411yescharacteristic, complemented
56C22×D4×C11—21no—
57C22×D4×C11—21no—
58C22×D4×C11—21no—
59C22×D4×C11—21no—
60C22×D4×C11—21no—
61C22×D4×C11—21no—
62C22×D4×C11—21no—
63C22×D4×C11—21no—
64C22×D4×C11C2×C412yes—
65C22×D4×C11C2×C412yes—
66C22×D4×C11C2×C411yescharacteristic, complemented
67C22×D4×C11D412yes—
68C22×D4×C11D412yes—
69C22×D4×C11D412yes—
70C22×D4×C11D412yes—
71C22×D4×C11C2312yes—
72C23×C4×C11—21no—
73C23×C4×C11C2311yescharacteristic
74C23×Dic11—24no—
75C11×AGL(1,ℤ/8)—28no—
76C11×AGL(1,ℤ/8)—28no—
77C11×AGL(1,ℤ/8)—28no—
78C11×AGL(1,ℤ/8)—28no—
79C2×C11×SD16—24no—
80C2×C11×SD16—24no—
81C2×C11×SD16C2×C418yescomplemented
82C2×C11×D8—24no—
83C2×C11×D8—24no—
84C2×C11×D8C2×C418yescomplemented
85C2×C11×M16—21no—
86C2×C11×M16—21no—
87C2×C11×M16—21no—
88C2×C11×M16—21no—
89C2×C11×M16C2×C412yescomplemented
90C2×C11×M16C2312yes—
91C22×C8×C11C2×C412yescomplemented
92C2×C22⋊Dic11—24no—
93C2×C22⋊Dic11—28no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—28no—
96C2×C22⋊Dic11—21no—
97C2×C22⋊Dic11D412yes—
98D4×Dic11—28no—
99D4×Dic11—28no—
100D4×Dic11—28no—
101D4×Dic11—28no—
102#66979—21no—
103#66979—21no—
104#66979—21no—
105#66979—21no—
106#66979—21no—
107#66979—21no—
108#66979—21no—
109#66979D412yes—
110#66979D412yes—
111#66979C2312yes—
112#66979C2312yes—
113#66979C2312yes—
114C2×C4⋊Dic11—21no—
115C2×C4⋊Dic11—21no—
116C2×C4⋊Dic11—21no—
117C2×C4×Dic11—21no—
118C2×C4×Dic11—21no—
119C2×C4×Dic11D412yes—
120C2×#4318—21no—
121C2×#4318—21no—
122C2×#4318—21no—
123C2×#4318—21no—
124C2×#4318—21no—
125C2×#4318C2312yes—
126C22×C11⋊C8—21no—
127#66901—28no—
128#66898—28no—
129#66896—28no—
130C2×#1904—111nomaximal, Sylow
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—22no—
135C24×C11—22no—
136C24×C11—22no—
137C24×C11—22no—
138C24×C11—21no—
139C24×C11—84no—
140C24×C11C2×D411yescharacteristic
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—22no—
144C11×#41—22no—
145C11×#41—22no—
146C11×#41—22no—
147C11×#41—22no—
148C11×#41—22no—
149C11×#41—41no—
150C11×#41—41no—
151C11×#41—41no—
152C11×#41—41no—
153C11×#41—41no—
154C11×#41—41no—
155C11×#41—41no—
156C11×#41—41no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11C22×C412yescomplemented
163C2×D4×C11—22no—
164C2×D4×C11—22no—
165C2×D4×C11—21no—
166C2×D4×C11—21no—
167C2×D4×C11—22no—
168C2×D4×C11—22no—
169C2×D4×C11—22no—
170C2×D4×C11—22no—
171C2×D4×C11—22no—
172C2×D4×C11—22no—
173C2×D4×C11—21no—
174C2×D4×C11—21no—
175C2×D4×C11—21no—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—22no—
180C2×D4×C11—22no—
181C2×D4×C11—22no—
182C2×D4×C11—22no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11—22no—
186C2×D4×C11—22no—
187C2×D4×C11—22no—
188C2×D4×C11—22no—
189C2×D4×C11—22no—
190C2×D4×C11—22no—
191C2×D4×C11—41no—
192C2×D4×C11—41no—
193C2×D4×C11—41no—
194C2×D4×C11—41no—
195C2×D4×C11C22⋊C414yes—
196C2×D4×C11C22⋊C414yes—
197C2×D4×C11C22⋊C414yes—
198C2×D4×C11C22⋊C414yes—
199C2×D4×C11C22×C414yes—
200C2×D4×C11C22×C412yescomplemented
201C2×D4×C11C2×D414yes—
202C2×D4×C11C2×D414yes—
203C22×C4×C11—21no—
204C22×C4×C11—22no—
205C22×C4×C11—22no—
206C22×C4×C11—41no—
207C22×C4×C11—41no—
208C22×C4×C11—41no—
209C22×C4×C11—41no—
210C22×C4×C11C22×C411yescharacteristic
211C22×C4×C11C22×C411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D411yescharacteristic
214C22×C4×C11C2×D411yescharacteristic
215C22×C4×C11C2×D411yescharacteristic
216C22×C4×C11C2×D411yescharacteristic
217C22×C4×C11C2×D411yescharacteristic
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11#4111yescharacteristic
220C22×C4×C11#4111yescharacteristic
221C22×C4×C11#4111yescharacteristic
222C22×C4×C11#4111yescharacteristic
223C22×C4×C11C2411yescharacteristic
224C22×Dic11—216no—
225C22×Dic11—22no—
226C22×Dic11—22no—
227C22×Dic11—41no—
228C22×Dic11—88no—
229C11×SD16—216no—
230C11×D8—216no—
231C11×M16—22no—
232C11×M16—22no—
233C11×M16—22no—
234C11×M16—22no—
235C2×C8×C11—22no—
236C2×C8×C11—22no—
237C2×C8×C11C22×C414yescomplemented
238C22⋊Dic11—216no—
239C22⋊Dic11—22no—
240C22⋊Dic11—22no—
241C22⋊Dic11—22no—
242C22⋊Dic11—22no—
243C22⋊Dic11—41no—
244C22⋊Dic11C2×D414yes—
245C4⋊Dic11—22no—
246C4⋊Dic11—22no—
247C4⋊Dic11—22no—
248C4⋊Dic11—22no—
249C4⋊Dic11—22no—
250C4⋊Dic11—41no—
251C4×Dic11—22no—
252C4×Dic11—22no—
253C4×Dic11—22no—
254C4×Dic11—22no—
255C4×Dic11—41no—
256C4×Dic11C2×D414yes—
257#4318—22no—
258#4318—22no—
259#4318—41no—
260#4318—41no—
261C2×C11⋊C8—22no—
262C2×C11⋊C8—41no—
263C2×C11⋊C8—41no—
264C22×AGL(1,ℤ/8)D1111yescharacteristic
265C2×#518—111no—
266C2×#421—111no—
267C2×#418—111no—
268C2×#410—111no—
269#1904—118no—
270C2×#344—111no—
271C2×H(3,ℤ/4)—111no—
272C23×C11—24no—
273C23×C11—24no—
274C23×C11—24no—
275C23×C11—24no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—24no—
279C23×C11—22no—
280C23×C11—42no—
281C23×C11—48no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11—84no—
285C23×C11—84no—
286C23×C11—82no—
287C23×C11—84no—
288C23×C11—84no—
289C23×C11—84no—
290C23×C11—84no—
291C23×C11C4×D411yescharacteristic
292C23×C11C4×D411yescharacteristic
293C23×C11#12011yescharacteristic
294C23×C11#12011yescharacteristic
295C23×C11#12111yescharacteristic
296C23×C11#12111yescharacteristic
297C23×C11C22×D411yescharacteristic
298Q8×C11—22no—
299Q8×C11—22no—
300Q8×C11—41no—
301Q8×C11—41no—
302D4×C11—22no—
303D4×C11—24no—
304D4×C11—22no—
305D4×C11—24no—
306D4×C11—24no—
307D4×C11—24no—
308D4×C11—24no—
309D4×C11—24no—
310D4×C11—24no—
311D4×C11—42no—
312D4×C11—42no—
313D4×C11—42no—
314D4×C11—42no—
315D4×C11—41no—
316D4×C11—41no—
317D4×C11C2×C22⋊C418yes—
318C2×C4×C11—22no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—42no—
322C2×C4×C11—42no—
323C2×C4×C11—42no—
324C2×C4×C11—42no—
325C2×C4×C11C2×C22⋊C411yescharacteristic
326C2×C4×C11C2×C22⋊C411yescharacteristic
327C2×C4×C11C2×C22⋊C411yescharacteristic
328C2×C4×C11C2×C22⋊C411yescharacteristic
329C2×C4×C11C4×D411yescharacteristic
330C2×C4×C11C4×D411yescharacteristic
331C2×C4×C11C4×D411yescharacteristic
332C2×C4×C11C4×D411yescharacteristic
333C2×C4×C11C4×D411yescharacteristic
334C2×C4×C11C4×D411yescharacteristic
335C2×C4×C11#12011yescharacteristic
336C2×C4×C11#12011yescharacteristic
337C2×C4×C11#12111yescharacteristic
338C2×C4×C11#12111yescharacteristic
339C2×C4×C11#12111yescharacteristic
340C2×C4×C11#12111yescharacteristic
341C2×C4×C11#12111yescharacteristic
342C2×C4×C11#12111yescharacteristic
343C2×C4×C11#12311yescharacteristic
344C2×C4×C11#12311yescharacteristic
345C2×C4×C11#12311yescharacteristic
346C2×C4×C11#12311yescharacteristic
347C2×C4×C11C23×C411yescharacteristic
348C2×C4×C11C22×D411yescharacteristic
349C2×C4×C11C22×D411yescharacteristic
350C2×C4×C11C22×D411yescharacteristic
351C2×C4×C11C2×#4111yescharacteristic
352C2×C4×C11C2×#4111yescharacteristic
353C2×Dic11—24no—
354C2×Dic11—24no—
355C2×Dic11—44no—
356C2×Dic11—44no—
357C2×Dic11—42no—
358C2×Dic11—816no—
359C2×Dic11—82no—
360C8×C11—24no—
361C11⋊C8—42no—
362C22×#41C2×D1111yescharacteristic
363C23×D4C2×D1111yescharacteristic
364C2×AGL(1,ℤ/8)—22no—
365C2×AGL(1,ℤ/8)—22no—
366C2×AGL(1,ℤ/8)—22no—
367C2×AGL(1,ℤ/8)—22no—
368C2×AGL(1,ℤ/8)Dic1114yescomplemented
369C2×AGL(1,ℤ/8)C2×D1114yes—
370C22×SD16Dic1112yescomplemented
371C22×D8Dic1112yescomplemented
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×#117—111no—
382C2×#117—111no—
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)—114no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—22no—
398C22×C11—28no—
399C22×C11—41no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—41no—
403C22×C11—48no—
404C22×C11—48no—
405C22×C11—48no—
406C22×C11—42no—
407C22×C11—84no—
408C22×C11—84no—
409C22×C11—84no—
410C22×C11—84no—
411C22×C11—82no—
412C22×C11—82no—
413C22×C11—82no—
414C22×C11#38611yescharacteristic
415C22×C11#38611yescharacteristic
416C22×C11#38611yescharacteristic
417C22×C11#38611yescharacteristic
418C22×C11C2×C4×D411yescharacteristic
419C22×C11C2×#12011yescharacteristic
420C22×C11C2×#12111yescharacteristic
421C4×C11—42no—
422C4×C11#38611yescharacteristic
423C4×C11#38611yescharacteristic
424C4×C11#38611yescharacteristic
425C4×C11#38611yescharacteristic
426C4×C11C22×C22⋊C411yescharacteristic
427C4×C11C2×C4×D411yescharacteristic
428C4×C11C2×#12111yescharacteristic
429C4×C11C2×#12311yescharacteristic
430Dic11—44no—
431Dic11—44no—
432Dic11—82no—
433C25—21no—
434C2×#41—21no—
435C2×#41—21no—
436C2×#41—21no—
437C2×#41—21no—
438C2×#41—21no—
439C2×#41—21no—
440C2×#41—21no—
441C2×#41—21no—
442C2×#41—21no—
443C2×#41—21no—
444C2×#41C2×Dic1112yescomplemented
445C2×#41C22×D1112yes—
446C22×Q8C2×Dic1111yescharacteristic, complemented
447C22×D4—21no—
448C22×D4—21no—
449C22×D4—21no—
450C22×D4—21no—
451C22×D4—21no—
452C22×D4—21no—
453C22×D4—21no—
454C22×D4—21no—
455C22×D4C2×Dic1112yes—
456C22×D4C2×Dic1112yes—
457C22×D4C2×Dic1111yescharacteristic, complemented
458C22×D4C22⋊D1112yes—
459C22×D4C22⋊D1112yes—
460C22×D4C22⋊D1112yes—
461C22×D4C22⋊D1112yes—
462C22×D4C22×D1112yes—
463C23×C4—21no—
464C23×C4—224no—
465C23×C4C22×D1111yescharacteristic
466AGL(1,ℤ/8)—28no—
467AGL(1,ℤ/8)—28no—
468AGL(1,ℤ/8)—28no—
469AGL(1,ℤ/8)—28no—
470C2×SD16—24no—
471C2×SD16—24no—
472C2×SD16C2×Dic1118yescomplemented
473C2×D8—24no—
474C2×D8—24no—
475C2×D8C2×Dic1118yescomplemented
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×M16C2×Dic1112yescomplemented
487C2×M16C22×D1112yes—
488C22×C8—221no—
489C22×C8C2×Dic1112yescomplemented
490C4×D4—228no—
491C4×D4—228no—
492C4×D4—228no—
493C4×D4—228no—
494#117—112no—
495#117—112no—
496#117—112no—
497#117—112no—
498#117—112no—
499#117—221no—
500#117—221no—
501#117—221no—
502#117—221no—
503#117—221no—
504#117—221no—
505#117—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C22⋊C4—112no—
510C2×C22⋊C4—228no—
511C2×C22⋊C4—224no—
512C2×C22⋊C4—228no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C42—112no—
516C2×C42—221no—
517C2×C42—221no—
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—48no—
528C2×C11—82no—
529C2×C11#190412yescomplemented
530C2×C11C2×#38611yescharacteristic
531C24—22no—
532C24—22no—
533C24—22no—
534C24—22no—
535C24—22no—
536C24—22no—
537C24—22no—
538C24—21no—
539C24—84no—
540C24D4×D1111yescharacteristic
541#41—22no—
542#41—22no—
543#41—22no—
544#41—22no—
545#41—22no—
546#41—22no—
547#41—22no—
548#41—22no—
549#41—41no—
550#41—41no—
551#41—41no—
552#41—41no—
553#41—41no—
554#41—41no—
555#41—41no—
556#41—41no—
557C2×Q8—21no—
558C2×Q8—21no—
559C2×Q8—21no—
560C2×Q8—21no—
561C2×Q8—21no—
562C2×Q8C22×Dic1112yescomplemented
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—22no—
566C2×D4—22no—
567C2×D4—22no—
568C2×D4—22no—
569C2×D4—22no—
570C2×D4—22no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—22no—
575C2×D4—22no—
576C2×D4—22no—
577C2×D4—22no—
578C2×D4—22no—
579C2×D4—22no—
580C2×D4—22no—
581C2×D4—22no—
582C2×D4—22no—
583C2×D4—22no—
584C2×D4—22no—
585C2×D4—22no—
586C2×D4—21no—
587C2×D4—21no—
588C2×D4—22no—
589C2×D4—22no—
590C2×D4—22no—
591C2×D4—41no—
592C2×D4—41no—
593C2×D4—41no—
594C2×D4—41no—
595C2×D4C22⋊Dic1114yes—
596C2×D4C22⋊Dic1114yes—
597C2×D4C22⋊Dic1114yes—
598C2×D4C22⋊Dic1114yes—
599C2×D4C22×Dic1114yes—
600C2×D4C22×Dic1112yescomplemented
601C2×D4C2×C22⋊D1114yes—
602C2×D4C2×C22⋊D1114yes—
603C22×C4—21no—
604C22×C4—22no—
605C22×C4—22no—
606C22×C4—41no—
607C22×C4—41no—
608C22×C4—41no—
609C22×C4—41no—
610C22×C4—222no—
611C22×C4—222no—
612C22×C4—2216no—
613C22×C4—441no—
614C22×C4—888no—
615C22×C4D4×D1111yescharacteristic
616C22×C4D4×D1111yescharacteristic
617C22×C4D4×D1111yescharacteristic
618C22×C4#434111yescharacteristic
619C22×C4#434111yescharacteristic
620C22×C4#434111yescharacteristic
621C22×C4#434111yescharacteristic
622C22×C4C22×Dic1111yescharacteristic
623C22×C4C22×Dic1111yescharacteristic
624C22×C4C2×C22⋊D1111yescharacteristic
625C22×C4C2×C22⋊D1111yescharacteristic
626C22×C4C2×C22⋊D1111yescharacteristic
627C22×C4C2×C22⋊D1111yescharacteristic
628C22×C4C23×D1111yescharacteristic
629SD16—216no—
630D8—216no—
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×C8C22×Dic1114yescomplemented
645C4⋊C4—222no—
646C4⋊C4—222no—
647C4⋊C4—222no—
648C4⋊C4—222no—
649C4⋊C4—222no—
650C4⋊C4—441no—
651C22⋊C4—114no—
652C22⋊C4—2216no—
653C22⋊C4—222no—
654C22⋊C4—222no—
655C22⋊C4—222no—
656C22⋊C4—222no—
657C22⋊C4—441no—
658C42—114no—
659C42—222no—
660C42—222no—
661C42—222no—
662C42—222no—
663C42—441no—
664C11C2×#190411yescharacteristic, complemented, Sylow
665C23—24no—
666C23—24no—
667C23—24no—
668C23—24no—
669C23—24no—
670C23—24no—
671C23—24no—
672C23—22no—
673C23—42no—
674C23—48no—
675C23—41no—
676C23—41no—
677C23—84no—
678C23—84no—
679C23—82no—
680C23—84no—
681C23—84no—
682C23—84no—
683C23—84no—
684C23D4×Dic1111yescharacteristic
685C23D4×Dic1111yescharacteristic
686C23#6699011yescharacteristic
687C23#6699011yescharacteristic
688C23#6699211yescharacteristic
689C23#6699211yescharacteristic
690C23C2×D4×D1111yescharacteristic
691Q8—22no—
692Q8—22no—
693Q8—41no—
694Q8—41no—
695D4—24no—
696D4—22no—
697D4—24no—
698D4—24no—
699D4—24no—
700D4—24no—
701D4—24no—
702D4—24no—
703D4—22no—
704D4—42no—
705D4—42no—
706D4—42no—
707D4—42no—
708D4—41no—
709D4—41no—
710D4C2×C22⋊Dic1118yes—
711C2×C4—22no—
712C2×C4—41no—
713C2×C4—41no—
714C2×C4—42no—
715C2×C4—42no—
716C2×C4—42no—
717C2×C4—42no—
718C2×C4—224no—
719C2×C4—224no—
720C2×C4—444no—
721C2×C4—444no—
722C2×C4—442no—
723C2×C4—8816no—
724C2×C4—882no—
725C2×C4D4×Dic1111yescharacteristic
726C2×C4D4×Dic1111yescharacteristic
727C2×C4D4×Dic1111yescharacteristic
728C2×C4D4×Dic1111yescharacteristic
729C2×C4D4×Dic1111yescharacteristic
730C2×C4D4×Dic1111yescharacteristic
731C2×C4#6698811yescharacteristic
732C2×C4#6698811yescharacteristic
733C2×C4#6698811yescharacteristic
734C2×C4#6698811yescharacteristic
735C2×C4#6699011yescharacteristic
736C2×C4#6699011yescharacteristic
737C2×C4#6699211yescharacteristic
738C2×C4#6699211yescharacteristic
739C2×C4#6699211yescharacteristic
740C2×C4#6699211yescharacteristic
741C2×C4#6699211yescharacteristic
742C2×C4#6699211yescharacteristic
743C2×C4C2×C22⋊Dic1111yescharacteristic
744C2×C4C2×C22⋊Dic1111yescharacteristic
745C2×C4C2×C22⋊Dic1111yescharacteristic
746C2×C4C2×C22⋊Dic1111yescharacteristic
747C2×C4C2×D4×D1111yescharacteristic
748C2×C4C2×#434111yescharacteristic
749C2×C4C2×#434111yescharacteristic
750C2×C4C23×Dic1111yescharacteristic
751C2×C4C22×C22⋊D1111yescharacteristic
752C2×C4C22×C22⋊D1111yescharacteristic
753C8—24no—
754C8—442no—
755C22—22no—
756C22—22no—
757C22—22no—
758C22—28no—
759C22—41no—
760C22—41no—
761C22—41no—
762C22—41no—
763C22—48no—
764C22—48no—
765C22—48no—
766C22—42no—
767C22—84no—
768C22—84no—
769C22—84no—
770C22—84no—
771C22—82no—
772C22—82no—
773C22—82no—
774C22#1062283311yescharacteristic
775C22#1062283311yescharacteristic
776C22#1062283311yescharacteristic
777C22#1062283311yescharacteristic
778C22C2×D4×Dic1111yescharacteristic
779C22C2×#6699011yescharacteristic
780C22C2×#6699211yescharacteristic
781C4—42no—
782C4—444no—
783C4—444no—
784C4—882no—
785C4#1062283311yescharacteristic
786C4#1062283311yescharacteristic
787C4#1062283311yescharacteristic
788C4#1062283311yescharacteristic
789C4C2×D4×Dic1111yescharacteristic
790C4C2×#6698811yescharacteristic
791C4C2×#6699211yescharacteristic
792C4C22×C22⋊Dic1111yescharacteristic
793C2—21no—
794C2—21no—
795C2—21no—
796C2—21no—
797C2—21no—
798C2—21no—
799C2—48no—
800C2—82no—
801C2#1306910512yesdirect product factor
802C2C2×#1062283311yescharacteristic
subgroupG/H
centerC22#10622833
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC22×C11#386
cosocleC22×C4×C11C24
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11C2×#1904
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C22 ◁ C23×C4 ◁ C22×AGL(1,ℤ/8)

Complements

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

NH ≅ G/Ntype
1. C2×#10623329C2semidirect
2. C2×#10622849C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622853C2semidirect
5. #13069105C2direct (N × H)
6. C2×#10622194C2semidirect
7. C2×#10622195C2semidirect
15. C2×C11×AGL(1,ℤ/8)C4semidirect
17. C22×C11×SD16C4semidirect
18. C22×C11×D8C4semidirect
24. #10623329C22semidirect
32. #10622853C22semidirect
34. #10622849C22semidirect
38. #10622828C22semidirect
40. #10622195C22semidirect
41. #10622194C22semidirect
53. C2×C11×#41C2×C4semidirect
55. C22×Q8×C11C2×C4semidirect
66. C22×D4×C11C2×C4semidirect
81. C2×C11×SD16C2×C4semidirect
84. C2×C11×D8C2×C4semidirect
89. C2×C11×M16C2×C4semidirect
91. C22×C8×C11C2×C4semidirect
162. C2×Q8×C11C22×C4semidirect
200. C2×D4×C11C22×C4semidirect
237. C2×C8×C11C22×C4semidirect
368. C2×AGL(1,ℤ/8)Dic11semidirect
370. C22×SD16Dic11semidirect
371. C22×D8Dic11semidirect
444. C2×#41C2×Dic11semidirect
446. C22×Q8C2×Dic11semidirect
457. C22×D4C2×Dic11semidirect
472. C2×SD16C2×Dic11semidirect
475. C2×D8C2×Dic11semidirect
486. C2×M16C2×Dic11semidirect
489. C22×C8C2×Dic11semidirect
529. C2×C11#1904semidirect
562. C2×Q8C22×Dic11semidirect
600. C2×D4C22×Dic11semidirect
644. C2×C8C22×Dic11semidirect
664. C11C2×#1904semidirect
801. C2#13069105direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106233292
C2×#106228492
C2×#106228282
C2×#106228532
#130691052
C2×#106221942
C2×#106221952
C22×C11×AGL(1,ℤ/8)2
C2×#190411