Finite Group Databasebeta

← #14797511

Subgroups — #14797511

Order 2816.

1232 conjugacy classes of subgroups.

The subgroup lattice has 818 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622769C211yesmaximal, characteristic
2C2×D8×Dic11C211yesmaximal, characteristic, complemented
3#13072128C211yesmaximal, characteristic, complemented
4D4×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
5#13070143C211yesmaximal, characteristic, complemented
6#13070041C211yesmaximal, characteristic, complemented
7#13069926C211yesmaximal, characteristic, complemented
8#13069797C211yesmaximal, characteristic, complemented
9#13069300C211yesmaximal, characteristic, complemented
10#13069223C211yesmaximal, characteristic, complemented
11#13068962C211yesmaximal, characteristic, complemented
12#13068865C211yesmaximal, characteristic, complemented
13#13068616C211yesmaximal, characteristic, complemented
14#13068545C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic
19C2×#66991C2211yescharacteristic
20C2×D4×Dic11C2211yescharacteristic
21C2×D4×Dic11C2211yescharacteristic, complemented
22C22×#4323C2211yescharacteristic
23C22×(C2×D11)⋊C4—21no—
24C2×#66939—21no—
25C2×C11×#102C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic, complemented
27C11×#390C2211yescharacteristic, complemented
28C2×#66896C2211yescharacteristic
29C2×#66896C2211yescharacteristic
30C2×#66896C2211yescharacteristic, complemented
31#10622826—21no—
32#10622769—24no—
33D8×Dic11—24no—
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×(C2×D11)⋊C8C2211yescharacteristic
38C2×#66882C2211yescharacteristic, complemented
39C2×#66882C2211yescharacteristic, complemented
40C2×C8×Dic11C2211yescharacteristic, complemented
41#10622601C2211yescharacteristic
42#10622600C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622598C2211yescharacteristic, complemented
45C2×#66873C2211yescharacteristic
46#10622574—21no—
47#10622571—21no—
48#10622568—21no—
49#10622566—21no—
50#10622563—21no—
51#10622552C2211yescharacteristic
52C4×(C2×D11)⋊C4C2211yescharacteristic
53#10622548C2211yescharacteristic, complemented
54C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
55C11×#340C2211yescharacteristic, complemented
56C11×#336C2211yescharacteristic, complemented
57#10622188C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61C24×D11—21no—
62C22×D4×C11C2311yescharacteristic
63C22×D4×C11C2311yescharacteristic
64C23×C4×C11—21no—
65C22×C22⋊D11—21no—
66C22×C22⋊D11—21no—
67C23×Dic11—21no—
68C23×Dic11—21no—
69C2×D4×D11—22no—
70C2×D4×D11—22no—
71C2×D4×D11—22no—
72C2×D4×D11—22no—
73C2×D4×D11—41no—
74C2×D4×D11—41no—
75C22×D44C2311yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C2×C11×D8—22no—
78C2×C11×D8—22no—
79C2×C11×D8D414yes—
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11—22no—
83C4×D4×C11—41no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C22⋊C4—21no—
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C42×C11C2311yescharacteristic
90C2×C22⋊Dic11—21no—
91C2×C22⋊Dic11—21no—
92C2×C22⋊Dic11—21no—
93#66991—22no—
94#66991—41no—
95D4×Dic11—22no—
96D4×Dic11—22no—
97D4×Dic11—41no—
98D4×Dic11—41no—
99C2×#4323—22no—
100C2×#4323—22no—
101C2×#4323—41no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—44no—
109C2×(C2×D11)⋊C4D411yescharacteristic
110C2×(C2×D11)⋊C4D411yescharacteristic
111C2×C4⋊Dic11—21no—
112C2×C4⋊Dic11—21no—
113C2×C4⋊Dic11—21no—
114C2×C4⋊Dic11C2311yescharacteristic
115C2×C4⋊Dic11C2311yescharacteristic
116C2×C4⋊Dic11C2311yescharacteristic
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120#66939—44no—
121C11×#102—22no—
122C11×#102—41no—
123#66896—22no—
124#66896—22no—
125#66896—22no—
126C11⋊#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95D411yescharacteristic
130C11⋊#95D411yescharacteristic
131#66885—22no—
132#66885—41no—
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8—41no—
135#66882—22no—
136#66882—41no—
137C8×Dic11—22no—
138#66873—22no—
139C4⋊(C11⋊C8)—41no—
140#24893—111nomaximal, Sylow
141C24×C11—21no—
142C24×C11—21no—
143C23×D11—21no—
144C23×D11—24no—
145C23×D11—42no—
146C23×D11—42no—
147C23×D11—42no—
148C23×D11—42no—
149C23×D11—81no—
150C23×D11—81no—
151C23×D11C2×D411yescharacteristic
152C2×D4×C11—21no—
153C2×D4×C11—21no—
154C2×D4×C11—21no—
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C2×D412yes—
161C2×D4×C11C2×D412yes—
162C2×D4×C11#4112yes—
163C2×D4×C11#4112yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—81no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—42no—
174C2×C22⋊D11—42no—
175C2×C22⋊D11—42no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—81no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11—42no—
182C22×Dic11—42no—
183C22×Dic11—42no—
184C22×Dic11—42no—
185C22×Dic11—81no—
186C22×Dic11—81no—
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
189C22×Dic11C2×D411yescharacteristic
190D4×D11—44no—
191D4×D11—44no—
192D4×D11—44no—
193D4×D11—44no—
194C2×D44—21no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44#4112yes—
200C2×C4×D11—21no—
201C2×C4×D11—21no—
202C2×C4×D11—21no—
203C2×C4×D11—21no—
204C2×C4×D11—21no—
205C2×C4×D11—21no—
206C11×D8—28no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11C2×D412yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C22⋊C4—42no—
218C11×C22⋊C4—42no—
219C11×C22⋊C4—42no—
220C42×C11—21no—
221C42×C11—21no—
222C22⋊Dic11—42no—
223C22⋊Dic11—42no—
224C22⋊Dic11—42no—
225#4323—44no—
226(C2×D11)⋊C4—41no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—42no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—81no—
232(C2×D11)⋊C4—81no—
233(C2×D11)⋊C4D814yescomplemented
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—42no—
241C4⋊Dic11—42no—
242C4⋊Dic11—81no—
243C4×Dic11—21no—
244C4×Dic11—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×#447—111no—
252C2×C4×D8—111no—
253#2422—111no—
254D4×C22⋊C4—111no—
255#2093—111no—
256#2075—111no—
257#2054—111no—
258#2033—111no—
259#1934—111no—
260#1923—111no—
261#1879—111no—
262#1879D1111yescharacteristic, complemented
263#1862—111no—
264#1802—111no—
265#1786—111no—
266C23×C11—22no—
267C23×C11—22no—
268C23×C11—22no—
269C23×C11—22no—
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—41no—
280C23×C11C22×D411yescharacteristic
281C22×D11—21no—
282C22×D11—21no—
283C22×D11—21no—
284C22×D11—21no—
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—22no—
288C22×D11—48no—
289C22×D11—48no—
290C22×D11—41no—
291C22×D11—41no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—84no—
297C22×D11—84no—
298C22×D11—84no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11C2×D812yes—
302D4×C11—22no—
303D4×C11—22no—
304D4×C11—22no—
305D4×C11—22no—
306D4×C11—22no—
307D4×C11—41no—
308D4×C11—41no—
309D4×C11#12314yescomplemented
310C2×C4×C11—21no—
311C2×C4×C11—21no—
312C2×C4×C11—21no—
313C2×C4×C11—21no—
314C2×C4×C11—21no—
315C2×C4×C11—41no—
316C2×C4×C11—41no—
317C2×C4×C11—41no—
318C2×C4×C11—41no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—84no—
322C2×C4×C11C2×D812yes—
323C2×C4×C11C22×D411yescharacteristic
324C2×C4×C11C2×#4111yescharacteristic
325C2×C4×C11C2×#4111yescharacteristic
326C2×C4×C11C2×#4111yescharacteristic
327C2×C4×C11H(5,𝔽2)11yescharacteristic
328C2×C4×C11H(5,𝔽2)11yescharacteristic
329C22⋊D11—48no—
330C22⋊D11—84no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—41no—
340C2×Dic11—41no—
341C2×Dic11—41no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—84no—
349C2×Dic11—84no—
350C2×Dic11C2×D812yes—
351D44—22no—
352D44—22no—
353D44—41no—
354D44—41no—
355C4×D11—41no—
356C4×D11—41no—
357C4×D11—41no—
358C4×D11—41no—
359C8×C11—22no—
360C8×C11—41no—
361C11⋊C8—41no—
362C11⋊C8—41no—
363C23×D4—111no—
364C22×D8—111no—
365C22×D8C2×D1111yescharacteristic
366C2×#123—221no—
367C2×#121—111no—
368C2×C4×D4—111no—
369C2×C4×D4—111no—
370C2×C4×D4C2×D1111yescharacteristic
371C22×C22⋊C4—221no—
372#447—224no—
373C4×D8—224no—
374C2×#107—111no—
375C2×#107—111no—
376C2×C4⋊C8—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—111no—
380C2×#102—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102C2×D1111yescharacteristic
384C2×#102C2×D1111yescharacteristic, complemented
385C2×C22⋊C8—111no—
386C2×C22⋊C8—111no—
387C2×C4×C8—111no—
388#397—221no—
389#394—221no—
390#390—111no—
391#390—111no—
392#390C2×D1111yescharacteristic, complemented
393#389—111no—
394#386—221no—
395#386—221no—
396#385—221no—
397#384—111no—
398#380—111no—
399#380—111no—
400#379—221no—
401C4×C22⋊C4—111no—
402#340—111no—
403#340—111no—
404#340—111no—
405#340C2×D1111yescharacteristic, complemented
406#336—111no—
407#336C2×D1111yescharacteristic, complemented
408C22×C11—24no—
409C22×C11—42no—
410C22×C11—42no—
411C22×C11—42no—
412C22×C11—42no—
413C22×C11—42no—
414C22×C11—42no—
415C22×C11—42no—
416C22×C11—42no—
417C22×C11—42no—
418C22×C11—81no—
419C22×C11—81no—
420C22×C11—81no—
421C22×C11—81no—
422C22×C11#52511yescharacteristic
423C22×C11D4211yescharacteristic
424C22×C11#54611yescharacteristic
425C22×C11C22×D811yescharacteristic
426C22×C11#57511yescharacteristic
427C22×C11#57611yescharacteristic
428C22×C11#57711yescharacteristic
429C2×D11—22no—
430C2×D11—22no—
431C2×D11—22no—
432C2×D11—41no—
433C2×D11—41no—
434C2×D11—41no—
435C2×D11—41no—
436C2×D11—42no—
437C2×D11—42no—
438C2×D11—42no—
439C2×D11—816no—
440C2×D11—81no—
441C2×D11—81no—
442C2×D11—81no—
443C2×D11—81no—
444C4×C11—22no—
445C4×C11—41no—
446C4×C11—81no—
447C4×C11—81no—
448C4×C11C2×#12311yescharacteristic
449C4×C11#53811yescharacteristic
450C4×C11#54611yescharacteristic
451C4×C11#55111yescharacteristic
452Dic11—22no—
453Dic11—41no—
454Dic11—41no—
455Dic11—81no—
456Dic11—81no—
457Dic11—81no—
458C25—221no—
459C22×D4—111no—
460C22×D4—221no—
461C22×D4—222no—
462C22×D4—222no—
463C22×D4—222no—
464C22×D4—222no—
465C22×D4—221no—
466C22×D4—441no—
467C22×D4—441no—
468C22×D4C22×D1111yescharacteristic
469C22×D4C22×D1111yescharacteristic
470C23×C4—21no—
471C23×C4—111no—
472C23×C4—221no—
473C23×C4—221no—
474C2×D8—22no—
475C2×D8—22no—
476C2×D8—222no—
477C2×D8—222no—
478C2×D8—441no—
479C2×D8D4414yes—
480C22×C8—111no—
481C22×C8—111no—
482C22×C8C22×D1111yescharacteristic
483C22×C8C22×D1111yescharacteristic
484#123—444no—
485#121—222no—
486#121—441no—
487C4×D4—22no—
488C4×D4—41no—
489C4×D4—222no—
490C4×D4—222no—
491C4×D4—441no—
492C4×D4—441no—
493C2×C4⋊C4—111no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—221no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4C22×D1111yescharacteristic
500C2×C4⋊C4C22×D1111yescharacteristic
501C2×C22⋊C4—21no—
502C2×C22⋊C4—21no—
503C2×C22⋊C4—21no—
504C2×C22⋊C4—111no—
505C2×C22⋊C4—111no—
506C2×C22⋊C4—221no—
507C2×C22⋊C4—221no—
508C2×C22⋊C4—221no—
509C2×C22⋊C4—221no—
510C2×C22⋊C4—221no—
511C2×C22⋊C4—221no—
512C2×C22⋊C4—221no—
513C2×C22⋊C4—221no—
514C2×C22⋊C4—221no—
515C2×C22⋊C4—444no—
516C2×C42—111no—
517C2×C42C22×D1111yescharacteristic
518#107—222no—
519#107—441no—
520C4⋊C8—441no—
521#102—22no—
522#102—41no—
523#102—222no—
524#102—222no—
525#102—222no—
526#102—222no—
527#102—222no—
528#102—441no—
529C22⋊C8—222no—
530C22⋊C8—441no—
531C4×C8—222no—
532#95—111no—
533#95—111no—
534#95—221no—
535#95—221no—
536#95—221no—
537C2×C11—44no—
538C2×C11—82no—
539C2×C11#241811yescharacteristic
540C2×C11#310011yescharacteristic
541C2×C11#311811yescharacteristic
542C2×C11#326711yescharacteristic
543C2×C11D4×D811yescharacteristic
544C2×C11#329411yescharacteristic
545C2×C11#332211yescharacteristic
546D11—42no—
547D11—82no—
548C24—21no—
549C24—21no—
550C24—111no—
551C24—224no—
552C24—221no—
553C24—442no—
554C24—442no—
555C24—442no—
556C24—442no—
557C24—881no—
558C24—881no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—21no—
563C2×D4—21no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—112no—
568C2×D4—224no—
569C2×D4—221no—
570C2×D4—221no—
571C2×D4—221no—
572C2×D4—221no—
573C2×D4—221no—
574C2×D4—442no—
575C2×D4—442no—
576C2×D4—444no—
577C2×D4—444no—
578C2×D4—444no—
579C2×D4—444no—
580C2×D4—442no—
581C2×D4—442no—
582C2×D4—881no—
583C2×D4C2×D4412yes—
584C2×D4C2×D4412yes—
585C2×D4#434112yes—
586C2×D4#434112yes—
587C22×C4—21no—
588C22×C4—21no—
589C22×C4—42no—
590C22×C4—42no—
591C22×C4—81no—
592C22×C4—111no—
593C22×C4—111no—
594C22×C4—111no—
595C22×C4—221no—
596C22×C4—221no—
597C22×C4—221no—
598C22×C4—221no—
599C22×C4—221no—
600C22×C4—221no—
601C22×C4—221no—
602C22×C4—221no—
603C22×C4—221no—
604C22×C4—442no—
605C22×C4—442no—
606C22×C4—442no—
607C22×C4—442no—
608C22×C4—881no—
609C22×C4—881no—
610C22×C4D4×D1111yescharacteristic
611C22×C4D4×D1111yescharacteristic
612C22×C4C23×D1111yescharacteristic
613D8—28no—
614D8—444no—
615C2×C8—21no—
616C2×C8—21no—
617C2×C8—21no—
618C2×C8—21no—
619C2×C8—21no—
620C2×C8—221no—
621C2×C8—221no—
622C2×C8—221no—
623C2×C8—221no—
624C2×C8—221no—
625C2×C8—221no—
626C2×C8C2×D4412yes—
627C4⋊C4—21no—
628C4⋊C4—21no—
629C4⋊C4—21no—
630C4⋊C4—21no—
631C4⋊C4—221no—
632C4⋊C4—221no—
633C4⋊C4—221no—
634C4⋊C4—221no—
635C4⋊C4—221no—
636C4⋊C4—221no—
637C4⋊C4—442no—
638C4⋊C4—442no—
639C4⋊C4—881no—
640C22⋊C4—42no—
641C22⋊C4—42no—
642C22⋊C4—42no—
643C22⋊C4—114no—
644C22⋊C4—441no—
645C22⋊C4—442no—
646C22⋊C4—442no—
647C22⋊C4—442no—
648C22⋊C4—442no—
649C22⋊C4—442no—
650C22⋊C4—442no—
651C22⋊C4—442no—
652C22⋊C4—881no—
653C22⋊C4—881no—
654C42—21no—
655C42—21no—
656C42—221no—
657C42—221no—
658C11#2489311yescharacteristic, complemented, Sylow
659C23—22no—
660C23—22no—
661C23—22no—
662C23—22no—
663C23—41no—
664C23—41no—
665C23—41no—
666C23—41no—
667C23—41no—
668C23—41no—
669C23—41no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—112no—
674C23—221no—
675C23—221no—
676C23—221no—
677C23—221no—
678C23—221no—
679C23—221no—
680C23—222no—
681C23—448no—
682C23—448no—
683C23—441no—
684C23—441no—
685C23—441no—
686C23—441no—
687C23—441no—
688C23—441no—
689C23—884no—
690C23—884no—
691C23—884no—
692C23—884no—
693C23—884no—
694C23C2×D4×D1111yescharacteristic
695D4—22no—
696D4—22no—
697D4—22no—
698D4—22no—
699D4—22no—
700D4—41no—
701D4—41no—
702D4—222no—
703D4—222no—
704D4—448no—
705D4—441no—
706D4—441no—
707D4—884no—
708D4#6693914yescomplemented
709C2×C4—21no—
710C2×C4—21no—
711C2×C4—21no—
712C2×C4—21no—
713C2×C4—21no—
714C2×C4—41no—
715C2×C4—41no—
716C2×C4—41no—
717C2×C4—41no—
718C2×C4—41no—
719C2×C4—41no—
720C2×C4—84no—
721C2×C4—112no—
722C2×C4—221no—
723C2×C4—221no—
724C2×C4—221no—
725C2×C4—221no—
726C2×C4—221no—
727C2×C4—221no—
728C2×C4—221no—
729C2×C4—221no—
730C2×C4—441no—
731C2×C4—441no—
732C2×C4—441no—
733C2×C4—441no—
734C2×C4—441no—
735C2×C4—441no—
736C2×C4—441no—
737C2×C4—441no—
738C2×C4—441no—
739C2×C4—441no—
740C2×C4—441no—
741C2×C4—441no—
742C2×C4—441no—
743C2×C4—884no—
744C2×C4—884no—
745C2×C4D8×D1112yes—
746C2×C4C22×D4411yescharacteristic
747C2×C4C2×#434111yescharacteristic
748C2×C4C2×#434111yescharacteristic
749C2×C4#6703711yescharacteristic
750C2×C4#41×D1111yescharacteristic
751C2×C4#6704211yescharacteristic
752C8—22no—
753C8—41no—
754C8—441no—
755C8—441no—
756C22—24no—
757C22—42no—
758C22—42no—
759C22—42no—
760C22—42no—
761C22—42no—
762C22—42no—
763C22—42no—
764C22—42no—
765C22—42no—
766C22—81no—
767C22—81no—
768C22—81no—
769C22—81no—
770C22—222no—
771C22—222no—
772C22—222no—
773C22—441no—
774C22—441no—
775C22—441no—
776C22—441no—
777C22—442no—
778C22—442no—
779C22—442no—
780C22—8816no—
781C22—881no—
782C22—881no—
783C22—881no—
784C22—881no—
785C22D4×D4411yescharacteristic
786C22#1062312211yescharacteristic
787C22#1062313711yescharacteristic
788C22C2×D8×D1111yescharacteristic
789C22#1062330011yescharacteristic
790C22#1062330411yescharacteristic
791C22#1062330611yescharacteristic
792C4—22no—
793C4—41no—
794C4—81no—
795C4—81no—
796C4—222no—
797C4—441no—
798C4—441no—
799C4—881no—
800C4—881no—
801C4—881no—
802C4C2×#6693911yescharacteristic
803C4#1062308511yescharacteristic
804C4#1062314811yescharacteristic
805C4#1062318911yescharacteristic
806C2—44no—
807C2—82no—
808C2—442no—
809C2—882no—
810C2#1307207611yescharacteristic
811C2#1307861511yescharacteristic
812C2#1307879711yescharacteristic
813C2#1308014311yescharacteristic
814C2D8×D4411yescharacteristic
815C2#1308042211yescharacteristic
816C2#1308081011yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC22×C4×C11C24
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
hypercenter#1879D11
hypocenterC11#24893
LCSG ▷ C22×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1879

Complements

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

NH ≅ G/Ntype
2. C2×D8×Dic11C2semidirect
3. #13072128C2semidirect
4. D4×(C2×D11)⋊C4C2semidirect
5. #13070143C2semidirect
6. #13070041C2semidirect
7. #13069926C2semidirect
8. #13069797C2semidirect
9. #13069300C2semidirect
10. #13069223C2semidirect
11. #13068962C2semidirect
12. #13068865C2semidirect
13. #13068616C2semidirect
14. #13068545C2semidirect
15. C11×#1879C2semidirect
21. C2×D4×Dic11C22semidirect
26. C2×C11×#102C22semidirect
27. C11×#390C22semidirect
30. C2×#66896C22semidirect
38. C2×#66882C22semidirect
39. C2×#66882C22semidirect
40. C2×C8×Dic11C22semidirect
44. #10622598C22semidirect
53. #10622548C22semidirect
54. C2×C4⋊(C11⋊C8)C22semidirect
55. C11×#340C22semidirect
56. C11×#336C22semidirect
57. #10622188C22semidirect
58. #10622167C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
233. (C2×D11)⋊C4D8semidirect
262. #1879D11semidirect
309. D4×C11#123semidirect
384. C2×#102C2×D11semidirect
392. #390C2×D11semidirect
405. #340C2×D11semidirect
407. #336C2×D11semidirect
658. C11#24893semidirect
708. D4#66939semidirect

Maximal subgroups

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

subgroupindex
C2×#106227692
C2×D8×Dic112
#130721282
D4×(C2×D11)⋊C42
#130701432
#130700412
#130699262
#130697972
#130693002
#130692232
#130689622
#130688652
#130686162
#130685452
C11×#18792
#2489311