Finite Group Databasebeta

← #19143814

Subgroups — #19143814

Order 5504.

764 conjugacy classes of subgroups; only the 141 normal subgroups are shown.

normal subgroups only

This group has 764 conjugacy classes of subgroups — too many to draw. Only its 141 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
1C22×#10621900C211yesmaximal, characteristic, complemented
2C2×#13063346C212yesmaximal, complemented
3#14583412C211yesmaximal, characteristic, complemented
4#14583058C212yesmaximal, complemented
5#14583054C211yesmaximal, characteristic, complemented
6#14583045C212yesmaximal, complemented
7#14583040C211yesmaximal, characteristic, complemented
8#14583033C211yesmaximal, characteristic, complemented
9#14582892C212yesmaximal, complemented
10C22⋊C8×D43C211yesmaximal, characteristic, complemented
11C43×#450C211yesmaximal, characteristic, complemented
12C2×#10621902C2211yescharacteristic, complemented
13C2×#10621900—28no—
14C2×#10621900—21no—
15C2×#10621900—21no—
16C2×#10621900C2212yes—
17C2×#10621900C2212yes—
18C22×Dic86C2211yescharacteristic
19C22×C22⋊D43—21no—
20C23×Dic43—21no—
21C22×C4×D43C2211yescharacteristic
22#13063346—28no—
23C2×#10621885C2212yescomplemented
24C2×#10621873C2212yescomplemented
25C2×#10621882C2212yescomplemented
26C2×C8×D43C2212yescomplemented
27#13063310—21no—
28#13063301C2211yescharacteristic, complemented
29#13063300C2211yescharacteristic, complemented
30#13063299C2211yescharacteristic
31#13063295—21no—
32#13063287—21no—
33(C22⋊D43)⋊C4—21no—
34#13063283C2211yescharacteristic, complemented
35#13063250C2212yescomplemented
36#13063248C2212yescomplemented
37#13063246C2212yescomplemented
38C22⋊(C43⋊C8)C2211yescharacteristic
39(C2×D43)⋊C8C2212yescomplemented
40C22×D4×C43C2211yescharacteristic
41C2×SD16×C43C2212yescomplemented
42C22⋊Q8×C43C2211yescharacteristic
43#102×C43C2212yescomplemented
44C22⋊C8×C43C2211yescharacteristic
45C24×C43—21no—
46C23×D43D411yescharacteristic
47C2×Q8×C43C2311yescharacteristic
48C2×D4×C43—24no—
49C2×D4×C43—21no—
50C2×D4×C43C2312yes—
51C22×C4×C43C2311yescharacteristic
52C2×C22⋊D43—28no—
53C2×C22⋊D43—21no—
54C2×C22⋊D43—22no—
55C2×C22⋊D43—22no—
56C22×Dic43—28no—
57C22×Dic43—22no—
58C22×Dic43—22no—
59C22×Dic43—21no—
60C22×Dic43D411yescharacteristic
61#10621902—24no—
62#10621900—28no—
63#10621900—28no—
64#10621900—24no—
65#10621900—24no—
66#10621900—24no—
67#10621900D418yescomplemented
68C2×D172—21no—
69C2×D172—21no—
70C2×D172C2311yescharacteristic
71C2×C4×D43—24no—
72C2×C4×D43—21no—
73C2×C4×D43D411yescharacteristic
74C2×C4×D43D411yescharacteristic
75C2×C4×D43C2311yescharacteristic
76C2×C4×D43C2311yescharacteristic
77C2×Dic86—21no—
78C2×Dic86—24no—
79C2×Dic86C2312yes—
80SD16×C43—24no—
81C2×C8×C43C2312yes—
82C4⋊C4×C43—21no—
83C4⋊C4×C43C2311yescharacteristic
84C22⋊C4×C43—21no—
85#10621885—24no—
86#10621882—24no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91C4⋊Dic43C2311yescharacteristic
92Dic43⋊C4—21no—
93C4×Dic43—21no—
94C2×C43⋊C8C2312yes—
95#10621873—24no—
96C8×D43—24no—
97C23×C43—24no—
98C23×C43—22no—
99C23×C43—42no—
100C23×C43—42no—
101C23×C43C2×D411yescharacteristic
102C22×D43—22no—
103C22×D43—22no—
104C22×D43—21no—
105C22×D43—41no—
106C22×D43C2×D411yescharacteristic
107C22×D43C2×D411yescharacteristic
108Q8×C43—22no—
109D4×C43—24no—
110D4×C43—22no—
111D4×C43C2×D414yes—
112C2×C4×C43—22no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43C2×D411yescharacteristic
116C2×C4×C43C2411yescharacteristic
117C22⋊D43—28no—
118C22⋊D43—28no—
119C22⋊D43—42no—
120C2×Dic43—24no—
121C2×Dic43—28no—
122C2×Dic43—22no—
123C2×Dic43—22no—
124C2×Dic43—28no—
125C2×Dic43—21no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128D172—22no—
129D172—42no—
130D172—42no—
131C4×D43—22no—
132C4×D43—22no—
133C4×D43—22no—
134C4×D43—42no—
135C4×D43C2×D414yes—
136Dic86—24no—
137Dic86—22no—
138Dic86C2×D414yes—
139C8×C43—22no—
140C43⋊C8—22no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—24no—
144C22×C43—48no—
145C22×C43—42no—
146C22×C43—42no—
147C22×C43#13512yescomplemented
148C22×C43C22×D411yescharacteristic
149C2×D43—21no—
150C2×D43—21no—
151C2×D43—21no—
152C2×D43—21no—
153C2×D43—21no—
154C2×D43—44no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
158C2×D43#12012yes—
159C4×C43—21no—
160C4×C43—41no—
161C4×C43—41no—
162C4×C43C22×D412yes—
163Dic43—24no—
164Dic43—21no—
165Dic43—41no—
166Dic43#12012yes—
167#3002—431nomaximal, Sylow
168C2×C43—22no—
169C2×C43—44no—
170C2×C43C2×#12011yescharacteristic
171C2×C43C2×#13511yescharacteristic
172C2×C43#57511yescharacteristic
173D43—22no—
174D43—41no—
175D43—81no—
176C22×#41—431no—
177C2×#135—432no—
178#525—431no—
179#452—432no—
180#451—431no—
181#450D4311yescharacteristic, complemented
182#449—432no—
183#448—431no—
184#447—431no—
185#416—432no—
186C2×C22⋊C8—431no—
187C43#300211yescharacteristic, complemented, Sylow
188C2×#41—431no—
189C2×#41—432no—
190C2×#41—432no—
191C2×#41—861no—
192C2×#41—861no—
193C2×#41—868no—
194C22×Q8—431no—
195C22×D4—861no—
196C22×D4C2×D4311yescharacteristic
197C23×C4—431no—
198C23×C4—861no—
199#135—868no—
200C2×Q16—432no—
201C2×SD16—432no—
202C2×SD16C2×D4312yescomplemented
203C2×D8—432no—
204C22×C8—432no—
205#123—861no—
206C22⋊Q8—431no—
207C22⋊Q8C2×D4311yescharacteristic
208#121—431no—
209#121—431no—
210#120—861no—
211C4×D4—861no—
212C4×D4—861no—
213#117—431no—
214#103—432no—
215#103—432no—
216#102—432no—
217#102C2×D4312yescomplemented
218C22⋊C8—431no—
219C22⋊C8—432no—
220C22⋊C8C2×D4311yescharacteristic
221C24—21no—
222C24—431no—
223#41—438no—
224#41—864no—
225#41—864no—
226#41—864no—
227#41—868no—
228#41—868no—
229#41—864no—
230C2×Q8—432no—
231C2×Q8—864no—
232C2×Q8—861no—
233C2×Q8C22×D4311yescharacteristic
234C2×D4—24no—
235C2×D4—21no—
236C2×D4—431no—
237C2×D4—861no—
238C2×D4—861no—
239C2×D4—862no—
240C2×D4—862no—
241C2×D4—868no—
242C2×D4—861no—
243C2×D4C22×D4312yes—
244C22×C4—431no—
245C22×C4—431no—
246C22×C4—431no—
247C22×C4—431no—
248C22×C4—431no—
249C22×C4—864no—
250C22×C4—861no—
251C22×C4—862no—
252C22×C4—862no—
253C22×C4—868no—
254C22×C4—861no—
255C22×C4C22×D4311yescharacteristic
256Q16—864no—
257SD16—24no—
258SD16—864no—
259D8—864no—
260C2×C8—432no—
261C2×C8—864no—
262C2×C8C22×D4312yes—
263C4⋊C4—21no—
264C4⋊C4—431no—
265C4⋊C4—861no—
266C4⋊C4C22×D4311yescharacteristic
267C22⋊C4—21no—
268C22⋊C4—861no—
269C22⋊C4—861no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C42—861no—
273C23—24no—
274C23—22no—
275C23—42no—
276C23—42no—
277C23—431no—
278C23—431no—
279C23—862no—
280C23—862no—
281C23—861no—
282C23—1721no—
283C23D4×D4311yescharacteristic
284Q8—22no—
285Q8—434no—
286Q8—864no—
287Q8—862no—
288D4—24no—
289D4—22no—
290D4—868no—
291D4—868no—
292D4—862no—
293D4—1722no—
294D4—1722no—
295D4—1722no—
296D4D4×D4314yes—
297C2×C4—22no—
298C2×C4—21no—
299C2×C4—21no—
300C2×C4—431no—
301C2×C4—434no—
302C2×C4—431no—
303C2×C4—862no—
304C2×C4—862no—
305C2×C4—862no—
306C2×C4—868no—
307C2×C4—864no—
308C2×C4—868no—
309C2×C4—862no—
310C2×C4—862no—
311C2×C4—861no—
312C2×C4—1722no—
313C2×C4D4×D4311yescharacteristic
314C2×C4C23×D4311yescharacteristic
315C8—22no—
316C8—862no—
317C22—21no—
318C22—21no—
319C22—24no—
320C22—48no—
321C22—42no—
322C22—42no—
323C22—432no—
324C22—861no—
325C22—861no—
326C22—861no—
327C22—861no—
328C22—861no—
329C22—1724no—
330C22—1721no—
331C22—1721no—
332C22—1721no—
333C22#1306334612yescomplemented
334C22C2×D4×D4311yescharacteristic
335C4—21no—
336C4—41no—
337C4—41no—
338C4—432no—
339C4—861no—
340C4—864no—
341C4—1721no—
342C4C2×D4×D4312yes—
343C2—22no—
344C2—44no—
345C2—862no—
346C2—3441no—
347C2—1721no—
348C2#120×D4311yescharacteristic
349C2C2×#1306334611yescharacteristic
350C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#450C2
socleC22×C43C22×D4
hypercenter#450D43
hypocenterC43#3002
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #450

Complements

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

NH ≅ G/Ntype
1. C22×#10621900C2semidirect
2. C2×#13063346C2semidirect
3. #14583412C2semidirect
4. #14583058C2semidirect
5. #14583054C2semidirect
6. #14583045C2semidirect
7. #14583040C2semidirect
8. #14583033C2semidirect
9. #14582892C2semidirect
10. C22⋊C8×D43C2semidirect
11. C43×#450C2semidirect
12. C2×#10621902C22semidirect
23. C2×#10621885C22semidirect
24. C2×#10621873C22semidirect
25. C2×#10621882C22semidirect
26. C2×C8×D43C22semidirect
28. #13063301C22semidirect
29. #13063300C22semidirect
34. #13063283C22semidirect
35. #13063250C22semidirect
36. #13063248C22semidirect
37. #13063246C22semidirect
39. (C2×D43)⋊C8C22semidirect
41. C2×SD16×C43C22semidirect
43. #102×C43C22semidirect
67. #10621900D4semidirect
147. C22×C43#135semidirect
181. #450D43semidirect
187. C43#3002semidirect
202. C2×SD16C2×D43semidirect
217. #102C2×D43semidirect
333. C22#13063346semidirect