Finite Group Databasebeta

← C2×#19132957 #25062566

Subgroups — C2×#19132957 #25062566

Order 11008.

1426 conjugacy classes of subgroups.

The subgroup lattice has 624 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063303C211yesmaximal, characteristic
2C2×#14582861C211yesmaximal, characteristic
3C2×C22⋊C8×D43C211yesmaximal, characteristic
4#19132957C218yesmaximal, direct product factor
5C2×#14582625C211yesmaximal, characteristic, complemented
6C2×#14582624C211yesmaximal, characteristic, complemented
7C2×#14582624C211yesmaximal, characteristic, complemented
8C2×C43×#324C211yesmaximal, characteristic, complemented
9C23×Dic86C411yescharacteristic
10C23×C4×D43C2211yescharacteristic
11C22×#10621872—21no—
12C22×C8×D43—21no—
13C2×#13063303—21no—
14C2×#13063303—21no—
15C2×#13063303—22no—
16C2×#13063303—21no—
17C2×#13063303—21no—
18C2×#13063303—22no—
19C2×#13063303C414yes—
20C2×#13063303C2214yes—
21C22×Dic43⋊C4C411yescharacteristic
22C22×Dic43⋊C4C2211yescharacteristic
23C22×(C2×D43)⋊C4C411yescharacteristic
24C22×(C2×D43)⋊C4C411yescharacteristic
25#14582861—22no—
26#14582861C2214yes—
27C2×C22⋊(C43⋊C8)C2211yescharacteristic
28C2×C22⋊(C43⋊C8)C2211yescharacteristic
29C2×(C2×D43)⋊C8—21no—
30C2×(C2×D43)⋊C8—21no—
31C22⋊C8×D43—22no—
32C22⋊C8×D43C2214yes—
33#14582625C2214yescomplemented
34#14582624C2214yescomplemented
35#14582624C2214yescomplemented
36C22×C4⋊C4×C43C2211yescharacteristic
37C2×C22⋊C8×C43C2211yescharacteristic
38C2×C22⋊C8×C43C2211yescharacteristic
39C43×#324C2214yescomplemented
40C24×D43C2×C411yescharacteristic
41C22×Dic86—22no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—44no—
45C22×Dic86C2×C414yes—
46C23×Dic43C2×C411yescharacteristic
47C23×Dic43C2×C411yescharacteristic
48C23×Dic43C2×C411yescharacteristic
49C22×C4×D43—44no—
50C22×C4×D43C2×C412yes—
51C22×C4×D43D411yescharacteristic
52C22×C4×D43D411yescharacteristic
53C22×C4×D43D412yes—
54C22×C4×D43D411yescharacteristic
55C22×C4×D43D411yescharacteristic
56C22×C4×D43D412yes—
57C22×C4×D43C2312yes—
58C2×#10621872—24no—
59C2×#10621872—44no—
60C22×C43⋊C8—21no—
61C22×C43⋊C8—21no—
62C2×C8×D43—24no—
63C2×C8×D43—44no—
64#13063303—24no—
65#13063303—24no—
66#13063303—24no—
67#13063303—24no—
68#13063303—24no—
69#13063303—24no—
70#13063303—24no—
71#13063303—24no—
72C2×Dic43⋊C4—21no—
73C2×Dic43⋊C4—21no—
74C2×Dic43⋊C4—21no—
75C2×Dic43⋊C4—21no—
76C2×Dic43⋊C4—22no—
77C2×Dic43⋊C4—21no—
78C2×Dic43⋊C4—21no—
79C2×Dic43⋊C4C2×C414yes—
80C2×Dic43⋊C4C2×C412yes—
81C2×Dic43⋊C4C2312yes—
82C2×(C2×D43)⋊C4—21no—
83C2×(C2×D43)⋊C4—22no—
84C2×(C2×D43)⋊C4—21no—
85C2×(C2×D43)⋊C4—21no—
86C2×(C2×D43)⋊C4—22no—
87C2×(C2×D43)⋊C4—21no—
88C2×(C2×D43)⋊C4C2×C414yes—
89C2×(C2×D43)⋊C4C2×C414yes—
90C22⋊(C43⋊C8)—21no—
91C22⋊(C43⋊C8)—21no—
92C22⋊(C43⋊C8)C2312yes—
93C22⋊(C43⋊C8)C2312yes—
94(C2×D43)⋊C8—24no—
95(C2×D43)⋊C8—24no—
96C23×C4×C43C2×C411yescharacteristic
97C23×C4×C43C2×C411yescharacteristic
98C23×C4×C43C2311yescharacteristic
99C22×C8×C43—21no—
100C22×C8×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43—21no—
103C2×C4⋊C4×C43—21no—
104C2×C4⋊C4×C43—21no—
105C2×C4⋊C4×C43C2×C412yes—
106C2×C4⋊C4×C43C2312yes—
107C22⋊C8×C43—21no—
108C22⋊C8×C43—21no—
109C22⋊C8×C43C2312yes—
110C22⋊C8×C43C2312yes—
111C24×C43C22×C411yescharacteristic
112C23×D43—22no—
113C23×D43—22no—
114C23×D43—24no—
115C23×D43—42no—
116C23×D43C22⋊C411yescharacteristic
117C23×D43C22⋊C412yes—
118C23×D43C22⋊C411yescharacteristic
119C23×D43C22×C412yes—
120C22×C4×C43—21no—
121C22×C4×C43—21no—
122C22×C4×C43—21no—
123C22×C4×C43—21no—
124C22×C4×C43—22no—
125C22×C4×C43—22no—
126C22×C4×C43—42no—
127C22×C4×C43—42no—
128C22×C4×C43C22×C412yes—
129C22×C4×C43C22×C412yes—
130C22×C4×C43C22×C411yescharacteristic
131C22×C4×C43C2×D411yescharacteristic
132C22×C4×C43C2×D411yescharacteristic
133C22×C4×C43C2×D411yescharacteristic
134C22×C4×C43C2×D411yescharacteristic
135C22×C4×C43C2411yescharacteristic
136C22×Dic43—24no—
137C22×Dic43—21no—
138C22×Dic43—21no—
139C22×Dic43—21no—
140C22×Dic43—21no—
141C22×Dic43—22no—
142C22×Dic43—22no—
143C22×Dic43—42no—
144C22×Dic43C22⋊C412yes—
145C22×Dic43C22⋊C411yescharacteristic
146C22×Dic43C22⋊C411yescharacteristic
147C22×Dic43C22×C412yes—
148C22×Dic43C22×C412yes—
149C22×Dic43C22×C412yes—
150C2×C4×D43—24no—
151C2×C4×D43—24no—
152C2×C4×D43—42no—
153C2×C4×D43—42no—
154C2×C4×D43—44no—
155C2×C4×D43—44no—
156C2×C4×D43—44no—
157C2×C4×D43—44no—
158C2×C4×D43C22⋊C412yes—
159C2×C4×D43C22⋊C412yes—
160C2×C4×D43C22⋊C412yes—
161C2×C4×D43C22⋊C412yes—
162C2×C4×D43C2×D412yes—
163C2×C4×D43C2×D412yes—
164C2×C4×D43C2×D412yes—
165C2×C4×D43C2×D412yes—
166C2×Dic86—24no—
167C2×Dic86—24no—
168C2×Dic86—44no—
169C2×Dic86—48no—
170C2×Dic86—44no—
171C2×Dic86—48no—
172C2×C8×C43—22no—
173C2×C8×C43—22no—
174C2×C8×C43—42no—
175C2×C8×C43—42no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43—22no—
178C4⋊C4×C43—22no—
179C4⋊C4×C43—22no—
180(C2×D43)⋊C4—24no—
181(C2×D43)⋊C4—24no—
182(C2×D43)⋊C4—24no—
183(C2×D43)⋊C4—24no—
184Dic43⋊C4—22no—
185Dic43⋊C4—22no—
186Dic43⋊C4—22no—
187Dic43⋊C4—22no—
188Dic43⋊C4—24no—
189Dic43⋊C4—24no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—42no—
193C2×C43⋊C8—42no—
194#10621872—48no—
195C8×D43—48no—
196C23×C43—22no—
197C23×C43—22no—
198C23×C43C2×C22⋊C411yescharacteristic
199C23×C43C2×C22⋊C411yescharacteristic
200C23×C43#13112yes—
201C23×C43#13112yes—
202C23×C43C23×C411yescharacteristic
203C22×D43—22no—
204C22×D43—22no—
205C22×D43—22no—
206C22×D43—22no—
207C22×D43—24no—
208C22×D43—22no—
209C22×D43—22no—
210C22×D43—22no—
211C22×D43—24no—
212C22×D43—24no—
213C22×D43—42no—
214C22×D43—42no—
215C22×D43—48no—
216C22×D43—48no—
217C22×D43#10114yes—
218C22×D43C2×C22⋊C412yes—
219C22×D43C2×C22⋊C412yes—
220C2×C4×C43—22no—
221C2×C4×C43—22no—
222C2×C4×C43—22no—
223C2×C4×C43—22no—
224C2×C4×C43—22no—
225C2×C4×C43—22no—
226C2×C4×C43—41no—
227C2×C4×C43—41no—
228C2×C4×C43—41no—
229C2×C4×C43—41no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—42no—
233C2×C4×C43—42no—
234C2×C4×C43—42no—
235C2×C4×C43C2×C22⋊C411yescharacteristic
236C2×C4×C43C2×C22⋊C411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×C4×C43C22×D411yescharacteristic
239C2×Dic43—22no—
240C2×Dic43—24no—
241C2×Dic43—24no—
242C2×Dic43—22no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—22no—
246C2×Dic43—42no—
247C2×Dic43—42no—
248C2×Dic43—42no—
249C2×Dic43—42no—
250C2×Dic43—42no—
251C2×Dic43#9914yes—
252C2×Dic43C2×C22⋊C412yes—
253C2×Dic43C2×C22⋊C412yes—
254C4×D43—24no—
255C4×D43—24no—
256C4×D43—24no—
257C4×D43—24no—
258C4×D43—42no—
259C4×D43—42no—
260C4×D43—42no—
261C4×D43—42no—
262Dic86—48no—
263Dic86—48no—
264C8×C43—42no—
265C8×C43—42no—
266C43⋊C8—42no—
267C43⋊C8—42no—
268C2×#1472—431nomaximal, Sylow
269C22×C43—21no—
270C22×C43—21no—
271C22×C43—21no—
272C22×C43—21no—
273C22×C43—24no—
274C22×C43—24no—
275C22×C43#40812yes—
276C22×C43#40812yes—
277C22×C43C2×#9912yes—
278C22×C43C2×#10112yes—
279C22×C43C22×C22⋊C411yescharacteristic
280C22×C43C2×#13111yescharacteristic
281C22×C43C2×#13111yescharacteristic
282C2×D43—22no—
283C2×D43—22no—
284C2×D43—28no—
285C2×D43—22no—
286C2×D43—22no—
287C2×D43—22no—
288C2×D43—44no—
289C2×D43—44no—
290C2×D43—48no—
291C2×D43—44no—
292C2×D43C2×#10114yes—
293C4×C43—21no—
294C4×C43—21no—
295C4×C43—21no—
296C4×C43—21no—
297C4×C43—42no—
298C4×C43—42no—
299Dic43—22no—
300Dic43—42no—
301Dic43—42no—
302Dic43C2×#9914yes—
303C22×C22⋊Q8—431no—
304C2×#407—431no—
305C22×C22⋊C8—431no—
306#1472—438no—
307C2×#324—431no—
308C2×#324—431no—
309C2×#324—431no—
310C2×#324D4311yescharacteristic, complemented
311C2×C43—21no—
312C2×C43—21no—
313C2×C43—22no—
314C2×C43#147214yescomplemented
315C2×C43C2×#40811yescharacteristic
316C2×C43C22×#9911yescharacteristic
317C2×C43C22×#10111yescharacteristic
318D43—24no—
319D43—42no—
320C23×Q8—431no—
321C24×C4—431no—
322C22×M16—861no—
323C23×C8—861no—
324C2×C22⋊Q8—434no—
325C2×C22⋊Q8—434no—
326C2×C22⋊Q8—861no—
327C2×C22⋊Q8—861no—
328C2×C22⋊Q8—862no—
329C2×C22⋊Q8—861no—
330C2×C22⋊Q8—861no—
331C2×C22⋊Q8—862no—
332C22×C4⋊C4—431no—
333C22×C4⋊C4—431no—
334C22×C4⋊C4C2×D4311yescharacteristic
335C22×C22⋊C4—431no—
336C22×C22⋊C4—431no—
337#407—434no—
338#407—862no—
339C2×C22⋊C8—431no—
340C2×C22⋊C8—431no—
341C2×C22⋊C8—434no—
342C2×C22⋊C8—862no—
343C2×C22⋊C8—861no—
344C2×C22⋊C8—861no—
345C2×C22⋊C8C2×D4311yescharacteristic
346C2×C22⋊C8C2×D4311yescharacteristic
347#324—434no—
348#324—434no—
349#324—434no—
350#324C2×D4314yescomplemented
351C43C2×#147211yescharacteristic, complemented, Sylow
352C25—431no—
353C22×Q8—434no—
354C22×Q8—862no—
355C22×Q8—861no—
356C22×Q8—861no—
357C22×Q8—1724no—
358C23×C4—431no—
359C23×C4—431no—
360C23×C4—431no—
361C23×C4—432no—
362C23×C4—432no—
363C23×C4—431no—
364C23×C4—431no—
365C23×C4—432no—
366C23×C4—432no—
367C23×C4—431no—
368C23×C4—431no—
369C23×C4—1724no—
370C23×C4C4×D4311yescharacteristic
371C23×C4C4×D4311yescharacteristic
372C23×C4C22×D4311yescharacteristic
373C2×M16—864no—
374C2×M16—1724no—
375C22×C8—21no—
376C22×C8—21no—
377C22×C8—864no—
378C22×C8—861no—
379C22×C8—861no—
380C22×C8—1724no—
381C22⋊Q8—864no—
382C22⋊Q8—864no—
383C22⋊Q8—864no—
384C22⋊Q8—864no—
385C22⋊Q8—864no—
386C22⋊Q8—864no—
387C22⋊Q8—864no—
388C22⋊Q8—864no—
389C2×C4⋊C4—21no—
390C2×C4⋊C4—21no—
391C2×C4⋊C4—21no—
392C2×C4⋊C4—21no—
393C2×C4⋊C4—434no—
394C2×C4⋊C4—432no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—862no—
397C2×C4⋊C4—861no—
398C2×C4⋊C4—861no—
399C2×C4⋊C4—861no—
400C2×C4⋊C4—861no—
401C2×C4⋊C4—861no—
402C2×C4⋊C4—861no—
403C2×C4⋊C4C4×D4312yes—
404C2×C4⋊C4C22×D4312yes—
405C2×C22⋊C4—434no—
406C2×C22⋊C4—434no—
407C2×C22⋊C4—862no—
408C2×C22⋊C4—862no—
409C2×C22⋊C4—861no—
410C2×C22⋊C4—861no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C22⋊C8—21no—
414C22⋊C8—21no—
415C22⋊C8—432no—
416C22⋊C8—432no—
417C22⋊C8—864no—
418C22⋊C8—864no—
419C22⋊C8—861no—
420C22⋊C8—861no—
421C22⋊C8C22×D4312yes—
422C22⋊C8C22×D4312yes—
423C24—431no—
424C24—431no—
425C24—432no—
426C24—432no—
427C24—864no—
428C24—862no—
429C24—862no—
430C24—1722no—
431C24C2×C4×D4311yescharacteristic
432C2×Q8—864no—
433C2×Q8—864no—
434C2×Q8—1724no—
435C2×Q8—1728no—
436C2×Q8—1728no—
437C2×Q8—1724no—
438C22×C4—21no—
439C22×C4—21no—
440C22×C4—21no—
441C22×C4—21no—
442C22×C4—22no—
443C22×C4—22no—
444C22×C4—42no—
445C22×C4—42no—
446C22×C4—431no—
447C22×C4—432no—
448C22×C4—431no—
449C22×C4—432no—
450C22×C4—432no—
451C22×C4—432no—
452C22×C4—432no—
453C22×C4—432no—
454C22×C4—432no—
455C22×C4—432no—
456C22×C4—432no—
457C22×C4—432no—
458C22×C4—432no—
459C22×C4—432no—
460C22×C4—864no—
461C22×C4—864no—
462C22×C4—864no—
463C22×C4—861no—
464C22×C4—861no—
465C22×C4—861no—
466C22×C4—861no—
467C22×C4—862no—
468C22×C4—862no—
469C22×C4—1722no—
470C22×C4—1722no—
471C22×C4—1724no—
472C22×C4—1724no—
473C22×C4—1724no—
474C22×C4—1724no—
475C22×C4—1722no—
476C22×C4C2×C4×D4312yes—
477C22×C4C2×C4×D4312yes—
478C22×C4C2×C4×D4311yescharacteristic
479C22×C4D4×D4311yescharacteristic
480C22×C4D4×D4311yescharacteristic
481C22×C4D4×D4311yescharacteristic
482C22×C4D4×D4311yescharacteristic
483C22×C4C23×D4311yescharacteristic
484M16—1728no—
485C2×C8—22no—
486C2×C8—22no—
487C2×C8—42no—
488C2×C8—42no—
489C2×C8—862no—
490C2×C8—862no—
491C2×C8—1728no—
492C2×C8—1722no—
493C2×C8—1722no—
494C4⋊C4—22no—
495C4⋊C4—22no—
496C4⋊C4—22no—
497C4⋊C4—22no—
498C4⋊C4—864no—
499C4⋊C4—864no—
500C4⋊C4—862no—
501C4⋊C4—862no—
502C4⋊C4—862no—
503C4⋊C4—862no—
504C22⋊C4—864no—
505C22⋊C4—864no—
506C22⋊C4—864no—
507C22⋊C4—864no—
508C23—22no—
509C23—22no—
510C23—432no—
511C23—434no—
512C23—432no—
513C23—864no—
514C23—864no—
515C23—862no—
516C23—862no—
517C23—864no—
518C23—862no—
519C23—862no—
520C23—862no—
521C23—862no—
522C23—862no—
523C23—1722no—
524C23—1722no—
525C23—1728no—
526C23—1728no—
527C23C22⋊C4×D4311yescharacteristic
528C23C22⋊C4×D4311yescharacteristic
529C23#1306333112yes—
530C23#1306333312yes—
531C23C22×C4×D4311yescharacteristic
532Q8—1728no—
533Q8—1728no—
534C2×C4—22no—
535C2×C4—22no—
536C2×C4—22no—
537C2×C4—22no—
538C2×C4—22no—
539C2×C4—22no—
540C2×C4—41no—
541C2×C4—41no—
542C2×C4—41no—
543C2×C4—41no—
544C2×C4—42no—
545C2×C4—42no—
546C2×C4—42no—
547C2×C4—42no—
548C2×C4—42no—
549C2×C4—432no—
550C2×C4—434no—
551C2×C4—432no—
552C2×C4—864no—
553C2×C4—864no—
554C2×C4—864no—
555C2×C4—864no—
556C2×C4—864no—
557C2×C4—864no—
558C2×C4—862no—
559C2×C4—862no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—1722no—
564C2×C4—1722no—
565C2×C4—1722no—
566C2×C4—1722no—
567C2×C4—1722no—
568C2×C4—1722no—
569C2×C4—1722no—
570C2×C4—1722no—
571C2×C4—1722no—
572C2×C4C22⋊C4×D4311yescharacteristic
573C2×C4C22⋊C4×D4311yescharacteristic
574C2×C4C2×D4×D4311yescharacteristic
575C2×C4C2×D4×D4311yescharacteristic
576C8—42no—
577C8—42no—
578C8—1722no—
579C8—1722no—
580C22—24no—
581C22—24no—
582C22—21no—
583C22—21no—
584C22—21no—
585C22—21no—
586C22—434no—
587C22—868no—
588C22—862no—
589C22—862no—
590C22—862no—
591C22—862no—
592C22—862no—
593C22—1728no—
594C22—1724no—
595C22—1724no—
596C22—1724no—
597C22#1458286412yes—
598C22#1458286412yes—
599C22#99×D4312yes—
600C22#101×D4312yes—
601C22C2×C22⋊C4×D4311yescharacteristic
602C22C2×#1306333111yescharacteristic
603C22C2×#1306333311yescharacteristic
604C4—21no—
605C4—21no—
606C4—21no—
607C4—21no—
608C4—42no—
609C4—42no—
610C4—434no—
611C4—862no—
612C4—1722no—
613C4—1722no—
614C2—22no—
615C2—21no—
616C2—21no—
617C2—864no—
618C2—1722no—
619C2#1913295714yesdirect product factor
620C2C2×#1458286411yescharacteristic
621C2C2×#99×D4311yescharacteristic
622C2C2×#101×D4311yescharacteristic
subgroupG/H
centerC23C22⋊C4×D43
commutatorC23×C43C23×C4
FrattiniC22×C4C23×D43
FittingC2×C43×#324C2
socleC23×C43C2×C22⋊C4
prime radicalC24×D43C2×C4
cosocleC22×C4×C43C24
hypercenterC2×#324D43
hypocenterC43C2×#1472
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#324

Complements

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

NH ≅ G/Ntype
4. #19132957C2direct (N × H)
5. C2×#14582625C2semidirect
6. C2×#14582624C2semidirect
7. C2×#14582624C2semidirect
8. C2×C43×#324C2semidirect
33. #14582625C22semidirect
34. #14582624C22semidirect
35. #14582624C22semidirect
39. C43×#324C22semidirect
310. C2×#324D43semidirect
314. C2×C43#1472semidirect
350. #324C2×D43semidirect
351. C43C2×#1472semidirect
619. C2#19132957direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633032
C2×#145828612
C2×C22⋊C8×D432
#191329572
C2×#145826252
C2×#145826242
C2×C43×#3242
C2×#147243