Finite Group Databasebeta

← C2×#13069886 #14781600

Subgroups — C2×#13069886 #14781600

Order 2816.

1450 conjugacy classes of subgroups.

The subgroup lattice has 776 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622737C211yesmaximal, characteristic, complemented
2C2×#10622849C211yesmaximal, characteristic, complemented
3C2×#10622828C211yesmaximal, characteristic, complemented
4C2×#10622850C211yesmaximal, characteristic, complemented
5C22×#66897C211yesmaximal, characteristic, complemented
6#13069886C218yesmaximal, direct product factor
7C2×#10622197C211yesmaximal, 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)—22no—
16C2×C11×AGL(1,ℤ/8)C2214yes—
17C22×C11×SD16—21no—
18C22×C11×D8—21no—
19C22×C11×M16C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C22×#4318C2211yescharacteristic
22C22×#4318C2211yescharacteristic
23C22×#4318C2211yescharacteristic
24#10622850—22no—
25#10622850C2214yescomplemented
26#10622849—22no—
27#10622849C2214yescomplemented
28C2×#66901—22no—
29C2×#66900—21no—
30C2×#66897—21no—
31C2×#66897—22no—
32C2×#66897—22no—
33C2×#66897C2214yescomplemented
34#10622828—22no—
35#10622828C2214yescomplemented
36C2×#66896—22no—
37#10622737—22no—
38#10622737C2214yescomplemented
39C2×#66886—22no—
40#10622197C2214yescomplemented
41C25×C11—21no—
42C2×C11×#41—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×#41D412yes—
53C2×C11×#41C2312yes—
54C22×Q8×C11D411yescharacteristic
55C22×D4×C11—21no—
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×C11—21no—
65C22×D4×C11—21no—
66C22×D4×C11—21no—
67C22×D4×C11D412yes—
68C22×D4×C11D412yes—
69C22×D4×C11D411yescharacteristic
70C22×D4×C11C2312yes—
71C23×C4×C11—21no—
72C23×C4×C11C2311yescharacteristic
73C11×AGL(1,ℤ/8)—28no—
74C11×AGL(1,ℤ/8)—28no—
75C11×AGL(1,ℤ/8)—28no—
76C11×AGL(1,ℤ/8)—28no—
77C2×C11×SD16—24no—
78C2×C11×SD16—24no—
79C2×C11×SD16—24no—
80C2×C11×D8—24no—
81C2×C11×D8—24no—
82C2×C11×D8—24no—
83C2×C11×M16—21no—
84C2×C11×M16—21no—
85C2×C11×M16—21no—
86C2×C11×M16D412yes—
87C2×C11×M16D412yes—
88C2×C11×M16C2312yes—
89C22×C8×C11—21no—
90C2×C22⋊Dic11—21no—
91#66979—21no—
92#66979—21no—
93#66979—21no—
94#66979C2312yes—
95C2×C4⋊Dic11—21no—
96C2×C4×Dic11—21no—
97C2×#4318—21no—
98C2×#4318—21no—
99C2×#4318—21no—
100C2×#4318—21no—
101C2×#4318—21no—
102C2×#4318—21no—
103C2×#4318—21no—
104C2×#4318—21no—
105C2×#4318—21no—
106C2×#4318—21no—
107C2×#4318—21no—
108C2×#4318—21no—
109C2×#4318—21no—
110C2×#4318D412yes—
111C2×#4318D412yes—
112C2×#4318C2312yes—
113C2×#4318C2312yes—
114C2×#4318C2312yes—
115C22×C11⋊C8—21no—
116C22×C11⋊C8—21no—
117C22×C11⋊C8—21no—
118#66901—28no—
119#66900—24no—
120#66897—24no—
121#66897—28no—
122#66896—28no—
123#66886—28no—
124C2×#2048—111nomaximal, Sylow
125C24×C11—22no—
126C24×C11—22no—
127C24×C11—21no—
128C24×C11—22no—
129C24×C11—41no—
130C24×C11—41no—
131C24×C11—41no—
132C24×C11—41no—
133C24×C11—84no—
134C24×C11#4111yescharacteristic
135C11×#41—22no—
136C11×#41—22no—
137C11×#41—22no—
138C11×#41—22no—
139C11×#41—22no—
140C11×#41—22no—
141C11×#41—22no—
142C11×#41—22no—
143C11×#41—41no—
144C11×#41—41no—
145C11×#41—41no—
146C11×#41—41no—
147C11×#41—41no—
148C11×#41—41no—
149C11×#41—41no—
150C11×#41—41no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11—21no—
156C2×Q8×C11C2×D412yes—
157C2×D4×C11—22no—
158C2×D4×C11—22no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—22no—
162C2×D4×C11—22no—
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—22no—
175C2×D4×C11—22no—
176C2×D4×C11—22no—
177C2×D4×C11—22no—
178C2×D4×C11—22no—
179C2×D4×C11—41no—
180C2×D4×C11—41no—
181C2×D4×C11—41no—
182C2×D4×C11—41no—
183C2×D4×C11—41no—
184C2×D4×C11—41no—
185C2×D4×C11—41no—
186C2×D4×C11—41no—
187C2×D4×C11—41no—
188C2×D4×C11—41no—
189C2×D4×C11—41no—
190C2×D4×C11—41no—
191C2×D4×C11—41no—
192C2×D4×C11—41no—
193C2×D4×C11—41no—
194C2×D4×C11—41no—
195C2×D4×C11C2×D414yes—
196C2×D4×C11C2×D412yes—
197C22×C4×C11—21no—
198C22×C4×C11—22no—
199C22×C4×C11—22no—
200C22×C4×C11—41no—
201C22×C4×C11—41no—
202C22×C4×C11—41no—
203C22×C4×C11—41no—
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2×D411yescharacteristic
207C22×C4×C11C2×D411yescharacteristic
208C22×C4×C11C2×D411yescharacteristic
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11#4111yescharacteristic
213C22×C4×C11#4111yescharacteristic
214C22×C4×C11#4111yescharacteristic
215C22×C4×C11#4111yescharacteristic
216C22×C4×C11#4111yescharacteristic
217C22×C4×C11C2411yescharacteristic
218C22×Dic11—41no—
219C11×SD16—216no—
220C11×D8—216no—
221C11×M16—22no—
222C11×M16—22no—
223C11×M16—22no—
224C11×M16C2×D414yes—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11—22no—
228C22⋊Dic11—22no—
229C22⋊Dic11—41no—
230C4⋊Dic11—22no—
231C4⋊Dic11—41no—
232C4×Dic11—22no—
233C4×Dic11—41no—
234#4318—22no—
235#4318—22no—
236#4318—22no—
237#4318—22no—
238#4318—22no—
239#4318—22no—
240#4318—22no—
241#4318—41no—
242#4318—41no—
243#4318—41no—
244#4318—41no—
245#4318C2×D414yes—
246C2×C11⋊C8—22no—
247C2×C11⋊C8—22no—
248C2×C11⋊C8—22no—
249C2×C11⋊C8—22no—
250C2×C11⋊C8—22no—
251C2×C11⋊C8—41no—
252C2×C11⋊C8—41no—
253C2×C11⋊C8—41no—
254C2×C11⋊C8—41no—
255C22×AGL(1,ℤ/8)D1111yescharacteristic
256C2×#430—111no—
257C2×#421—111no—
258C2×#418—111no—
259C2×#413—111no—
260C22×#100—111no—
261#2048—118no—
262C2×#344—111no—
263C23×C11—24no—
264C23×C11—22no—
265C23×C11—42no—
266C23×C11—42no—
267C23×C11—42no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—42no—
271C23×C11—42no—
272C23×C11—42no—
273C23×C11—42no—
274C23×C11—82no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11—84no—
282C23×C11#12111yescharacteristic
283C23×C11#12111yescharacteristic
284C23×C11#12311yescharacteristic
285C23×C11#12311yescharacteristic
286C23×C11#12411yescharacteristic
287C23×C11#12411yescharacteristic
288C23×C11C2×#4111yescharacteristic
289Q8×C11—22no—
290Q8×C11—22no—
291Q8×C11—41no—
292Q8×C11—41no—
293D4×C11—22no—
294D4×C11—24no—
295D4×C11—22no—
296D4×C11—24no—
297D4×C11—42no—
298D4×C11—42no—
299D4×C11—42no—
300D4×C11—42no—
301D4×C11—42no—
302D4×C11—42no—
303D4×C11—42no—
304D4×C11—42no—
305D4×C11—42no—
306D4×C11—42no—
307D4×C11—41no—
308D4×C11—41no—
309C2×C4×C11—22no—
310C2×C4×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11—42no—
313C2×C4×C11—42no—
314C2×C4×C11—42no—
315C2×C4×C11—42no—
316C2×C4×C11#12011yescharacteristic
317C2×C4×C11#12011yescharacteristic
318C2×C4×C11#12011yescharacteristic
319C2×C4×C11#12011yescharacteristic
320C2×C4×C11#12111yescharacteristic
321C2×C4×C11#12111yescharacteristic
322C2×C4×C11#12111yescharacteristic
323C2×C4×C11#12111yescharacteristic
324C2×C4×C11#12111yescharacteristic
325C2×C4×C11#12111yescharacteristic
326C2×C4×C11#12111yescharacteristic
327C2×C4×C11#12111yescharacteristic
328C2×C4×C11#12111yescharacteristic
329C2×C4×C11#12111yescharacteristic
330C2×C4×C11#12311yescharacteristic
331C2×C4×C11#12311yescharacteristic
332C2×C4×C11#12311yescharacteristic
333C2×C4×C11#12311yescharacteristic
334C2×C4×C11#12311yescharacteristic
335C2×C4×C11#12311yescharacteristic
336C2×C4×C11#12411yescharacteristic
337C2×C4×C11#12411yescharacteristic
338C2×C4×C11C22×D411yescharacteristic
339C2×C4×C11C22×D411yescharacteristic
340C2×C4×C11C22×D411yescharacteristic
341C2×C4×C11C22×D411yescharacteristic
342C2×C4×C11C2×#4111yescharacteristic
343C2×C4×C11C2×#4111yescharacteristic
344C2×Dic11—42no—
345C2×Dic11—82no—
346C8×C11—24no—
347C11⋊C8—24no—
348C11⋊C8—42no—
349C11⋊C8—42no—
350C22×#41C2×D1111yescharacteristic
351C23×D4C2×D1111yescharacteristic
352C2×AGL(1,ℤ/8)—22no—
353C2×AGL(1,ℤ/8)—22no—
354C2×AGL(1,ℤ/8)—22no—
355C2×AGL(1,ℤ/8)—22no—
356C2×AGL(1,ℤ/8)—22no—
357C2×AGL(1,ℤ/8)C2×D1114yes—
358C22×SD16—21no—
359C22×D8—21no—
360C22×M16—111no—
361C22×M16—111no—
362C22×M16—111no—
363C22×M16C2×D1111yescharacteristic
364C2×#117—111no—
365#430—114no—
366#430—222no—
367C2×#108—222no—
368#421—114no—
369#421—222no—
370C2×#104—222no—
371#418—114no—
372#418—222no—
373C2×#102—222no—
374#413—114no—
375#413—222no—
376C2×#101—221no—
377C2×#100—114no—
378C2×#100—222no—
379C2×#100—222no—
380C2×#100—221no—
381#344—114no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—41no—
386C22×C11—41no—
387C22×C11—41no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—44no—
391C22×C11—82no—
392C22×C11—84no—
393C22×C11—82no—
394C22×C11—84no—
395C22×C11—84no—
396C22×C11—84no—
397C22×C11—84no—
398C22×C11—84no—
399C22×C11—82no—
400C22×C11—84no—
401C22×C11#39411yescharacteristic
402C22×C11#39411yescharacteristic
403C22×C11#39411yescharacteristic
404C22×C11#39411yescharacteristic
405C22×C11C2×#12111yescharacteristic
406C22×C11C2×#12311yescharacteristic
407C22×C11C2×#12411yescharacteristic
408C4×C11—42no—
409C4×C11#39411yescharacteristic
410C4×C11#39411yescharacteristic
411C4×C11#39411yescharacteristic
412C4×C11#39411yescharacteristic
413C4×C11C2×#12011yescharacteristic
414C4×C11C2×#12111yescharacteristic
415C4×C11C2×#12111yescharacteristic
416C4×C11C2×#12311yescharacteristic
417Dic11—82no—
418C25—21no—
419C2×#41—21no—
420C2×#41—21no—
421C2×#41—21no—
422C2×#41—21no—
423C2×#41—21no—
424C2×#41—21no—
425C2×#41—21no—
426C2×#41—21no—
427C2×#41—21no—
428C2×#41—21no—
429C2×#41C22⋊D1112yes—
430C2×#41C22×D1112yes—
431C22×Q8C22⋊D1111yescharacteristic
432C22×D4—21no—
433C22×D4—21no—
434C22×D4—21no—
435C22×D4—21no—
436C22×D4—21no—
437C22×D4—21no—
438C22×D4—21no—
439C22×D4—21no—
440C22×D4—21no—
441C22×D4—21no—
442C22×D4—21no—
443C22×D4—21no—
444C22×D4C22⋊D1111yescharacteristic
445C22×D4C22⋊D1112yes—
446C22×D4C22⋊D1112yes—
447C22×D4C22×D1112yes—
448C23×C4—21no—
449C23×C4C22×D1111yescharacteristic
450AGL(1,ℤ/8)—28no—
451AGL(1,ℤ/8)—28no—
452AGL(1,ℤ/8)—28no—
453AGL(1,ℤ/8)—28no—
454C2×SD16—24no—
455C2×SD16—24no—
456C2×SD16—24no—
457C2×D8—24no—
458C2×D8—24no—
459C2×D8—24no—
460C2×M16—21no—
461C2×M16—21no—
462C2×M16—21no—
463C2×M16—112no—
464C2×M16—112no—
465C2×M16—112no—
466C2×M16—112no—
467C2×M16—112no—
468C2×M16—221no—
469C2×M16—221no—
470C2×M16—221no—
471C2×M16—221no—
472C2×M16—221no—
473C2×M16—221no—
474C2×M16—221no—
475C2×M16—221no—
476C2×M16—221no—
477C2×M16—221no—
478C2×M16—221no—
479C2×M16—221no—
480C2×M16—221no—
481C2×M16C22⋊D1112yes—
482C2×M16C22⋊D1112yes—
483C2×M16C22×D1112yes—
484C22×C8—21no—
485C22×C8—221no—
486C22×C8—221no—
487C22×C8—221no—
488#117—112no—
489#117—221no—
490#117—221no—
491#117—221no—
492C2×C4⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C42—221no—
495#108—228no—
496#104—228no—
497#102—228no—
498#101—224no—
499#100—228no—
500#100—224no—
501C2×C11—21no—
502C2×C11—21no—
503C2×C11—21no—
504C2×C11—21no—
505C2×C11—21no—
506C2×C11—21no—
507C2×C11—82no—
508C2×C11—84no—
509C2×C11#204812yescomplemented
510C2×C11C2×#39411yescharacteristic
511C24—21no—
512C24—22no—
513C24—22no—
514C24—22no—
515C24—41no—
516C24—41no—
517C24—41no—
518C24—41no—
519C24—84no—
520C24#434111yescharacteristic
521#41—22no—
522#41—22no—
523#41—22no—
524#41—22no—
525#41—22no—
526#41—22no—
527#41—22no—
528#41—22no—
529#41—41no—
530#41—41no—
531#41—41no—
532#41—41no—
533#41—41no—
534#41—41no—
535#41—41no—
536#41—41no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C22⋊D1112yes—
543C2×D4—22no—
544C2×D4—22no—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—22no—
548C2×D4—22no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4—21no—
555C2×D4—21no—
556C2×D4—22no—
557C2×D4—22no—
558C2×D4—22no—
559C2×D4—22no—
560C2×D4—22no—
561C2×D4—22no—
562C2×D4—22no—
563C2×D4—22no—
564C2×D4—22no—
565C2×D4—41no—
566C2×D4—41no—
567C2×D4—41no—
568C2×D4—41no—
569C2×D4—41no—
570C2×D4—41no—
571C2×D4—41no—
572C2×D4—41no—
573C2×D4—41no—
574C2×D4—41no—
575C2×D4—41no—
576C2×D4—41no—
577C2×D4—41no—
578C2×D4—41no—
579C2×D4—41no—
580C2×D4—41no—
581C2×D4C2×C22⋊D1112yes—
582C2×D4C2×C22⋊D1114yes—
583C22×C4—21no—
584C22×C4—22no—
585C22×C4—22no—
586C22×C4—41no—
587C22×C4—41no—
588C22×C4—41no—
589C22×C4—41no—
590C22×C4—441no—
591C22×C4D4×D1111yescharacteristic
592C22×C4D4×D1111yescharacteristic
593C22×C4#434111yescharacteristic
594C22×C4#434111yescharacteristic
595C22×C4#434111yescharacteristic
596C22×C4#434111yescharacteristic
597C22×C4#434111yescharacteristic
598C22×C4C2×C22⋊D1111yescharacteristic
599C22×C4C2×C22⋊D1111yescharacteristic
600C22×C4C2×C22⋊D1111yescharacteristic
601C22×C4C2×C22⋊D1111yescharacteristic
602C22×C4C2×C22⋊D1111yescharacteristic
603C22×C4C2×C22⋊D1111yescharacteristic
604C22×C4C23×D1111yescharacteristic
605SD16—216no—
606D8—216no—
607M16—22no—
608M16—22no—
609M16—22no—
610M16—114no—
611M16—222no—
612M16—222no—
613M16—222no—
614M16—222no—
615M16—222no—
616M16—222no—
617M16—222no—
618M16—441no—
619M16—441no—
620M16—441no—
621M16—441no—
622M16C2×C22⋊D1114yes—
623C2×C8—22no—
624C2×C8—22no—
625C2×C8—22no—
626C2×C8—222no—
627C2×C8—222no—
628C2×C8—222no—
629C2×C8—222no—
630C2×C8—222no—
631C2×C8—441no—
632C2×C8—441no—
633C2×C8—441no—
634C2×C8—441no—
635C4⋊C4—222no—
636C4⋊C4—441no—
637C22⋊C4—222no—
638C22⋊C4—441no—
639C42—222no—
640C42—441no—
641C11C2×#204811yescharacteristic, complemented, Sylow
642C23—22no—
643C23—24no—
644C23—42no—
645C23—42no—
646C23—42no—
647C23—41no—
648C23—42no—
649C23—42no—
650C23—42no—
651C23—41no—
652C23—42no—
653C23—82no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23—84no—
660C23—84no—
661C23#6698811yescharacteristic
662C23#6698811yescharacteristic
663C23#6698911yescharacteristic
664C23#6698911yescharacteristic
665C23#6699211yescharacteristic
666C23#6699211yescharacteristic
667C23C2×#434111yescharacteristic
668Q8—22no—
669Q8—22no—
670Q8—41no—
671Q8—41no—
672D4—24no—
673D4—22no—
674D4—22no—
675D4—24no—
676D4—42no—
677D4—42no—
678D4—42no—
679D4—42no—
680D4—42no—
681D4—42no—
682D4—42no—
683D4—42no—
684D4—42no—
685D4—42no—
686D4—41no—
687D4—41no—
688C2×C4—22no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—42no—
692C2×C4—42no—
693C2×C4—42no—
694C2×C4—42no—
695C2×C4—442no—
696C2×C4—882no—
697C2×C4#6698811yescharacteristic
698C2×C4#6698811yescharacteristic
699C2×C4#6698811yescharacteristic
700C2×C4#6698811yescharacteristic
701C2×C4#6698811yescharacteristic
702C2×C4#6698811yescharacteristic
703C2×C4#6698911yescharacteristic
704C2×C4#6698911yescharacteristic
705C2×C4#6699111yescharacteristic
706C2×C4#6699111yescharacteristic
707C2×C4#6699111yescharacteristic
708C2×C4#6699111yescharacteristic
709C2×C4#6699211yescharacteristic
710C2×C4#6699211yescharacteristic
711C2×C4#6699211yescharacteristic
712C2×C4#6699211yescharacteristic
713C2×C4#6699211yescharacteristic
714C2×C4#6699211yescharacteristic
715C2×C4#6700611yescharacteristic
716C2×C4#6700611yescharacteristic
717C2×C4#6700611yescharacteristic
718C2×C4#6700611yescharacteristic
719C2×C4C2×D4×D1111yescharacteristic
720C2×C4C2×#434111yescharacteristic
721C2×C4C2×#434111yescharacteristic
722C2×C4C22×C22⋊D1111yescharacteristic
723C2×C4C22×C22⋊D1111yescharacteristic
724C2×C4C22×C22⋊D1111yescharacteristic
725C8—24no—
726C8—224no—
727C8—442no—
728C8—442no—
729C22—22no—
730C22—22no—
731C22—22no—
732C22—41no—
733C22—41no—
734C22—41no—
735C22—41no—
736C22—42no—
737C22—44no—
738C22—84no—
739C22—82no—
740C22—84no—
741C22—84no—
742C22—84no—
743C22—84no—
744C22—84no—
745C22—82no—
746C22—84no—
747C22—82no—
748C22#1062283511yescharacteristic
749C22#1062283511yescharacteristic
750C22#1062283511yescharacteristic
751C22#1062283511yescharacteristic
752C22C2×#6698811yescharacteristic
753C22C2×#6698911yescharacteristic
754C22C2×#6699211yescharacteristic
755C4—42no—
756C4—882no—
757C4#1062283511yescharacteristic
758C4#1062283511yescharacteristic
759C4#1062283511yescharacteristic
760C4#1062283511yescharacteristic
761C4C2×#6698811yescharacteristic
762C4C2×#6699111yescharacteristic
763C4C2×#6699211yescharacteristic
764C4C2×#6700611yescharacteristic
765C2—21no—
766C2—21no—
767C2—21no—
768C2—21no—
769C2—21no—
770C2—21no—
771C2—84no—
772C2—82no—
773C2#1306988612yesdirect product factor
774C2C2×#1062283511yescharacteristic
subgroupG/H
centerC22#10622835
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
Fitting, prime radicalC22×C11×AGL(1,ℤ/8)C2
socleC22×C11#394
hypercenterC22×AGL(1,ℤ/8)D11
hypocenterC11C2×#2048
LCSG ▷ C22×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×#10622737C2semidirect
2. C2×#10622849C2semidirect
3. C2×#10622828C2semidirect
4. C2×#10622850C2semidirect
5. C22×#66897C2semidirect
6. #13069886C2direct (N × H)
7. C2×#10622197C2semidirect
25. #10622850C22semidirect
27. #10622849C22semidirect
33. C2×#66897C22semidirect
35. #10622828C22semidirect
38. #10622737C22semidirect
40. #10622197C22semidirect
509. C2×C11#2048semidirect
641. C11C2×#2048semidirect
773. C2#13069886direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106227372
C2×#106228492
C2×#106228282
C2×#106228502
C22×#668972
#130698862
C2×#106221972
C22×C11×AGL(1,ℤ/8)2
C2×#204811