Finite Group Databasebeta

← C2×#19133512 #25068660

Subgroups — C2×#19133512 #25068660

Order 11008.

2040 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 2040 conjugacy classes of subgroups — too many to draw. Only its 203 normal subgroups are shown.

Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1C2×#14583461C211yesmaximal, characteristic, complemented
2C2×#14583033C212yesmaximal, complemented
3#19133512C218yesmaximal, direct product factor
4C2×#14582632C212yesmaximal, complemented
5C2×#14582623C211yesmaximal, characteristic, complemented
6C2×C43×#392C211yesmaximal, characteristic, complemented
7C23×C22⋊D43—21no—
8C22×#10621882—22no—
9#14583461—24no—
10#14583461—22no—
11#14583461C2214yescomplemented
12C2×#13063309—22no—
13C2×#13063299—21no—
14C2×#13063299C2212yes—
15C2×#13063295—22no—
16#14583033—24no—
17#14583033C2218yescomplemented
18C2×#13063246—22no—
19C2×C22⋊(C43⋊C8)C2212yescomplemented
20#14582632C2218yescomplemented
21#14582623C2214yescomplemented
22C23×D4×C43—21no—
23C23×D4×C43C2211yescharacteristic, complemented
24C22×C22⋊C4×C43—21no—
25C22×C22⋊C4×C43C2211yescharacteristic
26C43×#392—22no—
27C43×#392C2214yescomplemented
28C2×#95×C43C2211yescharacteristic, complemented
29C24×D43—21no—
30C22×D172—21no—
31C22×D172D412yescomplemented
32C22×C22⋊D43—22no—
33C22×C22⋊D43—24no—
34C22×C22⋊D43—22no—
35C22×C22⋊D43—24no—
36C22×C22⋊D43—44no—
37C22×C22⋊D43—44no—
38C23×Dic43—21no—
39C2×#10621882—28no—
40C2×#10621882—48no—
41C22×C43⋊C8—22no—
42#13063309—28no—
43#13063309—28no—
44#13063299—24no—
45#13063299—24no—
46#13063299—22no—
47#13063299—22no—
48#13063299D414yescomplemented
49#13063299C2314yes—
50#13063295—28no—
51#13063295—28no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43D412yescomplemented
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56#13063246—28no—
57C22⋊(C43⋊C8)—22no—
58C22⋊(C43⋊C8)C2314yescomplemented
59C25×C43—21no—
60C25×C43D411yescharacteristic
61C22×D4×C43—24no—
62C22×D4×C43—22no—
63C22×D4×C43—22no—
64C22×D4×C43—21no—
65C22×D4×C43—44no—
66C22×D4×C43—44no—
67C22×D4×C43—44no—
68C22×D4×C43—44no—
69C22×D4×C43C2312yescomplemented
70C23×C4×C43—21no—
71C23×C4×C43D411yescharacteristic
72C23×C4×C43C2311yescharacteristic
73C2×C22⋊C4×C43—22no—
74C2×C22⋊C4×C43—22no—
75C2×C22⋊C4×C43—24no—
76C2×C22⋊C4×C43—44no—
77C2×C22⋊C4×C43D412yes—
78C2×C22⋊C4×C43C2312yes—
79#95×C43—21no—
80#95×C43C2312yescomplemented
81C24×C43—21no—
82C24×C43—21no—
83C24×C43—22no—
84C24×C43—24no—
85C24×C43—22no—
86C24×C43—42no—
87C24×C43—42no—
88C24×C43—42no—
89C24×C43—42no—
90C24×C43—42no—
91C24×C43—41no—
92C24×C43—41no—
93C24×C43—42no—
94C24×C43—42no—
95C24×C43D814yescomplemented
96C24×C43C2×D411yescharacteristic
97C24×C43C2×D412yes—
98C23×D43—22no—
99C23×D43—24no—
100C23×D43—44no—
101C23×D43—82no—
102C23×D43—82no—
103C2×D4×C43—28no—
104C2×D4×C43—24no—
105C2×D4×C43—44no—
106C2×D4×C43—48no—
107C2×D4×C43—44no—
108C2×D4×C43—48no—
109C2×D4×C43—44no—
110C2×D4×C43—48no—
111C2×D4×C43—432no—
112C2×D4×C43—42no—
113C2×D4×C43—48no—
114C22×C4×C43—24no—
115C22×C4×C43—21no—
116C22×C4×C43—21no—
117C22×C4×C43—22no—
118C22×C4×C43—42no—
119C22×C4×C43—42no—
120C22×C4×C43—42no—
121C22×C4×C43—42no—
122C22×C4×C43C2×D412yes—
123C22×C4×C43C2×D412yes—
124C22×C4×C43C2×D412yes—
125C22×C4×C43C2×D411yescharacteristic
126C22×C4×C43C2411yescharacteristic
127C2×C22⋊D43—28no—
128C2×C22⋊D43—24no—
129C2×C22⋊D43—24no—
130C2×C22⋊D43—48no—
131C2×C22⋊D43—416no—
132C2×C22⋊D43—48no—
133C2×C22⋊D43—44no—
134C2×C22⋊D43—48no—
135C2×C22⋊D43—44no—
136C22×Dic43—24no—
137C22×Dic43—22no—
138C22×Dic43—44no—
139C2×D172—24no—
140C2×D172—22no—
141C2×D172—44no—
142C2×D172—82no—
143C2×D172C2×D414yescomplemented
144C22⋊C4×C43—24no—
145C22⋊C4×C43—24no—
146C22⋊C4×C43—48no—
147#10621882—416no—
148(C2×D43)⋊C4—28no—
149(C2×D43)⋊C4—24no—
150(C2×D43)⋊C4—24no—
151C4⋊Dic43—24no—
152C4⋊Dic43—22no—
153C4⋊Dic43C2×D414yescomplemented
154C2×C43⋊C8—24no—
155C2×C43⋊C8—44no—
156C23×C43—22no—
157C23×C43—22no—
158C23×C43—22no—
159C23×C43—24no—
160C23×C43—22no—
161C23×C43—24no—
162C23×C43—24no—
163C23×C43—48no—
164C23×C43—42no—
165C23×C43—42no—
166C23×C43—42no—
167C23×C43—48no—
168C23×C43—42no—
169C23×C43—42no—
170C23×C43—44no—
171C23×C43—48no—
172C23×C43—42no—
173C23×C43—42no—
174C23×C43—42no—
175C23×C43—42no—
176C23×C43—42no—
177C23×C43—44no—
178C23×C43—84no—
179C23×C43—81no—
180C23×C43—81no—
181C23×C43—84no—
182C23×C43—84no—
183C23×C43—82no—
184C23×C43—82no—
185C23×C43—82no—
186C23×C43—82no—
187C23×C43#12011yescharacteristic
188C23×C43#12011yescharacteristic
189C23×C43C2×D812yes—
190C23×C43C2×D814yescomplemented
191C23×C43AGL(1,ℤ/8)12yes—
192C23×C43C22×D411yescharacteristic
193C22×D43—24no—
194C22×D43—48no—
195C22×D43—44no—
196C22×D43—44no—
197C22×D43—44no—
198C22×D43—84no—
199C22×D43—84no—
200C22×D43—816no—
201D4×C43—28no—
202D4×C43—44no—
203D4×C43—48no—
204D4×C43—432no—
205C2×C4×C43—24no—
206C2×C4×C43—24no—
207C2×C4×C43—22no—
208C2×C4×C43—42no—
209C2×C4×C43—41no—
210C2×C4×C43—41no—
211C2×C4×C43—48no—
212C2×C4×C43—42no—
213C2×C4×C43—42no—
214C2×C4×C43—42no—
215C2×C4×C43—42no—
216C2×C4×C43—81no—
217C2×C4×C43#12012yes—
218C2×C4×C43C22×D412yes—
219C22⋊D43—416no—
220C22⋊D43—44no—
221C22⋊D43—44no—
222C22⋊D43—48no—
223C2×Dic43—24no—
224C2×Dic43—48no—
225C2×Dic43—44no—
226D172—44no—
227D172—82no—
228D172—84no—
229C43⋊C8—44no—
230C2×#1595—431nomaximal, Sylow
231C22×C43—24no—
232C22×C43—24no—
233C22×C43—21no—
234C22×C43—21no—
235C22×C43—21no—
236C22×C43—21no—
237C22×C43—24no—
238C22×C43—44no—
239C22×C43—44no—
240C22×C43—44no—
241C22×C43—48no—
242C22×C43—42no—
243C22×C43—42no—
244C22×C43—44no—
245C22×C43—82no—
246C22×C43—84no—
247C22×C43—82no—
248C22×C43—82no—
249C22×C43—88no—
250C22×C43—88no—
251C22×C43—82no—
252C22×C43—82no—
253C22×C43#44712yes—
254C22×C43#44712yes—
255C22×C43#45312yes—
256C22×C43B(4,𝔽2)12yes—
257C22×C43C2×#12011yescharacteristic
258C22×C43C22×D811yescharacteristic
259C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
260C2×D43—44no—
261C2×D43—44no—
262C2×D43—44no—
263C2×D43—816no—
264C2×D43—88no—
265C4×C43—22no—
266C4×C43—22no—
267C4×C43—44no—
268C4×C43—42no—
269Dic43—44no—
270C2×#534—431no—
271C2×#447—432no—
272C2×#392D4311yescharacteristic, complemented
273#1595—438no—
274C2×#327—432no—
275C2×#323—431no—
276C2×C43—21no—
277C2×C43—21no—
278C2×C43—22no—
279C2×C43—44no—
280C2×C43—84no—
281C2×C43#159514yescomplemented
282C2×C43C2×#44711yescharacteristic
283C2×C43C2×#45311yescharacteristic
284C2×C43C2×B(4,𝔽2)11yescharacteristic
285D43—84no—
286C23×D4—21no—
287C23×D4—861no—
288C23×D4C2×D4311yescharacteristic, complemented
289C22×D8—862no—
290#534—434no—
291#534—864no—
292#534—862no—
293C2×#123—862no—
294C2×#121—432no—
295C2×#121—861no—
296C2×#120—862no—
297C22×C22⋊C4—21no—
298C22×C22⋊C4C2×D4311yescharacteristic
299#447—438no—
300#447—864no—
301C2×#102—862no—
302C2×C22⋊C8—432no—
303#392—22no—
304#392C2×D4314yescomplemented
305C2×#95C2×D4311yescharacteristic, complemented
306#327—438no—
307#323—434no—
308C43C2×#159511yescharacteristic, complemented, Sylow
309C25—21no—
310C25—861no—
311C25C22⋊D4311yescharacteristic
312C22×D4—24no—
313C22×D4—22no—
314C22×D4—22no—
315C22×D4—21no—
316C22×D4—44no—
317C22×D4—44no—
318C22×D4—44no—
319C22×D4—44no—
320C22×D4—432no—
321C22×D4—861no—
322C22×D4—862no—
323C22×D4—864no—
324C22×D4—862no—
325C22×D4—864no—
326C22×D4—1724no—
327C22×D4—1724no—
328C22×D4C22×D4312yescomplemented
329C23×C4—21no—
330C23×C4—861no—
331C23×C4C22⋊D4311yescharacteristic
332C23×C4C22×D4311yescharacteristic
333C2×D8—868no—
334C2×D8—1728no—
335C22×C8—862no—
336#123—868no—
337#123—868no—
338#121—434no—
339#121—434no—
340#121—864no—
341#121—862no—
342#121—862no—
343#121—864no—
344#120—868no—
345#120—868no—
346C2×C4⋊C4—432no—
347C2×C4⋊C4—861no—
348C2×C22⋊C4—22no—
349C2×C22⋊C4—22no—
350C2×C22⋊C4—24no—
351C2×C22⋊C4—44no—
352C2×C22⋊C4—862no—
353C2×C22⋊C4—862no—
354C2×C22⋊C4C22⋊D4312yes—
355C2×C22⋊C4C22×D4312yes—
356#102—868no—
357C22⋊C8—434no—
358C22⋊C8—862no—
359#95—21no—
360#95C22×D4312yescomplemented
361C24—21no—
362C24—21no—
363C24—22no—
364C24—24no—
365C24—22no—
366C24—42no—
367C24—42no—
368C24—42no—
369C24—42no—
370C24—42no—
371C24—41no—
372C24—41no—
373C24—42no—
374C24—42no—
375C24—864no—
376C24—862no—
377C24—3442no—
378C24—3442no—
379C24—1724no—
380C24#1062188214yescomplemented
381C24C2×C22⋊D4311yescharacteristic
382C24C2×C22⋊D4312yes—
383C2×D4—28no—
384C2×D4—24no—
385C2×D4—44no—
386C2×D4—48no—
387C2×D4—44no—
388C2×D4—48no—
389C2×D4—44no—
390C2×D4—48no—
391C2×D4—432no—
392C2×D4—48no—
393C2×D4—42no—
394C2×D4—434no—
395C2×D4—864no—
396C2×D4—868no—
397C2×D4—864no—
398C2×D4—864no—
399C2×D4—862no—
400C2×D4—3442no—
401C2×D4—1724no—
402C2×D4—1728no—
403C2×D4—17216no—
404C2×D4—1728no—
405C2×D4—1724no—
406C2×D4—1728no—
407C2×D4—1724no—
408C22×C4—24no—
409C22×C4—21no—
410C22×C4—22no—
411C22×C4—21no—
412C22×C4—42no—
413C22×C4—42no—
414C22×C4—42no—
415C22×C4—42no—
416C22×C4—864no—
417C22×C4—862no—
418C22×C4—1724no—
419C22×C4D4×D4312yes—
420C22×C4D4×D4312yes—
421C22×C4C2×C22⋊D4312yes—
422C22×C4C2×C22⋊D4311yescharacteristic
423C22×C4C23×D4311yescharacteristic
424D8—17216no—
425C2×C8—864no—
426C2×C8—1724no—
427C4⋊C4—434no—
428C4⋊C4—864no—
429C4⋊C4—862no—
430C22⋊C4—24no—
431C22⋊C4—24no—
432C22⋊C4—48no—
433C22⋊C4—868no—
434C22⋊C4—864no—
435C22⋊C4—864no—
436C23—22no—
437C23—22no—
438C23—22no—
439C23—24no—
440C23—22no—
441C23—24no—
442C23—24no—
443C23—48no—
444C23—42no—
445C23—42no—
446C23—42no—
447C23—42no—
448C23—44no—
449C23—48no—
450C23—42no—
451C23—48no—
452C23—42no—
453C23—42no—
454C23—44no—
455C23—42no—
456C23—42no—
457C23—42no—
458C23—81no—
459C23—84no—
460C23—81no—
461C23—84no—
462C23—84no—
463C23—82no—
464C23—82no—
465C23—82no—
466C23—82no—
467C23—864no—
468C23—34416no—
469C23—3444no—
470C23—3444no—
471C23—1728no—
472C23—1724no—
473C23—1724no—
474C23—1724no—
475C23#1306329311yescharacteristic
476C23#1306329311yescharacteristic
477C23C2×#1062188212yes—
478C23C2×#1062188214yescomplemented
479C23#1306335012yes—
480C23C22×C22⋊D4311yescharacteristic
481D4—28no—
482D4—44no—
483D4—48no—
484D4—432no—
485D4—3442no—
486D4—3444no—
487D4—1724no—
488D4—17216no—
489D4—1724no—
490D4—1724no—
491D4—1728no—
492C2×C4—24no—
493C2×C4—24no—
494C2×C4—22no—
495C2×C4—42no—
496C2×C4—41no—
497C2×C4—41no—
498C2×C4—42no—
499C2×C4—48no—
500C2×C4—42no—
501C2×C4—42no—
502C2×C4—42no—
503C2×C4—81no—
504C2×C4—864no—
505C2×C4—1728no—
506C2×C4—1724no—
507C2×C4#1306329312yes—
508C2×C4C2×D4×D4312yes—
509C8—1724no—
510C22—21no—
511C22—21no—
512C22—24no—
513C22—24no—
514C22—21no—
515C22—21no—
516C22—24no—
517C22—44no—
518C22—44no—
519C22—44no—
520C22—42no—
521C22—48no—
522C22—42no—
523C22—44no—
524C22—82no—
525C22—84no—
526C22—82no—
527C22—82no—
528C22—88no—
529C22—88no—
530C22—82no—
531C22—82no—
532C22—34416no—
533C22—3448no—
534C22—1724no—
535C22—1724no—
536C22—1724no—
537C22#1458303212yes—
538C22#1458303212yes—
539C22#1458306612yes—
540C22#1458308512yes—
541C22C2×#1306329311yescharacteristic
542C22C22×#1062188211yescharacteristic
543C22C2×#1306335011yescharacteristic
544C4—22no—
545C4—22no—
546C4—44no—
547C4—42no—
548C4—1724no—
549C2—21no—
550C2—21no—
551C2—22no—
552C2—44no—
553C2—84no—
554C2—3444no—
555C2#1913351214yesdirect product factor
556C2C2×#1458303211yescharacteristic
557C2C2×#1458306611yescharacteristic
558C2C2×#1458308511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#392C2
socleC23×C43#120
hypercenterC2×#392D43
hypocenterC43C2×#1595
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#392

Complements

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

NH ≅ G/Ntype
1. C2×#14583461C2semidirect
2. C2×#14583033C2semidirect
3. #19133512C2direct (N × H)
4. C2×#14582632C2semidirect
5. C2×#14582623C2semidirect
6. C2×C43×#392C2semidirect
11. #14583461C22semidirect
17. #14583033C22semidirect
19. C2×C22⋊(C43⋊C8)C22semidirect
20. #14582632C22semidirect
21. #14582623C22semidirect
23. C23×D4×C43C22semidirect
27. C43×#392C22semidirect
28. C2×#95×C43C22semidirect
31. C22×D172D4semidirect
48. #13063299D4semidirect
53. C2×C4⋊Dic43D4semidirect
58. C22⋊(C43⋊C8)C23semidirect
69. C22×D4×C43C23semidirect
80. #95×C43C23semidirect
95. C24×C43D8semidirect
143. C2×D172C2×D4semidirect
153. C4⋊Dic43C2×D4semidirect
190. C23×C43C2×D8semidirect
272. C2×#392D43semidirect
281. C2×C43#1595semidirect
288. C23×D4C2×D43semidirect
304. #392C2×D43semidirect
305. C2×#95C2×D43semidirect
308. C43C2×#1595semidirect
328. C22×D4C22×D43semidirect
360. #95C22×D43semidirect
380. C24#10621882semidirect
478. C23C2×#10621882semidirect
555. C2#19133512direct (N × H)

Maximal subgroups

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

subgroupindex
C2×#145834612
C2×#145830332
#191335122
C2×#145826322
C2×#145826232
C2×C43×#3922
C2×#159543