Finite Group Databasebeta

← #14797929

Subgroups — #14797929

Order 2816.

1150 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×#10622777C211yesmaximal, characteristic, complemented
2#13072137C211yesmaximal, characteristic, complemented
3D4×C22⋊Dic11C211yesmaximal, characteristic
4#13070142C211yesmaximal, characteristic, complemented
5#13070044C211yesmaximal, characteristic, complemented
6#13069929C211yesmaximal, characteristic, complemented
7#13069816C211yesmaximal, characteristic, complemented
8#13069310C211yesmaximal, characteristic, complemented
9#13069226C211yesmaximal, characteristic, complemented
10#13068973C211yesmaximal, characteristic, complemented
11#13068952C211yesmaximal, characteristic, complemented
12#13068861C211yesmaximal, characteristic, complemented
13#13068614C211yesmaximal, 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
44#10622777—24no—
45C2×#66882C2211yescharacteristic, complemented
46C2×#66879C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48#10622596—21no—
49#10622591—21no—
50#10622589C2211yescharacteristic, complemented
51#10622586C2211yescharacteristic, complemented
52C2×#66871C2211yescharacteristic, complemented
53#10622562—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×Dic11⋊C4—21no—
112C2×Dic11⋊C4—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11C2311yescharacteristic
115C2×C4×Dic11C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C11×#102—22no—
119C11×#102—22no—
120C11×C22⋊C8—22no—
121#66899—22no—
122#66899—41no—
123#66896—22no—
124#66896—22no—
125#66896—22no—
126#66896—41no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95D411yescharacteristic
133C11⋊#95D411yescharacteristic
134C22⋊(C11⋊C8)—41no—
135#66882—22no—
136#66879—22no—
137Dic11⋊C8—41no—
138#66871—41no—
139#24921—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—81no—
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—
231Dic11⋊C4—81no—
232Dic11⋊C4—81no—
233C4×Dic11—21no—
234C4×Dic11—21no—
235C4×Dic11—21no—
236C4×Dic11—21no—
237C4×Dic11—42no—
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×#450D1111yescharacteristic
245C2×#440—111no—
246#2423—111no—
247D4×C22⋊C4—111no—
248#2093—111no—
249#2076—111no—
250#2055—111no—
251#2036—111no—
252#1936—111no—
253#1924—111no—
254#1880—111no—
255#1877—111no—
256#1862—111no—
257#1802—111no—
258#1786—111no—
259C23×C11—21no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—21no—
263C23×C11—22no—
264C23×C11—21no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—22no—
269C23×C11—48no—
270C23×C11—48no—
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—41no—
280C23×C11—41no—
281C23×C11—84no—
282C23×C11—84no—
283C23×C11—84no—
284C23×C11—84no—
285C23×C11—84no—
286C23×C11#13712yes—
287C23×C11C22×D411yescharacteristic
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—41no—
291Q8×C11—41no—
292D4×C11—22no—
293D4×C11—22no—
294D4×C11—22no—
295D4×C11—22no—
296D4×C11—22no—
297D4×C11—48no—
298D4×C11—41no—
299D4×C11—41no—
300D4×C11#12314yes—
301C2×C4×C11—21no—
302C2×C4×C11—22no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
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×C11—41no—
313C2×C4×C11—41no—
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11C2×#4111yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11H(5,𝔽2)11yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
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—21no—
330C2×Dic11—21no—
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—41no—
342C2×Dic11—41no—
343C2×Dic11—84no—
344C2×Dic11—84no—
345C2×Dic11AGL(1,ℤ/8)12yes—
346C8×C11—22no—
347C8×C11—41no—
348C11⋊C8—41no—
349C11⋊C8—41no—
350C23×D4C2×D1111yescharacteristic
351C22×SD16C2×D1111yescharacteristic
352C22×SD16C2×D1111yescharacteristic
353C2×C22⋊Q8C2×D1111yescharacteristic
354C2×C4×Q8—111no—
355C2×C4×D4—111no—
356C2×C4×D4—111no—
357C22×C22⋊C4—221no—
358#450—24no—
359#440—224no—
360C2×#107—111no—
361C2×#107—111no—
362C2×C4⋊C8—111no—
363C2×#103—111no—
364C2×#103—111no—
365C2×#102—111no—
366C2×#102—111no—
367C2×#102—111no—
368C2×#102—111no—
369C2×#102C2×D1111yescharacteristic
370C2×#102C2×D1111yescharacteristic
371C2×C22⋊C8—111no—
372C2×C22⋊C8C2×D1111yescharacteristic
373C2×#97—111no—
374#399—221no—
375#398—221no—
376#391—111no—
377#390—111no—
378#390—111no—
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#340—111no—
393#336—111no—
394#336—111no—
395C22×C11—22no—
396C22×C11—24no—
397C22×C11—22no—
398C22×C11—22no—
399C22×C11—42no—
400C22×C11—41no—
401C22×C11—42no—
402C22×C11—41no—
403C22×C11—42no—
404C22×C11—41no—
405C22×C11—42no—
406C22×C11—41no—
407C22×C11—42no—
408C22×C11—42no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—816no—
413C22×C11—81no—
414C22×C11—81no—
415C22×C11—81no—
416C22×C11—81no—
417C22×C11#52511yescharacteristic
418C22×C11D4211yescharacteristic
419C22×C11#54611yescharacteristic
420C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
421C22×C11C2×#13711yescharacteristic
422C22×C11#57611yescharacteristic
423C22×C11#57711yescharacteristic
424C4×C11—41no—
425C4×C11—42no—
426C4×C11—81no—
427C4×C11C2×#12311yescharacteristic
428C4×C11#53811yescharacteristic
429C4×C11#54611yescharacteristic
430C4×C11#55111yescharacteristic
431Dic11—22no—
432Dic11—41no—
433Dic11—41no—
434Dic11—41no—
435Dic11—81no—
436Dic11—81no—
437Dic11—81no—
438Dic11—81no—
439C25—21no—
440C22×Q8C22×D1111yescharacteristic
441C22×D4—22no—
442C22×D4—22no—
443C22×D4—22no—
444C22×D4—22no—
445C22×D4—21no—
446C22×D4—41no—
447C22×D4—41no—
448C22×D4C22×D1111yescharacteristic
449C22×D4C22×D1111yescharacteristic
450C23×C4—221no—
451C23×C4—221no—
452C23×C4C22×D1111yescharacteristic
453C2×SD16—22no—
454C2×SD16—22no—
455C2×SD16—22no—
456C2×SD16—22no—
457C2×SD16—41no—
458C2×SD16C22⋊D1114yes—
459C22×C8—111no—
460C22×C8—111no—
461C22×C8C22×D1111yescharacteristic
462C22×C8C22×D1111yescharacteristic
463C22⋊Q8—22no—
464C22⋊Q8—41no—
465C4×Q8—222no—
466C4×Q8—441no—
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—111no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—221no—
480C2×C4⋊C4C22×D1111yescharacteristic
481C2×C22⋊C4—21no—
482C2×C22⋊C4—111no—
483C2×C22⋊C4—111no—
484C2×C22⋊C4—221no—
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—111no—
494C2×C42—111no—
495C2×C42—221no—
496#107—222no—
497#107—441no—
498C4⋊C8—441no—
499#103—222no—
500#103—441no—
501#102—22no—
502#102—22no—
503#102—222no—
504#102—222no—
505#102—222no—
506#102—441no—
507C22⋊C8—22no—
508C22⋊C8—441no—
509#97—222no—
510#95—111no—
511#95—111no—
512#95—221no—
513#95—221no—
514#95—221no—
515#95—221no—
516#95—221no—
517C2×C11—42no—
518C2×C11—44no—
519C2×C11—82no—
520C2×C11#241811yescharacteristic
521C2×C11#311011yescharacteristic
522C2×C11#311811yescharacteristic
523C2×C11#326611yescharacteristic
524C2×C11#327411yescharacteristic
525C2×C11#331011yescharacteristic
526C2×C11#331411yescharacteristic
527C24—21no—
528C24—24no—
529C24—21no—
530C24—42no—
531C24—42no—
532C24—42no—
533C24—42no—
534C24—81no—
535C24—81no—
536C24D4×D1111yescharacteristic
537C2×Q8—21no—
538C2×Q8—21no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8C2×C22⋊D1112yes—
543C2×D4—24no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—21no—
547C2×D4—21no—
548C2×D4—21no—
549C2×D4—21no—
550C2×D4—21no—
551C2×D4—21no—
552C2×D4—42no—
553C2×D4—42no—
554C2×D4—44no—
555C2×D4—44no—
556C2×D4—44no—
557C2×D4—44no—
558C2×D4#434112yes—
559C2×D4#434112yes—
560C2×D4#434112yes—
561C2×D4C2×C22⋊D1112yes—
562C22×C4—21no—
563C22×C4—21no—
564C22×C4—21no—
565C22×C4—21no—
566C22×C4—21no—
567C22×C4—21no—
568C22×C4—21no—
569C22×C4—21no—
570C22×C4—111no—
571C22×C4—111no—
572C22×C4—111no—
573C22×C4—111no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—221no—
578C22×C4—442no—
579C22×C4—442no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4—881no—
583C22×C4—881no—
584C22×C4D4×D1111yescharacteristic
585C22×C4C23×D1111yescharacteristic
586SD16—28no—
587SD16—44no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—21no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8—221no—
599C2×C8C2×C22⋊D1112yes—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—42no—
603C4⋊C4—221no—
604C4⋊C4—221no—
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—222no—
617C22⋊C4—222no—
618C22⋊C4—442no—
619C22⋊C4—442no—
620C22⋊C4—442no—
621C22⋊C4—442no—
622C22⋊C4—442no—
623C22⋊C4—881no—
624C22⋊C4—881no—
625C22⋊C4—881no—
626C42—221no—
627C42—221no—
628C42—221no—
629C42—221no—
630C42—442no—
631C11#2492111yescharacteristic, complemented, Sylow
632C23—21no—
633C23—21no—
634C23—21no—
635C23—21no—
636C23—22no—
637C23—21no—
638C23—22no—
639C23—22no—
640C23—21no—
641C23—22no—
642C23—48no—
643C23—48no—
644C23—41no—
645C23—41no—
646C23—41no—
647C23—41no—
648C23—41no—
649C23—41no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—84no—
655C23—84no—
656C23—84no—
657C23—84no—
658C23—84no—
659C23#6696812yes—
660C23C2×D4×D1111yescharacteristic
661Q8—22no—
662Q8—22no—
663Q8—41no—
664Q8—41no—
665D4—22no—
666D4—22no—
667D4—22no—
668D4—22no—
669D4—22no—
670D4—48no—
671D4—41no—
672D4—41no—
673D4#6698814yes—
674C2×C4—22no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—41no—
679C2×C4—41no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—112no—
688C2×C4—221no—
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—221no—
698C2×C4—221no—
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—441no—
711C2×C4—884no—
712C2×C4—884no—
713C2×C4C2×#434111yescharacteristic
714C2×C4C2×#434111yescharacteristic
715C2×C4C2×#434111yescharacteristic
716C2×C4#6703711yescharacteristic
717C2×C4#6703711yescharacteristic
718C2×C4C22×C22⋊D1111yescharacteristic
719C8—22no—
720C8—41no—
721C8—441no—
722C8—441no—
723C22—22no—
724C22—22no—
725C22—22no—
726C22—24no—
727C22—41no—
728C22—42no—
729C22—42no—
730C22—41no—
731C22—42no—
732C22—42no—
733C22—42no—
734C22—41no—
735C22—42no—
736C22—41no—
737C22—42no—
738C22—42no—
739C22—42no—
740C22—816no—
741C22—81no—
742C22—81no—
743C22—81no—
744C22—81no—
745C22#1062311711yescharacteristic
746C22#1062312211yescharacteristic
747C22C2×#6696811yescharacteristic
748C22#1062329311yescharacteristic
749C22D11×AGL(1,ℤ/8)11yescharacteristic
750C22#1062330511yescharacteristic
751C22D4×C22⋊D1111yescharacteristic
752C4—41no—
753C4—42no—
754C4—81no—
755C4—222no—
756C4—441no—
757C4—441no—
758C4—441no—
759C4—881no—
760C4—881no—
761C4—881no—
762C4—881no—
763C4#1062311811yescharacteristic
764C4#1062312411yescharacteristic
765C4C2×#6698811yescharacteristic
766C4#1062333711yescharacteristic
767C2—42no—
768C2—44no—
769C2—82no—
770C2#1307207411yescharacteristic
771C2#1307871011yescharacteristic
772C2#1307880111yescharacteristic
773C2#1308012611yescharacteristic
774C2#1308023011yescharacteristic
775C2#1308063011yescharacteristic
776C2#1308070111yescharacteristic
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#24921
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×#10622777C2semidirect
2. #13072137C2semidirect
4. #13070142C2semidirect
5. #13070044C2semidirect
6. #13069929C2semidirect
7. #13069816C2semidirect
8. #13069310C2semidirect
9. #13069226C2semidirect
10. #13068973C2semidirect
11. #13068952C2semidirect
12. #13068861C2semidirect
13. #13068614C2semidirect
21. C2×Q8×Dic11C22semidirect
29. #10622843C22semidirect
30. C2×#66899C22semidirect
31. C2×#66899C22semidirect
45. C2×#66882C22semidirect
46. C2×#66879C22semidirect
47. C2×Dic11⋊C8C22semidirect
50. #10622589C22semidirect
51. #10622586C22semidirect
52. C2×#66871C22semidirect
55. #10622189C22semidirect
56. #10622189C22semidirect
57. #10622189C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
631. C11#24921semidirect

Maximal subgroups

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

subgroupindex
C2×#106227772
#130721372
D4×C22⋊Dic112
#130701422
#130700442
#130699292
#130698162
#130693102
#130692262
#130689732
#130689522
#130688612
#130686142
#130685472
C2×C11×#4502
#2492111