Finite Group Databasebeta

← #14759451

Subgroups — #14759451

Order 2816.

1436 conjugacy classes of subgroups.

The subgroup lattice has 750 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×C4×Q8×D11C211yesmaximal, characteristic
2C2×#10622421C211yesmaximal, characteristic
3C2×#10622329C211yesmaximal, characteristic, complemented
4C2×#10622643C211yesmaximal, characteristic, complemented
5C4×#66950C211yesmaximal, characteristic
6#13068958C211yesmaximal, characteristic, complemented
7#13068955C211yesmaximal, characteristic, complemented
8#13068922C211yesmaximal, characteristic
9#13068886C211yesmaximal, characteristic, complemented
10#13068885C211yesmaximal, characteristic, complemented
11#13068810C211yesmaximal, characteristic
12#13068549C211yesmaximal, characteristic
13#13068449C211yesmaximal, characteristic, complemented
14#13068379C211yesmaximal, characteristic
15C11×#1763C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C2×C4×Q8×C11C2211yescharacteristic
18C2×Q8×Dic11C2211yescharacteristic
19C22×#4326C2211yescharacteristic
20C22×Dic44C2211yescharacteristic
21C4×Q8×D11—24no—
22C4×Q8×D11—24no—
23C2×#66950C2211yescharacteristic
24C2×C4⋊C4×D11—21no—
25C2×C4⋊C4×D11C2211yescharacteristic
26C2×#66940—21no—
27C2×#66940C2211yescharacteristic
28C2×C42×D11—21no—
29C2×C42×D11C2211yescharacteristic
30C2×C4×Dic22—21no—
31C2×C4×Dic22C2211yescharacteristic
32C2×C4×Dic22C2211yescharacteristic
33C2×C11×#103C2211yescharacteristic
34C2×C11×#103C2211yescharacteristic
35C2×C11×#97C2211yescharacteristic
36C4×C11×C4⋊C4C2211yescharacteristic
37C2×#66899C2211yescharacteristic
38C2×(C2×D11)⋊C8C2211yescharacteristic
39C2×(C2×D11)⋊C8C2211yescharacteristic
40C2×#66881C2211yescharacteristic
41C2×#66880C2211yescharacteristic
42C2×#66880C2211yescharacteristic
43#10622643—24no—
44#10622600C2211yescharacteristic
45#10622598C2211yescharacteristic
46#10622587C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66874C2211yescharacteristic
49C2×#66874C2211yescharacteristic
50C2×#66872C2211yescharacteristic
51C4×(C2×D11)⋊C4—21no—
52C4×C4⋊Dic11—21no—
53C2×#66867C2211yescharacteristic
54#10622421C418yescomplemented
55#10622329—24no—
56#10622281—21no—
57#10622266—21no—
58C11×#340C2211yescharacteristic
59C11×#340C2211yescharacteristic
60#10622188C2211yescharacteristic
61#10622188C2211yescharacteristic
62#10622167C2211yescharacteristic
63#10622167C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C2×Q8×D11—22no—
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11C2×C414yes—
71C22×C4×D11—21no—
72C22×C4×D11—21no—
73C22×C4×D11D411yescharacteristic
74C22×C4×D11D411yescharacteristic
75C22×C4×D11C2311yescharacteristic
76C22×Dic22—21no—
77C22×Dic22C2311yescharacteristic
78C22×Dic22C2311yescharacteristic
79C22×C8×C11C2311yescharacteristic
80C22×C8×C11C2311yescharacteristic
81C4×Q8×C11—22no—
82C4×Q8×C11D414yes—
83C2×C11×C4⋊C4—21no—
84C2×C11×C4⋊C4C2311yescharacteristic
85C2×C11×C4⋊C4C2311yescharacteristic
86C2×C11×C4⋊C4C2311yescharacteristic
87C2×C42×C11—21no—
88C2×C42×C11—21no—
89C2×C42×C11C2311yescharacteristic
90Q8×Dic11—22no—
91Q8×Dic11—22no—
92C2×#4326—22no—
93C2×#4326—22no—
94C2×#4326C2×C414yescomplemented
95C2×(C2×D11)⋊C4—21no—
96C2×(C2×D11)⋊C4—21no—
97C2×C4⋊Dic11—21no—
98C2×C4⋊Dic11—21no—
99C2×C4⋊Dic11—21no—
100C2×C4⋊Dic11C2311yescharacteristic
101C2×C4⋊Dic11C2311yescharacteristic
102C2×Dic11⋊C4—21no—
103C2×Dic11⋊C4—21no—
104C2×Dic11⋊C4—21no—
105C2×Dic11⋊C4—21no—
106C2×C4×Dic11—21no—
107C2×C4×Dic11—21no—
108C2×C4×Dic11—21no—
109C2×C4×Dic11—21no—
110C2×C4×Dic11D411yescharacteristic
111C2×C4×Dic11D411yescharacteristic
112C2×C4×Dic11C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
114C22×C11⋊C8C2311yescharacteristic
115C2×Dic44—22no—
116C2×Dic44—22no—
117C2×Dic44C2×C414yescomplemented
118#66950—22no—
119#66950C2×C414yes—
120C4⋊C4×D11—28no—
121C4⋊C4×D11—22no—
122C4⋊C4×D11—22no—
123#66940—28no—
124#66940—22no—
125#66940—22no—
126C42×D11—28no—
127C42×D11—22no—
128C42×D11—22no—
129C4×Dic22—28no—
130C4×Dic22—22no—
131C4×Dic22—22no—
132C4×Dic22—22no—
133C4×Dic22D414yes—
134C11×#103—22no—
135C11×#103C2×C414yescomplemented
136C11×#97—22no—
137C11×#95—21no—
138#66899—22no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143(C2×D11)⋊C8—22no—
144(C2×D11)⋊C8C2×C414yes—
145#66881—22no—
146#66880—22no—
147#66880—22no—
148#66874—22no—
149#66874—22no—
150#66874C2×C414yescomplemented
151#66872—22no—
152#66867—22no—
153#21455—111nomaximal, Sylow
154C23×D11C2×D411yescharacteristic
155C2×Q8×C11—21no—
156C2×Q8×C11—21no—
157C2×Q8×C11—21no—
158C2×Q8×C11C22×C412yes—
159C2×Q8×C11C2×D412yes—
160C2×Q8×C11#4112yes—
161C22×C4×C11—21no—
162C22×C4×C11—21no—
163C22×C4×C11—21no—
164C22×C4×C11—21no—
165C22×C4×C11C2×D411yescharacteristic
166C22×C4×C11C2×D411yescharacteristic
167C22×C4×C11C2411yescharacteristic
168C22×Dic11—21no—
169C22×Dic11—21no—
170C22×Dic11—21no—
171C22×Dic11—21no—
172C22×Dic11C2×D411yescharacteristic
173C22×Dic11C2×D411yescharacteristic
174C22×Dic11C2×D411yescharacteristic
175Q8×D11—28no—
176Q8×D11—28no—
177Q8×D11—28no—
178Q8×D11—28no—
179C2×C4×D11—24no—
180C2×C4×D11—24no—
181C2×C4×D11—22no—
182C2×C4×D11—24no—
183C2×C4×D11—24no—
184C2×C4×D11—22no—
185C2×C4×D11—22no—
186C2×C4×D11—22no—
187C2×C4×D11—22no—
188C2×C4×D11—21no—
189C2×C4×D11—21no—
190C2×C4×D11—21no—
191C2×C4×D11—21no—
192C2×C4×D11—41no—
193C2×C4×D11—42no—
194C2×C4×D11—42no—
195C2×C4×D11C22×C412yes—
196C2×C4×D11#4112yes—
197C2×Dic22—24no—
198C2×Dic22—24no—
199C2×Dic22—24no—
200C2×Dic22—21no—
201C2×Dic22—21no—
202C2×Dic22—21no—
203C2×Dic22—21no—
204C2×Dic22—21no—
205C2×Dic22—21no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22C22×C412yes—
209C2×Dic22C22×C412yes—
210C2×Dic22C2×D412yes—
211C2×Dic22#4112yes—
212C2×C8×C11—21no—
213C2×C8×C11—21no—
214C2×C8×C11—21no—
215C2×C8×C11—21no—
216C2×C8×C11—21no—
217C2×C8×C11C22×C412yes—
218C11×C4⋊C4—24no—
219C11×C4⋊C4—21no—
220C11×C4⋊C4—21no—
221C11×C4⋊C4—21no—
222C11×C4⋊C4—21no—
223C11×C4⋊C4C22×C412yes—
224C11×C4⋊C4C2×D412yes—
225C42×C11—24no—
226C42×C11—42no—
227C42×C11C2×D412yes—
228C42×C11C2×D412yes—
229#4326—28no—
230(C2×D11)⋊C4—24no—
231(C2×D11)⋊C4—42no—
232C4⋊Dic11—24no—
233C4⋊Dic11—24no—
234C4⋊Dic11—21no—
235C4⋊Dic11—21no—
236C4⋊Dic11—21no—
237C4⋊Dic11—42no—
238C4⋊Dic11C2×D412yes—
239Dic11⋊C4—24no—
240Dic11⋊C4—24no—
241Dic11⋊C4—24no—
242Dic11⋊C4—42no—
243C4×Dic11—24no—
244C4×Dic11—24no—
245C4×Dic11—22no—
246C4×Dic11—24no—
247C4×Dic11—22no—
248C4×Dic11—21no—
249C4×Dic11—21no—
250C4×Dic11—42no—
251C2×C11⋊C8—21no—
252C2×C11⋊C8—21no—
253C2×C11⋊C8—21no—
254C2×C11⋊C8—21no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8C22×C412yes—
257Dic44—28no—
258C22×C4×Q8—111no—
259C2×#451—111no—
260C2×#441—111no—
261C2×#441—111no—
262C4×C22⋊Q8—111no—
263#1878—111no—
264#1878—111no—
265#1872—111no—
266#1865—111no—
267#1865—111no—
268#1853—111no—
269#1787—111no—
270#1763—111no—
271#1763D1111yescharacteristic, complemented
272#1749—111no—
273C23×C11C22×D411yescharacteristic
274C22×D11—21no—
275C22×D11—21no—
276C22×D11—21no—
277C22×D11—21no—
278C22×D11C4×D412yes—
279C22×D11#13712yes—
280C22×D11#13712yes—
281Q8×C11—22no—
282Q8×C11—22no—
283Q8×C11—22no—
284Q8×C11C4×D414yes—
285C2×C4×C11—22no—
286C2×C4×C11—22no—
287C2×C4×C11—22no—
288C2×C4×C11—21no—
289C2×C4×C11—21no—
290C2×C4×C11—21no—
291C2×C4×C11—21no—
292C2×C4×C11—22no—
293C2×C4×C11—22no—
294C2×C4×C11—41no—
295C2×C4×C11—41no—
296C2×C4×C11—41no—
297C2×C4×C11—41no—
298C2×C4×C11—41no—
299C2×C4×C11—41no—
300C2×C4×C11—41no—
301C2×C4×C11#12012yes—
302C2×C4×C11#12012yes—
303C2×C4×C11C23×C411yescharacteristic
304C2×C4×C11C22×D411yescharacteristic
305C2×C4×C11C22×D411yescharacteristic
306C2×C4×C11C2×#4111yescharacteristic
307C2×C4×C11C2×#4111yescharacteristic
308C2×C4×C11C2×#4111yescharacteristic
309C2×Dic11—22no—
310C2×Dic11—21no—
311C2×Dic11—21no—
312C2×Dic11—22no—
313C2×Dic11—21no—
314C2×Dic11—22no—
315C2×Dic11—21no—
316C2×Dic11—22no—
317C2×Dic11—21no—
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—21no—
321C2×Dic11—41no—
322C2×Dic11—41no—
323C2×Dic11—41no—
324C2×Dic11—41no—
325C2×Dic11—41no—
326C2×Dic11—41no—
327C2×Dic11—41no—
328C2×Dic11C4×D412yes—
329C2×Dic11#13712yes—
330C4×D11—28no—
331C4×D11—216no—
332C4×D11—22no—
333C4×D11—22no—
334C4×D11—22no—
335C4×D11—22no—
336C4×D11—44no—
337C4×D11—48no—
338Dic22—216no—
339Dic22—22no—
340Dic22—22no—
341Dic22—22no—
342Dic22—22no—
343Dic22—22no—
344Dic22—41no—
345Dic22—41no—
346Dic22C4×D414yes—
347C8×C11—22no—
348C8×C11—41no—
349C11⋊C8—22no—
350C11⋊C8—41no—
351C23×Q8—111no—
352C22×Q16—111no—
353C22×Q16—111no—
354C2×C22⋊Q8—111no—
355C2×C4×Q8—111no—
356C2×C4×Q8—111no—
357C2×C4×Q8—111no—
358C2×C4×Q8—111no—
359C2×C4×Q8—221no—
360C2×C4×Q8—221no—
361C2×C4×Q8—224no—
362C2×C4×Q8—224no—
363C2×C4×Q8C2×D1111yescharacteristic
364C22×C4⋊C4—111no—
365C22×C4⋊C4—221no—
366C22×C42—111no—
367C22×C42—221no—
368#451—118no—
369#441—224no—
370#441—224no—
371C2×#106—111no—
372C2×#106—111no—
373C2×#103—111no—
374C2×#103—111no—
375C2×#103—111no—
376C2×#103—111no—
377C2×#103—111no—
378C2×#103—111no—
379C2×#103C2×D1111yescharacteristic
380C2×#103C2×D1111yescharacteristic
381C2×C22⋊C8—111no—
382C2×C22⋊C8—111no—
383C2×#97—111no—
384C2×#97C2×D1111yescharacteristic
385#391—111no—
386#389—111no—
387#387—221no—
388#385—221no—
389#380—111no—
390C4×C4⋊C4—221no—
391C4×C4⋊C4C2×D1111yescharacteristic
392C4×C22⋊C4—221no—
393#340—111no—
394#340—111no—
395#340C2×D1111yescharacteristic
396#340C2×D1111yescharacteristic
397#336—111no—
398#336—111no—
399C22×C11C2×C4×D411yescharacteristic
400C22×C11C2×#12011yescharacteristic
401C22×C11#52511yescharacteristic
402C22×C11C2×#13711yescharacteristic
403C22×C11C2×#13711yescharacteristic
404C22×C11C2×#13711yescharacteristic
405C22×C11#57511yescharacteristic
406C2×D11—22no—
407C2×D11—22no—
408C2×D11—22no—
409C2×D11—22no—
410C2×D11—22no—
411C2×D11—22no—
412C2×D11#44114yescomplemented
413C4×C11—22no—
414C4×C11—22no—
415C4×C11—24no—
416C4×C11—42no—
417C4×C11—42no—
418C4×C11—81no—
419C4×C11C2×C4×D411yescharacteristic
420C4×C11C2×C4×D411yescharacteristic
421C4×C11#52511yescharacteristic
422C4×C11#52511yescharacteristic
423Dic11—22no—
424Dic11—22no—
425Dic11—24no—
426Dic11—41no—
427Dic11—42no—
428Dic11—42no—
429Dic11—81no—
430C22×Q8—114no—
431C22×Q8—111no—
432C22×Q8—111no—
433C22×Q8—221no—
434C22×Q8—222no—
435C22×Q8—222no—
436C22×Q8—222no—
437C22×Q8—222no—
438C22×Q8—222no—
439C22×Q8C22×D1111yescharacteristic
440C23×C4—111no—
441C23×C4—111no—
442C23×C4—111no—
443C23×C4—221no—
444C23×C4—221no—
445C2×Q16—114no—
446C2×Q16—114no—
447C2×Q16—222no—
448C2×Q16—222no—
449C2×Q16—222no—
450C2×Q16—222no—
451C22×C8—111no—
452C22×C8—111no—
453C22×C8C22×D1111yescharacteristic
454C22×C8C22×D1111yescharacteristic
455C22⋊Q8—114no—
456C22⋊Q8—222no—
457C4×Q8—22no—
458C4×Q8—114no—
459C4×Q8—228no—
460C4×Q8—222no—
461C4×Q8—228no—
462C4×Q8—222no—
463C4×Q8—222no—
464C4×Q8—222no—
465C4×Q8—222no—
466C4×Q8—222no—
467C4×Q8—222no—
468C4×Q8D4414yes—
469C2×C4⋊C4—21no—
470C2×C4⋊C4—111no—
471C2×C4⋊C4—111no—
472C2×C4⋊C4—222no—
473C2×C4⋊C4—228no—
474C2×C4⋊C4—221no—
475C2×C4⋊C4—221no—
476C2×C4⋊C4—221no—
477C2×C4⋊C4—221no—
478C2×C4⋊C4—221no—
479C2×C4⋊C4—222no—
480C2×C4⋊C4—221no—
481C2×C4⋊C4—221no—
482C2×C4⋊C4C22×D1111yescharacteristic
483C2×C4⋊C4C22×D1111yescharacteristic
484C2×C4⋊C4C22×D1111yescharacteristic
485C2×C22⋊C4—221no—
486C2×C22⋊C4—221no—
487C2×C42—21no—
488C2×C42—21no—
489C2×C42—111no—
490C2×C42—111no—
491C2×C42—111no—
492C2×C42—228no—
493C2×C42—221no—
494C2×C42—221no—
495C2×C42—221no—
496C2×C42—222no—
497C2×C42—222no—
498C2×C42—221no—
499C2×C42C22×D1111yescharacteristic
500#106—222no—
501#106—222no—
502#103—22no—
503#103—114no—
504#103—222no—
505#103—222no—
506#103—222no—
507#103—222no—
508#103—222no—
509#103C4×D1114yescomplemented
510C22⋊C8—114no—
511C22⋊C8—222no—
512#97—22no—
513#97—222no—
514#95—21no—
515#95—221no—
516#95—221no—
517#95—221no—
518#95—221no—
519C2×C11C4×#12011yescharacteristic
520C2×C11C2×#44111yescharacteristic
521C2×C11C4×#13711yescharacteristic
522C2×C11#300411yescharacteristic
523C2×C11#300711yescharacteristic
524C2×C11#311311yescharacteristic
525C2×C11#311711yescharacteristic
526D11—24no—
527C24—111no—
528C2×Q8—21no—
529C2×Q8—21no—
530C2×Q8—21no—
531C2×Q8—112no—
532C2×Q8—112no—
533C2×Q8—112no—
534C2×Q8—112no—
535C2×Q8—224no—
536C2×Q8—224no—
537C2×Q8—224no—
538C2×Q8—228no—
539C2×Q8—228no—
540C2×Q8—228no—
541C2×Q8—228no—
542C2×Q8—221no—
543C2×Q8—221no—
544C2×Q8—221no—
545C2×Q8—221no—
546C2×Q8—221no—
547C2×Q8—221no—
548C2×Q8—221no—
549C2×Q8—221no—
550C2×Q8C2×C4×D1112yes—
551C2×Q8C2×D4412yes—
552C2×Q8#433912yes—
553C22×C4—21no—
554C22×C4—21no—
555C22×C4—21no—
556C22×C4—21no—
557C22×C4—111no—
558C22×C4—111no—
559C22×C4—112no—
560C22×C4—112no—
561C22×C4—111no—
562C22×C4—222no—
563C22×C4—222no—
564C22×C4—224no—
565C22×C4—224no—
566C22×C4—224no—
567C22×C4—222no—
568C22×C4—224no—
569C22×C4—221no—
570C22×C4—222no—
571C22×C4—221no—
572C22×C4—221no—
573C22×C4—221no—
574C22×C4—221no—
575C22×C4—221no—
576C22×C4—221no—
577C22×C4—222no—
578C22×C4—221no—
579C22×C4—441no—
580C22×C4—442no—
581C22×C4—442no—
582C22×C4D4×D1111yescharacteristic
583C22×C4D4×D1111yescharacteristic
584C22×C4C23×D1111yescharacteristic
585Q16—228no—
586Q16—228no—
587C2×C8—21no—
588C2×C8—21no—
589C2×C8—21no—
590C2×C8—21no—
591C2×C8—21no—
592C2×C8—112no—
593C2×C8—221no—
594C2×C8—221no—
595C2×C8—221no—
596C2×C8—221no—
597C2×C8—221no—
598C2×C8C2×C4×D1112yes—
599C4⋊C4—24no—
600C4⋊C4—21no—
601C4⋊C4—21no—
602C4⋊C4—21no—
603C4⋊C4—21no—
604C4⋊C4—112no—
605C4⋊C4—224no—
606C4⋊C4—224no—
607C4⋊C4—224no—
608C4⋊C4—224no—
609C4⋊C4—224no—
610C4⋊C4—221no—
611C4⋊C4—221no—
612C4⋊C4—221no—
613C4⋊C4—442no—
614C4⋊C4—442no—
615C4⋊C4C2×C4×D1112yes—
616C4⋊C4C2×D4412yes—
617C22⋊C4—224no—
618C22⋊C4—442no—
619C42—24no—
620C42—42no—
621C42—224no—
622C42—224no—
623C42—222no—
624C42—222no—
625C42—224no—
626C42—221no—
627C42—221no—
628C42—442no—
629C42C2×D4412yes—
630C42D4×D1112yes—
631C11#2145511yescharacteristic, complemented, Sylow
632C23—112no—
633C23—112no—
634C23—112no—
635C23—221no—
636C23—221no—
637C23—221no—
638C23—221no—
639C23C2×D4×D1111yescharacteristic
640Q8—22no—
641Q8—22no—
642Q8—22no—
643Q8—114no—
644Q8—2216no—
645Q8—222no—
646Q8—222no—
647Q8—222no—
648Q8—222no—
649Q8—222no—
650Q8—441no—
651Q8—441no—
652Q8C4×D4414yes—
653C2×C4—22no—
654C2×C4—21no—
655C2×C4—21no—
656C2×C4—21no—
657C2×C4—21no—
658C2×C4—22no—
659C2×C4—22no—
660C2×C4—22no—
661C2×C4—22no—
662C2×C4—41no—
663C2×C4—41no—
664C2×C4—41no—
665C2×C4—41no—
666C2×C4—41no—
667C2×C4—41no—
668C2×C4—41no—
669C2×C4—112no—
670C2×C4—112no—
671C2×C4—2216no—
672C2×C4—228no—
673C2×C4—221no—
674C2×C4—221no—
675C2×C4—222no—
676C2×C4—221no—
677C2×C4—222no—
678C2×C4—221no—
679C2×C4—222no—
680C2×C4—222no—
681C2×C4—222no—
682C2×C4—222no—
683C2×C4—222no—
684C2×C4—222no—
685C2×C4—221no—
686C2×C4—221no—
687C2×C4—221no—
688C2×C4—222no—
689C2×C4—444no—
690C2×C4—448no—
691C2×C4—441no—
692C2×C4—441no—
693C2×C4—441no—
694C2×C4—441no—
695C2×C4—441no—
696C2×C4—441no—
697C2×C4—441no—
698C2×C4#6693512yes—
699C2×C4#6693512yes—
700C2×C4C22×C4×D1111yescharacteristic
701C2×C4C22×D4411yescharacteristic
702C2×C4C2×#433911yescharacteristic
703C2×C4C2×D4×D1111yescharacteristic
704C2×C4#41×D1111yescharacteristic
705C2×C4#41×D1111yescharacteristic
706C8—22no—
707C8—41no—
708C8—222no—
709C8—441no—
710C22—114no—
711C22—222no—
712C22—222no—
713C22—222no—
714C22—222no—
715C22—222no—
716C22—222no—
717C22C2×#6693511yescharacteristic
718C22C4×D4×D1111yescharacteristic
719C22#1062307811yescharacteristic
720C22#1062330411yescharacteristic
721C22D11×#13711yescharacteristic
722C22D11×#13711yescharacteristic
723C22D11×#13711yescharacteristic
724C4—24no—
725C4—22no—
726C4—22no—
727C4—42no—
728C4—42no—
729C4—81no—
730C4—222no—
731C4—224no—
732C4—222no—
733C4—442no—
734C4—441no—
735C4—442no—
736C4—881no—
737C4C2×C4×D4411yescharacteristic
738C4#1062305511yescharacteristic
739C4C4×D4×D1111yescharacteristic
740C4#1062307811yescharacteristic
741C2—224no—
742C2C4×#6693511yescharacteristic
743C2D11×#44111yescharacteristic
744C2#1307743811yescharacteristic
745C2#1307785211yescharacteristic
746C2#1307787711yescharacteristic
747C2#1307874411yescharacteristic
748C2#1307878511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1763C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1763D11
hypocenterC11#21455
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1763

Complements

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

NH ≅ G/Ntype
3. C2×#10622329C2semidirect
4. C2×#10622643C2semidirect
6. #13068958C2semidirect
7. #13068955C2semidirect
9. #13068886C2semidirect
10. #13068885C2semidirect
13. #13068449C2semidirect
15. C11×#1763C2semidirect
54. #10622421C4semidirect
94. C2×#4326C2×C4semidirect
117. C2×Dic44C2×C4semidirect
135. C11×#103C2×C4semidirect
150. #66874C2×C4semidirect
271. #1763D11semidirect
412. C2×D11#441semidirect
509. #103C4×D11semidirect
631. C11#21455semidirect

Maximal subgroups

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

subgroupindex
C2×C4×Q8×D112
C2×#106224212
C2×#106223292
C2×#106226432
C4×#669502
#130689582
#130689552
#130689222
#130688862
#130688852
#130688102
#130685492
#130684492
#130683792
C11×#17632
#2145511