Finite Group Databasebeta

← C2×#19134582 #25095991

Subgroups — C2×#19134582 #25095991

Order 11008.

2066 conjugacy classes of subgroups.

The subgroup lattice has 620 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×(C22⋊D43)⋊C4C211yesmaximal, characteristic
2C22×#13063239C212yesmaximal
3C2×#14582757C212yesmaximal, complemented
4#19134582C218yesmaximal, direct product factor
5C2×#14582666C211yesmaximal, characteristic, complemented
6C2×C43×#342C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C2211yescharacteristic
8C24×Dic43C2211yescharacteristic
9C23×C4×D43C411yescharacteristic, complemented
10C2×(C22⋊D43)⋊C4—22no—
11C2×(C22⋊D43)⋊C4—22no—
12C2×(C22⋊D43)⋊C4—24no—
13C2×(C22⋊D43)⋊C4C414yescomplemented
14C2×(C22⋊D43)⋊C4C2214yes—
15C22×Dic43⋊C4—22no—
16C22×Dic43⋊C4C411yescharacteristic, complemented
17C22×C22⋊Dic43C2212yes—
18C22×(C2×D43)⋊C4C411yescharacteristic, complemented
19C22×C4×Dic43C411yescharacteristic, complemented
20C2×#13063239—28no—
21C2×#13063239C2218yes—
22#14582757—24no—
23#14582757C2218yescomplemented
24C2×C43⋊#95—22no—
25#14582666C2214yescomplemented
26C22×C22⋊C4×C43C2212yes—
27C22×C22⋊C4×C43C2211yescharacteristic
28C43×#342C2214yescomplemented
29C24×D43C2×C411yescharacteristic
30C22×C22⋊D43—22no—
31C22×C22⋊D43—22no—
32C22×C22⋊D43—24no—
33C22×C22⋊D43C2×C412yes—
34C22×C22⋊D43D414yes—
35C22×C22⋊D43Q814yes—
36C22×C22⋊D43C2312yes—
37C23×Dic43—22no—
38C23×Dic43—44no—
39C23×Dic43C2×C411yescharacteristic
40C23×Dic43C2×C411yescharacteristic
41C23×Dic43C2×C411yescharacteristic
42C23×Dic43C2×C412yes—
43C23×Dic43D412yes—
44C23×Dic43D412yes—
45C23×Dic43D414yes—
46C23×Dic43C2312yes—
47C22×C4×D43—22no—
48C22×C4×D43—21no—
49C22×C4×D43—21no—
50C22×C4×D43—44no—
51C22×C4×D43C2×C414yescomplemented
52(C22⋊D43)⋊C4—28no—
53(C22⋊D43)⋊C4—28no—
54(C22⋊D43)⋊C4—28no—
55(C22⋊D43)⋊C4—28no—
56C2×Dic43⋊C4—22no—
57C2×Dic43⋊C4—22no—
58C2×Dic43⋊C4—28no—
59C2×Dic43⋊C4—48no—
60C2×Dic43⋊C4C2×C414yescomplemented
61C2×C22⋊Dic43—24no—
62C2×C22⋊Dic43—24no—
63C2×C22⋊Dic43—22no—
64C2×C22⋊Dic43C2314yes—
65C2×(C2×D43)⋊C4—22no—
66C2×(C2×D43)⋊C4—22no—
67C2×(C2×D43)⋊C4C2×C414yescomplemented
68C2×C4×Dic43—22no—
69C2×C4×Dic43—21no—
70C2×C4×Dic43—21no—
71C2×C4×Dic43C2×C414yescomplemented
72#13063239—216no—
73C43⋊#95—28no—
74C25×C43C2311yescharacteristic
75C23×C4×C43—22no—
76C23×C4×C43C2×C411yescharacteristic
77C23×C4×C43C2×C411yescharacteristic
78C2×C22⋊C4×C43—22no—
79C2×C22⋊C4×C43—22no—
80C2×C22⋊C4×C43—24no—
81C2×C22⋊C4×C43—24no—
82C2×C22⋊C4×C43—22no—
83C2×C22⋊C4×C43C2×C412yes—
84C2×C22⋊C4×C43C2314yes—
85C2×C22⋊C4×C43C2312yes—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43C22×C411yescharacteristic
89C24×C43C22×C411yescharacteristic
90C24×C43C2×D412yes—
91C24×C43C2×D412yes—
92C24×C43C2×D412yes—
93C24×C43C2×Q812yes—
94C24×C43#4114yes—
95C24×C43C2411yescharacteristic
96C23×D43—21no—
97C23×D43—21no—
98C23×D43—22no—
99C23×D43—42no—
100C23×D43—42no—
101C23×D43C4⋊C414yescomplemented
102C23×D43C22×C412yes—
103C22×C4×C43—21no—
104C22×C4×C43—21no—
105C22×C4×C43—21no—
106C22×C4×C43—21no—
107C22×C4×C43—24no—
108C22×C4×C43—42no—
109C22×C4×C43—42no—
110C22×C4×C43—44no—
111C22×C4×C43—44no—
112C22×C4×C43—44no—
113C22×C4×C43C22×C412yes—
114C22×C4×C43C22×C412yes—
115C2×C22⋊D43—24no—
116C2×C22⋊D43—24no—
117C2×C22⋊D43—28no—
118C2×C22⋊D43—28no—
119C2×C22⋊D43—28no—
120C2×C22⋊D43—28no—
121C2×C22⋊D43—24no—
122C2×C22⋊D43—24no—
123C2×C22⋊D43C4⋊C418yescomplemented
124C2×C22⋊D43C2×D414yes—
125C2×C22⋊D43C2×Q814yes—
126C22×Dic43—28no—
127C22×Dic43—24no—
128C22×Dic43—21no—
129C22×Dic43—21no—
130C22×Dic43—22no—
131C22×Dic43—24no—
132C22×Dic43—42no—
133C22×Dic43—44no—
134C22×Dic43—44no—
135C22×Dic43—44no—
136C22×Dic43—44no—
137C22×Dic43—48no—
138C22×Dic43—44no—
139C22×Dic43—44no—
140C22×Dic43C22⋊C412yes—
141C22×Dic43C22⋊C411yescharacteristic
142C22×Dic43C22⋊C412yes—
143C22×Dic43C22⋊C414yes—
144C22×Dic43C22⋊C412yes—
145C22×Dic43C22⋊C414yes—
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C4⋊C414yescomplemented
148C22×Dic43C22×C412yes—
149C22×Dic43C22×C412yes—
150C22×Dic43C22×C412yes—
151C22×Dic43C2×D414yes—
152C22×Dic43C2×D414yes—
153C2×C4×D43—24no—
154C2×C4×D43—24no—
155C2×C4×D43—48no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43—48no—
159C22⋊C4×C43—24no—
160C22⋊C4×C43—24no—
161C22⋊C4×C43—24no—
162C22⋊C4×C43—24no—
163C22⋊C4×C43—44no—
164C22⋊Dic43—24no—
165C22⋊Dic43—24no—
166C22⋊Dic43—44no—
167(C2×D43)⋊C4—28no—
168Dic43⋊C4—28no—
169Dic43⋊C4—416no—
170C4×Dic43—24no—
171C4×Dic43—24no—
172C23×C43—24no—
173C23×C43—22no—
174C23×C43—24no—
175C23×C43—22no—
176C23×C43—41no—
177C23×C43—42no—
178C23×C43—41no—
179C23×C43—41no—
180C23×C43—44no—
181C23×C43—42no—
182C23×C43—44no—
183C23×C43—48no—
184C23×C43—41no—
185C23×C43C2×C22⋊C412yes—
186C23×C43C2×C22⋊C411yescharacteristic
187C23×C43C2×C22⋊C411yescharacteristic
188C23×C43C2×C4⋊C412yes—
189C23×C43C2×C4⋊C412yes—
190C23×C43#11712yes—
191C23×C43#11712yes—
192C23×C43#12114yes—
193C23×C43#12114yes—
194C23×C43C22⋊Q814yes—
195C23×C43C22⋊Q814yes—
196C23×C43C23×C411yescharacteristic
197C23×C43C22×D412yes—
198C23×C43C22×D411yescharacteristic
199C23×C43C22×Q811yescharacteristic
200C23×C43C2×#4112yes—
201C22×D43—22no—
202C22×D43—22no—
203C22×D43—24no—
204C22×D43—24no—
205C22×D43—42no—
206C22×D43—48no—
207C22×D43—42no—
208C22×D43—42no—
209C22×D43—42no—
210C22×D43—42no—
211C22×D43—48no—
212C22×D43—42no—
213C22×D43C2×C4⋊C414yescomplemented
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—42no—
217C2×C4×C43—42no—
218C2×C4×C43—42no—
219C2×C4×C43—42no—
220C2×C4×C43—42no—
221C2×C4×C43—42no—
222C2×C4×C43—44no—
223C2×C4×C43—44no—
224C2×C4×C43—44no—
225C2×C4×C43—88no—
226C22⋊D43—28no—
227C22⋊D43—28no—
228C22⋊D43—216no—
229C2×Dic43—22no—
230C2×Dic43—22no—
231C2×Dic43—24no—
232C2×Dic43—24no—
233C2×Dic43—22no—
234C2×Dic43—24no—
235C2×Dic43—28no—
236C2×Dic43—24no—
237C2×Dic43—24no—
238C2×Dic43—28no—
239C2×Dic43—44no—
240C2×Dic43—42no—
241C2×Dic43—42no—
242C2×Dic43—44no—
243C2×Dic43—44no—
244C2×Dic43—44no—
245C2×Dic43—44no—
246C2×Dic43—88no—
247C2×Dic43#9914yescomplemented
248C2×Dic43C2×C22⋊C412yes—
249C2×Dic43C2×C22⋊C414yes—
250C2×Dic43C2×C22⋊C412yes—
251C2×Dic43C2×C4⋊C414yescomplemented
252C4×D43—48no—
253C4×D43—48no—
254C2×#1799—431nomaximal, Sylow
255C22×C43—24no—
256C22×C43—24no—
257C22×C43—28no—
258C22×C43—28no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—22no—
262C22×C43—22no—
263C22×C43—21no—
264C22×C43—21no—
265C22×C43—22no—
266C22×C43—22no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—44no—
270C22×C43—44no—
271C22×C43—41no—
272C22×C43—41no—
273C22×C43—42no—
274C22×C43#38012yes—
275C22×C43#38014yes—
276C22×C43#38012yes—
277C22×C43C2×#9912yes—
278C22×C43#41012yes—
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43C22×C4⋊C411yescharacteristic
281C22×C43C2×#11711yescharacteristic
282C22×C43C2×#12112yes—
283C22×C43C2×C22⋊Q812yes—
284C2×D43—24no—
285C2×D43—44no—
286C2×D43—48no—
287C2×D43—48no—
288C2×D43—42no—
289C2×D43—42no—
290C2×D43—44no—
291C4×C43—42no—
292C4×C43—42no—
293C4×C43—84no—
294Dic43—22no—
295Dic43—24no—
296Dic43—24no—
297Dic43—84no—
298Dic43C2×#9914yescomplemented
299C22×C4×D4—431no—
300C22×#99—432no—
301C2×#380—432no—
302#1799—438no—
303C2×#342—431no—
304C2×#342D4311yescharacteristic, complemented
305C2×C43—22no—
306C2×C43—21no—
307C2×C43—21no—
308C2×C43—22no—
309C2×C43—22no—
310C2×C43—24no—
311C2×C43#179914yescomplemented
312C2×C43C2×#38011yescharacteristic
313C2×C43C22×#9911yescharacteristic
314C2×C43C2×#41011yescharacteristic
315D43—44no—
316C23×D4—431no—
317C24×C4—431no—
318C24×C4—431no—
319C2×C4×D4—434no—
320C2×C4×D4—434no—
321C2×C4×D4—862no—
322C2×C4×D4—862no—
323C2×C4×D4—864no—
324C22×C4⋊C4—431no—
325C22×C4⋊C4—862no—
326C22×C22⋊C4—431no—
327C22×C22⋊C4—432no—
328C22×C22⋊C4C2×D4312yes—
329C22×C22⋊C4C2×D4311yescharacteristic
330C22×C42—431no—
331C2×#99—438no—
332C2×#99—868no—
333#380—438no—
334#380—864no—
335C2×#95—862no—
336#342—434no—
337#342C2×D4314yescomplemented
338C43C2×#179911yescharacteristic, complemented, Sylow
339C25—431no—
340C25C22×D4311yescharacteristic
341C22×D4—432no—
342C22×D4—434no—
343C22×D4—434no—
344C22×D4—432no—
345C22×D4—864no—
346C22×D4—862no—
347C22×D4—862no—
348C23×C4—22no—
349C23×C4—431no—
350C23×C4—431no—
351C23×C4—432no—
352C23×C4—431no—
353C23×C4—432no—
354C23×C4—432no—
355C23×C4—434no—
356C23×C4—432no—
357C23×C4—434no—
358C23×C4—862no—
359C23×C4—861no—
360C23×C4—861no—
361C23×C4—862no—
362C23×C4—1724no—
363C23×C4—1724no—
364C23×C4C4×D4311yescharacteristic
365C23×C4C4×D4311yescharacteristic
366C4×D4—868no—
367C4×D4—868no—
368C4×D4—868no—
369C4×D4—868no—
370C2×C4⋊C4—434no—
371C2×C4⋊C4—862no—
372C2×C4⋊C4—862no—
373C2×C4⋊C4—868no—
374C2×C4⋊C4—1728no—
375C2×C22⋊C4—22no—
376C2×C22⋊C4—22no—
377C2×C22⋊C4—24no—
378C2×C22⋊C4—24no—
379C2×C22⋊C4—22no—
380C2×C22⋊C4—434no—
381C2×C22⋊C4—434no—
382C2×C22⋊C4—862no—
383C2×C22⋊C4—862no—
384C2×C22⋊C4—864no—
385C2×C22⋊C4—864no—
386C2×C22⋊C4—862no—
387C2×C22⋊C4C4×D4312yes—
388C2×C22⋊C4C22×D4314yes—
389C2×C22⋊C4C22×D4312yes—
390C2×C42—434no—
391C2×C42—862no—
392C2×C42—861no—
393C2×C42—861no—
394#99—8616no—
395#95—868no—
396C24—42no—
397C24—42no—
398C24—434no—
399C24—432no—
400C24—861no—
401C24—861no—
402C24—862no—
403C24—1722no—
404C24—1722no—
405C24C2×C4×D4311yescharacteristic
406C24C2×C4×D4311yescharacteristic
407C24#1062189814yes—
408C24D4×D4312yes—
409C24D4×D4312yes—
410C24D4×D4312yes—
411C24Q8×D4312yes—
412C24C23×D4311yescharacteristic
413C2×D4—438no—
414C2×D4—434no—
415C2×D4—434no—
416C2×D4—864no—
417C2×D4—864no—
418C2×D4—868no—
419C2×D4—868no—
420C2×D4—868no—
421C2×D4—868no—
422C2×D4—864no—
423C2×D4—864no—
424C22×C4—21no—
425C22×C4—21no—
426C22×C4—21no—
427C22×C4—21no—
428C22×C4—24no—
429C22×C4—42no—
430C22×C4—42no—
431C22×C4—44no—
432C22×C4—44no—
433C22×C4—44no—
434C22×C4—431no—
435C22×C4—432no—
436C22×C4—434no—
437C22×C4—431no—
438C22×C4—432no—
439C22×C4—434no—
440C22×C4—432no—
441C22×C4—432no—
442C22×C4—434no—
443C22×C4—432no—
444C22×C4—434no—
445C22×C4—432no—
446C22×C4—434no—
447C22×C4—864no—
448C22×C4—864no—
449C22×C4—868no—
450C22×C4—864no—
451C22×C4—861no—
452C22×C4—861no—
453C22×C4—862no—
454C22×C4—864no—
455C22×C4—1724no—
456C22×C4—1728no—
457C22×C4—1724no—
458C22×C4—1728no—
459C22×C4—1724no—
460C22×C4—1728no—
461C22×C4—1724no—
462C22×C4—1724no—
463C22×C4—1722no—
464C22×C4—1724no—
465C22×C4—1724no—
466C22×C4—1724no—
467C22×C4C2×C4×D4312yes—
468C22×C4C2×C4×D4312yes—
469C4⋊C4—868no—
470C4⋊C4—17216no—
471C22⋊C4—24no—
472C22⋊C4—24no—
473C22⋊C4—24no—
474C22⋊C4—24no—
475C22⋊C4—44no—
476C22⋊C4—868no—
477C22⋊C4—864no—
478C22⋊C4—864no—
479C22⋊C4—1724no—
480C42—864no—
481C42—864no—
482C23—24no—
483C23—22no—
484C23—24no—
485C23—22no—
486C23—41no—
487C23—42no—
488C23—41no—
489C23—41no—
490C23—48no—
491C23—44no—
492C23—42no—
493C23—44no—
494C23—41no—
495C23—434no—
496C23—862no—
497C23—862no—
498C23—864no—
499C23—864no—
500C23—1722no—
501C23—1728no—
502C23—1722no—
503C23—1722no—
504C23—1728no—
505C23—1722no—
506C23—1722no—
507C23—1722no—
508C23C22⋊C4×D4312yes—
509C23C22⋊C4×D4311yescharacteristic
510C23C22⋊C4×D4311yescharacteristic
511C23C4⋊C4×D4312yes—
512C23C4⋊C4×D4312yes—
513C23#1306328212yes—
514C23#1306328212yes—
515C23#1306329814yes—
516C23#1306329814yes—
517C23#1306330314yes—
518C23#1306330314yes—
519C23C22×C4×D4311yescharacteristic
520C23C2×D4×D4312yes—
521C23C2×D4×D4311yescharacteristic
522C23C2×Q8×D4311yescharacteristic
523C23C2×#1062189812yes—
524D4—868no—
525D4—868no—
526D4—8616no—
527C2×C4—22no—
528C2×C4—22no—
529C2×C4—42no—
530C2×C4—42no—
531C2×C4—42no—
532C2×C4—42no—
533C2×C4—42no—
534C2×C4—42no—
535C2×C4—44no—
536C2×C4—44no—
537C2×C4—44no—
538C2×C4—88no—
539C2×C4—432no—
540C2×C4—434no—
541C2×C4—432no—
542C2×C4—434no—
543C2×C4—434no—
544C2×C4—868no—
545C2×C4—864no—
546C2×C4—864no—
547C2×C4—868no—
548C2×C4—862no—
549C2×C4—862no—
550C2×C4—862no—
551C2×C4—864no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—3448no—
555C2×C4—1728no—
556C2×C4—1728no—
557C2×C4—1724no—
558C2×C4—1724no—
559C2×C4—1722no—
560C2×C4—1722no—
561C2×C4—1724no—
562C2×C4—1724no—
563C2×C4—1724no—
564C22—28no—
565C22—24no—
566C22—24no—
567C22—28no—
568C22—22no—
569C22—21no—
570C22—21no—
571C22—22no—
572C22—22no—
573C22—21no—
574C22—21no—
575C22—22no—
576C22—42no—
577C22—42no—
578C22—44no—
579C22—44no—
580C22—41no—
581C22—41no—
582C22—42no—
583C22—864no—
584C22—1724no—
585C22—1724no—
586C22—1728no—
587C22—1728no—
588C22—1722no—
589C22—1722no—
590C22#1458275812yes—
591C22#1458275814yes—
592C22#1458275812yes—
593C22#99×D4312yes—
594C22#1458287112yes—
595C22C2×C22⋊C4×D4311yescharacteristic
596C22C2×C4⋊C4×D4311yescharacteristic
597C22C2×#1306328211yescharacteristic
598C22C2×#1306329812yes—
599C22C2×#1306330312yes—
600C4—42no—
601C4—42no—
602C4—84no—
603C4—434no—
604C4—862no—
605C4—864no—
606C4—864no—
607C4—3444no—
608C2—22no—
609C2—21no—
610C2—21no—
611C2—22no—
612C2—22no—
613C2—24no—
614C2—1724no—
615C2#1913458214yesdirect product factor
616C2C2×#1458275811yescharacteristic
617C2C2×#99×D4311yescharacteristic
618C2C2×#1458287111yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC24C23×D43
FittingC2×C43×#342C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C22
cosocleC24×C43C24
hypercenterC2×#342D43
hypocenterC43C2×#1799
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C25 ◁ C2×#342

Complements

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

NH ≅ G/Ntype
3. C2×#14582757C2semidirect
4. #19134582C2direct (N × H)
5. C2×#14582666C2semidirect
6. C2×C43×#342C2semidirect
9. C23×C4×D43C4semidirect
13. C2×(C22⋊D43)⋊C4C4semidirect
16. C22×Dic43⋊C4C4semidirect
18. C22×(C2×D43)⋊C4C4semidirect
19. C22×C4×Dic43C4semidirect
23. #14582757C22semidirect
25. #14582666C22semidirect
28. C43×#342C22semidirect
51. C22×C4×D43C2×C4semidirect
60. C2×Dic43⋊C4C2×C4semidirect
67. C2×(C2×D43)⋊C4C2×C4semidirect
71. C2×C4×Dic43C2×C4semidirect
101. C23×D43C4⋊C4semidirect
123. C2×C22⋊D43C4⋊C4semidirect
147. C22×Dic43C4⋊C4semidirect
213. C22×D43C2×C4⋊C4semidirect
247. C2×Dic43#99semidirect
251. C2×Dic43C2×C4⋊C4semidirect
298. Dic43C2×#99semidirect
304. C2×#342D43semidirect
311. C2×C43#1799semidirect
337. #342C2×D43semidirect
338. C43C2×#1799semidirect
615. C2#19134582direct (N × H)

Maximal subgroups

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

subgroupindex
C22×(C22⋊D43)⋊C42
C22×#130632392
C2×#145827572
#191345822
C2×#145826662
C2×C43×#3422
C2×#179943