Finite Group Databasebeta

← #14769319

Subgroups — #14769319

Order 2816.

1930 conjugacy classes of subgroups.

The subgroup lattice has 960 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623140C211yesmaximal, characteristic
2C2×#10622724C211yesmaximal, characteristic, complemented
3C2×#10622383C211yesmaximal, characteristic, complemented
4C22×#66885C211yesmaximal, characteristic, complemented
5#13071547C211yesmaximal, characteristic, complemented
6#13069541C211yesmaximal, characteristic, complemented
7#13069438C211yesmaximal, characteristic, complemented
8#13069053C211yesmaximal, characteristic, complemented
9#13068937C211yesmaximal, characteristic, complemented
10#13068934C211yesmaximal, characteristic, complemented
11#13068625C211yesmaximal, characteristic, complemented
12#13068546C211yesmaximal, characteristic, complemented
13#13068545C211yesmaximal, characteristic, complemented
14#13068440C211yesmaximal, characteristic, complemented
15C11×#1893C211yesmaximal, characteristic, complemented
16C22×D4×D11—21no—
17C22×D4×D11C2211yescharacteristic
18C23×D44C2211yescharacteristic
19C23×C8×C11C2211yescharacteristic, complemented
20C2×C11×#121C2211yescharacteristic
21C2×#66993C2211yescharacteristic
22C2×#66990—21no—
23C2×C4×C22⋊D11C2211yescharacteristic
24C22×C4⋊Dic11C2211yescharacteristic, complemented
25C22×#4313C2211yescharacteristic, complemented
26#10623140—24no—
27#10623140C418yescomplemented
28C2×#66948C2211yescharacteristic
29C2×#66946C2211yescharacteristic
30C2×#66945C2211yescharacteristic, complemented
31C2×#66937—21no—
32C2×#66935—21no—
33C2×C11×#102C2211yescharacteristic, complemented
34C2×C11×#102C2211yescharacteristic, complemented
35C11×#380C2211yescharacteristic, complemented
36C2×#66896C2211yescharacteristic, complemented
37C2×#66896C2211yescharacteristic, complemented
38C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
39C2×#66885—24no—
40C2×#66885C2211yescharacteristic
41C2×#66885C2211yescharacteristic
42C2×#66885C2211yescharacteristic, complemented
43C2×#66885C2211yescharacteristic, complemented
44#10622724—24no—
45C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
46C2×#66879C2211yescharacteristic, complemented
47C2×Dic11⋊C8C2211yescharacteristic, complemented
48#10622600C2211yescharacteristic, complemented
49#10622590C2211yescharacteristic, complemented
50C4⋊C4×Dic11C2211yescharacteristic, complemented
51C2×#66873C2211yescharacteristic
52C2×#66873C2211yescharacteristic
53C2×#66873C2211yescharacteristic, complemented
54C2×#66873C2211yescharacteristic, complemented
55#10622571—21no—
56C22⋊C4×Dic11—21no—
57#10622383—24no—
58#10622283—21no—
59#10622268—21no—
60C11×#340C2211yescharacteristic, complemented
61C11×#340C2211yescharacteristic, complemented
62#10622167C2211yescharacteristic, complemented
63#10622167C2211yescharacteristic, complemented
64C24×D11—21no—
65C24×D11—21no—
66C22×D4×C11—21no—
67C22×D4×C11C2311yescharacteristic
68C23×C4×C11C2311yescharacteristic
69C22×C22⋊D11—21no—
70C22×C22⋊D11—21no—
71C22×C22⋊D11—21no—
72C22×C22⋊D11D411yescharacteristic
73C23×Dic11—21no—
74C2×D4×D11—28no—
75C2×D4×D11—22no—
76C2×D4×D11—22no—
77C2×D4×D11—22no—
78C2×D4×D11—41no—
79C2×D4×D11—41no—
80C2×D4×D11—44no—
81C2×D4×D11—44no—
82C2×D4×D11C2×C414yescomplemented
83C22×D44—22no—
84C22×D44—22no—
85C22×D44—21no—
86C22×D44—21no—
87C22×D44—22no—
88C22×D44—41no—
89C22×D44—41no—
90C22×D44C2×C414yes—
91C22×D44C2311yescharacteristic
92C22×D44C2311yescharacteristic
93C22×C4×D11—21no—
94C22×C4×D11C2311yescharacteristic
95C22×C8×C11—22no—
96C22×C8×C11—22no—
97C22×C8×C11—41no—
98C22×C8×C11C2311yescharacteristic
99C22×C8×C11C2311yescharacteristic
100C11×#121—22no—
101C11×#121C2×C414yes—
102C2×C11×C4⋊C4C2311yescharacteristic
103C2×C11×C4⋊C4C2311yescharacteristic
104C2×C11×C4⋊C4C2311yescharacteristic
105C2×C11×C22⋊C4—21no—
106C2×C11×C22⋊C4—21no—
107C2×C22⋊Dic11D411yescharacteristic
108#66993—22no—
109#66993C2×C414yescomplemented
110#66990—28no—
111C4×C22⋊D11C2×C414yes—
112C4×C22⋊D11D414yes—
113C2×(C2×D11)⋊C4—21no—
114C2×(C2×D11)⋊C4—21no—
115C2×(C2×D11)⋊C4—21no—
116C2×(C2×D11)⋊C4—21no—
117C2×(C2×D11)⋊C4D411yescharacteristic
118C2×C4⋊Dic11—22no—
119C2×C4⋊Dic11—21no—
120C2×C4⋊Dic11—41no—
121C2×C4⋊Dic11C2311yescharacteristic
122C2×C4⋊Dic11C2311yescharacteristic
123C2×Dic11⋊C4D411yescharacteristic
124C2×C4×Dic11—21no—
125C2×C4×Dic11—21no—
126C2×C4×Dic11C2311yescharacteristic
127C22×C11⋊C8C2311yescharacteristic
128C22×C11⋊C8C2311yescharacteristic
129C2×#4313—22no—
130C2×#4313—22no—
131C2×#4313—41no—
132#66948—22no—
133#66948C2×C414yescomplemented
134#66946—22no—
135#66946C2×C414yescomplemented
136#66945—22no—
137#66945—41no—
138#66937—28no—
139#66935—28no—
140C11×#102—22no—
141C11×#102—41no—
142C11×#95—21no—
143#66896—22no—
144#66896—41no—
145C11⋊#95—21no—
146C11⋊#95—21no—
147C11⋊#95—21no—
148C11⋊#95—21no—
149C22⋊(C11⋊C8)—22no—
150#66885—22no—
151#66885—22no—
152#66885—22no—
153#66885D414yescomplemented
154(C2×D11)⋊C8—22no—
155#66879—22no—
156Dic11⋊C8—22no—
157#66873—22no—
158#66873—22no—
159#66873—41no—
160#66873—41no—
161#22423—111nomaximal, Sylow
162C24×C11—21no—
163C24×C11C2×D411yescharacteristic
164C23×D11—21no—
165C23×D11—21no—
166C23×D11—24no—
167C23×D11—24no—
168C23×D11—42no—
169C23×D11—42no—
170C23×D11—42no—
171C23×D11—42no—
172C23×D11—42no—
173C23×D11—42no—
174C23×D11—42no—
175C23×D11—42no—
176C23×D11—81no—
177C23×D11—81no—
178C23×D11—81no—
179C23×D11—81no—
180C23×D11C2×D411yescharacteristic
181C2×D4×C11—24no—
182C2×D4×C11—21no—
183C2×D4×C11—21no—
184C2×D4×C11—21no—
185C2×D4×C11—21no—
186C2×D4×C11—21no—
187C2×D4×C11—42no—
188C2×D4×C11—42no—
189C2×D4×C11C22×C412yes—
190C22×C4×C11—21no—
191C22×C4×C11—21no—
192C22×C4×C11—21no—
193C22×C4×C11—21no—
194C22×C4×C11—21no—
195C22×C4×C11—21no—
196C22×C4×C11—21no—
197C22×C4×C11C22×C412yes—
198C22×C4×C11C2×D411yescharacteristic
199C22×C4×C11C2×D412yes—
200C22×C4×C11C2411yescharacteristic
201C2×C22⋊D11—24no—
202C2×C22⋊D11—24no—
203C2×C22⋊D11—24no—
204C2×C22⋊D11—22no—
205C2×C22⋊D11—22no—
206C2×C22⋊D11—42no—
207C2×C22⋊D11—42no—
208C2×C22⋊D11—42no—
209C2×C22⋊D11—42no—
210C2×C22⋊D11—81no—
211C2×C22⋊D11—81no—
212C2×C22⋊D11C22⋊C414yes—
213C22×Dic11—21no—
214C22×Dic11—21no—
215C22×Dic11—42no—
216C22×Dic11—42no—
217C22×Dic11—81no—
218C22×Dic11C2×D411yescharacteristic
219C22×Dic11C2×D411yescharacteristic
220C22×Dic11C2×D411yescharacteristic
221D4×D11—28no—
222D4×D11—44no—
223D4×D11—44no—
224D4×D11—44no—
225D4×D11—432no—
226C2×D44—24no—
227C2×D44—28no—
228C2×D44—24no—
229C2×D44—21no—
230C2×D44—21no—
231C2×D44—21no—
232C2×D44—21no—
233C2×D44—21no—
234C2×D44—21no—
235C2×D44—21no—
236C2×D44—21no—
237C2×D44—42no—
238C2×D44—42no—
239C2×D44—44no—
240C2×D44—44no—
241C2×D44—44no—
242C2×D44—42no—
243C2×D44—42no—
244C2×D44C22×C412yes—
245C2×D44C22×C412yes—
246C2×D44C2×D412yes—
247C2×D44#4112yes—
248C2×C4×D11—24no—
249C2×C4×D11—21no—
250C2×C4×D11—21no—
251C2×C4×D11—21no—
252C2×C4×D11—21no—
253C2×C4×D11—42no—
254C2×C4×D11—42no—
255C2×C4×D11C22×C412yes—
256C2×C4×D11C2×D412yes—
257C2×C8×C11—21no—
258C2×C8×C11—21no—
259C2×C8×C11—21no—
260C2×C8×C11—21no—
261C2×C8×C11—21no—
262C2×C8×C11—44no—
263C2×C8×C11C2×D412yescomplemented
264C11×C4⋊C4—21no—
265C11×C4⋊C4—21no—
266C11×C4⋊C4—21no—
267C11×C4⋊C4—21no—
268C11×C4⋊C4—21no—
269C11×C4⋊C4C22×C412yes—
270C11×C22⋊C4—24no—
271C11×C22⋊C4—42no—
272C22⋊Dic11C22⋊C414yes—
273(C2×D11)⋊C4—24no—
274(C2×D11)⋊C4—24no—
275(C2×D11)⋊C4—42no—
276(C2×D11)⋊C4—81no—
277(C2×D11)⋊C4C22⋊C414yes—
278C4⋊Dic11—21no—
279C4⋊Dic11—21no—
280C4⋊Dic11—21no—
281C4⋊Dic11—42no—
282C4⋊Dic11C2×D412yescomplemented
283Dic11⋊C4C22⋊C414yes—
284C4×Dic11—42no—
285C4×Dic11—81no—
286C4×Dic11C22×C412yes—
287C4×Dic11C2×D412yes—
288C2×C11⋊C8—21no—
289C2×C11⋊C8—21no—
290C2×C11⋊C8—21no—
291C2×C11⋊C8—21no—
292C2×C11⋊C8—21no—
293C2×C11⋊C8—21no—
294#4313—44no—
295C2×D42—111no—
296C2×#435—111no—
297C2×#418—111no—
298C22×#102—111no—
299#2352—111no—
300#1982—111no—
301#1961—111no—
302#1895—111no—
303#1893D1111yescharacteristic, complemented
304#1875—111no—
305#1874—111no—
306#1804—111no—
307#1786—111no—
308#1786—111no—
309#1762—111no—
310C23×C11—21no—
311C23×C11—21no—
312C23×C11—21no—
313C23×C11—21no—
314C23×C11—22no—
315C23×C11—41no—
316C23×C11—41no—
317C23×C11—41no—
318C23×C11—41no—
319C23×C11—41no—
320C23×C11—41no—
321C23×C11C2×C22⋊C412yes—
322C23×C11AGL(1,ℤ/8)12yes—
323C23×C11AGL(1,ℤ/8)12yes—
324C23×C11C22×D411yescharacteristic
325C22×D11—22no—
326C22×D11—21no—
327C22×D11—22no—
328C22×D11—21no—
329C22×D11—22no—
330C22×D11—21no—
331C22×D11—21no—
332C22×D11—21no—
333C22×D11—21no—
334C22×D11—22no—
335C22×D11—48no—
336C22×D11—48no—
337C22×D11—48no—
338C22×D11—41no—
339C22×D11—41no—
340C22×D11—41no—
341C22×D11—41no—
342C22×D11—41no—
343C22×D11—41no—
344C22×D11—41no—
345C22×D11—41no—
346C22×D11—41no—
347C22×D11—41no—
348C22×D11—48no—
349C22×D11—84no—
350C22×D11—84no—
351C22×D11—84no—
352C22×D11—84no—
353C22×D11—84no—
354C22×D11—84no—
355C22×D11—84no—
356C22×D11—84no—
357C22×D11—84no—
358C22×D11—84no—
359C22×D11C2×C22⋊C412yes—
360D4×C11—22no—
361D4×C11—22no—
362D4×C11—48no—
363D4×C11—41no—
364D4×C11—41no—
365C2×C4×C11—21no—
366C2×C4×C11—21no—
367C2×C4×C11—22no—
368C2×C4×C11—22no—
369C2×C4×C11—22no—
370C2×C4×C11—22no—
371C2×C4×C11—22no—
372C2×C4×C11—41no—
373C2×C4×C11—41no—
374C2×C4×C11—41no—
375C2×C4×C11—41no—
376C2×C4×C11—41no—
377C2×C4×C11—41no—
378C2×C4×C11—41no—
379C2×C4×C11—41no—
380C2×C4×C11C2×C22⋊C412yes—
381C2×C4×C11C23×C411yescharacteristic
382C2×C4×C11C22×D411yescharacteristic
383C2×C4×C11C22×D411yescharacteristic
384C2×C4×C11C2×#4111yescharacteristic
385C2×C4×C11H(5,𝔽2)11yescharacteristic
386C2×C4×C11H(5,𝔽2)11yescharacteristic
387C22⋊D11—28no—
388C22⋊D11—48no—
389C22⋊D11—48no—
390C22⋊D11—84no—
391C2×Dic11—21no—
392C2×Dic11—21no—
393C2×Dic11—21no—
394C2×Dic11—21no—
395C2×Dic11—21no—
396C2×Dic11—21no—
397C2×Dic11—22no—
398C2×Dic11—41no—
399C2×Dic11—41no—
400C2×Dic11—41no—
401C2×Dic11—41no—
402C2×Dic11—41no—
403C2×Dic11—84no—
404C2×Dic11C2×C22⋊C412yes—
405C2×Dic11C2×C22⋊C412yes—
406C2×Dic11C2×C22⋊C412yes—
407D44—22no—
408D44—22no—
409D44—22no—
410D44—22no—
411D44—22no—
412D44—48no—
413D44—48no—
414D44—41no—
415D44—41no—
416D44C4×D414yes—
417C4×D11—22no—
418C4×D11—22no—
419C4×D11—22no—
420C4×D11—22no—
421C4×D11—48no—
422C8×C11—22no—
423C8×C11—41no—
424C11⋊C8—41no—
425C11⋊C8—41no—
426C23×D4—111no—
427C23×D4—111no—
428C23×D4—221no—
429C22×M16—111no—
430C23×C8C2×D1111yescharacteristic, complemented
431D42—118no—
432D42—224no—
433C2×#127—111no—
434C2×#121—111no—
435C2×#121—221no—
436C2×#121C2×D1111yescharacteristic
437C2×#120—221no—
438C2×#120—221no—
439C2×C4×D4—111no—
440C2×C4×D4—111no—
441C2×#117—111no—
442C22×C4⋊C4—111no—
443#435—224no—
444C2×C4⋊C8—111no—
445#418—224no—
446C2×#102—111no—
447C2×#102—111no—
448C2×#102—111no—
449C2×#102—111no—
450C2×#102—111no—
451C2×#102—111no—
452C2×#102—111no—
453C2×#102—111no—
454C2×#102—111no—
455C2×#102—111no—
456C2×#102—224no—
457C2×#102C2×D1111yescharacteristic, complemented
458C2×#102C2×D1111yescharacteristic, complemented
459C2×C22⋊C8—111no—
460C2×C22⋊C8—111no—
461C2×#97—111no—
462#388—221no—
463#387—221no—
464#386—221no—
465#382—111no—
466#380—111no—
467#380C2×D1111yescharacteristic, complemented
468C4×C4⋊C4—111no—
469C4×C22⋊C4—221no—
470#340—111no—
471#340—111no—
472#340C2×D1111yescharacteristic, complemented
473#340C2×D1111yescharacteristic, complemented
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—22no—
479C22×C11—22no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—81no—
484C22×C11—81no—
485C22×C11—81no—
486C22×C11—81no—
487C22×C11#41814yescomplemented
488C22×C11C22×C22⋊C411yescharacteristic
489C22×C11D4211yescharacteristic
490C22×C11#54611yescharacteristic
491C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
492C22×C11C2×AGL(1,ℤ/8)11yescharacteristic
493C22×C11#57611yescharacteristic
494C22×C11#57711yescharacteristic
495C2×D11—24no—
496C2×D11—22no—
497C2×D11—22no—
498C2×D11—22no—
499C2×D11—42no—
500C2×D11—42no—
501C2×D11—41no—
502C2×D11—42no—
503C2×D11—41no—
504C2×D11—42no—
505C2×D11—41no—
506C2×D11—42no—
507C2×D11—41no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—816no—
513C2×D11—816no—
514C2×D11—81no—
515C2×D11—81no—
516C2×D11—81no—
517C2×D11—81no—
518C4×C11—22no—
519C4×C11—42no—
520C4×C11—81no—
521C4×C11—81no—
522C4×C11C2×C4×D411yescharacteristic
523C4×C11#51811yescharacteristic
524C4×C11D4211yescharacteristic
525C4×C11#54611yescharacteristic
526Dic11—22no—
527Dic11—22no—
528Dic11—22no—
529Dic11—42no—
530Dic11—81no—
531C25—221no—
532C25—221no—
533C22×D4—21no—
534C22×D4—111no—
535C22×D4—114no—
536C22×D4—114no—
537C22×D4—111no—
538C22×D4—111no—
539C22×D4—222no—
540C22×D4—222no—
541C22×D4—221no—
542C22×D4—222no—
543C22×D4—221no—
544C22×D4—221no—
545C22×D4—221no—
546C22×D4—222no—
547C22×D4—222no—
548C22×D4—228no—
549C22×D4—221no—
550C22×D4—222no—
551C22×D4—441no—
552C22×D4—441no—
553C22×D4—441no—
554C22×D4—441no—
555C22×D4—444no—
556C22×D4—444no—
557C22×D4C22×D1111yescharacteristic
558C23×C4—111no—
559C23×C4—221no—
560C23×C4—221no—
561C23×C4C22×D1111yescharacteristic
562C2×M16—222no—
563C2×M16—222no—
564C2×M16—441no—
565C22×C8—22no—
566C22×C8—22no—
567C22×C8—41no—
568C22×C8—111no—
569C22×C8—111no—
570C22×C8C22×D1111yescharacteristic
571C22×C8C22×D1111yescharacteristic
572#127—114no—
573#127—222no—
574#121—22no—
575#121—114no—
576#121—228no—
577#121—222no—
578#121C4×D1114yes—
579#120—228no—
580#120—228no—
581C4×D4—114no—
582C4×D4—114no—
583C4×D4—114no—
584C4×D4—222no—
585#117—222no—
586#117—441no—
587C2×C4⋊C4—111no—
588C2×C4⋊C4—111no—
589C2×C4⋊C4—111no—
590C2×C4⋊C4—222no—
591C2×C4⋊C4—221no—
592C2×C4⋊C4—441no—
593C2×C4⋊C4C22×D1111yescharacteristic
594C2×C4⋊C4C22×D1111yescharacteristic
595C2×C4⋊C4C22×D1111yescharacteristic
596C2×C22⋊C4—21no—
597C2×C22⋊C4—21no—
598C2×C22⋊C4—111no—
599C2×C22⋊C4—111no—
600C2×C22⋊C4—221no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—111no—
605C2×C42—221no—
606C2×C42—221no—
607C4⋊C8—222no—
608#102—22no—
609#102—41no—
610#102—114no—
611#102—222no—
612#102—222no—
613#102—222no—
614#102—222no—
615#102—222no—
616#102—222no—
617#102—441no—
618#102—441no—
619#102—441no—
620C22⋊C8—222no—
621C22⋊C8—222no—
622#97—222no—
623#95—21no—
624#95—221no—
625#95—221no—
626#95—221no—
627#95—221no—
628C2×C11—24no—
629C2×C11—82no—
630C2×C11D4×C22⋊C411yescharacteristic
631C2×C11C2×#41811yescharacteristic
632C2×C11#289711yescharacteristic
633C2×C11#326411yescharacteristic
634C2×C11#326511yescharacteristic
635C2×C11#331011yescharacteristic
636C2×C11#331811yescharacteristic
637D11—42no—
638D11—44no—
639D11—82no—
640C24—21no—
641C24—111no—
642C24—224no—
643C24—221no—
644C24—221no—
645C24—224no—
646C24—442no—
647C24—442no—
648C24—442no—
649C24—442no—
650C24—442no—
651C24—442no—
652C24—442no—
653C24—442no—
654C24—881no—
655C24—881no—
656C24—881no—
657C24—881no—
658C24D4×D1111yescharacteristic
659C2×D4—24no—
660C2×D4—21no—
661C2×D4—21no—
662C2×D4—21no—
663C2×D4—21no—
664C2×D4—21no—
665C2×D4—42no—
666C2×D4—42no—
667C2×D4—114no—
668C2×D4—112no—
669C2×D4—112no—
670C2×D4—112no—
671C2×D4—112no—
672C2×D4—228no—
673C2×D4—224no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—224no—
677C2×D4—228no—
678C2×D4—222no—
679C2×D4—222no—
680C2×D4—224no—
681C2×D4—221no—
682C2×D4—221no—
683C2×D4—221no—
684C2×D4—221no—
685C2×D4—221no—
686C2×D4—221no—
687C2×D4—221no—
688C2×D4—221no—
689C2×D4—444no—
690C2×D4—444no—
691C2×D4—444no—
692C2×D4—442no—
693C2×D4—442no—
694C2×D4—442no—
695C2×D4—442no—
696C2×D4—444no—
697C2×D4—444no—
698C2×D4—444no—
699C2×D4—442no—
700C2×D4—442no—
701C2×D4—442no—
702C2×D4—442no—
703C2×D4—4432no—
704C2×D4—881no—
705C2×D4—881no—
706C2×D4C2×C4×D1112yes—
707C22×C4—21no—
708C22×C4—21no—
709C22×C4—21no—
710C22×C4—21no—
711C22×C4—21no—
712C22×C4—21no—
713C22×C4—21no—
714C22×C4—111no—
715C22×C4—111no—
716C22×C4—111no—
717C22×C4—112no—
718C22×C4—112no—
719C22×C4—224no—
720C22×C4—221no—
721C22×C4—221no—
722C22×C4—221no—
723C22×C4—221no—
724C22×C4—221no—
725C22×C4—221no—
726C22×C4—442no—
727C22×C4—442no—
728C22×C4—442no—
729C22×C4—442no—
730C22×C4—881no—
731C22×C4C2×C4×D1112yes—
732C22×C4D4×D1111yescharacteristic
733C22×C4D4×D1112yes—
734C22×C4C23×D1111yescharacteristic
735M16—444no—
736C2×C8—21no—
737C2×C8—21no—
738C2×C8—21no—
739C2×C8—21no—
740C2×C8—21no—
741C2×C8—44no—
742C2×C8—221no—
743C2×C8—221no—
744C2×C8—221no—
745C2×C8—221no—
746C2×C8—221no—
747C2×C8—221no—
748C2×C8D4×D1112yescomplemented
749C4⋊C4—21no—
750C4⋊C4—21no—
751C4⋊C4—21no—
752C4⋊C4—21no—
753C4⋊C4—21no—
754C4⋊C4—114no—
755C4⋊C4—112no—
756C4⋊C4—221no—
757C4⋊C4—221no—
758C4⋊C4—221no—
759C4⋊C4—442no—
760C4⋊C4C2×C4×D1112yes—
761C22⋊C4—24no—
762C22⋊C4—42no—
763C22⋊C4—114no—
764C22⋊C4—114no—
765C22⋊C4—224no—
766C22⋊C4—224no—
767C22⋊C4—442no—
768C22⋊C4—881no—
769C42—112no—
770C42—112no—
771C42—442no—
772C42—881no—
773C11#2242311yescharacteristic, complemented, Sylow
774C23—21no—
775C23—21no—
776C23—21no—
777C23—21no—
778C23—22no—
779C23—41no—
780C23—41no—
781C23—41no—
782C23—41no—
783C23—41no—
784C23—41no—
785C23—112no—
786C23—222no—
787C23—221no—
788C23—221no—
789C23—221no—
790C23—221no—
791C23—221no—
792C23—222no—
793C23—221no—
794C23—222no—
795C23—222no—
796C23—448no—
797C23—448no—
798C23—448no—
799C23—441no—
800C23—441no—
801C23—441no—
802C23—441no—
803C23—441no—
804C23—441no—
805C23—441no—
806C23—441no—
807C23—441no—
808C23—441no—
809C23—448no—
810C23—884no—
811C23—884no—
812C23—884no—
813C23—884no—
814C23—884no—
815C23—884no—
816C23—884no—
817C23—884no—
818C23—884no—
819C23—884no—
820C23C22⋊C4×D1112yes—
821C23#6696412yes—
822C23#6696712yes—
823C23C2×D4×D1111yescharacteristic
824D4—22no—
825D4—22no—
826D4—48no—
827D4—41no—
828D4—41no—
829D4—114no—
830D4—228no—
831D4—222no—
832D4—222no—
833D4—222no—
834D4—222no—
835D4—222no—
836D4—448no—
837D4—448no—
838D4—448no—
839D4—448no—
840D4—441no—
841D4—441no—
842D4—884no—
843C2×C4—21no—
844C2×C4—21no—
845C2×C4—22no—
846C2×C4—22no—
847C2×C4—22no—
848C2×C4—22no—
849C2×C4—22no—
850C2×C4—41no—
851C2×C4—41no—
852C2×C4—41no—
853C2×C4—41no—
854C2×C4—41no—
855C2×C4—41no—
856C2×C4—41no—
857C2×C4—41no—
858C2×C4—112no—
859C2×C4—112no—
860C2×C4—112no—
861C2×C4—221no—
862C2×C4—221no—
863C2×C4—221no—
864C2×C4—221no—
865C2×C4—221no—
866C2×C4—221no—
867C2×C4—222no—
868C2×C4—222no—
869C2×C4—222no—
870C2×C4—222no—
871C2×C4—222no—
872C2×C4—448no—
873C2×C4—441no—
874C2×C4—441no—
875C2×C4—441no—
876C2×C4—441no—
877C2×C4—441no—
878C2×C4—884no—
879C2×C4C22⋊C4×D1112yes—
880C2×C4C22×C4×D1111yescharacteristic
881C2×C4C2×D4×D1111yescharacteristic
882C2×C4C2×D4×D1111yescharacteristic
883C2×C4#6703711yescharacteristic
884C2×C4#41×D1111yescharacteristic
885C2×C4#6704211yescharacteristic
886C8—22no—
887C8—41no—
888C8—441no—
889C8—441no—
890C22—22no—
891C22—22no—
892C22—22no—
893C22—22no—
894C22—22no—
895C22—22no—
896C22—42no—
897C22—42no—
898C22—42no—
899C22—81no—
900C22—81no—
901C22—81no—
902C22—81no—
903C22—222no—
904C22—224no—
905C22—222no—
906C22—222no—
907C22—441no—
908C22—442no—
909C22—441no—
910C22—442no—
911C22—441no—
912C22—442no—
913C22—442no—
914C22—442no—
915C22—441no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—8816no—
921C22—8816no—
922C22—881no—
923C22—881no—
924C22—881no—
925C22—881no—
926C22#1062238314yescomplemented
927C22C2×C22⋊C4×D1111yescharacteristic
928C22#1062314011yescharacteristic
929C22#1062314111yescharacteristic
930C22C2×#6696411yescharacteristic
931C22C2×#6696711yescharacteristic
932C22#1062330011yescharacteristic
933C22#1062330111yescharacteristic
934C4—22no—
935C4—42no—
936C4—81no—
937C4—81no—
938C4—222no—
939C4—222no—
940C4—222no—
941C4—442no—
942C4—881no—
943C4C4×D4×D1111yescharacteristic
944C4#1062307611yescharacteristic
945C4#1062312111yescharacteristic
946C4#1062318511yescharacteristic
947C2—24no—
948C2—82no—
949C2—442no—
950C2—444no—
951C2—882no—
952C2#1307143411yescharacteristic
953C2C2×#1062238311yescharacteristic
954C2#1307713811yescharacteristic
955C2#1308009311yescharacteristic
956C2#1308010811yescharacteristic
957C2#1308064311yescharacteristic
958C2#1308076311yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutatorC2×C4×C11C23×C4
FrattiniC22×C4C23×D11
FittingC11×#1893C2
socleC23×C11C22×D4
prime radicalC2×#10623140C2
cosocleC22×C4×C11C24
hypercenter#1893D11
hypocenterC11#22423
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ #1893

Complements

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

NH ≅ G/Ntype
2. C2×#10622724C2semidirect
3. C2×#10622383C2semidirect
4. C22×#66885C2semidirect
5. #13071547C2semidirect
6. #13069541C2semidirect
7. #13069438C2semidirect
8. #13069053C2semidirect
9. #13068937C2semidirect
10. #13068934C2semidirect
11. #13068625C2semidirect
12. #13068546C2semidirect
13. #13068545C2semidirect
14. #13068440C2semidirect
15. C11×#1893C2semidirect
19. C23×C8×C11C22semidirect
24. C22×C4⋊Dic11C22semidirect
25. C22×#4313C22semidirect
27. #10623140C4semidirect
30. C2×#66945C22semidirect
33. C2×C11×#102C22semidirect
34. C2×C11×#102C22semidirect
35. C11×#380C22semidirect
36. C2×#66896C22semidirect
37. C2×#66896C22semidirect
38. C2×C22⋊(C11⋊C8)C22semidirect
42. C2×#66885C22semidirect
43. C2×#66885C22semidirect
45. C2×(C2×D11)⋊C8C22semidirect
46. C2×#66879C22semidirect
47. C2×Dic11⋊C8C22semidirect
48. #10622600C22semidirect
49. #10622590C22semidirect
50. C4⋊C4×Dic11C22semidirect
53. C2×#66873C22semidirect
54. C2×#66873C22semidirect
60. C11×#340C22semidirect
61. C11×#340C22semidirect
62. #10622167C22semidirect
63. #10622167C22semidirect
82. C2×D4×D11C2×C4semidirect
109. #66993C2×C4semidirect
133. #66948C2×C4semidirect
135. #66946C2×C4semidirect
153. #66885D4semidirect
263. C2×C8×C11C2×D4semidirect
282. C4⋊Dic11C2×D4semidirect
303. #1893D11semidirect
430. C23×C8C2×D11semidirect
457. C2×#102C2×D11semidirect
458. C2×#102C2×D11semidirect
467. #380C2×D11semidirect
472. #340C2×D11semidirect
473. #340C2×D11semidirect
487. C22×C11#418semidirect
748. C2×C8D4×D11semidirect
773. C11#22423semidirect
926. C22#10622383semidirect

Maximal subgroups

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

subgroupindex
C2×#106231402
C2×#106227242
C2×#106223832
C22×#668852
#130715472
#130695412
#130694382
#130690532
#130689372
#130689342
#130686252
#130685462
#130685452
#130684402
C11×#18932
#2242311