Finite Group Databasebeta

← #14769375

Subgroups — #14769375

Order 2816.

1606 conjugacy classes of subgroups.

The subgroup lattice has 892 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623081C211yesmaximal, characteristic
2C2×#10622746C211yesmaximal, characteristic, complemented
3C2×#10622744C211yesmaximal, characteristic, complemented
4#13071545C211yesmaximal, characteristic, complemented
5#13069546C211yesmaximal, characteristic, complemented
6#13069427C211yesmaximal, characteristic, complemented
7#13069054C211yesmaximal, characteristic, complemented
8#13069049C211yesmaximal, characteristic, complemented
9#13068931C211yesmaximal, characteristic, complemented
10#13068926C211yesmaximal, characteristic, complemented
11#13068627C211yesmaximal, characteristic, complemented
12#13068557C211yesmaximal, characteristic, complemented
13#13068548C211yesmaximal, characteristic, complemented
14C4×#66885C211yesmaximal, characteristic, complemented
15C2×C11×#436C211yesmaximal, characteristic, complemented
16C22×#4339C2211yescharacteristic
17C23×D44C2211yescharacteristic
18C22×C11×M16C2211yescharacteristic
19C22×C11×M16C2211yescharacteristic, complemented
20C2×C4×D4×C11C2211yescharacteristic
21C2×#66990—21no—
22C2×#66983C2211yescharacteristic
23C2×#66979C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C2×#66977C2211yescharacteristic
26#10623081—24no—
27#10623081C418yescomplemented
28C2×#66947—21no—
29C2×#66937—21no—
30C2×C22⋊C4×D11—21no—
31C2×#66928C2211yescharacteristic
32C2×C4×D44C2211yescharacteristic
33C11×#436—24no—
34C2×C11×C4⋊C8C2211yescharacteristic, complemented
35C2×C11×C22⋊C8C2211yescharacteristic
36C2×C11×C22⋊C8C2211yescharacteristic, complemented
37C2×C4×C8×C11C2211yescharacteristic, complemented
38#10622833—21no—
39#10622825C2211yescharacteristic
40#10622825C2211yescharacteristic, complemented
41#10622746—24no—
42#10622744—24no—
43C2×#66885C2211yescharacteristic
44C2×#66885C2211yescharacteristic
45C2×#66885C2211yescharacteristic
46C2×#66885C2211yescharacteristic
47C2×#66885C2211yescharacteristic
48C2×#66885C2211yescharacteristic
49C2×#66885C2211yescharacteristic
50C2×#66885C2211yescharacteristic
51C2×#66880C2211yescharacteristic, complemented
52C2×#66880C2211yescharacteristic, complemented
53C2×#66880C2211yescharacteristic, complemented
54C2×#66880C2211yescharacteristic, complemented
55#10622594—21no—
56#10622564—21no—
57C22⋊C4×Dic11—21no—
58#10622549C2211yescharacteristic, complemented
59C4×C4⋊Dic11C2211yescharacteristic, complemented
60#10622189C2211yescharacteristic, complemented
61#10622189C2211yescharacteristic, complemented
62#10622189C2211yescharacteristic, complemented
63#10622189C2211yescharacteristic, complemented
64C24×D11—21no—
65C22×D4×C11D411yescharacteristic
66C23×C4×C11C2311yescharacteristic
67C23×C4×C11C2311yescharacteristic
68C22×C22⋊D11—21no—
69C22×C22⋊D11—21no—
70C23×Dic11—21no—
71C2×#4339—22no—
72C2×#4339—22no—
73C2×#4339—22no—
74C2×#4339—41no—
75C2×#4339—41no—
76C2×#4339C2×C414yes—
77C22×D44—22no—
78C22×D44—22no—
79C22×D44—21no—
80C22×D44—22no—
81C22×D44—41no—
82C22×D44—41no—
83C22×D44C2×C414yescomplemented
84C22×D44C2311yescharacteristic
85C22×D44C2311yescharacteristic
86C22×C4×D11—21no—
87C22×C4×D11—21no—
88C22×Dic22C2311yescharacteristic
89C2×C11×M16—22no—
90C2×C11×M16—22no—
91C2×C11×M16—22no—
92C2×C11×M16—22no—
93C2×C11×M16—41no—
94C2×C11×M16—41no—
95C22×C8×C11C2311yescharacteristic
96C22×C8×C11C2311yescharacteristic
97C22×C8×C11C2311yescharacteristic
98C22×C8×C11C2311yescharacteristic
99C4×D4×C11C2×C414yes—
100C4×D4×C11D414yes—
101C2×C11×C4⋊C4D411yescharacteristic
102C2×C11×C22⋊C4D411yescharacteristic
103C2×C11×C22⋊C4D411yescharacteristic
104C2×C42×C11C2311yescharacteristic
105C2×C22⋊Dic11—21no—
106C2×C22⋊Dic11—21no—
107C2×C22⋊Dic11—21no—
108C2×C22⋊Dic11—21no—
109#66990—28no—
110#66983—22no—
111#66983C2×C414yes—
112C2×(C2×D11)⋊C4—21no—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116#66979—22no—
117#66979—41no—
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×C4⋊Dic11C2311yescharacteristic
124C2×C4⋊Dic11C2311yescharacteristic
125C2×C4⋊Dic11C2311yescharacteristic
126#66977—22no—
127#66977C2×C414yescomplemented
128C2×Dic11⋊C4—21no—
129C2×C4×Dic11—21no—
130C2×C4×Dic11—21no—
131#66947—28no—
132#66937—28no—
133C22⋊C4×D11—28no—
134#66928—22no—
135#66928C2×C414yescomplemented
136C4×D44—22no—
137C4×D44C2×C414yescomplemented
138C11×C4⋊C8—22no—
139C11×C22⋊C8—22no—
140C11×C22⋊C8—22no—
141C4×C8×C11—22no—
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—22no—
152#66885—41no—
153#66885—41no—
154#66885D414yescomplemented
155#66880—22no—
156#66880—22no—
157#66880—41no—
158#66880—41no—
159#22427—111nomaximal, Sylow
160C24×C11C2×D411yescharacteristic
161C24×C11C2×D411yescharacteristic
162C23×D11—21no—
163C23×D11—21no—
164C23×D11—24no—
165C23×D11—42no—
166C23×D11—42no—
167C23×D11—42no—
168C23×D11—42no—
169C23×D11—81no—
170C23×D11—81no—
171C2×D4×C11—41no—
172C2×D4×C11—41no—
173C2×D4×C11C22⋊C414yes—
174C22×C4×C11—21no—
175C22×C4×C11—21no—
176C22×C4×C11—21no—
177C22×C4×C11—21no—
178C22×C4×C11—21no—
179C22×C4×C11—21no—
180C22×C4×C11—21no—
181C22×C4×C11—21no—
182C22×C4×C11C22×C412yes—
183C22×C4×C11C22×C412yes—
184C22×C4×C11C2×D411yescharacteristic
185C22×C4×C11C2×D411yescharacteristic
186C22×C4×C11C2×D411yescharacteristic
187C22×C4×C11C2×D411yescharacteristic
188C22×C4×C11C2×D412yes—
189C22×C4×C11C2×D412yes—
190C22×C4×C11C2411yescharacteristic
191C2×C22⋊D11—24no—
192C2×C22⋊D11—24no—
193C2×C22⋊D11—42no—
194C2×C22⋊D11—42no—
195C2×C22⋊D11—81no—
196C2×C22⋊D11—81no—
197C22×Dic11—21no—
198C22×Dic11—21no—
199C22×Dic11—21no—
200C22×Dic11—21no—
201C22×Dic11—21no—
202C22×Dic11—21no—
203C22×Dic11—42no—
204C22×Dic11—42no—
205C22×Dic11—81no—
206#4339—28no—
207#4339—44no—
208#4339—44no—
209#4339—44no—
210C2×D44—28no—
211C2×D44—24no—
212C2×D44—21no—
213C2×D44—21no—
214C2×D44—21no—
215C2×D44—21no—
216C2×D44—21no—
217C2×D44—21no—
218C2×D44—21no—
219C2×D44—21no—
220C2×D44—42no—
221C2×D44—42no—
222C2×D44—44no—
223C2×D44—44no—
224C2×D44—44no—
225C2×D44C22×C412yes—
226C2×D44C22×C412yes—
227C2×D44C2×D412yes—
228C2×D44#4112yes—
229C2×C4×D11—24no—
230C2×C4×D11—24no—
231C2×C4×D11—42no—
232C2×C4×D11—42no—
233C2×C4×D11—81no—
234C2×C4×D11—81no—
235C2×Dic22—21no—
236C2×Dic22—21no—
237C2×Dic22—21no—
238C2×Dic22—21no—
239C2×Dic22—21no—
240C2×Dic22C22×C412yes—
241C11×M16—44no—
242C11×M16—44no—
243C2×C8×C11—21no—
244C2×C8×C11—21no—
245C2×C8×C11—21no—
246C2×C8×C11—21no—
247C2×C8×C11—21no—
248C2×C8×C11—21no—
249C2×C8×C11—21no—
250C2×C8×C11—21no—
251C2×C8×C11—21no—
252C2×C8×C11—21no—
253C2×C8×C11—21no—
254C2×C8×C11C2×D412yes—
255C11×C4⋊C4C22⋊C414yes—
256C11×C22⋊C4C22⋊C414yes—
257C11×C22⋊C4C22⋊C414yes—
258C42×C11C22×C412yes—
259C42×C11C2×D412yes—
260C22⋊Dic11—24no—
261C22⋊Dic11—42no—
262C22⋊Dic11—42no—
263C22⋊Dic11—81no—
264(C2×D11)⋊C4—24no—
265(C2×D11)⋊C4—24no—
266(C2×D11)⋊C4—24no—
267(C2×D11)⋊C4—24no—
268C4⋊Dic11—21no—
269C4⋊Dic11—21no—
270C4⋊Dic11—21no—
271C4⋊Dic11—21no—
272C4⋊Dic11—21no—
273C4⋊Dic11—21no—
274C4⋊Dic11—21no—
275C4⋊Dic11—21no—
276C4⋊Dic11—42no—
277C4⋊Dic11C22×C412yes—
278C4⋊Dic11C2×D412yes—
279Dic11⋊C4—24no—
280C4×Dic11—42no—
281C4×Dic11—81no—
282C2×#546—111no—
283C2×#436D1111yescharacteristic, complemented
284C2×#417—111no—
285C2×#418—111no—
286#2352—111no—
287#1983—111no—
288#1958—111no—
289#1895—111no—
290#1894—111no—
291#1874—111no—
292#1873—111no—
293#1804—111no—
294#1788—111no—
295#1786—111no—
296C4×#102—111no—
297C23×C11—21no—
298C23×C11—21no—
299C23×C11—21no—
300C23×C11—21no—
301C23×C11—21no—
302C23×C11—21no—
303C23×C11—21no—
304C23×C11—21no—
305C23×C11—21no—
306C23×C11—21no—
307C23×C11—21no—
308C23×C11—21no—
309C23×C11C2×C22⋊C412yes—
310C23×C11C2×C22⋊C412yes—
311C23×C11C22×D411yescharacteristic
312C22×D11—22no—
313C22×D11—22no—
314C22×D11—22no—
315C22×D11—22no—
316C22×D11—48no—
317C22×D11—41no—
318C22×D11—41no—
319C22×D11—41no—
320C22×D11—41no—
321C22×D11—48no—
322C22×D11—41no—
323C22×D11—41no—
324C22×D11—41no—
325C22×D11—41no—
326C22×D11—41no—
327C22×D11—41no—
328C22×D11—84no—
329C22×D11—84no—
330C22×D11—84no—
331C22×D11—84no—
332C22×D11—84no—
333D4×C11—44no—
334C2×C4×C11—21no—
335C2×C4×C11—21no—
336C2×C4×C11—21no—
337C2×C4×C11—21no—
338C2×C4×C11—21no—
339C2×C4×C11—21no—
340C2×C4×C11—21no—
341C2×C4×C11—21no—
342C2×C4×C11—22no—
343C2×C4×C11—22no—
344C2×C4×C11—22no—
345C2×C4×C11—22no—
346C2×C4×C11—22no—
347C2×C4×C11—22no—
348C2×C4×C11—22no—
349C2×C4×C11—22no—
350C2×C4×C11C2×C22⋊C412yes—
351C2×C4×C11C2×C22⋊C412yes—
352C2×C4×C11C2×C22⋊C412yes—
353C2×C4×C11C2×C22⋊C412yes—
354C2×C4×C11C23×C411yescharacteristic
355C2×C4×C11C22×D411yescharacteristic
356C2×C4×C11C22×D411yescharacteristic
357C2×C4×C11C2×#4111yescharacteristic
358C2×C4×C11H(5,𝔽2)11yescharacteristic
359C2×C4×C11H(5,𝔽2)11yescharacteristic
360C22⋊D11—48no—
361C22⋊D11—84no—
362C2×Dic11—22no—
363C2×Dic11—22no—
364C2×Dic11—22no—
365C2×Dic11—41no—
366C2×Dic11—41no—
367C2×Dic11—41no—
368C2×Dic11—41no—
369C2×Dic11—41no—
370C2×Dic11—41no—
371C2×Dic11—41no—
372C2×Dic11—41no—
373C2×Dic11—41no—
374C2×Dic11—41no—
375C2×Dic11—41no—
376C2×Dic11—41no—
377C2×Dic11—41no—
378C2×Dic11—41no—
379C2×Dic11—41no—
380C2×Dic11—84no—
381D44—22no—
382D44—22no—
383D44—22no—
384D44—22no—
385D44—22no—
386D44—48no—
387D44—41no—
388D44—41no—
389D44C4×D414yes—
390C4×D11—48no—
391C4×D11—84no—
392Dic22—22no—
393Dic22—22no—
394Dic22—41no—
395Dic22—41no—
396C8×C11—22no—
397C8×C11—41no—
398C8×C11—41no—
399C8×C11—41no—
400C22×#41—111no—
401C23×D4—111no—
402C22×M16C2×D1111yescharacteristic
403C22×M16C2×D1111yescharacteristic, complemented
404#546—118no—
405#546—224no—
406C2×#124—111no—
407C2×#123—221no—
408C2×C22⋊Q8—111no—
409C2×#121—111no—
410C2×#121—221no—
411C2×#120—221no—
412C2×C4×D4—111no—
413C2×C4×D4C2×D1111yescharacteristic
414C2×#117—111no—
415C22×C4⋊C4—111no—
416C22×C22⋊C4—221no—
417#436—24no—
418C2×C4⋊C8C2×D1111yescharacteristic, complemented
419#418—224no—
420#417—224no—
421C2×#103—111no—
422C2×#103—111no—
423C2×#103—111no—
424C2×#103—111no—
425C2×#102—111no—
426C2×#102—111no—
427C2×#102—111no—
428C2×#102—111no—
429C2×#102—111no—
430C2×#102—111no—
431C2×#102—111no—
432C2×#102—111no—
433C2×C22⋊C8C2×D1111yescharacteristic
434C2×C22⋊C8C2×D1111yescharacteristic, complemented
435C2×C4×C8C2×D1111yescharacteristic, complemented
436#388—221no—
437#387—221no—
438#386—221no—
439#382—111no—
440#380—111no—
441#380—111no—
442C4×C4⋊C4—111no—
443C4×C22⋊C4—221no—
444#340—111no—
445#340—111no—
446#340—111no—
447#340—111no—
448C22×C11—22no—
449C22×C11—22no—
450C22×C11—22no—
451C22×C11—22no—
452C22×C11—22no—
453C22×C11—22no—
454C22×C11—41no—
455C22×C11—41no—
456C22×C11—41no—
457C22×C11—41no—
458C22×C11—41no—
459C22×C11—41no—
460C22×C11—41no—
461C22×C11—41no—
462C22×C11C22×C22⋊C411yescharacteristic
463C22×C11D4211yescharacteristic
464C22×C11#54611yescharacteristic
465C22×C11#57511yescharacteristic
466C22×C11#57511yescharacteristic
467C22×C11#57611yescharacteristic
468C22×C11#57711yescharacteristic
469C2×D11—24no—
470C2×D11—42no—
471C2×D11—42no—
472C2×D11—42no—
473C2×D11—42no—
474C2×D11—42no—
475C2×D11—42no—
476C2×D11—42no—
477C2×D11—42no—
478C2×D11—42no—
479C2×D11—816no—
480C2×D11—81no—
481C2×D11—81no—
482C2×D11—81no—
483C2×D11—81no—
484C4×C11—22no—
485C4×C11—22no—
486C4×C11—22no—
487C4×C11—22no—
488C4×C11C2×C4×D411yescharacteristic
489C4×C11#51811yescharacteristic
490C4×C11D4211yescharacteristic
491C4×C11#54611yescharacteristic
492Dic11—42no—
493Dic11—42no—
494Dic11—42no—
495Dic11—81no—
496Dic11—81no—
497Dic11—81no—
498C25—221no—
499C2×#41—114no—
500C2×#41—222no—
501C2×#41—222no—
502C2×#41—222no—
503C2×#41—441no—
504C2×#41—441no—
505C22×Q8—111no—
506C22×D4—114no—
507C22×D4—111no—
508C22×D4—111no—
509C22×D4—222no—
510C22×D4—222no—
511C22×D4—221no—
512C22×D4—221no—
513C22×D4—221no—
514C22×D4—222no—
515C22×D4—441no—
516C22×D4—441no—
517C22×D4D4411yescharacteristic
518C23×C4—221no—
519C23×C4—221no—
520C23×C4—221no—
521C23×C4C22×D1111yescharacteristic
522C23×C4C22×D1111yescharacteristic
523C2×M16—22no—
524C2×M16—22no—
525C2×M16—22no—
526C2×M16—22no—
527C2×M16—41no—
528C2×M16—41no—
529C22×C8C22×D1111yescharacteristic
530C22×C8C22×D1111yescharacteristic
531C22×C8C22×D1111yescharacteristic
532C22×C8C22×D1111yescharacteristic
533#124—114no—
534#124—222no—
535#123—228no—
536C22⋊Q8—114no—
537C22⋊Q8—222no—
538#121—114no—
539#121—222no—
540#121—228no—
541#120—228no—
542C4×D4—114no—
543C4×D4—222no—
544C4×D4C4×D1114yes—
545C4×D4C22⋊D1114yes—
546#117—222no—
547#117—441no—
548C2×C4⋊C4—111no—
549C2×C4⋊C4—111no—
550C2×C4⋊C4—111no—
551C2×C4⋊C4—111no—
552C2×C4⋊C4—111no—
553C2×C4⋊C4—222no—
554C2×C4⋊C4—221no—
555C2×C4⋊C4—221no—
556C2×C4⋊C4—441no—
557C2×C4⋊C4D4411yescharacteristic
558C2×C22⋊C4—221no—
559C2×C22⋊C4—221no—
560C2×C22⋊C4—221no—
561C2×C22⋊C4—221no—
562C2×C22⋊C4—221no—
563C2×C22⋊C4—228no—
564C2×C22⋊C4—221no—
565C2×C22⋊C4—221no—
566C2×C22⋊C4—221no—
567C2×C22⋊C4D4411yescharacteristic
568C2×C22⋊C4D4411yescharacteristic
569C2×C42—221no—
570C2×C42—221no—
571C2×C42C22×D1111yescharacteristic
572C4⋊C8—22no—
573#103—222no—
574#103—222no—
575#103—441no—
576#103—441no—
577#102—114no—
578#102—222no—
579#102—222no—
580#102—222no—
581#102—222no—
582#102—222no—
583#102—441no—
584#102—441no—
585C22⋊C8—22no—
586C22⋊C8—22no—
587C4×C8—22no—
588#95—221no—
589#95—221no—
590#95—221no—
591#95—221no—
592#95—221no—
593C2×C11—42no—
594C2×C11—42no—
595C2×C11D4×C22⋊C411yescharacteristic
596C2×C11#289611yescharacteristic
597C2×C11#289711yescharacteristic
598C2×C11#327311yescharacteristic
599C2×C11#327511yescharacteristic
600C2×C11#332211yescharacteristic
601C2×C11#332311yescharacteristic
602D11—44no—
603D11—82no—
604C24—221no—
605C24—221no—
606C24—224no—
607C24—442no—
608C24—442no—
609C24—442no—
610C24—442no—
611C24—881no—
612C24—881no—
613C24C2×D4411yescharacteristic
614C24C2×D4411yescharacteristic
615#41—228no—
616#41—444no—
617#41—444no—
618#41—444no—
619C2×Q8—112no—
620C2×Q8—221no—
621C2×Q8—221no—
622C2×Q8—221no—
623C2×Q8—221no—
624C2×Q8—221no—
625C2×D4—41no—
626C2×D4—41no—
627C2×D4—112no—
628C2×D4—112no—
629C2×D4—112no—
630C2×D4—112no—
631C2×D4—228no—
632C2×D4—224no—
633C2×D4—224no—
634C2×D4—224no—
635C2×D4—221no—
636C2×D4—221no—
637C2×D4—221no—
638C2×D4—221no—
639C2×D4—221no—
640C2×D4—221no—
641C2×D4—221no—
642C2×D4—221no—
643C2×D4—444no—
644C2×D4—444no—
645C2×D4—444no—
646C2×D4—442no—
647C2×D4—442no—
648C2×D4—442no—
649C2×D4—442no—
650C2×D4—881no—
651C2×D4—881no—
652C2×D4(C2×D11)⋊C414yes—
653C22×C4—21no—
654C22×C4—21no—
655C22×C4—21no—
656C22×C4—21no—
657C22×C4—21no—
658C22×C4—21no—
659C22×C4—21no—
660C22×C4—21no—
661C22×C4—221no—
662C22×C4—221no—
663C22×C4—221no—
664C22×C4—224no—
665C22×C4—224no—
666C22×C4—221no—
667C22×C4—221no—
668C22×C4—221no—
669C22×C4—442no—
670C22×C4—442no—
671C22×C4—442no—
672C22×C4—442no—
673C22×C4—881no—
674C22×C4—881no—
675C22×C4—881no—
676C22×C4C2×C4×D1112yes—
677C22×C4C2×C4×D1112yes—
678C22×C4C2×D4411yescharacteristic
679C22×C4C2×D4411yescharacteristic
680C22×C4C2×D4411yescharacteristic
681C22×C4C2×D4411yescharacteristic
682C22×C4C2×C22⋊D1112yes—
683C22×C4C2×C22⋊D1112yes—
684C22×C4C23×D1111yescharacteristic
685M16—44no—
686M16—44no—
687C2×C8—21no—
688C2×C8—21no—
689C2×C8—21no—
690C2×C8—21no—
691C2×C8—21no—
692C2×C8—21no—
693C2×C8—21no—
694C2×C8—21no—
695C2×C8—21no—
696C2×C8—21no—
697C2×C8—21no—
698C2×C8D4×D1112yes—
699C4⋊C4—112no—
700C4⋊C4—112no—
701C4⋊C4—224no—
702C4⋊C4—221no—
703C4⋊C4—221no—
704C4⋊C4—221no—
705C4⋊C4—221no—
706C4⋊C4—221no—
707C4⋊C4—221no—
708C4⋊C4—221no—
709C4⋊C4—221no—
710C4⋊C4—442no—
711C4⋊C4(C2×D11)⋊C414yes—
712C22⋊C4—224no—
713C22⋊C4—224no—
714C22⋊C4—224no—
715C22⋊C4—224no—
716C22⋊C4—224no—
717C22⋊C4—442no—
718C22⋊C4—442no—
719C22⋊C4—881no—
720C22⋊C4(C2×D11)⋊C414yes—
721C22⋊C4(C2×D11)⋊C414yes—
722C42—442no—
723C42—881no—
724C42C2×C4×D1112yes—
725C42C2×C22⋊D1112yes—
726C11#2242711yescharacteristic, complemented, Sylow
727C23—21no—
728C23—21no—
729C23—21no—
730C23—21no—
731C23—21no—
732C23—21no—
733C23—21no—
734C23—21no—
735C23—21no—
736C23—21no—
737C23—21no—
738C23—21no—
739C23—222no—
740C23—222no—
741C23—222no—
742C23—222no—
743C23—448no—
744C23—448no—
745C23—441no—
746C23—441no—
747C23—441no—
748C23—441no—
749C23—441no—
750C23—441no—
751C23—441no—
752C23—441no—
753C23—441no—
754C23—441no—
755C23—884no—
756C23—884no—
757C23—884no—
758C23—884no—
759C23—884no—
760C23C2×(C2×D11)⋊C412yes—
761C23C2×(C2×D11)⋊C412yes—
762C23C22×D4411yescharacteristic
763Q8—222no—
764Q8—222no—
765Q8—441no—
766Q8—441no—
767D4—44no—
768D4—114no—
769D4—222no—
770D4—222no—
771D4—222no—
772D4—222no—
773D4—222no—
774D4—448no—
775D4—448no—
776D4—441no—
777D4—441no—
778D4—884no—
779C2×C4—21no—
780C2×C4—21no—
781C2×C4—21no—
782C2×C4—21no—
783C2×C4—21no—
784C2×C4—21no—
785C2×C4—21no—
786C2×C4—21no—
787C2×C4—22no—
788C2×C4—22no—
789C2×C4—22no—
790C2×C4—22no—
791C2×C4—22no—
792C2×C4—22no—
793C2×C4—22no—
794C2×C4—22no—
795C2×C4—222no—
796C2×C4—222no—
797C2×C4—222no—
798C2×C4—448no—
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—441no—
811C2×C4—441no—
812C2×C4—441no—
813C2×C4—441no—
814C2×C4—884no—
815C2×C4—884no—
816C2×C4C2×(C2×D11)⋊C412yes—
817C2×C4C2×(C2×D11)⋊C412yes—
818C2×C4C2×(C2×D11)⋊C412yes—
819C2×C4C2×(C2×D11)⋊C412yes—
820C2×C4C22×C4×D1111yescharacteristic
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4#6703711yescharacteristic
823C2×C4#41×D1111yescharacteristic
824C2×C4#6704211yescharacteristic
825C2×C4C22×C22⋊D1111yescharacteristic
826C8—22no—
827C8—41no—
828C8—41no—
829C8—41no—
830C22—22no—
831C22—22no—
832C22—22no—
833C22—22no—
834C22—22no—
835C22—22no—
836C22—41no—
837C22—41no—
838C22—41no—
839C22—41no—
840C22—41no—
841C22—41no—
842C22—41no—
843C22—41no—
844C22—224no—
845C22—442no—
846C22—442no—
847C22—442no—
848C22—442no—
849C22—442no—
850C22—442no—
851C22—442no—
852C22—442no—
853C22—442no—
854C22—8816no—
855C22—881no—
856C22—881no—
857C22—881no—
858C22—881no—
859C22D4×D4411yescharacteristic
860C22#1062308511yescharacteristic
861C22#1062327911yescharacteristic
862C22#1062327911yescharacteristic
863C22#1062328211yescharacteristic
864C22#1062328311yescharacteristic
865C22C22×(C2×D11)⋊C411yescharacteristic
866C4—22no—
867C4—22no—
868C4—22no—
869C4—22no—
870C4—442no—
871C4—442no—
872C4—442no—
873C4—881no—
874C4—881no—
875C4—881no—
876C4C4×D4×D1111yescharacteristic
877C4#1062307611yescharacteristic
878C4D4×C22⋊D1111yescharacteristic
879C4#1062336011yescharacteristic
880C2—42no—
881C2—42no—
882C2—444no—
883C2—882no—
884C2D4×(C2×D11)⋊C411yescharacteristic
885C2#1307713611yescharacteristic
886C2#1307714311yescharacteristic
887C2#1308022811yescharacteristic
888C2#1308025211yescharacteristic
889C2#1308081911yescharacteristic
890C2#1308083411yescharacteristic
subgroupG/H
centerC23C22×D44
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC2×C11×#436C2
socleC23×C11C22×D4
prime radicalC2×#10623081C2
cosocleC22×C4×C11C24
hypercenterC2×#436D11
hypocenterC11#22427
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#436

Complements

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

NH ≅ G/Ntype
2. C2×#10622746C2semidirect
3. C2×#10622744C2semidirect
4. #13071545C2semidirect
5. #13069546C2semidirect
6. #13069427C2semidirect
7. #13069054C2semidirect
8. #13069049C2semidirect
9. #13068931C2semidirect
10. #13068926C2semidirect
11. #13068627C2semidirect
12. #13068557C2semidirect
13. #13068548C2semidirect
14. C4×#66885C2semidirect
15. C2×C11×#436C2semidirect
19. C22×C11×M16C22semidirect
24. C22×C4⋊Dic11C22semidirect
27. #10623081C4semidirect
34. C2×C11×C4⋊C8C22semidirect
36. C2×C11×C22⋊C8C22semidirect
37. C2×C4×C8×C11C22semidirect
40. #10622825C22semidirect
51. C2×#66880C22semidirect
52. C2×#66880C22semidirect
53. C2×#66880C22semidirect
54. C2×#66880C22semidirect
58. #10622549C22semidirect
59. C4×C4⋊Dic11C22semidirect
60. #10622189C22semidirect
61. #10622189C22semidirect
62. #10622189C22semidirect
63. #10622189C22semidirect
83. C22×D44C2×C4semidirect
127. #66977C2×C4semidirect
135. #66928C2×C4semidirect
137. C4×D44C2×C4semidirect
154. #66885D4semidirect
283. C2×#436D11semidirect
403. C22×M16C2×D11semidirect
418. C2×C4⋊C8C2×D11semidirect
434. C2×C22⋊C8C2×D11semidirect
435. C2×C4×C8C2×D11semidirect
726. C11#22427semidirect

Maximal subgroups

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

subgroupindex
C2×#106230812
C2×#106227462
C2×#106227442
#130715452
#130695462
#130694272
#130690542
#130690492
#130689312
#130689262
#130686272
#130685572
#130685482
C4×#668852
C2×C11×#4362
#2242711