Finite Group Databasebeta

← #14792614

Subgroups — #14792614

Order 2816.

1056 conjugacy classes of subgroups.

The subgroup lattice has 764 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622333C211yesmaximal, characteristic, complemented
2#13074414C211yesmaximal, characteristic, complemented
3#13071198C211yesmaximal, characteristic
4#13070002C211yesmaximal, characteristic, complemented
5#13069988C211yesmaximal, characteristic, complemented
6#13069929C211yesmaximal, characteristic, complemented
7#13069929C211yesmaximal, characteristic, complemented
8#13069499C211yesmaximal, characteristic, complemented
9#13069472C211yesmaximal, characteristic, complemented
10#13069310C211yesmaximal, characteristic, complemented
11#13069296C211yesmaximal, characteristic, complemented
12#13068929C211yesmaximal, characteristic, complemented
13#13068817C211yesmaximal, characteristic, complemented
14#13068547C211yesmaximal, characteristic
15C2×C11×#450C211yesmaximal, characteristic
16C23×D4×C11C2211yescharacteristic
17C22×C11×SD16C2211yescharacteristic
18C22×C11×SD16C2211yescharacteristic
19C2×C11×C22⋊Q8C2211yescharacteristic
20C2×#66979C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C11×#450—24no—
23C2×C11×#102C2211yescharacteristic
24C2×C11×#102C2211yescharacteristic
25C2×C11×C22⋊C8C2211yescharacteristic
26#10622860—21no—
27#10622860—21no—
28#10622843C2211yescharacteristic, complemented
29#10622843C2211yescharacteristic, complemented
30C2×#66899C2211yescharacteristic, complemented
31C2×#66899C2211yescharacteristic, complemented
32#10622834—21no—
33#10622834—21no—
34#10622834C2211yescharacteristic
35#10622834C2211yescharacteristic
36#10622834C2211yescharacteristic
37#10622834C2211yescharacteristic
38C2×#66896C2211yescharacteristic
39C2×#66896C2211yescharacteristic
40C2×#66896C2211yescharacteristic
41C2×#66896C2211yescharacteristic
42#10622825C2211yescharacteristic
43C2×C22⋊(C11⋊C8)C2211yescharacteristic
44C2×#66882C2211yescharacteristic, complemented
45C2×#66881C2211yescharacteristic, complemented
46C2×#66879C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48C2×Dic11⋊C8C2211yescharacteristic, complemented
49C2×C8×Dic11C2211yescharacteristic, complemented
50#10622599—21no—
51#10622596—21no—
52#10622586C2211yescharacteristic, complemented
53#10622586C2211yescharacteristic, complemented
54#10622565—21no—
55#10622565—21no—
56#10622333—24no—
57#10622189C2211yescharacteristic, complemented
58#10622189C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C25×C11—21no—
62C22×Q8×C11C2311yescharacteristic
63C22×D4×C11—22no—
64C22×D4×C11—22no—
65C22×D4×C11—21no—
66C22×D4×C11—22no—
67C22×D4×C11—22no—
68C22×D4×C11—41no—
69C22×D4×C11—41no—
70C22×D4×C11C2311yescharacteristic
71C22×D4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C2×C11×SD16—22no—
74C2×C11×SD16—22no—
75C2×C11×SD16—22no—
76C2×C11×SD16—22no—
77C2×C11×SD16—41no—
78C2×C11×SD16—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8—22no—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—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⋊Dic11D411yescharacteristic
97C2×C22⋊Dic11D411yescharacteristic
98#66979—22no—
99#66979—22no—
100#66979—41no—
101#66979—41no—
102C2×C4⋊Dic11D411yescharacteristic
103C2×C4⋊Dic11D411yescharacteristic
104C2×C4⋊Dic11C2311yescharacteristic
105C2×C4⋊Dic11C2311yescharacteristic
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×Dic11⋊C4—21no—
109C2×Dic11⋊C4—21no—
110C2×C4×Dic11—21no—
111C2×C4×Dic11C2311yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C11×#102—22no—
116C11×#102—22no—
117C11×C22⋊C8D414yes—
118#66899—41no—
119#66899—41no—
120#66896—22no—
121#66896—22no—
122#66896—41no—
123#66896—41no—
124C11⋊#95—21no—
125C11⋊#95—21no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C22⋊(C11⋊C8)—22no—
132#66882—41no—
133#66881—41no—
134#66879—22no—
135Dic11⋊C8—22no—
136Dic11⋊C8—22no—
137C8×Dic11—22no—
138#24516—111nomaximal, Sylow
139C24×C11—24no—
140C24×C11—21no—
141C24×C11—21no—
142C24×C11—42no—
143C24×C11—42no—
144C24×C11—81no—
145C24×C11—81no—
146C24×C11—81no—
147C24×C11—81no—
148C24×C11C2×D411yescharacteristic
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C2×D4×C11—24no—
156C2×D4×C11—21no—
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—21no—
166C2×D4×C11—44no—
167C2×D4×C11—44no—
168C2×D4×C11—44no—
169C2×D4×C11—44no—
170C2×D4×C11—42no—
171C2×D4×C11—42no—
172C2×D4×C11#4112yes—
173C2×D4×C11#4112yes—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11C2×D411yescharacteristic
181C22×C4×C11C2×D412yes—
182C22×C4×C11#4112yes—
183C22×C4×C11C2411yescharacteristic
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11C2×D411yescharacteristic
189C22×Dic11C2×D411yescharacteristic
190C22×Dic11C2×D411yescharacteristic
191C22×Dic11C2×D411yescharacteristic
192C11×SD16—44no—
193C11×SD16—44no—
194C2×C8×C11—21no—
195C2×C8×C11—21no—
196C2×C8×C11—21no—
197C2×C8×C11—21no—
198C2×C8×C11C2×D412yes—
199C2×C8×C11C2×D412yes—
200C11×C4⋊C4—21no—
201C11×C4⋊C4—21no—
202C11×C4⋊C4—42no—
203C11×C22⋊C4—42no—
204C22⋊Dic11—22no—
205C22⋊Dic11—22no—
206C22⋊Dic11—42no—
207C22⋊Dic11—81no—
208C22⋊Dic11—81no—
209C22⋊Dic11—81no—
210C22⋊Dic11—81no—
211C22⋊Dic11—81no—
212C22⋊Dic11—81no—
213C22⋊Dic11—81no—
214C22⋊Dic11—81no—
215C22⋊Dic11—81no—
216C4⋊Dic11—22no—
217C4⋊Dic11—22no—
218C4⋊Dic11—21no—
219C4⋊Dic11—21no—
220C4⋊Dic11—21no—
221C4⋊Dic11—21no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226Dic11⋊C4—81no—
227Dic11⋊C4—81no—
228C4×Dic11—21no—
229C4×Dic11—21no—
230C4×Dic11—21no—
231C4×Dic11—21no—
232C4×Dic11—42no—
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×#450D1111yescharacteristic
240C2×#433—111no—
241#2625—111no—
242#2309—111no—
243#2067—111no—
244#2065—111no—
245#2055—111no—
246#2055—111no—
247#1973—111no—
248#1968—111no—
249#1936—111no—
250#1934—111no—
251#1873—111no—
252#1854—111no—
253#1786—111no—
254C23×C11—21no—
255C23×C11—21no—
256C23×C11—21no—
257C23×C11—21no—
258C23×C11—21no—
259C23×C11—21no—
260C23×C11—22no—
261C23×C11—22no—
262C23×C11—48no—
263C23×C11—41no—
264C23×C11—41no—
265C23×C11—41no—
266C23×C11—41no—
267C23×C11—41no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11—41no—
275C23×C11—84no—
276C23×C11—84no—
277C23×C11—84no—
278C23×C11—84no—
279C23×C11—84no—
280C23×C11—84no—
281C23×C11#12112yes—
282C23×C11C22×D411yescharacteristic
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286Q8×C11—41no—
287D4×C11—22no—
288D4×C11—22no—
289D4×C11—22no—
290D4×C11—22no—
291D4×C11—48no—
292D4×C11—41no—
293D4×C11—41no—
294D4×C11—41no—
295D4×C11—41no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
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#12112yes—
309C2×C4×C11C22×D411yescharacteristic
310C2×C4×C11C2×#4111yescharacteristic
311C2×C4×C11C2×#4111yescharacteristic
312C2×C4×C11C2×#4111yescharacteristic
313C2×C4×C11H(5,𝔽2)11yescharacteristic
314C2×C4×C11H(5,𝔽2)11yescharacteristic
315C2×Dic11—21no—
316C2×Dic11—21no—
317C2×Dic11—21no—
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—41no—
328C2×Dic11—41no—
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—
339C8×C11—22no—
340C8×C11—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C23×D4C2×D1111yescharacteristic
344C22×SD16C2×D1111yescharacteristic
345C22×SD16C2×D1111yescharacteristic
346C2×C22⋊Q8C2×D1111yescharacteristic
347C2×#117—111no—
348C2×#117—111no—
349#450—24no—
350#433—224no—
351C2×#107—111no—
352C2×#106—111no—
353C2×C4⋊C8—111no—
354C2×C4⋊C8—111no—
355C2×#103—111no—
356C2×#103—111no—
357C2×#102—111no—
358C2×#102—111no—
359C2×#102—111no—
360C2×#102—111no—
361C2×#102C2×D1111yescharacteristic
362C2×#102C2×D1111yescharacteristic
363C2×C22⋊C8—111no—
364C2×C22⋊C8C2×D1111yescharacteristic
365C2×#97—111no—
366C2×C4×C8—111no—
367#400—221no—
368#398—221no—
369#397—221no—
370#397—221no—
371#391—111no—
372#391—111no—
373#390—111no—
374#390—111no—
375#390—111no—
376#390—111no—
377#390—221no—
378#390—221no—
379#389—111no—
380#389—111no—
381#380—111no—
382#379—221no—
383#379—221no—
384#340—111no—
385#340—111no—
386#340—111no—
387#340—111no—
388C22×C11—22no—
389C22×C11—22no—
390C22×C11—22no—
391C22×C11—41no—
392C22×C11—41no—
393C22×C11—41no—
394C22×C11—41no—
395C22×C11—42no—
396C22×C11—42no—
397C22×C11—42no—
398C22×C11—42no—
399C22×C11—42no—
400C22×C11—42no—
401C22×C11—816no—
402C22×C11—81no—
403C22×C11—81no—
404C22×C11—81no—
405C22×C11—81no—
406C22×C11—81no—
407C22×C11—81no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11C2×#12111yescharacteristic
411C22×C11#52511yescharacteristic
412C22×C11#53511yescharacteristic
413C22×C11#57611yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57711yescharacteristic
416C22×C11#57711yescharacteristic
417C4×C11—22no—
418C4×C11—81no—
419C4×C11—81no—
420C4×C11#54611yescharacteristic
421C4×C11#54611yescharacteristic
422C4×C11#55111yescharacteristic
423C4×C11#55111yescharacteristic
424Dic11—41no—
425Dic11—41no—
426Dic11—41no—
427Dic11—41no—
428Dic11—81no—
429Dic11—81no—
430Dic11—81no—
431Dic11—81no—
432C25—21no—
433C22×Q8C22×D1111yescharacteristic
434C22×D4—22no—
435C22×D4—22no—
436C22×D4—21no—
437C22×D4—22no—
438C22×D4—22no—
439C22×D4—41no—
440C22×D4—41no—
441C22×D4C22×D1111yescharacteristic
442C22×D4C22×D1111yescharacteristic
443C23×C4C22×D1111yescharacteristic
444C2×SD16—22no—
445C2×SD16—22no—
446C2×SD16—22no—
447C2×SD16—22no—
448C2×SD16—41no—
449C2×SD16—41no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8C22×D1111yescharacteristic
453C22×C8C22×D1111yescharacteristic
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456#117—222no—
457#117—222no—
458#117—441no—
459#117—441no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—111no—
462C2×C4⋊C4—111no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4—111no—
466C2×C4⋊C4—111no—
467C2×C4⋊C4—221no—
468C2×C4⋊C4—221no—
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—111no—
472C2×C22⋊C4—111no—
473C2×C22⋊C4—221no—
474C2×C22⋊C4—221no—
475C2×C22⋊C4—221no—
476C2×C22⋊C4—221no—
477C2×C22⋊C4—221no—
478C2×C22⋊C4—221no—
479C2×C22⋊C4—221no—
480C2×C22⋊C4—221no—
481C2×C22⋊C4—221no—
482C2×C22⋊C4—221no—
483C2×C42—111no—
484C2×C42—111no—
485C2×C42—221no—
486#107—441no—
487#106—441no—
488C4⋊C8—222no—
489C4⋊C8—222no—
490#103—441no—
491#103—441no—
492#102—22no—
493#102—22no—
494#102—222no—
495#102—222no—
496#102—441no—
497#102—441no—
498C22⋊C8—222no—
499C22⋊C8C22⋊D1114yes—
500#97—222no—
501C4×C8—222no—
502#95—221no—
503#95—221no—
504#95—221no—
505#95—221no—
506#95—221no—
507#95—221no—
508#95—221no—
509C2×C11—42no—
510C2×C11—82no—
511C2×C11—82no—
512C2×C11#241111yescharacteristic
513C2×C11#305711yescharacteristic
514C2×C11#306211yescharacteristic
515C2×C11#311811yescharacteristic
516C2×C11#312311yescharacteristic
517C2×C11#322211yescharacteristic
518C2×C11#322411yescharacteristic
519C24—24no—
520C24—21no—
521C24—21no—
522C24—42no—
523C24—42no—
524C24—81no—
525C24—81no—
526C24—81no—
527C24—81no—
528C24D4×D1111yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×D4—24no—
536C2×D4—21no—
537C2×D4—21no—
538C2×D4—21no—
539C2×D4—21no—
540C2×D4—21no—
541C2×D4—21no—
542C2×D4—21no—
543C2×D4—21no—
544C2×D4—21no—
545C2×D4—21no—
546C2×D4—44no—
547C2×D4—44no—
548C2×D4—44no—
549C2×D4—44no—
550C2×D4—42no—
551C2×D4—42no—
552C2×D4#434112yes—
553C2×D4#434112yes—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—111no—
561C22×C4—111no—
562C22×C4—111no—
563C22×C4—111no—
564C22×C4—221no—
565C22×C4—221no—
566C22×C4—221no—
567C22×C4—221no—
568C22×C4D4×D1111yescharacteristic
569C22×C4#434112yes—
570C22×C4C2×C22⋊D1112yes—
571C22×C4C23×D1111yescharacteristic
572SD16—44no—
573SD16—44no—
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—
584C2×C8C2×C22⋊D1112yes—
585C2×C8C2×C22⋊D1112yes—
586C4⋊C4—21no—
587C4⋊C4—21no—
588C4⋊C4—42no—
589C4⋊C4—222no—
590C4⋊C4—222no—
591C4⋊C4—221no—
592C4⋊C4—221no—
593C4⋊C4—221no—
594C4⋊C4—221no—
595C4⋊C4—221no—
596C4⋊C4—221no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—881no—
600C4⋊C4—881no—
601C22⋊C4—42no—
602C22⋊C4—222no—
603C22⋊C4—222no—
604C22⋊C4—442no—
605C22⋊C4—881no—
606C22⋊C4—881no—
607C22⋊C4—881no—
608C22⋊C4—881no—
609C22⋊C4—881no—
610C22⋊C4—881no—
611C22⋊C4—881no—
612C22⋊C4—881no—
613C22⋊C4—881no—
614C42—221no—
615C42—221no—
616C42—221no—
617C42—221no—
618C42—442no—
619C11#2451611yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—22no—
627C23—22no—
628C23—48no—
629C23—41no—
630C23—41no—
631C23—41no—
632C23—41no—
633C23—41no—
634C23—41no—
635C23—41no—
636C23—41no—
637C23—41no—
638C23—41no—
639C23—41no—
640C23—41no—
641C23—84no—
642C23—84no—
643C23—84no—
644C23—84no—
645C23—84no—
646C23—84no—
647C23#6699112yes—
648C23C2×D4×D1111yescharacteristic
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653D4—22no—
654D4—22no—
655D4—22no—
656D4—22no—
657D4—48no—
658D4—41no—
659D4—41no—
660D4—41no—
661D4—41no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—41no—
669C2×C4—41no—
670C2×C4—41no—
671C2×C4—41no—
672C2×C4—41no—
673C2×C4—41no—
674C2×C4—221no—
675C2×C4—221no—
676C2×C4—221no—
677C2×C4—221no—
678C2×C4—221no—
679C2×C4—221no—
680C2×C4—221no—
681C2×C4—221no—
682C2×C4—221no—
683C2×C4—221no—
684C2×C4—221no—
685C2×C4—221no—
686C2×C4—441no—
687C2×C4—441no—
688C2×C4—441no—
689C2×C4—441no—
690C2×C4—441no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4#6699112yes—
699C2×C4C2×#434111yescharacteristic
700C2×C4C2×#434111yescharacteristic
701C2×C4C2×#434111yescharacteristic
702C2×C4#6703711yescharacteristic
703C2×C4#6703711yescharacteristic
704C2×C4C22×C22⋊D1111yescharacteristic
705C8—22no—
706C8—22no—
707C8—441no—
708C8—441no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—42no—
717C22—42no—
718C22—42no—
719C22—42no—
720C22—42no—
721C22—42no—
722C22—816no—
723C22—81no—
724C22—81no—
725C22—81no—
726C22—81no—
727C22—81no—
728C22—81no—
729C22—81no—
730C22—81no—
731C22#1062311711yescharacteristic
732C22#1062312311yescharacteristic
733C22#1062329311yescharacteristic
734C22#1062329311yescharacteristic
735C22#1062330511yescharacteristic
736C22#1062330611yescharacteristic
737C22C2×#6699111yescharacteristic
738C4—22no—
739C4—81no—
740C4—81no—
741C4—441no—
742C4—441no—
743C4—441no—
744C4—441no—
745C4—881no—
746C4—881no—
747C4—881no—
748C4—881no—
749C4#1062311811yescharacteristic
750C4#1062311811yescharacteristic
751C4#1062333711yescharacteristic
752C4#1062333711yescharacteristic
753C2—42no—
754C2—82no—
755C2—82no—
756C2#1307199711yescharacteristic
757C2#1307825111yescharacteristic
758C2#1307829011yescharacteristic
759C2#1307880111yescharacteristic
760C2#1307886211yescharacteristic
761C2#1307968411yescharacteristic
762C2#1307971411yescharacteristic
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#24516
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×#10622333C2semidirect
2. #13074414C2semidirect
4. #13070002C2semidirect
5. #13069988C2semidirect
6. #13069929C2semidirect
7. #13069929C2semidirect
8. #13069499C2semidirect
9. #13069472C2semidirect
10. #13069310C2semidirect
11. #13069296C2semidirect
12. #13068929C2semidirect
13. #13068817C2semidirect
28. #10622843C22semidirect
29. #10622843C22semidirect
30. C2×#66899C22semidirect
31. C2×#66899C22semidirect
44. C2×#66882C22semidirect
45. C2×#66881C22semidirect
46. C2×#66879C22semidirect
47. C2×Dic11⋊C8C22semidirect
48. C2×Dic11⋊C8C22semidirect
49. C2×C8×Dic11C22semidirect
52. #10622586C22semidirect
53. #10622586C22semidirect
57. #10622189C22semidirect
58. #10622189C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
619. C11#24516semidirect

Maximal subgroups

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

subgroupindex
C2×#106223332
#130744142
#130711982
#130700022
#130699882
#130699292
#130694992
#130694722
#130693102
#130692962
#130689292
#130688172
#130685472
C2×C11×#4502
#2451611