Finite Group Databasebeta

← C2×C22⋊C4×C22⋊D11 #14912944

Subgroups — C2×C22⋊C4×C22⋊D11 #14912944

Order 2816.

8774 conjugacy classes of subgroups.

The subgroup lattice has 792 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C24×C22⋊D11C211yesmaximal, characteristic
2C22×C4×C22⋊D11C212yesmaximal, complemented
3C22×C22⋊C4×D11C211yesmaximal, characteristic, complemented
4C22⋊C4×C22⋊D11C2116yesmaximal, direct product factor
5C2×#10622570C212yesmaximal, complemented
6C2×#10622826C212yesmaximal, complemented
7C2×#10622569C212yesmaximal, complemented
8C2×#10622555C211yesmaximal, characteristic, complemented
9C2×#10622860C211yesmaximal, characteristic, complemented
10C2×#10622568C211yesmaximal, characteristic, complemented
11C2×C22⋊C4×Dic11C211yesmaximal, characteristic, complemented
12C23×C11×C22⋊C4C211yesmaximal, characteristic, complemented
13C26×C11C2211yescharacteristic
14C25×D11C2211yescharacteristic
15C24×C4×C11C2212yescomplemented
16C23×C22⋊D11—216no—
17C23×C22⋊D11C4116yescomplemented
18C23×C22⋊D11C2218yes—
19C23×C22⋊D11C2211yescharacteristic
20C23×C22⋊D11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic
23C24×Dic11C2211yescharacteristic
24C23×C4×D11C2212yescomplemented
25C22×C11×C22⋊C4—28no—
26C22×C11×C22⋊C4C2211yescharacteristic
27C22×C11×C22⋊C4C2211yescharacteristic
28C22×C11×C22⋊C4C2218yescomplemented
29C22×C11×C22⋊C4C2212yescomplemented
30C22×C22⋊Dic11C2211yescharacteristic
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2212yescomplemented
33C22×C22⋊Dic11C2212yescomplemented
34C2×C4×C22⋊D11—216no—
35C2×C4×C22⋊D11C22116yescomplemented
36C22×(C2×D11)⋊C4C2212yescomplemented
37C22×(C2×D11)⋊C4C2212yescomplemented
38C22×(C2×D11)⋊C4C2212yescomplemented
39C22×Dic11⋊C4C2212yescomplemented
40C22×C4×Dic11C2212yescomplemented
41C2×C22⋊C4×D11—28no—
42C2×C22⋊C4×D11C2218yescomplemented
43#10622860C2218yescomplemented
44#10622826C22116yescomplemented
45C2×C11⋊#95C2212yescomplemented
46C2×C11⋊#95C2212yescomplemented
47#10622570C22116yescomplemented
48#10622569C22116yescomplemented
49#10622568C2218yescomplemented
50#10622555C2218yescomplemented
51C22⋊C4×Dic11C2218yescomplemented
52C25×C11—24no—
53C25×C11—28no—
54C25×C11—24no—
55C25×C11—44no—
56C25×C11C2×C418yescomplemented
57C25×C11C2311yescharacteristic
58C25×C11C2314yes—
59C25×C11C2311yescharacteristic
60C25×C11C2311yescharacteristic
61C24×D11—24no—
62C24×D11—24no—
63C24×D11—28no—
64C24×D11—44no—
65C24×D11C2×C418yescomplemented
66C24×D11C2311yescharacteristic
67C24×D11C2314yes—
68C24×D11C2311yescharacteristic
69C23×C4×C11—28no—
70C23×C4×C11—28no—
71C23×C4×C11—44no—
72C23×C4×C11C2312yes—
73C23×C4×C11C2312yes—
74C23×C4×C11C2318yescomplemented
75C22×C22⋊D11—28no—
76C22×C22⋊D11—28no—
77C22×C22⋊D11—2128no—
78C22×C22⋊D11—264no—
79C22×C22⋊D11—28no—
80C22×C22⋊D11C2×C418yes—
81C22×C22⋊D11C2×C418yescomplemented
82C22×C22⋊D11C2×C418yescomplemented
83C22×C22⋊D11C2×C418yescomplemented
84C22×C22⋊D11C2×C4164yescomplemented
85C22×C22⋊D11D4116yes—
86C22×C22⋊D11C2314yes—
87C22×C22⋊D11C2314yes—
88C22×C22⋊D11C2314yes—
89C22×C22⋊D11C2314yes—
90C23×Dic11—28no—
91C23×Dic11C2×C418yescomplemented
92C23×Dic11C2312yes—
93C23×Dic11C2312yes—
94C23×Dic11C2311yescharacteristic
95C23×Dic11C2314yes—
96C23×Dic11C2311yescharacteristic
97C22×C4×D11—28no—
98C22×C4×D11—28no—
99C22×C4×D11—44no—
100C22×C4×D11C2318yescomplemented
101C2×C11×C22⋊C4—24no—
102C2×C11×C22⋊C4—28no—
103C2×C11×C22⋊C4—232no—
104C2×C11×C22⋊C4D418yescomplemented
105C2×C11×C22⋊C4C2314yes—
106C2×C11×C22⋊C4C2314yes—
107C2×C11×C22⋊C4C2318yescomplemented
108C2×C22⋊Dic11—24no—
109C2×C22⋊Dic11—28no—
110C2×C22⋊Dic11—24no—
111C2×C22⋊Dic11—44no—
112C2×C22⋊Dic11C2314yes—
113C2×C22⋊Dic11C2314yes—
114C2×C22⋊Dic11C2318yescomplemented
115C2×C22⋊Dic11C2318yescomplemented
116C4×C22⋊D11—264no—
117C2×(C2×D11)⋊C4—28no—
118C2×(C2×D11)⋊C4—28no—
119C2×(C2×D11)⋊C4—44no—
120C2×(C2×D11)⋊C4C2318yescomplemented
121C2×(C2×D11)⋊C4C2318yescomplemented
122C2×(C2×D11)⋊C4C2318yescomplemented
123C2×Dic11⋊C4—28no—
124C2×Dic11⋊C4C2318yescomplemented
125C2×C4×Dic11—28no—
126C2×C4×Dic11C2318yescomplemented
127C22⋊C4×D11—232no—
128C11⋊#95C2318yescomplemented
129C11⋊#95C2318yescomplemented
130C2×D4×C22⋊C4—111nomaximal, Sylow
131C24×C11—24no—
132C24×C11—22no—
133C24×C11—22no—
134C24×C11—24no—
135C24×C11—24no—
136C24×C11—232no—
137C24×C11—232no—
138C24×C11—28no—
139C24×C11—22no—
140C24×C11—216no—
141C24×C11—24no—
142C24×C11—28no—
143C24×C11—22no—
144C24×C11—24no—
145C24×C11—416no—
146C24×C11—48no—
147C24×C11—432no—
148C24×C11—432no—
149C24×C11C22×C414yes—
150C24×C11C22×C414yes—
151C24×C11C22×C414yes—
152C24×C11C22×C4116yescomplemented
153C24×C11C2×D418yes—
154C24×C11C2×D414yes—
155C24×C11#4114yes—
156C24×C11C2412yes—
157C24×C11C2412yes—
158C24×C11C2412yes—
159C24×C11C2411yescharacteristic
160C23×D11—22no—
161C23×D11—22no—
162C23×D11—24no—
163C23×D11—232no—
164C23×D11—28no—
165C23×D11—22no—
166C23×D11—24no—
167C23×D11—28no—
168C23×D11—22no—
169C23×D11—24no—
170C23×D11—232no—
171C23×D11—216no—
172C23×D11—416no—
173C23×D11—48no—
174C23×D11—432no—
175C23×D11—432no—
176C23×D11C22×C414yes—
177C23×D11C22×C414yes—
178C23×D11C22×C4116yescomplemented
179C23×D11C2×D418yes—
180C23×D11C2412yes—
181C23×D11C2412yes—
182C22×C4×C11—24no—
183C22×C4×C11—24no—
184C22×C4×C11—24no—
185C22×C4×C11—216no—
186C22×C4×C11—24no—
187C22×C4×C11—24no—
188C22×C4×C11—216no—
189C22×C4×C11—48no—
190C22×C4×C11—432no—
191C22×C4×C11C2×D418yescomplemented
192C22×C4×C11C2414yes—
193C22×C4×C11C2414yes—
194C2×C22⋊D11—2256no—
195C2×C22⋊D11—232no—
196C2×C22⋊D11—216no—
197C2×C22⋊D11—232no—
198C2×C22⋊D11—216no—
199C2×C22⋊D11—232no—
200C2×C22⋊D11—216no—
201C2×C22⋊D11C22⋊C4164yesdirect product factor
202C2×C22⋊D11C22×C4116yes—
203C2×C22⋊D11C22×C4116yescomplemented
204C2×C22⋊D11C22×C4116yescomplemented
205C2×C22⋊D11C22×C4116yescomplemented
206C2×C22⋊D11C2×D4132yes—
207C22×Dic11—232no—
208C22×Dic11—216no—
209C22×Dic11—24no—
210C22×Dic11—24no—
211C22×Dic11—24no—
212C22×Dic11—24no—
213C22×Dic11—24no—
214C22×Dic11—24no—
215C22×Dic11—24no—
216C22×Dic11C22×C414yes—
217C22×Dic11C22×C414yes—
218C22×Dic11C22×C4116yescomplemented
219C22×Dic11C2×D418yes—
220C22×Dic11C2414yes—
221C22×Dic11C2414yes—
222C22×Dic11C2412yes—
223C22×Dic11C2412yes—
224C2×C4×D11—216no—
225C2×C4×D11—216no—
226C2×C4×D11—48no—
227C2×C4×D11—432no—
228C11×C22⋊C4—28no—
229C11×C22⋊C4—216no—
230C11×C22⋊C4C2×D4116yescomplemented
231C22⋊Dic11—28no—
232C22⋊Dic11—216no—
233C22⋊Dic11—28no—
234C22⋊Dic11—48no—
235(C2×D11)⋊C4—216no—
236(C2×D11)⋊C4—216no—
237(C2×D11)⋊C4—48no—
238Dic11⋊C4—216no—
239C4×Dic11—216no—
240C24×D4—111no—
241C22×C4×D4—112no—
242C23×C22⋊C4—111no—
243C23×C22⋊C4D1111yescharacteristic, complemented
244D4×C22⋊C4—1116no—
245C2×#390—112no—
246C2×#386—112no—
247C2×#386—112no—
248C2×#380—111no—
249C2×#379—111no—
250C2×#379—111no—
251C2×C4×C22⋊C4—111no—
252C23×C11—28no—
253C23×C11—28no—
254C23×C11—28no—
255C23×C11—28no—
256C23×C11—216no—
257C23×C11—216no—
258C23×C11—216no—
259C23×C11—216no—
260C23×C11—24no—
261C23×C11—22no—
262C23×C11—22no—
263C23×C11—24no—
264C23×C11—24no—
265C23×C11—28no—
266C23×C11—232no—
267C23×C11—28no—
268C23×C11—232no—
269C23×C11—28no—
270C23×C11—22no—
271C23×C11—24no—
272C23×C11—22no—
273C23×C11—24no—
274C23×C11—416no—
275C23×C11—4128no—
276C23×C11—432no—
277C23×C11—432no—
278C23×C11—48no—
279C23×C11—48no—
280C23×C11C2×C22⋊C4116yescomplemented
281C23×C11C4×D4116yescomplemented
282C23×C11C23×C414yes—
283C23×C11C23×C414yes—
284C23×C11C23×C414yes—
285C23×C11C23×C412yes—
286C23×C11C22×D418yes—
287C23×C11C22×D414yes—
288C23×C11C22×D414yes—
289C23×C11C22×D412yes—
290C23×C11C2×#4114yes—
291C23×C11C2×#4112yes—
292C23×C11H(5,𝔽2)14yes—
293C23×C11C2511yescharacteristic
294C22×D11—28no—
295C22×D11—28no—
296C22×D11—216no—
297C22×D11—216no—
298C22×D11—22no—
299C22×D11—22no—
300C22×D11—24no—
301C22×D11—28no—
302C22×D11—28no—
303C22×D11—232no—
304C22×D11—28no—
305C22×D11—22no—
306C22×D11—24no—
307C22×D11—22no—
308C22×D11—24no—
309C22×D11—232no—
310C22×D11—416no—
311C22×D11—4128no—
312C22×D11—432no—
313C22×D11—432no—
314C22×D11—48no—
315C22×D11—48no—
316C22×D11C2×C22⋊C4116yescomplemented
317C22×D11C23×C414yes—
318C22×D11C23×C414yes—
319C22×D11C22×D418yes—
320C2×C4×C11—216no—
321C2×C4×C11—24no—
322C2×C4×C11—24no—
323C2×C4×C11—24no—
324C2×C4×C11—24no—
325C2×C4×C11—24no—
326C2×C4×C11—432no—
327C2×C4×C11—48no—
328C2×C4×C11C22×D418yescomplemented
329C22⋊D11—232no—
330C22⋊D11—232no—
331C22⋊D11—232no—
332C22⋊D11C2×C22⋊C4164yesdirect product factor
333C2×Dic11—28no—
334C2×Dic11—24no—
335C2×Dic11—232no—
336C2×Dic11—24no—
337C2×Dic11—24no—
338C2×Dic11—24no—
339C2×Dic11—24no—
340C2×Dic11—24no—
341C2×Dic11—24no—
342C2×Dic11—48no—
343C2×Dic11—48no—
344C2×Dic11C2×C22⋊C4116yescomplemented
345C2×Dic11C23×C414yes—
346C2×Dic11C23×C414yes—
347C2×Dic11C22×D418yes—
348C4×D11—432no—
349C26—111no—
350C26C2×D1111yescharacteristic
351C23×D4—111no—
352C23×D4—118no—
353C23×D4—111no—
354C23×D4—111no—
355C23×D4—111no—
356C23×D4—1116no—
357C23×D4—2216no—
358C24×C4—111no—
359C24×C4—112no—
360C24×C4C2×D1112yescomplemented
361C2×C4×D4—1116no—
362C2×C4×D4—2216no—
363C22×C4⋊C4—112no—
364C22×C22⋊C4—28no—
365C22×C22⋊C4—111no—
366C22×C22⋊C4—112no—
367C22×C22⋊C4—111no—
368C22×C22⋊C4—112no—
369C22×C22⋊C4—112no—
370C22×C22⋊C4—112no—
371C22×C22⋊C4—112no—
372C22×C22⋊C4—118no—
373C22×C22⋊C4—228no—
374C22×C22⋊C4C2×D1111yescharacteristic
375C22×C22⋊C4C2×D1111yescharacteristic
376C22×C22⋊C4C2×D1118yescomplemented
377C22×C22⋊C4C2×D1112yescomplemented
378C22×C42—112no—
379#390—1116no—
380#386—1116no—
381#386—1116no—
382#380—118no—
383#379—118no—
384#379—118no—
385C4×C22⋊C4—118no—
386C2×#95—112no—
387C2×#95—112no—
388C22×C11—232no—
389C22×C11—232no—
390C22×C11—24no—
391C22×C11—24no—
392C22×C11—24no—
393C22×C11—24no—
394C22×C11—28no—
395C22×C11—28no—
396C22×C11—28no—
397C22×C11—28no—
398C22×C11—24no—
399C22×C11—24no—
400C22×C11—24no—
401C22×C11—464no—
402C22×C11—416no—
403C22×C11—44no—
404C22×C11—44no—
405C22×C11C22×C22⋊C414yes—
406C22×C11C22×C22⋊C418yescomplemented
407C22×C11C2×C4×D414yes—
408C22×C11C2×C4×D418yescomplemented
409C22×C11#51814yes—
410C22×C11D4218yes—
411C22×C11#54618yes—
412C22×C11C24×C411yescharacteristic
413C22×C11C23×D412yes—
414C22×C11C23×D411yescharacteristic
415C22×C11C22×#4111yescharacteristic
416C22×C11C2×H(5,𝔽2)12yes—
417C2×D11—232no—
418C2×D11—24no—
419C2×D11—24no—
420C2×D11—28no—
421C2×D11—28no—
422C2×D11—24no—
423C2×D11—24no—
424C2×D11—24no—
425C2×D11—464no—
426C2×D11—416no—
427C2×D11—44no—
428C2×D11—44no—
429C2×D11C22×C22⋊C418yescomplemented
430C4×C11—28no—
431C4×C11—44no—
432Dic11—24no—
433Dic11—44no—
434Dic11—44no—
435Dic11C22×C22⋊C418yescomplemented
436C25—24no—
437C25—28no—
438C25—24no—
439C25—44no—
440C25—111no—
441C25—111no—
442C25—118no—
443C25—114no—
444C25—228no—
445C25—224no—
446C25—224no—
447C25—444no—
448C25C4×D1118yescomplemented
449C25C22×D1111yescharacteristic
450C25C22×D1114yes—
451C25C22×D1111yescharacteristic
452C25C22×D1111yescharacteristic
453C22×D4—118no—
454C22×D4—1116no—
455C22×D4—114no—
456C22×D4—118no—
457C22×D4—118no—
458C22×D4—118no—
459C22×D4—1164no—
460C22×D4—114no—
461C22×D4—114no—
462C22×D4—114no—
463C22×D4—228no—
464C22×D4—22128no—
465C22×D4—2264no—
466C22×D4—228no—
467C22×D4—228no—
468C23×C4—28no—
469C23×C4—28no—
470C23×C4—44no—
471C23×C4—111no—
472C23×C4—118no—
473C23×C4—114no—
474C23×C4—111no—
475C23×C4—112no—
476C23×C4—112no—
477C23×C4—118no—
478C23×C4—228no—
479C23×C4—228no—
480C23×C4—228no—
481C23×C4—444no—
482C23×C4C22×D1112yes—
483C23×C4C22×D1112yes—
484C23×C4C22×D1118yescomplemented
485C4×D4—2264no—
486C2×C4⋊C4—118no—
487C2×C4⋊C4—228no—
488C2×C22⋊C4—24no—
489C2×C22⋊C4—28no—
490C2×C22⋊C4—232no—
491C2×C22⋊C4—114no—
492C2×C22⋊C4—118no—
493C2×C22⋊C4—114no—
494C2×C22⋊C4—118no—
495C2×C22⋊C4—118no—
496C2×C22⋊C4—118no—
497C2×C22⋊C4—118no—
498C2×C22⋊C4—228no—
499C2×C22⋊C4—224no—
500C2×C22⋊C4—228no—
501C2×C22⋊C4—224no—
502C2×C22⋊C4—228no—
503C2×C22⋊C4—2232no—
504C2×C22⋊C4—444no—
505C2×C22⋊C4—444no—
506C2×C22⋊C4C22⋊D1118yesdirect product factor
507C2×C22⋊C4C22×D1114yes—
508C2×C22⋊C4C22×D1114yes—
509C2×C22⋊C4C22×D1118yescomplemented
510C2×C42—118no—
511C2×C42—228no—
512#95—118no—
513#95—118no—
514C2×C11—28no—
515C2×C11—28no—
516C2×C11—44no—
517C2×C11D4×C22⋊C418yescomplemented
518C2×C11C23×C22⋊C411yescharacteristic
519C2×C11C22×C4×D411yescharacteristic
520C2×C11C2×#51811yescharacteristic
521C2×C11C2×D4212yes—
522C2×C11C2×#54612yes—
523D11—28no—
524D11—44no—
525C24—22no—
526C24—24no—
527C24—24no—
528C24—24no—
529C24—22no—
530C24—232no—
531C24—232no—
532C24—28no—
533C24—22no—
534C24—216no—
535C24—24no—
536C24—24no—
537C24—28no—
538C24—22no—
539C24—48no—
540C24—416no—
541C24—432no—
542C24—432no—
543C24—114no—
544C24—118no—
545C24—112no—
546C24—114no—
547C24—112no—
548C24—1116no—
549C24—2232no—
550C24—2216no—
551C24—222no—
552C24—224no—
553C24—222no—
554C24—2232no—
555C24—228no—
556C24—222no—
557C24—224no—
558C24—224no—
559C24—228no—
560C24—222no—
561C24—4416no—
562C24—448no—
563C24—4432no—
564C24—4432no—
565C24C2×C4×D1114yes—
566C24C2×C4×D1114yes—
567C24C2×C4×D1114yes—
568C24C2×C4×D11116yescomplemented
569C24#433914yes—
570C24D4×D1118yes—
571C24C2×C22⋊D1114yes—
572C24C23×D1112yes—
573C24C23×D1112yes—
574C24C23×D1112yes—
575C24C23×D1111yescharacteristic
576C2×D4—1164no—
577C2×D4—1116no—
578C2×D4—1132no—
579C2×D4—1116no—
580C2×D4—1116no—
581C2×D4—1116no—
582C2×D4—2232no—
583C2×D4—2216no—
584C2×D4—22256no—
585C2×D4—2232no—
586C2×D4—2216no—
587C2×D4—2232no—
588C2×D4—2216no—
589C22×C4—24no—
590C22×C4—24no—
591C22×C4—24no—
592C22×C4—216no—
593C22×C4—24no—
594C22×C4—24no—
595C22×C4—216no—
596C22×C4—48no—
597C22×C4—432no—
598C22×C4—114no—
599C22×C4—118no—
600C22×C4—112no—
601C22×C4—114no—
602C22×C4—1116no—
603C22×C4—112no—
604C22×C4—114no—
605C22×C4—114no—
606C22×C4—2216no—
607C22×C4—2232no—
608C22×C4—2216no—
609C22×C4—224no—
610C22×C4—224no—
611C22×C4—224no—
612C22×C4—224no—
613C22×C4—224no—
614C22×C4—224no—
615C22×C4—224no—
616C22×C4—2216no—
617C22×C4—448no—
618C22×C4—4432no—
619C22×C4C2×C22⋊D1118yescomplemented
620C22×C4C23×D1114yes—
621C22×C4C23×D1114yes—
622C4⋊C4—2216no—
623C22⋊C4—28no—
624C22⋊C4—216no—
625C22⋊C4—2216no—
626C22⋊C4—228no—
627C22⋊C4—2216no—
628C22⋊C4—228no—
629C22⋊C4—2216no—
630C22⋊C4—448no—
631C22⋊C4—448no—
632C22⋊C4C2×C22⋊D11116yesdirect product factor
633C42—2216no—
634C11C2×D4×C22⋊C411yescharacteristic, complemented, Sylow
635C23—28no—
636C23—28no—
637C23—28no—
638C23—216no—
639C23—216no—
640C23—28no—
641C23—216no—
642C23—216no—
643C23—22no—
644C23—24no—
645C23—24no—
646C23—24no—
647C23—22no—
648C23—28no—
649C23—232no—
650C23—28no—
651C23—28no—
652C23—232no—
653C23—22no—
654C23—24no—
655C23—24no—
656C23—22no—
657C23—416no—
658C23—4128no—
659C23—432no—
660C23—432no—
661C23—48no—
662C23—48no—
663C23—1116no—
664C23—114no—
665C23—118no—
666C23—114no—
667C23—2232no—
668C23—228no—
669C23—2216no—
670C23—228no—
671C23—2216no—
672C23—222no—
673C23—224no—
674C23—222no—
675C23—228no—
676C23—228no—
677C23—228no—
678C23—2232no—
679C23—222no—
680C23—224no—
681C23—224no—
682C23—222no—
683C23—4416no—
684C23—44128no—
685C23—4432no—
686C23—4432no—
687C23—448no—
688C23—448no—
689C23C22⋊C4×D11116yescomplemented
690C23C4×C22⋊D11116yescomplemented
691C23C22×C4×D1114yes—
692C23C22×C4×D1114yes—
693C23C22×C4×D1114yes—
694C23C22×C4×D1112yes—
695C23C2×#433914yes—
696C23C2×#433912yes—
697C23C2×D4×D1118yes—
698C23C2×D4×D1114yes—
699C23#6703714yes—
700C23C22×C22⋊D1114yes—
701C23C22×C22⋊D1112yes—
702C23C24×D1111yescharacteristic
703D4—1164no—
704D4—2232no—
705D4—2232no—
706D4—2232no—
707C2×C4—216no—
708C2×C4—24no—
709C2×C4—24no—
710C2×C4—24no—
711C2×C4—24no—
712C2×C4—24no—
713C2×C4—432no—
714C2×C4—48no—
715C2×C4—1116no—
716C2×C4—114no—
717C2×C4—118no—
718C2×C4—114no—
719C2×C4—2232no—
720C2×C4—228no—
721C2×C4—224no—
722C2×C4—224no—
723C2×C4—224no—
724C2×C4—224no—
725C2×C4—224no—
726C2×C4—224no—
727C2×C4—224no—
728C2×C4—4432no—
729C2×C4—448no—
730C2×C4—448no—
731C2×C4C22×C22⋊D1118yescomplemented
732C22—232no—
733C22—232no—
734C22—24no—
735C22—24no—
736C22—28no—
737C22—28no—
738C22—24no—
739C22—24no—
740C22—28no—
741C22—28no—
742C22—24no—
743C22—24no—
744C22—24no—
745C22—464no—
746C22—416no—
747C22—44no—
748C22—44no—
749C22—118no—
750C22—2232no—
751C22—224no—
752C22—228no—
753C22—224no—
754C22—228no—
755C22—224no—
756C22—224no—
757C22—224no—
758C22—4464no—
759C22—4416no—
760C22—444no—
761C22—444no—
762C22C2×C22⋊C4×D1114yes—
763C22C2×C22⋊C4×D1118yescomplemented
764C22#1062301714yes—
765C22#1062302118yes—
766C22C2×C4×C22⋊D1114yes—
767C22C2×C4×C22⋊D1118yescomplemented
768C22D4×C22⋊D1118yes—
769C22C23×C4×D1111yescharacteristic
770C22C22×#433911yescharacteristic
771C22C22×D4×D1112yes—
772C22C2×#6703712yes—
773C22C23×C22⋊D1111yescharacteristic
774C4—28no—
775C4—44no—
776C4—118no—
777C4—224no—
778C4—444no—
779C4—444no—
780C2—28no—
781C2—28no—
782C2—44no—
783C2—228no—
784C2—444no—
785C2C22⋊C4×C22⋊D1118yesdirect product factor
786C2C22×C22⋊C4×D1111yescharacteristic
787C2C22×C4×C22⋊D1111yescharacteristic
788C2C2×#1062301711yescharacteristic
789C2C2×D4×C22⋊D1112yes—
790C2C2×#1062302112yes—
subgroupG/H
centerC24C23×D11
commutatorC22×C11C24×C4
FrattiniC23C24×D11
FittingC23×C11×C22⋊C4C2
socleC24×C11C24
prime radicalC24×C22⋊D11C2
cosocleC23×C11C25
hypercenterC23×C22⋊C4D11
hypocenterC11C2×D4×C22⋊C4
LCSG ▷ C22×C11 ▷ C11
UCSC1 ◁ C24 ◁ C23×C22⋊C4

Complements

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

NH ≅ G/Ntype
2. C22×C4×C22⋊D11C2semidirect
3. C22×C22⋊C4×D11C2semidirect
4. C22⋊C4×C22⋊D11C2direct (N × H)
5. C2×#10622570C2semidirect
6. C2×#10622826C2semidirect
7. C2×#10622569C2semidirect
8. C2×#10622555C2semidirect
9. C2×#10622860C2semidirect
10. C2×#10622568C2semidirect
11. C2×C22⋊C4×Dic11C2semidirect
12. C23×C11×C22⋊C4C2semidirect
15. C24×C4×C11C22semidirect
17. C23×C22⋊D11C4semidirect
24. C23×C4×D11C22semidirect
28. C22×C11×C22⋊C4C22semidirect
29. C22×C11×C22⋊C4C22semidirect
32. C22×C22⋊Dic11C22semidirect
33. C22×C22⋊Dic11C22semidirect
35. C2×C4×C22⋊D11C22semidirect
36. C22×(C2×D11)⋊C4C22semidirect
37. C22×(C2×D11)⋊C4C22semidirect
38. C22×(C2×D11)⋊C4C22semidirect
39. C22×Dic11⋊C4C22semidirect
40. C22×C4×Dic11C22semidirect
42. C2×C22⋊C4×D11C22semidirect
43. #10622860C22semidirect
44. #10622826C22semidirect
45. C2×C11⋊#95C22semidirect
46. C2×C11⋊#95C22semidirect
47. #10622570C22semidirect
48. #10622569C22semidirect
49. #10622568C22semidirect
50. #10622555C22semidirect
51. C22⋊C4×Dic11C22semidirect
56. C25×C11C2×C4semidirect
65. C24×D11C2×C4semidirect
74. C23×C4×C11C23semidirect
81. C22×C22⋊D11C2×C4semidirect
82. C22×C22⋊D11C2×C4semidirect
83. C22×C22⋊D11C2×C4semidirect
84. C22×C22⋊D11C2×C4semidirect
91. C23×Dic11C2×C4semidirect
100. C22×C4×D11C23semidirect
104. C2×C11×C22⋊C4D4semidirect
107. C2×C11×C22⋊C4C23semidirect
114. C2×C22⋊Dic11C23semidirect
115. C2×C22⋊Dic11C23semidirect
120. C2×(C2×D11)⋊C4C23semidirect
121. C2×(C2×D11)⋊C4C23semidirect
122. C2×(C2×D11)⋊C4C23semidirect
124. C2×Dic11⋊C4C23semidirect
126. C2×C4×Dic11C23semidirect
128. C11⋊#95C23semidirect
129. C11⋊#95C23semidirect
152. C24×C11C22×C4semidirect
178. C23×D11C22×C4semidirect
191. C22×C4×C11C2×D4semidirect
201. C2×C22⋊D11C22⋊C4direct (N × H)
203. C2×C22⋊D11C22×C4semidirect
204. C2×C22⋊D11C22×C4semidirect
205. C2×C22⋊D11C22×C4semidirect
218. C22×Dic11C22×C4semidirect
230. C11×C22⋊C4C2×D4semidirect
243. C23×C22⋊C4D11semidirect
280. C23×C11C2×C22⋊C4semidirect
281. C23×C11C4×D4semidirect
316. C22×D11C2×C22⋊C4semidirect
328. C2×C4×C11C22×D4semidirect
332. C22⋊D11C2×C22⋊C4direct (N × H)
344. C2×Dic11C2×C22⋊C4semidirect
360. C24×C4C2×D11semidirect
376. C22×C22⋊C4C2×D11semidirect
377. C22×C22⋊C4C2×D11semidirect
406. C22×C11C22×C22⋊C4semidirect
408. C22×C11C2×C4×D4semidirect
429. C2×D11C22×C22⋊C4semidirect
435. Dic11C22×C22⋊C4semidirect
448. C25C4×D11semidirect
484. C23×C4C22×D11semidirect
506. C2×C22⋊C4C22⋊D11direct (N × H)
509. C2×C22⋊C4C22×D11semidirect
517. C2×C11D4×C22⋊C4semidirect
568. C24C2×C4×D11semidirect
619. C22×C4C2×C22⋊D11semidirect
632. C22⋊C4C2×C22⋊D11direct (N × H)
634. C11C2×D4×C22⋊C4semidirect
689. C23C22⋊C4×D11semidirect
690. C23C4×C22⋊D11semidirect
731. C2×C4C22×C22⋊D11semidirect
763. C22C2×C22⋊C4×D11semidirect
767. C22C2×C4×C22⋊D11semidirect
785. C2C22⋊C4×C22⋊D11direct (N × H)

Maximal subgroups

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

subgroupindex
C24×C22⋊D112
C22×C4×C22⋊D112
C22×C22⋊C4×D112
C22⋊C4×C22⋊D112
C2×#106225702
C2×#106228262
C2×#106225692
C2×#106225552
C2×#106228602
C2×#106225682
C2×C22⋊C4×Dic112
C23×C11×C22⋊C42
C2×D4×C22⋊C411