Finite Group Databasebeta

← C2×#13080191 #15628823

Subgroups — C2×#13080191 #15628823

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×#66962C211yesmaximal, characteristic, complemented
2C23×Dic44C211yesmaximal, characteristic, complemented
3C2×D4×Dic22C211yesmaximal, characteristic, complemented
4C2×#10623083C211yesmaximal, characteristic
5#13080191C2116yesmaximal, direct product factor
6C2×#10622328C211yesmaximal, characteristic, complemented
7C2×#10622750C211yesmaximal, characteristic, complemented
8C2×#10622727C211yesmaximal, characteristic, complemented
9C2×#10622458C211yesmaximal, characteristic, complemented
10C2×#10622462C211yesmaximal, characteristic, complemented
11C2×#10622346C211yesmaximal, characteristic, complemented
12C2×#10622352C211yesmaximal, characteristic, complemented
13C2×#10622352C211yesmaximal, characteristic, complemented
14C2×#10622351C211yesmaximal, characteristic, complemented
15C2×#10622329C211yesmaximal, characteristic, complemented
16C2×C11×#435C211yesmaximal, characteristic, complemented
17C22×#4339C2211yescharacteristic
18C23×Dic22C2211yescharacteristic
19C23×Dic22C2211yescharacteristic
20C23×Dic22C2211yescharacteristic
21C22×C11×M16C2211yescharacteristic
22C23×C8×C11C2211yescharacteristic
23C2×C4×D4×C11C2211yescharacteristic
24C2×#66992—21no—
25C2×D4×Dic11—21no—
26C2×#66983C2211yescharacteristic
27C2×#66977C2211yescharacteristic
28C2×#66977C2211yescharacteristic
29C2×#66977C2211yescharacteristic
30C2×#66962—28no—
31C2×#66962C2218yescomplemented
32C22×Dic44—28no—
33C22×Dic44C2211yescharacteristic
34C22×Dic44C2211yescharacteristic
35C22×Dic44C2211yescharacteristic
36C22×Dic44C2211yescharacteristic
37C22×Dic44C2211yescharacteristic
38C22×Dic44C2211yescharacteristic
39C22×Dic44C2218yescomplemented
40C22×#4314C2211yescharacteristic
41C22×#4314C2211yescharacteristic
42C22×#4314C2211yescharacteristic
43#10623083—24no—
44#10623083C2218yes—
45D4×Dic22—24no—
46D4×Dic22C2218yescomplemented
47C2×#66949—21no—
48C2×#66941—21no—
49C2×#66938—21no—
50C2×(C22⋊D11)⋊C4—21no—
51C2×#66931—21no—
52C2×#66931—21no—
53C2×#66928C2211yescharacteristic
54C2×#66922C2211yescharacteristic
55C2×C4×Dic22C2211yescharacteristic
56C2×C4×Dic22C2211yescharacteristic
57C11×#435C2218yescomplemented
58C2×C11×C4⋊C8C2211yescharacteristic
59C2×C11×C22⋊C8C2211yescharacteristic
60C2×C11×C22⋊C8C2211yescharacteristic
61C2×C11×#97C2211yescharacteristic
62#10622750C2218yescomplemented
63#10622727C2218yescomplemented
64C2×#66885C2211yescharacteristic
65C2×#66881C2211yescharacteristic
66C2×#66880C2211yescharacteristic
67C2×#66880C2211yescharacteristic
68C2×#66880C2211yescharacteristic
69C2×#66880C2211yescharacteristic
70C2×#66880C2211yescharacteristic
71#10622462C2218yescomplemented
72#10622458C2218yescomplemented
73#10622352C2218yescomplemented
74#10622352C2218yescomplemented
75#10622351C2218yescomplemented
76#10622346C2218yescomplemented
77#10622329C2218yescomplemented
78#10622328C2218yescomplemented
79C22×D4×C11D411yescharacteristic
80C23×C4×C11C2311yescharacteristic
81C23×C4×C11C2311yescharacteristic
82C22×C22⋊D11—21no—
83C22×C22⋊D11—21no—
84C23×Dic11—21no—
85C23×Dic11—21no—
86C23×Dic11—21no—
87C2×#4339—22no—
88C2×#4339—24no—
89C2×#4339—42no—
90C2×#4339C2314yes—
91C22×D44C2311yescharacteristic
92C22×C4×D11—21no—
93C22×Dic22—24no—
94C22×Dic22—24no—
95C22×Dic22—24no—
96C22×Dic22—21no—
97C22×Dic22—21no—
98C22×Dic22—21no—
99C22×Dic22—22no—
100C22×Dic22—22no—
101C22×Dic22—22no—
102C22×Dic22—42no—
103C22×Dic22—42no—
104C22×Dic22—42no—
105C22×Dic22C2311yescharacteristic
106C22×Dic22C2311yescharacteristic
107C22×Dic22C2311yescharacteristic
108C22×Dic22C2314yes—
109C22×Dic22C2314yes—
110C22×Dic22C2314yes—
111C22×Dic22C2311yescharacteristic
112C22×Dic22C2311yescharacteristic
113C2×C11×M16—24no—
114C2×C11×M16C2314yes—
115C22×C8×C11—24no—
116C22×C8×C11C2311yescharacteristic
117C22×C8×C11C2314yes—
118C22×C8×C11C2311yescharacteristic
119C22×C8×C11C2311yescharacteristic
120C22×C8×C11C2311yescharacteristic
121C4×D4×C11D414yes—
122C4×D4×C11C2314yes—
123C2×C11×C4⋊C4D411yescharacteristic
124C2×C11×C22⋊C4D411yescharacteristic
125C2×C11×C22⋊C4D411yescharacteristic
126C2×C42×C11C2311yescharacteristic
127C2×C22⋊Dic11—21no—
128C2×C22⋊Dic11—21no—
129C2×C22⋊Dic11—21no—
130#66992—28no—
131D4×Dic11—28no—
132#66983—22no—
133#66983C2314yes—
134C2×(C2×D11)⋊C4—21no—
135C2×(C2×D11)⋊C4—21no—
136C2×(C2×D11)⋊C4—21no—
137C2×C4⋊Dic11—21no—
138C2×C4⋊Dic11—21no—
139C2×C4⋊Dic11C2311yescharacteristic
140C2×C4⋊Dic11C2311yescharacteristic
141#66977—22no—
142#66977—22no—
143#66977—22no—
144#66977C2314yes—
145#66977C2314yes—
146#66977C2314yes—
147C2×Dic11⋊C4—21no—
148C2×Dic11⋊C4—21no—
149C2×Dic11⋊C4—21no—
150C2×Dic11⋊C4—21no—
151C2×Dic11⋊C4—21no—
152C2×C4×Dic11—21no—
153C2×C4×Dic11—21no—
154#66962—232no—
155C2×Dic44—24no—
156C2×Dic44—24no—
157C2×Dic44—24no—
158C2×Dic44—24no—
159C2×Dic44—232no—
160C2×Dic44—42no—
161C2×Dic44D418yescomplemented
162C2×Dic44C2314yes—
163C2×Dic44C2314yes—
164C2×Dic44C2314yes—
165C2×Dic44C2314yes—
166C2×Dic44C2314yes—
167C2×Dic44C2314yes—
168C2×#4314—24no—
169C2×#4314—24no—
170C2×#4314—42no—
171C2×#4314C2314yes—
172C2×#4314C2314yes—
173C2×#4314C2314yes—
174#66949—28no—
175#66941—28no—
176#66938—28no—
177(C22⋊D11)⋊C4—28no—
178#66931—28no—
179#66931—28no—
180#66928—22no—
181#66928C2314yes—
182#66922—22no—
183#66922C2314yes—
184C4×Dic22—22no—
185C4×Dic22—22no—
186C4×Dic22C2314yes—
187C4×Dic22C2314yes—
188C11×C4⋊C8C2314yes—
189C11×C22⋊C8C2314yes—
190C11×C22⋊C8C2314yes—
191C11×#97C2314yes—
192#66885C2314yes—
193#66881C2314yes—
194#66880C2314yes—
195#66880C2314yes—
196#66880C2314yes—
197#66880C2314yes—
198#66880C2314yes—
199C2×#3270—111nomaximal, Sylow
200C24×C11C2×D411yescharacteristic
201C24×C11C2×D411yescharacteristic
202C23×D11—21no—
203C2×D4×C11—24no—
204C2×D4×C11C2×D414yes—
205C22×C4×C11—22no—
206C22×C4×C11—22no—
207C22×C4×C11—22no—
208C22×C4×C11—22no—
209C22×C4×C11C2×D411yescharacteristic
210C22×C4×C11C2×D411yescharacteristic
211C22×C4×C11C2×D411yescharacteristic
212C22×C4×C11C2×D411yescharacteristic
213C22×C4×C11C2×D412yes—
214C22×C4×C11C2×D412yes—
215C22×C4×C11C2412yes—
216C22×C4×C11C2412yes—
217C22×C4×C11C2411yescharacteristic
218C2×C22⋊D11—24no—
219C2×C22⋊D11—24no—
220C2×C22⋊D11—44no—
221C2×C22⋊D11—44no—
222C22×Dic11—21no—
223C22×Dic11—21no—
224C22×Dic11—24no—
225C22×Dic11—24no—
226C22×Dic11—24no—
227C22×Dic11—21no—
228C22×Dic11—21no—
229C22×Dic11—21no—
230C22×Dic11—21no—
231C22×Dic11—21no—
232C22×Dic11—44no—
233C22×Dic11—44no—
234C22×Dic11—44no—
235#4339—28no—
236#4339—44no—
237#4339—48no—
238C2×D44—21no—
239C2×D44—22no—
240C2×D44—22no—
241C2×D44C2412yes—
242C2×C4×D11—24no—
243C2×C4×D11—44no—
244C2×Dic22—28no—
245C2×Dic22—28no—
246C2×Dic22—28no—
247C2×Dic22—21no—
248C2×Dic22—21no—
249C2×Dic22—22no—
250C2×Dic22—22no—
251C2×Dic22—22no—
252C2×Dic22—21no—
253C2×Dic22—21no—
254C2×Dic22—21no—
255C2×Dic22—24no—
256C2×Dic22—24no—
257C2×Dic22—24no—
258C2×Dic22—22no—
259C2×Dic22—22no—
260C2×Dic22—22no—
261C2×Dic22—22no—
262C2×Dic22—22no—
263C2×Dic22—44no—
264C2×Dic22—44no—
265C2×Dic22—44no—
266C2×Dic22—48no—
267C2×Dic22—48no—
268C2×Dic22—48no—
269C2×Dic22—44no—
270C2×Dic22—44no—
271C2×Dic22—44no—
272C2×Dic22C2×D414yes—
273C2×Dic22C2×D414yes—
274C2×Dic22C2412yes—
275C2×Dic22C2412yes—
276C2×Dic22C2412yes—
277C2×Dic22C2412yes—
278C2×Dic22C2412yes—
279C11×M16—28no—
280C2×C8×C11—28no—
281C2×C8×C11—22no—
282C2×C8×C11—22no—
283C2×C8×C11—22no—
284C2×C8×C11C2×D414yes—
285C2×C8×C11C2412yes—
286C2×C8×C11C2412yes—
287C2×C8×C11C2412yes—
288C2×C8×C11C2412yes—
289C11×C4⋊C4C2×D414yes—
290C11×C22⋊C4C2×D414yes—
291C11×C22⋊C4C2×D414yes—
292C42×C11C2×D412yes—
293C42×C11C2412yes—
294C22⋊Dic11—24no—
295C22⋊Dic11—24no—
296C22⋊Dic11—24no—
297(C2×D11)⋊C4—24no—
298(C2×D11)⋊C4—24no—
299(C2×D11)⋊C4—24no—
300C4⋊Dic11—21no—
301C4⋊Dic11—21no—
302C4⋊Dic11—24no—
303C4⋊Dic11—24no—
304C4⋊Dic11C2412yes—
305C4⋊Dic11C2412yes—
306Dic11⋊C4—24no—
307Dic11⋊C4—24no—
308Dic11⋊C4—24no—
309Dic11⋊C4—24no—
310Dic11⋊C4—24no—
311C4×Dic11—24no—
312C4×Dic11—24no—
313Dic44—28no—
314Dic44—28no—
315Dic44—28no—
316Dic44—28no—
317Dic44—44no—
318Dic44C2×D4116yescomplemented
319#4314—28no—
320#4314—28no—
321#4314—44no—
322C22×#137—111no—
323C23×Q16—111no—
324C2×D4×Q8—111no—
325C2×#548—111no—
326#3270—1116no—
327C2×#497—111no—
328C2×#470—111no—
329C2×#465—111no—
330C2×#464—111no—
331C2×#462—111no—
332C2×#452—111no—
333C2×#451—111no—
334C2×#451—111no—
335C2×#448—111no—
336C2×#441—111no—
337C2×#435D1111yescharacteristic, complemented
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—22no—
341C23×C11—22no—
342C23×C11—22no—
343C23×C11#13714yescomplemented
344C23×C11C22×D412yes—
345C23×C11C22×D412yes—
346C23×C11C22×D411yescharacteristic
347C22×D11—22no—
348C22×D11—42no—
349C22×D11—42no—
350C22×D11—42no—
351D4×C11—28no—
352C2×C4×C11—22no—
353C2×C4×C11—22no—
354C2×C4×C11—22no—
355C2×C4×C11—22no—
356C2×C4×C11—24no—
357C2×C4×C11—24no—
358C2×C4×C11—22no—
359C2×C4×C11—22no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11C22×D412yes—
363C2×C4×C11C22×D412yes—
364C2×C4×C11C22×D412yes—
365C2×C4×C11C22×D412yes—
366C2×C4×C11C22×D411yescharacteristic
367C2×C4×C11C22×D412yes—
368C2×C4×C11H(5,𝔽2)12yes—
369C2×C4×C11C2511yescharacteristic
370C22⋊D11—48no—
371C22⋊D11—48no—
372C2×Dic11—24no—
373C2×Dic11—24no—
374C2×Dic11—22no—
375C2×Dic11—22no—
376C2×Dic11—22no—
377C2×Dic11—22no—
378C2×Dic11—22no—
379C2×Dic11—22no—
380C2×Dic11—22no—
381C2×Dic11—48no—
382C2×Dic11—48no—
383C2×Dic11—48no—
384C2×Dic11—42no—
385C2×Dic11—42no—
386C2×Dic11—42no—
387C2×Dic11—42no—
388C2×Dic11—42no—
389D44—22no—
390D44—22no—
391D44—42no—
392C4×D11—48no—
393Dic22—24no—
394Dic22—24no—
395Dic22—22no—
396Dic22—22no—
397Dic22—22no—
398Dic22—22no—
399Dic22—22no—
400Dic22—22no—
401Dic22—22no—
402Dic22—22no—
403Dic22—48no—
404Dic22—48no—
405Dic22—48no—
406Dic22—42no—
407Dic22—42no—
408Dic22—42no—
409Dic22C22×D414yes—
410Dic22C22×D414yes—
411C8×C11—22no—
412C8×C11—22no—
413C8×C11—22no—
414C8×C11C22×D414yes—
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—118no—
427C22×Q16—111no—
428C22×Q16—228no—
429C22×SD16—111no—
430C22×SD16—111no—
431C22×SD16—111no—
432C22×M16C2×D1111yescharacteristic
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—111no—
445C2×C22⋊Q8—221no—
446C2×C22⋊Q8—221no—
447C2×C22⋊Q8—221no—
448C2×#121—111no—
449C2×#121—221no—
450C2×C4×Q8—111no—
451C2×C4×Q8—111no—
452C2×C4×D4—221no—
453C2×C4×D4—221no—
454C2×C4×D4C2×D1111yescharacteristic
455#497—118no—
456#470—118no—
457#465—118no—
458#464—118no—
459#462—118no—
460#452—118no—
461#451—118no—
462#451—118no—
463#448—118no—
464#441—118no—
465#435C2×D1118yescomplemented
466C2×#106—111no—
467C2×C4⋊C8C2×D1111yescharacteristic
468C2×#103—111no—
469C2×#103—111no—
470C2×#103—111no—
471C2×#103—111no—
472C2×#103—111no—
473C2×#102—111no—
474C2×C22⋊C8C2×D1111yescharacteristic
475C2×C22⋊C8C2×D1111yescharacteristic
476C2×#97C2×D1111yescharacteristic
477C22×C11—22no—
478C22×C11—28no—
479C22×C11—22no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—44no—
484C22×C11D4212yes—
485C22×C11C2×#13712yes—
486C22×C11C2×#13714yescomplemented
487C22×C11#57812yes—
488C22×C11C23×D411yescharacteristic
489C2×D11—42no—
490C2×D11—42no—
491C2×D11—42no—
492C2×D11—84no—
493C4×C11—22no—
494C4×C11—22no—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11D4212yes—
498C4×C11C23×D411yescharacteristic
499C4×C11C2×H(5,𝔽2)11yescharacteristic
500Dic11—24no—
501Dic11—24no—
502Dic11—42no—
503Dic11—42no—
504Dic11—42no—
505Dic11—42no—
506Dic11—42no—
507C2×#41—114no—
508C2×#41—224no—
509C2×#41—222no—
510C2×#41—442no—
511C22×Q8—111no—
512C22×Q8—111no—
513C22×Q8—111no—
514C22×Q8—111no—
515C22×Q8—111no—
516C22×Q8—114no—
517C22×Q8—114no—
518C22×Q8—114no—
519C22×Q8—224no—
520C22×Q8—224no—
521C22×Q8—224no—
522C22×Q8—221no—
523C22×Q8—221no—
524C22×Q8—221no—
525C22×Q8—222no—
526C22×Q8—222no—
527C22×Q8—222no—
528C22×Q8—442no—
529C22×Q8—442no—
530C22×Q8—442no—
531C22×D4—111no—
532C22×D4—221no—
533C22×D4—221no—
534C22×D4D4411yescharacteristic
535C23×C4—221no—
536C23×C4—221no—
537C23×C4—221no—
538C23×C4—221no—
539C23×C4C22×D1111yescharacteristic
540C23×C4C22×D1111yescharacteristic
541#137—2232no—
542C2×Q16—118no—
543C2×Q16—114no—
544C2×Q16—114no—
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—114no—
556C2×SD16—114no—
557C2×SD16—114no—
558C2×SD16—224no—
559C2×SD16—224no—
560C2×SD16—442no—
561C2×M16—24no—
562C2×M16C22×D1114yes—
563C22×C8—24no—
564C22×C8C22×D1111yescharacteristic
565C22×C8C22×D1114yes—
566C22×C8C22×D1111yescharacteristic
567C22×C8C22×D1111yescharacteristic
568C22×C8C22×D1111yescharacteristic
569C4⋊Q8—114no—
570C4⋊Q8—228no—
571C4⋊Q8—222no—
572#124—114no—
573#124—228no—
574#124—222no—
575C22⋊Q8—114no—
576C22⋊Q8—114no—
577C22⋊Q8—114no—
578C22⋊Q8—222no—
579C22⋊Q8—222no—
580C22⋊Q8—222no—
581C22⋊Q8—228no—
582C22⋊Q8—228no—
583C22⋊Q8—228no—
584#121—114no—
585#121—228no—
586#121—222no—
587C4×Q8—114no—
588C4×Q8—114no—
589C4×Q8—222no—
590C4×Q8—222no—
591C4×D4—228no—
592C4×D4—228no—
593C4×D4D4414yes—
594C4×D4C22×D1114yes—
595C2×C4⋊C4—111no—
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⋊C4—221no—
604C2×C4⋊C4D4411yescharacteristic
605C2×C22⋊C4—221no—
606C2×C22⋊C4—221no—
607C2×C22⋊C4—221no—
608C2×C22⋊C4—221no—
609C2×C22⋊C4—221no—
610C2×C22⋊C4—221no—
611C2×C22⋊C4D4411yescharacteristic
612C2×C22⋊C4D4411yescharacteristic
613C2×C42—221no—
614C2×C42—221no—
615C2×C42C22×D1111yescharacteristic
616#106—114no—
617C4⋊C8C22×D1114yes—
618#103—114no—
619#103—114no—
620#103—114no—
621#103—114no—
622#103—114no—
623#102—114no—
624C22⋊C8C22×D1114yes—
625C22⋊C8C22×D1114yes—
626#97C22×D1114yes—
627C2×C11—24no—
628C2×C11—42no—
629C2×C11#327014yescomplemented
630C2×C11C2×D4211yescharacteristic
631C2×C11C22×#13711yescharacteristic
632C2×C11C2×#57811yescharacteristic
633D11—82no—
634C24—221no—
635C24C2×D4411yescharacteristic
636C24C2×D4411yescharacteristic
637#41—228no—
638#41—444no—
639#41—448no—
640C2×Q8—114no—
641C2×Q8—114no—
642C2×Q8—112no—
643C2×Q8—112no—
644C2×Q8—112no—
645C2×Q8—112no—
646C2×Q8—112no—
647C2×Q8—228no—
648C2×Q8—228no—
649C2×Q8—228no—
650C2×Q8—221no—
651C2×Q8—221no—
652C2×Q8—224no—
653C2×Q8—221no—
654C2×Q8—224no—
655C2×Q8—224no—
656C2×Q8—221no—
657C2×Q8—221no—
658C2×Q8—222no—
659C2×Q8—222no—
660C2×Q8—222no—
661C2×Q8—222no—
662C2×Q8—222no—
663C2×Q8—222no—
664C2×Q8—222no—
665C2×Q8—222no—
666C2×Q8—444no—
667C2×Q8—444no—
668C2×Q8—444no—
669C2×Q8—444no—
670C2×Q8—444no—
671C2×Q8—444no—
672C2×Q8—448no—
673C2×Q8—448no—
674C2×Q8—448no—
675C2×D4—24no—
676C2×D4—112no—
677C2×D4—224no—
678C2×D4—224no—
679C2×D4—221no—
680C2×D4—222no—
681C2×D4—222no—
682C2×D4—444no—
683C2×D4—444no—
684C2×D4C2×D4414yes—
685C22×C4—22no—
686C22×C4—22no—
687C22×C4—22no—
688C22×C4—22no—
689C22×C4—221no—
690C22×C4—221no—
691C22×C4—224no—
692C22×C4—224no—
693C22×C4—224no—
694C22×C4—221no—
695C22×C4—221no—
696C22×C4—221no—
697C22×C4—221no—
698C22×C4—221no—
699C22×C4—224no—
700C22×C4—444no—
701C22×C4—444no—
702C22×C4—444no—
703C22×C4—444no—
704C22×C4C2×D4412yes—
705C22×C4C2×D4412yes—
706C22×C4C2×D4411yescharacteristic
707C22×C4C2×D4411yescharacteristic
708C22×C4C2×D4411yescharacteristic
709C22×C4C2×D4411yescharacteristic
710C22×C4C23×D1112yes—
711C22×C4C23×D1112yes—
712C22×C4C23×D1111yescharacteristic
713Q16—1116no—
714Q16—228no—
715Q16—228no—
716Q16—228no—
717Q16—228no—
718Q16—444no—
719SD16—228no—
720SD16—228no—
721SD16—444no—
722M16—28no—
723C2×C8—22no—
724C2×C8—22no—
725C2×C8—22no—
726C2×C8—28no—
727C2×C8D4×D1114yes—
728C2×C8C23×D1112yes—
729C2×C8C23×D1112yes—
730C2×C8C23×D1112yes—
731C2×C8C23×D1112yes—
732C4⋊C4—112no—
733C4⋊C4—112no—
734C4⋊C4—221no—
735C4⋊C4—221no—
736C4⋊C4—224no—
737C4⋊C4—224no—
738C4⋊C4—224no—
739C4⋊C4—224no—
740C4⋊C4—224no—
741C4⋊C4—224no—
742C4⋊C4—224no—
743C4⋊C4C2×D4414yes—
744C22⋊C4—224no—
745C22⋊C4—224no—
746C22⋊C4—224no—
747C22⋊C4—224no—
748C22⋊C4—224no—
749C22⋊C4—224no—
750C22⋊C4C2×D4414yes—
751C22⋊C4C2×D4414yes—
752C42—224no—
753C42—224no—
754C42C2×D4412yes—
755C42C23×D1112yes—
756C11C2×#327011yescharacteristic, complemented, Sylow
757C23—22no—
758C23—22no—
759C23—22no—
760C23—22no—
761C23—22no—
762C23—222no—
763C23—442no—
764C23—442no—
765C23—442no—
766C23#6696214yescomplemented
767C23C22×D4412yes—
768C23C22×D4412yes—
769C23C22×D4411yescharacteristic
770Q8—114no—
771Q8—114no—
772Q8—224no—
773Q8—224no—
774Q8—222no—
775Q8—222no—
776Q8—222no—
777Q8—222no—
778Q8—222no—
779Q8—222no—
780Q8—222no—
781Q8—222no—
782Q8—448no—
783Q8—448no—
784Q8—448no—
785Q8—442no—
786Q8—442no—
787Q8—442no—
788D4—28no—
789D4—222no—
790D4—222no—
791D4—448no—
792D4—448no—
793D4—442no—
794C2×C4—22no—
795C2×C4—22no—
796C2×C4—22no—
797C2×C4—22no—
798C2×C4—24no—
799C2×C4—24no—
800C2×C4—22no—
801C2×C4—22no—
802C2×C4—22no—
803C2×C4—22no—
804C2×C4—224no—
805C2×C4—224no—
806C2×C4—222no—
807C2×C4—222no—
808C2×C4—222no—
809C2×C4—222no—
810C2×C4—222no—
811C2×C4—222no—
812C2×C4—222no—
813C2×C4—448no—
814C2×C4—448no—
815C2×C4—448no—
816C2×C4—448no—
817C2×C4—442no—
818C2×C4—442no—
819C2×C4—442no—
820C2×C4—442no—
821C2×C4—442no—
822C2×C4C22×D4412yes—
823C2×C4C22×D4412yes—
824C2×C4C22×D4412yes—
825C2×C4C22×D4412yes—
826C2×C4C22×D4411yescharacteristic
827C2×C4C2×D4×D1112yes—
828C2×C4#6704212yes—
829C2×C4C24×D1111yescharacteristic
830C8—22no—
831C8—22no—
832C8—22no—
833C8C2×D4×D1114yes—
834C22—28no—
835C22—22no—
836C22—22no—
837C22—22no—
838C22—22no—
839C22—22no—
840C22—44no—
841C22—442no—
842C22—442no—
843C22—442no—
844C22—884no—
845C22D4×D4412yes—
846C22C2×#6696212yes—
847C22C2×#6696214yescomplemented
848C22#1062328412yes—
849C22C23×D4411yescharacteristic
850C4—22no—
851C4—22no—
852C4—22no—
853C4—22no—
854C4—224no—
855C4—224no—
856C4—442no—
857C4—442no—
858C4—442no—
859C4—442no—
860C4—442no—
861C4D4×D4412yes—
862C4C22×D4×D1111yescharacteristic
863C4C2×#6704211yescharacteristic
864C2—24no—
865C2—42no—
866C2—882no—
867C2#1308019114yesdirect product factor
868C2C2×D4×D4411yescharacteristic
869C2C22×#6696211yescharacteristic
870C2C2×#1062328411yescharacteristic
subgroupG/H
centerC23C22×D44
commutator, cosocleC2×C4×C11C25
FrattiniC2×C4C24×D11
FittingC2×C11×#435C2
socleC23×C11C22×D4
prime radicalC2×#10623083C2
hypercenterC2×#435D11
hypocenterC11C2×#3270
LCSG ▷ C2×C4×C11 ▷ C2×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×C4×D4 ◁ C2×#435

Complements

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

NH ≅ G/Ntype
1. C22×#66962C2semidirect
2. C23×Dic44C2semidirect
3. C2×D4×Dic22C2semidirect
5. #13080191C2direct (N × H)
6. C2×#10622328C2semidirect
7. C2×#10622750C2semidirect
8. C2×#10622727C2semidirect
9. C2×#10622458C2semidirect
10. C2×#10622462C2semidirect
11. C2×#10622346C2semidirect
12. C2×#10622352C2semidirect
13. C2×#10622352C2semidirect
14. C2×#10622351C2semidirect
15. C2×#10622329C2semidirect
16. C2×C11×#435C2semidirect
31. C2×#66962C22semidirect
39. C22×Dic44C22semidirect
46. D4×Dic22C22semidirect
57. C11×#435C22semidirect
62. #10622750C22semidirect
63. #10622727C22semidirect
71. #10622462C22semidirect
72. #10622458C22semidirect
73. #10622352C22semidirect
74. #10622352C22semidirect
75. #10622351C22semidirect
76. #10622346C22semidirect
77. #10622329C22semidirect
78. #10622328C22semidirect
161. C2×Dic44D4semidirect
318. Dic44C2×D4semidirect
337. C2×#435D11semidirect
343. C23×C11#137semidirect
465. #435C2×D11semidirect
486. C22×C11C2×#137semidirect
629. C2×C11#3270semidirect
756. C11C2×#3270semidirect
766. C23#66962semidirect
847. C22C2×#66962semidirect
867. C2#13080191direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669622
C23×Dic442
C2×D4×Dic222
C2×#106230832
#130801912
C2×#106223282
C2×#106227502
C2×#106227272
C2×#106224582
C2×#106224622
C2×#106223462
C2×#106223522
C2×#106223512
C2×#106223292
C2×C11×#4352
C2×#327011