Finite Group Databasebeta

← C2×#13082861 #15661021

Subgroups — C2×#13082861 #15661021

Order 2816.

7162 conjugacy classes of subgroups.

The subgroup lattice has 848 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#13082861C2132yesmaximal, direct product factor
2C2×#10623177C214yesmaximal, complemented
3C2×#10623173C212yesmaximal, complemented
4C2×#10623044C212yesmaximal, complemented
5C2×#10623026C214yesmaximal, complemented
6C2×Q8×C22⋊D11C212yesmaximal, complemented
7C2×#10623163C212yesmaximal, complemented
8C2×#10623031C212yesmaximal, complemented
9C2×#10623154C212yesmaximal, complemented
10C2×#10623156C212yesmaximal, complemented
11C2×#10623176C212yesmaximal, complemented
12C2×#10623046C212yesmaximal, complemented
13C2×#10623159C212yesmaximal, complemented
14C2×#10623322C211yesmaximal, characteristic
15C22×#66977C211yesmaximal, characteristic, complemented
16C22×C11×C22⋊Q8C211yesmaximal, characteristic, complemented
17C23×Q8×C11C2211yescharacteristic
18C24×C4×C11C2211yescharacteristic
19C22×Q8×D11C2212yescomplemented
20C22×#4339C2211yescharacteristic
21C23×Dic22C2211yescharacteristic
22C2×C11×C22⋊Q8C2212yes—
23C2×C11×C22⋊Q8C2212yes—
24C2×C11×C22⋊Q8C2212yes—
25C2×C11×C22⋊Q8C2212yes—
26C2×C11×C22⋊Q8C22116yescomplemented
27C22×C11×C4⋊C4C2211yescharacteristic
28C22×C11×C4⋊C4C2212yes—
29C22×C11×C22⋊C4C2212yes—
30C2×#67006C2212yes—
31C22×C22⋊Dic11C2212yes—
32Q8×C22⋊D11C22132yescomplemented
33C2×#66999C2212yescomplemented
34C2×#66999C2214yescomplemented
35C2×Q8×Dic11C2212yescomplemented
36C2×#66997C2214yescomplemented
37C2×#66997C2212yescomplemented
38#10623322C22116yes—
39C2×#66983C2211yescharacteristic
40C2×#66983C2211yescharacteristic
41C2×#66982C2214yes—
42C2×#66982C2212yes—
43C2×C4×C22⋊D11C2214yes—
44C2×C4×C22⋊D11C2212yes—
45C2×C4×C22⋊D11C2212yes—
46C2×#66979C2214yes—
47C2×#66979C2211yescharacteristic
48C22×C4⋊Dic11C2211yescharacteristic
49C2×#66977C2214yes—
50C2×#66977C2211yescharacteristic
51C2×#66977C2211yescharacteristic
52C2×#66977C2212yes—
53C2×#66977C2212yes—
54C2×#66977C2212yes—
55C2×#66977C2212yes—
56C2×#66977C22116yescomplemented
57C22×Dic11⋊C4C2212yes—
58#10623177C22164yescomplemented
59#10623176C22132yescomplemented
60#10623173C22132yescomplemented
61#10623163C22132yescomplemented
62#10623159C22132yescomplemented
63#10623156C22132yescomplemented
64#10623154C22132yescomplemented
65#10623046C22132yescomplemented
66#10623044C22132yescomplemented
67C2×#66951C2214yescomplemented
68C2×#66951C2214yescomplemented
69C2×#66950C2212yescomplemented
70C2×#66949C2214yescomplemented
71C2×#66947C2214yescomplemented
72C2×#66945C2212yescomplemented
73#10623031C22132yescomplemented
74C2×#66943C2212yescomplemented
75C2×#66943C2214yescomplemented
76C2×#66943C2214yescomplemented
77C2×#66942C2214yescomplemented
78C2×#66942C2214yescomplemented
79C2×#66941C2214yescomplemented
80C2×#66941C2214yescomplemented
81C2×#66940C2212yescomplemented
82#10623026C22164yescomplemented
83C2×#66939C2214yes—
84C2×#66938C2214yes—
85C2×#66936C2214yes—
86C2×(C22⋊D11)⋊C4C2214yes—
87C2×#66932C2214yes—
88C2×#66932C2214yes—
89C2×#66931C2214yes—
90C2×#66930C2214yes—
91C25×C11C2311yescharacteristic
92C22×Q8×C11—44no—
93C22×Q8×C11C2312yes—
94C22×Q8×C11C2312yes—
95C22×Q8×C11C2318yes—
96C23×C4×C11—44no—
97C23×C4×C11C2311yescharacteristic
98C23×C4×C11C2311yescharacteristic
99C23×C4×C11C2311yescharacteristic
100C23×C4×C11C2312yes—
101C23×C4×C11C2311yescharacteristic
102C23×C4×C11C2311yescharacteristic
103C23×C4×C11C2312yes—
104C23×C4×C11C2311yescharacteristic
105C23×C4×C11C2318yes—
106C22×C22⋊D11C2312yes—
107C22×C22⋊D11C2312yes—
108C22×C22⋊D11C2312yes—
109C23×Dic11C2312yes—
110C23×Dic11C2312yes—
111C2×Q8×D11—48no—
112C2×Q8×D11C23116yescomplemented
113C2×#4339—44no—
114C2×#4339C2318yes—
115C22×D44C2311yescharacteristic
116C22×C4×D11C2312yes—
117C22×C4×D11C2314yes—
118C22×Dic22—44no—
119C22×Dic22C2312yes—
120C22×Dic22C2314yes—
121C22×Dic22C2311yescharacteristic
122C22×Dic22C2312yes—
123C22×Dic22C2318yes—
124C11×C22⋊Q8C23116yes—
125C11×C22⋊Q8C23116yes—
126C11×C22⋊Q8C23116yes—
127C11×C22⋊Q8C23116yes—
128C2×C11×C4⋊C4C2312yes—
129C2×C11×C4⋊C4C2314yes—
130C2×C11×C4⋊C4C2314yes—
131C2×C11×C4⋊C4C2312yes—
132C2×C11×C4⋊C4C23116yes—
133C2×C11×C4⋊C4C2318yes—
134C2×C11×C22⋊C4C2314yes—
135C2×C11×C22⋊C4C2314yes—
136C2×C11×C22⋊C4C23116yes—
137#67006C23116yes—
138C2×C22⋊Dic11C2312yes—
139C2×C22⋊Dic11C2312yes—
140C2×C22⋊Dic11C2314yes—
141C2×C22⋊Dic11C23116yes—
142C2×C22⋊Dic11C2312yes—
143C2×C22⋊Dic11C2314yes—
144#66999C23116yescomplemented
145#66999C23132yescomplemented
146Q8×Dic11C23116yescomplemented
147#66997C23132yescomplemented
148#66997C23116yescomplemented
149#66983C2318yes—
150#66983C2318yes—
151#66982C23132yes—
152#66982C23116yes—
153C4×C22⋊D11C23132yes—
154C4×C22⋊D11C23116yes—
155C4×C22⋊D11C23116yes—
156C2×(C2×D11)⋊C4C2314yes—
157C2×(C2×D11)⋊C4C2314yes—
158C2×(C2×D11)⋊C4C2314yes—
159C2×(C2×D11)⋊C4C2312yes—
160C2×(C2×D11)⋊C4C2312yes—
161#66979C23132yes—
162#66979C2318yes—
163C2×C4⋊Dic11C2314yes—
164C2×C4⋊Dic11C2314yes—
165C2×C4⋊Dic11C2314yes—
166C2×C4⋊Dic11C2311yescharacteristic
167C2×C4⋊Dic11C2311yescharacteristic
168C2×C4⋊Dic11C2312yes—
169C2×C4⋊Dic11C2312yes—
170C2×C4⋊Dic11C2318yes—
171#66977C23132yes—
172#66977C2318yes—
173#66977C23116yes—
174#66977C23116yes—
175#66977C23116yes—
176#66977C23116yes—
177#66977C2318yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2314yes—
181C2×Dic11⋊C4C2314yes—
182C2×Dic11⋊C4C2314yes—
183C2×Dic11⋊C4C2312yes—
184C2×Dic11⋊C4C2314yes—
185C2×Dic11⋊C4C2312yes—
186C2×Dic11⋊C4C2314yes—
187C2×Dic11⋊C4C23116yes—
188C2×C4×Dic11C2314yes—
189C2×C4×Dic11C2314yes—
190C2×C4×Dic11C2314yes—
191C2×C4×Dic11C2312yes—
192#66951C23132yescomplemented
193#66951C23132yescomplemented
194#66950C23116yescomplemented
195#66949C23132yescomplemented
196#66947C23132yescomplemented
197#66945C23116yescomplemented
198#66943C23132yescomplemented
199#66943C23132yescomplemented
200#66943C23116yescomplemented
201#66942C23132yescomplemented
202#66942C23132yescomplemented
203#66941C23132yescomplemented
204#66941C23132yescomplemented
205#66940C23116yescomplemented
206#66939C23132yes—
207#66938C23132yes—
208#66936C23132yes—
209(C22⋊D11)⋊C4C23132yes—
210#66932C23132yes—
211#66932C23132yes—
212#66931C23132yes—
213#66930C23132yes—
214C2×#3538—111nomaximal, Sylow
215C24×C11—24no—
216C24×C11—24no—
217C24×C11—42no—
218C24×C11C2411yescharacteristic
219C24×C11C2414yes—
220C24×C11C2411yescharacteristic
221C24×C11C2411yescharacteristic
222C23×D11C2412yes—
223C2×Q8×C11—28no—
224C2×Q8×C11—44no—
225C2×Q8×C11—416no—
226C2×Q8×C11C2418yes—
227C2×Q8×C11C2418yes—
228C22×C4×C11—28no—
229C22×C4×C11—24no—
230C22×C4×C11—24no—
231C22×C4×C11—24no—
232C22×C4×C11—416no—
233C22×C4×C11—42no—
234C22×C4×C11—42no—
235C22×C4×C11—42no—
236C22×C4×C11—44no—
237C22×C4×C11C2414yes—
238C22×C4×C11C2414yes—
239C22×C4×C11C2411yescharacteristic
240C22×C4×C11C2411yescharacteristic
241C22×C4×C11C2411yescharacteristic
242C22×C4×C11C2414yes—
243C22×C4×C11C2414yes—
244C22×C4×C11C2414yes—
245C22×C4×C11C2418yes—
246C22×C4×C11C2414yes—
247C22×C4×C11C2414yes—
248C22×C4×C11C2418yes—
249C22×C4×C11C2414yes—
250C22×C4×C11C2411yescharacteristic
251C2×C22⋊D11—28no—
252C2×C22⋊D11—28no—
253C2×C22⋊D11—44no—
254C2×C22⋊D11C2418yes—
255C2×C22⋊D11C2418yes—
256C2×C22⋊D11C2418yes—
257C22×Dic11—28no—
258C22×Dic11—44no—
259C22×Dic11C2418yes—
260C22×Dic11C2412yes—
261C22×Dic11C2412yes—
262C22×Dic11C2414yes—
263C22×Dic11C2412yes—
264C22×Dic11C2414yes—
265C22×Dic11C2418yes—
266Q8×D11—432no—
267#4339—416no—
268C2×D44—42no—
269C2×D44C2414yes—
270C2×C4×D11—28no—
271C2×C4×D11—48no—
272C2×C4×D11C2418yes—
273C2×C4×D11C24116yes—
274C2×Dic22—28no—
275C2×Dic22—416no—
276C2×Dic22—44no—
277C2×Dic22—42no—
278C2×Dic22—48no—
279C2×Dic22C2418yes—
280C2×Dic22C24116yes—
281C2×Dic22C2414yes—
282C2×Dic22C2418yes—
283C11×C4⋊C4C2418yes—
284C11×C4⋊C4C24116yes—
285C11×C4⋊C4C24116yes—
286C11×C4⋊C4C2418yes—
287C11×C22⋊C4C24116yes—
288C11×C22⋊C4C24116yes—
289C22⋊Dic11C2418yes—
290C22⋊Dic11C2418yes—
291C22⋊Dic11C24116yes—
292C22⋊Dic11C2418yes—
293C22⋊Dic11C24116yes—
294(C2×D11)⋊C4C24116yes—
295(C2×D11)⋊C4C24116yes—
296(C2×D11)⋊C4C24116yes—
297(C2×D11)⋊C4C2418yes—
298(C2×D11)⋊C4C2418yes—
299C4⋊Dic11C24116yes—
300C4⋊Dic11C24116yes—
301C4⋊Dic11C24116yes—
302C4⋊Dic11C2414yes—
303C4⋊Dic11C2414yes—
304C4⋊Dic11C2418yes—
305C4⋊Dic11C2418yes—
306Dic11⋊C4C24116yes—
307Dic11⋊C4C24116yes—
308Dic11⋊C4C24116yes—
309Dic11⋊C4C24116yes—
310Dic11⋊C4C24116yes—
311Dic11⋊C4C2418yes—
312Dic11⋊C4C24116yes—
313Dic11⋊C4C2418yes—
314Dic11⋊C4C24116yes—
315C4×Dic11C24116yes—
316C4×Dic11C24116yes—
317C4×Dic11C24116yes—
318C4×Dic11C2418yes—
319#3538—1132no—
320C2×#563—114no—
321C2×#552—112no—
322C2×#552—112no—
323C2×#551—114no—
324C2×D4×Q8—112no—
325C2×D4×Q8—112no—
326C2×#544—112no—
327C2×#544—112no—
328C2×#541—112no—
329C2×#539—112no—
330C2×#539—112no—
331C2×#536—112no—
332C2×#525—111no—
333C22×C22⋊Q8—111no—
334C22×C22⋊Q8D1111yescharacteristic, complemented
335C23×C11—22no—
336C23×C11—22no—
337C23×C11—22no—
338C23×C11—22no—
339C23×C11—22no—
340C23×C11—28no—
341C23×C11—22no—
342C23×C11—28no—
343C23×C11—22no—
344C23×C11—44no—
345C23×C11—416no—
346C23×C112−1+414yes—
347C23×C112−1+414yes—
348C23×C11C2512yes—
349C23×C11C2512yes—
350C23×C11C2512yes—
351C23×C11C2511yescharacteristic
352C22×D11—24no—
353C22×D11—24no—
354C22×D11—24no—
355C22×D11C2514yes—
356Q8×C11—216no—
357Q8×C11—48no—
358C2×C4×C11—22no—
359C2×C4×C11—28no—
360C2×C4×C11—22no—
361C2×C4×C11—22no—
362C2×C4×C11—216no—
363C2×C4×C11—28no—
364C2×C4×C11—28no—
365C2×C4×C11—28no—
366C2×C4×C11—28no—
367C2×C4×C11—44no—
368C2×C4×C11—44no—
369C2×C4×C11—44no—
370C2×C4×C11—48no—
371C2×C4×C11H(5,𝔽2)14yes—
372C2×C4×C11C2518yes—
373C2×C4×C11C2518yes—
374C2×C4×C11C2512yes—
375C2×C4×C11C2512yes—
376C2×C4×C11C2512yes—
377C2×C4×C11C2512yes—
378C22⋊D11—216no—
379C22⋊D11—216no—
380C22⋊D11—48no—
381C2×Dic11—28no—
382C2×Dic11—24no—
383C2×Dic11—216no—
384C2×Dic11—28no—
385C2×Dic11—24no—
386C2×Dic11—24no—
387C2×Dic11—48no—
388C2×Dic11C2514yes—
389C2×Dic11C2514yes—
390C2×Dic11C2518yes—
391C2×Dic11C2514yes—
392C2×Dic11C2518yes—
393D44—44no—
394C4×D11—216no—
395C4×D11—416no—
396Dic22—216no—
397Dic22—48no—
398Dic22—44no—
399Dic22—416no—
400C22×#41—111no—
401C23×Q8—112no—
402C23×Q8—111no—
403C23×Q8C2×D1111yescharacteristic
404C24×C4C2×D1111yescharacteristic
405#563—1164no—
406#552—1132no—
407#552—1132no—
408#551—1164no—
409D4×Q8—1132no—
410D4×Q8—1132no—
411#544—1132no—
412#544—1132no—
413#541—1132no—
414#539—1132no—
415#539—1132no—
416#536—1132no—
417C2×C4⋊Q8—112no—
418C2×C4⋊Q8—114no—
419C2×C4⋊Q8—114no—
420C2×C4⋊Q8—114no—
421C2×#126—114no—
422C2×#126—114no—
423C2×#126—114no—
424C2×#126—114no—
425C2×#125—114no—
426C2×#125—114no—
427C2×#125—114no—
428C2×#125—112no—
429C2×#125—114no—
430C2×#124—114no—
431#525—1116no—
432C2×#123—112no—
433C2×#123—114no—
434C2×#123—114no—
435C2×#123—114no—
436C2×#123—114no—
437C2×C22⋊Q8—112no—
438C2×C22⋊Q8—114no—
439C2×C22⋊Q8—112no—
440C2×C22⋊Q8—112no—
441C2×C22⋊Q8—112no—
442C2×C22⋊Q8—112no—
443C2×C22⋊Q8—111no—
444C2×C22⋊Q8—111no—
445C2×C22⋊Q8—114no—
446C2×C22⋊Q8—1116no—
447C2×C22⋊Q8—114no—
448C2×C22⋊Q8—112no—
449C2×C22⋊Q8—114no—
450C2×C22⋊Q8C2×D1112yes—
451C2×C22⋊Q8C2×D1112yes—
452C2×C22⋊Q8C2×D1112yes—
453C2×C22⋊Q8C2×D1112yes—
454C2×C22⋊Q8C2×D11116yescomplemented
455C2×#121—111no—
456C2×#121—111no—
457C2×#120—112no—
458C2×C4×Q8—112no—
459C2×C4×Q8—112no—
460C2×C4×D4—112no—
461C2×C4×D4—112no—
462C2×C4×D4—114no—
463C2×C4×D4—114no—
464C2×#117—111no—
465C2×#117—114no—
466C2×#117—112no—
467C2×#117—114no—
468C22×C4⋊C4—112no—
469C22×C4⋊C4—111no—
470C22×C4⋊C4C2×D1112yes—
471C22×C4⋊C4C2×D1111yescharacteristic
472C22×C22⋊C4—112no—
473C22×C22⋊C4C2×D1112yes—
474C22×C11—22no—
475C22×C11—22no—
476C22×C11—22no—
477C22×C11—22no—
478C22×C11—28no—
479C22×C11—28no—
480C22×C11—22no—
481C22×C11—22no—
482C22×C11—22no—
483C22×C11—416no—
484C22×C11—44no—
485C22×C11C2×H(5,𝔽2)12yes—
486C22×C11C2×2−1+414yes—
487C22×C11C2×2−1+412yes—
488C22×C11C2×2−1+414yes—
489C22×C11C2×2−1+412yes—
490C22×C11C2611yescharacteristic
491C2×D11—24no—
492C2×D11—24no—
493C2×D11—24no—
494C2×D11—48no—
495C4×C11—22no—
496C4×C11—22no—
497C4×C11—22no—
498C4×C11—28no—
499C4×C11—28no—
500C4×C11C2×H(5,𝔽2)14yes—
501Dic11—28no—
502Dic11—24no—
503Dic11—28no—
504Dic11—24no—
505Dic11—24no—
506C25C22×D1111yescharacteristic
507C2×#41—118no—
508C2×#41—444no—
509C22×Q8—44no—
510C22×Q8—1116no—
511C22×Q8—112no—
512C22×Q8—112no—
513C22×Q8—114no—
514C22×Q8—111no—
515C22×Q8—118no—
516C22×Q8—444no—
517C22×Q8—448no—
518C22×Q8C22×D1112yes—
519C22×Q8C22×D1112yes—
520C22×Q8C22×D1118yes—
521C22×D4—112no—
522C22×D4—112no—
523C22×D4—112no—
524C22×D4—111no—
525C23×C4—44no—
526C23×C4—112no—
527C23×C4—112no—
528C23×C4—112no—
529C23×C4—114no—
530C23×C4C22×D1112yes—
531C23×C4C22×D1111yescharacteristic
532C23×C4C22×D1111yescharacteristic
533C23×C4C22×D1111yescharacteristic
534C23×C4C22×D1112yes—
535C23×C4C22×D1111yescharacteristic
536C23×C4C22×D1111yescharacteristic
537C23×C4C22×D1111yescharacteristic
538C23×C4C22×D1118yes—
539C4⋊Q8—1116no—
540C4⋊Q8—1132no—
541C4⋊Q8—1132no—
542C4⋊Q8—1132no—
543#126—1132no—
544#126—1132no—
545#126—1132no—
546#126—1132no—
547#125—1132no—
548#125—1132no—
549#125—1116no—
550#125—1132no—
551#125—1132no—
552#124—1132no—
553#123—1116no—
554#123—1132no—
555#123—1132no—
556#123—1132no—
557#123—1132no—
558C22⋊Q8—1116no—
559C22⋊Q8—1132no—
560C22⋊Q8—1116no—
561C22⋊Q8—1116no—
562C22⋊Q8—1116no—
563C22⋊Q8—1116no—
564C22⋊Q8—118no—
565C22⋊Q8—118no—
566C22⋊Q8—1132no—
567C22⋊Q8—1116no—
568C22⋊Q8—1132no—
569C22⋊Q8—1132no—
570C22⋊Q8C22×D11116yes—
571C22⋊Q8C22×D11116yes—
572C22⋊Q8C22×D11116yes—
573C22⋊Q8C22×D11116yes—
574#121—118no—
575#121—118no—
576#120—1116no—
577C4×Q8—1116no—
578C4×Q8—1116no—
579C4×D4—1116no—
580C4×D4—1116no—
581C4×D4—1132no—
582C4×D4—1132no—
583#117—118no—
584#117—1132no—
585#117—1116no—
586#117—1132no—
587C2×C4⋊C4—112no—
588C2×C4⋊C4—114no—
589C2×C4⋊C4—114no—
590C2×C4⋊C4—112no—
591C2×C4⋊C4—1116no—
592C2×C4⋊C4—118no—
593C2×C4⋊C4—111no—
594C2×C4⋊C4—111no—
595C2×C4⋊C4—114no—
596C2×C4⋊C4—114no—
597C2×C4⋊C4—114no—
598C2×C4⋊C4—114no—
599C2×C4⋊C4—114no—
600C2×C4⋊C4—114no—
601C2×C4⋊C4—112no—
602C2×C4⋊C4—112no—
603C2×C4⋊C4—114no—
604C2×C4⋊C4—114no—
605C2×C4⋊C4C22×D1112yes—
606C2×C4⋊C4C22×D1114yes—
607C2×C4⋊C4C22×D1114yes—
608C2×C4⋊C4C22×D1112yes—
609C2×C4⋊C4C22×D11116yes—
610C2×C4⋊C4C22×D1118yes—
611C2×C22⋊C4—114no—
612C2×C22⋊C4—114no—
613C2×C22⋊C4—1116no—
614C2×C22⋊C4—112no—
615C2×C22⋊C4—112no—
616C2×C22⋊C4—112no—
617C2×C22⋊C4—114no—
618C2×C22⋊C4—112no—
619C2×C22⋊C4—112no—
620C2×C22⋊C4—114no—
621C2×C22⋊C4—114no—
622C2×C22⋊C4C22×D1114yes—
623C2×C22⋊C4C22×D1114yes—
624C2×C22⋊C4C22×D11116yes—
625C2×C42—114no—
626C2×C42—112no—
627C2×C42—114no—
628C2×C42—114no—
629C2×C11—24no—
630C2×C11—24no—
631C2×C11—42no—
632C2×C11#353814yescomplemented
633C2×C11C22×H(5,𝔽2)11yescharacteristic
634C2×C11C22×2−1+411yescharacteristic
635C2×C11C22×2−1+411yescharacteristic
636D11—44no—
637C24—24no—
638C24—24no—
639C24—42no—
640C24—112no—
641C24C23×D1111yescharacteristic
642C24C23×D1114yes—
643C24C23×D1111yescharacteristic
644C24C23×D1111yescharacteristic
645#41—4416no—
646C2×Q8—28no—
647C2×Q8—44no—
648C2×Q8—416no—
649C2×Q8—118no—
650C2×Q8—118no—
651C2×Q8—1116no—
652C2×Q8—114no—
653C2×Q8—228no—
654C2×Q8—444no—
655C2×Q8—448no—
656C2×Q8—442no—
657C2×Q8—4416no—
658C2×Q8—4432no—
659C2×Q8C23×D1118yes—
660C2×Q8C23×D1118yes—
661C2×D4—118no—
662C2×D4—118no—
663C2×D4—118no—
664C2×D4—114no—
665C2×D4—228no—
666C2×D4—228no—
667C2×D4—442no—
668C2×D4—444no—
669C22×C4—28no—
670C22×C4—24no—
671C22×C4—24no—
672C22×C4—24no—
673C22×C4—416no—
674C22×C4—42no—
675C22×C4—42no—
676C22×C4—42no—
677C22×C4—44no—
678C22×C4—118no—
679C22×C4—112no—
680C22×C4—112no—
681C22×C4—114no—
682C22×C4—112no—
683C22×C4—114no—
684C22×C4—118no—
685C22×C4—118no—
686C22×C4—1116no—
687C22×C4—228no—
688C22×C4—228no—
689C22×C4—448no—
690C22×C4—444no—
691C22×C4C23×D1118yes—
692C22×C4C23×D1114yes—
693C22×C4C23×D1114yes—
694C22×C4C23×D1114yes—
695C22×C4C23×D1114yes—
696C22×C4C23×D1114yes—
697C22×C4C23×D1111yescharacteristic
698C22×C4C23×D1111yescharacteristic
699C22×C4C23×D1111yescharacteristic
700C22×C4C23×D1118yes—
701C22×C4C23×D1114yes—
702C22×C4C23×D1114yes—
703C22×C4C23×D1114yes—
704C22×C4C23×D1111yescharacteristic
705C4⋊C4—118no—
706C4⋊C4—1116no—
707C4⋊C4—1116no—
708C4⋊C4—118no—
709C4⋊C4—114no—
710C4⋊C4—114no—
711C4⋊C4—1116no—
712C4⋊C4—1116no—
713C4⋊C4—1116no—
714C4⋊C4—1116no—
715C4⋊C4—1116no—
716C4⋊C4—1116no—
717C4⋊C4—118no—
718C4⋊C4—118no—
719C4⋊C4—1116no—
720C4⋊C4—1116no—
721C4⋊C4C23×D1118yes—
722C4⋊C4C23×D11116yes—
723C4⋊C4C23×D11116yes—
724C4⋊C4C23×D1118yes—
725C22⋊C4—1116no—
726C22⋊C4—1116no—
727C22⋊C4—118no—
728C22⋊C4—118no—
729C22⋊C4—118no—
730C22⋊C4—1116no—
731C22⋊C4—118no—
732C22⋊C4—118no—
733C22⋊C4—1116no—
734C22⋊C4—1116no—
735C22⋊C4C23×D11116yes—
736C22⋊C4C23×D11116yes—
737C42—1116no—
738C42—118no—
739C42—1116no—
740C42—1116no—
741C11C2×#353811yescharacteristic, complemented, Sylow
742C23—22no—
743C23—22no—
744C23—22no—
745C23—22no—
746C23—22no—
747C23—28no—
748C23—22no—
749C23—28no—
750C23—22no—
751C23—44no—
752C23—416no—
753C23—114no—
754C23—224no—
755C23—224no—
756C23—224no—
757C23#6704014yes—
758C23#6704314yes—
759C23C24×D1112yes—
760C23C24×D1112yes—
761C23C24×D1112yes—
762C23C24×D1111yescharacteristic
763Q8—216no—
764Q8—48no—
765Q8—2216no—
766Q8—448no—
767Q8—4416no—
768Q8—444no—
769D4—2216no—
770D4—2216no—
771D4—444no—
772D4—448no—
773C2×C4—22no—
774C2×C4—22no—
775C2×C4—22no—
776C2×C4—28no—
777C2×C4—216no—
778C2×C4—28no—
779C2×C4—28no—
780C2×C4—28no—
781C2×C4—28no—
782C2×C4—44no—
783C2×C4—44no—
784C2×C4—44no—
785C2×C4—48no—
786C2×C4—114no—
787C2×C4—114no—
788C2×C4—118no—
789C2×C4—114no—
790C2×C4—118no—
791C2×C4—224no—
792C2×C4—228no—
793C2×C4—2216no—
794C2×C4—228no—
795C2×C4—224no—
796C2×C4—224no—
797C2×C4—2216no—
798C2×C4—4416no—
799C2×C4—448no—
800C2×C4#6703714yes—
801C2×C4C24×D1118yes—
802C2×C4C24×D1118yes—
803C2×C4C24×D1112yes—
804C2×C4C24×D1112yes—
805C2×C4C24×D1112yes—
806C2×C4C24×D1112yes—
807C22—22no—
808C22—22no—
809C22—22no—
810C22—22no—
811C22—28no—
812C22—28no—
813C22—22no—
814C22—22no—
815C22—22no—
816C22—416no—
817C22—44no—
818C22—224no—
819C22—224no—
820C22—224no—
821C22—448no—
822C22C2×#6703712yes—
823C22C2×#6704014yes—
824C22C2×#6704012yes—
825C22C2×#6704314yes—
826C22C2×#6704312yes—
827C22C25×D1111yescharacteristic
828C4—22no—
829C4—22no—
830C4—22no—
831C4—28no—
832C4—28no—
833C4—224no—
834C4—228no—
835C4—224no—
836C4—228no—
837C4—224no—
838C4C2×#6703714yes—
839C2—24no—
840C2—24no—
841C2—42no—
842C2—444no—
843C2#1308286114yesdirect product factor
844C2C22×#6703711yescharacteristic
845C2C22×#6704311yescharacteristic
846C2C22×#6704011yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×C22⋊Q8C2
socleC23×C11C25
prime radicalC2×#10623322C2
hypercenterC22×C22⋊Q8D11
hypocenterC11C2×#3538
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C22×C22⋊Q8

Complements

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

NH ≅ G/Ntype
1. #13082861C2direct (N × H)
2. C2×#10623177C2semidirect
3. C2×#10623173C2semidirect
4. C2×#10623044C2semidirect
5. C2×#10623026C2semidirect
6. C2×Q8×C22⋊D11C2semidirect
7. C2×#10623163C2semidirect
8. C2×#10623031C2semidirect
9. C2×#10623154C2semidirect
10. C2×#10623156C2semidirect
11. C2×#10623176C2semidirect
12. C2×#10623046C2semidirect
13. C2×#10623159C2semidirect
15. C22×#66977C2semidirect
16. C22×C11×C22⋊Q8C2semidirect
19. C22×Q8×D11C22semidirect
26. C2×C11×C22⋊Q8C22semidirect
32. Q8×C22⋊D11C22semidirect
33. C2×#66999C22semidirect
34. C2×#66999C22semidirect
35. C2×Q8×Dic11C22semidirect
36. C2×#66997C22semidirect
37. C2×#66997C22semidirect
56. C2×#66977C22semidirect
58. #10623177C22semidirect
59. #10623176C22semidirect
60. #10623173C22semidirect
61. #10623163C22semidirect
62. #10623159C22semidirect
63. #10623156C22semidirect
64. #10623154C22semidirect
65. #10623046C22semidirect
66. #10623044C22semidirect
67. C2×#66951C22semidirect
68. C2×#66951C22semidirect
69. C2×#66950C22semidirect
70. C2×#66949C22semidirect
71. C2×#66947C22semidirect
72. C2×#66945C22semidirect
73. #10623031C22semidirect
74. C2×#66943C22semidirect
75. C2×#66943C22semidirect
76. C2×#66943C22semidirect
77. C2×#66942C22semidirect
78. C2×#66942C22semidirect
79. C2×#66941C22semidirect
80. C2×#66941C22semidirect
81. C2×#66940C22semidirect
82. #10623026C22semidirect
112. C2×Q8×D11C23semidirect
144. #66999C23semidirect
145. #66999C23semidirect
146. Q8×Dic11C23semidirect
147. #66997C23semidirect
148. #66997C23semidirect
192. #66951C23semidirect
193. #66951C23semidirect
194. #66950C23semidirect
195. #66949C23semidirect
196. #66947C23semidirect
197. #66945C23semidirect
198. #66943C23semidirect
199. #66943C23semidirect
200. #66943C23semidirect
201. #66942C23semidirect
202. #66942C23semidirect
203. #66941C23semidirect
204. #66941C23semidirect
205. #66940C23semidirect
334. C22×C22⋊Q8D11semidirect
454. C2×C22⋊Q8C2×D11semidirect
632. C2×C11#3538semidirect
741. C11C2×#3538semidirect
843. C2#13082861direct (N × H)

Maximal subgroups

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

subgroupindex
#130828612
C2×#106231772
C2×#106231732
C2×#106230442
C2×#106230262
C2×Q8×C22⋊D112
C2×#106231632
C2×#106230312
C2×#106231542
C2×#106231562
C2×#106231762
C2×#106230462
C2×#106231592
C2×#106233222
C22×#669772
C22×C11×C22⋊Q82
C2×#353811