Finite Group Databasebeta

← #14769631

Subgroups — #14769631

Order 2816.

1398 conjugacy classes of subgroups.

The subgroup lattice has 766 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×Q16×D11C211yesmaximal, characteristic
2C2×C4×#4326C211yesmaximal, characteristic, complemented
3C2×#10622403C211yesmaximal, characteristic, complemented
4#13071450C211yesmaximal, characteristic
5Q8×(C2×D11)⋊C4C211yesmaximal, characteristic
6#13069476C211yesmaximal, characteristic, complemented
7#13069474C211yesmaximal, characteristic, complemented
8#13068959C211yesmaximal, characteristic, complemented
9#13068958C211yesmaximal, characteristic, complemented
10#13068956C211yesmaximal, characteristic, complemented
11#13068644C211yesmaximal, characteristic
12#13068549C211yesmaximal, characteristic
13#13068549C211yesmaximal, characteristic
14#13068386C211yesmaximal, characteristic
15C11×#1878C211yesmaximal, characteristic, complemented
16C22×Q8×D11C2211yescharacteristic
17C22×Q8×D11C2211yescharacteristic
18C22×C11×Q16C2211yescharacteristic
19C2×C4×Q8×C11C2211yescharacteristic
20C2×Q8×Dic11C2211yescharacteristic
21C22×#4326C2211yescharacteristic
22C22×#4326C2211yescharacteristic
23C2×Q16×D11—24no—
24C2×Q16×D11—24no—
25C2×Q16×D11C418yescomplemented
26C22×Dic44C2211yescharacteristic
27C22×C8×D11C2211yescharacteristic
28C2×#66940C2211yescharacteristic
29C2×C4×Dic22C2211yescharacteristic
30C2×C11×#103C2211yescharacteristic
31C2×C11×#103C2211yescharacteristic
32C11×#391C2211yescharacteristic
33#10622843C2211yescharacteristic
34C2×#66899C2211yescharacteristic
35C2×#66899C2211yescharacteristic
36C2×(C2×D11)⋊C8C2211yescharacteristic
37C2×#66880C2211yescharacteristic
38C2×#66880C2211yescharacteristic
39C2×C8×Dic11C2211yescharacteristic
40C4×#4326—24no—
41#10622600—21no—
42#10622600C2211yescharacteristic
43#10622600C2211yescharacteristic
44#10622587—21no—
45#10622587C2211yescharacteristic
46C2×#66874C2211yescharacteristic
47C2×#66874C2211yescharacteristic
48C2×#66871C2211yescharacteristic
49C2×#66871C2211yescharacteristic
50C4×(C2×D11)⋊C4—21no—
51C4×(C2×D11)⋊C4C2211yescharacteristic
52#10622542—21no—
53#10622542C2211yescharacteristic
54C2×C4×C11⋊C8C2211yescharacteristic
55#10622403—24no—
56#10622280—21no—
57#10622279—21no—
58#10622259—21no—
59#10622259—21no—
60C11×#340C2211yescharacteristic
61C11×#336C2211yescharacteristic
62#10622189C2211yescharacteristic
63#10622188C2211yescharacteristic
64C22×Q8×C11C2311yescharacteristic
65C22×Q8×C11C2311yescharacteristic
66C2×Q8×D11—22no—
67C2×Q8×D11—22no—
68C2×Q8×D11—22no—
69C2×Q8×D11—22no—
70C2×Q8×D11—22no—
71C2×Q8×D11—22no—
72C2×Q8×D11—41no—
73C2×Q8×D11—41no—
74C2×Q8×D11—41no—
75C2×Q8×D11—41no—
76C2×Q8×D11C2×C414yes—
77C2×Q8×D11C2×C414yes—
78C22×C4×D11—21no—
79C22×C4×D11—21no—
80C22×C4×D11C2311yescharacteristic
81C22×Dic22—21no—
82C22×Dic22—21no—
83C22×Dic22C2311yescharacteristic
84C22×Dic22C2311yescharacteristic
85C2×C11×Q16—22no—
86C2×C11×Q16—22no—
87C2×C11×Q16C2×C414yes—
88C22×C8×C11C2311yescharacteristic
89C22×C8×C11C2311yescharacteristic
90C4×Q8×C11—22no—
91C4×Q8×C11—41no—
92C2×C11×C4⋊C4—21no—
93C2×C11×C4⋊C4C2311yescharacteristic
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C42×C11—21no—
96C2×C42×C11C2311yescharacteristic
97Q8×Dic11—22no—
98Q8×Dic11—41no—
99C2×#4326—22no—
100C2×#4326—22no—
101C2×#4326C2×C414yes—
102C2×#4326C2×C414yes—
103C2×#4326D414yes—
104C2×#4326D414yes—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4D411yescharacteristic
108C2×(C2×D11)⋊C4D411yescharacteristic
109C2×C4⋊Dic11—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×Dic11⋊C4—21no—
113C2×Dic11⋊C4—21no—
114C2×C4×Dic11—21no—
115C2×C4×Dic11—21no—
116C2×C4×Dic11—21no—
117C2×C4×Dic11C2311yescharacteristic
118C22×C11⋊C8C2311yescharacteristic
119C22×C11⋊C8C2311yescharacteristic
120Q16×D11—232no—
121C2×Dic44—22no—
122C2×Dic44—22no—
123C2×Dic44C2×C414yes—
124C2×C8×D11—22no—
125C2×C8×D11—22no—
126C2×C8×D11C2×C414yes—
127#66940—22no—
128#66940—41no—
129C4×Dic22—22no—
130C4×Dic22—41no—
131C11×#103—22no—
132C11×#103—41no—
133C11×#95—21no—
134C11×#95—21no—
135#66899—22no—
136#66899—41no—
137C11⋊#95—21no—
138C11⋊#95—21no—
139C11⋊#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95D411yescharacteristic
146C11⋊#95D411yescharacteristic
147(C2×D11)⋊C8—22no—
148#66880—22no—
149#66880—41no—
150C8×Dic11—22no—
151#66874—22no—
152#66874—41no—
153#66871—22no—
154#66871—22no—
155C4×C11⋊C8—22no—
156C22⋊C4×Q16—111nomaximal, Sylow
157C23×D11C2×D411yescharacteristic
158C2×Q8×C11—21no—
159C2×Q8×C11—21no—
160C2×Q8×C11—21no—
161C2×Q8×C11—21no—
162C2×Q8×C11—21no—
163C2×Q8×C11—21no—
164C2×Q8×C11—21no—
165C2×Q8×C11—21no—
166C2×Q8×C11C22×C412yes—
167C2×Q8×C11C22×C412yes—
168C2×Q8×C11C2×D412yes—
169C2×Q8×C11C2×D412yes—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11—21no—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2411yescharacteristic
177C22×Dic11—21no—
178C22×Dic11—21no—
179C22×Dic11—21no—
180C22×Dic11—21no—
181C22×Dic11C2×D411yescharacteristic
182C22×Dic11C2×D411yescharacteristic
183C22×Dic11C2×D411yescharacteristic
184Q8×D11—28no—
185Q8×D11—28no—
186Q8×D11—44no—
187Q8×D11—44no—
188Q8×D11—44no—
189Q8×D11—44no—
190Q8×D11—44no—
191Q8×D11—44no—
192C2×C4×D11—24no—
193C2×C4×D11—24no—
194C2×C4×D11—21no—
195C2×C4×D11—21no—
196C2×C4×D11—21no—
197C2×C4×D11—21no—
198C2×C4×D11—42no—
199C2×C4×D11—42no—
200C2×C4×D11—42no—
201C2×C4×D11—42no—
202C2×C4×D11C22×C412yes—
203C2×C4×D11#4112yes—
204C2×Dic22—24no—
205C2×Dic22—24no—
206C2×Dic22—21no—
207C2×Dic22—21no—
208C2×Dic22—21no—
209C2×Dic22—21no—
210C2×Dic22—21no—
211C2×Dic22—21no—
212C2×Dic22—21no—
213C2×Dic22—21no—
214C2×Dic22—42no—
215C2×Dic22—42no—
216C2×Dic22—42no—
217C2×Dic22—42no—
218C2×Dic22C22×C412yes—
219C2×Dic22C22×C412yes—
220C2×Dic22C2×D412yes—
221C2×Dic22C2×D412yes—
222C11×Q16—28no—
223C2×C8×C11—21no—
224C2×C8×C11—21no—
225C2×C8×C11—21no—
226C2×C8×C11—21no—
227C2×C8×C11—21no—
228C2×C8×C11C22×C412yes—
229C11×C4⋊C4—21no—
230C11×C4⋊C4—21no—
231C11×C4⋊C4—21no—
232C11×C4⋊C4—21no—
233C11×C4⋊C4—42no—
234C42×C11—21no—
235C42×C11—21no—
236C42×C11—42no—
237#4326—28no—
238#4326C22⋊C4116yescomplemented
239(C2×D11)⋊C4—22no—
240(C2×D11)⋊C4—42no—
241(C2×D11)⋊C4—42no—
242(C2×D11)⋊C4Q1614yescomplemented
243C4⋊Dic11—21no—
244C4⋊Dic11—21no—
245C4⋊Dic11—21no—
246C4⋊Dic11—21no—
247C4⋊Dic11—42no—
248Dic11⋊C4—42no—
249Dic11⋊C4—42no—
250C4×Dic11—21no—
251C4×Dic11—21no—
252C4×Dic11—42no—
253C4×Dic11—42no—
254C4×Dic11—42no—
255C2×C11⋊C8—21no—
256C2×C11⋊C8—21no—
257C2×C11⋊C8—21no—
258C2×C11⋊C8C22×C412yes—
259C2×C11⋊C8C2×D412yes—
260C2×C11⋊C8C2×D412yes—
261Dic44—28no—
262C8×D11—28no—
263C23×Q16—111no—
264C2×C4×Q16—111no—
265C2×C4×Q16—111no—
266Q8×C22⋊C4—111no—
267Q8×C22⋊C4—111no—
268#1969—111no—
269#1969—111no—
270#1878—111no—
271#1878—111no—
272#1878—111no—
273#1878D1111yescharacteristic, complemented
274#1808—111no—
275#1787—111no—
276#1787—111no—
277C8×C22⋊C4—111no—
278C23×C11C22×D411yescharacteristic
279C22×D11—21no—
280C22×D11—21no—
281C22×D11—21no—
282C22×D11—21no—
283C22×D11C4×D412yes—
284C22×D11C2×Q1612yes—
285C22×D11#13512yes—
286Q8×C11—22no—
287Q8×C11—22no—
288Q8×C11—22no—
289Q8×C11—22no—
290Q8×C11—22no—
291Q8×C11—41no—
292Q8×C11—41no—
293Q8×C11C2×C22⋊C414yes—
294C2×C4×C11—22no—
295C2×C4×C11—21no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—21no—
299C2×C4×C11—22no—
300C2×C4×C11—21no—
301C2×C4×C11—21no—
302C2×C4×C11—21no—
303C2×C4×C11—41no—
304C2×C4×C11—41no—
305C2×C4×C11—41no—
306C2×C4×C11—41no—
307C2×C4×C11—41no—
308C2×C4×C11—41no—
309C2×C4×C11—41no—
310C2×C4×C11—41no—
311C2×C4×C11C2×Q1612yescomplemented
312C2×C4×C11C23×C411yescharacteristic
313C2×C4×C11C22×D411yescharacteristic
314C2×C4×C11C22×D411yescharacteristic
315C2×C4×C11C2×#4111yescharacteristic
316C2×C4×C11H(5,𝔽2)11yescharacteristic
317C2×C4×C11H(5,𝔽2)11yescharacteristic
318C2×Dic11—22no—
319C2×Dic11—21no—
320C2×Dic11—22no—
321C2×Dic11—22no—
322C2×Dic11—21no—
323C2×Dic11—21no—
324C2×Dic11—21no—
325C2×Dic11—22no—
326C2×Dic11—21no—
327C2×Dic11—21no—
328C2×Dic11—21no—
329C2×Dic11—41no—
330C2×Dic11—41no—
331C2×Dic11—41no—
332C2×Dic11—41no—
333C2×Dic11—41no—
334C2×Dic11—41no—
335C2×Dic11—41no—
336C2×Dic11—41no—
337C2×Dic11C4×D412yes—
338C2×Dic11C2×Q1612yescomplemented
339C4×D11—22no—
340C4×D11—22no—
341C4×D11—22no—
342C4×D11—22no—
343C4×D11—48no—
344C4×D11—48no—
345Dic22—22no—
346Dic22—22no—
347Dic22—22no—
348Dic22—22no—
349Dic22—22no—
350Dic22—48no—
351Dic22—48no—
352Dic22—41no—
353Dic22—41no—
354Dic22C2×C22⋊C414yes—
355C8×C11—22no—
356C8×C11—41no—
357C11⋊C8—41no—
358C11⋊C8C2×C22⋊C414yes—
359C23×Q8—111no—
360C23×Q8—111no—
361C22×Q16—111no—
362C22×Q16—111no—
363C22×Q16—118no—
364C22×Q16—111no—
365C22×Q16—224no—
366C22×Q16—224no—
367C22×Q16C2×D1111yescharacteristic
368C23×C8—111no—
369C2×C4×Q8—111no—
370C2×C4×Q8—111no—
371C2×C4×Q8—111no—
372C2×C4×Q8C2×D1111yescharacteristic
373C4×Q16—224no—
374C4×Q16—224no—
375C2×#107—111no—
376C2×#107—111no—
377C2×#103—111no—
378C2×#103—111no—
379C2×#103—111no—
380C2×#103—111no—
381C2×#103—111no—
382C2×#103—111no—
383C2×#103C2×D1111yescharacteristic
384C2×#103C2×D1111yescharacteristic
385C2×C22⋊C8—111no—
386C2×C4×C8—111no—
387C2×C4×C8—111no—
388#391—111no—
389#391—111no—
390#391—111no—
391#391—221no—
392#391—221no—
393#391—221no—
394#391—221no—
395#391C2×D1111yescharacteristic
396#380—111no—
397#380—111no—
398#380—221no—
399#380—221no—
400C4×C22⋊C4—111no—
401C4×C22⋊C4—221no—
402C4×C22⋊C4—221no—
403#340—111no—
404#340C2×D1111yescharacteristic
405#336—111no—
406#336C2×D1111yescharacteristic
407C22×C11C2×C4×D411yescharacteristic
408C22×C11D4211yescharacteristic
409C22×C11D4211yescharacteristic
410C22×C11C22×Q1611yescharacteristic
411C22×C11C2×#13511yescharacteristic
412C22×C11#57811yescharacteristic
413C22×C11#57811yescharacteristic
414C2×D11—22no—
415C2×D11—22no—
416C2×D11—22no—
417C2×D11—22no—
418C2×D11—22no—
419C2×D11—22no—
420C2×D11C4×Q1614yescomplemented
421C4×C11—24no—
422C4×C11—22no—
423C4×C11—42no—
424C4×C11—41no—
425C4×C11—81no—
426C4×C11—81no—
427C4×C11C22×C22⋊C411yescharacteristic
428C4×C11#51811yescharacteristic
429C4×C11#54611yescharacteristic
430C4×C11#54611yescharacteristic
431Dic11—24no—
432Dic11—22no—
433Dic11—22no—
434Dic11—42no—
435Dic11—41no—
436Dic11—81no—
437Dic11—81no—
438C22×Q8—114no—
439C22×Q8—114no—
440C22×Q8—111no—
441C22×Q8—111no—
442C22×Q8—221no—
443C22×Q8—221no—
444C22×Q8—222no—
445C22×Q8—222no—
446C22×Q8—222no—
447C22×Q8—222no—
448C22×Q8—222no—
449C22×Q8—222no—
450C22×Q8—441no—
451C22×Q8—441no—
452C22×Q8—441no—
453C22×Q8—441no—
454C22×Q8C22×D1111yescharacteristic
455C22×Q8C22×D1111yescharacteristic
456C23×C4—111no—
457C23×C4—221no—
458C23×C4—221no—
459C2×Q16—22no—
460C2×Q16—22no—
461C2×Q16—114no—
462C2×Q16—114no—
463C2×Q16—114no—
464C2×Q16—114no—
465C2×Q16—114no—
466C2×Q16—222no—
467C2×Q16—222no—
468C2×Q16—222no—
469C2×Q16—222no—
470C2×Q16—2232no—
471C2×Q16C4×D1114yes—
472C22×C8—111no—
473C22×C8—114no—
474C22×C8—111no—
475C22×C8—222no—
476C22×C8—222no—
477C22×C8C22×D1111yescharacteristic
478C22×C8C22×D1111yescharacteristic
479C4×Q8—22no—
480C4×Q8—41no—
481C4×Q8—222no—
482C4×Q8—222no—
483C4×Q8—222no—
484C4×Q8—441no—
485C4×Q8—441no—
486C4×Q8—441no—
487C2×C4⋊C4—21no—
488C2×C4⋊C4—111no—
489C2×C4⋊C4—111no—
490C2×C4⋊C4—221no—
491C2×C4⋊C4—221no—
492C2×C4⋊C4—221no—
493C2×C4⋊C4C22×D1111yescharacteristic
494C2×C4⋊C4C22×D1111yescharacteristic
495C2×C22⋊C4—111no—
496C2×C22⋊C4—111no—
497C2×C22⋊C4—221no—
498C2×C22⋊C4—221no—
499C2×C42—21no—
500C2×C42—111no—
501C2×C42—221no—
502C2×C42—221no—
503C2×C42—221no—
504C2×C42C22×D1111yescharacteristic
505#107—222no—
506#107—222no—
507#103—22no—
508#103—41no—
509#103—222no—
510#103—222no—
511#103—222no—
512#103—441no—
513#103—441no—
514#103—441no—
515C22⋊C8—222no—
516C4×C8—222no—
517C4×C8—222no—
518#95—21no—
519#95—21no—
520#95—111no—
521#95—111no—
522#95—221no—
523#95—221no—
524#95—221no—
525#95—221no—
526#95—221no—
527#95—221no—
528#95—221no—
529#95—221no—
530C2×C11D4×C22⋊C411yescharacteristic
531C2×C11C2×C4×Q1611yescharacteristic
532C2×C11#295011yescharacteristic
533C2×C11#328511yescharacteristic
534C2×C11#328511yescharacteristic
535C2×C11D4×Q1611yescharacteristic
536C2×C11D4×Q1611yescharacteristic
537D11—24no—
538C24—111no—
539C2×Q8—21no—
540C2×Q8—21no—
541C2×Q8—21no—
542C2×Q8—21no—
543C2×Q8—21no—
544C2×Q8—21no—
545C2×Q8—21no—
546C2×Q8—21no—
547C2×Q8—112no—
548C2×Q8—112no—
549C2×Q8—112no—
550C2×Q8—112no—
551C2×Q8—224no—
552C2×Q8—224no—
553C2×Q8—221no—
554C2×Q8—221no—
555C2×Q8—221no—
556C2×Q8—221no—
557C2×Q8—228no—
558C2×Q8—228no—
559C2×Q8—221no—
560C2×Q8—221no—
561C2×Q8—221no—
562C2×Q8—221no—
563C2×Q8—442no—
564C2×Q8—442no—
565C2×Q8—442no—
566C2×Q8—442no—
567C2×Q8—444no—
568C2×Q8—444no—
569C2×Q8—444no—
570C2×Q8—444no—
571C2×Q8—444no—
572C2×Q8—444no—
573C2×Q8C2×C4×D1112yes—
574C2×Q8C2×C4×D1112yes—
575C2×Q8D4×D1112yes—
576C2×Q8D4×D1112yes—
577C22×C4—21no—
578C22×C4—21no—
579C22×C4—21no—
580C22×C4—21no—
581C22×C4—111no—
582C22×C4—111no—
583C22×C4—112no—
584C22×C4—112no—
585C22×C4—111no—
586C22×C4—224no—
587C22×C4—224no—
588C22×C4—221no—
589C22×C4—221no—
590C22×C4—221no—
591C22×C4—221no—
592C22×C4—221no—
593C22×C4—221no—
594C22×C4—221no—
595C22×C4—221no—
596C22×C4—442no—
597C22×C4—442no—
598C22×C4—442no—
599C22×C4—442no—
600C22×C4D4×D1111yescharacteristic
601C22×C4D4×D1111yescharacteristic
602C22×C4C23×D1111yescharacteristic
603Q16—28no—
604Q16—1116no—
605Q16—228no—
606Q16—228no—
607C2×C8—21no—
608C2×C8—21no—
609C2×C8—21no—
610C2×C8—21no—
611C2×C8—21no—
612C2×C8—112no—
613C2×C8—112no—
614C2×C8—112no—
615C2×C8—228no—
616C2×C8—221no—
617C2×C8—221no—
618C2×C8—221no—
619C2×C8C2×C4×D1112yes—
620C4⋊C4—21no—
621C4⋊C4—21no—
622C4⋊C4—21no—
623C4⋊C4—21no—
624C4⋊C4—42no—
625C4⋊C4—221no—
626C4⋊C4—221no—
627C4⋊C4—221no—
628C4⋊C4—221no—
629C4⋊C4—442no—
630C4⋊C4—442no—
631C4⋊C4—442no—
632C22⋊C4—114no—
633C22⋊C4—222no—
634C22⋊C4—442no—
635C22⋊C4—442no—
636C42—21no—
637C42—21no—
638C42—42no—
639C42—221no—
640C42—221no—
641C42—442no—
642C42—442no—
643C42—442no—
644C11C22⋊C4×Q1611yescharacteristic, complemented, Sylow
645C23—112no—
646C23—112no—
647C23—112no—
648C23—221no—
649C23—221no—
650C23—221no—
651C23—221no—
652C23C2×D4×D1111yescharacteristic
653Q8—22no—
654Q8—22no—
655Q8—22no—
656Q8—22no—
657Q8—22no—
658Q8—41no—
659Q8—41no—
660Q8—114no—
661Q8—222no—
662Q8—222no—
663Q8—222no—
664Q8—222no—
665Q8—222no—
666Q8—448no—
667Q8—448no—
668Q8—441no—
669Q8—441no—
670Q8C22⋊C4×D1114yes—
671C2×C4—21no—
672C2×C4—22no—
673C2×C4—21no—
674C2×C4—22no—
675C2×C4—22no—
676C2×C4—21no—
677C2×C4—21no—
678C2×C4—22no—
679C2×C4—21no—
680C2×C4—41no—
681C2×C4—41no—
682C2×C4—41no—
683C2×C4—41no—
684C2×C4—41no—
685C2×C4—41no—
686C2×C4—41no—
687C2×C4—41no—
688C2×C4—112no—
689C2×C4—112no—
690C2×C4—221no—
691C2×C4—222no—
692C2×C4—222no—
693C2×C4—221no—
694C2×C4—221no—
695C2×C4—222no—
696C2×C4—221no—
697C2×C4—222no—
698C2×C4—222no—
699C2×C4—222no—
700C2×C4—222no—
701C2×C4—221no—
702C2×C4—221no—
703C2×C4—222no—
704C2×C4—221no—
705C2×C4—448no—
706C2×C4—448no—
707C2×C4—441no—
708C2×C4—441no—
709C2×C4—441no—
710C2×C4—441no—
711C2×C4—441no—
712C2×C4—441no—
713C2×C4—441no—
714C2×C4—441no—
715C2×C4Q16×D1112yescomplemented
716C2×C4C22×C4×D1111yescharacteristic
717C2×C4C2×D4×D1111yescharacteristic
718C2×C4C2×D4×D1111yescharacteristic
719C2×C4#6703711yescharacteristic
720C2×C4#41×D1111yescharacteristic
721C2×C4#6704211yescharacteristic
722C8—22no—
723C8—41no—
724C8—114no—
725C8—441no—
726C22—114no—
727C22—222no—
728C22—222no—
729C22—222no—
730C22—222no—
731C22—222no—
732C22—222no—
733C22C4×D4×D1111yescharacteristic
734C22#1062312111yescharacteristic
735C22#1062314011yescharacteristic
736C22C2×Q16×D1111yescharacteristic
737C22D11×#13511yescharacteristic
738C22#1062331011yescharacteristic
739C22#1062331011yescharacteristic
740C4—22no—
741C4—24no—
742C4—41no—
743C4—42no—
744C4—81no—
745C4—81no—
746C4—222no—
747C4—222no—
748C4—224no—
749C4—441no—
750C4—442no—
751C4—881no—
752C4—881no—
753C4C2×C22⋊C4×D1111yescharacteristic
754C4#1062307611yescharacteristic
755C4#1062314111yescharacteristic
756C4#1062318511yescharacteristic
757C2—224no—
758C2#1307143411yescharacteristic
759C2C4×Q16×D1111yescharacteristic
760C2#1307748111yescharacteristic
761C2#1308035211yescharacteristic
762C2#1308035511yescharacteristic
763C2#1308036111yescharacteristic
764C2#1308036311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1878C2
socleC23×C11C22×D4
prime radicalC23×D11C2×D4
cosocleC22×C4×C11C24
hypercenter#1878D11
hypocenterC11C22⋊C4×Q16
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ #1878

Complements

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

NH ≅ G/Ntype
2. C2×C4×#4326C2semidirect
3. C2×#10622403C2semidirect
6. #13069476C2semidirect
7. #13069474C2semidirect
8. #13068959C2semidirect
9. #13068958C2semidirect
10. #13068956C2semidirect
15. C11×#1878C2semidirect
25. C2×Q16×D11C4semidirect
238. #4326C22⋊C4semidirect
242. (C2×D11)⋊C4Q16semidirect
273. #1878D11semidirect
311. C2×C4×C11C2×Q16semidirect
338. C2×Dic11C2×Q16semidirect
420. C2×D11C4×Q16semidirect
644. C11C22⋊C4×Q16semidirect
715. C2×C4Q16×D11semidirect

Maximal subgroups

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

subgroupindex
C22×Q16×D112
C2×C4×#43262
C2×#106224032
#130714502
Q8×(C2×D11)⋊C42
#130694762
#130694742
#130689592
#130689582
#130689562
#130686442
#130685492
#130683862
C11×#18782
C22⋊C4×Q1611