Finite Group Databasebeta

← #14797632

Subgroups — #14797632

Order 2816.

1156 conjugacy classes of subgroups.

The subgroup lattice has 778 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622782C211yesmaximal, characteristic
2C2×C4×#4325C211yesmaximal, characteristic, complemented
3#13072135C211yesmaximal, characteristic, complemented
4#13071437C211yesmaximal, characteristic
5#13070147C211yesmaximal, characteristic, complemented
6#13070055C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069811C211yesmaximal, characteristic, complemented
9#13069302C211yesmaximal, characteristic, complemented
10#13069220C211yesmaximal, characteristic, complemented
11#13068947C211yesmaximal, characteristic, complemented
12#13068880C211yesmaximal, characteristic, complemented
13#13068615C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic
15C11×#1880C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C2×C4×Q8×C11C2211yescharacteristic, complemented
19C2×#66999C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C22⋊C4×D11—21no—
23C2×C4×D44C2211yescharacteristic
24C2×C11×#103C2211yescharacteristic, complemented
25C2×C11×#102C2211yescharacteristic
26C11×#390C2211yescharacteristic
27#10622843C2211yescharacteristic, complemented
28C2×#66899C2211yescharacteristic, complemented
29#10622834C2211yescharacteristic
30C2×#66896C2211yescharacteristic
31C2×#66896C2211yescharacteristic
32#10622782—24no—
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×(C2×D11)⋊C8C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66881C2211yescharacteristic, complemented
38C2×Dic11⋊C8C2211yescharacteristic, complemented
39C4×#4325—24no—
40#10622605—21no—
41#10622600C2211yescharacteristic
42#10622600C2211yescharacteristic
43#10622593—21no—
44#10622589C2211yescharacteristic, complemented
45C2×#66873C2211yescharacteristic
46C2×#66872C2211yescharacteristic, complemented
47#10622569—21no—
48#10622569—21no—
49#10622568—21no—
50#10622553—21no—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52#10622546—21no—
53#10622541C2211yescharacteristic, complemented
54C2×C4×C11⋊C8C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C2×D4×D11—22no—
66C2×D4×D11—22no—
67C2×D4×D11—22no—
68C2×D4×D11—22no—
69C2×D4×D11—41no—
70C2×D4×D11—41no—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11C2311yescharacteristic
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—41no—
78C22×C8×C11C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C4×Q8×C11—22no—
81C4×Q8×C11—41no—
82C2×C11×C4⋊C4—21no—
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C42×C11—21no—
88C2×C42×C11C2311yescharacteristic
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91#66999—22no—
92#66999—41no—
93C2×#4325—22no—
94C2×#4325—22no—
95C2×#4325D414yes—
96C2×(C2×D11)⋊C4—21no—
97C2×(C2×D11)⋊C4—21no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4D411yescharacteristic
102C2×(C2×D11)⋊C4D411yescharacteristic
103C2×C4⋊Dic11C2311yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×Dic11⋊C4—21no—
107C2×Dic11⋊C4—21no—
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11C2311yescharacteristic
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113#66946—22no—
114#66946—41no—
115C22⋊C4×D11—44no—
116C4×D44—22no—
117C4×D44—41no—
118C11×#103—41no—
119C11×#102—41no—
120#66899—22no—
121#66896—22no—
122#66896—22no—
123C11⋊#95—21no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95D411yescharacteristic
129C11⋊#95D411yescharacteristic
130#66885—22no—
131#66885—22no—
132(C2×D11)⋊C8—22no—
133(C2×D11)⋊C8—41no—
134#66881—41no—
135Dic11⋊C8—41no—
136#66873—22no—
137#66872—22no—
138C4×C11⋊C8—22no—
139#24901—111nomaximal, Sylow
140C24×C11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—81no—
148C23×D11—81no—
149C23×D11C2×D411yescharacteristic
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×Q8×C11C2×D412yes—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11#4112yes—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C2×C22⋊D11—24no—
169C2×C22⋊D11—42no—
170C2×C22⋊D11—42no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11—21no—
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177D4×D11—44no—
178D4×D11—44no—
179D4×D11—44no—
180D4×D11—44no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44C2×D412yes—
185C2×D44#4112yes—
186C2×D44#4112yes—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—21no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—42no—
197C2×C4×D11—81no—
198C2×C4×D11—81no—
199C11×SD16—44no—
200C2×C8×C11—21no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C11×C4⋊C4—21no—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—21no—
210C11×C4⋊C4—42no—
211C11×C22⋊C4—42no—
212C11×C22⋊C4—81no—
213C42×C11—21no—
214C42×C11—21no—
215C42×C11—42no—
216C22⋊Dic11—42no—
217C22⋊Dic11—81no—
218#4325—28no—
219(C2×D11)⋊C4—41no—
220(C2×D11)⋊C4—42no—
221(C2×D11)⋊C4—42no—
222(C2×D11)⋊C4—42no—
223(C2×D11)⋊C4—42no—
224(C2×D11)⋊C4—81no—
225(C2×D11)⋊C4SD1614yescomplemented
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—21no—
230C4⋊Dic11—21no—
231C4⋊Dic11—21no—
232Dic11⋊C4—42no—
233Dic11⋊C4—42no—
234Dic11⋊C4—81no—
235Dic11⋊C4—81no—
236C4×Dic11—21no—
237C4×Dic11—21no—
238C2×C11⋊C8—21no—
239C2×C11⋊C8—21no—
240C2×C11⋊C8—21no—
241C2×C11⋊C8—21no—
242C2×C11⋊C8—21no—
243C2×C11⋊C8C2×D412yes—
244C2×#450—111no—
245C2×C4×SD16—111no—
246#2423—111no—
247D4×C22⋊C4—111no—
248#2094—111no—
249#2077—111no—
250#2055—111no—
251#2035—111no—
252#1934—111no—
253#1923—111no—
254#1880D1111yescharacteristic, complemented
255#1877—111no—
256#1864—111no—
257#1802—111no—
258#1786—111no—
259C23×C11—22no—
260C23×C11—41no—
261C23×C11—41no—
262C23×C11—41no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11C22×D411yescharacteristic
267C22×D11—21no—
268C22×D11—22no—
269C22×D11—21no—
270C22×D11—22no—
271C22×D11—22no—
272C22×D11—21no—
273C22×D11—21no—
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—48no—
277C22×D11—48no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—84no—
283C22×D11—84no—
284C22×D11—84no—
285C22×D11—84no—
286C22×D11—84no—
287C22×D11C2×SD1612yes—
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—41no—
291Q8×C11—41no—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—41no—
295D4×C11—41no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—41no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11C2×SD1612yes—
311C2×C4×C11C22×D411yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11H(5,𝔽2)11yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C22⋊D11—48no—
318C2×Dic11—21no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—21no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11C2×SD1612yes—
336D44—22no—
337D44—22no—
338D44—22no—
339D44#12314yes—
340C4×D11—41no—
341C4×D11—41no—
342C4×D11—41no—
343C4×D11—41no—
344C4×D11—84no—
345C4×D11—84no—
346C8×C11—41no—
347C8×C11—41no—
348C11⋊C8—22no—
349C11⋊C8—41no—
350C23×D4—111no—
351C22×SD16—111no—
352C22×SD16C2×D1111yescharacteristic
353C2×C22⋊Q8—111no—
354C2×C4×Q8C2×D1111yescharacteristic, complemented
355C2×C4×D4—111no—
356C2×C4×D4—111no—
357C22×C22⋊C4—221no—
358#450—224no—
359C4×SD16—224no—
360C2×#106—111no—
361C2×#106—111no—
362C2×C4⋊C8—111no—
363C2×#103—111no—
364C2×#103C2×D1111yescharacteristic, complemented
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102—111no—
370C2×#102C2×D1111yescharacteristic
371C2×C22⋊C8—111no—
372C2×C22⋊C8—111no—
373C2×C4×C8—111no—
374#399—221no—
375#398—221no—
376#391—111no—
377#390—111no—
378#390C2×D1111yescharacteristic
379#389—111no—
380#388—221no—
381#387—221no—
382#386—221no—
383#386—221no—
384#384—111no—
385#380—111no—
386#380—111no—
387#379—221no—
388C4×C22⋊C4—111no—
389#340—111no—
390#340—111no—
391#340—111no—
392#340C2×D1111yescharacteristic, complemented
393#336—111no—
394#336C2×D1111yescharacteristic, complemented
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—81no—
399C22×C11—81no—
400C22×C11—81no—
401C22×C11—81no—
402C22×C11#52511yescharacteristic
403C22×C11D4211yescharacteristic
404C22×C11#54611yescharacteristic
405C22×C11C22×SD1611yescharacteristic
406C22×C11#57511yescharacteristic
407C22×C11#57611yescharacteristic
408C22×C11#57711yescharacteristic
409C2×D11—22no—
410C2×D11—24no—
411C2×D11—22no—
412C2×D11—22no—
413C2×D11—42no—
414C2×D11—41no—
415C2×D11—42no—
416C2×D11—41no—
417C2×D11—41no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—41no—
422C2×D11—42no—
423C2×D11—816no—
424C4×C11—22no—
425C4×C11—42no—
426C4×C11—41no—
427C4×C11—81no—
428C4×C11—81no—
429C4×C11C2×#12311yescharacteristic
430C4×C11#53811yescharacteristic
431C4×C11#54611yescharacteristic
432C4×C11#55111yescharacteristic
433Dic11—22no—
434Dic11—41no—
435Dic11—41no—
436Dic11—81no—
437Dic11—81no—
438Dic11—81no—
439C25—221no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—111no—
442C22×D4—221no—
443C22×D4—222no—
444C22×D4—222no—
445C22×D4—222no—
446C22×D4—222no—
447C22×D4—441no—
448C22×D4—441no—
449C22×D4C22×D1111yescharacteristic
450C23×C4—111no—
451C23×C4—221no—
452C23×C4—221no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—41no—
456C2×SD16—114no—
457C2×SD16—222no—
458C2×SD16—222no—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C22⋊Q8—222no—
464C22⋊Q8—441no—
465C4×Q8—22no—
466C4×Q8—41no—
467C4×D4—222no—
468C4×D4—222no—
469C4×D4—441no—
470C4×D4—441no—
471C2×C4⋊C4—21no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—111no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4C22×D1111yescharacteristic
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—21no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—111no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—221no—
489C2×C22⋊C4—221no—
490C2×C22⋊C4—221no—
491C2×C22⋊C4—221no—
492C2×C22⋊C4—444no—
493C2×C42—21no—
494C2×C42—111no—
495C2×C42C22×D1111yescharacteristic
496#106—222no—
497#106—441no—
498C4⋊C8—441no—
499#103—41no—
500#103—222no—
501#102—41no—
502#102—222no—
503#102—222no—
504#102—222no—
505#102—222no—
506#102—222no—
507C22⋊C8—222no—
508C22⋊C8—441no—
509C4×C8—222no—
510#95—111no—
511#95—111no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—82no—
518C2×C11#241811yescharacteristic
519C2×C11#310111yescharacteristic
520C2×C11#311811yescharacteristic
521C2×C11#326811yescharacteristic
522C2×C11D4×SD1611yescharacteristic
523C2×C11#329511yescharacteristic
524C2×C11#332311yescharacteristic
525D11—42no—
526D11—44no—
527C24—21no—
528C24—111no—
529C24—224no—
530C24—221no—
531C24—442no—
532C24—442no—
533C24—442no—
534C24—442no—
535C24—881no—
536C24—881no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8D4×D1112yes—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—112no—
549C2×D4—112no—
550C2×D4—112no—
551C2×D4—224no—
552C2×D4—221no—
553C2×D4—221no—
554C2×D4—221no—
555C2×D4—442no—
556C2×D4—442no—
557C2×D4—444no—
558C2×D4—444no—
559C2×D4—444no—
560C2×D4—444no—
561C2×D4#433912yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—111no—
566C22×C4—111no—
567C22×C4—111no—
568C22×C4—221no—
569C22×C4—221no—
570C22×C4—221no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—442no—
581C22×C4—881no—
582C22×C4—881no—
583C22×C4D4×D1111yescharacteristic
584C22×C4D4×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586SD16—44no—
587SD16—228no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—21no—
594C2×C8—112no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8—221no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—42no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—221no—
610C4⋊C4—221no—
611C4⋊C4—442no—
612C4⋊C4—442no—
613C4⋊C4—881no—
614C4⋊C4—881no—
615C22⋊C4—42no—
616C22⋊C4—81no—
617C22⋊C4—114no—
618C22⋊C4—441no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—442no—
622C22⋊C4—442no—
623C22⋊C4—442no—
624C22⋊C4—881no—
625C22⋊C4—881no—
626C42—21no—
627C42—21no—
628C42—42no—
629C42—221no—
630C42—221no—
631C11#2490111yescharacteristic, complemented, Sylow
632C23—22no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—112no—
640C23—221no—
641C23—221no—
642C23—221no—
643C23—221no—
644C23—222no—
645C23—221no—
646C23—222no—
647C23—222no—
648C23—221no—
649C23—448no—
650C23—448no—
651C23—441no—
652C23—441no—
653C23—441no—
654C23—441no—
655C23—884no—
656C23—884no—
657C23—884no—
658C23—884no—
659C23—884no—
660C23C2×D4×D1111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—41no—
668D4—41no—
669D4—114no—
670D4—222no—
671D4—222no—
672D4—222no—
673D4—448no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—22no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—112no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—221no—
696C2×C4—221no—
697C2×C4—441no—
698C2×C4—441no—
699C2×C4—441no—
700C2×C4—441no—
701C2×C4—441no—
702C2×C4—441no—
703C2×C4—441no—
704C2×C4—441no—
705C2×C4—441no—
706C2×C4—441no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—884no—
711C2×C4—884no—
712C2×C4SD16×D1112yes—
713C2×C4C2×#433911yescharacteristic
714C2×C4C2×D4×D1111yescharacteristic
715C2×C4#6703711yescharacteristic
716C2×C4#6703711yescharacteristic
717C2×C4#41×D1111yescharacteristic
718C2×C4#41×D1111yescharacteristic
719C8—41no—
720C8—41no—
721C8—222no—
722C8—441no—
723C22—42no—
724C22—42no—
725C22—42no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—222no—
731C22—222no—
732C22—224no—
733C22—222no—
734C22—441no—
735C22—442no—
736C22—441no—
737C22—442no—
738C22—441no—
739C22—442no—
740C22—442no—
741C22—442no—
742C22—441no—
743C22—442no—
744C22—8816no—
745C22#1062307811yescharacteristic
746C22#1062312111yescharacteristic
747C22#1062314311yescharacteristic
748C22C2×SD16×D1111yescharacteristic
749C22#1062329911yescharacteristic
750C22#1062330511yescharacteristic
751C22#1062330911yescharacteristic
752C4—22no—
753C4—41no—
754C4—42no—
755C4—81no—
756C4—81no—
757C4—222no—
758C4—441no—
759C4—441no—
760C4—881no—
761C4—881no—
762C4—881no—
763C4#1062302111yescharacteristic
764C4#1062308711yescharacteristic
765C4#1062314411yescharacteristic
766C4D11×#12311yescharacteristic
767C2—82no—
768C2—442no—
769C2—444no—
770C2#1307207711yescharacteristic
771C2#1307862211yescharacteristic
772C2#1307880411yescharacteristic
773C2#1308014911yescharacteristic
774C2#1308030511yescharacteristic
775C2#1308044311yescharacteristic
776C2#1308083911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1880C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
hypercenter#1880D11
hypocenterC11#24901
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1880

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4325C2semidirect
3. #13072135C2semidirect
5. #13070147C2semidirect
6. #13070055C2semidirect
7. #13069929C2semidirect
8. #13069811C2semidirect
9. #13069302C2semidirect
10. #13069220C2semidirect
11. #13068947C2semidirect
12. #13068880C2semidirect
13. #13068615C2semidirect
15. C11×#1880C2semidirect
18. C2×C4×Q8×C11C22semidirect
24. C2×C11×#103C22semidirect
27. #10622843C22semidirect
28. C2×#66899C22semidirect
37. C2×#66881C22semidirect
38. C2×Dic11⋊C8C22semidirect
44. #10622589C22semidirect
46. C2×#66872C22semidirect
53. #10622541C22semidirect
54. C2×C4×C11⋊C8C22semidirect
55. C11×#340C22semidirect
56. C11×#336C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
225. (C2×D11)⋊C4SD16semidirect
254. #1880D11semidirect
354. C2×C4×Q8C2×D11semidirect
364. C2×#103C2×D11semidirect
392. #340C2×D11semidirect
394. #336C2×D11semidirect
631. C11#24901semidirect

Maximal subgroups

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

subgroupindex
C2×#106227822
C2×C4×#43252
#130721352
#130714372
#130701472
#130700552
#130699292
#130698112
#130693022
#130692202
#130689472
#130688802
#130686152
#130685452
C11×#18802
#2490111