Finite Group Databasebeta

← #14792620

Subgroups — #14792620

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×#10622659C211yesmaximal, characteristic
2C2×#10622613C211yesmaximal, characteristic, complemented
3#13071196C211yesmaximal, characteristic
4#13070001C211yesmaximal, characteristic, complemented
5#13069987C211yesmaximal, characteristic, complemented
6#13069931C211yesmaximal, characteristic, complemented
7#13069931C211yesmaximal, characteristic, complemented
8#13069500C211yesmaximal, characteristic, complemented
9#13069473C211yesmaximal, characteristic, complemented
10#13069312C211yesmaximal, characteristic, complemented
11#13069298C211yesmaximal, characteristic, complemented
12#13068929C211yesmaximal, characteristic, complemented
13#13068813C211yesmaximal, characteristic, complemented
14#13068546C211yesmaximal, characteristic
15C11×#2625C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C2×C11×C22⋊Q8C2211yescharacteristic
18C2×C11×#117C2211yescharacteristic
19C22×#4325C2211yescharacteristic
20C22×#4325C2211yescharacteristic
21C2×#66979C2211yescharacteristic
22C11×#400—21no—
23C11×#398—21no—
24C11×#397—21no—
25C11×#397—21no—
26C11×#391C2211yescharacteristic, complemented
27C11×#391C2211yescharacteristic, complemented
28C11×#389C2211yescharacteristic, complemented
29C11×#389C2211yescharacteristic, complemented
30C11×#380C2211yescharacteristic
31C2×#66899C2211yescharacteristic, complemented
32C2×#66899C2211yescharacteristic, complemented
33C2×C22⋊(C11⋊C8)C2211yescharacteristic
34C2×C22⋊(C11⋊C8)C2211yescharacteristic
35#10622659—24no—
36#10622613—24no—
37#10622601—21no—
38#10622601—21no—
39C2×#66873C2211yescharacteristic
40C2×#66873C2211yescharacteristic
41C2×#66873C2211yescharacteristic
42C2×#66873C2211yescharacteristic
43C2×#66873C2211yescharacteristic
44C2×#66873C2211yescharacteristic
45C2×#66872C2211yescharacteristic, complemented
46C2×#66871C2211yescharacteristic, complemented
47#10622568—21no—
48#10622568—21no—
49#10622552C2211yescharacteristic
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622552C2211yescharacteristic
53C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
55C2×#66867C2211yescharacteristic, complemented
56C2×C4×C11⋊C8C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×Q8×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C22×D44—21no—
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—22no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2311yescharacteristic
72C22×D44C2311yescharacteristic
73C11×C22⋊Q8—22no—
74C11×C22⋊Q8—22no—
75C11×#117—22no—
76C11×#117—22no—
77C2×C11×C4⋊C4—21no—
78C2×C11×C4⋊C4—21no—
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4D411yescharacteristic
81C2×C11×C4⋊C4D411yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C4⋊C4C2311yescharacteristic
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C22⋊C4—21no—
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4D411yescharacteristic
88C2×C11×C22⋊C4D411yescharacteristic
89C2×C42×C11C2311yescharacteristic
90C2×C42×C11C2311yescharacteristic
91C2×C22⋊Dic11—21no—
92C2×#4325—22no—
93C2×#4325—22no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325—41no—
97C2×#4325—41no—
98C2×(C2×D11)⋊C4—21no—
99C2×(C2×D11)⋊C4—21no—
100C2×(C2×D11)⋊C4—21no—
101C2×(C2×D11)⋊C4—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106#66979—41no—
107#66979—41no—
108C2×C4⋊Dic11C2311yescharacteristic
109C2×C4⋊Dic11C2311yescharacteristic
110C2×C4×Dic11—21no—
111C22×C11⋊C8C2311yescharacteristic
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C11×#95—21no—
116C11×#95—21no—
117C11×#95—21no—
118C11×#95—21no—
119C11×#95—21no—
120C11×#95—21no—
121C11×#95—21no—
122#66899—41no—
123#66899—41no—
124C22⋊(C11⋊C8)—22no—
125C22⋊(C11⋊C8)D414yes—
126#66873—22no—
127#66873—22no—
128#66873—22no—
129#66873—22no—
130#66873—41no—
131#66873—41no—
132#66872—41no—
133#66871—41no—
134C4⋊(C11⋊C8)—22no—
135C4⋊(C11⋊C8)—22no—
136#66867—22no—
137C4×C11⋊C8—22no—
138#24516—111nomaximal, Sylow
139C24×C11C2×D411yescharacteristic
140C23×D11—21no—
141C23×D11—21no—
142C23×D11—24no—
143C23×D11—42no—
144C23×D11—42no—
145C23×D11—81no—
146C23×D11—81no—
147C23×D11—81no—
148C23×D11—81no—
149C2×Q8×C11—21no—
150C2×Q8×C11—21no—
151C2×Q8×C11—21no—
152C2×Q8×C11—21no—
153C2×Q8×C11—21no—
154C2×Q8×C11—21no—
155C22×C4×C11—21no—
156C22×C4×C11—21no—
157C22×C4×C11—21no—
158C22×C4×C11—21no—
159C22×C4×C11—21no—
160C22×C4×C11—21no—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11C2×D411yescharacteristic
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2×D411yescharacteristic
168C22×C4×C11C2×D412yes—
169C22×C4×C11#4112yes—
170C22×C4×C11C2411yescharacteristic
171C22×Dic11—21no—
172C22×Dic11—21no—
173C2×D44—24no—
174C2×D44—21no—
175C2×D44—21no—
176C2×D44—21no—
177C2×D44—21no—
178C2×D44—21no—
179C2×D44—21no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—44no—
185C2×D44—44no—
186C2×D44—44no—
187C2×D44—44no—
188C2×D44—42no—
189C2×D44—42no—
190C2×D44#4112yes—
191C2×D44#4112yes—
192C11×C4⋊C4—22no—
193C11×C4⋊C4—22no—
194C11×C4⋊C4—21no—
195C11×C4⋊C4—21no—
196C11×C4⋊C4—21no—
197C11×C4⋊C4—21no—
198C11×C4⋊C4—21no—
199C11×C4⋊C4—21no—
200C11×C4⋊C4—42no—
201C11×C4⋊C4—81no—
202C11×C4⋊C4—81no—
203C11×C22⋊C4—22no—
204C11×C22⋊C4—22no—
205C11×C22⋊C4—42no—
206C11×C22⋊C4—81no—
207C42×C11—21no—
208C42×C11—21no—
209C42×C11—21no—
210C42×C11—21no—
211C22⋊Dic11—42no—
212#4325—44no—
213#4325—44no—
214(C2×D11)⋊C4—81no—
215(C2×D11)⋊C4—81no—
216(C2×D11)⋊C4—81no—
217(C2×D11)⋊C4—81no—
218(C2×D11)⋊C4—81no—
219(C2×D11)⋊C4—81no—
220(C2×D11)⋊C4—81no—
221(C2×D11)⋊C4—81no—
222C4⋊Dic11—21no—
223C4⋊Dic11—21no—
224C4⋊Dic11—21no—
225C4⋊Dic11—21no—
226C4×Dic11—42no—
227C2×C11⋊C8—21no—
228C2×C11⋊C8—21no—
229C2×C11⋊C8—21no—
230C2×C11⋊C8—21no—
231C2×C11⋊C8—21no—
232C2×C11⋊C8—21no—
233C2×C11⋊C8—21no—
234C2×C11⋊C8—21no—
235C2×C11⋊C8—21no—
236C2×C11⋊C8—21no—
237C2×C11⋊C8C2×D412yes—
238C2×C11⋊C8C2×D412yes—
239C2×#450—111no—
240C2×#433—111no—
241#2625D1111yescharacteristic, complemented
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#12112yes—
261C23×C11C22×D411yescharacteristic
262C22×D11—22no—
263C22×D11—22no—
264C22×D11—48no—
265C22×D11—41no—
266C22×D11—41no—
267C22×D11—41no—
268C22×D11—41no—
269C22×D11—41no—
270C22×D11—41no—
271C22×D11—41no—
272C22×D11—41no—
273C22×D11—41no—
274C22×D11—41no—
275C22×D11—41no—
276C22×D11—41no—
277C22×D11—84no—
278C22×D11—84no—
279C22×D11—84no—
280C22×D11—84no—
281C22×D11—84no—
282C22×D11—84no—
283Q8×C11—41no—
284Q8×C11—41no—
285Q8×C11—41no—
286Q8×C11—41no—
287C2×C4×C11—21no—
288C2×C4×C11—21no—
289C2×C4×C11—22no—
290C2×C4×C11—22no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—21no—
294C2×C4×C11—21no—
295C2×C4×C11—21no—
296C2×C4×C11—21no—
297C2×C4×C11—21no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
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×C11—41no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11#12112yes—
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11C2×#4111yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×C4×C11H(5,𝔽2)11yescharacteristic
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11—41no—
329C2×Dic11—41no—
330D44—22no—
331D44—22no—
332D44—22no—
333D44—22no—
334D44—48no—
335D44—41no—
336D44—41no—
337D44—41no—
338D44—41no—
339C11⋊C8—22no—
340C11⋊C8—22no—
341C11⋊C8—41no—
342C11⋊C8—41no—
343C23×D4—111no—
344C22×SD16—111no—
345C22×SD16—111no—
346C2×C22⋊Q8C2×D1111yescharacteristic
347C2×#117—111no—
348C2×#117C2×D1111yescharacteristic
349#450—224no—
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×#102—111no—
362C2×#102—111no—
363C2×C22⋊C8—111no—
364C2×C22⋊C8—111no—
365C2×#97—111no—
366C2×C4×C8—111no—
367#400—21no—
368#398—21no—
369#397—21no—
370#397—21no—
371#391C2×D1111yescharacteristic, complemented
372#391C2×D1111yescharacteristic, complemented
373#390—111no—
374#390—111no—
375#390—111no—
376#390—111no—
377#390—221no—
378#390—221no—
379#389C2×D1111yescharacteristic, complemented
380#389C2×D1111yescharacteristic, complemented
381#380C2×D1111yescharacteristic
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×C11C2×#12111yescharacteristic
396C22×C11#52511yescharacteristic
397C22×C11#53511yescharacteristic
398C22×C11#57611yescharacteristic
399C22×C11#57711yescharacteristic
400C22×C11#57711yescharacteristic
401C22×C11#57711yescharacteristic
402C2×D11—42no—
403C2×D11—42no—
404C2×D11—42no—
405C2×D11—42no—
406C2×D11—42no—
407C2×D11—42no—
408C2×D11—816no—
409C2×D11—81no—
410C2×D11—81no—
411C2×D11—81no—
412C2×D11—81no—
413C2×D11—81no—
414C2×D11—81no—
415C2×D11—81no—
416C2×D11—81no—
417C4×C11—22no—
418C4×C11—41no—
419C4×C11—41no—
420C4×C11—41no—
421C4×C11—41no—
422C4×C11—81no—
423C4×C11—81no—
424C4×C11—81no—
425C4×C11—81no—
426C4×C11#54611yescharacteristic
427C4×C11#54611yescharacteristic
428C4×C11#55111yescharacteristic
429C4×C11#55111yescharacteristic
430Dic11—81no—
431Dic11—81no—
432C25—221no—
433C22×Q8C22×D1111yescharacteristic
434C22×D4—111no—
435C22×D4—111no—
436C22×D4—222no—
437C22×D4—222no—
438C22×D4—222no—
439C22×D4—222no—
440C22×D4—221no—
441C22×D4—441no—
442C22×D4—441no—
443C23×C4C22×D1111yescharacteristic
444C2×SD16—222no—
445C2×SD16—222no—
446C2×SD16—222no—
447C2×SD16—222no—
448C2×SD16—441no—
449C2×SD16—441no—
450C22×C8—111no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8—111no—
454C22⋊Q8—22no—
455C22⋊Q8—22no—
456#117—22no—
457#117—22no—
458#117—441no—
459#117—441no—
460C2×C4⋊C4—21no—
461C2×C4⋊C4—21no—
462C2×C4⋊C4—21no—
463C2×C4⋊C4—111no—
464C2×C4⋊C4—111no—
465C2×C4⋊C4C22⋊D1111yescharacteristic
466C2×C4⋊C4C22⋊D1111yescharacteristic
467C2×C4⋊C4C22×D1111yescharacteristic
468C2×C4⋊C4C22×D1111yescharacteristic
469C2×C4⋊C4C22×D1111yescharacteristic
470C2×C22⋊C4—21no—
471C2×C22⋊C4—21no—
472C2×C22⋊C4—221no—
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⋊C4C22⋊D1111yescharacteristic
482C2×C22⋊C4C22⋊D1111yescharacteristic
483C2×C42—221no—
484C2×C42C22×D1111yescharacteristic
485C2×C42C22×D1111yescharacteristic
486#107—441no—
487#106—441no—
488C4⋊C8—222no—
489C4⋊C8—222no—
490#103—441no—
491#103—441no—
492#102—222no—
493#102—222no—
494#102—222no—
495#102—222no—
496#102—441no—
497#102—441no—
498C22⋊C8—114no—
499C22⋊C8—222no—
500#97—222no—
501C4×C8—222no—
502#95—21no—
503#95—21no—
504#95—21no—
505#95—21no—
506#95—21no—
507#95—21no—
508#95—21no—
509C2×C11—42no—
510C2×C11#241111yescharacteristic
511C2×C11#305711yescharacteristic
512C2×C11#306211yescharacteristic
513C2×C11#311811yescharacteristic
514C2×C11#312311yescharacteristic
515C2×C11#322211yescharacteristic
516C2×C11#322411yescharacteristic
517D11—82no—
518D11—82no—
519C24—224no—
520C24—221no—
521C24—221no—
522C24—442no—
523C24—442no—
524C24—881no—
525C24—881no—
526C24—881no—
527C24—881no—
528C24C2×C22⋊D1111yescharacteristic
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—21no—
532C2×Q8—21no—
533C2×Q8—21no—
534C2×Q8—21no—
535C2×D4—112no—
536C2×D4—112no—
537C2×D4—224no—
538C2×D4—221no—
539C2×D4—221no—
540C2×D4—221no—
541C2×D4—221no—
542C2×D4—221no—
543C2×D4—221no—
544C2×D4—221no—
545C2×D4—221no—
546C2×D4—221no—
547C2×D4—221no—
548C2×D4—444no—
549C2×D4—444no—
550C2×D4—444no—
551C2×D4—444no—
552C2×D4—442no—
553C2×D4—442no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—21no—
558C22×C4—21no—
559C22×C4—21no—
560C22×C4—21no—
561C22×C4—21no—
562C22×C4—221no—
563C22×C4—221no—
564C22×C4D4×D1112yes—
565C22×C4#434112yes—
566C22×C4C2×C22⋊D1111yescharacteristic
567C22×C4C2×C22⋊D1111yescharacteristic
568C22×C4C2×C22⋊D1111yescharacteristic
569C22×C4C2×C22⋊D1111yescharacteristic
570C22×C4C2×C22⋊D1111yescharacteristic
571C22×C4C23×D1111yescharacteristic
572SD16—444no—
573SD16—444no—
574C2×C8—112no—
575C2×C8—112no—
576C2×C8—221no—
577C2×C8—221no—
578C2×C8—221no—
579C2×C8—221no—
580C2×C8—221no—
581C2×C8—221no—
582C2×C8—221no—
583C2×C8—221no—
584C2×C8—221no—
585C2×C8—221no—
586C4⋊C4—22no—
587C4⋊C4—22no—
588C4⋊C4—21no—
589C4⋊C4—21no—
590C4⋊C4—21no—
591C4⋊C4—21no—
592C4⋊C4—21no—
593C4⋊C4—21no—
594C4⋊C4—42no—
595C4⋊C4—81no—
596C4⋊C4—81no—
597C4⋊C4—221no—
598C4⋊C4—221no—
599C4⋊C4—221no—
600C4⋊C4—221no—
601C22⋊C4—22no—
602C22⋊C4—22no—
603C22⋊C4—42no—
604C22⋊C4—81no—
605C22⋊C4—442no—
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—21no—
615C42—21no—
616C42—21no—
617C42—21no—
618C42—442no—
619C11#2451611yescharacteristic, complemented, Sylow
620C23—21no—
621C23—21no—
622C23—21no—
623C23—21no—
624C23—21no—
625C23—21no—
626C23—222no—
627C23—222no—
628C23—448no—
629C23—441no—
630C23—441no—
631C23—441no—
632C23—441no—
633C23—441no—
634C23—441no—
635C23—441no—
636C23—441no—
637C23—441no—
638C23—441no—
639C23—441no—
640C23—441no—
641C23—884no—
642C23—884no—
643C23—884no—
644C23—884no—
645C23—884no—
646C23—884no—
647C23#6699212yes—
648C23C22×C22⋊D1111yescharacteristic
649Q8—41no—
650Q8—41no—
651Q8—41no—
652Q8—41no—
653D4—222no—
654D4—222no—
655D4—222no—
656D4—222no—
657D4—448no—
658D4—441no—
659D4—441no—
660D4—441no—
661D4—441no—
662C2×C4—21no—
663C2×C4—21no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—21no—
669C2×C4—21no—
670C2×C4—21no—
671C2×C4—21no—
672C2×C4—21no—
673C2×C4—21no—
674C2×C4—21no—
675C2×C4—21no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—21no—
679C2×C4—21no—
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—41no—
689C2×C4—41no—
690C2×C4—41no—
691C2×C4—41no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4#6699212yes—
699C2×C4C2×D4×D1111yescharacteristic
700C2×C4C2×#434111yescharacteristic
701C2×C4#41×D1111yescharacteristic
702C2×C4#41×D1111yescharacteristic
703C2×C4#6704211yescharacteristic
704C2×C4#6704211yescharacteristic
705C8—222no—
706C8—222no—
707C8—441no—
708C8—441no—
709C22—22no—
710C22—22no—
711C22—22no—
712C22—41no—
713C22—41no—
714C22—41no—
715C22—41no—
716C22—442no—
717C22—442no—
718C22—442no—
719C22—442no—
720C22—442no—
721C22—442no—
722C22—8816no—
723C22—881no—
724C22—881no—
725C22—881no—
726C22—881no—
727C22—881no—
728C22—881no—
729C22—881no—
730C22—881no—
731C22C2×#6699211yescharacteristic
732C22#1062335911yescharacteristic
733C22#1062336111yescharacteristic
734C22#1062336611yescharacteristic
735C22#1062336811yescharacteristic
736C22#1062336811yescharacteristic
737C22#1062336811yescharacteristic
738C4—22no—
739C4—41no—
740C4—41no—
741C4—41no—
742C4—41no—
743C4—81no—
744C4—81no—
745C4—81no—
746C4—81no—
747C4—881no—
748C4—881no—
749C4#1062318511yescharacteristic
750C4#1062318511yescharacteristic
751C4#1062318911yescharacteristic
752C4#1062318911yescharacteristic
753C2—42no—
754C2—882no—
755C2—882no—
756C2#1307200211yescharacteristic
757C2#1307825711yescharacteristic
758C2#1307829811yescharacteristic
759C2#1307879411yescharacteristic
760C2#1307886311yescharacteristic
761C2#1307968211yescharacteristic
762C2#1307970411yescharacteristic
subgroupG/H
centerC23C22×C22⋊D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#2625C2
socleC23×C11C22×D4
prime radicalC23×D44C22
hypercenter#2625D11
hypocenterC11#24516
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#117 ◁ #2625

Complements

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

NH ≅ G/Ntype
2. C2×#10622613C2semidirect
4. #13070001C2semidirect
5. #13069987C2semidirect
6. #13069931C2semidirect
7. #13069931C2semidirect
8. #13069500C2semidirect
9. #13069473C2semidirect
10. #13069312C2semidirect
11. #13069298C2semidirect
12. #13068929C2semidirect
13. #13068813C2semidirect
15. C11×#2625C2semidirect
26. C11×#391C22semidirect
27. C11×#391C22semidirect
28. C11×#389C22semidirect
29. C11×#389C22semidirect
31. C2×#66899C22semidirect
32. C2×#66899C22semidirect
45. C2×#66872C22semidirect
46. C2×#66871C22semidirect
53. C2×C4⋊(C11⋊C8)C22semidirect
54. C2×C4⋊(C11⋊C8)C22semidirect
55. C2×#66867C22semidirect
56. C2×C4×C11⋊C8C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
241. #2625D11semidirect
371. #391C2×D11semidirect
372. #391C2×D11semidirect
379. #389C2×D11semidirect
380. #389C2×D11semidirect
619. C11#24516semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106226132
#130711962
#130700012
#130699872
#130699312
#130695002
#130694732
#130693122
#130692982
#130689292
#130688132
#130685462
C11×#26252
#2451611