Finite Group Databasebeta

← C2×#13078135 #15620676

Subgroups — C2×#13078135 #15620676

Order 2816.

2858 conjugacy classes of subgroups.

The subgroup lattice has 872 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66971C211yesmaximal, characteristic, complemented
2C22×SD16×D11C211yesmaximal, characteristic, complemented
3C2×#10623205C211yesmaximal, characteristic
4C2×#10623103C211yesmaximal, characteristic, complemented
5#13078135C2116yesmaximal, direct product factor
6C2×#10622411C211yesmaximal, characteristic, complemented
7C2×#10622798C211yesmaximal, characteristic, complemented
8C2×#10622667C211yesmaximal, characteristic, complemented
9C2×#10622461C211yesmaximal, characteristic, complemented
10C2×#10622640C211yesmaximal, characteristic, complemented
11C2×#10622375C211yesmaximal, characteristic, complemented
12C2×#10622776C211yesmaximal, characteristic, complemented
13C2×#10622452C211yesmaximal, characteristic, complemented
14C2×#10622383C211yesmaximal, characteristic, complemented
15C2×#10622417C211yesmaximal, characteristic, complemented
16C2×C11×#464C211yesmaximal, characteristic, complemented
17C22×#4343C2211yescharacteristic
18C22×Q8×D11C2211yescharacteristic
19C22×D4×D11C2211yescharacteristic
20C22×C11×Q16C2211yescharacteristic, complemented
21C22×C11×SD16C2211yescharacteristic
22C2×C11×#124C2211yescharacteristic
23C2×C4×Q8×C11C2211yescharacteristic, complemented
24C2×#67000C2211yescharacteristic
25C2×Q8×Dic11C2211yescharacteristic, complemented
26C22×#4326C2211yescharacteristic, complemented
27C22×#4325C2211yescharacteristic
28C22×#4325C2211yescharacteristic, complemented
29C2×#66993C2211yescharacteristic
30C22×#4324C2211yescharacteristic
31C2×#66971—28no—
32C2×#66971C2218yescomplemented
33C2×SD16×D11—28no—
34C2×SD16×D11C2218yescomplemented
35C22×#4314C2211yescharacteristic
36C22×#4314C2211yescharacteristic, complemented
37C22×#4313C2211yescharacteristic
38C22×C8×D11C2211yescharacteristic
39#10623205—24no—
40#10623205C2218yes—
41#10623103—24no—
42#10623103C2218yescomplemented
43C2×#66945—21no—
44C2×#66945C2211yescharacteristic
45C2×#66940—21no—
46C2×#66940C2211yescharacteristic, complemented
47C2×#66937—21no—
48C2×#66937—21no—
49C2×#66935—21no—
50C2×#66935—21no—
51C2×#66927C2211yescharacteristic
52C2×#66925—21no—
53C2×#66925C2211yescharacteristic
54C2×C4×Dic22—21no—
55C2×C4×Dic22C2211yescharacteristic, complemented
56C11×#464C2218yescomplemented
57C2×C11×C4⋊C8C2211yescharacteristic, complemented
58C2×C11×#103C2211yescharacteristic, complemented
59C2×C11×#102C2211yescharacteristic
60C2×#66899C2211yescharacteristic, complemented
61C2×#66896C2211yescharacteristic
62#10622798C2218yescomplemented
63#10622776C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66885C2211yescharacteristic, complemented
66C2×Dic11⋊C8C2211yescharacteristic, complemented
67C2×Dic11⋊C8C2211yescharacteristic, complemented
68#10622667C2218yescomplemented
69#10622640C2218yescomplemented
70C2×#66873C2211yescharacteristic
71C2×#66873C2211yescharacteristic, complemented
72C2×C4⋊(C11⋊C8)C2211yescharacteristic, complemented
73#10622461C2218yescomplemented
74#10622452C2218yescomplemented
75#10622417C2218yescomplemented
76#10622411C2218yescomplemented
77#10622383C2218yescomplemented
78#10622375C2218yescomplemented
79C24×D11—21no—
80C22×Q8×C11C2311yescharacteristic
81C22×Q8×C11C2311yescharacteristic
82C22×D4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11—21no—
85C22×C22⋊D11—21no—
86C2×#4343—22no—
87C2×#4343—24no—
88C2×#4343—24no—
89C2×#4343C2314yes—
90C2×Q8×D11—22no—
91C2×Q8×D11—24no—
92C2×Q8×D11D418yescomplemented
93C2×Q8×D11C2314yes—
94C2×D4×D11—24no—
95C2×D4×D11—22no—
96C2×D4×D11—24no—
97C2×D4×D11C2314yes—
98C22×D44—21no—
99C22×D44—21no—
100C22×D44—21no—
101C22×D44C2311yescharacteristic
102C22×D44C2311yescharacteristic
103C22×C4×D11—21no—
104C22×C4×D11—21no—
105C22×C4×D11C2311yescharacteristic
106C22×Dic22—21no—
107C22×Dic22C2311yescharacteristic
108C2×C11×Q16—24no—
109C2×C11×Q16C2314yescomplemented
110C2×C11×SD16—24no—
111C2×C11×SD16C2314yes—
112C22×C8×C11C2311yescharacteristic
113C22×C8×C11C2311yescharacteristic
114C11×#124—22no—
115C11×#124C2314yes—
116C4×Q8×C11—22no—
117C4×Q8×C11C2314yescomplemented
118C2×C11×C4⋊C4—21no—
119C2×C11×C4⋊C4C2311yescharacteristic
120C2×C11×C22⋊C4—21no—
121C2×C11×C22⋊C4—21no—
122C2×C42×C11—21no—
123C2×C42×C11C2311yescharacteristic
124#67000—22no—
125#67000C2314yes—
126Q8×Dic11—22no—
127Q8×Dic11C2314yescomplemented
128C2×#4326—24no—
129C2×#4326C2314yescomplemented
130C2×#4325—24no—
131C2×#4325—24no—
132C2×#4325C2314yes—
133C2×#4325C2314yescomplemented
134#66993—22no—
135#66993C2314yes—
136C2×#4324—24no—
137C2×#4324C2314yes—
138C2×(C2×D11)⋊C4—21no—
139C2×(C2×D11)⋊C4—21no—
140C2×(C2×D11)⋊C4—21no—
141C2×(C2×D11)⋊C4D411yescharacteristic
142C2×(C2×D11)⋊C4D411yescharacteristic
143C2×C4⋊Dic11—21no—
144C2×C4⋊Dic11C2311yescharacteristic
145C2×Dic11⋊C4—21no—
146C2×Dic11⋊C4—21no—
147C2×Dic11⋊C4D411yescharacteristic
148C2×Dic11⋊C4D411yescharacteristic
149C2×C4×Dic11—21no—
150C2×C4×Dic11—21no—
151C2×C4×Dic11—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11C2311yescharacteristic
154C22×C11⋊C8C2311yescharacteristic
155C22×C11⋊C8C2311yescharacteristic
156#66971—232no—
157SD16×D11—232no—
158C2×#4314—24no—
159C2×#4314—24no—
160C2×#4314C2314yes—
161C2×#4314C2314yescomplemented
162C2×#4313—24no—
163C2×#4313C2314yes—
164C2×C8×D11—24no—
165C2×C8×D11C2314yes—
166#66945—22no—
167#66945—28no—
168#66945C2314yes—
169#66940—28no—
170#66940—22no—
171#66940C2314yescomplemented
172#66937—28no—
173#66937—28no—
174#66935—28no—
175#66935—28no—
176#66927—22no—
177#66927C2314yes—
178#66925—28no—
179#66925D414yes—
180#66925C2314yes—
181C4×Dic22—22no—
182C4×Dic22—28no—
183C4×Dic22C2314yescomplemented
184C11×C4⋊C8C2314yescomplemented
185C11×#103C2314yescomplemented
186C11×#102C2314yes—
187#66899C2314yescomplemented
188#66896C2314yes—
189#66885C2314yes—
190#66885C2314yescomplemented
191Dic11⋊C8C2314yescomplemented
192Dic11⋊C8C2314yescomplemented
193#66873C2314yes—
194#66873C2314yescomplemented
195C4⋊(C11⋊C8)C2314yescomplemented
196C2×#3043—111nomaximal, Sylow
197C24×C11—21no—
198C23×D11—21no—
199C23×D11—21no—
200C23×D11—24no—
201C23×D11—44no—
202C23×D11—82no—
203C23×D11—82no—
204C23×D11C2×D411yescharacteristic
205C2×Q8×C11—21no—
206C2×Q8×C11—21no—
207C2×Q8×C11—22no—
208C2×Q8×C11—22no—
209C2×Q8×C11—22no—
210C2×Q8×C11C2×D414yes—
211C2×Q8×C11C2412yes—
212C2×Q8×C11C2412yes—
213C2×D4×C11—22no—
214C2×D4×C11—21no—
215C2×D4×C11—22no—
216C2×D4×C11C2412yes—
217C22×C4×C11—21no—
218C22×C4×C11—21no—
219C22×C4×C11—21no—
220C22×C4×C11C2×D411yescharacteristic
221C22×C4×C11C2×D411yescharacteristic
222C22×C4×C11C2411yescharacteristic
223C2×C22⋊D11—24no—
224C2×C22⋊D11—24no—
225C2×C22⋊D11—24no—
226C2×C22⋊D11—44no—
227C2×C22⋊D11—82no—
228C2×C22⋊D11—82no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11C2×D411yescharacteristic
232C22×Dic11C2×D411yescharacteristic
233C22×Dic11C2×D411yescharacteristic
234#4343—28no—
235#4343—28no—
236#4343—48no—
237Q8×D11—216no—
238Q8×D11—28no—
239Q8×D11C2×D4116yescomplemented
240D4×D11—28no—
241D4×D11—28no—
242D4×D11—48no—
243C2×D44—24no—
244C2×D44—21no—
245C2×D44—21no—
246C2×D44—24no—
247C2×D44—24no—
248C2×D44—22no—
249C2×D44—22no—
250C2×D44—22no—
251C2×D44—22no—
252C2×D44—44no—
253C2×D44—82no—
254C2×D44—82no—
255C2×D44C2412yes—
256C2×D44C2412yes—
257C2×C4×D11—24no—
258C2×C4×D11—28no—
259C2×C4×D11—24no—
260C2×C4×D11—44no—
261C2×C4×D11C2×D414yes—
262C2×C4×D11C2×D412yes—
263C2×C4×D11#4114yes—
264C2×C4×D11C2412yes—
265C2×Dic22—28no—
266C2×Dic22—24no—
267C2×Dic22—21no—
268C2×Dic22—22no—
269C2×Dic22C2×D414yes—
270C2×Dic22C2412yes—
271C11×Q16—28no—
272C11×SD16—28no—
273C2×C8×C11—22no—
274C2×C8×C11—22no—
275C2×C8×C11C2412yes—
276C2×C8×C11C2412yes—
277C11×C4⋊C4—24no—
278C11×C4⋊C4—21no—
279C11×C4⋊C4C2412yes—
280C11×C22⋊C4—24no—
281C11×C22⋊C4—24no—
282C42×C11—24no—
283C42×C11C2×D412yes—
284C42×C11C2412yes—
285#4326—28no—
286#4325—28no—
287#4325—28no—
288#4324—28no—
289(C2×D11)⋊C4—24no—
290(C2×D11)⋊C4—24no—
291(C2×D11)⋊C4—24no—
292(C2×D11)⋊C4C2×D414yes—
293(C2×D11)⋊C4C2×D414yes—
294C4⋊Dic11—24no—
295C4⋊Dic11—21no—
296C4⋊Dic11C2412yes—
297Dic11⋊C4—24no—
298Dic11⋊C4—24no—
299Dic11⋊C4C2×D414yes—
300Dic11⋊C4C2×D414yes—
301C4×Dic11—24no—
302C4×Dic11—24no—
303C4×Dic11—24no—
304C4×Dic11—24no—
305C4×Dic11C2×D412yes—
306C4×Dic11C2412yes—
307C2×C11⋊C8—22no—
308C2×C11⋊C8—22no—
309C2×C11⋊C8C2412yes—
310C2×C11⋊C8C2412yes—
311#4314—28no—
312#4314—28no—
313#4313—28no—
314C8×D11—28no—
315C22×#137—111no—
316C23×SD16—111no—
317C2×#535—111no—
318C2×#519—111no—
319#3043—1116no—
320C2×#464—111no—
321C2×#464—111no—
322C2×#464—111no—
323C2×#464D1111yescharacteristic, complemented
324C2×#460—111no—
325C2×#460—111no—
326C2×#460—111no—
327C2×#460—111no—
328C2×#424—111no—
329C2×#418—111no—
330C2×#416—111no—
331C23×C11—22no—
332C23×C11—42no—
333C23×C11—42no—
334C23×C11—42no—
335C23×C11C22×D411yescharacteristic
336C22×D11—22no—
337C22×D11—22no—
338C22×D11—22no—
339C22×D11—22no—
340C22×D11—42no—
341C22×D11—42no—
342C22×D11—42no—
343C22×D11—42no—
344C22×D11—42no—
345C22×D11—42no—
346C22×D11—48no—
347C22×D11—84no—
348C22×D11—84no—
349C22×D11—816no—
350C22×D11#12114yes—
351C22×D11C22×D412yes—
352Q8×C11—24no—
353Q8×C11—22no—
354Q8×C11—22no—
355Q8×C11—22no—
356Q8×C11—42no—
357Q8×C11C22×D414yes—
358D4×C11—22no—
359D4×C11—22no—
360D4×C11—42no—
361C2×C4×C11—24no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—22no—
366C2×C4×C11—22no—
367C2×C4×C11—42no—
368C2×C4×C11—42no—
369C2×C4×C11C22×D412yes—
370C2×C4×C11C22×D412yes—
371C2×C4×C11C22×D411yescharacteristic
372C2×C4×C11C22×D412yes—
373C2×C4×C11C2×#4112yes—
374C2×C4×C11C2511yescharacteristic
375C22⋊D11—48no—
376C22⋊D11—84no—
377C22⋊D11—84no—
378C2×Dic11—24no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—42no—
384C2×Dic11#12114yes—
385C2×Dic11C22×D412yes—
386C2×Dic11C22×D412yes—
387C2×Dic11C22×D412yes—
388D44—22no—
389D44—22no—
390D44—22no—
391D44—22no—
392D44—48no—
393D44—42no—
394D44—42no—
395D44—84no—
396D44—84no—
397C4×D11—216no—
398C4×D11—48no—
399C4×D11#12118yes—
400C4×D11C22×D414yes—
401C4×D11C2×#4114yes—
402Dic22—24no—
403Dic22—22no—
404Dic22—216no—
405Dic22C22×D414yes—
406C8×C11—22no—
407C8×C11—22no—
408C11⋊C8—22no—
409C11⋊C8—22no—
410C22×#41—111no—
411C23×Q8—111no—
412C23×D4—111no—
413C2×#137—118no—
414C2×#137—228no—
415C22×Q16—111no—
416C22×Q16C2×D1111yescharacteristic, complemented
417C22×SD16—111no—
418C22×SD16—111no—
419C22×SD16—111no—
420C22×SD16—118no—
421C22×SD16—111no—
422C22×SD16—111no—
423C22×SD16—228no—
424C22×SD16C2×D1111yescharacteristic
425C22×M16—111no—
426C23×C8—111no—
427#535—118no—
428#535—224no—
429C2×#127—111no—
430C2×#127—111no—
431C2×#124—111no—
432C2×#124C2×D1111yescharacteristic
433C2×#121—221no—
434C2×#121—221no—
435C2×#120—221no—
436C2×#120—221no—
437#519—118no—
438#519—224no—
439C2×C4×Q8—111no—
440C2×C4×Q8—111no—
441C2×C4×Q8—111no—
442C2×C4×Q8—221no—
443C2×C4×Q8—221no—
444C2×C4×Q8C2×D1111yescharacteristic, complemented
445C2×#117—111no—
446C2×#117—111no—
447C2×#117—221no—
448C2×#117—221no—
449#464—118no—
450#464—118no—
451#464—118no—
452#464C2×D1118yescomplemented
453#460—118no—
454#460—118no—
455#460—118no—
456#460—118no—
457#424—118no—
458C2×C4⋊C8—111no—
459C2×C4⋊C8—111no—
460C2×C4⋊C8—111no—
461C2×C4⋊C8C2×D1111yescharacteristic, complemented
462#418—118no—
463#416—118no—
464C2×#103—111no—
465C2×#103C2×D1111yescharacteristic, complemented
466C2×#102—111no—
467C2×#102—111no—
468C2×#102—111no—
469C2×#102—111no—
470C2×#102—111no—
471C2×#102C2×D1111yescharacteristic
472C22×C11—42no—
473C22×C11—42no—
474C22×C11—42no—
475C22×C11—84no—
476C22×C11C2×#12112yes—
477C22×C11#57712yes—
478C22×C11#57712yes—
479C22×C11C23×D411yescharacteristic
480C2×D11—28no—
481C2×D11—22no—
482C2×D11—22no—
483C2×D11—42no—
484C2×D11—42no—
485C2×D11—42no—
486C2×D11—42no—
487C2×D11—42no—
488C2×D11—42no—
489C2×D11—816no—
490C2×D11—84no—
491C2×D11—84no—
492C2×D11C2×#12114yes—
493C4×C11—24no—
494C4×C11—22no—
495C4×C11—22no—
496C4×C11—42no—
497C4×C11—42no—
498C4×C11C2×#12112yes—
499C4×C11C23×D411yescharacteristic
500C4×C11C22×#4111yescharacteristic
501Dic11—24no—
502Dic11—22no—
503Dic11—22no—
504Dic11—42no—
505Dic11C2×#12114yes—
506C25—221no—
507C2×#41—114no—
508C2×#41—222no—
509C2×#41—224no—
510C2×#41—224no—
511C22×Q8—118no—
512C22×Q8—114no—
513C22×Q8—111no—
514C22×Q8—221no—
515C22×Q8—222no—
516C22×Q8—224no—
517C22×Q8C22×D1111yescharacteristic
518C22×Q8C22×D1111yescharacteristic
519C22×D4—114no—
520C22×D4—111no—
521C22×D4—111no—
522C22×D4—221no—
523C22×D4—224no—
524C22×D4—224no—
525C22×D4—222no—
526C22×D4—221no—
527C22×D4—221no—
528C22×D4—221no—
529C22×D4—221no—
530C22×D4—221no—
531C22×D4C22×D1111yescharacteristic
532C23×C4—111no—
533C23×C4—221no—
534C23×C4—221no—
535#137—2232no—
536C2×Q16—24no—
537C2×Q16—114no—
538C2×Q16—224no—
539C2×Q16C22×D1114yescomplemented
540C2×SD16—24no—
541C2×SD16—114no—
542C2×SD16—114no—
543C2×SD16—114no—
544C2×SD16—114no—
545C2×SD16—114no—
546C2×SD16—224no—
547C2×SD16—224no—
548C2×SD16—2232no—
549C2×SD16—224no—
550C2×SD16—224no—
551C2×SD16—224no—
552C2×SD16C22×D1114yes—
553C2×M16—114no—
554C2×M16—224no—
555C22×C8—111no—
556C22×C8—111no—
557C22×C8—114no—
558C22×C8—224no—
559C22×C8C22×D1111yescharacteristic
560C22×C8C22×D1111yescharacteristic
561#127—114no—
562#127—114no—
563#127—222no—
564#127—222no—
565#124—22no—
566#124—114no—
567#124—222no—
568#124C22×D1114yes—
569#121—228no—
570#121—228no—
571#120—228no—
572#120—228no—
573C4×Q8—22no—
574C4×Q8—114no—
575C4×Q8—114no—
576C4×Q8—114no—
577C4×Q8—228no—
578C4×Q8—222no—
579C4×Q8—222no—
580C4×Q8—228no—
581C4×Q8—222no—
582C4×Q8C22×D1114yescomplemented
583#117—114no—
584#117—114no—
585#117—114no—
586#117—228no—
587#117—228no—
588#117—222no—
589C2×C4⋊C4—21no—
590C2×C4⋊C4—111no—
591C2×C4⋊C4—111no—
592C2×C4⋊C4—111no—
593C2×C4⋊C4—221no—
594C2×C4⋊C4—221no—
595C2×C4⋊C4—221no—
596C2×C4⋊C4C22×D1111yescharacteristic
597C2×C22⋊C4—21no—
598C2×C22⋊C4—21no—
599C2×C22⋊C4—111no—
600C2×C22⋊C4—111no—
601C2×C22⋊C4—221no—
602C2×C22⋊C4—221no—
603C2×C22⋊C4—221no—
604C2×C42—21no—
605C2×C42—111no—
606C2×C42—221no—
607C2×C42—221no—
608C2×C42—221no—
609C2×C42—221no—
610C2×C42C22×D1111yescharacteristic
611C4⋊C8—114no—
612C4⋊C8—114no—
613C4⋊C8—114no—
614C4⋊C8C22×D1114yescomplemented
615#103—114no—
616#103C22×D1114yescomplemented
617#102—114no—
618#102—114no—
619#102—114no—
620#102—114no—
621#102—114no—
622#102C22×D1114yes—
623C2×C11—82no—
624C2×C11#304314yescomplemented
625C2×C11C22×#12111yescharacteristic
626C2×C11C2×#57711yescharacteristic
627C2×C11C2×#57711yescharacteristic
628D11—24no—
629D11—82no—
630D11—82no—
631C24—21no—
632C24—111no—
633C24—224no—
634C24—221no—
635C24—221no—
636C24—444no—
637C24—882no—
638C24—882no—
639#41—228no—
640#41—228no—
641#41—448no—
642C2×Q8—21no—
643C2×Q8—21no—
644C2×Q8—22no—
645C2×Q8—22no—
646C2×Q8—22no—
647C2×Q8—1116no—
648C2×Q8—114no—
649C2×Q8—112no—
650C2×Q8—224no—
651C2×Q8—228no—
652C2×Q8—2216no—
653C2×Q8—228no—
654C2×Q8—221no—
655C2×Q8—222no—
656C2×Q8D4×D1114yes—
657C2×Q8C23×D1112yes—
658C2×Q8C23×D1112yes—
659C2×D4—22no—
660C2×D4—21no—
661C2×D4—22no—
662C2×D4—112no—
663C2×D4—112no—
664C2×D4—224no—
665C2×D4—228no—
666C2×D4—228no—
667C2×D4—224no—
668C2×D4—224no—
669C2×D4—224no—
670C2×D4—222no—
671C2×D4—222no—
672C2×D4—221no—
673C2×D4—221no—
674C2×D4—224no—
675C2×D4—224no—
676C2×D4—222no—
677C2×D4—222no—
678C2×D4—444no—
679C2×D4—448no—
680C2×D4—444no—
681C2×D4—882no—
682C2×D4—882no—
683C2×D4—882no—
684C2×D4—882no—
685C2×D4C23×D1112yes—
686C22×C4—21no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—111no—
690C22×C4—112no—
691C22×C4—114no—
692C22×C4—114no—
693C22×C4—112no—
694C22×C4—111no—
695C22×C4—111no—
696C22×C4—224no—
697C22×C4—224no—
698C22×C4—228no—
699C22×C4—221no—
700C22×C4—221no—
701C22×C4—444no—
702C22×C4D4×D1111yescharacteristic
703C22×C4D4×D1111yescharacteristic
704C22×C4C23×D1111yescharacteristic
705Q16—28no—
706Q16—228no—
707SD16—28no—
708SD16—228no—
709SD16—228no—
710SD16—228no—
711SD16—228no—
712SD16—228no—
713M16—228no—
714C2×C8—22no—
715C2×C8—22no—
716C2×C8—112no—
717C2×C8—112no—
718C2×C8—228no—
719C2×C8—222no—
720C2×C8—222no—
721C2×C8C23×D1112yes—
722C2×C8C23×D1112yes—
723C4⋊C4—24no—
724C4⋊C4—21no—
725C4⋊C4—114no—
726C4⋊C4—114no—
727C4⋊C4—112no—
728C4⋊C4—224no—
729C4⋊C4—224no—
730C4⋊C4—221no—
731C4⋊C4—224no—
732C4⋊C4C23×D1112yes—
733C22⋊C4—24no—
734C22⋊C4—24no—
735C22⋊C4—114no—
736C22⋊C4—114no—
737C22⋊C4—224no—
738C22⋊C4—224no—
739C22⋊C4—224no—
740C42—24no—
741C42—112no—
742C42—112no—
743C42—224no—
744C42—224no—
745C42—224no—
746C42—224no—
747C42D4×D1112yes—
748C42C23×D1112yes—
749C11C2×#304311yescharacteristic, complemented, Sylow
750C23—22no—
751C23—42no—
752C23—42no—
753C23—42no—
754C23—114no—
755C23—112no—
756C23—222no—
757C23—222no—
758C23—222no—
759C23—222no—
760C23—448no—
761C23—442no—
762C23—442no—
763C23—442no—
764C23—442no—
765C23—442no—
766C23—442no—
767C23—884no—
768C23—884no—
769C23—8816no—
770C23C2×D4×D1111yescharacteristic
771Q8—24no—
772Q8—22no—
773Q8—22no—
774Q8—22no—
775Q8—42no—
776Q8—114no—
777Q8—2216no—
778Q8—224no—
779Q8—222no—
780Q8C2×D4×D1114yes—
781D4—22no—
782D4—22no—
783D4—42no—
784D4—222no—
785D4—222no—
786D4—222no—
787D4—222no—
788D4—448no—
789D4—448no—
790D4—442no—
791D4—442no—
792D4—884no—
793D4—884no—
794D4—884no—
795D4—884no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—114no—
805C2×C4—112no—
806C2×C4—118no—
807C2×C4—114no—
808C2×C4—114no—
809C2×C4—112no—
810C2×C4—112no—
811C2×C4—2216no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—224no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—448no—
818C2×C4—442no—
819C2×C4C2×D4×D1112yes—
820C2×C4C2×D4×D1112yes—
821C2×C4C2×D4×D1111yescharacteristic
822C2×C4C2×D4×D1112yes—
823C2×C4#41×D1112yes—
824C2×C4C24×D1111yescharacteristic
825C8—22no—
826C8—22no—
827C8—222no—
828C8—222no—
829C22—42no—
830C22—42no—
831C22—42no—
832C22—84no—
833C22—114no—
834C22—228no—
835C22—222no—
836C22—222no—
837C22—442no—
838C22—442no—
839C22—442no—
840C22—442no—
841C22—442no—
842C22—442no—
843C22—8816no—
844C22—884no—
845C22—884no—
846C22D11×#12112yes—
847C22#1062330112yes—
848C22#1062330912yes—
849C22C22×D4×D1111yescharacteristic
850C4—24no—
851C4—22no—
852C4—22no—
853C4—42no—
854C4—42no—
855C4—114no—
856C4—224no—
857C4—222no—
858C4—222no—
859C4—442no—
860C4D11×#12112yes—
861C4C22×D4×D1111yescharacteristic
862C4C2×#41×D1111yescharacteristic
863C2—82no—
864C2—224no—
865C2—882no—
866C2—882no—
867C2#1307813514yesdirect product factor
868C2C2×D11×#12111yescharacteristic
869C2C2×#1062330111yescharacteristic
870C2C2×#1062330911yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#464C2
socleC23×C11C22×D4
prime radicalC2×#10623205C2
hypercenterC2×#464D11
hypocenterC11C2×#3043
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C42 ◁ C2×#464

Complements

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

NH ≅ G/Ntype
1. C22×#66971C2semidirect
2. C22×SD16×D11C2semidirect
4. C2×#10623103C2semidirect
5. #13078135C2direct (N × H)
6. C2×#10622411C2semidirect
7. C2×#10622798C2semidirect
8. C2×#10622667C2semidirect
9. C2×#10622461C2semidirect
10. C2×#10622640C2semidirect
11. C2×#10622375C2semidirect
12. C2×#10622776C2semidirect
13. C2×#10622452C2semidirect
14. C2×#10622383C2semidirect
15. C2×#10622417C2semidirect
16. C2×C11×#464C2semidirect
20. C22×C11×Q16C22semidirect
23. C2×C4×Q8×C11C22semidirect
25. C2×Q8×Dic11C22semidirect
26. C22×#4326C22semidirect
28. C22×#4325C22semidirect
32. C2×#66971C22semidirect
34. C2×SD16×D11C22semidirect
36. C22×#4314C22semidirect
42. #10623103C22semidirect
46. C2×#66940C22semidirect
55. C2×C4×Dic22C22semidirect
56. C11×#464C22semidirect
57. C2×C11×C4⋊C8C22semidirect
58. C2×C11×#103C22semidirect
60. C2×#66899C22semidirect
62. #10622798C22semidirect
63. #10622776C22semidirect
65. C2×#66885C22semidirect
66. C2×Dic11⋊C8C22semidirect
67. C2×Dic11⋊C8C22semidirect
68. #10622667C22semidirect
69. #10622640C22semidirect
71. C2×#66873C22semidirect
72. C2×C4⋊(C11⋊C8)C22semidirect
73. #10622461C22semidirect
74. #10622452C22semidirect
75. #10622417C22semidirect
76. #10622411C22semidirect
77. #10622383C22semidirect
78. #10622375C22semidirect
92. C2×Q8×D11D4semidirect
109. C2×C11×Q16C23semidirect
117. C4×Q8×C11C23semidirect
127. Q8×Dic11C23semidirect
129. C2×#4326C23semidirect
133. C2×#4325C23semidirect
161. C2×#4314C23semidirect
171. #66940C23semidirect
183. C4×Dic22C23semidirect
184. C11×C4⋊C8C23semidirect
185. C11×#103C23semidirect
187. #66899C23semidirect
190. #66885C23semidirect
191. Dic11⋊C8C23semidirect
192. Dic11⋊C8C23semidirect
194. #66873C23semidirect
195. C4⋊(C11⋊C8)C23semidirect
239. Q8×D11C2×D4semidirect
323. C2×#464D11semidirect
416. C22×Q16C2×D11semidirect
444. C2×C4×Q8C2×D11semidirect
452. #464C2×D11semidirect
461. C2×C4⋊C8C2×D11semidirect
465. C2×#103C2×D11semidirect
539. C2×Q16C22×D11semidirect
582. C4×Q8C22×D11semidirect
614. C4⋊C8C22×D11semidirect
616. #103C22×D11semidirect
624. C2×C11#3043semidirect
749. C11C2×#3043semidirect
867. C2#13078135direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669712
C22×SD16×D112
C2×#106232052
C2×#106231032
#130781352
C2×#106224112
C2×#106227982
C2×#106226672
C2×#106224612
C2×#106226402
C2×#106223752
C2×#106227762
C2×#106224522
C2×#106223832
C2×#106224172
C2×C11×#4642
C2×#304311