Finite Group Databasebeta

← C2×#19132941 #25062539

Subgroups — C2×#19132941 #25062539

Order 11008.

1490 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063308C211yesmaximal, characteristic
2C2×#14582863C211yesmaximal, characteristic, complemented
3#19132941C218yesmaximal, direct product factor
4C2×#14582624C212yesmaximal, complemented
5C2×#14582622C212yesmaximal, complemented
6C22×C22⋊C8×C43C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C411yescharacteristic
8C22×#10621877—21no—
9C2×#13063308—21no—
10C2×#13063308—21no—
11C2×#13063308—22no—
12C2×#13063308—21no—
13C2×#13063308—21no—
14C2×#13063308—22no—
15C2×#13063308C414yes—
16C2×#13063308C2214yes—
17C22×Dic43⋊C4C411yescharacteristic
18C22×Dic43⋊C4C2211yescharacteristic
19C22×C22⋊Dic43C411yescharacteristic
20C22×(C2×D43)⋊C4C411yescharacteristic
21C22×(C2×D43)⋊C4C2211yescharacteristic
22#14582863—22no—
23#14582863C2214yescomplemented
24C2×C22⋊(C43⋊C8)—21no—
25C2×C22⋊(C43⋊C8)C2212yes—
26#14582624C2218yescomplemented
27#14582622C2218yescomplemented
28C24×C4×C43C2211yescharacteristic
29C23×C8×C43—21no—
30C2×C22⋊C8×C43—22no—
31C2×C22⋊C8×C43—21no—
32C2×C22⋊C8×C43C2212yes—
33C2×C22⋊C8×C43C2214yescomplemented
34C24×D43C2×C411yescharacteristic
35C22×C22⋊D43—21no—
36C22×C22⋊D43—22no—
37C22×C22⋊D43—21no—
38C22×C22⋊D43—44no—
39C22×C22⋊D43C2×C414yes—
40C23×Dic43C2×C411yescharacteristic
41C23×Dic43C2×C411yescharacteristic
42C23×Dic43C2×C411yescharacteristic
43C2×#10621877—24no—
44C2×#10621877—44no—
45C22×C43⋊C8—22no—
46#13063308—24no—
47#13063308—24no—
48#13063308—24no—
49#13063308—24no—
50#13063308—24no—
51#13063308—24no—
52#13063308—24no—
53#13063308—24no—
54C2×Dic43⋊C4—21no—
55C2×Dic43⋊C4—21no—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—21no—
58C2×Dic43⋊C4—21no—
59C2×Dic43⋊C4—21no—
60C2×Dic43⋊C4—21no—
61C2×Dic43⋊C4C2×C414yes—
62C2×Dic43⋊C4C2×C412yes—
63C2×Dic43⋊C4C2312yes—
64C2×C22⋊Dic43—21no—
65C2×C22⋊Dic43—22no—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43C2×C414yes—
68C2×(C2×D43)⋊C4—21no—
69C2×(C2×D43)⋊C4—21no—
70C2×(C2×D43)⋊C4—22no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4—21no—
75C2×(C2×D43)⋊C4C2×C414yes—
76C2×(C2×D43)⋊C4C2×C412yes—
77C2×(C2×D43)⋊C4C2312yes—
78C22⋊(C43⋊C8)—24no—
79C22⋊(C43⋊C8)—22no—
80C22⋊(C43⋊C8)C2314yes—
81C25×C43C2×C411yescharacteristic
82C23×C4×C43—44no—
83C23×C4×C43C2×C411yescharacteristic
84C23×C4×C43C2×C412yes—
85C23×C4×C43D411yescharacteristic
86C23×C4×C43D411yescharacteristic
87C23×C4×C43D412yes—
88C23×C4×C43D411yescharacteristic
89C23×C4×C43D411yescharacteristic
90C23×C4×C43D412yes—
91C23×C4×C43C2311yescharacteristic
92C23×C4×C43C2312yes—
93C22×C8×C43—22no—
94C22×C8×C43—24no—
95C22×C8×C43—44no—
96C22⋊C8×C43—22no—
97C22⋊C8×C43—24no—
98C22⋊C8×C43C2314yes—
99C24×C43—24no—
100C24×C43—24no—
101C24×C43—42no—
102C24×C43C22⋊C411yescharacteristic
103C24×C43C22⋊C412yes—
104C24×C43C22⋊C411yescharacteristic
105C24×C43C22×C412yes—
106C24×C43C22×C411yescharacteristic
107C23×D43—21no—
108C23×D43—21no—
109C23×D43—24no—
110C23×D43—42no—
111C23×D43—42no—
112C23×D43C22×C412yes—
113C22×C4×C43—24no—
114C22×C4×C43—24no—
115C22×C4×C43—42no—
116C22×C4×C43—44no—
117C22×C4×C43—42no—
118C22×C4×C43—44no—
119C22×C4×C43—44no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—44no—
123C22×C4×C43C22⋊C411yescharacteristic
124C22×C4×C43C22⋊C411yescharacteristic
125C22×C4×C43C22⋊C412yes—
126C22×C4×C43C22⋊C412yes—
127C22×C4×C43C22⋊C412yes—
128C22×C4×C43C22⋊C412yes—
129C22×C4×C43C22⋊C412yes—
130C22×C4×C43C22×C412yes—
131C22×C4×C43C22×C411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D412yes—
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2×D412yes—
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2411yescharacteristic
141C2×C22⋊D43—24no—
142C2×C22⋊D43—24no—
143C2×C22⋊D43—48no—
144C2×C22⋊D43—48no—
145C2×C22⋊D43—44no—
146C2×C22⋊D43—44no—
147C22×Dic43—21no—
148C22×Dic43—21no—
149C22×Dic43—21no—
150C22×Dic43—21no—
151C22×Dic43—21no—
152C22×Dic43—21no—
153C22×Dic43—24no—
154C22×Dic43—42no—
155C22×Dic43—42no—
156C22×Dic43C22×C412yes—
157C22×Dic43C22×C412yes—
158C22×Dic43C22×C412yes—
159C2×C8×C43—24no—
160C2×C8×C43—44no—
161C2×C8×C43—48no—
162C22⋊Dic43—24no—
163C22⋊Dic43—24no—
164(C2×D43)⋊C4—24no—
165(C2×D43)⋊C4—24no—
166(C2×D43)⋊C4—22no—
167(C2×D43)⋊C4—22no—
168(C2×D43)⋊C4—22no—
169(C2×D43)⋊C4—22no—
170Dic43⋊C4—24no—
171Dic43⋊C4—24no—
172Dic43⋊C4—22no—
173Dic43⋊C4—22no—
174Dic43⋊C4—22no—
175Dic43⋊C4—22no—
176#10621877—48no—
177C2×C43⋊C8—24no—
178C2×C43⋊C8—44no—
179C23×C43—22no—
180C23×C43—22no—
181C23×C43—22no—
182C23×C43—22no—
183C23×C43—24no—
184C23×C43—24no—
185C23×C43—22no—
186C23×C43—24no—
187C23×C43—22no—
188C23×C43—24no—
189C23×C43—22no—
190C23×C43—42no—
191C23×C43—42no—
192C23×C43—416no—
193C23×C43#9914yes—
194C23×C43C2×C22⋊C412yes—
195C23×C43C2×C22⋊C411yescharacteristic
196C23×C43C2×C22⋊C412yes—
197C23×C43C2×C22⋊C411yescharacteristic
198C23×C43#13114yes—
199C23×C43C23×C411yescharacteristic
200C22×D43—22no—
201C22×D43—24no—
202C22×D43—42no—
203C22×D43—42no—
204C22×D43—42no—
205C22×D43—42no—
206C22×D43—42no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—88no—
211C2×C4×C43—22no—
212C2×C4×C43—24no—
213C2×C4×C43—24no—
214C2×C4×C43—22no—
215C2×C4×C43—24no—
216C2×C4×C43—24no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—41no—
223C2×C4×C43—42no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—41no—
227C2×C4×C43—42no—
228C2×C4×C43—41no—
229C2×C4×C43C2×C22⋊C412yes—
230C2×C4×C43C2×C22⋊C412yes—
231C2×C4×C43C2×C22⋊C411yescharacteristic
232C2×C4×C43C2×C22⋊C411yescharacteristic
233C2×C4×C43C22×D411yescharacteristic
234C2×C4×C43C22×D411yescharacteristic
235C22⋊D43—48no—
236C22⋊D43—48no—
237C2×Dic43—22no—
238C2×Dic43—22no—
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—42no—
242C2×Dic43—42no—
243C2×Dic43—42no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C8×C43—44no—
250C43⋊C8—44no—
251C2×#1468—431nomaximal, Sylow
252C22×C43—22no—
253C22×C43—21no—
254C22×C43—21no—
255C22×C43—21no—
256C22×C43—21no—
257C22×C43—22no—
258C22×C43—28no—
259C22×C43—28no—
260C22×C43—22no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—48no—
264C22×C43—48no—
265C22×C43—44no—
266C22×C43#40812yes—
267C22×C43#40812yes—
268C22×C43C2×#9914yes—
269C22×C43C2×#9912yes—
270C22×C43#41312yes—
271C22×C43C22×C22⋊C411yescharacteristic
272C22×C43C2×#13112yes—
273C2×D43—42no—
274C2×D43—42no—
275C2×D43—42no—
276C2×D43—84no—
277C2×D43—84no—
278C2×D43—84no—
279C4×C43—21no—
280C4×C43—21no—
281C4×C43—21no—
282C4×C43—22no—
283C4×C43—22no—
284C4×C43—21no—
285Dic43—42no—
286Dic43—42no—
287Dic43—42no—
288C22×#123—431no—
289C2×#407—431no—
290C22×C22⋊C8D4311yescharacteristic, complemented
291#1468—438no—
292C2×#324—432no—
293C2×#323—432no—
294C2×C43—22no—
295C2×C43—22no—
296C2×C43—24no—
297C2×C43—42no—
298C2×C43#146814yescomplemented
299C2×C43C2×#40811yescharacteristic
300C2×C43C22×#9911yescharacteristic
301C2×C43C2×#41311yescharacteristic
302D43—82no—
303C23×D4—431no—
304C24×C4C2×D4311yescharacteristic
305C22×M16—861no—
306C23×C8—21no—
307C2×#123—434no—
308C2×#123—434no—
309C2×#123—861no—
310C2×#123—861no—
311C2×#123—862no—
312C2×#123—861no—
313C2×#123—862no—
314C2×#123—861no—
315C22×C4⋊C4—431no—
316C22×C4⋊C4—431no—
317C22×C22⋊C4—431no—
318C22×C22⋊C4—431no—
319C22×C22⋊C4—431no—
320#407—434no—
321#407—862no—
322C2×C22⋊C8—22no—
323C2×C22⋊C8—21no—
324C2×C22⋊C8—432no—
325C2×C22⋊C8—861no—
326C2×C22⋊C8C2×D4312yes—
327C2×C22⋊C8C2×D4314yescomplemented
328#324—438no—
329#323—438no—
330C43C2×#146811yescharacteristic, complemented, Sylow
331C25—431no—
332C25C4×D4311yescharacteristic
333C22×D4—434no—
334C22×D4—862no—
335C22×D4—861no—
336C22×D4—861no—
337C22×D4—1724no—
338C23×C4—44no—
339C23×C4—431no—
340C23×C4—431no—
341C23×C4—431no—
342C23×C4C4×D4311yescharacteristic
343C23×C4C4×D4312yes—
344C23×C4D17211yescharacteristic
345C23×C4D17211yescharacteristic
346C23×C4D17212yes—
347C23×C4C22⋊D4311yescharacteristic
348C23×C4C22⋊D4312yes—
349C23×C4C22⋊D4311yescharacteristic
350C23×C4C22×D4311yescharacteristic
351C23×C4C22×D4312yes—
352C2×M16—864no—
353C2×M16—1724no—
354C22×C8—22no—
355C22×C8—24no—
356C22×C8—44no—
357C22×C8—862no—
358#123—864no—
359#123—864no—
360#123—864no—
361#123—864no—
362#123—864no—
363#123—864no—
364#123—864no—
365#123—864no—
366C2×C4⋊C4—432no—
367C2×C4⋊C4—434no—
368C2×C4⋊C4—432no—
369C2×C4⋊C4—862no—
370C2×C4⋊C4—861no—
371C2×C4⋊C4—861no—
372C2×C4⋊C4—861no—
373C2×C4⋊C4—861no—
374C2×C4⋊C4—861no—
375C2×C4⋊C4—861no—
376C2×C22⋊C4—434no—
377C2×C22⋊C4—434no—
378C2×C22⋊C4—432no—
379C2×C22⋊C4—432no—
380C2×C22⋊C4—862no—
381C2×C22⋊C4—861no—
382C2×C22⋊C4—861no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—861no—
385C2×C22⋊C4—861no—
386C2×C22⋊C4—861no—
387C2×C22⋊C4—861no—
388C2×C22⋊C4—861no—
389C2×C22⋊C4—861no—
390C22⋊C8—22no—
391C22⋊C8—24no—
392C22⋊C8—434no—
393C22⋊C8—862no—
394C22⋊C8—864no—
395C22⋊C8C22×D4314yes—
396C24—24no—
397C24—24no—
398C24—42no—
399C24—432no—
400C24—864no—
401C24—861no—
402C24—861no—
403C24—1722no—
404C24—1722no—
405C24(C2×D43)⋊C411yescharacteristic
406C24(C2×D43)⋊C412yes—
407C24(C2×D43)⋊C411yescharacteristic
408C24C2×C4×D4312yes—
409C24C2×C4×D4311yescharacteristic
410C2×D4—864no—
411C2×D4—864no—
412C2×D4—1728no—
413C2×D4—1724no—
414C2×D4—1724no—
415C2×D4—1728no—
416C22×C4—24no—
417C22×C4—24no—
418C22×C4—42no—
419C22×C4—44no—
420C22×C4—42no—
421C22×C4—44no—
422C22×C4—42no—
423C22×C4—44no—
424C22×C4—44no—
425C22×C4—42no—
426C22×C4—432no—
427C22×C4—432no—
428C22×C4—432no—
429C22×C4—861no—
430C22×C4—861no—
431C22×C4—861no—
432C22×C4—861no—
433C22×C4—861no—
434C22×C4—861no—
435C22×C4—864no—
436C22×C4—1722no—
437C22×C4—1722no—
438C22×C4(C2×D43)⋊C412yes—
439C22×C4(C2×D43)⋊C412yes—
440C22×C4(C2×D43)⋊C411yescharacteristic
441C22×C4(C2×D43)⋊C411yescharacteristic
442C22×C4(C2×D43)⋊C412yes—
443C22×C4(C2×D43)⋊C412yes—
444C22×C4(C2×D43)⋊C412yes—
445C22×C4C2×C4×D4311yescharacteristic
446C22×C4C2×C4×D4312yes—
447C22×C4C2×D17212yes—
448C22×C4C2×D17211yescharacteristic
449C22×C4C2×D17211yescharacteristic
450C22×C4C2×D17212yes—
451C22×C4C2×C22⋊D4312yes—
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4311yescharacteristic
454C22×C4C2×C22⋊D4312yes—
455C22×C4C23×D4311yescharacteristic
456M16—1728no—
457C2×C8—24no—
458C2×C8—44no—
459C2×C8—48no—
460C2×C8—864no—
461C2×C8—1724no—
462C4⋊C4—864no—
463C4⋊C4—864no—
464C4⋊C4—862no—
465C4⋊C4—862no—
466C4⋊C4—862no—
467C4⋊C4—862no—
468C22⋊C4—864no—
469C22⋊C4—864no—
470C22⋊C4—864no—
471C22⋊C4—864no—
472C22⋊C4—862no—
473C22⋊C4—862no—
474C22⋊C4—862no—
475C22⋊C4—862no—
476C23—22no—
477C23—22no—
478C23—22no—
479C23—22no—
480C23—24no—
481C23—22no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—24no—
487C23—42no—
488C23—42no—
489C23—416no—
490C23—864no—
491C23—862no—
492C23—3448no—
493C23—1722no—
494C23—1722no—
495C23—1722no—
496C23—1722no—
497C23—1722no—
498C23—1722no—
499C23—1722no—
500C23—1722no—
501C23#1306323914yes—
502C23C2×(C2×D43)⋊C412yes—
503C23C2×(C2×D43)⋊C411yescharacteristic
504C23C2×(C2×D43)⋊C412yes—
505C23C2×(C2×D43)⋊C411yescharacteristic
506C23#1306333114yes—
507C23C22×C4×D4311yescharacteristic
508D4—1728no—
509D4—1728no—
510C2×C4—24no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—24no—
514C2×C4—24no—
515C2×C4—24no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—42no—
519C2×C4—42no—
520C2×C4—42no—
521C2×C4—41no—
522C2×C4—42no—
523C2×C4—41no—
524C2×C4—42no—
525C2×C4—41no—
526C2×C4—42no—
527C2×C4—41no—
528C2×C4—862no—
529C2×C4—862no—
530C2×C4—862no—
531C2×C4—864no—
532C2×C4—1722no—
533C2×C4—1722no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1722no—
537C2×C4—1722no—
538C2×C4—1722no—
539C2×C4—1722no—
540C2×C4C2×(C2×D43)⋊C411yescharacteristic
541C2×C4C2×(C2×D43)⋊C411yescharacteristic
542C2×C4C2×(C2×D43)⋊C412yes—
543C2×C4C2×(C2×D43)⋊C412yes—
544C2×C4C22×C22⋊D4311yescharacteristic
545C2×C4C22×D17211yescharacteristic
546C8—44no—
547C8—1724no—
548C22—28no—
549C22—28no—
550C22—22no—
551C22—21no—
552C22—21no—
553C22—21no—
554C22—21no—
555C22—22no—
556C22—22no—
557C22—22no—
558C22—22no—
559C22—48no—
560C22—48no—
561C22—44no—
562C22—3444no—
563C22—3444no—
564C22—3444no—
565C22—1722no—
566C22—1722no—
567C22—1722no—
568C22#1458286512yes—
569C22#1458286512yes—
570C22C2×#1306323914yes—
571C22C2×#1306323912yes—
572C22#1458288112yes—
573C22C22×(C2×D43)⋊C411yescharacteristic
574C22C2×#1306333112yes—
575C4—21no—
576C4—21no—
577C4—22no—
578C4—21no—
579C4—21no—
580C4—22no—
581C4—1722no—
582C4—1722no—
583C4—1722no—
584C2—22no—
585C2—22no—
586C2—24no—
587C2—42no—
588C2—3442no—
589C2#1913294114yesdirect product factor
590C2C2×#1458286511yescharacteristic
591C2C22×#1306323911yescharacteristic
592C2C2×#1458288111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC22×C22⋊C8×C43C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC22×C4×C43C24
hypercenterC22×C22⋊C8D43
hypocenterC43C2×#1468
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C22×C22⋊C8

Complements

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

NH ≅ G/Ntype
2. C2×#14582863C2semidirect
3. #19132941C2direct (N × H)
4. C2×#14582624C2semidirect
5. C2×#14582622C2semidirect
6. C22×C22⋊C8×C43C2semidirect
23. #14582863C22semidirect
26. #14582624C22semidirect
27. #14582622C22semidirect
33. C2×C22⋊C8×C43C22semidirect
290. C22×C22⋊C8D43semidirect
298. C2×C43#1468semidirect
327. C2×C22⋊C8C2×D43semidirect
330. C43C2×#1468semidirect
589. C2#19132941direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633082
C2×#145828632
#191329412
C2×#145826242
C2×#145826222
C22×C22⋊C8×C432
C2×#146843