Finite Group Databasebeta

← C2×#13081516 #15634251

Subgroups — C2×#13081516 #15634251

Order 2816.

2082 conjugacy classes of subgroups.

The subgroup lattice has 720 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623070C211yesmaximal, characteristic, complemented
2C2×D4×Dic22C211yesmaximal, characteristic, complemented
3#13081516C2116yesmaximal, direct product factor
4C2×#10622315C211yesmaximal, characteristic, complemented
5C2×#10622469C211yesmaximal, characteristic, complemented
6C2×#10622468C211yesmaximal, characteristic, complemented
7C2×#10622622C211yesmaximal, characteristic, complemented
8C2×#10622379C211yesmaximal, characteristic, complemented
9C2×#10622621C211yesmaximal, characteristic, complemented
10C2×#10622374C211yesmaximal, characteristic, complemented
11C2×#10622374C211yesmaximal, characteristic, complemented
12C2×#10622372C211yesmaximal, characteristic, complemented
13C2×#10622314C211yesmaximal, characteristic, complemented
14C2×#10622765C211yesmaximal, characteristic
15C2×D8×Dic11C211yesmaximal, characteristic
16C2×C11×#442C211yesmaximal, characteristic
17C23×Dic22—21no—
18C22×C11×D8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×C4×D4×C11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C2×D4×Dic11C2211yescharacteristic
25C2×#66977—21no—
26C2×#66977—21no—
27C22×Dic11⋊C4—21no—
28#10623070—24no—
29#10623070C2218yescomplemented
30D4×Dic22—24no—
31D4×Dic22C2218yescomplemented
32C2×#66943C2211yescharacteristic
33C2×#66941C2211yescharacteristic
34C2×#66941C2211yescharacteristic
35C2×#66941C2211yescharacteristic
36C2×#66931—21no—
37C2×#66931—21no—
38C2×#66931—21no—
39C2×#66931—21no—
40C2×#66923C2211yescharacteristic
41C2×#66922C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C11×#442C2218yes—
44C2×C11×#106C2211yescharacteristic
45C2×C11×#102C2211yescharacteristic
46C2×C11×#102C2211yescharacteristic
47C2×C11×#97C2211yescharacteristic
48C2×#66896C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66896C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52#10622765C2218yes—
53D8×Dic11C2218yes—
54C2×#66882C2211yescharacteristic
55C2×#66882C2211yescharacteristic
56C2×#66881C2211yescharacteristic
57C2×#66881C2211yescharacteristic
58C2×#66879C2211yescharacteristic
59C2×Dic11⋊C8C2211yescharacteristic
60C2×Dic11⋊C8C2211yescharacteristic
61C2×C8×Dic11C2211yescharacteristic
62#10622622C2218yescomplemented
63#10622621C2218yescomplemented
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×C4⋊(C11⋊C8)C2211yescharacteristic
69#10622469C2218yescomplemented
70#10622468C2218yescomplemented
71#10622379C2218yescomplemented
72#10622374C2218yescomplemented
73#10622374C2218yescomplemented
74#10622372C2218yescomplemented
75#10622315C2218yescomplemented
76#10622314C2218yescomplemented
77C22×D4×C11C2311yescharacteristic
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×C4×C11—21no—
81C23×Dic11—21no—
82C23×Dic11—21no—
83C23×Dic11—21no—
84C23×Dic11—21no—
85C22×Dic22—21no—
86C22×Dic22—21no—
87C22×Dic22—21no—
88C22×Dic22—21no—
89C22×Dic22—28no—
90C22×Dic22—48no—
91C22×Dic22D411yescharacteristic
92C2×C11×D8Q818yescomplemented
93C2×C11×D8C2314yes—
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C4×D4×C11—22no—
97C4×D4×C11—22no—
98C4×D4×C11C2314yes—
99C4×D4×C11C2314yes—
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C11×C22⋊C4—21no—
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109D4×Dic11—22no—
110D4×Dic11—22no—
111D4×Dic11—22no—
112D4×Dic11—22no—
113D4×Dic11C2314yes—
114D4×Dic11C2314yes—
115D4×Dic11C2314yes—
116D4×Dic11C2314yes—
117C2×C4⋊Dic11—21no—
118C2×C4⋊Dic11—21no—
119C2×C4⋊Dic11D411yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124#66977—28no—
125#66977—28no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—21no—
129C2×Dic11⋊C4—21no—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—28no—
133C2×Dic11⋊C4D411yescharacteristic
134C2×Dic11⋊C4D411yescharacteristic
135C2×C4×Dic11C2311yescharacteristic
136C2×C4×Dic11C2311yescharacteristic
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139#66943—22no—
140#66943C2314yes—
141#66941—22no—
142#66941—22no—
143#66941—22no—
144#66941C2314yes—
145#66941C2314yes—
146#66941C2314yes—
147#66931—28no—
148#66931—28no—
149#66931—28no—
150#66931—28no—
151#66923—22no—
152#66923C2314yes—
153#66922—22no—
154#66922C2314yes—
155C4×Dic22D414yes—
156C4×Dic22C2314yes—
157C11×#106C2314yes—
158C11×#102C2314yes—
159C11×#102C2314yes—
160C11×#97C2314yes—
161#66896C2314yes—
162#66896C2314yes—
163#66896C2314yes—
164#66896C2314yes—
165#66882C2314yes—
166#66882C2314yes—
167#66881C2314yes—
168#66881C2314yes—
169#66879C2314yes—
170Dic11⋊C8C2314yes—
171Dic11⋊C8C2314yes—
172C8×Dic11C2314yes—
173#66872C2314yes—
174#66872C2314yes—
175#66872C2314yes—
176#66871C2314yes—
177C4⋊(C11⋊C8)C2314yes—
178C2×#3384—111nomaximal, Sylow
179C24×C11—21no—
180C24×C11—21no—
181C2×D4×C11—21no—
182C2×D4×C11—21no—
183C2×D4×C11—22no—
184C2×D4×C11—22no—
185C2×D4×C11C2×Q814yes—
186C2×D4×C11C2×Q814yescomplemented
187C2×D4×C11C2412yes—
188C2×D4×C11C2412yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—24no—
192C22×C4×C11—24no—
193C22×C4×C11—44no—
194C22×C4×C11—82no—
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—24no—
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—24no—
202C22×Dic11—21no—
203C22×Dic11—21no—
204C22×Dic11—21no—
205C22×Dic11—21no—
206C22×Dic11—44no—
207C22×Dic11—44no—
208C22×Dic11—44no—
209C22×Dic11—82no—
210C22×Dic11C2×D411yescharacteristic
211C22×Dic11C2×D411yescharacteristic
212C22×Dic11C2×D411yescharacteristic
213C22×Dic11C2×D411yescharacteristic
214C2×Dic22—24no—
215C2×Dic22—24no—
216C2×Dic22—24no—
217C2×Dic22—24no—
218C2×Dic22—24no—
219C2×Dic22—44no—
220C2×Dic22—432no—
221C2×Dic22—44no—
222C2×Dic22—44no—
223C2×Dic22—82no—
224C2×Dic22C2×D414yes—
225C11×D8C2×Q8116yescomplemented
226C2×C8×C11—22no—
227C2×C8×C11C2×Q814yescomplemented
228C2×C8×C11C2412yes—
229C2×C8×C11C2412yes—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4C2412yes—
233C11×C4⋊C4C2412yes—
234C11×C22⋊C4—24no—
235C11×C22⋊C4—24no—
236C42×C11C2×D412yes—
237C42×C11C2412yes—
238C22⋊Dic11—24no—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241C22⋊Dic11—24no—
242C4⋊Dic11—24no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11C2×D414yes—
249C4⋊Dic11C2412yes—
250C4⋊Dic11C2412yes—
251C4⋊Dic11C2412yes—
252C4⋊Dic11C2412yes—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256Dic11⋊C4—24no—
257Dic11⋊C4—24no—
258Dic11⋊C4—24no—
259Dic11⋊C4C2×D414yes—
260Dic11⋊C4C2×D414yes—
261C4×Dic11C2×D412yes—
262C4×Dic11C2×D412yes—
263C4×Dic11C2412yes—
264C4×Dic11C2412yes—
265C2×C11⋊C8—22no—
266C2×C11⋊C8—22no—
267C2×C11⋊C8C2412yes—
268C2×C11⋊C8C2412yes—
269C2×#554—111no—
270C2×D4×Q8—111no—
271#3384—1116no—
272C2×#501—111no—
273C2×#501—111no—
274C2×#498—111no—
275C2×#478—111no—
276C2×#478—111no—
277C2×#476—111no—
278C2×#476—111no—
279C2×#476—111no—
280C2×#474—111no—
281C2×#446—111no—
282C2×#442—111no—
283C2×#442D1111yescharacteristic
284C2×C4×D8—111no—
285C23×C11—24no—
286C23×C11—24no—
287C23×C11—22no—
288C23×C11—22no—
289C23×C11—42no—
290C23×C11—42no—
291C23×C11—42no—
292C23×C11—42no—
293C23×C11C22×D411yescharacteristic
294D4×C11—24no—
295D4×C11—24no—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11C22×Q814yes—
299D4×C11C22×Q814yescomplemented
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—48no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11—84no—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C22×Q812yes—
312C2×C4×C112−1+412yes—
313C2×C4×C11C2511yescharacteristic
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—48no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—48no—
327C2×Dic11—48no—
328C2×Dic11—84no—
329C2×Dic11AGL(1,ℤ/8)14yes—
330C2×Dic11C22×D412yes—
331C2×Dic11C22×D412yes—
332C2×Dic11C22×D412yes—
333C2×Dic11C22×D412yes—
334Dic22—28no—
335Dic22—48no—
336Dic22—48no—
337Dic22—48no—
338Dic22—84no—
339C8×C11—22no—
340C8×C11C22×Q814yescomplemented
341C11⋊C8—22no—
342C11⋊C8—22no—
343C23×Q8—221no—
344C22×D8C2×D1111yescharacteristic
345#554—118no—
346#554—224no—
347D4×Q8—118no—
348D4×Q8—224no—
349C2×C4⋊Q8—111no—
350C2×C4⋊Q8—111no—
351C2×C4⋊Q8—111no—
352C2×C4⋊Q8—111no—
353C2×#125—111no—
354C2×#125—111no—
355C2×C22⋊Q8—221no—
356C2×C22⋊Q8—221no—
357C2×C22⋊Q8—221no—
358C2×C22⋊Q8—221no—
359C2×C22⋊Q8—221no—
360C2×C22⋊Q8—221no—
361C2×C4×Q8—111no—
362C2×C4×D4—111no—
363C2×C4×D4—111no—
364C2×C4×D4—111no—
365C2×C4×D4—111no—
366C2×C4×D4C2×D1111yescharacteristic
367C2×C4×D4C2×D1111yescharacteristic
368C22×C4⋊C4—221no—
369#501—118no—
370#501—118no—
371#498—118no—
372#478—118no—
373#478—118no—
374#476—118no—
375#476—118no—
376#476—118no—
377#474—118no—
378#446—118no—
379#442—118no—
380#442C2×D1118yes—
381C4×D8—118no—
382C2×#107—111no—
383C2×#107—111no—
384C2×#107—111no—
385C2×#106—111no—
386C2×#106—111no—
387C2×#106—111no—
388C2×#106—111no—
389C2×#106—111no—
390C2×#106C2×D1111yescharacteristic
391C2×C4⋊C8—111no—
392C2×C4⋊C8—111no—
393C2×C4⋊C8—111no—
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102C2×D1111yescharacteristic
399C2×#102C2×D1111yescharacteristic
400C2×#97—111no—
401C2×#97C2×D1111yescharacteristic
402C2×C4×C8—111no—
403C22×C11—24no—
404C22×C11—24no—
405C22×C11—48no—
406C22×C11—48no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11D4×Q812yes—
412C22×C11C2×AGL(1,ℤ/8)12yes—
413C22×C11#57712yes—
414C22×C11C23×D411yescharacteristic
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11D4×Q812yes—
420C4×C11C23×Q811yescharacteristic
421C4×C11C2×2−1+411yescharacteristic
422Dic11—22no—
423Dic11—22no—
424Dic11—22no—
425Dic11—42no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11C2×AGL(1,ℤ/8)14yes—
430C22×Q8—111no—
431C22×Q8—221no—
432C22×Q8—221no—
433C22×Q8—221no—
434C22×Q8—228no—
435C22×Q8—221no—
436C22×Q8—448no—
437C22×D4C22×D1111yescharacteristic
438C22×D4C22×D1111yescharacteristic
439C23×C4—21no—
440C23×C4—21no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4—221no—
444C23×C4—221no—
445C2×D8Dic2218yescomplemented
446C2×D8C22×D1114yes—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8C22×D1111yescharacteristic
450C22×C8C22×D1111yescharacteristic
451C4⋊Q8—114no—
452C4⋊Q8—114no—
453C4⋊Q8—114no—
454C4⋊Q8—114no—
455C4⋊Q8—222no—
456C4⋊Q8—222no—
457C4⋊Q8—222no—
458C4⋊Q8—222no—
459#125—114no—
460#125—114no—
461#125—222no—
462#125—222no—
463C22⋊Q8—228no—
464C22⋊Q8—228no—
465C22⋊Q8—228no—
466C22⋊Q8—228no—
467C22⋊Q8—228no—
468C22⋊Q8—228no—
469C4×Q8—114no—
470C4×Q8—114no—
471C4×D4—22no—
472C4×D4—22no—
473C4×D4—114no—
474C4×D4—114no—
475C4×D4—114no—
476C4×D4—114no—
477C4×D4—222no—
478C4×D4—222no—
479C4×D4—222no—
480C4×D4—222no—
481C4×D4C22×D1114yes—
482C4×D4C22×D1114yes—
483C2×C4⋊C4—111no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—228no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4—221no—
494C2×C4⋊C4—221no—
495C2×C4⋊C4—221no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—221no—
507C2×C42—111no—
508C2×C42—111no—
509C2×C42C22×D1111yescharacteristic
510#107—114no—
511#107—114no—
512#107—114no—
513#106—114no—
514#106—114no—
515#106—114no—
516#106—114no—
517#106—114no—
518#106C22×D1114yes—
519C4⋊C8—114no—
520C4⋊C8—114no—
521C4⋊C8—114no—
522#102—114no—
523#102—114no—
524#102—114no—
525#102—114no—
526#102C22×D1114yes—
527#102C22×D1114yes—
528#97—114no—
529#97C22×D1114yes—
530C4×C8—114no—
531C2×C11—44no—
532C2×C11—44no—
533C2×C11#338414yescomplemented
534C2×C11C2×D4×Q811yescharacteristic
535C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
536C2×C11C2×#57711yescharacteristic
537C24—21no—
538C24—21no—
539C2×Q8—114no—
540C2×Q8—224no—
541C2×Q8—224no—
542C2×Q8—224no—
543C2×Q8—224no—
544C2×Q8—224no—
545C2×Q8—444no—
546C2×Q8—444no—
547C2×Q8—444no—
548C2×Q8—4432no—
549C2×Q8—882no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—22no—
553C2×D4—22no—
554C2×D4C2×Dic2214yes—
555C2×D4C2×Dic2214yescomplemented
556C2×D4C23×D1112yes—
557C2×D4C23×D1112yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—24no—
561C22×C4—24no—
562C22×C4—44no—
563C22×C4—82no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—224no—
569C22×C4—224no—
570C22×C4—224no—
571C22×C4—224no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—444no—
577C22×C4—444no—
578C22×C4—444no—
579C22×C4—882no—
580C22×C4D4×D1111yescharacteristic
581C22×C4D4×D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583D8C2×Dic22116yescomplemented
584C2×C8—22no—
585C2×C8—112no—
586C2×C8—112no—
587C2×C8—222no—
588C2×C8—222no—
589C2×C8C2×Dic2214yescomplemented
590C2×C8C23×D1112yes—
591C2×C8C23×D1112yes—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—114no—
595C4⋊C4—114no—
596C4⋊C4—114no—
597C4⋊C4—112no—
598C4⋊C4—112no—
599C4⋊C4—112no—
600C4⋊C4—112no—
601C4⋊C4—224no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—224no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4—224no—
613C4⋊C4C23×D1112yes—
614C4⋊C4C23×D1112yes—
615C22⋊C4—24no—
616C22⋊C4—24no—
617C22⋊C4—224no—
618C22⋊C4—224no—
619C22⋊C4—224no—
620C22⋊C4—224no—
621C42—112no—
622C42—112no—
623C42—112no—
624C42—112no—
625C42D4×D1112yes—
626C42C23×D1112yes—
627C11C2×#338411yescharacteristic, complemented, Sylow
628C23—24no—
629C23—24no—
630C23—22no—
631C23—22no—
632C23—42no—
633C23—42no—
634C23—42no—
635C23—42no—
636C23C2×D4×D1111yescharacteristic
637Q8—228no—
638Q8—448no—
639Q8—448no—
640Q8—448no—
641Q8—884no—
642D4—24no—
643D4—24no—
644D4—22no—
645D4—22no—
646D4C22×Dic2214yes—
647D4C22×Dic2214yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—48no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—84no—
656C2×C4—114no—
657C2×C4—112no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—222no—
665C2×C4—222no—
666C2×C4—222no—
667C2×C4—222no—
668C2×C4—448no—
669C2×C4—448no—
670C2×C4—448no—
671C2×C4—442no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—884no—
676C2×C4C22×Dic2212yes—
677C2×C4C2×D4×D1112yes—
678C2×C4C2×D4×D1112yes—
679C2×C4C2×D4×D1111yescharacteristic
680C2×C4#6704312yes—
681C2×C4C24×D1111yescharacteristic
682C8—22no—
683C8—222no—
684C8—222no—
685C8C22×Dic2214yescomplemented
686C22—24no—
687C22—24no—
688C22—48no—
689C22—48no—
690C22—42no—
691C22—42no—
692C22—42no—
693C22—42no—
694C22D4×Dic2212yes—
695C22D11×AGL(1,ℤ/8)12yes—
696C22#1062330612yes—
697C22C22×D4×D1111yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—114no—
703C4—222no—
704C4—222no—
705C4—222no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4—442no—
710C4D4×Dic2212yes—
711C4C23×Dic2211yescharacteristic
712C4C2×#6704311yescharacteristic
713C2—44no—
714C2—44no—
715C2#1308151614yesdirect product factor
716C2C2×D4×Dic2211yescharacteristic
717C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
718C2C2×#1062330611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#442C2
socleC23×C11C22×D4
prime radicalC22×C11×D8C22
hypercenterC2×#442D11
hypocenterC11C2×#3384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#442

Complements

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

NH ≅ G/Ntype
1. C2×#10623070C2semidirect
2. C2×D4×Dic22C2semidirect
3. #13081516C2direct (N × H)
4. C2×#10622315C2semidirect
5. C2×#10622469C2semidirect
6. C2×#10622468C2semidirect
7. C2×#10622622C2semidirect
8. C2×#10622379C2semidirect
9. C2×#10622621C2semidirect
10. C2×#10622374C2semidirect
11. C2×#10622374C2semidirect
12. C2×#10622372C2semidirect
13. C2×#10622314C2semidirect
29. #10623070C22semidirect
31. D4×Dic22C22semidirect
62. #10622622C22semidirect
63. #10622621C22semidirect
69. #10622469C22semidirect
70. #10622468C22semidirect
71. #10622379C22semidirect
72. #10622374C22semidirect
73. #10622374C22semidirect
74. #10622372C22semidirect
75. #10622315C22semidirect
76. #10622314C22semidirect
92. C2×C11×D8Q8semidirect
186. C2×D4×C11C2×Q8semidirect
225. C11×D8C2×Q8semidirect
227. C2×C8×C11C2×Q8semidirect
299. D4×C11C22×Q8semidirect
340. C8×C11C22×Q8semidirect
445. C2×D8Dic22semidirect
533. C2×C11#3384semidirect
555. C2×D4C2×Dic22semidirect
583. D8C2×Dic22semidirect
589. C2×C8C2×Dic22semidirect
627. C11C2×#3384semidirect
647. D4C22×Dic22semidirect
685. C8C22×Dic22semidirect
715. C2#13081516direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230702
C2×D4×Dic222
#130815162
C2×#106223152
C2×#106224692
C2×#106224682
C2×#106226222
C2×#106223792
C2×#106226212
C2×#106223742
C2×#106223722
C2×#106223142
C2×#106227652
C2×D8×Dic112
C2×C11×#4422
C2×#338411