Finite Group Databasebeta

← C2×#19145782 #25968699

Subgroups — C2×#19145782 #25968699

Order 11008.

2050 conjugacy classes of subgroups.

The subgroup lattice has 594 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583444C211yesmaximal, characteristic
2C22×#13063316C211yesmaximal, characteristic, complemented
3#19145782C2116yesmaximal, direct product factor
4C2×#14583307C212yesmaximal, complemented
5C2×#14583262C212yesmaximal, complemented
6C2×#14583218C211yesmaximal, characteristic, complemented
7C2×#14583215C211yesmaximal, characteristic, complemented
8C2×#14583212C211yesmaximal, characteristic, complemented
9C2×#14583202C212yesmaximal, complemented
10C2×#14583201C212yesmaximal, complemented
11C2×#14582953C211yesmaximal, characteristic, complemented
12C2×C43×#480C211yesmaximal, characteristic, complemented
13C22×#10621900—21no—
14#14583444—24no—
15#14583444C2218yes—
16C2×#13063324C2211yescharacteristic
17C2×#13063321C2211yescharacteristic
18C2×#13063316—21no—
19C2×#13063316—21no—
20C2×#13063316—24no—
21C2×#13063316C2212yes—
22C2×#13063316C2212yes—
23C2×#13063316C2218yescomplemented
24C2×#13063311—21no—
25C2×#13063299C2211yescharacteristic
26C2×#13063297—21no—
27C2×D4×Dic43C2211yescharacteristic
28C2×#13063287C2211yescharacteristic
29C2×(C22⋊D43)⋊C4—21no—
30C22×C4⋊Dic43—21no—
31C22×C4⋊Dic43C2211yescharacteristic
32C22×Dic43⋊C4—21no—
33C22×C4×Dic43C2211yescharacteristic
34#14583307C22116yescomplemented
35#14583262C22116yescomplemented
36#14583218C2218yescomplemented
37#14583215C2218yescomplemented
38#14583212C2218yescomplemented
39#14583202C22116yescomplemented
40#14583201C22116yescomplemented
41#14582953C2218yescomplemented
42C2×#13063258C2212yes—
43C2×#13063257C2212yes—
44C2×#13063256C2212yes—
45C2×Dic43⋊C8C2212yes—
46C2×#13063247C2212yes—
47C2×#13063246C2212yes—
48C2×#13063245C2212yes—
49C2×C22⋊(C43⋊C8)C2211yescharacteristic
50C2×#13063235C2212yes—
51C2×#121×C43C2211yescharacteristic
52C22×C4⋊C4×C43C2211yescharacteristic
53C43×#480C2218yescomplemented
54C2×#107×C43C2212yes—
55C2×#102×C43C2212yes—
56C2×C22⋊C8×C43C2211yescharacteristic
57C2×#10621900—28no—
58C2×#10621900—48no—
59C22×Dic86—21no—
60C22×D172C2311yescharacteristic
61C22×C22⋊D43—21no—
62C22×C22⋊D43—21no—
63C22×C22⋊D43—21no—
64C23×Dic43—21no—
65C23×Dic43—21no—
66C23×Dic43D411yescharacteristic
67C23×Dic43D411yescharacteristic
68C22×C4×D43—21no—
69C22×C43⋊C8C2312yes—
70#13063324—22no—
71#13063324C2314yes—
72#13063321—22no—
73#13063321C2314yes—
74#13063316—24no—
75#13063316—24no—
76#13063316—28no—
77#13063316—28no—
78#13063316C2318yes—
79#13063316C2318yes—
80#13063311—28no—
81#13063299—22no—
82#13063299C2314yes—
83#13063297—28no—
84D4×Dic43—22no—
85D4×Dic43C2314yes—
86#13063287—22no—
87#13063287C2314yes—
88(C22⋊D43)⋊C4—28no—
89C2×C4⋊Dic43—21no—
90C2×C4⋊Dic43—22no—
91C2×C4⋊Dic43—22no—
92C2×C4⋊Dic43—22no—
93C2×C4⋊Dic43—28no—
94C2×C4⋊Dic43C2312yes—
95C2×C4⋊Dic43C2314yes—
96C2×C4⋊Dic43C2311yescharacteristic
97C2×Dic43⋊C4—22no—
98C2×Dic43⋊C4—22no—
99C2×Dic43⋊C4—28no—
100C2×Dic43⋊C4—21no—
101C2×C22⋊Dic43—21no—
102C2×(C2×D43)⋊C4—21no—
103C2×(C2×D43)⋊C4—21no—
104C2×C4×Dic43D411yescharacteristic
105C2×C4×Dic43D411yescharacteristic
106C2×C4×Dic43D414yes—
107C2×C4×Dic43C2311yescharacteristic
108C2×C4×Dic43C2311yescharacteristic
109C2×C4×Dic43C2314yes—
110#13063258C2318yes—
111#13063257C2318yes—
112#13063256C2318yes—
113Dic43⋊C8C2318yes—
114#13063247C2318yes—
115#13063246C2318yes—
116#13063245C2318yes—
117C22⋊(C43⋊C8)C2314yes—
118#13063235C2318yes—
119C22×D4×C43—21no—
120C22×D4×C43C2311yescharacteristic
121C23×C4×C43—21no—
122C23×C4×C43C2311yescharacteristic
123C22×C8×C43C2312yes—
124#121×C43—22no—
125#121×C43C2314yes—
126C2×C4⋊C4×C43—21no—
127C2×C4⋊C4×C43—22no—
128C2×C4⋊C4×C43C2312yes—
129C2×C4⋊C4×C43C2314yes—
130C2×C4⋊C4×C43C2311yescharacteristic
131C2×C22⋊C4×C43—21no—
132#107×C43C2318yes—
133#102×C43C2318yes—
134C22⋊C8×C43C2314yes—
135C24×C43—21no—
136C24×C43C2×D411yescharacteristic
137C23×D43—21no—
138C2×D4×C43—21no—
139C2×D4×C43—24no—
140C2×D4×C43—24no—
141C2×D4×C43—44no—
142C2×D4×C43C2412yes—
143C22×C4×C43—24no—
144C22×C4×C43—21no—
145C22×C4×C43—24no—
146C22×C4×C43—22no—
147C22×C4×C43—44no—
148C22×C4×C43C2×D411yescharacteristic
149C22×C4×C43C2×D412yes—
150C22×C4×C43C2412yes—
151C22×C4×C43C2411yescharacteristic
152C2×C22⋊D43—24no—
153C2×C22⋊D43—24no—
154C2×C22⋊D43—24no—
155C2×C22⋊D43—44no—
156C2×C22⋊D43—44no—
157C2×C22⋊D43—44no—
158C22×Dic43—24no—
159C22×Dic43—24no—
160C22×Dic43—21no—
161C22×Dic43—24no—
162C22×Dic43—22no—
163C22×Dic43—42no—
164C22×Dic43—44no—
165C22×Dic43—44no—
166C22×Dic43C2×D411yescharacteristic
167C22×Dic43C2×D411yescharacteristic
168C22×Dic43C2×D411yescharacteristic
169C22×Dic43C2×D414yes—
170C22×Dic43C2×D411yescharacteristic
171C22×Dic43C2×D414yes—
172#10621900—432no—
173C2×D172—21no—
174C2×D172—24no—
175C2×D172C2412yes—
176C2×C4×D43—24no—
177C2×C4×D43—44no—
178C2×Dic86—24no—
179C2×Dic86—44no—
180C2×C8×C43—24no—
181C2×C8×C43C2414yes—
182C4⋊C4×C43—24no—
183C4⋊C4×C43—22no—
184C4⋊C4×C43—21no—
185C4⋊C4×C43C2414yes—
186C4⋊C4×C43C2412yes—
187C22⋊C4×C43—24no—
188C22⋊Dic43—24no—
189(C2×D43)⋊C4—24no—
190(C2×D43)⋊C4—24no—
191C4⋊Dic43—24no—
192C4⋊Dic43—22no—
193C4⋊Dic43—21no—
194C4⋊Dic43—28no—
195C4⋊Dic43—28no—
196C4⋊Dic43C2414yes—
197C4⋊Dic43C2412yes—
198Dic43⋊C4—28no—
199Dic43⋊C4—28no—
200Dic43⋊C4—24no—
201C4×Dic43C2×D414yes—
202C4×Dic43C2×D412yes—
203C4×Dic43C2×D414yes—
204C4×Dic43C2×D412yes—
205C4×Dic43C2412yes—
206C4×Dic43C2412yes—
207C2×C43⋊C8—24no—
208C2×C43⋊C8C2414yes—
209C23×C43—22no—
210C23×C43—22no—
211C23×C43—22no—
212C23×C43—42no—
213C23×C43—42no—
214C23×C43—42no—
215C23×C43AGL(1,ℤ/8)14yes—
216C23×C43C22×D412yes—
217C23×C43C22×D411yescharacteristic
218C22×D43—22no—
219C22×D43—42no—
220C22×D43—42no—
221C22×D43—42no—
222D4×C43—24no—
223D4×C43—48no—
224D4×C43—42no—
225C2×C4×C43—22no—
226C2×C4×C43—24no—
227C2×C4×C43—24no—
228C2×C4×C43—24no—
229C2×C4×C43—22no—
230C2×C4×C43—42no—
231C2×C4×C43—48no—
232C2×C4×C43—44no—
233C2×C4×C43C22×D412yes—
234C2×C4×C43C22×D411yescharacteristic
235C2×C4×C432−1+414yes—
236C2×C4×C43C2511yescharacteristic
237C22⋊D43—48no—
238C22⋊D43—48no—
239C22⋊D43—48no—
240C2×Dic43—22no—
241C2×Dic43—22no—
242C2×Dic43—28no—
243C2×Dic43—22no—
244C2×Dic43—22no—
245C2×Dic43—24no—
246C2×Dic43—22no—
247C2×Dic43—44no—
248C2×Dic43—48no—
249C2×Dic43—48no—
250C2×Dic43—42no—
251C2×Dic43—44no—
252C2×Dic43C22×D412yes—
253C2×Dic43C22×D412yes—
254C2×Dic43C22×D412yes—
255C2×Dic43C22×D412yes—
256D172—24no—
257D172—42no—
258C4×D43—48no—
259Dic86—48no—
260C8×C43—24no—
261C43⋊C8—24no—
262C2×#3234—431nomaximal, Sylow
263C22×C43—22no—
264C22×C43—28no—
265C22×C43—22no—
266C22×C43—42no—
267C22×C43—42no—
268C22×C43—42no—
269C22×C43—84no—
270C22×C43#53612yes—
271C22×C43C2×AGL(1,ℤ/8)14yes—
272C22×C43C2×AGL(1,ℤ/8)12yes—
273C22×C43#57512yes—
274C22×C43C23×D411yescharacteristic
275C2×D43—42no—
276C2×D43—42no—
277C2×D43—42no—
278C2×D43—84no—
279C4×C43—22no—
280C4×C43—42no—
281C4×C43—44no—
282C4×C43#53612yes—
283C4×C43C2×2−1+412yes—
284Dic43—22no—
285Dic43—22no—
286Dic43—22no—
287Dic43—22no—
288Dic43—42no—
289Dic43—44no—
290C2×#532—431no—
291C22×#125—431no—
292#3234—4316no—
293C2×#501—432no—
294C2×#490—432no—
295C2×#481—431no—
296C2×#481—431no—
297C2×#480—431no—
298C2×#480D4311yescharacteristic, complemented
299C2×#478—432no—
300C2×#478—432no—
301C2×#432—431no—
302C2×C43—24no—
303C2×C43—82no—
304C2×C43#323414yescomplemented
305C2×C43C2×#53611yescharacteristic
306C2×C43C22×AGL(1,ℤ/8)11yescharacteristic
307C2×C43C2×#57511yescharacteristic
308D43—82no—
309C22×#41—861no—
310#532—438no—
311#532—864no—
312C2×C4⋊Q8—431no—
313C2×#127—431no—
314C2×#125—432no—
315C2×#125—432no—
316C2×#125—438no—
317C2×#125—861no—
318C2×#125—861no—
319C2×#125—864no—
320C2×#124—861no—
321C2×#121—431no—
322C2×#121—861no—
323C2×#121C2×D4311yescharacteristic
324C2×C4×D4—431no—
325C2×C4×D4—431no—
326C2×C4×D4—861no—
327C22×C4⋊C4—431no—
328C22×C4⋊C4—861no—
329C22×C4⋊C4—861no—
330C22×C4⋊C4C2×D4311yescharacteristic
331C22×C42—431no—
332#501—4316no—
333#490—4316no—
334#481—438no—
335#481—438no—
336#480—438no—
337#480C2×D4318yescomplemented
338#478—4316no—
339#478—4316no—
340#432—438no—
341C2×#107—432no—
342C2×#107C2×D4312yes—
343C2×#106—432no—
344C2×#106—432no—
345C2×C4⋊C8—432no—
346C2×#102—432no—
347C2×#102—432no—
348C2×#102—432no—
349C2×#102C2×D4312yes—
350C2×C22⋊C8—431no—
351C2×C22⋊C8C2×D4311yescharacteristic
352C2×#97—432no—
353C43C2×#323411yescharacteristic, complemented, Sylow
354C2×#41—868no—
355C2×#41—1728no—
356C22×Q8—861no—
357C22×D4—21no—
358C22×D4—431no—
359C22×D4—861no—
360C22×D4—861no—
361C22×D4—861no—
362C22×D4C22×D4311yescharacteristic
363C23×C4—21no—
364C23×C4—431no—
365C23×C4—431no—
366C23×C4—861no—
367C23×C4—861no—
368C23×C4—861no—
369C23×C4C22×D4311yescharacteristic
370C22×C8—432no—
371C22×C8C22×D4312yes—
372C4⋊Q8—434no—
373C4⋊Q8—862no—
374#127—434no—
375#127—862no—
376#125—438no—
377#125—438no—
378#125—864no—
379#125—868no—
380#125—868no—
381#125—864no—
382#124—868no—
383#121—22no—
384#121—434no—
385#121—868no—
386#121—862no—
387#121C22×D4314yes—
388C4×D4—434no—
389C4×D4—434no—
390C4×D4—868no—
391C4×D4—862no—
392C4×D4—862no—
393C2×C4⋊C4—22no—
394C2×C4⋊C4—21no—
395C2×C4⋊C4—432no—
396C2×C4⋊C4—434no—
397C2×C4⋊C4—431no—
398C2×C4⋊C4—868no—
399C2×C4⋊C4—862no—
400C2×C4⋊C4—862no—
401C2×C4⋊C4—868no—
402C2×C4⋊C4—862no—
403C2×C4⋊C4—862no—
404C2×C4⋊C4—861no—
405C2×C4⋊C4—862no—
406C2×C4⋊C4—861no—
407C2×C4⋊C4C22×D4312yes—
408C2×C4⋊C4C22×D4314yes—
409C2×C4⋊C4C22×D4311yescharacteristic
410C2×C22⋊C4—21no—
411C2×C22⋊C4—861no—
412C2×C22⋊C4—861no—
413C2×C22⋊C4—861no—
414C2×C42—431no—
415C2×C42—431no—
416C2×C42—434no—
417C2×C42—431no—
418C2×C42—431no—
419C2×C42—434no—
420#107—438no—
421#107C22×D4318yes—
422#106—438no—
423#106—438no—
424C4⋊C8—438no—
425#102—438no—
426#102—438no—
427#102—438no—
428#102C22×D4318yes—
429C22⋊C8—434no—
430C22⋊C8C22×D4314yes—
431#97—438no—
432C24—21no—
433C24—861no—
434C24D4×D4311yescharacteristic
435#41—17232no—
436C2×Q8—864no—
437C2×Q8—1724no—
438C2×D4—24no—
439C2×D4—21no—
440C2×D4—24no—
441C2×D4—44no—
442C2×D4—432no—
443C2×D4—864no—
444C2×D4—864no—
445C2×D4—864no—
446C2×D4—861no—
447C2×D4—864no—
448C2×D4—1724no—
449C2×D4—1724no—
450C2×D4—1724no—
451C2×D4C23×D4312yes—
452C22×C4—24no—
453C22×C4—24no—
454C22×C4—21no—
455C22×C4—22no—
456C22×C4—44no—
457C22×C4—434no—
458C22×C4—431no—
459C22×C4—431no—
460C22×C4—431no—
461C22×C4—431no—
462C22×C4—434no—
463C22×C4—864no—
464C22×C4—864no—
465C22×C4—864no—
466C22×C4—864no—
467C22×C4—861no—
468C22×C4—862no—
469C22×C4—1724no—
470C22×C4—1722no—
471C22×C4—1724no—
472C22×C4—1724no—
473C22×C4D4×D4312yes—
474C22×C4D4×D4311yescharacteristic
475C22×C4C23×D4312yes—
476C22×C4C23×D4311yescharacteristic
477C2×C8—24no—
478C2×C8—434no—
479C2×C8—864no—
480C2×C8C23×D4314yes—
481C4⋊C4—24no—
482C4⋊C4—22no—
483C4⋊C4—21no—
484C4⋊C4—434no—
485C4⋊C4—432no—
486C4⋊C4—868no—
487C4⋊C4—868no—
488C4⋊C4—868no—
489C4⋊C4—868no—
490C4⋊C4—864no—
491C4⋊C4—864no—
492C4⋊C4—862no—
493C4⋊C4—861no—
494C4⋊C4C23×D4314yes—
495C4⋊C4C23×D4312yes—
496C22⋊C4—24no—
497C22⋊C4—864no—
498C22⋊C4—864no—
499C22⋊C4—864no—
500C42—432no—
501C42—434no—
502C42—434no—
503C42—432no—
504C42—432no—
505C42—432no—
506C23—22no—
507C23—22no—
508C23—22no—
509C23—42no—
510C23—42no—
511C23—42no—
512C23—862no—
513C23—1722no—
514C23—1722no—
515C23—1722no—
516C23#1306334914yes—
517C23C2×D4×D4312yes—
518C23C2×D4×D4311yescharacteristic
519Q8—1728no—
520D4—24no—
521D4—48no—
522D4—42no—
523D4—864no—
524D4—1728no—
525D4—1728no—
526D4—1728no—
527D4—1722no—
528C2×C4—22no—
529C2×C4—24no—
530C2×C4—24no—
531C2×C4—22no—
532C2×C4—24no—
533C2×C4—48no—
534C2×C4—44no—
535C2×C4—42no—
536C2×C4—432no—
537C2×C4—432no—
538C2×C4—432no—
539C2×C4—432no—
540C2×C4—862no—
541C2×C4—862no—
542C2×C4—868no—
543C2×C4—862no—
544C2×C4—862no—
545C2×C4—862no—
546C2×C4—864no—
547C2×C4—1728no—
548C2×C4—1724no—
549C2×C4—1728no—
550C2×C4—1728no—
551C2×C4—1722no—
552C2×C4—1724no—
553C2×C4C2×D4×D4312yes—
554C2×C4C2×D4×D4311yescharacteristic
555C2×C4#1306337214yes—
556C2×C4C24×D4311yescharacteristic
557C8—24no—
558C8—864no—
559C22—22no—
560C22—28no—
561C22—22no—
562C22—42no—
563C22—42no—
564C22—42no—
565C22—84no—
566C22—3444no—
567C22—1722no—
568C22—1722no—
569C22—1722no—
570C22#1458347112yes—
571C22C2×#1306334914yes—
572C22C2×#1306334912yes—
573C22#1458369812yes—
574C22C22×D4×D4311yescharacteristic
575C4—22no—
576C4—44no—
577C4—42no—
578C4—862no—
579C4—862no—
580C4—862no—
581C4—862no—
582C4—1722no—
583C4—1724no—
584C4#1458347112yes—
585C4C2×#1306337212yes—
586C2—24no—
587C2—82no—
588C2—3442no—
589C2#1914578214yesdirect product factor
590C2C2×#1458347111yescharacteristic
591C2C22×#1306334911yescharacteristic
592C2C2×#1458369811yescharacteristic
subgroupG/H
centerC23C2×D4×D43
commutator, cosocleC2×C4×C43C25
FrattiniC2×C4C24×D43
FittingC2×C43×#480C2
socleC23×C43C22×D4
prime radicalC2×#14583444C2
hypercenterC2×#480D43
hypocenterC43C2×#3234
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#480

Complements

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

NH ≅ G/Ntype
2. C22×#13063316C2semidirect
3. #19145782C2direct (N × H)
4. C2×#14583307C2semidirect
5. C2×#14583262C2semidirect
6. C2×#14583218C2semidirect
7. C2×#14583215C2semidirect
8. C2×#14583212C2semidirect
9. C2×#14583202C2semidirect
10. C2×#14583201C2semidirect
11. C2×#14582953C2semidirect
12. C2×C43×#480C2semidirect
23. C2×#13063316C22semidirect
34. #14583307C22semidirect
35. #14583262C22semidirect
36. #14583218C22semidirect
37. #14583215C22semidirect
38. #14583212C22semidirect
39. #14583202C22semidirect
40. #14583201C22semidirect
41. #14582953C22semidirect
53. C43×#480C22semidirect
298. C2×#480D43semidirect
304. C2×C43#3234semidirect
337. #480C2×D43semidirect
353. C43C2×#3234semidirect
589. C2#19145782direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834442
C22×#130633162
#191457822
C2×#145833072
C2×#145832622
C2×#145832182
C2×#145832152
C2×#145832122
C2×#145832022
C2×#145832012
C2×#145829532
C2×C43×#4802
C2×#323443