Finite Group Databasebeta

← C2×D11×#556 #15660781

Subgroups — C2×D11×#556 #15660781

Order 2816.

7846 conjugacy classes of subgroups.

The subgroup lattice has 896 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623263C211yesmaximal, characteristic, complemented
2C2×#10623115C211yesmaximal, characteristic, complemented
3C2×#10623099C212yesmaximal, complemented
4C2×#10623172C212yesmaximal, complemented
5C2×#10623073C211yesmaximal, characteristic, complemented
6C2×#10623202C212yesmaximal, complemented
7C2×#10623064C212yesmaximal, complemented
8C2×#10623233C214yesmaximal, complemented
9D11×#556C2132yesmaximal, direct product factor
10C2×D11×C4⋊Q8C211yesmaximal, characteristic, complemented
11C2×D11×#126C214yesmaximal, complemented
12C2×D11×#124C212yesmaximal
13C2×D11×C22⋊Q8C212yesmaximal, complemented
14C2×C4×Q8×D11C212yesmaximal, complemented
15C2×C4×Q8×D11C211yesmaximal, characteristic, complemented
16C2×C4×D4×D11C211yesmaximal, characteristic
17C2×D11×#117C212yesmaximal, complemented
18C2×C11×#556C211yesmaximal, characteristic, complemented
19C22×Q8×D11C2212yes—
20C22×Q8×D11C2211yescharacteristic
21C22×D4×D11C2211yescharacteristic
22C23×C4×D11C2212yes—
23C11×#556C22116yescomplemented
24C2×C11×C4⋊Q8C2211yescharacteristic, complemented
25C2×C11×#126C2214yescomplemented
26C2×C11×#124C2212yes—
27C2×C11×C22⋊Q8C2212yescomplemented
28C2×C4×Q8×C11C2212yescomplemented
29C2×C4×Q8×C11C2211yescharacteristic, complemented
30C2×C4×D4×C11C2211yescharacteristic
31C2×C11×#117C2212yescomplemented
32C2×#67000C2212yes—
33C2×#66999C2212yescomplemented
34C2×Q8×Dic11C2212yescomplemented
35C2×Q8×Dic11C2211yescharacteristic, complemented
36C2×#66997C2212yescomplemented
37C2×#66989C2212yes—
38C2×D4×Dic11C2211yescharacteristic
39C2×C4×C22⋊D11C2212yes—
40C2×#66979C2212yescomplemented
41C2×#66977C2212yescomplemented
42#10623263C22116yescomplemented
43D11×C4⋊Q8C22116yescomplemented
44D11×#126C22164yescomplemented
45#10623233C22164yescomplemented
46D11×#124C22132yes—
47#10623202C22132yescomplemented
48#10623172C22132yescomplemented
49D11×C22⋊Q8C22132yescomplemented
50#10623115C22116yescomplemented
51C4×Q8×D11C22132yescomplemented
52C4×Q8×D11C22116yescomplemented
53#10623099C22132yescomplemented
54C4×D4×D11C22116yes—
55#10623073C22116yescomplemented
56#10623064C22132yescomplemented
57D11×#117C22132yescomplemented
58C2×#66951C2214yescomplemented
59C2×#66951C2214yescomplemented
60C2×#66951C2214yescomplemented
61C2×#66950C2212yescomplemented
62C2×#66949C2214yescomplemented
63C2×#66946C2211yescharacteristic
64C2×#66945C2212yescomplemented
65C2×#66945C2212yescomplemented
66C2×C4⋊C4×D11C2212yes—
67C2×C4⋊C4×D11C2212yes—
68C2×C4⋊C4×D11C2214yes—
69C2×C4⋊C4×D11C2212yes—
70C2×C4⋊C4×D11C2211yescharacteristic
71C2×C4⋊C4×D11C2211yescharacteristic
72C2×#66941C2212yescomplemented
73C2×#66941C2212yescomplemented
74C2×#66940C2212yescomplemented
75C2×#66940C2214yescomplemented
76C2×#66940C2211yescharacteristic, complemented
77C2×#66940C2212yescomplemented
78C2×#66938C2214yes—
79C2×#66938C2214yes—
80C2×(C22⋊D11)⋊C4C2212yes—
81C2×C22⋊C4×D11C2214yes—
82C2×C22⋊C4×D11C2214yes—
83C2×C22⋊C4×D11C2212yes—
84C2×#66932C2214yescomplemented
85C2×#66932C2214yescomplemented
86C2×#66932C2214yescomplemented
87C2×#66931C2214yescomplemented
88C2×#66930C2214yescomplemented
89C2×#66929C2214yescomplemented
90C2×#66928C2212yes—
91C2×C4×D44C2211yescharacteristic
92C2×#66925C2214yescomplemented
93C2×C42×D11C2212yes—
94C2×C42×D11C2214yes—
95C2×C42×D11C2211yescharacteristic
96C2×#66922C2211yescharacteristic, complemented
97C2×C4×Dic22C2214yescomplemented
98C2×C4×Dic22C2212yescomplemented
99C2×C4×Dic22C2212yescomplemented
100C2×C4×Dic22C2211yescharacteristic, complemented
101C24×D11C2312yes—
102C22×Q8×C11C2312yes—
103C22×Q8×C11C2311yescharacteristic
104C22×D4×C11C2311yescharacteristic
105C23×C4×C11C2312yes—
106C22×C22⋊D11C2312yes—
107C23×Dic11C2312yes—
108C2×Q8×D11—28no—
109C2×Q8×D11—216no—
110C2×Q8×D11C23116yes—
111C2×Q8×D11C2318yes—
112C2×D4×D11—28no—
113C2×D4×D11C2318yes—
114C22×D44C2311yescharacteristic
115C22×C4×D11—216no—
116C22×C4×D11C2312yes—
117C22×C4×D11C2312yes—
118C22×C4×D11C2311yescharacteristic
119C22×C4×D11C2312yes—
120C22×C4×D11C2314yes—
121C22×C4×D11C2312yes—
122C22×C4×D11C2312yes—
123C22×C4×D11C23116yes—
124C22×C4×D11C2311yescharacteristic
125C22×C4×D11C2311yescharacteristic
126C22×Dic22C2312yes—
127C22×Dic22C2312yes—
128C22×Dic22C2314yes—
129C22×Dic22C2311yescharacteristic
130C11×C4⋊Q8C2318yescomplemented
131C11×#126C23132yescomplemented
132C11×#124C23116yes—
133C11×C22⋊Q8C23116yescomplemented
134C4×Q8×C11C23116yescomplemented
135C4×Q8×C11C2318yescomplemented
136C4×D4×C11C2318yes—
137C11×#117C23116yescomplemented
138C2×C11×C4⋊C4C2311yescharacteristic
139C2×C11×C4⋊C4C2311yescharacteristic
140C2×C11×C4⋊C4C2314yes—
141C2×C11×C4⋊C4C2312yes—
142C2×C11×C4⋊C4C2312yes—
143C2×C11×C4⋊C4C2312yes—
144C2×C11×C22⋊C4C2314yes—
145C2×C11×C22⋊C4C2314yes—
146C2×C11×C22⋊C4C2312yes—
147C2×C42×C11C2312yes—
148C2×C42×C11C2311yescharacteristic
149C2×C42×C11C2314yes—
150C2×C22⋊Dic11C2314yes—
151C2×C22⋊Dic11C2314yes—
152C2×C22⋊Dic11C2312yes—
153#67000C23116yes—
154#66999C23116yescomplemented
155Q8×Dic11C23116yescomplemented
156Q8×Dic11C2318yescomplemented
157#66997C23116yescomplemented
158#66989C23116yes—
159D4×Dic11C2318yes—
160C4×C22⋊D11C23116yes—
161C2×(C2×D11)⋊C4C2314yes—
162C2×(C2×D11)⋊C4C2314yes—
163C2×(C2×D11)⋊C4C2312yes—
164C2×(C2×D11)⋊C4C2314yes—
165C2×(C2×D11)⋊C4C2312yes—
166C2×(C2×D11)⋊C4C2314yes—
167#66979C23116yescomplemented
168C2×C4⋊Dic11C2311yescharacteristic
169C2×C4⋊Dic11C2314yes—
170C2×C4⋊Dic11C2312yes—
171C2×C4⋊Dic11C2311yescharacteristic
172C2×C4⋊Dic11C2312yes—
173C2×C4⋊Dic11C2312yes—
174#66977C23116yescomplemented
175C2×Dic11⋊C4C2312yes—
176C2×Dic11⋊C4C2312yes—
177C2×Dic11⋊C4C2312yes—
178C2×Dic11⋊C4C2314yes—
179C2×Dic11⋊C4C2314yes—
180C2×Dic11⋊C4C2312yes—
181C2×Dic11⋊C4C2314yes—
182C2×Dic11⋊C4C2314yes—
183C2×C4×Dic11C2314yes—
184C2×C4×Dic11C2312yes—
185C2×C4×Dic11C2312yes—
186C2×C4×Dic11C2311yescharacteristic
187C2×C4×Dic11C2314yes—
188C2×C4×Dic11C2314yes—
189C2×C4×Dic11C2311yescharacteristic
190C2×C4×Dic11C2312yes—
191C2×C4×Dic11C2311yescharacteristic
192#66951C23132yescomplemented
193#66951C23132yescomplemented
194#66951C23132yescomplemented
195#66950C23116yescomplemented
196#66949C23132yescomplemented
197#66946C2318yes—
198#66945C23116yescomplemented
199#66945C23116yescomplemented
200C4⋊C4×D11C23116yes—
201C4⋊C4×D11C23116yes—
202C4⋊C4×D11C23132yes—
203C4⋊C4×D11C23116yes—
204C4⋊C4×D11C2318yes—
205C4⋊C4×D11C2318yes—
206#66941C23116yescomplemented
207#66941C23116yescomplemented
208#66940C23116yescomplemented
209#66940C23132yescomplemented
210#66940C2318yescomplemented
211#66940C23116yescomplemented
212#66938C23132yes—
213#66938C23132yes—
214(C22⋊D11)⋊C4C23116yes—
215C22⋊C4×D11C23116yes—
216C22⋊C4×D11C23132yes—
217C22⋊C4×D11C23132yes—
218#66932C23132yescomplemented
219#66932C23132yescomplemented
220#66932C23132yescomplemented
221#66931C23132yescomplemented
222#66930C23132yescomplemented
223#66929C23132yescomplemented
224#66928C23116yes—
225C4×D44C2318yes—
226#66925C23132yescomplemented
227C42×D11C23132yes—
228C42×D11C2318yes—
229C42×D11C23116yes—
230#66922C2318yescomplemented
231C4×Dic22C23132yescomplemented
232C4×Dic22C2318yescomplemented
233C4×Dic22C23116yescomplemented
234C4×Dic22C23116yescomplemented
235C22×#556—111nomaximal, Sylow
236C24×C11C2412yes—
237C23×D11—28no—
238C23×D11—28no—
239C23×D11—28no—
240C23×D11C2418yes—
241C23×D11C2412yes—
242C23×D11C2411yescharacteristic
243C2×Q8×C11—28no—
244C2×Q8×C11—24no—
245C2×Q8×C11C2418yes—
246C2×Q8×C11C2414yes—
247C2×D4×C11—24no—
248C2×D4×C11C2414yes—
249C22×C4×C11—28no—
250C22×C4×C11C2412yes—
251C22×C4×C11C2412yes—
252C22×C4×C11C2411yescharacteristic
253C22×C4×C11C2414yes—
254C22×C4×C11C2412yes—
255C22×C4×C11C2418yes—
256C22×C4×C11C2411yescharacteristic
257C22×C4×C11C2411yescharacteristic
258C2×C22⋊D11—28no—
259C2×C22⋊D11C2418yes—
260C22×Dic11—28no—
261C22×Dic11C2418yes—
262C22×Dic11C2412yes—
263C22×Dic11C2412yes—
264C22×Dic11C2411yescharacteristic
265C22×Dic11C2414yes—
266C22×Dic11C2412yes—
267C22×Dic11C2411yescharacteristic
268C22×Dic11C2411yescharacteristic
269Q8×D11—232no—
270Q8×D11—264no—
271D4×D11—232no—
272C2×D44—24no—
273C2×D44C2414yes—
274C2×C4×D11—28no—
275C2×C4×D11—264no—
276C2×C4×D11—28no—
277C2×C4×D11—28no—
278C2×C4×D11—216no—
279C2×C4×D11—28no—
280C2×C4×D11—24no—
281C2×C4×D11—28no—
282C2×C4×D11#4118yes—
283C2×C4×D11#4118yes—
284C2×C4×D11C2418yes—
285C2×C4×D11C2418yes—
286C2×C4×D11C2414yes—
287C2×C4×D11C24116yes—
288C2×C4×D11C2418yes—
289C2×C4×D11C2418yes—
290C2×C4×D11C2418yes—
291C2×C4×D11C2414yes—
292C2×C4×D11C2414yes—
293C2×Dic22—216no—
294C2×Dic22—28no—
295C2×Dic22—28no—
296C2×Dic22—24no—
297C2×Dic22C2418yes—
298C2×Dic22C2418yes—
299C2×Dic22C24116yes—
300C2×Dic22C2414yes—
301C11×C4⋊C4C2414yes—
302C11×C4⋊C4C2414yes—
303C11×C4⋊C4C24116yes—
304C11×C4⋊C4C2418yes—
305C11×C4⋊C4C2418yes—
306C11×C4⋊C4C2418yes—
307C11×C22⋊C4C24116yes—
308C11×C22⋊C4C24116yes—
309C11×C22⋊C4C2418yes—
310C42×C11C2418yes—
311C42×C11C2414yes—
312C42×C11C24116yes—
313C22⋊Dic11C24116yes—
314C22⋊Dic11C24116yes—
315C22⋊Dic11C2418yes—
316(C2×D11)⋊C4C24116yes—
317(C2×D11)⋊C4C24116yes—
318(C2×D11)⋊C4C2418yes—
319(C2×D11)⋊C4C24116yes—
320(C2×D11)⋊C4C2418yes—
321(C2×D11)⋊C4C24116yes—
322C4⋊Dic11C2414yes—
323C4⋊Dic11C24116yes—
324C4⋊Dic11C2418yes—
325C4⋊Dic11C2414yes—
326C4⋊Dic11C2418yes—
327C4⋊Dic11C2418yes—
328Dic11⋊C4C2418yes—
329Dic11⋊C4C2418yes—
330Dic11⋊C4C2418yes—
331Dic11⋊C4C24116yes—
332Dic11⋊C4C24116yes—
333Dic11⋊C4C2418yes—
334Dic11⋊C4C24116yes—
335Dic11⋊C4C24116yes—
336C4×Dic11C24116yes—
337C4×Dic11C2418yes—
338C4×Dic11C2418yes—
339C4×Dic11C2414yes—
340C4×Dic11C24116yes—
341C4×Dic11C24116yes—
342C4×Dic11C2414yes—
343C4×Dic11C2418yes—
344C4×Dic11C2414yes—
345C2×#556—1132no—
346C2×#556—111no—
347C2×#556—114no—
348C2×#556—112no—
349C2×#556—112no—
350C2×#556—112no—
351C2×#556—111no—
352C2×#556—111no—
353C2×#556—112no—
354C2×#556D1111yescharacteristic, direct product factor
355C22×C4⋊Q8—111no—
356C22×#126—114no—
357C22×#124—112no—
358C22×C22⋊Q8—112no—
359C22×C4×Q8—111no—
360C22×C4×Q8—112no—
361C22×C4×D4—111no—
362C22×#117—112no—
363C23×C11—24no—
364C23×C11—24no—
365C23×C11—24no—
366C23×C11C2514yes—
367C23×C11C2511yescharacteristic
368C22×D11—24no—
369C22×D11—24no—
370C22×D11—24no—
371C22×D11—216no—
372C22×D11—216no—
373C22×D11—216no—
374C22×D11—432no—
375C22×D11C2×#4114yes—
376C22×D11C2×#4114yes—
377C22×D112−1+414yes—
378C22×D11C2514yes—
379C22×D11C2512yes—
380Q8×C11—28no—
381Q8×C11—216no—
382D4×C11—28no—
383C2×C4×C11—28no—
384C2×C4×C11—24no—
385C2×C4×C11—24no—
386C2×C4×C11—24no—
387C2×C4×C11—22no—
388C2×C4×C11—216no—
389C2×C4×C11C2×#4114yes—
390C2×C4×C11C2×#4114yes—
391C2×C4×C11C2514yes—
392C2×C4×C11C2514yes—
393C2×C4×C11C2512yes—
394C2×C4×C11C2518yes—
395C2×C4×C11C2514yes—
396C2×C4×C11C2512yes—
397C2×C4×C11C2512yes—
398C22⋊D11—216no—
399C2×Dic11—28no—
400C2×Dic11—24no—
401C2×Dic11—24no—
402C2×Dic11—24no—
403C2×Dic11—22no—
404C2×Dic11—216no—
405C2×Dic11C2×#4114yes—
406C2×Dic11C2×#4114yes—
407C2×Dic11C2514yes—
408C2×Dic11C2514yes—
409C2×Dic11C2512yes—
410C2×Dic11C2518yes—
411C2×Dic11C2514yes—
412C2×Dic11C2512yes—
413C2×Dic11C2512yes—
414D44—28no—
415C4×D11—216no—
416C4×D11—216no—
417C4×D11—232no—
418C4×D11—216no—
419C4×D11—28no—
420C4×D11—216no—
421C4×D11—216no—
422C4×D11C2×#41116yes—
423C4×D11C2×#41116yes—
424Dic22—28no—
425Dic22—216no—
426Dic22—232no—
427Dic22—216no—
428C23×Q8—111no—
429C23×Q8—112no—
430C23×D4—111no—
431C24×C4—112no—
432#556—1116no—
433#556—1164no—
434#556—1132no—
435#556—1132no—
436#556—1132no—
437#556—1116no—
438#556—1116no—
439#556—1132no—
440#556C2×D11116yesdirect product factor
441C2×C4⋊Q8—112no—
442C2×C4⋊Q8—1116no—
443C2×C4⋊Q8—112no—
444C2×C4⋊Q8—112no—
445C2×C4⋊Q8—111no—
446C2×C4⋊Q8C2×D1111yescharacteristic, complemented
447C2×#126—1164no—
448C2×#126—114no—
449C2×#126—114no—
450C2×#126—114no—
451C2×#126—114no—
452C2×#126—114no—
453C2×#126—114no—
454C2×#126—114no—
455C2×#126C2×D1114yescomplemented
456C2×#124—112no—
457C2×#124—112no—
458C2×#124—1132no—
459C2×#124—114no—
460C2×#124—114no—
461C2×#124—112no—
462C2×#124C2×D1112yes—
463C2×C22⋊Q8—112no—
464C2×C22⋊Q8—112no—
465C2×C22⋊Q8—1132no—
466C2×C22⋊Q8—114no—
467C2×C22⋊Q8—112no—
468C2×C22⋊Q8—114no—
469C2×C22⋊Q8C2×D1112yescomplemented
470C2×C4×Q8—112no—
471C2×C4×Q8—111no—
472C2×C4×Q8—1132no—
473C2×C4×Q8—1116no—
474C2×C4×Q8—114no—
475C2×C4×Q8—112no—
476C2×C4×Q8—112no—
477C2×C4×Q8—111no—
478C2×C4×Q8—112no—
479C2×C4×Q8—114no—
480C2×C4×Q8—112no—
481C2×C4×Q8—111no—
482C2×C4×Q8C2×D1112yescomplemented
483C2×C4×Q8C2×D1111yescharacteristic, complemented
484C2×C4×D4—111no—
485C2×C4×D4—112no—
486C2×C4×D4—1116no—
487C2×C4×D4—111no—
488C2×C4×D4—112no—
489C2×C4×D4—111no—
490C2×C4×D4C2×D1111yescharacteristic
491C2×#117—112no—
492C2×#117—1132no—
493C2×#117—112no—
494C2×#117—112no—
495C2×#117—114no—
496C2×#117—114no—
497C2×#117C2×D1112yescomplemented
498C22×C4⋊C4—111no—
499C22×C4⋊C4—112no—
500C22×C4⋊C4—111no—
501C22×C4⋊C4—114no—
502C22×C4⋊C4—112no—
503C22×C4⋊C4—112no—
504C22×C22⋊C4—114no—
505C22×C22⋊C4—112no—
506C22×C22⋊C4—114no—
507C22×C42—114no—
508C22×C42—111no—
509C22×C42—112no—
510C22×C11—24no—
511C22×C11—24no—
512C22×C11—24no—
513C22×C11—48no—
514C22×C11C22×#4112yes—
515C22×C11C22×#4112yes—
516C22×C11C2×2−1+412yes—
517C22×C11C2611yescharacteristic
518C2×D11—24no—
519C2×D11—24no—
520C2×D11—24no—
521C2×D11—48no—
522C2×D11—432no—
523C2×D11#556116yesdirect product factor
524C2×D11C22×#4114yes—
525C2×D11C22×#4114yes—
526C2×D11C2×2−1+414yes—
527C4×C11—24no—
528C4×C11—28no—
529C4×C11—24no—
530C4×C11—24no—
531C4×C11—22no—
532C4×C11C22×#4114yes—
533C4×C11C22×#4114yes—
534Dic11—28no—
535Dic11—24no—
536Dic11—24no—
537Dic11—24no—
538Dic11—22no—
539Dic11C22×#4114yes—
540Dic11C22×#4114yes—
541C25—112no—
542C22×Q8—118no—
543C22×Q8—1116no—
544C22×Q8—112no—
545C22×Q8—111no—
546C22×Q8—114no—
547C22×Q8—112no—
548C22×Q8—228no—
549C22×Q8—2216no—
550C22×Q8C22×D1111yescharacteristic
551C22×Q8C22×D1112yes—
552C22×D4—112no—
553C22×D4—118no—
554C22×D4—111no—
555C22×D4—228no—
556C22×D4C22×D1111yescharacteristic
557C23×C4—111no—
558C23×C4—111no—
559C23×C4—112no—
560C23×C4—111no—
561C23×C4—114no—
562C23×C4—112no—
563C23×C4—112no—
564C23×C4—112no—
565C23×C4—112no—
566C23×C4—1116no—
567C23×C4—112no—
568C23×C4—2216no—
569C23×C4C22×D1112yes—
570C4⋊Q8—1116no—
571C4⋊Q8—1116no—
572C4⋊Q8—1116no—
573C4⋊Q8—118no—
574C4⋊Q8C22×D1118yescomplemented
575#126—1132no—
576#126—1132no—
577#126—1132no—
578#126—1132no—
579#126—1132no—
580#126—1132no—
581#126—1132no—
582#126C22×D11132yescomplemented
583#124—1116no—
584#124—1116no—
585#124—1132no—
586#124—1132no—
587#124—1116no—
588#124C22×D11116yes—
589C22⋊Q8—1116no—
590C22⋊Q8—1116no—
591C22⋊Q8—1132no—
592C22⋊Q8—1116no—
593C22⋊Q8—1132no—
594C22⋊Q8C22×D11116yescomplemented
595C4×Q8—1116no—
596C4×Q8—118no—
597C4×Q8—1132no—
598C4×Q8—1116no—
599C4×Q8—1116no—
600C4×Q8—118no—
601C4×Q8—1116no—
602C4×Q8—1132no—
603C4×Q8—1116no—
604C4×Q8—118no—
605C4×Q8C22×D11116yescomplemented
606C4×Q8C22×D1118yescomplemented
607C4×D4—118no—
608C4×D4—1116no—
609C4×D4—118no—
610C4×D4—1116no—
611C4×D4—118no—
612C4×D4C22×D1118yes—
613#117—1116no—
614#117—1116no—
615#117—1116no—
616#117—1132no—
617#117—1132no—
618#117C22×D11116yescomplemented
619C2×C4⋊C4—112no—
620C2×C4⋊C4—111no—
621C2×C4⋊C4—114no—
622C2×C4⋊C4—112no—
623C2×C4⋊C4—112no—
624C2×C4⋊C4—111no—
625C2×C4⋊C4—114no—
626C2×C4⋊C4—114no—
627C2×C4⋊C4—114no—
628C2×C4⋊C4—112no—
629C2×C4⋊C4—112no—
630C2×C4⋊C4—112no—
631C2×C4⋊C4—114no—
632C2×C4⋊C4—112no—
633C2×C4⋊C4—118no—
634C2×C4⋊C4—1116no—
635C2×C4⋊C4—118no—
636C2×C4⋊C4—1132no—
637C2×C4⋊C4—1116no—
638C2×C4⋊C4—1116no—
639C2×C4⋊C4C22×D1111yescharacteristic
640C2×C4⋊C4C22×D1112yes—
641C2×C4⋊C4C22×D1111yescharacteristic
642C2×C4⋊C4C22×D1114yes—
643C2×C4⋊C4C22×D1112yes—
644C2×C4⋊C4C22×D1112yes—
645C2×C22⋊C4—114no—
646C2×C22⋊C4—112no—
647C2×C22⋊C4—114no—
648C2×C22⋊C4—114no—
649C2×C22⋊C4—114no—
650C2×C22⋊C4—112no—
651C2×C22⋊C4—112no—
652C2×C22⋊C4—114no—
653C2×C22⋊C4—114no—
654C2×C22⋊C4—1132no—
655C2×C22⋊C4—1116no—
656C2×C22⋊C4—1132no—
657C2×C22⋊C4C22×D1114yes—
658C2×C22⋊C4C22×D1112yes—
659C2×C22⋊C4C22×D1114yes—
660C2×C42—114no—
661C2×C42—114no—
662C2×C42—114no—
663C2×C42—111no—
664C2×C42—111no—
665C2×C42—111no—
666C2×C42—112no—
667C2×C42—112no—
668C2×C42—112no—
669C2×C42—1132no—
670C2×C42—118no—
671C2×C42—1116no—
672C2×C42C22×D1114yes—
673C2×C42C22×D1111yescharacteristic
674C2×C42C22×D1112yes—
675C2×C11—44no—
676C2×C11C2×#55614yescomplemented
677C2×C11C23×#4111yescharacteristic
678C2×C11C23×#4111yescharacteristic
679C2×C11C22×2−1+411yescharacteristic
680D11—44no—
681D11C2×#55618yesdirect product factor
682C24—111no—
683C24—118no—
684C24—112no—
685C24—228no—
686C24—228no—
687C24—228no—
688C24C23×D1112yes—
689C2×Q8—24no—
690C2×Q8—28no—
691C2×Q8—118no—
692C2×Q8—114no—
693C2×Q8—1116no—
694C2×Q8—118no—
695C2×Q8—228no—
696C2×Q8—2216no—
697C2×Q8—2232no—
698C2×Q8—2264no—
699C2×Q8—224no—
700C2×Q8—228no—
701C2×Q8C23×D1114yes—
702C2×Q8C23×D1118yes—
703C2×D4—24no—
704C2×D4—118no—
705C2×D4—114no—
706C2×D4—2232no—
707C2×D4—228no—
708C2×D4—224no—
709C2×D4C23×D1114yes—
710C22×C4—28no—
711C22×C4—111no—
712C22×C4—111no—
713C22×C4—118no—
714C22×C4—118no—
715C22×C4—114no—
716C22×C4—114no—
717C22×C4—118no—
718C22×C4—112no—
719C22×C4—112no—
720C22×C4—111no—
721C22×C4—114no—
722C22×C4—112no—
723C22×C4—118no—
724C22×C4—118no—
725C22×C4—114no—
726C22×C4—1116no—
727C22×C4—118no—
728C22×C4—118no—
729C22×C4—118no—
730C22×C4—228no—
731C22×C4—2264no—
732C22×C4—228no—
733C22×C4—228no—
734C22×C4—2216no—
735C22×C4—224no—
736C22×C4—228no—
737C22×C4—228no—
738C22×C4—228no—
739C22×C4C23×D1118yes—
740C22×C4C23×D1112yes—
741C22×C4C23×D1112yes—
742C22×C4C23×D1111yescharacteristic
743C22×C4C23×D1114yes—
744C22×C4C23×D1112yes—
745C22×C4C23×D1111yescharacteristic
746C22×C4C23×D1111yescharacteristic
747C4⋊C4—118no—
748C4⋊C4—114no—
749C4⋊C4—1116no—
750C4⋊C4—118no—
751C4⋊C4—118no—
752C4⋊C4—114no—
753C4⋊C4—1116no—
754C4⋊C4—1116no—
755C4⋊C4—1116no—
756C4⋊C4—118no—
757C4⋊C4—118no—
758C4⋊C4—118no—
759C4⋊C4—1116no—
760C4⋊C4—118no—
761C4⋊C4C23×D1114yes—
762C4⋊C4C23×D1118yes—
763C4⋊C4C23×D1114yes—
764C4⋊C4C23×D11116yes—
765C4⋊C4C23×D1118yes—
766C4⋊C4C23×D1118yes—
767C22⋊C4—1116no—
768C22⋊C4—118no—
769C22⋊C4—1116no—
770C22⋊C4—1116no—
771C22⋊C4—1116no—
772C22⋊C4—118no—
773C22⋊C4—118no—
774C22⋊C4—1116no—
775C22⋊C4—1116no—
776C22⋊C4C23×D11116yes—
777C22⋊C4C23×D1118yes—
778C22⋊C4C23×D11116yes—
779C42—1116no—
780C42—1116no—
781C42—1116no—
782C42—114no—
783C42—114no—
784C42—114no—
785C42—118no—
786C42—118no—
787C42—118no—
788C42C23×D11116yes—
789C42C23×D1114yes—
790C42C23×D1118yes—
791C11C22×#55611yescharacteristic, complemented, Sylow
792C23—24no—
793C23—24no—
794C23—24no—
795C23—114no—
796C23—114no—
797C23—114no—
798C23—112no—
799C23—114no—
800C23—2216no—
801C23—2216no—
802C23—2216no—
803C23—224no—
804C23—224no—
805C23—224no—
806C23—4432no—
807C23C24×D1114yes—
808C23C24×D1111yescharacteristic
809Q8—28no—
810Q8—216no—
811Q8—2216no—
812Q8—2232no—
813Q8—228no—
814Q8—2216no—
815D4—28no—
816D4—2216no—
817D4—228no—
818C2×C4—24no—
819C2×C4—24no—
820C2×C4—28no—
821C2×C4—24no—
822C2×C4—22no—
823C2×C4—216no—
824C2×C4—114no—
825C2×C4—114no—
826C2×C4—112no—
827C2×C4—112no—
828C2×C4—1116no—
829C2×C4—1116no—
830C2×C4—114no—
831C2×C4—114no—
832C2×C4—112no—
833C2×C4—118no—
834C2×C4—114no—
835C2×C4—2216no—
836C2×C4—2216no—
837C2×C4—2216no—
838C2×C4—2232no—
839C2×C4—2216no—
840C2×C4—228no—
841C2×C4—2216no—
842C2×C4—224no—
843C2×C4—224no—
844C2×C4—228no—
845C2×C4—224no—
846C2×C4—222no—
847C2×C4—2216no—
848C2×C4#41×D1114yes—
849C2×C4#41×D1114yes—
850C2×C4C24×D1114yes—
851C2×C4C24×D1114yes—
852C2×C4C24×D1112yes—
853C2×C4C24×D1118yes—
854C2×C4C24×D1114yes—
855C2×C4C24×D1112yes—
856C2×C4C24×D1112yes—
857C22—24no—
858C22—24no—
859C22—24no—
860C22—48no—
861C22—114no—
862C22—114no—
863C22—114no—
864C22—1116no—
865C22—224no—
866C22—224no—
867C22—224no—
868C22—4432no—
869C22—448no—
870C22C2×#41×D1112yes—
871C22C2×#41×D1112yes—
872C22D11×2−1+412yes—
873C22C25×D1111yescharacteristic
874C4—24no—
875C4—24no—
876C4—28no—
877C4—24no—
878C4—22no—
879C4—114no—
880C4—114no—
881C4—224no—
882C4—224no—
883C4—228no—
884C4—224no—
885C4—222no—
886C4C2×#41×D1114yes—
887C4C2×#41×D1114yes—
888C2—44no—
889C2—118no—
890C2—444no—
891C2D11×#55614yesdirect product factor
892C2C22×#41×D1111yescharacteristic
893C2C22×#41×D1111yescharacteristic
894C2C2×D11×2−1+411yescharacteristic
subgroupG/H
centerC23C24×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC2×C11×#556C2
socleC23×C11C25
prime radicalC22×D4×D11C22
hypercenterC2×#556D11
hypocenterC11C22×#556
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23 ◁ C2×#556

Complements

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

NH ≅ G/Ntype
1. C2×#10623263C2semidirect
2. C2×#10623115C2semidirect
3. C2×#10623099C2semidirect
4. C2×#10623172C2semidirect
5. C2×#10623073C2semidirect
6. C2×#10623202C2semidirect
7. C2×#10623064C2semidirect
8. C2×#10623233C2semidirect
9. D11×#556C2direct (N × H)
10. C2×D11×C4⋊Q8C2semidirect
11. C2×D11×#126C2semidirect
13. C2×D11×C22⋊Q8C2semidirect
14. C2×C4×Q8×D11C2semidirect
15. C2×C4×Q8×D11C2semidirect
17. C2×D11×#117C2semidirect
18. C2×C11×#556C2semidirect
23. C11×#556C22semidirect
24. C2×C11×C4⋊Q8C22semidirect
25. C2×C11×#126C22semidirect
27. C2×C11×C22⋊Q8C22semidirect
28. C2×C4×Q8×C11C22semidirect
29. C2×C4×Q8×C11C22semidirect
31. C2×C11×#117C22semidirect
33. C2×#66999C22semidirect
34. C2×Q8×Dic11C22semidirect
35. C2×Q8×Dic11C22semidirect
36. C2×#66997C22semidirect
40. C2×#66979C22semidirect
41. C2×#66977C22semidirect
42. #10623263C22semidirect
43. D11×C4⋊Q8C22semidirect
44. D11×#126C22semidirect
45. #10623233C22semidirect
47. #10623202C22semidirect
48. #10623172C22semidirect
49. D11×C22⋊Q8C22semidirect
50. #10623115C22semidirect
51. C4×Q8×D11C22semidirect
52. C4×Q8×D11C22semidirect
53. #10623099C22semidirect
55. #10623073C22semidirect
56. #10623064C22semidirect
57. D11×#117C22semidirect
58. C2×#66951C22semidirect
59. C2×#66951C22semidirect
60. C2×#66951C22semidirect
61. C2×#66950C22semidirect
62. C2×#66949C22semidirect
64. C2×#66945C22semidirect
65. C2×#66945C22semidirect
72. C2×#66941C22semidirect
73. C2×#66941C22semidirect
74. C2×#66940C22semidirect
75. C2×#66940C22semidirect
76. C2×#66940C22semidirect
77. C2×#66940C22semidirect
84. C2×#66932C22semidirect
85. C2×#66932C22semidirect
86. C2×#66932C22semidirect
87. C2×#66931C22semidirect
88. C2×#66930C22semidirect
89. C2×#66929C22semidirect
92. C2×#66925C22semidirect
96. C2×#66922C22semidirect
97. C2×C4×Dic22C22semidirect
98. C2×C4×Dic22C22semidirect
99. C2×C4×Dic22C22semidirect
100. C2×C4×Dic22C22semidirect
130. C11×C4⋊Q8C23semidirect
131. C11×#126C23semidirect
133. C11×C22⋊Q8C23semidirect
134. C4×Q8×C11C23semidirect
135. C4×Q8×C11C23semidirect
137. C11×#117C23semidirect
154. #66999C23semidirect
155. Q8×Dic11C23semidirect
156. Q8×Dic11C23semidirect
157. #66997C23semidirect
167. #66979C23semidirect
174. #66977C23semidirect
192. #66951C23semidirect
193. #66951C23semidirect
194. #66951C23semidirect
195. #66950C23semidirect
196. #66949C23semidirect
198. #66945C23semidirect
199. #66945C23semidirect
206. #66941C23semidirect
207. #66941C23semidirect
208. #66940C23semidirect
209. #66940C23semidirect
210. #66940C23semidirect
211. #66940C23semidirect
218. #66932C23semidirect
219. #66932C23semidirect
220. #66932C23semidirect
221. #66931C23semidirect
222. #66930C23semidirect
223. #66929C23semidirect
226. #66925C23semidirect
230. #66922C23semidirect
231. C4×Dic22C23semidirect
232. C4×Dic22C23semidirect
233. C4×Dic22C23semidirect
234. C4×Dic22C23semidirect
354. C2×#556D11direct (N × H)
440. #556C2×D11direct (N × H)
446. C2×C4⋊Q8C2×D11semidirect
455. C2×#126C2×D11semidirect
469. C2×C22⋊Q8C2×D11semidirect
482. C2×C4×Q8C2×D11semidirect
483. C2×C4×Q8C2×D11semidirect
497. C2×#117C2×D11semidirect
523. C2×D11#556direct (N × H)
574. C4⋊Q8C22×D11semidirect
582. #126C22×D11semidirect
594. C22⋊Q8C22×D11semidirect
605. C4×Q8C22×D11semidirect
606. C4×Q8C22×D11semidirect
618. #117C22×D11semidirect
676. C2×C11C2×#556semidirect
681. D11C2×#556direct (N × H)
791. C11C22×#556semidirect
891. C2D11×#556direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106232632
C2×#106231152
C2×#106230992
C2×#106231722
C2×#106230732
C2×#106232022
C2×#106230642
C2×#106232332
D11×#5562
C2×D11×C4⋊Q82
C2×D11×#1262
C2×D11×#1242
C2×D11×C22⋊Q82
C2×C4×Q8×D112
C2×C4×D4×D112
C2×D11×#1172
C2×C11×#5562
C22×#55611