Finite Group Databasebeta

← C2×#13080233 #15628888

Subgroups — C2×#13080233 #15628888

Order 2816.

3278 conjugacy classes of subgroups.

The subgroup lattice has 980 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66961C211yesmaximal, characteristic, complemented
2C22×#66964C211yesmaximal, characteristic, complemented
3C2×#10623130C211yesmaximal, characteristic, complemented
4C2×#10623140C211yesmaximal, characteristic, complemented
5#13080233C2116yesmaximal, direct product factor
6C2×#10622764C211yesmaximal, characteristic, complemented
7C2×#10622478C211yesmaximal, characteristic, complemented
8C2×#10622375C211yesmaximal, characteristic, complemented
9C2×#10622399C211yesmaximal, characteristic, complemented
10C2×#10622394C211yesmaximal, characteristic, complemented
11C2×#10622650C211yesmaximal, characteristic, complemented
12C2×#10622386C211yesmaximal, characteristic, complemented
13C2×#10622649C211yesmaximal, characteristic, complemented
14C2×#10622465C211yesmaximal, characteristic, complemented
15C2×#10622741C211yesmaximal, characteristic, complemented
16C2×C11×#469C211yesmaximal, characteristic, complemented
17C22×#4341C2211yescharacteristic, complemented
18C22×D4×D11—21no—
19C22×D4×D11C2211yescharacteristic
20C22×#4339C2211yescharacteristic, complemented
21C23×D44C2211yescharacteristic
22C22×C11×D8C2211yescharacteristic, complemented
23C22×C11×M16C2211yescharacteristic, complemented
24C2×C11×#121C2211yescharacteristic
25C2×C11×#121C2211yescharacteristic, complemented
26C2×#66993—21no—
27C2×#66993C2211yescharacteristic
28C2×#66993C2211yescharacteristic, complemented
29C2×#66992—21no—
30C2×#66990—21no—
31C22×#4324C2211yescharacteristic, complemented
32C22×#4323C2211yescharacteristic
33C22×#4323C2211yescharacteristic, complemented
34C22×#4323C2211yescharacteristic, complemented
35C2×C4×C22⋊D11C2211yescharacteristic
36C2×#66964—28no—
37C2×#66964C2218yescomplemented
38C2×#66961—28no—
39C2×#66961C2218yescomplemented
40C22×D88C2211yescharacteristic
41C22×D88C2211yescharacteristic, complemented
42C22×#4314C2211yescharacteristic
43C22×#4314C2211yescharacteristic, complemented
44C22×#4313C2211yescharacteristic, complemented
45#10623140—24no—
46#10623140C2218yescomplemented
47#10623130—24no—
48#10623130C2218yescomplemented
49C2×#66948C2211yescharacteristic
50C2×#66948C2211yescharacteristic, complemented
51C2×#66946C2211yescharacteristic
52C2×#66940C2211yescharacteristic, complemented
53C2×#66937—21no—
54C2×#66937—21no—
55C2×#66935—21no—
56C2×(C22⋊D11)⋊C4—21no—
57C11×#469C2218yescomplemented
58C2×C11×#106C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic, complemented
60C2×C11×#102C2211yescharacteristic, complemented
61C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
62#10622764C2218yescomplemented
63#10622741C2218yescomplemented
64C2×(C2×D11)⋊C8C2211yescharacteristic, complemented
65C2×Dic11⋊C8C2211yescharacteristic, complemented
66C2×C8×Dic11C2211yescharacteristic, complemented
67#10622650C2218yescomplemented
68#10622649C2218yescomplemented
69C2×#66874C2211yescharacteristic, complemented
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic, complemented
72C2×#66873C2211yescharacteristic, complemented
73#10622478C2218yescomplemented
74#10622465C2218yescomplemented
75#10622399C2218yescomplemented
76#10622394C2218yescomplemented
77#10622386C2218yescomplemented
78#10622375C2218yescomplemented
79C24×D11—21no—
80C24×D11—21no—
81C22×D4×C11—21no—
82C22×D4×C11—21no—
83C22×D4×C11C2311yescharacteristic
84C22×D4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C22×C22⋊D11—21no—
87C22×C22⋊D11—21no—
88C22×C22⋊D11—21no—
89C22×C22⋊D11—21no—
90C22×C22⋊D11—21no—
91C22×C22⋊D11—21no—
92C22×C22⋊D11—21no—
93C22×C22⋊D11D411yescharacteristic
94C23×Dic11—21no—
95C2×#4341—22no—
96C2×#4341—24no—
97C2×#4341—42no—
98C2×#4341C2314yescomplemented
99C2×D4×D11—28no—
100C2×D4×D11—24no—
101C2×D4×D11—22no—
102C2×D4×D11—42no—
103C2×D4×D11—48no—
104C2×D4×D11C2314yes—
105C2×#4339—22no—
106C2×#4339—24no—
107C2×#4339—42no—
108C2×#4339C2314yescomplemented
109C22×D44—24no—
110C22×D44—21no—
111C22×D44—21no—
112C22×D44—22no—
113C22×D44—21no—
114C22×D44—42no—
115C22×D44C2311yescharacteristic
116C22×D44C2311yescharacteristic
117C22×D44C2314yes—
118C22×D44C2311yescharacteristic
119C22×C4×D11—21no—
120C22×C4×D11—21no—
121C22×C4×D11C2311yescharacteristic
122C22×Dic22C2311yescharacteristic
123C2×C11×D8—24no—
124C2×C11×D8C2314yescomplemented
125C2×C11×M16—24no—
126C2×C11×M16C2314yescomplemented
127C22×C8×C11C2311yescharacteristic
128C22×C8×C11C2311yescharacteristic
129C11×#121—22no—
130C11×#121—22no—
131C11×#121C2314yes—
132C11×#121C2314yescomplemented
133C2×C11×C4⋊C4C2311yescharacteristic
134C2×C11×C4⋊C4C2311yescharacteristic
135C2×C11×C22⋊C4—21no—
136C2×C11×C22⋊C4—21no—
137C2×C22⋊Dic11D411yescharacteristic
138#66993—28no—
139#66993—22no—
140#66993—22no—
141#66993C2314yes—
142#66993C2314yescomplemented
143#66992—28no—
144#66990—28no—
145C2×#4324—24no—
146C2×#4324C2314yescomplemented
147C2×#4323—24no—
148C2×#4323—42no—
149C2×#4323—42no—
150C2×#4323C2314yes—
151C2×#4323C2314yescomplemented
152C2×#4323C2314yescomplemented
153C4×C22⋊D11D414yes—
154C4×C22⋊D11C2314yes—
155C2×(C2×D11)⋊C4—21no—
156C2×(C2×D11)⋊C4—21no—
157C2×(C2×D11)⋊C4—21no—
158C2×(C2×D11)⋊C4D411yescharacteristic
159C2×Dic11⋊C4—21no—
160C2×Dic11⋊C4D411yescharacteristic
161C2×C4×Dic11—21no—
162C2×C4×Dic11C2311yescharacteristic
163C22×C11⋊C8C2311yescharacteristic
164C22×C11⋊C8C2311yescharacteristic
165#66964—232no—
166#66961—232no—
167C2×D88—24no—
168C2×D88—24no—
169C2×D88C2314yes—
170C2×D88C2314yescomplemented
171C2×#4314—24no—
172C2×#4314D418yescomplemented
173C2×#4314C2314yes—
174C2×#4314C2314yescomplemented
175C2×#4313—24no—
176C2×#4313C2314yescomplemented
177#66948—22no—
178#66948—22no—
179#66948C2314yes—
180#66948C2314yescomplemented
181#66946—22no—
182#66946C2314yes—
183#66940—22no—
184#66940C2314yescomplemented
185#66937—28no—
186#66937—28no—
187#66935—28no—
188(C22⋊D11)⋊C4—28no—
189C11×#106C2314yescomplemented
190C11×#102C2314yescomplemented
191C11×#102C2314yescomplemented
192C22⋊(C11⋊C8)C2314yescomplemented
193(C2×D11)⋊C8C2314yescomplemented
194Dic11⋊C8C2314yescomplemented
195C8×Dic11C2314yescomplemented
196#66874C2314yescomplemented
197#66873C2314yes—
198#66873C2314yescomplemented
199#66873C2314yescomplemented
200C2×#3274—111nomaximal, Sylow
201C24×C11—21no—
202C24×C11—21no—
203C24×C11C2×D411yescharacteristic
204C23×D11—21no—
205C23×D11—21no—
206C23×D11—21no—
207C23×D11—24no—
208C23×D11—24no—
209C23×D11—44no—
210C23×D11—44no—
211C23×D11—44no—
212C23×D11—44no—
213C23×D11—82no—
214C23×D11—82no—
215C23×D11C2×D411yescharacteristic
216C2×D4×C11—24no—
217C2×D4×C11—24no—
218C2×D4×C11—22no—
219C2×D4×C11—22no—
220C2×D4×C11—21no—
221C2×D4×C11—21no—
222C2×D4×C11—22no—
223C2×D4×C11—22no—
224C2×D4×C11—44no—
225C2×D4×C11—82no—
226C2×D4×C11C2412yes—
227C2×D4×C11C2412yes—
228C22×C4×C11—22no—
229C22×C4×C11—22no—
230C22×C4×C11—21no—
231C22×C4×C11—21no—
232C22×C4×C11C2×D411yescharacteristic
233C22×C4×C11C2×D412yes—
234C22×C4×C11C2412yes—
235C22×C4×C11C2411yescharacteristic
236C2×C22⋊D11—24no—
237C2×C22⋊D11—24no—
238C2×C22⋊D11—24no—
239C2×C22⋊D11—24no—
240C2×C22⋊D11—24no—
241C2×C22⋊D11—24no—
242C2×C22⋊D11—24no—
243C2×C22⋊D11—24no—
244C2×C22⋊D11—44no—
245C2×C22⋊D11—44no—
246C2×C22⋊D11—44no—
247C2×C22⋊D11—44no—
248C2×C22⋊D11—44no—
249C2×C22⋊D11—82no—
250C2×C22⋊D11—82no—
251C2×C22⋊D11C2×D414yes—
252C22×Dic11—24no—
253C22×Dic11—21no—
254C22×Dic11—44no—
255C22×Dic11C2×D411yescharacteristic
256C22×Dic11C2×D411yescharacteristic
257C22×Dic11C2×D411yescharacteristic
258#4341—28no—
259#4341—44no—
260#4341—48no—
261D4×D11—28no—
262D4×D11—44no—
263D4×D11—48no—
264D4×D11—432no—
265#4339—28no—
266#4339—44no—
267#4339—48no—
268C2×D44—24no—
269C2×D44—24no—
270C2×D44—28no—
271C2×D44—21no—
272C2×D44—24no—
273C2×D44—21no—
274C2×D44—21no—
275C2×D44—22no—
276C2×D44—22no—
277C2×D44—22no—
278C2×D44—22no—
279C2×D44—22no—
280C2×D44—44no—
281C2×D44—44no—
282C2×D44—48no—
283C2×D44—44no—
284C2×D44—82no—
285C2×D44C2×D414yes—
286C2×D44C2412yes—
287C2×D44C2412yes—
288C2×D44C2412yes—
289C2×C4×D11—24no—
290C2×C4×D11—22no—
291C2×C4×D11—24no—
292C2×C4×D11—22no—
293C2×C4×D11—44no—
294C2×C4×D11—44no—
295C2×C4×D11C2×D412yes—
296C2×C4×D11C2412yes—
297C2×Dic22—21no—
298C2×Dic22—22no—
299C2×Dic22C2×D414yescomplemented
300C2×Dic22C2412yes—
301C11×D8—28no—
302C11×M16—28no—
303C2×C8×C11—22no—
304C2×C8×C11C2×D414yescomplemented
305C2×C8×C11C2412yes—
306C2×C8×C11C2412yes—
307C11×C4⋊C4—21no—
308C11×C4⋊C4—21no—
309C11×C4⋊C4C2412yes—
310C11×C4⋊C4C2412yes—
311C11×C22⋊C4—24no—
312C11×C22⋊C4—24no—
313C22⋊Dic11C2×D414yes—
314#4324—28no—
315#4323—28no—
316#4323—44no—
317#4323—44no—
318(C2×D11)⋊C4—24no—
319(C2×D11)⋊C4—24no—
320(C2×D11)⋊C4—24no—
321(C2×D11)⋊C4C2×D414yes—
322Dic11⋊C4—24no—
323Dic11⋊C4C2×D414yes—
324C4×Dic11—24no—
325C4×Dic11C2×D412yes—
326C4×Dic11C2412yes—
327C2×C11⋊C8—22no—
328C2×C11⋊C8—22no—
329C2×C11⋊C8C2412yes—
330C2×C11⋊C8C2412yes—
331D88—28no—
332D88—28no—
333#4314—28no—
334#4314C2×D4116yescomplemented
335#4313—28no—
336C22×AGL(1,ℤ/8)—111no—
337C22×AGL(1,ℤ/8)—111no—
338C2×#550—111no—
339C2×D42—111no—
340#3274—1116no—
341C2×#493—111no—
342C2×#469—111no—
343C2×#469D1111yescharacteristic, complemented
344C2×#460—111no—
345C2×#459—111no—
346C2×#449—111no—
347C2×#449—111no—
348C2×#447—111no—
349C2×#447—111no—
350C2×C4×SD16—111no—
351C2×#436—111no—
352C23×C11—22no—
353C23×C11—22no—
354C23×C11—22no—
355C23×C11—22no—
356C23×C11—22no—
357C23×C11—42no—
358C23×C11—42no—
359C23×C11—42no—
360C23×C11—42no—
361C23×C11—42no—
362C23×C11—42no—
363C23×C11C22×D412yes—
364C23×C11C22×D411yescharacteristic
365C22×D11—22no—
366C22×D11—24no—
367C22×D11—22no—
368C22×D11—22no—
369C22×D11—22no—
370C22×D11—22no—
371C22×D11—22no—
372C22×D11—48no—
373C22×D11—48no—
374C22×D11—48no—
375C22×D11—42no—
376C22×D11—42no—
377C22×D11—48no—
378C22×D11—42no—
379C22×D11—42no—
380C22×D11—42no—
381C22×D11—42no—
382C22×D11—42no—
383C22×D11—42no—
384C22×D11—84no—
385C22×D11—84no—
386C22×D11—816no—
387C22×D11—816no—
388C22×D11C22×D412yes—
389D4×C11—22no—
390D4×C11—22no—
391D4×C11—22no—
392D4×C11—22no—
393D4×C11—48no—
394D4×C11—42no—
395D4×C11—42no—
396D4×C11—84no—
397C2×C4×C11—22no—
398C2×C4×C11—24no—
399C2×C4×C11—22no—
400C2×C4×C11—22no—
401C2×C4×C11—22no—
402C2×C4×C11—22no—
403C2×C4×C11—42no—
404C2×C4×C11—42no—
405C2×C4×C11C22×D412yes—
406C2×C4×C11C22×D411yescharacteristic
407C2×C4×C11C22×D412yes—
408C2×C4×C11H(5,𝔽2)12yes—
409C2×C4×C11C2511yescharacteristic
410C22⋊D11—28no—
411C22⋊D11—48no—
412C22⋊D11—48no—
413C22⋊D11—48no—
414C22⋊D11—48no—
415C22⋊D11—48no—
416C22⋊D11—84no—
417C22⋊D11—84no—
418C2×Dic11—24no—
419C2×Dic11—22no—
420C2×Dic11—22no—
421C2×Dic11—22no—
422C2×Dic11—48no—
423C2×Dic11AGL(1,ℤ/8)14yescomplemented
424C2×Dic11C22×D412yes—
425C2×Dic11C22×D412yes—
426C2×Dic11C22×D412yes—
427D44—24no—
428D44—22no—
429D44—22no—
430D44—22no—
431D44—22no—
432D44—22no—
433D44—48no—
434D44—48no—
435D44—42no—
436D44—42no—
437D44—84no—
438D44C22×D414yes—
439C4×D11—24no—
440C4×D11—22no—
441C4×D11—22no—
442C4×D11—48no—
443C4×D11—48no—
444Dic22—24no—
445Dic22—22no—
446Dic22C22×D414yescomplemented
447C8×C11—22no—
448C8×C11C22×D414yescomplemented
449C11⋊C8—22no—
450C11⋊C8—22no—
451C22×#41—111no—
452C22×#41—111no—
453C23×D4—111no—
454C23×D4—111no—
455C23×D4—221no—
456C2×AGL(1,ℤ/8)—118no—
457C2×AGL(1,ℤ/8)—118no—
458C2×AGL(1,ℤ/8)—228no—
459C2×AGL(1,ℤ/8)—228no—
460C22×SD16—111no—
461C22×SD16—111no—
462C22×SD16—111no—
463C22×D8—111no—
464C22×D8—111no—
465C22×D8—111no—
466C22×D8—111no—
467C22×D8—111no—
468C22×D8C2×D1111yescharacteristic, complemented
469C22×M16—111no—
470C22×M16C2×D1111yescharacteristic, complemented
471#550—118no—
472#550—224no—
473D42—118no—
474D42—224no—
475C2×#127—111no—
476C2×#127—111no—
477C2×#127—221no—
478C2×#121—111no—
479C2×#121—111no—
480C2×#121—221no—
481C2×#121—221no—
482C2×#121—221no—
483C2×#121C2×D1111yescharacteristic
484C2×#121C2×D1111yescharacteristic, complemented
485C2×#120—221no—
486C2×#120—221no—
487C2×C4×Q8—111no—
488C2×C4×D4—111no—
489C2×C4×D4—111no—
490C2×C4×D4—221no—
491#493—118no—
492#469—118no—
493#469C2×D1118yescomplemented
494#460—118no—
495#459—118no—
496#449—118no—
497#449—118no—
498#447—118no—
499#447—118no—
500C4×SD16—118no—
501#436—118no—
502C2×#106C2×D1111yescharacteristic, complemented
503C2×C4⋊C8—111no—
504C2×#103—111no—
505C2×#102—111no—
506C2×#102—111no—
507C2×#102—111no—
508C2×#102C2×D1111yescharacteristic, complemented
509C2×#102C2×D1111yescharacteristic, complemented
510C2×C22⋊C8—111no—
511C2×C22⋊C8—111no—
512C2×C4×C8—111no—
513C22×C11—22no—
514C22×C11—22no—
515C22×C11—22no—
516C22×C11—44no—
517C22×C11—42no—
518C22×C11—42no—
519C22×C11—42no—
520C22×C11—42no—
521C22×C11—42no—
522C22×C11—42no—
523C22×C11—84no—
524C22×C11—84no—
525C22×C11D4212yes—
526C22×C11C2×AGL(1,ℤ/8)12yes—
527C22×C11#57612yes—
528C22×C11C23×D411yescharacteristic
529C2×D11—24no—
530C2×D11—22no—
531C2×D11—22no—
532C2×D11—22no—
533C2×D11—44no—
534C2×D11—48no—
535C2×D11—42no—
536C2×D11—42no—
537C2×D11—42no—
538C2×D11—42no—
539C2×D11—42no—
540C2×D11—42no—
541C2×D11—42no—
542C2×D11—42no—
543C2×D11—816no—
544C2×D11—816no—
545C2×D11—84no—
546C2×D11—84no—
547C4×C11—22no—
548C4×C11—42no—
549C4×C11—42no—
550C4×C11D4212yes—
551C4×C11C23×D411yescharacteristic
552C4×C11C2×H(5,𝔽2)11yescharacteristic
553Dic11—24no—
554Dic11—22no—
555Dic11—22no—
556Dic11C2×AGL(1,ℤ/8)14yescomplemented
557C25—221no—
558C25—221no—
559C2×#41—114no—
560C2×#41—114no—
561C2×#41—224no—
562C2×#41—222no—
563C2×#41—222no—
564C2×#41—224no—
565C2×#41—442no—
566C2×#41—442no—
567C22×Q8—111no—
568C22×D4—21no—
569C22×D4—21no—
570C22×D4—111no—
571C22×D4—114no—
572C22×D4—111no—
573C22×D4—111no—
574C22×D4—111no—
575C22×D4—114no—
576C22×D4—224no—
577C22×D4—221no—
578C22×D4—221no—
579C22×D4—222no—
580C22×D4—221no—
581C22×D4—221no—
582C22×D4—221no—
583C22×D4—221no—
584C22×D4—221no—
585C22×D4—224no—
586C22×D4—228no—
587C22×D4—221no—
588C22×D4—221no—
589C22×D4—221no—
590C22×D4—222no—
591C22×D4—442no—
592C22×D4—442no—
593C22×D4—448no—
594C22×D4C22×D1111yescharacteristic
595C22×D4C22×D1111yescharacteristic
596C23×C4—111no—
597C23×C4—221no—
598C23×C4—221no—
599C23×C4—221no—
600C23×C4C22×D1111yescharacteristic
601AGL(1,ℤ/8)—2232no—
602AGL(1,ℤ/8)—2232no—
603C2×SD16—114no—
604C2×SD16—118no—
605C2×SD16—114no—
606C2×SD16—114no—
607C2×SD16—224no—
608C2×SD16—224no—
609C2×D8—24no—
610C2×D8—114no—
611C2×D8—114no—
612C2×D8—114no—
613C2×D8—114no—
614C2×D8—114no—
615C2×D8—224no—
616C2×D8—224no—
617C2×D8—224no—
618C2×D8—442no—
619C2×D8—442no—
620C2×D8C22×D1114yescomplemented
621C2×M16—24no—
622C2×M16—114no—
623C2×M16—224no—
624C2×M16C22×D1114yescomplemented
625C22×C8—111no—
626C22×C8—111no—
627C22×C8C22×D1111yescharacteristic
628C22×C8C22×D1111yescharacteristic
629#127—114no—
630#127—114no—
631#127—222no—
632#127—222no—
633#127—228no—
634#121—22no—
635#121—22no—
636#121—114no—
637#121—114no—
638#121—228no—
639#121—228no—
640#121—228no—
641#121—222no—
642#121—222no—
643#121C22×D1114yes—
644#121C22×D1114yescomplemented
645#120—228no—
646#120—228no—
647C4×Q8—114no—
648C4×Q8—222no—
649C4×D4—114no—
650C4×D4—114no—
651C4×D4—114no—
652C4×D4—222no—
653C4×D4—228no—
654C2×C4⋊C4—111no—
655C2×C4⋊C4—221no—
656C2×C4⋊C4C22×D1111yescharacteristic
657C2×C4⋊C4C22×D1111yescharacteristic
658C2×C22⋊C4—21no—
659C2×C22⋊C4—21no—
660C2×C22⋊C4—111no—
661C2×C22⋊C4—111no—
662C2×C22⋊C4—221no—
663C2×C22⋊C4—221no—
664C2×C22⋊C4—221no—
665C2×C42—111no—
666C2×C42—221no—
667#106C22×D1114yescomplemented
668C4⋊C8—114no—
669#103—114no—
670#102—114no—
671#102—114no—
672#102—114no—
673#102C22×D1114yescomplemented
674#102C22×D1114yescomplemented
675C22⋊C8—114no—
676C22⋊C8—114no—
677C4×C8—114no—
678C2×C11—42no—
679C2×C11—82no—
680C2×C11—82no—
681C2×C11#327414yescomplemented
682C2×C11C2×D4211yescharacteristic
683C2×C11C22×AGL(1,ℤ/8)11yescharacteristic
684C2×C11C2×#57611yescharacteristic
685D11—42no—
686D11—44no—
687D11—82no—
688D11—82no—
689C24—21no—
690C24—21no—
691C24—111no—
692C24—224no—
693C24—221no—
694C24—221no—
695C24—221no—
696C24—224no—
697C24—444no—
698C24—444no—
699C24—444no—
700C24—444no—
701C24—882no—
702C24—882no—
703C24D4×D1111yescharacteristic
704#41—228no—
705#41—228no—
706#41—444no—
707#41—448no—
708#41—444no—
709#41—448no—
710C2×Q8—114no—
711C2×Q8—112no—
712C2×Q8—221no—
713C2×Q8—222no—
714C2×D4—24no—
715C2×D4—24no—
716C2×D4—22no—
717C2×D4—22no—
718C2×D4—21no—
719C2×D4—21no—
720C2×D4—22no—
721C2×D4—22no—
722C2×D4—44no—
723C2×D4—82no—
724C2×D4—114no—
725C2×D4—114no—
726C2×D4—112no—
727C2×D4—112no—
728C2×D4—112no—
729C2×D4—228no—
730C2×D4—224no—
731C2×D4—224no—
732C2×D4—224no—
733C2×D4—224no—
734C2×D4—224no—
735C2×D4—224no—
736C2×D4—224no—
737C2×D4—224no—
738C2×D4—228no—
739C2×D4—224no—
740C2×D4—224no—
741C2×D4—221no—
742C2×D4—222no—
743C2×D4—222no—
744C2×D4—224no—
745C2×D4—221no—
746C2×D4—221no—
747C2×D4—222no—
748C2×D4—222no—
749C2×D4—222no—
750C2×D4—444no—
751C2×D4—448no—
752C2×D4—444no—
753C2×D4—444no—
754C2×D4—444no—
755C2×D4—444no—
756C2×D4—444no—
757C2×D4—448no—
758C2×D4—444no—
759C2×D4—444no—
760C2×D4—444no—
761C2×D4—4432no—
762C2×D4—882no—
763C2×D4—882no—
764C2×D4—882no—
765C2×D4C23×D1112yes—
766C2×D4C23×D1112yes—
767C22×C4—22no—
768C22×C4—22no—
769C22×C4—21no—
770C22×C4—21no—
771C22×C4—111no—
772C22×C4—111no—
773C22×C4—111no—
774C22×C4—112no—
775C22×C4—112no—
776C22×C4—224no—
777C22×C4—224no—
778C22×C4—221no—
779C22×C4—222no—
780C22×C4—222no—
781C22×C4—224no—
782C22×C4—444no—
783C22×C4—444no—
784C22×C4—444no—
785C22×C4D4×D1112yes—
786C22×C4D4×D1111yescharacteristic
787C22×C4C23×D1112yes—
788C22×C4C23×D1111yescharacteristic
789SD16—1116no—
790SD16—228no—
791SD16—228no—
792D8—28no—
793D8—228no—
794D8—228no—
795D8—228no—
796D8—444no—
797D8—444no—
798M16—28no—
799M16—228no—
800C2×C8—22no—
801C2×C8—112no—
802C2×C8—112no—
803C2×C8—222no—
804C2×C8—222no—
805C2×C8D4×D1114yescomplemented
806C2×C8C23×D1112yes—
807C2×C8C23×D1112yes—
808C4⋊C4—21no—
809C4⋊C4—21no—
810C4⋊C4—114no—
811C4⋊C4—224no—
812C4⋊C4C23×D1112yes—
813C4⋊C4C23×D1112yes—
814C22⋊C4—24no—
815C22⋊C4—24no—
816C22⋊C4—114no—
817C22⋊C4—114no—
818C22⋊C4—224no—
819C22⋊C4—224no—
820C22⋊C4—224no—
821C42—112no—
822C42—112no—
823C42—224no—
824C11C2×#327411yescharacteristic, complemented, Sylow
825C23—22no—
826C23—22no—
827C23—22no—
828C23—22no—
829C23—22no—
830C23—42no—
831C23—42no—
832C23—42no—
833C23—42no—
834C23—42no—
835C23—42no—
836C23—112no—
837C23—222no—
838C23—222no—
839C23—222no—
840C23—224no—
841C23—222no—
842C23—222no—
843C23—222no—
844C23—448no—
845C23—448no—
846C23—448no—
847C23—448no—
848C23—442no—
849C23—442no—
850C23—442no—
851C23—442no—
852C23—442no—
853C23—442no—
854C23—442no—
855C23—442no—
856C23—884no—
857C23—884no—
858C23—8816no—
859C23—8816no—
860C23C2×D4×D1112yes—
861C23C2×D4×D1111yescharacteristic
862Q8—114no—
863Q8—224no—
864Q8—222no—
865D4—22no—
866D4—22no—
867D4—22no—
868D4—22no—
869D4—48no—
870D4—42no—
871D4—42no—
872D4—84no—
873D4—114no—
874D4—228no—
875D4—224no—
876D4—222no—
877D4—222no—
878D4—222no—
879D4—222no—
880D4—222no—
881D4—448no—
882D4—448no—
883D4—448no—
884D4—448no—
885D4—448no—
886D4—448no—
887D4—448no—
888D4—442no—
889D4—442no—
890D4—884no—
891D4—884no—
892D4—884no—
893C2×C4—22no—
894C2×C4—24no—
895C2×C4—22no—
896C2×C4—22no—
897C2×C4—22no—
898C2×C4—22no—
899C2×C4—42no—
900C2×C4—42no—
901C2×C4—114no—
902C2×C4—112no—
903C2×C4—112no—
904C2×C4—112no—
905C2×C4—222no—
906C2×C4—222no—
907C2×C4—224no—
908C2×C4—222no—
909C2×C4—224no—
910C2×C4—222no—
911C2×C4—222no—
912C2×C4—448no—
913C2×C4—448no—
914C2×C4—448no—
915C2×C4C2×D4×D1112yes—
916C2×C4C2×D4×D1111yescharacteristic
917C2×C4C2×D4×D1112yes—
918C2×C4#6704212yes—
919C2×C4C24×D1111yescharacteristic
920C8—22no—
921C8—222no—
922C8—222no—
923C8C2×D4×D1114yescomplemented
924C22—22no—
925C22—22no—
926C22—22no—
927C22—44no—
928C22—42no—
929C22—42no—
930C22—42no—
931C22—42no—
932C22—42no—
933C22—42no—
934C22—84no—
935C22—84no—
936C22—222no—
937C22—224no—
938C22—222no—
939C22—222no—
940C22—444no—
941C22—448no—
942C22—442no—
943C22—442no—
944C22—442no—
945C22—442no—
946C22—442no—
947C22—442no—
948C22—442no—
949C22—442no—
950C22—8816no—
951C22—8816no—
952C22—884no—
953C22—884no—
954C22#1062314012yes—
955C22D11×AGL(1,ℤ/8)12yes—
956C22#1062330512yes—
957C22C22×D4×D1111yescharacteristic
958C4—22no—
959C4—42no—
960C4—42no—
961C4—114no—
962C4—222no—
963C4—224no—
964C4—222no—
965C4#1062314012yes—
966C4C22×D4×D1111yescharacteristic
967C4C2×#6704211yescharacteristic
968C2—42no—
969C2—82no—
970C2—82no—
971C2—442no—
972C2—444no—
973C2—882no—
974C2—882no—
975C2#1308023314yesdirect product factor
976C2C2×#1062314011yescharacteristic
977C2C2×D11×AGL(1,ℤ/8)11yescharacteristic
978C2C2×#1062330511yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#469C2
socleC23×C11C22×D4
hypercenterC2×#469D11
hypocenterC11C2×#3274
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#469

Complements

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

NH ≅ G/Ntype
1. C22×#66961C2semidirect
2. C22×#66964C2semidirect
3. C2×#10623130C2semidirect
4. C2×#10623140C2semidirect
5. #13080233C2direct (N × H)
6. C2×#10622764C2semidirect
7. C2×#10622478C2semidirect
8. C2×#10622375C2semidirect
9. C2×#10622399C2semidirect
10. C2×#10622394C2semidirect
11. C2×#10622650C2semidirect
12. C2×#10622386C2semidirect
13. C2×#10622649C2semidirect
14. C2×#10622465C2semidirect
15. C2×#10622741C2semidirect
16. C2×C11×#469C2semidirect
17. C22×#4341C22semidirect
20. C22×#4339C22semidirect
22. C22×C11×D8C22semidirect
23. C22×C11×M16C22semidirect
25. C2×C11×#121C22semidirect
28. C2×#66993C22semidirect
31. C22×#4324C22semidirect
33. C22×#4323C22semidirect
34. C22×#4323C22semidirect
37. C2×#66964C22semidirect
39. C2×#66961C22semidirect
41. C22×D88C22semidirect
43. C22×#4314C22semidirect
44. C22×#4313C22semidirect
46. #10623140C22semidirect
48. #10623130C22semidirect
50. C2×#66948C22semidirect
52. C2×#66940C22semidirect
57. C11×#469C22semidirect
58. C2×C11×#106C22semidirect
59. C2×C11×#102C22semidirect
60. C2×C11×#102C22semidirect
61. C2×C22⋊(C11⋊C8)C22semidirect
62. #10622764C22semidirect
63. #10622741C22semidirect
64. C2×(C2×D11)⋊C8C22semidirect
65. C2×Dic11⋊C8C22semidirect
66. C2×C8×Dic11C22semidirect
67. #10622650C22semidirect
68. #10622649C22semidirect
69. C2×#66874C22semidirect
71. C2×#66873C22semidirect
72. C2×#66873C22semidirect
73. #10622478C22semidirect
74. #10622465C22semidirect
75. #10622399C22semidirect
76. #10622394C22semidirect
77. #10622386C22semidirect
78. #10622375C22semidirect
98. C2×#4341C23semidirect
108. C2×#4339C23semidirect
124. C2×C11×D8C23semidirect
126. C2×C11×M16C23semidirect
132. C11×#121C23semidirect
142. #66993C23semidirect
146. C2×#4324C23semidirect
151. C2×#4323C23semidirect
152. C2×#4323C23semidirect
170. C2×D88C23semidirect
172. C2×#4314D4semidirect
174. C2×#4314C23semidirect
176. C2×#4313C23semidirect
180. #66948C23semidirect
184. #66940C23semidirect
189. C11×#106C23semidirect
190. C11×#102C23semidirect
191. C11×#102C23semidirect
192. C22⋊(C11⋊C8)C23semidirect
193. (C2×D11)⋊C8C23semidirect
194. Dic11⋊C8C23semidirect
195. C8×Dic11C23semidirect
196. #66874C23semidirect
198. #66873C23semidirect
199. #66873C23semidirect
299. C2×Dic22C2×D4semidirect
304. C2×C8×C11C2×D4semidirect
334. #4314C2×D4semidirect
343. C2×#469D11semidirect
423. C2×Dic11AGL(1,ℤ/8)semidirect
446. Dic22C22×D4semidirect
448. C8×C11C22×D4semidirect
468. C22×D8C2×D11semidirect
470. C22×M16C2×D11semidirect
484. C2×#121C2×D11semidirect
493. #469C2×D11semidirect
502. C2×#106C2×D11semidirect
508. C2×#102C2×D11semidirect
509. C2×#102C2×D11semidirect
556. Dic11C2×AGL(1,ℤ/8)semidirect
620. C2×D8C22×D11semidirect
624. C2×M16C22×D11semidirect
644. #121C22×D11semidirect
667. #106C22×D11semidirect
673. #102C22×D11semidirect
674. #102C22×D11semidirect
681. C2×C11#3274semidirect
805. C2×C8D4×D11semidirect
824. C11C2×#3274semidirect
923. C8C2×D4×D11semidirect
975. C2#13080233direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669612
C22×#669642
C2×#106231302
C2×#106231402
#130802332
C2×#106227642
C2×#106224782
C2×#106223752
C2×#106223992
C2×#106223942
C2×#106226502
C2×#106223862
C2×#106226492
C2×#106224652
C2×#106227412
C2×C11×#4692
C2×#327411