Finite Group Databasebeta

← #19144793

Subgroups — #19144793

Order 5504.

396 conjugacy classes of subgroups.

The subgroup lattice has 362 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583503C211yesmaximal, characteristic, complemented
2#14583381C211yesmaximal, characteristic, complemented
3#14583216C211yesmaximal, characteristic, complemented
4#14583211C211yesmaximal, characteristic, complemented
5#14583206C211yesmaximal, characteristic, complemented
6#14583200C211yesmaximal, characteristic, complemented
7#14583091C211yesmaximal, characteristic, complemented
8#14583043C211yesmaximal, characteristic, complemented
9#14583043C211yesmaximal, characteristic, complemented
10#14583008C211yesmaximal, characteristic, complemented
11#14583000C211yesmaximal, characteristic, complemented
12SD16×Dic43C211yesmaximal, characteristic, complemented
13#14582979C211yesmaximal, characteristic, complemented
14#14582959C211yesmaximal, characteristic, complemented
15C43×#460C211yesmaximal, characteristic, complemented
16C2×#10621902C2211yescharacteristic
17C2×#10621882C2211yescharacteristic
18C2×#10621882C2211yescharacteristic
19#13063317C2211yescharacteristic
20#13063306—21no—
21#13063306—21no—
22#13063297—21no—
23#13063297—21no—
24#13063296C2211yescharacteristic
25#13063296C2211yescharacteristic
26Q8×Dic43C2211yescharacteristic
27C4×D172—21no—
28C4×D172C2211yescharacteristic
29D4×Dic43C2211yescharacteristic
30D4×Dic43C2211yescharacteristic
31#13063287—21no—
32#13063287C2211yescharacteristic
33#13063282—21no—
34#13063282C2211yescharacteristic
35C4⋊C4×D43—21no—
36C4⋊C4×D43C2211yescharacteristic
37#13063259C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063257C2211yescharacteristic
40#13063256C2211yescharacteristic
41C4⋊(C43⋊C8)C2211yescharacteristic
42#13063249C2211yescharacteristic
43#13063249C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063247C2211yescharacteristic
46#13063246C2211yescharacteristic
47#13063246C2211yescharacteristic
48(C2×D43)⋊C8C2211yescharacteristic
49(C2×D43)⋊C8C2211yescharacteristic
50#13063235C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×SD16×C43C2211yescharacteristic
53C2×SD16×C43C2211yescharacteristic
54#127×C43C2211yescharacteristic
55C4×Q8×C43C2211yescharacteristic
56C4⋊C8×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58#102×C43C2211yescharacteristic
59C2×Q8×C43C2311yescharacteristic
60C2×D4×C43—21no—
61C2×D4×C43—21no—
62C2×D4×C43C2311yescharacteristic
63C2×D4×C43C2311yescharacteristic
64C2×C22⋊D43—21no—
65C2×C22⋊D43—21no—
66C22×Dic43—21no—
67C22×Dic43—21no—
68#10621902—22no—
69#10621902—22no—
70C2×D172—21no—
71C2×D172C2311yescharacteristic
72C2×C4×D43—21no—
73C2×C4×D43—21no—
74C2×C4×D43—21no—
75C2×C4×D43—21no—
76C2×C4×D43C2311yescharacteristic
77SD16×C43—22no—
78SD16×C43—22no—
79C2×C8×C43C2311yescharacteristic
80C2×C8×C43C2311yescharacteristic
81C4⋊C4×C43—21no—
82C4⋊C4×C43C2311yescharacteristic
83C42×C43—21no—
84C42×C43C2311yescharacteristic
85C22⋊Dic43—21no—
86C22⋊Dic43—21no—
87C22⋊Dic43—21no—
88C22⋊Dic43—21no—
89#10621882—22no—
90#10621882—22no—
91(C2×D43)⋊C4—21no—
92(C2×D43)⋊C4—21no—
93(C2×D43)⋊C4D411yescharacteristic
94(C2×D43)⋊C4D411yescharacteristic
95C4⋊Dic43—21no—
96C4⋊Dic43C2311yescharacteristic
97C4⋊Dic43C2311yescharacteristic
98C4⋊Dic43C2311yescharacteristic
99Dic43⋊C4—21no—
100Dic43⋊C4—21no—
101Dic43⋊C4—21no—
102Dic43⋊C4D411yescharacteristic
103Dic43⋊C4D411yescharacteristic
104C4×Dic43—21no—
105C4×Dic43C2311yescharacteristic
106C2×C43⋊C8C2311yescharacteristic
107C2×C43⋊C8C2311yescharacteristic
108C23×C43—21no—
109C23×C43—21no—
110C22×D43—21no—
111C22×D43C2×D411yescharacteristic
112Q8×C43—21no—
113Q8×C43#4112yes—
114D4×C43—21no—
115D4×C43—21no—
116D4×C43—21no—
117D4×C43—21no—
118D4×C43—81no—
119D4×C43—81no—
120C2×C4×C43—21no—
121C2×C4×C43—21no—
122C2×C4×C43C2×D411yescharacteristic
123C2×C4×C43C2×D411yescharacteristic
124C2×C4×C43C2411yescharacteristic
125C22⋊D43—81no—
126C22⋊D43—81no—
127C2×Dic43—21no—
128C2×Dic43—21no—
129C2×Dic43—21no—
130C2×Dic43—81no—
131C2×Dic43—81no—
132C2×Dic43C2×D411yescharacteristic
133C2×Dic43C2×D411yescharacteristic
134C2×Dic43C2×D411yescharacteristic
135D172—24no—
136D172—21no—
137D172#4112yes—
138C4×D43—24no—
139C4×D43—21no—
140C4×D43—21no—
141C4×D43—81no—
142C4×D43—81no—
143C4×D43—81no—
144C8×C43—21no—
145C8×C43—21no—
146C43⋊C8—21no—
147C43⋊C8—21no—
148C22×C43—41no—
149C22×C43—41no—
150C22×C43—41no—
151C22×C43—41no—
152C22×C43—41no—
153C22×C43—41no—
154C22×C43C22×D411yescharacteristic
155C2×D43—22no—
156C2×D43—21no—
157C2×D43—21no—
158C2×D43—21no—
159C2×D43—41no—
160C2×D43—41no—
161C4×C43—22no—
162C4×C43—21no—
163C4×C43—21no—
164C4×C43—41no—
165C4×C43C2×#4111yescharacteristic
166C4×C43C2×#4111yescharacteristic
167Dic43—21no—
168Dic43—21no—
169Dic43—21no—
170Dic43—41no—
171Dic43—41no—
172Dic43—41no—
173#3119—431nomaximal, Sylow
174C2×C43—81no—
175C2×C43—81no—
176C2×C43#52511yescharacteristic
177C2×C43#57611yescharacteristic
178C2×C43#57711yescharacteristic
179D43—41no—
180D43—42no—
181#540—431no—
182#520—431no—
183#481—431no—
184#480—431no—
185#479—431no—
186#478—431no—
187#460D4311yescharacteristic, complemented
188#459—431no—
189#449—431no—
190#449—431no—
191#442—431no—
192#440—431no—
193C4×SD16—431no—
194C4×D8—431no—
195#433—431no—
196C43#311911yescharacteristic, complemented, Sylow
197C2×#41—431no—
198C2×SD16C2×D4311yescharacteristic
199C2×SD16C2×D4311yescharacteristic
200C2×D8—431no—
201C2×D8—431no—
202#127C2×D4311yescharacteristic
203#125—431no—
204#123—861no—
205#123—861no—
206#121—431no—
207#121—431no—
208#121—861no—
209#121—861no—
210C4×Q8—431no—
211C4×Q8C2×D4311yescharacteristic
212C4×D4—431no—
213C4×D4—431no—
214C4×D4—431no—
215C4×D4—431no—
216C4×D4—861no—
217C4×D4—861no—
218#117—431no—
219#117—861no—
220C2×C4⋊C4—431no—
221C2×C4⋊C4—861no—
222#107—431no—
223#107—431no—
224#106—431no—
225#106—431no—
226C4⋊C8—431no—
227C4⋊C8C2×D4311yescharacteristic
228#103—431no—
229#103—431no—
230#102—431no—
231#102—431no—
232#102—431no—
233#102—431no—
234#102C2×D4311yescharacteristic
235#102C2×D4311yescharacteristic
236C22⋊C8—431no—
237C22⋊C8—431no—
238#97—431no—
239C4×C8—431no—
240#41—862no—
241#41—862no—
242C2×Q8C22×D4311yescharacteristic
243C2×D4—21no—
244C2×D4—21no—
245C2×D4—431no—
246C2×D4—861no—
247C2×D4—861no—
248C2×D4—861no—
249C2×D4C22×D4311yescharacteristic
250C2×D4C22×D4311yescharacteristic
251C22×C4—431no—
252C22×C4—861no—
253C22×C4—861no—
254C22×C4—861no—
255C22×C4—861no—
256C22×C4—861no—
257C22×C4—861no—
258SD16—22no—
259SD16—22no—
260D8—862no—
261D8—862no—
262C2×C8—431no—
263C2×C8—431no—
264C2×C8C22×D4311yescharacteristic
265C2×C8C22×D4311yescharacteristic
266C4⋊C4—21no—
267C4⋊C4—431no—
268C4⋊C4—431no—
269C4⋊C4—431no—
270C4⋊C4—431no—
271C4⋊C4—431no—
272C4⋊C4—861no—
273C4⋊C4—861no—
274C4⋊C4—861no—
275C4⋊C4—861no—
276C4⋊C4C22×D4311yescharacteristic
277C22⋊C4—431no—
278C22⋊C4—431no—
279C22⋊C4—861no—
280C22⋊C4—861no—
281C22⋊C4—861no—
282C22⋊C4—861no—
283C22⋊C4—861no—
284C22⋊C4—861no—
285C42—21no—
286C42—431no—
287C42—861no—
288C42C22×D4311yescharacteristic
289C23—21no—
290C23—21no—
291C23—431no—
292C23—861no—
293Q8—21no—
294Q8#1062190012yes—
295D4—21no—
296D4—21no—
297D4—21no—
298D4—21no—
299D4—81no—
300D4—81no—
301D4—432no—
302D4—864no—
303D4—861no—
304D4—3441no—
305D4—3441no—
306C2×C4—21no—
307C2×C4—21no—
308C2×C4—431no—
309C2×C4—431no—
310C2×C4—431no—
311C2×C4—864no—
312C2×C4—861no—
313C2×C4—861no—
314C2×C4—861no—
315C2×C4—861no—
316C2×C4—861no—
317C2×C4—3441no—
318C2×C4—3441no—
319C2×C4—3441no—
320C2×C4—3441no—
321C2×C4—3441no—
322C2×C4D4×D4311yescharacteristic
323C2×C4D4×D4311yescharacteristic
324C2×C4C23×D4311yescharacteristic
325C8—21no—
326C8—21no—
327C8—861no—
328C8—861no—
329C22—41no—
330C22—41no—
331C22—41no—
332C22—41no—
333C22—41no—
334C22—41no—
335C22—862no—
336C22—861no—
337C22—861no—
338C22—861no—
339C22—1721no—
340C22—1721no—
341C22C2×D4×D4311yescharacteristic
342C4—22no—
343C4—21no—
344C4—21no—
345C4—41no—
346C4—861no—
347C4—861no—
348C4—861no—
349C4—1721no—
350C4—1721no—
351C4—1721no—
352C4#41×D4311yescharacteristic
353C4C2×#1062190011yescharacteristic
354C2—81no—
355C2—81no—
356C2—1721no—
357C2—1722no—
358C2#1458340911yescharacteristic
359C2#1458370311yescharacteristic
360C2#1458370511yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#460C2
socleC22×C43C22×D4
hypercenter#460D43
hypocenterC43#3119
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C42 ◁ #460

Complements

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

NH ≅ G/Ntype
1. #14583503C2semidirect
2. #14583381C2semidirect
3. #14583216C2semidirect
4. #14583211C2semidirect
5. #14583206C2semidirect
6. #14583200C2semidirect
7. #14583091C2semidirect
8. #14583043C2semidirect
9. #14583043C2semidirect
10. #14583008C2semidirect
11. #14583000C2semidirect
12. SD16×Dic43C2semidirect
13. #14582979C2semidirect
14. #14582959C2semidirect
15. C43×#460C2semidirect
187. #460D43semidirect
196. C43#3119semidirect