Finite Group Databasebeta

← #14774177

Subgroups — #14774177

Order 2816.

1274 conjugacy classes of subgroups.

The subgroup lattice has 790 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10622659C211yesmaximal, characteristic
2C2×#10622430C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic
4#13071647C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic
6#13069467C211yesmaximal, characteristic, complemented
7#13069314C211yesmaximal, characteristic, complemented
8#13069234C211yesmaximal, characteristic, complemented
9#13068969C211yesmaximal, characteristic, complemented
10#13068947C211yesmaximal, characteristic, complemented
11#13068878C211yesmaximal, characteristic, complemented
12#13068813C211yesmaximal, characteristic, complemented
13#13068430C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#1894C211yesmaximal, characteristic, complemented
16C23×D44C2211yescharacteristic
17C22×C11×M16C2211yescharacteristic
18C2×C11×C22⋊Q8C2211yescharacteristic
19C2×Q8×Dic11C2211yescharacteristic, complemented
20C22×#4325C2211yescharacteristic
21C22×#4325C2211yescharacteristic
22C2×#66979C2211yescharacteristic
23C2×#66946C2211yescharacteristic
24C2×#66946C2211yescharacteristic
25C2×C22⋊C4×D11—21no—
26C2×C11×#103C2211yescharacteristic, complemented
27C2×C11×#103C2211yescharacteristic, complemented
28C11×#380C2211yescharacteristic
29#10622843C2211yescharacteristic, complemented
30C4×C22⋊Dic11C2211yescharacteristic
31C2×C22⋊(C11⋊C8)C2211yescharacteristic
32#10622744—24no—
33C2×#66885C2211yescharacteristic
34C2×#66885C2211yescharacteristic
35C2×#66885C2211yescharacteristic
36C2×#66885C2211yescharacteristic
37C2×#66879C2211yescharacteristic, complemented
38C2×C8×Dic11C2211yescharacteristic, complemented
39#10622659C418yescomplemented
40#10622601C2211yescharacteristic
41#10622601C2211yescharacteristic
42#10622598C2211yescharacteristic, complemented
43#10622594—21no—
44C4⋊C4×Dic11—21no—
45C4⋊C4×Dic11C2211yescharacteristic, complemented
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66872C2211yescharacteristic, complemented
49C2×#66871C2211yescharacteristic, complemented
50#10622568—21no—
51#10622564—21no—
52#10622564—21no—
53#10622430—24no—
54#10622278—21no—
55#10622278—21no—
56C11×#340C2211yescharacteristic, complemented
57C11×#340C2211yescharacteristic, complemented
58#10622188C2211yescharacteristic, complemented
59#10622188C2211yescharacteristic, complemented
60#10622167C2211yescharacteristic, complemented
61#10622167C2211yescharacteristic, complemented
62C24×D11—21no—
63C22×Q8×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×D44—22no—
66C22×D44—22no—
67C22×D44—21no—
68C22×D44—22no—
69C22×D44—41no—
70C22×D44—41no—
71C22×D44C2×C414yes—
72C22×D44C2311yescharacteristic
73C22×D44C2311yescharacteristic
74C22×C4×D11—21no—
75C22×C4×D11—21no—
76C2×C11×M16—22no—
77C2×C11×M16—22no—
78C2×C11×M16—41no—
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C11×C22⋊Q8—22no—
82C11×C22⋊Q8C2×C414yescomplemented
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C11×C22⋊C4—21no—
88C2×C11×C22⋊C4—21no—
89C2×C22⋊Dic11—21no—
90C2×C22⋊Dic11D411yescharacteristic
91C2×C22⋊Dic11D411yescharacteristic
92Q8×Dic11—22no—
93Q8×Dic11—41no—
94C2×#4325—22no—
95C2×#4325—22no—
96C2×#4325—41no—
97C2×#4325—41no—
98C2×#4325C2×C414yes—
99C2×#4325C2×C414yescomplemented
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—22no—
107#66979—41no—
108C2×C4⋊Dic11—21no—
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4×Dic11—21no—
113C2×C4×Dic11—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11C2311yescharacteristic
116C2×C4×Dic11C2311yescharacteristic
117C22×C11⋊C8C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119#66946—22no—
120#66946—22no—
121#66946—41no—
122#66946—41no—
123C22⋊C4×D11—44no—
124C11×#103—22no—
125C11×#103—41no—
126C11×#95—21no—
127C11⋊#95—21no—
128C11⋊#95—21no—
129C11⋊#95—21no—
130C11⋊#95—21no—
131C11⋊#95D411yescharacteristic
132C11⋊#95D411yescharacteristic
133C22⋊(C11⋊C8)C2×C414yescomplemented
134#66885—22no—
135#66885—22no—
136#66885—22no—
137#66885D414yes—
138#66879—22no—
139C8×Dic11—41no—
140#66873C2×C414yes—
141#66873C2×C414yescomplemented
142#66872—41no—
143#66871—22no—
144#22864—111nomaximal, Sylow
145C24×C11C2×D411yescharacteristic
146C23×D11—21no—
147C23×D11—21no—
148C23×D11—24no—
149C23×D11—42no—
150C23×D11—42no—
151C23×D11—42no—
152C23×D11—42no—
153C23×D11—81no—
154C23×D11—81no—
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11C22×C412yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11—21no—
166C22×C4×C11—21no—
167C22×C4×C11—21no—
168C22×C4×C11—21no—
169C22×C4×C11C22×C412yes—
170C22×C4×C11C2×D411yescharacteristic
171C22×C4×C11#4112yes—
172C22×C4×C11C2411yescharacteristic
173C22×Dic11—21no—
174C22×Dic11—21no—
175C22×Dic11C2×D411yescharacteristic
176C22×Dic11C2×D411yescharacteristic
177C22×Dic11C2×D411yescharacteristic
178C22×Dic11C2×D411yescharacteristic
179C2×D44—28no—
180C2×D44—24no—
181C2×D44—21no—
182C2×D44—21no—
183C2×D44—21no—
184C2×D44—21no—
185C2×D44—21no—
186C2×D44—21no—
187C2×D44—21no—
188C2×D44—21no—
189C2×D44—42no—
190C2×D44—42no—
191C2×D44—44no—
192C2×D44—44no—
193C2×D44—44no—
194C2×D44C22×C412yes—
195C2×D44C22×C412yes—
196C2×D44C2×D412yes—
197C2×D44#4112yes—
198C2×C4×D11—42no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11—81no—
203C2×C4×D11—81no—
204C11×M16—44no—
205C2×C8×C11—21no—
206C2×C8×C11—21no—
207C2×C8×C11—21no—
208C2×C8×C11—21no—
209C2×C8×C11—21no—
210C2×C8×C11C2×D412yes—
211C11×C4⋊C4—24no—
212C11×C4⋊C4—21no—
213C11×C4⋊C4—21no—
214C11×C4⋊C4—21no—
215C11×C4⋊C4—21no—
216C11×C4⋊C4—21no—
217C11×C4⋊C4C22×C412yes—
218C11×C22⋊C4—24no—
219C11×C22⋊C4—42no—
220C22⋊Dic11—22no—
221C22⋊Dic11—41no—
222C22⋊Dic11—42no—
223#4325—28no—
224#4325—44no—
225(C2×D11)⋊C4—42no—
226(C2×D11)⋊C4—42no—
227(C2×D11)⋊C4—42no—
228(C2×D11)⋊C4—42no—
229(C2×D11)⋊C4—81no—
230(C2×D11)⋊C4—81no—
231C4⋊Dic11—21no—
232C4⋊Dic11—21no—
233C4⋊Dic11—21no—
234C4⋊Dic11—42no—
235C4⋊Dic11—42no—
236C4⋊Dic11C2×D412yes—
237C4×Dic11—21no—
238C4×Dic11—21no—
239C4×Dic11—21no—
240C4×Dic11—21no—
241C4×Dic11—42no—
242C4×Dic11—42no—
243C4×Dic11—42no—
244C2×C11⋊C8—21no—
245C2×C11⋊C8—21no—
246C2×C11⋊C8—21no—
247C2×C11⋊C8—21no—
248C2×C11⋊C8C22×C412yes—
249C2×C11⋊C8C22×C412yes—
250C2×#450—111no—
251C2×#440—111no—
252C2×#418—111no—
253#2362—111no—
254D4×C22⋊C4—111no—
255#1968—111no—
256#1936—111no—
257#1925—111no—
258#1894D1111yescharacteristic, complemented
259#1880—111no—
260#1877—111no—
261#1864—111no—
262#1854—111no—
263C4×#102—111no—
264#1753—111no—
265C23×C11—21no—
266C23×C11—21no—
267C23×C11—21no—
268C23×C11—21no—
269C23×C11—21no—
270C23×C11—21no—
271C23×C11C4×D412yes—
272C23×C11C22×D411yescharacteristic
273C22×D11—22no—
274C22×D11—22no—
275C22×D11—22no—
276C22×D11—22no—
277C22×D11—48no—
278C22×D11—41no—
279C22×D11—41no—
280C22×D11—41no—
281C22×D11—41no—
282C22×D11—48no—
283C22×D11—41no—
284C22×D11—41no—
285C22×D11—41no—
286C22×D11—41no—
287C22×D11—41no—
288C22×D11—41no—
289C22×D11—84no—
290C22×D11—84no—
291C22×D11—84no—
292C22×D11—84no—
293C22×D11—84no—
294Q8×C11—22no—
295Q8×C11—22no—
296Q8×C11—41no—
297Q8×C11—41no—
298C2×C4×C11—21no—
299C2×C4×C11—21no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
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×C11C4×D412yes—
317C2×C4×C11C23×C411yescharacteristic
318C2×C4×C11C22×D411yescharacteristic
319C2×C4×C11C2×#4111yescharacteristic
320C2×C4×C11C2×#4111yescharacteristic
321C2×C4×C11H(5,𝔽2)11yescharacteristic
322C2×C4×C11H(5,𝔽2)11yescharacteristic
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—21no—
326C2×Dic11—21no—
327C2×Dic11—22no—
328C2×Dic11—21no—
329C2×Dic11—21no—
330C2×Dic11—21no—
331C2×Dic11—21no—
332C2×Dic11—21no—
333C2×Dic11—21no—
334C2×Dic11—21no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11—41no—
338C2×Dic11—41no—
339C2×Dic11—41no—
340C2×Dic11AGL(1,ℤ/8)12yes—
341D44—22no—
342D44—22no—
343D44—22no—
344D44—22no—
345D44—22no—
346D44—48no—
347D44—41no—
348D44—41no—
349D44C4×D414yes—
350C4×D11—84no—
351C4×D11—84no—
352C8×C11—22no—
353C8×C11—41no—
354C11⋊C8—22no—
355C11⋊C8—22no—
356C23×D4—111no—
357C22×SD16—111no—
358C22×SD16—111no—
359C22×M16C2×D1111yescharacteristic
360C2×C22⋊Q8C2×D1111yescharacteristic
361C2×C4×Q8—111no—
362C2×C4×D4—111no—
363C2×C4×D4—111no—
364C2×#117—111no—
365C22×C22⋊C4—221no—
366#450—118no—
367#440—224no—
368C2×#107—111no—
369C2×#106—111no—
370#418—224no—
371C2×#103C2×D1111yescharacteristic, complemented
372C2×#103C2×D1111yescharacteristic, complemented
373C2×#102—111no—
374C2×#102—111no—
375C2×#102—111no—
376C2×#102—111no—
377C2×#102—111no—
378C2×#102—111no—
379C2×C22⋊C8—111no—
380C2×#97—111no—
381C2×C4×C8—111no—
382#391—111no—
383#390—111no—
384#390—111no—
385#389—111no—
386#388—221no—
387#388—221no—
388#387—221no—
389#386—221no—
390#386—221no—
391#380C2×D1111yescharacteristic
392#379—221no—
393C4×C4⋊C4—111no—
394C4×C4⋊C4—221no—
395C4×C22⋊C4—111no—
396#340—111no—
397#340—111no—
398#340C2×D1111yescharacteristic, complemented
399#340C2×D1111yescharacteristic, complemented
400#336—111no—
401#336—111no—
402C22×C11—22no—
403C22×C11—22no—
404C22×C11—22no—
405C22×C11—41no—
406C22×C11—41no—
407C22×C11—41no—
408C22×C11—41no—
409C22×C11C2×C4×D411yescharacteristic
410C22×C11D4211yescharacteristic
411C22×C11#54611yescharacteristic
412C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
413C22×C11#57511yescharacteristic
414C22×C11#57711yescharacteristic
415C22×C11#57711yescharacteristic
416C2×D11—24no—
417C2×D11—42no—
418C2×D11—42no—
419C2×D11—42no—
420C2×D11—42no—
421C2×D11—42no—
422C2×D11—42no—
423C2×D11—42no—
424C2×D11—42no—
425C2×D11—42no—
426C2×D11—816no—
427C2×D11—81no—
428C2×D11—81no—
429C2×D11—81no—
430C2×D11—81no—
431C4×C11—22no—
432C4×C11—42no—
433C4×C11—42no—
434C4×C11—81no—
435C4×C11—81no—
436C4×C11C2×C4×D411yescharacteristic
437C4×C11#51811yescharacteristic
438C4×C11#54611yescharacteristic
439C4×C11#55111yescharacteristic
440Dic11—22no—
441Dic11—41no—
442Dic11—42no—
443Dic11—41no—
444Dic11—41no—
445Dic11—81no—
446C25—221no—
447C22×Q8C22×D1111yescharacteristic
448C22×D4—114no—
449C22×D4—111no—
450C22×D4—111no—
451C22×D4—222no—
452C22×D4—222no—
453C22×D4—221no—
454C22×D4—222no—
455C22×D4—441no—
456C22×D4—441no—
457C23×C4—221no—
458C23×C4—221no—
459C23×C4C22×D1111yescharacteristic
460C2×SD16—114no—
461C2×SD16—114no—
462C2×SD16—222no—
463C2×SD16—222no—
464C2×SD16—441no—
465C2×SD16—441no—
466C2×M16—22no—
467C2×M16—22no—
468C2×M16—41no—
469C22×C8—111no—
470C22×C8—111no—
471C22×C8C22×D1111yescharacteristic
472C22×C8C22×D1111yescharacteristic
473C22⋊Q8—22no—
474C22⋊Q8C4×D1114yescomplemented
475C4×Q8—222no—
476C4×Q8—441no—
477C4×D4—222no—
478C4×D4—222no—
479C4×D4—441no—
480C4×D4—441no—
481#117—222no—
482#117—441no—
483C2×C4⋊C4—21no—
484C2×C4⋊C4—111no—
485C2×C4⋊C4—111no—
486C2×C4⋊C4—221no—
487C2×C4⋊C4—221no—
488C2×C4⋊C4C22×D1111yescharacteristic
489C2×C4⋊C4C22×D1111yescharacteristic
490C2×C4⋊C4C22×D1111yescharacteristic
491C2×C22⋊C4—21no—
492C2×C22⋊C4—21no—
493C2×C22⋊C4—111no—
494C2×C22⋊C4—111no—
495C2×C22⋊C4—221no—
496C2×C22⋊C4—221no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C22⋊C4—221no—
500C2×C22⋊C4—221no—
501C2×C22⋊C4—221no—
502C2×C22⋊C4—444no—
503C2×C42—111no—
504C2×C42—111no—
505C2×C42—221no—
506C2×C42—221no—
507C2×C42—221no—
508#107—222no—
509#106—441no—
510#103—22no—
511#103—41no—
512#102—114no—
513#102—114no—
514#102—114no—
515#102—222no—
516#102—222no—
517#102—222no—
518C22⋊C8—114no—
519#97—222no—
520C4×C8—441no—
521#95—21no—
522#95—111no—
523#95—111no—
524#95—221no—
525#95—221no—
526#95—221no—
527#95—221no—
528C2×C11—42no—
529C2×C11#235811yescharacteristic
530C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
531C2×C11#294911yescharacteristic
532C2×C11#327211yescharacteristic
533C2×C11#327511yescharacteristic
534C2×C11#331011yescharacteristic
535C2×C11#331111yescharacteristic
536D11—44no—
537D11—82no—
538C24—221no—
539C24—221no—
540C24—224no—
541C24—442no—
542C24—442no—
543C24—442no—
544C24—442no—
545C24—881no—
546C24—881no—
547C24D4×D1111yescharacteristic
548C2×Q8—21no—
549C2×Q8—21no—
550C2×Q8—21no—
551C2×Q8—21no—
552C2×Q8—21no—
553C2×Q8C2×C4×D1112yes—
554C2×D4—112no—
555C2×D4—112no—
556C2×D4—112no—
557C2×D4—112no—
558C2×D4—228no—
559C2×D4—224no—
560C2×D4—221no—
561C2×D4—221no—
562C2×D4—221no—
563C2×D4—221no—
564C2×D4—221no—
565C2×D4—221no—
566C2×D4—221no—
567C2×D4—221no—
568C2×D4—444no—
569C2×D4—444no—
570C2×D4—444no—
571C2×D4—442no—
572C2×D4—442no—
573C22×C4—21no—
574C22×C4—21no—
575C22×C4—21no—
576C22×C4—21no—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—111no—
584C22×C4—111no—
585C22×C4—221no—
586C22×C4—221no—
587C22×C4—442no—
588C22×C4—442no—
589C22×C4—442no—
590C22×C4—442no—
591C22×C4—881no—
592C22×C4—881no—
593C22×C4C2×C4×D1112yes—
594C22×C4D4×D1111yescharacteristic
595C22×C4#434112yes—
596C22×C4C23×D1111yescharacteristic
597SD16—228no—
598SD16—444no—
599M16—44no—
600C2×C8—21no—
601C2×C8—21no—
602C2×C8—21no—
603C2×C8—21no—
604C2×C8—21no—
605C2×C8—112no—
606C2×C8—112no—
607C2×C8—221no—
608C2×C8—221no—
609C2×C8—221no—
610C2×C8—221no—
611C2×C8D4×D1112yes—
612C4⋊C4—24no—
613C4⋊C4—21no—
614C4⋊C4—21no—
615C4⋊C4—21no—
616C4⋊C4—21no—
617C4⋊C4—21no—
618C4⋊C4—112no—
619C4⋊C4—221no—
620C4⋊C4—221no—
621C4⋊C4—221no—
622C4⋊C4—442no—
623C4⋊C4—442no—
624C4⋊C4C2×C4×D1112yes—
625C22⋊C4—24no—
626C22⋊C4—42no—
627C22⋊C4—222no—
628C22⋊C4—442no—
629C22⋊C4—442no—
630C22⋊C4—442no—
631C22⋊C4—442no—
632C22⋊C4—441no—
633C22⋊C4—442no—
634C22⋊C4—881no—
635C22⋊C4—881no—
636C42—221no—
637C42—221no—
638C42—221no—
639C42—221no—
640C42—442no—
641C42—442no—
642C42—442no—
643C11#2286411yescharacteristic, complemented, Sylow
644C23—21no—
645C23—21no—
646C23—21no—
647C23—21no—
648C23—21no—
649C23—21no—
650C23—222no—
651C23—222no—
652C23—222no—
653C23—222no—
654C23—448no—
655C23—448no—
656C23—441no—
657C23—441no—
658C23—441no—
659C23—441no—
660C23—441no—
661C23—441no—
662C23—441no—
663C23—441no—
664C23—441no—
665C23—441no—
666C23—884no—
667C23—884no—
668C23—884no—
669C23—884no—
670C23—884no—
671C23(C22⋊D11)⋊C412yes—
672C23C2×D4×D1111yescharacteristic
673Q8—22no—
674Q8—22no—
675Q8—41no—
676Q8—41no—
677D4—114no—
678D4—222no—
679D4—222no—
680D4—222no—
681D4—222no—
682D4—222no—
683D4—448no—
684D4—441no—
685D4—441no—
686C2×C4—21no—
687C2×C4—21no—
688C2×C4—22no—
689C2×C4—22no—
690C2×C4—22no—
691C2×C4—22no—
692C2×C4—22no—
693C2×C4—22no—
694C2×C4—41no—
695C2×C4—41no—
696C2×C4—41no—
697C2×C4—41no—
698C2×C4—41no—
699C2×C4—41no—
700C2×C4—41no—
701C2×C4—41no—
702C2×C4—41no—
703C2×C4—41no—
704C2×C4—112no—
705C2×C4—221no—
706C2×C4—221no—
707C2×C4—221no—
708C2×C4—221no—
709C2×C4—221no—
710C2×C4—221no—
711C2×C4—221no—
712C2×C4—221no—
713C2×C4—221no—
714C2×C4—221no—
715C2×C4—222no—
716C2×C4—221no—
717C2×C4—441no—
718C2×C4—441no—
719C2×C4—441no—
720C2×C4—441no—
721C2×C4—441no—
722C2×C4—884no—
723C2×C4—884no—
724C2×C4(C22⋊D11)⋊C412yes—
725C2×C4C22×C4×D1111yescharacteristic
726C2×C4C2×D4×D1111yescharacteristic
727C2×C4C2×#434111yescharacteristic
728C2×C4#6703711yescharacteristic
729C2×C4#41×D1111yescharacteristic
730C2×C4#6704211yescharacteristic
731C8—22no—
732C8—41no—
733C8—222no—
734C8—222no—
735C22—22no—
736C22—22no—
737C22—22no—
738C22—41no—
739C22—41no—
740C22—41no—
741C22—41no—
742C22—224no—
743C22—442no—
744C22—442no—
745C22—442no—
746C22—442no—
747C22—442no—
748C22—442no—
749C22—442no—
750C22—442no—
751C22—442no—
752C22—8816no—
753C22—881no—
754C22—881no—
755C22—881no—
756C22—881no—
757C22C2×(C22⋊D11)⋊C411yescharacteristic
758C22#1062314011yescharacteristic
759C22#1062314111yescharacteristic
760C22D11×AGL(1,ℤ/8)11yescharacteristic
761C22#1062330811yescharacteristic
762C22#1062330911yescharacteristic
763C22#1062330911yescharacteristic
764C4—22no—
765C4—42no—
766C4—42no—
767C4—81no—
768C4—81no—
769C4—222no—
770C4—441no—
771C4—441no—
772C4—442no—
773C4—441no—
774C4—881no—
775C4C4×D4×D1111yescharacteristic
776C4#1062307611yescharacteristic
777C4#1062312211yescharacteristic
778C4#1062318911yescharacteristic
779C2—42no—
780C2—444no—
781C2—882no—
782C2#1307159611yescharacteristic
783C2#1307742911yescharacteristic
784C2#1307747111yescharacteristic
785C2#1308021311yescharacteristic
786C2#1308024411yescharacteristic
787C2#1308063211yescharacteristic
788C2#1308064711yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1894C2
socleC23×C11C22×D4
prime radicalC23×D44C22
cosocleC22×C4×C11C24
hypercenter#1894D11
hypocenterC11#22864
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1894

Complements

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

NH ≅ G/Ntype
2. C2×#10622430C2semidirect
4. #13071647C2semidirect
6. #13069467C2semidirect
7. #13069314C2semidirect
8. #13069234C2semidirect
9. #13068969C2semidirect
10. #13068947C2semidirect
11. #13068878C2semidirect
12. #13068813C2semidirect
13. #13068430C2semidirect
14. #13068397C2semidirect
15. C11×#1894C2semidirect
19. C2×Q8×Dic11C22semidirect
26. C2×C11×#103C22semidirect
27. C2×C11×#103C22semidirect
29. #10622843C22semidirect
37. C2×#66879C22semidirect
38. C2×C8×Dic11C22semidirect
39. #10622659C4semidirect
42. #10622598C22semidirect
45. C4⋊C4×Dic11C22semidirect
48. C2×#66872C22semidirect
49. C2×#66871C22semidirect
56. C11×#340C22semidirect
57. C11×#340C22semidirect
58. #10622188C22semidirect
59. #10622188C22semidirect
60. #10622167C22semidirect
61. #10622167C22semidirect
82. C11×C22⋊Q8C2×C4semidirect
99. C2×#4325C2×C4semidirect
133. C22⋊(C11⋊C8)C2×C4semidirect
141. #66873C2×C4semidirect
258. #1894D11semidirect
371. C2×#103C2×D11semidirect
372. C2×#103C2×D11semidirect
398. #340C2×D11semidirect
399. #340C2×D11semidirect
474. C22⋊Q8C4×D11semidirect
643. C11#22864semidirect

Maximal subgroups

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

subgroupindex
C2×#106226592
C2×#106224302
C2×#106227442
#130716472
#130714362
#130694672
#130693142
#130692342
#130689692
#130689472
#130688782
#130688132
#130684302
#130683972
C11×#18942
#2286411