Finite Group Databasebeta

← C2×#13081458 #15633570

Subgroups — C2×#13081458 #15633570

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×#10623115C211yesmaximal, characteristic
2#13081458C2116yesmaximal, direct product factor
3C2×#10622682C211yesmaximal, characteristic, complemented
4C2×#10622702C211yesmaximal, characteristic
5C2×#10622681C211yesmaximal, characteristic
6C2×#10622676C211yesmaximal, characteristic, complemented
7C2×#10622704C211yesmaximal, characteristic, complemented
8C2×#10622679C211yesmaximal, characteristic
9C2×#10622641C211yesmaximal, characteristic
10C2×#10622641C211yesmaximal, characteristic
11C2×#10622644C211yesmaximal, characteristic, complemented
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622643C211yesmaximal, characteristic, complemented
14C2×#10622639C211yesmaximal, characteristic
15C2×C4×#4326C211yesmaximal, characteristic, complemented
16C2×C11×#557C211yesmaximal, characteristic, complemented
17C11×#557—24no—
18C11×#557C2218yescomplemented
19C2×C11×C4⋊Q8—21no—
20C2×C11×C4⋊Q8C2211yescharacteristic
21C2×C11×#125—21no—
22C2×C11×#125—21no—
23C2×C11×#125C2211yescharacteristic
24C2×C11×#125C2211yescharacteristic
25C2×C4×Q8×C11—21no—
26C2×C4×Q8×C11C2211yescharacteristic
27C2×C4×Q8×C11C2211yescharacteristic
28C2×C4×Q8×C11C2211yescharacteristic
29C2×C4×Q8×C11C2211yescharacteristic
30C2×#66999—21no—
31C22×#4326C2211yescharacteristic
32C22×#4326C2211yescharacteristic
33C22×#4325C2211yescharacteristic
34#10623115—24no—
35#10623115C2218yes—
36C2×#66951—21no—
37C2×#66951—21no—
38C2×#66945—21no—
39C2×#66928C2211yescharacteristic
40C2×#66928C2211yescharacteristic
41C2×C4×D44C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C2×C4×Dic22C2211yescharacteristic
44C2×C4×Dic22C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46#10622704C2218yescomplemented
47#10622702C2218yes—
48#10622682C2218yescomplemented
49#10622681C2218yes—
50#10622679C2218yes—
51#10622676C2218yescomplemented
52#10622644C2218yescomplemented
53#10622643C2218yescomplemented
54C4×#4326C2218yescomplemented
55#10622641C2218yes—
56#10622641C2218yes—
57#10622639C2218yes—
58#10622637C2218yescomplemented
59C2×#66874C2211yescharacteristic
60C2×#66874C2211yescharacteristic
61C2×#66874C2211yescharacteristic
62C2×#66874C2211yescharacteristic
63C2×#66874C2211yescharacteristic
64C2×#66874C2211yescharacteristic
65C2×#66873C2211yescharacteristic
66C2×#66873C2211yescharacteristic
67C2×#66873C2211yescharacteristic
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×C11—21no—
78C22×Q8×C11D411yescharacteristic
79C22×Q8×C11C2311yescharacteristic
80C22×D44C2311yescharacteristic
81C22×C4×D11—21no—
82C22×Dic22C2311yescharacteristic
83C22×Dic22C2311yescharacteristic
84C11×C4⋊Q8—28no—
85C11×C4⋊Q8—22no—
86C11×C4⋊Q8C2314yes—
87C11×#125—28no—
88C11×#125—28no—
89C11×#125—22no—
90C11×#125—22no—
91C11×#125C2314yes—
92C11×#125C2314yes—
93C4×Q8×C11—28no—
94C4×Q8×C11—22no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11D414yes—
98C4×Q8×C11C2314yes—
99C4×Q8×C11C2314yes—
100C4×Q8×C11C2314yes—
101C4×Q8×C11C2314yes—
102C2×C11×C4⋊C4—21no—
103C2×C11×C4⋊C4—21no—
104C2×C11×C4⋊C4—21no—
105C2×C11×C4⋊C4—21no—
106C2×C11×C4⋊C4—21no—
107C2×C11×C4⋊C4—21no—
108C2×C11×C4⋊C4—21no—
109C2×C11×C4⋊C4—21no—
110C2×C11×C4⋊C4D411yescharacteristic
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4C2311yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C42×C11—21no—
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11C2311yescharacteristic
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122#66999—28no—
123C2×#4326—24no—
124C2×#4326—24no—
125C2×#4326C2314yes—
126C2×#4326C2314yes—
127C2×#4325—24no—
128C2×#4325C2314yes—
129C2×(C2×D11)⋊C4—21no—
130C2×(C2×D11)⋊C4—21no—
131C2×(C2×D11)⋊C4—21no—
132C2×(C2×D11)⋊C4—21no—
133C2×(C2×D11)⋊C4—21no—
134C2×C4⋊Dic11—21no—
135C2×C4⋊Dic11—21no—
136C2×C4⋊Dic11C2311yescharacteristic
137C2×Dic11⋊C4—21no—
138C2×Dic11⋊C4—21no—
139C2×C4×Dic11—21no—
140C2×C4×Dic11—21no—
141C22×C11⋊C8C2311yescharacteristic
142C22×C11⋊C8C2311yescharacteristic
143C22×C11⋊C8C2311yescharacteristic
144C22×C11⋊C8C2311yescharacteristic
145#66951—28no—
146#66951—28no—
147#66945—28no—
148#66928—22no—
149#66928—22no—
150#66928C2314yes—
151#66928C2314yes—
152C4×D44—22no—
153C4×D44C2314yes—
154#66922—22no—
155#66922C2314yes—
156C4×Dic22—22no—
157C4×Dic22—22no—
158C4×Dic22C2314yes—
159C4×Dic22C2314yes—
160#66899C2314yes—
161#66874C2314yes—
162#66874C2314yes—
163#66874C2314yes—
164#66874C2314yes—
165#66874C2314yes—
166#66874C2314yes—
167#66873C2314yes—
168#66873C2314yes—
169#66873C2314yes—
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
180C23×D11—21no—
181C2×Q8×C11—21no—
182C2×Q8×C11—24no—
183C2×Q8×C11—22no—
184C2×Q8×C11—42no—
185C2×Q8×C11—44no—
186C2×Q8×C11C2×D414yes—
187C2×Q8×C11#4114yes—
188C2×Q8×C11C2412yes—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2×D411yescharacteristic
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2411yescharacteristic
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C2×D44—21no—
204C2×D44—22no—
205C2×D44—22no—
206C2×D44C2412yes—
207C2×C4×D11—24no—
208C2×C4×D11—44no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—22no—
212C2×Dic22—22no—
213C2×Dic22—22no—
214C2×Dic22—22no—
215C2×Dic22C2412yes—
216C2×Dic22C2412yes—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—24no—
222C11×C4⋊C4—24no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—24no—
225C11×C4⋊C4—21no—
226C11×C4⋊C4—21no—
227C11×C4⋊C4—21no—
228C11×C4⋊C4C2×D414yes—
229C11×C4⋊C4C2×D414yes—
230C11×C4⋊C4C2×D414yes—
231C11×C4⋊C4C2412yes—
232C11×C4⋊C4C2412yes—
233C11×C4⋊C4C2412yes—
234C42×C11—24no—
235C42×C11—24no—
236C42×C11—24no—
237C42×C11C2×D412yes—
238C42×C11C2×D412yes—
239C42×C11C2×D412yes—
240C42×C11C2412yes—
241C42×C11C2412yes—
242C42×C11C2412yes—
243#4326—28no—
244#4326—28no—
245#4325—28no—
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—
251C4⋊Dic11—21no—
252C4⋊Dic11—24no—
253C4⋊Dic11—24no—
254C4⋊Dic11C2412yes—
255Dic11⋊C4—24no—
256Dic11⋊C4—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×#557D1111yescharacteristic, complemented
268C2×#556—111no—
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×C11C22×D411yescharacteristic
284C22×D11—22no—
285C22×D11—42no—
286C22×D11—42no—
287C22×D11—42no—
288Q8×C11—24no—
289Q8×C11—22no—
290Q8×C11—44no—
291Q8×C11—48no—
292Q8×C11C2×#4114yes—
293C2×C4×C11—24no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
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—42no—
305C2×C4×C11—42no—
306C2×C4×C11—42no—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D412yes—
312C2×C4×C11C22×D412yes—
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C2×#4112yes—
315C2×C4×C112−1+412yes—
316C2×C4×C11C2511yescharacteristic
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—42no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323D44—22no—
324D44—22no—
325D44—42no—
326C4×D11—48no—
327Dic22—22no—
328Dic22—22no—
329Dic22—22no—
330Dic22—22no—
331Dic22—42no—
332Dic22—42no—
333C11⋊C8—22no—
334C11⋊C8—22no—
335C11⋊C8—22no—
336C11⋊C8—22no—
337C22×Q16—111no—
338C22×Q16—111no—
339C22×SD16—111no—
340#557—24no—
341#557C2×D1118yescomplemented
342#556—118no—
343#556—224no—
344C2×C4⋊Q8—21no—
345C2×C4⋊Q8—111no—
346C2×C4⋊Q8C2×D1111yescharacteristic
347C2×#126—221no—
348C2×#126—221no—
349C2×#125—21no—
350C2×#125—21no—
351C2×#125C2×D1111yescharacteristic
352C2×#125C2×D1111yescharacteristic
353C2×#124—111no—
354C2×#124—111no—
355C2×C22⋊Q8—221no—
356C2×C4×Q8—21no—
357C2×C4×Q8—111no—
358C2×C4×Q8—111no—
359C2×C4×Q8C2×D1111yescharacteristic
360C2×C4×Q8C2×D1111yescharacteristic
361C2×C4×Q8C2×D1111yescharacteristic
362C2×C4×Q8C2×D1111yescharacteristic
363C2×C4×D4—111no—
364C2×#117—221no—
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#54812yes—
398C22×C11#57512yes—
399C22×C11#57812yes—
400C22×C11C23×D411yescharacteristic
401C2×D11—42no—
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—84no—
405C4×C11—24no—
406C4×C11—22no—
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—22no—
410C4×C11—22no—
411C4×C11—22no—
412C4×C11—42no—
413C4×C11—42no—
414C4×C11—42no—
415C4×C11#54812yes—
416C4×C11C22×#4111yescharacteristic
417C4×C11C2×2−1+411yescharacteristic
418Dic11—42no—
419Dic11—42no—
420Dic11—42no—
421C22×Q8—21no—
422C22×Q8—111no—
423C22×Q8—111no—
424C22×Q8C22⋊D1111yescharacteristic
425C22×Q8C22×D1111yescharacteristic
426C22×D4—111no—
427C23×C4—221no—
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—28no—
439C4⋊Q8—22no—
440C4⋊Q8—114no—
441C4⋊Q8—222no—
442C4⋊Q8C22×D1114yes—
443#126—228no—
444#126—228no—
445#125—28no—
446#125—28no—
447#125—22no—
448#125—22no—
449#125C22×D1114yes—
450#125C22×D1114yes—
451#124—114no—
452#124—114no—
453#124—222no—
454#124—222no—
455C22⋊Q8—228no—
456C4×Q8—28no—
457C4×Q8—22no—
458C4×Q8—22no—
459C4×Q8—22no—
460C4×Q8—114no—
461C4×Q8—114no—
462C4×Q8—222no—
463C4×Q8—222no—
464C4×Q8C22⋊D1114yes—
465C4×Q8C22×D1114yes—
466C4×Q8C22×D1114yes—
467C4×Q8C22×D1114yes—
468C4×Q8C22×D1114yes—
469C4×D4—114no—
470C4×D4—222no—
471#117—228no—
472C2×C4⋊C4—21no—
473C2×C4⋊C4—21no—
474C2×C4⋊C4—21no—
475C2×C4⋊C4—21no—
476C2×C4⋊C4—21no—
477C2×C4⋊C4—21no—
478C2×C4⋊C4—21no—
479C2×C4⋊C4—21no—
480C2×C4⋊C4—111no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4—221no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4C22⋊D1111yescharacteristic
486C2×C4⋊C4C22⋊D1111yescharacteristic
487C2×C4⋊C4C22⋊D1111yescharacteristic
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C22⋊C4—221no—
496C2×C42—21no—
497C2×C42—21no—
498C2×C42—21no—
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#337714yescomplemented
524C2×C11C2×#54811yescharacteristic
525C2×C11C2×#57511yescharacteristic
526C2×C11C2×#57811yescharacteristic
527D11—82no—
528C24—221no—
529C2×Q8—22no—
530C2×Q8—21no—
531C2×Q8—24no—
532C2×Q8—42no—
533C2×Q8—44no—
534C2×Q8—112no—
535C2×Q8—112no—
536C2×Q8—221no—
537C2×Q8—221no—
538C2×Q8—222no—
539C2×Q8—222no—
540C2×Q8—222no—
541C2×Q8—222no—
542C2×Q8#434314yes—
543C2×Q8C2×C22⋊D1114yes—
544C2×Q8C23×D1112yes—
545C2×D4—112no—
546C2×D4—222no—
547C2×D4—222no—
548C2×D4—221no—
549C22×C4—21no—
550C22×C4—21no—
551C22×C4—21no—
552C22×C4—21no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4—224no—
557C22×C4—444no—
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—24no—
581C4⋊C4—24no—
582C4⋊C4—24no—
583C4⋊C4—24no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—112no—
588C4⋊C4—221no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4C2×C22⋊D1114yes—
594C4⋊C4C2×C22⋊D1114yes—
595C4⋊C4C2×C22⋊D1114yes—
596C4⋊C4C23×D1112yes—
597C4⋊C4C23×D1112yes—
598C4⋊C4C23×D1112yes—
599C22⋊C4—224no—
600C22⋊C4—224no—
601C22⋊C4—224no—
602C22⋊C4—224no—
603C22⋊C4—224no—
604C42—24no—
605C42—24no—
606C42—24no—
607C42—224no—
608C42—224no—
609C42C2×C22⋊D1112yes—
610C42C2×C22⋊D1112yes—
611C42C2×C22⋊D1112yes—
612C42C23×D1112yes—
613C42C23×D1112yes—
614C42C23×D1112yes—
615C11C2×#337711yescharacteristic, complemented, Sylow
616C23—222no—
617C23—442no—
618C23—442no—
619C23—442no—
620C23C22×C22⋊D1111yescharacteristic
621Q8—24no—
622Q8—22no—
623Q8—44no—
624Q8—48no—
625Q8—222no—
626Q8—222no—
627Q8—222no—
628Q8—222no—
629Q8—442no—
630Q8—442no—
631Q8C2×#434314yes—
632D4—222no—
633D4—222no—
634D4—442no—
635C2×C4—24no—
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—22no—
645C2×C4—22no—
646C2×C4—42no—
647C2×C4—42no—
648C2×C4—42no—
649C2×C4—222no—
650C2×C4—222no—
651C2×C4—222no—
652C2×C4—448no—
653C2×C4—442no—
654C2×C4—442no—
655C2×C4—442no—
656C2×C4C2×#434312yes—
657C2×C4#6704012yes—
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—442no—
671C22—442no—
672C22—442no—
673C22—884no—
674C22#1062334812yes—
675C22#1062335312yes—
676C22#1062336912yes—
677C22C23×C22⋊D1111yescharacteristic
678C4—22no—
679C4—22no—
680C4—22no—
681C4—24no—
682C4—22no—
683C4—22no—
684C4—22no—
685C4—42no—
686C4—42no—
687C4—42no—
688C4—442no—
689C4—442no—
690C4—442no—
691C4#1062334812yes—
692C4C22×#434311yescharacteristic
693C4C2×#6704011yescharacteristic
694C2—882no—
695C2#1308145814yesdirect product factor
696C2C2×#1062334811yescharacteristic
697C2C2×#1062335311yescharacteristic
698C2C2×#1062336911yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11C2×#3377
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×Q8 ◁ C2×#557

Complements

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

NH ≅ G/Ntype
2. #13081458C2direct (N × H)
3. C2×#10622682C2semidirect
6. C2×#10622676C2semidirect
7. C2×#10622704C2semidirect
11. C2×#10622644C2semidirect
12. C2×#10622637C2semidirect
13. C2×#10622643C2semidirect
15. C2×C4×#4326C2semidirect
16. C2×C11×#557C2semidirect
18. C11×#557C22semidirect
46. #10622704C22semidirect
48. #10622682C22semidirect
51. #10622676C22semidirect
52. #10622644C22semidirect
53. #10622643C22semidirect
54. C4×#4326C22semidirect
58. #10622637C22semidirect
267. C2×#557D11semidirect
341. #557C2×D11semidirect
523. C2×C11#3377semidirect
615. C11C2×#3377semidirect
695. C2#13081458direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231152
#130814582
C2×#106226822
C2×#106227022
C2×#106226812
C2×#106226762
C2×#106227042
C2×#106226792
C2×#106226412
C2×#106226442
C2×#106226372
C2×#106226432
C2×#106226392
C2×C4×#43262
C2×C11×#5572
C2×#337711