Finite Group Databasebeta

← #14774037

Subgroups — #14774037

Order 2816.

1302 conjugacy classes of subgroups.

The subgroup lattice has 796 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622389C211yesmaximal, characteristic
2C2×#10622323C211yesmaximal, characteristic, complemented
3C2×D11×#102C211yesmaximal, characteristic
4#13071620C211yesmaximal, characteristic, complemented
5#13071437C211yesmaximal, characteristic
6#13069498C211yesmaximal, characteristic, complemented
7#13069238C211yesmaximal, characteristic, complemented
8#13069038C211yesmaximal, characteristic, complemented
9#13068974C211yesmaximal, characteristic, complemented
10#13068951C211yesmaximal, characteristic, complemented
11#13068862C211yesmaximal, characteristic, complemented
12#13068805C211yesmaximal, characteristic, complemented
13#13068440C211yesmaximal, characteristic, complemented
14#13068393C211yesmaximal, characteristic, complemented
15C11×#1936C211yesmaximal, characteristic, complemented
16C22×D4×D11C2211yescharacteristic
17C22×#4324C2211yescharacteristic
18C22×#4314C2211yescharacteristic
19C22×C8×D11C2211yescharacteristic
20C2×#66950C2211yescharacteristic
21C2×#66946C2211yescharacteristic
22C2×C4⋊C4×D11C2211yescharacteristic
23C2×C22⋊C4×D11—21no—
24C2×C4×D44C2211yescharacteristic
25C2×C4×Dic22C2211yescharacteristic, complemented
26C2×C11×#102C2211yescharacteristic
27C2×C11×#102C2211yescharacteristic
28C2×C11×#97C2211yescharacteristic, complemented
29C11×#390C2211yescharacteristic
30C11×#389C2211yescharacteristic, complemented
31#10622834C2211yescharacteristic
32C2×#66896C2211yescharacteristic
33C2×#66885C2211yescharacteristic
34C2×(C2×D11)⋊C8C2211yescharacteristic
35C2×#66882C2211yescharacteristic, complemented
36C2×#66880C2211yescharacteristic, complemented
37C2×#66879C2211yescharacteristic, complemented
38#10622602—21no—
39#10622600C2211yescharacteristic
40C4⋊C4×Dic11C2211yescharacteristic, complemented
41#10622587C2211yescharacteristic, complemented
42#10622586—21no—
43C2×#66874C2211yescharacteristic, complemented
44C2×#66873C2211yescharacteristic
45C2×#66873C2211yescharacteristic
46C2×#66871C2211yescharacteristic, complemented
47#10622569—21no—
48#10622569—21no—
49#10622568—21no—
50C4×(C2×D11)⋊C4C2211yescharacteristic
51#10622389C418yescomplemented
52D11×#102—24no—
53#10622323—24no—
54#10622279—21no—
55#10622267—21no—
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622167C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622162C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×D4×C11C2311yescharacteristic
64C22×C22⋊D11—21no—
65C2×D4×D11—22no—
66C2×D4×D11—22no—
67C2×D4×D11—22no—
68C2×D4×D11—41no—
69C2×D4×D11—41no—
70C2×D4×D11C2×C414yes—
71C22×D44C2311yescharacteristic
72C22×C4×D11—21no—
73C22×C4×D11—21no—
74C22×C4×D11—21no—
75C22×C4×D11C2311yescharacteristic
76C22×Dic22C2311yescharacteristic
77C22×C8×C11C2311yescharacteristic
78C22×C8×C11C2311yescharacteristic
79C2×C11×C4⋊C4—21no—
80C2×C11×C4⋊C4C2311yescharacteristic
81C2×C11×C4⋊C4C2311yescharacteristic
82C2×C11×C4⋊C4C2311yescharacteristic
83C2×C11×C22⋊C4—21no—
84C2×C11×C22⋊C4—21no—
85C2×C42×C11C2311yescharacteristic
86C2×C22⋊Dic11—21no—
87C2×C22⋊Dic11—21no—
88C2×#4324—41no—
89C2×#4324—41no—
90C2×#4324C2×C414yescomplemented
91C2×(C2×D11)⋊C4—21no—
92C2×(C2×D11)⋊C4—21no—
93C2×(C2×D11)⋊C4—21no—
94C2×(C2×D11)⋊C4—21no—
95C2×(C2×D11)⋊C4D411yescharacteristic
96C2×(C2×D11)⋊C4D411yescharacteristic
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11C2311yescharacteristic
99C2×C4⋊Dic11C2311yescharacteristic
100C2×Dic11⋊C4—21no—
101C2×Dic11⋊C4—21no—
102C2×C4×Dic11—21no—
103C2×C4×Dic11—21no—
104C2×C4×Dic11C2311yescharacteristic
105C22×C11⋊C8C2311yescharacteristic
106C22×C11⋊C8C2311yescharacteristic
107C2×#4314—22no—
108C2×#4314—22no—
109C2×#4314C2×C414yescomplemented
110C2×C8×D11—22no—
111C2×C8×D11—22no—
112C2×C8×D11—41no—
113#66950—22no—
114#66950C2×C414yescomplemented
115#66946—22no—
116#66946—41no—
117C4⋊C4×D11—22no—
118C4⋊C4×D11—41no—
119C22⋊C4×D11—44no—
120C4×D44—22no—
121C4×D44—41no—
122C4×Dic22—22no—
123C4×Dic22—41no—
124C11×#102—22no—
125C11×#102C2×C414yescomplemented
126C11×#97—22no—
127C11×#95—21no—
128#66896—22no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95—21no—
132C11⋊#95—21no—
133C11⋊#95D411yescharacteristic
134C11⋊#95D411yescharacteristic
135#66885D414yes—
136(C2×D11)⋊C8C2×C414yescomplemented
137#66882—22no—
138#66880—22no—
139#66879—41no—
140#66874—41no—
141#66873—22no—
142#66873C2×C414yescomplemented
143#66871—41no—
144#22854—111nomaximal, Sylow
145C24×C11—21no—
146C23×D11—21no—
147C23×D11—24no—
148C23×D11—42no—
149C23×D11—42no—
150C23×D11—42no—
151C23×D11—42no—
152C23×D11—81no—
153C23×D11—81no—
154C23×D11C2×D411yescharacteristic
155C2×D4×C11—21no—
156C2×D4×C11—21no—
157C2×D4×C11—21no—
158C2×D4×C11—21no—
159C2×D4×C11—21no—
160C2×D4×C11C22×C412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11C2×D411yescharacteristic
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2411yescharacteristic
167C2×C22⋊D11—24no—
168C2×C22⋊D11—42no—
169C2×C22⋊D11—42no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11—21no—
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175C22×Dic11C2×D411yescharacteristic
176D4×D11—28no—
177D4×D11—44no—
178D4×D11—44no—
179D4×D11—44no—
180C2×D44—21no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44C22×C412yes—
184C2×D44C2×D412yes—
185C2×D44#4112yes—
186C2×C4×D11—21no—
187C2×C4×D11—21no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—42no—
191C2×C4×D11—42no—
192C2×C4×D11—42no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11—42no—
196C2×C4×D11—81no—
197C2×C4×D11—81no—
198C2×C4×D11—81no—
199C2×C4×D11C22×C412yes—
200C2×C4×D11#4112yes—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22C22×C412yes—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11—21no—
211C2×C8×C11C22×C412yes—
212C2×C8×C11C2×D412yes—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4—21no—
218C11×C4⋊C4—81no—
219C11×C4⋊C4C22×C412yes—
220C11×C22⋊C4—42no—
221C11×C22⋊C4—81no—
222C42×C11—21no—
223C42×C11—21no—
224C22⋊Dic11—42no—
225C22⋊Dic11—81no—
226#4324—44no—
227(C2×D11)⋊C4—24no—
228(C2×D11)⋊C4—22no—
229(C2×D11)⋊C4—22no—
230(C2×D11)⋊C4—42no—
231(C2×D11)⋊C4—42no—
232(C2×D11)⋊C4—42no—
233C4⋊Dic11—24no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11C2×D412yes—
238Dic11⋊C4—42no—
239Dic11⋊C4—42no—
240C4×Dic11—21no—
241C4×Dic11—21no—
242C4×Dic11—42no—
243C4×Dic11—81no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8—21no—
249C2×C11⋊C8C22×C412yes—
250#4314—28no—
251C8×D11—44no—
252C2×#450—111no—
253C2×#440—111no—
254C22×#102—111no—
255#2360—111no—
256D4×C22⋊C4—111no—
257#1973—111no—
258#1936D1111yescharacteristic, complemented
259#1925—111no—
260#1892—111no—
261#1880—111no—
262#1877—111no—
263#1862—111no—
264#1852—111no—
265#1762—111no—
266#1752—111no—
267C23×C11—22no—
268C23×C11—41no—
269C23×C11—41no—
270C23×C11—41no—
271C23×C11—41no—
272C23×C11—41no—
273C23×C11—41no—
274C23×C11C22×D411yescharacteristic
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11—21no—
279C22×D11—22no—
280C22×D11—22no—
281C22×D11—22no—
282C22×D11—48no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—48no—
288C22×D11—84no—
289C22×D11—84no—
290C22×D11—84no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11C4×D412yes—
294C22×D11AGL(1,ℤ/8)12yes—
295C22×D11#13712yes—
296D4×C11—22no—
297D4×C11—22no—
298D4×C11—41no—
299D4×C11—41no—
300C2×C4×C11—22no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—21no—
304C2×C4×C11—21no—
305C2×C4×C11—21no—
306C2×C4×C11—21no—
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×C11C23×C411yescharacteristic
316C2×C4×C11C22×D411yescharacteristic
317C2×C4×C11C2×#4111yescharacteristic
318C2×C4×C11C2×#4111yescharacteristic
319C2×C4×C11H(5,𝔽2)11yescharacteristic
320C2×C4×C11H(5,𝔽2)11yescharacteristic
321C22⋊D11—48no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—22no—
325C2×Dic11—22no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11C4×D412yes—
340D44—22no—
341D44—22no—
342D44—22no—
343D44C4×D414yes—
344C4×D11—22no—
345C4×D11—22no—
346C4×D11—22no—
347C4×D11—22no—
348C4×D11—84no—
349C4×D11—84no—
350C4×D11—84no—
351Dic22—22no—
352Dic22—22no—
353Dic22—41no—
354Dic22—41no—
355C8×C11—22no—
356C8×C11—22no—
357C11⋊C8—22no—
358C11⋊C8—41no—
359C23×D4—111no—
360C22×SD16—111no—
361C22×SD16—111no—
362C23×C8—111no—
363C2×C22⋊Q8—111no—
364C2×C4×Q8—111no—
365C2×C4×D4—111no—
366C2×C4×D4—111no—
367C22×C4⋊C4—111no—
368C22×C22⋊C4—221no—
369#450—118no—
370#440—224no—
371C2×#107—111no—
372C2×#107—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×#102—224no—
380C2×#102C2×D1111yescharacteristic
381C2×#102C2×D1111yescharacteristic
382C2×C22⋊C8—111no—
383C2×#97—111no—
384C2×#97C2×D1111yescharacteristic, complemented
385#391—111no—
386#390—111no—
387#390C2×D1111yescharacteristic
388#389—221no—
389#389C2×D1111yescharacteristic, complemented
390#387—221no—
391#386—221no—
392#386—221no—
393#385—221no—
394#380—111no—
395#379—221no—
396C4×C4⋊C4—111no—
397C4×C22⋊C4—111no—
398C4×C22⋊C4—221no—
399#340—111no—
400#340—111no—
401#340C2×D1111yescharacteristic, complemented
402#340C2×D1111yescharacteristic, complemented
403#336—111no—
404#336—111no—
405C22×C11—42no—
406C22×C11—42no—
407C22×C11—42no—
408C22×C11—81no—
409C22×C11—81no—
410C22×C11—81no—
411C22×C11—81no—
412C22×C11C2×C4×D411yescharacteristic
413C22×C11D4211yescharacteristic
414C22×C11#54611yescharacteristic
415C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
416C22×C11C2×#13711yescharacteristic
417C22×C11#57611yescharacteristic
418C22×C11#57711yescharacteristic
419C2×D11—22no—
420C2×D11—22no—
421C2×D11—22no—
422C2×D11—22no—
423C2×D11—22no—
424C2×D11—22no—
425C2×D11—24no—
426C2×D11—42no—
427C2×D11—42no—
428C2×D11—42no—
429C2×D11—42no—
430C2×D11—42no—
431C2×D11—42no—
432C2×D11—816no—
433C2×D11#44014yescomplemented
434C4×C11—42no—
435C4×C11—41no—
436C4×C11—41no—
437C4×C11—81no—
438C4×C11—81no—
439C4×C11C2×C4×D411yescharacteristic
440C4×C11#51811yescharacteristic
441C4×C11#54611yescharacteristic
442C4×C11#55111yescharacteristic
443Dic11—22no—
444Dic11—42no—
445Dic11—42no—
446Dic11—41no—
447Dic11—41no—
448Dic11—81no—
449C25—221no—
450C22×Q8—111no—
451C22×D4—114no—
452C22×D4—111no—
453C22×D4—222no—
454C22×D4—221no—
455C22×D4—222no—
456C22×D4—222no—
457C22×D4—441no—
458C22×D4—441no—
459C22×D4C22×D1111yescharacteristic
460C23×C4—111no—
461C23×C4—221no—
462C23×C4—221no—
463C23×C4—221no—
464C2×SD16—114no—
465C2×SD16—114no—
466C2×SD16—222no—
467C2×SD16—222no—
468C2×SD16—441no—
469C2×SD16—441no—
470C22×C8—111no—
471C22×C8—111no—
472C22×C8—222no—
473C22×C8—222no—
474C22×C8—441no—
475C22×C8C22×D1111yescharacteristic
476C22×C8C22×D1111yescharacteristic
477C22⋊Q8—114no—
478C22⋊Q8—222no—
479C4×Q8—222no—
480C4×Q8—441no—
481C4×D4—222no—
482C4×D4—222no—
483C4×D4—441no—
484C4×D4—441no—
485C2×C4⋊C4—21no—
486C2×C4⋊C4—111no—
487C2×C4⋊C4—111no—
488C2×C4⋊C4—222no—
489C2×C4⋊C4—221no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—441no—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C4⋊C4C22×D1111yescharacteristic
496C2×C22⋊C4—21no—
497C2×C22⋊C4—21no—
498C2×C22⋊C4—111no—
499C2×C22⋊C4—111no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—221no—
503C2×C22⋊C4—221no—
504C2×C22⋊C4—221no—
505C2×C22⋊C4—221no—
506C2×C22⋊C4—444no—
507C2×C42—111no—
508C2×C42—221no—
509C2×C42—221no—
510C2×C42C22×D1111yescharacteristic
511#107—222no—
512#107—441no—
513#103—222no—
514#103—441no—
515#102—22no—
516#102—114no—
517#102—114no—
518#102—222no—
519#102—222no—
520#102C4×D1114yescomplemented
521C22⋊C8—114no—
522#97—22no—
523#97—441no—
524#95—21no—
525#95—111no—
526#95—111no—
527#95—221no—
528#95—221no—
529#95—221no—
530#95—221no—
531C2×C11—82no—
532C2×C11#235811yescharacteristic
533C2×C11C2×#44011yescharacteristic
534C2×C11#294611yescharacteristic
535C2×C11#326411yescharacteristic
536C2×C11#326611yescharacteristic
537C2×C11#331011yescharacteristic
538C2×C11#331411yescharacteristic
539D11—24no—
540D11—44no—
541C24—21no—
542C24—111no—
543C24—224no—
544C24—221no—
545C24—442no—
546C24—442no—
547C24—442no—
548C24—442no—
549C24—881no—
550C24—881no—
551C2×Q8—112no—
552C2×Q8—221no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×D4—21no—
558C2×D4—21no—
559C2×D4—21no—
560C2×D4—21no—
561C2×D4—21no—
562C2×D4—112no—
563C2×D4—112no—
564C2×D4—112no—
565C2×D4—224no—
566C2×D4—228no—
567C2×D4—221no—
568C2×D4—221no—
569C2×D4—221no—
570C2×D4—444no—
571C2×D4—444no—
572C2×D4—444no—
573C2×D4—442no—
574C2×D4—442no—
575C2×D4C2×C4×D1112yes—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—111no—
580C22×C4—112no—
581C22×C4—112no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—221no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—221no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—442no—
592C22×C4—442no—
593C22×C4—442no—
594C22×C4—442no—
595C22×C4—442no—
596C22×C4—442no—
597C22×C4—881no—
598C22×C4—881no—
599C22×C4—881no—
600C22×C4D4×D1111yescharacteristic
601C22×C4D4×D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603SD16—228no—
604SD16—444no—
605C2×C8—21no—
606C2×C8—21no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—112no—
610C2×C8—221no—
611C2×C8—221no—
612C2×C8—221no—
613C2×C8—221no—
614C2×C8—221no—
615C2×C8—444no—
616C2×C8C2×C4×D1112yes—
617C2×C8D4×D1112yes—
618C4⋊C4—21no—
619C4⋊C4—21no—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—81no—
624C4⋊C4—112no—
625C4⋊C4—224no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—442no—
630C4⋊C4—442no—
631C4⋊C4C2×C4×D1112yes—
632C22⋊C4—42no—
633C22⋊C4—81no—
634C22⋊C4—222no—
635C22⋊C4—222no—
636C22⋊C4—224no—
637C22⋊C4—442no—
638C22⋊C4—442no—
639C22⋊C4—442no—
640C22⋊C4—442no—
641C22⋊C4—881no—
642C42—21no—
643C42—21no—
644C42—221no—
645C42—221no—
646C42—442no—
647C42—881no—
648C11#2285411yescharacteristic, complemented, Sylow
649C23—22no—
650C23—41no—
651C23—41no—
652C23—41no—
653C23—41no—
654C23—41no—
655C23—41no—
656C23—112no—
657C23—112no—
658C23—112no—
659C23—221no—
660C23—221no—
661C23—221no—
662C23—221no—
663C23—222no—
664C23—222no—
665C23—222no—
666C23—448no—
667C23—448no—
668C23—441no—
669C23—441no—
670C23—441no—
671C23—441no—
672C23—884no—
673C23—884no—
674C23—884no—
675C23—884no—
676C23—884no—
677C23C2×D4×D1111yescharacteristic
678Q8—222no—
679Q8—222no—
680Q8—441no—
681Q8—441no—
682D4—22no—
683D4—22no—
684D4—41no—
685D4—41no—
686D4—114no—
687D4—222no—
688D4—222no—
689D4—222no—
690D4—448no—
691C2×C4—21no—
692C2×C4—21no—
693C2×C4—21no—
694C2×C4—21no—
695C2×C4—22no—
696C2×C4—21no—
697C2×C4—21no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—41no—
705C2×C4—41no—
706C2×C4—112no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—222no—
710C2×C4—222no—
711C2×C4—222no—
712C2×C4—222no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—221no—
716C2×C4—221no—
717C2×C4—222no—
718C2×C4—222no—
719C2×C4—221no—
720C2×C4—221no—
721C2×C4—441no—
722C2×C4—441no—
723C2×C4—441no—
724C2×C4—441no—
725C2×C4—441no—
726C2×C4—441no—
727C2×C4—441no—
728C2×C4—884no—
729C2×C4—884no—
730C2×C4—884no—
731C2×C4C22×C4×D1111yescharacteristic
732C2×C4C2×D4×D1111yescharacteristic
733C2×C4#41×D1111yescharacteristic
734C2×C4#41×D1111yescharacteristic
735C2×C4#6704211yescharacteristic
736C2×C4#6704211yescharacteristic
737C8—22no—
738C8—22no—
739C8—222no—
740C8—441no—
741C22—42no—
742C22—42no—
743C22—42no—
744C22—81no—
745C22—81no—
746C22—81no—
747C22—81no—
748C22—114no—
749C22—222no—
750C22—222no—
751C22—222no—
752C22—222no—
753C22—222no—
754C22—222no—
755C22—224no—
756C22—442no—
757C22—442no—
758C22—442no—
759C22—442no—
760C22—442no—
761C22—442no—
762C22—8816no—
763C22C4×D4×D1111yescharacteristic
764C22#1062314011yescharacteristic
765C22#1062320711yescharacteristic
766C22D11×AGL(1,ℤ/8)11yescharacteristic
767C22#1062330511yescharacteristic
768C22#1062330611yescharacteristic
769C22D11×#13711yescharacteristic
770C4—41no—
771C4—41no—
772C4—42no—
773C4—81no—
774C4—81no—
775C4—222no—
776C4—442no—
777C4—441no—
778C4—441no—
779C4—442no—
780C4—881no—
781C4#1062305211yescharacteristic
782C4C4×D4×D1111yescharacteristic
783C4#1062318511yescharacteristic
784C4#1062323611yescharacteristic
785C2—82no—
786C2—224no—
787C2—444no—
788C2#1307159411yescharacteristic
789C2D11×#44011yescharacteristic
790C2#1307744511yescharacteristic
791C2#1308010311yescharacteristic
792C2#1308013311yescharacteristic
793C2#1308063611yescharacteristic
794C2#1308069611yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1936C2
socleC23×C11C22×D4
prime radicalC22×D4×D11C22
cosocleC22×C4×C11C24
hypercenter#1936D11
hypocenterC11#22854
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1936

Complements

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

NH ≅ G/Ntype
2. C2×#10622323C2semidirect
4. #13071620C2semidirect
6. #13069498C2semidirect
7. #13069238C2semidirect
8. #13069038C2semidirect
9. #13068974C2semidirect
10. #13068951C2semidirect
11. #13068862C2semidirect
12. #13068805C2semidirect
13. #13068440C2semidirect
14. #13068393C2semidirect
15. C11×#1936C2semidirect
25. C2×C4×Dic22C22semidirect
28. C2×C11×#97C22semidirect
30. C11×#389C22semidirect
35. C2×#66882C22semidirect
36. C2×#66880C22semidirect
37. C2×#66879C22semidirect
40. C4⋊C4×Dic11C22semidirect
41. #10622587C22semidirect
43. C2×#66874C22semidirect
46. C2×#66871C22semidirect
51. #10622389C4semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. #10622188C22semidirect
59. #10622167C22semidirect
60. #10622167C22semidirect
61. #10622162C22semidirect
90. C2×#4324C2×C4semidirect
109. C2×#4314C2×C4semidirect
114. #66950C2×C4semidirect
125. C11×#102C2×C4semidirect
136. (C2×D11)⋊C8C2×C4semidirect
142. #66873C2×C4semidirect
258. #1936D11semidirect
384. C2×#97C2×D11semidirect
389. #389C2×D11semidirect
401. #340C2×D11semidirect
402. #340C2×D11semidirect
433. C2×D11#440semidirect
520. #102C4×D11semidirect
648. C11#22854semidirect

Maximal subgroups

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

subgroupindex
C2×#106223892
C2×#106223232
C2×D11×#1022
#130716202
#130714372
#130694982
#130692382
#130690382
#130689742
#130689512
#130688622
#130688052
#130684402
#130683932
C11×#19362
#2285411