Finite Group Databasebeta

← #14764902

Subgroups — #14764902

Order 2816.

1308 conjugacy classes of subgroups.

The subgroup lattice has 828 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622769C211yesmaximal, characteristic
2C4×#66991C211yesmaximal, characteristic, complemented
3D11×#390C211yesmaximal, characteristic, complemented
4#13069483C211yesmaximal, characteristic, complemented
5#13069479C211yesmaximal, characteristic, complemented
6#13069297C211yesmaximal, characteristic, complemented
7#13069296C211yesmaximal, characteristic, complemented
8#13069237C211yesmaximal, characteristic, complemented
9#13069233C211yesmaximal, characteristic, complemented
10#13068964C211yesmaximal, characteristic, complemented
11#13068930C211yesmaximal, characteristic, complemented
12#13068805C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068373C211yesmaximal, characteristic, complemented
15C11×#1879C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×C11×D8C2211yescharacteristic
18C2×C4×D4×C11C2211yescharacteristic, complemented
19C2×#66991C2211yescharacteristic
20C22×#4323C2211yescharacteristic
21C2×C4×C22⋊D11—21no—
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C22⋊C4×D11—21no—
24C2×C22⋊C4×D11—21no—
25C2×C42×D11C2211yescharacteristic
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic, complemented
28C11×#390C2211yescharacteristic
29#10622834C2211yescharacteristic
30#10622834C2211yescharacteristic, complemented
31C2×#66896C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66896C2211yescharacteristic, complemented
34C4×C22⋊Dic11—21no—
35#10622769C418yescomplemented
36C2×#66885C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66882C2211yescharacteristic, complemented
41C2×C8×Dic11C2211yescharacteristic, complemented
42C2×C8×Dic11C2211yescharacteristic, complemented
43#10622601C2211yescharacteristic
44#10622600C2211yescharacteristic
45#10622586C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66871C2211yescharacteristic, complemented
48#10622570—21no—
49#10622570—21no—
50#10622569—21no—
51#10622557—21no—
52#10622552C2211yescharacteristic
53C4×C4⋊Dic11C2211yescharacteristic, complemented
54C11×#340C2211yescharacteristic, complemented
55C11×#336C2211yescharacteristic, complemented
56#10622189C2211yescharacteristic, complemented
57#10622167C2211yescharacteristic, complemented
58#10622167C2211yescharacteristic, complemented
59#10622162C2211yescharacteristic, complemented
60C24×D11—21no—
61C22×D4×C11C2311yescharacteristic
62C22×D4×C11C2311yescharacteristic
63C23×C4×C11—21no—
64C22×C22⋊D11—21no—
65C22×C22⋊D11—21no—
66C2×D4×D11—22no—
67C2×D4×D11—41no—
68C2×D4×D11—41no—
69C2×D4×D11—41no—
70C2×D4×D11—41no—
71C2×D4×D11C2×C414yescomplemented
72C22×D44C2311yescharacteristic
73C22×C4×D11—21no—
74C22×C4×D11D411yescharacteristic
75C22×C4×D11D411yescharacteristic
76C22×C4×D11C2311yescharacteristic
77C2×C11×D8—41no—
78C2×C11×D8—41no—
79C2×C11×D8C2×C414yescomplemented
80C22×C8×C11C2311yescharacteristic
81C22×C8×C11C2311yescharacteristic
82C4×D4×C11—41no—
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—
93C2×C22⋊Dic11—21no—
94C2×C22⋊Dic11—21no—
95#66991—22no—
96#66991C2×C414yes—
97C2×#4323—41no—
98C2×#4323—41no—
99C2×#4323C2×C414yescomplemented
100C4×C22⋊D11—44no—
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—
106C2×C4⋊Dic11C2311yescharacteristic
107C2×C4⋊Dic11C2311yescharacteristic
108C2×C4⋊Dic11C2311yescharacteristic
109C2×Dic11⋊C4—21no—
110C2×Dic11⋊C4—21no—
111C2×C4×Dic11—21no—
112C2×C4×Dic11D411yescharacteristic
113C2×C4×Dic11D411yescharacteristic
114C2×C4×Dic11C2311yescharacteristic
115C22×C11⋊C8C2311yescharacteristic
116C22×C11⋊C8C2311yescharacteristic
117C4⋊C4×D11—41no—
118C4⋊C4×D11—41no—
119C22⋊C4×D11—44no—
120C22⋊C4×D11—44no—
121C42×D11—41no—
122C42×D11—41no—
123C11×#102—41no—
124C11×#102—41no—
125#66896—41no—
126#66896—41no—
127#66896C2×C414yescomplemented
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131#66885—41no—
132#66885C2×C414yescomplemented
133(C2×D11)⋊C8—22no—
134(C2×D11)⋊C8C2×C414yescomplemented
135#66882—41no—
136C8×Dic11—41no—
137C8×Dic11—41no—
138#66873—41no—
139#66871—41no—
140#22040—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—42no—
150C23×D11—42no—
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×C11—21no—
161C2×D4×C11—21no—
162C2×D4×C11C22×C412yes—
163C2×D4×C11C22×C412yes—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—42no—
167C22×C4×C11—42no—
168C22×C4×C11—42no—
169C22×C4×C11C2×D411yescharacteristic
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11C2411yescharacteristic
172C2×C22⋊D11—24no—
173C2×C22⋊D11—24no—
174C2×C22⋊D11—42no—
175C2×C22⋊D11—42no—
176C2×C22⋊D11—42no—
177C2×C22⋊D11—42no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184D4×D11—44no—
185D4×D11—44no—
186D4×D11—44no—
187D4×D11—44no—
188C2×D44—21no—
189C2×D44—21no—
190C2×D44—21no—
191C2×D44—21no—
192C2×D44—21no—
193C2×D44C22×C412yes—
194C2×C4×D11—22no—
195C2×C4×D11—22no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—21no—
199C2×C4×D11—21no—
200C2×C4×D11—41no—
201C2×C4×D11—41no—
202C2×C4×D11—41no—
203C2×C4×D11—42no—
204C2×C4×D11—42no—
205C2×C4×D11—42no—
206C2×C4×D11D814yescomplemented
207C2×C4×D11C22×C412yes—
208C2×C4×D11#4112yes—
209C11×D8—44no—
210C2×C8×C11—21no—
211C2×C8×C11—21no—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11C22×C412yes—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—21no—
219C11×C4⋊C4—21no—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—42no—
222C11×C22⋊C4—42no—
223C42×C11—21no—
224C42×C11—21no—
225C22⋊Dic11—24no—
226C22⋊Dic11—42no—
227C22⋊Dic11—42no—
228C22⋊Dic11—42no—
229C22⋊Dic11—42no—
230#4323—44no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233(C2×D11)⋊C4—42no—
234(C2×D11)⋊C4—42no—
235(C2×D11)⋊C4—42no—
236C4⋊Dic11—21no—
237C4⋊Dic11—21no—
238C4⋊Dic11—21no—
239C4⋊Dic11—21no—
240C4⋊Dic11—21no—
241C4⋊Dic11C22×C412yes—
242Dic11⋊C4—42no—
243Dic11⋊C4—42no—
244C4×Dic11—21no—
245C4×Dic11—21no—
246C4×Dic11—41no—
247C4×Dic11—41no—
248C4×Dic11—42no—
249C2×C11⋊C8—21no—
250C2×C11⋊C8—21no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8C22×C412yes—
255C2×#447—111no—
256C4×#121—111no—
257C2×#390—111no—
258#1970—111no—
259#1970—111no—
260#1934—111no—
261#1934—111no—
262#1925—111no—
263#1925—111no—
264#1879—111no—
265#1879D1111yescharacteristic, complemented
266#1874—111no—
267#1852—111no—
268#1786—111no—
269C4×C22⋊C8—111no—
270C23×C11—22no—
271C23×C11—22no—
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—41no—
282C23×C11—41no—
283C23×C11—41no—
284C23×C11C22×D411yescharacteristic
285C22×D11—21no—
286C22×D11—21no—
287C22×D11—21no—
288C22×D11—21no—
289C22×D11—22no—
290C22×D11—48no—
291C22×D11—48no—
292C22×D11—41no—
293C22×D11—41no—
294C22×D11—41no—
295C22×D11—41no—
296C22×D11—41no—
297C22×D11—41no—
298C22×D11—48no—
299C22×D11—84no—
300C22×D11—84no—
301C22×D11—84no—
302C22×D11—84no—
303C22×D11C4×D412yes—
304C22×D11C2×D812yes—
305C22×D11#13512yes—
306D4×C11—22no—
307D4×C11—22no—
308D4×C11—22no—
309D4×C11—22no—
310D4×C11—41no—
311D4×C11—41no—
312D4×C11—41no—
313D4×C11—41no—
314C2×C4×C11—21no—
315C2×C4×C11—21no—
316C2×C4×C11—21no—
317C2×C4×C11—21no—
318C2×C4×C11—21no—
319C2×C4×C11—41no—
320C2×C4×C11—41no—
321C2×C4×C11—41no—
322C2×C4×C11—41no—
323C2×C4×C11—41no—
324C2×C4×C11—41no—
325C2×C4×C11—84no—
326C2×C4×C11C2×D812yes—
327C2×C4×C11C23×C411yescharacteristic
328C2×C4×C11C2×#4111yescharacteristic
329C2×C4×C11H(5,𝔽2)11yescharacteristic
330C2×C4×C11H(5,𝔽2)11yescharacteristic
331C2×C4×C11H(5,𝔽2)11yescharacteristic
332C2×C4×C11H(5,𝔽2)11yescharacteristic
333C22⋊D11—48no—
334C22⋊D11—48no—
335C2×Dic11—21no—
336C2×Dic11—21no—
337C2×Dic11—21no—
338C2×Dic11—21no—
339C2×Dic11—21no—
340C2×Dic11—21no—
341C2×Dic11—22no—
342C2×Dic11—41no—
343C2×Dic11—41no—
344C2×Dic11—41no—
345C2×Dic11—41no—
346C2×Dic11—41no—
347C2×Dic11—41no—
348C2×Dic11—41no—
349C2×Dic11—41no—
350C2×Dic11C4×D412yes—
351C2×Dic11C2×D812yes—
352C2×Dic11AGL(1,ℤ/8)12yes—
353D44—22no—
354D44—22no—
355D44—41no—
356D44—41no—
357C4×D11—22no—
358C4×D11—22no—
359C4×D11—22no—
360C4×D11—22no—
361C4×D11—44no—
362C4×D11—44no—
363C4×D11—84no—
364C8×C11—22no—
365C8×C11—41no—
366C11⋊C8—22no—
367C11⋊C8—41no—
368C23×D4—111no—
369C22×D8—111no—
370C22×D8C2×D1111yescharacteristic
371C2×#121—111no—
372C2×C4×D4—221no—
373C2×C4×D4C2×D1111yescharacteristic, complemented
374C22×C4⋊C4—111no—
375C22×C22⋊C4—221no—
376C22×C22⋊C4—221no—
377C22×C42—111no—
378#447—118no—
379C2×#107—111no—
380C2×#107—111no—
381C2×#102—111no—
382C2×#102—111no—
383C2×#102—111no—
384C2×#102—111no—
385C2×#102—111no—
386C2×#102—111no—
387C2×#102C2×D1111yescharacteristic
388C2×#102C2×D1111yescharacteristic, complemented
389C2×C22⋊C8—111no—
390C2×C22⋊C8—111no—
391C2×C4×C8—111no—
392C2×C4×C8—111no—
393#390—111no—
394#390—111no—
395#390—111no—
396#390—111no—
397#390—221no—
398#390—221no—
399#390C2×D1111yescharacteristic
400#389—111no—
401#388—221no—
402#386—221no—
403#380—111no—
404C4×C4⋊C4—111no—
405C4×C22⋊C4—221no—
406#340—111no—
407#340—111no—
408#340—111no—
409#340C2×D1111yescharacteristic, complemented
410#336—111no—
411#336C2×D1111yescharacteristic, complemented
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—81no—
423C22×C11—81no—
424C22×C11—81no—
425C22×C11—81no—
426C22×C11C2×C4×D411yescharacteristic
427C22×C11#53411yescharacteristic
428C22×C11#53511yescharacteristic
429C22×C11C22×D811yescharacteristic
430C22×C11C2×#13511yescharacteristic
431C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
432C22×C11#57511yescharacteristic
433C2×D11—22no—
434C2×D11—22no—
435C2×D11—22no—
436C2×D11—22no—
437C2×D11—22no—
438C2×D11—22no—
439C2×D11—42no—
440C2×D11—42no—
441C2×D11—42no—
442C2×D11—816no—
443C2×D11—81no—
444C2×D11—81no—
445C2×D11—81no—
446C2×D11—81no—
447C2×D11C4×D814yes—
448C4×C11—22no—
449C4×C11—41no—
450C4×C11—81no—
451C4×C11—81no—
452C4×C11#51811yescharacteristic
453C4×C11#51811yescharacteristic
454C4×C11#53811yescharacteristic
455C4×C11#53811yescharacteristic
456Dic11—22no—
457Dic11—22no—
458Dic11—22no—
459Dic11—42no—
460Dic11—81no—
461Dic11—81no—
462C25—221no—
463C22×D4—114no—
464C22×D4—111no—
465C22×D4—222no—
466C22×D4—221no—
467C22×D4—221no—
468C22×D4—441no—
469C22×D4—441no—
470C22×D4—441no—
471C22×D4—441no—
472C22×D4C22×D1111yescharacteristic
473C22×D4C22×D1111yescharacteristic
474C23×C4—21no—
475C23×C4—111no—
476C23×C4—111no—
477C23×C4—111no—
478C23×C4—221no—
479C2×D8—41no—
480C2×D8—41no—
481C2×D8—114no—
482C2×D8—441no—
483C2×D8—441no—
484C2×D8C4×D1114yescomplemented
485C22×C8—111no—
486C22×C8—111no—
487C22×C8C22×D1111yescharacteristic
488C22×C8C22×D1111yescharacteristic
489#121—114no—
490#121—222no—
491C4×D4—41no—
492C4×D4—41no—
493C4×D4—444no—
494C2×C4⋊C4—111no—
495C2×C4⋊C4—111no—
496C2×C4⋊C4—111no—
497C2×C4⋊C4—221no—
498C2×C4⋊C4—221no—
499C2×C4⋊C4—441no—
500C2×C4⋊C4—441no—
501C2×C4⋊C4C22×D1111yescharacteristic
502C2×C4⋊C4C22×D1111yescharacteristic
503C2×C22⋊C4—21no—
504C2×C22⋊C4—21no—
505C2×C22⋊C4—21no—
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—221no—
516C2×C22⋊C4—444no—
517C2×C22⋊C4—444no—
518C2×C42—111no—
519C2×C42—111no—
520C2×C42—111no—
521C2×C42—221no—
522C2×C42—441no—
523C2×C42—441no—
524C2×C42C22×D1111yescharacteristic
525#107—441no—
526#107—441no—
527#102—41no—
528#102—41no—
529#102—114no—
530#102—114no—
531#102—441no—
532#102—441no—
533#102—441no—
534#102—441no—
535C22⋊C8—114no—
536C22⋊C8—222no—
537C4×C8—441no—
538C4×C8—441no—
539#95—221no—
540#95—221no—
541#95—221no—
542C2×C11—82no—
543C2×C11—82no—
544C2×C11#232111yescharacteristic
545C2×C11C2×C4×D811yescharacteristic
546C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
547C2×C11#318611yescharacteristic
548C2×C11#318811yescharacteristic
549C2×C11#320511yescharacteristic
550C2×C11#321111yescharacteristic
551D11—24no—
552D11—82no—
553C24—21no—
554C24—21no—
555C24—111no—
556C24—224no—
557C24—221no—
558C24—442no—
559C24—442no—
560C24—442no—
561C24—442no—
562C24—442no—
563C24—442no—
564C2×D4—21no—
565C2×D4—21no—
566C2×D4—21no—
567C2×D4—21no—
568C2×D4—21no—
569C2×D4—21no—
570C2×D4—21no—
571C2×D4—21no—
572C2×D4—21no—
573C2×D4—21no—
574C2×D4—112no—
575C2×D4—224no—
576C2×D4—224no—
577C2×D4—221no—
578C2×D4—221no—
579C2×D4—221no—
580C2×D4—221no—
581C2×D4—221no—
582C2×D4—444no—
583C2×D4—444no—
584C2×D4—444no—
585C2×D4—444no—
586C2×D4—442no—
587C2×D4—442no—
588C2×D4—442no—
589C2×D4—442no—
590C2×D4C2×C4×D1112yes—
591C2×D4C2×C4×D1112yes—
592C22×C4—21no—
593C22×C4—21no—
594C22×C4—42no—
595C22×C4—42no—
596C22×C4—42no—
597C22×C4—111no—
598C22×C4—111no—
599C22×C4—111no—
600C22×C4—112no—
601C22×C4—112no—
602C22×C4—114no—
603C22×C4—222no—
604C22×C4—222no—
605C22×C4—221no—
606C22×C4—221no—
607C22×C4—221no—
608C22×C4—221no—
609C22×C4—221no—
610C22×C4—221no—
611C22×C4—221no—
612C22×C4—441no—
613C22×C4—441no—
614C22×C4—441no—
615C22×C4—442no—
616C22×C4—442no—
617C22×C4—442no—
618C22×C4D4×D1111yescharacteristic
619C22×C4D4×D1111yescharacteristic
620C22×C4C23×D1111yescharacteristic
621D8—44no—
622D8—444no—
623C2×C8—21no—
624C2×C8—21no—
625C2×C8—21no—
626C2×C8—21no—
627C2×C8—21no—
628C2×C8—112no—
629C2×C8—221no—
630C2×C8—221no—
631C2×C8—221no—
632C2×C8—221no—
633C2×C8—221no—
634C2×C8C2×C4×D1112yes—
635C4⋊C4—21no—
636C4⋊C4—21no—
637C4⋊C4—21no—
638C4⋊C4—21no—
639C4⋊C4—112no—
640C4⋊C4—221no—
641C4⋊C4—221no—
642C4⋊C4—221no—
643C4⋊C4—221no—
644C4⋊C4—221no—
645C4⋊C4—442no—
646C4⋊C4—442no—
647C22⋊C4—42no—
648C22⋊C4—42no—
649C22⋊C4—42no—
650C22⋊C4—224no—
651C22⋊C4—442no—
652C22⋊C4—442no—
653C22⋊C4—442no—
654C22⋊C4—442no—
655C22⋊C4—442no—
656C22⋊C4—442no—
657C22⋊C4—442no—
658C22⋊C4—442no—
659C22⋊C4—442no—
660C42—21no—
661C42—21no—
662C42—221no—
663C42—221no—
664C42—441no—
665C42—441no—
666C42—442no—
667C11#2204011yescharacteristic, complemented, Sylow
668C23—22no—
669C23—22no—
670C23—41no—
671C23—41no—
672C23—41no—
673C23—41no—
674C23—41no—
675C23—41no—
676C23—41no—
677C23—41no—
678C23—41no—
679C23—41no—
680C23—41no—
681C23—41no—
682C23—112no—
683C23—112no—
684C23—112no—
685C23—221no—
686C23—221no—
687C23—221no—
688C23—221no—
689C23—222no—
690C23—448no—
691C23—448no—
692C23—448no—
693C23—441no—
694C23—441no—
695C23—441no—
696C23—441no—
697C23—441no—
698C23—441no—
699C23—884no—
700C23—884no—
701C23—884no—
702C23—884no—
703C23C2×D4×D1111yescharacteristic
704D4—22no—
705D4—22no—
706D4—22no—
707D4—22no—
708D4—41no—
709D4—41no—
710D4—41no—
711D4—41no—
712D4—222no—
713D4—222no—
714D4—448no—
715D4—448no—
716D4—441no—
717D4—441no—
718C2×C4—21no—
719C2×C4—21no—
720C2×C4—21no—
721C2×C4—21no—
722C2×C4—21no—
723C2×C4—41no—
724C2×C4—41no—
725C2×C4—41no—
726C2×C4—41no—
727C2×C4—41no—
728C2×C4—41no—
729C2×C4—84no—
730C2×C4—112no—
731C2×C4—112no—
732C2×C4—112no—
733C2×C4—221no—
734C2×C4—221no—
735C2×C4—221no—
736C2×C4—221no—
737C2×C4—221no—
738C2×C4—221no—
739C2×C4—222no—
740C2×C4—222no—
741C2×C4—222no—
742C2×C4—222no—
743C2×C4—222no—
744C2×C4—444no—
745C2×C4—444no—
746C2×C4—441no—
747C2×C4—441no—
748C2×C4—441no—
749C2×C4—441no—
750C2×C4—441no—
751C2×C4—441no—
752C2×C4—441no—
753C2×C4—441no—
754C2×C4—884no—
755C2×C4D8×D1112yes—
756C2×C4C22×C4×D1111yescharacteristic
757C2×C4#6703711yescharacteristic
758C2×C4#6703711yescharacteristic
759C2×C4#6703711yescharacteristic
760C2×C4#41×D1111yescharacteristic
761C2×C4#6704211yescharacteristic
762C8—22no—
763C8—41no—
764C8—222no—
765C8—441no—
766C22—42no—
767C22—42no—
768C22—42no—
769C22—42no—
770C22—42no—
771C22—42no—
772C22—81no—
773C22—81no—
774C22—81no—
775C22—81no—
776C22—81no—
777C22—81no—
778C22—81no—
779C22—81no—
780C22—114no—
781C22—222no—
782C22—222no—
783C22—222no—
784C22—222no—
785C22—222no—
786C22—222no—
787C22—442no—
788C22—442no—
789C22—442no—
790C22—8816no—
791C22—881no—
792C22—881no—
793C22—881no—
794C22—881no—
795C22C4×D4×D1111yescharacteristic
796C22#1062312011yescharacteristic
797C22#1062313811yescharacteristic
798C22C2×D8×D1111yescharacteristic
799C22D11×#13511yescharacteristic
800C22D11×AGL(1,ℤ/8)11yescharacteristic
801C22#1062330411yescharacteristic
802C4—22no—
803C4—41no—
804C4—81no—
805C4—81no—
806C4—222no—
807C4—222no—
808C4—222no—
809C4—442no—
810C4—881no—
811C4—881no—
812C4#1062301711yescharacteristic
813C4#1062307611yescharacteristic
814C4#1062314411yescharacteristic
815C4#1062318811yescharacteristic
816C2—82no—
817C2—82no—
818C2—224no—
819C2—882no—
820C2#1307127211yescharacteristic
821C2C4×D8×D1111yescharacteristic
822C2#1307742711yescharacteristic
823C2#1307936511yescharacteristic
824C2#1307937911yescharacteristic
825C2#1307953311yescharacteristic
826C2#1307957911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1879C2
socleC23×C11C22×D4
prime radicalC2×#10622769C2
cosocleC22×C4×C11C24
hypercenter#1879D11
hypocenterC11#22040
LCSG ▷ C2×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. C4×#66991C2semidirect
3. D11×#390C2semidirect
4. #13069483C2semidirect
5. #13069479C2semidirect
6. #13069297C2semidirect
7. #13069296C2semidirect
8. #13069237C2semidirect
9. #13069233C2semidirect
10. #13068964C2semidirect
11. #13068930C2semidirect
12. #13068805C2semidirect
13. #13068545C2semidirect
14. #13068373C2semidirect
15. C11×#1879C2semidirect
18. C2×C4×D4×C11C22semidirect
27. C2×C11×#102C22semidirect
30. #10622834C22semidirect
33. C2×#66896C22semidirect
35. #10622769C4semidirect
40. C2×#66882C22semidirect
41. C2×C8×Dic11C22semidirect
42. C2×C8×Dic11C22semidirect
45. #10622586C22semidirect
47. C2×#66871C22semidirect
53. C4×C4⋊Dic11C22semidirect
54. C11×#340C22semidirect
55. C11×#336C22semidirect
56. #10622189C22semidirect
57. #10622167C22semidirect
58. #10622167C22semidirect
59. #10622162C22semidirect
71. C2×D4×D11C2×C4semidirect
79. C2×C11×D8C2×C4semidirect
99. C2×#4323C2×C4semidirect
127. #66896C2×C4semidirect
132. #66885C2×C4semidirect
134. (C2×D11)⋊C8C2×C4semidirect
206. C2×C4×D11D8semidirect
265. #1879D11semidirect
373. C2×C4×D4C2×D11semidirect
388. C2×#102C2×D11semidirect
409. #340C2×D11semidirect
411. #336C2×D11semidirect
484. C2×D8C4×D11semidirect
667. C11#22040semidirect

Maximal subgroups

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

subgroupindex
C2×#106227692
C4×#669912
D11×#3902
#130694832
#130694792
#130692972
#130692962
#130692372
#130692332
#130689642
#130689302
#130688052
#130685452
#130683732
C11×#18792
#2204011