Finite Group Databasebeta

← #14769543

Subgroups — #14769543

Order 2816.

1650 conjugacy classes of subgroups.

The subgroup lattice has 888 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic
2C2×#10622324C211yesmaximal, characteristic, complemented
3C2×C4×D88C211yesmaximal, characteristic, complemented
4#13071447C211yesmaximal, characteristic, complemented
5C22⋊C4×D44C211yesmaximal, characteristic, complemented
6#13069497C211yesmaximal, characteristic, complemented
7#13069470C211yesmaximal, characteristic, complemented
8#13068963C211yesmaximal, characteristic, complemented
9#13068963C211yesmaximal, characteristic, complemented
10#13068949C211yesmaximal, characteristic, complemented
11#13068949C211yesmaximal, characteristic, complemented
12#13068649C211yesmaximal, characteristic, complemented
13#13068557C211yesmaximal, characteristic, complemented
14#13068548C211yesmaximal, characteristic, complemented
15C11×#1753C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C2×#66961—24no—
20C2×#66961—24no—
21C2×#66961C418yescomplemented
22C22×D88C2211yescharacteristic
23C22×D88C2211yescharacteristic
24C22×#4314C2211yescharacteristic
25C22×#4314C2211yescharacteristic
26C2×C22⋊C4×D11—21no—
27C2×C4×D44C2211yescharacteristic
28C2×C4×D44C2211yescharacteristic
29C2×C4×D44C2211yescharacteristic, complemented
30C2×C4×D44C2211yescharacteristic, complemented
31C2×C11×C22⋊C8C2211yescharacteristic
32C2×C11×#97C2211yescharacteristic, complemented
33C2×C4×C8×C11C2211yescharacteristic, complemented
34C4×C11×C22⋊C4C2211yescharacteristic
35#10622825C2211yescharacteristic
36#10622825C2211yescharacteristic
37C2×#66885C2211yescharacteristic
38C2×#66885C2211yescharacteristic
39C2×#66885C2211yescharacteristic
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic, complemented
42C2×#66885C2211yescharacteristic, complemented
43C2×#66882C2211yescharacteristic, complemented
44C2×#66881C2211yescharacteristic, complemented
45C2×#66880C2211yescharacteristic, complemented
46C2×#66880C2211yescharacteristic, complemented
47#10622569—21no—
48#10622569—21no—
49#10622568—21no—
50#10622552C2211yescharacteristic
51#10622552C2211yescharacteristic
52#10622542C2211yescharacteristic, complemented
53#10622542C2211yescharacteristic, complemented
54#10622324—24no—
55C4×D88—24no—
56#10622278—21no—
57#10622278—21no—
58#10622277—21no—
59D11×#95—21no—
60C11×#336C2211yescharacteristic, complemented
61C11×#336C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622189C2211yescharacteristic, complemented
64C24×D11—21no—
65C23×C4×C11C2311yescharacteristic
66C22×C22⋊D11—21no—
67C2×#4339—22no—
68C2×#4339—22no—
69C2×#4339—22no—
70C2×#4339—41no—
71C2×#4339—41no—
72C2×#4339C2×C414yescomplemented
73C22×D44—22no—
74C22×D44—22no—
75C22×D44—21no—
76C22×D44—22no—
77C22×D44—41no—
78C22×D44—41no—
79C22×D44C2×C414yescomplemented
80C22×D44C2311yescharacteristic
81C22×D44C2311yescharacteristic
82C22×D44C2311yescharacteristic
83C22×C4×D11—21no—
84C22×C4×D11—21no—
85C22×C4×D11—21no—
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×Dic22C2311yescharacteristic
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16C2×C414yescomplemented
92C22×C8×C11C2311yescharacteristic
93C22×C8×C11C2311yescharacteristic
94C22×C8×C11C2311yescharacteristic
95C22×C8×C11C2311yescharacteristic
96C2×C11×C22⋊C4D411yescharacteristic
97C2×C11×C22⋊C4D411yescharacteristic
98C2×C42×C11C2311yescharacteristic
99C2×C42×C11C2311yescharacteristic
100C2×C22⋊Dic11—21no—
101C2×C22⋊Dic11—21no—
102C2×(C2×D11)⋊C4—21no—
103C2×(C2×D11)⋊C4—21no—
104C2×(C2×D11)⋊C4—21no—
105C2×(C2×D11)⋊C4—21no—
106C2×(C2×D11)⋊C4—21no—
107C2×(C2×D11)⋊C4—21no—
108C2×(C2×D11)⋊C4—21no—
109C2×(C2×D11)⋊C4—21no—
110C2×C4⋊Dic11C2311yescharacteristic
111C2×C4⋊Dic11C2311yescharacteristic
112C2×C4⋊Dic11C2311yescharacteristic
113C2×C4⋊Dic11C2311yescharacteristic
114#66961—232no—
115C2×D88—22no—
116C2×D88—22no—
117C2×D88C2×C414yes—
118C2×D88C2×C414yescomplemented
119C2×D88D414yes—
120C2×D88D414yes—
121C2×#4314—22no—
122C2×#4314—22no—
123C2×#4314—22no—
124C2×#4314—22no—
125C2×#4314C2×C414yescomplemented
126C2×#4314C2×C414yescomplemented
127C22⋊C4×D11—44no—
128C4×D44—22no—
129C4×D44—22no—
130C4×D44—22no—
131C4×D44—22no—
132C4×D44—41no—
133C4×D44—41no—
134C4×D44—41no—
135C4×D44—41no—
136C11×C22⋊C8—22no—
137C11×#97—22no—
138C4×C8×C11—22no—
139C11×#95D411yescharacteristic
140C11×#95D411yescharacteristic
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95—21no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147#66885—22no—
148#66885—22no—
149#66885—22no—
150#66885—22no—
151#66885—41no—
152#66885—41no—
153#66882—22no—
154#66881—22no—
155#66880—41no—
156#66880—41no—
157#22442—111nomaximal, Sylow
158C24×C11C2×D411yescharacteristic
159C23×D11—21no—
160C23×D11—21no—
161C23×D11—21no—
162C23×D11—24no—
163C23×D11—42no—
164C23×D11—42no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—81no—
168C23×D11—81no—
169C22×C4×C11—21no—
170C22×C4×C11—21no—
171C22×C4×C11—21no—
172C22×C4×C11—21no—
173C22×C4×C11C22×C412yes—
174C22×C4×C11C2×D411yescharacteristic
175C22×C4×C11C2×D411yescharacteristic
176C22×C4×C11C2×D411yescharacteristic
177C22×C4×C11C2×D411yescharacteristic
178C22×C4×C11C2×D411yescharacteristic
179C22×C4×C11#4112yes—
180C22×C4×C11C2411yescharacteristic
181C2×C22⋊D11—24no—
182C2×C22⋊D11—42no—
183C2×C22⋊D11—42no—
184C22×Dic11—21no—
185C22×Dic11—21no—
186C22×Dic11—21no—
187C22×Dic11—21no—
188C22×Dic11—21no—
189#4339—28no—
190#4339—44no—
191#4339—44no—
192#4339—44no—
193C2×D44—28no—
194C2×D44—24no—
195C2×D44—21no—
196C2×D44—21no—
197C2×D44—21no—
198C2×D44—21no—
199C2×D44—21no—
200C2×D44—21no—
201C2×D44—21no—
202C2×D44—21no—
203C2×D44—21no—
204C2×D44—21no—
205C2×D44—21no—
206C2×D44—42no—
207C2×D44—42no—
208C2×D44—44no—
209C2×D44—44no—
210C2×D44—44no—
211C2×D44C22×C412yes—
212C2×D44C22×C412yes—
213C2×D44C22×C412yes—
214C2×D44C2×D412yes—
215C2×D44C2×D412yes—
216C2×D44C2×D412yes—
217C2×D44C2×D412yes—
218C2×C4×D11—24no—
219C2×C4×D11—42no—
220C2×C4×D11—42no—
221C2×C4×D11—42no—
222C2×C4×D11—42no—
223C2×C4×D11—42no—
224C2×C4×D11—42no—
225C2×C4×D11—42no—
226C2×C4×D11—42no—
227C2×C4×D11—42no—
228C2×C4×D11—42no—
229C2×C4×D11—81no—
230C2×C4×D11—81no—
231C2×C4×D11—81no—
232C2×C4×D11—81no—
233C2×Dic22—21no—
234C2×Dic22—21no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22C22×C412yes—
239C11×M16—28no—
240C2×C8×C11—21no—
241C2×C8×C11—21no—
242C2×C8×C11—21no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11C22×C412yes—
249C2×C8×C11C22×C412yes—
250C2×C8×C11C2×D412yes—
251C2×C8×C11C2×D412yes—
252C11×C22⋊C4—22no—
253C11×C22⋊C4—41no—
254C42×C11—21no—
255C42×C11—21no—
256C42×C11—21no—
257C42×C11—21no—
258C22⋊Dic11—42no—
259C22⋊Dic11—81no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4—42no—
264(C2×D11)⋊C4—42no—
265(C2×D11)⋊C4—42no—
266(C2×D11)⋊C4—81no—
267(C2×D11)⋊C4—81no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276D88—28no—
277D88C22⋊C4116yescomplemented
278#4314—28no—
279#4314—28no—
280C22×AGL(1,ℤ/8)—111no—
281C2×#442—111no—
282C2×C4×D8—111no—
283#2339—111no—
284D4×C22⋊C4—111no—
285#1973—111no—
286#1968—111no—
287#1879—111no—
288#1879—111no—
289#1877—111no—
290#1877—111no—
291#1809—111no—
292#1788—111no—
293#1786—111no—
294#1753D1111yescharacteristic, complemented
295C23×C11—21no—
296C23×C11—21no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11C4×D412yes—
302C23×C11C22×D411yescharacteristic
303C22×D11—22no—
304C22×D11—22no—
305C22×D11—22no—
306C22×D11—22no—
307C22×D11—22no—
308C22×D11—22no—
309C22×D11—22no—
310C22×D11—48no—
311C22×D11—41no—
312C22×D11—41no—
313C22×D11—41no—
314C22×D11—41no—
315C22×D11—41no—
316C22×D11—41no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—48no—
320C22×D11—41no—
321C22×D11—41no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—84no—
327C22×D11—84no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C2×C4×C11—21no—
332C2×C4×C11—21no—
333C2×C4×C11—21no—
334C2×C4×C11—21no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—22no—
338C2×C4×C11—22no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—21no—
343C2×C4×C11—21no—
344C2×C4×C11—21no—
345C2×C4×C11—21no—
346C2×C4×C11—21no—
347C2×C4×C11—21no—
348C2×C4×C11C4×D412yes—
349C2×C4×C11AGL(1,ℤ/8)12yescomplemented
350C2×C4×C11C23×C411yescharacteristic
351C2×C4×C11C22×D411yescharacteristic
352C2×C4×C11C22×D411yescharacteristic
353C2×C4×C11C2×#4111yescharacteristic
354C2×C4×C11H(5,𝔽2)11yescharacteristic
355C2×C4×C11H(5,𝔽2)11yescharacteristic
356C22⋊D11—48no—
357C2×Dic11—22no—
358C2×Dic11—41no—
359C2×Dic11—41no—
360C2×Dic11—41no—
361C2×Dic11—41no—
362C2×Dic11—41no—
363C2×Dic11—41no—
364C2×Dic11—41no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372D44—22no—
373D44—22no—
374D44—22no—
375D44—22no—
376D44—22no—
377D44—22no—
378D44—22no—
379D44—22no—
380D44—48no—
381D44—41no—
382D44—41no—
383D44C2×C22⋊C414yes—
384D44C2×C22⋊C414yescomplemented
385C4×D11—48no—
386C4×D11—84no—
387C4×D11—84no—
388C4×D11—84no—
389C4×D11—84no—
390Dic22—22no—
391Dic22—22no—
392Dic22—41no—
393Dic22—41no—
394C8×C11—22no—
395C8×C11—41no—
396C8×C11—41no—
397C8×C11C2×C22⋊C414yescomplemented
398C22×#41—111no—
399C23×D4—111no—
400C2×AGL(1,ℤ/8)—118no—
401C2×AGL(1,ℤ/8)—224no—
402C2×AGL(1,ℤ/8)—224no—
403C22×SD16—111no—
404C22×SD16—111no—
405C22×D8—111no—
406C22×D8—111no—
407C22×M16C2×D1111yescharacteristic
408C2×C4×D4—111no—
409C2×C4×D4—111no—
410C2×C4×D4—111no—
411C2×C4×D4—111no—
412C22×C22⋊C4—221no—
413#442—224no—
414C4×D8—224no—
415C2×#107—111no—
416C2×#106—111no—
417C2×#103—111no—
418C2×#103—111no—
419C2×#102—111no—
420C2×#102—111no—
421C2×#102—111no—
422C2×#102—111no—
423C2×#102—111no—
424C2×#102—111no—
425C2×C22⋊C8C2×D1111yescharacteristic
426C2×#97C2×D1111yescharacteristic, complemented
427C2×C4×C8C2×D1111yescharacteristic, complemented
428#391—111no—
429#391—111no—
430#390—111no—
431#390—111no—
432#386—221no—
433#386—221no—
434#386—221no—
435#386—221no—
436#381—221no—
437#380—111no—
438#380—111no—
439#379—221no—
440C4×C22⋊C4C2×D1111yescharacteristic
441C2×#95—221no—
442#340—111no—
443#340—111no—
444#336C2×D1111yescharacteristic, complemented
445#336C2×D1111yescharacteristic, complemented
446C22×C11—22no—
447C22×C11—22no—
448C22×C11—22no—
449C22×C11—41no—
450C22×C11—41no—
451C22×C11—41no—
452C22×C11—41no—
453C22×C11C2×C4×D411yescharacteristic
454C22×C11D4211yescharacteristic
455C22×C11D4211yescharacteristic
456C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
457C22×C11#57511yescharacteristic
458C22×C11#57611yescharacteristic
459C22×C11#57711yescharacteristic
460C2×D11—24no—
461C2×D11—24no—
462C2×D11—42no—
463C2×D11—42no—
464C2×D11—42no—
465C2×D11—42no—
466C2×D11—42no—
467C2×D11—42no—
468C2×D11—42no—
469C2×D11—42no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—816no—
478C2×D11—81no—
479C2×D11—81no—
480C2×D11—81no—
481C2×D11—81no—
482C4×C11—22no—
483C4×C11—22no—
484C4×C11—41no—
485C4×C11—41no—
486C4×C11—41no—
487C4×C11C22×C22⋊C411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—42no—
492Dic11—81no—
493Dic11—81no—
494Dic11—81no—
495Dic11—81no—
496C25—221no—
497C2×#41—114no—
498C2×#41—222no—
499C2×#41—222no—
500C2×#41—222no—
501C2×#41—441no—
502C2×#41—441no—
503C22×Q8—111no—
504C22×D4—114no—
505C22×D4—111no—
506C22×D4—111no—
507C22×D4—111no—
508C22×D4—222no—
509C22×D4—222no—
510C22×D4—221no—
511C22×D4—221no—
512C22×D4—222no—
513C22×D4—441no—
514C22×D4—441no—
515C23×C4—221no—
516C23×C4—221no—
517C23×C4—221no—
518C23×C4—221no—
519C23×C4—221no—
520C23×C4C22×D1111yescharacteristic
521AGL(1,ℤ/8)—2232no—
522C2×SD16—114no—
523C2×SD16—114no—
524C2×SD16—222no—
525C2×SD16—222no—
526C2×SD16—222no—
527C2×SD16—222no—
528C2×D8—114no—
529C2×D8—114no—
530C2×D8—114no—
531C2×D8—114no—
532C2×D8—222no—
533C2×D8—222no—
534C2×M16—22no—
535C2×M16—22no—
536C2×M16C4×D1114yescomplemented
537C22×C8C22×D1111yescharacteristic
538C22×C8C22×D1111yescharacteristic
539C22×C8C22×D1111yescharacteristic
540C22×C8C22×D1111yescharacteristic
541C4×D4—222no—
542C4×D4—222no—
543C4×D4—222no—
544C4×D4—222no—
545C4×D4—441no—
546C4×D4—441no—
547C4×D4—441no—
548C4×D4—441no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C22⋊C4—221no—
554C2×C22⋊C4—221no—
555C2×C22⋊C4—221no—
556C2×C22⋊C4—221no—
557C2×C22⋊C4—221no—
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—444no—
564C2×C22⋊C4D4411yescharacteristic
565C2×C22⋊C4D4411yescharacteristic
566C2×C42C22×D1111yescharacteristic
567C2×C42C22×D1111yescharacteristic
568#107—222no—
569#106—222no—
570#103—441no—
571#103—441no—
572#102—222no—
573#102—222no—
574#102—222no—
575#102—222no—
576#102—441no—
577#102—441no—
578C22⋊C8—22no—
579#97—22no—
580C4×C8—22no—
581#95—221no—
582#95—221no—
583#95—221no—
584#95—221no—
585#95—221no—
586#95—221no—
587#95D4411yescharacteristic
588#95D4411yescharacteristic
589C2×C11—42no—
590C2×C11D4×C22⋊C411yescharacteristic
591C2×C11C4×AGL(1,ℤ/8)11yescharacteristic
592C2×C11#294611yescharacteristic
593C2×C11#326411yescharacteristic
594C2×C11#326711yescharacteristic
595C2×C11#327211yescharacteristic
596C2×C11#327311yescharacteristic
597D11—44no—
598D11—44no—
599D11—82no—
600C24—221no—
601C24—221no—
602C24—221no—
603C24—224no—
604C24—442no—
605C24—442no—
606C24—442no—
607C24—442no—
608C24—881no—
609C24—881no—
610C24C2×D4411yescharacteristic
611#41—228no—
612#41—444no—
613#41—444no—
614#41—444no—
615C2×Q8—112no—
616C2×Q8—221no—
617C2×Q8—221no—
618C2×Q8—221no—
619C2×Q8—221no—
620C2×Q8—221no—
621C2×D4—112no—
622C2×D4—112no—
623C2×D4—112no—
624C2×D4—112no—
625C2×D4—112no—
626C2×D4—112no—
627C2×D4—112no—
628C2×D4—228no—
629C2×D4—224no—
630C2×D4—224no—
631C2×D4—221no—
632C2×D4—221no—
633C2×D4—221no—
634C2×D4—221no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—444no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—442no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C22×C4—21no—
650C22×C4—21no—
651C22×C4—21no—
652C22×C4—21no—
653C22×C4—221no—
654C22×C4—224no—
655C22×C4—221no—
656C22×C4—221no—
657C22×C4—221no—
658C22×C4—221no—
659C22×C4—442no—
660C22×C4—442no—
661C22×C4—442no—
662C22×C4—442no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—881no—
670C22×C4—881no—
671C22×C4—881no—
672C22×C4—881no—
673C22×C4C2×C4×D1112yes—
674C22×C4C2×D4411yescharacteristic
675C22×C4C2×D4411yescharacteristic
676C22×C4C2×D4411yescharacteristic
677C22×C4C2×D4411yescharacteristic
678C22×C4C2×D4411yescharacteristic
679C22×C4#433912yes—
680C22×C4C23×D1111yescharacteristic
681SD16—228no—
682SD16—228no—
683D8—1116no—
684D8—228no—
685M16—28no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8C2×C4×D1112yes—
695C2×C8C2×C4×D1112yes—
696C2×C8D4×D1112yes—
697C2×C8D4×D1112yes—
698C4⋊C4—221no—
699C4⋊C4—221no—
700C4⋊C4—221no—
701C4⋊C4—221no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C22⋊C4—22no—
707C22⋊C4—41no—
708C22⋊C4—442no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—881no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C42—21no—
719C42—21no—
720C42—21no—
721C42—21no—
722C11#2244211yescharacteristic, complemented, Sylow
723C23—21no—
724C23—21no—
725C23—21no—
726C23—21no—
727C23—21no—
728C23—21no—
729C23—222no—
730C23—222no—
731C23—222no—
732C23—222no—
733C23—222no—
734C23—222no—
735C23—222no—
736C23—448no—
737C23—448no—
738C23—441no—
739C23—441no—
740C23—441no—
741C23—441no—
742C23—441no—
743C23—441no—
744C23—441no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—884no—
753C23—884no—
754C23—884no—
755C23—884no—
756C23—884no—
757C23C4×D4412yes—
758C23C22×D4411yescharacteristic
759Q8—222no—
760Q8—222no—
761Q8—441no—
762Q8—441no—
763D4—114no—
764D4—114no—
765D4—222no—
766D4—222no—
767D4—222no—
768D4—222no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—448no—
774D4—448no—
775D4—441no—
776D4—441no—
777C2×C4—21no—
778C2×C4—21no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—22no—
784C2×C4—22no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—21no—
788C2×C4—21no—
789C2×C4—21no—
790C2×C4—21no—
791C2×C4—21no—
792C2×C4—21no—
793C2×C4—21no—
794C2×C4—222no—
795C2×C4—448no—
796C2×C4—441no—
797C2×C4—441no—
798C2×C4—441no—
799C2×C4—441no—
800C2×C4—441no—
801C2×C4—441no—
802C2×C4—441no—
803C2×C4—441no—
804C2×C4—441no—
805C2×C4—441no—
806C2×C4—441no—
807C2×C4—441no—
808C2×C4—441no—
809C2×C4—441no—
810C2×C4—884no—
811C2×C4—884no—
812C2×C4—884no—
813C2×C4—884no—
814C2×C4C4×D4412yes—
815C2×C4#6696112yescomplemented
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×#433911yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4C2×D4×D1111yescharacteristic
820C2×C4#6704211yescharacteristic
821C2×C4#6704211yescharacteristic
822C8—22no—
823C8—41no—
824C8—41no—
825C8C22⋊C4×D1114yescomplemented
826C22—22no—
827C22—22no—
828C22—22no—
829C22—41no—
830C22—41no—
831C22—41no—
832C22—41no—
833C22—224no—
834C22—224no—
835C22—442no—
836C22—442no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—442no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—8816no—
851C22—881no—
852C22—881no—
853C22—881no—
854C22—881no—
855C22C2×C4×D4411yescharacteristic
856C22D4×D4411yescharacteristic
857C22D4×D4411yescharacteristic
858C22C2×#6696111yescharacteristic
859C22#1062327911yescharacteristic
860C22#1062328211yescharacteristic
861C22#1062328311yescharacteristic
862C4—22no—
863C4—22no—
864C4—41no—
865C4—41no—
866C4—41no—
867C4—442no—
868C4—881no—
869C4—881no—
870C4—881no—
871C4—881no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062305211yescharacteristic
874C4#1062308111yescharacteristic
875C4#1062308111yescharacteristic
876C2—42no—
877C2—444no—
878C2—444no—
879C2—882no—
880C2C22⋊C4×D4411yescharacteristic
881C2C4×#6696111yescharacteristic
882C2#1307745011yescharacteristic
883C2#1308010111yescharacteristic
884C2#1308014611yescharacteristic
885C2#1308021811yescharacteristic
886C2#1308022811yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1753C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenter#1753D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C4×C22⋊C4 ◁ #1753

Complements

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

NH ≅ G/Ntype
2. C2×#10622324C2semidirect
3. C2×C4×D88C2semidirect
4. #13071447C2semidirect
5. C22⋊C4×D44C2semidirect
6. #13069497C2semidirect
7. #13069470C2semidirect
8. #13068963C2semidirect
9. #13068963C2semidirect
10. #13068949C2semidirect
11. #13068949C2semidirect
12. #13068649C2semidirect
13. #13068557C2semidirect
14. #13068548C2semidirect
15. C11×#1753C2semidirect
21. C2×#66961C4semidirect
29. C2×C4×D44C22semidirect
30. C2×C4×D44C22semidirect
32. C2×C11×#97C22semidirect
33. C2×C4×C8×C11C22semidirect
41. C2×#66885C22semidirect
42. C2×#66885C22semidirect
43. C2×#66882C22semidirect
44. C2×#66881C22semidirect
45. C2×#66880C22semidirect
46. C2×#66880C22semidirect
52. #10622542C22semidirect
53. #10622542C22semidirect
60. C11×#336C22semidirect
61. C11×#336C22semidirect
62. #10622189C22semidirect
63. #10622189C22semidirect
72. C2×#4339C2×C4semidirect
79. C22×D44C2×C4semidirect
91. C2×C11×M16C2×C4semidirect
118. C2×D88C2×C4semidirect
125. C2×#4314C2×C4semidirect
126. C2×#4314C2×C4semidirect
277. D88C22⋊C4semidirect
294. #1753D11semidirect
349. C2×C4×C11AGL(1,ℤ/8)semidirect
384. D44C2×C22⋊C4semidirect
397. C8×C11C2×C22⋊C4semidirect
426. C2×#97C2×D11semidirect
427. C2×C4×C8C2×D11semidirect
444. #336C2×D11semidirect
445. #336C2×D11semidirect
536. C2×M16C4×D11semidirect
722. C11#22442semidirect
815. C2×C4#66961semidirect
825. C8C22⋊C4×D11semidirect

Maximal subgroups

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

subgroupindex
C22×#669612
C2×#106223242
C2×C4×D882
#130714472
C22⋊C4×D442
#130694972
#130694702
#130689632
#130689492
#130686492
#130685572
#130685482
C11×#17532
#2244211