Finite Group Databasebeta

← C2×C4×#66990 #14912185

Subgroups — C2×C4×#66990 #14912185

Order 2816.

8582 conjugacy classes of subgroups.

The subgroup lattice has 708 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C4×D11C211yesmaximal, characteristic, complemented
2C22×#66990C211yesmaximal, characteristic
3C22×C4×C22⋊D11C212yesmaximal, complemented
4C4×#66990C2116yesmaximal, direct product factor
5C2×#10622833C211yesmaximal, characteristic, complemented
6C2×#10622569C212yesmaximal, complemented
7C2×#10622559C211yesmaximal, characteristic, complemented
8C2×#10622602C212yesmaximal, complemented
9C2×#10622568C211yesmaximal, characteristic, complemented
10C2×C4×(C2×D11)⋊C4C212yesmaximal, complemented
11C2×C4×C22⋊Dic11C211yesmaximal, characteristic, complemented
12C22×C4×D4×C11C211yesmaximal, characteristic, complemented
13C25×D11C2211yescharacteristic
14C23×D4×C11C2211yescharacteristic
15C24×C4×C11C2211yescharacteristic
16C24×C4×C11C2211yescharacteristic, complemented
17C23×C22⋊D11C2212yes—
18C24×Dic11C2211yescharacteristic
19C23×C4×D11—28no—
20C23×C4×D11—216no—
21C23×C4×D11C2212yes—
22C23×C4×D11C2212yes—
23C23×C4×D11C2218yescomplemented
24C2×C4×D4×C11—28no—
25C2×C4×D4×C11C2218yescomplemented
26C22×C11×C4⋊C4C2211yescharacteristic, complemented
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2211yescharacteristic, complemented
29C22×C42×C11C2211yescharacteristic, complemented
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2212yescomplemented
33C2×#66990C4116yesdirect product factor
34C2×#66990C2218yes—
35C2×C4×C22⋊D11—216no—
36C2×C4×C22⋊D11C22116yescomplemented
37C22×(C2×D11)⋊C4C2212yes—
38C22×(C2×D11)⋊C4C2212yes—
39C22×(C2×D11)⋊C4C2212yes—
40C22×Dic11⋊C4C2212yescomplemented
41C22×C4×Dic11C2212yescomplemented
42#10622833C2218yescomplemented
43C4×C22⋊Dic11C2218yescomplemented
44C2×C11⋊#95C2212yescomplemented
45C2×C11⋊#95C2212yescomplemented
46C2×C11⋊#95C2212yescomplemented
47#10622602C22116yescomplemented
48#10622569C22116yescomplemented
49#10622568C2218yescomplemented
50#10622559C2218yescomplemented
51C4×(C2×D11)⋊C4C22116yescomplemented
52C25×C11C2311yescharacteristic
53C25×C11C2311yescharacteristic
54C24×D11—24no—
55C24×D11—24no—
56C24×D11—28no—
57C24×D11—28no—
58C24×D11C2×C418yescomplemented
59C24×D11C2314yes—
60C24×D11C2312yes—
61C22×D4×C11—24no—
62C22×D4×C11—24no—
63C22×D4×C11C2×C418yescomplemented
64C22×D4×C11C2314yes—
65C23×C4×C11—28no—
66C23×C4×C11—28no—
67C23×C4×C11—24no—
68C23×C4×C11D418yescomplemented
69C23×C4×C11C2311yescharacteristic
70C23×C4×C11C2311yescharacteristic
71C23×C4×C11C2311yescharacteristic
72C23×C4×C11C2311yescharacteristic
73C23×C4×C11C2314yes—
74C23×C4×C11C2311yescharacteristic
75C23×C4×C11C2314yescomplemented
76C22×C22⋊D11—28no—
77C22×C22⋊D11—28no—
78C22×C22⋊D11C2×C4116yescomplemented
79C22×C22⋊D11C2318yes—
80C23×Dic11—24no—
81C23×Dic11—28no—
82C23×Dic11C2312yes—
83C23×Dic11C2314yes—
84C23×Dic11C2312yes—
85C23×Dic11C2312yes—
86C22×C4×D11—2128no—
87C22×C4×D11—28no—
88C22×C4×D11—28no—
89C22×C4×D11—28no—
90C22×C4×D11—28no—
91C22×C4×D11—232no—
92C22×C4×D11—28no—
93C22×C4×D11—264no—
94C22×C4×D11D4116yescomplemented
95C22×C4×D11C2318yes—
96C22×C4×D11C2318yes—
97C4×D4×C11—232no—
98C2×C11×C4⋊C4—24no—
99C2×C11×C4⋊C4C2314yescomplemented
100C2×C11×C22⋊C4—24no—
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4C2314yes—
103C2×C11×C22⋊C4C2314yescomplemented
104C2×C42×C11—24no—
105C2×C42×C11C2314yescomplemented
106C2×C22⋊Dic11—24no—
107C2×C22⋊Dic11—28no—
108C2×C22⋊Dic11C2×C418yescomplemented
109C2×C22⋊Dic11C2314yes—
110C2×C22⋊Dic11C2314yes—
111C2×C22⋊Dic11C2318yescomplemented
112#66990C2×C4164yesdirect product factor
113C4×C22⋊D11—264no—
114C2×(C2×D11)⋊C4—28no—
115C2×(C2×D11)⋊C4—28no—
116C2×(C2×D11)⋊C4C2×C4116yescomplemented
117C2×(C2×D11)⋊C4C2318yes—
118C2×(C2×D11)⋊C4C2318yes—
119C2×(C2×D11)⋊C4C2318yes—
120C2×Dic11⋊C4—28no—
121C2×Dic11⋊C4C2318yescomplemented
122C2×C4×Dic11—28no—
123C2×C4×Dic11C2318yescomplemented
124C11⋊#95C2318yescomplemented
125C11⋊#95C2318yescomplemented
126C11⋊#95C2318yescomplemented
127C2×C4×#120—111nomaximal, Sylow
128C24×C11—24no—
129C24×C11—24no—
130C24×C11—24no—
131C24×C11—22no—
132C24×C11—24no—
133C24×C11—22no—
134C24×C11C22×C414yes—
135C24×C11C22×C414yescomplemented
136C24×C11C2×D414yes—
137C24×C11#4114yes—
138C24×C11C2412yes—
139C24×C11C2412yes—
140C24×C11C2411yescharacteristic
141C23×D11—232no—
142C23×D11—264no—
143C23×D11—232no—
144C23×D11—232no—
145C23×D11—28no—
146C23×D11—24no—
147C23×D11—24no—
148C23×D11—28no—
149C23×D11—24no—
150C23×D11—24no—
151C23×D11—264no—
152C23×D11—216no—
153C23×D11—216no—
154C23×D11C22×C418yes—
155C23×D11C22×C4116yescomplemented
156C23×D11C2×D418yes—
157C23×D11#4118yes—
158C23×D11C2414yes—
159C2×D4×C11—232no—
160C2×D4×C11—28no—
161C2×D4×C11—28no—
162C2×D4×C11C22×C4116yescomplemented
163C22×C4×C11—22no—
164C22×C4×C11—24no—
165C22×C4×C11—22no—
166C22×C4×C11—232no—
167C22×C4×C11—216no—
168C22×C4×C11—24no—
169C22×C4×C11—22no—
170C22×C4×C11—22no—
171C22×C4×C11—24no—
172C22×C4×C11—216no—
173C22×C4×C11—28no—
174C22×C4×C11—416no—
175C22×C4×C11C22×C414yescomplemented
176C22×C4×C11C2×D414yes—
177C22×C4×C11C2×D418yes—
178C22×C4×C11C2×D414yes—
179C22×C4×C11C2×D4116yescomplemented
180C22×C4×C11C2412yes—
181C22×C4×C11C2412yes—
182C22×C4×C11C2412yes—
183C22×C4×C11C2412yes—
184C22×C4×C11C2412yes—
185C2×C22⋊D11—264no—
186C2×C22⋊D11—216no—
187C2×C22⋊D11—216no—
188C2×C22⋊D11C22×C4132yescomplemented
189C22×Dic11—232no—
190C22×Dic11—216no—
191C22×Dic11—24no—
192C22×Dic11—24no—
193C22×Dic11—28no—
194C22×Dic11—24no—
195C22×Dic11—24no—
196C22×Dic11—24no—
197C22×Dic11—24no—
198C22×Dic11—24no—
199C22×Dic11C22×C418yescomplemented
200C22×Dic11C2×D418yes—
201C22×Dic11C2414yes—
202C22×Dic11C2414yes—
203C22×Dic11C2414yes—
204C2×C4×D11—264no—
205C2×C4×D11—2256no—
206C2×C4×D11—216no—
207C2×C4×D11—216no—
208C2×C4×D11—264no—
209C2×C4×D11—216no—
210C2×C4×D11—216no—
211C2×C4×D11—216no—
212C2×C4×D11C2×D4132yescomplemented
213C11×C4⋊C4—28no—
214C11×C22⋊C4—28no—
215C11×C22⋊C4—28no—
216C42×C11—28no—
217C22⋊Dic11—216no—
218C22⋊Dic11—28no—
219C22⋊Dic11C22×C4116yescomplemented
220(C2×D11)⋊C4—216no—
221(C2×D11)⋊C4—216no—
222(C2×D11)⋊C4C22×C4132yescomplemented
223Dic11⋊C4—216no—
224C4×Dic11—216no—
225C25×C4—111no—
226C22×#120—111no—
227C22×C4×D4—112no—
228C22×C4×D4D1111yescharacteristic, complemented
229C4×#120—1116no—
230C2×#386—111no—
231C2×#386—112no—
232C2×#385—112no—
233C2×#385—111no—
234C2×#379—111no—
235C2×C4×C22⋊C4—112no—
236C2×C4×C22⋊C4—111no—
237C23×C11—216no—
238C23×C11—28no—
239C23×C11—28no—
240C23×C11—216no—
241C23×C11—24no—
242C23×C11—24no—
243C23×C11—216no—
244C23×C11—28no—
245C23×C11—24no—
246C23×C11—22no—
247C23×C11—24no—
248C23×C11—22no—
249C23×C11—44no—
250C23×C11—48no—
251C23×C11—44no—
252C23×C11C4×D4116yescomplemented
253C23×C11C23×C414yes—
254C23×C11C23×C412yes—
255C23×C11C23×C414yescomplemented
256C23×C11C22×D414yes—
257C23×C11C22×D414yes—
258C23×C11C22×D412yes—
259C23×C11C2×#4114yes—
260C23×C11C2×#4112yes—
261C23×C11C2×#4114yes—
262C23×C11C2511yescharacteristic
263C22×D11—232no—
264C22×D11—264no—
265C22×D11—232no—
266C22×D11—2256no—
267C22×D11—216no—
268C22×D11—216no—
269C22×D11—232no—
270C22×D11—216no—
271C22×D11—216no—
272C22×D11—216no—
273C22×D11—216no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—24no—
278C22×D11—264no—
279C22×D11C4×D4132yescomplemented
280C22×D11C23×C418yes—
281C22×D11C22×D418yes—
282C22×D11C2×#4118yes—
283D4×C11—232no—
284C2×C4×C11—28no—
285C2×C4×C11—28no—
286C2×C4×C11—22no—
287C2×C4×C11—24no—
288C2×C4×C11—22no—
289C2×C4×C11—232no—
290C2×C4×C11—24no—
291C2×C4×C11—22no—
292C2×C4×C11—22no—
293C2×C4×C11—24no—
294C2×C4×C11—44no—
295C2×C4×C11—44no—
296C2×C4×C11—416no—
297C2×C4×C11#120116yescomplemented
298C2×C4×C11C23×C414yescomplemented
299C2×C4×C11C22×D418yes—
300C2×C4×C11C22×D414yes—
301C2×C4×C11C22×D414yes—
302C22⋊D11—264no—
303C2×Dic11—232no—
304C2×Dic11—216no—
305C2×Dic11—216no—
306C2×Dic11—24no—
307C2×Dic11—24no—
308C2×Dic11—24no—
309C2×Dic11—24no—
310C2×Dic11—24no—
311C2×Dic11—24no—
312C2×Dic11—24no—
313C2×Dic11—48no—
314C2×Dic11C23×C418yescomplemented
315C2×Dic11C22×D418yes—
316C4×D11—264no—
317C4×D11—264no—
318C26—111no—
319C23×D4—112no—
320C23×D4C2×D1111yescharacteristic
321C24×C4—112no—
322C24×C4—111no—
323C24×C4—112no—
324C24×C4—118no—
325C24×C4—2216no—
326C24×C4—228no—
327C24×C4C2×D1111yescharacteristic
328C24×C4C2×D1111yescharacteristic, complemented
329C2×#120—118no—
330C2×#120—1116no—
331C2×C4×D4—28no—
332C2×C4×D4—1116no—
333C2×C4×D4—2216no—
334C2×C4×D4C2×D1118yescomplemented
335C22×C4⋊C4—112no—
336C22×C4⋊C4C2×D1111yescharacteristic, complemented
337C22×C22⋊C4—111no—
338C22×C22⋊C4—112no—
339C22×C22⋊C4—112no—
340C22×C22⋊C4—111no—
341C22×C22⋊C4—112no—
342C22×C22⋊C4—112no—
343C22×C22⋊C4C2×D1111yescharacteristic
344C22×C22⋊C4C2×D1111yescharacteristic, complemented
345C22×C42—112no—
346C22×C42C2×D1111yescharacteristic, complemented
347#386—118no—
348#386—1116no—
349#385—1116no—
350#385—118no—
351#379—118no—
352C4×C22⋊C4—118no—
353C4×C22⋊C4—1116no—
354C2×#95—112no—
355C2×#95—112no—
356C2×#95—112no—
357C22×C11—28no—
358C22×C11—24no—
359C22×C11—24no—
360C22×C11—28no—
361C22×C11—232no—
362C22×C11—24no—
363C22×C11—28no—
364C22×C11—42no—
365C22×C11—44no—
366C22×C11—42no—
367C22×C11—416no—
368C22×C11C2×C4×D414yes—
369C22×C11C2×C4×D418yes—
370C22×C11C2×C4×D418yescomplemented
371C22×C11C2×#12014yes—
372C22×C11#52518yes—
373C22×C11#52514yes—
374C22×C11C24×C411yescharacteristic
375C22×C11C23×D412yes—
376C22×C11C23×D411yescharacteristic
377C22×C11C22×#4111yescharacteristic
378C22×C11C22×#4112yes—
379C2×D11—2128no—
380C2×D11—28no—
381C2×D11—28no—
382C2×D11—28no—
383C2×D11—28no—
384C2×D11—28no—
385C2×D11—28no—
386C2×D11—264no—
387C2×D11C2×C4×D4116yescomplemented
388C4×C11—24no—
389C4×C11—24no—
390C4×C11—42no—
391C4×C11—42no—
392C4×C11C2×#12018yescomplemented
393Dic11—28no—
394Dic11—28no—
395Dic11—44no—
396C25—112no—
397C25—118no—
398C25—114no—
399C25—228no—
400C25—228no—
401C25—224no—
402C25—224no—
403C25C22×D1111yescharacteristic
404C25C22×D1111yescharacteristic
405C22×D4—24no—
406C22×D4—24no—
407C22×D4—1116no—
408C22×D4—118no—
409C22×D4—228no—
410C22×D4—228no—
411C22×D4C4×D1118yescomplemented
412C22×D4C22×D1114yes—
413C23×C4—28no—
414C23×C4—28no—
415C23×C4—24no—
416C23×C4—112no—
417C23×C4—112no—
418C23×C4—1116no—
419C23×C4—118no—
420C23×C4—112no—
421C23×C4—114no—
422C23×C4—118no—
423C23×C4—228no—
424C23×C4—2264no—
425C23×C4—228no—
426C23×C4—22128no—
427C23×C4—228no—
428C23×C4—224no—
429C23×C4—228no—
430C23×C4—228no—
431C23×C4—228no—
432C23×C4—2232no—
433C23×C4C22⋊D1118yescomplemented
434C23×C4C22×D1111yescharacteristic
435C23×C4C22×D1111yescharacteristic
436C23×C4C22×D1111yescharacteristic
437C23×C4C22×D1111yescharacteristic
438C23×C4C22×D1114yes—
439C23×C4C22×D1111yescharacteristic
440C23×C4C22×D1114yescomplemented
441#120—1164no—
442C4×D4—232no—
443C4×D4—2264no—
444C2×C4⋊C4—24no—
445C2×C4⋊C4—118no—
446C2×C4⋊C4—228no—
447C2×C4⋊C4C22×D1114yescomplemented
448C2×C22⋊C4—24no—
449C2×C22⋊C4—24no—
450C2×C22⋊C4—118no—
451C2×C22⋊C4—114no—
452C2×C22⋊C4—1116no—
453C2×C22⋊C4—118no—
454C2×C22⋊C4—118no—
455C2×C22⋊C4—114no—
456C2×C22⋊C4—118no—
457C2×C22⋊C4—118no—
458C2×C22⋊C4—228no—
459C2×C22⋊C4—228no—
460C2×C22⋊C4—228no—
461C2×C22⋊C4—224no—
462C2×C22⋊C4C22×D1114yes—
463C2×C22⋊C4C22×D1114yescomplemented
464C2×C42—24no—
465C2×C42—118no—
466C2×C42—228no—
467C2×C42C22×D1114yescomplemented
468#95—118no—
469#95—118no—
470#95—118no—
471C2×C11—28no—
472C2×C11—44no—
473C2×C11C4×#12018yescomplemented
474C2×C11C22×C4×D412yes—
475C2×C11C22×C4×D411yescharacteristic
476C2×C11C22×#12011yescharacteristic
477C2×C11C2×#52512yes—
478C2×C11C2×#52511yescharacteristic
479D11—216no—
480C24—24no—
481C24—24no—
482C24—22no—
483C24—24no—
484C24—24no—
485C24—22no—
486C24—118no—
487C24—118no—
488C24—118no—
489C24—114no—
490C24—1116no—
491C24—2216no—
492C24—2264no—
493C24—2216no—
494C24—2232no—
495C24—2264no—
496C24—2232no—
497C24—2232no—
498C24—228no—
499C24—224no—
500C24—224no—
501C24—224no—
502C24—228no—
503C24—224no—
504C24C2×C4×D1114yes—
505C24C2×C4×D1114yescomplemented
506C24#433914yes—
507C24C2×C22⋊D1114yes—
508C24C23×D1112yes—
509C24C23×D1112yes—
510C24C23×D1111yescharacteristic
511C2×D4—232no—
512C2×D4—28no—
513C2×D4—28no—
514C2×D4—1132no—
515C2×D4—2216no—
516C2×D4—2264no—
517C2×D4—2216no—
518C2×D4C2×C4×D11116yescomplemented
519C22×C4—22no—
520C22×C4—24no—
521C22×C4—22no—
522C22×C4—232no—
523C22×C4—216no—
524C22×C4—24no—
525C22×C4—24no—
526C22×C4—22no—
527C22×C4—22no—
528C22×C4—216no—
529C22×C4—28no—
530C22×C4—416no—
531C22×C4—118no—
532C22×C4—118no—
533C22×C4—114no—
534C22×C4—114no—
535C22×C4—1132no—
536C22×C4—114no—
537C22×C4—2216no—
538C22×C4—2216no—
539C22×C4—2264no—
540C22×C4—22256no—
541C22×C4—2216no—
542C22×C4—2232no—
543C22×C4—224no—
544C22×C4—224no—
545C22×C4—224no—
546C22×C4—228no—
547C22×C4—224no—
548C22×C4—2264no—
549C22×C4—2216no—
550C22×C4—2216no—
551C22×C4—2216no—
552C22×C4—224no—
553C22×C4—224no—
554C22×C4—224no—
555C22×C4C2×C4×D1114yescomplemented
556C22×C4D4×D1118yes—
557C22×C4C2×C22⋊D1114yes—
558C22×C4C2×C22⋊D1114yes—
559C22×C4C2×C22⋊D11116yescomplemented
560C22×C4C23×D1112yes—
561C22×C4C23×D1112yes—
562C22×C4C23×D1112yes—
563C22×C4C23×D1112yes—
564C22×C4C23×D1112yes—
565C4⋊C4—28no—
566C4⋊C4—2216no—
567C22⋊C4—28no—
568C22⋊C4—28no—
569C22⋊C4—1116no—
570C22⋊C4—1132no—
571C22⋊C4—2216no—
572C22⋊C4—2216no—
573C22⋊C4—2216no—
574C22⋊C4—228no—
575C42—28no—
576C42—2216no—
577C11C2×C4×#12011yescharacteristic, complemented, Sylow
578C23—28no—
579C23—216no—
580C23—216no—
581C23—28no—
582C23—24no—
583C23—24no—
584C23—28no—
585C23—216no—
586C23—22no—
587C23—24no—
588C23—24no—
589C23—22no—
590C23—44no—
591C23—48no—
592C23—44no—
593C23—1132no—
594C23—118no—
595C23—118no—
596C23—118no—
597C23—2264no—
598C23—2232no—
599C23—2264no—
600C23—22256no—
601C23—2232no—
602C23—2216no—
603C23—2232no—
604C23—2216no—
605C23—2216no—
606C23—2216no—
607C23—2216no—
608C23—2216no—
609C23—224no—
610C23—224no—
611C23—224no—
612C23—224no—
613C23C4×C22⋊D11116yescomplemented
614C23C22×C4×D1114yes—
615C23C22×C4×D1112yes—
616C23C22×C4×D1114yescomplemented
617C23C2×#433914yes—
618C23C2×#433912yes—
619C23C2×D4×D1114yes—
620C23#41×D1114yes—
621C23C22×C22⋊D1114yes—
622C23C22×C22⋊D1112yes—
623C23C24×D1111yescharacteristic
624D4—232no—
625D4—2264no—
626C2×C4—28no—
627C2×C4—28no—
628C2×C4—22no—
629C2×C4—24no—
630C2×C4—22no—
631C2×C4—232no—
632C2×C4—24no—
633C2×C4—24no—
634C2×C4—22no—
635C2×C4—22no—
636C2×C4—44no—
637C2×C4—44no—
638C2×C4—416no—
639C2×C4—118no—
640C2×C4—118no—
641C2×C4—2264no—
642C2×C4—2232no—
643C2×C4—2216no—
644C2×C4—2216no—
645C2×C4—224no—
646C2×C4—224no—
647C2×C4—224no—
648C2×C4—224no—
649C2×C4—2264no—
650C2×C4—224no—
651C2×C4—224no—
652C2×C4—224no—
653C2×C4—448no—
654C2×C4#66990116yesdirect product factor
655C2×C4C22×C4×D1114yescomplemented
656C2×C4C2×D4×D1118yes—
657C2×C4C22×C22⋊D1114yes—
658C2×C4C22×C22⋊D1114yes—
659C22—28no—
660C22—232no—
661C22—28no—
662C22—24no—
663C22—24no—
664C22—28no—
665C22—24no—
666C22—44no—
667C22—416no—
668C22—42no—
669C22—42no—
670C22—1116no—
671C22—22128no—
672C22—228no—
673C22—228no—
674C22—2264no—
675C22—228no—
676C22—228no—
677C22—228no—
678C22—228no—
679C22C4×D4×D1118yes—
680C22#1062307818yes—
681C22C2×C4×C22⋊D1114yes—
682C22C2×C4×C22⋊D1118yescomplemented
683C22C2×#6699014yes—
684C22#1062335914yes—
685C22C23×C4×D1111yescharacteristic
686C22C22×#433911yescharacteristic
687C22C22×D4×D1112yes—
688C22C2×#41×D1112yes—
689C22C23×C22⋊D1111yescharacteristic
690C4—24no—
691C4—24no—
692C4—42no—
693C4—42no—
694C4—228no—
695C4—228no—
696C4—444no—
697C4C2×#6699018yesdirect product factor
698C2—28no—
699C2—44no—
700C2—2216no—
701C2C4×#6699018yesdirect product factor
702C2C2×C4×D4×D1112yes—
703C2C22×C4×C22⋊D1111yescharacteristic
704C2C22×#6699011yescharacteristic
705C2C2×#1062335911yescharacteristic
706C2C2×#1062307812yes—
subgroupG/H
centerC23×C4C22×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC22×C4×D4×C11C2
socleC24×C11C24
prime radicalC22×#66990C2
cosocleC23×C11C25
hypercenterC22×C4×D4D11
hypocenterC11C2×C4×#120
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C23×C4 ◁ C22×C4×D4

Complements

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

NH ≅ G/Ntype
1. C24×C4×D11C2semidirect
3. C22×C4×C22⋊D11C2semidirect
4. C4×#66990C2direct (N × H)
5. C2×#10622833C2semidirect
6. C2×#10622569C2semidirect
7. C2×#10622559C2semidirect
8. C2×#10622602C2semidirect
9. C2×#10622568C2semidirect
10. C2×C4×(C2×D11)⋊C4C2semidirect
11. C2×C4×C22⋊Dic11C2semidirect
12. C22×C4×D4×C11C2semidirect
16. C24×C4×C11C22semidirect
23. C23×C4×D11C22semidirect
25. C2×C4×D4×C11C22semidirect
26. C22×C11×C4⋊C4C22semidirect
28. C22×C11×C22⋊C4C22semidirect
29. C22×C42×C11C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C2×#66990C4direct (N × H)
36. C2×C4×C22⋊D11C22semidirect
40. C22×Dic11⋊C4C22semidirect
41. C22×C4×Dic11C22semidirect
42. #10622833C22semidirect
43. C4×C22⋊Dic11C22semidirect
44. C2×C11⋊#95C22semidirect
45. C2×C11⋊#95C22semidirect
46. C2×C11⋊#95C22semidirect
47. #10622602C22semidirect
48. #10622569C22semidirect
49. #10622568C22semidirect
50. #10622559C22semidirect
51. C4×(C2×D11)⋊C4C22semidirect
58. C24×D11C2×C4semidirect
63. C22×D4×C11C2×C4semidirect
68. C23×C4×C11D4semidirect
75. C23×C4×C11C23semidirect
78. C22×C22⋊D11C2×C4semidirect
94. C22×C4×D11D4semidirect
99. C2×C11×C4⋊C4C23semidirect
103. C2×C11×C22⋊C4C23semidirect
105. C2×C42×C11C23semidirect
108. C2×C22⋊Dic11C2×C4semidirect
111. C2×C22⋊Dic11C23semidirect
112. #66990C2×C4direct (N × H)
116. C2×(C2×D11)⋊C4C2×C4semidirect
121. C2×Dic11⋊C4C23semidirect
123. C2×C4×Dic11C23semidirect
124. C11⋊#95C23semidirect
125. C11⋊#95C23semidirect
126. C11⋊#95C23semidirect
135. C24×C11C22×C4semidirect
155. C23×D11C22×C4semidirect
162. C2×D4×C11C22×C4semidirect
175. C22×C4×C11C22×C4semidirect
179. C22×C4×C11C2×D4semidirect
188. C2×C22⋊D11C22×C4semidirect
199. C22×Dic11C22×C4semidirect
212. C2×C4×D11C2×D4semidirect
219. C22⋊Dic11C22×C4semidirect
222. (C2×D11)⋊C4C22×C4semidirect
228. C22×C4×D4D11semidirect
252. C23×C11C4×D4semidirect
255. C23×C11C23×C4semidirect
279. C22×D11C4×D4semidirect
297. C2×C4×C11#120semidirect
298. C2×C4×C11C23×C4semidirect
314. C2×Dic11C23×C4semidirect
328. C24×C4C2×D11semidirect
334. C2×C4×D4C2×D11semidirect
336. C22×C4⋊C4C2×D11semidirect
344. C22×C22⋊C4C2×D11semidirect
346. C22×C42C2×D11semidirect
370. C22×C11C2×C4×D4semidirect
387. C2×D11C2×C4×D4semidirect
392. C4×C11C2×#120semidirect
411. C22×D4C4×D11semidirect
433. C23×C4C22⋊D11semidirect
440. C23×C4C22×D11semidirect
447. C2×C4⋊C4C22×D11semidirect
463. C2×C22⋊C4C22×D11semidirect
467. C2×C42C22×D11semidirect
473. C2×C11C4×#120semidirect
505. C24C2×C4×D11semidirect
518. C2×D4C2×C4×D11semidirect
555. C22×C4C2×C4×D11semidirect
559. C22×C4C2×C22⋊D11semidirect
577. C11C2×C4×#120semidirect
613. C23C4×C22⋊D11semidirect
616. C23C22×C4×D11semidirect
654. C2×C4#66990direct (N × H)
655. C2×C4C22×C4×D11semidirect
682. C22C2×C4×C22⋊D11semidirect
697. C4C2×#66990direct (N × H)
701. C2C4×#66990direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C4×D112
C22×#669902
C22×C4×C22⋊D112
C4×#669902
C2×#106228332
C2×#106225692
C2×#106225592
C2×#106226022
C2×#106225682
C2×C4×(C2×D11)⋊C42
C2×C4×C22⋊Dic112
C22×C4×D4×C112
C2×C4×#12011