Finite Group Databasebeta

← C2×#13081452 #15633564

Subgroups — C2×#13081452 #15633564

Order 2816.

1810 conjugacy classes of subgroups.

The subgroup lattice has 700 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623098C211yesmaximal, characteristic, complemented
2#13081452C2116yesmaximal, direct product factor
3C2×#10622695C211yesmaximal, characteristic, complemented
4C2×#10622668C211yesmaximal, characteristic
5C2×#10622669C211yesmaximal, characteristic
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622634C211yesmaximal, characteristic, complemented
8C2×#10622622C211yesmaximal, characteristic
9C2×#10622667C211yesmaximal, characteristic
10C2×#10622667C211yesmaximal, characteristic
11C2×#10622703C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622643C211yesmaximal, characteristic, complemented
14C2×#10622631C211yesmaximal, characteristic
15C2×C4×#4326C211yesmaximal, characteristic, complemented
16C2×C11×#556C211yesmaximal, characteristic
17C11×#556—24no—
18C11×#556C2218yes—
19C2×C11×C4⋊Q8C2211yescharacteristic
20C2×C11×#126—21no—
21C2×C11×#126—21no—
22C2×C11×#124C2211yescharacteristic
23C2×C11×#124C2211yescharacteristic
24C2×C11×C22⋊Q8—21no—
25C2×C4×Q8×C11C2211yescharacteristic
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×D4×C11C2211yescharacteristic
29C2×C11×#117—21no—
30C2×#66997—21no—
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4324C2211yescharacteristic
34#10623098—24no—
35#10623098C2218yescomplemented
36C2×#66942—21no—
37C2×#66942—21no—
38C2×#66940—21no—
39C2×#66923C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C2×#66922C2211yescharacteristic
42C2×C4×Dic22C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46C2×#66899C2211yescharacteristic
47C2×#66899C2211yescharacteristic
48C2×#66899C2211yescharacteristic
49C2×#66899C2211yescharacteristic
50C2×#66899C2211yescharacteristic
51C2×#66896C2211yescharacteristic
52C2×#66896C2211yescharacteristic
53C2×#66896C2211yescharacteristic
54#10622703C2218yescomplemented
55#10622695C2218yescomplemented
56#10622669C2218yes—
57#10622668C2218yes—
58#10622667C2218yes—
59#10622667C2218yes—
60#10622643C2218yescomplemented
61C4×#4326C2218yescomplemented
62#10622637C2218yescomplemented
63#10622635C2218yescomplemented
64#10622634C2218yescomplemented
65#10622631C2218yes—
66#10622622C2218yes—
67C2×#66874C2211yescharacteristic
68C2×#66872C2211yescharacteristic
69C2×#66871C2211yescharacteristic
70C2×#66871C2211yescharacteristic
71C2×C4⋊(C11⋊C8)C2211yescharacteristic
72C2×C4⋊(C11⋊C8)C2211yescharacteristic
73C2×C4⋊(C11⋊C8)C2211yescharacteristic
74C2×#66867C2211yescharacteristic
75C2×#66867C2211yescharacteristic
76C2×C4×C11⋊C8C2211yescharacteristic
77C22×Q8×C11D411yescharacteristic
78C22×Q8×C11C2311yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11C2311yescharacteristic
81C23×C4×C11—21no—
82C22×Dic22—21no—
83C22×Dic22C2311yescharacteristic
84C11×C4⋊Q8—22no—
85C11×C4⋊Q8C2314yes—
86C11×#126—28no—
87C11×#126—28no—
88C11×#124—22no—
89C11×#124—22no—
90C11×#124C2314yes—
91C11×#124C2314yes—
92C11×C22⋊Q8—28no—
93C4×Q8×C11—22no—
94C4×Q8×C11—22no—
95C4×Q8×C11D414yes—
96C4×Q8×C11C2314yes—
97C4×Q8×C11C2314yes—
98C4×Q8×C11C2314yes—
99C4×D4×C11—22no—
100C4×D4×C11C2314yes—
101C11×#117—28no—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4D411yescharacteristic
107C2×C11×C4⋊C4D411yescharacteristic
108C2×C11×C4⋊C4D411yescharacteristic
109C2×C11×C4⋊C4C2311yescharacteristic
110C2×C11×C22⋊C4—21no—
111C2×C11×C22⋊C4—21no—
112C2×C11×C22⋊C4—21no—
113C2×C11×C22⋊C4—21no—
114C2×C11×C22⋊C4—21no—
115C2×C42×C11—21no—
116C2×C42×C11—21no—
117C2×C42×C11C2311yescharacteristic
118C2×C42×C11C2311yescharacteristic
119C2×C42×C11C2311yescharacteristic
120#66997—28no—
121C2×#4326—24no—
122C2×#4326—24no—
123C2×#4326C2314yes—
124C2×#4326C2314yes—
125C2×#4324—24no—
126C2×#4324C2314yes—
127C2×C4⋊Dic11—21no—
128C2×C4⋊Dic11C2311yescharacteristic
129C2×C4⋊Dic11C2311yescharacteristic
130C2×C4⋊Dic11C2311yescharacteristic
131C2×Dic11⋊C4—21no—
132C2×Dic11⋊C4—21no—
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C2×Dic11⋊C4—21no—
138C2×C4×Dic11—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145#66942—28no—
146#66942—28no—
147#66940—28no—
148#66923—22no—
149#66923—22no—
150#66923C2314yes—
151#66923C2314yes—
152#66922—22no—
153#66922C2314yes—
154C4×Dic22—22no—
155C4×Dic22—22no—
156C4×Dic22—22no—
157C4×Dic22C2314yes—
158C4×Dic22C2314yes—
159C4×Dic22C2314yes—
160#66899C2314yes—
161#66899C2314yes—
162#66899C2314yes—
163#66899C2314yes—
164#66899C2314yes—
165#66899C2314yes—
166#66896C2314yes—
167#66896C2314yes—
168#66896C2314yes—
169#66874C2314yes—
170#66872C2314yes—
171#66871C2314yes—
172#66871C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174C4⋊(C11⋊C8)C2314yes—
175C4⋊(C11⋊C8)C2314yes—
176#66867C2314yes—
177#66867C2314yes—
178C4×C11⋊C8C2314yes—
179C2×#3377—111nomaximal, Sylow
180C24×C11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—21no—
183C2×Q8×C11—22no—
184C2×Q8×C11—22no—
185C2×Q8×C11—22no—
186C2×Q8×C11—22no—
187C2×Q8×C11—42no—
188C2×Q8×C11C2×D414yes—
189C2×Q8×C11C2412yes—
190C2×Q8×C11C2412yes—
191C2×D4×C11—21no—
192C2×D4×C11—22no—
193C2×D4×C11—22no—
194C2×D4×C11C2412yes—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11—21no—
198C22×C4×C11—24no—
199C22×C4×C11—44no—
200C22×C4×C11C2×D411yescharacteristic
201C22×C4×C11C2×D411yescharacteristic
202C22×C4×C11C2×D411yescharacteristic
203C22×C4×C11C2×D411yescharacteristic
204C22×C4×C11C2×D411yescharacteristic
205C22×C4×C11C2×D411yescharacteristic
206C22×C4×C11C2411yescharacteristic
207C22×Dic11—21no—
208C22×Dic11—21no—
209C22×Dic11—21no—
210C22×Dic11—21no—
211C2×Dic22—21no—
212C2×Dic22—24no—
213C2×Dic22—22no—
214C2×Dic22—44no—
215C2×Dic22#4114yes—
216C2×Dic22C2412yes—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4C2×D414yes—
223C11×C4⋊C4C2×D414yes—
224C11×C4⋊C4C2×D414yes—
225C11×C4⋊C4C2412yes—
226C11×C22⋊C4—24no—
227C11×C22⋊C4—24no—
228C11×C22⋊C4—24no—
229C11×C22⋊C4—24no—
230C11×C22⋊C4—24no—
231C42×C11—24no—
232C42×C11—24no—
233C42×C11C2×D412yes—
234C42×C11C2×D412yes—
235C42×C11C2×D412yes—
236C42×C11C2412yes—
237C42×C11C2412yes—
238C42×C11C2412yes—
239#4326—28no—
240#4326—28no—
241#4324—28no—
242C4⋊Dic11—21no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—24no—
246C4⋊Dic11C2412yes—
247C4⋊Dic11C2412yes—
248C4⋊Dic11C2412yes—
249Dic11⋊C4—24no—
250Dic11⋊C4—24no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254Dic11⋊C4—24no—
255Dic11⋊C4—24no—
256C4×Dic11—24no—
257C4×Dic11—24no—
258C4×Dic11—24no—
259C2×C11⋊C8—22no—
260C2×C11⋊C8—22no—
261C2×C11⋊C8—22no—
262C2×C11⋊C8—22no—
263C2×C11⋊C8C2412yes—
264C2×C11⋊C8C2412yes—
265C2×C11⋊C8C2412yes—
266C2×C11⋊C8C2412yes—
267C2×#557—111no—
268C2×#556D1111yescharacteristic
269#3377—1116no—
270C2×#491—111no—
271C2×#489—111no—
272C2×#488—111no—
273C2×#479—111no—
274C2×#477—111no—
275C2×#478—111no—
276C2×#464—111no—
277C2×#464—111no—
278C2×#462—111no—
279C2×#446—111no—
280C2×#441—111no—
281C2×#440—111no—
282C2×C4×Q16—111no—
283C23×C11—22no—
284C23×C11—42no—
285C23×C11—42no—
286C23×C11—42no—
287C23×C11C22×D411yescharacteristic
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—22no—
291Q8×C11—22no—
292Q8×C11—44no—
293Q8×C11—42no—
294Q8×C11—42no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—42no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—22no—
307C2×C4×C11—48no—
308C2×C4×C11—42no—
309C2×C4×C11—42no—
310C2×C4×C11—42no—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D412yes—
314C2×C4×C11C22×D412yes—
315C2×C4×C11C22×D412yes—
316C2×C4×C11C22×D412yes—
317C2×C4×C11C22×D411yescharacteristic
318C2×C4×C11C2×#4112yes—
319C2×C4×C112−1+412yes—
320C2×C4×C11C2511yescharacteristic
321C2×Dic11—24no—
322C2×Dic11—22no—
323C2×Dic11—22no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—42no—
327C2×Dic11—42no—
328C2×Dic11—42no—
329Dic22—24no—
330Dic22—22no—
331Dic22—48no—
332Dic22C2×#4114yes—
333C11⋊C8—22no—
334C11⋊C8—22no—
335C11⋊C8—22no—
336C11⋊C8—22no—
337C22×Q16—111no—
338C22×Q16—111no—
339C22×SD16—111no—
340#557—118no—
341#557—224no—
342#556—24no—
343#556C2×D1118yes—
344C2×C4⋊Q8—111no—
345C2×C4⋊Q8—221no—
346C2×C4⋊Q8C2×D1111yescharacteristic
347C2×#126—21no—
348C2×#126—21no—
349C2×#125—111no—
350C2×#125—111no—
351C2×#125—221no—
352C2×#125—221no—
353C2×#124C2×D1111yescharacteristic
354C2×#124C2×D1111yescharacteristic
355C2×C22⋊Q8—21no—
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×Q8—111no—
359C2×C4×Q8—221no—
360C2×C4×Q8C2×D1111yescharacteristic
361C2×C4×Q8C2×D1111yescharacteristic
362C2×C4×Q8C2×D1111yescharacteristic
363C2×C4×D4C2×D1111yescharacteristic
364C2×#117—21no—
365#491—118no—
366#489—118no—
367#488—118no—
368#479—118no—
369#478—118no—
370#477—118no—
371#464—118no—
372#464—118no—
373#462—118no—
374#446—118no—
375#441—118no—
376#440—118no—
377C4×Q16—118no—
378C2×#107—111no—
379C2×#107—111no—
380C2×#106—111no—
381C2×C4⋊C8—111no—
382C2×C4⋊C8—111no—
383C2×C4⋊C8—111no—
384C2×#103—111no—
385C2×#103—111no—
386C2×#103—111no—
387C2×#103—111no—
388C2×#103—111no—
389C2×#103—111no—
390C2×#103—111no—
391C2×#102—111no—
392C2×#102—111no—
393C2×#102—111no—
394C2×#97—111no—
395C2×#97—111no—
396C2×C4×C8—111no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—84no—
401C22×C11#54812yes—
402C22×C11#57512yes—
403C22×C11#57812yes—
404C22×C11C23×D411yescharacteristic
405C4×C11—22no—
406C4×C11—22no—
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11#54812yes—
415C4×C11C22×#4111yescharacteristic
416C4×C11C2×2−1+411yescharacteristic
417Dic11—24no—
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421C22×Q8—111no—
422C22×Q8—221no—
423C22×Q8C22⋊D1111yescharacteristic
424C22×Q8C22×D1111yescharacteristic
425C22×Q8C22×D1111yescharacteristic
426C22×D4C22×D1111yescharacteristic
427C23×C4—21no—
428C2×Q16—114no—
429C2×Q16—114no—
430C2×Q16—224no—
431C2×Q16—224no—
432C2×SD16—114no—
433C2×SD16—224no—
434C22×C8—111no—
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—111no—
438C4⋊Q8—22no—
439C4⋊Q8—114no—
440C4⋊Q8—228no—
441C4⋊Q8—222no—
442C4⋊Q8C22×D1114yes—
443#126—28no—
444#126—28no—
445#125—114no—
446#125—114no—
447#125—228no—
448#125—228no—
449#125—222no—
450#125—222no—
451#124—22no—
452#124—22no—
453#124C22×D1114yes—
454#124C22×D1114yes—
455C22⋊Q8—28no—
456C4×Q8—22no—
457C4×Q8—22no—
458C4×Q8—114no—
459C4×Q8—114no—
460C4×Q8—114no—
461C4×Q8—228no—
462C4×Q8—222no—
463C4×Q8—222no—
464C4×Q8—222no—
465C4×Q8C22⋊D1114yes—
466C4×Q8C22×D1114yes—
467C4×Q8C22×D1114yes—
468C4×Q8C22×D1114yes—
469C4×D4—22no—
470C4×D4C22×D1114yes—
471#117—28no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—111no—
477C2×C4⋊C4—111no—
478C2×C4⋊C4—111no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4—221no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4C22⋊D1111yescharacteristic
488C2×C4⋊C4C22⋊D1111yescharacteristic
489C2×C4⋊C4C22⋊D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—21no—
494C2×C22⋊C4—21no—
495C2×C22⋊C4—21no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—221no—
499C2×C42—221no—
500C2×C42—221no—
501C2×C42C22×D1111yescharacteristic
502C2×C42C22×D1111yescharacteristic
503C2×C42C22×D1111yescharacteristic
504#107—114no—
505#107—114no—
506#106—114no—
507C4⋊C8—114no—
508C4⋊C8—114no—
509C4⋊C8—114no—
510#103—114no—
511#103—114no—
512#103—114no—
513#103—114no—
514#103—114no—
515#103—114no—
516#103—114no—
517#102—114no—
518#102—114no—
519#102—114no—
520#97—114no—
521#97—114no—
522C4×C8—114no—
523C2×C11—82no—
524C2×C11#337714yescomplemented
525C2×C11C2×#54811yescharacteristic
526C2×C11C2×#57511yescharacteristic
527C2×C11C2×#57811yescharacteristic
528C24—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—22no—
532C2×Q8—22no—
533C2×Q8—22no—
534C2×Q8—22no—
535C2×Q8—42no—
536C2×Q8—114no—
537C2×Q8—112no—
538C2×Q8—222no—
539C2×Q8—221no—
540C2×Q8—224no—
541C2×Q8—444no—
542C2×Q8C2×C22⋊D1114yes—
543C2×Q8C23×D1112yes—
544C2×Q8C23×D1112yes—
545C2×D4—22no—
546C2×D4—22no—
547C2×D4—21no—
548C2×D4C23×D1112yes—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—24no—
553C22×C4—44no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C2×C22⋊D1111yescharacteristic
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C2×C22⋊D1111yescharacteristic
562C22×C4C2×C22⋊D1111yescharacteristic
563C22×C4C2×C22⋊D1111yescharacteristic
564C22×C4C23×D1111yescharacteristic
565Q16—228no—
566Q16—228no—
567SD16—228no—
568C2×C8—112no—
569C2×C8—112no—
570C2×C8—112no—
571C2×C8—112no—
572C2×C8—222no—
573C2×C8—222no—
574C2×C8—222no—
575C2×C8—222no—
576C4⋊C4—24no—
577C4⋊C4—24no—
578C4⋊C4—24no—
579C4⋊C4—24no—
580C4⋊C4—21no—
581C4⋊C4—112no—
582C4⋊C4—112no—
583C4⋊C4—112no—
584C4⋊C4—221no—
585C4⋊C4—221no—
586C4⋊C4—221no—
587C4⋊C4—224no—
588C4⋊C4—224no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—224no—
595C4⋊C4C2×C22⋊D1114yes—
596C4⋊C4C2×C22⋊D1114yes—
597C4⋊C4C2×C22⋊D1114yes—
598C4⋊C4C23×D1112yes—
599C22⋊C4—24no—
600C22⋊C4—24no—
601C22⋊C4—24no—
602C22⋊C4—24no—
603C22⋊C4—24no—
604C42—24no—
605C42—24no—
606C42—224no—
607C42—224no—
608C42—224no—
609C42C2×C22⋊D1112yes—
610C42C2×C22⋊D1112yes—
611C42C2×C22⋊D1112yes—
612C42C23×D1112yes—
613C42C23×D1112yes—
614C42C23×D1112yes—
615C11C2×#337711yescharacteristic, complemented, Sylow
616C23—22no—
617C23—42no—
618C23—42no—
619C23—42no—
620C23C22×C22⋊D1111yescharacteristic
621Q8—22no—
622Q8—22no—
623Q8—22no—
624Q8—22no—
625Q8—44no—
626Q8—42no—
627Q8—42no—
628Q8—114no—
629Q8—224no—
630Q8—222no—
631Q8—448no—
632D4—22no—
633D4—22no—
634D4—42no—
635C2×C4—22no—
636C2×C4—22no—
637C2×C4—22no—
638C2×C4—22no—
639C2×C4—22no—
640C2×C4—22no—
641C2×C4—22no—
642C2×C4—22no—
643C2×C4—22no—
644C2×C4—48no—
645C2×C4—42no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—224no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—222no—
653C2×C4—442no—
654C2×C4—442no—
655C2×C4—442no—
656C2×C4#41×D1112yes—
657C2×C4#6704312yes—
658C2×C4C22×C22⋊D1112yes—
659C2×C4C22×C22⋊D1112yes—
660C2×C4C22×C22⋊D1112yes—
661C2×C4C22×C22⋊D1112yes—
662C2×C4C22×C22⋊D1112yes—
663C2×C4C22×C22⋊D1112yes—
664C2×C4C22×C22⋊D1111yescharacteristic
665C2×C4C24×D1111yescharacteristic
666C8—222no—
667C8—222no—
668C8—222no—
669C8—222no—
670C22—42no—
671C22—42no—
672C22—42no—
673C22—84no—
674C22#1062335312yes—
675C22#1062336212yes—
676C22#1062336912yes—
677C22C23×C22⋊D1111yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—22no—
682C4—22no—
683C4—22no—
684C4—42no—
685C4—42no—
686C4—42no—
687C4—224no—
688C4—442no—
689C4—442no—
690C4—442no—
691C4#1062336212yes—
692C4C2×#41×D1111yescharacteristic
693C4C2×#6704311yescharacteristic
694C2—82no—
695C2#1308145214yesdirect product factor
696C2C2×#1062336211yescharacteristic
697C2C2×#1062335311yescharacteristic
698C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#556C2
socleC23×C11C22×D4
prime radicalC22×D4×C11C23
hypercenterC2×#556D11
hypocenterC11C2×#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623098C2semidirect
2. #13081452C2direct (N × H)
3. C2×#10622695C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622634C2semidirect
11. C2×#10622703C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622643C2semidirect
15. C2×C4×#4326C2semidirect
35. #10623098C22semidirect
54. #10622703C22semidirect
55. #10622695C22semidirect
60. #10622643C22semidirect
61. C4×#4326C22semidirect
62. #10622637C22semidirect
63. #10622635C22semidirect
64. #10622634C22semidirect
524. C2×C11#3377semidirect
615. C11C2×#3377semidirect
695. C2#13081452direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230982
#130814522
C2×#106226952
C2×#106226682
C2×#106226692
C2×#106226352
C2×#106226342
C2×#106226222
C2×#106226672
C2×#106227032
C2×#106226372
C2×#106226432
C2×#106226312
C2×C4×#43262
C2×C11×#5562
C2×#337711