Finite Group Databasebeta

← #14769535

Subgroups — #14769535

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×#10622482C211yesmaximal, characteristic, complemented
3C2×#10622485C211yesmaximal, characteristic, complemented
4#13071444C211yesmaximal, characteristic, complemented
5#13071436C211yesmaximal, characteristic, complemented
6#13069495C211yesmaximal, characteristic, complemented
7#13069468C211yesmaximal, characteristic, complemented
8#13068965C211yesmaximal, characteristic, complemented
9#13068965C211yesmaximal, characteristic, complemented
10#13068951C211yesmaximal, characteristic, complemented
11#13068951C211yesmaximal, characteristic, complemented
12#13068554C211yesmaximal, characteristic, complemented
13#13068546C211yesmaximal, characteristic, complemented
14#13068397C211yesmaximal, characteristic, complemented
15C11×#1809C211yesmaximal, 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×#66946C2211yescharacteristic
27C2×#66946C2211yescharacteristic
28C2×#66946C2211yescharacteristic, complemented
29C2×#66946C2211yescharacteristic, complemented
30C2×C22⋊C4×D11—21no—
31C2×C11×#107C2211yescharacteristic, complemented
32C2×C11×#106C2211yescharacteristic, complemented
33C11×#380C2211yescharacteristic
34C11×#380C2211yescharacteristic
35C4×C22⋊Dic11C2211yescharacteristic
36C2×C22⋊(C11⋊C8)C2211yescharacteristic
37C2×#66879C2211yescharacteristic, complemented
38C2×C8×Dic11C2211yescharacteristic, complemented
39#10622601C2211yescharacteristic
40#10622601C2211yescharacteristic
41#10622587C2211yescharacteristic, complemented
42#10622587C2211yescharacteristic, complemented
43C2×#66874C2211yescharacteristic, complemented
44C2×#66874C2211yescharacteristic, complemented
45C2×#66873C2211yescharacteristic
46C2×#66873C2211yescharacteristic
47C2×#66873C2211yescharacteristic
48C2×#66873C2211yescharacteristic
49C2×#66873C2211yescharacteristic, complemented
50C2×#66873C2211yescharacteristic, complemented
51#10622569—21no—
52#10622569—21no—
53#10622568—21no—
54#10622485—24no—
55#10622482—24no—
56#10622278—21no—
57#10622278—21no—
58#10622277—21no—
59D11×#95—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622188C2211yescharacteristic, complemented
63#10622188C2211yescharacteristic, 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
94C2×C11×C4⋊C4C2311yescharacteristic
95C2×C11×C4⋊C4C2311yescharacteristic
96C2×C11×C4⋊C4C2311yescharacteristic
97C2×C11×C4⋊C4C2311yescharacteristic
98C2×C11×C22⋊C4—21no—
99C2×C11×C22⋊C4—21no—
100C2×C22⋊Dic11D411yescharacteristic
101C2×C22⋊Dic11D411yescharacteristic
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
112C22×C11⋊C8C2311yescharacteristic
113C22×C11⋊C8C2311yescharacteristic
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
127#66946—22no—
128#66946—22no—
129#66946—22no—
130#66946—22no—
131#66946—41no—
132#66946—41no—
133#66946—41no—
134#66946—41no—
135C22⋊C4×D11—44no—
136C11×#107—22no—
137C11×#106—22no—
138C11×#95—21no—
139C11×#95—21no—
140C11⋊#95—21no—
141C11⋊#95—21no—
142C11⋊#95—21no—
143C11⋊#95—21no—
144C11⋊#95D411yescharacteristic
145C11⋊#95D411yescharacteristic
146C22⋊(C11⋊C8)—22no—
147#66879—22no—
148C8×Dic11—22no—
149#66874—41no—
150#66874—41no—
151#66873—22no—
152#66873—22no—
153#66873—22no—
154#66873—22no—
155#66873—41no—
156#66873—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×C11—21no—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11C22×C412yes—
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×Dic11C2×D411yescharacteristic
186C22×Dic11C2×D411yescharacteristic
187C22×Dic11C2×D411yescharacteristic
188C22×Dic11C2×D411yescharacteristic
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×C11C22×C412yes—
243C2×C8×C11C22×C412yes—
244C2×C8×C11C2×D412yes—
245C2×C8×C11C2×D412yes—
246C11×C4⋊C4—21no—
247C11×C4⋊C4—21no—
248C11×C4⋊C4—21no—
249C11×C4⋊C4—21no—
250C11×C4⋊C4—21no—
251C11×C4⋊C4—21no—
252C11×C4⋊C4—21no—
253C11×C4⋊C4—21no—
254C11×C22⋊C4—42no—
255C11×C22⋊C4—81no—
256C22⋊Dic11—22no—
257C22⋊Dic11—41no—
258(C2×D11)⋊C4—42no—
259(C2×D11)⋊C4—42no—
260(C2×D11)⋊C4—42no—
261(C2×D11)⋊C4—42no—
262(C2×D11)⋊C4—42no—
263(C2×D11)⋊C4—42no—
264(C2×D11)⋊C4—81no—
265(C2×D11)⋊C4—81no—
266C4×Dic11—21no—
267C4×Dic11—21no—
268C4×Dic11—21no—
269C4×Dic11—21no—
270C2×C11⋊C8—21no—
271C2×C11⋊C8—21no—
272C2×C11⋊C8—21no—
273C2×C11⋊C8—21no—
274C2×C11⋊C8—21no—
275C2×C11⋊C8—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#1809D1111yescharacteristic, complemented
292#1788—111no—
293#1786—111no—
294#1753—111no—
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—22no—
334C2×C4×C11—22no—
335C2×C4×C11—22no—
336C2×C4×C11—22no—
337C2×C4×C11—41no—
338C2×C4×C11—41no—
339C2×C4×C11—41no—
340C2×C4×C11—41no—
341C2×C4×C11—41no—
342C2×C4×C11—41no—
343C2×C4×C11—41no—
344C2×C4×C11—41no—
345C2×C4×C11—41no—
346C2×C4×C11—41no—
347C2×C4×C11—41no—
348C2×C4×C11—41no—
349C2×C4×C11C4×D412yes—
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—21no—
358C2×Dic11—21no—
359C2×Dic11—22no—
360C2×Dic11—21no—
361C2×Dic11—21no—
362C2×Dic11—21no—
363C2×Dic11—21no—
364C2×Dic11—21no—
365C2×Dic11—21no—
366C2×Dic11—21no—
367C2×Dic11—21no—
368C2×Dic11—21no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11AGL(1,ℤ/8)12yescomplemented
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×C11C2×C22⋊C414yescomplemented
396C11⋊C8—41no—
397C11⋊C8—41no—
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×#107C2×D1111yescharacteristic, complemented
416C2×#106C2×D1111yescharacteristic, complemented
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⋊C8—111no—
426C2×#97—111no—
427C2×C4×C8—111no—
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#380C2×D1111yescharacteristic
438#380C2×D1111yescharacteristic
439#379—221no—
440C4×C22⋊C4—111no—
441C2×#95—221no—
442#340C2×D1111yescharacteristic, complemented
443#340C2×D1111yescharacteristic, complemented
444#336—111no—
445#336—111no—
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—81no—
484C4×C11—81no—
485C4×C11—81no—
486C4×C11—81no—
487C4×C11C22×C22⋊C411yescharacteristic
488C4×C11#51811yescharacteristic
489C4×C11#54611yescharacteristic
490C4×C11#54611yescharacteristic
491Dic11—22no—
492Dic11—42no—
493Dic11—41no—
494Dic11—41no—
495Dic11—41no—
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×C8—111no—
538C22×C8—111no—
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⋊C4C22×D1111yescharacteristic
550C2×C4⋊C4C22×D1111yescharacteristic
551C2×C4⋊C4C22×D1111yescharacteristic
552C2×C4⋊C4C22×D1111yescharacteristic
553C2×C22⋊C4—21no—
554C2×C22⋊C4—21no—
555C2×C22⋊C4—111no—
556C2×C22⋊C4—111no—
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—221no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—444no—
566C2×C42—111no—
567C2×C42—111no—
568#107—22no—
569#106—22no—
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—222no—
579#97—222no—
580C4×C8—222no—
581#95—21no—
582#95—21no—
583#95—111no—
584#95—111no—
585#95—221no—
586#95—221no—
587#95—221no—
588#95—221no—
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—
610C24D4×D1111yescharacteristic
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—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—111no—
658C22×C4—111no—
659C22×C4—111no—
660C22×C4—111no—
661C22×C4—221no—
662C22×C4—224no—
663C22×C4—442no—
664C22×C4—442no—
665C22×C4—442no—
666C22×C4—442no—
667C22×C4—442no—
668C22×C4—442no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—881no—
674C22×C4—881no—
675C22×C4—881no—
676C22×C4—881no—
677C22×C4C2×C4×D1112yes—
678C22×C4D4×D1111yescharacteristic
679C22×C4#434312yes—
680C22×C4C23×D1111yescharacteristic
681SD16—228no—
682SD16—228no—
683D8—1116no—
684D8—228no—
685M16—28no—
686C2×C8—21no—
687C2×C8—21no—
688C2×C8—221no—
689C2×C8—221no—
690C2×C8—221no—
691C2×C8—221no—
692C2×C8—221no—
693C2×C8—221no—
694C2×C8C2×C4×D1112yes—
695C2×C8C2×C4×D1112yes—
696C2×C8D4×D1112yes—
697C2×C8D4×D1112yes—
698C4⋊C4—21no—
699C4⋊C4—21no—
700C4⋊C4—21no—
701C4⋊C4—21no—
702C4⋊C4—21no—
703C4⋊C4—21no—
704C4⋊C4—21no—
705C4⋊C4—21no—
706C22⋊C4—42no—
707C22⋊C4—81no—
708C22⋊C4—222no—
709C22⋊C4—442no—
710C22⋊C4—442no—
711C22⋊C4—442no—
712C22⋊C4—442no—
713C22⋊C4—442no—
714C22⋊C4—442no—
715C22⋊C4—441no—
716C22⋊C4—881no—
717C22⋊C4—881no—
718C42—221no—
719C42—221no—
720C42—221no—
721C42—221no—
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—
757C23#6694612yes—
758C23C2×D4×D1111yescharacteristic
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—22no—
780C2×C4—22no—
781C2×C4—22no—
782C2×C4—22no—
783C2×C4—41no—
784C2×C4—41no—
785C2×C4—41no—
786C2×C4—41no—
787C2×C4—41no—
788C2×C4—41no—
789C2×C4—41no—
790C2×C4—41no—
791C2×C4—41no—
792C2×C4—41no—
793C2×C4—41no—
794C2×C4—41no—
795C2×C4—112no—
796C2×C4—221no—
797C2×C4—221no—
798C2×C4—222no—
799C2×C4—221no—
800C2×C4—221no—
801C2×C4—221no—
802C2×C4—221no—
803C2×C4—221no—
804C2×C4—221no—
805C2×C4—221no—
806C2×C4—221no—
807C2×C4—221no—
808C2×C4—448no—
809C2×C4—441no—
810C2×C4—441no—
811C2×C4—884no—
812C2×C4—884no—
813C2×C4—884no—
814C2×C4—884no—
815C2×C4#6694612yes—
816C2×C4C22×C4×D1111yescharacteristic
817C2×C4C2×D4×D1111yescharacteristic
818C2×C4C2×D4×D1111yescharacteristic
819C2×C4C2×#434311yescharacteristic
820C2×C4#6704211yescharacteristic
821C2×C4#6704211yescharacteristic
822C8—22no—
823C8—441no—
824C8—441no—
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×#6694611yescharacteristic
856C22#1062314011yescharacteristic
857C22#1062314011yescharacteristic
858C22D11×AGL(1,ℤ/8)11yescharacteristic
859C22#1062330511yescharacteristic
860C22#1062330811yescharacteristic
861C22#1062330911yescharacteristic
862C4—22no—
863C4—81no—
864C4—81no—
865C4—81no—
866C4—81no—
867C4—222no—
868C4—442no—
869C4—441no—
870C4—441no—
871C4—441no—
872C4C2×C22⋊C4×D1111yescharacteristic
873C4#1062305211yescharacteristic
874C4#1062316111yescharacteristic
875C4#1062316111yescharacteristic
876C2—42no—
877C2—444no—
878C2—444no—
879C2—882no—
880C2#1307143611yescharacteristic
881C2#1307742311yescharacteristic
882C2#1307744611yescharacteristic
883C2#1308010311yescharacteristic
884C2#1308014811yescharacteristic
885C2#1308021311yescharacteristic
886C2#1308022411yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1809C2
socleC23×C11C22×D4
prime radicalC22×#66961C2
cosocleC22×C4×C11C24
hypercenter#1809D11
hypocenterC11#22442
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1809

Complements

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

NH ≅ G/Ntype
2. C2×#10622482C2semidirect
3. C2×#10622485C2semidirect
4. #13071444C2semidirect
5. #13071436C2semidirect
6. #13069495C2semidirect
7. #13069468C2semidirect
8. #13068965C2semidirect
9. #13068965C2semidirect
10. #13068951C2semidirect
11. #13068951C2semidirect
12. #13068554C2semidirect
13. #13068546C2semidirect
14. #13068397C2semidirect
15. C11×#1809C2semidirect
21. C2×#66961C4semidirect
28. C2×#66946C22semidirect
29. C2×#66946C22semidirect
31. C2×C11×#107C22semidirect
32. C2×C11×#106C22semidirect
37. C2×#66879C22semidirect
38. C2×C8×Dic11C22semidirect
41. #10622587C22semidirect
42. #10622587C22semidirect
43. C2×#66874C22semidirect
44. C2×#66874C22semidirect
49. C2×#66873C22semidirect
50. C2×#66873C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622188C22semidirect
63. #10622188C22semidirect
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
291. #1809D11semidirect
371. C2×Dic11AGL(1,ℤ/8)semidirect
384. D44C2×C22⋊C4semidirect
395. C8×C11C2×C22⋊C4semidirect
415. C2×#107C2×D11semidirect
416. C2×#106C2×D11semidirect
442. #340C2×D11semidirect
443. #340C2×D11semidirect
536. C2×M16C4×D11semidirect
722. C11#22442semidirect
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×#106224822
C2×#106224852
#130714442
#130714362
#130694952
#130694682
#130689652
#130689512
#130685542
#130685462
#130683972
C11×#18092
#2244211