Finite Group Databasebeta

← C2×#19133546 #25068666

Subgroups — C2×#19133546 #25068666

Order 11008.

1652 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1652 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
2C2×#14583038C212yesmaximal, complemented
3#19133546C218yesmaximal, direct product factor
4C2×#14582632C212yesmaximal, complemented
5C2×#14582623C211yesmaximal, characteristic, complemented
6C2×C43×#393C211yesmaximal, characteristic, complemented
7C23×C22⋊D43—21no—
8C22×#10621884—22no—
9#14583461—24no—
10#14583461—22no—
11#14583461C2214yes—
12C2×#13063309—22no—
13C2×#13063299—21no—
14C2×#13063299C2212yes—
15C2×#13063295—22no—
16#14583038—24no—
17#14583038C2218yescomplemented
18C2×#13063249—22no—
19C2×C22⋊(C43⋊C8)C2212yescomplemented
20#14582632C2218yescomplemented
21#14582623C2214yescomplemented
22C23×Q8×C43C2211yescharacteristic, complemented
23C22×C22⋊C4×C43—21no—
24C22×C22⋊C4×C43C2211yescharacteristic
25C43×#393—22no—
26C43×#393C2214yescomplemented
27C2×#95×C43—21no—
28C2×#95×C43C2211yescharacteristic, complemented
29C24×D43—21no—
30C22×D172—21no—
31C22×D172D412yes—
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×#10621884—28no—
40C2×#10621884—48no—
41C22×C43⋊C8—22no—
42#13063309—28no—
43#13063309—28no—
44#13063299—24no—
45#13063299—24no—
46#13063299—22no—
47#13063299—22no—
48#13063299D414yes—
49#13063299C2314yes—
50#13063295—28no—
51#13063295—28no—
52C2×C4⋊Dic43—21no—
53C2×C4⋊Dic43D412yes—
54C2×(C2×D43)⋊C4—22no—
55C2×(C2×D43)⋊C4—22no—
56#13063249—28no—
57C22⋊(C43⋊C8)—22no—
58C22⋊(C43⋊C8)C2314yescomplemented
59C25×C43D411yescharacteristic
60C22×Q8×C43—21no—
61C22×Q8×C43—22no—
62C22×Q8×C43—22no—
63C22×Q8×C43—44no—
64C22×Q8×C43C2312yescomplemented
65C23×C4×C43—21no—
66C23×C4×C43—21no—
67C23×C4×C43D411yescharacteristic
68C23×C4×C43C2311yescharacteristic
69C2×C22⋊C4×C43—22no—
70C2×C22⋊C4×C43—22no—
71C2×C22⋊C4×C43—24no—
72C2×C22⋊C4×C43—44no—
73C2×C22⋊C4×C43D412yes—
74C2×C22⋊C4×C43C2312yes—
75#95×C43—24no—
76#95×C43—21no—
77#95×C43C2312yescomplemented
78C24×C43—21no—
79C24×C43—21no—
80C24×C43—22no—
81C24×C43—42no—
82C24×C43—42no—
83C24×C43SD1614yescomplemented
84C24×C43C2×D411yescharacteristic
85C24×C43C2×D412yes—
86C23×D43—22no—
87C23×D43—24no—
88C23×D43—44no—
89C23×D43—82no—
90C23×D43—82no—
91C2×Q8×C43—28no—
92C2×Q8×C43—24no—
93C2×Q8×C43—44no—
94C2×Q8×C43—44no—
95C2×Q8×C43—44no—
96C2×Q8×C43—48no—
97C2×Q8×C43—42no—
98C22×C4×C43—24no—
99C22×C4×C43—21no—
100C22×C4×C43—21no—
101C22×C4×C43—22no—
102C22×C4×C43—22no—
103C22×C4×C43—42no—
104C22×C4×C43—42no—
105C22×C4×C43—42no—
106C22×C4×C43—42no—
107C22×C4×C43—42no—
108C22×C4×C43—41no—
109C22×C4×C43—41no—
110C22×C4×C43—42no—
111C22×C4×C43C2×D412yes—
112C22×C4×C43C2×D412yes—
113C22×C4×C43C2×D412yes—
114C22×C4×C43C2×D411yescharacteristic
115C22×C4×C43C2411yescharacteristic
116C2×C22⋊D43—28no—
117C2×C22⋊D43—24no—
118C2×C22⋊D43—24no—
119C2×C22⋊D43—48no—
120C2×C22⋊D43—416no—
121C2×C22⋊D43—48no—
122C2×C22⋊D43—44no—
123C2×C22⋊D43—48no—
124C2×C22⋊D43—44no—
125C22×Dic43—24no—
126C22×Dic43—22no—
127C22×Dic43—44no—
128C2×D172—24no—
129C2×D172—22no—
130C2×D172—44no—
131C2×D172—82no—
132C2×D172C2×D414yes—
133C22⋊C4×C43—24no—
134C22⋊C4×C43—24no—
135C22⋊C4×C43—48no—
136#10621884—416no—
137(C2×D43)⋊C4—28no—
138(C2×D43)⋊C4—24no—
139(C2×D43)⋊C4—24no—
140C4⋊Dic43—24no—
141C4⋊Dic43—22no—
142C4⋊Dic43C2×D414yes—
143C2×C43⋊C8—24no—
144C2×C43⋊C8—44no—
145C23×C43—22no—
146C23×C43—22no—
147C23×C43—22no—
148C23×C43—24no—
149C23×C43—22no—
150C23×C43—24no—
151C23×C43—42no—
152C23×C43—48no—
153C23×C43—42no—
154C23×C43—42no—
155C23×C43—42no—
156C23×C43—84no—
157C23×C43—81no—
158C23×C43—81no—
159C23×C43#12011yescharacteristic
160C23×C43#12011yescharacteristic
161C23×C43C2×SD1612yes—
162C23×C43C2×SD1614yescomplemented
163C23×C43AGL(1,ℤ/8)12yes—
164C23×C43C22×D411yescharacteristic
165C22×D43—24no—
166C22×D43—48no—
167C22×D43—44no—
168C22×D43—44no—
169C22×D43—44no—
170C22×D43—84no—
171C22×D43—84no—
172C22×D43—816no—
173Q8×C43—28no—
174Q8×C43—44no—
175Q8×C43—48no—
176C2×C4×C43—24no—
177C2×C4×C43—24no—
178C2×C4×C43—22no—
179C2×C4×C43—42no—
180C2×C4×C43—41no—
181C2×C4×C43—41no—
182C2×C4×C43—42no—
183C2×C4×C43—44no—
184C2×C4×C43—42no—
185C2×C4×C43—42no—
186C2×C4×C43—44no—
187C2×C4×C43—42no—
188C2×C4×C43—42no—
189C2×C4×C43—42no—
190C2×C4×C43—42no—
191C2×C4×C43—81no—
192C2×C4×C43—84no—
193C2×C4×C43#12012yes—
194C2×C4×C43C22×D412yes—
195C22⋊D43—416no—
196C22⋊D43—44no—
197C22⋊D43—44no—
198C22⋊D43—48no—
199C2×Dic43—24no—
200C2×Dic43—48no—
201C2×Dic43—44no—
202D172—44no—
203D172—82no—
204D172—84no—
205C43⋊C8—44no—
206C2×#1601—431nomaximal, Sylow
207C22×C43—24no—
208C22×C43—24no—
209C22×C43—21no—
210C22×C43—21no—
211C22×C43—21no—
212C22×C43—21no—
213C22×C43—24no—
214C22×C43—44no—
215C22×C43—48no—
216C22×C43—42no—
217C22×C43—42no—
218C22×C43—82no—
219C22×C43—84no—
220C22×C43#45012yes—
221C22×C43#45012yes—
222C22×C43#45512yes—
223C22×C43B(4,𝔽2)12yes—
224C22×C43C2×#12011yescharacteristic
225C22×C43C22×SD1611yescharacteristic
226C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
227C2×D43—44no—
228C2×D43—44no—
229C2×D43—44no—
230C2×D43—816no—
231C2×D43—88no—
232C4×C43—22no—
233C4×C43—22no—
234C4×C43—42no—
235C4×C43—44no—
236C4×C43—82no—
237Dic43—44no—
238C2×#534—431no—
239C2×#448—432no—
240C2×#393D4311yescharacteristic, complemented
241#1601—438no—
242C2×#327—432no—
243C2×#323—431no—
244C2×C43—21no—
245C2×C43—21no—
246C2×C43—22no—
247C2×C43—44no—
248C2×C43#160114yescomplemented
249C2×C43C2×#45011yescharacteristic
250C2×C43C2×#45511yescharacteristic
251C2×C43C2×B(4,𝔽2)11yescharacteristic
252D43—84no—
253C23×Q8C2×D4311yescharacteristic, complemented
254C23×D4—861no—
255C22×SD16—862no—
256#534—434no—
257#534—864no—
258#534—862no—
259C2×#123—862no—
260C2×#121—432no—
261C2×#121—861no—
262C2×#120—862no—
263C22×C22⋊C4—21no—
264C22×C22⋊C4C2×D4311yescharacteristic
265#448—438no—
266#448—864no—
267C2×#103—862no—
268C2×C22⋊C8—432no—
269#393—22no—
270#393C2×D4314yescomplemented
271C2×#95—21no—
272C2×#95C2×D4311yescharacteristic, complemented
273#327—438no—
274#323—434no—
275C43C2×#160111yescharacteristic, complemented, Sylow
276C25—861no—
277C25C22⋊D4311yescharacteristic
278C22×Q8—21no—
279C22×Q8—22no—
280C22×Q8—22no—
281C22×Q8—44no—
282C22×Q8C22×D4312yescomplemented
283C22×D4—432no—
284C22×D4—861no—
285C22×D4—862no—
286C22×D4—864no—
287C22×D4—862no—
288C22×D4—864no—
289C22×D4—1724no—
290C22×D4—1724no—
291C23×C4—21no—
292C23×C4—21no—
293C23×C4—861no—
294C23×C4C22⋊D4311yescharacteristic
295C23×C4C22×D4311yescharacteristic
296C2×SD16—868no—
297C2×SD16—1728no—
298C22×C8—862no—
299#123—868no—
300#123—868no—
301#121—434no—
302#121—434no—
303#121—864no—
304#121—862no—
305#121—862no—
306#121—864no—
307#120—868no—
308#120—868no—
309C2×C4⋊C4—432no—
310C2×C4⋊C4—861no—
311C2×C22⋊C4—22no—
312C2×C22⋊C4—22no—
313C2×C22⋊C4—24no—
314C2×C22⋊C4—44no—
315C2×C22⋊C4—862no—
316C2×C22⋊C4—862no—
317C2×C22⋊C4C22⋊D4312yes—
318C2×C22⋊C4C22×D4312yes—
319#103—868no—
320C22⋊C8—434no—
321C22⋊C8—862no—
322#95—24no—
323#95—21no—
324#95C22×D4312yescomplemented
325C24—21no—
326C24—21no—
327C24—22no—
328C24—42no—
329C24—42no—
330C24—864no—
331C24—862no—
332C24—3442no—
333C24—3442no—
334C24—1724no—
335C24#1062188414yescomplemented
336C24C2×C22⋊D4311yescharacteristic
337C24C2×C22⋊D4312yes—
338C2×Q8—28no—
339C2×Q8—24no—
340C2×Q8—44no—
341C2×Q8—44no—
342C2×Q8—44no—
343C2×Q8—48no—
344C2×Q8—42no—
345C2×D4—434no—
346C2×D4—864no—
347C2×D4—868no—
348C2×D4—864no—
349C2×D4—864no—
350C2×D4—862no—
351C2×D4—3442no—
352C2×D4—1724no—
353C2×D4—17216no—
354C2×D4—1728no—
355C2×D4—1728no—
356C2×D4—1724no—
357C2×D4—1728no—
358C2×D4—1724no—
359C22×C4—24no—
360C22×C4—21no—
361C22×C4—22no—
362C22×C4—21no—
363C22×C4—22no—
364C22×C4—42no—
365C22×C4—42no—
366C22×C4—41no—
367C22×C4—41no—
368C22×C4—42no—
369C22×C4—42no—
370C22×C4—42no—
371C22×C4—42no—
372C22×C4—864no—
373C22×C4—862no—
374C22×C4—1724no—
375C22×C4D4×D4312yes—
376C22×C4D4×D4312yes—
377C22×C4C2×C22⋊D4312yes—
378C22×C4C2×C22⋊D4311yescharacteristic
379C22×C4C23×D4311yescharacteristic
380SD16—17216no—
381C2×C8—864no—
382C2×C8—1724no—
383C4⋊C4—434no—
384C4⋊C4—864no—
385C4⋊C4—862no—
386C22⋊C4—24no—
387C22⋊C4—24no—
388C22⋊C4—48no—
389C22⋊C4—868no—
390C22⋊C4—864no—
391C22⋊C4—864no—
392C23—22no—
393C23—22no—
394C23—24no—
395C23—22no—
396C23—24no—
397C23—22no—
398C23—42no—
399C23—48no—
400C23—42no—
401C23—42no—
402C23—42no—
403C23—81no—
404C23—84no—
405C23—81no—
406C23—864no—
407C23—34416no—
408C23—3444no—
409C23—3444no—
410C23—1728no—
411C23—1724no—
412C23—1724no—
413C23—1724no—
414C23#1306329311yescharacteristic
415C23#1306329311yescharacteristic
416C23C2×#1062188412yes—
417C23C2×#1062188414yescomplemented
418C23#1306335012yes—
419C23C22×C22⋊D4311yescharacteristic
420Q8—28no—
421Q8—44no—
422Q8—48no—
423D4—3442no—
424D4—3444no—
425D4—1724no—
426D4—17216no—
427D4—1728no—
428D4—1724no—
429D4—1724no—
430C2×C4—24no—
431C2×C4—24no—
432C2×C4—22no—
433C2×C4—42no—
434C2×C4—41no—
435C2×C4—41no—
436C2×C4—42no—
437C2×C4—44no—
438C2×C4—42no—
439C2×C4—44no—
440C2×C4—42no—
441C2×C4—42no—
442C2×C4—42no—
443C2×C4—42no—
444C2×C4—42no—
445C2×C4—81no—
446C2×C4—84no—
447C2×C4—864no—
448C2×C4—1728no—
449C2×C4—1724no—
450C2×C4#1306329312yes—
451C2×C4C2×D4×D4312yes—
452C8—1724no—
453C22—21no—
454C22—21no—
455C22—24no—
456C22—24no—
457C22—21no—
458C22—21no—
459C22—24no—
460C22—44no—
461C22—42no—
462C22—48no—
463C22—42no—
464C22—82no—
465C22—84no—
466C22—34416no—
467C22—3448no—
468C22—1724no—
469C22—1724no—
470C22—1724no—
471C22#1458304912yes—
472C22#1458304912yes—
473C22#1458307612yes—
474C22#1458308512yes—
475C22C2×#1306329311yescharacteristic
476C22C22×#1062188411yescharacteristic
477C22C2×#1306335011yescharacteristic
478C4—22no—
479C4—22no—
480C4—44no—
481C4—42no—
482C4—82no—
483C4—1724no—
484C2—21no—
485C2—21no—
486C2—22no—
487C2—44no—
488C2—3444no—
489C2#1913354614yesdirect product factor
490C2C2×#1458304911yescharacteristic
491C2C2×#1458307611yescharacteristic
492C2C2×#1458308511yescharacteristic
subgroupG/H
centerC23#13063293
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#393C2
socleC23×C43#120
prime radicalC2×#14583461C2
hypercenterC2×#393D43
hypocenterC43C2×#1601
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#393

Complements

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

NH ≅ G/Ntype
2. C2×#14583038C2semidirect
3. #19133546C2direct (N × H)
4. C2×#14582632C2semidirect
5. C2×#14582623C2semidirect
6. C2×C43×#393C2semidirect
17. #14583038C22semidirect
19. C2×C22⋊(C43⋊C8)C22semidirect
20. #14582632C22semidirect
21. #14582623C22semidirect
22. C23×Q8×C43C22semidirect
26. C43×#393C22semidirect
28. C2×#95×C43C22semidirect
58. C22⋊(C43⋊C8)C23semidirect
64. C22×Q8×C43C23semidirect
77. #95×C43C23semidirect
83. C24×C43SD16semidirect
162. C23×C43C2×SD16semidirect
240. C2×#393D43semidirect
248. C2×C43#1601semidirect
253. C23×Q8C2×D43semidirect
270. #393C2×D43semidirect
272. C2×#95C2×D43semidirect
275. C43C2×#1601semidirect
282. C22×Q8C22×D43semidirect
324. #95C22×D43semidirect
335. C24#10621884semidirect
417. C23C2×#10621884semidirect
489. C2#19133546direct (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×#145830382
#191335462
C2×#145826322
C2×#145826232
C2×C43×#3932
C2×#160143