Finite Group Databasebeta

← C2×#19133558 #25068694

Subgroups — C2×#19133558 #25068694

Order 11008.

1232 conjugacy classes of subgroups.

The subgroup lattice has 584 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583054C211yesmaximal, characteristic, complemented
2C2×#14583037C211yesmaximal, characteristic
3C2×#14582819C211yesmaximal, characteristic, complemented
4#19133558C218yesmaximal, direct product factor
5C2×#14582636C211yesmaximal, characteristic, complemented
6C2×#14582633C211yesmaximal, characteristic
7C2×#14582625C211yesmaximal, characteristic, complemented
8C2×C43×#539C211yesmaximal, characteristic
9C23×Dic86C2211yescharacteristic
10C22×#10621885—21no—
11C22×#10621883—21no—
12C22×Dic43⋊C4—21no—
13#14583054—22no—
14#14583054C2214yescomplemented
15#14583037—22no—
16#14583037C2214yes—
17C2×#13063248—21no—
18C2×#13063248—21no—
19C2×C22⋊(C43⋊C8)C2211yescharacteristic
20C2×C22⋊(C43⋊C8)C2211yescharacteristic
21#14582819—22no—
22#14582819C2214yescomplemented
23C2×C43⋊#95—21no—
24C2×C43⋊#95C2211yescharacteristic
25#14582636C2214yescomplemented
26#14582633C2214yes—
27#14582625C2214yescomplemented
28C43×#539—22no—
29C43×#539—22no—
30C43×#539—22no—
31C43×#539C2214yes—
32C2×#126×C43—21no—
33C2×#125×C43—21no—
34C2×#123×C43—21no—
35C2×#123×C43—21no—
36C2×C22⋊Q8×C43—21no—
37C2×C22⋊Q8×C43C2211yescharacteristic
38C2×#121×C43C2211yescharacteristic
39C2×C4×D4×C43—21no—
40C22×C4⋊C4×C43C2211yescharacteristic
41C22×Dic86—21no—
42C22×Dic86—21no—
43C22×Dic86—21no—
44C22×Dic86—21no—
45C22×Dic86—21no—
46C22×Dic86—44no—
47C22×Dic86C2312yes—
48C23×Dic43—21no—
49C23×Dic43—21no—
50C2×#10621885—24no—
51C2×#10621885—44no—
52C2×#10621883—24no—
53C2×#10621883—44no—
54C22×C43⋊C8—21no—
55C22×C43⋊C8—21no—
56C2×Dic43⋊C4—24no—
57C2×Dic43⋊C4—44no—
58#13063248—24no—
59#13063248—24no—
60C22⋊(C43⋊C8)—21no—
61C22⋊(C43⋊C8)—21no—
62C22⋊(C43⋊C8)C2312yes—
63C22⋊(C43⋊C8)C2312yes—
64C43⋊#95—21no—
65C43⋊#95—24no—
66C43⋊#95C2312yes—
67C22×Q8×C43D411yescharacteristic
68C22×D4×C43—21no—
69C22×D4×C43D411yescharacteristic
70C23×C4×C43—21no—
71C23×C4×C43D411yescharacteristic
72C23×C4×C43D411yescharacteristic
73C23×C4×C43C2311yescharacteristic
74#126×C43—24no—
75#126×C43—24no—
76#125×C43—24no—
77#125×C43—24no—
78#123×C43—24no—
79#123×C43—24no—
80#123×C43—24no—
81#123×C43—24no—
82C22⋊Q8×C43—24no—
83C22⋊Q8×C43—24no—
84C22⋊Q8×C43—21no—
85C22⋊Q8×C43—21no—
86C22⋊Q8×C43D412yes—
87C22⋊Q8×C43C2312yes—
88#121×C43—21no—
89#121×C43—21no—
90#121×C43D412yes—
91#121×C43C2312yes—
92C4×D4×C43—24no—
93C4×D4×C43—24no—
94C2×C4⋊C4×C43—21no—
95C2×C4⋊C4×C43—21no—
96C2×C4⋊C4×C43—21no—
97C2×C4⋊C4×C43—21no—
98C2×C4⋊C4×C43—21no—
99C2×C4⋊C4×C43—21no—
100C2×C4⋊C4×C43—21no—
101C2×C4⋊C4×C43—21no—
102C2×C4⋊C4×C43D412yes—
103C2×C4⋊C4×C43D411yescharacteristic
104C2×C4⋊C4×C43D411yescharacteristic
105C2×C4⋊C4×C43C2312yes—
106C2×C22⋊C4×C43—21no—
107C2×C22⋊C4×C43—21no—
108C2×C22⋊C4×C43—21no—
109C2×C22⋊C4×C43—21no—
110C2×C22⋊C4×C43—21no—
111C2×C42×C43—21no—
112C24×C43—21no—
113C24×C43C2×D411yescharacteristic
114C2×Q8×C43—21no—
115C2×Q8×C43—42no—
116C2×Q8×C43C2×D412yes—
117C2×D4×C43—21no—
118C2×D4×C43—22no—
119C2×D4×C43—22no—
120C2×D4×C43—42no—
121C2×D4×C43—42no—
122C2×D4×C43—42no—
123C2×D4×C43C2×D412yes—
124C22×C4×C43—24no—
125C22×C4×C43—21no—
126C22×C4×C43—21no—
127C22×C4×C43—21no—
128C22×C4×C43—21no—
129C22×C4×C43—21no—
130C22×C4×C43—21no—
131C22×C4×C43—21no—
132C22×C4×C43—22no—
133C22×C4×C43—22no—
134C22×C4×C43—42no—
135C22×C4×C43—42no—
136C22×C4×C43—82no—
137C22×C4×C43C2×D411yescharacteristic
138C22×C4×C43C2×D411yescharacteristic
139C22×C4×C43C2×D411yescharacteristic
140C22×C4×C43C2×D411yescharacteristic
141C22×C4×C43C2×D412yes—
142C22×C4×C43C2×D412yes—
143C22×C4×C43C2×D411yescharacteristic
144C22×C4×C43C2411yescharacteristic
145C22×Dic43—24no—
146C22×Dic43—24no—
147C22×Dic43—22no—
148C22×Dic43—22no—
149C22×Dic43—42no—
150C22×Dic43—42no—
151C22×Dic43—41no—
152C22×Dic43—41no—
153C22×Dic43—42no—
154C2×Dic86—24no—
155C2×Dic86—24no—
156C2×Dic86—22no—
157C2×Dic86—22no—
158C2×Dic86—44no—
159C2×Dic86—44no—
160C2×Dic86—44no—
161C2×Dic86—44no—
162C2×Dic86—42no—
163C2×Dic86—42no—
164C2×Dic86—41no—
165C2×Dic86—41no—
166C4⋊C4×C43—24no—
167C4⋊C4×C43—24no—
168C4⋊C4×C43—24no—
169C4⋊C4×C43—22no—
170C4⋊C4×C43—22no—
171C4⋊C4×C43—22no—
172C4⋊C4×C43—21no—
173C4⋊C4×C43—21no—
174C4⋊C4×C43—22no—
175C4⋊C4×C43—22no—
176C4⋊C4×C43—22no—
177C4⋊C4×C43C2×D412yes—
178C4⋊C4×C43C2×D412yes—
179C22⋊C4×C43—24no—
180C22⋊C4×C43—24no—
181C22⋊C4×C43—24no—
182C22⋊C4×C43—22no—
183C22⋊C4×C43—22no—
184C22⋊C4×C43—22no—
185C22⋊C4×C43—22no—
186C42×C43—24no—
187#10621885—48no—
188#10621883—48no—
189Dic43⋊C4—48no—
190C2×C43⋊C8—22no—
191C2×C43⋊C8—22no—
192C2×C43⋊C8—42no—
193C2×C43⋊C8—42no—
194C23×C43—22no—
195C23×C43—22no—
196C23×C43—22no—
197C23×C43—42no—
198C23×C43—42no—
199C23×C43—42no—
200C23×C43#12011yescharacteristic
201C23×C43#12011yescharacteristic
202C23×C43#13512yes—
203C23×C43#13712yes—
204C23×C43C22×D411yescharacteristic
205Q8×C43—42no—
206Q8×C43—81no—
207D4×C43—42no—
208D4×C43—42no—
209D4×C43—42no—
210D4×C43—44no—
211D4×C43—81no—
212C2×C4×C43—22no—
213C2×C4×C43—22no—
214C2×C4×C43—22no—
215C2×C4×C43—22no—
216C2×C4×C43—22no—
217C2×C4×C43—22no—
218C2×C4×C43—22no—
219C2×C4×C43—22no—
220C2×C4×C43—22no—
221C2×C4×C43—41no—
222C2×C4×C43—41no—
223C2×C4×C43—41no—
224C2×C4×C43—41no—
225C2×C4×C43—42no—
226C2×C4×C43—42no—
227C2×C4×C43—42no—
228C2×C4×C43—42no—
229C2×C4×C43—42no—
230C2×C4×C43—42no—
231C2×C4×C43—42no—
232C2×C4×C43—81no—
233C2×C4×C43—84no—
234C2×C4×C43#12011yescharacteristic
235C2×C4×C43#12011yescharacteristic
236C2×C4×C43C22×D411yescharacteristic
237C2×C4×C43C22×D411yescharacteristic
238C2×Dic43—24no—
239C2×Dic43—24no—
240C2×Dic43—42no—
241C2×Dic43—44no—
242C2×Dic43—42no—
243C2×Dic43—48no—
244C2×Dic43—42no—
245C2×Dic43—42no—
246C2×Dic43—44no—
247Dic86—24no—
248Dic86—24no—
249Dic86—42no—
250Dic86—42no—
251Dic86—44no—
252Dic86—44no—
253C43⋊C8—42no—
254C43⋊C8—42no—
255C2×#1603—431nomaximal, Sylow
256C22×C43—24no—
257C22×C43—24no—
258C22×C43—21no—
259C22×C43—21no—
260C22×C43—21no—
261C22×C43—21no—
262C22×C43—42no—
263C22×C43—42no—
264C22×C43—42no—
265C22×C43—84no—
266C22×C43#45212yes—
267C22×C43#45212yes—
268C22×C43#45612yes—
269C22×C43B(4,𝔽2)12yes—
270C22×C43C2×#12011yescharacteristic
271C22×C43C2×#13511yescharacteristic
272C22×C43C2×#13711yescharacteristic
273C4×C43—21no—
274C4×C43—21no—
275C4×C43—21no—
276C4×C43—21no—
277C4×C43—42no—
278C4×C43—42no—
279C4×C43—42no—
280C4×C43—42no—
281C4×C43—42no—
282Dic43—44no—
283Dic43—44no—
284C2×#539D4311yescharacteristic
285C2×#451—431no—
286C2×#448—431no—
287C2×#395—431no—
288#1603—438no—
289C2×#328—431no—
290C2×#327—431no—
291C2×#324—431no—
292C2×C43—21no—
293C2×C43—21no—
294C2×C43—22no—
295C2×C43—82no—
296C2×C43#160314yescomplemented
297C2×C43C2×#45211yescharacteristic
298C2×C43C2×#45611yescharacteristic
299C2×C43C2×B(4,𝔽2)11yescharacteristic
300C23×Q8—431no—
301C22×Q16—861no—
302C22×SD16—861no—
303#539—22no—
304#539—22no—
305#539—22no—
306#539C2×D4314yes—
307C2×#126—21no—
308C2×#125—21no—
309C2×#123—21no—
310C2×#123—21no—
311C2×C22⋊Q8—21no—
312C2×C22⋊Q8C2×D4311yescharacteristic
313C2×#121C2×D4311yescharacteristic
314C2×C4×D4—21no—
315C22×C4⋊C4—861no—
316C22×C4⋊C4C2×D4311yescharacteristic
317#451—434no—
318#451—862no—
319#448—434no—
320#448—862no—
321C2×#103—861no—
322C2×#103—861no—
323C2×C22⋊C8—431no—
324C2×C22⋊C8—431no—
325#395—434no—
326#395—862no—
327C2×#95—431no—
328C2×#95—861no—
329#328—434no—
330#327—434no—
331#324—434no—
332C43C2×#160311yescharacteristic, complemented, Sylow
333C22×Q8—432no—
334C22×Q8—861no—
335C22×Q8—861no—
336C22×Q8—861no—
337C22×Q8—861no—
338C22×Q8—861no—
339C22×Q8—1724no—
340C22×Q8C22⋊D4311yescharacteristic
341C22×D4—21no—
342C22×D4C22⋊D4311yescharacteristic
343C23×C4—21no—
344C23×C4—861no—
345C23×C4—861no—
346C23×C4C22⋊D4311yescharacteristic
347C23×C4C22⋊D4311yescharacteristic
348C23×C4C22×D4311yescharacteristic
349C2×Q16—864no—
350C2×Q16—1724no—
351C2×SD16—864no—
352C2×SD16—1724no—
353C22×C8—861no—
354C22×C8—861no—
355#126—24no—
356#126—24no—
357#125—24no—
358#125—24no—
359#123—24no—
360#123—24no—
361#123—24no—
362#123—24no—
363C22⋊Q8—24no—
364C22⋊Q8—24no—
365C22⋊Q8—21no—
366C22⋊Q8—21no—
367C22⋊Q8C22⋊D4312yes—
368C22⋊Q8C22×D4312yes—
369#121—21no—
370#121—21no—
371#121C22⋊D4312yes—
372#121C22×D4312yes—
373C4×D4—24no—
374C4×D4—24no—
375C2×C4⋊C4—21no—
376C2×C4⋊C4—21no—
377C2×C4⋊C4—21no—
378C2×C4⋊C4—21no—
379C2×C4⋊C4—21no—
380C2×C4⋊C4—21no—
381C2×C4⋊C4—21no—
382C2×C4⋊C4—21no—
383C2×C4⋊C4—864no—
384C2×C4⋊C4—1724no—
385C2×C4⋊C4C22⋊D4312yes—
386C2×C4⋊C4C22⋊D4311yescharacteristic
387C2×C4⋊C4C22⋊D4311yescharacteristic
388C2×C4⋊C4C22×D4312yes—
389C2×C22⋊C4—21no—
390C2×C22⋊C4—21no—
391C2×C22⋊C4—21no—
392C2×C22⋊C4—21no—
393C2×C22⋊C4—21no—
394C2×C42—21no—
395#103—864no—
396#103—864no—
397C22⋊C8—432no—
398C22⋊C8—432no—
399C22⋊C8—861no—
400C22⋊C8—861no—
401#95—432no—
402#95—861no—
403#95—864no—
404C24—21no—
405C24C2×C22⋊D4311yescharacteristic
406C2×Q8—21no—
407C2×Q8—42no—
408C2×Q8—864no—
409C2×Q8—864no—
410C2×Q8—862no—
411C2×Q8—862no—
412C2×Q8—1722no—
413C2×Q8—1722no—
414C2×Q8—1724no—
415C2×Q8—1724no—
416C2×Q8—1724no—
417C2×Q8—1724no—
418C2×Q8—1721no—
419C2×Q8—1721no—
420C2×Q8C2×C22⋊D4312yes—
421C2×D4—22no—
422C2×D4—22no—
423C2×D4—21no—
424C2×D4—42no—
425C2×D4—42no—
426C2×D4—42no—
427C2×D4C2×C22⋊D4312yes—
428C22×C4—21no—
429C22×C4—21no—
430C22×C4—21no—
431C22×C4—21no—
432C22×C4—21no—
433C22×C4—21no—
434C22×C4—22no—
435C22×C4—22no—
436C22×C4—24no—
437C22×C4—21no—
438C22×C4—42no—
439C22×C4—42no—
440C22×C4—82no—
441C22×C4—864no—
442C22×C4—864no—
443C22×C4—862no—
444C22×C4—862no—
445C22×C4—1722no—
446C22×C4—1722no—
447C22×C4—1721no—
448C22×C4—1721no—
449C22×C4—1722no—
450C22×C4C2×C22⋊D4312yes—
451C22×C4C2×C22⋊D4311yescharacteristic
452C22×C4C2×C22⋊D4311yescharacteristic
453C22×C4C2×C22⋊D4312yes—
454C22×C4C2×C22⋊D4311yescharacteristic
455C22×C4C2×C22⋊D4311yescharacteristic
456C22×C4C2×C22⋊D4311yescharacteristic
457C22×C4C23×D4311yescharacteristic
458Q16—1728no—
459SD16—1728no—
460C2×C8—862no—
461C2×C8—862no—
462C2×C8—1722no—
463C2×C8—1722no—
464C4⋊C4—24no—
465C4⋊C4—24no—
466C4⋊C4—24no—
467C4⋊C4—22no—
468C4⋊C4—22no—
469C4⋊C4—22no—
470C4⋊C4—21no—
471C4⋊C4—21no—
472C4⋊C4—22no—
473C4⋊C4—22no—
474C4⋊C4—22no—
475C4⋊C4—1728no—
476C4⋊C4C2×C22⋊D4312yes—
477C4⋊C4C2×C22⋊D4312yes—
478C22⋊C4—24no—
479C22⋊C4—24no—
480C22⋊C4—24no—
481C22⋊C4—22no—
482C22⋊C4—22no—
483C22⋊C4—22no—
484C22⋊C4—22no—
485C42—24no—
486C23—22no—
487C23—22no—
488C23—22no—
489C23—42no—
490C23—42no—
491C23—42no—
492C23#1306329411yescharacteristic
493C23#1306329411yescharacteristic
494C23#1306334512yes—
495C23#1306335512yes—
496C23C22×C22⋊D4311yescharacteristic
497Q8—42no—
498Q8—81no—
499Q8—864no—
500Q8—864no—
501Q8—1722no—
502Q8—1722no—
503Q8—1724no—
504Q8—1724no—
505D4—42no—
506D4—44no—
507D4—42no—
508D4—42no—
509D4—81no—
510C2×C4—22no—
511C2×C4—22no—
512C2×C4—22no—
513C2×C4—22no—
514C2×C4—22no—
515C2×C4—22no—
516C2×C4—22no—
517C2×C4—22no—
518C2×C4—22no—
519C2×C4—41no—
520C2×C4—41no—
521C2×C4—41no—
522C2×C4—41no—
523C2×C4—42no—
524C2×C4—42no—
525C2×C4—42no—
526C2×C4—42no—
527C2×C4—42no—
528C2×C4—42no—
529C2×C4—42no—
530C2×C4—81no—
531C2×C4—84no—
532C2×C4—864no—
533C2×C4—864no—
534C2×C4—1722no—
535C2×C4—1722no—
536C2×C4—1724no—
537C2×C4—1728no—
538C2×C4—1724no—
539C2×C4—1722no—
540C2×C4—1722no—
541C2×C4#1306329411yescharacteristic
542C2×C4#1306329411yescharacteristic
543C2×C4C22×C22⋊D4311yescharacteristic
544C2×C4C22×C22⋊D4311yescharacteristic
545C8—1722no—
546C8—1722no—
547C22—21no—
548C22—21no—
549C22—21no—
550C22—21no—
551C22—24no—
552C22—24no—
553C22—42no—
554C22—42no—
555C22—42no—
556C22—84no—
557C22#1458306112yes—
558C22#1458306112yes—
559C22#1458308212yes—
560C22#1458308612yes—
561C22C2×#1306329411yescharacteristic
562C22C2×#1306334511yescharacteristic
563C22C2×#1306335511yescharacteristic
564C4—21no—
565C4—21no—
566C4—21no—
567C4—21no—
568C4—42no—
569C4—42no—
570C4—42no—
571C4—42no—
572C4—42no—
573C4—1724no—
574C4—1724no—
575C2—21no—
576C2—22no—
577C2—21no—
578C2—82no—
579C2#1913355814yesdirect product factor
580C2C2×#1458306111yescharacteristic
581C2C2×#1458308211yescharacteristic
582C2C2×#1458308611yescharacteristic
subgroupG/H
centerC23#13063294
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#539C2
socleC23×C43#120
prime radicalC2×#121×C43C22
hypercenterC2×#539D43
hypocenterC43C2×#1603
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#539

Complements

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

NH ≅ G/Ntype
1. C2×#14583054C2semidirect
3. C2×#14582819C2semidirect
4. #19133558C2direct (N × H)
5. C2×#14582636C2semidirect
7. C2×#14582625C2semidirect
14. #14583054C22semidirect
22. #14582819C22semidirect
25. #14582636C22semidirect
27. #14582625C22semidirect
296. C2×C43#1603semidirect
332. C43C2×#1603semidirect
579. C2#19133558direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145830542
C2×#145830372
C2×#145828192
#191335582
C2×#145826362
C2×#145826332
C2×#145826252
C2×C43×#5392
C2×#160343