Finite Group Databasebeta

← #14763555

Subgroups — #14763555

Order 2816.

1150 conjugacy classes of subgroups.

The subgroup lattice has 756 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623093C211yesmaximal, characteristic
2C2×#10622453C211yesmaximal, characteristic, complemented
3#13071241C211yesmaximal, characteristic, complemented
4#13069583C211yesmaximal, characteristic, complemented
5#13069579C211yesmaximal, characteristic, complemented
6#13069438C211yesmaximal, characteristic, complemented
7#13069420C211yesmaximal, characteristic, complemented
8#13068937C211yesmaximal, characteristic, complemented
9#13068935C211yesmaximal, characteristic, complemented
10#13068932C211yesmaximal, characteristic, complemented
11#13068930C211yesmaximal, characteristic, complemented
12#13068623C211yesmaximal, characteristic, complemented
13#13068617C211yesmaximal, characteristic, complemented
14#13068616C211yesmaximal, characteristic, complemented
15C11×#1804C211yesmaximal, characteristic, complemented
16C2×C4×D4×C11C2211yescharacteristic
17C2×#66993C2211yescharacteristic
18C2×#66991C2211yescharacteristic
19C2×#66983—21no—
20C2×#66982—21no—
21#10623093—24no—
22#10623093C418yescomplemented
23C2×#66948C2211yescharacteristic
24C2×#66945C2211yescharacteristic
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×#66943C2211yescharacteristic
27C2×#66937—21no—
28C2×#66936—21no—
29C2×C4×D44C2211yescharacteristic
30C2×#66925C2211yescharacteristic
31C2×C11×C4⋊C8C2211yescharacteristic
32C2×C11×#102C2211yescharacteristic
33C2×C11×#102C2211yescharacteristic
34C11×#382C2211yescharacteristic
35C2×#66896C2211yescharacteristic
36C2×#66896C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×(C2×D11)⋊C8C2211yescharacteristic
41C2×#66879C2211yescharacteristic
42C2×C8×Dic11C2211yescharacteristic
43#10622590C2211yescharacteristic
44#10622589C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47#10622548C2211yescharacteristic
48C2×C4⋊(C11⋊C8)C2211yescharacteristic
49#10622453—24no—
50#10622281—21no—
51#10622281—21no—
52#10622260—21no—
53#10622260—21no—
54C11×#340C2211yescharacteristic
55C11×#340C2211yescharacteristic
56#10622189C2211yescharacteristic
57#10622189C2211yescharacteristic
58#10622167C2211yescharacteristic
59#10622167C2211yescharacteristic
60#10622167C2211yescharacteristic
61#10622167C2211yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C22×C22⋊D11—21no—
67C22×D44—21no—
68C22×D44C2311yescharacteristic
69C22×C4×D11—21no—
70C22×C4×D11—21no—
71C22×C4×D11C2311yescharacteristic
72C22×C8×C11C2311yescharacteristic
73C22×C8×C11C2311yescharacteristic
74C4×D4×C11—22no—
75C4×D4×C11C2×C414yescomplemented
76C2×C11×C4⋊C4C2311yescharacteristic
77C2×C11×C4⋊C4C2311yescharacteristic
78C2×C11×C4⋊C4C2311yescharacteristic
79C2×C11×C22⋊C4—21no—
80C2×C42×C11C2311yescharacteristic
81C2×C22⋊Dic11—21no—
82#66993—22no—
83#66993C2×C414yescomplemented
84#66991—22no—
85#66991C2×C414yes—
86#66983—28no—
87#66982—28no—
88C2×(C2×D11)⋊C4—21no—
89C2×(C2×D11)⋊C4—21no—
90C2×(C2×D11)⋊C4—21no—
91C2×(C2×D11)⋊C4D411yescharacteristic
92C2×(C2×D11)⋊C4D411yescharacteristic
93C2×C4⋊Dic11—21no—
94C2×C4⋊Dic11—21no—
95C2×C4⋊Dic11—21no—
96C2×C4⋊Dic11C2311yescharacteristic
97C2×C4⋊Dic11C2311yescharacteristic
98C2×C4⋊Dic11C2311yescharacteristic
99C2×Dic11⋊C4—21no—
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4D411yescharacteristic
104C2×Dic11⋊C4D411yescharacteristic
105C2×C4×Dic11—21no—
106C2×C4×Dic11C2311yescharacteristic
107C22×C11⋊C8C2311yescharacteristic
108C22×C11⋊C8C2311yescharacteristic
109#66948—22no—
110#66948C2×C414yes—
111#66945—41no—
112#66945—41no—
113C4⋊C4×D11—41no—
114C4⋊C4×D11—41no—
115#66943—22no—
116#66943C2×C414yescomplemented
117#66937—28no—
118#66936—28no—
119C4×D44—22no—
120C4×D44C2×C414yescomplemented
121#66925C2×C414yes—
122#66925D414yes—
123C11×C4⋊C8—22no—
124C11×#102—41no—
125C11×#102—41no—
126C11×#95—21no—
127C11×#95—21no—
128#66896—41no—
129#66896—41no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132#66885—41no—
133#66885—41no—
134(C2×D11)⋊C8—22no—
135(C2×D11)⋊C8—22no—
136#66879—22no—
137C8×Dic11—22no—
138#66873—41no—
139#66873—41no—
140C4⋊(C11⋊C8)—22no—
141#21872—111nomaximal, Sylow
142C24×C11—21no—
143C23×D11—21no—
144C23×D11C2×D411yescharacteristic
145C2×D4×C11—21no—
146C2×D4×C11—21no—
147C2×D4×C11—21no—
148C2×D4×C11—21no—
149C2×D4×C11—21no—
150C2×D4×C11C22×C412yes—
151C22×C4×C11—21no—
152C22×C4×C11—24no—
153C22×C4×C11—21no—
154C22×C4×C11—21no—
155C22×C4×C11—81no—
156C22×C4×C11—81no—
157C22×C4×C11C2×D411yescharacteristic
158C22×C4×C11C2×D411yescharacteristic
159C22×C4×C11C2411yescharacteristic
160C2×C22⋊D11—24no—
161C2×C22⋊D11—24no—
162C2×C22⋊D11—24no—
163C2×C22⋊D11—81no—
164C2×C22⋊D11—81no—
165C2×C22⋊D11—81no—
166C2×C22⋊D11—81no—
167C2×C22⋊D11—81no—
168C2×C22⋊D11—81no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C2×D44—24no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—81no—
182C2×D44—81no—
183C2×D44C22×C412yes—
184C2×C4×D11—24no—
185C2×C4×D11—21no—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—42no—
190C2×C4×D11—81no—
191C2×C4×D11—81no—
192C2×C4×D11—81no—
193C2×C4×D11—81no—
194C2×C4×D11C22×C412yes—
195C2×C4×D11C2×D412yes—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11—21no—
199C2×C8×C11—21no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C11×C4⋊C4—21no—
203C11×C4⋊C4—21no—
204C11×C4⋊C4—21no—
205C11×C4⋊C4—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4C22×C412yes—
208C11×C22⋊C4—24no—
209C42×C11C22×C412yes—
210C42×C11C2×D412yes—
211C22⋊Dic11—24no—
212(C2×D11)⋊C4—24no—
213(C2×D11)⋊C4—24no—
214(C2×D11)⋊C4—42no—
215(C2×D11)⋊C4C22⋊C414yes—
216(C2×D11)⋊C4C22⋊C414yes—
217C4⋊Dic11—24no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—81no—
224C4⋊Dic11—81no—
225C4⋊Dic11C22×C412yes—
226Dic11⋊C4—24no—
227Dic11⋊C4—42no—
228Dic11⋊C4—81no—
229Dic11⋊C4—81no—
230Dic11⋊C4C22⋊C414yes—
231Dic11⋊C4C22⋊C414yes—
232C4×Dic11—42no—
233C4×Dic11C22×C412yes—
234C4×Dic11C2×D412yes—
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×#540—111no—
242C2×#433—111no—
243#2317—111no—
244#1992—111no—
245#1991—111no—
246#1961—111no—
247#1957—111no—
248#1875—111no—
249#1875—111no—
250#1874—111no—
251#1874—111no—
252#1804—111no—
253#1804D1111yescharacteristic, complemented
254#1802—111no—
255#1802—111no—
256C23×C11—22no—
257C23×C11—41no—
258C23×C11—41no—
259C23×C11—41no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11C22×D411yescharacteristic
264C22×D11—21no—
265C22×D11—21no—
266C22×D11—21no—
267C22×D11—21no—
268C22×D11—21no—
269C22×D11—21no—
270C22×D11—22no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11C2×C22⋊C412yes—
278D4×C11—22no—
279D4×C11—22no—
280D4×C11—41no—
281D4×C11—41no—
282C2×C4×C11—21no—
283C2×C4×C11—21no—
284C2×C4×C11—21no—
285C2×C4×C11—21no—
286C2×C4×C11—22no—
287C2×C4×C11—41no—
288C2×C4×C11—41no—
289C2×C4×C11—41no—
290C2×C4×C11—41no—
291C2×C4×C11—41no—
292C2×C4×C11—41no—
293C2×C4×C11—41no—
294C2×C4×C11—41no—
295C2×C4×C11—84no—
296C2×C4×C11C2×C22⋊C412yes—
297C2×C4×C11C2×C22⋊C412yes—
298C2×C4×C11C23×C411yescharacteristic
299C2×C4×C11C22×D411yescharacteristic
300C2×C4×C11H(5,𝔽2)11yescharacteristic
301C2×C4×C11H(5,𝔽2)11yescharacteristic
302C2×C4×C112−1+411yescharacteristic
303C2×C4×C112−1+411yescharacteristic
304C22⋊D11—84no—
305C22⋊D11—84no—
306C22⋊D11—84no—
307C2×Dic11—21no—
308C2×Dic11—21no—
309C2×Dic11—21no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—21no—
313C2×Dic11—22no—
314C2×Dic11—41no—
315C2×Dic11—41no—
316C2×Dic11—41no—
317C2×Dic11—41no—
318C2×Dic11—41no—
319C2×Dic11—41no—
320C2×Dic11—41no—
321C2×Dic11—41no—
322C2×Dic11C2×C22⋊C412yes—
323C2×Dic11C2×C22⋊C412yes—
324C2×Dic11C2×C22⋊C412yes—
325D44—22no—
326D44—22no—
327D44—41no—
328D44—41no—
329D44—84no—
330C4×D11—22no—
331C4×D11—22no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—84no—
335C4×D11—84no—
336C8×C11—41no—
337C8×C11—41no—
338C11⋊C8—41no—
339C11⋊C8—41no—
340#540—118no—
341#540—224no—
342C2×#127—111no—
343C2×#125—111no—
344C2×#123—221no—
345C2×#123—221no—
346C2×#121—111no—
347C2×#121—111no—
348C2×#121—221no—
349C2×#121—221no—
350C2×C4×D4—111no—
351C2×C4×D4C2×D1111yescharacteristic
352C2×#117—111no—
353C2×#117—111no—
354C22×C4⋊C4—111no—
355#433—224no—
356C2×C4⋊C8—111no—
357C2×C4⋊C8C2×D1111yescharacteristic
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102—111no—
362C2×#102—111no—
363C2×#102—111no—
364C2×#102C2×D1111yescharacteristic
365C2×#102C2×D1111yescharacteristic
366C2×C22⋊C8—111no—
367C2×C22⋊C8—111no—
368C2×#97—111no—
369C2×C4×C8—111no—
370#389—221no—
371#389—221no—
372#385—221no—
373#385—221no—
374#384—111no—
375#384—111no—
376#382—111no—
377#382C2×D1111yescharacteristic
378#340—111no—
379#340—111no—
380#340—111no—
381#340—111no—
382#340—111no—
383#340—111no—
384#340C2×D1111yescharacteristic
385#340C2×D1111yescharacteristic
386C22×C11—42no—
387C22×C11—42no—
388C22×C11—42no—
389C22×C11—81no—
390C22×C11—81no—
391C22×C11—81no—
392C22×C11—81no—
393C22×C11C22×C22⋊C411yescharacteristic
394C22×C11#53511yescharacteristic
395C22×C11#53611yescharacteristic
396C22×C11#57611yescharacteristic
397C22×C11#57611yescharacteristic
398C22×C11#57711yescharacteristic
399C22×C11#57711yescharacteristic
400C2×D11—22no—
401C2×D11—22no—
402C2×D11—22no—
403C2×D11—41no—
404C2×D11—41no—
405C2×D11—41no—
406C2×D11—41no—
407C2×D11—42no—
408C2×D11—42no—
409C2×D11—42no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C4×C11—22no—
415C4×C11—22no—
416C4×C11—42no—
417C4×C11—81no—
418C4×C11—81no—
419C4×C11#52011yescharacteristic
420C4×C11#52011yescharacteristic
421C4×C11#53711yescharacteristic
422C4×C11#53711yescharacteristic
423Dic11—22no—
424Dic11—22no—
425Dic11—22no—
426Dic11—42no—
427Dic11—81no—
428Dic11—81no—
429C22×D4—111no—
430C22×D4—221no—
431C22×D4—221no—
432C22×D4—221no—
433C22×D4—221no—
434C22×D4C22×D1111yescharacteristic
435C23×C4—21no—
436C23×C4—111no—
437C23×C4—221no—
438C23×C4—221no—
439C22×C8—111no—
440C22×C8—111no—
441C22×C8C22×D1111yescharacteristic
442C22×C8C22×D1111yescharacteristic
443#127—114no—
444#127—222no—
445#125—114no—
446#125—222no—
447#123—228no—
448#123—228no—
449#121—114no—
450#121—114no—
451#121—228no—
452#121—228no—
453#121—222no—
454#121—222no—
455C4×D4—22no—
456C4×D4—114no—
457C4×D4—222no—
458C4×D4C4×D1114yescomplemented
459#117—114no—
460#117—114no—
461#117—441no—
462#117—441no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—111no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4—221no—
470C2×C4⋊C4—221no—
471C2×C4⋊C4—221no—
472C2×C4⋊C4—221no—
473C2×C4⋊C4—221no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—441no—
476C2×C4⋊C4—441no—
477C2×C4⋊C4C22×D1111yescharacteristic
478C2×C4⋊C4C22×D1111yescharacteristic
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C22⋊C4—21no—
481C2×C22⋊C4—111no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C42—111no—
488C2×C42—221no—
489C2×C42C22×D1111yescharacteristic
490C4⋊C8—22no—
491C4⋊C8—222no—
492#102—41no—
493#102—41no—
494#102—441no—
495#102—441no—
496#102—441no—
497#102—441no—
498#102—441no—
499#102—441no—
500C22⋊C8—222no—
501C22⋊C8—222no—
502#97—222no—
503C4×C8—222no—
504#95—21no—
505#95—21no—
506#95—221no—
507#95—221no—
508C2×C11—82no—
509C2×C11#231111yescharacteristic
510C2×C11#289711yescharacteristic
511C2×C11#289711yescharacteristic
512C2×C11#322011yescharacteristic
513C2×C11#322111yescharacteristic
514C2×C11#324111yescharacteristic
515C2×C11#324111yescharacteristic
516D11—42no—
517D11—82no—
518C24—21no—
519C24—111no—
520C24—221no—
521C2×D4—21no—
522C2×D4—21no—
523C2×D4—21no—
524C2×D4—21no—
525C2×D4—21no—
526C2×D4—112no—
527C2×D4—224no—
528C2×D4—224no—
529C2×D4—224no—
530C2×D4—224no—
531C2×D4—221no—
532C2×D4—221no—
533C2×D4—221no—
534C2×D4—221no—
535C2×D4—221no—
536C2×D4—881no—
537C2×D4—881no—
538C2×D4—881no—
539C2×D4—881no—
540C2×D4—881no—
541C2×D4—881no—
542C2×D4—881no—
543C2×D4—881no—
544C2×D4C2×C4×D1112yes—
545C22×C4—21no—
546C22×C4—24no—
547C22×C4—21no—
548C22×C4—21no—
549C22×C4—81no—
550C22×C4—81no—
551C22×C4—111no—
552C22×C4—111no—
553C22×C4—111no—
554C22×C4—112no—
555C22×C4—112no—
556C22×C4—221no—
557C22×C4—221no—
558C22×C4—221no—
559C22×C4—221no—
560C22×C4—221no—
561C22×C4—224no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4—442no—
565C22×C4—881no—
566C22×C4—881no—
567C22×C4—881no—
568C22×C4—881no—
569C22×C4D4×D1111yescharacteristic
570C22×C4D4×D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572C2×C8—21no—
573C2×C8—21no—
574C2×C8—21no—
575C2×C8—21no—
576C2×C8—21no—
577C2×C8—21no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C4⋊C4—21no—
585C4⋊C4—21no—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—21no—
589C4⋊C4—114no—
590C4⋊C4—114no—
591C4⋊C4—112no—
592C4⋊C4—224no—
593C4⋊C4—224no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—442no—
600C4⋊C4—881no—
601C4⋊C4—881no—
602C4⋊C4—881no—
603C4⋊C4—881no—
604C4⋊C4C2×C4×D1112yes—
605C22⋊C4—24no—
606C22⋊C4—114no—
607C22⋊C4—114no—
608C22⋊C4—224no—
609C22⋊C4—224no—
610C22⋊C4—224no—
611C22⋊C4—442no—
612C42—112no—
613C42—112no—
614C42—442no—
615C42C2×C4×D1112yes—
616C42D4×D1112yes—
617C11#2187211yescharacteristic, complemented, Sylow
618C23—22no—
619C23—41no—
620C23—41no—
621C23—41no—
622C23—41no—
623C23—41no—
624C23—41no—
625C23—112no—
626C23—221no—
627C23—221no—
628C23—221no—
629C23—221no—
630C23—221no—
631C23—221no—
632C23—222no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23C2×D4×D1111yescharacteristic
640D4—22no—
641D4—22no—
642D4—41no—
643D4—41no—
644D4—222no—
645D4—222no—
646D4—441no—
647D4—441no—
648D4—884no—
649D4—884no—
650D4—884no—
651D4—884no—
652C2×C4—21no—
653C2×C4—21no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—22no—
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—84no—
666C2×C4—112no—
667C2×C4—112no—
668C2×C4—112no—
669C2×C4—221no—
670C2×C4—221no—
671C2×C4—221no—
672C2×C4—221no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—222no—
676C2×C4—222no—
677C2×C4—222no—
678C2×C4—222no—
679C2×C4—222no—
680C2×C4—441no—
681C2×C4—441no—
682C2×C4—441no—
683C2×C4—441no—
684C2×C4—441no—
685C2×C4—441no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—884no—
689C2×C4—884no—
690C2×C4C22⋊C4×D1112yes—
691C2×C4C22⋊C4×D1112yes—
692C2×C4C22×C4×D1111yescharacteristic
693C2×C4C2×D4×D1111yescharacteristic
694C2×C4#6703711yescharacteristic
695C2×C4#6704011yescharacteristic
696C2×C4#6704211yescharacteristic
697C2×C4#6704311yescharacteristic
698C8—41no—
699C8—41no—
700C8—441no—
701C8—441no—
702C22—42no—
703C22—42no—
704C22—42no—
705C22—81no—
706C22—81no—
707C22—81no—
708C22—81no—
709C22—222no—
710C22—222no—
711C22—222no—
712C22—441no—
713C22—441no—
714C22—441no—
715C22—441no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—881no—
720C22—881no—
721C22—881no—
722C22—881no—
723C22C2×C22⋊C4×D1111yescharacteristic
724C22#1062313811yescharacteristic
725C22#1062315911yescharacteristic
726C22#1062330011yescharacteristic
727C22#1062330111yescharacteristic
728C22#1062330511yescharacteristic
729C22#1062330611yescharacteristic
730C4—22no—
731C4—22no—
732C4—42no—
733C4—81no—
734C4—81no—
735C4—222no—
736C4—222no—
737C4—222no—
738C4—442no—
739C4—881no—
740C4—881no—
741C4#1062303511yescharacteristic
742C4#1062305411yescharacteristic
743C4#1062313911yescharacteristic
744C4#1062316011yescharacteristic
745C2—82no—
746C2—442no—
747C2—882no—
748C2#1307120511yescharacteristic
749C2#1307713811yescharacteristic
750C2#1307714111yescharacteristic
751C2#1307966311yescharacteristic
752C2#1307967411yescharacteristic
753C2#1307986611yescharacteristic
754C2#1307987411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1804C2
socleC23×C11C22×D4
prime radicalC2×#10623093C2
cosocleC22×C4×C11C24
hypercenter#1804D11
hypocenterC11#21872
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1804

Complements

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

NH ≅ G/Ntype
2. C2×#10622453C2semidirect
3. #13071241C2semidirect
4. #13069583C2semidirect
5. #13069579C2semidirect
6. #13069438C2semidirect
7. #13069420C2semidirect
8. #13068937C2semidirect
9. #13068935C2semidirect
10. #13068932C2semidirect
11. #13068930C2semidirect
12. #13068623C2semidirect
13. #13068617C2semidirect
14. #13068616C2semidirect
15. C11×#1804C2semidirect
22. #10623093C4semidirect
75. C4×D4×C11C2×C4semidirect
83. #66993C2×C4semidirect
116. #66943C2×C4semidirect
120. C4×D44C2×C4semidirect
253. #1804D11semidirect
458. C4×D4C4×D11semidirect
617. C11#21872semidirect

Maximal subgroups

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

subgroupindex
C2×#106230932
C2×#106224532
#130712412
#130695832
#130695792
#130694382
#130694202
#130689372
#130689352
#130689322
#130689302
#130686232
#130686172
#130686162
C11×#18042
#2187211