Finite Group Databasebeta

← C2×#14583068 #19143920

Subgroups — C2×#14583068 #19143920

Order 5504.

844 conjugacy classes of subgroups; only the 149 normal subgroups are shown.

normal subgroups only

This group has 844 conjugacy classes of subgroups — too many to draw. Only its 149 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×#13063371C211yesmaximal, characteristic, complemented
2C2×#13063353C211yesmaximal, characteristic, complemented
3C2×#13063350C211yesmaximal, characteristic, complemented
4C2×#13063322C211yesmaximal, characteristic, complemented
5#14583068C218yesmaximal, direct product factor
6C2×#13063253C211yesmaximal, characteristic, complemented
7C2×#13063241C211yesmaximal, characteristic, complemented
8C2×#104×C43C211yesmaximal, characteristic, complemented
9#13063371—22no—
10#13063371—22no—
11#13063371—22no—
12#13063371C2214yescomplemented
13C2×#10621902—21no—
14C2×#10621898—21no—
15C2×#10621898C2211yescharacteristic
16C22×D172—21no—
17C22×D172—22no—
18C22×D172C2211yescharacteristic
19C22×D172C2211yescharacteristic, complemented
20C2×D4×D43—22no—
21C2×D4×D43—21no—
22#13063353—22no—
23#13063353C2214yescomplemented
24#13063350—22no—
25#13063350C2214yescomplemented
26C2×#10621873—21no—
27C2×#10621884—21no—
28C2×D344—21no—
29C2×#10621882—21no—
30C2×#10621877C2211yescharacteristic, complemented
31#13063322—22no—
32#13063322C2214yescomplemented
33#13063253C2214yescomplemented
34#13063241C2214yescomplemented
35C2×#41×C43C2211yescharacteristic
36C2×M16×C43C2211yescharacteristic, complemented
37C2×C42×C43C2211yescharacteristic, complemented
38#104×C43C2214yescomplemented
39C23×D43—22no—
40C23×D43—21no—
41C23×D43D412yes—
42#41×C43—21no—
43#41×C43—21no—
44#41×C43D412yescomplemented
45#41×C43C2312yes—
46C2×Q8×C43D411yescharacteristic, complemented
47C2×D4×C43—21no—
48C2×D4×C43D411yescharacteristic, complemented
49C22×C4×C43—21no—
50C22×C4×C43—21no—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—22no—
53C2×C22⋊D43—21no—
54#10621902—24no—
55#10621902—24no—
56D4×D43—24no—
57D4×D43—28no—
58D4×D43—24no—
59D4×D43—28no—
60#10621898—24no—
61#10621898—21no—
62#10621898—21no—
63#10621898—24no—
64#10621898D412yescomplemented
65#10621898C2312yes—
66C2×D172—22no—
67C2×D172—24no—
68C2×D172—21no—
69C2×D172—21no—
70C2×D172—21no—
71C2×D172—21no—
72C2×D172—24no—
73C2×D172—21no—
74C2×D172—28no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—48no—
80C2×D172D412yes—
81C2×D172D411yescharacteristic, complemented
82C2×D172C2312yes—
83C2×D172C2312yescomplemented
84C2×C4×D43—22no—
85C2×C4×D43—21no—
86C2×Dic86D411yescharacteristic, complemented
87M16×C43—21no—
88M16×C43C2312yescomplemented
89C2×C8×C43—21no—
90C42×C43—21no—
91C42×C43C2312yescomplemented
92#10621884—24no—
93#10621882—24no—
94#10621877—21no—
95#10621877C2312yescomplemented
96C2×C43⋊C8—21no—
97D344—24no—
98#10621873—24no—
99C23×C43—21no—
100C23×C43C2×D411yescharacteristic
101C22×D43—22no—
102C22×D43—21no—
103C22×D43—28no—
104C22×D43—22no—
105C22×D43—22no—
106C22×D43—44no—
107C22×D43—44no—
108C22×D43—41no—
109C22×D43—41no—
110C22×D43—84no—
111C22×D43C2×D414yes—
112Q8×C43—21no—
113Q8×C43C2×D412yescomplemented
114D4×C43—22no—
115D4×C43—22no—
116D4×C43—21no—
117D4×C43C2×D412yescomplemented
118C2×C4×C43—24no—
119C2×C4×C43—21no—
120C2×C4×C43—22no—
121C2×C4×C43—22no—
122C2×C4×C43—22no—
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2×D411yescharacteristic
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2×D411yescharacteristic
127C2×C4×C43C2×D411yescharacteristic
128C2×C4×C43C2411yescharacteristic
129C22⋊D43—28no—
130C22⋊D43—22no—
131C22⋊D43—22no—
132C2×Dic43—21no—
133D172—28no—
134D172—22no—
135D172—21no—
136D172—22no—
137D172—22no—
138D172—22no—
139D172—22no—
140D172—22no—
141D172—416no—
142D172—41no—
143D172—41no—
144D172C2×D412yescomplemented
145C4×D43—28no—
146C4×D43—22no—
147C4×D43—22no—
148Dic86—21no—
149Dic86C2×D412yescomplemented
150C8×C43—22no—
151C43⋊C8—22no—
152C22×C43—22no—
153C22×C43—22no—
154C22×C43—42no—
155C22×C43#12011yescharacteristic
156C22×C43#12011yescharacteristic
157C22×C43C22×D411yescharacteristic
158C2×D43—22no—
159C2×D43—24no—
160C2×D43—44no—
161C2×D43—42no—
162C2×D43—44no—
163C2×D43—44no—
164C2×D43—42no—
165C2×D43—82no—
166C2×D43—88no—
167C2×D43—82no—
168C2×D43—82no—
169C4×C43—24no—
170C4×C43—22no—
171C4×C43#12011yescharacteristic
172C4×C43#12011yescharacteristic
173C4×C43C22×D411yescharacteristic
174C4×C43C22×D411yescharacteristic
175Dic43—22no—
176C2×#453—431nomaximal, Sylow
177C2×C43—21no—
178C2×C43—21no—
179C2×C43—42no—
180C2×C43#45312yescomplemented
181C2×C43C2×#12011yescharacteristic
182D43—44no—
183D43—42no—
184D43—82no—
185C2×H(5,𝔽2)—431no—
186C2×AGL(1,ℤ/8)—431no—
187C2×AGL(1,ℤ/8)—431no—
188C2×#127—431no—
189#453—438no—
190C2×#104—431no—
191C2×#104D4311yescharacteristic, complemented
192C2×#100—431no—
193C43C2×#45311yescharacteristic, complemented, Sylow
194H(5,𝔽2)—434no—
195H(5,𝔽2)—862no—
196H(5,𝔽2)—862no—
197H(5,𝔽2)—862no—
198C2×#41—431no—
199C2×#41—861no—
200C2×#41—861no—
201C2×#41C2×D4311yescharacteristic
202C22×D4—431no—
203C22×D4—431no—
204C22×D4—861no—
205C22×D4—862no—
206C22×D4—862no—
207C22×D4—861no—
208AGL(1,ℤ/8)—434no—
209AGL(1,ℤ/8)—434no—
210AGL(1,ℤ/8)—862no—
211AGL(1,ℤ/8)—862no—
212C2×SD16—861no—
213C2×SD16—861no—
214C2×D8—861no—
215C2×D8—861no—
216C2×M16—431no—
217C2×M16C2×D4311yescharacteristic, complemented
218#127—434no—
219#127—862no—
220C2×C42C2×D4311yescharacteristic, complemented
221#104—434no—
222#104C2×D4314yescomplemented
223#100—434no—
224C24—432no—
225C24—862no—
226C24—861no—
227#41—21no—
228#41—21no—
229#41—432no—
230#41—432no—
231#41—864no—
232#41—864no—
233#41—864no—
234#41—864no—
235#41—861no—
236#41—861no—
237#41D17212yescomplemented
238#41C22×D4312yes—
239C2×Q8—431no—
240C2×Q8D17211yescharacteristic, complemented
241C2×D4—21no—
242C2×D4—431no—
243C2×D4—432no—
244C2×D4—432no—
245C2×D4—432no—
246C2×D4—864no—
247C2×D4—862no—
248C2×D4—864no—
249C2×D4—868no—
250C2×D4—868no—
251C2×D4—868no—
252C2×D4—864no—
253C2×D4—862no—
254C2×D4—861no—
255C2×D4—864no—
256C2×D4—861no—
257C2×D4—861no—
258C2×D4—861no—
259C2×D4—861no—
260C2×D4—861no—
261C2×D4—861no—
262C2×D4—861no—
263C2×D4—861no—
264C2×D4—861no—
265C2×D4—1728no—
266C2×D4D17211yescharacteristic, complemented
267C22×C4—21no—
268C22×C4—21no—
269C22×C4—862no—
270C22×C4—861no—
271C22×C4C22×D4311yescharacteristic
272SD16—864no—
273SD16—864no—
274D8—864no—
275D8—864no—
276M16—21no—
277M16—432no—
278M16—861no—
279M16C22×D4312yescomplemented
280C2×C8—21no—
281C2×C8—861no—
282C42—21no—
283C42C22×D4312yescomplemented
284C23—21no—
285C23—434no—
286C23—868no—
287C23—862no—
288C23—861no—
289C23—862no—
290C23—862no—
291C23—3444no—
292C23—1724no—
293C23—1724no—
294C23—1721no—
295C23—1721no—
296C23D4×D4311yescharacteristic
297Q8—21no—
298Q8—432no—
299Q8—861no—
300Q8C2×D17212yescomplemented
301D4—22no—
302D4—22no—
303D4—21no—
304D4—432no—
305D4—868no—
306D4—868no—
307D4—862no—
308D4—862no—
309D4—861no—
310D4—862no—
311D4—862no—
312D4—862no—
313D4—862no—
314D4—862no—
315D4—862no—
316D4—17216no—
317D4—1721no—
318D4—1721no—
319D4C2×D17212yescomplemented
320C2×C4—24no—
321C2×C4—21no—
322C2×C4—22no—
323C2×C4—22no—
324C2×C4—22no—
325C2×C4—868no—
326C2×C4—861no—
327C2×C4—862no—
328C2×C4—862no—
329C2×C4C2×D17211yescharacteristic
330C2×C4C2×D17211yescharacteristic
331C2×C4D4×D4311yescharacteristic
332C2×C4D4×D4311yescharacteristic
333C2×C4D4×D4311yescharacteristic
334C2×C4C23×D4311yescharacteristic
335C8—22no—
336C8—862no—
337C22—22no—
338C22—22no—
339C22—42no—
340C22—862no—
341C22—864no—
342C22—3442no—
343C22—3442no—
344C22—3448no—
345C22—3442no—
346C22—1724no—
347C22—1724no—
348C22—1722no—
349C22—1722no—
350C22—1724no—
351C22#1306329511yescharacteristic
352C22#1306329511yescharacteristic
353C22C2×D4×D4311yescharacteristic
354C4—24no—
355C4—22no—
356C4—862no—
357C4#1306329511yescharacteristic
358C4#1306329511yescharacteristic
359C4C2×D4×D4311yescharacteristic
360C4C22×D17211yescharacteristic
361C2—21no—
362C2—21no—
363C2—42no—
364C2—3442no—
365C2—1722no—
366C2—1724no—
367C2#1458306812yesdirect product factor
368C2C2×#1306329511yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#104×C43C2
socleC22×C43#120
hypercenterC2×#104D43
hypocenterC43C2×#453
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ C2×#104

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. C2×#13063353C2semidirect
3. C2×#13063350C2semidirect
4. C2×#13063322C2semidirect
5. #14583068C2direct (N × H)
6. C2×#13063253C2semidirect
7. C2×#13063241C2semidirect
8. C2×#104×C43C2semidirect
12. #13063371C22semidirect
19. C22×D172C22semidirect
23. #13063353C22semidirect
25. #13063350C22semidirect
30. C2×#10621877C22semidirect
32. #13063322C22semidirect
33. #13063253C22semidirect
34. #13063241C22semidirect
36. C2×M16×C43C22semidirect
37. C2×C42×C43C22semidirect
38. #104×C43C22semidirect
44. #41×C43D4semidirect
46. C2×Q8×C43D4semidirect
48. C2×D4×C43D4semidirect
64. #10621898D4semidirect
81. C2×D172D4semidirect
83. C2×D172C23semidirect
86. C2×Dic86D4semidirect
88. M16×C43C23semidirect
91. C42×C43C23semidirect
95. #10621877C23semidirect
113. Q8×C43C2×D4semidirect
117. D4×C43C2×D4semidirect
144. D172C2×D4semidirect
149. Dic86C2×D4semidirect
180. C2×C43#453semidirect
191. C2×#104D43semidirect
193. C43C2×#453semidirect
217. C2×M16C2×D43semidirect
220. C2×C42C2×D43semidirect
222. #104C2×D43semidirect
237. #41D172semidirect
240. C2×Q8D172semidirect
266. C2×D4D172semidirect
279. M16C22×D43semidirect
283. C42C22×D43semidirect
300. Q8C2×D172semidirect
319. D4C2×D172semidirect
367. C2#14583068direct (N × H)