Finite Group Databasebeta

← C2×#13071990 #14921189

Subgroups — C2×#13071990 #14921189

Order 2816.

8730 conjugacy classes of subgroups.

The subgroup lattice has 832 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#66992C212yesmaximal, complemented
2C22×#67006C211yesmaximal, characteristic, complemented
3C22×#67006C211yesmaximal, characteristic, complemented
4C23×C22⋊Dic11C211yesmaximal, characteristic, complemented
5#13071990C2116yesmaximal, direct product factor
6C2×#10622835C212yesmaximal, complemented
7C2×#10622836C212yesmaximal, complemented
8C2×#10622833C212yesmaximal, complemented
9C2×#10622826C211yesmaximal, characteristic, complemented
10C2×#10622823C211yesmaximal, characteristic, complemented
11C2×#10622860C211yesmaximal, characteristic, complemented
12C24×D4×C11C211yesmaximal, characteristic, complemented
13C26×C11C2211yescharacteristic
14C26×C11C2211yescharacteristic
15C23×D4×C11—28no—
16C23×D4×C11—216no—
17C23×D4×C11C2212yes—
18C23×D4×C11C2212yes—
19C23×D4×C11C2218yescomplemented
20C24×C4×C11C2211yescharacteristic
21C23×C22⋊D11C2211yescharacteristic
22C23×C22⋊D11C2211yescharacteristic, complemented
23C23×C22⋊D11C2212yescomplemented
24C23×C22⋊D11C2211yescharacteristic, complemented
25C24×Dic11C2212yescomplemented
26C2×#67006—28no—
27C2×#67006—28no—
28C2×#67006C2218yescomplemented
29C2×#67006C2218yescomplemented
30C22×C22⋊Dic11—28no—
31C22×C22⋊Dic11C2211yescharacteristic
32C22×C22⋊Dic11C2211yescharacteristic
33C22×C22⋊Dic11C2211yescharacteristic
34C22×C22⋊Dic11C2218yescomplemented
35C22×C22⋊Dic11C2212yescomplemented
36C22×C22⋊Dic11C2212yescomplemented
37C22×C22⋊Dic11C2211yescharacteristic, complemented
38C22×C22⋊Dic11C2212yescomplemented
39C22×C22⋊Dic11C2211yescharacteristic, complemented
40C22×C22⋊Dic11C2212yescomplemented
41C2×#66992—216no—
42C2×#66992C22116yescomplemented
43C22×(C2×D11)⋊C4C2212yescomplemented
44C22×Dic11⋊C4C2212yescomplemented
45#10622860C2218yescomplemented
46#10622836C22116yescomplemented
47#10622835C22116yescomplemented
48#10622833C22116yescomplemented
49#10622826C2218yescomplemented
50#10622823C2218yescomplemented
51C2×C11⋊#95C2212yescomplemented
52C2×C11⋊#95C2212yescomplemented
53C25×C11—24no—
54C25×C11—28no—
55C25×C11—28no—
56C25×C11—24no—
57C25×C11—24no—
58C25×C11—24no—
59C25×C11—24no—
60C25×C11—44no—
61C25×C11—44no—
62C25×C11D418yescomplemented
63C25×C11C2311yescharacteristic
64C25×C11C2312yes—
65C25×C11C2314yes—
66C25×C11C2314yes—
67C25×C11C2311yescharacteristic
68C25×C11C2311yescharacteristic
69C24×D11C2311yescharacteristic
70C22×D4×C11—2128no—
71C22×D4×C11—28no—
72C22×D4×C11—28no—
73C22×D4×C11—28no—
74C22×D4×C11—28no—
75C22×D4×C11—232no—
76C22×D4×C11—264no—
77C22×D4×C11—28no—
78C22×D4×C11D4116yescomplemented
79C22×D4×C11C2318yes—
80C22×D4×C11C2318yes—
81C23×C4×C11—24no—
82C23×C4×C11—28no—
83C23×C4×C11C2314yes—
84C23×C4×C11C2312yes—
85C22×C22⋊D11—28no—
86C22×C22⋊D11—28no—
87C22×C22⋊D11—24no—
88C22×C22⋊D11—24no—
89C22×C22⋊D11—24no—
90C22×C22⋊D11—24no—
91C22×C22⋊D11—24no—
92C22×C22⋊D11—28no—
93C22×C22⋊D11—44no—
94C22×C22⋊D11—44no—
95C22×C22⋊D11C2314yes—
96C22×C22⋊D11C2314yescomplemented
97C22×C22⋊D11C2318yescomplemented
98C22×C22⋊D11C2314yescomplemented
99C23×Dic11—28no—
100C23×Dic11—28no—
101C23×Dic11—44no—
102C23×Dic11C2311yescharacteristic
103C23×Dic11C2312yes—
104C23×Dic11C2311yescharacteristic
105C23×Dic11C2311yescharacteristic
106C23×Dic11C2312yes—
107C23×Dic11C2318yescomplemented
108#67006—232no—
109#67006—232no—
110C2×C22⋊Dic11—28no—
111C2×C22⋊Dic11—24no—
112C2×C22⋊Dic11—24no—
113C2×C22⋊Dic11—24no—
114C2×C22⋊Dic11—24no—
115C2×C22⋊Dic11—28no—
116C2×C22⋊Dic11—28no—
117C2×C22⋊Dic11—232no—
118C2×C22⋊Dic11—44no—
119C2×C22⋊Dic11D418yescomplemented
120C2×C22⋊Dic11C2314yes—
121C2×C22⋊Dic11C2314yes—
122C2×C22⋊Dic11C2314yes—
123C2×C22⋊Dic11C2318yescomplemented
124C2×C22⋊Dic11C2314yescomplemented
125C2×C22⋊Dic11C2318yescomplemented
126C2×C22⋊Dic11C2314yescomplemented
127C2×C22⋊Dic11C2318yescomplemented
128C2×C22⋊Dic11C2318yescomplemented
129#66992—264no—
130C2×(C2×D11)⋊C4—28no—
131C2×(C2×D11)⋊C4C2318yescomplemented
132C2×Dic11⋊C4—28no—
133C2×Dic11⋊C4C2318yescomplemented
134C11⋊#95C2318yescomplemented
135C11⋊#95C2318yescomplemented
136C2×#2410—111nomaximal, Sylow
137C24×C11—22no—
138C24×C11—24no—
139C24×C11—22no—
140C24×C11—24no—
141C24×C11—24no—
142C24×C11—232no—
143C24×C11—232no—
144C24×C11—232no—
145C24×C11—28no—
146C24×C11—22no—
147C24×C11—24no—
148C24×C11—216no—
149C24×C11—216no—
150C24×C11—28no—
151C24×C11—24no—
152C24×C11—24no—
153C24×C11—24no—
154C24×C11—28no—
155C24×C11—22no—
156C24×C11—24no—
157C24×C11—24no—
158C24×C11—24no—
159C24×C11—24no—
160C24×C11—28no—
161C24×C11—28no—
162C24×C11—416no—
163C24×C11—48no—
164C24×C11—48no—
165C24×C11—432no—
166C24×C11—432no—
167C24×C11—432no—
168C24×C11—432no—
169C24×C11—416no—
170C24×C11—416no—
171C24×C11C2×D414yes—
172C24×C11C2×D418yes—
173C24×C11C2×D414yes—
174C24×C11C2×D418yes—
175C24×C11C2×D414yes—
176C24×C11C2×D414yes—
177C24×C11C2×D4116yescomplemented
178C24×C11#4114yes—
179C24×C11C2412yes—
180C24×C11C2414yes—
181C24×C11C2412yes—
182C24×C11C2412yes—
183C24×C11C2411yescharacteristic
184C23×D11—24no—
185C23×D11—22no—
186C23×D11—22no—
187C23×D11—22no—
188C23×D11—24no—
189C23×D11C2412yes—
190C2×D4×C11—2256no—
191C2×D4×C11—264no—
192C2×D4×C11—264no—
193C2×D4×C11—216no—
194C2×D4×C11—216no—
195C2×D4×C11—216no—
196C2×D4×C11—216no—
197C2×D4×C11—216no—
198C2×D4×C11C2×D4132yescomplemented
199C22×C4×C11—232no—
200C22×C4×C11—28no—
201C22×C4×C11—24no—
202C22×C4×C11—24no—
203C22×C4×C11—216no—
204C22×C4×C11C2×D418yes—
205C22×C4×C11C2414yes—
206C2×C22⋊D11—216no—
207C2×C22⋊D11—216no—
208C2×C22⋊D11—216no—
209C2×C22⋊D11—28no—
210C2×C22⋊D11—28no—
211C2×C22⋊D11—28no—
212C2×C22⋊D11—28no—
213C2×C22⋊D11—28no—
214C2×C22⋊D11—48no—
215C2×C22⋊D11—48no—
216C2×C22⋊D11—432no—
217C2×C22⋊D11—416no—
218C2×C22⋊D11—416no—
219C2×C22⋊D11—416no—
220C22×Dic11—216no—
221C22×Dic11—24no—
222C22×Dic11—24no—
223C22×Dic11—24no—
224C22×Dic11—216no—
225C22×Dic11—24no—
226C22×Dic11—22no—
227C22×Dic11—22no—
228C22×Dic11—22no—
229C22×Dic11—22no—
230C22×Dic11—22no—
231C22×Dic11—24no—
232C22×Dic11—24no—
233C22×Dic11—24no—
234C22×Dic11—48no—
235C22×Dic11—432no—
236C22×Dic11C2×D418yescomplemented
237C22×Dic11C2412yes—
238C22×Dic11C2412yes—
239C22×Dic11C2414yes—
240C22×Dic11C2412yes—
241C22×Dic11C2414yes—
242C22⋊Dic11—216no—
243C22⋊Dic11—216no—
244C22⋊Dic11—216no—
245C22⋊Dic11—28no—
246C22⋊Dic11—28no—
247C22⋊Dic11—28no—
248C22⋊Dic11—28no—
249C22⋊Dic11—48no—
250C22⋊Dic11C2×D4116yescomplemented
251(C2×D11)⋊C4—216no—
252Dic11⋊C4—216no—
253C24×D4D1111yescharacteristic, complemented
254C22×#121—112no—
255C22×#120—111no—
256C22×#120—111no—
257C23×C22⋊C4—111no—
258#2410—1116no—
259C2×#394—112no—
260C2×#392—112no—
261C2×#386—112no—
262C2×#386—111no—
263C2×#385—111no—
264C2×#379—111no—
265C23×C11—28no—
266C23×C11—28no—
267C23×C11—28no—
268C23×C11—28no—
269C23×C11—216no—
270C23×C11—216no—
271C23×C11—216no—
272C23×C11—216no—
273C23×C11—22no—
274C23×C11—24no—
275C23×C11—22no—
276C23×C11—24no—
277C23×C11—24no—
278C23×C11—232no—
279C23×C11—28no—
280C23×C11—216no—
281C23×C11—232no—
282C23×C11—28no—
283C23×C11—232no—
284C23×C11—28no—
285C23×C11—216no—
286C23×C11—216no—
287C23×C11—22no—
288C23×C11—24no—
289C23×C11—24no—
290C23×C11—24no—
291C23×C11—24no—
292C23×C11—22no—
293C23×C11—24no—
294C23×C11—24no—
295C23×C11—24no—
296C23×C11—24no—
297C23×C11—416no—
298C23×C11—4128no—
299C23×C11—432no—
300C23×C11—432no—
301C23×C11—432no—
302C23×C11—432no—
303C23×C11—4128no—
304C23×C11—416no—
305C23×C11—48no—
306C23×C11—416no—
307C23×C11—48no—
308C23×C11—48no—
309C23×C11—48no—
310C23×C11—48no—
311C23×C11—48no—
312C23×C11#120116yescomplemented
313C23×C11#121116yescomplemented
314C23×C11C22×D414yes—
315C23×C11C22×D412yes—
316C23×C11C22×D414yes—
317C23×C11C22×D418yes—
318C23×C11C22×D414yes—
319C23×C11C22×D418yes—
320C23×C11C22×D414yes—
321C23×C11C22×D412yes—
322C23×C11C22×D414yes—
323C23×C11C2×#4114yes—
324C23×C11C2×#4112yes—
325C23×C11H(5,𝔽2)14yes—
326C23×C11C2511yescharacteristic
327C22×D11—24no—
328C22×D11—22no—
329C22×D11—22no—
330C22×D11—22no—
331C22×D11—24no—
332C22×D11—44no—
333C22×D11—44no—
334C22×D11—44no—
335C22×D11—48no—
336C22×D11—48no—
337D4×C11—264no—
338D4×C11—264no—
339C2×C4×C11—232no—
340C2×C4×C11—216no—
341C2×C4×C11—24no—
342C2×C4×C11—24no—
343C2×C4×C11C22×D418yes—
344C22⋊D11—432no—
345C22⋊D11—416no—
346C22⋊D11—416no—
347C22⋊D11—416no—
348C2×Dic11—216no—
349C2×Dic11—24no—
350C2×Dic11—24no—
351C2×Dic11—24no—
352C2×Dic11—24no—
353C2×Dic11—24no—
354C2×Dic11—22no—
355C2×Dic11—22no—
356C2×Dic11—22no—
357C2×Dic11—22no—
358C2×Dic11—22no—
359C2×Dic11—24no—
360C2×Dic11—24no—
361C2×Dic11—432no—
362C2×Dic11—44no—
363C2×Dic11—44no—
364C2×Dic11—44no—
365C2×Dic11—48no—
366C2×Dic11C22×D418yescomplemented
367C26C2×D1111yescharacteristic
368C26C2×D1111yescharacteristic
369C23×D4—28no—
370C23×D4—216no—
371C23×D4—111no—
372C23×D4—111no—
373C23×D4—112no—
374C23×D4—111no—
375C23×D4C2×D1112yes—
376C23×D4C2×D1112yes—
377C23×D4C2×D1118yescomplemented
378C24×C4—112no—
379C24×C4C2×D1111yescharacteristic
380C2×#121—1116no—
381C2×#121—2216no—
382C2×#120—118no—
383C2×#120—118no—
384C2×#120—228no—
385C2×#120—228no—
386C22×C4⋊C4—112no—
387C22×C22⋊C4—111no—
388C22×C22⋊C4—112no—
389C22×C22⋊C4—111no—
390C22×C22⋊C4—112no—
391C22×C22⋊C4—112no—
392C22×C22⋊C4—118no—
393C22×C22⋊C4—111no—
394C22×C22⋊C4—111no—
395C22×C22⋊C4—111no—
396C22×C22⋊C4—112no—
397C22×C22⋊C4—112no—
398C22×C22⋊C4—228no—
399#394—1116no—
400#392—1116no—
401#386—1116no—
402#386—118no—
403#385—118no—
404#379—118no—
405C2×#95—112no—
406C2×#95—112no—
407C22×C11—24no—
408C22×C11—24no—
409C22×C11—232no—
410C22×C11—232no—
411C22×C11—24no—
412C22×C11—24no—
413C22×C11—28no—
414C22×C11—28no—
415C22×C11—28no—
416C22×C11—28no—
417C22×C11—24no—
418C22×C11—28no—
419C22×C11—24no—
420C22×C11—24no—
421C22×C11—28no—
422C22×C11—28no—
423C22×C11—464no—
424C22×C11—464no—
425C22×C11—44no—
426C22×C11—416no—
427C22×C11—432no—
428C22×C11—44no—
429C22×C11—44no—
430C22×C11—44no—
431C22×C11—44no—
432C22×C11—44no—
433C22×C11C2×#12014yes—
434C22×C11C2×#12018yescomplemented
435C22×C11C2×#12114yes—
436C22×C11C2×#12118yescomplemented
437C22×C11#53414yes—
438C22×C11D4218yes—
439C22×C11#54618yes—
440C22×C11C23×D411yescharacteristic
441C22×C11C23×D411yescharacteristic
442C22×C11C23×D412yes—
443C22×C11C22×#4111yescharacteristic
444C22×C11C2×H(5,𝔽2)12yes—
445C2×D11—42no—
446C2×D11—42no—
447C2×D11—42no—
448C2×D11—44no—
449C2×D11—44no—
450C2×D11—88no—
451C4×C11—28no—
452Dic11—28no—
453Dic11—42no—
454Dic11—42no—
455Dic11—42no—
456Dic11—44no—
457C25—24no—
458C25—24no—
459C25—28no—
460C25—28no—
461C25—24no—
462C25—24no—
463C25—24no—
464C25—44no—
465C25—44no—
466C25—111no—
467C25C22⋊D1118yescomplemented
468C25C22×D1111yescharacteristic
469C25C22×D1112yes—
470C25C22×D1114yes—
471C25C22×D1114yes—
472C25C22×D1111yescharacteristic
473C25C22×D1111yescharacteristic
474C22×D4—2128no—
475C22×D4—28no—
476C22×D4—28no—
477C22×D4—28no—
478C22×D4—28no—
479C22×D4—232no—
480C22×D4—264no—
481C22×D4—28no—
482C22×D4—114no—
483C22×D4—114no—
484C22×D4—118no—
485C22×D4—114no—
486C22×D4—228no—
487C22×D4—224no—
488C22×D4—224no—
489C22×D4—224no—
490C22×D4—224no—
491C22×D4—224no—
492C22×D4—228no—
493C22×D4—228no—
494C22×D4—444no—
495C22×D4—444no—
496C22×D4C22⋊D11116yescomplemented
497C22×D4C22×D1118yes—
498C22×D4C22×D1118yes—
499C23×C4—24no—
500C23×C4—28no—
501C23×C4—112no—
502C23×C4—112no—
503C23×C4—111no—
504C23×C4—111no—
505C23×C4—111no—
506C23×C4—118no—
507C23×C4—228no—
508C23×C4—228no—
509C23×C4—444no—
510C23×C4C22×D1114yes—
511C23×C4C22×D1112yes—
512#121—2264no—
513#120—2232no—
514#120—2232no—
515C2×C4⋊C4—118no—
516C2×C4⋊C4—228no—
517C2×C22⋊C4—118no—
518C2×C22⋊C4—114no—
519C2×C22⋊C4—114no—
520C2×C22⋊C4—118no—
521C2×C22⋊C4—114no—
522C2×C22⋊C4—114no—
523C2×C22⋊C4—118no—
524C2×C22⋊C4—114no—
525C2×C22⋊C4—118no—
526C2×C22⋊C4—118no—
527C2×C22⋊C4—118no—
528C2×C22⋊C4—2232no—
529C2×C22⋊C4—228no—
530C2×C22⋊C4—228no—
531C2×C22⋊C4—224no—
532C2×C22⋊C4—224no—
533C2×C22⋊C4—224no—
534C2×C22⋊C4—224no—
535C2×C22⋊C4—228no—
536C2×C22⋊C4—228no—
537C2×C22⋊C4—444no—
538#95—118no—
539#95—118no—
540C2×C11—28no—
541C2×C11—28no—
542C2×C11—44no—
543C2×C11—48no—
544C2×C11#241018yescomplemented
545C2×C11C22×#12011yescharacteristic
546C2×C11C22×#12111yescharacteristic
547C2×C11C2×#53411yescharacteristic
548C2×C11C2×D4212yes—
549C2×C11C2×#54612yes—
550D11—82no—
551C24—22no—
552C24—22no—
553C24—24no—
554C24—24no—
555C24—24no—
556C24—232no—
557C24—232no—
558C24—232no—
559C24—28no—
560C24—22no—
561C24—24no—
562C24—28no—
563C24—22no—
564C24—24no—
565C24—24no—
566C24—24no—
567C24—24no—
568C24—216no—
569C24—216no—
570C24—28no—
571C24—24no—
572C24—24no—
573C24—24no—
574C24—28no—
575C24—28no—
576C24—48no—
577C24—48no—
578C24—416no—
579C24—432no—
580C24—432no—
581C24—432no—
582C24—432no—
583C24—416no—
584C24—416no—
585C24—112no—
586C24—222no—
587C24—222no—
588C24—224no—
589C24—224no—
590C24—222no—
591C24D4×D1114yes—
592C24#434114yes—
593C24C2×C22⋊D1114yes—
594C24C2×C22⋊D1118yes—
595C24C2×C22⋊D1114yes—
596C24C2×C22⋊D1114yes—
597C24C2×C22⋊D1118yes—
598C24C2×C22⋊D11116yescomplemented
599C24C23×D1112yes—
600C24C23×D1114yes—
601C24C23×D1112yes—
602C24C23×D1112yes—
603C24C23×D1111yescharacteristic
604C2×D4—2256no—
605C2×D4—264no—
606C2×D4—264no—
607C2×D4—216no—
608C2×D4—216no—
609C2×D4—216no—
610C2×D4—216no—
611C2×D4—216no—
612C2×D4—2216no—
613C2×D4—228no—
614C2×D4—228no—
615C2×D4—228no—
616C2×D4—228no—
617C2×D4—228no—
618C2×D4—2216no—
619C2×D4—2216no—
620C2×D4—448no—
621C2×D4—448no—
622C2×D4—4432no—
623C2×D4—4416no—
624C2×D4—4416no—
625C2×D4—4416no—
626C2×D4C2×C22⋊D11132yescomplemented
627C22×C4—232no—
628C22×C4—28no—
629C22×C4—24no—
630C22×C4—24no—
631C22×C4—216no—
632C22×C4—118no—
633C22×C4—114no—
634C22×C4—112no—
635C22×C4—112no—
636C22×C4—114no—
637C22×C4—112no—
638C22×C4—2216no—
639C22×C4—224no—
640C22×C4—224no—
641C22×C4—224no—
642C22×C4—222no—
643C22×C4—222no—
644C22×C4—224no—
645C22×C4—224no—
646C22×C4—224no—
647C22×C4—222no—
648C22×C4—222no—
649C22×C4—222no—
650C22×C4—224no—
651C22×C4—2216no—
652C22×C4—448no—
653C22×C4—4432no—
654C22×C4C2×C22⋊D1118yes—
655C22×C4C23×D1114yes—
656C4⋊C4—2216no—
657C22⋊C4—1116no—
658C22⋊C4—2216no—
659C22⋊C4—2216no—
660C22⋊C4—228no—
661C22⋊C4—228no—
662C22⋊C4—228no—
663C22⋊C4—228no—
664C22⋊C4—2216no—
665C22⋊C4—2216no—
666C22⋊C4—448no—
667C11C2×#241011yescharacteristic, complemented, Sylow
668C23—216no—
669C23—216no—
670C23—28no—
671C23—28no—
672C23—28no—
673C23—216no—
674C23—216no—
675C23—28no—
676C23—22no—
677C23—22no—
678C23—24no—
679C23—24no—
680C23—24no—
681C23—232no—
682C23—216no—
683C23—28no—
684C23—232no—
685C23—28no—
686C23—216no—
687C23—28no—
688C23—216no—
689C23—232no—
690C23—22no—
691C23—24no—
692C23—24no—
693C23—22no—
694C23—24no—
695C23—24no—
696C23—24no—
697C23—24no—
698C23—24no—
699C23—24no—
700C23—416no—
701C23—4128no—
702C23—432no—
703C23—432no—
704C23—432no—
705C23—432no—
706C23—416no—
707C23—4128no—
708C23—48no—
709C23—48no—
710C23—48no—
711C23—416no—
712C23—48no—
713C23—48no—
714C23—48no—
715C23—222no—
716C23—222no—
717C23—224no—
718C23—224no—
719C23—222no—
720C23—448no—
721C23—444no—
722C23—444no—
723C23—448no—
724C23—444no—
725C23#66992116yescomplemented
726C23#67006116yescomplemented
727C23C2×D4×D1114yes—
728C23C2×D4×D1112yes—
729C23C2×#434114yes—
730C23C2×#434112yes—
731C23#6703714yes—
732C23C22×C22⋊D1114yes—
733C23C22×C22⋊D1118yes—
734C23C22×C22⋊D1114yes—
735C23C22×C22⋊D1114yes—
736C23C22×C22⋊D1118yes—
737C23C22×C22⋊D1114yes—
738C23C22×C22⋊D1112yes—
739C23C24×D1111yescharacteristic
740D4—264no—
741D4—264no—
742D4—4432no—
743D4—4416no—
744D4—4416no—
745D4—4416no—
746C2×C4—232no—
747C2×C4—216no—
748C2×C4—24no—
749C2×C4—24no—
750C2×C4—118no—
751C2×C4—2216no—
752C2×C4—224no—
753C2×C4—224no—
754C2×C4—224no—
755C2×C4—222no—
756C2×C4—222no—
757C2×C4—224no—
758C2×C4—224no—
759C2×C4—224no—
760C2×C4—222no—
761C2×C4—222no—
762C2×C4—222no—
763C2×C4—224no—
764C2×C4—4432no—
765C2×C4—448no—
766C2×C4—444no—
767C2×C4—444no—
768C2×C4—444no—
769C2×C4C22×C22⋊D1118yes—
770C22—24no—
771C22—24no—
772C22—232no—
773C22—232no—
774C22—28no—
775C22—28no—
776C22—28no—
777C22—28no—
778C22—24no—
779C22—24no—
780C22—24no—
781C22—28no—
782C22—28no—
783C22—24no—
784C22—28no—
785C22—24no—
786C22—464no—
787C22—464no—
788C22—44no—
789C22—432no—
790C22—416no—
791C22—44no—
792C22—44no—
793C22—44no—
794C22—44no—
795C22—44no—
796C22—442no—
797C22—444no—
798C22—444no—
799C22—442no—
800C22—442no—
801C22—888no—
802C22D4×C22⋊D1118yes—
803C22C2×#6699214yes—
804C22C2×#6699218yescomplemented
805C22#1062333514yes—
806C22#1062333718yes—
807C22C2×#6700614yes—
808C22C2×#6700618yescomplemented
809C22C22×D4×D1111yescharacteristic
810C22C22×#434111yescharacteristic
811C22C2×#6703712yes—
812C22C23×C22⋊D1111yescharacteristic
813C22C23×C22⋊D1112yes—
814C4—28no—
815C4—228no—
816C4—442no—
817C4—444no—
818C4—442no—
819C4—442no—
820C2—28no—
821C2—28no—
822C2—44no—
823C2—48no—
824C2—882no—
825C2#1307199018yesdirect product factor
826C2C22×#6700611yescharacteristic
827C2C22×#6699211yescharacteristic
828C2C2×#1062333511yescharacteristic
829C2C2×D4×C22⋊D1112yes—
830C2C2×#1062333712yes—
subgroupG/H
centerC24C23×D11
commutator, cosocleC23×C11C25
FrattiniC23C24×D11
FittingC24×D4×C11C2
socleC24×C11C24
hypercenterC24×D4D11
hypocenterC11C2×#2410
LCSG ▷ C23×C11 ▷ C11
UCSC1 ◁ C24 ◁ C24×D4

Complements

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

NH ≅ G/Ntype
1. C22×#66992C2semidirect
2. C22×#67006C2semidirect
3. C22×#67006C2semidirect
4. C23×C22⋊Dic11C2semidirect
5. #13071990C2direct (N × H)
6. C2×#10622835C2semidirect
7. C2×#10622836C2semidirect
8. C2×#10622833C2semidirect
9. C2×#10622826C2semidirect
10. C2×#10622823C2semidirect
11. C2×#10622860C2semidirect
12. C24×D4×C11C2semidirect
19. C23×D4×C11C22semidirect
22. C23×C22⋊D11C22semidirect
23. C23×C22⋊D11C22semidirect
24. C23×C22⋊D11C22semidirect
25. C24×Dic11C22semidirect
28. C2×#67006C22semidirect
29. C2×#67006C22semidirect
34. C22×C22⋊Dic11C22semidirect
35. C22×C22⋊Dic11C22semidirect
36. C22×C22⋊Dic11C22semidirect
37. C22×C22⋊Dic11C22semidirect
38. C22×C22⋊Dic11C22semidirect
39. C22×C22⋊Dic11C22semidirect
40. C22×C22⋊Dic11C22semidirect
42. C2×#66992C22semidirect
43. C22×(C2×D11)⋊C4C22semidirect
44. C22×Dic11⋊C4C22semidirect
45. #10622860C22semidirect
46. #10622836C22semidirect
47. #10622835C22semidirect
48. #10622833C22semidirect
49. #10622826C22semidirect
50. #10622823C22semidirect
51. C2×C11⋊#95C22semidirect
52. C2×C11⋊#95C22semidirect
62. C25×C11D4semidirect
78. C22×D4×C11D4semidirect
96. C22×C22⋊D11C23semidirect
97. C22×C22⋊D11C23semidirect
98. C22×C22⋊D11C23semidirect
107. C23×Dic11C23semidirect
119. C2×C22⋊Dic11D4semidirect
123. C2×C22⋊Dic11C23semidirect
124. C2×C22⋊Dic11C23semidirect
125. C2×C22⋊Dic11C23semidirect
126. C2×C22⋊Dic11C23semidirect
127. C2×C22⋊Dic11C23semidirect
128. C2×C22⋊Dic11C23semidirect
131. C2×(C2×D11)⋊C4C23semidirect
133. C2×Dic11⋊C4C23semidirect
134. C11⋊#95C23semidirect
135. C11⋊#95C23semidirect
177. C24×C11C2×D4semidirect
198. C2×D4×C11C2×D4semidirect
236. C22×Dic11C2×D4semidirect
250. C22⋊Dic11C2×D4semidirect
253. C24×D4D11semidirect
312. C23×C11#120semidirect
313. C23×C11#121semidirect
366. C2×Dic11C22×D4semidirect
377. C23×D4C2×D11semidirect
434. C22×C11C2×#120semidirect
436. C22×C11C2×#121semidirect
467. C25C22⋊D11semidirect
496. C22×D4C22⋊D11semidirect
544. C2×C11#2410semidirect
598. C24C2×C22⋊D11semidirect
626. C2×D4C2×C22⋊D11semidirect
667. C11C2×#2410semidirect
725. C23#66992semidirect
726. C23#67006semidirect
804. C22C2×#66992semidirect
808. C22C2×#67006semidirect
825. C2#13071990direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#669922
C22×#670062
C23×C22⋊Dic112
#130719902
C2×#106228352
C2×#106228362
C2×#106228332
C2×#106228262
C2×#106228232
C2×#106228602
C24×D4×C112
C2×#241011