Finite Group Databasebeta

← C2×#13081555 #15634294

Subgroups — C2×#13081555 #15634294

Order 2816.

1822 conjugacy classes of subgroups.

The subgroup lattice has 684 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623110C211yesmaximal, characteristic
2#13081555C2116yesmaximal, direct product factor
3C2×#10622678C211yesmaximal, characteristic, complemented
4C2×#10622693C211yesmaximal, characteristic, complemented
5C2×#10622677C211yesmaximal, characteristic, complemented
6C2×#10622635C211yesmaximal, characteristic, complemented
7C2×#10622635C211yesmaximal, characteristic, complemented
8C2×#10622633C211yesmaximal, characteristic, complemented
9C2×#10622679C211yesmaximal, characteristic
10C2×#10622679C211yesmaximal, characteristic
11C2×#10622697C211yesmaximal, characteristic
12C2×#10622637C211yesmaximal, characteristic, complemented
13C2×#10622639C211yesmaximal, characteristic
14C2×#10622639C211yesmaximal, characteristic
15C2×C4×#4325C211yesmaximal, characteristic
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×#4325C2211yescharacteristic
32#10623110—24no—
33#10623110C2218yes—
34C2×#66949—21no—
35C2×#66949—21no—
36C2×C4⋊C4×D11—21no—
37C2×C4×D44C2211yescharacteristic
38C2×C4×D44C2211yescharacteristic
39C2×C4×D44C2211yescharacteristic
40C2×#66923C2211yescharacteristic
41C2×#66923C2211yescharacteristic
42C2×#66922C2211yescharacteristic
43C2×#66899C2211yescharacteristic
44C2×#66899C2211yescharacteristic
45C2×#66899C2211yescharacteristic
46#10622697C2218yes—
47#10622693C2218yescomplemented
48#10622679C2218yes—
49#10622679C2218yes—
50#10622678C2218yescomplemented
51#10622677C2218yescomplemented
52#10622639C2218yes—
53#10622639C2218yes—
54C4×#4325C2218yes—
55#10622637C2218yescomplemented
56#10622635C2218yescomplemented
57#10622635C2218yescomplemented
58#10622633C2218yescomplemented
59C2×#66873C2211yescharacteristic
60C2×#66873C2211yescharacteristic
61C2×#66873C2211yescharacteristic
62C2×#66872C2211yescharacteristic
63C2×#66872C2211yescharacteristic
64C2×#66872C2211yescharacteristic
65C2×#66872C2211yescharacteristic
66C2×#66872C2211yescharacteristic
67C2×#66871C2211yescharacteristic
68C2×#66871C2211yescharacteristic
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×C4×D11—21no—
83C22×C4×D11—21no—
84C22×Dic22—21no—
85C11×C4⋊Q8—28no—
86C11×C4⋊Q8—22no—
87C11×C4⋊Q8C2314yes—
88C11×#125—28no—
89C11×#125—28no—
90C11×#125—22no—
91C11×#125—22no—
92C11×#125C2314yes—
93C11×#125C2314yes—
94C4×Q8×C11—28no—
95C4×Q8×C11—22no—
96C4×Q8×C11—22no—
97C4×Q8×C11—22no—
98C4×Q8×C11D414yes—
99C4×Q8×C11C2314yes—
100C4×Q8×C11C2314yes—
101C4×Q8×C11C2314yes—
102C4×Q8×C11C2314yes—
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⋊C4—21no—
111C2×C11×C4⋊C4D411yescharacteristic
112C2×C11×C4⋊C4D411yescharacteristic
113C2×C11×C4⋊C4D411yescharacteristic
114C2×C11×C4⋊C4C2311yescharacteristic
115C2×C11×C4⋊C4C2311yescharacteristic
116C2×C11×C4⋊C4C2311yescharacteristic
117C2×C42×C11—21no—
118C2×C42×C11—21no—
119C2×C42×C11—21no—
120C2×C42×C11C2311yescharacteristic
121C2×C42×C11C2311yescharacteristic
122C2×C42×C11C2311yescharacteristic
123#66999—28no—
124C2×#4325Q818yescomplemented
125C2×#4325C2314yes—
126C2×(C2×D11)⋊C4—21no—
127C2×(C2×D11)⋊C4—21no—
128C2×(C2×D11)⋊C4—21no—
129C2×C4⋊Dic11—21no—
130C2×C4⋊Dic11C2311yescharacteristic
131C2×C4⋊Dic11C2311yescharacteristic
132C2×C4⋊Dic11C2311yescharacteristic
133C2×Dic11⋊C4—21no—
134C2×Dic11⋊C4—21no—
135C2×Dic11⋊C4—21no—
136C2×Dic11⋊C4—21no—
137C22×C11⋊C8C2311yescharacteristic
138C22×C11⋊C8C2311yescharacteristic
139C22×C11⋊C8C2311yescharacteristic
140C22×C11⋊C8C2311yescharacteristic
141#66949—28no—
142#66949—28no—
143C4⋊C4×D11—28no—
144C4×D44—22no—
145C4×D44—22no—
146C4×D44—22no—
147C4×D44C2314yes—
148C4×D44C2314yes—
149C4×D44C2314yes—
150#66923—22no—
151#66923—22no—
152#66923C2314yes—
153#66923C2314yes—
154#66922—22no—
155#66922C2314yes—
156#66899C2314yes—
157#66899C2314yes—
158#66899C2314yes—
159#66873C2314yes—
160#66873C2314yes—
161#66873C2314yes—
162#66872C2314yes—
163#66872C2314yes—
164#66872C2314yes—
165#66872C2314yes—
166#66872C2314yes—
167#66871C2314yes—
168#66871C2314yes—
169#66871C2314yes—
170#66871C2314yes—
171C4⋊(C11⋊C8)C2314yes—
172C4⋊(C11⋊C8)C2314yes—
173C4⋊(C11⋊C8)C2314yes—
174#66867C2314yes—
175#66867C2314yes—
176C4×C11⋊C8C2314yes—
177C2×#3388—111nomaximal, Sylow
178C23×D11—21no—
179C2×Q8×C11—21no—
180C2×Q8×C11—24no—
181C2×Q8×C11—22no—
182C2×Q8×C11—42no—
183C2×Q8×C11—44no—
184C2×Q8×C11C2×D414yes—
185C2×Q8×C11C2×Q814yes—
186C2×Q8×C11C2412yes—
187C22×C4×C11—21no—
188C22×C4×C11—21no—
189C22×C4×C11—21no—
190C22×C4×C11—21no—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D411yescharacteristic
193C22×C4×C11C2×D411yescharacteristic
194C22×C4×C11C2×D411yescharacteristic
195C22×C4×C11C2×D411yescharacteristic
196C22×C4×C11C2×D411yescharacteristic
197C22×C4×C11C2411yescharacteristic
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C2×D44—21no—
202C2×D44—22no—
203C2×D44C2×Q814yes—
204C2×D44C2412yes—
205C2×C4×D11—24no—
206C2×C4×D11—24no—
207C2×C4×D11—24no—
208C2×C4×D11—44no—
209C2×C4×D11—82no—
210C2×C4×D11—82no—
211C2×Dic22—24no—
212C2×Dic22—82no—
213C11×C4⋊C4—24no—
214C11×C4⋊C4—24no—
215C11×C4⋊C4—24no—
216C11×C4⋊C4—24no—
217C11×C4⋊C4—24no—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—24no—
220C11×C4⋊C4—24no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4—21no—
224C11×C4⋊C4C2×D414yes—
225C11×C4⋊C4C2×D414yes—
226C11×C4⋊C4C2×D414yes—
227C11×C4⋊C4C2412yes—
228C11×C4⋊C4C2412yes—
229C11×C4⋊C4C2412yes—
230C42×C11—24no—
231C42×C11—24no—
232C42×C11—24no—
233C42×C11C2×D412yes—
234C42×C11C2×D412yes—
235C42×C11C2×D412yes—
236C42×C11C2412yes—
237C42×C11C2412yes—
238C42×C11C2412yes—
239#4325C2×Q8116yescomplemented
240(C2×D11)⋊C4—24no—
241(C2×D11)⋊C4—24no—
242(C2×D11)⋊C4—24no—
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—24no—
246C4⋊Dic11—21no—
247C4⋊Dic11C2412yes—
248C4⋊Dic11C2412yes—
249C4⋊Dic11C2412yes—
250Dic11⋊C4—24no—
251Dic11⋊C4—24no—
252Dic11⋊C4—24no—
253Dic11⋊C4—24no—
254C2×C11⋊C8—22no—
255C2×C11⋊C8—22no—
256C2×C11⋊C8—22no—
257C2×C11⋊C8C2×Q814yes—
258C2×C11⋊C8C2412yes—
259C2×C11⋊C8C2412yes—
260C2×C11⋊C8C2412yes—
261C2×C11⋊C8C2412yes—
262C2×#557D1111yescharacteristic, complemented
263C2×#554—111no—
264#3388—1116no—
265C2×#501—111no—
266C2×#501—111no—
267C2×#499—111no—
268C2×#479—111no—
269C2×#479—111no—
270C2×#475—111no—
271C2×#478—111no—
272C2×#478—111no—
273C2×#476—111no—
274C2×#446—111no—
275C2×#440—111no—
276C2×#440—111no—
277C2×C4×SD16—111no—
278C23×C11C22×D411yescharacteristic
279C22×D11—24no—
280C22×D11—22no—
281C22×D11—42no—
282C22×D11—42no—
283Q8×C11—24no—
284Q8×C11—22no—
285Q8×C11—44no—
286Q8×C11—48no—
287Q8×C11C22×Q814yes—
288C2×C4×C11—24no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—42no—
300C2×C4×C11—42no—
301C2×C4×C11—42no—
302C2×C4×C11C22×D412yes—
303C2×C4×C11C22×D412yes—
304C2×C4×C11C22×D412yes—
305C2×C4×C11C22×D412yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D412yes—
308C2×C4×C11C22×D411yescharacteristic
309C2×C4×C11C22×Q812yes—
310C2×C4×C112−1+412yes—
311C2×C4×C11C2511yescharacteristic
312C2×Dic11—22no—
313C2×Dic11—22no—
314C2×Dic11—22no—
315C2×Dic11—42no—
316C2×Dic11—42no—
317C2×Dic11—42no—
318D44—24no—
319D44—22no—
320D44C22×Q814yes—
321C4×D11—48no—
322C4×D11—84no—
323C4×D11—84no—
324Dic22—84no—
325C11⋊C8—22no—
326C11⋊C8—22no—
327C11⋊C8—22no—
328C11⋊C8C22×Q814yes—
329C22×SD16—111no—
330#557—24no—
331#557C2×D1118yescomplemented
332#554—118no—
333#554—224no—
334C2×C4⋊Q8—21no—
335C2×C4⋊Q8—111no—
336C2×C4⋊Q8C2×D1111yescharacteristic
337C2×#125—21no—
338C2×#125—21no—
339C2×#125—111no—
340C2×#125—111no—
341C2×#125C2×D1111yescharacteristic
342C2×#125C2×D1111yescharacteristic
343C2×C22⋊Q8—221no—
344C2×C22⋊Q8—221no—
345C2×C22⋊Q8—221no—
346C2×C4×Q8—21no—
347C2×C4×Q8C2×D1111yescharacteristic
348C2×C4×Q8C2×D1111yescharacteristic
349C2×C4×Q8C2×D1111yescharacteristic
350C2×C4×Q8C2×D1111yescharacteristic
351C2×C4×D4—111no—
352C2×C4×D4—111no—
353C2×C4×D4—111no—
354C22×C4⋊C4—221no—
355#501—118no—
356#501—118no—
357#499—118no—
358#479—118no—
359#479—118no—
360#478—118no—
361#478—118no—
362#476—118no—
363#475—118no—
364#446—118no—
365#440—118no—
366#440—118no—
367C4×SD16—118no—
368C2×#107—111no—
369C2×#107—111no—
370C2×#107—111no—
371C2×#107—111no—
372C2×#106—111no—
373C2×#106—111no—
374C2×#106—111no—
375C2×#106—111no—
376C2×#106—111no—
377C2×C4⋊C8—111no—
378C2×C4⋊C8—111no—
379C2×C4⋊C8—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#97—111no—
387C2×#97—111no—
388C2×C4×C8—111no—
389C22×C11D4×Q812yes—
390C22×C11#57512yes—
391C22×C11#57712yes—
392C22×C11C23×D411yescharacteristic
393C2×D11—24no—
394C2×D11—48no—
395C2×D11—42no—
396C2×D11—42no—
397C4×C11—24no—
398C4×C11—22no—
399C4×C11—22no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—22no—
403C4×C11—22no—
404C4×C11—42no—
405C4×C11—42no—
406C4×C11—42no—
407C4×C11D4×Q812yes—
408C4×C11C23×Q811yescharacteristic
409C4×C11C2×2−1+411yescharacteristic
410Dic11—42no—
411Dic11—42no—
412Dic11—42no—
413C22×Q8—21no—
414C22×Q8—221no—
415C22×Q8C22⋊D1111yescharacteristic
416C22×Q8C22×D1111yescharacteristic
417C22×D4—111no—
418C23×C4—221no—
419C23×C4—221no—
420C23×C4—221no—
421C2×SD16—118no—
422C2×SD16—114no—
423C22×C8—111no—
424C22×C8—111no—
425C22×C8—111no—
426C22×C8—111no—
427C4⋊Q8—28no—
428C4⋊Q8—22no—
429C4⋊Q8—114no—
430C4⋊Q8—222no—
431C4⋊Q8C22×D1114yes—
432#125—28no—
433#125—28no—
434#125—22no—
435#125—22no—
436#125—114no—
437#125—114no—
438#125—222no—
439#125—222no—
440#125C22×D1114yes—
441#125C22×D1114yes—
442C22⋊Q8—228no—
443C22⋊Q8—228no—
444C22⋊Q8—228no—
445C4×Q8—28no—
446C4×Q8—22no—
447C4×Q8—22no—
448C4×Q8—22no—
449C4×Q8C22⋊D1114yes—
450C4×Q8C22×D1114yes—
451C4×Q8C22×D1114yes—
452C4×Q8C22×D1114yes—
453C4×Q8C22×D1114yes—
454C4×D4—114no—
455C4×D4—114no—
456C4×D4—114no—
457C4×D4—222no—
458C4×D4—222no—
459C4×D4—222no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—21no—
464C2×C4⋊C4—21no—
465C2×C4⋊C4—21no—
466C2×C4⋊C4—21no—
467C2×C4⋊C4—21no—
468C2×C4⋊C4—111no—
469C2×C4⋊C4—111no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—228no—
477C2×C4⋊C4C22⋊D1111yescharacteristic
478C2×C4⋊C4C22⋊D1111yescharacteristic
479C2×C4⋊C4C22⋊D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C4⋊C4C22×D1111yescharacteristic
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C42—21no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42C22×D1111yescharacteristic
490C2×C42C22×D1111yescharacteristic
491C2×C42C22×D1111yescharacteristic
492#107—114no—
493#107—114no—
494#107—114no—
495#107—114no—
496#106—114no—
497#106—114no—
498#106—114no—
499#106—114no—
500#106—114no—
501C4⋊C8—114no—
502C4⋊C8—114no—
503C4⋊C8—114no—
504#103—114no—
505#103—114no—
506#103—114no—
507#102—114no—
508#102—114no—
509#102—114no—
510#97—114no—
511#97—114no—
512C4×C8—114no—
513C2×C11#338814yescomplemented
514C2×C11C2×D4×Q811yescharacteristic
515C2×C11C2×#57511yescharacteristic
516C2×C11C2×#57711yescharacteristic
517D11—44no—
518C24—221no—
519C2×Q8—22no—
520C2×Q8—21no—
521C2×Q8—24no—
522C2×Q8—42no—
523C2×Q8—44no—
524C2×Q8—224no—
525C2×Q8—882no—
526C2×Q8Q8×D1114yes—
527C2×Q8C2×C22⋊D1114yes—
528C2×Q8C23×D1112yes—
529C2×D4—114no—
530C2×D4—112no—
531C2×D4—222no—
532C2×D4—221no—
533C22×C4—21no—
534C22×C4—21no—
535C22×C4—21no—
536C22×C4—21no—
537C22×C4—221no—
538C22×C4—221no—
539C22×C4—221no—
540C22×C4—224no—
541C22×C4—224no—
542C22×C4—224no—
543C22×C4—444no—
544C22×C4—882no—
545C22×C4—882no—
546C22×C4C2×C22⋊D1111yescharacteristic
547C22×C4C2×C22⋊D1111yescharacteristic
548C22×C4C2×C22⋊D1111yescharacteristic
549C22×C4C2×C22⋊D1111yescharacteristic
550C22×C4C2×C22⋊D1111yescharacteristic
551C22×C4C2×C22⋊D1111yescharacteristic
552C22×C4C23×D1111yescharacteristic
553SD16—1116no—
554C2×C8—114no—
555C2×C8—112no—
556C2×C8—112no—
557C2×C8—112no—
558C2×C8—112no—
559C2×C8—222no—
560C2×C8—222no—
561C2×C8—222no—
562C4⋊C4—24no—
563C4⋊C4—24no—
564C4⋊C4—24no—
565C4⋊C4—24no—
566C4⋊C4—24no—
567C4⋊C4—24no—
568C4⋊C4—24no—
569C4⋊C4—24no—
570C4⋊C4—21no—
571C4⋊C4—21no—
572C4⋊C4—21no—
573C4⋊C4—112no—
574C4⋊C4—112no—
575C4⋊C4—112no—
576C4⋊C4—221no—
577C4⋊C4—221no—
578C4⋊C4—221no—
579C4⋊C4—224no—
580C4⋊C4—224no—
581C4⋊C4—224no—
582C4⋊C4—224no—
583C4⋊C4—224no—
584C4⋊C4C2×C22⋊D1114yes—
585C4⋊C4C2×C22⋊D1114yes—
586C4⋊C4C2×C22⋊D1114yes—
587C4⋊C4C23×D1112yes—
588C4⋊C4C23×D1112yes—
589C4⋊C4C23×D1112yes—
590C22⋊C4—224no—
591C22⋊C4—224no—
592C22⋊C4—224no—
593C42—24no—
594C42—24no—
595C42—24no—
596C42C2×C22⋊D1112yes—
597C42C2×C22⋊D1112yes—
598C42C2×C22⋊D1112yes—
599C42C23×D1112yes—
600C42C23×D1112yes—
601C42C23×D1112yes—
602C11C2×#338811yescharacteristic, complemented, Sylow
603C23—224no—
604C23—222no—
605C23—442no—
606C23—442no—
607C23C22×C22⋊D1111yescharacteristic
608Q8—24no—
609Q8—22no—
610Q8—44no—
611Q8—48no—
612Q8—884no—
613Q8C2×Q8×D1114yes—
614D4—114no—
615D4—224no—
616D4—222no—
617C2×C4—24no—
618C2×C4—22no—
619C2×C4—22no—
620C2×C4—22no—
621C2×C4—22no—
622C2×C4—22no—
623C2×C4—22no—
624C2×C4—22no—
625C2×C4—22no—
626C2×C4—22no—
627C2×C4—22no—
628C2×C4—42no—
629C2×C4—42no—
630C2×C4—42no—
631C2×C4—222no—
632C2×C4—222no—
633C2×C4—222no—
634C2×C4—448no—
635C2×C4—442no—
636C2×C4—442no—
637C2×C4—442no—
638C2×C4—884no—
639C2×C4—884no—
640C2×C4C2×Q8×D1112yes—
641C2×C4#6704012yes—
642C2×C4C22×C22⋊D1112yes—
643C2×C4C22×C22⋊D1112yes—
644C2×C4C22×C22⋊D1112yes—
645C2×C4C22×C22⋊D1112yes—
646C2×C4C22×C22⋊D1112yes—
647C2×C4C22×C22⋊D1112yes—
648C2×C4C22×C22⋊D1111yescharacteristic
649C2×C4C24×D1111yescharacteristic
650C8—114no—
651C8—222no—
652C8—222no—
653C8—222no—
654C22—224no—
655C22—448no—
656C22—442no—
657C22—442no—
658C22Q8×C22⋊D1112yes—
659C22#1062335312yes—
660C22#1062336812yes—
661C22C23×C22⋊D1111yescharacteristic
662C4—22no—
663C4—22no—
664C4—22no—
665C4—24no—
666C4—22no—
667C4—22no—
668C4—22no—
669C4—42no—
670C4—42no—
671C4—42no—
672C4—442no—
673C4—442no—
674C4—442no—
675C4Q8×C22⋊D1112yes—
676C4C22×Q8×D1111yescharacteristic
677C4C2×#6704011yescharacteristic
678C2—444no—
679C2#1308155514yesdirect product factor
680C2C2×Q8×C22⋊D1111yescharacteristic
681C2C2×#1062335311yescharacteristic
682C2C2×#1062336811yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#557C2
socleC23×C11C22×D4
prime radicalC22×D44C23
hypercenterC2×#557D11
hypocenterC11C2×#3388
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. #13081555C2direct (N × H)
3. C2×#10622678C2semidirect
4. C2×#10622693C2semidirect
5. C2×#10622677C2semidirect
6. C2×#10622635C2semidirect
7. C2×#10622635C2semidirect
8. C2×#10622633C2semidirect
12. C2×#10622637C2semidirect
16. C2×C11×#557C2semidirect
18. C11×#557C22semidirect
47. #10622693C22semidirect
50. #10622678C22semidirect
51. #10622677C22semidirect
55. #10622637C22semidirect
56. #10622635C22semidirect
57. #10622635C22semidirect
58. #10622633C22semidirect
124. C2×#4325Q8semidirect
239. #4325C2×Q8semidirect
262. C2×#557D11semidirect
331. #557C2×D11semidirect
513. C2×C11#3388semidirect
602. C11C2×#3388semidirect
679. C2#13081555direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231102
#130815552
C2×#106226782
C2×#106226932
C2×#106226772
C2×#106226352
C2×#106226332
C2×#106226792
C2×#106226972
C2×#106226372
C2×#106226392
C2×C4×#43252
C2×C11×#5572
C2×#338811