Finite Group Databasebeta

← C2×#19144408 #25964126

Subgroups — C2×#19144408 #25964126

Order 11008.

2358 conjugacy classes of subgroups.

The subgroup lattice has 612 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C22×#13063324C211yesmaximal, characteristic, complemented
2C2×#14583367C211yesmaximal, characteristic
3#19144408C2116yesmaximal, direct product factor
4C2×#14583193C212yesmaximal, complemented
5C2×#14583183C212yesmaximal, complemented
6C2×#14583188C212yesmaximal, complemented
7C2×#14583178C212yesmaximal, complemented
8C2×#14582942C211yesmaximal, characteristic, complemented
9C2×#14582922C211yesmaximal, characteristic, complemented
10C2×#14582901C211yesmaximal, characteristic
11C2×#14582898C211yesmaximal, characteristic
12C2×C43×#428C211yesmaximal, characteristic, complemented
13C22×#10621898C2211yescharacteristic
14C23×Dic86—21no—
15C22×#10621877C2211yescharacteristic
16C2×#13063324—21no—
17C2×#13063324—21no—
18C2×#13063324—24no—
19C2×#13063324C2212yes—
20C2×#13063324C2212yes—
21C2×#13063324C2218yescomplemented
22#14583367—24no—
23#14583367C2218yes—
24C2×#13063290C2211yescharacteristic
25C2×#13063290C2211yescharacteristic
26C2×#13063287C2211yescharacteristic
27C2×#13063287C2211yescharacteristic
28C2×(C22⋊D43)⋊C4—21no—
29C2×(C22⋊D43)⋊C4—21no—
30C2×#13063282—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32C22×Dic43⋊C4—21no—
33C22×C4×Dic43C2211yescharacteristic
34C2×C42×D43—21no—
35#14583193C22116yescomplemented
36#14583188C22116yescomplemented
37#14583183C22116yescomplemented
38#14583178C22116yescomplemented
39#14582942C2218yescomplemented
40C2×#13063258C2212yes—
41C2×#13063256C2212yes—
42#14582922C2218yescomplemented
43C2×Dic43⋊C8C2212yes—
44C2×Dic43⋊C8C2212yes—
45#14582901C2218yes—
46#14582898C2218yes—
47C2×#13063250C2212yes—
48C2×#13063248C2212yes—
49C2×#13063247C2212yes—
50C2×#13063245C2212yes—
51C22×M16×C43C2211yescharacteristic
52C2×#117×C43C2211yescharacteristic
53C22×C4⋊C4×C43C2211yescharacteristic
54C43×#428C2218yescomplemented
55C2×#107×C43C2212yes—
56C2×#106×C43C2212yes—
57C2×#10621898—22no—
58C2×#10621898—24no—
59C2×#10621898Q818yescomplemented
60C2×#10621898C2314yes—
61C22×Dic86—22no—
62C22×Dic86—22no—
63C22×Dic86—28no—
64C22×Dic86—48no—
65C22×Dic86C2311yescharacteristic
66C22×D172C2311yescharacteristic
67C22×C22⋊D43—21no—
68C23×Dic43—21no—
69C23×Dic43D411yescharacteristic
70C23×Dic43D411yescharacteristic
71C22×C4×D43—21no—
72C22×C4×D43—21no—
73C22×C4×D43—21no—
74C2×#10621877—24no—
75C2×#10621877C2314yes—
76C22×C43⋊C8C2312yes—
77#13063324—24no—
78#13063324—24no—
79#13063324—28no—
80#13063324—28no—
81#13063324C2318yes—
82#13063324C2318yes—
83#13063290—22no—
84#13063290—22no—
85#13063290C2314yes—
86#13063290C2314yes—
87#13063287—22no—
88#13063287—22no—
89#13063287C2314yes—
90#13063287C2314yes—
91(C22⋊D43)⋊C4—28no—
92(C22⋊D43)⋊C4—28no—
93#13063282—28no—
94C2×C4⋊Dic43—21no—
95C2×C4⋊Dic43—22no—
96C2×C4⋊Dic43C2312yes—
97C2×C4⋊Dic43C2314yes—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—22no—
100C2×Dic43⋊C4—28no—
101C2×Dic43⋊C4—21no—
102C2×Dic43⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×(C2×D43)⋊C4—21no—
105C2×C4×Dic43—21no—
106C2×C4×Dic43—21no—
107C2×C4×Dic43D411yescharacteristic
108C2×C4×Dic43D411yescharacteristic
109C2×C4×Dic43D414yes—
110C2×C4×Dic43C2311yescharacteristic
111C2×C4×Dic43C2311yescharacteristic
112C2×C4×Dic43C2314yes—
113C42×D43—28no—
114#13063258C2318yes—
115#13063256C2318yes—
116Dic43⋊C8C2318yes—
117Dic43⋊C8C2318yes—
118#13063250C2318yes—
119#13063248C2318yes—
120#13063247C2318yes—
121#13063245C2318yes—
122C23×C4×C43—21no—
123C23×C4×C43C2311yescharacteristic
124C2×M16×C43—24no—
125C2×M16×C43C2314yes—
126C22×C8×C43C2312yes—
127#117×C43—22no—
128#117×C43C2314yes—
129C2×C4⋊C4×C43—21no—
130C2×C4⋊C4×C43—22no—
131C2×C4⋊C4×C43C2312yes—
132C2×C4⋊C4×C43C2314yes—
133C2×C4⋊C4×C43C2311yescharacteristic
134C2×C4⋊C4×C43C2311yescharacteristic
135C2×C22⋊C4×C43—21no—
136C2×C42×C43—21no—
137#107×C43C2318yes—
138#106×C43C2318yes—
139C24×C43C2×D411yescharacteristic
140C23×D43—21no—
141C22×C4×C43—21no—
142C22×C4×C43—21no—
143C22×C4×C43—24no—
144C22×C4×C43—22no—
145C22×C4×C43—44no—
146C22×C4×C43C2×D411yescharacteristic
147C22×C4×C43C2×D412yes—
148C22×C4×C43C2×Q814yes—
149C22×C4×C43#4114yes—
150C22×C4×C43C2411yescharacteristic
151C22×C4×C43C2412yes—
152C2×C22⋊D43—28no—
153C2×C22⋊D43—24no—
154C22×Dic43—24no—
155C22×Dic43—24no—
156C22×Dic43—21no—
157C22×Dic43—24no—
158C22×Dic43—22no—
159C22×Dic43—44no—
160C22×Dic43C2×D411yescharacteristic
161C22×Dic43C2×D411yescharacteristic
162C22×Dic43C2×D414yes—
163C22×Dic43C2×D414yes—
164C22×Dic43C2×D411yescharacteristic
165C22×Dic43C2×D411yescharacteristic
166#10621898—216no—
167#10621898—28no—
168#10621898C2×Q8116yescomplemented
169C2×D172—21no—
170C2×D172—22no—
171C2×D172C2×Q814yescomplemented
172C2×D172C2412yes—
173C2×C4×D43—28no—
174C2×C4×D43—24no—
175C2×C4×D43—24no—
176C2×C4×D43—24no—
177C2×C4×D43—44no—
178C2×C4×D43—44no—
179C2×Dic86—21no—
180C2×Dic86—22no—
181C2×Dic86—28no—
182C2×Dic86—28no—
183C2×Dic86—48no—
184C2×Dic86—432no—
185C2×Dic86—48no—
186C2×Dic86C2×Q814yescomplemented
187C2×Dic86C2412yes—
188M16×C43—28no—
189C2×C8×C43—24no—
190C2×C8×C43C2414yes—
191C4⋊C4×C43—24no—
192C4⋊C4×C43—22no—
193C4⋊C4×C43—21no—
194C4⋊C4×C43—21no—
195C4⋊C4×C43C2412yes—
196C4⋊C4×C43C2414yes—
197C4⋊C4×C43C2412yes—
198C22⋊C4×C43—24no—
199C42×C43—24no—
200(C2×D43)⋊C4—24no—
201(C2×D43)⋊C4—24no—
202C4⋊Dic43—24no—
203C4⋊Dic43—22no—
204C4⋊Dic43C2414yes—
205Dic43⋊C4—28no—
206Dic43⋊C4—28no—
207Dic43⋊C4—24no—
208Dic43⋊C4—24no—
209C4×Dic43—24no—
210C4×Dic43—24no—
211C4×Dic43C2×D414yes—
212C4×Dic43C2×D414yes—
213C4×Dic43C2×D412yes—
214C4×Dic43C2×D412yes—
215C4×Dic43C2412yes—
216C4×Dic43C2412yes—
217#10621877—28no—
218C2×C43⋊C8—24no—
219C2×C43⋊C8C2414yes—
220C23×C43—22no—
221C23×C43—22no—
222C23×C43C22⋊Q814yes—
223C23×C43C22×D412yes—
224C23×C43C22×D411yescharacteristic
225C22×D43—24no—
226C22×D43—22no—
227C22×D43—42no—
228C22×D43—42no—
229C2×C4×C43—22no—
230C2×C4×C43—22no—
231C2×C4×C43—24no—
232C2×C4×C43—48no—
233C2×C4×C43—44no—
234C2×C4×C43—42no—
235C2×C4×C43—42no—
236C2×C4×C43C22⋊Q814yes—
237C2×C4×C43C22⋊Q818yes—
238C2×C4×C43C22×D412yes—
239C2×C4×C43C22×D411yescharacteristic
240C2×C4×C43C22×Q812yes—
241C2×C4×C43C22×Q814yes—
242C2×C4×C43C2×#4112yes—
243C2×C4×C43C2×#4114yes—
244C2×C4×C43C2511yescharacteristic
245C22⋊D43—216no—
246C2×Dic43—24no—
247C2×Dic43—22no—
248C2×Dic43—22no—
249C2×Dic43—22no—
250C2×Dic43—28no—
251C2×Dic43—28no—
252C2×Dic43—24no—
253C2×Dic43—48no—
254C2×Dic43—44no—
255C2×Dic43AGL(1,ℤ/8)14yes—
256C2×Dic43#13714yes—
257C2×Dic43C22×D412yes—
258C2×Dic43C22×D412yes—
259C2×Dic43C22×D412yes—
260C2×Dic43C22×D412yes—
261D172—24no—
262D172—22no—
263D172C22×Q814yescomplemented
264C4×D43—216no—
265C4×D43—48no—
266C4×D43—48no—
267Dic86—24no—
268Dic86—22no—
269Dic86—416no—
270Dic86—416no—
271Dic86C22×Q814yescomplemented
272C8×C43—24no—
273C43⋊C8—24no—
274C2×#3079—431nomaximal, Sylow
275C22×C43—28no—
276C22×C43—22no—
277C22×C43—22no—
278C22×C43C2×C22⋊Q814yes—
279C22×C43C2×C22⋊Q812yes—
280C22×C43C2×AGL(1,ℤ/8)12yes—
281C22×C43C2×#13712yes—
282C22×C43C23×D411yescharacteristic
283C2×D43—24no—
284C2×D43—48no—
285C2×D43—42no—
286C2×D43—42no—
287C4×C43—44no—
288C4×C43—42no—
289C4×C43—42no—
290C4×C43C2×C22⋊Q812yes—
291C4×C43C2×C22⋊Q814yes—
292C4×C43C23×Q811yescharacteristic
293C4×C43C22×#4111yescharacteristic
294Dic43—24no—
295Dic43—22no—
296Dic43—22no—
297Dic43—44no—
298Dic43C2×AGL(1,ℤ/8)14yes—
299Dic43C2×#13714yes—
300C22×C4⋊Q8—431no—
301C2×C4×#41—431no—
302#3079—4316no—
303C2×#477—432no—
304C2×#475—432no—
305C2×#476—432no—
306C2×#474—432no—
307C2×#428—431no—
308C2×#428D4311yescharacteristic, complemented
309C2×#423—431no—
310C2×#417—431no—
311C2×#417—431no—
312C2×C43—24no—
313C2×C43#307914yescomplemented
314C2×C43C22×C22⋊Q811yescharacteristic
315C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
316C2×C43C22×#13711yescharacteristic
317D43—44no—
318C22×#41—431no—
319C23×Q8—861no—
320C22×M16—431no—
321C22×M16C2×D4311yescharacteristic
322C2×C4⋊Q8—432no—
323C2×C4⋊Q8—432no—
324C2×C4⋊Q8—438no—
325C2×C4⋊Q8—861no—
326C2×C4⋊Q8—864no—
327C2×C4⋊Q8—861no—
328C4×#41—438no—
329C4×#41—864no—
330C2×C4×Q8—431no—
331C2×C4×Q8—431no—
332C2×C4×D4—431no—
333C2×C4×D4—431no—
334C2×C4×D4—861no—
335C2×C4×D4—861no—
336C2×#117—861no—
337C2×#117C2×D4311yescharacteristic
338C22×C4⋊C4—431no—
339C22×C4⋊C4—861no—
340C22×C4⋊C4C2×D4311yescharacteristic
341C22×C42—431no—
342C22×C42—861no—
343#477—4316no—
344#476—4316no—
345#475—4316no—
346#474—4316no—
347#428—438no—
348#428C2×D4318yescomplemented
349C2×#107—432no—
350C2×#107C2×D4312yes—
351C2×#106—432no—
352C2×#106C2×D4312yes—
353#423—438no—
354C2×C4⋊C8—432no—
355C2×C4⋊C8—432no—
356#417—438no—
357#417—438no—
358C2×#103—432no—
359C2×#103—432no—
360C2×#102—432no—
361C2×#102—432no—
362C43C2×#307911yescharacteristic, complemented, Sylow
363C2×#41—438no—
364C2×#41—434no—
365C2×#41—864no—
366C2×#41—862no—
367C22×Q8—431no—
368C22×Q8—868no—
369C22×Q8—862no—
370C22×Q8—862no—
371C22×Q8—1728no—
372C22×D4—431no—
373C22×D4—861no—
374C23×C4—21no—
375C23×C4—431no—
376C23×C4—431no—
377C23×C4—861no—
378C23×C4—861no—
379C23×C4—861no—
380C23×C4—861no—
381C23×C4C22×D4311yescharacteristic
382C2×M16—24no—
383C2×M16—434no—
384C2×M16—864no—
385C2×M16C22×D4314yes—
386C22×C8—432no—
387C22×C8C22×D4312yes—
388C4⋊Q8—438no—
389C4⋊Q8—438no—
390C4⋊Q8—868no—
391C4⋊Q8—868no—
392C4⋊Q8—864no—
393C4⋊Q8—864no—
394C4×Q8—434no—
395C4×Q8—434no—
396C4×Q8—862no—
397C4×Q8—862no—
398C4×D4—434no—
399C4×D4—434no—
400C4×D4—862no—
401C4×D4—862no—
402C4×D4—868no—
403C4×D4—868no—
404#117—22no—
405#117—868no—
406#117C22×D4314yes—
407C2×C4⋊C4—22no—
408C2×C4⋊C4—21no—
409C2×C4⋊C4—432no—
410C2×C4⋊C4—434no—
411C2×C4⋊C4—868no—
412C2×C4⋊C4—862no—
413C2×C4⋊C4—862no—
414C2×C4⋊C4—861no—
415C2×C4⋊C4—861no—
416C2×C4⋊C4—862no—
417C2×C4⋊C4—861no—
418C2×C4⋊C4C22×D4312yes—
419C2×C4⋊C4C22×D4314yes—
420C2×C4⋊C4C22×D4311yescharacteristic
421C2×C4⋊C4C22×D4311yescharacteristic
422C2×C22⋊C4—21no—
423C2×C22⋊C4—861no—
424C2×C22⋊C4—861no—
425C2×C42—21no—
426C2×C42—431no—
427C2×C42—434no—
428C2×C42—431no—
429C2×C42—431no—
430C2×C42—431no—
431C2×C42—434no—
432C2×C42—868no—
433C2×C42—861no—
434C2×C42—861no—
435#107—438no—
436#107C22×D4318yes—
437#106—438no—
438#106C22×D4318yes—
439C4⋊C8—438no—
440C4⋊C8—438no—
441#103—438no—
442#103—438no—
443#102—438no—
444#102—438no—
445C24—861no—
446C24D4×D4311yescharacteristic
447#41—4316no—
448#41—8616no—
449#41—868no—
450C2×Q8—434no—
451C2×Q8—432no—
452C2×Q8—868no—
453C2×Q8—868no—
454C2×Q8—861no—
455C2×Q8—862no—
456C2×Q8—1728no—
457C2×Q8—17232no—
458C2×Q8—1728no—
459C2×D4—434no—
460C2×D4—432no—
461C2×D4—868no—
462C2×D4—864no—
463C2×D4—861no—
464C2×D4—862no—
465C22×C4—24no—
466C22×C4—21no—
467C22×C4—21no—
468C22×C4—22no—
469C22×C4—44no—
470C22×C4—431no—
471C22×C4—431no—
472C22×C4—434no—
473C22×C4—434no—
474C22×C4—431no—
475C22×C4—431no—
476C22×C4—864no—
477C22×C4—864no—
478C22×C4—864no—
479C22×C4—864no—
480C22×C4—861no—
481C22×C4—868no—
482C22×C4—864no—
483C22×C4—864no—
484C22×C4—862no—
485C22×C4—1724no—
486C22×C4—1724no—
487C22×C4—1724no—
488C22×C4#1062189814yes—
489C22×C4D4×D4312yes—
490C22×C4D4×D4311yescharacteristic
491C22×C4Q8×D4314yes—
492C22×C4C23×D4312yes—
493C22×C4C23×D4311yescharacteristic
494M16—28no—
495M16—868no—
496C2×C8—24no—
497C2×C8—434no—
498C2×C8—864no—
499C2×C8C23×D4314yes—
500C4⋊C4—24no—
501C4⋊C4—22no—
502C4⋊C4—21no—
503C4⋊C4—21no—
504C4⋊C4—434no—
505C4⋊C4—868no—
506C4⋊C4—868no—
507C4⋊C4—864no—
508C4⋊C4—864no—
509C4⋊C4—864no—
510C4⋊C4—862no—
511C4⋊C4C23×D4314yes—
512C4⋊C4C23×D4312yes—
513C4⋊C4C23×D4312yes—
514C22⋊C4—24no—
515C22⋊C4—864no—
516C22⋊C4—864no—
517C42—24no—
518C42—434no—
519C42—434no—
520C42—432no—
521C42—432no—
522C42—432no—
523C42—432no—
524C42—864no—
525C42—864no—
526C23—22no—
527C23—22no—
528C23—864no—
529C23—862no—
530C23—1722no—
531C23—1722no—
532C23#1306330314yes—
533C23C2×D4×D4312yes—
534C23C2×D4×D4311yescharacteristic
535Q8—434no—
536Q8—864no—
537Q8—862no—
538Q8—17216no—
539Q8—17216no—
540D4—434no—
541D4—8616no—
542D4—864no—
543D4—862no—
544C2×C4—22no—
545C2×C4—22no—
546C2×C4—24no—
547C2×C4—48no—
548C2×C4—44no—
549C2×C4—42no—
550C2×C4—42no—
551C2×C4—434no—
552C2×C4—434no—
553C2×C4—432no—
554C2×C4—432no—
555C2×C4—432no—
556C2×C4—432no—
557C2×C4—868no—
558C2×C4—868no—
559C2×C4—864no—
560C2×C4—862no—
561C2×C4—862no—
562C2×C4—862no—
563C2×C4—8616no—
564C2×C4—864no—
565C2×C4—1728no—
566C2×C4—1728no—
567C2×C4—1728no—
568C2×C4—1724no—
569C2×C4#1306330314yes—
570C2×C4#1306330318yes—
571C2×C4C2×D4×D4312yes—
572C2×C4C2×D4×D4311yescharacteristic
573C2×C4C2×Q8×D4312yes—
574C2×C4C2×Q8×D4314yes—
575C2×C4C2×#1062189812yes—
576C2×C4C2×#1062189814yes—
577C2×C4C24×D4311yescharacteristic
578C8—24no—
579C8—864no—
580C22—22no—
581C22—22no—
582C22—28no—
583C22—864no—
584C22—1722no—
585C22—1722no—
586C22—1728no—
587C22C2×#1306330314yes—
588C22C2×#1306330312yes—
589C22AGL(1,ℤ/8)×D4312yes—
590C22#137×D4312yes—
591C22C22×D4×D4311yescharacteristic
592C4—44no—
593C4—42no—
594C4—42no—
595C4—434no—
596C4—434no—
597C4—862no—
598C4—862no—
599C4—864no—
600C4—1724no—
601C4C2×#1306330314yes—
602C4C2×#1306330312yes—
603C4C22×Q8×D4311yescharacteristic
604C4C22×#1062189811yescharacteristic
605C2—24no—
606C2—1724no—
607C2#1914440814yesdirect product factor
608C2C22×#1306330311yescharacteristic
609C2C2×AGL(1,ℤ/8)×D4311yescharacteristic
610C2C2×#137×D4311yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#428C2
socleC23×C43C22×D4
prime radicalC22×#10621898C22
hypercenterC2×#428D43
hypocenterC43C2×#3079
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#428

Complements

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

NH ≅ G/Ntype
1. C22×#13063324C2semidirect
3. #19144408C2direct (N × H)
4. C2×#14583193C2semidirect
5. C2×#14583183C2semidirect
6. C2×#14583188C2semidirect
7. C2×#14583178C2semidirect
8. C2×#14582942C2semidirect
9. C2×#14582922C2semidirect
12. C2×C43×#428C2semidirect
21. C2×#13063324C22semidirect
35. #14583193C22semidirect
36. #14583188C22semidirect
37. #14583183C22semidirect
38. #14583178C22semidirect
39. #14582942C22semidirect
42. #14582922C22semidirect
54. C43×#428C22semidirect
59. C2×#10621898Q8semidirect
168. #10621898C2×Q8semidirect
171. C2×D172C2×Q8semidirect
186. C2×Dic86C2×Q8semidirect
263. D172C22×Q8semidirect
271. Dic86C22×Q8semidirect
308. C2×#428D43semidirect
313. C2×C43#3079semidirect
348. #428C2×D43semidirect
362. C43C2×#3079semidirect
607. C2#19144408direct (N × H)

Maximal subgroups

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

subgroupindex
C22×#130633242
C2×#145833672
#191444082
C2×#145831932
C2×#145831832
C2×#145831882
C2×#145831782
C2×#145829422
C2×#145829222
C2×#145829012
C2×#145828982
C2×C43×#4282
C2×#307943