Finite Group Databasebeta

← #14788243

Subgroups — #14788243

Order 2816.

1078 conjugacy classes of subgroups.

The subgroup lattice has 740 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623049C211yesmaximal, characteristic, complemented
2C2×#10622622C211yesmaximal, characteristic, complemented
3C2×#10622632C211yesmaximal, characteristic, complemented
4#13069819C211yesmaximal, characteristic, complemented
5#13069812C211yesmaximal, characteristic, complemented
6#13069619C211yesmaximal, characteristic
7#13069619C211yesmaximal, characteristic
8#13069573C211yesmaximal, characteristic, complemented
9#13069539C211yesmaximal, characteristic, complemented
10#13068974C211yesmaximal, characteristic, complemented
11#13068974C211yesmaximal, characteristic, complemented
12#13068883C211yesmaximal, characteristic, complemented
13#13068869C211yesmaximal, characteristic, complemented
14#13068600C211yesmaximal, characteristic, complemented
15C11×#2324C211yesmaximal, characteristic
16C2×C11×#121C2211yescharacteristic
17C2×C4×D4×C11C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4324C2211yescharacteristic
20C22×#4324C2211yescharacteristic
21C2×#66977C2211yescharacteristic
22C2×#66977C2211yescharacteristic
23#10623049—24no—
24#10623049—24no—
25C2×#66942—21no—
26C2×#66942—21no—
27C2×#66932—21no—
28C2×#66932—21no—
29C2×#66923C2211yescharacteristic
30C2×#66922C2211yescharacteristic
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C11×#390—21no—
34C11×#390C2211yescharacteristic
35C11×#389C2211yescharacteristic
36C11×#388—21no—
37C11×#386—21no—
38C11×#385—21no—
39C11×#380C2211yescharacteristic
40C4×C11×C4⋊C4C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42C2×#66896C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×C22⋊(C11⋊C8)C2211yescharacteristic
45#10622632—24no—
46#10622622—24no—
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66874C2211yescharacteristic
51C2×#66874C2211yescharacteristic
52C2×#66874C2211yescharacteristic
53C2×#66872C2211yescharacteristic
54C2×#66871C2211yescharacteristic
55C2×C4⋊(C11⋊C8)C2211yescharacteristic
56C2×C4⋊(C11⋊C8)C2211yescharacteristic
57#10622167C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622162C2211yescharacteristic
62#10622162C2211yescharacteristic
63C22×D4×C11—21no—
64C22×D4×C11C2311yescharacteristic
65C23×C4×C11—21no—
66C23×C4×C11C2311yescharacteristic
67C22×Dic22C2311yescharacteristic
68C22×Dic22C2311yescharacteristic
69C11×#121—22no—
70C11×#121—22no—
71C4×D4×C11—22no—
72C4×D4×C11—22no—
73C11×#117—22no—
74C11×#117—22no—
75C2×C11×C4⋊C4—21no—
76C2×C11×C4⋊C4D411yescharacteristic
77C2×C11×C4⋊C4D411yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C4⋊C4C2311yescharacteristic
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C22⋊C4—21no—
82C2×C11×C22⋊C4—21no—
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4D411yescharacteristic
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×#4324—22no—
94C2×#4324—22no—
95C2×#4324—22no—
96C2×#4324—22no—
97C2×#4324—41no—
98C2×#4324—41no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11—21no—
101C2×C4⋊Dic11C2311yescharacteristic
102C2×C4⋊Dic11C2311yescharacteristic
103#66977—22no—
104#66977—22no—
105#66977—22no—
106#66977—22no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119#66942—28no—
120#66942—28no—
121#66932—28no—
122#66932—28no—
123#66923—22no—
124#66923D414yescomplemented
125#66922—22no—
126#66922D414yescomplemented
127C4×Dic22—22no—
128C4×Dic22—22no—
129C4×Dic22—22no—
130C4×Dic22—22no—
131C11×#95—21no—
132C11×#95—21no—
133C11×#95—21no—
134#66896—22no—
135#66896—22no—
136C22⋊(C11⋊C8)—41no—
137C22⋊(C11⋊C8)—41no—
138#66874—22no—
139#66874—22no—
140#66874—22no—
141#66874—22no—
142#66874—41no—
143#66874—41no—
144#66872—22no—
145#66871—22no—
146C4⋊(C11⋊C8)—22no—
147C4⋊(C11⋊C8)—22no—
148#24163—111nomaximal, Sylow
149C24×C11—21no—
150C24×C11C2×D411yescharacteristic
151C2×D4×C11—24no—
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—81no—
158C2×D4×C11—81no—
159C2×D4×C11#4112yes—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11—42no—
170C22×C4×C11—81no—
171C22×C4×C11—81no—
172C22×C4×C11C2×D411yescharacteristic
173C22×C4×C11C2×D411yescharacteristic
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2411yescharacteristic
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—21no—
182C2×Dic22—21no—
183C2×Dic22—21no—
184C2×Dic22—21no—
185C2×Dic22—21no—
186C2×Dic22—21no—
187C2×Dic22—21no—
188C2×Dic22—21no—
189C2×Dic22—21no—
190C2×Dic22—21no—
191C2×Dic22—21no—
192C2×Dic22C2×D412yes—
193C2×Dic22C2×D412yes—
194C11×C4⋊C4—22no—
195C11×C4⋊C4—22no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—81no—
202C11×C4⋊C4#4112yes—
203C11×C22⋊C4—24no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—22no—
206C11×C22⋊C4—42no—
207C11×C22⋊C4—81no—
208C11×C22⋊C4—81no—
209C11×C22⋊C4—81no—
210C42×C11—21no—
211C42×C11—21no—
212C42×C11—81no—
213C42×C11C2×D412yes—
214C42×C11C2×D412yes—
215C22⋊Dic11—24no—
216C22⋊Dic11—24no—
217#4324—44no—
218#4324—44no—
219C4⋊Dic11—24no—
220C4⋊Dic11—24no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11C2×D412yes—
224C4⋊Dic11C2×D412yes—
225Dic11⋊C4—24no—
226Dic11⋊C4—24no—
227Dic11⋊C4—24no—
228Dic11⋊C4—24no—
229Dic11⋊C4—24no—
230Dic11⋊C4—24no—
231C4×Dic11—24no—
232C4×Dic11—24no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8—21no—
244C2×C11⋊C8—21no—
245C2×#541—111no—
246C2×#478—111no—
247C2×#461—111no—
248#2324D1111yescharacteristic
249#2036—111no—
250#2035—111no—
251#2000—111no—
252#2000—111no—
253#1989—111no—
254#1981—111no—
255#1880—111no—
256#1880—111no—
257#1865—111no—
258#1863—111no—
259#1798—111no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C22×D411yescharacteristic
275D4×C11—22no—
276D4×C11—22no—
277D4×C11—41no—
278D4×C11—41no—
279D4×C11—84no—
280C2×C4×C11—21no—
281C2×C4×C11—21no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—21no—
287C2×C4×C11—21no—
288C2×C4×C11—22no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—21no—
293C2×C4×C11—21no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11—41no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—84no—
307C2×C4×C11#12012yes—
308C2×C4×C11#12012yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C22×D411yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C112−1+411yescharacteristic
315C2×Dic11—22no—
316C2×Dic11—22no—
317C2×Dic11—22no—
318C2×Dic11—22no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327Dic22—22no—
328Dic22—22no—
329Dic22—22no—
330Dic22—22no—
331Dic22—41no—
332Dic22—41no—
333Dic22—41no—
334Dic22—41no—
335C11⋊C8—41no—
336C11⋊C8—41no—
337C11⋊C8—41no—
338C11⋊C8—41no—
339C22×SD16—111no—
340C22×SD16—111no—
341#541—224no—
342#541—224no—
343C2×C4⋊Q8—111no—
344C2×#126—221no—
345C2×#126—221no—
346C2×#125—111no—
347C2×#125—221no—
348C2×#125—221no—
349C2×C22⋊Q8—111no—
350C2×C22⋊Q8—111no—
351C2×#121C2×D1111yescharacteristic
352C2×C4×Q8—111no—
353C2×C4×Q8—111no—
354C2×C4×D4C2×D1111yescharacteristic
355C2×#117C2×D1111yescharacteristic
356#478—224no—
357#461—224no—
358C2×#107—111no—
359C2×#106—111no—
360C2×C4⋊C8—111no—
361C2×C4⋊C8—111no—
362C2×#103—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#103—111no—
366C2×#103—111no—
367C2×#103—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×C22⋊C8—111no—
371C2×C22⋊C8—111no—
372#390—21no—
373#390C2×D1111yescharacteristic
374#389C2×D1111yescharacteristic
375#388—21no—
376#386—21no—
377#385—21no—
378#380C2×D1111yescharacteristic
379C4×C4⋊C4C2×D1111yescharacteristic
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#336—111no—
385#336—111no—
386C22×C11—41no—
387C22×C11—42no—
388C22×C11—41no—
389C22×C11—42no—
390C22×C11—41no—
391C22×C11—42no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—41no—
396C22×C11—81no—
397C22×C11—81no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11C2×#12011yescharacteristic
401C22×C11#52511yescharacteristic
402C22×C11#53711yescharacteristic
403C22×C11#57711yescharacteristic
404C22×C11#57711yescharacteristic
405C22×C11#57711yescharacteristic
406C22×C11#57811yescharacteristic
407C4×C11—22no—
408C4×C11—22no—
409C4×C11—42no—
410C4×C11—41no—
411C4×C11—41no—
412C4×C11—41no—
413C4×C11—81no—
414C4×C11—81no—
415C4×C11#54611yescharacteristic
416C4×C11#54711yescharacteristic
417C4×C11#54811yescharacteristic
418C4×C11#55011yescharacteristic
419Dic11—42no—
420Dic11—42no—
421Dic11—42no—
422Dic11—42no—
423C22×Q8—111no—
424C22×Q8—111no—
425C22×D4—21no—
426C22×D4C22×D1111yescharacteristic
427C23×C4—21no—
428C23×C4C22×D1111yescharacteristic
429C2×SD16—222no—
430C2×SD16—222no—
431C2×SD16—222no—
432C2×SD16—222no—
433C2×SD16—441no—
434C2×SD16—441no—
435C22×C8—111no—
436C22×C8—111no—
437C22×C8—111no—
438C22×C8—111no—
439C4⋊Q8—114no—
440C4⋊Q8—222no—
441#126—228no—
442#126—228no—
443#125—114no—
444#125—228no—
445#125—228no—
446#125—222no—
447C22⋊Q8—222no—
448C22⋊Q8—222no—
449C22⋊Q8—222no—
450C22⋊Q8—222no—
451#121—22no—
452#121—22no—
453C4×Q8—222no—
454C4×Q8—222no—
455C4×Q8—222no—
456C4×Q8—222no—
457C4×D4—22no—
458C4×D4—22no—
459#117—22no—
460#117—22no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—221no—
465C2×C4⋊C4—221no—
466C2×C4⋊C4—221no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4C22⋊D1111yescharacteristic
473C2×C4⋊C4C22⋊D1111yescharacteristic
474C2×C4⋊C4C22×D1111yescharacteristic
475C2×C4⋊C4C22×D1111yescharacteristic
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—21no—
479C2×C22⋊C4—21no—
480C2×C22⋊C4—21no—
481C2×C22⋊C4—21no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4C22⋊D1111yescharacteristic
485C2×C22⋊C4C22⋊D1111yescharacteristic
486C2×C42—21no—
487C2×C42—221no—
488C2×C42—221no—
489C2×C42C22×D1111yescharacteristic
490C2×C42C22×D1111yescharacteristic
491#107—222no—
492#106—222no—
493C4⋊C8—222no—
494C4⋊C8—222no—
495#103—222no—
496#103—222no—
497#103—222no—
498#103—222no—
499#103—441no—
500#103—441no—
501#102—222no—
502#102—222no—
503C22⋊C8—441no—
504C22⋊C8—441no—
505#95—21no—
506#95—21no—
507#95—21no—
508C2×C11—81no—
509C2×C11—82no—
510C2×C11#240711yescharacteristic
511C2×C11#301011yescharacteristic
512C2×C11#301311yescharacteristic
513C2×C11#312011yescharacteristic
514C2×C11#312311yescharacteristic
515C2×C11#325811yescharacteristic
516C2×C11#326011yescharacteristic
517C24—21no—
518C24C2×C22⋊D1111yescharacteristic
519C2×Q8—112no—
520C2×Q8—112no—
521C2×Q8—221no—
522C2×Q8—221no—
523C2×Q8—221no—
524C2×Q8—221no—
525C2×Q8—221no—
526C2×Q8—221no—
527C2×Q8—221no—
528C2×Q8—221no—
529C2×Q8—221no—
530C2×Q8—221no—
531C2×D4—24no—
532C2×D4—21no—
533C2×D4—21no—
534C2×D4—21no—
535C2×D4—21no—
536C2×D4—21no—
537C2×D4—81no—
538C2×D4—81no—
539C2×D4#433912yes—
540C22×C4—21no—
541C22×C4—21no—
542C22×C4—21no—
543C22×C4—21no—
544C22×C4—21no—
545C22×C4—21no—
546C22×C4—21no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—42no—
550C22×C4—81no—
551C22×C4—81no—
552C22×C4—221no—
553C22×C4—221no—
554C22×C4—221no—
555C22×C4—221no—
556C22×C4C2×C22⋊D1111yescharacteristic
557C22×C4C2×C22⋊D1111yescharacteristic
558C22×C4C2×C22⋊D1111yescharacteristic
559C22×C4C2×C22⋊D1111yescharacteristic
560C22×C4C2×C22⋊D1111yescharacteristic
561C22×C4C23×D1111yescharacteristic
562SD16—444no—
563SD16—444no—
564C2×C8—221no—
565C2×C8—221no—
566C2×C8—221no—
567C2×C8—221no—
568C2×C8—221no—
569C2×C8—221no—
570C2×C8—221no—
571C2×C8—221no—
572C2×C8—221no—
573C2×C8—221no—
574C2×C8—221no—
575C2×C8—221no—
576C4⋊C4—22no—
577C4⋊C4—22no—
578C4⋊C4—21no—
579C4⋊C4—21no—
580C4⋊C4—21no—
581C4⋊C4—21no—
582C4⋊C4—21no—
583C4⋊C4—81no—
584C4⋊C4—112no—
585C4⋊C4—112no—
586C4⋊C4—224no—
587C4⋊C4—224no—
588C4⋊C4—224no—
589C4⋊C4—224no—
590C4⋊C4—224no—
591C4⋊C4—224no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4#433912yes—
597C22⋊C4—24no—
598C22⋊C4—22no—
599C22⋊C4—22no—
600C22⋊C4—42no—
601C22⋊C4—81no—
602C22⋊C4—81no—
603C22⋊C4—81no—
604C22⋊C4—224no—
605C22⋊C4—224no—
606C42—21no—
607C42—21no—
608C42—81no—
609C42—224no—
610C42—224no—
611C42D4×D1112yes—
612C42D4×D1112yes—
613C11#2416311yescharacteristic, complemented, Sylow
614C23—22no—
615C23—21no—
616C23—21no—
617C23—21no—
618C23—21no—
619C23—21no—
620C23—21no—
621C23—21no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—41no—
626C23—41no—
627C23—41no—
628C23C22×C22⋊D1111yescharacteristic
629Q8—222no—
630Q8—222no—
631Q8—222no—
632Q8—222no—
633Q8—441no—
634Q8—441no—
635Q8—441no—
636Q8—441no—
637D4—22no—
638D4—22no—
639D4—41no—
640D4—41no—
641D4—84no—
642C2×C4—21no—
643C2×C4—21no—
644C2×C4—21no—
645C2×C4—21no—
646C2×C4—21no—
647C2×C4—22no—
648C2×C4—21no—
649C2×C4—21no—
650C2×C4—21no—
651C2×C4—21no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—41no—
657C2×C4—41no—
658C2×C4—41no—
659C2×C4—41no—
660C2×C4—41no—
661C2×C4—41no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—84no—
669C2×C4—222no—
670C2×C4—222no—
671C2×C4—222no—
672C2×C4—222no—
673C2×C4—441no—
674C2×C4—441no—
675C2×C4—441no—
676C2×C4—441no—
677C2×C4—441no—
678C2×C4—441no—
679C2×C4—441no—
680C2×C4—441no—
681C2×C4#6699012yes—
682C2×C4#6699012yes—
683C2×C4C2×#433911yescharacteristic
684C2×C4C2×#433911yescharacteristic
685C2×C4C2×D4×D1111yescharacteristic
686C2×C4C2×D4×D1111yescharacteristic
687C2×C4#6704211yescharacteristic
688C2×C4#6704311yescharacteristic
689C8—441no—
690C8—441no—
691C8—441no—
692C8—441no—
693C22—41no—
694C22—42no—
695C22—41no—
696C22—42no—
697C22—41no—
698C22—42no—
699C22—41no—
700C22—41no—
701C22—41no—
702C22—41no—
703C22—81no—
704C22—81no—
705C22—81no—
706C22—81no—
707C22#1062332211yescharacteristic
708C22C2×#6699011yescharacteristic
709C22#1062336411yescharacteristic
710C22#1062336711yescharacteristic
711C22#1062336711yescharacteristic
712C22#1062336711yescharacteristic
713C22#1062336911yescharacteristic
714C4—22no—
715C4—22no—
716C4—42no—
717C4—41no—
718C4—41no—
719C4—41no—
720C4—81no—
721C4—81no—
722C4—442no—
723C4—442no—
724C4—442no—
725C4—442no—
726C4#1062308111yescharacteristic
727C4#1062308211yescharacteristic
728C4#1062308311yescharacteristic
729C4#1062308411yescharacteristic
730C2—81no—
731C2—82no—
732C2#1307196111yescharacteristic
733C2#1307790011yescharacteristic
734C2#1307792811yescharacteristic
735C2#1307883011yescharacteristic
736C2#1307886811yescharacteristic
737C2#1308004211yescharacteristic
738C2#1308006211yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2324C2
socleC23×C11C22×D4
prime radicalC2×C11×#121C22
hypercenter#2324D11
hypocenterC11#24163
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2324

Complements

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

NH ≅ G/Ntype
1. C2×#10623049C2semidirect
2. C2×#10622622C2semidirect
3. C2×#10622632C2semidirect
4. #13069819C2semidirect
5. #13069812C2semidirect
8. #13069573C2semidirect
9. #13069539C2semidirect
10. #13068974C2semidirect
11. #13068974C2semidirect
12. #13068883C2semidirect
13. #13068869C2semidirect
14. #13068600C2semidirect
124. #66923D4semidirect
126. #66922D4semidirect
613. C11#24163semidirect

Maximal subgroups

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

subgroupindex
C2×#106230492
C2×#106226222
C2×#106226322
#130698192
#130698122
#130696192
#130695732
#130695392
#130689742
#130688832
#130688692
#130686002
C11×#23242
#2416311