Finite Group Databasebeta

← #19145291

Subgroups — #19145291

Order 5504.

410 conjugacy classes of subgroups.

The subgroup lattice has 364 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583446C211yesmaximal, characteristic, complemented
2#14583431C211yesmaximal, characteristic, complemented
3#14583306C211yesmaximal, characteristic, complemented
4#14583287C211yesmaximal, characteristic, complemented
5#14583262C211yesmaximal, characteristic, complemented
6#14583257C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583132C211yesmaximal, characteristic, complemented
9#14583129C211yesmaximal, characteristic, complemented
10#14583127C211yesmaximal, characteristic, complemented
11#14583009C211yesmaximal, characteristic, complemented
12#14583001C211yesmaximal, characteristic, complemented
13#14582999C211yesmaximal, characteristic, complemented
14#97×D43C211yesmaximal, characteristic, complemented
15C43×#442C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×#10621882C2211yescharacteristic
20C2×C8×D43C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22#13063324C2211yescharacteristic
23#13063321C2211yescharacteristic
24#13063318—21no—
25#13063316C2211yescharacteristic
26#13063312C2211yescharacteristic
27#13063311—21no—
28#13063307—21no—
29#13063305C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063298—21no—
32#13063296C2211yescharacteristic
33#13063296C2211yescharacteristic
34C4×Dic86C2211yescharacteristic
35C4×D172C2211yescharacteristic
36C4×C22⋊D43—21no—
37C4×C22⋊D43—21no—
38#13063284—21no—
39C42×D43C2211yescharacteristic
40#13063259C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063256C2211yescharacteristic
43#13063250C2211yescharacteristic
44#13063248C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48#13063245C2211yescharacteristic
49#13063236C2211yescharacteristic
50#13063235C2211yescharacteristic
51#13063235C2211yescharacteristic
52C2×D8×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54C4×D4×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#97×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43—21no—
62C22×C4×C43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C2×C22⋊D43—21no—
67#10621898—44no—
68C2×D172—21no—
69C2×D172C2311yescharacteristic
70C2×C4×D43—21no—
71C2×C4×D43D411yescharacteristic
72C2×C4×D43D411yescharacteristic
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86C2311yescharacteristic
76D8×C43—22no—
77C2×C8×C43C2311yescharacteristic
78C2×C8×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C4⋊C4×C43C2311yescharacteristic
81C22⋊C4×C43—21no—
82C22⋊C4×C43—21no—
83C42×C43C2311yescharacteristic
84C22⋊Dic43—21no—
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88#10621883—22no—
89#10621882—22no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93C4⋊Dic43—21no—
94C4⋊Dic43—21no—
95C4⋊Dic43C2311yescharacteristic
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99Dic43⋊C4—21no—
100C4×Dic43—21no—
101C4×Dic43D411yescharacteristic
102C4×Dic43D411yescharacteristic
103C4×Dic43C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105C2×C43⋊C8C2311yescharacteristic
106#10621873—22no—
107C8×D43—22no—
108C8×D43—22no—
109C23×C43—21no—
110C23×C43—21no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113D4×C43—21no—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—21no—
119C2×C4×C43—42no—
120C2×C4×C43—42no—
121C2×C4×C43C2×D411yescharacteristic
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2411yescharacteristic
124C22⋊D43—42no—
125C22⋊D43—42no—
126C22⋊D43—42no—
127C22⋊D43—42no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—21no—
131C2×Dic43C2×D411yescharacteristic
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134D172—21no—
135D172—21no—
136D172—42no—
137C4×D43—22no—
138C4×D43—21no—
139C4×D43—21no—
140C4×D43—41no—
141C4×D43—42no—
142Dic86—21no—
143Dic86—21no—
144Dic86—42no—
145C8×C43—21no—
146C8×C43#4112yescomplemented
147C43⋊C8—21no—
148C43⋊C8#4112yescomplemented
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43—41no—
155C22×C43C22×D411yescharacteristic
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—41no—
159C2×D43—41no—
160C2×D43—41no—
161C2×D43AGL(1,ℤ/8)12yes—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43—41no—
166C4×C43C2×#4111yescharacteristic
167C4×C43C2×#4111yescharacteristic
168Dic43—21no—
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43—41no—
174#3180—431nomaximal, Sylow
175C2×C43—81no—
176C2×C43—81no—
177C2×C43#53211yescharacteristic
178C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
179C2×C43#57511yescharacteristic
180D43—22no—
181D43—81no—
182#532—431no—
183#529—431no—
184#501—431no—
185#496—431no—
186#490—431no—
187#489—431no—
188#466—431no—
189#466—431no—
190#465—431no—
191#465—431no—
192#442—431no—
193#442D4311yescharacteristic, complemented
194#440—431no—
195#440—431no—
196C2×#97—431no—
197C43#318011yescharacteristic, complemented, Sylow
198C2×#41—861no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
202C2×D8C2×D4311yescharacteristic
203C22×C8—431no—
204C22×C8—431no—
205C4⋊Q8—431no—
206#127—431no—
207#126—861no—
208#125—431no—
209#124—431no—
210#124—861no—
211#123—861no—
212C22⋊Q8—431no—
213#121—431no—
214#121—431no—
215#121—431no—
216#121—861no—
217C4×Q8—431no—
218C4×D4—431no—
219C4×D4—861no—
220C4×D4—861no—
221C4×D4C2×D4311yescharacteristic
222C4×D4C2×D4311yescharacteristic
223#117—861no—
224C2×C42—431no—
225#107—431no—
226#107—431no—
227#106—431no—
228#106C2×D4311yescharacteristic
229#103—431no—
230#103—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102—431no—
235#102C2×D4311yescharacteristic
236#102C2×D4311yescharacteristic
237#97—431no—
238#97—431no—
239#97—431no—
240#97C2×D4311yescharacteristic
241#41—1724no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—431no—
245C2×D4—861no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4C22×D4311yescharacteristic
251C2×D4C22×D4311yescharacteristic
252C22×C4—21no—
253C22×C4—21no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—431no—
257C22×C4—861no—
258SD16—862no—
259SD16—862no—
260D8—22no—
261D8—862no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8—862no—
265C2×C8—862no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—861no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—21no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C22⋊C4—861no—
286C42—431no—
287C42—431no—
288C42—431no—
289C42—861no—
290C42C22×D4311yescharacteristic
291C23—21no—
292C23—21no—
293C23—431no—
294C23—861no—
295Q8—861no—
296Q8—861no—
297Q8—1722no—
298D4—21no—
299D4—21no—
300D4—21no—
301D4—21no—
302D4—861no—
303D4—861no—
304D4—1722no—
305D4—1722no—
306D4—1722no—
307D4—1722no—
308D4—1722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—42no—
312C2×C4—42no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—862no—
317C2×C4—861no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—1721no—
323C2×C4—1722no—
324C2×C4D4×D4311yescharacteristic
325C2×C4D4×D4311yescharacteristic
326C2×C4C23×D4311yescharacteristic
327C8—21no—
328C8—432no—
329C8—861no—
330C8#1062189812yescomplemented
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—41no—
336C22—41no—
337C22—432no—
338C22—861no—
339C22—861no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—861no—
349C4—861no—
350C4—861no—
351C4—1721no—
352C4—1721no—
353C4—1721no—
354C4#41×D4311yescharacteristic
355C4C2×#1062189811yescharacteristic
356C2—81no—
357C2—81no—
358C2—862no—
359C2—3441no—
360C2#1458344611yescharacteristic
361C2AGL(1,ℤ/8)×D4311yescharacteristic
362C2#1458369511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#442C2
socleC22×C43C22×D4
hypercenter#442D43
hypocenterC43#3180
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #442

Complements

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

NH ≅ G/Ntype
1. #14583446C2semidirect
2. #14583431C2semidirect
3. #14583306C2semidirect
4. #14583287C2semidirect
5. #14583262C2semidirect
6. #14583257C2semidirect
7. #14583134C2semidirect
8. #14583132C2semidirect
9. #14583129C2semidirect
10. #14583127C2semidirect
11. #14583009C2semidirect
12. #14583001C2semidirect
13. #14582999C2semidirect
14. #97×D43C2semidirect
15. C43×#442C2semidirect
146. C8×C43#41semidirect
148. C43⋊C8#41semidirect
193. #442D43semidirect
197. C43#3180semidirect
330. C8#10621898semidirect