Finite Group Databasebeta

← C2×#13080241 #15628897

Subgroups — C2×#13080241 #15628897

Order 2816.

2902 conjugacy classes of subgroups.

The subgroup lattice has 916 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66967C211yesmaximal, characteristic, complemented
2C2×#10623348C211yesmaximal, characteristic, complemented
3C2×#10623360C211yesmaximal, characteristic, complemented
4#13080241C2116yesmaximal, direct product factor
5C2×#10622804C211yesmaximal, characteristic, complemented
6C2×#10622802C211yesmaximal, characteristic, complemented
7C2×#10622748C211yesmaximal, characteristic, complemented
8C2×#10622798C211yesmaximal, characteristic, complemented
9C2×#10622778C211yesmaximal, characteristic, complemented
10C2×#10622800C211yesmaximal, characteristic, complemented
11C2×#10622851C211yesmaximal, characteristic, complemented
12C2×#10622840C211yesmaximal, characteristic, complemented
13C2×#10622782C211yesmaximal, characteristic, complemented
14C2×SD16×Dic11C211yesmaximal, characteristic, complemented
15C2×#10622741C211yesmaximal, characteristic, complemented
16C22×C11×#137C211yesmaximal, characteristic, complemented
17C22×C11×#41C2211yescharacteristic
18C23×Q8×C11C2211yescharacteristic, complemented
19C22×#4343C2211yescharacteristic
20C22×D4×D11C2211yescharacteristic
21C2×C11×#137—28no—
22C2×C11×#137C2218yescomplemented
23C22×C11×Q16C2211yescharacteristic, complemented
24C22×C11×Q16C2211yescharacteristic, complemented
25C22×C11×SD16C2211yescharacteristic
26C22×C11×SD16C2211yescharacteristic
27C22×C11×M16C2211yescharacteristic, complemented
28#10623360—24no—
29#10623360C2218yescomplemented
30#10623348—24no—
31#10623348C2218yescomplemented
32C2×#67000—21no—
33C2×#67000C2211yescharacteristic
34C2×#67000C2211yescharacteristic, complemented
35C2×#66999—21no—
36C2×#66999C2211yescharacteristic
37C2×#66999C2211yescharacteristic
38C2×Q8×Dic11C2211yescharacteristic, complemented
39C22×#4325C2211yescharacteristic
40C22×#4325C2211yescharacteristic
41C22×#4325C2211yescharacteristic, complemented
42C2×#66992—21no—
43C2×#66990—21no—
44C2×D4×Dic11C2211yescharacteristic
45C22×#4323C2211yescharacteristic
46C2×#66983—21no—
47C2×#66983C2211yescharacteristic
48C2×#66983C2211yescharacteristic, complemented
49C2×#66982—21no—
50C2×C4×C22⋊D11—21no—
51C2×C4×C22⋊D11C2211yescharacteristic
52C22×(C2×D11)⋊C4—21no—
53C2×#66967—28no—
54C2×#66967C2218yescomplemented
55C22×D88C2211yescharacteristic
56C22×#4313C2211yescharacteristic
57#10622851C2218yescomplemented
58#10622840C2218yescomplemented
59C2×#66899C2211yescharacteristic, complemented
60C2×#66899C2211yescharacteristic, complemented
61C2×#66899C2211yescharacteristic, complemented
62C2×#66896C2211yescharacteristic
63C2×C22⋊(C11⋊C8)C2211yescharacteristic, complemented
64#10622804C2218yescomplemented
65#10622802C2218yescomplemented
66#10622800C2218yescomplemented
67#10622798C2218yescomplemented
68#10622782C2218yescomplemented
69#10622778C2218yescomplemented
70SD16×Dic11C2218yescomplemented
71#10622748C2218yescomplemented
72#10622741C2218yescomplemented
73C2×#66885C2211yescharacteristic
74C2×#66885C2211yescharacteristic, complemented
75C2×(C2×D11)⋊C8C2211yescharacteristic
76C2×#66881C2211yescharacteristic, complemented
77C2×Dic11⋊C8C2211yescharacteristic, complemented
78C2×C8×Dic11C2211yescharacteristic, complemented
79C24×D11—21no—
80C2×C11×#41—22no—
81C2×C11×#41—24no—
82C2×C11×#41—42no—
83C2×C11×#41C2314yes—
84C22×Q8×C11—21no—
85C22×Q8×C11—22no—
86C22×Q8×C11—24no—
87C22×Q8×C11—42no—
88C22×Q8×C11C2311yescharacteristic
89C22×Q8×C11C2311yescharacteristic
90C22×Q8×C11C2311yescharacteristic
91C22×Q8×C11C2314yescomplemented
92C22×D4×C11—21no—
93C22×D4×C11C2311yescharacteristic
94C23×C4×C11—21no—
95C23×C4×C11—21no—
96C23×C4×C11C2311yescharacteristic
97C22×C22⋊D11—21no—
98C22×C22⋊D11—21no—
99C22×C22⋊D11—21no—
100C22×C22⋊D11D411yescharacteristic
101C23×Dic11—21no—
102C2×#4343—22no—
103C2×#4343—24no—
104C2×#4343—42no—
105C2×#4343C2314yes—
106C2×D4×D11—24no—
107C2×D4×D11—22no—
108C2×D4×D11—42no—
109C2×D4×D11C2314yes—
110C22×D44—21no—
111C22×D44C2311yescharacteristic
112C22×D44C2311yescharacteristic
113C22×C4×D11—21no—
114C22×C4×D11C2311yescharacteristic
115C11×#137—232no—
116C2×C11×Q16—24no—
117C2×C11×Q16—24no—
118C2×C11×Q16C2314yescomplemented
119C2×C11×Q16C2314yescomplemented
120C2×C11×SD16—24no—
121C2×C11×SD16D418yescomplemented
122C2×C11×SD16C2314yes—
123C2×C11×SD16C2314yes—
124C2×C11×M16—24no—
125C2×C11×M16C2314yescomplemented
126C22×C8×C11C2311yescharacteristic
127C22×C8×C11C2311yescharacteristic
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11D411yescharacteristic
130#67000—28no—
131#67000—22no—
132#67000—22no—
133#67000C2314yes—
134#67000C2314yescomplemented
135#66999—22no—
136#66999—22no—
137#66999—28no—
138#66999C2314yes—
139#66999C2314yes—
140Q8×Dic11—22no—
141Q8×Dic11C2314yescomplemented
142C2×#4325—24no—
143C2×#4325—42no—
144C2×#4325—42no—
145C2×#4325C2314yes—
146C2×#4325C2314yes—
147C2×#4325C2314yescomplemented
148#66992—28no—
149#66990—28no—
150D4×Dic11—22no—
151D4×Dic11C2314yes—
152C2×#4323—24no—
153C2×#4323C2314yes—
154#66983—22no—
155#66983—22no—
156#66983—28no—
157#66983C2314yes—
158#66983C2314yescomplemented
159#66982—28no—
160C4×C22⋊D11—28no—
161C4×C22⋊D11D414yes—
162C4×C22⋊D11C2314yes—
163C2×(C2×D11)⋊C4—21no—
164C2×(C2×D11)⋊C4—21no—
165C2×(C2×D11)⋊C4—21no—
166C2×(C2×D11)⋊C4—21no—
167C2×(C2×D11)⋊C4—21no—
168C2×(C2×D11)⋊C4—21no—
169C2×(C2×D11)⋊C4—21no—
170C2×(C2×D11)⋊C4—21no—
171C2×(C2×D11)⋊C4—28no—
172C2×(C2×D11)⋊C4D411yescharacteristic
173C2×C4⋊Dic11—21no—
174C2×C4⋊Dic11C2311yescharacteristic
175C2×C4⋊Dic11C2311yescharacteristic
176C2×Dic11⋊C4—21no—
177C2×Dic11⋊C4—21no—
178C2×Dic11⋊C4D411yescharacteristic
179C2×C4×Dic11—21no—
180C2×C4×Dic11C2311yescharacteristic
181C22×C11⋊C8C2311yescharacteristic
182C22×C11⋊C8C2311yescharacteristic
183#66967—232no—
184C2×D88—24no—
185C2×D88C2314yes—
186C2×#4313—24no—
187C2×#4313C2314yes—
188#66899C2314yescomplemented
189#66899C2314yescomplemented
190#66899C2314yescomplemented
191#66896C2314yes—
192C22⋊(C11⋊C8)C2314yescomplemented
193#66885C2314yes—
194#66885C2314yescomplemented
195(C2×D11)⋊C8C2314yes—
196#66881C2314yescomplemented
197Dic11⋊C8C2314yescomplemented
198C8×Dic11C2314yescomplemented
199C2×#3275—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C23×D11—21no—
204C23×D11—24no—
205C23×D11—44no—
206C23×D11—44no—
207C23×D11—82no—
208C23×D11C2×D411yescharacteristic
209C11×#41—28no—
210C11×#41—44no—
211C11×#41—48no—
212C2×Q8×C11—21no—
213C2×Q8×C11—21no—
214C2×Q8×C11—24no—
215C2×Q8×C11—21no—
216C2×Q8×C11—22no—
217C2×Q8×C11—28no—
218C2×Q8×C11—22no—
219C2×Q8×C11—22no—
220C2×Q8×C11—22no—
221C2×Q8×C11—22no—
222C2×Q8×C11—44no—
223C2×Q8×C11—44no—
224C2×Q8×C11—48no—
225C2×Q8×C11C2×D414yes—
226C2×Q8×C11C2412yes—
227C2×Q8×C11C2412yes—
228C2×Q8×C11C2412yes—
229C2×D4×C11—24no—
230C2×D4×C11—21no—
231C2×D4×C11—22no—
232C2×D4×C11—44no—
233C2×D4×C11C2×D414yes—
234C2×D4×C11C2412yes—
235C22×C4×C11—21no—
236C22×C4×C11—22no—
237C22×C4×C11—22no—
238C22×C4×C11—21no—
239C22×C4×C11—21no—
240C22×C4×C11—24no—
241C22×C4×C11—24no—
242C22×C4×C11—44no—
243C22×C4×C11—44no—
244C22×C4×C11C2×D411yescharacteristic
245C22×C4×C11C2×D412yes—
246C22×C4×C11C2412yes—
247C22×C4×C11C2411yescharacteristic
248C2×C22⋊D11—24no—
249C2×C22⋊D11—24no—
250C2×C22⋊D11—24no—
251C2×C22⋊D11—42no—
252C2×C22⋊D11—44no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11—82no—
255C2×C22⋊D11C2×D414yes—
256C22×Dic11—24no—
257C22×Dic11—21no—
258C22×Dic11—21no—
259C22×Dic11—82no—
260C22×Dic11C2×D411yescharacteristic
261C22×Dic11C2×D411yescharacteristic
262C22×Dic11C2×D411yescharacteristic
263#4343—28no—
264#4343—44no—
265#4343—48no—
266D4×D11—28no—
267D4×D11—44no—
268D4×D11—48no—
269C2×D44—24no—
270C2×D44—21no—
271C2×D44—21no—
272C2×D44—22no—
273C2×D44—22no—
274C2×D44—22no—
275C2×D44—22no—
276C2×D44—44no—
277C2×D44C2412yes—
278C2×D44C2412yes—
279C2×C4×D11—24no—
280C2×C4×D11—22no—
281C2×C4×D11—22no—
282C2×C4×D11—44no—
283C2×C4×D11C2×D412yes—
284C2×C4×D11C2412yes—
285C11×Q16—28no—
286C11×Q16—28no—
287C11×SD16—28no—
288C11×SD16C2×D4116yescomplemented
289C11×M16—28no—
290C2×C8×C11—22no—
291C2×C8×C11C2×D414yes—
292C2×C8×C11C2412yes—
293C2×C8×C11C2412yes—
294C22⋊Dic11—24no—
295C22⋊Dic11C2×D414yes—
296#4325—28no—
297#4325—44no—
298#4325—44no—
299#4323—28no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4—24no—
302(C2×D11)⋊C4—24no—
303(C2×D11)⋊C4—24no—
304(C2×D11)⋊C4—24no—
305(C2×D11)⋊C4—24no—
306(C2×D11)⋊C4—24no—
307(C2×D11)⋊C4—24no—
308(C2×D11)⋊C4C2×D414yes—
309C4⋊Dic11—24no—
310C4⋊Dic11—21no—
311C4⋊Dic11—21no—
312C4⋊Dic11C2412yes—
313C4⋊Dic11C2412yes—
314Dic11⋊C4—24no—
315Dic11⋊C4—24no—
316Dic11⋊C4C2×D414yes—
317C4×Dic11—24no—
318C4×Dic11C2×D412yes—
319C4×Dic11C2412yes—
320C2×C11⋊C8—22no—
321C2×C11⋊C8—22no—
322C2×C11⋊C8C2412yes—
323C2×C11⋊C8C2412yes—
324D88—28no—
325#4313—28no—
326C22×#137D1111yescharacteristic, complemented
327C22×AGL(1,ℤ/8)—111no—
328C2×#548—111no—
329C2×#546—111no—
330#3275—1116no—
331C2×#495—111no—
332C2×#470—111no—
333C2×#469—111no—
334C2×#464—111no—
335C2×#463—111no—
336C2×#452—111no—
337C2×#449—111no—
338C2×#448—111no—
339C2×#450—111no—
340C2×C4×SD16—111no—
341C2×#436—111no—
342C23×C11—24no—
343C23×C11—22no—
344C23×C11—22no—
345C23×C11—22no—
346C23×C11—22no—
347C23×C11—42no—
348C23×C11—42no—
349C23×C11C22×D412yes—
350C23×C11C22×D411yescharacteristic
351C22×D11—22no—
352C22×D11—22no—
353C22×D11—22no—
354C22×D11—22no—
355C22×D11—22no—
356C22×D11—48no—
357C22×D11—48no—
358C22×D11—42no—
359C22×D11—42no—
360C22×D11—42no—
361C22×D11—42no—
362C22×D11—42no—
363C22×D11—42no—
364C22×D11—84no—
365C22×D11—816no—
366C22×D11C22×D412yes—
367Q8×C11—24no—
368Q8×C11—22no—
369Q8×C11—22no—
370Q8×C11—22no—
371Q8×C11—22no—
372Q8×C11—22no—
373Q8×C11—48no—
374Q8×C11—42no—
375Q8×C11—42no—
376Q8×C11C22×D414yes—
377D4×C11—24no—
378D4×C11—22no—
379D4×C11—48no—
380D4×C11C22×D414yes—
381C2×C4×C11—24no—
382C2×C4×C11—22no—
383C2×C4×C11—22no—
384C2×C4×C11—24no—
385C2×C4×C11—22no—
386C2×C4×C11—22no—
387C2×C4×C11—22no—
388C2×C4×C11—22no—
389C2×C4×C11—48no—
390C2×C4×C11—48no—
391C2×C4×C11—42no—
392C2×C4×C11—42no—
393C2×C4×C11C22×D412yes—
394C2×C4×C11C22×D411yescharacteristic
395C2×C4×C11C22×D412yes—
396C2×C4×C11H(5,𝔽2)12yes—
397C2×C4×C11C2511yescharacteristic
398C22⋊D11—44no—
399C22⋊D11—48no—
400C22⋊D11—48no—
401C22⋊D11—84no—
402C2×Dic11—22no—
403C2×Dic11—22no—
404C2×Dic11—22no—
405C2×Dic11—22no—
406C2×Dic11—22no—
407C2×Dic11—42no—
408C2×Dic11—42no—
409C2×Dic11—84no—
410C2×Dic11C22×D412yes—
411C2×Dic11C22×D412yes—
412C2×Dic11C22×D412yes—
413D44—22no—
414D44—22no—
415D44—22no—
416D44—22no—
417D44—48no—
418D44—42no—
419D44—42no—
420C4×D11—24no—
421C4×D11—22no—
422C4×D11—22no—
423C4×D11—48no—
424C8×C11—22no—
425C8×C11C22×D414yes—
426C11⋊C8—22no—
427C11⋊C8—22no—
428C22×#41—111no—
429C22×#41C2×D1111yescharacteristic
430C23×Q8C2×D1111yescharacteristic, complemented
431C23×D4—111no—
432C2×#137—28no—
433C2×#137C2×D1118yescomplemented
434C2×AGL(1,ℤ/8)—118no—
435C2×AGL(1,ℤ/8)—228no—
436C22×Q16C2×D1111yescharacteristic, complemented
437C22×Q16C2×D1111yescharacteristic, complemented
438C22×SD16—111no—
439C22×SD16—111no—
440C22×SD16—111no—
441C22×SD16C2×D1111yescharacteristic
442C22×SD16C2×D1111yescharacteristic
443C22×D8—111no—
444C22×D8—111no—
445C22×M16—111no—
446C22×M16C2×D1111yescharacteristic, complemented
447#548—118no—
448#548—224no—
449#546—118no—
450#546—224no—
451C2×#124—111no—
452C2×#124—111no—
453C2×#124—221no—
454C2×#123—221no—
455C2×C22⋊Q8—111no—
456C2×C22⋊Q8—111no—
457C2×C22⋊Q8—221no—
458C2×#121—111no—
459C2×#121—111no—
460C2×#121—221no—
461C2×#121—221no—
462C2×#120—221no—
463C2×C4×Q8—111no—
464C2×C4×D4—111no—
465C2×C4×D4—111no—
466C2×C4×D4—221no—
467C22×C22⋊C4—221no—
468#495—118no—
469#470—118no—
470#469—118no—
471#464—118no—
472#463—118no—
473#452—118no—
474#450—118no—
475#449—118no—
476#448—118no—
477C4×SD16—118no—
478#436—118no—
479C2×#106—111no—
480C2×C4⋊C8—111no—
481C2×#103—111no—
482C2×#103—111no—
483C2×#103—111no—
484C2×#102—111no—
485C2×#102—111no—
486C2×#102—111no—
487C2×C22⋊C8—111no—
488C2×C22⋊C8—111no—
489C2×C4×C8—111no—
490C22×C11—22no—
491C22×C11—24no—
492C22×C11—22no—
493C22×C11—22no—
494C22×C11—48no—
495C22×C11—44no—
496C22×C11—42no—
497C22×C11—42no—
498C22×C11D4212yes—
499C22×C11#57512yes—
500C22×C11#57712yes—
501C22×C11C23×D411yescharacteristic
502C2×D11—22no—
503C2×D11—22no—
504C2×D11—22no—
505C2×D11—44no—
506C2×D11—42no—
507C2×D11—42no—
508C2×D11—42no—
509C2×D11—42no—
510C2×D11—42no—
511C2×D11—42no—
512C2×D11—816no—
513C2×D11—84no—
514C2×D11—84no—
515C4×C11—22no—
516C4×C11—24no—
517C4×C11—42no—
518C4×C11—42no—
519C4×C11D4212yes—
520C4×C11C23×D411yescharacteristic
521C4×C11C2×H(5,𝔽2)11yescharacteristic
522Dic11—22no—
523Dic11—22no—
524Dic11—22no—
525Dic11—42no—
526Dic11—42no—
527C25—221no—
528C2×#41—22no—
529C2×#41—24no—
530C2×#41—42no—
531C2×#41—114no—
532C2×#41—222no—
533C2×#41—224no—
534C2×#41—442no—
535C2×#41C22×D1114yes—
536C22×Q8—21no—
537C22×Q8—22no—
538C22×Q8—24no—
539C22×Q8—42no—
540C22×Q8C22×D1111yescharacteristic
541C22×Q8C22×D1111yescharacteristic
542C22×Q8C22×D1111yescharacteristic
543C22×Q8C22×D1114yescomplemented
544C22×D4—21no—
545C22×D4—111no—
546C22×D4—114no—
547C22×D4—111no—
548C22×D4—111no—
549C22×D4—221no—
550C22×D4—222no—
551C22×D4—221no—
552C22×D4—224no—
553C22×D4—221no—
554C22×D4—221no—
555C22×D4—442no—
556C22×D4C22×D1111yescharacteristic
557C23×C4—21no—
558C23×C4—21no—
559C23×C4—111no—
560C23×C4—221no—
561C23×C4—221no—
562C23×C4C22×D1111yescharacteristic
563#137—232no—
564AGL(1,ℤ/8)—2232no—
565C2×Q16—24no—
566C2×Q16—24no—
567C2×Q16C22×D1114yescomplemented
568C2×Q16C22×D1114yescomplemented
569C2×SD16—24no—
570C2×SD16—114no—
571C2×SD16—114no—
572C2×SD16—114no—
573C2×SD16—224no—
574C2×SD16—442no—
575C2×SD16—442no—
576C2×SD16C22⋊D1118yescomplemented
577C2×SD16C22×D1114yes—
578C2×SD16C22×D1114yes—
579C2×D8—114no—
580C2×D8—114no—
581C2×D8—224no—
582C2×D8—224no—
583C2×M16—24no—
584C2×M16—114no—
585C2×M16—224no—
586C2×M16C22×D1114yescomplemented
587C22×C8—111no—
588C22×C8—111no—
589C22×C8C22×D1111yescharacteristic
590C22×C8C22×D1111yescharacteristic
591#124—114no—
592#124—114no—
593#124—222no—
594#124—222no—
595#124—228no—
596#123—228no—
597C22⋊Q8—114no—
598C22⋊Q8—114no—
599C22⋊Q8—228no—
600C22⋊Q8—222no—
601C22⋊Q8—222no—
602#121—114no—
603#121—114no—
604#121—228no—
605#121—228no—
606#121—222no—
607#121—222no—
608#120—228no—
609C4×Q8—114no—
610C4×Q8—222no—
611C4×D4—114no—
612C4×D4—114no—
613C4×D4—114no—
614C4×D4—222no—
615C4×D4—228no—
616C2×C4⋊C4—111no—
617C2×C4⋊C4—111no—
618C2×C4⋊C4—111no—
619C2×C4⋊C4—221no—
620C2×C4⋊C4—221no—
621C2×C4⋊C4—221no—
622C2×C22⋊C4—111no—
623C2×C22⋊C4—111no—
624C2×C22⋊C4—228no—
625C2×C22⋊C4—221no—
626C2×C22⋊C4—221no—
627C2×C22⋊C4—221no—
628C2×C22⋊C4—221no—
629C2×C22⋊C4—221no—
630C2×C22⋊C4—221no—
631C2×C22⋊C4—221no—
632C2×C22⋊C4—221no—
633C2×C22⋊C4—221no—
634C2×C42—111no—
635C2×C42—221no—
636#106—114no—
637C4⋊C8—114no—
638#103—114no—
639#103—114no—
640#103—114no—
641#102—114no—
642#102—114no—
643#102—114no—
644C22⋊C8—114no—
645C22⋊C8—114no—
646C4×C8—114no—
647C2×C11—44no—
648C2×C11—42no—
649C2×C11#327514yescomplemented
650C2×C11C2×D4211yescharacteristic
651C2×C11C2×#57511yescharacteristic
652C2×C11C2×#57711yescharacteristic
653D11—42no—
654D11—82no—
655D11—82no—
656C24—21no—
657C24—111no—
658C24—224no—
659C24—221no—
660C24—221no—
661C24—444no—
662C24—444no—
663C24—882no—
664C24D4×D1111yescharacteristic
665#41—28no—
666#41—44no—
667#41—48no—
668#41—228no—
669#41—444no—
670#41—448no—
671C2×Q8—21no—
672C2×Q8—21no—
673C2×Q8—24no—
674C2×Q8—21no—
675C2×Q8—22no—
676C2×Q8—28no—
677C2×Q8—22no—
678C2×Q8—22no—
679C2×Q8—22no—
680C2×Q8—22no—
681C2×Q8—44no—
682C2×Q8—44no—
683C2×Q8—48no—
684C2×Q8C2×C22⋊D1114yes—
685C2×Q8C23×D1112yes—
686C2×Q8C23×D1112yes—
687C2×Q8C23×D1112yes—
688C2×D4—24no—
689C2×D4—21no—
690C2×D4—22no—
691C2×D4—44no—
692C2×D4—114no—
693C2×D4—112no—
694C2×D4—112no—
695C2×D4—224no—
696C2×D4—224no—
697C2×D4—228no—
698C2×D4—224no—
699C2×D4—224no—
700C2×D4—221no—
701C2×D4—221no—
702C2×D4—222no—
703C2×D4—222no—
704C2×D4—222no—
705C2×D4—222no—
706C2×D4—444no—
707C2×D4—444no—
708C2×D4—448no—
709C2×D4—442no—
710C2×D4—444no—
711C2×D4—444no—
712C2×D4—882no—
713C2×D4C2×C22⋊D1114yes—
714C2×D4C23×D1112yes—
715C22×C4—21no—
716C22×C4—22no—
717C22×C4—22no—
718C22×C4—24no—
719C22×C4—21no—
720C22×C4—21no—
721C22×C4—24no—
722C22×C4—44no—
723C22×C4—44no—
724C22×C4—111no—
725C22×C4—111no—
726C22×C4—111no—
727C22×C4—112no—
728C22×C4—112no—
729C22×C4—224no—
730C22×C4—224no—
731C22×C4—222no—
732C22×C4—222no—
733C22×C4—221no—
734C22×C4—221no—
735C22×C4—444no—
736C22×C4—882no—
737C22×C4D4×D1112yes—
738C22×C4D4×D1111yescharacteristic
739C22×C4C23×D1112yes—
740C22×C4C23×D1111yescharacteristic
741Q16—28no—
742Q16—28no—
743SD16—28no—
744SD16—228no—
745SD16—444no—
746SD16—444no—
747SD16C2×C22⋊D11116yescomplemented
748D8—228no—
749D8—228no—
750M16—28no—
751M16—228no—
752C2×C8—22no—
753C2×C8—112no—
754C2×C8—112no—
755C2×C8—222no—
756C2×C8—222no—
757C2×C8C2×C22⋊D1114yes—
758C2×C8C23×D1112yes—
759C2×C8C23×D1112yes—
760C4⋊C4—114no—
761C4⋊C4—112no—
762C4⋊C4—112no—
763C4⋊C4—224no—
764C4⋊C4—224no—
765C4⋊C4—224no—
766C4⋊C4—221no—
767C4⋊C4—221no—
768C22⋊C4—114no—
769C22⋊C4—114no—
770C22⋊C4—224no—
771C22⋊C4—224no—
772C22⋊C4—224no—
773C22⋊C4—224no—
774C22⋊C4—224no—
775C22⋊C4—224no—
776C22⋊C4—224no—
777C22⋊C4—224no—
778C22⋊C4—224no—
779C42—112no—
780C42—112no—
781C42—224no—
782C11C2×#327511yescharacteristic, complemented, Sylow
783C23—22no—
784C23—22no—
785C23—22no—
786C23—24no—
787C23—22no—
788C23—42no—
789C23—42no—
790C23—112no—
791C23—222no—
792C23—222no—
793C23—222no—
794C23—222no—
795C23—222no—
796C23—448no—
797C23—448no—
798C23—442no—
799C23—442no—
800C23—442no—
801C23—442no—
802C23—442no—
803C23—442no—
804C23—884no—
805C23—8816no—
806C23C2×D4×D1112yes—
807C23C2×D4×D1111yescharacteristic
808Q8—24no—
809Q8—22no—
810Q8—22no—
811Q8—22no—
812Q8—22no—
813Q8—22no—
814Q8—48no—
815Q8—42no—
816Q8—42no—
817Q8C22×C22⋊D1114yes—
818D4—24no—
819D4—22no—
820D4—48no—
821D4—222no—
822D4—222no—
823D4—222no—
824D4—222no—
825D4—448no—
826D4—444no—
827D4—448no—
828D4—448no—
829D4—442no—
830D4—442no—
831D4—884no—
832D4C22×C22⋊D1114yes—
833C2×C4—22no—
834C2×C4—24no—
835C2×C4—22no—
836C2×C4—24no—
837C2×C4—22no—
838C2×C4—22no—
839C2×C4—22no—
840C2×C4—22no—
841C2×C4—48no—
842C2×C4—48no—
843C2×C4—42no—
844C2×C4—42no—
845C2×C4—112no—
846C2×C4—112no—
847C2×C4—112no—
848C2×C4—222no—
849C2×C4—222no—
850C2×C4—222no—
851C2×C4—224no—
852C2×C4—222no—
853C2×C4—222no—
854C2×C4—222no—
855C2×C4—222no—
856C2×C4—448no—
857C2×C4—442no—
858C2×C4—442no—
859C2×C4—884no—
860C2×C4C2×D4×D1112yes—
861C2×C4C2×D4×D1111yescharacteristic
862C2×C4#6703712yes—
863C2×C4C22×C22⋊D1112yes—
864C2×C4C24×D1111yescharacteristic
865C8—22no—
866C8—222no—
867C8—222no—
868C8C22×C22⋊D1114yes—
869C22—22no—
870C22—24no—
871C22—22no—
872C22—22no—
873C22—44no—
874C22—48no—
875C22—42no—
876C22—42no—
877C22—222no—
878C22—222no—
879C22—222no—
880C22—444no—
881C22—442no—
882C22—442no—
883C22—442no—
884C22—442no—
885C22—442no—
886C22—442no—
887C22—8816no—
888C22—884no—
889C22—884no—
890C22#1062330812yes—
891C22#1062330912yes—
892C22D4×C22⋊D1112yes—
893C22C22×D4×D1111yescharacteristic
894C4—22no—
895C4—24no—
896C4—42no—
897C4—42no—
898C4—222no—
899C4—222no—
900C4—222no—
901C4—442no—
902C4—442no—
903C4D4×C22⋊D1112yes—
904C4C2×#6703711yescharacteristic
905C4C23×C22⋊D1111yescharacteristic
906C2—42no—
907C2—44no—
908C2—442no—
909C2—882no—
910C2—882no—
911C2#1308024114yesdirect product factor
912C2C2×D4×C22⋊D1111yescharacteristic
913C2C2×#1062330811yescharacteristic
914C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC22×C11×#137C2
socleC23×C11C22×D4
hypercenterC22×#137D11
hypocenterC11C2×#3275
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C22×#137

Complements

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

NH ≅ G/Ntype
1. C22×#66967C2semidirect
2. C2×#10623348C2semidirect
3. C2×#10623360C2semidirect
4. #13080241C2direct (N × H)
5. C2×#10622804C2semidirect
6. C2×#10622802C2semidirect
7. C2×#10622748C2semidirect
8. C2×#10622798C2semidirect
9. C2×#10622778C2semidirect
10. C2×#10622800C2semidirect
11. C2×#10622851C2semidirect
12. C2×#10622840C2semidirect
13. C2×#10622782C2semidirect
14. C2×SD16×Dic11C2semidirect
15. C2×#10622741C2semidirect
16. C22×C11×#137C2semidirect
18. C23×Q8×C11C22semidirect
22. C2×C11×#137C22semidirect
23. C22×C11×Q16C22semidirect
24. C22×C11×Q16C22semidirect
27. C22×C11×M16C22semidirect
29. #10623360C22semidirect
31. #10623348C22semidirect
34. C2×#67000C22semidirect
38. C2×Q8×Dic11C22semidirect
41. C22×#4325C22semidirect
48. C2×#66983C22semidirect
54. C2×#66967C22semidirect
57. #10622851C22semidirect
58. #10622840C22semidirect
59. C2×#66899C22semidirect
60. C2×#66899C22semidirect
61. C2×#66899C22semidirect
63. C2×C22⋊(C11⋊C8)C22semidirect
64. #10622804C22semidirect
65. #10622802C22semidirect
66. #10622800C22semidirect
67. #10622798C22semidirect
68. #10622782C22semidirect
69. #10622778C22semidirect
70. SD16×Dic11C22semidirect
71. #10622748C22semidirect
72. #10622741C22semidirect
74. C2×#66885C22semidirect
76. C2×#66881C22semidirect
77. C2×Dic11⋊C8C22semidirect
78. C2×C8×Dic11C22semidirect
91. C22×Q8×C11C23semidirect
118. C2×C11×Q16C23semidirect
119. C2×C11×Q16C23semidirect
121. C2×C11×SD16D4semidirect
125. C2×C11×M16C23semidirect
134. #67000C23semidirect
141. Q8×Dic11C23semidirect
147. C2×#4325C23semidirect
158. #66983C23semidirect
188. #66899C23semidirect
189. #66899C23semidirect
190. #66899C23semidirect
192. C22⋊(C11⋊C8)C23semidirect
194. #66885C23semidirect
196. #66881C23semidirect
197. Dic11⋊C8C23semidirect
198. C8×Dic11C23semidirect
288. C11×SD16C2×D4semidirect
326. C22×#137D11semidirect
430. C23×Q8C2×D11semidirect
433. C2×#137C2×D11semidirect
436. C22×Q16C2×D11semidirect
437. C22×Q16C2×D11semidirect
446. C22×M16C2×D11semidirect
543. C22×Q8C22×D11semidirect
567. C2×Q16C22×D11semidirect
568. C2×Q16C22×D11semidirect
576. C2×SD16C22⋊D11semidirect
586. C2×M16C22×D11semidirect
649. C2×C11#3275semidirect
747. SD16C2×C22⋊D11semidirect
782. C11C2×#3275semidirect
911. C2#13080241direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669672
C2×#106233482
C2×#106233602
#130802412
C2×#106228042
C2×#106228022
C2×#106227482
C2×#106227982
C2×#106227782
C2×#106228002
C2×#106228512
C2×#106228402
C2×#106227822
C2×SD16×Dic112
C2×#106227412
C22×C11×#1372
C2×#327511