Finite Group Databasebeta

← C22×#10623144 #15660497

Subgroups — C22×#10623144 #15660497

Order 2816.

9566 conjugacy classes of subgroups.

The subgroup lattice has 702 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#10623144C2148yesmaximal, direct product factor
2C22×#66951C211yesmaximal, characteristic, complemented
3C22×#66932C211yesmaximal, characteristic, complemented
4C22×#66989C211yesmaximal, characteristic, complemented
5C22×#66938C211yesmaximal, characteristic, complemented
6C22×#66982C211yesmaximal, characteristic, complemented
7C22×#66988C211yesmaximal, characteristic, complemented
8C22×#66949C211yesmaximal, characteristic, complemented
9C22×#66992C211yesmaximal, characteristic, complemented
10C22×#66991C211yesmaximal, characteristic, complemented
11C22×#66990C211yesmaximal, characteristic, complemented
12C22×#66990C211yesmaximal, characteristic, complemented
13C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
14C22×(C22⋊D11)⋊C4C211yesmaximal, characteristic, complemented
15C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
16C22×C11×#121C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C23×D4×C11C2211yescharacteristic
20C23×D4×C11C2211yescharacteristic, complemented
21C24×C4×C11C2211yescharacteristic, complemented
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic
25C23×C22⋊D11C2211yescharacteristic
26C24×Dic11C2211yescharacteristic, complemented
27C23×C4×D11C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic
29C23×Dic22C2211yescharacteristic, complemented
30C2×C11×#121C22124yescomplemented
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic, complemented
34C22×C22⋊Dic11C2211yescharacteristic
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic
37C22×C22⋊Dic11C2211yescharacteristic, complemented
38C22×C22⋊Dic11C2211yescharacteristic, complemented
39C22×C22⋊Dic11C2211yescharacteristic, complemented
40C2×#66992C22124yescomplemented
41C2×#66991C22124yescomplemented
42C2×#66990C22124yescomplemented
43C2×#66990C22124yescomplemented
44C2×#66989C22124yescomplemented
45C2×#66988C22124yescomplemented
46C2×#66982C22124yescomplemented
47C2×C4×C22⋊D11C22124yescomplemented
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C2211yescharacteristic
51C22×(C2×D11)⋊C4C2211yescharacteristic
52C22×(C2×D11)⋊C4C2211yescharacteristic
53C22×(C2×D11)⋊C4C2211yescharacteristic
54C22×C4⋊Dic11C2211yescharacteristic, complemented
55C22×Dic11⋊C4C2211yescharacteristic, complemented
56C22×Dic11⋊C4C2211yescharacteristic, complemented
57C22×Dic11⋊C4C2211yescharacteristic, complemented
58C22×Dic11⋊C4C2211yescharacteristic, complemented
59C22×C4×Dic11C2211yescharacteristic, complemented
60C22×C4×Dic11C2211yescharacteristic, complemented
61#10623144C221256yesdirect product factor
62C2×#66951C22124yescomplemented
63C2×#66949C22124yescomplemented
64C2×#66938C22124yescomplemented
65C2×(C22⋊D11)⋊C4C22124yescomplemented
66C2×C22⋊C4×D11C22124yescomplemented
67C2×#66932C22124yescomplemented
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C25×C11C2311yescharacteristic
71C24×D11—28no—
72C24×D11—44no—
73C24×D11—44no—
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C23112yes—
77C22×D4×C11—44no—
78C22×D4×C11—44no—
79C22×D4×C11—44no—
80C22×D4×C11C23112yes—
81C22×D4×C11C23112yes—
82C22×D4×C11C23112yescomplemented
83C23×C4×C11—44no—
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C2311yescharacteristic
87C23×C4×C11C2311yescharacteristic
88C23×C4×C11C23112yescomplemented
89C22×C22⋊D11—28no—
90C22×C22⋊D11—28no—
91C22×C22⋊D11—44no—
92C22×C22⋊D11—44no—
93C22×C22⋊D11C23112yes—
94C22×C22⋊D11C23112yes—
95C22×C22⋊D11C23112yes—
96C22×C22⋊D11C23112yes—
97C23×Dic11—44no—
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2311yescharacteristic
104C23×Dic11C23112yescomplemented
105C22×C4×D11—44no—
106C22×C4×D11—44no—
107C22×C4×D11C23112yes—
108C22×C4×D11C23112yes—
109C22×Dic22—44no—
110C22×Dic22C23112yescomplemented
111C11×#121C23164yescomplemented
112C2×C11×C4⋊C4C23112yescomplemented
113C2×C11×C22⋊C4C23112yes—
114C2×C11×C22⋊C4C23112yescomplemented
115C2×C22⋊Dic11C23112yes—
116C2×C22⋊Dic11C23112yes—
117C2×C22⋊Dic11C23112yes—
118C2×C22⋊Dic11C23112yescomplemented
119C2×C22⋊Dic11C23112yescomplemented
120C2×C22⋊Dic11C23112yescomplemented
121#66992C23164yescomplemented
122#66991C23164yescomplemented
123#66990C23164yescomplemented
124#66990C23164yescomplemented
125#66989C23164yescomplemented
126#66988C23164yescomplemented
127#66982C23164yescomplemented
128C4×C22⋊D11C23164yescomplemented
129C2×(C2×D11)⋊C4C23112yes—
130C2×(C2×D11)⋊C4C23112yes—
131C2×(C2×D11)⋊C4C23112yes—
132C2×(C2×D11)⋊C4C23112yes—
133C2×(C2×D11)⋊C4C23112yes—
134C2×(C2×D11)⋊C4C23112yes—
135C2×C4⋊Dic11C23112yescomplemented
136C2×Dic11⋊C4C23112yescomplemented
137C2×Dic11⋊C4C23112yescomplemented
138C2×Dic11⋊C4C23112yescomplemented
139C2×Dic11⋊C4C23112yescomplemented
140C2×C4×Dic11C23112yescomplemented
141C2×C4×Dic11C23112yescomplemented
142#66951C23164yescomplemented
143#66949C23164yescomplemented
144#66938C23164yescomplemented
145(C22⋊D11)⋊C4C23164yescomplemented
146C22⋊C4×D11C23164yescomplemented
147#66932C23164yescomplemented
148C22×#538—111nomaximal, Sylow
149C24×C11—24no—
150C24×C11—24no—
151C24×C11—24no—
152C24×C11—24no—
153C24×C11—24no—
154C24×C11—24no—
155C24×C11—24no—
156C24×C11—24no—
157C24×C11—24no—
158C24×C11C2416yes—
159C24×C11C2416yes—
160C24×C11C2416yes—
161C24×C11C2411yescharacteristic
162C23×D11—24no—
163C23×D11—24no—
164C23×D11—24no—
165C23×D11—24no—
166C23×D11—24no—
167C23×D11—248no—
168C23×D11—424no—
169C23×D11—424no—
170C23×D11—464no—
171C23×D11#4118yes—
172C23×D11C2416yes—
173C23×D11C2416yes—
174C23×D11C24116yes—
175C2×D4×C11—424no—
176C2×D4×C11—424no—
177C2×D4×C11—424no—
178C2×D4×C11C24116yes—
179C2×D4×C11C24116yes—
180C2×D4×C11C24116yescomplemented
181C22×C4×C11—24no—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11—424no—
186C22×C4×C11C2416yes—
187C22×C4×C11C2416yes—
188C22×C4×C11C2416yes—
189C22×C4×C11C2416yes—
190C22×C4×C11C24116yescomplemented
191C2×C22⋊D11—248no—
192C2×C22⋊D11—248no—
193C2×C22⋊D11—424no—
194C2×C22⋊D11—424no—
195C2×C22⋊D11C24116yes—
196C2×C22⋊D11C24116yes—
197C2×C22⋊D11C24116yes—
198C2×C22⋊D11C24116yes—
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—24no—
202C22×Dic11—24no—
203C22×Dic11—24no—
204C22×Dic11—24no—
205C22×Dic11—424no—
206C22×Dic11C2416yes—
207C22×Dic11C2416yes—
208C22×Dic11C2416yes—
209C22×Dic11C2416yes—
210C22×Dic11C2416yes—
211C22×Dic11C2416yes—
212C22×Dic11C24116yescomplemented
213C2×C4×D11—424no—
214C2×C4×D11—424no—
215C2×C4×D11C24116yes—
216C2×C4×D11C24116yes—
217C2×Dic22—424no—
218C2×Dic22C24116yescomplemented
219C11×C4⋊C4C24116yescomplemented
220C11×C22⋊C4C24116yes—
221C11×C22⋊C4C24116yescomplemented
222C22⋊Dic11C24116yes—
223C22⋊Dic11C24116yes—
224C22⋊Dic11C24116yes—
225C22⋊Dic11C24116yescomplemented
226C22⋊Dic11C24116yescomplemented
227C22⋊Dic11C24116yescomplemented
228(C2×D11)⋊C4C24116yes—
229(C2×D11)⋊C4C24116yes—
230(C2×D11)⋊C4C24116yes—
231(C2×D11)⋊C4C24116yes—
232(C2×D11)⋊C4C24116yes—
233(C2×D11)⋊C4C24116yes—
234C4⋊Dic11C24116yescomplemented
235Dic11⋊C4C24116yescomplemented
236Dic11⋊C4C24116yescomplemented
237Dic11⋊C4C24116yescomplemented
238Dic11⋊C4C24116yescomplemented
239C4×Dic11C24116yescomplemented
240C4×Dic11C24116yescomplemented
241C2×#538—1148no—
242C22×#126—111no—
243C22×#126—111no—
244C22×#124—111no—
245C22×#124—111no—
246C22×#123—111no—
247C22×#123—111no—
248C22×C22⋊Q8—111no—
249C22×#121—111no—
250C22×#121—111no—
251C22×#121D1111yescharacteristic, complemented
252C22×#120—111no—
253C22×#120—111no—
254C22×C4×D4—111no—
255C22×C4×D4—111no—
256C23×C22⋊C4—111no—
257C23×C11—212no—
258C23×C11—212no—
259C23×C11—212no—
260C23×C11—212no—
261C23×C11—212no—
262C23×C11—212no—
263C23×C11—212no—
264C23×C11—212no—
265C23×C11—212no—
266C23×C11—416no—
267C23×C11—416no—
268C23×C11—416no—
269C23×C11C2×#4114yes—
270C23×C11H(5,𝔽2)14yes—
271C23×C11H(5,𝔽2)14yes—
272C23×C11C2514yes—
273C23×C11C2514yes—
274C23×C11C2514yes—
275C23×C11C2513yes—
276C22×D11—232no—
277C22×D11—212no—
278C22×D11—212no—
279C22×D11—212no—
280C22×D11—212no—
281C22×D11—212no—
282C22×D11—232no—
283C22×D11—416no—
284C22×D11—416no—
285C22×D11—4192no—
286C22×D11—416no—
287C22×D11C2×#41124yes—
288C22×D11C2514yes—
289C22×D11C2514yes—
290D4×C11—416no—
291D4×C11—416no—
292D4×C11—416no—
293C2×C4×C11—212no—
294C2×C4×C11—212no—
295C2×C4×C11—212no—
296C2×C4×C11—212no—
297C2×C4×C11—416no—
298C2×C4×C11C2514yes—
299C2×C4×C11C2514yes—
300C2×C4×C11C2514yes—
301C2×C4×C11C2514yes—
302C22⋊D11—232no—
303C22⋊D11—232no—
304C22⋊D11—416no—
305C22⋊D11—416no—
306C2×Dic11—212no—
307C2×Dic11—212no—
308C2×Dic11—212no—
309C2×Dic11—212no—
310C2×Dic11—212no—
311C2×Dic11—212no—
312C2×Dic11—416no—
313C2×Dic11C2514yes—
314C2×Dic11C2514yes—
315C2×Dic11C2514yes—
316C2×Dic11C2514yes—
317C2×Dic11C2514yes—
318C2×Dic11C2514yes—
319C4×D11—416no—
320C4×D11—416no—
321Dic22—416no—
322C26—111no—
323C23×Q8—111no—
324C23×D4—111no—
325C23×D4—111no—
326C23×D4—111no—
327C23×D4—111no—
328C23×D4C2×D1111yescharacteristic
329C23×D4C2×D1111yescharacteristic
330C23×D4C2×D1111yescharacteristic, complemented
331C24×C4—111no—
332C24×C4—111no—
333C24×C4—111no—
334C24×C4C2×D1111yescharacteristic, complemented
335#538—11256no—
336C2×#126—1124no—
337C2×#126—1124no—
338C2×#124—1124no—
339C2×#124—1124no—
340C2×#123—1124no—
341C2×#123—1124no—
342C2×C22⋊Q8—1124no—
343C2×#121—1124no—
344C2×#121—1124no—
345C2×#121C2×D11124yescomplemented
346C2×#120—1124no—
347C2×#120—1124no—
348C2×C4×D4—1124no—
349C2×C4×D4—1124no—
350C22×C4⋊C4—111no—
351C22×C4⋊C4—111no—
352C22×C4⋊C4—111no—
353C22×C4⋊C4—111no—
354C22×C4⋊C4—111no—
355C22×C4⋊C4C2×D1111yescharacteristic, complemented
356C22×C22⋊C4—111no—
357C22×C22⋊C4—111no—
358C22×C22⋊C4—111no—
359C22×C22⋊C4—111no—
360C22×C22⋊C4—111no—
361C22×C22⋊C4—111no—
362C22×C22⋊C4—111no—
363C22×C22⋊C4—111no—
364C22×C22⋊C4—111no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—111no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—1124no—
369C22×C22⋊C4C2×D1111yescharacteristic
370C22×C22⋊C4C2×D1111yescharacteristic, complemented
371C22×C42—111no—
372C22×C42—111no—
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—24no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—24no—
379C22×C11—24no—
380C22×C11—24no—
381C22×C11—24no—
382C22×C11—424no—
383C22×C11—424no—
384C22×C11—424no—
385C22×C11#538116yescomplemented
386C22×C11C22×#4116yes—
387C22×C11C2×H(5,𝔽2)16yes—
388C22×C11C2×H(5,𝔽2)16yes—
389C22×C11C2611yescharacteristic
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—248no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—24no—
396C2×D11—464no—
397C2×D11—424no—
398C2×D11C22×#4118yes—
399C4×C11—24no—
400C4×C11—24no—
401C4×C11—24no—
402C4×C11—24no—
403Dic11—24no—
404Dic11—24no—
405Dic11—24no—
406Dic11—24no—
407Dic11—24no—
408Dic11—24no—
409C25—111no—
410C25—111no—
411C25—1112no—
412C25—228no—
413C25—444no—
414C25—444no—
415C25C22×D1111yescharacteristic
416C25C22×D1111yescharacteristic
417C25C22×D1111yescharacteristic
418C22×Q8—1112no—
419C22×Q8—444no—
420C22×D4—44no—
421C22×D4—44no—
422C22×D4—44no—
423C22×D4—1112no—
424C22×D4—1112no—
425C22×D4—1112no—
426C22×D4—1112no—
427C22×D4—228no—
428C22×D4—228no—
429C22×D4—444no—
430C22×D4—444no—
431C22×D4C22×D11112yes—
432C22×D4C22×D11112yes—
433C22×D4C22×D11112yescomplemented
434C23×C4—44no—
435C23×C4—111no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—1112no—
442C23×C4—1112no—
443C23×C4—1112no—
444C23×C4—444no—
445C23×C4—444no—
446C23×C4—444no—
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D1111yescharacteristic
451C23×C4C22×D11112yescomplemented
452#126—1164no—
453#126—1164no—
454#124—1164no—
455#124—1164no—
456#123—1164no—
457#123—1164no—
458C22⋊Q8—1164no—
459#121—1164no—
460#121—1164no—
461#121C22×D11164yescomplemented
462#120—1164no—
463#120—1164no—
464C4×D4—1164no—
465C4×D4—1164no—
466C2×C4⋊C4—1112no—
467C2×C4⋊C4—1112no—
468C2×C4⋊C4—1112no—
469C2×C4⋊C4—1112no—
470C2×C4⋊C4—1112no—
471C2×C4⋊C4C22×D11112yescomplemented
472C2×C22⋊C4—1112no—
473C2×C22⋊C4—1112no—
474C2×C22⋊C4—1112no—
475C2×C22⋊C4—1112no—
476C2×C22⋊C4—1112no—
477C2×C22⋊C4—1112no—
478C2×C22⋊C4—1112no—
479C2×C22⋊C4—1112no—
480C2×C22⋊C4—1112no—
481C2×C22⋊C4—1112no—
482C2×C22⋊C4—1112no—
483C2×C22⋊C4—1112no—
484C2×C22⋊C4—1164no—
485C2×C22⋊C4C22×D11112yes—
486C2×C22⋊C4C22×D11112yescomplemented
487C2×C42—1112no—
488C2×C42—1112no—
489C2×C11—44no—
490C2×C11—44no—
491C2×C11—44no—
492C2×C11C2×#538112yescomplemented
493C2×C11C23×#4111yescharacteristic
494C2×C11C22×H(5,𝔽2)11yescharacteristic
495C2×C11C22×H(5,𝔽2)11yescharacteristic
496D11—28no—
497D11—44no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—24no—
504C24—24no—
505C24—24no—
506C24—24no—
507C24—118no—
508C24—116no—
509C24—116no—
510C24—1116no—
511C24—2248no—
512C24—224no—
513C24—224no—
514C24—224no—
515C24—224no—
516C24—224no—
517C24—4424no—
518C24—4424no—
519C24—4464no—
520C24C23×D1116yes—
521C24C23×D1116yes—
522C24C23×D1116yes—
523C24C23×D1111yescharacteristic
524C2×Q8—1116no—
525C2×Q8—4424no—
526C2×D4—424no—
527C2×D4—424no—
528C2×D4—424no—
529C2×D4—1116no—
530C2×D4—1116no—
531C2×D4—1116no—
532C2×D4—1116no—
533C2×D4—2248no—
534C2×D4—2248no—
535C2×D4—4424no—
536C2×D4—4424no—
537C2×D4C23×D11116yes—
538C2×D4C23×D11116yes—
539C2×D4C23×D11116yescomplemented
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—424no—
545C22×C4—116no—
546C22×C4—116no—
547C22×C4—116no—
548C22×C4—116no—
549C22×C4—116no—
550C22×C4—116no—
551C22×C4—1116no—
552C22×C4—1116no—
553C22×C4—1116no—
554C22×C4—224no—
555C22×C4—224no—
556C22×C4—224no—
557C22×C4—224no—
558C22×C4—224no—
559C22×C4—224no—
560C22×C4—4424no—
561C22×C4—4424no—
562C22×C4—4424no—
563C22×C4C23×D1116yes—
564C22×C4C23×D1116yes—
565C22×C4C23×D1116yes—
566C22×C4C23×D1116yes—
567C22×C4C23×D11116yescomplemented
568C4⋊C4—1116no—
569C4⋊C4—1116no—
570C4⋊C4—1116no—
571C4⋊C4—1116no—
572C4⋊C4—1116no—
573C4⋊C4C23×D11116yescomplemented
574C22⋊C4—1116no—
575C22⋊C4—1116no—
576C22⋊C4—1116no—
577C22⋊C4—1116no—
578C22⋊C4—1116no—
579C22⋊C4—1116no—
580C22⋊C4—1116no—
581C22⋊C4—1116no—
582C22⋊C4—1116no—
583C22⋊C4—1116no—
584C22⋊C4—1116no—
585C22⋊C4—1116no—
586C22⋊C4C23×D11116yes—
587C22⋊C4C23×D11116yescomplemented
588C42—1116no—
589C42—1116no—
590C11C22×#53811yescharacteristic, complemented, Sylow
591C23—212no—
592C23—212no—
593C23—212no—
594C23—212no—
595C23—212no—
596C23—212no—
597C23—212no—
598C23—212no—
599C23—212no—
600C23—416no—
601C23—416no—
602C23—416no—
603C23—1124no—
604C23—114no—
605C23—114no—
606C23—2232no—
607C23—2232no—
608C23—2212no—
609C23—2212no—
610C23—2212no—
611C23—2212no—
612C23—2212no—
613C23—4416no—
614C23—4416no—
615C23—44192no—
616C23—4416no—
617C23#6703714yes—
618C23#6703714yes—
619C23#41×D1114yes—
620C23C24×D1114yes—
621C23C24×D1114yes—
622C23C24×D1114yes—
623C23C24×D1113yes—
624Q8—4416no—
625D4—416no—
626D4—416no—
627D4—416no—
628D4—2232no—
629D4—2232no—
630D4—4416no—
631D4—4416no—
632C2×C4—212no—
633C2×C4—212no—
634C2×C4—212no—
635C2×C4—212no—
636C2×C4—416no—
637C2×C4—114no—
638C2×C4—114no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—2212no—
644C2×C4—2212no—
645C2×C4—2212no—
646C2×C4—2212no—
647C2×C4—2212no—
648C2×C4—2212no—
649C2×C4—4416no—
650C2×C4—4416no—
651C2×C4—4416no—
652C2×C4C24×D1114yes—
653C2×C4C24×D1114yes—
654C2×C4C24×D1114yes—
655C2×C4C24×D1114yes—
656C22—24no—
657C22—24no—
658C22—24no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—24no—
663C22—24no—
664C22—24no—
665C22—424no—
666C22—424no—
667C22—424no—
668C22—118no—
669C22—224no—
670C22—224no—
671C22—2248no—
672C22—224no—
673C22—224no—
674C22—224no—
675C22—4464no—
676C22—4424no—
677C22#10623144116yesdirect product factor
678C22C2×#6703716yes—
679C22C2×#6703716yes—
680C22C2×#41×D1116yes—
681C22C25×D1111yescharacteristic
682C4—24no—
683C4—24no—
684C4—24no—
685C4—24no—
686C4—224no—
687C4—224no—
688C4—224no—
689C4—224no—
690C4—224no—
691C4—224no—
692C2—44no—
693C2—44no—
694C2—44no—
695C2—228no—
696C2—444no—
697C2C2×#10623144112yesdirect product factor
698C2C22×#41×D1111yescharacteristic
699C2C22×#6703711yescharacteristic
700C2C22×#6703711yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C11×#121C2
socleC24×C11C24
hypercenterC22×#121D11
hypocenterC11C22×#538
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×#121

Complements

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

NH ≅ G/Ntype
1. C2×#10623144C2direct (N × H)
2. C22×#66951C2semidirect
3. C22×#66932C2semidirect
4. C22×#66989C2semidirect
5. C22×#66938C2semidirect
6. C22×#66982C2semidirect
7. C22×#66988C2semidirect
8. C22×#66949C2semidirect
9. C22×#66992C2semidirect
10. C22×#66991C2semidirect
11. C22×#66990C2semidirect
12. C22×#66990C2semidirect
13. C22×C4×C22⋊D11C2semidirect
14. C22×(C22⋊D11)⋊C4C2semidirect
15. C22×C22⋊C4×D11C2semidirect
16. C22×C11×#121C2semidirect
20. C23×D4×C11C22semidirect
21. C24×C4×C11C22semidirect
26. C24×Dic11C22semidirect
29. C23×Dic22C22semidirect
30. C2×C11×#121C22semidirect
31. C22×C11×C4⋊C4C22semidirect
33. C22×C11×C22⋊C4C22semidirect
37. C22×C22⋊Dic11C22semidirect
38. C22×C22⋊Dic11C22semidirect
39. C22×C22⋊Dic11C22semidirect
40. C2×#66992C22semidirect
41. C2×#66991C22semidirect
42. C2×#66990C22semidirect
43. C2×#66990C22semidirect
44. C2×#66989C22semidirect
45. C2×#66988C22semidirect
46. C2×#66982C22semidirect
47. C2×C4×C22⋊D11C22semidirect
54. C22×C4⋊Dic11C22semidirect
55. C22×Dic11⋊C4C22semidirect
56. C22×Dic11⋊C4C22semidirect
57. C22×Dic11⋊C4C22semidirect
58. C22×Dic11⋊C4C22semidirect
59. C22×C4×Dic11C22semidirect
60. C22×C4×Dic11C22semidirect
61. #10623144C22direct (N × H)
62. C2×#66951C22semidirect
63. C2×#66949C22semidirect
64. C2×#66938C22semidirect
65. C2×(C22⋊D11)⋊C4C22semidirect
66. C2×C22⋊C4×D11C22semidirect
67. C2×#66932C22semidirect
82. C22×D4×C11C23semidirect
88. C23×C4×C11C23semidirect
104. C23×Dic11C23semidirect
110. C22×Dic22C23semidirect
111. C11×#121C23semidirect
112. C2×C11×C4⋊C4C23semidirect
114. C2×C11×C22⋊C4C23semidirect
118. C2×C22⋊Dic11C23semidirect
119. C2×C22⋊Dic11C23semidirect
120. C2×C22⋊Dic11C23semidirect
121. #66992C23semidirect
122. #66991C23semidirect
123. #66990C23semidirect
124. #66990C23semidirect
125. #66989C23semidirect
126. #66988C23semidirect
127. #66982C23semidirect
128. C4×C22⋊D11C23semidirect
135. C2×C4⋊Dic11C23semidirect
136. C2×Dic11⋊C4C23semidirect
137. C2×Dic11⋊C4C23semidirect
138. C2×Dic11⋊C4C23semidirect
139. C2×Dic11⋊C4C23semidirect
140. C2×C4×Dic11C23semidirect
141. C2×C4×Dic11C23semidirect
142. #66951C23semidirect
143. #66949C23semidirect
144. #66938C23semidirect
145. (C22⋊D11)⋊C4C23semidirect
146. C22⋊C4×D11C23semidirect
147. #66932C23semidirect
180. C2×D4×C11C24semidirect
190. C22×C4×C11C24semidirect
212. C22×Dic11C24semidirect
218. C2×Dic22C24semidirect
219. C11×C4⋊C4C24semidirect
221. C11×C22⋊C4C24semidirect
225. C22⋊Dic11C24semidirect
226. C22⋊Dic11C24semidirect
227. C22⋊Dic11C24semidirect
234. C4⋊Dic11C24semidirect
235. Dic11⋊C4C24semidirect
236. Dic11⋊C4C24semidirect
237. Dic11⋊C4C24semidirect
238. Dic11⋊C4C24semidirect
239. C4×Dic11C24semidirect
240. C4×Dic11C24semidirect
251. C22×#121D11semidirect
330. C23×D4C2×D11semidirect
334. C24×C4C2×D11semidirect
345. C2×#121C2×D11semidirect
355. C22×C4⋊C4C2×D11semidirect
370. C22×C22⋊C4C2×D11semidirect
385. C22×C11#538semidirect
433. C22×D4C22×D11semidirect
451. C23×C4C22×D11semidirect
461. #121C22×D11semidirect
471. C2×C4⋊C4C22×D11semidirect
486. C2×C22⋊C4C22×D11semidirect
492. C2×C11C2×#538semidirect
539. C2×D4C23×D11semidirect
567. C22×C4C23×D11semidirect
573. C4⋊C4C23×D11semidirect
587. C22⋊C4C23×D11semidirect
590. C11C22×#538semidirect
677. C22#10623144direct (N × H)
697. C2C2×#10623144direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106231442
C22×#669512
C22×#669322
C22×#669892
C22×#669382
C22×#669822
C22×#669882
C22×#669492
C22×#669922
C22×#669912
C22×#669902
C22×C4×C22⋊D112
C22×(C22⋊D11)⋊C42
C22×C22⋊C4×D112
C22×C11×#1212
C22×#53811