Finite Group Databasebeta

← #19143971

Subgroups — #19143971

Order 5504.

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

normal subgroups only

This group has 704 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
1#14583735C211yesmaximal, characteristic
2C2×#13063356C211yesmaximal, characteristic, complemented
3#14583473C211yesmaximal, characteristic, complemented
4#14583080C214yesmaximal, complemented
5#14583075C214yesmaximal, complemented
6#14582916C211yesmaximal, characteristic, complemented
7#14582915C211yesmaximal, characteristic, complemented
8#14582881C211yesmaximal, characteristic, complemented
9C2×#137×C43C211yesmaximal, characteristic, complemented
10#13063373—21no—
11#13063372—21no—
12#13063372C2212yes—
13#13063371—21no—
14#13063371C2212yes—
15#13063370—21no—
16#13063370—22no—
17C2×#10621898—22no—
18C2×#10621898C2211yescharacteristic
19C2×#10621898C2211yescharacteristic
20#41×D43—22no—
21#41×D43—22no—
22#13063356—22no—
23#13063356C2214yescomplemented
24C2×#10621885—21no—
25C2×#10621884—21no—
26C2×#10621877C2211yescharacteristic, complemented
27#13063323C2212yescomplemented
28#13063314C2212yescomplemented
29#13063308—22no—
30#13063301—22no—
31#13063284C2211yescharacteristic, complemented
32#13063252C2214yescomplemented
33#13063251C2214yescomplemented
34#13063243C2212yescomplemented
35#13063241C2212yescomplemented
36C2×#41×C43C2211yescharacteristic
37C22×Q8×C43C2211yescharacteristic, complemented
38#137×C43—22no—
39#137×C43C2214yescomplemented
40C2×Q16×C43—21no—
41C2×SD16×C43—21no—
42C2×M16×C43C2211yescharacteristic, complemented
43#41×C43—21no—
44#41×C43—21no—
45#41×C43D412yes—
46#41×C43C2312yes—
47C2×Q8×C43—21no—
48C2×Q8×C43—21no—
49C2×Q8×C43—21no—
50C2×Q8×C43—21no—
51C2×Q8×C43—21no—
52C2×Q8×C43D411yescharacteristic
53C2×Q8×C43C2312yes—
54C2×D4×C43—21no—
55C2×D4×C43D411yescharacteristic
56C22×C4×C43—21no—
57C22×C4×C43—21no—
58C22×C4×C43C2311yescharacteristic
59C2×C22⋊D43—24no—
60C2×C22⋊D43—21no—
61C2×C22⋊D43D412yes—
62#10621902—22no—
63#10621902—22no—
64Q8×D43—22no—
65Q8×D43—22no—
66#10621900—24no—
67#10621900—22no—
68#10621900—22no—
69#10621900—24no—
70D4×D43—22no—
71D4×D43—24no—
72D4×D43—22no—
73D4×D43—24no—
74#10621898—24no—
75#10621898—24no—
76#10621898—21no—
77#10621898—21no—
78#10621898—21no—
79#10621898—21no—
80#10621898—21no—
81#10621898—21no—
82#10621898—22no—
83#10621898—22no—
84#10621898D412yes—
85#10621898C2312yes—
86C2×D172—22no—
87C2×D172D411yescharacteristic
88C2×D172C2311yescharacteristic
89C2×C4×D43—24no—
90C2×C4×D43—21no—
91C2×C4×D43D412yes—
92C2×Dic86—22no—
93C2×Dic86D411yescharacteristic
94C2×Dic86C2311yescharacteristic
95Q16×C43—24no—
96SD16×C43—24no—
97M16×C43—21no—
98M16×C43C2312yes—
99C2×C8×C43—21no—
100C22⋊Dic43—21no—
101#10621885—24no—
102#10621884—24no—
103(C2×D43)⋊C4—24no—
104C4⋊Dic43—21no—
105Dic43⋊C4—24no—
106C4×Dic43C2312yes—
107#10621877—21no—
108#10621877C2312yes—
109C2×C43⋊C8—21no—
110C23×C43—21no—
111C23×C43C2×D411yescharacteristic
112C22×D43—24no—
113C22×D43—21no—
114C22×D43C2×D412yes—
115Q8×C43—21no—
116Q8×C43—22no—
117Q8×C43—22no—
118Q8×C43—41no—
119Q8×C43—41no—
120Q8×C43C2×D412yes—
121D4×C43—22no—
122D4×C43—22no—
123D4×C43—21no—
124D4×C43C2×D412yes—
125C2×C4×C43—21no—
126C2×C4×C43—22no—
127C2×C4×C43—22no—
128C2×C4×C43—22no—
129C2×C4×C43—41no—
130C2×C4×C43—41no—
131C2×C4×C43C2×D411yescharacteristic
132C2×C4×C43C2×D411yescharacteristic
133C2×C4×C43C2×D411yescharacteristic
134C2×C4×C43C2×D411yescharacteristic
135C2×C4×C43C2×D411yescharacteristic
136C2×C4×C43C2411yescharacteristic
137C22⋊D43—24no—
138C22⋊D43—24no—
139C22⋊D43—22no—
140C22⋊D43—22no—
141C22⋊D43—22no—
142C22⋊D43—22no—
143C2×Dic43—24no—
144C2×Dic43—21no—
145C2×Dic43—22no—
146C2×Dic43C2×D412yes—
147D172—24no—
148D172—21no—
149D172—21no—
150D172—21no—
151D172C2×D412yes—
152C4×D43—24no—
153C4×D43—24no—
154C4×D43—22no—
155C4×D43—22no—
156C4×D43—22no—
157C4×D43—22no—
158Dic86—24no—
159Dic86—21no—
160Dic86—21no—
161Dic86—21no—
162Dic86C2×D412yes—
163C8×C43—22no—
164C43⋊C8—22no—
165C22×C43—22no—
166C22×C43—41no—
167C22×C43—81no—
168C22×C43#12011yescharacteristic
169C22×C43#12011yescharacteristic
170C22×C43C22×D411yescharacteristic
171C2×D43—22no—
172C2×D43—22no—
173C2×D43—42no—
174C2×D43—81no—
175C2×D43—84no—
176C4×C43—22no—
177C4×C43—42no—
178C4×C43#12011yescharacteristic
179C4×C43#12011yescharacteristic
180C4×C43C22×D411yescharacteristic
181C4×C43C22×D411yescharacteristic
182Dic43—22no—
183Dic43—22no—
184Dic43—42no—
185#3022—431nomaximal, Sylow
186C2×C43—21no—
187C2×C43—21no—
188C2×C43—21no—
189C2×C43—42no—
190C2×C43C2×#12011yescharacteristic
191D43—42no—
192D43—42no—
193#585—431no—
194C2×#137—431no—
195C2×#137D4311yescharacteristic, complemented
196#536—431no—
197#456—434no—
198#455—434no—
199#421—431no—
200#421—431no—
201#413—431no—
202C43#302211yescharacteristic, complemented, Sylow
2032−1+4—432no—
2042−1+4—861no—
2052−1+4—861no—
206H(5,𝔽2)—432no—
207H(5,𝔽2)—862no—
208H(5,𝔽2)—861no—
209H(5,𝔽2)—861no—
210C2×#41—431no—
211C2×#41—431no—
212C2×#41—862no—
213C2×#41—862no—
214C2×#41—862no—
215C2×#41C2×D4311yescharacteristic
216C22×Q8C2×D4311yescharacteristic, complemented
217#137—22no—
218#137—434no—
219#137—862no—
220#137C2×D4314yescomplemented
221C2×Q16—21no—
222C2×Q16—861no—
223C2×SD16—21no—
224C2×SD16—861no—
225C2×M16—431no—
226C2×M16C2×D4311yescharacteristic, complemented
227C4⋊Q8—432no—
228#124—432no—
229#123—862no—
230C22⋊Q8—862no—
231#117—431no—
232#104—434no—
233#104—434no—
234#101—432no—
235#100—432no—
236#41—21no—
237#41—21no—
238#41—432no—
239#41—432no—
240#41—862no—
241#41—862no—
242#41—864no—
243#41—864no—
244#41—864no—
245#41—864no—
246#41—862no—
247#41—862no—
248#41—862no—
249#41—862no—
250#41—861no—
251#41—861no—
252#41—861no—
253#41—861no—
254#41—861no—
255#41—861no—
256#41C22⋊D4312yes—
257#41C22×D4312yes—
258C2×Q8—21no—
259C2×Q8—21no—
260C2×Q8—21no—
261C2×Q8—21no—
262C2×Q8—21no—
263C2×Q8—431no—
264C2×Q8—431no—
265C2×Q8—862no—
266C2×Q8—862no—
267C2×Q8—862no—
268C2×Q8C22⋊D4311yescharacteristic
269C2×Q8C22×D4312yes—
270C2×D4—21no—
271C2×D4—432no—
272C2×D4—431no—
273C2×D4—431no—
274C2×D4—862no—
275C2×D4—864no—
276C2×D4—864no—
277C2×D4—862no—
278C2×D4—864no—
279C2×D4—861no—
280C2×D4—862no—
281C2×D4C22⋊D4311yescharacteristic
282C22×C4—21no—
283C22×C4—21no—
284C22×C4—432no—
285C22×C4—864no—
286C22×C4—861no—
287C22×C4C22×D4311yescharacteristic
288Q16—24no—
289Q16—864no—
290SD16—24no—
291SD16—864no—
292M16—21no—
293M16—432no—
294M16—861no—
295M16C22×D4312yes—
296C2×C8—21no—
297C2×C8—861no—
298C4⋊C4—864no—
299C4⋊C4—861no—
300C22⋊C4—864no—
301C22⋊C4—861no—
302C42—432no—
303C23—21no—
304C23—432no—
305C23—864no—
306C23—861no—
307C23D4×D4311yescharacteristic
308Q8—21no—
309Q8—22no—
310Q8—22no—
311Q8—41no—
312Q8—41no—
313Q8—432no—
314Q8—864no—
315Q8—861no—
316Q8—861no—
317Q8—861no—
318Q8C2×C22⋊D4312yes—
319D4—22no—
320D4—22no—
321D4—21no—
322D4—432no—
323D4—864no—
324D4—864no—
325D4—864no—
326D4—862no—
327D4—862no—
328D4—862no—
329D4—862no—
330D4—861no—
331D4—861no—
332D4—861no—
333D4C2×C22⋊D4312yes—
334C2×C4—21no—
335C2×C4—22no—
336C2×C4—22no—
337C2×C4—22no—
338C2×C4—41no—
339C2×C4—41no—
340C2×C4—432no—
341C2×C4—864no—
342C2×C4—864no—
343C2×C4—864no—
344C2×C4—861no—
345C2×C4—862no—
346C2×C4—862no—
347C2×C4—862no—
348C2×C4—862no—
349C2×C4—862no—
350C2×C4D4×D4311yescharacteristic
351C2×C4D4×D4311yescharacteristic
352C2×C4D4×D4311yescharacteristic
353C2×C4C2×C22⋊D4311yescharacteristic
354C2×C4C2×C22⋊D4311yescharacteristic
355C2×C4C23×D4311yescharacteristic
356C8—22no—
357C8—862no—
358C22—22no—
359C22—41no—
360C22—81no—
361C22—862no—
362C22—862no—
363C22—3441no—
364C22—3444no—
365C22—1722no—
366C22#1306329311yescharacteristic
367C22#1306329311yescharacteristic
368C22C2×D4×D4311yescharacteristic
369C4—22no—
370C4—42no—
371C4—862no—
372C4—862no—
373C4—1722no—
374C4#1306329311yescharacteristic
375C4#1306329311yescharacteristic
376C4C2×D4×D4311yescharacteristic
377C4C22×C22⋊D4311yescharacteristic
378C2—21no—
379C2—21no—
380C2—21no—
381C2—42no—
382C2—1722no—
383C2—1722no—
384C2C2×#1306329311yescharacteristic
subgroupG/H
centerC2C2×#13063293
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC2×#137×C43C2
socleC2×C43C2×#120
hypercenterC2×#137D43
hypocenterC43#3022
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C2 ◁ C22×C4 ◁ C2×#137

Complements

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

NH ≅ G/Ntype
2. C2×#13063356C2semidirect
3. #14583473C2semidirect
4. #14583080C2semidirect
5. #14583075C2semidirect
6. #14582916C2semidirect
7. #14582915C2semidirect
8. #14582881C2semidirect
9. C2×#137×C43C2semidirect
23. #13063356C22semidirect
26. C2×#10621877C22semidirect
27. #13063323C22semidirect
28. #13063314C22semidirect
31. #13063284C22semidirect
32. #13063252C22semidirect
33. #13063251C22semidirect
34. #13063243C22semidirect
35. #13063241C22semidirect
37. C22×Q8×C43C22semidirect
39. #137×C43C22semidirect
42. C2×M16×C43C22semidirect
195. C2×#137D43semidirect
202. C43#3022semidirect
216. C22×Q8C2×D43semidirect
220. #137C2×D43semidirect
226. C2×M16C2×D43semidirect