Finite Group Databasebeta

← #14797689

Subgroups — #14797689

Order 2816.

1148 conjugacy classes of subgroups.

The subgroup lattice has 774 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×SD16×Dic11C211yesmaximal, characteristic, complemented
2#13072115C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic11C211yesmaximal, characteristic
4#13070139C211yesmaximal, characteristic, complemented
5#13070049C211yesmaximal, characteristic, complemented
6#13069929C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069296C211yesmaximal, characteristic, complemented
9#13069219C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic, complemented
12#13068861C211yesmaximal, characteristic, complemented
13#13068624C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic
15C2×C11×#450C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C22×C22⋊Dic11—21no—
21C2×Q8×Dic11C2211yescharacteristic, complemented
22C2×D4×Dic11C2211yescharacteristic
23C2×D4×Dic11C2211yescharacteristic
24C11×#450—24no—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×C22⋊C8C2211yescharacteristic
28#10622860—21no—
29#10622843C2211yescharacteristic, complemented
30C2×#66899C2211yescharacteristic, complemented
31C2×#66899C2211yescharacteristic, complemented
32#10622834C2211yescharacteristic
33#10622834C2211yescharacteristic
34#10622833—21no—
35#10622833—21no—
36C2×#66896C2211yescharacteristic
37C2×#66896C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40#10622825C2211yescharacteristic
41#10622825C2211yescharacteristic
42C4×C22⋊Dic11C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44SD16×Dic11—24no—
45C2×#66881C2211yescharacteristic, complemented
46C2×Dic11⋊C8C2211yescharacteristic, complemented
47C2×C8×Dic11C2211yescharacteristic, complemented
48#10622599—21no—
49#10622591—21no—
50#10622590C2211yescharacteristic, complemented
51#10622586C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622566—21no—
54#10622557—21no—
55#10622189C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622189C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—22no—
66C22×D4×C11—22no—
67C22×D4×C11—21no—
68C22×D4×C11—41no—
69C22×D4×C11—41no—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×Dic11—21no—
74C23×Dic11—21no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—22no—
78C2×C11×SD16—22no—
79C2×C11×SD16—41no—
80C2×C11×SD16D414yes—
81C22×C8×C11C2311yescharacteristic
82C22×C8×C11C2311yescharacteristic
83C11×C22⋊Q8—22no—
84C11×C22⋊Q8—41no—
85C2×C11×C4⋊C4—21no—
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C22⋊Dic11—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95C2×C22⋊Dic11—21no—
96C2×C22⋊Dic11—44no—
97C2×C22⋊Dic11D411yescharacteristic
98C2×C22⋊Dic11D411yescharacteristic
99Q8×Dic11—22no—
100Q8×Dic11—41no—
101D4×Dic11—22no—
102D4×Dic11—22no—
103D4×Dic11—41no—
104D4×Dic11—41no—
105C2×C4⋊Dic11—21no—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11C2311yescharacteristic
113C2×C4×Dic11C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C11×#102—22no—
117C11×#102—22no—
118C11×C22⋊C8—22no—
119#66899—22no—
120#66899—41no—
121#66896—22no—
122#66896—22no—
123#66896—22no—
124#66896—41no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95D411yescharacteristic
133C11⋊#95D411yescharacteristic
134C22⋊(C11⋊C8)—41no—
135#66881—22no—
136Dic11⋊C8—41no—
137C8×Dic11—22no—
138#66871—41no—
139#24905—111nomaximal, Sylow
140C24×C11—21no—
141C24×C11—24no—
142C24×C11—21no—
143C24×C11—42no—
144C24×C11—42no—
145C24×C11—42no—
146C24×C11—42no—
147C24×C11—81no—
148C24×C11—81no—
149C24×C11C2×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—24no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11—21no—
163C2×D4×C11—21no—
164C2×D4×C11—21no—
165C2×D4×C11—42no—
166C2×D4×C11—42no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—44no—
171C2×D4×C11C2×D412yes—
172C2×D4×C11#4112yes—
173C2×D4×C11#4112yes—
174C2×D4×C11#4112yes—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11—21no—
183C22×C4×C11C2×D411yescharacteristic
184C22×C4×C11C2411yescharacteristic
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189C22×Dic11—42no—
190C22×Dic11—42no—
191C22×Dic11—42no—
192C22×Dic11—42no—
193C22×Dic11—81no—
194C22×Dic11—81no—
195C22×Dic11C2×D411yescharacteristic
196C22×Dic11C2×D411yescharacteristic
197C22×Dic11C2×D411yescharacteristic
198C22×Dic11C2×D411yescharacteristic
199C11×SD16—28no—
200C11×SD16—44no—
201C2×C8×C11—21no—
202C2×C8×C11—21no—
203C2×C8×C11—21no—
204C2×C8×C11—21no—
205C2×C8×C11—21no—
206C2×C8×C11C2×D412yes—
207C11×C4⋊C4—21no—
208C11×C4⋊C4—21no—
209C11×C4⋊C4—42no—
210C11×C22⋊C4—42no—
211C22⋊Dic11—22no—
212C22⋊Dic11—22no—
213C22⋊Dic11—42no—
214C22⋊Dic11—42no—
215C22⋊Dic11—42no—
216C22⋊Dic11—42no—
217C22⋊Dic11—42no—
218C22⋊Dic11—42no—
219C22⋊Dic11—81no—
220C22⋊Dic11—81no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4⋊Dic11—21no—
227C4⋊Dic11—21no—
228C4⋊Dic11—21no—
229C4⋊Dic11—42no—
230Dic11⋊C4—42no—
231C4×Dic11—21no—
232C4×Dic11—21no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—42no—
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×#450D1111yescharacteristic
243C2×C4×SD16—111no—
244#2421—111no—
245D4×C22⋊C4—111no—
246#2092—111no—
247#2077—111no—
248#2055—111no—
249#2036—111no—
250#1934—111no—
251#1923—111no—
252#1880—111no—
253#1877—111no—
254#1862—111no—
255#1804—111no—
256#1786—111no—
257C23×C11—21no—
258C23×C11—22no—
259C23×C11—22no—
260C23×C11—21no—
261C23×C11—22no—
262C23×C11—21no—
263C23×C11—21no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—22no—
267C23×C11—48no—
268C23×C11—48no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—41no—
276C23×C11—41no—
277C23×C11—41no—
278C23×C11—41no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11—84no—
282C23×C11—84no—
283C23×C11—84no—
284C23×C11#13512yes—
285C23×C11C22×D411yescharacteristic
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—41no—
289Q8×C11—41no—
290D4×C11—22no—
291D4×C11—22no—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—48no—
296D4×C11—41no—
297D4×C11—41no—
298D4×C11#12314yes—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
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×C11—41no—
311C2×C4×C11—41no—
312C2×C4×C11C22×D411yescharacteristic
313C2×C4×C11C2×#4111yescharacteristic
314C2×C4×C11C2×#4111yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
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—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—84no—
342C2×Dic11—84no—
343C2×Dic11AGL(1,ℤ/8)12yes—
344C8×C11—22no—
345C8×C11—41no—
346C11⋊C8—41no—
347C11⋊C8—41no—
348C23×D4C2×D1111yescharacteristic
349C22×SD16C2×D1111yescharacteristic
350C22×SD16C2×D1111yescharacteristic
351C2×C22⋊Q8C2×D1111yescharacteristic
352C2×C4×Q8—111no—
353C2×C4×D4—111no—
354C2×C4×D4—111no—
355C22×C22⋊C4—221no—
356#450—24no—
357C4×SD16—224no—
358C2×#107—111no—
359C2×#106—111no—
360C2×C4⋊C8—111no—
361C2×#103—111no—
362C2×#103—111no—
363C2×#102—111no—
364C2×#102—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102C2×D1111yescharacteristic
368C2×#102C2×D1111yescharacteristic
369C2×C22⋊C8—111no—
370C2×C22⋊C8C2×D1111yescharacteristic
371C2×C4×C8—111no—
372#400—221no—
373#397—221no—
374#391—111no—
375#390—111no—
376#390—111no—
377#389—111no—
378#388—221no—
379#387—221no—
380#386—221no—
381#386—221no—
382#382—111no—
383#380—111no—
384#380—111no—
385#379—221no—
386C4×C22⋊C4—111no—
387#340—111no—
388#340—111no—
389#340—111no—
390#340—111no—
391#336—111no—
392#336—111no—
393C22×C11—22no—
394C22×C11—24no—
395C22×C11—22no—
396C22×C11—22no—
397C22×C11—42no—
398C22×C11—41no—
399C22×C11—42no—
400C22×C11—41no—
401C22×C11—41no—
402C22×C11—42no—
403C22×C11—42no—
404C22×C11—42no—
405C22×C11—41no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—816no—
411C22×C11—81no—
412C22×C11—81no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11#52511yescharacteristic
416C22×C11D4211yescharacteristic
417C22×C11#54611yescharacteristic
418C22×C11C2×#13511yescharacteristic
419C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
420C22×C11#57711yescharacteristic
421C22×C11#57711yescharacteristic
422C4×C11—41no—
423C4×C11—42no—
424C4×C11—81no—
425C4×C11C2×#12311yescharacteristic
426C4×C11#53811yescharacteristic
427C4×C11#54611yescharacteristic
428C4×C11#55111yescharacteristic
429Dic11—22no—
430Dic11—41no—
431Dic11—41no—
432Dic11—41no—
433Dic11—81no—
434Dic11—81no—
435Dic11—81no—
436Dic11—81no—
437C25—21no—
438C22×Q8C22×D1111yescharacteristic
439C22×D4—22no—
440C22×D4—22no—
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—21no—
444C22×D4—41no—
445C22×D4—41no—
446C22×D4C22×D1111yescharacteristic
447C22×D4C22×D1111yescharacteristic
448C23×C4—221no—
449C23×C4—221no—
450C23×C4C22×D1111yescharacteristic
451C2×SD16—22no—
452C2×SD16—22no—
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—41no—
456C2×SD16C22⋊D1114yes—
457C22×C8—111no—
458C22×C8—111no—
459C22×C8C22×D1111yescharacteristic
460C22×C8C22×D1111yescharacteristic
461C22⋊Q8—22no—
462C22⋊Q8—41no—
463C4×Q8—222no—
464C4×Q8—441no—
465C4×D4—222no—
466C4×D4—222no—
467C4×D4—441no—
468C4×D4—441no—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—111no—
473C2×C4⋊C4—111no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4C22×D1111yescharacteristic
477C2×C22⋊C4—21no—
478C2×C22⋊C4—111no—
479C2×C22⋊C4—111no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C22⋊C4—221no—
484C2×C22⋊C4—221no—
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C22⋊C4—221no—
488C2×C22⋊C4—444no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—221no—
492#107—441no—
493#106—222no—
494C4⋊C8—441no—
495#103—222no—
496#103—441no—
497#102—22no—
498#102—22no—
499#102—222no—
500#102—222no—
501#102—222no—
502#102—441no—
503C22⋊C8—22no—
504C22⋊C8—441no—
505C4×C8—222no—
506#95—111no—
507#95—111no—
508#95—221no—
509#95—221no—
510#95—221no—
511#95—221no—
512#95—221no—
513#95—221no—
514#95—221no—
515C2×C11—42no—
516C2×C11—44no—
517C2×C11—82no—
518C2×C11#241811yescharacteristic
519C2×C11#310511yescharacteristic
520C2×C11#312311yescharacteristic
521C2×C11#326511yescharacteristic
522C2×C11#328211yescharacteristic
523C2×C11#329611yescharacteristic
524C2×C11#332411yescharacteristic
525C24—21no—
526C24—24no—
527C24—21no—
528C24—42no—
529C24—42no—
530C24—42no—
531C24—42no—
532C24—81no—
533C24—81no—
534C24D4×D1111yescharacteristic
535C2×Q8—21no—
536C2×Q8—21no—
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8C2×C22⋊D1112yes—
541C2×D4—24no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4—44no—
553C2×D4—44no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4#434112yes—
557C2×D4#434112yes—
558C2×D4#434112yes—
559C2×D4C2×C22⋊D1112yes—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—111no—
569C22×C4—111no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—442no—
577C22×C4—442no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—881no—
581C22×C4—881no—
582C22×C4D4×D1111yescharacteristic
583C22×C4C23×D1111yescharacteristic
584SD16—28no—
585SD16—44no—
586C2×C8—21no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—221no—
592C2×C8—221no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8C2×C22⋊D1112yes—
598C4⋊C4—21no—
599C4⋊C4—21no—
600C4⋊C4—42no—
601C4⋊C4—221no—
602C4⋊C4—221no—
603C4⋊C4—221no—
604C4⋊C4—221no—
605C4⋊C4—221no—
606C4⋊C4—221no—
607C4⋊C4—221no—
608C4⋊C4—221no—
609C4⋊C4—442no—
610C4⋊C4—442no—
611C22⋊C4—42no—
612C22⋊C4—222no—
613C22⋊C4—222no—
614C22⋊C4—442no—
615C22⋊C4—442no—
616C22⋊C4—442no—
617C22⋊C4—442no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—881no—
621C22⋊C4—881no—
622C42—221no—
623C42—221no—
624C42—221no—
625C42—221no—
626C42—442no—
627C11#2490511yescharacteristic, complemented, Sylow
628C23—21no—
629C23—21no—
630C23—21no—
631C23—21no—
632C23—22no—
633C23—21no—
634C23—22no—
635C23—22no—
636C23—21no—
637C23—22no—
638C23—48no—
639C23—48no—
640C23—41no—
641C23—41no—
642C23—41no—
643C23—41no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—84no—
651C23—84no—
652C23—84no—
653C23—84no—
654C23—84no—
655C23#6696912yes—
656C23C2×D4×D1111yescharacteristic
657Q8—22no—
658Q8—22no—
659Q8—41no—
660Q8—41no—
661D4—22no—
662D4—22no—
663D4—22no—
664D4—22no—
665D4—22no—
666D4—48no—
667D4—41no—
668D4—41no—
669D4#6698814yes—
670C2×C4—22no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—41no—
675C2×C4—41no—
676C2×C4—41no—
677C2×C4—41no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—112no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—221no—
689C2×C4—221no—
690C2×C4—221no—
691C2×C4—221no—
692C2×C4—221no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—441no—
696C2×C4—441no—
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—884no—
708C2×C4—884no—
709C2×C4C2×#434111yescharacteristic
710C2×C4C2×#434111yescharacteristic
711C2×C4C2×#434111yescharacteristic
712C2×C4#6703711yescharacteristic
713C2×C4#6703711yescharacteristic
714C2×C4C22×C22⋊D1111yescharacteristic
715C8—22no—
716C8—41no—
717C8—441no—
718C8—441no—
719C22—22no—
720C22—22no—
721C22—22no—
722C22—24no—
723C22—42no—
724C22—42no—
725C22—41no—
726C22—42no—
727C22—41no—
728C22—41no—
729C22—42no—
730C22—42no—
731C22—42no—
732C22—41no—
733C22—42no—
734C22—42no—
735C22—42no—
736C22—816no—
737C22—81no—
738C22—81no—
739C22—81no—
740C22—81no—
741C22#1062311711yescharacteristic
742C22#1062312211yescharacteristic
743C22C2×#6696911yescharacteristic
744C22#1062329311yescharacteristic
745C22D11×AGL(1,ℤ/8)11yescharacteristic
746C22#1062330611yescharacteristic
747C22D4×C22⋊D1111yescharacteristic
748C4—41no—
749C4—42no—
750C4—81no—
751C4—222no—
752C4—441no—
753C4—441no—
754C4—441no—
755C4—881no—
756C4—881no—
757C4—881no—
758C4—881no—
759C4#1062311811yescharacteristic
760C4#1062312411yescharacteristic
761C4C2×#6698811yescharacteristic
762C4#1062333711yescharacteristic
763C2—42no—
764C2—44no—
765C2—82no—
766C2#1307207411yescharacteristic
767C2#1307866411yescharacteristic
768C2#1307886211yescharacteristic
769C2#1308010511yescharacteristic
770C2#1308032311yescharacteristic
771C2#1308045511yescharacteristic
772C2#1308084011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC2×C11×#450C2
socleC23×C11C22×D4
prime radicalC23×D4×C11C22
hypercenterC2×#450D11
hypocenterC11#24905
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#450

Complements

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

NH ≅ G/Ntype
1. C2×SD16×Dic11C2semidirect
2. #13072115C2semidirect
4. #13070139C2semidirect
5. #13070049C2semidirect
6. #13069929C2semidirect
7. #13069816C2semidirect
8. #13069296C2semidirect
9. #13069219C2semidirect
10. #13068973C2semidirect
11. #13068952C2semidirect
12. #13068861C2semidirect
13. #13068624C2semidirect
21. C2×Q8×Dic11C22semidirect
29. #10622843C22semidirect
30. C2×#66899C22semidirect
31. C2×#66899C22semidirect
45. C2×#66881C22semidirect
46. C2×Dic11⋊C8C22semidirect
47. C2×C8×Dic11C22semidirect
50. #10622590C22semidirect
51. #10622586C22semidirect
52. C2×#66871C22semidirect
55. #10622189C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
627. C11#24905semidirect

Maximal subgroups

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

subgroupindex
C2×SD16×Dic112
#130721152
D4×C22⋊Dic112
#130701392
#130700492
#130699292
#130698162
#130692962
#130692192
#130689732
#130689522
#130688612
#130686242
#130685472
C2×C11×#4502
#2490511