Finite Group Databasebeta

← #19147197

Subgroups — #19147197

Order 5504.

360 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#14583597C211yesmaximal, characteristic, complemented
2#14583593C211yesmaximal, characteristic, complemented
3#14583299C211yesmaximal, characteristic, complemented
4#14583225C211yesmaximal, characteristic, complemented
5#14583223C211yesmaximal, characteristic, complemented
6#14583214C211yesmaximal, characteristic, complemented
7#14583212C211yesmaximal, characteristic, complemented
8#14583202C211yesmaximal, characteristic, complemented
9#14583198C211yesmaximal, characteristic, complemented
10#14583153C211yesmaximal, characteristic, complemented
11#14583152C211yesmaximal, characteristic, complemented
12#14582981C211yesmaximal, characteristic, complemented
13#14582975C211yesmaximal, characteristic, complemented
14#14582940C211yesmaximal, characteristic, complemented
15C43×#428C211yesmaximal, characteristic, complemented
16C2×D344C2211yescharacteristic
17C2×#10621872C2211yescharacteristic
18#13063320—21no—
19#13063319—21no—
20#13063316C2211yescharacteristic
21#13063316C2211yescharacteristic
22#13063310—21no—
23#13063307—21no—
24#13063300C2211yescharacteristic
25#13063300C2211yescharacteristic
26#13063299—21no—
27#13063299C2211yescharacteristic
28#13063299C2211yescharacteristic
29#13063298—21no—
30C4×D172—21no—
31#13063287C2211yescharacteristic
32#13063287C2211yescharacteristic
33C4×C22⋊D43—21no—
34C4×C22⋊D43C2211yescharacteristic
35#13063283C2211yescharacteristic
36C4⋊C4×D43C2211yescharacteristic
37#13063258C2211yescharacteristic
38#13063258C2211yescharacteristic
39#13063258C2211yescharacteristic
40#13063257C2211yescharacteristic
41#13063256C2211yescharacteristic
42Dic43⋊C8C2211yescharacteristic
43#13063247C2211yescharacteristic
44#13063247C2211yescharacteristic
45#13063245C2211yescharacteristic
46#13063245C2211yescharacteristic
47#13063245C2211yescharacteristic
48#13063245C2211yescharacteristic
49C22⋊(C43⋊C8)C2211yescharacteristic
50(C2×D43)⋊C8C2211yescharacteristic
51C8×Dic43C2211yescharacteristic
52C2×M16×C43C2211yescharacteristic
53#117×C43C2211yescharacteristic
54C2×C4⋊C4×C43C2211yescharacteristic
55#107×C43C2211yescharacteristic
56#107×C43C2211yescharacteristic
57#106×C43C2211yescharacteristic
58#106×C43C2211yescharacteristic
59C22×C4×C43—21no—
60C22×C4×C43C2311yescharacteristic
61C2×C22⋊D43—21no—
62C2×C22⋊D43—21no—
63C2×C22⋊D43D411yescharacteristic
64C2×D172—21no—
65C2×D172—21no—
66C2×D172C2311yescharacteristic
67C2×D172C2311yescharacteristic
68C2×C4×D43—21no—
69C2×C4×D43—21no—
70C2×C4×D43—21no—
71C2×C4×D43C2311yescharacteristic
72M16×C43—22no—
73C2×C8×C43C2311yescharacteristic
74C2×C8×C43C2311yescharacteristic
75C4⋊C4×C43—21no—
76C4⋊C4×C43C2311yescharacteristic
77C4⋊C4×C43C2311yescharacteristic
78C4⋊C4×C43C2311yescharacteristic
79C4⋊C4×C43C2311yescharacteristic
80C22⋊C4×C43—21no—
81C42×C43—21no—
82C22⋊Dic43D411yescharacteristic
83(C2×D43)⋊C4—21no—
84(C2×D43)⋊C4—21no—
85(C2×D43)⋊C4—21no—
86(C2×D43)⋊C4—21no—
87(C2×D43)⋊C4—21no—
88(C2×D43)⋊C4—21no—
89(C2×D43)⋊C4—21no—
90(C2×D43)⋊C4D411yescharacteristic
91C4⋊Dic43—21no—
92C4⋊Dic43—21no—
93C4⋊Dic43C2311yescharacteristic
94C4⋊Dic43C2311yescharacteristic
95Dic43⋊C4—21no—
96Dic43⋊C4—21no—
97Dic43⋊C4—21no—
98Dic43⋊C4D411yescharacteristic
99C4×Dic43—21no—
100C4×Dic43C2311yescharacteristic
101C2×C43⋊C8C2311yescharacteristic
102C2×C43⋊C8C2311yescharacteristic
103D344—22no—
104#10621872—22no—
105C23×C43C2×D411yescharacteristic
106C22×D43—21no—
107C22×D43—21no—
108C22×D43C2×D411yescharacteristic
109C2×C4×C43—21no—
110C2×C4×C43—21no—
111C2×C4×C43—21no—
112C2×C4×C43—21no—
113C2×C4×C43—21no—
114C2×C4×C43—21no—
115C2×C4×C43—81no—
116C2×C4×C43C2×D411yescharacteristic
117C2×C4×C43C2411yescharacteristic
118C22⋊D43—41no—
119C22⋊D43—42no—
120C22⋊D43—81no—
121C2×Dic43—21no—
122C2×Dic43—21no—
123C2×Dic43C2×D411yescharacteristic
124C2×Dic43C2×D411yescharacteristic
125C2×Dic43C2×D411yescharacteristic
126D172—21no—
127D172—21no—
128D172—21no—
129D172—21no—
130D172—42no—
131D172—81no—
132C4×D43—21no—
133C4×D43—21no—
134C4×D43—81no—
135C4×D43—81no—
136C4×D43—81no—
137C8×C43—21no—
138C8×C43#4112yes—
139C43⋊C8—21no—
140C43⋊C8—21no—
141C22×C43—21no—
142C22×C43—21no—
143C22×C43—21no—
144C22×C43C22×D411yescharacteristic
145C2×D43—21no—
146C2×D43—21no—
147C2×D43—21no—
148C2×D43—41no—
149C2×D43—41no—
150C2×D43—41no—
151C2×D43—41no—
152C2×D43—41no—
153C2×D43—41no—
154C4×C43—21no—
155C4×C43—41no—
156C4×C43—41no—
157C4×C43—41no—
158C4×C43—41no—
159C4×C43C2×#4111yescharacteristic
160C4×C432−1+411yescharacteristic
161Dic43—21no—
162Dic43—21no—
163Dic43—21no—
164Dic43—41no—
165Dic43—41no—
166#3355—431nomaximal, Sylow
167C2×C43—41no—
168C2×C43#54711yescharacteristic
169C2×C43#57511yescharacteristic
170C2×C43#57611yescharacteristic
171D43—41no—
172D43—81no—
173D43—81no—
174#553—431no—
175#553—431no—
176#499—431no—
177#482—431no—
178#482—431no—
179#480—431no—
180#480—431no—
181#478—431no—
182#478—431no—
183#469—431no—
184#469—431no—
185C4×D8—431no—
186#436—431no—
187#428—431no—
188#428D4311yescharacteristic, complemented
189C43#335511yescharacteristic, complemented, Sylow
190C2×D8—431no—
191C2×M16—431no—
192C2×M16C2×D4311yescharacteristic
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—431no—
203#121—861no—
204#121—861no—
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⋊C4C2×D4311yescharacteristic
214#107—431no—
215#107—431no—
216#107—431no—
217#107C2×D4311yescharacteristic
218#107C2×D4311yescharacteristic
219#106—431no—
220#106—431no—
221#106C2×D4311yescharacteristic
222#106C2×D4311yescharacteristic
223C4⋊C8—431no—
224#102—431no—
225#102—431no—
226#102—431no—
227#102—431no—
228#102—431no—
229#102—431no—
230C22⋊C8—431no—
231C22⋊C8—431no—
232C4×C8—431no—
233C2×D4—431no—
234C2×D4—431no—
235C2×D4—431no—
236C2×D4—861no—
237C2×D4—861no—
238C2×D4—861no—
239C2×D4—861no—
240C22×C4—21no—
241C22×C4—431no—
242C22×C4—861no—
243C22×C4—861no—
244C22×C4—861no—
245C22×C4C22×D4311yescharacteristic
246D8—862no—
247M16—22no—
248M16—862no—
249C2×C8—431no—
250C2×C8—431no—
251C2×C8C22×D4311yescharacteristic
252C2×C8C22×D4311yescharacteristic
253C4⋊C4—21no—
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⋊C4C22×D4311yescharacteristic
263C4⋊C4C22×D4311yescharacteristic
264C4⋊C4C22×D4311yescharacteristic
265C4⋊C4C22×D4311yescharacteristic
266C22⋊C4—21no—
267C22⋊C4—431no—
268C22⋊C4—431no—
269C22⋊C4—861no—
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—431no—
280C23—861no—
281C23—861no—
282C23D4×D4311yescharacteristic
283D4—861no—
284D4—861no—
285D4—861no—
286D4—861no—
287D4—3441no—
288D4—3441no—
289D4—1722no—
290D4—1721no—
291D4—1722no—
292C2×C4—21no—
293C2×C4—21no—
294C2×C4—21no—
295C2×C4—21no—
296C2×C4—21no—
297C2×C4—21no—
298C2×C4—81no—
299C2×C4—431no—
300C2×C4—431no—
301C2×C4—431no—
302C2×C4—861no—
303C2×C4—861no—
304C2×C4—861no—
305C2×C4—861no—
306C2×C4—3441no—
307C2×C4—3441no—
308C2×C4—3441no—
309C2×C4D4×D4311yescharacteristic
310C2×C4C23×D4311yescharacteristic
311C8—21no—
312C8—861no—
313C8—861no—
314C8#1062189812yes—
315C22—21no—
316C22—21no—
317C22—21no—
318C22—861no—
319C22—861no—
320C22—861no—
321C22—1721no—
322C22—1721no—
323C22—1721no—
324C22—1721no—
325C22—1721no—
326C22—1721no—
327C22C2×D4×D4311yescharacteristic
328C4—21no—
329C4—41no—
330C4—41no—
331C4—41no—
332C4—41no—
333C4—861no—
334C4—861no—
335C4—861no—
336C4—1721no—
337C4—1721no—
338C4C2×#1062189811yescharacteristic
339C4#1306337311yescharacteristic
340C2—41no—
341C2—3441no—
342C2—3441no—
343C2—1721no—
344C2#1458355011yescharacteristic
345C2#1458369811yescharacteristic
346C2#1458370311yescharacteristic
subgroupG/H
centerC22C2×D4×D43
commutatorC2×C4×C43C24
FrattiniC2×C4C23×D43
FittingC43×#428C2
socleC22×C43C22×D4
hypercenter#428D43
hypocenterC43#3355
LCSG ▷ C2×C4×C43 ▷ C2×C43 ▷ C43
UCSC1 ◁ C22 ◁ C22×C4 ◁ #428

Complements

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

NH ≅ G/Ntype
1. #14583597C2semidirect
2. #14583593C2semidirect
3. #14583299C2semidirect
4. #14583225C2semidirect
5. #14583223C2semidirect
6. #14583214C2semidirect
7. #14583212C2semidirect
8. #14583202C2semidirect
9. #14583198C2semidirect
10. #14583153C2semidirect
11. #14583152C2semidirect
12. #14582981C2semidirect
13. #14582975C2semidirect
14. #14582940C2semidirect
15. C43×#428C2semidirect
188. #428D43semidirect
189. C43#3355semidirect