Finite Group Databasebeta

← C22×#10623091 #15660500

Subgroups — C22×#10623091 #15660500

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×#10623091C2148yesmaximal, direct product factor
2C22×#66951C211yesmaximal, characteristic, complemented
3C22×#66929C211yesmaximal, characteristic, complemented
4C22×#66928C211yesmaximal, characteristic, complemented
5C22×#66938C211yesmaximal, characteristic, complemented
6C22×#66947C211yesmaximal, characteristic, complemented
7C22×#66982C211yesmaximal, characteristic, complemented
8C22×#66931C211yesmaximal, characteristic, complemented
9C22×#66983C211yesmaximal, characteristic, complemented
10C22×#66937C211yesmaximal, characteristic, complemented
11C22×#66992C211yesmaximal, characteristic, complemented
12C22×#66935C211yesmaximal, characteristic, complemented
13C22×#66990C211yesmaximal, characteristic, complemented
14C22×C4×C22⋊D11C211yesmaximal, characteristic, complemented
15C23×(C2×D11)⋊C4C211yesmaximal, characteristic, complemented
16C22×C4×D4×C11C211yesmaximal, characteristic, complemented
17C25×D11C2211yescharacteristic
18C23×D4×C11C2211yescharacteristic
19C24×C4×C11C2211yescharacteristic
20C24×C4×C11C2211yescharacteristic, complemented
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C23×C22⋊D11C2211yescharacteristic
24C23×C22⋊D11C2211yescharacteristic, complemented
25C24×Dic11C2211yescharacteristic
26C23×D44C2211yescharacteristic
27C23×D44C2211yescharacteristic
28C23×C4×D11C2211yescharacteristic, complemented
29C23×Dic22C2211yescharacteristic, complemented
30C2×C4×D4×C11C22124yescomplemented
31C22×C11×C4⋊C4C2211yescharacteristic, complemented
32C22×C11×C22⋊C4C2211yescharacteristic
33C22×C11×C22⋊C4C2211yescharacteristic, complemented
34C22×C42×C11C2211yescharacteristic, complemented
35C22×C22⋊Dic11C2211yescharacteristic
36C22×C22⋊Dic11C2211yescharacteristic, complemented
37C2×#66992C22124yescomplemented
38C2×#66990C22124yescomplemented
39C2×#66983C22124yescomplemented
40C2×#66982C22124yescomplemented
41C2×C4×C22⋊D11C22124yescomplemented
42C22×(C2×D11)⋊C4C2211yescharacteristic
43C22×(C2×D11)⋊C4C2211yescharacteristic
44C22×(C2×D11)⋊C4C2211yescharacteristic
45C22×(C2×D11)⋊C4C2211yescharacteristic
46C22×(C2×D11)⋊C4C2211yescharacteristic
47C22×(C2×D11)⋊C4C2211yescharacteristic
48C22×(C2×D11)⋊C4C2211yescharacteristic
49C22×(C2×D11)⋊C4C2211yescharacteristic
50C22×(C2×D11)⋊C4C22124yescomplemented
51C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
52C22×(C2×D11)⋊C4C2211yescharacteristic, complemented
53C22×C4⋊Dic11C2211yescharacteristic, complemented
54C22×Dic11⋊C4C2211yescharacteristic, complemented
55C22×Dic11⋊C4C2211yescharacteristic, complemented
56C22×Dic11⋊C4C2211yescharacteristic, complemented
57C22×Dic11⋊C4C2211yescharacteristic, complemented
58C22×C4×Dic11C2211yescharacteristic, complemented
59#10623091C221256yesdirect product factor
60C2×#66951C22124yescomplemented
61C2×#66947C22124yescomplemented
62C2×#66938C22124yescomplemented
63C2×#66937C22124yescomplemented
64C2×#66935C22124yescomplemented
65C2×#66931C22124yescomplemented
66C2×#66929C22124yescomplemented
67C2×#66928C22124yescomplemented
68C25×C11C2311yescharacteristic
69C25×C11C2311yescharacteristic
70C24×D11—28no—
71C24×D11—44no—
72C24×D11—44no—
73C24×D11C2311yescharacteristic
74C24×D11C2311yescharacteristic
75C24×D11C2311yescharacteristic
76C24×D11C23112yes—
77C22×D4×C11—28no—
78C22×D4×C11C23112yes—
79C23×C4×C11—44no—
80C23×C4×C11—44no—
81C23×C4×C11C2311yescharacteristic
82C23×C4×C11C2311yescharacteristic
83C23×C4×C11C2311yescharacteristic
84C23×C4×C11C2311yescharacteristic
85C23×C4×C11C2311yescharacteristic
86C23×C4×C11C23112yes—
87C23×C4×C11C23112yescomplemented
88C22×C22⋊D11—28no—
89C22×C22⋊D11—44no—
90C22×C22⋊D11—44no—
91C22×C22⋊D11—44no—
92C22×C22⋊D11C23112yes—
93C22×C22⋊D11C23112yes—
94C22×C22⋊D11C23112yes—
95C22×C22⋊D11C23112yescomplemented
96C23×Dic11—44no—
97C23×Dic11C2311yescharacteristic
98C23×Dic11C2311yescharacteristic
99C23×Dic11C2311yescharacteristic
100C23×Dic11C2311yescharacteristic
101C23×Dic11C2311yescharacteristic
102C23×Dic11C23112yes—
103C22×D44—44no—
104C22×D44—44no—
105C22×D44C23112yes—
106C22×D44C23112yes—
107C22×C4×D11—44no—
108C22×C4×D11C23112yescomplemented
109C22×Dic22—44no—
110C22×Dic22C23112yescomplemented
111C4×D4×C11C23164yescomplemented
112C2×C11×C4⋊C4C23112yescomplemented
113C2×C11×C22⋊C4C23112yes—
114C2×C11×C22⋊C4C23112yescomplemented
115C2×C42×C11C23112yescomplemented
116C2×C22⋊Dic11C23112yes—
117C2×C22⋊Dic11C23112yescomplemented
118#66992C23164yescomplemented
119#66990C23164yescomplemented
120#66983C23164yescomplemented
121#66982C23164yescomplemented
122C4×C22⋊D11C23164yescomplemented
123C2×(C2×D11)⋊C4C23112yes—
124C2×(C2×D11)⋊C4C23112yes—
125C2×(C2×D11)⋊C4C23112yes—
126C2×(C2×D11)⋊C4C23112yes—
127C2×(C2×D11)⋊C4C23112yes—
128C2×(C2×D11)⋊C4C23112yes—
129C2×(C2×D11)⋊C4C23112yes—
130C2×(C2×D11)⋊C4C23112yes—
131C2×(C2×D11)⋊C4C23164yescomplemented
132C2×(C2×D11)⋊C4C23112yescomplemented
133C2×(C2×D11)⋊C4C23112yescomplemented
134C2×C4⋊Dic11C23112yescomplemented
135C2×Dic11⋊C4C23112yescomplemented
136C2×Dic11⋊C4C23112yescomplemented
137C2×Dic11⋊C4C23112yescomplemented
138C2×Dic11⋊C4C23112yescomplemented
139C2×C4×Dic11C23112yescomplemented
140#66951C23164yescomplemented
141#66947C23164yescomplemented
142#66938C23164yescomplemented
143#66937C23164yescomplemented
144#66935C23164yescomplemented
145#66931C23164yescomplemented
146#66929C23164yescomplemented
147#66928C23164yescomplemented
148C22×#538—111nomaximal, Sylow
149C24×C11—24no—
150C24×C11—24no—
151C24×C11—24no—
152C24×C11—24no—
153C24×C11—24no—
154C24×C11#4118yes—
155C24×C11C2416yes—
156C24×C11C2416yes—
157C24×C11C2411yescharacteristic
158C23×D11—24no—
159C23×D11—248no—
160C23×D11—24no—
161C23×D11—24no—
162C23×D11—24no—
163C23×D11—24no—
164C23×D11—24no—
165C23×D11—24no—
166C23×D11—24no—
167C23×D11—24no—
168C23×D11—424no—
169C23×D11—424no—
170C23×D11—464no—
171C23×D11C2416yes—
172C23×D11C2416yes—
173C23×D11C2416yes—
174C23×D11C24116yes—
175C2×D4×C11—248no—
176C2×D4×C11C24116yes—
177C22×C4×C11—24no—
178C22×C4×C11—24no—
179C22×C4×C11—24no—
180C22×C4×C11—24no—
181C22×C4×C11—24no—
182C22×C4×C11—424no—
183C22×C4×C11—424no—
184C22×C4×C11C2416yes—
185C22×C4×C11C2416yes—
186C22×C4×C11C2416yes—
187C22×C4×C11C2416yes—
188C22×C4×C11C2416yes—
189C22×C4×C11C24116yes—
190C22×C4×C11C24116yescomplemented
191C2×C22⋊D11—248no—
192C2×C22⋊D11—424no—
193C2×C22⋊D11—424no—
194C2×C22⋊D11—424no—
195C2×C22⋊D11C24116yes—
196C2×C22⋊D11C24116yes—
197C2×C22⋊D11C24116yes—
198C2×C22⋊D11C24116yescomplemented
199C22×Dic11—24no—
200C22×Dic11—24no—
201C22×Dic11—24no—
202C22×Dic11—24no—
203C22×Dic11—24no—
204C22×Dic11—424no—
205C22×Dic11C2416yes—
206C22×Dic11C2416yes—
207C22×Dic11C2416yes—
208C22×Dic11C2416yes—
209C22×Dic11C2416yes—
210C22×Dic11C24116yes—
211C2×D44—424no—
212C2×D44—424no—
213C2×D44C24116yes—
214C2×D44C24116yes—
215C2×C4×D11—424no—
216C2×C4×D11C24116yescomplemented
217C2×Dic22—424no—
218C2×Dic22C24116yescomplemented
219C11×C4⋊C4C24116yescomplemented
220C11×C22⋊C4C24116yes—
221C11×C22⋊C4C24116yescomplemented
222C42×C11C24116yescomplemented
223C22⋊Dic11C24116yes—
224C22⋊Dic11C24116yescomplemented
225(C2×D11)⋊C4C24116yes—
226(C2×D11)⋊C4C24116yes—
227(C2×D11)⋊C4C24116yes—
228(C2×D11)⋊C4C24116yes—
229(C2×D11)⋊C4C24116yes—
230(C2×D11)⋊C4C24116yes—
231(C2×D11)⋊C4C24116yes—
232(C2×D11)⋊C4C24116yes—
233(C2×D11)⋊C4C24116yescomplemented
234(C2×D11)⋊C4C24116yescomplemented
235C4⋊Dic11C24116yescomplemented
236Dic11⋊C4C24116yescomplemented
237Dic11⋊C4C24116yescomplemented
238Dic11⋊C4C24116yescomplemented
239Dic11⋊C4C24116yescomplemented
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×#121—111no—
252C22×#120—111no—
253C22×#120—111no—
254C22×C4×D4—111no—
255C22×C4×D4D1111yescharacteristic, complemented
256C23×C22⋊C4—111no—
257C23×C11—232no—
258C23×C11—212no—
259C23×C11—212no—
260C23×C11—212no—
261C23×C11—212no—
262C23×C11—212no—
263C23×C11—416no—
264C23×C11C2×#41124yes—
265C23×C11C2×#4114yes—
266C23×C11H(5,𝔽2)14yes—
267C23×C11H(5,𝔽2)14yes—
268C23×C11C2514yes—
269C23×C11C2514yes—
270C23×C11C2513yes—
271C22×D11—212no—
272C22×D11—232no—
273C22×D11—212no—
274C22×D11—212no—
275C22×D11—212no—
276C22×D11—212no—
277C22×D11—212no—
278C22×D11—212no—
279C22×D11—212no—
280C22×D11—212no—
281C22×D11—416no—
282C22×D11—416no—
283C22×D11—4192no—
284C22×D11—416no—
285C22×D11—416no—
286C22×D11—416no—
287C22×D11C2514yes—
288C22×D11C2514yes—
289C22×D11C2514yes—
290D4×C11—232no—
291C2×C4×C11—212no—
292C2×C4×C11—212no—
293C2×C4×C11—212no—
294C2×C4×C11—212no—
295C2×C4×C11—212no—
296C2×C4×C11—416no—
297C2×C4×C11—416no—
298C2×C4×C11C2514yes—
299C2×C4×C11C2514yes—
300C2×C4×C11C2514yes—
301C2×C4×C11C2514yes—
302C2×C4×C11C2514yes—
303C22⋊D11—232no—
304C22⋊D11—416no—
305C22⋊D11—416no—
306C22⋊D11—416no—
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—
318D44—416no—
319D44—416no—
320C4×D11—416no—
321Dic22—416no—
322C26—111no—
323C23×Q8—111no—
324C23×D4—111no—
325C23×D4—111no—
326C23×D4—111no—
327C23×D4—111no—
328C23×D4—111no—
329C23×D4—111no—
330C23×D4C2×D1111yescharacteristic
331C24×C4—111no—
332C24×C4—111no—
333C24×C4C2×D1111yescharacteristic
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×#121—1124no—
346C2×#120—1124no—
347C2×#120—1124no—
348C2×C4×D4—1124no—
349C2×C4×D4C2×D11124yescomplemented
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—1124no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—111no—
369C22×C22⋊C4C2×D1111yescharacteristic
370C22×C22⋊C4C2×D1111yescharacteristic, complemented
371C22×C42—111no—
372C22×C42C2×D1111yescharacteristic, complemented
373C22×C11—24no—
374C22×C11—24no—
375C22×C11—248no—
376C22×C11—24no—
377C22×C11—24no—
378C22×C11—24no—
379C22×C11—424no—
380C22×C11#538116yescomplemented
381C22×C11C22×#4118yes—
382C22×C11C22×#4116yes—
383C22×C11C2×H(5,𝔽2)16yes—
384C22×C11C2×H(5,𝔽2)16yes—
385C22×C11C2611yescharacteristic
386C2×D11—24no—
387C2×D11—24no—
388C2×D11—24no—
389C2×D11—24no—
390C2×D11—24no—
391C2×D11—24no—
392C2×D11—24no—
393C2×D11—24no—
394C2×D11—24no—
395C2×D11—464no—
396C2×D11—424no—
397C2×D11—424no—
398C2×D11—424no—
399C4×C11—24no—
400C4×C11—24no—
401C4×C11—24no—
402C4×C11—24no—
403C4×C11—24no—
404Dic11—24no—
405Dic11—24no—
406Dic11—24no—
407Dic11—24no—
408Dic11—24no—
409C25—111no—
410C25—111no—
411C25—111no—
412C25—1112no—
413C25—228no—
414C25—444no—
415C25—444no—
416C25C22×D1111yescharacteristic
417C25C22×D1111yescharacteristic
418C22×Q8—1112no—
419C22×Q8—444no—
420C22×D4—28no—
421C22×D4—1112no—
422C22×D4—1112no—
423C22×D4—1112no—
424C22×D4—1112no—
425C22×D4—1112no—
426C22×D4—1112no—
427C22×D4—228no—
428C22×D4—444no—
429C22×D4—444no—
430C22×D4—444no—
431C22×D4—444no—
432C22×D4—444no—
433C22×D4C22×D11112yes—
434C23×C4—44no—
435C23×C4—44no—
436C23×C4—111no—
437C23×C4—111no—
438C23×C4—111no—
439C23×C4—111no—
440C23×C4—111no—
441C23×C4—1112no—
442C23×C4—1112no—
443C23×C4—444no—
444C23×C4—444no—
445C23×C4C22×D1111yescharacteristic
446C23×C4C22×D1111yescharacteristic
447C23×C4C22×D1111yescharacteristic
448C23×C4C22×D1111yescharacteristic
449C23×C4C22×D1111yescharacteristic
450C23×C4C22×D11112yes—
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#121—1164no—
462#120—1164no—
463#120—1164no—
464C4×D4—1164no—
465C4×D4C22×D11164yescomplemented
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—1164no—
479C2×C22⋊C4—1112no—
480C2×C22⋊C4—1112no—
481C2×C22⋊C4—1112no—
482C2×C22⋊C4—1112no—
483C2×C22⋊C4—1112no—
484C2×C22⋊C4—1112no—
485C2×C22⋊C4C22×D11112yes—
486C2×C22⋊C4C22×D11112yescomplemented
487C2×C42—1112no—
488C2×C42C22×D11112yescomplemented
489C2×C11—28no—
490C2×C11—44no—
491C2×C11C2×#538112yescomplemented
492C2×C11C23×#4111yescharacteristic
493C2×C11C22×H(5,𝔽2)11yescharacteristic
494C2×C11C22×H(5,𝔽2)11yescharacteristic
495D11—44no—
496D11—44no—
497D11—44no—
498C24—24no—
499C24—24no—
500C24—24no—
501C24—24no—
502C24—24no—
503C24—116no—
504C24—116no—
505C24—116no—
506C24—1116no—
507C24—224no—
508C24—2248no—
509C24—224no—
510C24—224no—
511C24—224no—
512C24—224no—
513C24—224no—
514C24—224no—
515C24—224no—
516C24—224no—
517C24—4424no—
518C24—4424no—
519C24—4464no—
520C24#433918yes—
521C24C23×D1116yes—
522C24C23×D1116yes—
523C24C23×D1111yescharacteristic
524C2×Q8—1116no—
525C2×Q8—4424no—
526C2×D4—248no—
527C2×D4—1116no—
528C2×D4—1116no—
529C2×D4—1116no—
530C2×D4—1116no—
531C2×D4—1116no—
532C2×D4—1116no—
533C2×D4—2248no—
534C2×D4—4424no—
535C2×D4—4424no—
536C2×D4—4424no—
537C2×D4—4424no—
538C2×D4—4424no—
539C2×D4C23×D11116yes—
540C22×C4—24no—
541C22×C4—24no—
542C22×C4—24no—
543C22×C4—24no—
544C22×C4—24no—
545C22×C4—424no—
546C22×C4—424no—
547C22×C4—116no—
548C22×C4—116no—
549C22×C4—116no—
550C22×C4—116no—
551C22×C4—116no—
552C22×C4—1116no—
553C22×C4—1116no—
554C22×C4—224no—
555C22×C4—224no—
556C22×C4—224no—
557C22×C4—224no—
558C22×C4—224no—
559C22×C4—4424no—
560C22×C4—4424no—
561C22×C4C23×D1116yes—
562C22×C4C23×D1116yes—
563C22×C4C23×D1116yes—
564C22×C4C23×D1116yes—
565C22×C4C23×D1116yes—
566C22×C4C23×D11116yes—
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—
589C42C23×D11116yescomplemented
590C11C22×#53811yescharacteristic, complemented, Sylow
591C23—232no—
592C23—212no—
593C23—212no—
594C23—212no—
595C23—212no—
596C23—212no—
597C23—416no—
598C23—114no—
599C23—114no—
600C23—114no—
601C23—2212no—
602C23—2232no—
603C23—2212no—
604C23—2212no—
605C23—2212no—
606C23—2212no—
607C23—2212no—
608C23—2212no—
609C23—2212no—
610C23—2212no—
611C23—4416no—
612C23—4416no—
613C23—44192no—
614C23—4416no—
615C23—4416no—
616C23—4416no—
617C23C2×#4339124yes—
618C23C2×#433914yes—
619C23#6703714yes—
620C23#6704214yes—
621C23C24×D1114yes—
622C23C24×D1114yes—
623C23C24×D1113yes—
624Q8—4416no—
625D4—232no—
626D4—2232no—
627D4—4416no—
628D4—4416no—
629D4—4416no—
630D4—4416no—
631D4—4416no—
632C2×C4—212no—
633C2×C4—212no—
634C2×C4—212no—
635C2×C4—212no—
636C2×C4—212no—
637C2×C4—416no—
638C2×C4—416no—
639C2×C4—114no—
640C2×C4—114no—
641C2×C4—114no—
642C2×C4—114no—
643C2×C4—114no—
644C2×C4—2212no—
645C2×C4—2212no—
646C2×C4—2212no—
647C2×C4—2212no—
648C2×C4—2212no—
649C2×C4—4416no—
650C2×C4—4416no—
651C2×C4C24×D1114yes—
652C2×C4C24×D1114yes—
653C2×C4C24×D1114yes—
654C2×C4C24×D1114yes—
655C2×C4C24×D1114yes—
656C22—24no—
657C22—24no—
658C22—248no—
659C22—24no—
660C22—24no—
661C22—24no—
662C22—424no—
663C22—224no—
664C22—224no—
665C22—224no—
666C22—224no—
667C22—224no—
668C22—224no—
669C22—224no—
670C22—224no—
671C22—224no—
672C22—4464no—
673C22—4424no—
674C22—4424no—
675C22—4424no—
676C22#10623091116yesdirect product factor
677C22C22×#433918yes—
678C22C22×#433916yes—
679C22C2×#6703716yes—
680C22C2×#6704216yes—
681C22C25×D1111yescharacteristic
682C4—24no—
683C4—24no—
684C4—24no—
685C4—24no—
686C4—24no—
687C4—224no—
688C4—224no—
689C4—224no—
690C4—224no—
691C4—224no—
692C2—28no—
693C2—44no—
694C2—444no—
695C2—444no—
696C2—444no—
697C2C2×#10623091112yesdirect product factor
698C2C23×#433911yescharacteristic
699C2C22×#6703711yescharacteristic
700C2C22×#6704211yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC22×C11C26
FrattiniC22C25×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
hypercenterC22×C4×D4D11
hypocenterC11C22×#538
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C2×#10623091C2direct (N × H)
2. C22×#66951C2semidirect
3. C22×#66929C2semidirect
4. C22×#66928C2semidirect
5. C22×#66938C2semidirect
6. C22×#66947C2semidirect
7. C22×#66982C2semidirect
8. C22×#66931C2semidirect
9. C22×#66983C2semidirect
10. C22×#66937C2semidirect
11. C22×#66992C2semidirect
12. C22×#66935C2semidirect
13. C22×#66990C2semidirect
14. C22×C4×C22⋊D11C2semidirect
15. C23×(C2×D11)⋊C4C2semidirect
16. C22×C4×D4×C11C2semidirect
20. C24×C4×C11C22semidirect
24. C23×C22⋊D11C22semidirect
28. C23×C4×D11C22semidirect
29. C23×Dic22C22semidirect
30. C2×C4×D4×C11C22semidirect
31. C22×C11×C4⋊C4C22semidirect
33. C22×C11×C22⋊C4C22semidirect
34. C22×C42×C11C22semidirect
36. C22×C22⋊Dic11C22semidirect
37. C2×#66992C22semidirect
38. C2×#66990C22semidirect
39. C2×#66983C22semidirect
40. C2×#66982C22semidirect
41. C2×C4×C22⋊D11C22semidirect
50. C22×(C2×D11)⋊C4C22semidirect
51. C22×(C2×D11)⋊C4C22semidirect
52. C22×(C2×D11)⋊C4C22semidirect
53. C22×C4⋊Dic11C22semidirect
54. C22×Dic11⋊C4C22semidirect
55. C22×Dic11⋊C4C22semidirect
56. C22×Dic11⋊C4C22semidirect
57. C22×Dic11⋊C4C22semidirect
58. C22×C4×Dic11C22semidirect
59. #10623091C22direct (N × H)
60. C2×#66951C22semidirect
61. C2×#66947C22semidirect
62. C2×#66938C22semidirect
63. C2×#66937C22semidirect
64. C2×#66935C22semidirect
65. C2×#66931C22semidirect
66. C2×#66929C22semidirect
67. C2×#66928C22semidirect
87. C23×C4×C11C23semidirect
95. C22×C22⋊D11C23semidirect
108. C22×C4×D11C23semidirect
110. C22×Dic22C23semidirect
111. C4×D4×C11C23semidirect
112. C2×C11×C4⋊C4C23semidirect
114. C2×C11×C22⋊C4C23semidirect
115. C2×C42×C11C23semidirect
117. C2×C22⋊Dic11C23semidirect
118. #66992C23semidirect
119. #66990C23semidirect
120. #66983C23semidirect
121. #66982C23semidirect
122. C4×C22⋊D11C23semidirect
131. C2×(C2×D11)⋊C4C23semidirect
132. C2×(C2×D11)⋊C4C23semidirect
133. C2×(C2×D11)⋊C4C23semidirect
134. C2×C4⋊Dic11C23semidirect
135. C2×Dic11⋊C4C23semidirect
136. C2×Dic11⋊C4C23semidirect
137. C2×Dic11⋊C4C23semidirect
138. C2×Dic11⋊C4C23semidirect
139. C2×C4×Dic11C23semidirect
140. #66951C23semidirect
141. #66947C23semidirect
142. #66938C23semidirect
143. #66937C23semidirect
144. #66935C23semidirect
145. #66931C23semidirect
146. #66929C23semidirect
147. #66928C23semidirect
190. C22×C4×C11C24semidirect
198. C2×C22⋊D11C24semidirect
216. C2×C4×D11C24semidirect
218. C2×Dic22C24semidirect
219. C11×C4⋊C4C24semidirect
221. C11×C22⋊C4C24semidirect
222. C42×C11C24semidirect
224. C22⋊Dic11C24semidirect
233. (C2×D11)⋊C4C24semidirect
234. (C2×D11)⋊C4C24semidirect
235. C4⋊Dic11C24semidirect
236. Dic11⋊C4C24semidirect
237. Dic11⋊C4C24semidirect
238. Dic11⋊C4C24semidirect
239. Dic11⋊C4C24semidirect
240. C4×Dic11C24semidirect
255. C22×C4×D4D11semidirect
334. C24×C4C2×D11semidirect
349. C2×C4×D4C2×D11semidirect
355. C22×C4⋊C4C2×D11semidirect
370. C22×C22⋊C4C2×D11semidirect
372. C22×C42C2×D11semidirect
380. C22×C11#538semidirect
451. C23×C4C22×D11semidirect
465. C4×D4C22×D11semidirect
471. C2×C4⋊C4C22×D11semidirect
486. C2×C22⋊C4C22×D11semidirect
488. C2×C42C22×D11semidirect
491. C2×C11C2×#538semidirect
567. C22×C4C23×D11semidirect
573. C4⋊C4C23×D11semidirect
587. C22⋊C4C23×D11semidirect
589. C42C23×D11semidirect
590. C11C22×#538semidirect
676. C22#10623091direct (N × H)
697. C2C2×#10623091direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#106230912
C22×#669512
C22×#669292
C22×#669282
C22×#669382
C22×#669472
C22×#669822
C22×#669312
C22×#669832
C22×#669372
C22×#669922
C22×#669352
C22×#669902
C22×C4×C22⋊D112
C23×(C2×D11)⋊C42
C22×C4×D4×C112
C22×#53811