Finite Group Databasebeta

← C2×#13080113 #15628740

Subgroups — C2×#13080113 #15628740

Order 2816.

3226 conjugacy classes of subgroups.

The subgroup lattice has 956 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C22×SD16×D11C211yesmaximal, characteristic, complemented
3C2×#10623107C211yesmaximal, characteristic, complemented
4C2×D4×D44C211yesmaximal, characteristic, complemented
5#13080113C2116yesmaximal, direct product factor
6C2×#10622325C211yesmaximal, characteristic, complemented
7C2×#10622499C211yesmaximal, characteristic, complemented
8C2×#10622496C211yesmaximal, characteristic, complemented
9C2×#10622640C211yesmaximal, characteristic, complemented
10C2×#10622629C211yesmaximal, characteristic, complemented
11C2×#10622424C211yesmaximal, characteristic, complemented
12C2×#10622419C211yesmaximal, characteristic, complemented
13C2×#10622389C211yesmaximal, characteristic, complemented
14C2×#10622386C211yesmaximal, characteristic, complemented
15C2×#10622319C211yesmaximal, characteristic, complemented
16C2×C11×#440C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic, complemented
18C22×Q8×D11C2211yescharacteristic, complemented
19C22×D4×D11C2211yescharacteristic
20C22×D4×D11C2211yescharacteristic
21C23×D44—21no—
22C22×C11×SD16C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic, complemented
24C2×C4×D4×C11C2211yescharacteristic
25C22×#4325C2211yescharacteristic, complemented
26C22×#4325C2211yescharacteristic, complemented
27C22×#4324C2211yescharacteristic
28C22×#4323C2211yescharacteristic
29C2×#66983—21no—
30C2×#66967—28no—
31C2×#66967C2218yescomplemented
32C2×SD16×D11—28no—
33C2×SD16×D11C2218yescomplemented
34C22×D88C2211yescharacteristic, complemented
35C22×D88C2211yescharacteristic, complemented
36C22×#4314C2211yescharacteristic, complemented
37C22×#4314C2211yescharacteristic, complemented
38C22×#4313C2211yescharacteristic, complemented
39C22×C8×D11C2211yescharacteristic, complemented
40#10623107—24no—
41#10623107C2218yescomplemented
42D4×D44—24no—
43D4×D44C2218yescomplemented
44C2×#66950—21no—
45C2×#66950C2211yescharacteristic, complemented
46C2×#66948—21no—
47C2×#66948C2211yescharacteristic
48C2×#66948C2211yescharacteristic
49C2×#66948C2211yescharacteristic, complemented
50C2×#66935—21no—
51C2×#66935—21no—
52C2×#66928—21no—
53C2×#66928C2211yescharacteristic, complemented
54C2×#66927C2211yescharacteristic
55C2×C4×D44—21no—
56C2×C4×D44C2211yescharacteristic
57C11×#440C2218yescomplemented
58C2×C11×#107C2211yescharacteristic, complemented
59C2×C11×#103C2211yescharacteristic, complemented
60C2×C11×#102C2211yescharacteristic
61C2×C11×#97C2211yescharacteristic, complemented
62C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
63C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
64#10622640C2218yescomplemented
65#10622629C2218yescomplemented
66C2×#66874C2211yescharacteristic, complemented
67C2×#66873C2211yescharacteristic, complemented
68C2×#66873C2211yescharacteristic, complemented
69C2×#66873C2211yescharacteristic, complemented
70C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
71#10622499C2218yescomplemented
72#10622496C2218yescomplemented
73#10622424C2218yescomplemented
74#10622419C2218yescomplemented
75#10622389C2218yescomplemented
76#10622386C2218yescomplemented
77#10622325C2218yescomplemented
78#10622319C2218yescomplemented
79C24×D11—21no—
80C24×D11—21no—
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C23×C4×C11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C2×#4343—22no—
87C2×#4343—24no—
88C2×#4343—42no—
89C2×#4343C2314yescomplemented
90C2×Q8×D11—22no—
91C2×Q8×D11—24no—
92C2×Q8×D11—42no—
93C2×Q8×D11C2314yescomplemented
94C2×D4×D11—24no—
95C2×D4×D11—24no—
96C2×D4×D11—22no—
97C2×D4×D11—22no—
98C2×D4×D11—42no—
99C2×D4×D11—42no—
100C2×D4×D11C2314yes—
101C2×D4×D11C2314yes—
102C22×D44—21no—
103C22×D44—21no—
104C22×D44—21no—
105C22×D44—21no—
106C22×D44—21no—
107C22×D44—21no—
108C22×D44—28no—
109C22×D44—48no—
110C22×D44D411yescharacteristic
111C22×D44C2311yescharacteristic
112C22×D44C2311yescharacteristic
113C22×D44C2311yescharacteristic
114C22×C4×D11—21no—
115C22×C4×D11—21no—
116C22×C4×D11C2311yescharacteristic
117C22×C4×D11C2311yescharacteristic
118C22×Dic22—21no—
119C22×Dic22C2311yescharacteristic
120C2×C11×SD16D418yescomplemented
121C2×C11×SD16C2314yes—
122C22×C8×C11C2311yescharacteristic
123C22×C8×C11C2311yescharacteristic
124C4×Q8×C11—22no—
125C4×Q8×C11C2314yescomplemented
126C4×D4×C11—22no—
127C4×D4×C11C2314yes—
128C2×C11×C4⋊C4—21no—
129C2×C11×C4⋊C4C2311yescharacteristic
130C2×C11×C4⋊C4C2311yescharacteristic
131C2×C11×C22⋊C4—21no—
132C2×C42×C11—21no—
133C2×C42×C11C2311yescharacteristic
134C2×#4325—24no—
135C2×#4325—24no—
136C2×#4325C2314yescomplemented
137C2×#4325C2314yescomplemented
138C2×#4324—24no—
139C2×#4324C2314yes—
140C2×#4323—24no—
141C2×#4323C2314yes—
142#66983—28no—
143C2×(C2×D11)⋊C4—21no—
144C2×(C2×D11)⋊C4—21no—
145C2×(C2×D11)⋊C4—21no—
146C2×(C2×D11)⋊C4—21no—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×(C2×D11)⋊C4D411yescharacteristic
151C2×C4⋊Dic11—21no—
152C2×C4⋊Dic11D411yescharacteristic
153C22×C11⋊C8C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155#66967—232no—
156SD16×D11—232no—
157C2×D88—24no—
158C2×D88—42no—
159C2×D88C2314yescomplemented
160C2×D88C2314yescomplemented
161C2×#4314—24no—
162C2×#4314—42no—
163C2×#4314C2314yescomplemented
164C2×#4314C2314yescomplemented
165C2×#4313—24no—
166C2×#4313C2314yescomplemented
167C2×C8×D11—24no—
168C2×C8×D11C2314yescomplemented
169#66950—22no—
170#66950—28no—
171#66950C2314yescomplemented
172#66948—28no—
173#66948—22no—
174#66948—22no—
175#66948—22no—
176#66948C2314yes—
177#66948C2314yes—
178#66948C2314yescomplemented
179#66935—28no—
180#66935—28no—
181#66928—22no—
182#66928—28no—
183#66928C2314yescomplemented
184#66927—22no—
185#66927C2314yes—
186C4×D44—28no—
187C4×D44D414yes—
188C4×D44C2314yes—
189C11×#107C2314yescomplemented
190C11×#103C2314yescomplemented
191C11×#102C2314yes—
192C11×#97C2314yescomplemented
193(C2×D11)⋊C8C2314yescomplemented
194(C2×D11)⋊C8C2314yescomplemented
195#66874C2314yescomplemented
196#66873C2314yescomplemented
197#66873C2314yescomplemented
198#66873C2314yescomplemented
199C4⋊(C11⋊C8)C2314yescomplemented
200C2×#3265—111nomaximal, Sylow
201C24×C11—21no—
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—21no—
205C23×D11—24no—
206C23×D11—24no—
207C23×D11—44no—
208C23×D11—44no—
209C23×D11—44no—
210C23×D11—44no—
211C23×D11—82no—
212C23×D11—82no—
213C23×D11C2×D411yescharacteristic
214C23×D11C2×D411yescharacteristic
215C2×Q8×C11—21no—
216C2×Q8×C11—22no—
217C2×Q8×C11C2×D414yescomplemented
218C2×Q8×C11C2412yes—
219C2×D4×C11—21no—
220C2×D4×C11—22no—
221C2×D4×C11C2×D414yes—
222C2×D4×C11C2412yes—
223C22×C4×C11—21no—
224C22×C4×C11—21no—
225C22×C4×C11—21no—
226C22×C4×C11—24no—
227C22×C4×C11—44no—
228C22×C4×C11C2×D411yescharacteristic
229C22×C4×C11C2×D411yescharacteristic
230C22×C4×C11C2411yescharacteristic
231C2×C22⋊D11—24no—
232C2×C22⋊D11—24no—
233C2×C22⋊D11—44no—
234C2×C22⋊D11—44no—
235C22×Dic11—21no—
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238#4343—28no—
239#4343—44no—
240#4343—48no—
241Q8×D11—28no—
242Q8×D11—44no—
243Q8×D11—48no—
244D4×D11—28no—
245D4×D11—28no—
246D4×D11—44no—
247D4×D11—44no—
248D4×D11—48no—
249D4×D11—48no—
250C2×D44—24no—
251C2×D44—24no—
252C2×D44—24no—
253C2×D44—24no—
254C2×D44—24no—
255C2×D44—21no—
256C2×D44—21no—
257C2×D44—24no—
258C2×D44—21no—
259C2×D44—24no—
260C2×D44—22no—
261C2×D44—22no—
262C2×D44—22no—
263C2×D44—22no—
264C2×D44—22no—
265C2×D44—22no—
266C2×D44—44no—
267C2×D44—44no—
268C2×D44—44no—
269C2×D44—432no—
270C2×D44—44no—
271C2×D44—44no—
272C2×D44—82no—
273C2×D44C2×D414yes—
274C2×D44C2412yes—
275C2×D44C2412yes—
276C2×D44C2412yes—
277C2×C4×D11—24no—
278C2×C4×D11—24no—
279C2×C4×D11—22no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—22no—
283C2×C4×D11—44no—
284C2×C4×D11—44no—
285C2×C4×D11C2×D412yes—
286C2×C4×D11C2×D412yes—
287C2×C4×D11C2412yes—
288C2×C4×D11C2412yes—
289C2×Dic22—24no—
290C2×Dic22—22no—
291C2×Dic22—21no—
292C2×Dic22—22no—
293C2×Dic22—44no—
294C2×Dic22C2412yes—
295C11×SD16C2×D4116yescomplemented
296C2×C8×C11—22no—
297C2×C8×C11C2×D414yescomplemented
298C2×C8×C11C2412yes—
299C2×C8×C11C2412yes—
300C11×C4⋊C4—21no—
301C11×C4⋊C4—24no—
302C11×C4⋊C4—21no—
303C11×C4⋊C4C2412yes—
304C11×C4⋊C4C2412yes—
305C11×C22⋊C4—24no—
306C42×C11—24no—
307C42×C11C2×D412yes—
308C42×C11C2412yes—
309#4325—28no—
310#4325—28no—
311#4324—28no—
312#4323—28no—
313(C2×D11)⋊C4—24no—
314(C2×D11)⋊C4—24no—
315(C2×D11)⋊C4—24no—
316(C2×D11)⋊C4—24no—
317(C2×D11)⋊C4—24no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4C2×D414yes—
320(C2×D11)⋊C4C2×D414yes—
321C4⋊Dic11—24no—
322C4⋊Dic11C2×D414yes—
323C2×C11⋊C8—22no—
324C2×C11⋊C8—22no—
325C2×C11⋊C8C2412yes—
326C2×C11⋊C8C2412yes—
327D88—28no—
328D88—44no—
329#4314—28no—
330#4314—44no—
331#4313—28no—
332C8×D11—28no—
333C22×AGL(1,ℤ/8)—111no—
334C23×SD16—111no—
335C2×#548—111no—
336C2×D42—111no—
337#3265—1116no—
338C2×#496—111no—
339C2×#468—111no—
340C2×#466—111no—
341C2×#460—111no—
342C2×#463—111no—
343C2×#449—111no—
344C2×#448—111no—
345C2×#450—111no—
346C2×#447—111no—
347C2×#440D1111yescharacteristic, complemented
348C2×#435—111no—
349C23×C11—24no—
350C23×C11—22no—
351C23×C11—42no—
352C23×C11—42no—
353C23×C11C22×D411yescharacteristic
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—22no—
357C22×D11—22no—
358C22×D11—22no—
359C22×D11—22no—
360C22×D11—22no—
361C22×D11—22no—
362C22×D11—48no—
363C22×D11—48no—
364C22×D11—48no—
365C22×D11—42no—
366C22×D11—42no—
367C22×D11—42no—
368C22×D11—42no—
369C22×D11—42no—
370C22×D11—42no—
371C22×D11—42no—
372C22×D11—42no—
373C22×D11—42no—
374C22×D11—48no—
375C22×D11—84no—
376C22×D11—84no—
377C22×D11—816no—
378C22×D11—816no—
379C22×D11AGL(1,ℤ/8)14yescomplemented
380C22×D11C22×D412yes—
381C22×D11C22×D412yes—
382Q8×C11—24no—
383Q8×C11—22no—
384Q8×C11C22×D414yescomplemented
385D4×C11—24no—
386D4×C11—22no—
387D4×C11C22×D414yes—
388C2×C4×C11—24no—
389C2×C4×C11—22no—
390C2×C4×C11—22no—
391C2×C4×C11—22no—
392C2×C4×C11—22no—
393C2×C4×C11—22no—
394C2×C4×C11—48no—
395C2×C4×C11—42no—
396C2×C4×C11—42no—
397C2×C4×C11C22×D412yes—
398C2×C4×C11C22×D412yes—
399C2×C4×C11C22×D412yes—
400C2×C4×C11C22×D411yescharacteristic
401C2×C4×C11H(5,𝔽2)12yes—
402C2×C4×C11C2511yescharacteristic
403C22⋊D11—48no—
404C22⋊D11—48no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—22no—
408C2×Dic11—42no—
409C2×Dic11C22×D412yes—
410C2×Dic11C22×D412yes—
411D44—28no—
412D44—22no—
413D44—22no—
414D44—22no—
415D44—22no—
416D44—22no—
417D44—22no—
418D44—48no—
419D44—48no—
420D44—48no—
421D44—48no—
422D44—48no—
423D44—42no—
424D44—42no—
425D44—42no—
426D44—84no—
427C4×D11—24no—
428C4×D11—24no—
429C4×D11—22no—
430C4×D11—22no—
431C4×D11—22no—
432C4×D11—22no—
433C4×D11—48no—
434C4×D11—48no—
435Dic22—22no—
436Dic22—22no—
437Dic22—48no—
438Dic22—42no—
439C8×C11—22no—
440C8×C11C22×D414yescomplemented
441C11⋊C8—22no—
442C11⋊C8—22no—
443C22×#41—111no—
444C23×Q8—111no—
445C23×D4—111no—
446C23×D4—111no—
447C23×D4—221no—
448C2×AGL(1,ℤ/8)—118no—
449C2×AGL(1,ℤ/8)—228no—
450C22×SD16—111no—
451C22×SD16—111no—
452C22×SD16—111no—
453C22×SD16—118no—
454C22×SD16—111no—
455C22×SD16—111no—
456C22×SD16—228no—
457C22×SD16C2×D1111yescharacteristic
458C22×D8—111no—
459C22×D8—111no—
460C22×D8—111no—
461C22×M16—111no—
462C23×C8—111no—
463#548—118no—
464#548—224no—
465D42—118no—
466D42—224no—
467C2×#127—111no—
468C2×#124—111no—
469C2×#124—221no—
470C2×C22⋊Q8—111no—
471C2×C22⋊Q8—221no—
472C2×#121—111no—
473C2×#121—111no—
474C2×#121—111no—
475C2×#121—221no—
476C2×#121—221no—
477C2×#120—221no—
478C2×#120—221no—
479C2×C4×Q8C2×D1111yescharacteristic, complemented
480C2×C4×D4—111no—
481C2×C4×D4—221no—
482C2×C4×D4C2×D1111yescharacteristic
483#496—118no—
484#468—118no—
485#466—118no—
486#463—118no—
487#460—118no—
488#450—118no—
489#449—118no—
490#448—118no—
491#447—118no—
492#440C2×D1118yescomplemented
493#435—118no—
494C2×#107C2×D1111yescharacteristic, complemented
495C2×C4⋊C8—111no—
496C2×#103—111no—
497C2×#103C2×D1111yescharacteristic, complemented
498C2×#102—111no—
499C2×#102—111no—
500C2×#102—111no—
501C2×#102C2×D1111yescharacteristic
502C2×C22⋊C8—111no—
503C2×C22⋊C8—111no—
504C2×#97C2×D1111yescharacteristic, complemented
505C22×C11—24no—
506C22×C11—48no—
507C22×C11—42no—
508C22×C11—42no—
509C22×C11D4212yes—
510C22×C11C2×AGL(1,ℤ/8)12yes—
511C22×C11#57712yes—
512C22×C11C23×D411yescharacteristic
513C2×D11—22no—
514C2×D11—28no—
515C2×D11—22no—
516C2×D11—22no—
517C2×D11—22no—
518C2×D11—22no—
519C2×D11—44no—
520C2×D11—42no—
521C2×D11—42no—
522C2×D11—42no—
523C2×D11—42no—
524C2×D11—42no—
525C2×D11—42no—
526C2×D11—42no—
527C2×D11—42no—
528C2×D11—42no—
529C2×D11—816no—
530C2×D11—816no—
531C2×D11—84no—
532C2×D11—84no—
533C2×D11—84no—
534C2×D11C2×AGL(1,ℤ/8)14yescomplemented
535C4×C11—24no—
536C4×C11—22no—
537C4×C11—22no—
538C4×C11—42no—
539C4×C11—42no—
540C4×C11D4212yes—
541C4×C11C23×D411yescharacteristic
542C4×C11C2×H(5,𝔽2)11yescharacteristic
543Dic11—22no—
544Dic11—22no—
545Dic11—42no—
546C25—221no—
547C25—221no—
548C2×#41—114no—
549C2×#41—222no—
550C2×#41—224no—
551C2×#41—442no—
552C22×Q8—114no—
553C22×Q8—111no—
554C22×Q8—221no—
555C22×Q8—222no—
556C22×Q8—224no—
557C22×Q8—442no—
558C22×Q8C22×D1111yescharacteristic
559C22×D4—114no—
560C22×D4—114no—
561C22×D4—111no—
562C22×D4—111no—
563C22×D4—111no—
564C22×D4—111no—
565C22×D4—228no—
566C22×D4—221no—
567C22×D4—221no—
568C22×D4—221no—
569C22×D4—221no—
570C22×D4—222no—
571C22×D4—222no—
572C22×D4—221no—
573C22×D4—221no—
574C22×D4—224no—
575C22×D4—224no—
576C22×D4—221no—
577C22×D4—221no—
578C22×D4—448no—
579C22×D4—442no—
580C22×D4—442no—
581C22×D4C22×D1111yescharacteristic
582C23×C4—21no—
583C23×C4—111no—
584C23×C4—111no—
585C23×C4—221no—
586C23×C4—221no—
587AGL(1,ℤ/8)—2232no—
588C2×SD16—114no—
589C2×SD16—114no—
590C2×SD16—114no—
591C2×SD16—114no—
592C2×SD16—114no—
593C2×SD16—224no—
594C2×SD16—224no—
595C2×SD16—224no—
596C2×SD16—2232no—
597C2×SD16—224no—
598C2×SD16—442no—
599C2×SD16D4418yescomplemented
600C2×SD16C22×D1114yes—
601C2×D8—114no—
602C2×D8—114no—
603C2×D8—114no—
604C2×D8—224no—
605C2×D8—224no—
606C2×D8—442no—
607C2×M16—114no—
608C2×M16—224no—
609C22×C8—111no—
610C22×C8—111no—
611C22×C8—114no—
612C22×C8—224no—
613C22×C8C22×D1111yescharacteristic
614C22×C8C22×D1111yescharacteristic
615#127—114no—
616#127—222no—
617#124—114no—
618#124—228no—
619#124—222no—
620C22⋊Q8—114no—
621C22⋊Q8—228no—
622C22⋊Q8—222no—
623#121—114no—
624#121—114no—
625#121—114no—
626#121—222no—
627#121—222no—
628#121—222no—
629#121—228no—
630#121—228no—
631#120—228no—
632#120—228no—
633C4×Q8—22no—
634C4×Q8C22×D1114yescomplemented
635C4×D4—22no—
636C4×D4—114no—
637C4×D4—114no—
638C4×D4—228no—
639C4×D4C22×D1114yes—
640C2×C4⋊C4—21no—
641C2×C4⋊C4—111no—
642C2×C4⋊C4—221no—
643C2×C4⋊C4C22×D1111yescharacteristic
644C2×C4⋊C4C22×D1111yescharacteristic
645C2×C22⋊C4—21no—
646C2×C22⋊C4—111no—
647C2×C22⋊C4—111no—
648C2×C22⋊C4—221no—
649C2×C22⋊C4—221no—
650C2×C22⋊C4—221no—
651C2×C22⋊C4—221no—
652C2×C22⋊C4—221no—
653C2×C22⋊C4—221no—
654C2×C42—21no—
655C2×C42C22×D1111yescharacteristic
656#107C22×D1114yescomplemented
657C4⋊C8—114no—
658#103—114no—
659#103C22×D1114yescomplemented
660#102—114no—
661#102—114no—
662#102—114no—
663#102C22×D1114yes—
664C22⋊C8—114no—
665C22⋊C8—114no—
666#97C22×D1114yescomplemented
667C2×C11—44no—
668C2×C11#326514yescomplemented
669C2×C11C2×D4211yescharacteristic
670C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
671C2×C11C2×#57711yescharacteristic
672D11—24no—
673D11—42no—
674D11—82no—
675D11—82no—
676D11—82no—
677C24—21no—
678C24—111no—
679C24—111no—
680C24—224no—
681C24—224no—
682C24—221no—
683C24—221no—
684C24—221no—
685C24—444no—
686C24—444no—
687C24—444no—
688C24—444no—
689C24—882no—
690C24—882no—
691#41—228no—
692#41—444no—
693#41—448no—
694C2×Q8—21no—
695C2×Q8—22no—
696C2×Q8—112no—
697C2×Q8—224no—
698C2×Q8—221no—
699C2×Q8—228no—
700C2×Q8—222no—
701C2×Q8—222no—
702C2×Q8—444no—
703C2×Q8—444no—
704C2×Q8—448no—
705C2×Q8C2×D4414yescomplemented
706C2×Q8C23×D1112yes—
707C2×D4—21no—
708C2×D4—22no—
709C2×D4—114no—
710C2×D4—112no—
711C2×D4—112no—
712C2×D4—112no—
713C2×D4—224no—
714C2×D4—224no—
715C2×D4—224no—
716C2×D4—224no—
717C2×D4—224no—
718C2×D4—224no—
719C2×D4—224no—
720C2×D4—228no—
721C2×D4—228no—
722C2×D4—222no—
723C2×D4—222no—
724C2×D4—222no—
725C2×D4—221no—
726C2×D4—224no—
727C2×D4—221no—
728C2×D4—221no—
729C2×D4—224no—
730C2×D4—222no—
731C2×D4—222no—
732C2×D4—222no—
733C2×D4—444no—
734C2×D4—444no—
735C2×D4—4432no—
736C2×D4—444no—
737C2×D4—444no—
738C2×D4—444no—
739C2×D4—444no—
740C2×D4—444no—
741C2×D4—448no—
742C2×D4—448no—
743C2×D4—444no—
744C2×D4—444no—
745C2×D4—882no—
746C2×D4C2×D4414yes—
747C2×D4C23×D1112yes—
748C22×C4—21no—
749C22×C4—21no—
750C22×C4—21no—
751C22×C4—24no—
752C22×C4—44no—
753C22×C4—111no—
754C22×C4—111no—
755C22×C4—112no—
756C22×C4—112no—
757C22×C4—112no—
758C22×C4—112no—
759C22×C4—224no—
760C22×C4—224no—
761C22×C4—222no—
762C22×C4—222no—
763C22×C4—222no—
764C22×C4—222no—
765C22×C4—221no—
766C22×C4—444no—
767C22×C4—444no—
768C22×C4D4×D1111yescharacteristic
769C22×C4D4×D1111yescharacteristic
770C22×C4C23×D1111yescharacteristic
771SD16—228no—
772SD16—228no—
773SD16—228no—
774SD16—228no—
775SD16—444no—
776SD16C2×D44116yescomplemented
777D8—228no—
778D8—228no—
779D8—444no—
780M16—228no—
781C2×C8—22no—
782C2×C8—112no—
783C2×C8—112no—
784C2×C8—222no—
785C2×C8—222no—
786C2×C8—228no—
787C2×C8C2×D4414yescomplemented
788C2×C8C23×D1112yes—
789C2×C8C23×D1112yes—
790C4⋊C4—24no—
791C4⋊C4—21no—
792C4⋊C4—21no—
793C4⋊C4—114no—
794C4⋊C4—224no—
795C4⋊C4C23×D1112yes—
796C4⋊C4C23×D1112yes—
797C22⋊C4—24no—
798C22⋊C4—114no—
799C22⋊C4—114no—
800C22⋊C4—224no—
801C22⋊C4—224no—
802C22⋊C4—224no—
803C22⋊C4—224no—
804C22⋊C4—224no—
805C22⋊C4—224no—
806C42—24no—
807C42D4×D1112yes—
808C42C23×D1112yes—
809C11C2×#326511yescharacteristic, complemented, Sylow
810C23—24no—
811C23—22no—
812C23—42no—
813C23—42no—
814C23—114no—
815C23—112no—
816C23—112no—
817C23—222no—
818C23—222no—
819C23—222no—
820C23—222no—
821C23—222no—
822C23—222no—
823C23—222no—
824C23—222no—
825C23—448no—
826C23—448no—
827C23—448no—
828C23—448no—
829C23—442no—
830C23—442no—
831C23—442no—
832C23—442no—
833C23—442no—
834C23—442no—
835C23—442no—
836C23—442no—
837C23—442no—
838C23—884no—
839C23—884no—
840C23—8816no—
841C23—8816no—
842C23C2×D4×D1111yescharacteristic
843Q8—24no—
844Q8—22no—
845Q8—222no—
846Q8—222no—
847Q8—448no—
848Q8—442no—
849Q8C22×D4414yescomplemented
850D4—24no—
851D4—22no—
852D4—228no—
853D4—222no—
854D4—222no—
855D4—222no—
856D4—222no—
857D4—222no—
858D4—222no—
859D4—448no—
860D4—448no—
861D4—448no—
862D4—448no—
863D4—448no—
864D4—448no—
865D4—448no—
866D4—442no—
867D4—442no—
868D4—442no—
869D4—884no—
870D4C22×D4414yes—
871C2×C4—22no—
872C2×C4—22no—
873C2×C4—24no—
874C2×C4—22no—
875C2×C4—22no—
876C2×C4—22no—
877C2×C4—48no—
878C2×C4—42no—
879C2×C4—42no—
880C2×C4—112no—
881C2×C4—112no—
882C2×C4—222no—
883C2×C4—222no—
884C2×C4—224no—
885C2×C4—224no—
886C2×C4—222no—
887C2×C4—222no—
888C2×C4—222no—
889C2×C4—222no—
890C2×C4—222no—
891C2×C4—448no—
892C2×C4—448no—
893C2×C4—442no—
894C2×C4C22×D4412yes—
895C2×C4C2×D4×D1112yes—
896C2×C4C2×D4×D1112yes—
897C2×C4C2×D4×D1111yescharacteristic
898C2×C4#6704212yes—
899C2×C4C24×D1111yescharacteristic
900C8—22no—
901C8—222no—
902C8—222no—
903C8C22×D4414yescomplemented
904C22—24no—
905C22—48no—
906C22—42no—
907C22—42no—
908C22—114no—
909C22—228no—
910C22—222no—
911C22—222no—
912C22—222no—
913C22—222no—
914C22—222no—
915C22—444no—
916C22—442no—
917C22—442no—
918C22—442no—
919C22—442no—
920C22—442no—
921C22—442no—
922C22—442no—
923C22—442no—
924C22—442no—
925C22—8816no—
926C22—8816no—
927C22—884no—
928C22—884no—
929C22—884no—
930C22D4×D4412yes—
931C22D11×AGL(1,ℤ/8)12yes—
932C22#1062330912yes—
933C22C22×D4×D1111yescharacteristic
934C4—24no—
935C4—22no—
936C4—22no—
937C4—42no—
938C4—42no—
939C4—222no—
940C4—222no—
941C4—442no—
942C4D4×D4412yes—
943C4C23×D4411yescharacteristic
944C4C2×#6704211yescharacteristic
945C2—44no—
946C2—224no—
947C2—442no—
948C2—882no—
949C2—882no—
950C2—882no—
951C2#1308011314yesdirect product factor
952C2C2×D4×D4411yescharacteristic
953C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
954C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#440C2
socleC23×C11C22×D4
hypercenterC2×#440D11
hypocenterC11C2×#3265
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#440

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C22×SD16×D11C2semidirect
3. C2×#10623107C2semidirect
4. C2×D4×D44C2semidirect
5. #13080113C2direct (N × H)
6. C2×#10622325C2semidirect
7. C2×#10622499C2semidirect
8. C2×#10622496C2semidirect
9. C2×#10622640C2semidirect
10. C2×#10622629C2semidirect
11. C2×#10622424C2semidirect
12. C2×#10622419C2semidirect
13. C2×#10622389C2semidirect
14. C2×#10622386C2semidirect
15. C2×#10622319C2semidirect
16. C2×C11×#440C2semidirect
17. C22×#4343C22semidirect
18. C22×Q8×D11C22semidirect
23. C2×C4×Q8×C11C22semidirect
25. C22×#4325C22semidirect
26. C22×#4325C22semidirect
31. C2×#66967C22semidirect
33. C2×SD16×D11C22semidirect
34. C22×D88C22semidirect
35. C22×D88C22semidirect
36. C22×#4314C22semidirect
37. C22×#4314C22semidirect
38. C22×#4313C22semidirect
39. C22×C8×D11C22semidirect
41. #10623107C22semidirect
43. D4×D44C22semidirect
45. C2×#66950C22semidirect
49. C2×#66948C22semidirect
53. C2×#66928C22semidirect
57. C11×#440C22semidirect
58. C2×C11×#107C22semidirect
59. C2×C11×#103C22semidirect
61. C2×C11×#97C22semidirect
62. C2×(C2×D11)⋊C8C22semidirect
63. C2×(C2×D11)⋊C8C22semidirect
64. #10622640C22semidirect
65. #10622629C22semidirect
66. C2×#66874C22semidirect
67. C2×#66873C22semidirect
68. C2×#66873C22semidirect
69. C2×#66873C22semidirect
70. C2×C4⋊(C11⋊C8)C22semidirect
71. #10622499C22semidirect
72. #10622496C22semidirect
73. #10622424C22semidirect
74. #10622419C22semidirect
75. #10622389C22semidirect
76. #10622386C22semidirect
77. #10622325C22semidirect
78. #10622319C22semidirect
89. C2×#4343C23semidirect
93. C2×Q8×D11C23semidirect
120. C2×C11×SD16D4semidirect
125. C4×Q8×C11C23semidirect
136. C2×#4325C23semidirect
137. C2×#4325C23semidirect
159. C2×D88C23semidirect
160. C2×D88C23semidirect
163. C2×#4314C23semidirect
164. C2×#4314C23semidirect
166. C2×#4313C23semidirect
168. C2×C8×D11C23semidirect
171. #66950C23semidirect
178. #66948C23semidirect
183. #66928C23semidirect
189. C11×#107C23semidirect
190. C11×#103C23semidirect
192. C11×#97C23semidirect
193. (C2×D11)⋊C8C23semidirect
194. (C2×D11)⋊C8C23semidirect
195. #66874C23semidirect
196. #66873C23semidirect
197. #66873C23semidirect
198. #66873C23semidirect
199. C4⋊(C11⋊C8)C23semidirect
217. C2×Q8×C11C2×D4semidirect
295. C11×SD16C2×D4semidirect
297. C2×C8×C11C2×D4semidirect
347. C2×#440D11semidirect
379. C22×D11AGL(1,ℤ/8)semidirect
384. Q8×C11C22×D4semidirect
440. C8×C11C22×D4semidirect
479. C2×C4×Q8C2×D11semidirect
492. #440C2×D11semidirect
494. C2×#107C2×D11semidirect
497. C2×#103C2×D11semidirect
504. C2×#97C2×D11semidirect
534. C2×D11C2×AGL(1,ℤ/8)semidirect
599. C2×SD16D44semidirect
634. C4×Q8C22×D11semidirect
656. #107C22×D11semidirect
659. #103C22×D11semidirect
666. #97C22×D11semidirect
668. C2×C11#3265semidirect
705. C2×Q8C2×D44semidirect
776. SD16C2×D44semidirect
787. C2×C8C2×D44semidirect
809. C11C2×#3265semidirect
849. Q8C22×D44semidirect
903. C8C22×D44semidirect
951. C2#13080113direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C22×SD16×D112
C2×#106231072
C2×D4×D442
#130801132
C2×#106223252
C2×#106224992
C2×#106224962
C2×#106226402
C2×#106226292
C2×#106224242
C2×#106224192
C2×#106223892
C2×#106223862
C2×#106223192
C2×C11×#4402
C2×#326511