Finite Group Databasebeta

← C2×#13080183 #15628815

Subgroups — C2×#13080183 #15628815

Order 2816.

2742 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×#66968C211yesmaximal, characteristic, complemented
2C23×Dic44C211yesmaximal, characteristic, complemented
3C2×#10623163C211yesmaximal, characteristic, complemented
4C2×#10623129C211yesmaximal, characteristic
5#13080183C2116yesmaximal, direct product factor
6C2×#10622780C211yesmaximal, characteristic, complemented
7C2×#10622481C211yesmaximal, characteristic, complemented
8C2×#10622380C211yesmaximal, characteristic, complemented
9C2×#10622406C211yesmaximal, characteristic, complemented
10C2×#10622396C211yesmaximal, characteristic, complemented
11C2×#10622421C211yesmaximal, characteristic, complemented
12C2×#10622663C211yesmaximal, characteristic, complemented
13C2×#10622653C211yesmaximal, characteristic, complemented
14C2×#10622466C211yesmaximal, characteristic, complemented
15C2×#10622724C211yesmaximal, characteristic, complemented
16C2×C11×#465C211yesmaximal, characteristic, complemented
17C22×Q8×D11C2211yescharacteristic
18C22×#4341C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×SD16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C2×C11×C22⋊Q8C2211yescharacteristic
24C2×C11×#121C2211yescharacteristic
25C2×#66997C2211yescharacteristic
26C22×#4326C2211yescharacteristic
27C22×#4326C2211yescharacteristic
28C2×#66992—21no—
29C2×#66989C2211yescharacteristic
30C2×D4×Dic11—21no—
31C22×#4324C2211yescharacteristic
32C22×#4324C2211yescharacteristic
33C2×C4×C22⋊D11C2211yescharacteristic
34C2×#66968—28no—
35C2×#66968C2218yescomplemented
36C22×Dic44—28no—
37C22×Dic44C2211yescharacteristic
38C22×Dic44C2211yescharacteristic
39C22×Dic44C2211yescharacteristic
40C22×Dic44C2211yescharacteristic
41C22×Dic44C2218yescomplemented
42C22×#4313C2211yescharacteristic
43#10623163—24no—
44#10623163C2218yescomplemented
45#10623129—24no—
46#10623129C2218yes—
47C2×#66950C2211yescharacteristic
48C2×#66950C2211yescharacteristic
49C2×#66949—21no—
50C2×#66941—21no—
51C2×#66940C2211yescharacteristic
52C2×#66940C2211yescharacteristic
53C2×#66938—21no—
54C2×(C22⋊D11)⋊C4—21no—
55C2×#66931—21no—
56C2×#66931—21no—
57C11×#465C2218yescomplemented
58C2×C11×#106C2211yescharacteristic
59C2×C11×#103C2211yescharacteristic
60C2×C11×#102C2211yescharacteristic
61C2×C22⋊(C11⋊C8)C2211yescharacteristic
62#10622780C2218yescomplemented
63#10622724C2218yescomplemented
64C2×(C2×D11)⋊C8C2211yescharacteristic
65C2×#66879C2211yescharacteristic
66C2×Dic11⋊C8C2211yescharacteristic
67#10622663C2218yescomplemented
68#10622653C2218yescomplemented
69C2×#66874C2211yescharacteristic
70C2×#66874C2211yescharacteristic
71C2×#66874C2211yescharacteristic
72C2×#66874C2211yescharacteristic
73#10622481C2218yescomplemented
74#10622466C2218yescomplemented
75#10622421C2218yescomplemented
76#10622406C2218yescomplemented
77#10622396C2218yescomplemented
78#10622380C2218yescomplemented
79C22×Q8×C11C2311yescharacteristic
80C22×D4×C11—21no—
81C22×D4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C22×C22⋊D11—21no—
84C22×C22⋊D11D411yescharacteristic
85C23×Dic11—21no—
86C23×Dic11—21no—
87C23×Dic11—21no—
88C2×Q8×D11—22no—
89C2×Q8×D11—24no—
90C2×Q8×D11—42no—
91C2×Q8×D11C2314yes—
92C2×#4341—22no—
93C2×#4341—24no—
94C2×#4341—42no—
95C2×#4341C2314yes—
96C22×C4×D11—21no—
97C22×C4×D11C2311yescharacteristic
98C22×Dic22—24no—
99C22×Dic22—24no—
100C22×Dic22—21no—
101C22×Dic22—21no—
102C22×Dic22—22no—
103C22×Dic22—22no—
104C22×Dic22—21no—
105C22×Dic22—42no—
106C22×Dic22—42no—
107C22×Dic22C2311yescharacteristic
108C22×Dic22C2311yescharacteristic
109C22×Dic22C2314yes—
110C22×Dic22C2314yes—
111C22×Dic22C2311yescharacteristic
112C22×Dic22C2311yescharacteristic
113C2×C11×SD16—24no—
114C2×C11×SD16C2314yes—
115C22×C8×C11—24no—
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2314yes—
118C22×C8×C11C2311yescharacteristic
119C11×C22⋊Q8—22no—
120C11×C22⋊Q8C2314yes—
121C11×#121—22no—
122C11×#121C2314yes—
123C2×C11×C4⋊C4—21no—
124C2×C11×C4⋊C4C2311yescharacteristic
125C2×C11×C4⋊C4C2311yescharacteristic
126C2×C11×C22⋊C4—21no—
127C2×C11×C22⋊C4—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130C2×C22⋊Dic11D411yescharacteristic
131#66997—22no—
132#66997C2314yes—
133C2×#4326—24no—
134C2×#4326—42no—
135C2×#4326C2314yes—
136C2×#4326C2314yes—
137#66992—28no—
138#66989—22no—
139#66989C2314yes—
140D4×Dic11—28no—
141C2×#4324—24no—
142C2×#4324—42no—
143C2×#4324C2314yes—
144C2×#4324C2314yes—
145C4×C22⋊D11D414yes—
146C4×C22⋊D11C2314yes—
147C2×(C2×D11)⋊C4—21no—
148C2×(C2×D11)⋊C4—21no—
149C2×(C2×D11)⋊C4D411yescharacteristic
150C2×C4⋊Dic11—21no—
151C2×C4⋊Dic11—21no—
152C2×Dic11⋊C4—21no—
153C2×Dic11⋊C4—21no—
154C2×Dic11⋊C4—21no—
155C2×Dic11⋊C4—21no—
156C2×Dic11⋊C4D411yescharacteristic
157C2×C4×Dic11—21no—
158C2×C4×Dic11—21no—
159C2×C4×Dic11C2311yescharacteristic
160C22×C11⋊C8C2311yescharacteristic
161C22×C11⋊C8C2311yescharacteristic
162#66968—232no—
163C2×Dic44—24no—
164C2×Dic44—24no—
165C2×Dic44—24no—
166C2×Dic44—232no—
167C2×Dic44D418yescomplemented
168C2×Dic44C2314yes—
169C2×Dic44C2314yes—
170C2×Dic44C2314yes—
171C2×Dic44C2314yes—
172C2×#4313—24no—
173C2×#4313C2314yes—
174#66950—22no—
175#66950—22no—
176#66950C2314yes—
177#66950C2314yes—
178#66949—28no—
179#66941—28no—
180#66940—22no—
181#66940—22no—
182#66940C2314yes—
183#66940C2314yes—
184#66938—28no—
185(C22⋊D11)⋊C4—28no—
186#66931—28no—
187#66931—28no—
188C11×#106C2314yes—
189C11×#103C2314yes—
190C11×#102C2314yes—
191C22⋊(C11⋊C8)C2314yes—
192(C2×D11)⋊C8C2314yes—
193#66879C2314yes—
194Dic11⋊C8C2314yes—
195#66874C2314yes—
196#66874C2314yes—
197#66874C2314yes—
198#66874C2314yes—
199C2×#3270—111nomaximal, Sylow
200C24×C11—21no—
201C24×C11C2×D411yescharacteristic
202C23×D11C2×D411yescharacteristic
203C2×Q8×C11—21no—
204C2×Q8×C11—22no—
205C2×Q8×C11—22no—
206C2×Q8×C11C2412yes—
207C2×D4×C11—24no—
208C2×D4×C11—22no—
209C2×D4×C11—21no—
210C2×D4×C11—22no—
211C2×D4×C11—44no—
212C2×D4×C11C2412yes—
213C22×C4×C11—22no—
214C22×C4×C11—22no—
215C22×C4×C11—21no—
216C22×C4×C11—21no—
217C22×C4×C11—21no—
218C22×C4×C11C2×D411yescharacteristic
219C22×C4×C11C2×D412yes—
220C22×C4×C11C2412yes—
221C22×C4×C11C2411yescharacteristic
222C2×C22⋊D11—24no—
223C2×C22⋊D11—24no—
224C2×C22⋊D11—44no—
225C2×C22⋊D11C2×D414yes—
226C22×Dic11—24no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—24no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—24no—
233C22×Dic11—44no—
234C22×Dic11—44no—
235C22×Dic11—44no—
236C22×Dic11C2×D411yescharacteristic
237C22×Dic11C2×D411yescharacteristic
238C22×Dic11C2×D411yescharacteristic
239Q8×D11—28no—
240Q8×D11—44no—
241Q8×D11—48no—
242#4341—28no—
243#4341—44no—
244#4341—48no—
245C2×C4×D11—24no—
246C2×C4×D11—22no—
247C2×C4×D11—22no—
248C2×C4×D11—44no—
249C2×C4×D11C2×D412yes—
250C2×C4×D11C2412yes—
251C2×Dic22—28no—
252C2×Dic22—28no—
253C2×Dic22—24no—
254C2×Dic22—21no—
255C2×Dic22—21no—
256C2×Dic22—22no—
257C2×Dic22—22no—
258C2×Dic22—24no—
259C2×Dic22—24no—
260C2×Dic22—21no—
261C2×Dic22—21no—
262C2×Dic22—22no—
263C2×Dic22—22no—
264C2×Dic22—22no—
265C2×Dic22—22no—
266C2×Dic22—44no—
267C2×Dic22—44no—
268C2×Dic22—48no—
269C2×Dic22—48no—
270C2×Dic22—44no—
271C2×Dic22—44no—
272C2×Dic22—44no—
273C2×Dic22C2×D414yes—
274C2×Dic22C2×D414yes—
275C2×Dic22C2412yes—
276C2×Dic22C2412yes—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×SD16—28no—
280C2×C8×C11—28no—
281C2×C8×C11—22no—
282C2×C8×C11C2×D414yes—
283C2×C8×C11C2412yes—
284C2×C8×C11C2412yes—
285C11×C4⋊C4—21no—
286C11×C4⋊C4—21no—
287C11×C4⋊C4—24no—
288C11×C4⋊C4C2412yes—
289C11×C4⋊C4C2412yes—
290C11×C22⋊C4—24no—
291C11×C22⋊C4—24no—
292C22⋊Dic11—24no—
293C22⋊Dic11—24no—
294C22⋊Dic11C2×D414yes—
295#4326—28no—
296#4326—44no—
297#4324—28no—
298#4324—44no—
299(C2×D11)⋊C4—24no—
300(C2×D11)⋊C4—24no—
301(C2×D11)⋊C4C2×D414yes—
302C4⋊Dic11—24no—
303C4⋊Dic11—24no—
304Dic11⋊C4—24no—
305Dic11⋊C4—24no—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4C2×D414yes—
309C4×Dic11—24no—
310C4×Dic11—24no—
311C4×Dic11C2×D412yes—
312C4×Dic11C2412yes—
313C2×C11⋊C8—22no—
314C2×C11⋊C8—22no—
315C2×C11⋊C8C2412yes—
316C2×C11⋊C8C2412yes—
317Dic44—28no—
318Dic44—28no—
319Dic44—28no—
320Dic44C2×D4116yescomplemented
321#4313—28no—
322C22×#137—111no—
323C23×Q16—111no—
324C2×D4×Q8—111no—
325C2×#548—111no—
326#3270—1116no—
327C2×#497—111no—
328C2×#470—111no—
329C2×#465D1111yescharacteristic, complemented
330C2×#464—111no—
331C2×#462—111no—
332C2×#452—111no—
333C2×#451—111no—
334C2×#451—111no—
335C2×#448—111no—
336C2×#441—111no—
337C2×#435—111no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—42no—
342C23×C11—42no—
343C23×C11—42no—
344C23×C11#13714yescomplemented
345C23×C11C22×D412yes—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—22no—
349C22×D11—22no—
350C22×D11C22×D412yes—
351Q8×C11—22no—
352Q8×C11—22no—
353Q8×C11—42no—
354D4×C11—22no—
355D4×C11—22no—
356D4×C11—48no—
357D4×C11—42no—
358C2×C4×C11—22no—
359C2×C4×C11—24no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—22no—
363C2×C4×C11—22no—
364C2×C4×C11—22no—
365C2×C4×C11—42no—
366C2×C4×C11—42no—
367C2×C4×C11—42no—
368C2×C4×C11C22×D412yes—
369C2×C4×C11C22×D411yescharacteristic
370C2×C4×C11C22×D412yes—
371C2×C4×C11H(5,𝔽2)12yes—
372C2×C4×C11C2511yescharacteristic
373C22⋊D11—28no—
374C22⋊D11—48no—
375C2×Dic11—24no—
376C2×Dic11—24no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—22no—
382C2×Dic11—22no—
383C2×Dic11—22no—
384C2×Dic11—48no—
385C2×Dic11—48no—
386C2×Dic11—48no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389C2×Dic11C22×D412yes—
390C2×Dic11C22×D412yes—
391C2×Dic11C22×D412yes—
392C4×D11—24no—
393C4×D11—22no—
394C4×D11—22no—
395C4×D11—48no—
396Dic22—24no—
397Dic22—24no—
398Dic22—22no—
399Dic22—22no—
400Dic22—22no—
401Dic22—22no—
402Dic22—22no—
403Dic22—22no—
404Dic22—48no—
405Dic22—48no—
406Dic22—48no—
407Dic22—42no—
408Dic22—42no—
409Dic22C22×D414yes—
410Dic22C22×D414yes—
411C8×C11—22no—
412C8×C11C22×D414yes—
413C11⋊C8—22no—
414C11⋊C8—22no—
415C22×#41—111no—
416C23×Q8—111no—
417C23×Q8—111no—
418C23×Q8—111no—
419C2×#137—118no—
420C2×#137—228no—
421C22×Q16—111no—
422C22×Q16—111no—
423C22×Q16—111no—
424C22×Q16—111no—
425C22×Q16—111no—
426C22×Q16—111no—
427C22×Q16—118no—
428C22×Q16—228no—
429C22×SD16—111no—
430C22×SD16—111no—
431C22×SD16C2×D1111yescharacteristic
432C22×M16—111no—
433C23×C8C2×D1111yescharacteristic
434D4×Q8—118no—
435D4×Q8—224no—
436#548—118no—
437#548—224no—
438C2×C4⋊Q8—111no—
439C2×C4⋊Q8—221no—
440C2×#124—111no—
441C2×#124—221no—
442C2×C22⋊Q8—111no—
443C2×C22⋊Q8—111no—
444C2×C22⋊Q8—221no—
445C2×C22⋊Q8—221no—
446C2×C22⋊Q8—221no—
447C2×C22⋊Q8C2×D1111yescharacteristic
448C2×#121—221no—
449C2×#121C2×D1111yescharacteristic
450C2×C4×Q8—111no—
451C2×C4×Q8—111no—
452C2×C4×D4—111no—
453C2×C4×D4—221no—
454C2×C4×D4—221no—
455#497—118no—
456#470—118no—
457#465C2×D1118yescomplemented
458#464—118no—
459#462—118no—
460#452—118no—
461#451—118no—
462#451—118no—
463#448—118no—
464#441—118no—
465#435—118no—
466C2×#106C2×D1111yescharacteristic
467C2×C4⋊C8—111no—
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103C2×D1111yescharacteristic
473C2×#102C2×D1111yescharacteristic
474C2×C22⋊C8—111no—
475C2×C22⋊C8—111no—
476C2×#97—111no—
477C22×C11—22no—
478C22×C11—28no—
479C22×C11—22no—
480C22×C11—42no—
481C22×C11—42no—
482C22×C11—42no—
483C22×C11—84no—
484C22×C11D4212yes—
485C22×C11C2×#13712yes—
486C22×C11C2×#13714yescomplemented
487C22×C11#57812yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—22no—
490C2×D11—22no—
491C2×D11—22no—
492C2×D11—44no—
493C4×C11—22no—
494C4×C11—42no—
495C4×C11—42no—
496C4×C11—42no—
497C4×C11D4212yes—
498C4×C11C23×D411yescharacteristic
499C4×C11C2×H(5,𝔽2)11yescharacteristic
500Dic11—24no—
501Dic11—24no—
502Dic11—22no—
503Dic11—22no—
504Dic11—22no—
505Dic11—42no—
506Dic11—42no—
507C2×#41—114no—
508C2×#41—222no—
509C2×#41—224no—
510C2×#41—442no—
511C22×Q8—114no—
512C22×Q8—111no—
513C22×Q8—111no—
514C22×Q8—111no—
515C22×Q8—111no—
516C22×Q8—114no—
517C22×Q8—114no—
518C22×Q8—221no—
519C22×Q8—224no—
520C22×Q8—224no—
521C22×Q8—222no—
522C22×Q8—221no—
523C22×Q8—221no—
524C22×Q8—222no—
525C22×Q8—222no—
526C22×Q8—224no—
527C22×Q8—442no—
528C22×Q8—442no—
529C22×Q8—442no—
530C22×Q8C22×D1111yescharacteristic
531C22×D4—21no—
532C22×D4—111no—
533C22×D4—221no—
534C22×D4C22×D1111yescharacteristic
535C23×C4—111no—
536C23×C4—221no—
537C23×C4—221no—
538C23×C4—221no—
539C23×C4—221no—
540C23×C4C22×D1111yescharacteristic
541#137—2232no—
542C2×Q16—114no—
543C2×Q16—114no—
544C2×Q16—118no—
545C2×Q16—114no—
546C2×Q16—114no—
547C2×Q16—114no—
548C2×Q16—114no—
549C2×Q16—2232no—
550C2×Q16—224no—
551C2×Q16—224no—
552C2×Q16—224no—
553C2×Q16—224no—
554C2×Q16—442no—
555C2×SD16—24no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—224no—
559C2×SD16—442no—
560C2×SD16C22×D1114yes—
561C2×M16—114no—
562C2×M16—224no—
563C22×C8—24no—
564C22×C8—111no—
565C22×C8—111no—
566C22×C8C22×D1111yescharacteristic
567C22×C8C22×D1114yes—
568C22×C8C22×D1111yescharacteristic
569C4⋊Q8—114no—
570C4⋊Q8—222no—
571C4⋊Q8—228no—
572#124—114no—
573#124—222no—
574#124—228no—
575C22⋊Q8—22no—
576C22⋊Q8—114no—
577C22⋊Q8—114no—
578C22⋊Q8—228no—
579C22⋊Q8—228no—
580C22⋊Q8—228no—
581C22⋊Q8—222no—
582C22⋊Q8—222no—
583C22⋊Q8C22×D1114yes—
584#121—22no—
585#121—228no—
586#121C22×D1114yes—
587C4×Q8—114no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×D4—114no—
592C4×D4—114no—
593C4×D4—228no—
594C4×D4—228no—
595C2×C4⋊C4—21no—
596C2×C4⋊C4—111no—
597C2×C4⋊C4—221no—
598C2×C4⋊C4—221no—
599C2×C4⋊C4—221no—
600C2×C4⋊C4—221no—
601C2×C4⋊C4—221no—
602C2×C4⋊C4—221no—
603C2×C4⋊C4C22×D1111yescharacteristic
604C2×C4⋊C4C22×D1111yescharacteristic
605C2×C22⋊C4—21no—
606C2×C22⋊C4—21no—
607C2×C22⋊C4—111no—
608C2×C22⋊C4—111no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4—221no—
612C2×C22⋊C4—221no—
613C2×C42—111no—
614C2×C42—221no—
615C2×C42—221no—
616#106C22×D1114yes—
617C4⋊C8—114no—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103C22×D1114yes—
623#102C22×D1114yes—
624C22⋊C8—114no—
625C22⋊C8—114no—
626#97—114no—
627C2×C11—24no—
628C2×C11—82no—
629C2×C11#327014yescomplemented
630C2×C11C2×D4211yescharacteristic
631C2×C11C22×#13711yescharacteristic
632C2×C11C2×#57811yescharacteristic
633D11—42no—
634C24—21no—
635C24—111no—
636C24D4×D1111yescharacteristic
637#41—228no—
638#41—444no—
639#41—448no—
640C2×Q8—21no—
641C2×Q8—22no—
642C2×Q8—22no—
643C2×Q8—114no—
644C2×Q8—114no—
645C2×Q8—112no—
646C2×Q8—112no—
647C2×Q8—112no—
648C2×Q8—112no—
649C2×Q8—224no—
650C2×Q8—228no—
651C2×Q8—228no—
652C2×Q8—221no—
653C2×Q8—221no—
654C2×Q8—224no—
655C2×Q8—221no—
656C2×Q8—224no—
657C2×Q8—221no—
658C2×Q8—222no—
659C2×Q8—222no—
660C2×Q8—228no—
661C2×Q8—222no—
662C2×Q8—222no—
663C2×Q8—222no—
664C2×Q8—222no—
665C2×Q8—444no—
666C2×Q8—444no—
667C2×Q8—444no—
668C2×Q8—444no—
669C2×Q8—448no—
670C2×Q8—448no—
671C2×Q8—444no—
672C2×Q8—444no—
673C2×Q8—448no—
674C2×Q8C23×D1112yes—
675C2×D4—24no—
676C2×D4—22no—
677C2×D4—21no—
678C2×D4—22no—
679C2×D4—44no—
680C2×D4—114no—
681C2×D4—224no—
682C2×D4—224no—
683C2×D4—444no—
684C2×D4C23×D1112yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—21no—
688C22×C4—21no—
689C22×C4—21no—
690C22×C4—111no—
691C22×C4—111no—
692C22×C4—111no—
693C22×C4—112no—
694C22×C4—112no—
695C22×C4—224no—
696C22×C4—224no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—222no—
700C22×C4—222no—
701C22×C4—224no—
702C22×C4—224no—
703C22×C4—221no—
704C22×C4—221no—
705C22×C4—444no—
706C22×C4—444no—
707C22×C4—444no—
708C22×C4—444no—
709C22×C4D4×D1112yes—
710C22×C4D4×D1111yescharacteristic
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713Q16—1116no—
714Q16—228no—
715Q16—228no—
716Q16—228no—
717Q16—228no—
718Q16—444no—
719SD16—28no—
720SD16—228no—
721SD16—444no—
722M16—228no—
723C2×C8—22no—
724C2×C8—28no—
725C2×C8—112no—
726C2×C8—112no—
727C2×C8—222no—
728C2×C8—222no—
729C2×C8D4×D1114yes—
730C2×C8C23×D1112yes—
731C2×C8C23×D1112yes—
732C4⋊C4—24no—
733C4⋊C4—21no—
734C4⋊C4—21no—
735C4⋊C4—114no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—224no—
741C4⋊C4—224no—
742C4⋊C4C23×D1112yes—
743C4⋊C4C23×D1112yes—
744C22⋊C4—24no—
745C22⋊C4—24no—
746C22⋊C4—114no—
747C22⋊C4—114no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4—224no—
751C22⋊C4—224no—
752C42—112no—
753C42—112no—
754C42—224no—
755C42—224no—
756C11C2×#327011yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—22no—
760C23—42no—
761C23—42no—
762C23—42no—
763C23—112no—
764C23—222no—
765C23—222no—
766C23—222no—
767C23#6696814yescomplemented
768C23C2×D4×D1112yes—
769C23C2×D4×D1111yescharacteristic
770Q8—22no—
771Q8—22no—
772Q8—42no—
773Q8—114no—
774Q8—114no—
775Q8—224no—
776Q8—224no—
777Q8—222no—
778Q8—222no—
779Q8—222no—
780Q8—222no—
781Q8—222no—
782Q8—222no—
783Q8—448no—
784Q8—448no—
785Q8—448no—
786Q8—442no—
787Q8—442no—
788D4—22no—
789D4—22no—
790D4—48no—
791D4—42no—
792D4—228no—
793D4—448no—
794C2×C4—22no—
795C2×C4—24no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—22no—
799C2×C4—22no—
800C2×C4—22no—
801C2×C4—42no—
802C2×C4—42no—
803C2×C4—42no—
804C2×C4—112no—
805C2×C4—112no—
806C2×C4—112no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—224no—
811C2×C4—224no—
812C2×C4—222no—
813C2×C4—222no—
814C2×C4—224no—
815C2×C4—222no—
816C2×C4—222no—
817C2×C4—222no—
818C2×C4—222no—
819C2×C4—448no—
820C2×C4—448no—
821C2×C4—448no—
822C2×C4—448no—
823C2×C4—442no—
824C2×C4—442no—
825C2×C4C2×D4×D1112yes—
826C2×C4C2×D4×D1111yescharacteristic
827C2×C4C2×D4×D1112yes—
828C2×C4#6704212yes—
829C2×C4C24×D1111yescharacteristic
830C8—22no—
831C8—222no—
832C8—222no—
833C8C2×D4×D1114yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—42no—
838C22—42no—
839C22—42no—
840C22—84no—
841C22—222no—
842C22—222no—
843C22—222no—
844C22—444no—
845C22#1062314012yes—
846C22C2×#6696812yes—
847C22C2×#6696814yescomplemented
848C22#1062330212yes—
849C22C22×D4×D1111yescharacteristic
850C4—22no—
851C4—42no—
852C4—42no—
853C4—42no—
854C4—222no—
855C4—224no—
856C4—224no—
857C4—222no—
858C4—222no—
859C4—442no—
860C4—442no—
861C4#1062314012yes—
862C4C22×D4×D1111yescharacteristic
863C4C2×#6704211yescharacteristic
864C2—24no—
865C2—82no—
866C2—442no—
867C2#1308018314yesdirect product factor
868C2C2×#1062314011yescharacteristic
869C2C22×#6696811yescharacteristic
870C2C2×#1062330211yescharacteristic
subgroupG/H
centerC23C2×D4×D11
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#465C2
socleC23×C11C22×D4
prime radicalC2×#10623129C2
hypercenterC2×#465D11
hypocenterC11C2×#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#465

Complements

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

NH ≅ G/Ntype
1. C22×#66968C2semidirect
2. C23×Dic44C2semidirect
3. C2×#10623163C2semidirect
5. #13080183C2direct (N × H)
6. C2×#10622780C2semidirect
7. C2×#10622481C2semidirect
8. C2×#10622380C2semidirect
9. C2×#10622406C2semidirect
10. C2×#10622396C2semidirect
11. C2×#10622421C2semidirect
12. C2×#10622663C2semidirect
13. C2×#10622653C2semidirect
14. C2×#10622466C2semidirect
15. C2×#10622724C2semidirect
16. C2×C11×#465C2semidirect
35. C2×#66968C22semidirect
41. C22×Dic44C22semidirect
44. #10623163C22semidirect
57. C11×#465C22semidirect
62. #10622780C22semidirect
63. #10622724C22semidirect
67. #10622663C22semidirect
68. #10622653C22semidirect
73. #10622481C22semidirect
74. #10622466C22semidirect
75. #10622421C22semidirect
76. #10622406C22semidirect
77. #10622396C22semidirect
78. #10622380C22semidirect
167. C2×Dic44D4semidirect
320. Dic44C2×D4semidirect
329. C2×#465D11semidirect
344. C23×C11#137semidirect
457. #465C2×D11semidirect
486. C22×C11C2×#137semidirect
629. C2×C11#3270semidirect
756. C11C2×#3270semidirect
767. C23#66968semidirect
847. C22C2×#66968semidirect
867. C2#13080183direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669682
C23×Dic442
C2×#106231632
C2×#106231292
#130801832
C2×#106227802
C2×#106224812
C2×#106223802
C2×#106224062
C2×#106223962
C2×#106224212
C2×#106226632
C2×#106226532
C2×#106224662
C2×#106227242
C2×C11×#4652
C2×#327011