Finite Group Databasebeta

← C2×#13072204 #14921660

Subgroups — C2×#13072204 #14921660

Order 2816.

5062 conjugacy classes of subgroups.

The subgroup lattice has 752 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66927C211yesmaximal, characteristic, complemented
2C22×#66983C211yesmaximal, characteristic, complemented
3C22×#66983C211yesmaximal, characteristic, complemented
4C22×#66937C212yesmaximal, complemented
5C22×C4×D44C211yesmaximal, characteristic, complemented
6#13072204C2116yesmaximal, direct product factor
7C2×#10622285C212yesmaximal, complemented
8C2×#10622573C212yesmaximal, complemented
9C2×#10622552C211yesmaximal, characteristic, complemented
10C2×#10622541C211yesmaximal, characteristic, complemented
11C2×#10622278C212yesmaximal, complemented
12C2×C4×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C24×C4×C11C2211yescharacteristic
14C23×C22⋊D11C2212yes—
15C23×C22⋊D11C2212yes—
16C23×D44C2211yescharacteristic
17C23×D44C2212yes—
18C23×D44C2212yes—
19C23×D44C2211yescharacteristic
20C23×C4×D11C2212yes—
21C22×C11×C22⋊C4C2211yescharacteristic
22C22×C11×C22⋊C4C2211yescharacteristic
23C22×C42×C11C2211yescharacteristic
24C22×C42×C11C2211yescharacteristic
25C2×#66983—28no—
26C2×#66983—28no—
27C2×#66983C2218yescomplemented
28C2×#66983C2218yescomplemented
29C22×(C2×D11)⋊C4C2212yes—
30C22×(C2×D11)⋊C4C2212yes—
31C22×(C2×D11)⋊C4C2212yes—
32C22×(C2×D11)⋊C4C2212yes—
33C22×(C2×D11)⋊C4C2212yes—
34C22×C4⋊Dic11C2211yescharacteristic
35C22×C4⋊Dic11C2211yescharacteristic
36C22×Dic11⋊C4C2212yes—
37C2×#66937—216no—
38C2×#66937C22116yescomplemented
39C2×#66927—28no—
40C2×#66927C2218yescomplemented
41C2×C4×D44—28no—
42C2×C4×D44C2218yescomplemented
43C4×C11×C22⋊C4C2218yescomplemented
44C2×C11×#95C2211yescharacteristic
45C2×C11×#95C2211yescharacteristic
46C2×C11⋊#95C2212yes—
47#10622573C22116yescomplemented
48#10622552C2218yescomplemented
49#10622541C2218yescomplemented
50#10622285C22116yescomplemented
51#10622278C22116yescomplemented
52C25×C11C2311yescharacteristic
53C24×D11C2312yes—
54C24×D11C2312yes—
55C23×C4×C11—24no—
56C23×C4×C11—24no—
57C23×C4×C11—24no—
58C23×C4×C11C2311yescharacteristic
59C23×C4×C11C2311yescharacteristic
60C23×C4×C11C2314yes—
61C23×C4×C11C2311yescharacteristic
62C23×C4×C11C2311yescharacteristic
63C23×C4×C11C2311yescharacteristic
64C23×C4×C11C2311yescharacteristic
65C22×C22⋊D11—28no—
66C22×C22⋊D11—28no—
67C22×C22⋊D11—28no—
68C22×C22⋊D11—28no—
69C22×C22⋊D11—44no—
70C22×C22⋊D11—44no—
71C22×C22⋊D11C2318yes—
72C22×C22⋊D11C2318yes—
73C23×Dic11C2312yes—
74C23×Dic11C2312yes—
75C22×D44—24no—
76C22×D44—24no—
77C22×D44—28no—
78C22×D44—28no—
79C22×D44—24no—
80C22×D44—28no—
81C22×D44—24no—
82C22×D44—28no—
83C22×D44—24no—
84C22×D44—44no—
85C22×D44—44no—
86C22×D44D418yescomplemented
87C22×D44C2314yes—
88C22×D44C2318yes—
89C22×D44C2318yes—
90C22×D44C2314yes—
91C22×C4×D11—28no—
92C22×C4×D11—28no—
93C22×C4×D11—44no—
94C22×C4×D11C2318yes—
95C2×C11×C22⋊C4—24no—
96C2×C11×C22⋊C4D418yescomplemented
97C2×C11×C22⋊C4C2314yes—
98C2×C11×C22⋊C4C2314yes—
99C2×C42×C11—24no—
100C2×C42×C11—24no—
101C2×C42×C11C2314yes—
102C2×C42×C11C2314yes—
103#66983—232no—
104#66983—232no—
105C2×(C2×D11)⋊C4—28no—
106C2×(C2×D11)⋊C4—28no—
107C2×(C2×D11)⋊C4—28no—
108C2×(C2×D11)⋊C4—28no—
109C2×(C2×D11)⋊C4—44no—
110C2×(C2×D11)⋊C4C2318yes—
111C2×(C2×D11)⋊C4C2318yes—
112C2×(C2×D11)⋊C4C2318yes—
113C2×(C2×D11)⋊C4C2318yes—
114C2×(C2×D11)⋊C4C2318yes—
115C2×C4⋊Dic11—24no—
116C2×C4⋊Dic11D418yescomplemented
117C2×C4⋊Dic11C2314yes—
118C2×C4⋊Dic11C2314yes—
119C2×Dic11⋊C4—28no—
120C2×Dic11⋊C4C2318yes—
121#66937—264no—
122#66927—232no—
123C4×D44—232no—
124C11×#95C2314yes—
125C11×#95C2314yes—
126C11⋊#95C2318yes—
127C2×#2428—111nomaximal, Sylow
128C24×C11—22no—
129C24×C11—22no—
130C24×C11—22no—
131C24×C11—22no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11C2×D414yes—
135C24×C11C2412yes—
136C24×C11C2411yescharacteristic
137C23×D11—24no—
138C23×D11—24no—
139C23×D11—24no—
140C23×D11—24no—
141C23×D11—24no—
142C23×D11—24no—
143C23×D11—24no—
144C23×D11—24no—
145C23×D11—24no—
146C23×D11—24no—
147C23×D11—24no—
148C23×D11—24no—
149C23×D11—24no—
150C23×D11C2×D418yes—
151C23×D11C2414yes—
152C23×D11C2414yes—
153C22×C4×C11—22no—
154C22×C4×C11—22no—
155C22×C4×C11—22no—
156C22×C4×C11—22no—
157C22×C4×C11—22no—
158C22×C4×C11—22no—
159C22×C4×C11—22no—
160C22×C4×C11—22no—
161C22×C4×C11—22no—
162C22×C4×C11—22no—
163C22×C4×C11—22no—
164C22×C4×C11—22no—
165C22×C4×C11—28no—
166C22×C4×C11—28no—
167C22×C4×C11—28no—
168C22×C4×C11—416no—
169C22×C4×C11C2×D414yes—
170C22×C4×C11C2×D414yes—
171C22×C4×C11C2×D414yes—
172C22×C4×C11C2×D414yes—
173C22×C4×C11#4114yes—
174C22×C4×C11#4114yes—
175C22×C4×C11C2412yes—
176C22×C4×C11C2412yes—
177C22×C4×C11C2412yes—
178C22×C4×C11C2412yes—
179C22×C4×C11C2412yes—
180C22×C4×C11C2412yes—
181C2×C22⋊D11—216no—
182C2×C22⋊D11—216no—
183C2×C22⋊D11—216no—
184C2×C22⋊D11—216no—
185C2×C22⋊D11—48no—
186C2×C22⋊D11—48no—
187C2×C22⋊D11—432no—
188C2×C22⋊D11—432no—
189C22×Dic11—24no—
190C22×Dic11—24no—
191C22×Dic11—24no—
192C22×Dic11—24no—
193C22×Dic11—24no—
194C22×Dic11C2×D418yes—
195C22×Dic11C2414yes—
196C22×Dic11C2414yes—
197C2×D44—216no—
198C2×D44—216no—
199C2×D44—232no—
200C2×D44—28no—
201C2×D44—28no—
202C2×D44—216no—
203C2×D44—28no—
204C2×D44—28no—
205C2×D44—216no—
206C2×D44—28no—
207C2×D44—48no—
208C2×D44—48no—
209C2×D44—432no—
210C2×D44—432no—
211C2×D44—416no—
212C2×D44C2×D4116yescomplemented
213C2×C4×D11—216no—
214C2×C4×D11—216no—
215C2×C4×D11—48no—
216C2×C4×D11—432no—
217C11×C22⋊C4—28no—
218C11×C22⋊C4C2×D4116yescomplemented
219C42×C11—28no—
220C42×C11—28no—
221(C2×D11)⋊C4—216no—
222(C2×D11)⋊C4—216no—
223(C2×D11)⋊C4—216no—
224(C2×D11)⋊C4—216no—
225(C2×D11)⋊C4—48no—
226C4⋊Dic11—28no—
227C4⋊Dic11C2×D4116yescomplemented
228Dic11⋊C4—216no—
229C22×#127—111no—
230C22×#121—111no—
231C22×#121—111no—
232C22×#121—112no—
233C22×C4×D4—111no—
234#2428—1116no—
235C2×#394—112no—
236C2×#392—112no—
237C2×#390—111no—
238C2×#389—111no—
239C2×#386—112no—
240C2×C4×C22⋊C4D1111yescharacteristic, complemented
241C23×C11—28no—
242C23×C11—28no—
243C23×C11—28no—
244C23×C11—22no—
245C23×C11—22no—
246C23×C11—22no—
247C23×C11—22no—
248C23×C11—22no—
249C23×C11—22no—
250C23×C11—44no—
251C23×C11—44no—
252C23×C11—44no—
253C23×C11—44no—
254C23×C11C22×D414yes—
255C23×C11C22×D412yes—
256C23×C11C22×D412yes—
257C23×C11C22×D412yes—
258C23×C11C2×#4112yes—
259C23×C11C2×#4112yes—
260C23×C11H(5,𝔽2)12yes—
261C23×C11H(5,𝔽2)12yes—
262C23×C11C2511yescharacteristic
263C22×D11—216no—
264C22×D11—216no—
265C22×D11—216no—
266C22×D11—24no—
267C22×D11—24no—
268C22×D11—24no—
269C22×D11—24no—
270C22×D11—24no—
271C22×D11—24no—
272C22×D11—24no—
273C22×D11—24no—
274C22×D11—24no—
275C22×D11—24no—
276C22×D11—24no—
277C22×D11—24no—
278C22×D11—24no—
279C22×D11—48no—
280C22×D11—48no—
281C22×D11—48no—
282C22×D11—48no—
283C22×D11—48no—
284C22×D11—48no—
285C22×D11—48no—
286C22×D11—48no—
287C22×D11—48no—
288C22×D11—48no—
289C22×D11—48no—
290C22×D11C22×D418yes—
291C2×C4×C11—28no—
292C2×C4×C11—28no—
293C2×C4×C11—28no—
294C2×C4×C11—22no—
295C2×C4×C11—22no—
296C2×C4×C11—22no—
297C2×C4×C11—22no—
298C2×C4×C11—22no—
299C2×C4×C11—22no—
300C2×C4×C11—22no—
301C2×C4×C11—22no—
302C2×C4×C11—22no—
303C2×C4×C11—22no—
304C2×C4×C11—22no—
305C2×C4×C11—22no—
306C2×C4×C11—44no—
307C2×C4×C11—44no—
308C2×C4×C11—416no—
309C2×C4×C11#121116yescomplemented
310C2×C4×C11C22×D414yes—
311C2×C4×C11C22×D414yes—
312C2×C4×C11C22×D414yes—
313C2×C4×C11C22×D414yes—
314C2×C4×C11C2×#4114yes—
315C2×C4×C11C2×#4114yes—
316C22⋊D11—432no—
317C22⋊D11—432no—
318C2×Dic11—216no—
319C2×Dic11—24no—
320C2×Dic11—24no—
321C2×Dic11—24no—
322C2×Dic11—24no—
323C2×Dic11—24no—
324C2×Dic11—48no—
325C2×Dic11C22×D418yes—
326D44—232no—
327D44—432no—
328D44—432no—
329D44—416no—
330C4×D11—432no—
331C23×D4—112no—
332C23×D4—112no—
333C23×D4—111no—
334C23×D4—111no—
335C23×D4—112no—
336C23×D4—112no—
337C24×C4—112no—
338C24×C4C2×D1111yescharacteristic
339C2×#127—118no—
340C2×#127—228no—
341C2×#121—118no—
342C2×#121—118no—
343C2×#121—1116no—
344C2×#121—228no—
345C2×#121—228no—
346C2×#121—2216no—
347C2×C4×D4—118no—
348C2×C4×D4—228no—
349C22×C4⋊C4—111no—
350C22×C4⋊C4—112no—
351C22×C4⋊C4—111no—
352C22×C22⋊C4—112no—
353C22×C22⋊C4—112no—
354C22×C22⋊C4—112no—
355C22×C22⋊C4—112no—
356C22×C22⋊C4—112no—
357C22×C22⋊C4C2×D1111yescharacteristic
358C22×C22⋊C4C2×D1111yescharacteristic
359C22×C42C2×D1111yescharacteristic
360C22×C42C2×D1111yescharacteristic
361#394—1116no—
362#392—1116no—
363#390—118no—
364#389—118no—
365#386—1116no—
366C4×C22⋊C4C2×D1118yescomplemented
367C2×#95—112no—
368C2×#95C2×D1111yescharacteristic
369C2×#95C2×D1111yescharacteristic
370C22×C11—24no—
371C22×C11—24no—
372C22×C11—24no—
373C22×C11—42no—
374C22×C11—416no—
375C22×C11—42no—
376C22×C11—42no—
377C22×C11—42no—
378C22×C11C2×#12114yes—
379C22×C11#53214yes—
380C22×C11#54014yes—
381C22×C11D4214yes—
382C22×C11D4214yes—
383C22×C11#54614yes—
384C22×C11#55014yes—
385C22×C11C23×D411yescharacteristic
386C22×C11C23×D411yescharacteristic
387C22×C11C23×D411yescharacteristic
388C22×C11C22×#4111yescharacteristic
389C22×C11C22×#4111yescharacteristic
390C22×C11C2×H(5,𝔽2)11yescharacteristic
391C22×C11C2×H(5,𝔽2)11yescharacteristic
392C2×D11—28no—
393C2×D11—28no—
394C2×D11—28no—
395C2×D11—44no—
396C2×D11—432no—
397C2×D11—44no—
398C2×D11—44no—
399C2×D11—44no—
400C2×D11—44no—
401C2×D11—44no—
402C2×D11—44no—
403C2×D11—44no—
404C2×D11—44no—
405C2×D11—44no—
406C2×D11—44no—
407C2×D11—816no—
408C4×C11—24no—
409C4×C11—24no—
410C4×C11—24no—
411C4×C11—42no—
412C4×C11—42no—
413C4×C11C2×#12118yescomplemented
414Dic11—28no—
415Dic11—44no—
416C25—112no—
417C25—112no—
418C25C22×D1111yescharacteristic
419C22×D4—118no—
420C22×D4—118no—
421C22×D4—118no—
422C22×D4—114no—
423C22×D4—114no—
424C22×D4—118no—
425C22×D4—118no—
426C22×D4—228no—
427C22×D4—228no—
428C22×D4—228no—
429C22×D4—228no—
430C22×D4—228no—
431C22×D4—228no—
432C22×D4—228no—
433C22×D4—224no—
434C22×D4—228no—
435C22×D4—224no—
436C22×D4—224no—
437C22×D4—224no—
438C22×D4—224no—
439C22×D4—444no—
440C22×D4—444no—
441C22×D4—444no—
442C22×D4—444no—
443C23×C4—24no—
444C23×C4—24no—
445C23×C4—24no—
446C23×C4—112no—
447C23×C4—112no—
448C23×C4—118no—
449C23×C4—228no—
450C23×C4—228no—
451C23×C4—444no—
452C23×C4C22×D1114yes—
453C23×C4C22×D1111yescharacteristic
454C23×C4C22×D1111yescharacteristic
455C23×C4C22×D1111yescharacteristic
456C23×C4C22×D1111yescharacteristic
457C23×C4C22×D1111yescharacteristic
458C23×C4C22×D1111yescharacteristic
459#127—2232no—
460#121—2232no—
461#121—2232no—
462#121—2264no—
463C4×D4—2232no—
464C2×C4⋊C4—118no—
465C2×C4⋊C4—114no—
466C2×C4⋊C4—114no—
467C2×C4⋊C4—118no—
468C2×C4⋊C4—228no—
469C2×C4⋊C4—224no—
470C2×C22⋊C4—24no—
471C2×C22⋊C4—118no—
472C2×C22⋊C4—118no—
473C2×C22⋊C4—118no—
474C2×C22⋊C4—118no—
475C2×C22⋊C4—118no—
476C2×C22⋊C4—228no—
477C2×C22⋊C4—228no—
478C2×C22⋊C4—228no—
479C2×C22⋊C4—228no—
480C2×C22⋊C4—444no—
481C2×C22⋊C4D4418yescomplemented
482C2×C22⋊C4C22×D1114yes—
483C2×C22⋊C4C22×D1114yes—
484C2×C42—24no—
485C2×C42—24no—
486C2×C42C22×D1114yes—
487C2×C42C22×D1114yes—
488#95—118no—
489#95C22×D1114yes—
490#95C22×D1114yes—
491C2×C11—44no—
492C2×C11#242818yescomplemented
493C2×C11C22×#12111yescharacteristic
494C2×C11C2×#53211yescharacteristic
495C2×C11C2×#54011yescharacteristic
496C2×C11C2×D4211yescharacteristic
497C2×C11C2×D4211yescharacteristic
498C2×C11C2×#54611yescharacteristic
499C2×C11C2×#55011yescharacteristic
500D11—48no—
501D11—84no—
502C24—22no—
503C24—22no—
504C24—22no—
505C24—22no—
506C24—22no—
507C24—22no—
508C24—118no—
509C24—114no—
510C24—114no—
511C24—224no—
512C24—224no—
513C24—224no—
514C24—224no—
515C24—224no—
516C24—224no—
517C24—224no—
518C24—224no—
519C24—224no—
520C24—224no—
521C24—224no—
522C24—224no—
523C24—224no—
524C24C2×D4414yes—
525C24C23×D1112yes—
526C24C23×D1111yescharacteristic
527C2×D4—1116no—
528C2×D4—2216no—
529C2×D4—2216no—
530C2×D4—2216no—
531C2×D4—2216no—
532C2×D4—2216no—
533C2×D4—2216no—
534C2×D4—2232no—
535C2×D4—2216no—
536C2×D4—228no—
537C2×D4—2216no—
538C2×D4—228no—
539C2×D4—228no—
540C2×D4—228no—
541C2×D4—228no—
542C2×D4—448no—
543C2×D4—448no—
544C2×D4—4432no—
545C2×D4—4432no—
546C2×D4—448no—
547C2×D4—448no—
548C2×D4—4432no—
549C2×D4—4432no—
550C2×D4—4416no—
551C22×C4—22no—
552C22×C4—22no—
553C22×C4—22no—
554C22×C4—22no—
555C22×C4—22no—
556C22×C4—22no—
557C22×C4—22no—
558C22×C4—22no—
559C22×C4—22no—
560C22×C4—22no—
561C22×C4—22no—
562C22×C4—22no—
563C22×C4—28no—
564C22×C4—28no—
565C22×C4—28no—
566C22×C4—416no—
567C22×C4—118no—
568C22×C4—114no—
569C22×C4—114no—
570C22×C4—2216no—
571C22×C4—224no—
572C22×C4—224no—
573C22×C4—224no—
574C22×C4—224no—
575C22×C4—224no—
576C22×C4—2216no—
577C22×C4—448no—
578C22×C4—4432no—
579C22×C4C2×D4414yes—
580C22×C4C2×D4414yes—
581C22×C4#433914yes—
582C22×C4#433914yes—
583C22×C4D4×D1114yes—
584C22×C4D4×D1114yes—
585C22×C4C23×D1112yes—
586C22×C4C23×D1112yes—
587C22×C4C23×D1112yes—
588C22×C4C23×D1112yes—
589C22×C4C23×D1112yes—
590C22×C4C23×D1112yes—
591C4⋊C4—1116no—
592C4⋊C4—2216no—
593C4⋊C4—228no—
594C22⋊C4—28no—
595C22⋊C4—2216no—
596C22⋊C4—2216no—
597C22⋊C4—2216no—
598C22⋊C4—2216no—
599C22⋊C4—448no—
600C22⋊C4C2×D44116yescomplemented
601C42—28no—
602C42—28no—
603C11C2×#242811yescharacteristic, complemented, Sylow
604C23—28no—
605C23—28no—
606C23—28no—
607C23—22no—
608C23—22no—
609C23—22no—
610C23—22no—
611C23—22no—
612C23—22no—
613C23—44no—
614C23—44no—
615C23—44no—
616C23—44no—
617C23—118no—
618C23—2216no—
619C23—2216no—
620C23—2216no—
621C23—224no—
622C23—224no—
623C23—224no—
624C23—224no—
625C23—224no—
626C23—224no—
627C23—224no—
628C23—224no—
629C23—224no—
630C23—224no—
631C23—224no—
632C23—224no—
633C23—224no—
634C23—448no—
635C23—448no—
636C23—448no—
637C23—448no—
638C23—448no—
639C23—448no—
640C23—448no—
641C23—448no—
642C23—448no—
643C23—448no—
644C23—448no—
645C23C22×D4414yes—
646C23C22×D4412yes—
647C23C2×#433912yes—
648C23C2×#433912yes—
649C23C2×D4×D1112yes—
650C23C2×D4×D1112yes—
651C23#6704212yes—
652C23#6704212yes—
653C23C24×D1111yescharacteristic
654D4—2232no—
655D4—4432no—
656D4—4432no—
657D4—4432no—
658D4—4432no—
659D4—4416no—
660C2×C4—28no—
661C2×C4—28no—
662C2×C4—28no—
663C2×C4—22no—
664C2×C4—22no—
665C2×C4—22no—
666C2×C4—22no—
667C2×C4—22no—
668C2×C4—22no—
669C2×C4—22no—
670C2×C4—22no—
671C2×C4—22no—
672C2×C4—22no—
673C2×C4—22no—
674C2×C4—22no—
675C2×C4—44no—
676C2×C4—44no—
677C2×C4—416no—
678C2×C4—118no—
679C2×C4—2216no—
680C2×C4—224no—
681C2×C4—224no—
682C2×C4—224no—
683C2×C4—224no—
684C2×C4—224no—
685C2×C4—4432no—
686C2×C4—448no—
687C2×C4#66937116yescomplemented
688C2×C4C22×D4414yes—
689C2×C4C22×D4414yes—
690C2×C4C2×#433914yes—
691C2×C4C2×#433914yes—
692C2×C4C2×D4×D1114yes—
693C2×C4C2×D4×D1114yes—
694C22—24no—
695C22—24no—
696C22—24no—
697C22—416no—
698C22—42no—
699C22—42no—
700C22—42no—
701C22—42no—
702C22—228no—
703C22—228no—
704C22—228no—
705C22—444no—
706C22—4432no—
707C22—444no—
708C22—444no—
709C22—444no—
710C22—444no—
711C22—444no—
712C22—444no—
713C22—444no—
714C22—444no—
715C22—444no—
716C22—444no—
717C22—8816no—
718C22#1062300814yes—
719C22C2×#6693714yes—
720C22#1062306614yes—
721C22D4×D4414yes—
722C22D4×D4414yes—
723C22#1062308114yes—
724C22#1062308414yes—
725C22C23×D4411yescharacteristic
726C22C22×#433911yescharacteristic
727C22C22×#433911yescharacteristic
728C22C22×D4×D1111yescharacteristic
729C22C22×D4×D1111yescharacteristic
730C22C2×#6704211yescharacteristic
731C22C2×#6704211yescharacteristic
732C4—24no—
733C4—24no—
734C4—24no—
735C4—42no—
736C4—42no—
737C4—228no—
738C4—444no—
739C4C2×#6693718yescomplemented
740C2—44no—
741C2—448no—
742C2—884no—
743C2#1307220418yesdirect product factor
744C2C22×#6693711yescharacteristic
745C2C2×#1062300811yescharacteristic
746C2C2×#1062306611yescharacteristic
747C2C2×D4×D4411yescharacteristic
748C2C2×D4×D4411yescharacteristic
749C2C2×#1062308111yescharacteristic
750C2C2×#1062308411yescharacteristic
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC2×C4×C11×C22⋊C4C2
socleC24×C11C24
hypercenterC2×C4×C22⋊C4D11
hypocenterC11C2×#2428
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C2×C4×C22⋊C4

Complements

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

NH ≅ G/Ntype
1. C22×#66927C2semidirect
2. C22×#66983C2semidirect
3. C22×#66983C2semidirect
4. C22×#66937C2semidirect
5. C22×C4×D44C2semidirect
6. #13072204C2direct (N × H)
7. C2×#10622285C2semidirect
8. C2×#10622573C2semidirect
9. C2×#10622552C2semidirect
10. C2×#10622541C2semidirect
11. C2×#10622278C2semidirect
12. C2×C4×C11×C22⋊C4C2semidirect
27. C2×#66983C22semidirect
28. C2×#66983C22semidirect
38. C2×#66937C22semidirect
40. C2×#66927C22semidirect
42. C2×C4×D44C22semidirect
43. C4×C11×C22⋊C4C22semidirect
47. #10622573C22semidirect
48. #10622552C22semidirect
49. #10622541C22semidirect
50. #10622285C22semidirect
51. #10622278C22semidirect
86. C22×D44D4semidirect
96. C2×C11×C22⋊C4D4semidirect
116. C2×C4⋊Dic11D4semidirect
212. C2×D44C2×D4semidirect
218. C11×C22⋊C4C2×D4semidirect
227. C4⋊Dic11C2×D4semidirect
240. C2×C4×C22⋊C4D11semidirect
309. C2×C4×C11#121semidirect
366. C4×C22⋊C4C2×D11semidirect
413. C4×C11C2×#121semidirect
481. C2×C22⋊C4D44semidirect
492. C2×C11#2428semidirect
600. C22⋊C4C2×D44semidirect
603. C11C2×#2428semidirect
687. C2×C4#66937semidirect
739. C4C2×#66937semidirect
743. C2#13072204direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669272
C22×#669832
C22×#669372
C22×C4×D442
#130722042
C2×#106222852
C2×#106225732
C2×#106225522
C2×#106225412
C2×#106222782
C2×C4×C11×C22⋊C42
C2×#242811