Finite Group Databasebeta

← C2×#13081510 #15634245

Subgroups — C2×#13081510 #15634245

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×#10623258C211yesmaximal, characteristic, complemented
3#13081510C2116yesmaximal, direct product factor
4C2×#10622469C211yesmaximal, characteristic, complemented
5C2×#10622693C211yesmaximal, characteristic, complemented
6C2×#10622468C211yesmaximal, characteristic, complemented
7C2×#10622460C211yesmaximal, characteristic, complemented
8C2×#10622484C211yesmaximal, characteristic, complemented
9C2×#10622483C211yesmaximal, characteristic, complemented
10C2×#10622374C211yesmaximal, characteristic, complemented
11C2×#10622372C211yesmaximal, characteristic, complemented
12C2×#10622441C211yesmaximal, characteristic, complemented
13C2×#10622627C211yesmaximal, characteristic
14C2×#10622398C211yesmaximal, characteristic
15C2×#10622369C211yesmaximal, characteristic
16C2×C11×#476C211yesmaximal, characteristic, complemented
17C22×Q8×D11—21no—
18C2×C11×C4⋊Q8C2211yescharacteristic
19C2×C4×D4×C11C2211yescharacteristic
20C2×#66999—21no—
21C2×D4×Dic11C2211yescharacteristic
22C2×D4×Dic11C2211yescharacteristic
23C22×#4323C2211yescharacteristic
24C2×#66977—21no—
25C22×Dic11⋊C4—21no—
26#10623258—24no—
27#10623258C2218yescomplemented
28#10623070—24no—
29#10623070C2218yescomplemented
30C2×#66949—21no—
31C2×#66949—21no—
32C2×#66946C2211yescharacteristic
33C2×#66946C2211yescharacteristic
34C2×#66943C2211yescharacteristic
35C2×#66941C2211yescharacteristic
36C2×#66941C2211yescharacteristic
37C2×#66941C2211yescharacteristic
38C2×#66931—21no—
39C2×#66931—21no—
40C2×C4×D44C2211yescharacteristic
41C2×#66923C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C11×#476C2218yescomplemented
44C2×C11×#106C2211yescharacteristic
45C2×C11×#106C2211yescharacteristic
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×#102C2211yescharacteristic
48C2×C11×#102C2211yescharacteristic
49C2×#66896C2211yescharacteristic
50C2×#66885C2211yescharacteristic
51C2×#66885C2211yescharacteristic
52C2×#66882C2211yescharacteristic
53C2×#66881C2211yescharacteristic
54C2×#66879C2211yescharacteristic
55C2×Dic11⋊C8C2211yescharacteristic
56C2×Dic11⋊C8C2211yescharacteristic
57C2×C8×Dic11C2211yescharacteristic
58#10622693C2218yescomplemented
59#10622627C2218yes—
60C2×#66873C2211yescharacteristic
61C2×#66872C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66871C2211yescharacteristic
65C2×#66871C2211yescharacteristic
66C2×#66867C2211yescharacteristic
67#10622484C2218yescomplemented
68#10622483C2218yescomplemented
69#10622469C2218yescomplemented
70#10622468C2218yescomplemented
71#10622460C2218yescomplemented
72#10622441C2218yescomplemented
73#10622398C2218yes—
74#10622374C2218yescomplemented
75#10622372C2218yescomplemented
76#10622369C2218yes—
77C22×Q8×C11—21no—
78C22×D4×C11C2311yescharacteristic
79C23×C4×C11—21no—
80C23×Dic11—21no—
81C23×Dic11—21no—
82C2×Q8×D11—28no—
83C2×Q8×D11—48no—
84C22×D44C2311yescharacteristic
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×Dic22—21no—
89C22×Dic22—21no—
90C22×Dic22—21no—
91C22×Dic22D411yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C11×C4⋊Q8—22no—
95C11×C4⋊Q8C2314yes—
96C4×D4×C11—22no—
97C4×D4×C11C2314yes—
98C2×C11×C4⋊C4—21no—
99C2×C11×C4⋊C4C2311yescharacteristic
100C2×C11×C4⋊C4C2311yescharacteristic
101C2×C11×C4⋊C4C2311yescharacteristic
102C2×C11×C22⋊C4—21no—
103C2×C42×C11C2311yescharacteristic
104C2×C22⋊Dic11—21no—
105C2×C22⋊Dic11—21no—
106#66999—28no—
107D4×Dic11—22no—
108D4×Dic11—22no—
109D4×Dic11C2314yes—
110D4×Dic11C2314yes—
111C2×#4323Q818yescomplemented
112C2×#4323C2314yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×C4⋊Dic11—21no—
117C2×C4⋊Dic11D411yescharacteristic
118C2×C4⋊Dic11C2311yescharacteristic
119C2×C4⋊Dic11C2311yescharacteristic
120C2×C4⋊Dic11C2311yescharacteristic
121#66977—28no—
122C2×Dic11⋊C4—21no—
123C2×Dic11⋊C4—21no—
124C2×Dic11⋊C4—21no—
125C2×Dic11⋊C4—21no—
126C2×Dic11⋊C4—21no—
127C2×Dic11⋊C4—21no—
128C2×Dic11⋊C4—28no—
129C2×Dic11⋊C4D411yescharacteristic
130C2×Dic11⋊C4D411yescharacteristic
131C2×C4×Dic11C2311yescharacteristic
132C2×C4×Dic11C2311yescharacteristic
133C22×C11⋊C8C2311yescharacteristic
134C22×C11⋊C8C2311yescharacteristic
135#66949—28no—
136#66949—28no—
137#66946—22no—
138#66946—22no—
139#66946C2314yes—
140#66946C2314yes—
141#66943—22no—
142#66943C2314yes—
143#66941—22no—
144#66941—22no—
145#66941—22no—
146#66941C2314yes—
147#66941C2314yes—
148#66941C2314yes—
149#66931—28no—
150#66931—28no—
151C4×D44—22no—
152C4×D44C2314yes—
153#66923—22no—
154#66923C2314yes—
155C4×Dic22D414yes—
156C4×Dic22C2314yes—
157C11×#106C2314yes—
158C11×#106C2314yes—
159C11×C4⋊C8C2314yes—
160C11×#102C2314yes—
161C11×#102C2314yes—
162#66896C2314yes—
163#66885C2314yes—
164#66885C2314yes—
165#66882C2314yes—
166#66881C2314yes—
167#66879C2314yes—
168Dic11⋊C8C2314yes—
169Dic11⋊C8C2314yes—
170C8×Dic11C2314yes—
171#66873C2314yes—
172#66872C2314yes—
173#66872C2314yes—
174#66872C2314yes—
175#66871C2314yes—
176#66871C2314yes—
177#66867C2314yes—
178C2×#3384—111nomaximal, Sylow
179C24×C11—21no—
180C23×D11—21no—
181C2×Q8×C11—24no—
182C2×Q8×C11—44no—
183C2×D4×C11—21no—
184C2×D4×C11—22no—
185C2×D4×C11C2×Q814yescomplemented
186C2×D4×C11C2412yes—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—24no—
191C22×C4×C11—82no—
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2411yescharacteristic
195C22×Dic11—24no—
196C22×Dic11—24no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—44no—
201C22×Dic11—82no—
202C22×Dic11C2×D411yescharacteristic
203C22×Dic11C2×D411yescharacteristic
204C22×Dic11C2×D411yescharacteristic
205C22×Dic11C2×D411yescharacteristic
206Q8×D11—432no—
207C2×D44—21no—
208C2×D44—22no—
209C2×D44C2×Q814yes—
210C2×D44C2412yes—
211C2×C4×D11—24no—
212C2×C4×D11—24no—
213C2×C4×D11—24no—
214C2×C4×D11—44no—
215C2×C4×D11—44no—
216C2×C4×D11—44no—
217C2×Dic22—24no—
218C2×Dic22—24no—
219C2×Dic22—24no—
220C2×Dic22—24no—
221C2×Dic22—44no—
222C2×Dic22—44no—
223C2×Dic22—82no—
224C2×Dic22C2×D414yes—
225C2×C8×C11—22no—
226C2×C8×C11—22no—
227C2×C8×C11C2412yes—
228C2×C8×C11C2412yes—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—24no—
233C11×C4⋊C4C2412yes—
234C11×C4⋊C4C2412yes—
235C11×C4⋊C4C2412yes—
236C11×C22⋊C4—24no—
237C42×C11C2×D412yes—
238C42×C11C2412yes—
239C22⋊Dic11—24no—
240C22⋊Dic11—24no—
241#4323C2×Q8116yescomplemented
242(C2×D11)⋊C4—24no—
243(C2×D11)⋊C4—24no—
244(C2×D11)⋊C4—24no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11—21no—
248C4⋊Dic11—21no—
249C4⋊Dic11C2×D414yes—
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⋊C8C2×Q814yescomplemented
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×#476D1111yescharacteristic, complemented
280C2×#474—111no—
281C2×#446—111no—
282C2×#442—111no—
283C2×#442—111no—
284C2×C4×D8—111no—
285C23×C11—24no—
286C23×C11—22no—
287C23×C11—42no—
288C23×C11—42no—
289C23×C11C22×D411yescharacteristic
290C22×D11—24no—
291C22×D11—22no—
292C22×D11—42no—
293C22×D11—42no—
294Q8×C11—48no—
295D4×C11—24no—
296D4×C11—22no—
297D4×C11C22×Q814yescomplemented
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—42no—
304C2×C4×C11—42no—
305C2×C4×C11—42no—
306C2×C4×C11—84no—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×Q812yes—
311C2×C4×C112−1+412yes—
312C2×C4×C11C2511yescharacteristic
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—42no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—48no—
323C2×Dic11—84no—
324C2×Dic11AGL(1,ℤ/8)14yes—
325C2×Dic11C22×D412yes—
326C2×Dic11C22×D412yes—
327C2×Dic11C22×D412yes—
328C2×Dic11C22×D412yes—
329D44—24no—
330D44—22no—
331D44C22×Q814yes—
332C4×D11—48no—
333C4×D11—48no—
334C4×D11—48no—
335Dic22—28no—
336Dic22—48no—
337Dic22—48no—
338Dic22—84no—
339C8×C11—22no—
340C8×C11—22no—
341C11⋊C8—22no—
342C11⋊C8C22×Q814yescomplemented
343C23×Q8—221no—
344C22×D8—111no—
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⋊Q8C2×D1111yescharacteristic
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×D4—111no—
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#476C2×D1118yescomplemented
377#474—118no—
378#446—118no—
379#442—118no—
380#442—118no—
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×#106C2×D1111yescharacteristic
390C2×#106C2×D1111yescharacteristic
391C2×C4⋊C8—111no—
392C2×C4⋊C8—111no—
393C2×C4⋊C8C2×D1111yescharacteristic
394C2×#102—111no—
395C2×#102—111no—
396C2×#102—111no—
397C2×#102—111no—
398C2×#102C2×D1111yescharacteristic
399C2×#102C2×D1111yescharacteristic
400C2×#97—111no—
401C2×#97—111no—
402C2×C4×C8—111no—
403C22×C11—24no—
404C22×C11—48no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11D4×Q812yes—
408C22×C11C2×AGL(1,ℤ/8)12yes—
409C22×C11#57712yes—
410C22×C11C23×D411yescharacteristic
411C2×D11—24no—
412C2×D11—48no—
413C2×D11—42no—
414C2×D11—42no—
415C4×C11—22no—
416C4×C11—22no—
417C4×C11—42no—
418C4×C11—42no—
419C4×C11—42no—
420C4×C11D4×Q812yes—
421C4×C11C23×Q811yescharacteristic
422C4×C11C2×2−1+411yescharacteristic
423Dic11—22no—
424Dic11—22no—
425Dic11—22no—
426Dic11—42no—
427Dic11—42no—
428Dic11—42no—
429Dic11C2×AGL(1,ℤ/8)14yes—
430C22×Q8—21no—
431C22×Q8—111no—
432C22×Q8—221no—
433C22×Q8—221no—
434C22×Q8—221no—
435C22×Q8—228no—
436C22×Q8—448no—
437C22×D4—111no—
438C22×D4C22×D1111yescharacteristic
439C23×C4—21no—
440C23×C4—221no—
441C23×C4—221no—
442C23×C4—221no—
443C23×C4—221no—
444C23×C4—221no—
445C2×D8—118no—
446C2×D8—114no—
447C22×C8—111no—
448C22×C8—111no—
449C22×C8C22×D1111yescharacteristic
450C22×C8C22×D1111yescharacteristic
451C4⋊Q8—22no—
452C4⋊Q8—114no—
453C4⋊Q8—114no—
454C4⋊Q8—114no—
455C4⋊Q8—222no—
456C4⋊Q8—222no—
457C4⋊Q8—222no—
458C4⋊Q8C22×D1114yes—
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—114no—
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×D4—222no—
482C4×D4C22×D1114yes—
483C2×C4⋊C4—21no—
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⋊C4C22×D1111yescharacteristic
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—221no—
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#106C22×D1114yes—
518#106C22×D1114yes—
519C4⋊C8—114no—
520C4⋊C8—114no—
521C4⋊C8C22×D1114yes—
522#102—114no—
523#102—114no—
524#102—114no—
525#102—114no—
526#102C22×D1114yes—
527#102C22×D1114yes—
528#97—114no—
529#97—114no—
530C4×C8—114no—
531C2×C11—44no—
532C2×C11#338414yescomplemented
533C2×C11C2×D4×Q811yescharacteristic
534C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
535C2×C11C2×#57711yescharacteristic
536D11—44no—
537C24—21no—
538C24—221no—
539C2×Q8—24no—
540C2×Q8—44no—
541C2×Q8—114no—
542C2×Q8—224no—
543C2×Q8—224no—
544C2×Q8—224no—
545C2×Q8—224no—
546C2×Q8—444no—
547C2×Q8—444no—
548C2×Q8—4432no—
549C2×Q8—882no—
550C2×D4—21no—
551C2×D4—22no—
552C2×D4—114no—
553C2×D4—112no—
554C2×D4—221no—
555C2×D4—222no—
556C2×D4Q8×D1114yescomplemented
557C2×D4C23×D1112yes—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—24no—
562C22×C4—82no—
563C22×C4—111no—
564C22×C4—111no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—224no—
568C22×C4—224no—
569C22×C4—224no—
570C22×C4—224no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—224no—
575C22×C4—444no—
576C22×C4—444no—
577C22×C4—444no—
578C22×C4—444no—
579C22×C4—882no—
580C22×C4D4×D1111yescharacteristic
581C22×C4D4×D1111yescharacteristic
582C22×C4C23×D1111yescharacteristic
583D8—1116no—
584C2×C8—22no—
585C2×C8—22no—
586C2×C8—114no—
587C2×C8—112no—
588C2×C8—112no—
589C2×C8—222no—
590C2×C8C23×D1112yes—
591C2×C8C23×D1112yes—
592C4⋊C4—24no—
593C4⋊C4—21no—
594C4⋊C4—21no—
595C4⋊C4—21no—
596C4⋊C4—114no—
597C4⋊C4—114no—
598C4⋊C4—114no—
599C4⋊C4—112no—
600C4⋊C4—112no—
601C4⋊C4—112no—
602C4⋊C4—224no—
603C4⋊C4—224no—
604C4⋊C4—224no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—224no—
611C4⋊C4—224no—
612C4⋊C4C23×D1112yes—
613C4⋊C4C23×D1112yes—
614C4⋊C4C23×D1112yes—
615C22⋊C4—24no—
616C22⋊C4—224no—
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—22no—
630C23—42no—
631C23—42no—
632C23—224no—
633C23—222no—
634C23—442no—
635C23—442no—
636C23C2×D4×D1111yescharacteristic
637Q8—48no—
638Q8—228no—
639Q8—448no—
640Q8—448no—
641Q8—884no—
642D4—24no—
643D4—22no—
644D4—114no—
645D4—224no—
646D4—222no—
647D4C2×Q8×D1114yescomplemented
648C2×C4—22no—
649C2×C4—22no—
650C2×C4—22no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—42no—
654C2×C4—42no—
655C2×C4—42no—
656C2×C4—84no—
657C2×C4—114no—
658C2×C4—112no—
659C2×C4—112no—
660C2×C4—112no—
661C2×C4—112no—
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—448no—
672C2×C4—442no—
673C2×C4—442no—
674C2×C4—442no—
675C2×C4—884no—
676C2×C4C2×D4×D1112yes—
677C2×C4C2×D4×D1112yes—
678C2×C4C2×D4×D1111yescharacteristic
679C2×C4C2×Q8×D1112yes—
680C2×C4#6704312yes—
681C2×C4C24×D1111yescharacteristic
682C8—22no—
683C8—22no—
684C8—114no—
685C8—222no—
686C22—24no—
687C22—48no—
688C22—42no—
689C22—42no—
690C22—224no—
691C22—448no—
692C22—442no—
693C22—442no—
694C22#1062316312yes—
695C22#1062329312yes—
696C22D11×AGL(1,ℤ/8)12yes—
697C22C22×D4×D1111yescharacteristic
698C4—22no—
699C4—22no—
700C4—42no—
701C4—42no—
702C4—42no—
703C4—114no—
704C4—222no—
705C4—222no—
706C4—222no—
707C4—442no—
708C4—442no—
709C4—442no—
710C4#1062316312yes—
711C4C22×Q8×D1111yescharacteristic
712C4C2×#6704311yescharacteristic
713C2—44no—
714C2—444no—
715C2#1308151014yesdirect product factor
716C2C2×#1062316311yescharacteristic
717C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
718C2C2×#1062329311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#476C2
socleC23×C11C22×D4
prime radicalC22×#4323C22
hypercenterC2×#476D11
hypocenterC11C2×#3384
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#476

Complements

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

NH ≅ G/Ntype
1. C2×#10623070C2semidirect
2. C2×#10623258C2semidirect
3. #13081510C2direct (N × H)
4. C2×#10622469C2semidirect
5. C2×#10622693C2semidirect
6. C2×#10622468C2semidirect
7. C2×#10622460C2semidirect
8. C2×#10622484C2semidirect
9. C2×#10622483C2semidirect
10. C2×#10622374C2semidirect
11. C2×#10622372C2semidirect
12. C2×#10622441C2semidirect
16. C2×C11×#476C2semidirect
27. #10623258C22semidirect
29. #10623070C22semidirect
43. C11×#476C22semidirect
58. #10622693C22semidirect
67. #10622484C22semidirect
68. #10622483C22semidirect
69. #10622469C22semidirect
70. #10622468C22semidirect
71. #10622460C22semidirect
72. #10622441C22semidirect
74. #10622374C22semidirect
75. #10622372C22semidirect
111. C2×#4323Q8semidirect
185. C2×D4×C11C2×Q8semidirect
241. #4323C2×Q8semidirect
266. C2×C11⋊C8C2×Q8semidirect
279. C2×#476D11semidirect
297. D4×C11C22×Q8semidirect
342. C11⋊C8C22×Q8semidirect
376. #476C2×D11semidirect
532. C2×C11#3384semidirect
556. C2×D4Q8×D11semidirect
627. C11C2×#3384semidirect
647. D4C2×Q8×D11semidirect
715. C2#13081510direct (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×#106232582
#130815102
C2×#106224692
C2×#106226932
C2×#106224682
C2×#106224602
C2×#106224842
C2×#106224832
C2×#106223742
C2×#106223722
C2×#106224412
C2×#106226272
C2×#106223982
C2×#106223692
C2×C11×#4762
C2×#338411