Finite Group Databasebeta

← #19145920

Subgroups — #19145920

Order 5504.

398 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#14583434C211yesmaximal, characteristic, complemented
3#14583196C211yesmaximal, characteristic, complemented
4#14583193C211yesmaximal, characteristic, complemented
5#14583188C211yesmaximal, characteristic, complemented
6#14583136C211yesmaximal, characteristic, complemented
7#14583134C211yesmaximal, characteristic, complemented
8#14583129C211yesmaximal, characteristic, complemented
9#14583127C211yesmaximal, characteristic, complemented
10#14583115C211yesmaximal, characteristic, complemented
11#14583114C211yesmaximal, characteristic, complemented
12#14583098C211yesmaximal, characteristic, complemented
13#14583093C211yesmaximal, characteristic, complemented
14C4⋊C8×D43C211yesmaximal, characteristic, complemented
15C43×#478C211yesmaximal, characteristic, complemented
16C2×#10621898—21no—
17C2×#10621873C2211yescharacteristic
18C2×#10621883C2211yescharacteristic
19C2×D344C2211yescharacteristic
20C2×#10621882C2211yescharacteristic
21C2×C8×D43C2211yescharacteristic
22C2×C8×D43C2211yescharacteristic
23#13063324C2211yescharacteristic
24#13063321C2211yescharacteristic
25#13063320—21no—
26#13063313C2211yescharacteristic
27#13063311—21no—
28#13063310—21no—
29#13063305C2211yescharacteristic
30#13063300C2211yescharacteristic
31#13063300C2211yescharacteristic
32#13063298—21no—
33#13063296C2211yescharacteristic
34#13063290C2211yescharacteristic
35C4×D172C2211yescharacteristic
36#13063287—21no—
37#13063287C2211yescharacteristic
38C4×C22⋊D43—21no—
39#13063283—21no—
40C42×D43C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063256C2211yescharacteristic
43C4⋊(C43⋊C8)C2211yescharacteristic
44Dic43⋊C8C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063250C2211yescharacteristic
47#13063248C2211yescharacteristic
48#13063247C2211yescharacteristic
49#13063245C2211yescharacteristic
50#13063245C2211yescharacteristic
51#13063245C2211yescharacteristic
52#125×C43C2211yescharacteristic
53C4×D4×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×D4×C43C2311yescharacteristic
60C22×C4×C43—21no—
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64#10621898—44no—
65C2×D172—21no—
66C2×D172—21no—
67C2×D172C2311yescharacteristic
68C2×D172C2311yescharacteristic
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43D411yescharacteristic
72C2×C4×D43D411yescharacteristic
73C2×C4×D43C2311yescharacteristic
74C2×Dic86—21no—
75C2×Dic86C2311yescharacteristic
76C2×C8×C43C2311yescharacteristic
77C2×C8×C43C2311yescharacteristic
78C4⋊C4×C43—21no—
79C4⋊C4×C43—21no—
80C4⋊C4×C43C2311yescharacteristic
81C4⋊C4×C43C2311yescharacteristic
82C4⋊C4×C43C2311yescharacteristic
83C22⋊C4×C43—21no—
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86#10621883—41no—
87#10621882—41no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4—21no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4—21no—
94(C2×D43)⋊C4—21no—
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97Dic43⋊C4—21no—
98Dic43⋊C4—21no—
99C4×Dic43—21no—
100C4×Dic43D411yescharacteristic
101C4×Dic43D411yescharacteristic
102C4×Dic43C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C2×C43⋊C8C2311yescharacteristic
105D344—41no—
106#10621873—41no—
107C8×D43—41no—
108C8×D43—41no—
109C23×C43—21no—
110C22×D43—21no—
111C22×D43—21no—
112C22×D43C2×D411yescharacteristic
113D4×C43—21no—
114D4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43—21no—
118C2×C4×C43—42no—
119C2×C4×C43C2×D411yescharacteristic
120C2×C4×C43C2×D411yescharacteristic
121C2×C4×C43C2411yescharacteristic
122C22⋊D43—42no—
123C22⋊D43—42no—
124C22⋊D43—42no—
125C2×Dic43—21no—
126C2×Dic43—21no—
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129C2×Dic43C2×D411yescharacteristic
130D172—21no—
131D172—21no—
132D172—21no—
133D172—21no—
134D172—42no—
135D172—42no—
136C4×D43—22no—
137C4×D43—21no—
138C4×D43—21no—
139C4×D43—22no—
140C4×D43—42no—
141C4×D43—42no—
142Dic86—21no—
143Dic86—21no—
144Dic86—42no—
145C8×C43—21no—
146C8×C43—21no—
147C43⋊C8—21no—
148C43⋊C8—21no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43C22×D411yescharacteristic
153C2×D43—21no—
154C2×D43—21no—
155C2×D43—41no—
156C2×D43—41no—
157C2×D43—41no—
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×C43—41no—
167C4×C43H(5,𝔽2)11yescharacteristic
168C4×C432−1+411yescharacteristic
169Dic43—21no—
170Dic43—21no—
171Dic43—41no—
172Dic43—41no—
173Dic43#13512yes—
174#3247—431nomaximal, Sylow
175C2×C43—81no—
176C2×C43#53711yescharacteristic
177C2×C43C2×#13511yescharacteristic
178C2×C43C2×AGL(1,ℤ/8)11yescharacteristic
179D43—22no—
180D43—81no—
181D43—81no—
182#532—431no—
183#529—431no—
184#478—431no—
185#478D4311yescharacteristic, complemented
186#477—431no—
187#476—431no—
188#466—431no—
189#466—431no—
190#465—431no—
191#465—431no—
192#463—431no—
193#463—431no—
194#460—431no—
195#459—431no—
196C2×C4⋊C8—431no—
197C43#324711yescharacteristic, complemented, Sylow
198C2×#41—861no—
199C2×SD16—431no—
200C2×SD16—431no—
201C2×D8—431no—
202C2×D8—431no—
203C22×C8—431no—
204C22×C8—431no—
205C4⋊Q8—431no—
206#127—431no—
207#126—861no—
208#125C2×D4311yescharacteristic
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—431no—
220C4×D4—861no—
221C4×D4—861no—
222C4×D4C2×D4311yescharacteristic
223#117—861no—
224C2×C42—431no—
225#107—431no—
226#107C2×D4311yescharacteristic
227#106—431no—
228#106C2×D4311yescharacteristic
229C4⋊C8—431no—
230C4⋊C8—431no—
231C4⋊C8—431no—
232C4⋊C8C2×D4311yescharacteristic
233#103—431no—
234#103—431no—
235#102—431no—
236#102—431no—
237#102—431no—
238#102—431no—
239#102C2×D4311yescharacteristic
240#102C2×D4311yescharacteristic
241#41—1724no—
242C2×Q8—431no—
243C2×Q8—861no—
244C2×D4—431no—
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4—861no—
250C2×D4—861no—
251C2×D4C22×D4311yescharacteristic
252C22×C4—21no—
253C22×C4—431no—
254C22×C4—431no—
255C22×C4—431no—
256C22×C4—861no—
257C22×C4—861no—
258SD16—1721no—
259SD16—1721no—
260D8—1721no—
261D8—1721no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8—1721no—
265C2×C8—1721no—
266C2×C8C22×D4311yescharacteristic
267C2×C8C22×D4311yescharacteristic
268C4⋊C4—21no—
269C4⋊C4—21no—
270C4⋊C4—431no—
271C4⋊C4—861no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4C22×D4311yescharacteristic
275C4⋊C4C22×D4311yescharacteristic
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—21no—
278C22⋊C4—861no—
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—431no—
293C23—861no—
294C23—861no—
295Q8—861no—
296Q8—861no—
297Q8—1722no—
298D4—21no—
299D4—21no—
300D4—861no—
301D4—861no—
302D4—861no—
303D4—861no—
304D4—1722no—
305D4—1722no—
306D4—1722no—
307D4—1722no—
308D4—1722no—
309C2×C4—21no—
310C2×C4—21no—
311C2×C4—21no—
312C2×C4—42no—
313C2×C4—431no—
314C2×C4—431no—
315C2×C4—431no—
316C2×C4—862no—
317C2×C4—862no—
318C2×C4—861no—
319C2×C4—861no—
320C2×C4—861no—
321C2×C4—861no—
322C2×C4—1722no—
323C2×C4—1722no—
324C2×C4D4×D4311yescharacteristic
325C2×C4D4×D4311yescharacteristic
326C2×C4C23×D4311yescharacteristic
327C8—21no—
328C8—21no—
329C8—861no—
330C8—861no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—432no—
335C22—861no—
336C22—861no—
337C22—1721no—
338C22—1721no—
339C22—1721no—
340C22—1721no—
341C22—1721no—
342C22—1721no—
343C22C2×D4×D4311yescharacteristic
344C4—21no—
345C4—21no—
346C4—41no—
347C4—41no—
348C4—41no—
349C4—432no—
350C4—861no—
351C4—861no—
352C4—1721no—
353C4—1721no—
354C4#1306337111yescharacteristic
355C4#1306337311yescharacteristic
356C2—81no—
357C2—862no—
358C2—3441no—
359C2—3441no—
360C2#1458347911yescharacteristic
361C2#135×D4311yescharacteristic
362C2AGL(1,ℤ/8)×D4311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#478C2
socleC22×C43C22×D4
hypercenter#478D43
hypocenterC43#3247
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #478

Complements

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

NH ≅ G/Ntype
1. #14583446C2semidirect
2. #14583434C2semidirect
3. #14583196C2semidirect
4. #14583193C2semidirect
5. #14583188C2semidirect
6. #14583136C2semidirect
7. #14583134C2semidirect
8. #14583129C2semidirect
9. #14583127C2semidirect
10. #14583115C2semidirect
11. #14583114C2semidirect
12. #14583098C2semidirect
13. #14583093C2semidirect
14. C4⋊C8×D43C2semidirect
15. C43×#478C2semidirect
185. #478D43semidirect
197. C43#3247semidirect