Finite Group Databasebeta

← C2×#13078242 #15620927

Subgroups — C2×#13078242 #15620927

Order 2816.

2898 conjugacy classes of subgroups.

The subgroup lattice has 722 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66995C211yesmaximal, characteristic, complemented
2C23×#4318C211yesmaximal, characteristic, complemented
3C2×#10623322C211yesmaximal, characteristic
4#13078242C2116yesmaximal, direct product factor
5C2×#10622665C212yesmaximal, complemented
6C2×#10622662C212yesmaximal, complemented
7C2×#10622664C212yesmaximal, complemented
8C2×#10622661C212yesmaximal, complemented
9C2×#10622577C211yesmaximal, characteristic, complemented
10C2×#10622579C211yesmaximal, characteristic, complemented
11C2×#10622838C211yesmaximal, characteristic, complemented
12C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
13C23×Q8×C11C2211yescharacteristic
14C24×C4×C11C2211yescharacteristic
15C22×#4339C2211yescharacteristic
16C2×C11×C22⋊Q8—21no—
17C2×C11×C22⋊Q8—21no—
18C2×C11×C22⋊Q8—24no—
19C2×C11×C22⋊Q8C2212yes—
20C2×C11×C22⋊Q8C2212yes—
21C2×C11×C22⋊Q8C2218yescomplemented
22C22×C11×C4⋊C4—21no—
23C22×C11×C4⋊C4C2211yescharacteristic
24C22×C11×C22⋊C4—21no—
25C2×#67006—21no—
26C22×#4326C2212yescomplemented
27C2×#66995—28no—
28C2×#66995C2218yescomplemented
29C22×#4325C2212yescomplemented
30#10623322—24no—
31#10623322C2218yes—
32C2×#66983C2211yescharacteristic
33C2×#66983C2211yescharacteristic
34C2×#66982—21no—
35C2×C4×C22⋊D11—21no—
36C2×C4×C22⋊D11—21no—
37C2×#66979C2211yescharacteristic
38C2×#66977C2211yescharacteristic
39C2×#66977C2211yescharacteristic
40C22×#4318—28no—
41C22×#4318C2211yescharacteristic
42C22×#4318C2212yes—
43C22×#4318C2211yescharacteristic
44C22×#4318C2218yescomplemented
45C23×C11⋊C8C2212yes—
46#10622838C2218yescomplemented
47C2×#66899C2212yescomplemented
48C2×#66899C2212yescomplemented
49#10622665C22116yescomplemented
50#10622664C22116yescomplemented
51#10622662C22116yescomplemented
52#10622661C22116yescomplemented
53C2×#66874C2212yescomplemented
54#10622579C2218yescomplemented
55C2×#66873C2212yescomplemented
56#10622577C2218yescomplemented
57C2×#66872C2212yescomplemented
58C2×#66871C2212yescomplemented
59C25×C11D411yescharacteristic
60C22×Q8×C11—21no—
61C22×Q8×C11—22no—
62C22×Q8×C11—24no—
63C22×Q8×C11—24no—
64C22×Q8×C11C2312yes—
65C22×Q8×C11C2314yes—
66C23×C4×C11—24no—
67C23×C4×C11—24no—
68C23×C4×C11—21no—
69C23×C4×C11—21no—
70C23×C4×C11D411yescharacteristic
71C23×C4×C11D411yescharacteristic
72C23×C4×C11D411yescharacteristic
73C23×C4×C11D414yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2311yescharacteristic
76C23×C4×C11C2314yes—
77C23×C4×C11C2311yescharacteristic
78C22×C22⋊D11—21no—
79C22×C22⋊D11—21no—
80C22×C22⋊D11—21no—
81C2×#4339—22no—
82C2×#4339—24no—
83C2×#4339—24no—
84C2×#4339C2314yes—
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×Dic22C2311yescharacteristic
88C11×C22⋊Q8—24no—
89C11×C22⋊Q8—24no—
90C11×C22⋊Q8—28no—
91C11×C22⋊Q8—28no—
92C11×C22⋊Q8C2318yes—
93C11×C22⋊Q8C2318yes—
94C2×C11×C4⋊C4—22no—
95C2×C11×C4⋊C4—22no—
96C2×C11×C4⋊C4—28no—
97C2×C11×C4⋊C4—21no—
98C2×C11×C4⋊C4—22no—
99C2×C11×C4⋊C4C2312yes—
100C2×C11×C4⋊C4C2314yes—
101C2×C11×C22⋊C4—22no—
102C2×C11×C22⋊C4—22no—
103C2×C11×C22⋊C4—28no—
104#67006—28no—
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×#4326—28no—
109C2×#4326C2318yescomplemented
110#66995—232no—
111C2×#4325—28no—
112C2×#4325C2318yescomplemented
113#66983—22no—
114#66983—22no—
115#66983C2314yes—
116#66983C2314yes—
117#66982—28no—
118C4×C22⋊D11—28no—
119C4×C22⋊D11—28no—
120C2×(C2×D11)⋊C4—21no—
121C2×(C2×D11)⋊C4—21no—
122#66979—22no—
123#66979C2314yes—
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126#66977—22no—
127#66977—22no—
128#66977C2314yes—
129#66977C2314yes—
130C2×Dic11⋊C4—21no—
131C2×Dic11⋊C4—21no—
132C2×C4×Dic11—21no—
133C2×#4318—24no—
134C2×#4318—232no—
135C2×#4318—28no—
136C2×#4318D418yescomplemented
137C2×#4318C2314yes—
138C2×#4318C2318yes—
139C2×#4318C2314yes—
140C22×C11⋊C8—28no—
141C22×C11⋊C8C2312yes—
142C22×C11⋊C8C2318yes—
143C22×C11⋊C8C2312yes—
144#66899C2318yescomplemented
145#66899C2318yescomplemented
146#66874C2318yescomplemented
147#66873C2318yescomplemented
148#66872C2318yescomplemented
149#66871C2318yescomplemented
150C2×#3056—111nomaximal, Sylow
151C24×C11—24no—
152C24×C11—24no—
153C24×C11—42no—
154C24×C11C2×D411yescharacteristic
155C24×C11C2×D414yes—
156C24×C11C2×D411yescharacteristic
157C24×C11C2×D411yescharacteristic
158C23×D11—21no—
159C2×Q8×C11—24no—
160C2×Q8×C11—22no—
161C2×Q8×C11—24no—
162C2×Q8×C11—28no—
163C2×Q8×C11—24no—
164C2×Q8×C11—28no—
165C2×Q8×C11—44no—
166C2×Q8×C11—48no—
167C2×Q8×C11C2414yes—
168C22×C4×C11—24no—
169C22×C4×C11—24no—
170C22×C4×C11—24no—
171C22×C4×C11—216no—
172C22×C4×C11—22no—
173C22×C4×C11—28no—
174C22×C4×C11—22no—
175C22×C4×C11—22no—
176C22×C4×C11—22no—
177C22×C4×C11—28no—
178C22×C4×C11—24no—
179C22×C4×C11—22no—
180C22×C4×C11—24no—
181C22×C4×C11—22no—
182C22×C4×C11—44no—
183C22×C4×C11—44no—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D412yes—
187C22×C4×C11C2×D412yes—
188C22×C4×C11C2×D414yes—
189C22×C4×C11C2×D414yes—
190C22×C4×C11C2×D414yes—
191C22×C4×C11C2×D411yescharacteristic
192C22×C4×C11C2×D412yes—
193C22×C4×C11C2×D414yes—
194C22×C4×C11#4114yes—
195C22×C4×C11C2412yes—
196C22×C4×C11C2412yes—
197C22×C4×C11C2411yescharacteristic
198C22×C4×C11C2412yes—
199C2×C22⋊D11—24no—
200C2×C22⋊D11—24no—
201C2×C22⋊D11—24no—
202C2×C22⋊D11—44no—
203C2×C22⋊D11—44no—
204C2×C22⋊D11—44no—
205C22×Dic11—21no—
206C22×Dic11—21no—
207C22×Dic11—21no—
208#4339—28no—
209#4339—28no—
210#4339—48no—
211C2×D44—21no—
212C2×D44—22no—
213C2×D44—22no—
214C2×D44C2412yes—
215C2×C4×D11—24no—
216C2×C4×D11—44no—
217C2×Dic22—22no—
218C2×Dic22—21no—
219C2×Dic22—22no—
220C2×Dic22C2412yes—
221C11×C4⋊C4—28no—
222C11×C4⋊C4—28no—
223C11×C4⋊C4—24no—
224C11×C4⋊C4—22no—
225C11×C4⋊C4C2414yes—
226C11×C22⋊C4—28no—
227C11×C22⋊C4—28no—
228C22⋊Dic11—24no—
229C22⋊Dic11—24no—
230C22⋊Dic11—24no—
231#4326—216no—
232#4325—216no—
233(C2×D11)⋊C4—24no—
234(C2×D11)⋊C4—24no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11C2412yes—
238C4⋊Dic11C2412yes—
239Dic11⋊C4—24no—
240Dic11⋊C4—24no—
241C4×Dic11—24no—
242#4318—216no—
243#4318—28no—
244#4318C2×D4116yescomplemented
245C2×C11⋊C8—216no—
246C2×C11⋊C8—24no—
247C2×C11⋊C8C2×D418yes—
248C2×C11⋊C8C2414yes—
249C2×C11⋊C8C2414yes—
250C22×#137—111no—
251C23×M16—111no—
252C2×#525—111no—
253C22×C22⋊Q8D1111yescharacteristic, complemented
254#3056—1116no—
255C2×#470—112no—
256C2×#468—112no—
257C2×#467—112no—
258C2×#465—112no—
259C2×#428—111no—
260C2×#417—111no—
261C2×#419—111no—
262C23×C11—22no—
263C23×C11—22no—
264C23×C11—22no—
265C23×C11—22no—
266C23×C11—28no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—28no—
270C23×C11—22no—
271C23×C11—44no—
272C23×C11—416no—
273C23×C11#12114yes—
274C23×C11#13714yescomplemented
275C23×C11C22×D412yes—
276C23×C11C22×D412yes—
277C23×C11C22×D412yes—
278C23×C11C22×D411yescharacteristic
279C22×D11—22no—
280C22×D11—42no—
281C22×D11—42no—
282C22×D11—42no—
283Q8×C11—24no—
284Q8×C11—24no—
285Q8×C11—44no—
286Q8×C11—48no—
287C2×C4×C11—28no—
288C2×C4×C11—22no—
289C2×C4×C11—22no—
290C2×C4×C11—24no—
291C2×C4×C11—24no—
292C2×C4×C11—28no—
293C2×C4×C11—28no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—24no—
299C2×C4×C11—24no—
300C2×C4×C11—48no—
301C2×C4×C11—48no—
302C2×C4×C11—44no—
303C2×C4×C11—44no—
304C2×C4×C11#12114yes—
305C2×C4×C11#12118yes—
306C2×C4×C11C22×D412yes—
307C2×C4×C11C22×D414yes—
308C2×C4×C11C22×D412yes—
309C2×C4×C11C22×D412yes—
310C2×C4×C11C22×D412yes—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4112yes—
313C2×C4×C11C2×#4114yes—
314C2×C4×C11C2511yescharacteristic
315C22⋊D11—48no—
316C22⋊D11—48no—
317C22⋊D11—48no—
318C2×Dic11—22no—
319C2×Dic11—22no—
320C2×Dic11—22no—
321C2×Dic11—42no—
322C2×Dic11—42no—
323C2×Dic11—42no—
324D44—22no—
325D44—22no—
326D44—42no—
327C4×D11—48no—
328Dic22—22no—
329Dic22—22no—
330Dic22—42no—
331C11⋊C8—24no—
332C11⋊C8C22×D418yes—
333C22×#41—111no—
334C23×Q8C2×D1111yescharacteristic
335C24×C4C2×D1111yescharacteristic
336C2×#137—118no—
337C2×#137—228no—
338C22×Q16—112no—
339C22×SD16—112no—
340C22×M16—111no—
341C22×M16—111no—
342C22×M16—112no—
343C22×M16—118no—
344C22×M16—228no—
345C23×C8—112no—
346#525—118no—
347#525—224no—
348C2×#123—221no—
349C2×C22⋊Q8—21no—
350C2×C22⋊Q8—21no—
351C2×C22⋊Q8—24no—
352C2×C22⋊Q8—111no—
353C2×C22⋊Q8—111no—
354C2×C22⋊Q8C2×D1112yes—
355C2×C22⋊Q8C2×D1112yes—
356C2×C22⋊Q8C2×D1118yescomplemented
357C2×#121—111no—
358C2×#121—111no—
359C2×#120—221no—
360C2×C4×D4—221no—
361C2×C4×D4—221no—
362C2×#117—111no—
363C22×C4⋊C4—21no—
364C22×C4⋊C4C2×D1111yescharacteristic
365C22×C22⋊C4—21no—
366#470—1116no—
367#468—1116no—
368#467—1116no—
369#465—1116no—
370#428—118no—
371C2×#107—112no—
372C2×#106—112no—
373#419—118no—
374#417—118no—
375C2×#103—112no—
376C2×#103—112no—
377C2×#103—112no—
378C2×#102—112no—
379C22×C11—22no—
380C22×C11—28no—
381C22×C11—28no—
382C22×C11—22no—
383C22×C11—22no—
384C22×C11—22no—
385C22×C11—22no—
386C22×C11—22no—
387C22×C11—22no—
388C22×C11—416no—
389C22×C11—44no—
390C22×C11C2×#12114yes—
391C22×C11C2×#12112yes—
392C22×C11C2×#13712yes—
393C22×C11C2×#13714yescomplemented
394C22×C11#57512yes—
395C22×C11C23×D411yescharacteristic
396C2×D11—42no—
397C2×D11—42no—
398C2×D11—42no—
399C2×D11—84no—
400C4×C11—22no—
401C4×C11—22no—
402C4×C11—44no—
403C4×C11—44no—
404C4×C11C2×#12112yes—
405C4×C11C2×#12114yes—
406C4×C11C23×D411yescharacteristic
407C4×C11C22×#4111yescharacteristic
408Dic11—42no—
409Dic11—42no—
410Dic11—42no—
411C25C22⋊D1111yescharacteristic
412C2×#41—114no—
413C2×#41—222no—
414C2×#41—224no—
415C2×#41—224no—
416C22×Q8—22no—
417C22×Q8—21no—
418C22×Q8—24no—
419C22×Q8—24no—
420C22×Q8—111no—
421C22×Q8C22×D1112yes—
422C22×Q8C22×D1114yes—
423C22×D4—111no—
424C22×D4—221no—
425C22×D4—221no—
426C22×D4—221no—
427C23×C4—24no—
428C23×C4—24no—
429C23×C4—21no—
430C23×C4—21no—
431C23×C4—221no—
432C23×C4C22⋊D1111yescharacteristic
433C23×C4C22⋊D1111yescharacteristic
434C23×C4C22⋊D1111yescharacteristic
435C23×C4C22⋊D1114yes—
436C23×C4C22×D1111yescharacteristic
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1114yes—
439C23×C4C22×D1111yescharacteristic
440#137—2232no—
441C2×Q16—118no—
442C2×Q16—228no—
443C2×SD16—118no—
444C2×SD16—228no—
445C2×M16—118no—
446C2×M16—114no—
447C2×M16—114no—
448C2×M16—118no—
449C2×M16—228no—
450C2×M16—2232no—
451C2×M16—224no—
452C22×C8—112no—
453C22×C8—112no—
454C22×C8—118no—
455C22×C8—228no—
456#123—228no—
457C22⋊Q8—24no—
458C22⋊Q8—24no—
459C22⋊Q8—28no—
460C22⋊Q8—28no—
461C22⋊Q8—114no—
462C22⋊Q8—114no—
463C22⋊Q8—222no—
464C22⋊Q8—222no—
465C22⋊Q8C22×D1118yes—
466C22⋊Q8C22×D1118yes—
467#121—114no—
468#121—114no—
469#121—222no—
470#121—222no—
471#120—228no—
472C4×D4—228no—
473C4×D4—228no—
474#117—114no—
475#117—222no—
476C2×C4⋊C4—22no—
477C2×C4⋊C4—22no—
478C2×C4⋊C4—28no—
479C2×C4⋊C4—22no—
480C2×C4⋊C4—21no—
481C2×C4⋊C4—111no—
482C2×C4⋊C4—111no—
483C2×C4⋊C4—221no—
484C2×C4⋊C4—221no—
485C2×C4⋊C4C22×D1112yes—
486C2×C4⋊C4C22×D1114yes—
487C2×C22⋊C4—22no—
488C2×C22⋊C4—22no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—221no—
493C2×C22⋊C4—221no—
494C2×C22⋊C4—221no—
495C2×C42—221no—
496#107—118no—
497#106—118no—
498#103—118no—
499#103—118no—
500#103—118no—
501#102—118no—
502C2×C11—24no—
503C2×C11—24no—
504C2×C11—42no—
505C2×C11#305614yescomplemented
506C2×C11C22×#12111yescharacteristic
507C2×C11C22×#13711yescharacteristic
508C2×C11C2×#57511yescharacteristic
509D11—82no—
510C24—24no—
511C24—24no—
512C24—42no—
513C24—221no—
514C24C2×C22⋊D1111yescharacteristic
515C24C2×C22⋊D1114yes—
516C24C2×C22⋊D1111yescharacteristic
517C24C2×C22⋊D1111yescharacteristic
518#41—228no—
519#41—228no—
520#41—448no—
521C2×Q8—24no—
522C2×Q8—22no—
523C2×Q8—24no—
524C2×Q8—28no—
525C2×Q8—24no—
526C2×Q8—28no—
527C2×Q8—44no—
528C2×Q8—48no—
529C2×Q8—112no—
530C2×Q8—221no—
531C2×Q8—222no—
532C2×Q8—222no—
533C2×Q8C23×D1114yes—
534C2×D4—112no—
535C2×D4—224no—
536C2×D4—224no—
537C2×D4—224no—
538C2×D4—222no—
539C2×D4—222no—
540C2×D4—221no—
541C2×D4—444no—
542C2×D4—444no—
543C2×D4—444no—
544C22×C4—24no—
545C22×C4—24no—
546C22×C4—24no—
547C22×C4—216no—
548C22×C4—22no—
549C22×C4—28no—
550C22×C4—22no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—28no—
554C22×C4—24no—
555C22×C4—24no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—44no—
559C22×C4—44no—
560C22×C4—221no—
561C22×C4—221no—
562C22×C4—221no—
563C22×C4—224no—
564C22×C4—444no—
565C22×C4D4×D1114yes—
566C22×C4#434114yes—
567C22×C4C2×C22⋊D1114yes—
568C22×C4C2×C22⋊D1114yes—
569C22×C4C2×C22⋊D1114yes—
570C22×C4C2×C22⋊D1112yes—
571C22×C4C2×C22⋊D1112yes—
572C22×C4C2×C22⋊D1111yescharacteristic
573C22×C4C2×C22⋊D1111yescharacteristic
574C22×C4C2×C22⋊D1112yes—
575C22×C4C2×C22⋊D1111yescharacteristic
576C22×C4C23×D1112yes—
577C22×C4C23×D1112yes—
578C22×C4C23×D1112yes—
579C22×C4C23×D1111yescharacteristic
580Q16—2216no—
581SD16—2216no—
582M16—1116no—
583M16—2216no—
584M16—228no—
585C2×C8—118no—
586C2×C8—114no—
587C2×C8—114no—
588C2×C8—2216no—
589C2×C8—224no—
590C4⋊C4—28no—
591C4⋊C4—28no—
592C4⋊C4—24no—
593C4⋊C4—22no—
594C4⋊C4—112no—
595C4⋊C4—112no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—224no—
599C4⋊C4—224no—
600C4⋊C4C23×D1114yes—
601C22⋊C4—28no—
602C22⋊C4—28no—
603C22⋊C4—224no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C22⋊C4—224no—
607C22⋊C4—224no—
608C42—224no—
609C11C2×#305611yescharacteristic, complemented, Sylow
610C23—22no—
611C23—22no—
612C23—22no—
613C23—22no—
614C23—28no—
615C23—22no—
616C23—22no—
617C23—28no—
618C23—22no—
619C23—44no—
620C23—416no—
621C23—222no—
622C23—442no—
623C23—442no—
624C23—442no—
625C23#6699214yes—
626C23#6699514yescomplemented
627C23C22×C22⋊D1112yes—
628C23C22×C22⋊D1112yes—
629C23C22×C22⋊D1112yes—
630C23C22×C22⋊D1111yescharacteristic
631Q8—24no—
632Q8—24no—
633Q8—48no—
634Q8—44no—
635Q8—222no—
636Q8—222no—
637Q8—442no—
638D4—222no—
639D4—222no—
640D4—448no—
641D4—448no—
642D4—448no—
643D4—442no—
644C2×C4—28no—
645C2×C4—22no—
646C2×C4—22no—
647C2×C4—28no—
648C2×C4—28no—
649C2×C4—24no—
650C2×C4—24no—
651C2×C4—22no—
652C2×C4—22no—
653C2×C4—22no—
654C2×C4—22no—
655C2×C4—24no—
656C2×C4—24no—
657C2×C4—48no—
658C2×C4—48no—
659C2×C4—44no—
660C2×C4—44no—
661C2×C4—222no—
662C2×C4—222no—
663C2×C4—222no—
664C2×C4—442no—
665C2×C4—442no—
666C2×C4—442no—
667C2×C4—448no—
668C2×C4#6699214yes—
669C2×C4#6699218yes—
670C2×C4C2×D4×D1112yes—
671C2×C4C2×D4×D1114yes—
672C2×C4C2×#434112yes—
673C2×C4C2×#434114yes—
674C2×C4C22×C22⋊D1112yes—
675C2×C4C22×C22⋊D1112yes—
676C2×C4C22×C22⋊D1112yes—
677C2×C4C22×C22⋊D1111yescharacteristic
678C2×C4C24×D1111yescharacteristic
679C8—118no—
680C8—224no—
681C22—22no—
682C22—22no—
683C22—22no—
684C22—28no—
685C22—28no—
686C22—22no—
687C22—22no—
688C22—22no—
689C22—22no—
690C22—416no—
691C22—44no—
692C22—442no—
693C22—442no—
694C22—442no—
695C22—884no—
696C22C2×#6699214yes—
697C22C2×#6699212yes—
698C22C2×#6699512yes—
699C22C2×#6699514yescomplemented
700C22#1062335312yes—
701C22C23×C22⋊D1111yescharacteristic
702C4—22no—
703C4—22no—
704C4—44no—
705C4—44no—
706C4—442no—
707C4—442no—
708C4—442no—
709C4C2×#6699214yes—
710C4C2×#6699212yes—
711C4C22×D4×D1111yescharacteristic
712C4C22×#434111yescharacteristic
713C2—24no—
714C2—24no—
715C2—42no—
716C2—882no—
717C2#1307824214yesdirect product factor
718C2C22×#6699211yescharacteristic
719C2C22×#6699511yescharacteristic
720C2C2×#1062335311yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C22×D4
prime radicalC2×#10623322C2
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#3056
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. C22×#66995C2semidirect
2. C23×#4318C2semidirect
4. #13078242C2direct (N × H)
5. C2×#10622665C2semidirect
6. C2×#10622662C2semidirect
7. C2×#10622664C2semidirect
8. C2×#10622661C2semidirect
9. C2×#10622577C2semidirect
10. C2×#10622579C2semidirect
11. C2×#10622838C2semidirect
12. C22×C11×C22⋊Q8C2semidirect
21. C2×C11×C22⋊Q8C22semidirect
26. C22×#4326C22semidirect
28. C2×#66995C22semidirect
29. C22×#4325C22semidirect
44. C22×#4318C22semidirect
46. #10622838C22semidirect
47. C2×#66899C22semidirect
48. C2×#66899C22semidirect
49. #10622665C22semidirect
50. #10622664C22semidirect
51. #10622662C22semidirect
52. #10622661C22semidirect
53. C2×#66874C22semidirect
54. #10622579C22semidirect
55. C2×#66873C22semidirect
56. #10622577C22semidirect
57. C2×#66872C22semidirect
58. C2×#66871C22semidirect
109. C2×#4326C23semidirect
112. C2×#4325C23semidirect
136. C2×#4318D4semidirect
144. #66899C23semidirect
145. #66899C23semidirect
146. #66874C23semidirect
147. #66873C23semidirect
148. #66872C23semidirect
149. #66871C23semidirect
244. #4318C2×D4semidirect
253. C22×C22⋊Q8D11semidirect
274. C23×C11#137semidirect
356. C2×C22⋊Q8C2×D11semidirect
393. C22×C11C2×#137semidirect
505. C2×C11#3056semidirect
609. C11C2×#3056semidirect
626. C23#66995semidirect
699. C22C2×#66995semidirect
717. C2#13078242direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669952
C23×#43182
C2×#106233222
#130782422
C2×#106226652
C2×#106226622
C2×#106226642
C2×#106226612
C2×#106225772
C2×#106225792
C2×#106228382
C22×C11×C22⋊Q82
C2×#305611