Finite Group Databasebeta

← #19146990

Subgroups — #19146990

Order 5504.

366 conjugacy classes of subgroups.

The subgroup lattice has 348 nodes — too large to display as a diagram.

Conjugacy classes of subgroups

#subgroupG/Hclass sizemultiplicitynormal?properties
1#14583596C211yesmaximal, characteristic, complemented
2#14583593C211yesmaximal, characteristic, complemented
3#14583299C211yesmaximal, characteristic, complemented
4#14583224C211yesmaximal, characteristic, complemented
5#14583219C211yesmaximal, characteristic, complemented
6#14583216C211yesmaximal, characteristic, complemented
7#14583202C211yesmaximal, characteristic, complemented
8#14583197C211yesmaximal, characteristic, complemented
9#14583134C211yesmaximal, characteristic, complemented
10#14583133C211yesmaximal, characteristic, complemented
11#14582979C211yesmaximal, characteristic, complemented
12(C22⋊D43)⋊C8C211yesmaximal, characteristic, complemented
13#14582935C211yesmaximal, characteristic, complemented
14#107×D43C211yesmaximal, characteristic, complemented
15C43×#482C211yesmaximal, characteristic, complemented
16C2×#10621882C2211yescharacteristic
17C22×C43⋊C8C2211yescharacteristic
18C2×C8×D43C2211yescharacteristic
19#13063319—21no—
20#13063318—21no—
21#13063316C2211yescharacteristic
22#13063316C2211yescharacteristic
23#13063307—21no—
24#13063306—21no—
25#13063300C2211yescharacteristic
26#13063299C2211yescharacteristic
27#13063298—21no—
28#13063296—21no—
29#13063296C2211yescharacteristic
30C4×D172—21no—
31D4×Dic43C2211yescharacteristic
32#13063287C2211yescharacteristic
33C4×C22⋊D43C2211yescharacteristic
34(C22⋊D43)⋊C4—21no—
35#13063284C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37C4⋊C4×D43C2211yescharacteristic
38#13063259C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063258C2211yescharacteristic
41#13063258C2211yescharacteristic
42#13063257C2211yescharacteristic
43#13063256C2211yescharacteristic
44#13063256C2211yescharacteristic
45Dic43⋊C8C2211yescharacteristic
46#13063247C2211yescharacteristic
47#13063247C2211yescharacteristic
48#13063246C2211yescharacteristic
49#13063245C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52#121×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54#107×C43C2211yescharacteristic
55#106×C43C2211yescharacteristic
56#102×C43C2211yescharacteristic
57#102×C43C2211yescharacteristic
58C22⋊C8×C43C2211yescharacteristic
59C2×D4×C43—21no—
60C2×D4×C43C2311yescharacteristic
61C22×C4×C43C2311yescharacteristic
62C2×C22⋊D43—21no—
63C2×C22⋊D43—21no—
64C2×C22⋊D43D411yescharacteristic
65C22×Dic43—21no—
66C2×D172—21no—
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72C2×C8×C43C2311yescharacteristic
73C2×C8×C43C2311yescharacteristic
74C4⋊C4×C43C2311yescharacteristic
75C4⋊C4×C43C2311yescharacteristic
76C4⋊C4×C43C2311yescharacteristic
77C22⋊C4×C43—21no—
78C22⋊C4×C43—21no—
79C42×C43—21no—
80C22⋊Dic43—21no—
81C22⋊Dic43—21no—
82C22⋊Dic43—21no—
83C22⋊Dic43D411yescharacteristic
84#10621882—22no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4D411yescharacteristic
89C4⋊Dic43—21no—
90C4⋊Dic43—21no—
91C4⋊Dic43C2311yescharacteristic
92C4⋊Dic43C2311yescharacteristic
93C4⋊Dic43C2311yescharacteristic
94Dic43⋊C4—21no—
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4D411yescharacteristic
99C4×Dic43—21no—
100C4×Dic43C2311yescharacteristic
101C2×C43⋊C8—22no—
102C2×C43⋊C8C2311yescharacteristic
103C2×C43⋊C8C2311yescharacteristic
104C8×D43—22no—
105C23×C43—21no—
106C23×C43C2×D411yescharacteristic
107C22×D43—21no—
108C22×D43C2×D411yescharacteristic
109D4×C43—21no—
110D4×C43—21no—
111D4×C43—81no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—21no—
116C2×C4×C43—21no—
117C2×C4×C43C2×D411yescharacteristic
118C2×C4×C43C2411yescharacteristic
119C22⋊D43—22no—
120C22⋊D43—42no—
121C22⋊D43—81no—
122C2×Dic43—21no—
123C2×Dic43—21no—
124C2×Dic43—21no—
125C2×Dic43—81no—
126C2×Dic43C2×D411yescharacteristic
127C2×Dic43C2×D411yescharacteristic
128C2×Dic43C2×D411yescharacteristic
129D172—21no—
130D172—21no—
131D172—42no—
132C4×D43—21no—
133C4×D43—21no—
134C4×D43—81no—
135C4×D43—81no—
136C4×D43—81no—
137C8×C43—21no—
138C8×C43—21no—
139C43⋊C8—21no—
140C43⋊C8#4112yes—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43—41no—
145C22×C43—41no—
146C22×C43—41no—
147C22×C43C22×D411yescharacteristic
148C2×D43—21no—
149C2×D43—21no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43#13512yes—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43C2×#4111yescharacteristic
159C4×C432−1+411yescharacteristic
160Dic43—21no—
161Dic43—21no—
162Dic43—21no—
163Dic43—41no—
164Dic43—41no—
165Dic43—41no—
166#3339—431nomaximal, Sylow
167C2×C43—41no—
168C2×C43—81no—
169C2×C43#54711yescharacteristic
170C2×C43C2×#13511yescharacteristic
171C2×C43#57611yescharacteristic
172D43—22no—
173D43—81no—
174#553—431no—
175#553—431no—
176#499—431no—
177#482—431no—
178#482D4311yescharacteristic, complemented
179#481—431no—
180#481—431no—
181#478—431no—
182#478—431no—
183#466—431no—
184#466—431no—
185C4×D8—431no—
186C8×D4—431no—
187#427—431no—
188C2×#107—431no—
189C43#333911yescharacteristic, complemented, Sylow
190C2×D8—431no—
191C22×C8—431no—
192C22×C8—431no—
193#126—861no—
194#126—861no—
195#125—431no—
196#125—431no—
197#123—861no—
198#123—861no—
199#121—431no—
200#121—431no—
201#121—431no—
202#121—861no—
203#121—861no—
204#121C2×D4311yescharacteristic
205C4×D4—431no—
206C4×D4—431no—
207C4×D4—431no—
208C4×D4—861no—
209C4×D4—861no—
210#117—431no—
211#117C2×D4311yescharacteristic
212C2×C4⋊C4—431no—
213C2×C4⋊C4—431no—
214#107—431no—
215#107—431no—
216#107—431no—
217#107—431no—
218#107C2×D4311yescharacteristic
219#106—431no—
220#106—431no—
221#106—431no—
222#106C2×D4311yescharacteristic
223C4⋊C8—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102C2×D4311yescharacteristic
229#102C2×D4311yescharacteristic
230C22⋊C8—431no—
231C22⋊C8C2×D4311yescharacteristic
232C4×C8—431no—
233C2×D4—21no—
234C2×D4—431no—
235C2×D4—431no—
236C2×D4—861no—
237C2×D4—861no—
238C2×D4—861no—
239C2×D4C22×D4311yescharacteristic
240C22×C4—431no—
241C22×C4—861no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4C22×D4311yescharacteristic
246D8—862no—
247C2×C8—431no—
248C2×C8—431no—
249C2×C8—862no—
250C2×C8—862no—
251C2×C8C22×D4311yescharacteristic
252C2×C8C22×D4311yescharacteristic
253C4⋊C4—431no—
254C4⋊C4—431no—
255C4⋊C4—431no—
256C4⋊C4—431no—
257C4⋊C4—861no—
258C4⋊C4—861no—
259C4⋊C4—861no—
260C4⋊C4—861no—
261C4⋊C4—861no—
262C4⋊C4—861no—
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C4⋊C4C22×D4311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—21no—
268C22⋊C4—431no—
269C22⋊C4—431no—
270C22⋊C4—861no—
271C22⋊C4—861no—
272C22⋊C4—861no—
273C22⋊C4—861no—
274C22⋊C4—861no—
275C22⋊C4—861no—
276C42—21no—
277C42—431no—
278C42—861no—
279C23—21no—
280C23—431no—
281C23—861no—
282C23D4×D4311yescharacteristic
283D4—21no—
284D4—21no—
285D4—81no—
286D4—862no—
287D4—861no—
288D4—861no—
289D4—3441no—
290D4—1722no—
291D4—1722no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—431no—
298C2×C4—431no—
299C2×C4—431no—
300C2×C4—861no—
301C2×C4—861no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—3441no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4D4×D4311yescharacteristic
310C2×C4C23×D4311yescharacteristic
311C8—21no—
312C8—21no—
313C8—432no—
314C8—861no—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—41no—
319C22—41no—
320C22—41no—
321C22—432no—
322C22—861no—
323C22—861no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C2×D4×D4311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—861no—
333C4—861no—
334C4—861no—
335C4—1721no—
336C4—1721no—
337C4—1721no—
338C4#41×D4311yescharacteristic
339C4#1306337211yescharacteristic
340C2—41no—
341C2—81no—
342C2—862no—
343C2—3441no—
344C2#1458354711yescharacteristic
345C2#135×D4311yescharacteristic
346C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#482C2
socleC22×C43C22×D4
hypercenter#482D43
hypocenterC43#3339
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #482

Complements

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

NH ≅ G/Ntype
1. #14583596C2semidirect
2. #14583593C2semidirect
3. #14583299C2semidirect
4. #14583224C2semidirect
5. #14583219C2semidirect
6. #14583216C2semidirect
7. #14583202C2semidirect
8. #14583197C2semidirect
9. #14583134C2semidirect
10. #14583133C2semidirect
11. #14582979C2semidirect
12. (C22⋊D43)⋊C8C2semidirect
13. #14582935C2semidirect
14. #107×D43C2semidirect
15. C43×#482C2semidirect
178. #482D43semidirect
189. C43#3339semidirect