Finite Group Databasebeta

← C2×#13081371 #15633524

Subgroups — C2×#13081371 #15633524

Order 2816.

1950 conjugacy classes of subgroups.

The subgroup lattice has 748 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623116C211yesmaximal, characteristic, complemented
2C2×#10623110C211yesmaximal, characteristic, complemented
3#13081371C2116yesmaximal, direct product factor
4C2×#10622326C211yesmaximal, characteristic, complemented
5C2×#10622327C211yesmaximal, characteristic, complemented
6C2×#10622310C211yesmaximal, characteristic, complemented
7C2×#10622442C211yesmaximal, characteristic, complemented
8C2×#10622460C211yesmaximal, characteristic, complemented
9C2×#10622459C211yesmaximal, characteristic, complemented
10C2×#10622457C211yesmaximal, characteristic, complemented
11C2×#10622457C211yesmaximal, characteristic, complemented
12C2×#10622456C211yesmaximal, characteristic
13C2×#10622324C211yesmaximal, characteristic, complemented
14C2×#10622323C211yesmaximal, characteristic, complemented
15C2×C4×D88C211yesmaximal, characteristic, complemented
16C2×C11×#446C211yesmaximal, characteristic, complemented
17C2×C4×Q8×C11C2211yescharacteristic
18C2×#67000—21no—
19C2×#66999—21no—
20C22×D88C2211yescharacteristic
21C22×D88C2211yescharacteristic
22C22×#4314C2211yescharacteristic
23#10623116—24no—
24#10623116C2218yescomplemented
25#10623110—24no—
26#10623110C2218yescomplemented
27C2×#66949—21no—
28C2×#66949—21no—
29C2×#66947—21no—
30C2×#66947—21no—
31C2×#66946—21no—
32C2×C4⋊C4×D11—21no—
33C2×#66928C2211yescharacteristic
34C2×#66928C2211yescharacteristic
35C2×#66927C2211yescharacteristic
36C2×C4×D44C2211yescharacteristic
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×C4×D44C2211yescharacteristic
41C2×#66923C2211yescharacteristic
42C2×#66923C2211yescharacteristic
43C2×#66922C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C11×#446C2218yescomplemented
46C2×C11×C4⋊C8C2211yescharacteristic
47C2×C11×C4⋊C8C2211yescharacteristic
48C2×C11×C4⋊C8C2211yescharacteristic
49C2×C11×#97C2211yescharacteristic
50C2×C11×#97C2211yescharacteristic
51C2×C4×C8×C11C2211yescharacteristic
52C2×#66885C2211yescharacteristic
53C2×#66885C2211yescharacteristic
54C2×#66885C2211yescharacteristic
55C2×#66885C2211yescharacteristic
56C2×#66885C2211yescharacteristic
57C2×#66885C2211yescharacteristic
58C2×#66885C2211yescharacteristic
59C2×#66882C2211yescharacteristic
60C2×#66882C2211yescharacteristic
61C2×#66881C2211yescharacteristic
62C2×#66880C2211yescharacteristic
63C2×#66880C2211yescharacteristic
64C2×#66880C2211yescharacteristic
65#10622460C2218yescomplemented
66#10622459C2218yescomplemented
67#10622457C2218yescomplemented
68#10622457C2218yescomplemented
69#10622456C2218yes—
70#10622442C2218yescomplemented
71#10622327C2218yescomplemented
72#10622326C2218yescomplemented
73#10622324C2218yescomplemented
74#10622323C2218yescomplemented
75#10622310C2218yescomplemented
76C4×D88C2218yescomplemented
77C22×Q8×C11D411yescharacteristic
78C22×D44—21no—
79C22×D44—21no—
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×Dic22—21no—
89C22×Dic22C2311yescharacteristic
90C22×C8×C11C2311yescharacteristic
91C22×C8×C11C2311yescharacteristic
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C4×Q8×C11D414yes—
95C4×Q8×C11C2314yes—
96C2×C11×C4⋊C4D411yescharacteristic
97C2×C11×C4⋊C4D411yescharacteristic
98C2×C11×C4⋊C4D411yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C42×C11C2311yescharacteristic
101C2×C42×C11C2311yescharacteristic
102#67000—28no—
103#66999—28no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×(C2×D11)⋊C4—21no—
111C2×(C2×D11)⋊C4—21no—
112C2×(C2×D11)⋊C4—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4⋊Dic11C2311yescharacteristic
118C2×Dic11⋊C4—21no—
119C2×Dic11⋊C4—21no—
120C2×Dic11⋊C4—21no—
121C2×Dic11⋊C4—21no—
122C2×Dic11⋊C4—21no—
123C2×C4×Dic11—21no—
124C2×D88—24no—
125C2×D88—24no—
126C2×D88C2314yes—
127C2×D88C2314yes—
128C2×#4314—24no—
129C2×#4314C2314yes—
130#66949—28no—
131#66949—28no—
132#66947—28no—
133#66947—28no—
134#66946—28no—
135C4⋊C4×D11—28no—
136#66928—22no—
137#66928—22no—
138#66928C2314yes—
139#66928C2314yes—
140#66927—22no—
141#66927C2314yes—
142C4×D44—22no—
143C4×D44—22no—
144C4×D44—22no—
145C4×D44—22no—
146C4×D44—22no—
147C4×D44C2314yes—
148C4×D44C2314yes—
149C4×D44C2314yes—
150C4×D44C2314yes—
151C4×D44C2314yes—
152#66923—22no—
153#66923—22no—
154#66923C2314yes—
155#66923C2314yes—
156#66922—22no—
157#66922C2314yes—
158C4×Dic22—22no—
159C4×Dic22C2314yes—
160C11×C4⋊C8C2314yes—
161C11×C4⋊C8C2314yes—
162C11×C4⋊C8C2314yes—
163C11×#97C2314yes—
164C11×#97C2314yes—
165C4×C8×C11C2314yes—
166#66885C2314yes—
167#66885C2314yes—
168#66885C2314yes—
169#66885C2314yes—
170#66885C2314yes—
171#66885C2314yes—
172#66885C2314yes—
173#66882C2314yes—
174#66882C2314yes—
175#66881C2314yes—
176#66880C2314yes—
177#66880C2314yes—
178#66880C2314yes—
179C2×#3370—111nomaximal, Sylow
180C23×D11—21no—
181C23×D11—21no—
182C23×D11—21no—
183C2×Q8×C11—42no—
184C2×Q8×C11C2×D414yes—
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D411yescharacteristic
189C22×C4×C11C2×D411yescharacteristic
190C22×C4×C11C2×D411yescharacteristic
191C22×C4×C11C2411yescharacteristic
192C22×Dic11—21no—
193C22×Dic11—21no—
194C22×Dic11—21no—
195C22×Dic11—21no—
196C22×Dic11—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—24no—
201C2×D44—24no—
202C2×D44—22no—
203C2×D44—22no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44—22no—
207C2×D44—44no—
208C2×D44—82no—
209C2×D44#4114yes—
210C2×D44C2412yes—
211C2×D44C2412yes—
212C2×D44C2412yes—
213C2×C4×D11—24no—
214C2×C4×D11—24no—
215C2×C4×D11—24no—
216C2×C4×D11—24no—
217C2×C4×D11—24no—
218C2×C4×D11—44no—
219C2×C4×D11—82no—
220C2×C4×D11—82no—
221C2×C4×D11—82no—
222C2×C4×D11—82no—
223C2×Dic22—21no—
224C2×Dic22—24no—
225C2×Dic22—22no—
226C2×Dic22—22no—
227C2×Dic22—82no—
228C2×Dic22C2412yes—
229C2×C8×C11—22no—
230C2×C8×C11—22no—
231C2×C8×C11—22no—
232C2×C8×C11—22no—
233C2×C8×C11C2412yes—
234C2×C8×C11C2412yes—
235C2×C8×C11C2412yes—
236C2×C8×C11C2412yes—
237C11×C4⋊C4C2×D414yes—
238C11×C4⋊C4C2×D414yes—
239C11×C4⋊C4C2×D414yes—
240C42×C11C2×D412yes—
241C42×C11C2×D412yes—
242C42×C11C2×D412yes—
243C42×C11C2412yes—
244C42×C11C2412yes—
245C42×C11C2412yes—
246(C2×D11)⋊C4—24no—
247(C2×D11)⋊C4—24no—
248(C2×D11)⋊C4—24no—
249(C2×D11)⋊C4—24no—
250(C2×D11)⋊C4—24no—
251(C2×D11)⋊C4—24no—
252(C2×D11)⋊C4—24no—
253(C2×D11)⋊C4—24no—
254(C2×D11)⋊C4—24no—
255C4⋊Dic11—21no—
256C4⋊Dic11—21no—
257C4⋊Dic11—21no—
258C4⋊Dic11—24no—
259C4⋊Dic11—21no—
260C4⋊Dic11C2412yes—
261C4⋊Dic11C2412yes—
262C4⋊Dic11C2412yes—
263C4⋊Dic11C2412yes—
264Dic11⋊C4—24no—
265Dic11⋊C4—24no—
266Dic11⋊C4—24no—
267Dic11⋊C4—24no—
268Dic11⋊C4—24no—
269C4×Dic11—24no—
270D88—28no—
271D88—28no—
272#4314—28no—
273C2×#559—111no—
274C2×#554—111no—
275#3370—1116no—
276C2×#490—111no—
277C2×#489—111no—
278C2×#488—111no—
279C2×#479—111no—
280C2×#478—111no—
281C2×#474—111no—
282C2×#463—111no—
283C2×#463—111no—
284C2×#459—111no—
285C2×#446D1111yescharacteristic, complemented
286C2×#442—111no—
287C2×#440—111no—
288C2×C4×D8—111no—
289C23×C11C22×D411yescharacteristic
290C22×D11—24no—
291C22×D11—22no—
292C22×D11—22no—
293C22×D11—22no—
294C22×D11—42no—
295C22×D11—42no—
296C22×D11—42no—
297C22×D11—42no—
298C22×D11—42no—
299C22×D11—42no—
300C22×D11—42no—
301C22×D11—42no—
302Q8×C11—44no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—22no—
308C2×C4×C11—22no—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D411yescharacteristic
316C2×C4×C11C2×#4112yes—
317C2×C4×C112−1+412yes—
318C2×C4×C11C2511yescharacteristic
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—42no—
325C2×Dic11—42no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329D44—24no—
330D44—22no—
331D44—22no—
332D44—22no—
333D44—22no—
334D44—22no—
335D44—48no—
336D44—42no—
337D44—42no—
338D44—84no—
339D44C2×#4114yes—
340C4×D11—48no—
341C4×D11—84no—
342C4×D11—84no—
343C4×D11—84no—
344C4×D11—84no—
345Dic22—22no—
346Dic22—22no—
347Dic22—42no—
348Dic22—84no—
349C8×C11—22no—
350C8×C11—22no—
351C8×C11—22no—
352C8×C11—22no—
353C22×SD16—111no—
354C22×D8—111no—
355C22×D8—111no—
356#559—118no—
357#559—224no—
358#554—118no—
359#554—224no—
360C2×C4⋊Q8—111no—
361C2×#127—111no—
362C2×#125—111no—
363C2×#125—111no—
364C2×#124—111no—
365C2×#124—111no—
366C2×#124—221no—
367C2×#123—221no—
368C2×#123—221no—
369C2×C22⋊Q8—221no—
370C2×C22⋊Q8—221no—
371C2×C22⋊Q8—221no—
372C2×C4×Q8—111no—
373C2×C4×Q8C2×D1111yescharacteristic
374C2×C4×D4—111no—
375C2×C4×D4—111no—
376C2×C4×D4—111no—
377C2×C4×D4—111no—
378C2×C4×D4—111no—
379C2×C4×D4—221no—
380C22×C4⋊C4—221no—
381#490—118no—
382#489—118no—
383#488—118no—
384#479—118no—
385#478—118no—
386#474—118no—
387#463—118no—
388#463—118no—
389#459—118no—
390#446C2×D1118yescomplemented
391#442—118no—
392#440—118no—
393C4×D8—118no—
394C2×#107—111no—
395C2×#107—111no—
396C2×#106—111no—
397C2×C4⋊C8C2×D1111yescharacteristic
398C2×C4⋊C8C2×D1111yescharacteristic
399C2×C4⋊C8C2×D1111yescharacteristic
400C2×#103—111no—
401C2×#103—111no—
402C2×#103—111no—
403C2×#102—111no—
404C2×#102—111no—
405C2×#102—111no—
406C2×#102—111no—
407C2×#102—111no—
408C2×#102—111no—
409C2×#102—111no—
410C2×#97C2×D1111yescharacteristic
411C2×#97C2×D1111yescharacteristic
412C2×C4×C8C2×D1111yescharacteristic
413C22×C11#54812yes—
414C22×C11#57512yes—
415C22×C11#57612yes—
416C22×C11C23×D411yescharacteristic
417C2×D11—24no—
418C2×D11—48no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—42no—
427C2×D11—84no—
428C2×D11—84no—
429C4×C11—22no—
430C4×C11—22no—
431C4×C11—22no—
432C4×C11—22no—
433C4×C11—22no—
434C4×C11—22no—
435C4×C11#54812yes—
436C4×C11C22×#4111yescharacteristic
437C4×C11C2×2−1+411yescharacteristic
438Dic11—42no—
439Dic11—42no—
440Dic11—42no—
441Dic11—42no—
442Dic11—42no—
443C22×Q8—111no—
444C22×Q8—221no—
445C22×Q8D4411yescharacteristic
446C22×D4—111no—
447C22×D4—111no—
448C22×D4—111no—
449C22×D4—221no—
450C22×D4—221no—
451C23×C4—221no—
452C23×C4—221no—
453C23×C4—221no—
454C23×C4—221no—
455C23×C4—221no—
456C2×SD16—114no—
457C2×SD16—224no—
458C2×D8—114no—
459C2×D8—114no—
460C2×D8—224no—
461C2×D8—224no—
462C22×C8C22×D1111yescharacteristic
463C22×C8C22×D1111yescharacteristic
464C22×C8C22×D1111yescharacteristic
465C22×C8C22×D1111yescharacteristic
466C4⋊Q8—114no—
467C4⋊Q8—222no—
468#127—114no—
469#127—222no—
470#125—114no—
471#125—114no—
472#125—222no—
473#125—222no—
474#124—114no—
475#124—114no—
476#124—228no—
477#124—222no—
478#124—222no—
479#123—228no—
480#123—228no—
481C22⋊Q8—228no—
482C22⋊Q8—228no—
483C22⋊Q8—228no—
484C4×Q8—114no—
485C4×Q8—222no—
486C4×Q8D4414yes—
487C4×Q8C22×D1114yes—
488C4×D4—114no—
489C4×D4—114no—
490C4×D4—114no—
491C4×D4—114no—
492C4×D4—114no—
493C4×D4—228no—
494C4×D4—222no—
495C4×D4—222no—
496C4×D4—222no—
497C4×D4—222no—
498C4×D4—222no—
499C2×C4⋊C4—111no—
500C2×C4⋊C4—111no—
501C2×C4⋊C4—111no—
502C2×C4⋊C4—111no—
503C2×C4⋊C4—221no—
504C2×C4⋊C4—221no—
505C2×C4⋊C4—221no—
506C2×C4⋊C4—221no—
507C2×C4⋊C4—221no—
508C2×C4⋊C4—221no—
509C2×C4⋊C4—228no—
510C2×C4⋊C4D4411yescharacteristic
511C2×C4⋊C4D4411yescharacteristic
512C2×C4⋊C4D4411yescharacteristic
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—221no—
516C2×C22⋊C4—221no—
517C2×C22⋊C4—221no—
518C2×C22⋊C4—221no—
519C2×C22⋊C4—221no—
520C2×C22⋊C4—221no—
521C2×C22⋊C4—221no—
522C2×C42—221no—
523C2×C42C22×D1111yescharacteristic
524C2×C42C22×D1111yescharacteristic
525C2×C42C22×D1111yescharacteristic
526#107—114no—
527#107—114no—
528#106—114no—
529C4⋊C8C22×D1114yes—
530C4⋊C8C22×D1114yes—
531C4⋊C8C22×D1114yes—
532#103—114no—
533#103—114no—
534#103—114no—
535#102—114no—
536#102—114no—
537#102—114no—
538#102—114no—
539#102—114no—
540#102—114no—
541#102—114no—
542#97C22×D1114yes—
543#97C22×D1114yes—
544C4×C8C22×D1114yes—
545C2×C11#337014yescomplemented
546C2×C11C2×#54811yescharacteristic
547C2×C11C2×#57511yescharacteristic
548C2×C11C2×#57611yescharacteristic
549D11—44no—
550D11—82no—
551D11—82no—
552C24—221no—
553C24—221no—
554C24—221no—
555C2×Q8—42no—
556C2×Q8—112no—
557C2×Q8—221no—
558C2×Q8—224no—
559C2×Q8—222no—
560C2×Q8—222no—
561C2×Q8—882no—
562C2×Q8C2×D4414yes—
563C2×D4—114no—
564C2×D4—112no—
565C2×D4—112no—
566C2×D4—112no—
567C2×D4—221no—
568C2×D4—224no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—224no—
572C2×D4—222no—
573C2×D4—222no—
574C2×D4—222no—
575C2×D4—222no—
576C2×D4—222no—
577C2×D4—444no—
578C2×D4—882no—
579C22×C4—221no—
580C22×C4—221no—
581C22×C4—221no—
582C22×C4—221no—
583C22×C4—221no—
584C22×C4—224no—
585C22×C4—224no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—224no—
589C22×C4—444no—
590C22×C4—882no—
591C22×C4—882no—
592C22×C4—882no—
593C22×C4—882no—
594C22×C4C2×D4411yescharacteristic
595C22×C4C2×D4411yescharacteristic
596C22×C4C2×D4411yescharacteristic
597C22×C4C2×D4411yescharacteristic
598C22×C4C2×D4411yescharacteristic
599C22×C4C2×D4411yescharacteristic
600C22×C4C23×D1111yescharacteristic
601SD16—228no—
602D8—228no—
603D8—228no—
604C2×C8—22no—
605C2×C8—22no—
606C2×C8—22no—
607C2×C8—22no—
608C2×C8C23×D1112yes—
609C2×C8C23×D1112yes—
610C2×C8C23×D1112yes—
611C2×C8C23×D1112yes—
612C4⋊C4—112no—
613C4⋊C4—112no—
614C4⋊C4—112no—
615C4⋊C4—112no—
616C4⋊C4—221no—
617C4⋊C4—221no—
618C4⋊C4—221no—
619C4⋊C4—221no—
620C4⋊C4—224no—
621C4⋊C4—224no—
622C4⋊C4—224no—
623C4⋊C4—224no—
624C4⋊C4—224no—
625C4⋊C4—224no—
626C4⋊C4C2×D4414yes—
627C4⋊C4C2×D4414yes—
628C4⋊C4C2×D4414yes—
629C22⋊C4—224no—
630C22⋊C4—224no—
631C22⋊C4—224no—
632C22⋊C4—224no—
633C22⋊C4—224no—
634C22⋊C4—224no—
635C22⋊C4—224no—
636C22⋊C4—224no—
637C22⋊C4—224no—
638C42—224no—
639C42C2×D4412yes—
640C42C2×D4412yes—
641C42C2×D4412yes—
642C42C23×D1112yes—
643C42C23×D1112yes—
644C42C23×D1112yes—
645C11C2×#337011yescharacteristic, complemented, Sylow
646C23—224no—
647C23—222no—
648C23—222no—
649C23—222no—
650C23—442no—
651C23—442no—
652C23—442no—
653C23—442no—
654C23—442no—
655C23—442no—
656C23—442no—
657C23—442no—
658C23C22×D4411yescharacteristic
659Q8—44no—
660Q8—222no—
661Q8—222no—
662Q8—442no—
663Q8—884no—
664D4—114no—
665D4—224no—
666D4—222no—
667D4—222no—
668D4—222no—
669D4—222no—
670D4—222no—
671D4—448no—
672D4—442no—
673D4—442no—
674D4—884no—
675C2×C4—22no—
676C2×C4—22no—
677C2×C4—22no—
678C2×C4—22no—
679C2×C4—22no—
680C2×C4—22no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—222no—
686C2×C4—448no—
687C2×C4—442no—
688C2×C4—442no—
689C2×C4—442no—
690C2×C4—442no—
691C2×C4—442no—
692C2×C4—884no—
693C2×C4—884no—
694C2×C4—884no—
695C2×C4—884no—
696C2×C4C22×D4412yes—
697C2×C4C22×D4412yes—
698C2×C4C22×D4412yes—
699C2×C4C22×D4412yes—
700C2×C4C22×D4412yes—
701C2×C4C22×D4412yes—
702C2×C4C22×D4411yescharacteristic
703C2×C4#6704012yes—
704C2×C4#41×D1112yes—
705C2×C4C24×D1111yescharacteristic
706C8—22no—
707C8—22no—
708C8—22no—
709C8—22no—
710C22—224no—
711C22—448no—
712C22—442no—
713C22—442no—
714C22—442no—
715C22—442no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—884no—
721C22—884no—
722C22#1062310712yes—
723C22#1062327912yes—
724C22#1062328312yes—
725C22C23×D4411yescharacteristic
726C4—22no—
727C4—22no—
728C4—22no—
729C4—22no—
730C4—22no—
731C4—22no—
732C4—442no—
733C4—442no—
734C4—442no—
735C4—442no—
736C4—442no—
737C4#1062310712yes—
738C4C2×#6704011yescharacteristic
739C4C2×#41×D1111yescharacteristic
740C2—444no—
741C2—882no—
742C2—882no—
743C2#1308137114yesdirect product factor
744C2C2×#1062310711yescharacteristic
745C2C2×#1062327911yescharacteristic
746C2C2×#1062328311yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#446C2
socleC23×C11C22×D4
prime radicalC2×#10622456C2
hypercenterC2×#446D11
hypocenterC11C2×#3370
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#446

Complements

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

NH ≅ G/Ntype
1. C2×#10623116C2semidirect
2. C2×#10623110C2semidirect
3. #13081371C2direct (N × H)
4. C2×#10622326C2semidirect
5. C2×#10622327C2semidirect
6. C2×#10622310C2semidirect
7. C2×#10622442C2semidirect
8. C2×#10622460C2semidirect
9. C2×#10622459C2semidirect
10. C2×#10622457C2semidirect
11. C2×#10622457C2semidirect
13. C2×#10622324C2semidirect
14. C2×#10622323C2semidirect
15. C2×C4×D88C2semidirect
16. C2×C11×#446C2semidirect
24. #10623116C22semidirect
26. #10623110C22semidirect
45. C11×#446C22semidirect
65. #10622460C22semidirect
66. #10622459C22semidirect
67. #10622457C22semidirect
68. #10622457C22semidirect
70. #10622442C22semidirect
71. #10622327C22semidirect
72. #10622326C22semidirect
73. #10622324C22semidirect
74. #10622323C22semidirect
75. #10622310C22semidirect
76. C4×D88C22semidirect
285. C2×#446D11semidirect
390. #446C2×D11semidirect
545. C2×C11#3370semidirect
645. C11C2×#3370semidirect
743. C2#13081371direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231162
C2×#106231102
#130813712
C2×#106223262
C2×#106223272
C2×#106223102
C2×#106224422
C2×#106224602
C2×#106224592
C2×#106224572
C2×#106224562
C2×#106223242
C2×#106223232
C2×C4×D882
C2×C11×#4462
C2×#337011