Finite Group Databasebeta

← #19143954

Subgroups — #19143954

Order 5504.

762 conjugacy classes of subgroups; only the 145 normal subgroups are shown.

normal subgroups only

This group has 762 conjugacy classes of subgroups — too many to draw. Only its 145 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
2#14583699C211yesmaximal, characteristic, complemented
3#14583697C211yesmaximal, characteristic, complemented
4#14583468C211yesmaximal, characteristic, complemented
5#14583078C214yesmaximal, complemented
6#14583068C214yesmaximal, complemented
7#14582917C211yesmaximal, characteristic, complemented
8C2×#13063241C211yesmaximal, characteristic, complemented
9C43×#421C211yesmaximal, characteristic, complemented
10#13063371—22no—
11#13063371—22no—
12#13063371—22no—
13#13063371C2214yes—
14C2×#10621902—21no—
15C2×#10621898—21no—
16C2×#10621898C2211yescharacteristic
17C2×#10621898C2211yescharacteristic, complemented
18C22×D172—21no—
19C22×D172C2211yescharacteristic
20C2×D4×D43—22no—
21C2×D4×D43—21no—
22#13063358—21no—
23#13063358C2212yescomplemented
24#13063356—21no—
25#13063355C2212yescomplemented
26#13063353—21no—
27#13063353C2212yescomplemented
28#13063351—21no—
29#13063350C2212yescomplemented
30#13063347—22no—
31#13063345—22no—
32C2×#10621877C2211yescharacteristic, complemented
33#13063322C2212yescomplemented
34#13063313C2212yescomplemented
35#13063300—22no—
36#13063295—22no—
37#13063253C2214yescomplemented
38#13063241C2214yescomplemented
39C2×#41×C43C2211yescharacteristic
40C2×M16×C43C2211yescharacteristic, complemented
41#117×C43C2211yescharacteristic, complemented
42#104×C43C2214yescomplemented
43C23×D43—22no—
44C23×D43D412yes—
45#41×C43—21no—
46#41×C43—21no—
47#41×C43D412yescomplemented
48#41×C43C2312yes—
49C2×Q8×C43D411yescharacteristic, complemented
50C2×D4×C43—21no—
51C2×D4×C43D411yescharacteristic, complemented
52C22×C4×C43—21no—
53C22×C4×C43C2311yescharacteristic
54C2×C22⋊D43—22no—
55C2×C22⋊D43—21no—
56C2×C22⋊D43—21no—
57#10621902—24no—
58#10621902—24no—
59D4×D43—24no—
60D4×D43—28no—
61D4×D43—24no—
62D4×D43—28no—
63#10621898—24no—
64#10621898—21no—
65#10621898—21no—
66#10621898—21no—
67#10621898—21no—
68#10621898—21no—
69#10621898—21no—
70#10621898—24no—
71#10621898D412yescomplemented
72#10621898C2312yes—
73C2×D172—22no—
74C2×D172—24no—
75C2×D172—21no—
76C2×D172—21no—
77C2×D172—21no—
78C2×D172—21no—
79C2×D172—24no—
80C2×D172—24no—
81C2×D172D412yes—
82C2×D172D411yescharacteristic, complemented
83C2×D172C2312yes—
84C2×D172C2311yescharacteristic, complemented
85C2×C4×D43—22no—
86C2×C4×D43—21no—
87C2×C4×D43—21no—
88C2×Dic86D411yescharacteristic, complemented
89C2×Dic86C2311yescharacteristic, complemented
90M16×C43—21no—
91M16×C43C2312yescomplemented
92C2×C8×C43—21no—
93C4⋊C4×C43—21no—
94C22⋊C4×C43—21no—
95C42×C43C2312yescomplemented
96#10621885—22no—
97#10621884—22no—
98#10621883—22no—
99#10621882—22no—
100(C2×D43)⋊C4—24no—
101#10621877—21no—
102#10621877C2312yescomplemented
103C2×C43⋊C8—21no—
104Dic172—22no—
105D344—22no—
106#10621873—22no—
107#10621873—22no—
108C23×C43—21no—
109C23×C43C2×D411yescharacteristic
110C22×D43—22no—
111C22×D43—21no—
112C22×D43—28no—
113C22×D43—22no—
114C22×D43—21no—
115C22×D43—82no—
116C22×D43—84no—
117C22×D43C2×D414yes—
118Q8×C43—21no—
119Q8×C43C2×D412yes—
120D4×C43—22no—
121D4×C43—22no—
122D4×C43—21no—
123D4×C43C2×D412yes—
124C2×C4×C43—21no—
125C2×C4×C43—22no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43C2×D411yescharacteristic
129C2×C4×C43C2×D411yescharacteristic
130C2×C4×C43C2×D411yescharacteristic
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2411yescharacteristic
134C22⋊D43—28no—
135C22⋊D43—22no—
136C22⋊D43—22no—
137C22⋊D43—41no—
138C22⋊D43—41no—
139C2×Dic43—21no—
140C2×Dic43—21no—
141D172—28no—
142D172—22no—
143D172—21no—
144D172—22no—
145D172—22no—
146D172—22no—
147D172—21no—
148D172—21no—
149D172—84no—
150D172C2×D412yes—
151C4×D43—28no—
152C4×D43—22no—
153C4×D43—22no—
154C4×D43—41no—
155C4×D43—41no—
156Dic86—21no—
157Dic86—21no—
158Dic86—21no—
159Dic86C2×D412yes—
160C8×C43—22no—
161C43⋊C8—22no—
162C22×C43—22no—
163C22×C43—41no—
164C22×C43—42no—
165C22×C43#12011yescharacteristic
166C22×C43#12011yescharacteristic
167C22×C43C22×D411yescharacteristic
168C2×D43—22no—
169C2×D43—24no—
170C2×D43—44no—
171C2×D43—42no—
172C2×D43—44no—
173C2×D43—42no—
174C2×D43—41no—
175C2×D43—82no—
176C2×D43—88no—
177C4×C43—22no—
178C4×C43—42no—
179C4×C43#12011yescharacteristic
180C4×C43#12011yescharacteristic
181C4×C43C22×D411yescharacteristic
182C4×C43C22×D411yescharacteristic
183Dic43—22no—
184Dic43—41no—
185#3019—431nomaximal, Sylow
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43C2×#12011yescharacteristic
191D43—44no—
192D43—42no—
193D43—81no—
194C2×H(5,𝔽2)—431no—
195#575—431no—
196#575—431no—
197#535—431no—
198#455—434no—
199#453—434no—
200#421—431no—
201#421D4311yescharacteristic, complemented
202C2×#100—431no—
203C43#301911yescharacteristic, complemented, Sylow
204H(5,𝔽2)—434no—
205H(5,𝔽2)—862no—
206H(5,𝔽2)—862no—
207H(5,𝔽2)—862no—
208C2×#41—431no—
209C2×#41—431no—
210C2×#41—861no—
211C2×#41—861no—
212C2×#41C2×D4311yescharacteristic
213C22×D4—431no—
214C22×D4—861no—
215C22×D4—862no—
216C22×D4—861no—
217#137—432no—
218#137—432no—
219#137—861no—
220#137—861no—
221AGL(1,ℤ/8)—432no—
222AGL(1,ℤ/8)—432no—
223AGL(1,ℤ/8)—861no—
224AGL(1,ℤ/8)—861no—
225#135—862no—
226#135—862no—
227C2×M16—431no—
228C2×M16C2×D4311yescharacteristic, complemented
229#127—432no—
230#124—432no—
231#121—862no—
232#120—862no—
233#117C2×D4311yescharacteristic, complemented
234#104—434no—
235#104C2×D4314yescomplemented
236#100—434no—
237C24—432no—
238C24—862no—
239#41—21no—
240#41—21no—
241#41—432no—
242#41—432no—
243#41—864no—
244#41—864no—
245#41—864no—
246#41—864no—
247#41—861no—
248#41—861no—
249#41—861no—
250#41—861no—
251#41—861no—
252#41—861no—
253#41D17212yescomplemented
254#41C22×D4312yes—
255C2×Q8—431no—
256C2×Q8—431no—
257C2×Q8D17211yescharacteristic, complemented
258C2×D4—21no—
259C2×D4—431no—
260C2×D4—432no—
261C2×D4—432no—
262C2×D4—431no—
263C2×D4—864no—
264C2×D4—862no—
265C2×D4—864no—
266C2×D4—864no—
267C2×D4—868no—
268C2×D4—868no—
269C2×D4—864no—
270C2×D4—862no—
271C2×D4—861no—
272C2×D4—864no—
273C2×D4—861no—
274C2×D4—861no—
275C2×D4—861no—
276C2×D4—861no—
277C2×D4—861no—
278C2×D4D17211yescharacteristic, complemented
279C22×C4—21no—
280C22×C4—862no—
281C22×C4—861no—
282C22×C4—861no—
283C22×C4C22×D4311yescharacteristic
284Q16—862no—
285Q16—862no—
286SD16—862no—
287SD16—862no—
288SD16—862no—
289SD16—862no—
290D8—862no—
291D8—862no—
292M16—21no—
293M16—432no—
294M16—861no—
295M16C22×D4312yescomplemented
296C2×C8—21no—
297C2×C8—861no—
298C4⋊C4—21no—
299C22⋊C4—21no—
300C22⋊C4—864no—
301C42C22×D4312yescomplemented
302C23—21no—
303C23—434no—
304C23—868no—
305C23—862no—
306C23—861no—
307C23—862no—
308C23—861no—
309C23—3444no—
310C23—3442no—
311C23D4×D4311yescharacteristic
312Q8—21no—
313Q8—432no—
314Q8—861no—
315Q8—861no—
316Q8—861no—
317Q8C2×D17212yes—
318D4—22no—
319D4—22no—
320D4—21no—
321D4—432no—
322D4—868no—
323D4—868no—
324D4—862no—
325D4—862no—
326D4—861no—
327D4—862no—
328D4—862no—
329D4—862no—
330D4—861no—
331D4—862no—
332D4—861no—
333D4—3444no—
334D4—1721no—
335D4—1721no—
336D4C2×D17212yes—
337C2×C4—21no—
338C2×C4—22no—
339C2×C4—22no—
340C2×C4—22no—
341C2×C4—868no—
342C2×C4—861no—
343C2×C4—862no—
344C2×C4—862no—
345C2×C4—861no—
346C2×C4—1721no—
347C2×C4—1721no—
348C2×C4C2×D17211yescharacteristic
349C2×C4C2×D17211yescharacteristic
350C2×C4D4×D4311yescharacteristic
351C2×C4D4×D4311yescharacteristic
352C2×C4D4×D4311yescharacteristic
353C2×C4C23×D4311yescharacteristic
354C8—22no—
355C8—862no—
356C22—22no—
357C22—41no—
358C22—42no—
359C22—862no—
360C22—864no—
361C22—3442no—
362C22—3448no—
363C22—1722no—
364C22—1724no—
365C22—1722no—
366C22—1724no—
367C22—1721no—
368C22#1306329511yescharacteristic
369C22#1306329511yescharacteristic
370C22C2×D4×D4311yescharacteristic
371C4—22no—
372C4—42no—
373C4—862no—
374C4—1721no—
375C4#1306329511yescharacteristic
376C4#1306329511yescharacteristic
377C4C2×D4×D4311yescharacteristic
378C4C22×D17211yescharacteristic
379C2—21no—
380C2—21no—
381C2—21no—
382C2—42no—
383C2—3441no—
384C2—1722no—
385C2—1724no—
386C2C2×#1306329511yescharacteristic
subgroupG/H
centerC2C2×#13063295
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#421C2
socleC2×C43C2×#120
hypercenter#421D43
hypocenterC43#3019
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ #421

Complements

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

NH ≅ G/Ntype
1. C2×#13063371C2semidirect
2. #14583699C2semidirect
3. #14583697C2semidirect
4. #14583468C2semidirect
5. #14583078C2semidirect
6. #14583068C2semidirect
7. #14582917C2semidirect
8. C2×#13063241C2semidirect
9. C43×#421C2semidirect
17. C2×#10621898C22semidirect
23. #13063358C22semidirect
25. #13063355C22semidirect
27. #13063353C22semidirect
29. #13063350C22semidirect
32. C2×#10621877C22semidirect
33. #13063322C22semidirect
34. #13063313C22semidirect
37. #13063253C22semidirect
38. #13063241C22semidirect
40. C2×M16×C43C22semidirect
41. #117×C43C22semidirect
42. #104×C43C22semidirect
47. #41×C43D4semidirect
49. C2×Q8×C43D4semidirect
51. C2×D4×C43D4semidirect
71. #10621898D4semidirect
82. C2×D172D4semidirect
84. C2×D172C23semidirect
88. C2×Dic86D4semidirect
89. C2×Dic86C23semidirect
91. M16×C43C23semidirect
95. C42×C43C23semidirect
102. #10621877C23semidirect
201. #421D43semidirect
203. C43#3019semidirect
228. C2×M16C2×D43semidirect
233. #117C2×D43semidirect
235. #104C2×D43semidirect
253. #41D172semidirect
257. C2×Q8D172semidirect
278. C2×D4D172semidirect
295. M16C22×D43semidirect
301. C42C22×D43semidirect