Finite Group Databasebeta

← C2×#19132931 #25062452

Subgroups — C2×#19132931 #25062452

Order 11008.

1738 conjugacy classes of subgroups.

The subgroup lattice has 640 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×C4×C22⋊D43C211yesmaximal, characteristic
2C2×#14582863C211yesmaximal, characteristic, complemented
3#19132931C218yesmaximal, direct product factor
4C2×#14582624C212yesmaximal, complemented
5C2×#14582622C212yesmaximal, complemented
6C2×C43×#407C211yesmaximal, characteristic, complemented
7C23×C22⋊D43C411yescharacteristic
8C23×C4×D43C411yescharacteristic
9C22×#10621877—21no—
10C2×C4×C22⋊D43—21no—
11C2×C4×C22⋊D43—21no—
12C2×C4×C22⋊D43—22no—
13C2×C4×C22⋊D43—21no—
14C2×C4×C22⋊D43—21no—
15C2×C4×C22⋊D43—22no—
16C2×C4×C22⋊D43C414yes—
17C2×C4×C22⋊D43C2214yes—
18C22×Dic43⋊C4C2211yescharacteristic
19C22×C22⋊Dic43C411yescharacteristic
20C22×(C2×D43)⋊C4C2211yescharacteristic
21C22×C4×Dic43C411yescharacteristic
22#14582863—22no—
23#14582863C2214yescomplemented
24C2×C22⋊(C43⋊C8)—21no—
25C2×C22⋊(C43⋊C8)C2212yes—
26#14582624C2218yescomplemented
27#14582622C2218yescomplemented
28C24×C4×C43C2211yescharacteristic
29C22×M16×C43—21no—
30C43×#407—22no—
31C43×#407C2214yescomplemented
32C2×C22⋊C8×C43—21no—
33C2×C22⋊C8×C43C2212yes—
34C24×D43C2×C411yescharacteristic
35C22×C22⋊D43—21no—
36C22×C22⋊D43—21no—
37C22×C22⋊D43—22no—
38C22×C22⋊D43—24no—
39C22×C22⋊D43—24no—
40C22×C22⋊D43C2×C414yes—
41C23×Dic43C2×C411yescharacteristic
42C23×Dic43C2×C411yescharacteristic
43C23×Dic43C2×C411yescharacteristic
44C22×C4×D43—22no—
45C22×C4×D43—21no—
46C22×C4×D43—21no—
47C22×C4×D43—44no—
48C22×C4×D43C2×C414yes—
49C2×#10621877—24no—
50C2×#10621877—44no—
51C22×C43⋊C8—22no—
52C4×C22⋊D43—24no—
53C4×C22⋊D43—24no—
54C4×C22⋊D43—24no—
55C4×C22⋊D43—24no—
56C4×C22⋊D43—24no—
57C4×C22⋊D43—24no—
58C4×C22⋊D43—24no—
59C4×C22⋊D43—24no—
60C2×Dic43⋊C4—21no—
61C2×Dic43⋊C4—21no—
62C2×Dic43⋊C4—21no—
63C2×Dic43⋊C4—21no—
64C2×Dic43⋊C4C2×C412yes—
65C2×Dic43⋊C4C2312yes—
66C2×C22⋊Dic43—21no—
67C2×C22⋊Dic43—21no—
68C2×C22⋊Dic43—22no—
69C2×C22⋊Dic43C2×C414yes—
70C2×(C2×D43)⋊C4—21no—
71C2×(C2×D43)⋊C4—21no—
72C2×(C2×D43)⋊C4—21no—
73C2×(C2×D43)⋊C4—21no—
74C2×(C2×D43)⋊C4C2×C412yes—
75C2×(C2×D43)⋊C4C2312yes—
76C2×C4×Dic43—22no—
77C2×C4×Dic43—21no—
78C2×C4×Dic43—21no—
79C2×C4×Dic43C2×C414yes—
80C22⋊(C43⋊C8)—24no—
81C22⋊(C43⋊C8)—22no—
82C22⋊(C43⋊C8)C2314yes—
83C25×C43C2×C411yescharacteristic
84C23×C4×C43—44no—
85C23×C4×C43C2×C411yescharacteristic
86C23×C4×C43C2×C412yes—
87C23×C4×C43D411yescharacteristic
88C23×C4×C43D411yescharacteristic
89C23×C4×C43D412yes—
90C23×C4×C43D411yescharacteristic
91C23×C4×C43D411yescharacteristic
92C23×C4×C43D412yes—
93C23×C4×C43C2311yescharacteristic
94C23×C4×C43C2312yes—
95C2×M16×C43—24no—
96C2×M16×C43—44no—
97C22×C8×C43—22no—
98C22⋊C8×C43—24no—
99C22⋊C8×C43—22no—
100C22⋊C8×C43C2314yes—
101C24×C43—22no—
102C24×C43—22no—
103C24×C43—42no—
104C24×C43—42no—
105C24×C43C22⋊C411yescharacteristic
106C24×C43C22⋊C411yescharacteristic
107C24×C43C22⋊C412yes—
108C24×C43C22×C411yescharacteristic
109C24×C43C22×C412yes—
110C23×D43—21no—
111C23×D43—21no—
112C23×D43—22no—
113C23×D43—42no—
114C23×D43—42no—
115C23×D43M1614yescomplemented
116C23×D43C22×C412yes—
117C22×C4×C43—24no—
118C22×C4×C43—24no—
119C22×C4×C43—24no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43—42no—
123C22×C4×C43—44no—
124C22×C4×C43—44no—
125C22×C4×C43—44no—
126C22×C4×C43—44no—
127C22×C4×C43C22⋊C412yes—
128C22×C4×C43C22⋊C411yescharacteristic
129C22×C4×C43C22⋊C412yes—
130C22×C4×C43C22⋊C412yes—
131C22×C4×C43C22⋊C412yes—
132C22×C4×C43C22⋊C412yes—
133C22×C4×C43C22⋊C411yescharacteristic
134C22×C4×C43C22×C412yes—
135C22×C4×C43C22×C411yescharacteristic
136C22×C4×C43C2×D411yescharacteristic
137C22×C4×C43C2×D412yes—
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D412yes—
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D411yescharacteristic
143C22×C4×C43C2×D412yes—
144C22×C4×C43C2411yescharacteristic
145C2×C22⋊D43—216no—
146C2×C22⋊D43—28no—
147C2×C22⋊D43—28no—
148C2×C22⋊D43—28no—
149C2×C22⋊D43—24no—
150C2×C22⋊D43—24no—
151C2×C22⋊D43—28no—
152C22×Dic43—21no—
153C22×Dic43—21no—
154C22×Dic43—21no—
155C22×Dic43—21no—
156C22×Dic43—21no—
157C22×Dic43—21no—
158C22×Dic43—22no—
159C22×Dic43—42no—
160C22×Dic43—42no—
161C22×Dic43M1614yescomplemented
162C22×Dic43C22×C412yes—
163C22×Dic43C22×C412yes—
164C22×Dic43C22×C412yes—
165C2×C4×D43—24no—
166C2×C4×D43—24no—
167C2×C4×D43—48no—
168C2×C4×D43—44no—
169C2×C4×D43—44no—
170C2×C4×D43—48no—
171M16×C43—48no—
172C2×C8×C43—24no—
173C2×C8×C43—44no—
174C22⋊Dic43—24no—
175C22⋊Dic43—24no—
176(C2×D43)⋊C4—22no—
177(C2×D43)⋊C4—22no—
178(C2×D43)⋊C4—22no—
179(C2×D43)⋊C4—22no—
180Dic43⋊C4—22no—
181Dic43⋊C4—22no—
182Dic43⋊C4—22no—
183Dic43⋊C4—22no—
184C4×Dic43—24no—
185C4×Dic43—24no—
186#10621877—48no—
187C2×C43⋊C8—24no—
188C2×C43⋊C8—44no—
189C23×C43—22no—
190C23×C43—22no—
191C23×C43—22no—
192C23×C43—22no—
193C23×C43—24no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43—22no—
199C23×C43—22no—
200C23×C43—42no—
201C23×C43—42no—
202C23×C43—42no—
203C23×C43—42no—
204C23×C43—48no—
205C23×C43—48no—
206C23×C43C2×C22⋊C412yes—
207C23×C43C2×C22⋊C412yes—
208C23×C43C2×C22⋊C411yescharacteristic
209C23×C43C2×C22⋊C411yescharacteristic
210C23×C43C2×M1612yes—
211C23×C43C2×M1612yes—
212C23×C43C23×C411yescharacteristic
213C22×D43—22no—
214C22×D43—22no—
215C22×D43—24no—
216C22×D43—24no—
217C22×D43—42no—
218C22×D43—42no—
219C22×D43—48no—
220C22×D43—42no—
221C22×D43—42no—
222C22×D43—42no—
223C22×D43—48no—
224C22×D43—42no—
225C22×D43C2×M1614yescomplemented
226C2×C4×C43—22no—
227C2×C4×C43—22no—
228C2×C4×C43—22no—
229C2×C4×C43—24no—
230C2×C4×C43—24no—
231C2×C4×C43—24no—
232C2×C4×C43—24no—
233C2×C4×C43—24no—
234C2×C4×C43—24no—
235C2×C4×C43—42no—
236C2×C4×C43—42no—
237C2×C4×C43—41no—
238C2×C4×C43—42no—
239C2×C4×C43—41no—
240C2×C4×C43—42no—
241C2×C4×C43—41no—
242C2×C4×C43—41no—
243C2×C4×C43#9914yes—
244C2×C4×C43C2×C22⋊C412yes—
245C2×C4×C43C2×C22⋊C411yescharacteristic
246C2×C4×C43C2×C22⋊C411yescharacteristic
247C2×C4×C43C2×C22⋊C412yes—
248C2×C4×C43C22×D411yescharacteristic
249C2×C4×C43C22×D411yescharacteristic
250C22⋊D43—216no—
251C22⋊D43—216no—
252C2×Dic43—22no—
253C2×Dic43—22no—
254C2×Dic43—24no—
255C2×Dic43—24no—
256C2×Dic43—22no—
257C2×Dic43—22no—
258C2×Dic43—42no—
259C2×Dic43—42no—
260C2×Dic43—42no—
261C2×Dic43—42no—
262C2×Dic43—42no—
263C2×Dic43—42no—
264C2×Dic43C2×M1614yescomplemented
265C4×D43—48no—
266C4×D43—48no—
267C8×C43—44no—
268C43⋊C8—44no—
269C2×#1465—431nomaximal, Sylow
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—21no—
274C22×C43—24no—
275C22×C43—24no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43—22no—
279C22×C43—22no—
280C22×C43—22no—
281C22×C43—22no—
282C22×C43—44no—
283C22×C43—44no—
284C22×C43—48no—
285C22×C43—44no—
286C22×C43—44no—
287C22×C43#40712yes—
288C22×C43#40712yes—
289C22×C43C2×#9912yes—
290C22×C43#41312yes—
291C22×C43C22×C22⋊C411yescharacteristic
292C22×C43C22×M1611yescharacteristic
293C22×C43C22×M1611yescharacteristic
294C2×D43—24no—
295C2×D43—44no—
296C2×D43—48no—
297C2×D43—42no—
298C2×D43—42no—
299C2×D43—48no—
300C2×D43—44no—
301C4×C43—21no—
302C4×C43—21no—
303C4×C43—22no—
304C4×C43—21no—
305C4×C43—21no—
306C4×C43C2×#9914yes—
307Dic43—24no—
308Dic43—42no—
309Dic43—42no—
310C22×C4×D4—431no—
311C2×#407—431no—
312C2×#407D4311yescharacteristic, complemented
313#1465—438no—
314C2×#324—432no—
315C2×#323—432no—
316C2×C43—21no—
317C2×C43—21no—
318C2×C43—22no—
319C2×C43—42no—
320C2×C43—42no—
321C2×C43#146514yescomplemented
322C2×C43C2×#40711yescharacteristic
323C2×C43C22×#9911yescharacteristic
324C2×C43C2×#41311yescharacteristic
325D43—44no—
326C23×D4—431no—
327C24×C4—431no—
328C24×C4C2×D4311yescharacteristic
329C22×M16—21no—
330C22×M16—861no—
331C2×C4×D4—434no—
332C2×C4×D4—434no—
333C2×C4×D4—861no—
334C2×C4×D4—861no—
335C2×C4×D4—862no—
336C2×C4×D4—861no—
337C2×C4×D4—861no—
338C2×C4×D4—862no—
339C22×C4⋊C4—431no—
340C22×C22⋊C4—431no—
341C22×C22⋊C4—431no—
342C22×C42—431no—
343#407—22no—
344#407—434no—
345#407—862no—
346#407C2×D4314yescomplemented
347C2×C22⋊C8—21no—
348C2×C22⋊C8—432no—
349C2×C22⋊C8—861no—
350C2×C22⋊C8C2×D4312yes—
351#324—438no—
352#323—438no—
353C43C2×#146511yescharacteristic, complemented, Sylow
354C25—431no—
355C25C4×D4311yescharacteristic
356C22×D4—434no—
357C22×D4—864no—
358C22×D4—864no—
359C22×D4—862no—
360C22×D4—861no—
361C22×D4—861no—
362C23×C4—44no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—434no—
367C23×C4—862no—
368C23×C4—861no—
369C23×C4—861no—
370C23×C4—1724no—
371C23×C4C4×D4311yescharacteristic
372C23×C4C4×D4312yes—
373C23×C4D17211yescharacteristic
374C23×C4D17211yescharacteristic
375C23×C4D17212yes—
376C23×C4C22⋊D4311yescharacteristic
377C23×C4C22⋊D4311yescharacteristic
378C23×C4C22⋊D4312yes—
379C23×C4C22×D4311yescharacteristic
380C23×C4C22×D4312yes—
381C2×M16—24no—
382C2×M16—44no—
383C2×M16—864no—
384C2×M16—1724no—
385C22×C8—22no—
386C22×C8—862no—
387C4×D4—864no—
388C4×D4—864no—
389C4×D4—864no—
390C4×D4—864no—
391C4×D4—864no—
392C4×D4—864no—
393C4×D4—864no—
394C4×D4—864no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—432no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C22⋊C4—434no—
402C2×C22⋊C4—432no—
403C2×C22⋊C4—432no—
404C2×C22⋊C4—862no—
405C2×C22⋊C4—861no—
406C2×C22⋊C4—861no—
407C2×C22⋊C4—861no—
408C2×C22⋊C4—861no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C42—434no—
412C2×C42—862no—
413C2×C42—861no—
414C2×C42—861no—
415C22⋊C8—24no—
416C22⋊C8—22no—
417C22⋊C8—434no—
418C22⋊C8—862no—
419C22⋊C8—864no—
420C22⋊C8C22×D4314yes—
421C24—22no—
422C24—22no—
423C24—42no—
424C24—42no—
425C24—434no—
426C24—432no—
427C24—861no—
428C24—861no—
429C24—862no—
430C24—1722no—
431C24—1722no—
432C24(C2×D43)⋊C411yescharacteristic
433C24(C2×D43)⋊C411yescharacteristic
434C24(C2×D43)⋊C412yes—
435C24C2×C4×D4311yescharacteristic
436C24C2×C4×D4312yes—
437C2×D4—868no—
438C2×D4—868no—
439C2×D4—8616no—
440C2×D4—868no—
441C2×D4—868no—
442C2×D4—864no—
443C2×D4—864no—
444C22×C4—24no—
445C22×C4—24no—
446C22×C4—24no—
447C22×C4—44no—
448C22×C4—44no—
449C22×C4—44no—
450C22×C4—44no—
451C22×C4—42no—
452C22×C4—42no—
453C22×C4—42no—
454C22×C4—434no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—861no—
459C22×C4—861no—
460C22×C4—862no—
461C22×C4—861no—
462C22×C4—861no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—864no—
466C22×C4—864no—
467C22×C4—1724no—
468C22×C4—1728no—
469C22×C4—1728no—
470C22×C4—1724no—
471C22×C4—1722no—
472C22×C4—1722no—
473C22×C4(C2×D43)⋊C412yes—
474C22×C4(C2×D43)⋊C412yes—
475C22×C4(C2×D43)⋊C412yes—
476C22×C4(C2×D43)⋊C411yescharacteristic
477C22×C4(C2×D43)⋊C412yes—
478C22×C4(C2×D43)⋊C412yes—
479C22×C4(C2×D43)⋊C411yescharacteristic
480C22×C4C2×C4×D4312yes—
481C22×C4C2×C4×D4311yescharacteristic
482C22×C4C2×D17212yes—
483C22×C4C2×D17211yescharacteristic
484C22×C4C2×D17211yescharacteristic
485C22×C4C2×D17212yes—
486C22×C4C2×C22⋊D4312yes—
487C22×C4C2×C22⋊D4311yescharacteristic
488C22×C4C2×C22⋊D4311yescharacteristic
489C22×C4C2×C22⋊D4312yes—
490C22×C4C23×D4311yescharacteristic
491M16—48no—
492M16—1728no—
493C2×C8—24no—
494C2×C8—44no—
495C2×C8—864no—
496C2×C8—1724no—
497C4⋊C4—862no—
498C4⋊C4—862no—
499C4⋊C4—862no—
500C4⋊C4—862no—
501C22⋊C4—864no—
502C22⋊C4—864no—
503C22⋊C4—862no—
504C22⋊C4—862no—
505C22⋊C4—862no—
506C22⋊C4—862no—
507C42—864no—
508C42—864no—
509C23—22no—
510C23—22no—
511C23—24no—
512C23—22no—
513C23—22no—
514C23—22no—
515C23—22no—
516C23—22no—
517C23—22no—
518C23—22no—
519C23—22no—
520C23—42no—
521C23—42no—
522C23—42no—
523C23—42no—
524C23—48no—
525C23—48no—
526C23—434no—
527C23—862no—
528C23—864no—
529C23—864no—
530C23—862no—
531C23—1722no—
532C23—1728no—
533C23—1722no—
534C23—1722no—
535C23—1728no—
536C23—1722no—
537C23—1722no—
538C23—1722no—
539C23C2×(C2×D43)⋊C412yes—
540C23C2×(C2×D43)⋊C412yes—
541C23C2×(C2×D43)⋊C411yescharacteristic
542C23C2×(C2×D43)⋊C411yescharacteristic
543C23M16×D4312yes—
544C23M16×D4312yes—
545C23C22×C4×D4311yescharacteristic
546D4—8616no—
547D4—8616no—
548C2×C4—22no—
549C2×C4—22no—
550C2×C4—22no—
551C2×C4—24no—
552C2×C4—24no—
553C2×C4—24no—
554C2×C4—24no—
555C2×C4—24no—
556C2×C4—24no—
557C2×C4—42no—
558C2×C4—42no—
559C2×C4—41no—
560C2×C4—42no—
561C2×C4—41no—
562C2×C4—42no—
563C2×C4—41no—
564C2×C4—41no—
565C2×C4—434no—
566C2×C4—862no—
567C2×C4—864no—
568C2×C4—864no—
569C2×C4—862no—
570C2×C4—862no—
571C2×C4—862no—
572C2×C4—1728no—
573C2×C4—1722no—
574C2×C4—1722no—
575C2×C4—1722no—
576C2×C4—1722no—
577C2×C4—1728no—
578C2×C4—1722no—
579C2×C4—1722no—
580C2×C4#1306323914yes—
581C2×C4C2×(C2×D43)⋊C412yes—
582C2×C4C2×(C2×D43)⋊C411yescharacteristic
583C2×C4C2×(C2×D43)⋊C411yescharacteristic
584C2×C4C2×(C2×D43)⋊C412yes—
585C2×C4C22×C22⋊D4311yescharacteristic
586C2×C4C22×D17211yescharacteristic
587C8—44no—
588C8—1724no—
589C22—24no—
590C22—24no—
591C22—21no—
592C22—21no—
593C22—21no—
594C22—21no—
595C22—22no—
596C22—22no—
597C22—22no—
598C22—22no—
599C22—22no—
600C22—22no—
601C22—48no—
602C22—44no—
603C22—44no—
604C22—44no—
605C22—44no—
606C22—864no—
607C22—1724no—
608C22—1728no—
609C22—1724no—
610C22—1728no—
611C22—1722no—
612C22—1722no—
613C22#1458286212yes—
614C22#1458286212yes—
615C22C2×#1306323912yes—
616C22#1458288112yes—
617C22C22×(C2×D43)⋊C411yescharacteristic
618C22C2×M16×D4311yescharacteristic
619C22C2×M16×D4311yescharacteristic
620C4—21no—
621C4—21no—
622C4—22no—
623C4—21no—
624C4—21no—
625C4—864no—
626C4—1722no—
627C4—1722no—
628C4C2×#1306323914yes—
629C2—22no—
630C2—21no—
631C2—21no—
632C2—42no—
633C2—42no—
634C2—1724no—
635C2#1913293114yesdirect product factor
636C2C2×#1458286211yescharacteristic
637C2C22×#1306323911yescharacteristic
638C2C2×#1458288111yescharacteristic
subgroupG/H
centerC23C2×(C2×D43)⋊C4
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#407C2
socleC23×C43C2×C22⋊C4
prime radicalC23×C22⋊D43C4
cosocleC22×C4×C43C24
hypercenterC2×#407D43
hypocenterC43C2×#1465
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C24×C4 ◁ C2×#407

Complements

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

NH ≅ G/Ntype
2. C2×#14582863C2semidirect
3. #19132931C2direct (N × H)
4. C2×#14582624C2semidirect
5. C2×#14582622C2semidirect
6. C2×C43×#407C2semidirect
23. #14582863C22semidirect
26. #14582624C22semidirect
27. #14582622C22semidirect
31. C43×#407C22semidirect
115. C23×D43M16semidirect
161. C22×Dic43M16semidirect
225. C22×D43C2×M16semidirect
264. C2×Dic43C2×M16semidirect
312. C2×#407D43semidirect
321. C2×C43#1465semidirect
346. #407C2×D43semidirect
353. C43C2×#1465semidirect
635. C2#19132931direct (N × H)

Maximal subgroups

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

subgroupindex
C22×C4×C22⋊D432
C2×#145828632
#191329312
C2×#145826242
C2×#145826222
C2×C43×#4072
C2×#146543