Finite Group Databasebeta

← C2×#19133617 #25068720

Subgroups — C2×#19133617 #25068720

Order 11008.

1524 conjugacy classes of subgroups; only the 203 normal subgroups are shown.

normal subgroups only

This group has 1524 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×#14583218C212yesmaximal, complemented
3C2×#14582835C211yesmaximal, characteristic, complemented
4#19133617C218yesmaximal, direct product factor
5C2×#14582634C212yesmaximal, complemented
6C2×C43×#323C211yesmaximal, characteristic, complemented
7C23×C22⋊D43—21no—
8#14583461—24no—
9#14583461—22no—
10#14583461C2214yes—
11C2×#13063309—22no—
12C2×#13063299—21no—
13C2×#13063299C2212yes—
14C2×#13063295—22no—
15C22×C4⋊Dic43C2211yescharacteristic, complemented
16C22×Dic43⋊C4—21no—
17C22×C22⋊Dic43—21no—
18#14583218—24no—
19#14583218C2218yescomplemented
20C2×#13063257—22no—
21C2×#13063247—22no—
22#14582835—22no—
23#14582835C2214yescomplemented
24C2×C43⋊#95C2211yescharacteristic, complemented
25#14582634C2218yescomplemented
26C22×C22⋊C4×C43C2211yescharacteristic
27C2×C22⋊C8×C43C2212yescomplemented
28C43×#323C2214yescomplemented
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—
39C23×Dic43—21no—
40C23×Dic43—21no—
41#13063309—28no—
42#13063309—28no—
43#13063299—24no—
44#13063299—24no—
45#13063299—22no—
46#13063299—22no—
47#13063299D414yes—
48#13063299C2314yes—
49#13063295—28no—
50#13063295—28no—
51C2×C4⋊Dic43—21no—
52C2×C4⋊Dic43—22no—
53C2×C4⋊Dic43—22no—
54C2×C4⋊Dic43—21no—
55C2×C4⋊Dic43D412yes—
56C2×C4⋊Dic43C2312yescomplemented
57C2×Dic43⋊C4—24no—
58C2×Dic43⋊C4—44no—
59C2×C22⋊Dic43—24no—
60C2×C22⋊Dic43—44no—
61C2×(C2×D43)⋊C4—22no—
62C2×(C2×D43)⋊C4—22no—
63#13063257—28no—
64#13063247—28no—
65C43⋊#95—21no—
66C43⋊#95C2312yescomplemented
67C25×C43D411yescharacteristic
68C23×C4×C43D411yescharacteristic
69C23×C4×C43C2311yescharacteristic
70C22×C8×C43—22no—
71C2×C22⋊C4×C43—22no—
72C2×C22⋊C4×C43—22no—
73C2×C22⋊C4×C43D412yes—
74C2×C22⋊C4×C43C2312yes—
75C22⋊C8×C43—22no—
76C22⋊C8×C43C2314yescomplemented
77C24×C43—21no—
78C24×C43—21no—
79C24×C43—22no—
80C24×C43—42no—
81C24×C43—42no—
82C24×C43SD1614yes—
83C24×C43C2×D411yescharacteristic
84C24×C43C2×D412yes—
85C23×D43—22no—
86C23×D43—24no—
87C23×D43—44no—
88C23×D43—82no—
89C23×D43—82no—
90C22×C4×C43—21no—
91C22×C4×C43—21no—
92C22×C4×C43—42no—
93C22×C4×C43—42no—
94C22×C4×C43C2×D412yes—
95C22×C4×C43C2×D412yes—
96C22×C4×C43C2×D412yes—
97C22×C4×C43C2×D411yescharacteristic
98C22×C4×C43C2411yescharacteristic
99C2×C22⋊D43—28no—
100C2×C22⋊D43—24no—
101C2×C22⋊D43—24no—
102C2×C22⋊D43—48no—
103C2×C22⋊D43—416no—
104C2×C22⋊D43—48no—
105C2×C22⋊D43—48no—
106C2×C22⋊D43—44no—
107C2×C22⋊D43—44no—
108C22×Dic43—24no—
109C22×Dic43—24no—
110C22×Dic43—22no—
111C22×Dic43—22no—
112C22×Dic43—22no—
113C22×Dic43—42no—
114C22×Dic43—44no—
115C22×Dic43—42no—
116C22×Dic43—42no—
117C22×Dic43—41no—
118C22×Dic43—41no—
119C22×Dic43—42no—
120C2×D172—24no—
121C2×D172—22no—
122C2×D172—44no—
123C2×D172—82no—
124C2×D172C2×D414yes—
125C2×C8×C43—24no—
126C2×C8×C43—44no—
127C22⋊C4×C43—24no—
128C22⋊C4×C43—24no—
129C22⋊Dic43—48no—
130(C2×D43)⋊C4—28no—
131(C2×D43)⋊C4—24no—
132(C2×D43)⋊C4—24no—
133C4⋊Dic43—24no—
134C4⋊Dic43—22no—
135C4⋊Dic43—24no—
136C4⋊Dic43—42no—
137C4⋊Dic43C2×D414yes—
138Dic43⋊C4—48no—
139C23×C43—22no—
140C23×C43—22no—
141C23×C43—22no—
142C23×C43—24no—
143C23×C43—22no—
144C23×C43—24no—
145C23×C43—42no—
146C23×C43—48no—
147C23×C43—42no—
148C23×C43—42no—
149C23×C43—42no—
150C23×C43—84no—
151C23×C43—81no—
152C23×C43—81no—
153C23×C43#12011yescharacteristic
154C23×C43#12011yescharacteristic
155C23×C43C2×SD1612yes—
156C23×C43C2×SD1614yes—
157C23×C43AGL(1,ℤ/8)12yes—
158C23×C43C22×D411yescharacteristic
159C22×D43—24no—
160C22×D43—48no—
161C22×D43—44no—
162C22×D43—44no—
163C22×D43—44no—
164C22×D43—84no—
165C22×D43—84no—
166C22×D43—816no—
167C2×C4×C43—24no—
168C2×C4×C43—22no—
169C2×C4×C43—41no—
170C2×C4×C43—42no—
171C2×C4×C43—41no—
172C2×C4×C43—42no—
173C2×C4×C43—42no—
174C2×C4×C43—81no—
175C2×C4×C43#12012yes—
176C2×C4×C43C22×D412yes—
177C22⋊D43—416no—
178C22⋊D43—44no—
179C22⋊D43—44no—
180C22⋊D43—48no—
181C2×Dic43—24no—
182C2×Dic43—24no—
183C2×Dic43—48no—
184C2×Dic43—42no—
185C2×Dic43—48no—
186C2×Dic43—42no—
187C2×Dic43—44no—
188C2×Dic43—42no—
189C2×Dic43—42no—
190C2×Dic43—42no—
191C2×Dic43—82no—
192C2×Dic43—82no—
193D172—44no—
194D172—82no—
195D172—84no—
196C8×C43—44no—
197C2×#1613—431nomaximal, Sylow
198C22×C43—24no—
199C22×C43—24no—
200C22×C43—21no—
201C22×C43—21no—
202C22×C43—21no—
203C22×C43—21no—
204C22×C43—24no—
205C22×C43—44no—
206C22×C43—48no—
207C22×C43—42no—
208C22×C43—42no—
209C22×C43—82no—
210C22×C43—84no—
211C22×C43#45012yes—
212C22×C43#45012yes—
213C22×C43#45312yes—
214C22×C43#45812yes—
215C22×C43C2×#12011yescharacteristic
216C22×C43C22×SD1611yescharacteristic
217C22×C43C2×AGL(1,ℤ/8)11yescharacteristic
218C2×D43—44no—
219C2×D43—44no—
220C2×D43—44no—
221C2×D43—816no—
222C2×D43—88no—
223C4×C43—22no—
224C4×C43—22no—
225C4×C43—42no—
226Dic43—44no—
227Dic43—44no—
228Dic43—82no—
229C2×#534—431no—
230C2×#481—432no—
231C2×#399—431no—
232#1613—438no—
233C2×#327—432no—
234C2×#323D4311yescharacteristic, complemented
235C2×C43—21no—
236C2×C43—21no—
237C2×C43—22no—
238C2×C43—44no—
239C2×C43#161314yescomplemented
240C2×C43C2×#45011yescharacteristic
241C2×C43C2×#45311yescharacteristic
242C2×C43C2×#45811yescharacteristic
243D43—84no—
244C23×D4—861no—
245#534—434no—
246#534—864no—
247#534—862no—
248C2×#123—862no—
249C2×#121—432no—
250C2×#121—861no—
251C2×#120—862no—
252C22×C4⋊C4—431no—
253C22×C4⋊C4—861no—
254C22×C22⋊C4—861no—
255C22×C22⋊C4C2×D4311yescharacteristic
256#481—438no—
257#481—864no—
258C2×#106—862no—
259C2×#102—862no—
260C2×C22⋊C8C2×D4312yescomplemented
261#399—434no—
262#399—862no—
263C2×#95—431no—
264#327—438no—
265#323C2×D4314yescomplemented
266C43C2×#161311yescharacteristic, complemented, Sylow
267C25—861no—
268C25D17211yescharacteristic
269C22×D4—432no—
270C22×D4—861no—
271C22×D4—862no—
272C22×D4—864no—
273C22×D4—862no—
274C22×D4—864no—
275C22×D4—1724no—
276C22×D4—1724no—
277C23×C4—861no—
278C23×C4—861no—
279C23×C4—861no—
280C23×C4D17211yescharacteristic
281C23×C4C22×D4311yescharacteristic
282C22×C8—22no—
283#123—868no—
284#123—868no—
285#121—434no—
286#121—434no—
287#121—864no—
288#121—862no—
289#121—864no—
290#121—862no—
291#120—868no—
292#120—868no—
293C2×C4⋊C4—432no—
294C2×C4⋊C4—432no—
295C2×C4⋊C4—861no—
296C2×C4⋊C4—862no—
297C2×C4⋊C4—862no—
298C2×C4⋊C4—861no—
299C2×C4⋊C4—864no—
300C2×C4⋊C4—1724no—
301C2×C22⋊C4—22no—
302C2×C22⋊C4—22no—
303C2×C22⋊C4—862no—
304C2×C22⋊C4—862no—
305C2×C22⋊C4—864no—
306C2×C22⋊C4—1724no—
307C2×C22⋊C4D17212yes—
308C2×C22⋊C4C22×D4312yes—
309#106—868no—
310#102—868no—
311C22⋊C8—22no—
312C22⋊C8C22×D4314yescomplemented
313#95—432no—
314#95—861no—
315C24—21no—
316C24—21no—
317C24—22no—
318C24—42no—
319C24—42no—
320C24—864no—
321C24—862no—
322C24—3442no—
323C24—3442no—
324C24—1724no—
325C24#1062187314yes—
326C24C2×D17211yescharacteristic
327C24C2×D17212yes—
328C2×D4—434no—
329C2×D4—864no—
330C2×D4—868no—
331C2×D4—864no—
332C2×D4—864no—
333C2×D4—862no—
334C2×D4—3442no—
335C2×D4—1724no—
336C2×D4—17216no—
337C2×D4—1728no—
338C2×D4—1728no—
339C2×D4—1728no—
340C2×D4—1724no—
341C2×D4—1724no—
342C22×C4—21no—
343C22×C4—21no—
344C22×C4—42no—
345C22×C4—42no—
346C22×C4—864no—
347C22×C4—864no—
348C22×C4—862no—
349C22×C4—862no—
350C22×C4—862no—
351C22×C4—1722no—
352C22×C4—1722no—
353C22×C4—1721no—
354C22×C4—1721no—
355C22×C4—1724no—
356C22×C4—1722no—
357C22×C4—1722no—
358C22×C4C2×D17212yes—
359C22×C4C2×D17211yescharacteristic
360C22×C4D4×D4312yes—
361C22×C4D4×D4312yes—
362C22×C4C23×D4311yescharacteristic
363C2×C8—24no—
364C2×C8—44no—
365C4⋊C4—434no—
366C4⋊C4—864no—
367C4⋊C4—862no—
368C4⋊C4—864no—
369C4⋊C4—1728no—
370C4⋊C4—1722no—
371C22⋊C4—24no—
372C22⋊C4—24no—
373C22⋊C4—868no—
374C22⋊C4—864no—
375C22⋊C4—864no—
376C22⋊C4—1728no—
377C23—22no—
378C23—22no—
379C23—24no—
380C23—22no—
381C23—24no—
382C23—22no—
383C23—42no—
384C23—48no—
385C23—42no—
386C23—42no—
387C23—42no—
388C23—81no—
389C23—84no—
390C23—81no—
391C23—864no—
392C23—34416no—
393C23—3444no—
394C23—3444no—
395C23—1728no—
396C23—1724no—
397C23—1724no—
398C23—1724no—
399C23#1306329511yescharacteristic
400C23#1306329511yescharacteristic
401C23C2×#1062187312yes—
402C23C2×#1062187314yes—
403C23#1306335312yes—
404C23C22×D17211yescharacteristic
405D4—3442no—
406D4—3444no—
407D4—1724no—
408D4—17216no—
409D4—1728no—
410D4—1724no—
411D4—1724no—
412C2×C4—24no—
413C2×C4—22no—
414C2×C4—41no—
415C2×C4—42no—
416C2×C4—41no—
417C2×C4—42no—
418C2×C4—42no—
419C2×C4—81no—
420C2×C4—864no—
421C2×C4—864no—
422C2×C4—3442no—
423C2×C4—3442no—
424C2×C4—1722no—
425C2×C4—1722no—
426C2×C4—1722no—
427C2×C4—1728no—
428C2×C4—1722no—
429C2×C4—1728no—
430C2×C4—1724no—
431C2×C4—1722no—
432C2×C4#1306329512yes—
433C2×C4C2×D4×D4312yes—
434C8—44no—
435C22—21no—
436C22—21no—
437C22—24no—
438C22—24no—
439C22—21no—
440C22—21no—
441C22—24no—
442C22—44no—
443C22—42no—
444C22—48no—
445C22—42no—
446C22—82no—
447C22—84no—
448C22—34416no—
449C22—3448no—
450C22—1724no—
451C22—1724no—
452C22—1724no—
453C22#1458305212yes—
454C22#1458305212yes—
455C22#1458306912yes—
456C22#1458309012yes—
457C22C2×#1306329511yescharacteristic
458C22C22×#1062187311yescharacteristic
459C22C2×#1306335311yescharacteristic
460C4—22no—
461C4—22no—
462C4—42no—
463C4—3442no—
464C4—1724no—
465C4—1724no—
466C2—21no—
467C2—21no—
468C2—22no—
469C2—44no—
470C2—3444no—
471C2#1913361714yesdirect product factor
472C2C2×#1458305211yescharacteristic
473C2C2×#1458306911yescharacteristic
474C2C2×#1458309011yescharacteristic
subgroupG/H
centerC23#13063295
commutator, cosocleC22×C4×C43C24
FrattiniC22×C4C23×D43
FittingC2×C43×#323C2
socleC23×C43#120
prime radicalC2×#14583461C2
hypercenterC2×#323D43
hypocenterC43C2×#1613
LCSG ▷ C22×C4×C43 ▷ C22×C43 ▷ C43
UCSC1 ◁ C23 ◁ C23×C4 ◁ C2×#323

Complements

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

NH ≅ G/Ntype
2. C2×#14583218C2semidirect
3. C2×#14582835C2semidirect
4. #19133617C2direct (N × H)
5. C2×#14582634C2semidirect
6. C2×C43×#323C2semidirect
15. C22×C4⋊Dic43C22semidirect
19. #14583218C22semidirect
23. #14582835C22semidirect
24. C2×C43⋊#95C22semidirect
25. #14582634C22semidirect
27. C2×C22⋊C8×C43C22semidirect
28. C43×#323C22semidirect
56. C2×C4⋊Dic43C23semidirect
66. C43⋊#95C23semidirect
76. C22⋊C8×C43C23semidirect
234. C2×#323D43semidirect
239. C2×C43#1613semidirect
260. C2×C22⋊C8C2×D43semidirect
265. #323C2×D43semidirect
266. C43C2×#1613semidirect
312. C22⋊C8C22×D43semidirect
471. C2#19133617direct (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×#145832182
C2×#145828352
#191336172
C2×#145826342
C2×C43×#3232
C2×#161343