Finite Group Databasebeta

← #19146776

Subgroups — #19146776

Order 5504.

392 conjugacy classes of subgroups.

The subgroup lattice has 370 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583613C211yesmaximal, characteristic, complemented
2#14583555C211yesmaximal, characteristic, complemented
3#14583257C211yesmaximal, characteristic, complemented
4#14583243C211yesmaximal, characteristic, complemented
5#14583220C211yesmaximal, characteristic, complemented
6#14583183C211yesmaximal, characteristic, complemented
7#14583127C211yesmaximal, characteristic, complemented
8#14583112C211yesmaximal, characteristic, complemented
9#14583041C211yesmaximal, characteristic, complemented
10#14583037C211yesmaximal, characteristic, complemented
11#14582996C211yesmaximal, characteristic, complemented
12#14582968C211yesmaximal, characteristic, complemented
13#14582909C211yesmaximal, characteristic, complemented
14#14582892C211yesmaximal, characteristic, complemented
15C43×#469C211yesmaximal, characteristic, complemented
16C2×#10621900C2211yescharacteristic
17C22×Dic86C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621883C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21#13063324C2211yescharacteristic
22#13063312—21no—
23#13063312C2211yescharacteristic
24#13063311—21no—
25#13063311—21no—
26#13063305C2211yescharacteristic
27#13063302—21no—
28#13063297—21no—
29#13063297—21no—
30#13063296C2211yescharacteristic
31#13063290C2211yescharacteristic
32D4×Dic43—21no—
33D4×Dic43C2211yescharacteristic
34C4×C22⋊D43C2211yescharacteristic
35#13063284C2211yescharacteristic
36#13063283C2211yescharacteristic
37#13063281—21no—
38#13063258C2211yescharacteristic
39#13063256C2211yescharacteristic
40Dic43⋊C8C2211yescharacteristic
41#13063250C2211yescharacteristic
42#13063250C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063250C2211yescharacteristic
45#13063248C2211yescharacteristic
46#13063248C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063246C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C2×M16×C43C2211yescharacteristic
54#121×C43C2211yescharacteristic
55#121×C43C2211yescharacteristic
56#106×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43—21no—
61C2×D4×C43C2311yescharacteristic
62C2×D4×C43C2311yescharacteristic
63C22×C4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43D411yescharacteristic
67C22×Dic43—21no—
68C22×Dic43—21no—
69C22×Dic43—21no—
70#10621900—22no—
71#10621900—41no—
72C2×C4×D43C2311yescharacteristic
73C2×Dic86—22no—
74C2×Dic86—21no—
75C2×Dic86—21no—
76C2×Dic86—41no—
77C2×Dic86C2311yescharacteristic
78C2×Dic86C2311yescharacteristic
79D8×C43—41no—
80M16×C43—41no—
81C2×C8×C43C2311yescharacteristic
82C2×C8×C43C2311yescharacteristic
83C4⋊C4×C43C2311yescharacteristic
84C4⋊C4×C43C2311yescharacteristic
85C22⋊C4×C43—21no—
86C22⋊C4×C43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89C22⋊Dic43—21no—
90C22⋊Dic43—21no—
91C22⋊Dic43—21no—
92C22⋊Dic43D411yescharacteristic
93#10621883—22no—
94#10621883—41no—
95(C2×D43)⋊C4—21no—
96(C2×D43)⋊C4—21no—
97(C2×D43)⋊C4D411yescharacteristic
98C4⋊Dic43—21no—
99C4⋊Dic43C2311yescharacteristic
100C4⋊Dic43C2311yescharacteristic
101Dic43⋊C4—21no—
102Dic43⋊C4—21no—
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43—21no—
106C4×Dic43—21no—
107C4×Dic43C2311yescharacteristic
108C2×C43⋊C8C2311yescharacteristic
109C2×C43⋊C8C2311yescharacteristic
110C8×D43—41no—
111C23×C43—21no—
112C23×C43—21no—
113C23×C43C2×D411yescharacteristic
114C22×D43C2×D411yescharacteristic
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—21no—
119D4×C43—42no—
120D4×C43—81no—
121C2×C4×C43—21no—
122C2×C4×C43—21no—
123C2×C4×C43—21no—
124C2×C4×C43—21no—
125C2×C4×C43C2×D411yescharacteristic
126C2×C4×C43C2411yescharacteristic
127C22⋊D43—41no—
128C22⋊D43—42no—
129C22⋊D43—81no—
130C2×Dic43—21no—
131C2×Dic43—21no—
132C2×Dic43—21no—
133C2×Dic43—21no—
134C2×Dic43—42no—
135C2×Dic43—42no—
136C2×Dic43—42no—
137C2×Dic43C2×D411yescharacteristic
138C2×Dic43C2×D411yescharacteristic
139C2×Dic43C2×D411yescharacteristic
140C4×D43—21no—
141C4×D43—21no—
142Dic86—21no—
143Dic86—21no—
144Dic86—21no—
145Dic86—42no—
146Dic86—81no—
147Dic86#4112yes—
148C8×C43—21no—
149C8×C43—21no—
150C43⋊C8—21no—
151C43⋊C8—21no—
152C22×C43—21no—
153C22×C43—21no—
154C22×C43—21no—
155C22×C43—41no—
156C22×C43—41no—
157C22×C43—41no—
158C22×C43—41no—
159C22×C43—41no—
160C22×C43—41no—
161C22×C43C22×D411yescharacteristic
162C2×D43—21no—
163C2×D43—21no—
164C2×D43—21no—
165C4×C43—21no—
166C4×C43—41no—
167C4×C43—41no—
168C4×C43C2×#4111yescharacteristic
169C4×C43H(5,𝔽2)11yescharacteristic
170Dic43—22no—
171Dic43—21no—
172Dic43—21no—
173Dic43—21no—
174Dic43—41no—
175Dic43—41no—
176Dic43—41no—
177#3321—431nomaximal, Sylow
178C2×C43—41no—
179C2×C43—81no—
180C2×C43—81no—
181C2×C43#54611yescharacteristic
182C2×C43#57511yescharacteristic
183C2×C43#57711yescharacteristic
184D43—41no—
185#555—431no—
186#548—431no—
187#489—431no—
188#485—431no—
189#482—431no—
190#475—431no—
191#469D4311yescharacteristic, complemented
192#465—431no—
193#463—431no—
194#449—431no—
195#448—431no—
196#440—431no—
197#435—431no—
198#419—431no—
199#416—431no—
200C43#332111yescharacteristic, complemented, Sylow
201C2×#41—431no—
202C22×Q8—431no—
203C2×SD16—431no—
204C2×SD16—431no—
205C2×D8C2×D4311yescharacteristic
206C2×M16C2×D4311yescharacteristic
207C22×C8—431no—
208C4⋊Q8—431no—
209#124—431no—
210#124—861no—
211#124—861no—
212#124—861no—
213C22⋊Q8—431no—
214C22⋊Q8—861no—
215#121—431no—
216#121—861no—
217#121—861no—
218#121C2×D4311yescharacteristic
219#121C2×D4311yescharacteristic
220C4×Q8—431no—
221C4×D4—431no—
222C4×D4—431no—
223C4×D4—861no—
224#117—431no—
225#117—431no—
226#117—861no—
227#107—431no—
228#106—431no—
229#106C2×D4311yescharacteristic
230C4⋊C8—431no—
231#103—431no—
232#103—431no—
233#103—431no—
234#103—431no—
235#103—431no—
236#103—431no—
237#102—431no—
238#102—431no—
239#102C2×D4311yescharacteristic
240#102C2×D4311yescharacteristic
241C22⋊C8—431no—
242C22⋊C8—431no—
243#97—431no—
244#41—862no—
245#41—1721no—
246C2×Q8—431no—
247C2×Q8—431no—
248C2×Q8—861no—
249C2×Q8—862no—
250C2×Q8—861no—
251C2×Q8—1721no—
252C2×D4—21no—
253C2×D4—21no—
254C2×D4—431no—
255C2×D4—861no—
256C2×D4—861no—
257C2×D4C22×D4311yescharacteristic
258C2×D4C22×D4311yescharacteristic
259C22×C4—431no—
260C22×C4—861no—
261C22×C4—861no—
262C22×C4—861no—
263C22×C4C22×D4311yescharacteristic
264SD16—862no—
265SD16—1721no—
266D8—41no—
267M16—41no—
268C2×C8—431no—
269C2×C8—431no—
270C2×C8—1721no—
271C2×C8C22×D4311yescharacteristic
272C2×C8C22×D4311yescharacteristic
273C4⋊C4—431no—
274C4⋊C4—431no—
275C4⋊C4—431no—
276C4⋊C4—861no—
277C4⋊C4—861no—
278C4⋊C4—861no—
279C4⋊C4C22×D4311yescharacteristic
280C4⋊C4C22×D4311yescharacteristic
281C22⋊C4—21no—
282C22⋊C4—21no—
283C22⋊C4—431no—
284C22⋊C4—431no—
285C22⋊C4—861no—
286C22⋊C4—861no—
287C22⋊C4—861no—
288C22⋊C4—861no—
289C22⋊C4—861no—
290C22⋊C4—861no—
291C22⋊C4—861no—
292C42—431no—
293C42—861no—
294C42—861no—
295C42—861no—
296C23—21no—
297C23—21no—
298C23—431no—
299C23D4×D4311yescharacteristic
300Q8—432no—
301Q8—861no—
302Q8—861no—
303Q8—861no—
304Q8—3441no—
305Q8—1722no—
306D4—21no—
307D4—21no—
308D4—21no—
309D4—21no—
310D4—42no—
311D4—81no—
312D4—3441no—
313D4—1721no—
314D4—1722no—
315C2×C4—21no—
316C2×C4—21no—
317C2×C4—21no—
318C2×C4—21no—
319C2×C4—431no—
320C2×C4—431no—
321C2×C4—431no—
322C2×C4—861no—
323C2×C4—861no—
324C2×C4—861no—
325C2×C4—861no—
326C2×C4—861no—
327C2×C4—861no—
328C2×C4—1722no—
329C2×C4—1722no—
330C2×C4—1722no—
331C2×C4D4×D4311yescharacteristic
332C2×C4C23×D4311yescharacteristic
333C8—21no—
334C8—21no—
335C8—861no—
336C8—861no—
337C22—21no—
338C22—21no—
339C22—21no—
340C22—41no—
341C22—41no—
342C22—41no—
343C22—41no—
344C22—41no—
345C22—41no—
346C22—861no—
347C22—861no—
348C22—861no—
349C22C2×D4×D4311yescharacteristic
350C4—21no—
351C4—41no—
352C4—41no—
353C4—861no—
354C4—861no—
355C4—861no—
356C4—862no—
357C4—1721no—
358C4—1721no—
359C4—1721no—
360C4#41×D4311yescharacteristic
361C4#1306337011yescharacteristic
362C2—41no—
363C2—81no—
364C2—81no—
365C2—1721no—
366C2#1458353811yescharacteristic
367C2#1458369511yescharacteristic
368C2#1458370911yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#469C2
socleC22×C43C22×D4
hypercenter#469D43
hypocenterC43#3321
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #469

Complements

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

NH ≅ G/Ntype
1. #14583613C2semidirect
2. #14583555C2semidirect
3. #14583257C2semidirect
4. #14583243C2semidirect
5. #14583220C2semidirect
6. #14583183C2semidirect
7. #14583127C2semidirect
8. #14583112C2semidirect
9. #14583041C2semidirect
10. #14583037C2semidirect
11. #14582996C2semidirect
12. #14582968C2semidirect
13. #14582909C2semidirect
14. #14582892C2semidirect
15. C43×#469C2semidirect
191. #469D43semidirect
200. C43#3321semidirect