Finite Group Databasebeta

← C2×#14583090 #19143984

Subgroups — C2×#14583090 #19143984

Order 5504.

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

normal subgroups only

This group has 794 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×#13063370C211yesmaximal, characteristic
2C2×#13063309C212yesmaximal, complemented
3C2×#13063306C211yesmaximal, characteristic, complemented
4#14583090C218yesmaximal, direct product factor
5C2×#13063239C212yesmaximal, complemented
6C2×#99×C43C211yesmaximal, characteristic, complemented
7#13063370—22no—
8#13063370—24no—
9#13063370C2214yes—
10C2×#10621898—21no—
11C2×#10621900—22no—
12C22×C22⋊D43—21no—
13C22×C22⋊D43C2212yes—
14C2×D4×D43—22no—
15C23×Dic43C2211yescharacteristic, complemented
16#13063309—24no—
17#13063309C2218yescomplemented
18#13063306—22no—
19#13063306C2214yescomplemented
20C2×C4⋊Dic43—22no—
21C2×Dic43⋊C4—21no—
22C2×C22⋊Dic43—21no—
23C2×C22⋊Dic43C2211yescharacteristic, complemented
24C2×(C2×D43)⋊C4—22no—
25#13063239C2218yescomplemented
26C22×D4×C43C2211yescharacteristic
27C2×C22⋊C4×C43C2212yescomplemented
28#99×C43C2214yescomplemented
29C24×C43D411yescharacteristic
30C24×C43C2311yescharacteristic
31C23×D43—21no—
32C23×D43D412yes—
33C2×D4×C43—22no—
34C2×D4×C43—22no—
35C2×D4×C43D412yes—
36C2×D4×C43C2312yes—
37C22×C4×C43—22no—
38C22×C4×C43D411yescharacteristic
39C2×C22⋊D43—22no—
40C2×C22⋊D43—24no—
41C2×C22⋊D43—22no—
42C2×C22⋊D43—22no—
43C2×C22⋊D43—24no—
44C2×C22⋊D43—22no—
45C2×C22⋊D43—22no—
46C2×C22⋊D43D414yes—
47C2×C22⋊D43C2314yes—
48C22×Dic43—21no—
49C22×Dic43—22no—
50C22×Dic43—21no—
51C22×Dic43—21no—
52C22×Dic43—21no—
53C22×Dic43—22no—
54C22×Dic43D412yes—
55C22×Dic43C2312yescomplemented
56#10621900—28no—
57#10621900—28no—
58D4×D43—28no—
59D4×D43—28no—
60#10621898—24no—
61#10621898—24no—
62C2×D172—21no—
63C2×C4×D43—22no—
64C2×Dic86—21no—
65C22⋊C4×C43—22no—
66C22⋊C4×C43C2314yescomplemented
67C22⋊Dic43—24no—
68C22⋊Dic43—21no—
69C22⋊Dic43C2312yescomplemented
70(C2×D43)⋊C4—28no—
71C4⋊Dic43—28no—
72Dic43⋊C4—24no—
73C23×C43—21no—
74C23×C43—21no—
75C23×C43—42no—
76C23×C43—42no—
77C23×C43C2×D411yescharacteristic
78C23×C43C2×D412yes—
79C23×C43C2×D411yescharacteristic
80C23×C43C2×D412yes—
81C23×C43C2×D412yes—
82C23×C43C2411yescharacteristic
83C22×D43—22no—
84C22×D43—24no—
85C22×D43—22no—
86C22×D43—44no—
87C22×D43—82no—
88C22×D43C2×D414yes—
89D4×C43—24no—
90D4×C43—24no—
91C2×C4×C43—21no—
92C2×C4×C43—21no—
93C2×C4×C43—24no—
94C2×C4×C43—44no—
95C2×C4×C43C2×D412yes—
96C22⋊D43—28no—
97C22⋊D43—24no—
98C22⋊D43—24no—
99C22⋊D43—24no—
100C22⋊D43—24no—
101C2×Dic43—24no—
102C2×Dic43—22no—
103C2×Dic43—22no—
104C2×Dic43—22no—
105C2×Dic43—22no—
106C2×Dic43—24no—
107C2×Dic43—42no—
108C2×Dic43—42no—
109C2×Dic43—41no—
110C2×Dic43—41no—
111C2×Dic43C2×D414yes—
112D172—24no—
113C4×D43—28no—
114Dic86—24no—
115C22×C43—24no—
116C22×C43—22no—
117C22×C43—22no—
118C22×C43—41no—
119C22×C43—42no—
120C22×C43—41no—
121C22×C43—42no—
122C22×C43—42no—
123C22×C43—81no—
124C22×C43#12012yes—
125C22×C43#12011yescharacteristic
126C22×C43#12011yescharacteristic
127C22×C43C22×D412yes—
128C22×C43C22×D411yescharacteristic
129C2×D43—24no—
130C2×D43—44no—
131C2×D43—44no—
132C2×D43—82no—
133C2×D43—84no—
134C4×C43—22no—
135C4×C43—44no—
136Dic43—24no—
137Dic43—42no—
138Dic43—42no—
139C2×#458—431nomaximal, Sylow
140C2×C43—21no—
141C2×C43—22no—
142C2×C43—22no—
143C2×C43—21no—
144C2×C43—42no—
145C2×C43#45812yescomplemented
146C2×C43C2×#12011yescharacteristic
147D43—44no—
148C2×H(5,𝔽2)—431no—
149C2×#123—431no—
150C2×#123—432no—
151#458—438no—
152C2×#99—432no—
153C2×#99D4311yescharacteristic, complemented
154C43C2×#45811yescharacteristic, complemented, Sylow
155H(5,𝔽2)—434no—
156H(5,𝔽2)—864no—
157H(5,𝔽2)—862no—
158C2×#41—862no—
159C2×#41—861no—
160C22×D4—432no—
161C22×D4—862no—
162C22×D4—861no—
163C22×D4C2×D4311yescharacteristic
164C23×C4—431no—
165#123—434no—
166#123—438no—
167#123—864no—
168#123—862no—
169C2×C4⋊C4—862no—
170C2×C4⋊C4—861no—
171C2×C22⋊C4—431no—
172C2×C22⋊C4—862no—
173C2×C22⋊C4—861no—
174C2×C22⋊C4C2×D4312yescomplemented
175#99—438no—
176#99C2×D4314yescomplemented
177C24—432no—
178C24—861no—
179C24D17211yescharacteristic
180C24C22×D4311yescharacteristic
181#41—864no—
182#41—868no—
183#41—868no—
184#41—864no—
185C2×Q8—861no—
186C2×D4—22no—
187C2×D4—22no—
188C2×D4—434no—
189C2×D4—434no—
190C2×D4—861no—
191C2×D4—868no—
192C2×D4—868no—
193C2×D4—862no—
194C2×D4—864no—
195C2×D4—862no—
196C2×D4—862no—
197C2×D4—864no—
198C2×D4—862no—
199C2×D4—862no—
200C2×D4D17212yes—
201C2×D4C22×D4312yes—
202C22×C4—22no—
203C22×C4—432no—
204C22×C4—432no—
205C22×C4—862no—
206C22×C4—861no—
207C22×C4—861no—
208C22×C4—861no—
209C22×C4—861no—
210C22×C4—862no—
211C22×C4—862no—
212C22×C4D17211yescharacteristic
213C4⋊C4—868no—
214C4⋊C4—864no—
215C22⋊C4—22no—
216C22⋊C4—432no—
217C22⋊C4—868no—
218C22⋊C4—861no—
219C22⋊C4—864no—
220C22⋊C4C22×D4314yescomplemented
221C23—21no—
222C23—21no—
223C23—42no—
224C23—42no—
225C23—434no—
226C23—864no—
227C23—862no—
228C23—862no—
229C23—3442no—
230C23—1724no—
231C23C2×D17211yescharacteristic
232C23C2×D17212yes—
233C23C2×D17211yescharacteristic
234C23D4×D4312yes—
235C23D4×D4312yes—
236C23C23×D4311yescharacteristic
237Q8—864no—
238D4—24no—
239D4—24no—
240D4—864no—
241D4—868no—
242D4—864no—
243D4—864no—
244D4—864no—
245D4—864no—
246C2×C4—21no—
247C2×C4—21no—
248C2×C4—24no—
249C2×C4—44no—
250C2×C4—434no—
251C2×C4—868no—
252C2×C4—864no—
253C2×C4—862no—
254C2×C4—862no—
255C2×C4—864no—
256C2×C4—862no—
257C2×C4—862no—
258C2×C4—1722no—
259C2×C4—1721no—
260C2×C4—1722no—
261C2×C4—1721no—
262C2×C4C2×D17212yes—
263C22—24no—
264C22—22no—
265C22—22no—
266C22—41no—
267C22—42no—
268C22—41no—
269C22—42no—
270C22—42no—
271C22—81no—
272C22—864no—
273C22—3442no—
274C22—3444no—
275C22—1724no—
276C22—1724no—
277C22#1306329511yescharacteristic
278C22#1306329512yes—
279C22#1306329511yescharacteristic
280C22C2×D4×D4312yes—
281C22C22×D17211yescharacteristic
282C4—22no—
283C4—44no—
284C4—864no—
285C4—1722no—
286C4—1722no—
287C2—22no—
288C2—21no—
289C2—21no—
290C2—22no—
291C2—42no—
292C2—1724no—
293C2#1458309012yesdirect product factor
294C2C2×#1306329511yescharacteristic
subgroupG/H
centerC22#13063295
commutatorC23×C43C24
FrattiniC23C23×D43
FittingC2×#99×C43C2
socleC22×C43#120
hypercenterC2×#99D43
hypocenterC43C2×#458
LCSG ▷ C23×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C24 ◁ C2×#99

Complements

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

NH ≅ G/Ntype
2. C2×#13063309C2semidirect
3. C2×#13063306C2semidirect
4. #14583090C2direct (N × H)
5. C2×#13063239C2semidirect
6. C2×#99×C43C2semidirect
15. C23×Dic43C22semidirect
17. #13063309C22semidirect
19. #13063306C22semidirect
23. C2×C22⋊Dic43C22semidirect
25. #13063239C22semidirect
27. C2×C22⋊C4×C43C22semidirect
28. #99×C43C22semidirect
55. C22×Dic43C23semidirect
66. C22⋊C4×C43C23semidirect
69. C22⋊Dic43C23semidirect
145. C2×C43#458semidirect
153. C2×#99D43semidirect
154. C43C2×#458semidirect
174. C2×C22⋊C4C2×D43semidirect
176. #99C2×D43semidirect
220. C22⋊C4C22×D43semidirect
293. C2#14583090direct (N × H)